PASSAGES FROM THE LIFE OF A PHILOSOPHER, by Charles Babbage

SIRE,

IN dedicating this volume to your Majesty, I am also doing an act of justice to the memory of your illustrious father.

In 1840, the King, Charles Albert, invited the learned of Italy to assemble in his capital. At the request of her most gifted Analyst, I brought with me the drawings and explanations of the Analytical Engine. These were thoroughly examined and their truth acknowledged by Italy’s choicest sons.

To the King, your father, I am indebted for the first public and official acknowledgment of this invention.

I am happy in thus expressing my deep sense of that obligation to his son, the Sovereign of united Italy, the country of Archimedes and of Galileo.

SOME men write their lives to save themselves from ennui, careless of the amount they inflict on their readers.

Others write their personal history, lest some kind friend should survive them, and, in showing off his own talent, unwittingly show them up.

Others, again, write their own life from a different motive—from fear that the vampires of literature might make it their prey.

I have frequently had applications to write my life, both from my countrymen and from foreigners. Some caterers for the public offered to pay me for it. Others required that I should pay them for its insertion; others offered to insert it without charge. One proposed to give me a quarter of a column gratis, and as many additional lines of eloge as I chose to write and pay for at ten-pence per line. To many of these I sent a list of my works, with the remark that they formed the best life of an author; but nobody cared to insert them.

I have no desire to write my own biography, as long as I have strength and means to do better work.

The remarkable circumstances attending those Calculating Machines, on which I have spent so large a portion of my life, make me wish to place on record some account of their past history. As, however, such a work would be utterly uninteresting to the greater part of my countrymen, I thought it might be rendered less unpalatable by relating some of my experience amongst various classes of society, widely differing from each other, in which I have oc­ca­sion­al­ly mixed.

This volume does not aspire to the name of an autobiography. It relates a variety of isolated circumstances in which I have taken part—some of them arranged in the order of time, and others grouped together in separate chapters, from similarity of subject.

The selection has been made in some cases from the importance of the matter. In others, from the celebrity of the persons concerned; whilst several of them furnish interesting illustrations of human character.

WHAT is there in a name? It is merely an empty basket, until you put something into it. My earliest visit to the Continent taught me the value of such a basket, filled with the name of my venerable friend the first Herschel, ere yet my younger friend his son, had adorned his distinguished patronymic with the additional laurels of his own well-earned fame.

The inheritance of a celebrated name is not, however, without its disadvantages. This truth I never found more fully appreciated, nor more admirably expressed, than in a conversation with the son of Filangieri, the author of the {2} celebrated Treatise on Legislation, with whom I became acquainted at Naples, and in whose company I visited several of the most interesting institutions of that capital.

In the course of one of our drives, I alluded to the advantages of inheriting a distinguished name, as in the case of the second Herschel. His remark was, “For my own part, I think it a great disadvantage. Such a man must feel in the position of one inheriting a vast estate, so deeply mortgaged that he can never hope, by any efforts of his own, to redeem it.”

Without reverting to the philosophic, but unromantic, views of our origin taken by Darwin, I shall pass over the long history of our progress from a monad up to man, and commence tracing my ancestry as the world generally do: namely, as soon as there is the slightest ground for conjecture. Although I have contended for the Mosaic date of the creation of man as long as I decently could, and have even endeavoured to explain away1 some of the facts relied upon to prove man’s long anterior origin; yet I must admit that the continual accumulation of evidence probably will, at last, compel me to acknowledge that, in this single instance, the writings of Moses may have been misapprehended.

Let us, therefore, take for granted that man and certain extinct races of animals lived together, thousands of years before Adam. We find, at that period, a race who formed knives, and hammers, and arrow-heads out of flint. Now, considering my own inveterate habit of contriving tools, it is more probable that I should derive my passion by hereditary transmission from these original tool-makers, than from any other inferior race existing at that period. {3}

Many years ago I met a very agreeable party at Mr. Rogers’ table. Somebody introduced the subject of ancestry. I remarked that most people are reluctant to acknowledge as their father or grandfather, any person who had committed a dishonest action or a crime. But that no one ever scrupled to be proud of a remote ancestor, even though he might have been a thief or a murderer. Various remarks were made, and reasons assigned, for this tendency of the educated mind. I then turned to my next neighbour, Sir Robert H. Inglis, and asked him what he would do, supposing he possessed undoubted documents, that he was lineally descended from Cain.

Sir Robert said he was at that moment proposing to himself the very same question. After some consideration, he said he should burn them; and then inquired what I should do in the same circumstances. My reply was, that I should preserve them: but simply because I thought the preservation of any fact might ultimately be useful.

I possess no evidence that I am descended from Cain. If any herald suppose that there may be such a presumption, I think it must arise from his confounding Cain with Tubal Cain, who was a great worker in iron. Still, however he might argue that, the probabilities are in favour of his opinion: for I, too, work in iron. But a friend of mine, to whose kind criticisms I am much indebted, suggests that as Tubal Cain invented the Organ, this probability is opposed to the former one.

The next step in my pedigree is to determine whence the origin of my modern family name.

Some have supposed it to be derived from the cry of sheep. If so, that would point to a descent from the Shepherd Kings. Others have supposed it is derived from the name of a place called Bab or Babb, as we have, in the West of England, Bab {4} Tor, Babbacombe, &c. But this is evidently erroneous; for, when a people took possession of a desert country, its various localities could possess no names; consequently, the colonists could not take names from the country to which they migrated, but would very naturally give their own names to the several lands they appropriated: “mais revenons à nos moutons.”

How my blood was trans­mit­ted to me through more modern races, is quite immaterial, seeing the admitted antiquity of the flint-workers.

In recent times, that is, since the Conquest, my knowledge of the history of my family is limited by the unfortunate omission of my name from the roll of William’s followers. Those who are curious about the subject, and are idlers, may, if they think it worth while, search all the parish registers in the West of England and elsewhere.

The light I can throw upon it is not great, and rests on a few documents, and on family tradition. During the past four generations I have no surviving collateral relatives of my own name.

The name of Babbage is not uncommon in the West of England. One day during my boyhood, I observed it over a small grocer’s shop, whilst riding through the town of Chudley. I dismounted, went into the shop, purchased some figs, and found a very old man of whom I made inquiry as to his family. He had not a good memory himself, but his wife told me that his name was Babb when she married him, and that it was only during the last twenty years he had adopted the name of Babbage, which, the old man thought, sounded better. Of course I told his wife that I entirely agreed with her husband, and thought him a very sensible fellow.

The craft most frequently practised by my ancestors seems {5} to have been that of a goldsmith, although several are believed to have practised less dignified trades.

In the time of Henry the Eighth one of my ancestors, together with a hundred men, were taken prisoners at the siege of Calais.

When William the Third landed in Torbay, another ancestor of mine, a yeoman possessing some small estate, undertook to distribute his proclamations. For this bit of high treason he was rewarded with a silver medal, which I well remember seeing, when I was a boy. It had descended to a very venerable and truthful old lady, an unmarried aunt, the historian of our family, on whose authority the identity of the medal I saw with that given by King William must rest.

Another ancestor married one of two daughters, the only children of a wealthy physician, Dr. Burthogge, an intimate friend and cor­res­pon­dent of John Locke.

Somewhere about 1700 a member of my family, one Richard Babbage, who appears to have been a very wild fellow, having tried his hand at various trades, and given them all up, offended a wealthy relative.

To punish this idleness, his relative entailed all his large estates upon eleven different people, after whom he gave it to this Richard Babbage, who, had there been no entail, would have taken them as heir-at-law.

Ten of these lives had dropped, and the eleventh was in a consumption, when Richard Babbage took it into his head to go off to America with Bamfylde Moore Carew, the King of the Beggars.

The last only of the eleven lives existed when he embarked, and that life expired within twelve months after Richard Babbage sailed. The estates remained in possession of the rep­re­sen­ta­tives of the eleventh in the entail. {6}

If it could have been proved that Richard Babbage had survived twelve months after his voyage to America, these estates would have remained in my own branch of the family.

I possess a letter from Richard Babbage, dated on board the ship in which he sailed for America.

In the year 1773 it became necessary to sell a portion of this property, for the purpose of building a church at Ashbrenton. A private Act of Parliament was passed for that purpose, in which the rights of the true heir were reserved.

FROM my earliest years I had a great desire to inquire into the causes of all those little things and events which astonish the childish mind. At a later period I commenced the still more important inquiry into those laws of thought and those aids which assist the human mind in passing from received knowledge to that other knowledge then unknown to our race. I now think it fit to record some of those views to which, at various periods of my life, my reasoning has led me. Truth only has been the object of my search, and I am not conscious of ever having turned aside in my inquiries from any fear of the conclusions to which they might lead.

As it may be interesting to some of those who will hereafter read these lines, I shall briefly mention a few events of my earliest, and even of my childish years. My parents being born at a certain period of history, and in a certain latitude and longitude, of course followed the religion {8} of their country. They brought me up in the Protestant form of the Christian faith. My excellent mother taught me the usual forms of my daily and nightly prayer; and neither in my father nor my mother was there any mixture of bigotry and intolerance on the one hand, nor on the other of that unbecoming and familiar mode of addressing the Almighty which afterwards so much disgusted me in my youthful years.

My invariable question on receiving any new toy, was “Mamma, what is inside of it?” Until this information was obtained those around me had no repose, and the toy itself, I have been told, was generally broken open if the answer did not satisfy my own little ideas of the “fitness of things.”

Two events which impressed themselves forcibly on my memory happened, I think, previously to my eighth year.

When about five years old, I was walking with my nurse, who had in her arms an infant brother of mine, across London Bridge, holding, as I thought, by her apron. I was looking at the ships in the river. On turning round to speak to her, I found that my nurse was not there, and that I was alone upon London Bridge. My mother had always impressed upon me the necessity of great caution in passing any street-crossing: I went on, therefore, quietly until I reached Tooley Street, where I remained watching the passing vehicles, in order to find a safe opportunity of crossing that very busy street.

In the mean time the nurse, having lost one of her charges, had gone to the crier, who proceeded immediately to call, by the ringing of his bell, the attention of the public to the fact that a young phi­los­o­pher was lost, and to the still more important fact that five shillings would be the reward of his fortunate discoverer. I well remember sitting on the steps of {9} the door of the linendraper’s shop on the opposite corner of Tooley Street, when the gold-laced crier was making proclamation of my loss; but I was too much occupied with eating some pears to attend to what he was saying.

The fact was, that one of the men in the linendraper’s shop, observing a little child by itself, went over to it, and asked what it wanted. Finding that it had lost its nurse, he brought it across the street, gave it some pears, and placed it on the steps at the door: having asked my name, the shopkeeper found it to be that of one of his own customers. He accordingly sent off a messenger, who announced to my mother the finding of young Pickle before she was aware of his loss.

Those who delight in observing coincidences may perhaps account for the following singular one. Several years ago when the houses in Tooley Street were being pulled down, I believe to make room for the new railway terminus, I happened to pass along the very spot on which I had been lost in my infancy. A slate of the largest size, called a Duchess,2 was thrown from the roof of one of the houses, and penetrated into the earth close to my feet.

The other event, which I believe happened some time after the one just related, is as follows. I give it from memory, as I have always repeated it.

I was walking with my nurse and my brother in a public garden, called Mont­pel­ier Gar­dens, in Wal­worth. On returning through the private road leading to the gardens, I gathered and swallowed some dark berries very like black currants:—these were poisonous. {10}

On my return home, I recollect being placed between my father’s knees, and his giving me a glass of castor oil, which I took from his hand.

My father at that time possessed a collection of pictures. He sat on a chair on the right hand side of the chimney-piece in the breakfast room, under a fine picture of our Saviour taken down from the cross. On the opposite wall was a still-celebrated “Interior of Antwerp Cathedral.”

In after-life I several times mentioned the subject both to my father and to my mother; but neither of them had the slightest recollection of the matter.

Having suffered in health at the age of five years, and again at that of ten by violent fevers, from which I was with difficulty saved, I was sent into Devonshire and placed under the care of a clergyman (who kept a school at Alphington, near Exeter), with in­struc­tions to attend to my health; but, not to press too much knowledge upon me: a mission which he faithfully accomplished. Perhaps great idleness may have led to some of my childish reasonings.

Relations of ghost stories often circulate amongst children, and also of visitations from the devil in a personal form. Of course I shared the belief of my comrades, but still had some doubts of the existence of these personages, although I greatly feared their appearance. Once, in conjunction with a companion, I frightened another boy, bigger than myself, with some pretended ghost; how prepared or how represented by natural objects I do not now remember: I believe it was by the accidental passing shadows of some external objects upon the walls of our common bedroom.

The effect of this on my playfellow was painful; he was much frightened for several days; and it naturally occurred to me, after some time, that as I had deluded him with ghosts, {11} I might myself have been deluded by older persons, and that, after all, it might be a doubtful point whether ghost or devil ever really existed. I gathered all the information I could on the subject from the other boys, and was soon informed that there was a peculiar process by which the devil might be raised and become personally visible. I carefully collected from the traditions of different boys the visible forms in which the Prince of Darkness had been recorded to have appeared. Amongst them were—

After long thinking over the subject, although checked by a belief that the inquiry was wicked, my curiosity at length over-balanced my fears, and I resolved to attempt to raise the devil. Naughty people, I was told, had made written compacts with the devil, and had signed them with their names written in their own blood. These had become very rich and great men during their life, a fact which might be well known. But, after death, they were described as having suffered and continuing to suffer physical torments throughout eternity, another fact which, to my uninstructed mind, it seemed difficult to prove.

As I only desired an interview with the gentleman in black simply to convince my senses of his existence, I declined adopting the legal forms of a bond, and preferred one more resembling that of leaving a visiting card, when, if not at home, I might expect the sat­is­fac­tion of a return of the visit by the devil in person. {12}

Accordingly, having selected a promising locality, I went one evening towards dusk up into a deserted garret. Having closed the door, and I believe opened the window, I proceeded to cut my finger and draw a circle on the floor with the blood which flowed from the incision.

I then placed myself in the centre of the circle, and either said or read the Lord’s Prayer backwards. This I accomplished at first with some trepidation and in great fear towards the close of the scene. I then stood still in the centre of that magic and superstitious circle, looking with intense anxiety in all directions, especially at the window and at the chimney. Fortunately for myself, and for the reader also, if he is interested in this narrative, no owl or black cat or unlucky raven came into the room.

In either case my then weakened frame might have expiated this foolish experiment by its own extinction, or by the alienation of that too curious spirit which controlled its feeble powers.

After waiting some time for my expected but dreaded visitor, I, in some degree, recovered my self-possession, and leaving the circle of my incantation, I gradually opened the door and gently closing it, descended the stairs, at first slowly, and by degrees much more quickly. I then rejoined my companions, but said nothing whatever of my recent attempt. After supper the boys retired to bed. When we were in bed and the candle removed, I proceeded as usual to repeat my prayers silently to myself. After the few first sentences of the Lord’s Prayer, I found that I had forgotten a sentence, and could not go on to the conclusion. This alarmed me very much, and having repeated another prayer or hymn, I remained long awake, and very unhappy. I thought that this forgetfulness was a punishment inflicted {13} upon me by the Almighty, and that I was a wicked little boy for having attempted to satisfy myself about the existence of a devil. The next night my memory was more faithful, and my prayers went on as usual. Still, however, I was unhappy, and continued to brood over the inquiry. My uninstructed faculties led me from doubts of the existence of a devil to doubts of the book and the religion which asserted him to be a living being. My sense of justice (whether it be innate or acquired) led me to believe that it was impossible that an almighty and all-merciful God could punish me, a poor little boy, with eternal torments because I had anxiously taken the only means I knew of to verify the truth or falsehood of the religion I had been taught. I thought over these things for a long time, and, in my own childish mind, wished and prayed that God would tell me what was true. After long meditation, I resolved to make an experiment to settle the question. I thought, if it was really of such immense importance to me here and hereafter to believe rightly, that the Almighty would not consign me to eternal misery because, after trying all means that I could devise, I was unable to know the truth. I took an odd mode of making the experiment; I resolved that at a certain hour of a certain day I would go to a certain room in the house, and that if I found the door open, I would believe the Bible; but that if it were closed, I should conclude that it was not true. I remember well that the ob­ser­va­tion was made, but I have no recollection as to the state of the door. I presume it was found open from the circumstance that, for many years after, I was no longer troubled by doubts, and indeed went through the usual religious forms with very little thought about their origin.

At length, as time went on, my bodily health was restored {14} by my native air: my mind, however, receiving but little in­struc­tion, began, I imagine, to prey upon itself—such at least I infer to have been the case from the following circumstance. One day, when uninterested in the sports of my little companions, I had retired into the shrubbery and was leaning my head, supported by my left arm, upon the lower branch of a thorn-tree. Listless and unoccupied, I imagined I had a head-ache. After a time I perceived, lying on the ground just under me, a small bright bit of metal. I instantly seized the precious discovery, and turning it over, examined both sides. I immediately concluded that I had discovered some valuable treasure, and running away to my deserted companions, showed them my golden coin. The little company became greatly excited, and declared that it must be gold, and that it was a piece of money of great value. We ran off to get the opinion of the usher; but whether he partook of the delusion, or we acquired our knowledge from the higher authority of the master, I know not. I only recollect the entire dissipation of my head-ache, and then my ultimate great disappointment when it was pronounced, upon the undoubted authority of the village doctor, that the square piece of brass I had found was a half-dram weight which had escaped from the box of a pair of medical scales. This little incident had an important effect upon my after-life. I reflected upon the extraordinary fact, that my head-ache had been entirely cured by the discovery of the piece of brass. Although I may not have put into words the principle, that occupation of the mind is such a source of pleasure that it can relieve even the pain of a head-ache; yet I am sure it practically gave an additional stimulus to me in many a difficult inquiry. Some few years after, when suffering under a form of tooth-ache, not acute though tediously {15} wearing, I often had recourse to a volume of Don Quixote, and still more frequently to one of Robinson Crusoe. Although at first it required a painful effort of attention, yet it almost always happened, after a time, that I had forgotten the moderate pain in the overpowering interest of the novel.

My most intimate companion and friend was a boy named Dacres, the son of Admiral Richard Dacres. We had often talked over such questions as those I have mentioned in this chapter, and we had made an agreement that whichever died first should, if possible, appear to the other after death, in order to satisfy the survivor about their solution.

After a year or two my young friend entered the navy, but we kept up our friendship, and when he was ashore I saw him frequently. He was in a ship of eighty guns at the passage of the Dardanelles, under the command of Sir Thomas Duckworth. Ultimately he was sent home in charge of a prize-ship, in which he suffered the severest hardships during a long and tempestuous voyage, and then died of consumption.

I saw him a few days before his death, at the age of about eighteen. We talked of former times, but neither of us mentioned the compact. I believe it occurred to his mind: it was certainly strongly present to my own.

He died a few days after. On the evening of that day I retired to my own room, which was partially detached from the house by an intervening conservatory. I sat up until after midnight, endeavouring to read, but found it impossible to fix my attention on any subject, except the overpowering feeling of curiosity, which absorbed my mind. I then undressed and went into bed; but sleep was entirely banished. I had previously carefully examined whether any cat, bird, or living animal might be accidentally concealed in my room, {16} and I had studied the forms of the furniture lest they should in the darkness mislead me.

I passed a night of perfect sleeplessness. The distant clock and a faithful dog, just outside my own door, produced the only sounds which disturbed the intense silence of that anxious night.

DURING my boyhood my mother took me to several exhibitions of machinery. I well remember one of them in Hanover Square, by a man who called himself Merlin. I was so greatly interested in it, that the Exhibitor remarked the circumstance, and after explaining some of the objects to which the public had access, proposed to my mother to take me up to his workshop, where I should see still more wonderful automata. We accordingly ascended to the attic. There were two uncovered female figures of silver, about twelve inches high.

One of these walked or rather glided along a space of about four feet, when she turned round and went back to her original place. She used an eye-glass oc­ca­sion­al­ly, and bowed frequently, as if recognizing her acquaintances. The motions of her limbs were singularly graceful.

The other silver figure was an admirable danseuse, with a bird on the fore finger of her right hand, which wagged its tail, flapped its wings, and opened its beak. This lady attitudinized in a most fascinating manner. Her eyes were full of imagination, and irresistible. {18}

These silver figures were the chef-d’œuvres of the artist: they had cost him years of unwearied labour, and were not even then finished.

After I left Devonshire I was placed at a school in the neighbourhood of London, in which there were about thirty boys.

My first experience was unfortunate, and prob­a­bly gave an un­fa­vour­a­ble turn to my whole career during my residence of three years.

After I had been at school a few weeks, I went with one of my companions into the play-ground in the dusk of the evening. We heard a noise, as of people talking in an orchard at some distance, which belonged to our master. As the orchard had recently been robbed, we thought that thieves were again at work. We accordingly climbed over the boundary wall, ran across the field, and saw in the orchard beyond a couple of fellows evidently running away. We pursued as fast as our legs could carry us, and just got up to the supposed thieves at the ditch on the opposite side of the orchard.

A roar of laughter then greeted us from two of our own companions, who had entered the orchard for the purpose of getting some manure for their flowers out of a rotten mulberry-tree. These boys were aware of our mistake, and had humoured it.

We now returned all together towards the play-ground, when we met our master, who immediately pronounced that we were each fined one shilling for being out of bounds. We two boys who had gone out of bounds to protect our master’s property, and who if thieves had really been there would probably have been half-killed by them, attempted to remonstrate and explain the case; but all {19} remonstrance was vain, and we were accordingly fined. I never forgot that injustice.

The school-room adjoined the house, but was not directly connected with it. It contained a library of about three hundred volumes on various subjects, generally very well selected; it also contained one or two works on subjects which do not usually attract at that period of life. I derived much advantage from this library; and I now mention it because I think it of great importance that a library should exist in every school-room.

Amongst the books was a treatise on Algebra, called “Ward’s Young Mathematician’s Guide.” I was always partial to my arithmetical lessons, but this book attracted my particular attention. After I had been at this school for about a twelvemonth, I proposed to one of my school-fellows, who was of a studious habit, that we should get up every morning at three o’clock, light a fire in the school-room, and work until five or half-past five. We accomplished this pretty regularly for several months. Our plan had, however, become partially known to a few of our companions. One of these, a tall boy, bigger than ourselves, having heard of it, asked me to allow him to get up with us, urging that his sole object was to study, and that it would be of great importance to him in after-life. I had the cruelty to refuse this very reasonable request. The subject has often recurred to my memory, but never without regret.

Another of my young companions, Frederick Marryat,3 made the same request, but not with the same motive. I told him we got up in order to work; that he would only play, and that we should then be found out. After some time, having exhausted all his arguments, Marryat told me he was {20} determined to get up, and would do it whether I liked it or not.

Marryat slept in the same room as myself: it contained five beds. Our room opened upon a landing, and its door was exactly opposite that of the master. A flight of stairs led up to a passage just over the room in which the master and mistress slept. Passing along this passage, another flight of stairs led down, on the other side of the master’s bed-room, to another landing, from which another flight of stairs led down to the external door of the house, leading by a long passage to the school-room.

Through this devious course I had cautiously threaded my way, calling up my companion in his room at the top of the last flight of stairs, almost every night for several months.

One night on trying to open the door of my own bed-room, I found Marryat’s bed projecting a little before the door, so that I could not open it. I perceived that this was done purposely, in order that I might awaken him. I therefore cautiously, and by degrees, pushed his bed back without awaking him, and went as usual to my work. This occurred two or three nights successively.

One night, however, I found a piece of pack-thread tied to the door lock, which I traced to Marryat’s bed, and concluded it was tied to his arm or hand. I merely untied the cord from the lock, and passed on.

A few nights after I found it impossible to untie the cord, so I cut it with my pocket-knife. The cord then became thicker and thicker for several nights, but still my pen-knife did its work.

One night I found a small chain fixed to the lock, and passing thence into Marryat’s bed. This defeated my efforts for that night, and I retired to my own bed. The next night {21} I was provided with a pair of plyers, and unbent one of the links, leaving the two portions attached to Marryat’s arm and to the lock of the door. This occurred several times, varying by stouter chains, and by having a padlock which I could not pick in the dark.

At last one morning I found a chain too strong for the tools I possessed; so I retired to my own bed, defeated. The next night, however, I provided myself with a ball of packthread. As soon as I heard by his breathing that Marryat was asleep, I crept over to the door, drew one end of my ball of packthread through a link of the too-powerful chain, and bringing it back with me to bed, gave it a sudden jerk by pulling both ends of the packthread passing through the link of the chain.

Marryat jumped up, put out his hand to the door, found his chain all right, and then lay down. As soon as he was asleep again, I repeated the operation. Having awakened him for the third time, I let go one end of the string, and drew it back by the other, so that he was unable at daylight to detect the cause.

At last, however, I found it expedient to enter into a treaty of peace, the basis of which was that I should allow Marryat to join the night party; but that nobody else should be admitted. This continued for a short time; but, one by one, three or four other boys, friends of Marryat, joined our party, and, as I had anticipated, no work was done. We all got to play; we let off fire-works in the play-ground, and were of course discovered.

Our master read us a very grave lecture at breakfast upon the impropriety of this irregular system of turning night into day, and pointed out its injurious effects upon the health. This, he said, was so remarkable that he could distinguish by {22} their pallid countenances those who had taken part in it. Now he certainly did point out every boy who had been up on the night we were detected. But it appeared to me very odd that the same means of judging had not enabled him long before to discover the two boys who had for several months habitually practised this system of turning night into day.

Another of our pranks never received its solution in our master’s mind; indeed I myself scarcely knew its early history. Somehow or other, a Russian young gentleman, who was a parlour-boarder, had I believe, expatiated to Marryat on the virtues of Cognac.

One evening my friend came to me with a quart bottle of what he called excellent stuff. A council was held amongst a few of us boys to decide how we should dispose of this treasure. I did not myself much admire the liquid, but suggested that it might be very good when mixed up with a lot of treacle. This thought was unanimously adopted, and a subscription made to purchase the treacle. Having no vessel sufficiently large to hold the intended mixture, I proposed to take one of our garden-pots, stopping up the hole in its bottom with a cork.

A good big earthen vessel, thus extemporised, was then filled with this wonderful mixture. A spoon or two, an oyster-shell, and various other contrivances delivered it to its numerous consumers, and all the boys got a greater or less share, according to their taste for this extraordinary liqueur.

The feast was over, the garden-pot was restored to its owner, and the treacled lips of the boys had been wiped with their handkerchiefs or on their coat-sleeves, when the bell announced that it was prayer-time. We all knelt in silence at our respective desks. As soon as the prayers were over, one of the oddest scenes occurred. {23}

Many boys rose up from their knees—but some fell down again. Some turned round several times, and then fell. Some turned round so often that they resembled spinning dervishes. Others were only more stupid than usual; some complained of being sick; many were very sleepy; others were sound asleep, and had to be carried to bed; some talked fast and heroically, two attempted psalmody, but none listened.

All investigation at the time was useless: we were sent off to bed as quickly as possible. It was only known that Count Cognac had married the sweet Miss Treacle, whom all the boys knew and loved, and who lodged at the grocer’s, in the neighbouring village. But I believe neither the pedigree of the bridegroom nor his domicile were ever discovered. It is probable that he was of French origin, and dwelt in a cellar.

After I left this school I was for a few years under the care of an excellent clergyman in the neighbourhood of Cambridge. There were only six boys; but I fear I did not derive from it all the advantage that I might have done. I came into frequent contact with the Rev. Charles Simeon, and with many of his enthusiastic disciples. Every Sunday I had to write from memory an abstract of the sermon he preached in our village. Even at that period of my life I had a taste for generalization. Accordingly, having generalized some of Mr. Simeon’s sermons up to a kind of skeleton form, I tried, by way of experiment, to fill up such a form in a sermon of my own composing from the text of “Alexander the coppersmith hath done us much harm.” As well as I remember, there were in my sermon some queer deductions from this text; but then they fulfilled all the usual conditions of our sermons: so thought also two of my companions to whom I communicated in confidence this new man­u­fac­ture. {24}

By some unexplained circumstance my sermon relating to copper being isomorphous with Simeon’s own productions, got by substitution into the hands of our master as the recollections of one of the other boys. Thereupon arose an awful explosion which I decline to paint.

I did, however, learn something at this school, for I observed a striking illustration of the Economy of Man­u­fac­tures. Mr. Simeon had the cure of a very wicked parish in Cambridge, whilst my instructor held that of a tolerably decent country village. If each minister had stuck to the in­struc­tion of his own parish, it would have necessitated the man­u­fac­ture of four sermons per week, whilst, by this beneficial interchange of duties, only two were required.

Each congregation enjoyed also another advantage from this arrangement—the advantage of variety, which, when moderately indulged in, excites the appetite.

MY father, with a view of acquiring some information which might be of use to me at Cambridge, had consulted a tutor of one of the colleges, who was passing his long vacation at the neighbouring watering-place, Teignmouth. He dined with us frequently. The advice of the Rev. Doctor was quite sound, but very limited. It might be summed up in one short sentence: “Advise your son not to purchase his wine in Cambridge.”

Previously to my entrance at Trinity College, Cambridge, I resided for a time at Totnes, under the guidance of an Oxford tutor, who undertook to superintend my classical studies only.

During my residence at this place I accidentally heard, for the first time, of an idea of forming a universal language. I was much fascinated by it, and, soon after, proceeded to write a kind of grammar, and then to devise a dictionary. Some trace of the former, I think, I still possess: but I was stopped in my idea of making a universal dictionary by the apparent impossibility of arranging signs in any consecutive {26} order, so as to find, as in a dictionary, the meaning of each when wanted. It was only after I had been some time at Cambridge that I became acquainted with the work of “Bishop Wilkins on Universal Language.”

Being passionately fond of algebra, I had instructed myself by means of Ward’s “Young Mathematician’s Guide,” which had casually fallen into my hands at school. I now employed all my leisure in studying such math­e­mat­i­cal works as accident brought to my knowledge. Amongst these were Humphrey Ditton’s “Fluxions,” of which I could make nothing; Madame Agnesi’s “Analytical Institutions,” from which I acquired some knowledge; Woodhouse’s “Principles of Analytical Calculation,” from which I learned the notation of Leibnitz; and Lagrange’s “Théorie des Fonctions.” I possessed also the Fluxions of Maclaurin and of Simpson.

Thus it happened that when I went to Cambridge I could work out such questions as the very moderate amount of mathematics which I then possessed admitted, with equal facility, in the dots of Newton, the d’s of Leibnitz, or the dashes of Lagrange. I had, however, met with many difficulties, and looked forward with intense delight to the certainty of having them all removed on my arrival at Cambridge. I had in my imagination formed a plan for the institution amongst my future friends of a chess club, and also of another club for the discussion of math­e­mat­i­cal subjects.

In 1811, during the war, it was very difficult to procure foreign books. I had heard of the great work of Lacroix, on the “Differential and Integral Calculus,” which I longed to possess, and being misinformed that its price was two guineas, I resolved to purchase it in London on my passage to Cambridge. As soon as I arrived I went to the French {27} bookseller, Dulau, and to my great surprise found that the price of the book was seven guineas. After much thought I made the costly purchase, went on immediately to Cambridge, saw my tutor, Hudson, got lodgings, and then spent the greater part of the night in turning over the pages of my newly-acquired purchase. After a few days, I went to my public tutor Hudson, to ask the explanation of one of my math­e­mat­i­cal difficulties. He listened to my question, said it would not be asked in the Senate House, and was of no sort of consequence, and advised me to get up the earlier subjects of the university studies.

After some little while I went to ask the explanation of another difficulty from one of the lecturers. He treated the question just in the same way. I made a third effort to be enlightened about what was really a doubtful question, and felt satisfied that the person I addressed knew nothing of the matter, although he took some pains to disguise his ignorance.

I thus acquired a distaste for the routine of the studies of the place, and devoured the papers of Euler and other mathematicians, scattered through innumerable volumes of the academies of Petersburgh, Berlin, and Paris, which the libraries I had recourse to contained.

Under these circumstances it was not surprising that I should perceive and be penetrated with the superior power of the notation of Leibnitz.

At an early period, probably at the commencement of the second year of my residence at Cambridge, a friend of mine, Michael Slegg, of Trinity, was taking wine with me, discussing math­e­mat­i­cal subjects, to which he also was enthusiastically attached. Hearing the chapel bell ring, he took leave of me, promising to return for a cup of coffee. {28}

At this period Cambridge was agitated by a fierce controversy. Societies had been formed for printing and circulating the Bible. One party proposed to circulate it with notes, in order to make it intelligible; whilst the other scornfully rejected all explanations of the word of God as profane attempts to mend that which was perfect.

The walls of the town were placarded with broadsides, and posters were sent from house to house. One of the latter form of advertisement was lying upon my table when Slegg left me. Taking up the paper, and looking through it, I thought it, from its exaggerated tone, a good subject for a parody.

I then drew up the sketch of a society to be instituted for translating the small work of Lacroix on the Differential and Integral Lacroix. It proposed that we should have periodical meetings for the propagation of d’s; and consigned to perdition all who supported the heresy of dots. It maintained that the work of Lacroix was so perfect that any comment was unnecessary.

On Slegg’s return from chapel I put the parody into his hands. My friend enjoyed the joke heartily, and at parting asked my permission to show the parody to a math­e­mat­i­cal friend of his, Mr. Bromhead.4

The next day Slegg called on me, and said that he had put the joke into the hand of his friend, who, after laughing heartily, remarked that it was too good a joke to be lost, and proposed seriously that we should form a society for the cultivation of mathematics.

The next day Bromhead called on me. We talked the subject over, and agreed to hold a meeting at his lodgings {29} for the purpose of forming a society for the promotion of analysis.

At that meeting, besides the projectors, there were present Herschel, Peacock, D’Arblay,5 Ryan,6 Robinson,7 Frederick Maule,8 and several others. We constituted ourselves “The Analytical Society;” hired a meeting-room, open daily; held meetings, read papers, and discussed them. Of course we were much ridiculed by the Dons; and, not being put down, it was darkly hinted that we were young infidels, and that no good would come of us.

In the meantime we quietly pursued our course, and at last resolved to publish a volume of our Transactions. Owing to the illness of one of the number, and to various other circumstances, the volume which was published was entirely contributed by Herschel and myself.

At last our work was printed, and it became necessary to decide upon a title. Recalling the slight imputation which had been made upon our faith, I suggested that the most appropriate title would be—

The Principles of pure D-ism in opposition to the Dot-age of the University.9

In thus reviving this wicked pun, I ought at the same time to record an instance of forgiveness unparalleled in history. Fourteen years after, being then at Rome, I accidentally read in Galignani’s newspaper the following paragraph, dated Cambridge:—“Yesterday the bells of St. Mary rang on the election of Mr. Babbage as Lucasian Professor of Mathematics.” {30}

If this event had happened during the lifetime of my father, it would have been most gratifying to myself, because, whilst it would have given him much pleasure, it would then also have afforded intense delight to my mother.

I concluded that the next post would bring me the official confirmation of this report, and after some consideration I sketched the draft of a letter, in which I proposed to thank the University sincerely for the honour they had done me, but to decline it.

This sketch of a letter was hardly dry when two of my intimate friends, the Rev. Mr. Lunn and Mr. Beilby Thompson,10 who resided close to me in the Piazza del Populo, came over to congratulate me on the appointment. I showed them my proposed reply, against which they earnestly protested. Their first, and as they believed their strongest, reason was that it would give so much pleasure to my mother. To this I answered that my mother’s opinion of her son had been confirmed by the reception he had met with in every foreign country he had visited, and that this, in her estimation, would add but little to it. To their next argument I had no sat­is­fac­tory answer. It was that this election could not have occurred unless some friends of mine in England had taken active measures to promote it; that some of these might have been personal friends, but that many others might have exerted themselves entirely upon principle, and that it would be harsh to disappoint such friends, and reject such a compliment.

My own feelings were of a mixed nature. I saw the vast field that the Difference Engine had opened out; for, before I left England in the previous year, I had extended its mechanism to the tabulation of functions having no constant {31} difference, and more par­tic­u­lar­ly I had arrived at the knowledge of the entire command it would have over the computation of the most important classes of tables, those of astronomy and of navigation. I was also most anxious to give my whole time to the completion of the mechanism of the Difference Engine No. 1 which I had then in hand. Small as the admitted duties of the Lucasian Chair were, I felt that they would absorb time which I thought better devoted to the completion of the Difference Engine. If I had then been aware that the lapse of a few years would have thrown upon me the enormous labour which the Analytical Engine absorbed, no motive short of absolute necessity would have induced me to accept any office which might, in the slightest degree, withdraw my attention from its contrivance.

The result of this consultation with my two friends was, that I determined to accept the Chair of Newton, and to hold it for a few years. In 1839 the demands of the Analytical Engine upon my attention had become so incessant and so exhausting, that even the few duties of the Lucasian Chair had a sensible effect in impairing my bodily strength. I therefore sent in my resignation.

In January, 1829, I visited Cambridge, to fulfil one of the first duties of my new office, the examination for Dr. Smith’s prizes.

These two prizes, of twenty-five pounds each, exercise a very curious and important influence. Usually three or four hundred young men are examined previously to taking their degree. The University officers examine and place them in the order of their math­e­mat­i­cal merit. The class called Wranglers is the highest; of these the first is called the senior wrangler, the others the second and third, &c., wranglers. {32}

All the young men who have just taken their degree, whether with or without honours, are qualified to compete for the Smith’s prizes by sending in notice to the electors, who consist of the three Professors of Geometry, Astronomy, and Physics, assisted oc­ca­sion­al­ly by two official electors, the Vice-Chancellor and the Master of Trinity College. However, in point of fact, generally three, and rarely above six young men compete.

It is manifest that the University officers, who examine several hundred young men, cannot bestow the same minute attention upon each as those who, at the utmost, only examine six. Nor is this of any importance, except to the few first wranglers, who usually are candidates for these prizes. The consequence is that the examiners of the Smith’s prizes constitute, as it were, a court of appeal from the decision of the University officers. The decision of the latter is thus therefore, necessarily appealed against upon every occasion. Perhaps in one out of five or six cases the second or third wrangler obtains the first Smith’s prize. I may add that in the few cases known to me previously to my becoming an examiner, the public opinion of the University always approved those decisions, without implying any censure on the officers of the University.

In forming my set of questions, I consulted the late Dean of Ely and another friend, in order that I might not suddenly deviate too much from the usual style of examinations.

After having examined the young men, I sat up the whole night, carefully weighing the relative merits of their answers. I found, with some mortification, that, according to my marks, the second wrangler ought to have the first prize. I therefore put aside the papers until the day before the decision. I then took an unmarked copy of my questions, and put new {33} numbers for their respective values. After very carefully going over the whole of the examination-papers again, I arrived almost exactly at my former conclusion.

On our meeting at the Vice-Chancellor’s, that functionary asked me, as the senior professor, what was my decision as to the two prizes. I stated that the result of my examination obliged me to award the first prize to the second wrangler. Professor Airy was then asked the same question. He made the same reply. Professor Lax being then asked, said he had arrived at the same conclusion as his two colleagues.

The Vice-Chancellor remarked that when we altered the arrangement of the University Examiners, it was very sat­is­fac­tory that we should be unanimous. Professor Airy observed that this sat­is­fac­tion was enhanced by the fact of the remarkable difference in the tastes of the three examiners.

The Vice-Chancellor, turning to me, asked whether it might be permitted to inquire the numbers we had respectively assigned to each candidate.

I and my colleagues immediately mentioned our numbers, which Professor Airy at once reduced to a common scale. On this it appeared that the number of marks assigned to each by Professor Airy and myself very nearly agreed, whilst that of Professor Lax differed but little.

On this occasion the first Smith’s prize was assigned to the second wrangler, Mr. Cavendish, now Duke of Devonshire, the present Chancellor of the University.

The result of the whole of my after-experience showed that amongst the highest men the peculiar tastes of the examiners had no effect in disturbing the proper decision.

I held the Chair of Newton for some few years, and still feel deeply grateful for the honour the University conferred {34} upon me—the only honour I ever received in my own country.11

I must now return to my pursuits during my residence at Cambridge, the account of which has been partially interrupted by the history of my appointment to the Chair of Newton.

Whilst I was an undergraduate, I lived probably in a greater variety of sets than any of my young companions. But my chief and choicest consisted of some ten or a dozen friends who usually breakfasted with me every Sunday after chapel; arriving at about nine, and remaining to between twelve and one o’clock. We discussed all knowable and many unknowable things.

At one time we resolved ourselves into a Ghost Club, and proceeded to collect evidence, and entered into a considerable correspondence upon the subject. Some of this was both interesting and instructive.

At another time we resolved ourselves into a Club which we called The Extractors. Its rules were as follows,—

It has often occurred to me to inquire of my legal friends whether, if the sanity of any member of the club had been questioned in after-life, he would have adduced the fact of membership of the Club of Extractors as an indication of sanity or of insanity.

During the first part of my residence at Cambridge, I played at chess very frequently, often with D’Arblay and with several other good players. There was at that period a fellow-commoner at Trinity named Brande, who devoted almost his whole time to the study of chess. I was invited to meet him one evening at the rooms of a common friend for the purpose of trying our strength.

On arriving at my friend’s rooms, I found a note informing me that he had gone to Newmarket, and had left coffee and the chessmen for us. I was myself tormented by great shyness, and my yet unseen adversary was, I understood, equally diffident. I was sitting before the chess-board when Brande entered. I rose, he advanced, sat down, and took a white and a black pawn from the board, which he held, one in either hand. I pointed with my finger to the left hand and won the move.

The game then commenced; it was rather a long one, and I won it: but not a word was exchanged until the end: when Brande uttered the first word. “Another?” To this I nodded assent.

How that game was decided I do not now remember; but the first sentence pronounced by either of us, was a remark by Brande, that he had lost the first game by a certain move of his white bishop. To this I replied, that I thought he was {36} mistaken, and that the real cause of his losing the game arose from the use I had made of my knight two moves previously to his white bishop’s move.

We then immediately began to replace the men on the board in the positions they occupied at that particular point of the game when the white bishop’s move was made. Each took up any piece indiscriminately, and placed it without hesitation on the exact square on which it had stood. It then became apparent that the effective move to which I had referred was that of my knight.

Brande, during his residence at Cambridge, studied chess regularly several hours each day, and read almost every treatise on the subject. After he left college he travelled abroad, took lessons from every celebrated teacher, and played with all the most eminent players on the Continent.

At intervals of three or four years I oc­ca­sion­al­ly met him in London. After the usual greeting he always proposed that we should play a game of chess.

I found on these occasions, that if I played any of the ordinary openings, such as are found in the books, I was sure to be beaten. The only way in which I had a chance of winning, was by making early in the game a move so bad that it had not been mentioned in any treatise. Brande possessed, and had read, almost every book upon the subject.

Another set which I frequently joined were addicted to sixpenny whist. It consisted of Higman, afterwards Tutor of Trinity; Follet, afterwards Attorney-General; of a learned and accomplished Dean still living, and I have no doubt still playing an excellent rubber, and myself. We not unfrequently sat from chapel-time in the evening until the sound {37} of the morning chapel bell again called us to our religious duties.

I mixed oc­ca­sion­al­ly with a different set of whist players at Jesus College. They played high: guinea points, and five guineas on the rubber. I was always a most welcome visitor, not from my skill at the game; but because I never played more than shilling points and five shillings on the rubber. Consequently my partner had what they considered an advantage: namely, that of playing guinea points with one of our adversaries and pound points with the other.

Totally different in character was another set in which I mixed. I was very fond of boating, not of the manual labour of rowing, but the more in­tel­lec­tual art of sailing. I kept a beautiful light, London-built boat, and oc­ca­sion­al­ly took long voyages down the river, beyond Ely into the fens. To accomplish these trips, it was necessary to have two or three strong fellows to row when the wind failed or was contrary. These were useful friends upon my aquatic expeditions, but not being of exactly the same calibre as my friends of the Ghost Club, were very cruelly and disrespectfully called by them “my Tom fools.”

The plan of our voyage was thus:—I sent my servant to the apothecary for a thing called an ægrotat, which I understood, for I never saw one, meant a certificate that I was indisposed, and that it would be injurious to my health to attend chapel, or hall, or lectures. This was forwarded to the college authorities.

I also directed my servant to order the cook to send me a large well-seasoned meat pie, a couple of fowls, &c. These were packed in a hamper with three or four bottles of wine and one of noyeau. We sailed when the wind was fair, and rowed when there was none. Whittlesea Mere was a very {38} favourite resort for sailing, fishing, and shooting. Sometimes we reached Lynn. After various adventures and five or six days of hard exercise in the open air, we returned with our health more renovated than if the best physician had prescribed for us.

During my residence at Cambridge, Smithson Tennant was the Professor of Chemistry, and I attended his lectures. Having a spare room, I turned it into a kind of laboratory, in which Herschel worked with me, until he set up a rival one of his own. We both oc­ca­sion­al­ly assisted the Professor in preparing his experiments. The science of chemistry had not then assumed the vast development it has now attained. I gave up its practical pursuit soon after I resided in London, but I have never regretted the time I bestowed upon it at the commencement of my career. I had hoped to have long continued to enjoy the friendship of my entertaining and valued instructor, and to have profited by his introducing me to the science of the metropolis, but his tragical fate deprived me of that advantage. Whilst riding with General Bulow across a drawbridge at Boulogne, the bolt having been displaced, Smithson Tennant was precipitated to the bottom, and killed on the spot. The General, having an earlier warning, set spurs to his horse, and just escaped a similar fate.

My views respecting the notation of Leibnitz now (1812) received confirmation from an extensive course of reading. I became convinced that the notation of fluxions must ultimately prove a strong impediment to the progress of English science. But I knew, also, that it was hopeless for any young and unknown author to attempt to introduce the notation of Leibnitz into an elementary work. This opinion naturally {39} suggested to me the idea of translating the smaller work of Lacroix. It is possible, although I have no recollection of it, that the same idea may have occurred to several of my colleagues of the Analytical Society, but most of them were so occupied, first with their degree, and then with their examination for fellowships, that no steps were at that time taken by any of them on that subject.

Unencumbered by these distractions, I commenced the task, but at what period of time I do not exactly recollect. I had finished a portion of the translation, and laid it aside, when, some years afterwards, Peacock called on me in Devonshire Street, and stated that both Herschel and himself were convinced that the change from the dots to the d’s would not be accomplished until some foreign work of eminence should be translated into English. Peacock then proposed that I should either finish the translation which I had commenced, or that Herschel and himself should complete the remainder of my translation. I suggested that we should toss up which alternative to take. It was determined by lot that we should make a joint translation. Some months after, the translation of the small work of Lacroix was published.

For several years after, the progress of the notation of Leibnitz at Cambridge was slow. It is true that the tutors of the two largest colleges had adopted it, but it was taught at none of the other colleges.

It is always difficult to think and reason in a new language, and this difficulty discouraged all but men of energetic minds. I saw, however, that, by making it their interest to do so, the change might be accomplished. I therefore proposed to make a large collection of examples of the differential and integral calculus, consisting merely of the statement of each problem and its final solution. I foresaw that if such a {40} publication existed, all those tutors who did not approve of the change of the Newtonian notation would yet, in order to save their own time and trouble, go to this collection of examples to find problems to set to their pupils. After a short time the use of the new signs would become familiar, and I anticipated their general adoption at Cambridge as a matter of course.

I commenced by copying out a large portion of the work of Hirsch. I then communicated to Peacock and Herschel my view, and proposed that they should each contribute a portion.

Peacock considerably modified my plan by giving the process of solution to a large number of the questions. Herschel prepared the questions in finite differences, and I supplied the examples to the calculus of functions. In a very few years the change was completely established; and thus at last the English cultivators of math­e­mat­i­cal science, untrammelled by a limited and imperfect system of signs, entered on equal terms into competition with their continental rivals.

CALCULATING MACHINES comprise various pieces of mechanism for assisting the human mind in executing the operations of arithmetic. Some few of these perform the whole operation without any mental attention when once the given numbers have been put into the machine.

Others require a moderate portion of mental attention: these latter are generally of much simpler construction than the former, and it may also be added, are less useful.

The simplest way of deciding to which of these two classes any calculating machine belongs is to ask its maker—Whether, when the numbers on which it is to operate are placed in the instrument, it is capable of arriving at its result by the mere motion of a spring, a descending weight, or any other constant force? If the answer be in the affirmative, the machine is really automatic; if otherwise, it is not self-acting.

Of the various machines I have had occasion to examine, many of those for Addition and Subtraction have been found {42} to be automatic. Of machines for Multiplication and Division, which have fully come under my examination, I cannot at present recall one to my memory as absolutely fulfilling this condition.

The earliest idea that I can trace in my own mind of calculating arithmetical Tables by machinery arose in this manner:—

One evening I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the Table in a kind of dreamy mood, with a Table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, “Well, Babbage, what are you dreaming about?” to which I replied, “I am thinking that all these Tables (pointing to the logarithms) might be calculated by machinery.”

I am indebted to my friend, the Rev. Dr. Robinson, the Master of the Temple, for this anecdote. The event must have happened either in 1812 or 1813.

About 1819 I was occupied with devising means for accurately dividing astronomical instruments, and had arrived at a plan which I thought was likely to succeed perfectly. I had also at that time been speculating about making machinery to compute arithmetical Tables.

One morning I called upon the late Dr. Wollaston, to consult him about my plan for dividing instruments. On talking over the matter, it turned out that my system was exactly that which had been described by the Duke de Chaulnes, in the Memoirs of the French Academy of Sciences, about fifty or sixty years before. I then mentioned my other idea of computing Tables by machinery, which Dr. Wollaston thought a more promising subject.

I considered that a machine to execute the mere isolated {43} operations of arithmetic, would be comparatively of little value, unless it were very easily set to do its work, and unless it executed not only accurately, but with great rapidity, whatever it was required to do.

On the other hand, the method of differences supplied a general principle by which all Tables might be computed through limited intervals, by one uniform process. Again, the method of differences required the use of mechanism for Addition only. In order, however, to insure accuracy in the printed Tables, it was necessary that the machine which computed Tables should also set them up in type, or else supply a mould in which stereotype plates of those Tables could be cast.

I now began to sketch out arrangements for accomplishing the several partial processes which were required. The arithmetical part must consist of two distinct processes—the power of adding one digit to another, and also of carrying the tens to the next digit, if it should be necessary.

The first idea was, naturally, to add each digit successively. This, however, would occupy much time if the numbers added together consisted of many places of figures.

The next step was to add all the digits of the two numbers each to each at the same instant, but reserving a certain mechanical memorandum, wherever a carriage became due. These carriages were then to be executed successively.

Having made various drawings, I now began to make models of some portions of the machine, to see how they would act. Each number was to be expressed upon wheels placed upon an axis; there being one wheel for each figure in the number operated upon.

Having arrived at a certain point in my progress, it became necessary to have teeth of a peculiar form cut upon these {44} wheels. As my own lathe was not fit for this job, I took the wheels to a wheel-cutter at Lambeth, to whom I carefully conveyed my in­struc­tions, leaving with him a drawing as his guide.

These wheels arrived late one night, and the next morning I began putting them in action with my other mechanism, when, to my utter astonishment, I found they were quite unfit for their task. I examined the shape of their teeth, compared them with those in the drawings, and found they agreed perfectly; yet they could not perform their intended work. I had been so certain of the truth of my previous reasoning, that I now began to be somewhat uneasy. I reflected that, if the reasoning about which I had been so certain should prove to have been really fallacious, I could then no longer trust the power of my own reason. I therefore went over with my wheels to the artist who had formed the teeth, in order that I might arrive at some explanation of this extraordinary contradiction.

On conferring with him, it turned out that, when he had understood fully the peculiar form of the teeth of wheels, he discovered that his wheel-cutting engine had not got amongst its divisions that precise number which I had required. He therefore had asked me whether another number, which his machine possessed, would not equally answer my object. I had inadvertently replied in the affirmative. He then made arrangements for the precise number of teeth I required; and the new wheels performed their expected duty perfectly.

The next step was to devise means for printing the tables to be computed by this machine. My first plan was to make it put together moveable type. I proposed to make metal boxes, each containing 3,000 types of one of the ten digits. These types were to be made to pass out one by one from the {45} bottom of their boxes, when required by the computing part of the machine.

But here a new difficulty arose. The attendant who put the types into the boxes might, by mistake, put a wrong type in one or more of them. This cause of error I removed in the following manner:—There are usually certain notches in the side of the type. I caused these notches to be so placed that all the types of any given digit possessed the same char­ac­ter­is­tic notches, which no other type had. Thus, when the boxes were filled, by passing a small wire down these peculiar notches, it would be impeded in its passage, if there were included in the row a single wrong figure. Also, if any digit were accidentally turned upside down, it would be indicated by the stoppage of the testing wire.

One notch was reserved as common to every species of type. The object of this was that, before the types which the Difference Engine had used for its computation were removed from the iron platform on which they were placed, a steel wire should be passed through this common notch, and remain there. The tables, composed of moveable types, thus interlocked, could never have any of their figures drawn out by adhesion to the inking-roller, and then by possibility be restored in an inverted order. A small block of such figures tied together by a bit of string, remained unbroken for several years, although it was rather roughly used as a plaything by my children. One such box was finished, and delivered its type satisfactorily.

Another plan for printing the tables, was to place the ordinary printing type round the edges of wheels. Then, as each successive number was produced by the arithmetical part, the type-wheels would move down upon a plate of soft composition, upon which the tabular number would be {46} impressed. This mould was formed of a mixture of plaster-of-Paris with other materials, so as to become hard in the course of a few hours.

The first difficulty arose from the impression of one tabular number on the mould being distorted by the succeeding one.

I was not then aware that a very slight depth of impression from the type would be quite sufficient. I surmounted the difficulty by previously passing a roller, having longitudinal wedge-shaped projections, over the plastic material. This formed a series of small depressions in the matrix between each line. Thus the expansion arising from the impression of one line partially filled up the small depression or ditch which occurred between each successive line.

The various minute difficulties of this kind were successively overcome; but subsequent experience has proved that the depth necessary for stereotype moulds is very small, and that even thick paper, prepared in a peculiar manner, is quite sufficient for the purpose.

Another series of experiments were, however, made for the purpose of punching the computed numbers upon copper plate. A special machine was contrived and constructed, which might be called a co-ordinate machine, because it moved the copper plate and steel punches in the direction of three rectangular co-ordinates. This machine was afterwards found very useful for many other purposes. It was, in fact, a general shaping machine, upon which many parts of the Difference Engine were formed.

Several specimens of surface and copper-plate printing, as well as of the copper plates, produced by these means, were exhibited at the Exhibition of 1862.

I have proposed and drawn various machines for the purpose of calculating a series of numbers forming Tables {47} by means of a certain system called “The Method of Differences,” which it is the object of this sketch to explain.

The first Difference Engine with which I am acquainted comprised a few figures, and was made by myself, between 1820 and June 1822. It consisted of from six to eight figures. A much larger and more perfect engine was sub­se­quent­ly commenced in 1823 for the Government.

It was proposed that this latter Difference Engine should have six orders of differences, each consisting of about twenty places of figures, and also that it should print the Tables it computed.

The small portion of it which was placed in the International Exhibition of 1862 was put together nearly thirty years ago. It was accompanied by various parts intended to enable it to print the results it calculated, either as a single copy on paper—or by putting together moveable types—or by stereotype plates taken from moulds punched by the machine—or from copper plates impressed by it. The parts necessary for the execution of each of these processes were made, but these were not at that time attached to the calculating part of the machine.

A considerable number of the parts by which the printing was to be accomplished, as also several specimens of portions of tables punched on copper, and of stereotype moulds, were exhibited in a glass case adjacent to the Engine.

In 1834 Dr. Lardner published, in the ‘Edinburgh Review,’12 a very elaborate description of this portion of the machine, in which he explained clearly the method of Differences.

It is very singular that two persons, one resident in London, the other in Sweden, should both have been struck, on reading this review, with the simplicity of the math­e­mat­i­cal principle {48} of differences as applied to the calculation of Tables, and should have been so fascinated with it as to have undertaken to construct a machine of the kind.

Mr. Deacon, of Beaufort House, Strand, whose mechanical skill is well known, made, for his own sat­is­fac­tion, a small model of the calculating part of such a machine, which was shown only to a few friends, and of the existence of which I was not aware until after the Swedish machine was brought to London.

Mr. Scheutz, an eminent printer at Stockholm, had far greater difficulties to encounter. The construction of mechanism, as well as the math­e­mat­i­cal part of the question, was entirely new to him. He, however, undertook to make a machine having four differences, and fourteen places of figures, and capable of printing its own Tables.

After many years’ indefatigable labour, and an almost ruinous expense, aided by grants from his Government, by the constant assistance of his son, and by the support of many enlightened members of the Swedish Academy, he completed his Difference Engine. It was brought to London, and some time afterwards exhibited at the great Exhibition at Paris. It was then purchased for the Dudley Observatory at Albany by an enlightened and public-spirited merchant of that city, John F. Rathbone, Esq.

An exact copy of this machine was made by Messrs. Donkin and Co., for the English Government, and is now in use in the Registrar-General’s Department at Somerset House. It is very much to be regretted that this specimen of English workmanship was not exhibited in the International Exhibition.

Those who are only familiar with ordinary arithmetic may, by following out with the pen some of the examples which will be given, easily make themselves acquainted with the simple principles on which the Difference Engine acts.

It is necessary to state distinctly at the outset, that the Difference Engine is not intended to answer special questions. Its object is to calculate and print a series of results formed according to given laws. These are called Tables—many such are in use in various trades. For example—there are collections of Tables of the amount of any number of pounds from 1 to 100 lbs. of butchers’ meat at various prices per lb. Let us examine one of these Tables: viz.—the price of meat 5 d. per lb., we find

There are two ways of computing this Table:—

Let us now examine the relative advantages of each plan. We shall find that if we had multiplied each number of lbs. in {50} the Table by 5, and put down the resulting amount, then every number in the Table would have been computed independently. If, therefore, an error had been committed, it would not have affected any but the single tabular number at which it had been made. On the other hand, if a single error had occurred in the system of computing by adding five at each step, any such error would have rendered the whole of the rest of the Table untrue.

Thus the system of calculating by differences, which is the easiest, is much more liable to error. It has, on the other hand, this great advantage: viz., that when the Table has been so computed, if we calculate its last term directly, and if it agree with the last term found by the continual addition of 5, we shall then be quite certain that every term throughout is correct. In the system of computing each term directly, we possess no such check upon our accuracy.

Now the Table we have been considering is, in fact, merely a Table whose first difference is constant and equal to five. If we express it in pence it becomes—

Any machine, therefore, which could add one number to another, and at the same time retain the original number called the first difference for the next operation, would be able to compute all such Tables.

Let us now consider another form of Table which might readily occur to a boy playing with his marbles, or to a young lady with the balls of her solitaire board. {51}

The boy may place a row of his marbles on the sand, at equal distances from each other, thus—

He might then, beginning with the second, place two other marbles under each, thus—

He might then, beginning with the third, place three other marbles under each group, and so on; commencing always one group later, and making the addition one marble more each time. The several groups would stand thus arranged—

He will not fail to observe that he has thus formed a series of triangular groups, every group having an equal number of marbles in each of its three sides. Also that the side of each successive group contains one more marble than that of its preceding group.

Now an inquisitive boy would naturally count the numbers in each group and he would find them thus—

He might also want to know how many marbles the thirtieth or any other distant group might contain. Perhaps he might go to papa to obtain this information; but I much fear papa would snub him, and would tell him that it was nonsense—that it was useless—that nobody knew the number, and so forth. If the boy is told by papa, that he is not able to answer the question, then I recommend him to pay careful attention to whatever that father may at any time say, for he has overcome two of the greatest obstacles to the acquisition {52} of knowledge—inasmuch as he possesses the consciousness that he does not know—and he has the moral courage to avow it.13

If papa fail to inform him, let him go to mamma, who will not fail to find means to satisfy her darling’s curiosity. In the meantime the author of this sketch will endeavour to lead his young friend to make use of his own common sense for the purpose of becoming better acquainted with the triangular figures he has formed with his marbles.

In the case of the Table of the price of butchers’ meat, it was obvious that it could be formed by adding the same constant difference continually to the first term. Now suppose we place the numbers of our groups of marbles in a column, as we did our prices of various weights of meat. Instead of adding a certain difference, as we did in the former case, let us subtract the figures representing each group of marbles from the figures of the succeeding group in the Table. The process will stand thus:—

It is usual to call the third column thus formed the column of {53} first dif­fer­ences. It is evident in the present instance that that column represents the natural numbers. But we already know that the first difference of the natural numbers is constant and equal to unity. It appears, therefore, that a Table of these numbers, representing the group of marbles, might be constructed to any extent by mere addition—using the number 1 as the first number of the Table, the number 1 as the first Difference, and also the number 1 as the second Difference, which last always remains constant.

Now as we could find the value of any given number of pounds of meat directly, without going through all the previous part of the Table, so by a somewhat different rule we can find at once the value of any group whose number is given.

Thus, if we require the number of marbles in the fifth group, proceed thus:—

If the reader will take the trouble to calculate with his pencil the five groups given above, he will soon perceive the general truth of this rule.

We have now arrived at the fact that this Table—like that of the price of butchers’ meat—can be calculated by two different methods. By the first, each number of the Table is calculated independently: by the second, the truth of each number depends upon the truth of all the previous numbers.

Perhaps my young friend may now ask me, What is the use of such Tables? Until he has advanced further in his {54} arithmetical studies, he must take for granted that they are of some use. The very Table about which he has been reasoning possesses a special name—it is called a Table of Triangular Numbers. Almost every general collection of Tables hitherto published contains portions of it of more or less extent.

Above a century ago, a volume in small quarto, containing the first 20,000 triangular numbers, was published at the Hague by E. De Joncourt, A.M., and Professor of Philosophy.14 I cannot resist quoting the author’s enthusiastic expression of the happiness he enjoyed in composing his celebrated work:

I hope my young friend is acquainted with the fact—that the product of any number multiplied by itself is called the square of that number. Thus 36 is the product of 6 multiplied by 6, and 36 is called the square of 6. I would now recommend him to examine the series of square numbers

{55} and to make, for his own in­struc­tion, the series of their first and second differences, and then to apply to it the same reasoning which has been already applied to the Table of Triangular Numbers.

When he feels that he has mastered that Table, I shall be happy to accompany mamma’s darling to Woolwich or to Portsmouth, where he will find some practical illustrations of the use of his newly-acquired numbers. He will find scattered about in the Arsenal various heaps of cannon balls, some of them triangular, others square or oblong pyramids.

Looking on the simplest form—the triangular pyramid—he will observe that it exactly represents his own heaps of marbles placed each successively above one another until the top of the pyramid contains only a single ball.

The new series thus formed by the addition of his own triangular numbers is—

He will at once perceive that this Table of the number of cannon balls contained in a triangular pyramid can be carried to any extent by simply adding successive differences, the third of which is constant.

The next step will naturally be to inquire how any number in this Table can be calculated by itself. A little consideration will lead him to a fair guess; a little industry will enable him to confirm his conjecture.

It will be observed at p. 49 that in order to find {56} independently any number of the Table of the price of butchers’ meat, the following rule was observed:—

Take the number whose tabular number is required.

Multiply it by the first difference.

This product is equal to the required tabular number.

Again, at p. 53, the rule for finding any triangular number was:—

This is the number of marbles in the 5th group.

Now let us make a bold conjecture respecting the Table of cannon balls, and try this rule:—

The real number in the 5th pyramid is 35. But the number 105 at which we have arrived is exactly three times as great. If, therefore, instead of dividing by 2 we had divided by 2 and also by 3, we should have arrived at a true result in this instance.

The amended rule is therefore— {57}

This rule will, upon trial, be found to give correctly every tabular number.

By similar reasoning we might arrive at the knowledge of the number of cannon balls in square and rectangular pyramids. But it is presumed that enough has been stated to enable the reader to form some general notion of the method of calculating arithmetical Tables by differences which are constant.

It may now be stated that mathematicians have discovered that all the Tables most important for practical purposes, such as those relating to Astronomy and Navigation, can, although they may not possess any constant differences, still be calculated in detached portions by that method.

Hence the importance of having machinery to calculate by differences, which, if well made, cannot err; and which, if carelessly set, presents in the last term it calculates the power of verification of every antecedent term.

From the preceding explanation it appears that all Tables may be calculated, to a greater or less extent, by the method of Differences. That method requires, for its successful {58} execution, little beyond mechanical means of performing the arithmetical operation of Addition. Subtraction can, by the aid of a well-known artifice, be converted into Addition.

The process of Addition includes two distinct parts—1st. The first consists of the addition of any one digit to another digit; 2nd. The second consists in carrying the tens to the next digit above.

Let us take the case of the addition of the two following numbers, in which no carriages occur:—

It will be observed that, in making this addition, the mind acts by successive steps. The person adding says to himself—

In the following addition there are several carriages:—

The person adding says to himself—

Now, the length of time required for adding one number to another is mainly dependent upon the number of figures to {59} be added. If we could tell the average time required by the mind to add two figures together, the time required for adding any given number of figures to another equal number would be found by multiplying that average time by the number of digits in either number.

When we attempt to perform such additions by machinery we might follow exactly the usual process of the human mind. In that case we might take a series of wheels, each having marked on its edges the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These wheels might be placed above each other upon an axis. The lowest would indicate the units’ figure, the next above the tens, and so on, as in the Difference Engine at the Exhibition, a woodcut of which faces the title-page.

Several such axes, with their figure wheels, might be placed around a system of central wheels, with which the wheels of any one or more axes might at times be made to gear. Thus the figures on any one axis might, by means of those central wheels, be added to the figure wheels of any other axis.

But it may fairly be expected, and it is indeed of great importance that calculations made by machinery should not merely be exact, but that they should be done in a much shorter time than those performed by the human mind. Suppose there were no tens to carry, as in the first of the two cases; then, if we possessed mechanism capable of adding any one digit to any other in the units’ place of figures, a similar mechanism might be placed above it to add the tens’ figures, and so on for as many figures as might be required.

But in this case, since there are no carriages, each digit might be added to its corresponding digit at the same time. Thus, the time of adding by means of mechanism, any two numbers, however many figures they might consist of, would {60} not exceed that of adding a single digit to another digit. If this could be accomplished it would render additions and subtractions with numbers having ten, twenty, fifty, or any number of figures, as rapid as those operations are with single figures.

Let us now examine the case in which there were several carriages. Its successive stages may be better explained, thus—

Now if, as in this case, all the carriages were known, it would then be possible to make all the additions of digits at the same time, provided we could also record each carriage as it became due. We might then complete the addition by adding, at the same instant, each carriage in its proper place. The process would then stand thus:— {61}

Now, whatever mechanism is contrived for adding any one digit to any other must, of course, be able to add the largest digit, nine, to that other digit. Supposing, therefore, one unit of number to be passed over in one second of time, it is evident that any number of pairs of digits may be added together in nine seconds, and that, when all the consequent carriages are known, as in the above case, it will cost one second more to make those carriages. Thus, addition and carriage would be completed in ten seconds, even though the numbers consisted each of a hundred figures.

But, unfortunately, there are multitudes of cases in which the carriages that become due are only known in successive periods of time. As an example, add together the two following numbers:—

In this case the carriages only become known successively, and they amount to the number of figures to be added; consequently, the mere addition of two numbers, each of fifty places of figures, would require only nine seconds of time, whilst the possible carriages would consume fifty seconds.

The mechanical means I employed to make these carriages bears some slight analogy to the operation of the faculty of memory. A toothed wheel had the ten digits marked upon its edge; between the nine and the zero a projecting tooth was placed. Whenever any wheel, in receiving addition, passed from nine to zero, the projecting tooth pushed over a certain lever. Thus, as soon as the nine seconds of time required for addition were ended, every carriage which had become due was indicated by the altered position of its lever. An arm now went round, which was so contrived that the act of replacing that lever caused the carriage which its position indicated to be made to the next figure above. But this figure might be a nine, in which case, in passing to zero, it would put over its lever, and so on. By placing the arms spirally round an axis, these successive carriages were accomplished.

Multitudes of contrivances were designed, and almost endless drawings made, for the purpose of economizing the time and simplifying the mechanism of carriage. In that portion of the Difference Engine in the Exhibition of 1862 the time of carriage has been reduced to about one-fourth part of what was at first required.

At last having exhausted, during years of labour, the principle of successive carriages, it occurred to me that it might be possible to teach mechanism to accomplish another mental process, namely—to foresee. This idea occurred to me in October, 1834. It cost me much thought, but the {63} principle was arrived at in a short time. As soon as that was attained, the next step was to teach the mechanism which could foresee to act upon that foresight. This was not so difficult: certain mechanical means were soon devised which, although very far from simple, were yet sufficient to dem­on­strate the possibility of constructing such machinery.

The process of simplifying this form of carriage occupied me, at intervals, during a long series of years. The demands of the Analytical Engine, for the mechanical execution of arithmetical operations, were of the most extensive kind. The multitude of similar parts required by the Analytical Engine, amounting in some instances to upwards of fifty thousand, rendered any, even the simplest, improvement of each part a matter of the highest importance, more especially as regarded the diminished amount of expenditure for its construction.

That portion of Difference Engine, No. 1, which during the last twenty years has been in the museum of King’s College, at Somerset House, is represented in the woodcut opposite the title page.

It consists of three columns; each column contains six cages; each cage contains one figure-wheel.

The column on the right hand has its lowest figure-wheel covered by a shade which is never removed, and to which the reader’s attention need not be directed.

The figure-wheel next above may be placed by hand at any one of the ten digits. In the woodcut it stands at zero.

The third, fourth, and fifth cages are exactly the same as the second.

The sixth cage contains exactly the same as the four just {64} described. It also contains two other figure-wheels, which with a similar one above the frame, may also be dismissed from the reader’s attention. Those wheels are entirely unconnected with the moving part of the engine, and are only used for memoranda.

It appears, therefore, that there are in the first column on the right hand five figure-wheels, each of which may be set by hand to any of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The lowest of these figure-wheels represents the unit’s figure of any number; the next above the ten’s figure, and so on. The highest figure-wheel will therefore represent tens of thousands.

Now, as each of these figure-wheels may be set by hand to any digit, it is possible to place on the first column any number up to 99999. It is on these wheels that the Table to be calculated by the engine is expressed. This column is called the Table column, and the axis of the wheels the Table axis.

The second or middle column has also six cages, in each of which a figure-wheel is placed. It will be observed that in the lowest cage, the figure on the wheel is concealed by a shade. It may therefore be dismissed from the attention. The five other figure-wheels are exactly like the figure-wheels on the Table axis, and can also represent any number up to 99999.

This column is called the First Difference column, and the axis is called the First Difference axis.

The third column, which is that on the left hand, has also six cages, in each of which is a figure-wheel capable of being set by hand to any digit.

The mechanism is so contrived that whatever may be the numbers placed respectively on the figure-wheels of each of {65} the three columns, the following succession of operations will take place as long as the handle is moved:—

It appears, therefore, that with this small portion of the Engine any Table may be computed by the method of differences, provided neither the Table itself, nor its first and second differences, exceed five places of figures.

If the whole Engine had been completed it would have had six orders of differences, each of twenty places of figures, whilst the three first columns would each have had half a dozen additional figures.

This is the simplest explanation of that portion of the Difference Engine No. 1, at the Exhibition of 1862. There are, however, certain modifications in this fragment which render its exhibition more instructive, and which even give a mechanical insight into those higher powers with which I had endowed it in its complete state.

As a matter of convenience in exhibiting it, there is an arrangement by which the three upper figures of the second difference are transformed into a small engine which counts the natural numbers.

By this means it can be set to compute any Table whose second difference is constant and less than 1000, whilst at the same time it thus shows the position in the Table of each tabular number.

In the existing portion there are three bells; they can be respectively ordered to ring when the Table, its first difference {66} and its second difference, pass from positive to negative. Several weeks after the machine had been placed in my drawing-room, a friend came by appointment to test its power of calculating Tables. After the Engine had computed several Tables, I remarked that it was evidently finding the root of a quadratic equation; I therefore set the bells to watch it. After some time the proper bell sounded twice, indicating, and giving the two positive roots to be 28 and 30. The Table thus calculated related to the barometer and really involved a quadratic equation, although its maker had not previously observed it. I afterwards set the Engine to tabulate a formula containing impossible roots, and of course the other bell warned me when it had attained those roots. I had never before used these bells, simply because I did not think the power it thus possessed to be of any practical utility.

Again, the lowest cages of the Table, and of the first difference, have been made use of for the purpose of illustrating three important faculties of the finished engine.

Amongst the various questions which have been asked respecting the Difference Engine, I will mention a few of the most remarkable:—One gentleman addressed me thus: {67} “Pray, Mr. Babbage, can you explain to me in two words what is the principle of this machine?” Had the querist possessed a moderate acquaintance with mathematics I might in four words have conveyed to him the required information by answering, “The method of differences.” The question might indeed have been answered with six characters thus—

but such information would have been unintelligible to such inquirers.

On two occasions I have been asked,—“Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” In one case a member of the Upper, and in the other a member of the Lower, House put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. I did, however, explain the following property, which might in some measure approach towards an answer to it.

It is possible to construct the Analytical Engine in such a manner that after the question is once communicated to the engine, it may be stopped at any turn of the handle and set on again as often as may be desired. At each stoppage every figure-wheel throughout the Engine, which is capable of being moved without breaking, may be moved on to any other digit. Yet after each of these apparent falsifications the engine will be found to make the next calculation with perfect truth.

The explanation is very simple, and the property itself useless. The whole of the mechanism ought of course to be enclosed in glass, and kept under lock and key, in which case the mechanism necessary to give it the property alluded to would be useless.

THE following statement was drawn up by the late Sir Harris Nicolas, G.S.M. & G., from papers and documents in my possession relating to the Difference Engine. I believe every paper I possessed at all bearing on the subject was in his hands for several months.

For some time previous to 1822, Mr. Babbage had been engaged in contriving machinery for the execution of extensive arithmetical operations, and in devising mechanism by which the machine that made the calculations might also print the results.

On the 3rd of July, 1822, he published a letter to Sir Humphry Davy, President of the Royal Society, containing a statement of his views on that subject; and more par­tic­u­lar­ly describing an Engine for calculating astronomical, nautical, and other Tables, by means of the “method of differences.” In that letter it is stated that a small Model, consisting of six figures, and capable of working two orders of differences, had been constructed; and that it performed its work in a sat­is­fac­tory manner.

The concluding paragraph of that letter is as follows:—

The Model alluded to had been shown to a large number of Mr. Babbage’s acquaintances, and to many other persons; and copies of his letter having been given to several of his friends, it is probable that one of the copies was sent to the Treasury.

On the 1st of April, 1823, the Lords of the Treasury referred that Letter to the Royal Society, requesting—

On the 1st of May the Royal Society reported to the Treasury, that—

On the 21st of May these papers were ordered to be printed by the House of Commons.

In July, 1823, Mr. Babbage had an interview with the Chancellor of the Exchequer (Mr. Robinson16 ), to ascertain if it was the wish of the Government that he should construct a large Engine of the kind, which would also print the results it calculated. {70}

From the conversation which took place on that occasion, Mr. Babbage apprehended that such was the wish of the Government. The Chancellor of the Exchequer remarked that the Government were in general unwilling to make grants of money for any inventions, however meritorious; because, if they really possessed the merit claimed for them, the sale of the article produced would be the best, as well as largest reward of the inventor: but that the present case was an exception; it being apparent that the construction of such a Machine could not be undertaken with a view to profit from the sale of its produce; and that, as math­e­mat­i­cal Tables were peculiarly valuable for nautical purposes, it was deemed a fit object of encouragement by the Government.

The Chancellor of the Exchequer mentioned two modes of advancing money for the construction:—either through the recommendation of a Committee of the House of Commons, or by taking a sum from the Civil Contingencies: and he observed that, as the Session of Parliament was near its termination, the latter course might, perhaps, be the most convenient.

Mr. Babbage thinks the Chancellor of the Exchequer also made some ob­ser­va­tion, indicating that the amount of money taken from the Civil Contingencies would be smaller than that which might be had by means of a Committee of the House of Commons: and he then proposed to take 1,000 l. as a commencement from the Civil Contingencies Fund. To this Mr. Babbage replied, in words which he distinctly remembers, “Would it be too much, in the first instance, to take 1,500 l.?” The Chancellor of the Exchequer immediately answered, that 1,500 l. should be advanced.

Mr. Babbage’s opinion at that time was, that the Engine would be completed in two, or at the most in three years; and that by having 1,500 l. in the first instance, he would be {71} enabled to advance, from his own private funds, the residue of the 3,000 l., or even 5,000 l., which he then imagined the Engine might possibly cost; so that he would not again have occasion to apply to Government until it was completed. Some ob­ser­va­tions were made by the Chancellor of the Exchequer about the mode of accounting for the money received, as well as about its expenditure; but it seemed to be admitted that it was not possible to prescribe any very definite system, and that much must be left to Mr. Babbage’s own judgment.

Very unfortunately, no Minute of that conversation was made at the time, nor was any sufficiently distinct understanding between the parties arrived at. Mr. Babbage’s conviction was, that whatever might be the labour and difficulty of the undertaking, the Engine itself would, of course, become the property of the Government, which had paid for its construction.

Soon after this interview with the Chancellor of the Exchequer, a letter was sent from the Treasury to the Royal Society, informing that body that the Lords of the Treasury

These latter words, “in the manner recommended,” can only refer to the previous recommendation of the Royal Society; but it does not appear, from the Report of the Royal Society, that any plan, terms, or conditions had been pointed out by that body.

Towards the end of July, 1823, Mr. Babbage took measures for the construction of the present Difference Engine,* and it was regularly proceeded with for four years. {72}

In October, 1827, the expense incurred had amounted to 3,475 l.; and Mr. Babbage having suffered severe domestic affliction, and being in a very ill state of health, was recommended by his medical advisers to travel on the Continent. He left, however, sufficient drawings to enable the work to be continued, and gave an order to his own banker to advance 1,000 l. during his absence: he also received, from time to time, drawings and inquiries relating to the mechanism, and returned in­struc­tions to the engineer who was constructing it.

As it now appeared probable that the expense would much exceed what Mr. Babbage had originally anticipated, he thought it desirable to inform the Government of that fact, and to procure a further grant. As a preliminary step, he wrote from Italy to his brother-in-law, Mr. Wolryche Whitmore, to request that he would see Lord Goderich upon the subject of the interview in July, 1823; but it is probable that he did not sufficiently inform Mr. Whitmore of all the circumstances of the case.

Mr. Whitmore, having had some conversation with Lord Goderich on the subject, addressed a letter, dated on the 29th of February, 1828, to Mr. Babbage, who was then at Rome, stating that

On Mr. Babbage’s return to England, towards the end of {73} 1828, he waited in person upon Lord Goderich, who admitted that the understanding of 1823 was not very definite. He then addressed a statement to the Duke of Wellington, as the head of the Government, explaining the previous steps in the affair; stating the reasons for his inferences from what took place at the interview with the Chancellor of the Exchequer in July, 1823; and referring his Grace for further information to Lord Goderich, to whom also he sent a copy of that statement.

The Duke of Wellington, in consequence of this application, requested the Royal Society to inquire—

The Royal Society reported, in February, 1829, that—

The Royal Society also expressed their hope that—

On the 28th of April, 1829, a Treasury Minute directed a further payment to Mr. Babbage of

At that time the sum expended on the Engine amounted to 6,697 l. 12 s., of which 3,000 l. had been received from the Treasury; so that Mr. Babbage had provided 3,697 l. 12 s. from his own private funds.

Under these circumstances, by the advice of Mr. Wolryche Whitmore, a meeting of Mr. Babbage’s personal friends was held on the 12th of May, 1829. It consisted of— {74}

Being satisfied, upon inquiry, of the following facts, they came to the annexed resolutions:—

Mr. Whitmore and Mr. Herschel accordingly had an interview with the Duke of Wellington; and some time after they were informed by the Chancellor of the Exchequer, to whom they had applied for his Grace’s answer, that the Duke of {75} Wellington intended to see the portion of the Engine which had been then made.

In November, 1829, the Duke of Wellington, accompanied by the Chancellor of the Exchequer (Mr. Goulburn) and Lord Ashley, saw the Model of the Engine, the drawings, and the parts in progress. On the 23rd of that month Mr. Babbage received a note from Mr. Goulburn, dated on the 20th, informing him that the Duke of Wellington and himself had recommended the Treasury to make a further payment towards the completion of the Machine; and that their Lordships had in consequence directed a payment of 3,000 l. to be made to him. This letter also contained a suggestion about separating the Calculating from the Printing part of the Machine, which was repeated in the letter from the Treasury of the 3rd of December, 1829, communicating officially the information contained in Mr. Goulburn’s private note, and stating that directions had been given—

Mr. Babbage inferred from this further grant, that Government had adopted his view of the arrangement entered into with the Chancellor of the Exchequer in July, 1823; but, to prevent the recurrence of difficulty from any remaining indistinctness, he wrote to Mr. Goulburn, stating that, before he received the 3,000 l., he wished to propose some general arrangements for expediting the completion of the Engine, further notes of which he would shortly submit to him. On the 25th of November, 1829, he addressed a letter to Lord {76} Ashley, to be communicated to the Chancellor of the Exchequer, stating the grounds on which he thought the following arrangements desirable:—

Mr. Babbage also stated that he had been obliged to suspend the work for nearly nine months; and that such delay risked the final completion of the Engine.

In reply to these suggestions, Mr. Goulburn wrote to Lord Ashley, stating—

Mr. Goulburn’s letter was enclosed by Lord Ashley to Mr. Babbage, with a note, in which his Lordship observed, with reference to Mr. Goulburn’s opinion, that it was

“The original intention” of the Government is here stated to have been communicated to Mr. Babbage, both in the letter from the Treasury of the 3rd of December, 1829, granting the 3,000 l., and also in Mr. Goulburn’s private letter of the 20th of November, 1829. These letters have been just given; and it certainly does not appear from either of them, that the “original intention” was then in any degree more apparent than it was at the commencement of the undertaking in July, 1823.

On the 16th of December, 1829, Mr. Babbage wrote to Lord Ashley, observing, that Mr. Goulburn seemed to think that he [Mr. Babbage] had commenced the machine on his own account; and that, pursuing it zealously, he had expended more than was prudent, and had then applied to Government for aid. He remarked, that a reference to papers and dates would confirm his own positive declaration, that this was never for one moment, in his apprehension, the ground on which the matter rested; and that the following facts would prove that it was absolutely impossible it could have been so:—

Having thus shown that the light in which Mr. Goulburn viewed these transactions was founded on a misconception, Mr. Babbage requested Lord Ashley to inquire whether the facts to which he had called Mr. Goulburn’s attention might not induce him to reconsider the subject. And in case Mr. Goulburn should decline revising his opinion, then he wished Lord Ashley to ascertain the opinion of Government, upon the contingent questions which he enclosed; viz.—

The following statement was also enclosed:—

In January, 1830, Mr. Babbage wrote to Lord Goderich, {79} stating that the Chancellor of the Exchequer (Mr. Goulburn) would probably apply to his Lordship respecting the interview in July, 1823. He therefore recalled some of the circumstances attending it to Lord Goderich, and concluded thus:—

In the mean time Mr. Babbage had encountered difficulties of another kind. The Engineer who had been constructing the Engine under Mr. Babbage’s direction had delivered his bills in such a state that it was impossible to judge how far the charges were just and reasonable; and although Mr. Babbage had paid several thousand pounds, yet there remained a considerable balance, which he was quite prepared and willing to pay, as soon as the accounts should be examined, and the charges approved of by pro­fes­sion­al engineers.

The delay in deciding whether the Engine was the property of Government, added greatly to this embarrassment. Mr. Babbage, therefore, wrote to Lord Ashley on the 8th of February, to mention these difficulties; and to point out the serious inconvenience which would arise, in the future progress of the Engine, from any dispute between the Engineer and himself relative to payments.

On the 24th of February, 1830, Mr. Babbage called on Lord Ashley, to request he would represent to the Duke of Wellington the facts of the case, and point out to his Grace {80} the importance of a decision. In the afternoon of the same day, he again saw Lord Ashley, who communicated to him the decision of the Government; to the following effect:—

Thus, after considerable discussion, the doubts arising from the indefiniteness of the understanding with the Chancellor of the Exchequer, in July, 1823, were at length removed. Mr. Babbage’s impression of the original arrangement entered into between Lord Goderich and himself was thus formally adopted in the first three propositions: and the Government voluntarily added the expression of their disposition to attend to any claim of his for remuneration when the Engine should be completed.

When the arrangements consequent upon this decision were made, the work of the Engine was resumed, and continued to advance.

After some time, the increasing amount of costly drawings, and of parts of the Engine already executed, remaining exposed to destruction from fire and from other casualties became a source of some anxiety.

These facts having been represented to Lord Althorp (then Chancellor of the Exchequer), an experienced surveyor {81} was directed to find a site adapted for a building for the reception of the Engine in the neighbourhood of Mr. Babbage’s residence.

On the 19th of January the Surveyor’s reports were forwarded to Lord Althorp (the Chancellor of the Exchequer), who referred the case to a committee of practical Engineers for their opinion. This committee reported strongly in favour of the removal, on the grounds of security, and of economy in completing the Engine; and also recommended the site which had been previously selected by the Surveyor. The Royal Society, also, to whom Lord Althorp had applied, examined the question, and likewise reported strongly to the same effect.

A lease of some property, adjacent to Mr. Babbage’s residence, was therefore sub­se­quent­ly granted by him to the Government; and a fire-proof building, capable of containing the Engine, with its drawings, and workshops necessary for its completion, were erected.

With respect to the expenses of constructing the Engine, the following plan was agreed upon and carried out:—The great bulk of the work was executed by the Engineer under the direction of Mr. Babbage. When the bills were sent in, they were immediately forwarded by him to two eminent Engineers, Messrs. Donkin and Field, who, at the request of Government, had undertaken to examine their accuracy. On these gentlemen certifying those bills to be correct, Mr. Babbage trans­mit­ted them to the Treasury; and after the usual forms, a warrant was issued directing the payment of the respective sums to Mr. Babbage. This course, however, required considerable time; and the Engineer having represented that he was unable to pay his workmen without more immediate advances, Mr. Babbage, to prevent delay in {82} completing the Engine, did himself, from time to time, advance from his own funds several sums of money; so that he was, in fact, usually in advance from 500 l. to 1,000 l. Those sums were, of course, repaid when the Treasury warrants were issued.

Early in the year 1833, an event of great importance in the history of the Engine occurred. Mr. Babbage had directed a portion of it, consisting of sixteen figures, to be put together. It was capable of calculating Tables having two or three orders of differences; and, to some extent, of forming other Tables. The action of this portion completely justified the expectations raised, and gave a most sat­is­fac­tory assurance of its final success.

The fire-proof building and workshops having been completed, arrangements were made for the removal of the Engine. Mr. Babbage finding it no longer convenient to make payments in advance, informed the Engineer that he should in future not pay him until the money was received from the Treasury. Upon receiving this intimation, the Engineer immediately discontinued the construction of the Engine, and dismissed the workmen employed on it; which fact Mr. Babbage immediately communicated to the Treasury.

In this state of affairs it appeared, both to the Treasury and to Mr. Babbage, that it would be better to complete the removal of the drawings, and all the parts of the Engine to the fire-proof building; and then make such arrangements between the Treasury and the Engineer, respecting the future payments, as might prevent further discussion on that subject.

After much delay and difficulty the whole of the drawings, and parts of the Engine, were at length removed to the fire-proof building in East-street, Manchester-square. Mr. Babbage wrote, on the 16th of July, 1834, to the Treasury, {83} informing their Lordships of the fact;—adding that no advance had been made in its construction for above a year and a quarter; and requesting further in­struc­tions on the subject.

Mr. Babbage received a letter from the Treasury, expressing their Lordships’ sat­is­fac­tion at learning that the drawings, and parts of the Calculating Engine were removed to the fire-proof building, and stating that as soon as Mr. Clement’s Accounts should be received and examined, they would

A few weeks afterwards Mr. Babbage received a letter from the Treasury, conveying their Lordships’ authority to proceed with the construction of the Engine.

During the time which had elapsed since the Engineer had ceased to proceed with the construction of the Engine, Mr. Babbage had been deprived of the use of his own drawings. Having, in the meanwhile, naturally speculated upon the general principles on which machinery for calculation might be constructed, a principle of an entirely new kind occurred to him, the power of which over the most complicated arithmetical operations seemed nearly unbounded. On re-examining his drawings when returned to him by the Engineer, the new principle appeared to be limited only by the extent of the mechanism it might require. The invention of simpler mechanical means for executing the elementary operations of the Engine now derived a far greater importance than it had hitherto possessed; and should such simp­li­fi­ca­tions be discovered, it seemed difficult to anticipate, or even to over-estimate, the vast results which might be attained. In the Engine for calculating by differences, such simp­li­fi­ca­tions affected only about a hundred and twenty {84} similar parts, whilst in the new or Analytical Engine, they would affect a great many thousand. The Difference Engine might be constructed with more or less advantage by employing various mechanical modes for the operation of addition: the Analytical Engine could not exist without inventing for it a method of mechanical addition possessed of the utmost simplicity. In fact, it was not until upwards of twenty different mechanical modes for performing the operation of addition had been designed and drawn, that the necessary degree of simplicity required for the Analytical Engine was ultimately attained. Hence, therefore, the powerful motive for simp­li­fi­ca­tion.

These new views acquired additional importance, from their bearings upon the Engine already partly executed for the Government. For, if such simp­li­fi­ca­tions should be discovered, it might happen that the Analytical Engine would execute more rapidly the calculations for which the Difference Engine was intended; or, that the Difference Engine would itself be superseded by a far simpler mode of construction. Though these views might, perhaps, at that period have appeared visionary, both have sub­se­quent­ly been completely realized.

To withhold those new views from the Government, and under such circumstances to have allowed the construction of the Engine to be resumed, would have been improper; yet the state of uncertainty in which those views were then necessarily involved rendered any written communication respecting their probable bearing on the Difference Engine a matter of very great difficulty. It appeared to Mr. Babbage that the most straightforward course was to ask for an interview on the subject with the Head of the Government, and to communicate to him the exact state of the case. {85}

Had that interview taken place, the First Lord of the Treasury might have ascertained from his inquiries, in a manner quite impracticable by any written communications, the degree of importance which Mr. Babbage attached to his new inventions, and his own opinion of their probable effect, in superseding the whole or any part of the original, or Difference, Engine. The First Lord of the Treasury would then have been in a position to decide, either on the immediate continuation and completion of the original design, or on its temporary suspension, until the character of the new views should be more fully developed by further drawings and examination.

There was another, although a far less material point, on which also it was desirable to obtain the opinion of the Government: the serious impediments to the progress of the Engine, arising from the Engineer’s conduct, as well as the consequent great expense, had induced Mr. Babbage to consider, whether it might not be possible to employ some other person as his agent for constructing it. His mind had gradually become convinced of the practicability of that measure; but he was also aware that however advantageous it might prove to the Government, from its greater economy, yet that it would add greatly to his own personal labour, responsibility, and anxiety.

On the 26th of September, 1834, Mr. Babbage therefore requested an interview with Lord Melbourne, for the purpose of placing before him these views. Lord Melbourne acceded to the proposed interview, but it was then postponed; and soon after, the Administration of which his Lordship was the Head went out of Office, without the interview having taken place.

For the same purpose, Mr. Babbage applied in December, {86} 1834, for an interview with the Duke of Wellington, who, in reply, expressed his wish to receive a written communication on the subject. He accordingly addressed a statement to his Grace, pointing out the only plans which, in his opinion, could be pursued for terminating the questions relative to the Difference Engine; namely,

He also stated to the Duke of Wellington, the circumstances which had led him to the invention of a new Engine, of far more extensive powers of calculation; which he then observed did not supersede the former one, but added greatly to its utility.

At this period, the impediments relating to the Difference Engine had been partially and temporarily removed. The chief difficulty would have been either the formation of new arrangements with the Engineer, or the appointment of some other person to supply his place. This latter alternative, which was of great importance for economy as well as for its speedy completion, Mr. Babbage had carefully examined, and was then prepared to point out means for its accomplishment. {87}

The duration of the Duke of Wellington’s Administration was short; and no decision on the subject of the Difference Engine was obtained.

On the 15th of May the Difference Engine was alluded to in the House of Commons; when the Chancellor of the Exchequer did Mr. Babbage the justice to state distinctly, that the whole of the money voted had been expended in paying the workmen and for the materials employed in constructing it, and that not one shilling of it had ever gone into his own pocket.

About this time several communications took place between the Chancellor of the Exchequer and Mr. Babbage, respecting a reference to the Royal Society for an opinion on the subject of the Engine.

A new and serious impediment to the possibility of executing one of the plans which had been suggested to the Duke of Wellington for completing the Difference Engine arose from these delays. The draftsman whom Mr. Babbage had, at his own expense, employed, both on the Difference and on the Analytical Engine, received an offer of a very liberal salary, if he would enter into an engagement abroad, which would occupy many years. His assistance was indispensable, and his services were retained only by Mr. Babbage considerably increasing his salary.

On the 14th of January, 1836, Mr. Babbage received a communication from the Chancellor of the Exchequer (Mr. Spring Rice19 ), expressing his desire to come to some definite result on the subject of the Calculating Engine, in which he remarked, that the conclusion to be drawn from Mr. Babbage’s statement to the Duke of Wellington was, that he {88} (Mr. Babbage) having invented a new machine, of far greater powers than the former one, wished to be informed if the Government would undertake to defray the expense of this new Engine.

The Chancellor of the Exchequer then pointed out reasons why he should feel himself bound to look to the completion of the first machine, before he could propose to Parliament to enter on the consideration of the second: and he proposed to refer to the Royal Society for their opinion, authorizing them, if they thought fit, to employ any practical mechanist or engineer to assist them in their inquiries. The Chancellor of the Exchequer concluded with expressing his readiness to communicate with Mr. Babbage respecting the best mode of attaining that result.

From these statements it is evident that Mr. Babbage had failed in making his own views distinctly understood by the Chancellor of the Exchequer. His first anxiety, when applying to Lord Melbourne, had been respecting the question, whether the Discoveries with which he was then advancing might not ultimately supersede the work already executed. His second object had been to point out a possible arrangement, by which great expense might be saved in the mechanical construction of the Difference Engine.

So far was Mr. Babbage from having proposed to the Government to defray the expenses of the new or Analytical Engine, that though he expressly pointed out in the statement to the Duke of Wellington20 four courses which it was possible for the Government to take,—yet in no one of them was the construction of the new Engine alluded to.

Those views of improved machinery for making calculations {89} which had appeared in but faint perspective in 1834, as likely to lead to important consequences, had, by this time, assumed a form and distinctness which fully justified the anticipations then made. By patient inquiry, aided by extensive drawings and notations, the projected Analytical Engine had acquired such powers, that it became necessary, for its further advancement, to simplify the elements of which it was composed. In the progress of this inquiry, Mr. Babbage had gradually arrived at simpler mechanical modes of performing those arithmetical operations on which the action of the Difference Engine depended; and he felt it necessary to communicate these new circumstances, as well as their consequences, to the Chancellor of the Exchequer.

On the 20th of January, 1836, Mr. Babbage wrote, in answer to the communication from the Chancellor of the Exchequer, that he did not, on re-examining the statement addressed to the Duke of Wellington, perceive that it contained any application to take up the new or Analytical Engine; and he accompanied this reply by a statement relative to the progress of the Analytical Engine, and its bearing upon the Difference Engine belonging to the Government. The former, it was said,

The Reply then referred to the statement laid before the Duke of Wellington in July, 1834, in which it was said,

and that the mechanical simplicity to which its elements had now been reduced was such, that it would probably cost more {90} to finish the old Difference Engine on its original plan than to construct a new Difference Engine with the simplified elements devised for the Analytical Engine.

It then proceeded to state that—

The reference to the Royal Society, proposed by the Chancellor of the Exchequer, in his letter of the 14th of January, 1836,21 did not take place; and during more than a year and a half no further measures appear to have been adopted by the Government respecting the Engine.

It was obviously of the greatest importance to Mr. Babbage that a final decision should be made by the Government. When he undertook to superintend the construction of the Difference Engine for the Government, it was, of course, understood that he would not leave it unfinished. He had now been engaged fourteen years upon an object which he {91} had anticipated would not require more than two or three; and there seemed no limit to the time his engagement with the Government might thus be supposed to endure, unless some steps were taken to terminate it. Without such a decision Mr. Babbage felt that he should be impeded in any plans he might form, and liable to the most serious in­ter­rup­tion, if he should venture to enter upon the execution of them. He therefore most earnestly pressed, both by his personal applications and by those of his friends, for the settlement of the question. Mr. Wolryche Whitmore, in particular, repeatedly urged upon the Chancellor of the Exchequer, personally, as well as by letter, the injustice of keeping Mr. Babbage so very long in a state of suspense.

Time, however, passed on, and during nearly two years the question remained in the same state. Mr. Babbage, wearied with this delay, determined upon making a last effort to obtain a decision. He wrote to the First Lord of the Treasury (Lord Melbourne) on the 26th of July, 1838, recalling to his Lordship’s attention the frequency of his applications on this subject, and urging the necessity of a final decision upon it. He observed, that if the question had become more difficult, because he had invented superior mechanism, which had superseded that which was already partly executed, this consequence had arisen from the very delay against which he had so repeatedly remonstrated. He then asked, for the last time, not for any favour, but for that which it was an injustice to withhold—a decision.

On the 16th of August Mr. Spring Rice (the Chancellor of the Exchequer) addressed a note to Mr. Babbage, in reference to his application to Lord Melbourne. After recapitulating his former statement of the subject, which had been shown to be founded on a misapprehension, viz., that Mr. Babbage {92} had made an application to the Government to construct for them the Analytical Engine, the Chancellor of the Exchequer inquired whether he was solicitous that steps should be taken for the completion of the old, or for the commencement of a new machine,—and what he considered would be the cost of the one proceeding, and of the other?

Being absent on a distant journey, Mr. Babbage could not reply to this note until the 21st of October. He then reminded the Chancellor of the Exchequer of his previous communication of the 20th of January, 1836 (see p. 89), in which it was expressly stated that he did not intend to make any application to construct a new machine; but that the communication to the Duke of Wellington and the one to himself were made, simply because he thought it would be unfair to conceal such important facts from those who were called upon to decide on the continuance or discontinuance of the construction of the Difference Engine.

With respect to the expense of either of the courses pointed out by the Chancellor of the Exchequer, Mr. Babbage observed that, not being a pro­fes­sion­al Engineer, and his past experience having taught him not to rely upon his own judgment on matters of that nature, he should be very reluctant to offer any opinion upon the subject.

In conclusion, Mr. Babbage stated that the question he wished to have settled was—

Whether the Government required him to superintend the completion of the Difference Engine, which had been suspended during the last five years, according to the original plan and principles; or whether they intended to discontinue it altogether ?

In November, 1841, Mr. Babbage, on his return from the Continent, finding that Sir Robert Peel had become First {93} Lord of the Treasury, determined upon renewing his application for a decision of the question. With this view the previous pages of this Statement were drawn up, and a copy of it was forwarded to him, accompanied by a letter from Mr. Babbage, in which he observed—

Mr. Babbage, in reply, received a note from Sir George Clerk (Secretary to the Treasury), stating that Sir Robert Peel feared that it would not be in his power to turn his attention to the subject for some days, but that he hoped, as soon as the great pressure of business previous to the opening of the session of Parliament was over, he might be able to determine on the best course to be pursued.

The session of Parliament closed in August, and Mr. Babbage had received no further communication on the subject. Having availed himself of several private channels for recalling the question to Sir Robert Peel’s attention without effect, Mr. Babbage, on the 8th of October, 1842, again wrote to him, requesting an early decision.

On the 4th of November, 1842, a note from Sir Robert Peel explained to Mr. Babbage that some delay had arisen, from his wish to communicate personally with the Chancellor of the Exchequer, who would shortly announce to him their joint conclusion on the subject.

On the same day Mr. Babbage received a letter from Mr. {94} Goulburn (the Chancellor of the Exchequer), who stated that he had communicated with Sir Robert Peel, and that they both regretted the necessity of abandoning the completion of a machine, on which so much scientific labour had been bestowed. He observed, that the expense necessary for rendering it either sat­is­fac­tory to Mr. Babbage or generally useful appeared, on the lowest calculation, so far to exceed what they should be justified in incurring, that they considered themselves as having no other alternative.

Mr. Goulburn concluded by expressing their hope, that by the Government withdrawing all claim to the machine as already constructed, and placing it entirely at Mr. Babbage’s disposal, they might in some degree assist him in his future exertions in the cause of Science.

On the 6th of November, 1842, Mr. Babbage wrote to Sir Robert Peel and the Chancellor of the Exchequer, acknowledging the receipt of their decision, thanking them for the offer of the machine as already constructed, but, under all the circumstances, declining to accept it.22

On the 11th of November Mr. Babbage obtained an interview with Sir Robert Peel, and stated, that having given the original Invention to the Government—having superintended for them its construction—having dem­on­strated the possibility of the undertaking by the completion of an important portion of it—and that the non-completion of the design arose neither from his fault nor his desire, but was the act of the Government itself, he felt that he had some claims on their consideration.

He rested those claims upon the sacrifices he had made, {95} both personal and pecuniary, in the advancement of the Mechanical Arts and of Science—on the anxiety and the injury he had experienced by the delay of eight years in the decision of the Government on the subject, and on the great annoyance he had constantly been exposed to by the prevailing belief in the public mind that he had been amply remunerated by large grants of public money. Nothing, he observed, but some public act of the Government could ever fully refute that opinion, or repair the injustice with which he had been treated.

The result of this interview was entirely unsat­is­fac­tory. Mr. Babbage went to it prepared, had his statement produced any effect, to have pointed out two courses, by either of which it was probable that not only a Difference Engine, but even the Analytical Engine, might in a few years have been completed. The state of Sir Robert Peel’s information on the subject, and the views he took of Mr. Babbage’s services and position, prevented Mr. Babbage from making any allusion to either of those plans.

Thus finally terminated an engagement, which had existed upwards of twenty years. During no part of the last eight of those years does there appear to have been any reason why the same decision should not have been arrived at by the Government as was at last actually pronounced.

It was during this last period that all the great principles on which the Analytical Engine rests were discovered, and that the mechanical contrivances in which they might be embodied were invented. The establishment which Mr. Babbage had long maintained in his own house, and at his own expense, was now directed with increased energy to the new inquiries required for its perfection.

In this Statement the heavy sacrifices, both pecuniary and {96} personal, which the invention of these machines has entailed upon their author, have been alluded to as slightly as possible. Few can imagine, and none will ever know their full extent. Some idea of those sacrifices must nevertheless have occurred to every one who has read this Statement. During upwards of twenty years Mr. Babbage has employed, in his own house, and at his own expense, workmen of various kinds, to assist him in making experiments necessary for attaining a knowledge of every art which could possibly tend to the perfection of those Engines; and with that object he has frequently visited the manufactories of the Continent, as well as our own.

Since the discontinuance of the Difference Engine belonging to the Government, Mr. Babbage has himself maintained an establishment for making drawings and descriptions dem­on­strat­ing the nature and power of the Analytical Engine, and for its construction at some future period, when its value may be appreciated.

IT was not until 1848, when I had mastered the subject of the Analytical Engine, that I resolved on making a complete set of drawings of the Difference Engine No. 2. In this I proposed to take advantage of all the improvements and simp­li­fi­ca­tions which years of unwearied study had produced for the Analytical Engine.

In 1852, the Earl of Rosse, who, from its commencement, had looked forward with the greatest interest to the application of mechanism to purposes of calculation, and who was well acquainted with the drawings and notations of the Difference Engine No. 2, inquired of me whether I was willing to give them to the Government, provided they would have the Engine constructed. My feeling was, after the sad experience of the past, that I ought not to think of sacrificing any further portion of my life upon the subject. If, however, they chose to have the Difference Engine made, I was ready to give them the whole of the drawings, and also the notations by which it was dem­on­strated that such a machine could be constructed, and that when made it would necessarily do the work prescribed for it. {98}

My much-valued friend, the late Sir Benjamin Hawes, had also been consulted, and it was agreed that the draft of a letter to Lord Derby, who was then prime minister, should be prepared; in which I should make this offer. Lord Rosse proposed to place my letter in Lord Derby’s hands, with his own statement of a plan by which the whole question might be determined.

Lord Rosse’s suggestion was, that the Government should apply to the President of the Institution of Civil Engineers to ascertain,

The Institution of Civil Engineers was undoubtedly the highest authority upon the first question. That being decided in the affirmative, no other body had equal power to find out those mechanical engineers who might be willing to undertake the contract.

Supposing both these questions, or even the latter only, answered in the negative, the proposition, of course, fell to the ground. But if they were both answered in the affirmative, then there would have arisen a further question for the consideration of the Government: namely, Whether the object to be obtained was worthy of the expenditure?

The final result of this eminently practical plan was communicated to the Royal Society by their President, in his address at their anniversary on the 30th November, 1854. The following is an extract:— {99}

“The progress of the work was suspended: there was a change of Government. Science was weighed against gold by a new standard, and it was resolved to proceed no further. No enterprise could have had its beginning under more auspicious circumstances: the Government had taken the initiative—they had called for advice, and the adviser was the highest scientific authority in this country;—your Council; guided by such men as Davy, Wollaston, and Herschel. By your Council the undertaking was inaugurated,—by your Council it was watched over in its progress. That the first great effort to employ the powers of calculating mechanism, in aid of the human intellect, should have been suffered in this great country to expire fruitless, because there was no tangible evidence of immediate profit, as a British subject I deeply regret, and as a Fellow my regret is accompanied with feelings of bitter disappointment. Where a question has once been disposed of, succeeding Governments rarely reopen it, still I thought I should not be doing my duty if I did not take some opportunity of bringing the facts once more before Government. Circumstances had changed, mechanical engineering had made much progress; the tools required and trained workmen were to be found in the workshops of the leading mechanists, the founder’s art was so advanced that casting had been substituted for cutting, in making the change wheels, even of screw-cutting engines, and therefore it was very probable that persons would be found willing to undertake to complete the Difference Engine for a specific sum.

“That finished, the question would then have arisen, how far it was advisable to endeavour, by the same means, to turn to account the great labour which had been expended under the guidance of inventive powers the most original, {100} controlled by mathematics of a very high order; and which had been wholly devoted for so many years to the great task of carrying the powers of calculating machinery to its utmost limits. Before I took any step I wrote to several very eminent men of science, inquiring whether, in their opinion, any great scientific object would be gained if Mr. Babbage’s views, as explained in Ménabrèa’s little essay, were completely realized. The answers I received were strongly in the affirmative. As it was necessary the subject should be laid before Government in a form as practical as possible, I wrote to one of our most eminent mechanical engineers to inquire whether I should be safe in stating to Government that the expense of the Calculating Engine had been more than repaid in the improvements in mechanism directly referable to it; he replied,—unquestionably. Fortified by these opinions, I submitted this proposition to Government:—that they should call upon the President of the Society of Civil Engineers to report whether it would be practicable to make a contract for the completion of Mr. Babbage’s Difference Engine, and if so, for what sum. This was in 1852, during the short administration of Lord Derby, and it led to no result. The time was unfortunate; a great political contest was impending, and before there was a lull in politics, so that the voice of Science could be heard, Lord Derby’s government was at an end.”

The following letter was then drawn up, and placed in Lord Derby’s hands by Lord Rosse:—

June 8, 1852.   MY LORD,

I TAKE the liberty of drawing your Lordship’s attention to the subject of the construction of a Difference Engine, for {101} calculating and printing Astronomical and Nautical Tables, which was brought under the notice of the Government so far back as the year 1823, and upon which the Government of that day desired the opinion of the Royal Society.

I annex a copy of the correspondence which took place at that time, and which your Lordship will observe was laid before Parliament.

The Committee of the Royal Society, to which the subject was referred, reported generally that the invention was one “fully adequate to the attainment of the objects proposed by the inventor, and that they considered Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking.”—Report of Royal Society, 1 st May, 1823. Parliamentary Paper, 370, 22 nd May, 1823.

And in a subsequent and more detailed Report, which I annex also, they state:—

“The Committee have no intention of entering into any consideration of the abstract math­e­mat­i­cal principle on which the practicability of such a machine as Mr. Babbage’s relies, nor of its public utility when completed. They consider the former as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. The latter they regard as obvious to every one who considers the immense advantage of accurate numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, and the great variety and extent of those which it is the object and within the compass of Mr. Babbage’s Engine to calculate and print with perfect accuracy.”—Report of Committee of Royal Society, 12th Feb., 1829.

Upon the first of these Reports, the Government determined to construct the machine, under my personal {102} superintendence and direction. The Engine was accordingly commenced and partially completed. Tables of figures were calculated, limited in extent only by the number of wheels put together.

Delays, from various causes arose in the progress of the work, and great expenses were incurred. The machine was altogether new in design and construction, and required the utmost mechanical skill which could be obtained for its execution. “It involved,” to quote again from the Report of the Committee of the Royal Society, “the necessity of constructing, and in many instances inventing, tools and machinery of great expense and complexity (and in many instances of ingenious contrivances likely to prove useful for other purposes hereafter), for forming with the requisite precision parts of the apparatus dissimilar to any used in ordinary mechanical works; that of making many previous trials to ascertain the validity of proposed movements; and that of altering, improving, and simplifying those already contrived and reduced to drawings. Your Committee are so far from being surprised at the time it has occupied to bring it to its present state, that they feel more disposed to wonder it has been possible to accomplish so much.” The true explanation both of the slow progress and of the cost of the work is clearly stated in this passage; and I may remark in passing, that the tools which were invented for the construction of the machine were afterwards found of utility, and that this anticipation of the Committee has been realized, as some of our most eminent mechanical engineers will readily testify.

Similar circumstances will, I apprehend, always attend and prolong the period of bringing to perfection inventions which have no parallel in the previous history of mechanical {103} construction. The necessary science and skill specially acquired in executing such works must also, as experience is gained, suggest deviations from, and improvements in, the original plan of those works; and the adoption or rejection of such changes, especially under circumstances similar to those in which I was placed, often involves questions of the greatest difficulty and anxiety.

From whatever cause, however, the delays and expenses arose, the result was that the Government was discouraged, and declined to proceed further with the work.

Mr. Goulburn’s letter, intimating this decision to me, in 1842, will be found in the accompanying printed Statement. And that the impediments to the completion of the engine, described by the Royal Society, were those which influenced the Government in the determination they came to, I infer from the reason assigned by Mr. Goulburn for its discontinuance, viz., “the expense which would be necessary in order to render it either sat­is­fac­tory to yourself or generally useful.” I readily admit that the work could not have been rendered sat­is­fac­tory to myself unless I was free to introduce every improvement which experience and thought could suggest. But that even with this additional source of expense its general usefulness would have been impaired, I cannot assent to, for I believe, in the words of the Report I have already quoted, the “immense advantage of accurate Numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, cannot, within any reasonable limits, be over-estimated.” As to the expense actually incurred upon the first Difference Engine, that of the Government was about 17,000 l. On my own part, and out of my own private resources, I have sacrificed upon this and other works of science upwards of 20,000 l. {104}

From the date of Mr. Goulburn’s letter, nothing has been done towards the further completion of the Difference Engine by the Government or myself. So much of it as was completed was deposited in the Museum of King’s College, where it now remains.

Three consequences have, however, resulted from my subsequent labours, to which I attach great importance.

First, I have been led to conceive the most important elements of another Engine upon a new principle (the details of which are reduced accurately to paper), the power of which over the most complicated analytical operations appears nearly unlimited; but no portion of which is yet commenced. I have called this engine, in contradistinction to the other, the Analytical Engine.

Secondly, I have invented and brought to maturity a system of signs for the explanation of machinery, which I have called Mechanical Notation, by means of which the drawings, the times of action, and the trains for the transmission of force, are expressed in a language at once simple and concise. Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or of some other equivalent language. The Difference Engine No. 2, to which I shall presently refer, is entirely described by its aid.

Thirdly, in labouring to perfect this Analytical Machine of greater power and wider range of computation, I have discovered the means of simplifying and expediting the mechanical processes of the first or Difference Engine.

After what has passed, I cannot expect the Government to undertake the construction of the Analytical Engine, and I do not offer it for that purpose. It is not so matured as to {105} enable any other person, without long previous training and application, even to attempt its execution; and on my own part, to superintend its construction would demand an amount of labour, anxiety, and time which could not, after the treatment I have received, be expected from me. I therefore make no such offer.

But that I may fulfil to the utmost of my power the original expectation that I should be able to complete, for the Government, an Engine capable of calculating astronomical and nautical Tables with perfect accuracy, such as that which is described in the Reports of the Royal Society, I am willing to place at the disposal of Government (if they will undertake to execute a new Difference Engine) all those improvements which I have invented and have applied to the Analytical Engine. These comprise a complete series of drawings and explanatory notations, finished in 1849, of the Difference Engine No. 2,—an instrument of greater power as well as of greater simplicity than that formerly commenced, and now in the possession of the Government.

I have sacrificed time, health, and fortune, in the desire to complete these Calculating Engines. I have also declined several offers of great personal advantage to myself. But, not­with­stand­ing the sacrifice of these advantages for the purpose of maturing an engine of almost in­tel­lec­tual power, and after expending from my own private fortune a larger sum than the Government of England has spent on that machine, the execution of which it only commenced, I have received neither an acknowledgment of my labours, nor even the offer of those honours or rewards which are allowed to fall within the reach of men who devote themselves to purely scientific investigations. I might, perhaps, advance some claims to consideration, founded on my works and {106} cont­ri­bu­tions in aid of various departments of industrial and physical science,—but it is for others to estimate those services.

I now, however, simply ask your Lordship to do me the honour to consider this statement and the offer I make. I prefer no claim to the distinctions or the advantages which it is in the power of the Crown or the Government to bestow. I desire only to discharge whatever imagined obligation may be supposed to rest upon me, in connexion with the original undertaking of the Difference Engine; though I cannot but feel that whilst the public has already derived advantage from my labours, I have myself experienced only loss and neglect.

If the work upon which I have bestowed so much time and thought were a mere triumph over mechanical difficulties, or simply curious, or if the execution of such engines were of doubtful practicability or utility, some justification might be found for the course which has been taken; but I venture to assert that no mathematician who has a reputation to lose will ever publicly express an opinion that such a machine would be useless if made, and that no man distinguished as a Civil Engineer will venture to declare the construction of such machinery impracticable. The names appended to the Report of the Committee of the Royal Society fully justify my expressing this opinion, which I apprehend will not be disputed.

And at a period when the progress of physical science is obstructed by that exhausting in­tel­lec­tual and manual labour, indispensable for its advancement, which it is the object of the Analytical Engine to relieve, I think the application of machinery in aid of the most complicated and abstruse calculations can no longer be deemed unworthy of the attention of the country. In fact, there is no reason why mental as {107} well as bodily labour should not be economized by the aid of machinery.

With these views I have addressed your Lordship, as the head of the Government; and whatever may be my sense of the injustice that has hitherto been done me, I feel, in laying this rep­re­sen­ta­tion before your Lordship, and in making the offer I now make, that I have discharged to the utmost limit every implied obligation I originally contracted with the country.

Dorset Street, Manchester Square.

June 8, 1852.

As this question was one of finance and of calculation, the sagacious Premier adroitly turned it over to his Chancellor of the Exchequer—that official being, from his office, supposed to be well versed in both subjects.

The opinion pronounced by the novelist and financier was, “That Mr. Babbage’s projects appear to be so indefinitely expensive, the ultimate success so problematical, and the expenditure certainly so large and so utterly incapable of being calculated, that the Government would not be justified in taking upon itself any further liability.”—Extract from the Reply of Earl Derby to the application of the Earl of Rosse, K.P., President of the Royal Society.

The answer of Lord Derby to Lord Rosse was in substance—

That he had consulted the Chancellor of the Exchequer, who pronounced Mr. Babbage’s project as— {108}

1. With regard to the “indefinite expense.” Lord Rosse had proposed to refer this question to the President of the Institution of Civil Engineers, who would have given his opinion after a careful examination of the drawings and notations. These had not been seen by the Chancellor of the Exchequer; and, if seen by him, would not have been comprehended.

The objection that its success was “problematical” may refer either to its mechanical construction or to its math­e­mat­i­cal principles.

Who, possessing one grain of common sense, could look upon the unrivalled workmanship of the then existing portion of the Difference Engine No. 1, and doubt whether a simplified form of the same engine could be executed?

As to any doubt of its math­e­mat­i­cal principles, this was excusable in the Chancellor of the Exchequer, who was himself too practically acquainted with the fallibility of his own figures, over which the severe duties of his office had stultified his brilliant imagination. Far other figures are dear to him—those of speech, in which it cannot be denied he is indeed pre-eminent.

Any junior clerk in his office might, however, have told him that the power of computing Tables by differences merely required a knowledge of simple addition.

As to the impossibility of ascertaining the expenditure, this merges into the first objection; but a poetical brain must be pardoned when it repeats or amplifies. I will recall to the ex-Chancellor of the Exchequer what Lord Rosse really {109} proposed, namely, that the Government should take the opinion of the President of the Institution of Civil Engineers upon the question, whether a contract could be made for constructing the Difference Engine, and if so, for what sum.

But the very plan proposed by Lord Rosse and refused by Lord Derby, for the construction of the English Difference Engine, was adopted some few years after by another administration for the Swedish Difference Engine. Messrs. Donkin, the eminent Engineers, made an estimate, and a contract was in consequence executed to construct for Government a fac-simile of the Swedish Difference Engine, which is now in use in the department of the Registrar-General, at Somerset House. There were far greater mechanical difficulties in the production of that machine than in the one the drawings of which I had offered to the Government.

From my own experience of the cost of executing such works, I have no doubt, although it was highly creditable to the skill of the able firm who constructed it, but that it must have been commercially unprofitable. Under such circumstances, surely it was harsh on the part of the Government to refuse Messrs. Donkin permission to exhibit it as a specimen of English workmanship at the Exhibition of 1862.

But the machine upon which everybody could calculate, had little chance of fair play from the man on whom nobody could calculate.

If the Chancellor of the Exchequer had read my letter to Lord Derby, he would have found the opinion of the Committee of the Royal Society expressed in these words:—

“They consider the former [the abstract math­e­mat­i­cal principle] as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. {110}

“The latter [its public utility] they consider as obvious to every one who considers the immense advantage of accurate numerical tables in all matters of calculation, especially in those which relate to astronomy and navigation.”—Report of the Royal Society, 12th Feb., 1829.

Thus it appears:—

This much-abused Difference Engine is, however, like its prouder relative the Analytical, a being of sensibility, of impulse, and of power.

It can not only calculate the millions the ex-Chancellor of the Exchequer squandered, but it can deal with the smallest quantities; nay, it feels even for zeros.23 It is as conscious as Lord Derby himself is of the presence of a negative quantity, and it is not beyond the ken of either of them to foresee the existence of impossible ones.24

Yet should any unexpected course of events ever raise the {111} ex-Chancellor of the Exchequer to his former dignity, I am sure he will be its friend as soon as he is convinced that it can be made useful to him.

It may possibly enable him to un-muddle even his own financial accounts, and to ———

But as I have no wish to crucify him, I will leave his name in obscurity.

The Herostratus of Science, if he escape oblivion, will be linked with the destroyer of the Ephesian Temple.

THE circular arrangement of the axes of the Difference Engine round large central wheels led to the most extended prospects. The whole of arithmetic now appeared within the grasp of mechanism. A vague glimpse even of an Analytical Engine at length opened out, and I pursued with enthusiasm the shadowy vision. The drawings and the experiments were of the most costly kind. Draftsmen of the highest order were necessary to economize the labour of my own head; whilst skilled workmen were required to execute the experimental machinery to which I was obliged constantly to have recourse.

In order to carry out my pursuits successfully, I had purchased a house with above a quarter of an acre of ground in a {113} very quiet locality. My coach-house was now converted into a forge and a foundry, whilst my stables were transformed into a workshop. I built other extensive workshops myself, and had a fire-proof building for my drawings and draftsmen. Having myself worked with a variety of tools, and having studied the art of constructing each of them, I at length laid it down as a principle—that, except in rare cases, I would never do anything myself if I could afford to hire another person who could do it for me.

The complicated relations which then arose amongst the various parts of the machinery would have baffled the most tenacious memory. I overcame that difficulty by improving and extending a language of signs, the Mechanical Notation, which in 1826 I had explained in a paper printed in the “Phil. Trans.” By such means I succeeded in mastering trains of investigation so vast in extent that no length of years ever allotted to one individual could otherwise have enabled me to control. By the aid of the Mechanical Notation, the Analytical Engine became a reality: for it became susceptible of demonstration.

Such works could not be carried on without great expenditure. The fluctuations in the demand and supply of skilled labour were considerable. The railroad mania withdrew from other pursuits the most in­tel­lec­tual and skilful draftsmen. One who had for some years been my chief assistant was tempted by an offer so advantageous that in justice to his own family he could scarcely have declined it. Under these circumstances I took into consideration the plan of advancing his salary to one guinea per day. Whilst this was in abeyance, I consulted my venerable surviving parent. When I had fully explained the circumstances, my excellent mother replied: “My dear son, you have advanced {114} far in the accomplishment of a great object, which is worthy of your ambition. You are capable of completing it. My advice is—pursue it, even if it should oblige you to live on bread and cheese.”

This advice entirely accorded with my own feelings. I therefore retained my chief assistant at his advanced salary.

The most important part of the Analytical Engine was undoubtedly the mechanical method of carrying the tens. On this I laboured incessantly, each succeeding improvement advancing me a step or two. The difficulty did not consist so much in the more or less complexity of the contrivance as in the reduction of the time required to effect the carriage. Twenty or thirty different plans and modifications had been drawn. At last I came to the conclusion that I had exhausted the principle of successive carriage. I concluded also that nothing but teaching the Engine to foresee and then to act upon that foresight could ever lead me to the object I desired, namely, to make the whole of any unlimited number of carriages in one unit of time. One morning, after I had spent many hours in the drawing-office in endeavouring to improve the system of successive carriages, I mentioned these views to my chief assistant, and added that I should retire to my library, and endeavour to work out the new principle. He gently expressed a doubt whether the plan was possible, to which I replied that, not being able to prove its impossibility, I should follow out a slight glimmering of light which I thought I perceived.

After about three hours’ examination, I returned to the drawing-office with much more definite ideas upon the subject. I had discovered a principle that proved the possibility, and I had contrived mechanism which, I thought, would accomplish my object. {115}

I now commenced the explanation of my views, which I soon found were but little understood by my assistant; nor was this surprising, since in the course of my own attempt at explanation, I found several defects in my plan, and was also led by his questions to perceive others. All these I removed one after another, and ultimately terminated at a late hour my morning’s work with the conviction that anticipating carriage was not only within my power, but that I had devised one mechanism at least by which it might be accomplished.

Many years after, my assistant, on his return from a long residence abroad, called upon me, and we talked over the progress of the Analytical Engine. I referred back to the day on which I had made that most important step, and asked him if he recollected it. His reply was that he perfectly remembered the circumstance; for that on retiring to my library, he seriously thought that my intellect was beginning to become deranged. The reader may perhaps be curious to know how I spent the rest of that remarkable day.

After working, as I constantly did, for ten or eleven hours a day, I had arrived at this sat­is­fac­tory conclusion, and was revising the rough sketches of the new contrivance, when my servant entered the drawing-office, and announced that it was seven o’clock—that I dined in Park Lane—and that it was time to dress. I usually arrived at the house of my friend about a quarter of an hour before the appointed time, in order that we might have a short conversation on subjects on which we were both much interested. Having mentioned my recent success, in which my host thoroughly sympathized, I remarked that it had produced an exhilaration of the spirits which not even his excellent champagne could rival. Having enjoyed the society of Hallam, of Rogers, and of some few {116} others of that delightful circle, I retired, and joined one or perhaps two much more extensive reunions. Having thus forgotten science, and enjoyed society for four or five hours, I returned home. About one o’clock I was asleep in my bed, and thus continued for the next five hours.

This new and rapid system of carrying the tens when two numbers are added together, reduced the actual time of the addition of any number of digits, however large, to nine units of time for the addition, and one unit for the carriage. Thus in ten’s units of time, any two numbers, however large, might be added together. A few more units of time, perhaps five or six, were required for making the requisite previous arrangements.

Having thus advanced as nearly as seemed possible to the minimum of time requisite for arithmetical operations, I felt renewed power and increased energy to pursue the far higher object I had in view.

To describe the successive improvements of the Analytical Engine would require many volumes. I only propose here to indicate a few of its more important functions, and to give to those whose minds are duly prepared for it some information which will remove those vague notions of wonder, and even of its impossibility, with which it is surrounded in the minds of some of the most enlightened.

To those who are acquainted with the principles of the Jacquard loom, and who are also familiar with analytical formulæ, a general idea of the means by which the Engine executes its operations may be obtained without much difficulty. In the Exhibition of 1862 there were many splendid examples of such looms.

It is known as a fact that the Jacquard loom is capable of {117} weaving any design which the imagination of man may conceive. It is also the constant practice for skilled artists to be employed by man­u­fac­turers in designing patterns. These patterns are then sent to a peculiar artist, who, by means of a certain machine, punches holes in a set of pasteboard cards in such a manner that when those cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.

Now the man­u­fac­turer may use, for the warp and weft of his work, threads which are all of the same colour; let us suppose them to be unbleached or white threads. In this case the cloth will be woven all of one colour; but there will be a damask pattern upon it such as the artist designed.

But the man­u­fac­turer might use the same cards, and put into the warp threads of any other colour. Every thread might even be of a different colour, or of a different shade of colour; but in all these cases the form of the pattern will be precisely the same—the colours only will differ.

The analogy of the Analytical Engine with this well-known process is nearly perfect.

The Analytical Engine consists of two parts:—

Every formula which the Analytical Engine can be required to compute consists of certain algebraical operations to be performed upon given letters, and of certain other modifications depending on the numerical value assigned to those letters.

There are therefore two sets of cards, the first to direct the {118} nature of the operations to be performed—these are called operation cards: the other to direct the particular variables on which those cards are required to operate—these latter are called variable cards. Now the symbol of each variable or constant, is placed at the top of a column capable of containing any required number of digits.

Under this arrangement, when any formula is required to be computed, a set of operation cards must be strung together, which contain the series of operations in the order in which they occur. Another set of cards must then be strung together, to call in the variables into the mill, the order in which they are required to be acted upon. Each operation card will require three other cards, two to represent the variables and constants and their numerical values upon which the previous operation card is to act, and one to indicate the variable on which the arithmetical result of this operation is to be placed.

But each variable has below it, on the same axis, a certain number of figure-wheels marked on their edges with the ten digits: upon these any number the machine is capable of holding can be placed. Whenever variables are ordered into the mill, these figures will be brought in, and the operation indicated by the preceding card will be performed upon them. The result of this operation will then be replaced in the store.

The Analytical Engine is therefore a machine of the most general nature. Whatever formula it is required to develop, the law of its development must be communicated to it by two sets of cards. When these have been placed, the engine is special for that particular formula. The numerical value of its constants must then be put on the columns of wheels below them, and on setting the Engine in motion it will calculate and print the numerical results of that formula. {119}

Every set of cards made for any formula will at any future time recalculate that formula with whatever constants may be required.

Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any future time reproduce the calculations for which it was first arranged. The numerical value of its constants may then be inserted.

It is perhaps difficult to apprehend these descriptions without a familiarity both with analytical forms and mechanical structures. I will now, therefore, confine myself to the math­e­mat­i­cal view of the Analytical Engine, and illustrate by example some of its supposed difficulties.

An excellent friend of mine, the late Professor MacCullagh, of Dublin, was discussing with me, at breakfast, the various powers of the Analytical Engine. After a long conversation on the subject, he inquired what the machine could do if, in the midst of algebraic operations, it was required to perform logarithmic or trigonometric operations.

My answer was, that whenever the Analytical Engine should exist, all the developments of formula would be directed by this condition—that the machine should be able to compute their numerical value in the shortest possible time. I then added that if this answer were not sat­is­fac­tory, I had provided means by which, with equal accuracy, it might compute by logarithmic or other Tables.

I explained that the Tables to be used must, of course, be computed and punched on cards by the machine, in which case they would undoubtedly be correct. I then added that when the machine wanted a tabular number, say the logarithm of a given number, that it would ring a bell and then stop itself. On this, the attendant would look at a certain part of the machine, and find that it wanted the logarithm of a given {120} number, say of 2303. The attendant would then go to the drawer containing the pasteboard cards representing its table of logarithms. From amongst these he would take the required logarithmic card, and place it in the machine. Upon this the engine would first ascertain whether the assistant had or had not given him the correct logarithm of the number; if so, it would use it and continue its work. But if the engine found the attendant had given him a wrong logarithm, it would then ring a louder bell, and stop itself. On the attendant again examining the engine, he would observe the words, “Wrong tabular number,” and then discover that he really had given the wrong logarithm, and of course he would have to replace it by the right one.

Upon this, Professor MacCullagh naturally asked why, if the machine could tell whether the logarithm was the right one, it should have asked the attendant at all? I told him that the means employed were so ridiculously simple that I would not at that moment explain them; but that if he would come again in the course of a few days, I should be ready to explain it. Three or four days after, Bessel and Jacobi, who had just arrived in England, were sitting with me, inquiring about the Analytical Engine, when fortunately my friend MacCullagh was announced. The meeting was equally agreeable to us all, and we continued our conversation. After some time Bessel put to me the very same question which MacCullagh had previously asked. On this Jacobi remarked that he, too, was about to make the same inquiry when Bessel had asked the question. I then explained to them the following very simple means by which that verification was accomplished.

Besides the sets of cards which direct the nature of the operations to be performed, and the variables or constants {121} which are to be operated upon, there is another class of cards called number cards. These are much less general in their uses than the others, although they are necessarily of much larger size.

Any number which the Analytical Engine is capable of using or of producing can, if required, be expressed by a card with certain holes in it; thus—

The above card contains eleven vertical rows for holes, each row having nine or any less number of holes. In this example the tabular number is 3 6 2 2 9 3 9, whilst its number in the order of the table is 2 3 0 3. In fact, the former number is the logarithm of the latter.

The Analytical Engine will contain,

Of course the Engine will compute all the Tables which {122} it may itself be required to use. These cards will therefore be entirely free from error. Now when the Engine requires a tabular number, it will stop, ring a bell, and ask for such number. In the case we have assumed, it asks for the logarithm of 2 3 0 3.

When the attendant has placed a tabular card in the Engine, the first step taken by it will be to verify the number of the card given it by subtracting its number from 2 3 0 3, the number whose logarithm it asked for. If the remainder is zero, then the engine is certain that the logarithm must be the right one, since it was computed and punched by itself.

Thus the Analytical Engine first computes and punches on cards its own tabular numbers. These are brought to it by its attendant when demanded. But the engine itself takes care that the right card is brought to it by verifying the number of that card by the number of the card which it demanded. The Engine will always reject a wrong card by continually ringing a loud bell and stopping itself until supplied with the precise in­tel­lec­tual food it demands.

It will be an interesting question, which time only can solve, to know whether such tables of cards will ever be required for the Engine. Tables are used for saving the time of continually computing individual numbers. But the computations to be made by the Engine are so rapid that it seems most probable that it will make shorter work by computing directly from proper formulæ than by having recourse even to its own Tables.

The Analytical Engine I propose will have the power of expressing every number it uses to fifty places of figures. It will multiply any two such numbers together, and then, if required, will divide the product of one hundred figures by number of fifty places of figures. {123}

Supposing the velocity of the moving parts of the Engine to be not greater than forty feet per minute, I have no doubt that

In the various sets of drawings of the modifications of the mechanical structure of the Analytical Engines, already numbering upwards of thirty, two great principles were embodied to an unlimited extent.

The difficulties which naturally occur to those capable of examining the question, as far as they relate to arithmetic, are these,—

The following conditions relate to the algebraic portion of the Analytical Engine:—

This enumeration includes eight conditions, each of which is absolutely unlimited as to the number of its combinations.

Now it is obvious that no finite machine can include infinity. It is also certain that no question necessarily involving infinity can ever be converted into any other in which the idea of infinity under some shape or other does not enter.

It is impossible to construct machinery occupying unlimited space; but it is possible to construct finite machinery, and to use it through unlimited time. It is this substitution of the infinity of time for the infinity of space which I have made use of, to limit the size of the engine and yet to retain its unlimited power.

(a). I shall now proceed briefly to point out the means by which I have effected this change.

Since every calculating machine must be constructed for the calculation of a definite number of figures, the first datum must be to fix upon that number. In order to be somewhat in advance of the greatest number that may ever be required, I chose fifty places of figures as the standard for the Analytical Engine. The intention being that in such a machine two numbers, each of fifty places of figures, might be multiplied together and the resultant product of one hundred places might then be divided by another number of fifty {125} places. It seems to me probable that a long period must elapse before the demands of science will exceed this limit. To this it may be added that the addition and subtraction of numbers in an engine constructed for n places of figures would be equally rapid whether n were equal to five or five thousand digits. With respect to multiplication and division, the time required is greater:—

Thus if a . 10⁵⁰ + b and a′ . 10⁵⁰ + b′ are two numbers each of less than a hundred places of figures, then each can be expressed upon two columns of fifty figures, and a, b, a′, b′ are each less than fifty places of figures: they can therefore be added and subtracted upon any column holding fifty places of figures.

The product of two such numbers is—

This expression contains four pair of factors, a a′, a b′, a′ b, b b′, each factor of which has less than fifty places of figures. Each multiplication can therefore be executed in the Engine. The time, however, of multiplying two numbers, each consisting of any number of digits between fifty and one hundred, will be nearly four times as long as that of two such numbers of less than fifty places of figures.

The same reasoning will show that if the numbers of digits of each factor are between one hundred and one hundred and fifty, then the time required for the operation will be nearly nine times that of a pair of factors having only fifty digits.

Thus it appears that whatever may be the number of digits the Analytical Engine is capable of holding, if it is required to make all the computations with k times that number of digits, then it can be executed by the same Engine, but in an amount of time equal to k² times the former. Hence the {126} condition (a), or the unlimited number of digits contained in each constant employed, is fulfilled.

It must, however, be admitted that this advantage is gained at the expense of diminishing the number of the constants the Engine can hold. An engine of fifty digits, when used as one of a hundred digits, can only contain half the number of variables. An engine containing m columns, each holding n digits, if used for computations requiring k n digits, can only hold m / k constants or variables.

(b). The next step is therefore to prove (b), viz.: to show that a finite engine can be used as if it contained an unlimited number of constants. The method of punching cards for tabular numbers has already been alluded to. Each Analytical Engine will contain one or more apparatus for printing any numbers put into it, and also an apparatus for punching on pasteboard cards the holes corresponding to those numbers. At another part of the machine a series of number cards, resembling those of Jacquard, but delivered to and computed by the machine itself, can be placed. These can be called for by the Engine itself in any order in which they may be placed, or according to any law the Engine may be directed to use. Hence the condition (b) is fulfilled, namely: an unlimited number of constants can be inserted in the machine in an unlimited time.

I propose in the Engine I am constructing to have places for only a thousand constants, because I think it will be more than sufficient. But if it were required to have ten, or even a hundred times that number, it would be quite possible to make it, such is the simplicity of its structure of that portion of the Engine.

(c). The next stage in the arithmetic is the number of times {127} the four processes of addition, subtraction, multiplication, and division can be repeated. It is obvious that four different cards thus punched

would give the orders for the four rules of arithmetic.

Now there is no limit to the number of such cards which may be strung together according to the nature of the operations required. Consequently the condition (c) is fulfilled.

(d). The fourth arithmetical condition (d), that the order of succession in which these operations can be varied, is itself unlimited, follows as a matter of course.

The four remaining conditions which must be fulfilled, in order to render the Analytical Engine as general as the science of which it is the powerful executive, relate to algebraic quantities with which it operates.

The thousand columns, each capable of holding any number of less than fifty-one places of figures, may each represent a constant or a variable quantity. These quantities I have called by the comprehensive title of variables, and have denoted them by V_n, with an index below. In the machine I have designed, n may vary from 0 to 999. But after any one or more columns have been used for variables, if those variables are not required afterwards, they may be printed upon paper, and the columns themselves again used for other variables. In such cases the variables must have a new index; thus, ^mVⁿ. I propose to make n vary from 0 to 99. If more variables are required, these may be supplied by Variable Cards, which may follow each other in unlimited succession. Each card will cause its symbol to be printed with its proper indices. {128}

For the sake of uniformity, I have used V with as many indices as may be required throughout the Engine. This, however, does not prevent the printed result of a development from being represented by any letters which may be thought to be more convenient. In that part in which the results are printed, type of any form may be used, according to the taste of the proposer of the question.

It thus appears that the two conditions, (e) and (f), which require that the number of constants and of variables should be unlimited, are both fulfilled.

The condition (g) requiring that the number of combinations of the four algebraic signs shall be unlimited, is easily fulfilled by placing them on cards in any order of succession the problem may require.

The last condition (h), namely, that the number of functions to be employed must be without limit, might seem at first sight to be difficult to fulfil. But when it is considered that any function of any number of operations performed upon any variables is but a combination of the four simple signs of operation with various quantities, it becomes apparent that any function whatever may be represented by two groups of cards, the first being signs of operation, placed in the order in which they succeed each other, and the second group of cards representing the variables and constants placed in the order of succession in which they are acted upon by the former.

Thus it appears that the whole of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled in the Analytical Engine. The means I have adopted are uniform. I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time. The means I have employed are in {129} daily use in the art of weaving patterns. It is accomplished by systems of cards punched with various holes strung together to any extent which may be demanded. Two large boxes, the one empty and the other filled with perforated cards, are placed before and behind a polygonal prism, which revolves at intervals upon its axis, and advances through a short space, after which it immediately returns.

A card passes over the prism just before each stroke of the shuttle; the cards that have passed hang down until they reach the empty box placed to receive them, into which they arrange themselves one over the other. When the box is full, another empty box is placed to receive the coming cards, and a new full box on the opposite side replaces the one just emptied. As the suspended cards on the entering side are exactly equal to those on the side at which the others are delivered, they are perfectly balanced, so that whether the formulæ to be computed be excessively complicated or very simple, the force to be exerted always remains nearly the same.

In 1840 I received from my friend M. Plana a letter pressing me strongly to visit Turin at the then approaching meeting of Italian phi­los­o­phers. In that letter M. Plana stated that he had inquired anxiously of many of my countrymen about the power and mechanism of the Analytical Engine. He remarked that from all the information he could collect the case seemed to stand thus:—

“Hitherto the legislative department of our analysis has been all powerful—the executive all feeble.

“Your engine seems to give us the same control over the executive which we have hitherto only possessed over the legislative department.”

Considering the exceedingly limited information which {130} could have reached my friend respecting the Analytical Engine, I was equally surprised and delighted at his exact prevision of its powers. Even at the present moment I could not express more clearly, and in fewer terms, its real object. I collected together such of my models, drawings, and notations as I conceived to be best adapted to give an insight into the principles and mode of operating of the Analytical Engine. On mentioning my intention to my excellent friend the late Professor MacCullagh, he resolved to give up a trip to the Tyrol, and join me at Turin.

We met at Turin at the appointed time, and as soon as the first bustle of the meeting had a little abated, I had the great pleasure of receiving at my own apartments, for several mornings, Messrs. Plana, Menabrea, Mossotti, MacCullagh, Plantamour, and others of the most eminent geometers and engineers of Italy.

Around the room were hung the formula, the drawings, notations, and other illustrations which I had brought with me. I began on the first day to give a short outline of the idea. My friends asked from time to time further explanations of parts I had not made sufficiently clear. M. Plana had at first proposed to make notes, in order to write an outline of the principles of the engine. But his own laborious pursuits induced him to give up this plan, and to transfer the task to a younger friend of his, M. Menabrea, who had already established his reputation as a profound analyst.

These discussions were of great value to me in several ways. I was thus obliged to put into language the various views I had taken, and I observed the effect of my explanations on different minds. My own ideas became clearer, and I profited by many of the remarks made by my highly-gifted friends. {131}

One day Mosotti, who had been unavoidably absent from the previous meeting, when a question of great importance had been discussed, again joined the party. Well aware of the acuteness and rapidity of my friend’s intellect, I asked my other friends to allow me five minutes to convey to Professor Mosotti the substance of the preceding sitting. After putting a few questions to Mosotti himself, he placed before me distinctly his greatest difficulty.

He remarked that he was now quite ready to admit the power of mechanism over numerical, and even over algebraical relations, to any extent. But he added that he had no conception how the machine could perform the act of judgment sometimes required during an analytical inquiry, when two or more different courses presented themselves, especially as the proper course to be adopted could not be known in many cases until all the previous portion had been gone through.

I then inquired whether the solution of a numerical equation of any degree by the usual, but very tedious proceeding of approximation would be a type of the difficulty to be explained. He at once admitted that it would be a very eminent one.

For the sake of perspicuity and brevity I shall confine my present explanation to possible roots.

I then mentioned the successive stages:—

Now it will be observed that Professor Mosotti was quite ready to admit at once that each of these different processes could be performed by the Analytical Machine through the medium of properly-arranged sets of Jacquard cards.

His real difficulty consisted in teaching the engine to know when to change from one set of cards to another, and back again repeatedly, at intervals not known to the person who gave the orders.

The dimensions of the algebraic equation being known, the number of arithmetical processes necessary for Sturm’s theorem is consequently known. A set of operation cards can therefore be prepared. These must be accompanied by a corresponding set of variable cards, which will represent the columns in the store, on which the several coefficients of the given equation, and the various combinations required amongst them, are to be placed.

The next stage is to find a number greater than the greatest root of the given equation. There are various courses for arriving at such a number. Any one of these being selected, another set of operation and variable cards can be prepared to execute this operation.

Now, as this second process invariably follows the first, the second set of cards may be attached to the first set, and the engine will pass on from the first to the second process, and again from the second to the third process. {134}

But here a difficulty arises: successive powers of ten are to be substituted for x in the equation, until a certain event happens. A set of cards may be provided to make the substitution of the highest power of ten, and similarly for the others; but on the occurrence of a certain event, namely, the change of a sign from + to −, this stage of the calculation is to terminate.

Now at a very early period of the inquiry I had found it necessary to teach the engine to know when any numbers it might be computing passed through zero or infinity.

The passage through zero can be easily ascertained, thus: Let the continually-decreasing number which is being computed be placed upon a column of wheels in connection with a carrying apparatus. After each process this number will be diminished, until at last a number is subtracted from it which is greater than the number expressed on those wheels.

Now in every case of a carriage becoming due, a certain lever is transferred from one position to another in the cage next above it.

Consequently in the highest cage of all (say the fiftieth in the Analytical Engine), an arm will be moved or not moved accordingly as the carriages do or do not run up beyond the highest wheel.

This arm can, of course, make any change which has previously been decided upon. In the instance we have been considering it would order the cards to be turned on to the next set.

If we wish to find when any number, which is increasing, {135} exceeds in the number of its digits the number of wheels on the columns of the machine, the same carrying arm can be employed. Hence any directions may be given which the circumstances require.

It will be remarked that this does not actually prove, even in the Analytical Engine of fifty figures, that the number computed has passed through infinity; but only that it has become greater than any number of fifty places of figures.

There are, however, methods by which any machine made for a given number of figures may be made to compute the same formulæ with double or any multiple of its original number. But the nature of this work prevents me from explaining that method.

It may here be remarked that in the process, the cards employed to make the substitutions of the powers of ten are operation cards. They are, therefore, quite independent of the numerical values substituted. Hence the same set of operation cards which order the substitutions 1 × 10ⁿ will, if backed, order the substitution of 2 × 10ⁿ, &c. We may, therefore, avail ourselves of mechanism for backing these cards, and call it into action whenever the circumstances themselves require it.

The explanation of M. Mosotti’s difficulty is this:—Mechanical means have been provided for backing or advancing the operation cards to any extent. There exist means of expressing the conditions under which these various processes are required to be called into play. It is not even necessary that two courses only should be possible. Any number of courses may be possible at the same time; and the choice of each may depend upon any number of conditions.

It was during these meetings that my highly valued friend, M. Menabrea, collected the materials for that lucid and {136} admirable description which he sub­se­quent­ly published in the Bibli. Univ. de Genève, t. xli. Oct. 1842.

The elementary principles on which the Analytical Engine rests were thus in the first instance brought before the public by General Menabrea.

Some time after the appearance of his memoir on the subject in the “Bibliothèque Universelle de Genève,” the late Countess of Lovelace25 informed me that she had translated the memoir of Menabrea. I asked why she had not herself written an original paper on a subject with which she was so intimately acquainted? To this Lady Lovelace replied that the thought had not occurred to her. I then suggested that she should add some notes to Menabrea’s memoir; an idea which was immediately adopted.

We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernouilli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject.

These two memoirs taken together furnish, to those who are capable of understanding the reasoning, a complete demonstration—That the whole of the developments and operations of analysis are now capable of being executed by machinery.

There are various methods by which these developments {137} are arrived at:—1. By the aid of the Differential and Integral Calculus. 2. By the Combinatorial Analysis of Hindenburg. 3. By the Calculus of Derivations of Arbogast.

Each of these systems professes to expand any function according to any laws. Theoretically each method may be admitted to be perfect; but practically the time and attention required are, in the greater number of cases, more than the human mind is able to bestow. Consequently, upon several highly interesting questions relative to the Lunar theory, some of the ablest and most indefatigable of existing analysts are at variance.

The Analytical Engine is capable of executing the laws prescribed by each of these methods. At one period I examined the Combinatorial Analysis, and also took some pains to ascertain from several of my German friends, who had had far more experience of it than myself, whether it could be used with greater facility than the Differential system. They seemed to think that it was more readily applicable to all the usual wants of analysis.

I have myself worked with the system of Arbogast, and if I were to decide from my own limited use of the three methods, I should, for the purposes of the Analytical Engine, prefer the Calcul des Derivations.

As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise—By what course of calculation can these results be arrived at by the machine in the shortest time?

In the drawings I have prepared I proposed to have a thousand variables, upon each of which any number not having more than fifty figures can be placed. This machine would multiply 50 figures by other 50, and print the product {138} of 100 figures. Or it would divide any number having 100 figures by any other of 50 figures, and print the quotient of 50 figures. Allowing but a moderate velocity for the machine, the time occupied by either of these operations would be about one minute.

The whole of the numerical constants throughout the works of Laplace, Plana, Le Verrier, Hansen, and other eminent men whose indefatigable labours have brought astronomy to its present advanced state, might easily be recomputed. They are but the numerical coefficients of the various terms of functions developed according to certain series. In all cases in which these numerical constants can be calculated by more than one method, it might be desirable to compute them by several processes until frequent practice shall have confirmed our belief in the infallibility of mechanism.

The great importance of having accurate Tables is admitted by all who understand their uses; but the multitude of errors really occurring is comparatively little known. Dr. Lardner, in the “Edinburgh Review,” has made some very instructive remarks on this subject.

I shall mention two within my own experience: these are selected because they occurred in works where neither care nor expense were spared on the part of the Government to insure perfect accuracy. It is, however, but just to the eminent men who presided over the preparation of these works for the press to observe, that the real fault lay not in them but in the nature of things.

In 1828 I lent the Government an original MS. of the table of Logarithmic Sines, Cosines, &c., computed to every second of the quadrant, in order that they might have it compared with Taylor’s Logarithms, 4to., 1792, of which they possessed a considerable number of copies. Nineteen {139} errors were thus detected, and a list of these errata was published in the Nautical Almanac for 1832: these may be called

An error being detected in one of these errata, in the following Nautical Almanac we find an

But in this very erratum of the second order a new mistake was introduced larger than any of the original mistakes. In the year next following there ought to have been found

In the “Tables de la Lune,” by M. P. A. Hansen, 4to, 1857, published at the expense of the English Government, under the direction of the Astronomer Royal, is to be found a list of errata amounting to 155. In the 21st of these original errata there have been found three mistakes. These are duly noted in a newly-printed list of errata discovered during computations made with them in the “Nautical Almanac;” so that we now have the errata of an erratum of the original work.

This list of errata from the office of the “Nautical Almanac” is larger than the original list. The total number of errors at present (1862) discovered in Hansen’s “Tables of the Moon” amounts to above three hundred and fifty. In making these remarks I have no intention of imputing the slightest blame to the Astronomer Royal, who, like other men, cannot avoid submitting to inevitable fate. The only circumstance which is really extraordinary is that, when it was dem­on­strated that all tables are capable of being computed by machinery, and even when a machine existed which {140} computed certain tables, that the Astronomer Royal did not become the most enthusiastic supporter of an instrument which could render such invaluable service to his own science.

In the Supplementary Notices of the Astronomical Society, No. 9, vol. xxiii., p. 259, 1863, there occurs a Paper by M. G. de Ponteculant, in which forty-nine numerical coefficients relative to the Longitude, Latitude, and Radius vector of the Moon are given as computed by Plana, Delaunay, and Ponteculant. The computations of Plana and Ponteculant agree in thirteen cases; those of Delaunay and Ponteculant in two; and in the remaining thirty-four cases they all three differ.

I am unwilling to terminate this chapter without reference to another difficulty now arising, which is calculated to impede the progress of Analytical Science. The extension of analysis is so rapid, its domain so unlimited, and so many inquirers are entering into its fields, that a variety of new symbols have been introduced, formed on no common principles. Many of these are merely new ways of expressing well-known functions. Unless some philosophical principles are generally admitted as the basis of all notation, there appears a great probability of introducing the confusion of Babel into the most accurate of all languages.

A few months ago I turned back to a paper in the Philosophical Transactions, 1844, to examine some analytical investigations of great interest by an author who has thought deeply on the subject. It related to the separation of symbols of operation from those of quantity, a question peculiarly interesting to me, since the Analytical Engine contains the embodiment of that method. There was no ready, sufficient, and simple mode of distinguishing letters which represented quantity from those which indicated operation. To {141} understand the results the author had arrived at, it became necessary to read the whole Memoir.

Although deeply interested in the subject, I was obliged, with great regret, to give up the attempt; for it not only occupied much time, but placed too great a strain on the memory.

Whenever I am thus perplexed it has often occurred to me that the very simple plan I have adopted in my Mechanical Notation for lettering drawings might be adopted in analysis.

On the geometrical drawings of machinery every piece of matter which represents framework is invariably denoted by an upright letter; whilst all letters indicating moveable parts are marked by inclined letters.

The analogous rule would be—

Let all letters indicating operations or modifications be expressed by upright letters;

Whilst all letters representing quantity should be represented by inclined letters.

The subject of the principles and laws of notation is so important that it is desireable, before it is too late, that the scientific academies of the world should each contribute the results of their own examination and conclusions, and that some congress should assemble to discuss them. Perhaps it might be still better if each academy would draw up its own views, illustrated by examples, and have a sufficient number printed to send to all other academies.

SOON after I had commenced the Difference Engine, my attention was strongly directed to the imperfection of all known modes of explaining and dem­on­strat­ing the construction of machinery. It soon became apparent that my progress would be seriously impeded unless I could devise more rapid means of understanding and recalling the interpretation of my own drawings.

By a new system of very simple signs I ultimately succeeded in rendering the most complicated machine capable of explanation almost without the aid of words.

In order thoroughly to understand the action of any machine, we must have full information upon the following subjects, and it is of the greatest importance that this information should be acquired in the shortest possible time.

I. The actual shape and relative position of every piece of matter of which the machine is composed.

This can be accomplished by the ordinary mechanical drawings. Such drawings usually have letters upon them for the sake of reference in the description of the machine. Hitherto such letters were chosen without any principle, {143} and in fact gave no indication of anything except the mere spot upon the paper on which they were written.

I then laid down rules for the selection of letters. I shall only mention one or two of them:—

By other rules it is rendered possible, when looking at a plan of any complicated machine, to perceive the relative order of super-position of any number of wheels, arms, &c., without referring to the elevation or end view.

II. The actual time and duration of every motion throughout the action of any machine can be ascertained almost instantly by a system of signs called the Notations of Periods.

It possesses equal facilities for ascertaining every contemporaneous as well as for every successive system of movements.

III. The actual connection of each moveable piece of the machine with every other on which it acts. Thus, taking from any special part of the drawing the indicating letter, and looking for it on a certain diagram, called the trains, the whole course of its movements may be traced, up to the prime mover, or down to the final result.

I have called this system of signs the Mechanical Notation. By its application to geometrical drawing it has given us a new demonstrative science, namely, that of proving that any given machine can or cannot exist; and if it can exist, that it will accomplish its desired object. {144}

It is singular that this addition to human knowledge should have been made just about the period when it was beginning to be felt by those most eminently skilled in analysis that the time has arrived when many of its conclusions rested only on probable evidence. This state of things arose chiefly from the enormous extent to which the developments were necessarily carried in the lunar and planetary theories.

After employing this language for several years, it was announced, in December 1825, that King William IV. had founded two medals of fifty guineas each, to be given annually by the Royal Society according to rules to be laid down by the Council.

On the 26th January 1826, it was resolved,

“That it is the opinion of the Council that the medals be awarded for the most important discoveries or series of investigations, completed and made known to the Royal Society in the year preceding the day of the award.”

This rule reduced the number of competitors to a very few. Although I had had some experience as to the mode in which medals were awarded, and therefore valued them accordingly, I was simple enough to expect that the Council of the Royal Society would not venture upon a fraud on the very first occasion of exercising the royal liberality. I had also another motive for taking a ticket in this philosophical lottery of medals.

In 1824, the Astronomical Society did me the honour to award to me the first gold medal they ever bestowed. It was rendered still more grateful by the address of that eminent man, the late Henry Thomas Colebrooke, the President, who in a spirit of prophecy anticipated the results of years, at that period, long future. {145}

“It may not, therefore, be deemed too sanguine an anticipation, when I express the hope that an instrument which in its simpler form attains to the extraction of the roots of numbers, and approximates to the roots of equations, may, in a more advanced state of improvement, rise to the approximate solutions of algebraic equations of elevated degrees. I refer to solutions of such equations proposed by Lagrange, and more recently by other analysts, which involve operations too tedious and intricate for use, and which must remain without efficacy, unless some mode be devised of abridging the labour or facilitating the means of performance.”26

I felt, therefore, that the first Royal Medal might fairly become an object of ambition, whatever might be the worth of subsequent ones.

In order to qualify myself for this chance, I carefully drew up a paper, “On a Method of expressing by Signs the Action of Machinery,” which I otherwise should not have published at that time.

This Memoir was read at the Royal Society on the 16th March, 1826. To the system of signs which it first expounded I afterwards gave the name of “Mechanical Notation.” It had been used in England and in Ireland, although not taught in its schools. It applies to the description of a combat by sea or by land. It can assist in representing the functions of animal life; and I have had both from the Continent and from the United States, specimens of such applications. Finally, to whatever degree of simplicity I may at last have reduced the Analytical Engine, the course {146} through which I arrived at it was the most entangled and perplexed which probably ever occupied the human mind. Through the aid of the Mechanical Notation I examined numberless plans and systems of computing, and I am sure, from the nature of its self-necessary verifications that it is impossible I can have been deceived.

On the 16th November, 1826, that very Council of the Royal Society which had made the law took the earliest opportunity to violate it by awarding the two Royal Medals, the first to Dalton, whose great discovery had been made nearly twenty years before, and the other to Ivory, for a paper published in their “Transactions” three years before. The history of their proceedings will be found in the “Decline of Science in England,” p. 115, 1830.

WHEN the construction of the Difference Engine No. 1 was abandoned by the Government in 1842, I was consulted respecting the place in which it should be deposited. Well aware of the unrivalled perfection of its workmanship, and {148} conscious that it formed the first great step towards reducing the whole science of number to the absolute control of mechanism, I wished it to be placed wherever the greatest number of persons could see it daily.

With this view, I advised that it should be placed in one of the much-frequented rooms of the British Museum. Another locality was, however, assigned to it, and it was confided by the Government to the care of King’s College, Somerset House. It remained in safe custody within its glass case in the Museum of that body for twenty years. It is remarkable that during that long period no person should have studied its structure, and, by explaining its nature and use, have acquired an amount of celebrity which the singularity of that knowledge would undoubtedly have produced.

The College authorities did justice to their charge. They put it in the place of honour, in the centre of their Museum, and would, no doubt have given facilities to any of their members or to other persons who might have wished to study it.

But the system quietly pursued by the Government, of ignoring the existence of the Difference Engine and its inventor doubtlessly exercised its deadening influence27 on those who were inclined, by taste or acquirements, to take such a course. {149}

I shall enumerate a few instances.

1. In 1850, the Government appointed a Commission to organize the Exhibition of 1851.

The name of the author of the Economy of Man­u­fac­tures was not thought worthy by the Government to be placed on that Commission.

2. In 1851, the Com­mis­sion­ers of the International Exhibition did not think proper to exhibit the Difference Engine, although it was the property of the nation. They were as insensible to the greatest mechanical as to, what has been regarded by some, the greatest in­tel­lec­tual triumph of their country.

3. When it was decided by the people of the United States to have an Exhibition at New York, they sent a Com­mis­sion­er to Europe to make arrangement for its success. He was authorized to apply for the loan of the Difference Engine for a few months, and was empowered to give any pecuniary guarantee which might be required for its safe return.

That Com­mis­sion­er, on his arrival, applied to me on the subject. I explained to him the state of the case, and advised him to apply to the Government, whose property it was. I added that, if his application was successful, I would at my own expense put the machine in good working order, and give him every information requisite for its safe conveyance and use. His application was, however, unsuccessful.

4. In 1847, Mr. Dargan nobly undertook at a vast expense to make an Exhibition in Dublin to aid in the relief of his starving countrymen. It was thought that the exhibition of the Difference Engine would be a great attraction. I was informed at the time that an application was made to the Government for its loan, and that it was also unsuccessful. {150}

5. In 1855 the great French Exhibition occurred. Previously to its opening, our Government sent Com­mis­sion­ers to arrange and superintend the English department.

These Com­mis­sion­ers reported that the English cont­ri­bu­tion was remarkably deficient in what in France are termed “instruments de précision,” a term which includes a variety of instruments for scientific purposes. They recommended that “a Committee should be appointed who could represent to the producers of Philosophical Instruments how necessary it was that they should, upon an occasion of this kind, maintain their credit in the eyes of Europe.” The Government also applied to the Royal Society for advice; but neither did the Royal Society advise, nor the Government propose, to exhibit the Difference Engine.

6. The French Exhibition of 1855 was remarkable beyond all former ones for the number and ingenuity of the machines which performed arithmetical operations.

Pre-eminently above all others stood the Swedish Machine for calculating and printing math­e­mat­i­cal Tables. It is honourable to France that its highest reward was deservedly given to the inventor of that machine; whilst it is somewhat remarkable that the English Com­mis­sion­ers appointed to report upon the French Exhibition omitted all notice of these Calculating Machines.

The appearance of the finished portion of the unfinished Difference Engine No. 1 at the Exhibition of 1862 is entirely due to Mr. Gravatt. That gentleman had a few years before paid great attention to the Swedish Calculating Engine of M. Scheutz, and was the main cause of its success in this country.

Being satisfied that it was possible to calculate and print all Tables by machinery, Mr. Gravatt became convinced that {151} the time must arrive when no Tables would ever be calculated or printed except by machines. He felt that it was of great importance to accelerate the arrival of that period, more especially as numerical Tables, which are at present the most expensive kind of printing, would then become the cheapest.

In furtherance of this idea, Mr. Gravatt wrote to Dr. Jelf, the Principal of King’s College, Somerset House, to suggest that the Difference Engine of Mr. Babbage, which had for so many years occupied a prominent place in the museum, should be exhibited in the International Exhibition of 1862. He at the same time offered his assistance in the removal and reinstatement of that instrument.

The authorities of the College readily acceded to this plan. On further inquiry, it appeared that the Difference Engine belonged to the Government, and was only deposited with the College. It was then found necessary to make an application to the Treasury for permission to exhibit it, which was accordingly done by the proper authorities.

The Government granted the permission, and referred it to the Board of Works to superintend its placement in the building.

The Board of Works sent to me a copy of the correspondence relative to this matter, asking my opinion whether any danger might be apprehended for the safety of the machine during its transport, and also inquiring whether I had any other suggestion to make upon the subject.

Knowing the great strength of the work, I immediately answered that I did not anticipate the slightest injury from its transport, and that, under the superintendence of Mr. Gravatt, I considered it might be removed with perfect safety. The only suggestion I ventured to offer was, that as the Government possessed in the department of the {152} Registrar-General a copy, made by English workmen, of the Swedish Difference Engine, that it should be exhibited by the side of mine: and that both the Engines should be kept constantly working with a very slow motion.

By a subsequent communication I was informed that the Swedish Machine could not be exhibited, because it was then in constant use, computing certain Tables relating to the values of lives. I regretted this very much. I had intended to alter the handle of my own Engine in order to make it moveable circularly by the same catgut which I had hoped might have driven both. The Tables which the Swedish Machine was employed in printing were not of any pressing necessity, and their execution could, upon such an occasion, have been postponed for a few months without loss or inconvenience.

Besides, if the Swedish Engine had, as I proposed, been placed at work, its superintendent might have continued his table-making with but little delay, and the public would have been highly gratified by the sight.

He could also have given information to the public by occasional explanations of its principles; thus might Her Majesty’s Com­mis­sion­ers have gratified thousands of her subjects who came, with intense curiosity, prepared to be pleased and instructed, and whom they sent away amazed and disappointed.

From the experience I had during the first week of the Exhibition, I am convinced that if a fit place had been provided for the two Calculating Machines, so that the public might have seen them both in constant but slow motion, and if the superintendent had oc­ca­sion­al­ly given a short explanation of the principles on which they acted, they would have been one of the greatest attractions within the building. {153}

On Mr. Gravatt applying to the Com­mis­sion­ers for space, it was stated that the Engine must be placed amongst philosophical instruments, Class XIII.

The only place offered for its reception was a small hole, 4 feet 4 inches in front by 5 feet deep. On one side of this was the only passage to the office of the superintendent of the class. The opposite side was occupied by a glass case in which I placed specimens of the separate parts of the unfinished engine. These, although executed by English workmen above thirty years ago, were yet, in the opinion of the most eminent engineers, unsurpassed by any work the building of 1862 contained. The back of this recess was closed in and dark, and only allowed a space on the wall of about five feet by four, on which to place the whole of the drawings and illustrations of the Difference Engine. Close above the top of the machine was a flat roof, which deprived the drawings and the work itself of much light.

The public at first flocked to it: but it was so placed that only three persons could conveniently see it at the same time. When Mr. Gravatt kindly explained and set it in motion, he was continually interrupted by the necessity of moving away in order to allow access to the numerous persons whose business called them to the superintendent’s office. At a very early period various rep­re­sen­ta­tions were made to the Com­mis­sion­ers by the Jury, the superintendent, and very strongly by the press, of the necessity of having some qualified person to explain the machine to the public. I was continually informed by the attendants that hundreds of persons had, during my absence asked, when they could get an opportunity of seeing the machine in motion.

Admiring the earnestness of purpose and the sagacity with which Mr. Gravatt had steadily followed out the convictions of {154} his own mind relative to the abolition of all tables except those made and stereotyped by machinery, I offered all the assistance in my power to accelerate the accomplishment of his task.

I lent him for exhibition numerous specimens of the unfinished portions of the Difference Engine No. 1. These I had purchased on the determination of the Government to abandon its construction in 1842.

I proposed also to lend him the Mechanical Notations of the Difference Engine, which had been made at my own expense, and were finished by myself and my eldest son, Mr. B. Herschel Babbage.

I had had several applications from foreigners28 for some account of my system of Mechanical Notation, and great desire was frequently expressed to see the illustrations of the method itself, and of its various applications.

These, however, were so extensive that it was impossible, without very great inconvenience, to exhibit them even in my own house.

I therefore wrote to Mr. Gravatt to offer him the loan of the following property for the Exhibition:—

These drawings and notations would have required for their exhibition about seven or eight hundred square feet of wall. My letter to Mr. Gravatt was forwarded to the Com­mis­sion­ers with his own application for space to exhibit them. The Com­mis­sion­ers declined this offer; yet during the first six weeks of the Exhibition there was at a short distance from the Difference Engine an empty space of wall large enough for the greater part of these instructive diagrams. This portion of wall was afterwards filled up by a vast oil-cloth. Other large portions of wall, to the amount of thousands of square feet, were given up to other oil-cloths, and to numberless carpets. It is evident the Royal Com­mis­sion­ers were much better qualified to judge of furniture for the feet than of furniture for the head.

I was myself frequently asked why I did not employ a person to explain the Difference Engine. In reply to some of my friends, I inquired whether, when they purchased a carriage, they expected the builder to pay the wages of their coachman.

But my greatest difficulty was with foreigners; no explanation I could devise, and I tried many, appeared at all {157} to satisfy their minds. The thing seemed to them entirely in­com­pre­hen­sible.

That the nation possessing the greatest military and commercial marine in the world—the nation which had spent so much in endeavouring to render perfect the means of finding the longitude—which had recently caused to be computed and published at considerable expense an entirely new set of lunar Tables should not have availed itself at any cost of mechanical means of computing and stereotyping such Tables, seemed entirely beyond their comprehension.

At last they asked me whether the Com­mis­sion­ers were bêtes. I assured them that the only one with whom I was personally acquainted certainly was not.

When hard pressed by difficult questions, I thought it my duty as an Englishman to save my country’s character, even at the expense of my own. So on one occasion I suggested to my unsatisfied friends that Com­mis­sion­ers were usually selected from the highest class of society, and that possibly four out of five had never heard of my name.

But here again my generous efforts to save the character of my country and its Com­mis­sion­ers entirely failed. Several of my foreign friends had known me in their own homes, and had seen the estimation in which I was held by their own countrymen and by their own sovereign. These were still more astonished.

On another occasion an anecdote was quoted against me to prove that my name was well known even in China. It may, perhaps, amuse the reader. A short time after the arrival of Count Strzelecki in England, I had the pleasure of meeting him at the table of a common friend. Many inquiries were made relative to his residence in China. Much interest was expressed by several of the party to learn on {158} what subject the Chinese were most anxious to have information. Count Strzelecki told them that the subject of most frequent inquiry was Babbage’s Calculating Machine. On being further asked as to the nature of the inquiries, he said they were most anxious to know whether it would go into the pocket. Our host now introduced me to Count Strzelecki, opposite to whom I was then sitting. After expressing my pleasure at the introduction, I told the Count that he might safely assure his friends in the Celestial Empire that it was in every sense of the word an out-of-pocket machine.

At last the Com­mis­sion­ers were moved, not to supply the deficiency themselves, but to address the Government, to whom the Difference Engine belonged, to send somebody to explain it. I received a communication from the Board of Works, inquiring whether I could make any suggestions for getting over this difficulty. I immediately made inquiries, and found a person who formerly had been my amanuensis, and had, under my direction, worked out many most intricate problems. He possessed very considerable knowledge of mathematics, and was willing, for the moderate remuneration of six shillings a day, to be present daily during nine hours to explain the Difference Engine.

I immediately sent this information to the Board of Works, with the name and address of the person I recommended. This, I have little doubt, was directly communicated to the Com­mis­sion­ers; but they did not avail themselves of his services.

It is difficult, upon any principle, to explain the conduct of the Royal Com­mis­sion­ers of the Exhibition of 1862. They were appointed by the Government, yet when the Government itself became an exhibitor, and sent for exhibition a {159} Difference Engine, the property of the nation, these Com­mis­sion­ers placed it in a small hole in a dark corner, where it could, with some difficulty, be seen by six people at the same time.

No remonstrance was of the slightest avail; it was “Hobson’s choice,” that or none. It was represented that all other space was occupied.

A trophy of children’s toys, whose merits, it is true, the Com­mis­sion­ers were somewhat more competent to appreciate, filled one of the most prominent positions in the building. On the other hand, a trophy of the workmanship of English engineers, executed by machine tools thirty years before, and admitted by the best judges to be unsurpassed by any rival, was placed in a position not very inappropriate for the authorities themselves who condemned it to that locality.

But no hired aristocratic30 agent was employed to excite the slumbering perceptions of the Com­mis­sion­ers, who might have secured a favourable position for the Difference Engine, by practising on their good nature, or by imposing upon their imbecility.

It has been urged, in extenuation of the con­duct of these Com­mis­sion­ers, that their duty as guardians of the funds intrusted to them, and of the interests of the Guarantors, compelled them to practise a rigid economy.

Rigid economy is to be respected only when it is under the control of judgment, not of favouritism. If the machinery for making arithmetical calculations which was placed at the disposal of the Com­mis­sion­ers had been properly arranged, it might have been made at once a source of high gratification to the public and even of profit to the Exhibition. {160}

Such a group of Calculating Machines might have been placed by themselves in a small court capable of holding a limited number of persons. Round the walls of this court might have been hung the drawings I had offered to lend, containing the whole of those necessary for the Difference Engine No. 2, as well as a large number of illustrations for the explanation of the Mechanical Notation. The Swedish Difference Engine and my own might have been slowly making calculations during the whole day.

This court should have been open to the public generally, except at two or three periods of half an hour each, during which it should have been accessible only to those who had previously secured tickets at a shilling apiece.

During each half hour the person whom I had recommended to the Com­mis­sion­ers might have given a short popular explanation of the subject.

This attraction might have been still further increased, and additional profit made, if a single sheet of paper had been printed containing a woodcut of the Swedish Machine, an impression from a page of the Tables computed and stereotyped by it at Somerset House, and also an impression from a stereotype plate of the Difference Engine exhibited by the Government.

A plate of the Swedish Machine is in existence in London. I am confident that, for such a purpose, I could have procured the loan of it for the Com­mis­sion­ers, and I would willingly have supplied them with the stereotype plate from which the frontispage of the present volume was printed, together with from ten to twenty lines of necessary explanation.

These illustrations of machinery used for computing and printing Tables might have been put up into packets of dozens and half dozens, and also have been sold in single {161} sheets at the rate of one penny each copy. There can be no doubt the sale of them would have been very considerable. As it was, I found the woodcut representing the Difference Engine No. 1 in great request, and during the exhibition I had numberless applications for it; having given away my whole stock of about 800 copies.

The calculating court might have held comfortably from sixty to eighty seats. Each lecture would have produced say 3 l. This being repeated three times each day, together with the sale of the woodcuts, would have produced about 10 l. per day, out of which the Com­mis­sion­ers would have had six shillings per day to pay the assistant who gave the required explanations.

If the dignity of the Com­mis­sion­ers would not permit them to make money by such means, they might have announced that the proceeds of the tickets would be given to the distressed population of the Manchester district, and there would then have been crowds of visitors.

But the rigid economy of the Com­mis­sion­ers, who refused to expend six shillings a day for an attendant, although it would most probably have produced a return of several hundred pounds, was entirely laid aside when their patronage was to be extended to a brother official.

Captain Fowke, an officer of engineers, whose high order of architectural talent became afterwards so well known to the public, and whose whole time and services were retained and paid for by the country, was employed to make a design for the Exhibition Building.

The Com­mis­sion­ers approved of this design, which comprised two lofty domes, uniting in themselves the threefold inconvenience of being ugly, useless, and expensive. They then proceeded to pay him five thousand pounds for the job. {162} This system of awarding large sums of money to certain favoured public officers who are already paid for their services by liberal salaries seems to be a growing evil. At the period of the Irish famine the under-secretary of the Treasury condescended to accept 2,500 l. out of the fund raised to save a famished nation. Some inquiries, even recently, were oc­ca­sion­al­ly made whether any similar deduction will be allowed from the liberal cont­ri­bu­tions to the sufferers by the cotton famine.

The question was raised and the practice reprobated in the House of Commons by men of opposite party politics. Mr. Gladstone remarked:—

“If there was one rule connected with the public service which more than any other ought to be scrupulously observed, it was this, that the salary of a public officer, more especially if he were of high rank, ought to cover all the services he might be called upon to render. Any departure from this rule must be dangerous.” Hansard, vol. 101, p. 138, 1848. Supply, 14 Aug. 1848. See also “The Exposition of 1851,” 8vo., p. 217.

The following paragraph appeared in “The Times”31 a short time since, under the head Naval Intelligence:—

“A reply has been received to the memorial trans­mit­ted to the Admiralty some few days since from the inspectors employed on the iron frigate ‘Achilles,’ building at Chatham dockyard, requesting that they may be placed on the same footing as regards increased pay as the junior officers and mechanics working on the iron frigate for the additional number of hours they are employed in the dockyard. The Lords of the Admiralty intimate that they cannot accede to the wishes of the memorialists, who are reminded that, as {163} salaried officers of the establishment, the whole of their time is at the disposal of the Admiralty. This decision has caused considerable dissat­is­fac­tion.”

It appears that the Admiralty wisely adopted the principle enunciated by Mr. Gladstone.

It may, however, not unreasonably have caused dis­sat­is­fac­tion to those who had no interest to back them on finding that such large sums are pocketed by those who are blessed with influential friends in high quarters.

If the Com­mis­sion­ers had really wished to have obtained a suitable building at a fair price their course was simple and obvious. They need only have stated the nature and amount of accommodation required, and then have selected half a dozen of the most eminent firms amongst our great contractors, who would each have given them an estimate of the plans they respectively suggested.

The Com­mis­sion­ers might have made it one of the conditions that they should not be absolutely bound to give the contract to the author of the plan accepted. But in case of not employing him a sum previously stipulated should have been assigned for the use of the design.

By such means they would have had a choice of various plans, and if those plans had, previously to the decision of the Com­mis­sion­ers, been publicly exhibited for a few weeks, they might have been enlightened by public criticism. Such a course would have prevented the gigantic job they afterwards perpetrated. It could therefore find no support from the Com­mis­sion­ers.

The present Com­mis­sion­ers, however, are fit successors to those who in 1851 ignored the existence of the author of the “Economy of Man­u­fac­tures” and his inventions. They seem to have been deluded into the belief that they possessed {164} the strength, as well as the desire, quietly to strangle the Difference Engine.

It would be idle to break such butterflies upon its matchless wheels, or to give permanence to such names by reflecting them from its diamond-graven plates.32 Though the steam-hammer can crack the coating without injuring the kernel of the filbert it drops upon—the admirable precision of its gigantic power could never be dem­on­strated by exhausting its energy upon an empty nut-shell.

Peace, then, to their memory, aptly enshrined in unknown characters within the penetralia of the temple of oblivion.

These celebrities may there at last console themselves in the enjoyment of one enviable privilege denied to them during their earthly career—exemption from the daily consciousness of being “found out.”

It is, however, not quite impossible, although deciphering is a brilliant art, that one or other of them may have heard of the dread power of the decipherer. Having myself had some slight acquaintance with that fascinating pursuit, it gives me real pleasure to relieve them from this very natural fear by assuring them that not even the most juvenile decipherer could be so stupid as to apply himself to the interpretation of—characters known to be meaningless.

Yet there is one name amongst, but not of them—a fellow-worshipper with myself at far other fanes, whose hands, like mine, have wielded the hammer, and whose pen, like mine, has endeavoured to communicate faithfully to his fellow-men {165} the measure of those truths he has himself laboriously extracted from the material world. With such endowments, it is impossible that he could have had any cognizance of this part of the proceedings of his colleagues.33

At the commencement of the Exhibition, Mr. Gravatt was constantly present, and was so kind as to explain to many anxious inquirers the nature and uses of the Difference Engine. This, however, interfered so much with his pro­fes­sion­al engagements as a Civil Engineer, that it would have been unreasonable to have expected its continuance. In fact, as not above half a dozen spectators could see the machine at once, it was a great sacrifice of valuable time for a very small result.

During the early part of my own examination of the Exhibition I had many opportunities of conversing with experienced workmen, well qualified to appreciate the workmanship of the Difference Engine; these I frequently accompanied to its narrow cell, and pointed out to them its use, as well as the means by which its various parts had received their destined form.

Oc­ca­sion­al­ly also I explained it to some few of my personal friends. When Mr. Gravatt or myself were thus engaged, a considerable crowd was often collected, who were anxious to hear about, although they could not see, the Engine itself.

Upon one of these occasions I was insulted by impertinent questions conveyed in a loud voice from a person at a distance in the crowd. My taste for music, and especially for organs, was questioned. I was charitable enough to suppose that this was an exceptional case; but in less than a week another instance {166} occurred. After this experience, of course, I seldom went near the Difference Engine. Mr. Gravatt who had generously sacrificed a considerable portion of his valuable time for the information and in­struc­tion of the public was now imperatively called away by pro­fes­sion­al engagements, and the public had no information whatever upon a subject on which it was really very anxious to be instructed.

Fortunately, however, the Exhibition took place during the long vacation; and a friend of mine, Mr. Wilmot Buxton, of the Chancery Bar, very frequently accompanied me in my visits. Possessing a profound knowledge of the math­e­mat­i­cal principles embodied in the mechanism, I had frequently pointed out to him its nature and relations. These I soon found he so well apprehended that I felt justified in intrusting him with one of my keys of the machine, in order that he might have access to it without the necessity of my presence.

Whenever he opened it for his own sat­is­fac­tion or for the in­struc­tion of his friends, he was speedily surrounded by a far larger portion of the public than could possibly see it, but who were still attracted by his lucid oral explanation.

It was fortunate for many of the visitors to the Exhibition that this occurred, for the demands on his time, when present, were incessant, and hundreds thus acquired from his explanations a popular view of the subject.

After the close of the Exhibition, Mr. Gravatt and myself attended to prepare the Difference Engine for its return to the Museum of King’s College. To our great astonishment, we found that it had already been removed to the Museum at South Kensington. Not only the Difference Engine itself, but also the illustrations and all the unfinished portions of exquisite workmanship which I had lent to the Exhibition for its explanation, were gone. {167}

On Mr. Gravatt applying to the Board of Works, it was stated that the Difference Engine itself had been placed in the Kensington Museum because the authorities of King’s College had declined receiving it, and immediate in­struc­tions were of course given for the restoration of my own property.

I have had one op­por­tun­i­ty of fairly estimating some por­tion of the char­ac­ter of the late justly-lamented Prince Con­sort; to this I will now ven­ture to al­lude.

In 1842 Count Mensdorf visited London. A few days after I had a note from the late Duke of Wellington, in which he informed me that on the previous evening he had met at the palace the Queen’s uncle, Count Mensdorf, who had expressed to the Duke his wish to see my Calculating Engine. The Duke then inquired whether I could conveniently make some arrangement for that purpose. I immediately wrote to the Duke, that if he would appoint an hour on any morning of the ensuing week, I should have great pleasure in showing and explaining the Difference Engine to Count Mensdorf. It was afterwards arranged that on the following Tuesday, at two o’clock, Count Mensdorf and the Duke should pay me a visit in Dorset Street. On Monday {169} morning I received another note from the Duke, informing me that Prince Albert had expressed his intention to accompany Count Mensdorf in the proposed visit, and that it would be more convenient if the hour were changed to one instead of two o’clock.

I must freely admit that I did not greatly rejoice at this addition to the party. I resolved, however, strictly to perform the duties thus thrown upon me as a host, as well as all those to which Prince Albert was entitled by his elevated position.

Before I took the Prince into the fire-proof building in which the Difference Engine was then deposited, I asked his Royal Highness to allow me to show him a portrait of Jacquard, which was at that time hanging up in my drawing-room, as it would greatly assist in explaining the nature of Calculating Machines.

When we had arrived in front of the portrait, I pointed it out as the object to which I solicited the Prince’s attention. “Oh! that engraving?” remarked the Duke of Wellington. “No!” said Prince Albert to the Duke; “it is not an engraving.” I felt for a moment very great surprise; but this was changed into a much more agreeable feeling, when the Prince instantly added, “I have seen it before.” I felt at once that the Prince was a “good man and true,” and I resolved that I would not confine myself to the rigid rules of etiquette, but that I would help him with all my heart in whatever line his inquiries might be directed.

The portrait of Jacquard was, in fact, a sheet of woven silk, framed and glazed, but looking so perfectly like an engraving, that it had been mistaken for such by two members of the Royal Academy.

A short time after I became possessed of this beautiful work of art, I met Wilkie, and invited him to come and see {170} my recent acquisition. He called on me one morning. I placed him at a short distance in front of the portrait, which he admired greatly. I then asked him what he thought it was. He answered, “An engraving!” On which I asked, “Of what kind?” To this he replied, “Line-engraving, to be sure!” I drew him a little nearer. He then mentioned another style of engraving. At last, having placed Wilkie close to the portrait, he said, after a considerable pause, “Can it be lithography?”

A splendid collection of arms from Afghanistan, recently sent to me from India by Sir Edward Ryan, was lying on the tables in one of the rooms we passed through. These had attracted the notice of the Prince, and on returning, the whole party examined them with the greatest interest

I now conducted my visitors to the fire-proof building in which the Difference Engine was placed. Prince Albert was, I understood, sufficiently acquainted with the higher departments of math­e­mat­i­cal science to appreciate the influence of such an instrument on its future progress. But the circumstance that charmed me was—his bearing towards his uncle, Count Mensdorf. It was perfectly natural: it could be felt, admired, and honoured—but not described.

When the sad fact of the nation’s loss became known to me, I immediately reverted with some anxiety to a work I had published ten years before on the Exhibition of 1851. I feared lest, in speaking of that event, I might have committed some injustice, whilst I was indignant at that under which I was myself suffering. I willingly reprint it here because it contained no empty words of flattery; but analysed the reasons which commanded our respect.

MY acquaintance with the late Duke of Wellington commenced in an official visit from himself and Mr. Goulburn, the Chancellor of the Exchequer, to inspect the drawings and works of the Difference Engine No. 1. This was in November, 1829. Afterwards I met the Duke in private society at the houses of one or two of his intimate friends, and sub­se­quent­ly I was honoured not unfrequently by receiving him at my own. During the Exhibition of 1851 I very often accompanied him in his examination of the contents of that building. I made no notes of any of the conversations, some of them highly interesting, which occurred on such occasions, because I felt that the habit of recording privately the conversations with our acquaintances was a breach of faith towards the individual, and tended to destroy all confidence in society. {174}

I now perceive, when it is too late, that a rigid adherence to that rule has deprived me of the power of relating circumstances of the greatest interest to survivors, and of the highest credit to himself. I should not even have adverted to the subject in the present work, had I not observed in the fourth volume of the life of the late General Sir Charles Napier of Scinde a passage which, if not explained, might lead to the erroneous inference that I had myself proposed to speak to the Duke of Wellington on a certain military subject, whereas I only did so at the repeated desire of Sir Charles himself.

The following is a portion of a letter from General Sir Charles Napier to his brother, General Sir William Napier, extracted from “The Life of Sir Charles Napier,” vol. iv., p. 347:—

The matter referred to arose thus. Several years ago a troop-ship, named the “Birkenhead,” was wrecked on the African coast, near the Cape of Good Hope. A very small portion only of the troops were saved. According to the testimony of the survivors, the discipline and order which prevailed on board up to the final catastrophe was admirable, and almost beyond example. If any human means could have saved those invaluable lives, such discipline would have largely contributed to the result.

Sharing the general regret at this severe loss, and sympathising deeply with the feelings of the surviving relatives, it occurred to me that very simple and inexpensive means were available, which if employed, would at the least afford a melancholy consolation to the afflicted relatives, might be retained with becoming pride in their families, and would also add to the respectability of the social position of the soldier.

Observing that military offences punished by a court-martial were made public by being read at the head of every regiment, I suggested that in certain cases publicity should be given by the same means to noble acts of forbearance or of self-devotion.

In the case of the “Birkenhead,” in which ship small detachments of several regiments were lost, I suggested that an order should be issued, stating—

The circumstances under which the loss occurred, and the nation’s approbation of the conduct of the departed.

That their names should be read at the head of their respective regiments.

That an official letter, signed by the colonel or other proper {176} officer of each regiment, describing the nature of the service under which the loss occurred, and conveying to the nearest surviving relative the expression of the high approbation the Government entertained of such heroic conduct.

Such official testimonials would soothe the feelings of many a relative, would become objects of just pride amongst the relations of the departed, and be handed down as heir-looms in many a village circle.

I mentioned these views to several of my acquaintances, and the idea seemed to meet with general approbation. I found my military friends fully alive to the advantage of such a course for the benefit of the service, and also as a consolation to surviving relatives. Amongst others, I proposed it to the late General Sir Charles Napier. He highly approved of the plan, about which we had several conversations. In one of these I suggested that he should mention it to the Duke of Wellington; to which Sir Charles replied, “No, I could not do that: you should tell him yourself.” I smiled at the notion, not thinking that my friend was in earnest.

A short time after I met Sir Charles Napier at a large evening party. We were sitting together on a sofa talking: he resumed the plan I had proposed, spoke of it with much approbation, and concluded by saying, “You ought to tell the Duke of it.”

I replied that I had thought he was only joking when he had on a former occasion made the same ob­ser­va­tion.

“No, indeed,” said Sir Charles; “I am serious. The Duke will attend to what you say more than to any of us.”

“If you really think so,” I replied, “I will follow your counsel. I hope,” I added, “the Duke may excuse me as a civilian for speaking about it, but after such an expression of your opinion I feel bound to take that course.” {177}

The conversation then turned upon other subjects, when shortly after the Duke of Wellington was announced.

“There,” observed Sir Charles, “is the Duke, now go and talk to him about it.” I promised to do so at a proper opportunity.

After the Duke had made his bow to the lady of the house, and recognised and conversed with many of his friends, I threw myself in his way. On the Duke shaking hands with me, I remarked that I was par­tic­u­lar­ly glad to meet him, because an idea had occurred to me in which I thought he would take an interest. He stepped with me a little out of the crowd, and I then stated shortly my views. The Duke paid great attention to the subject; made several remarks upon it; and when we separated, I felt satisfied that he took a strong interest in it. I thought, however, that he had applied the idea rather more to the officers, whilst my main object was the interests of the privates.

Much later in the evening I was taking some refreshment in another room, when the Duke entering, saw and rejoined me. He reverted to the subject; I observed that though officers and privates should have the same official acknowledgment, yet that the Commander-in-Chief and the Government possessed other more substantial means of benefiting the surviving relatives of the officers than of the privates. We had some further conversation about it, and I then felt quite satisfied that he both understood and approved of it.

I rather think the Duke of Wellington moved in the House of Lords for certain papers, on which he intended to found some measure of the kind; but his death, shortly after, put an end to the question.

During the year 1851 I very frequently accompanied the Duke of Wellington to the Exhibition, or met him there by {178} appointment at the crystal fountain. Sometimes one or two of his particular friends, usually ladies, were invited to join the party.

On the first occasion I spoke to one of the attending police, simply for the purpose of facilitating our passage if we should get into a great crowd, which, of course, did oc­ca­sion­al­ly happen. In these cases the policeman a little preceded us, and it was very interesting to observe the sudden changes in the countenances of those whom the constable gently touched in order to accelerate our passage. On the first slight pressure of the policeman’s hand upon the arm of John Bull, he looked round with indignation: but when the policeman quietly asked him to be so good as to allow the Duke of Wellington to pass, the muscles of John Bull’s countenance relaxed into a grateful smile: he immediately made way, and in several cases thanked the officer for giving him an opportunity of seeing the Duke. During the most crowded of those days we at one period became entirely blocked up and stationary for upwards of ten minutes. Our intelligent companion was himself wedged in, at a short distance from us. Just in front of us stood a woman with a child in her arms of about two years old, who was leaning over its mother’s shoulder.

The Duke began to play with the infant, pretending to touch its ear with his finger, and then to touch its nose. The mother was gratified,—the child was charmed. At last the crowd almost suddenly broke up, and we went on. After we had advanced about a dozen paces I said to the Duke of Wellington, “I must step back to speak to the mother of your young friend.” I then asked her if she knew the gentleman who had been playing with her child for the last ten minutes: she said “No, Sir.” I told her it was the Duke of Wellington. Her surprise and delight were equally great. {179} I desired her to tell her boy when he grew up that, when an infant, the Duke of Wellington had played with him. I then returned and told the Duke the object of my mission. His approbation was indicated by a happy smile.

One morning the Duke of Wellington called in Dorset Street with the late Countess of Wilton, to whom he wished me to show the Difference Engine. Its home was at that period in my drawing-room. We sat round it whilst I explained its mode of action, and made it calculate some small Table of numbers.

When I had concluded my explanation, Lady Wilton, addressing me, said, “Now, Mr. Babbage, can you tell me what was your greatest difficulty in contriving this machine?” I had never previously asked myself that question; but I knew the nature of it well.

It arose not from the difficulty of contriving mechanism to execute each individual movement, for I had contrived very many different modes of executing each: but it really arose from the almost innumerable combinations amongst all these contrivances—a number so vast, that no human mind could examine them all.

It instantly occurred to me that a similar difficulty must present itself to a general commanding a vast army, when about to engage in a conflict with another army of equal or of greater amount. I therefore thought it must have been felt by the Duke of Wellington, and I determined to make a kind of psychological experiment upon him.

Carefully abstaining from any military term, I commenced my explanation to Lady Wilton. I soon perceived by his countenance that the Duke was already in imagination again in Spain. I then went on boldly with the explanation of my {180} own mechanical difficulty; and when I had concluded, the Duke turned to Lady Wilton and said, “I know that difficulty well.”

The success of this experiment induced me in a subsequent publication34 to give an analysis of one portion of the Duke of Wellington’s in­tel­lec­tual character, although I made no mention of his name. Many of his admirers, however, perceived at once the truth of those views, and recognised the justice of their application. I therefore place them before my readers in the following extract from the work referred to:—

“It is now felt and admitted, that it is the civil capacity of the great commander which prepares the way for his military triumphs; that his knowledge of human nature enables him to select the fittest agents, and to place them in the situations best adapted to their powers; that his intimate acquaintance with all the accessories which contribute to the health and comfort of his troops, enables him to sustain their moral and physical energy. It has been seen that he must have studied and properly estimated the character of his foes as well as of his allies, and have made himself acquainted with the personal character of the chiefs of both; and still further, that he must have scrutinized the secret motives which regulated their respective governments.

“When directly engaged in the operations of contending armies occupying a wide extent of country, he must be able, with rapid glance, to ascertain the force it is possible to con­cen­trate upon each of many points in any given time, and the greater or less chance of fairing in the attempt. He must also be able to foresee, with something more than conjecture, what amount of the enemy’s force can be brought to the same spot in the same and in different times. With these elements {181} he must undertake one of the most difficult of mental tasks, that of classifying and grouping the innumerable combinations to which either party may have recourse for purposes of attack or defence. Out of the multitude of such combinations, which might baffle by their simple enumeration the strongest memory, throwing aside the less important, he must be able to discover, to fix his attention, and to act upon the most favourable. Finally, when the course thus selected having been pursued, and perhaps partially carried out, is found to be entirely deranged by one of those many chances inseparable from such operations, then, in the midst of action, he must be able suddenly to organise a different system of operations, new to all other minds, yet possibly, although unconsciously, anticipated by his own.

“The genius that can meet and overcome such difficulties must be in­tel­lec­tual, and would, under different circumstances, have been distinguished in many a different career.

“Nor even would it be very surprising that such a commander, estimating justly the extent of his own powers, and conscious of having planned the best combinations of which his mind is capable, should, having issued his orders, calmly lie down on the eve of the approaching conflict, and find in sleep that bodily restoration so indispensable to the full exercise of his faculties in the mighty struggle about to ensue.”

Soon after the Queen came to the throne, the two Uni­ver­si­ties pre­sent­ed ad­dresses to her Majesty. I ac­com­panied that of Cambridge. The depu­ta­tion was very numerous, and much unseemly pushing took place. I recollect a very short dumpy fellow pushing much more energetically than any other, for whom I made way, as I retired from the strife in which I was unwillingly involved. He not only pushed, but was {182} continually jumping up like a parched pea in a heated frying-pan: his object being to get a glimpse of her Majesty, and the effect accomplished being to alight on the toes or graze the heels of his colleagues.

I retired into a window close to the end of the position occupied by the gentlemen-at-arms. The Duke of Wellington, who had a short time before, as Chancellor of the University of Oxford, presented the address of that body, still remained in the state apartments. He joined me in the recess of the window, and we entered into conversation.

After a time the little dumpy fellow, who had been regularly turned out of the crowd for his pushing, came up to us, and, mistaking the Duke of Wellington for a beef-eater or some palace attendant, complained, almost in tears, that he wanted to see the Queen, and that they had pushed him out, and that he had not been able to see the Queen.

The Duke very good-naturedly said he would take him to a place where he could see her Majesty without being pushed about. Accordingly, the Duke led him behind the gentlemen-at-arms to a situation in which the little man’s wish was gratified, and then returned with him to the window, and resumed the conversation.

On another occasion the University of Cambridge presented an address to the Queen at Buckingham Palace. The crowd was very great. On descending one of the flights of stairs, a short Master of Arts was unluckily caught by the string of his gown hooking itself upon one of the large door-handles. He was carried off his legs by the advancing rush. To bring back the pendant Master of Arts a single inch was impossible from the pressure onwards. So whilst two or three of his colleagues with difficulty supported him, I took out my pen-knife and cut the imprisoning ribbon. {183}

When I published the “Ninth Bridgewater Treatise,” I sent my servant to Apsley House with a presentation copy for the Duke of Wellington. The next morning at breakfast my servant informed me that the porter absolutely refused to take it in, although he stated from whom it came.

I remarked to my brother-in-law, who was staying with me, that it was a very odd circumstance, and inquired what was to be done. He replied, “When a man refuses to receive a parcel, nothing more can be done.” I then observed, that if any other person than the Duke had done so, I should have taken no further step; but, I added, that I knew his character so well, that I was confident there was really a good and sufficient reason, although I could not conjecture its nature.

After breakfast I wrote a short note to the Duke, mentioning the circumstance, taking for granted that it arose entirely from some misconception of his orders. I then requested him not to take the trouble of writing to me to explain it; but added that I would send the volume to Apsley House on the following morning, when, I had no doubt, the mistaken interpretation of his orders would have been rectified.

About three o’clock the same day a servant of the Duke’s brought me a note, inquiring if there were any answer to take back. The Duke stated in his note that letters, books, parcels, maps, and even merchandise, were continually sent to him for the purpose of being forwarded to all parts of the world. This, he observed, threw upon his house-steward so great a responsibility, that he had been compelled to give directions that no parcel should be received at Apsley House without a written order with his signature, like that which he now enclosed. As the Duke’s servant was waiting, I gave him the book, which he took back, and I retained the slip of paper for any other similar occasion. {184}

The Duke was habitually an economist of time. One day I was going homeward in a cab to dress for a dinner engagement, when I thought I observed him riding down St. James’s Street towards the House of Lords. On reaching the house of the friend with whom I was to dine, I found that the Duke of Wellington was expected at dinner. He arrived punctually. In the course of the evening I took an opportunity of asking him whether I was mistaken in supposing I had seen him a short time before dinner riding down St. James’s Street. I then expressed my surprise at the rapidity of his movements in getting back to Apsley House in time to dress and be punctual to his engagement. He said, “No, I did not do that; I had ordered my carriage to meet me at the House of Lords, and I changed my dress whilst it was bringing me here.”

The most interesting conversations generally occurred when only a few of his intimate friends met together.

On one of these occasions, at a very small dinner-party, the characters of the French marshals became the subject of conversation. The Duke, being appealed to, pointed out freely their various qualities, and assigned to each his peculiar excellence.

One question, the most highly interesting of all, naturally presented itself to our minds. I was speculating how I could, without impropriety, suggest it, when, to my great relief, one of the party, addressing the Duke, said—

“Well, sir, how was it that, with such various great qualities, you licked them all, one after another?”

The Duke was evidently taken by surprise. He paused for a moment or two, and then said—

“Well, I don’t know exactly how it was; but I think that if any unexpected circumstance occurred in the midst of a {185} battle, which deranged its whole plan, I could perhaps organize another plan more quickly than most of them.”

This strongly confirms the view of the Duke of Wellington’s character given in the preceding pages. After examining all the more important combinations which might be made for the conflict, and having selected those which appeared the best, it is quite natural, if any accident deranged the original plan, that he should perceive, more quickly than another commander, one amongst the many plans previously rejected which was immediately applicable to the new and unexpected circumstances.

IN 1826, one of the secretaryships of the Royal Society became vacant. Dr. Wollaston and several others of the leading members of the Society and of the Council wished that I should be appointed. This would have been the more agreeable to me, because my early friend Herschel was at that time the senior Secretary.

This arrangement was agreed to by Sir H. Davy, and I left town with the full assurance that I was to have the appointment. In the mean time Sir H. Davy summoned a Council at an unusual hour—eight o’clock in the evening—for a special purpose, namely, some arrangement about the Treasurer’s accounts.

After the business relating to the Treasurer was got through, Sir H. Davy observed that there was a secretaryship vacant, and he proposed to fill it up.

Dr. Wollaston then asked Sir Humphry Davy if he claimed the nomination as a right of the President, to which {187} Sir H. Davy replied that he did, and then nominated Mr. Children. The President, as president, has no such right; and even if he had possessed it, he had promised Mr. Herschel that I should be his colleague. There were upright and eminent men on that council; yet no one of them had the moral courage to oppose the President’s dictation, or afterwards to set it aside on the ground of its irregularity.

A few years after, whilst I was on a visit at Wimbledon Park, Dr. and Mrs. Somerville came down to spend the day. Dr. Somerville mentioned a very pleasant dinner he had had with the late Mr. John Murray of Albemarle Street, and also a conversation relating to my book “On the Decline of Science in England.” Mr. Murray felt hurt at a remark I had made on himself (page 107) whilst criticizing a then unexplained job of Sir Humphry Davy’s. Dr. Somerville assured Mr. Murray that he knew me intimately, and that if I were convinced that I had done him an injustice, nobody would be more ready to repair it. A few days after, Mr. Murray put into Dr. Somerville’s hands papers explaining the whole of the transaction. These papers were now transferred to me. On examining them I found ample proof of what I had always suspected. The ob­ser­va­tion I had made which pained Mr. Murray fell to the ground as soon as the real facts were known, and I offered to retract it in any suitable manner. One plan I proposed was to print a supplemental page, and have it bound up with all the remaining copies of the “Decline of Science.”

Mr. Murray was satisfied with my explanation, but did not wish me to take the course I proposed, at least, not at that time. Various objections may have presented themselves to his mind, but the affair was adjourned with the understanding that at some future time I should explain the real state of {188} the facts which had led to this misinterpretation of Mr. Murray’s conduct.

The true history of the affair was this: Being on the Council of the Royal Society in 1827, I observed in our accounts a charge of 381 l. 5 s. as paid to Mr. Murray for 500 copies of Sir Humphry Davy’s Discourses.

I asked publicly at the Council for an explanation of this item. The answer given by Dr. Young and others was—

“That the Council had agreed to purchase these volumes at that price, in order to induce Mr. Murray to print the President’s speeches.”

To this I replied that such an explanation was entirely inadmissible. I then showed that even allowing a very high price for composing, printing, and paper, if the Council had wished to print 500 copies of those Discourses they could have done it themselves for 150 l. at the outside. I could not extract a single word to elucidate this mystery, about which, however, I had my own ideas.

It appeared by the papers put into my hands that Sir Humphry Davy had applied to Mr. Murray, and had sold him the copyright of the Discourses for 500 guineas, one of the conditions being that the Royal Society should purchase of him 500 copies at the trade price.

Mr. Murray paid Sir H. Davy the 500 guineas in three bills at six, twelve, and eighteen months. These bills passed through Drummond’s (Sir H. Davy’s banker), and I have had them in my own hands for examination.

Thus it appears that Mr. Murray treated the whole affair as a matter of business, and acted in this purchase in his usual liberal manner. I have had in my hand a statement of the winding-up of that account copied from Mr. Murray’s books, and I find that he was a considerable loser by his {189} purchase. Sir H. Davy, on the other hand, contrived to transfer between three and four hundred pounds from the funds of the Royal Society into his own pocket.35

It was my determination to have called for an explanation of this affair at the election of our President and officers at our anniversary on the 30th November if Sir H. Davy had been again proposed as President in 1827.

One day Herschel, sitting with me after dinner, amusing himself by spinning a pear upon the table, suddenly asked whether I could show him the two sides of a shilling at the same moment.

I took out of my pocket a shilling, and holding it up before the looking-glass, pointed out my method. “No,” said my friend, “that won’t do;” then spinning my shilling upon the table, he pointed out his method of seeing both sides at once. The next day I mentioned the anecdote to the late Dr. Fitton, who a few days after brought me a beautiful illustration of the principle. It consisted of a round disc of card suspended between the two pieces of sewing-silk. These threads being held between the finger and thumb of each hand, were then made to turn quickly, when the disc of card, of course, revolved also.

Upon one side of this disc of card was painted a bird; upon the other side, an empty bird-cage. On turning the thread rapidly, the bird appeared to have got inside the cage. We soon made numerous applications, as a rat on one side and a trap upon the other, &c. It was shown to Captain Kater, Dr. Wollaston, and many of our friends, and was, after the lapse of a short time, forgotten. {190}

Some months after, during dinner at the Royal Society Club, Sir Joseph Banks being in the chair, I heard Mr. Barrow, then Secretary to the Admiralty, talking very loudly about a wonderful invention of Dr. Paris, the object of which I could not quite understand. It was called the thaumatrope, and was said to be sold at the Royal Institution, in Albemarle-street. Suspecting that it had some connection with our unnamed toy, I went the next morning and purchased, for seven shillings and sixpence, a thaumatrope, which I afterwards sent down to Slough to the late Lady Herschel. It was precisely the thing which her son and Dr. Fitton had contributed to invent, which amused all their friends for a time and had then been forgotten. There was however one additional thaumatrope made afterwards. It consisted of the usual disc of paper. On one side was represented a thaumatrope (the design upon it being a penny-piece) with the motto, “How to turn a penny.”

On the other side was a gentleman in black, with his hands held out in the act of spinning a thaumatrope, the motto being, “A new trick from Paris.”

After my contest for Finsbury was decided, Mr. Rogers the banker, and the brother of the poet, who had been one of my warmest supporters, proposed accompanying me to the hustings at the declaration of the poll. He had also invited a party of some of the most influential electors of his district to dine with him in the course of the week, in order that they might meet me, and consider about measures for supporting me at the next opportunity.

On a cold drizzling rainy day in November the final state of the poll was declared. Mr. Rogers took me in his carriage to the hustings, and caught a cold, which seemed at first unimportant. On the day of the dinner, when we met at {191} Mr. Rogers’s, who resided at Islington, he was unable to leave his bed. Miss Rogers, his sister, who lived with him, and his brother the poet, received us, quite unconscious of the dangerous condition of their relative, who died the next day.

Thus commenced a friendship with both of my much-valued friends which remained unruffled by the slightest wave until their lamented loss. Miss Rogers removed to a house in the Regent’s Park, in which the paintings by modern artists collected by her elder brother, and increased by her own judicious taste, were arranged. The society at that house comprised all that was most eminent in literature and in art. The adjournment after her breakfasts to the delightful verandah overlooking the Park still clings to my fading memory, and the voices of her poet brother, of Jeffrey, and of Sidney Smith still survive in the vivid impressions of their wisdom and their wit.

I do not think the genuine kindness of the poet’s character was sufficiently appreciated. I oc­ca­sion­al­ly walked home with him from parties during the first years of our acquaintance. In later years, when his bodily strength began to fail, I always accompanied him, though sometimes not without a little contest.

I have frequently walked with him from his sister’s house, in the Regent’s Park, to his own in St. James’s Place, and he has sometimes insisted upon returning part of the way home with me.

On one of those occasions we were crossing a street near Cavendish Square: a cart coming rapidly round the corner, I almost dragged him over. As soon as we were safe, the poet said, very much as a child would, “There, now, that was all your fault; you would come with me, and so I was nearly run over.” However, I found less and less resistance to my {192} accompanying him, and only regretted that I could not be constantly at his side on those occasions.

Soon after the publication of the “Economy of Man­u­fac­tures,” Mr. Rogers told me that he had met one evening, at a very fashionable party, a young dandy, with whom he had had some conversation. The poet had asked him whether he had read that work. To this his reply was, “Yes: it is a very nice book—just the kind of book that anybody could have written.”

One day, when I was in great favour with the poet, we were talking about the preservation of health. He told me he would teach me how to live for ever; for which I thanked him in a compliment after his own style, rather than in mine. I answered, “Only embalm me in your poetry, and it is done.” Mr. Rogers invited me to breakfast with him the next morning, when he would communicate the receipt. We were alone, and I enjoyed a very entertaining breakfast. The receipt consisted mainly of cold ablutions and the frequent use of the flesh brush. Mr. Rogers himself used the latter to a moderate extent regularly, three times every day—before he dressed himself, when he dressed for dinner, and before he got into bed. About six or eight strokes of the flesh-brush completed each operation. We then adjourned to a shop, where I purchased a couple of the proper brushes, which I used for several years, and still use oc­ca­sion­al­ly, with, I believe, considerable advantage.

Once, at Mr. Rogers’s table, I was talking with one of his guests about the speed with which some authors composed, and the slowness of others. I then turned to our host, and, much to his surprise, inquired how many lines a-day on the average a poet usually wrote. My friend, when his astonishment had a little subsided, very good-naturedly gave us the result of his own experience. He said that he had never written {193} more than four36 lines of verse in any one day of his life. This I can easily understand; for Mr. Rogers’ taste was the most fastidious, as well as the most just, I ever met with. Another circumstance also, I think, contributed to this slowness of composition.

An author may adopt either of two modes of composing. He may write off the whole of his work roughly, so as to get upon paper the plan and general outline, without attending at all to the language. He may afterwards study minutely every clause of each sentence, and then every word of each clause.

Or the author may finish and polish each sentence as soon as it is written.

This latter process was, I think, employed by Mr. Rogers, at least in his poetry.

He then told us that Southey composed with much greater rapidity than himself, as well in poetry as in prose. Of the latter Southey frequently wrote a great many pages before breakfast.

Once, at a large dinner party, Mr. Rogers was speaking of an inconvenience arising from the custom, then commencing, of having windows formed of one large sheet of plate-glass. He said that a short time ago he sat at dinner with his back to one of these single panes of plate-glass: it appeared to him that the window was wide open, and such was the force of imagination, that he actually caught cold.

It so happened that I was sitting just opposite to the poet. Hearing this remark, I immediately said, “Dear me, how odd it is, Mr. Rogers, that you and I should make such a very different use of the faculty of imagination. When I go to the house of a friend in the country, and unexpectedly {194} remain for the night, having no night-cap, I should naturally catch cold. But by tying a bit of pack-thread tightly round my head, I go to sleep imagining that I have a night-cap on; consequently I catch no cold at all.” This sally produced much amusement in all around, who supposed I had improvised it; but, odd as it may appear, it is a practice I have often resorted to. Mr. Rogers, who knew full well the respect and regard I had for him, saw at once that I was relating a simple fact, and joined cordially in the merriment it excited.

In the latter part of Mr. Rogers’s life, when, being unable to walk, he was driven in his carriage round the Regent’s Park, he frequently called at my door, and, when I was able, I often accompanied him in his drive. On some one of these occasions, when I was unable to accompany him, I put into his hands a parcel of proof-sheets of a work I was then writing, thinking they might amuse him during his drive, and that I might profit by his criticism. Some years before, I had consulted him about a novel I had proposed to write solely for the purpose of making money to assist me in completing the Analytical Engine. I breakfasted alone with the poet, who entered fully into the subject. I proposed to give up a twelvemonth to writing the novel, but I determined not to commence it unless I saw pretty clearly that I could make about 5,000 l. by the sacrifice of my time. The novel was to have been in three volumes, and there would probably have been reprints of another work in two volumes. Both of these works would have had graphic illustrations. The poet gave me much information on all the subjects connected with the plan, and amongst other things, observed that when he published his beautifully illustrated work on Italy, that he had paid 9,000 l. out of his own pocket before he received any return for that work.

MY first visit to Paris was made in company with my friend John Herschel. On reaching Abbeville, we wanted breakfast, and I undertook to order it. Each of us usually required a couple of eggs. I preferred having mine moderately boiled, but my friend required his to be boiled quite hard. Having explained this matter to the waiter, I concluded by instructing him that each of us required two eggs thus cooked, concluding my order with the words, “pour chacun deux.”

The garçon ran along the passage half way towards the kitchen, and then called out in his loudest tone—

“Il faut faire bouillir cinquante-deux œufs pour Messieurs les Anglais.” I burst into such a fit of un­con­trol­lable laughter at this absurd mis­un­der­stand­ing of chacun deux, for cinquante-deux, that it was some time before I could explain it to Herschel, and but for his running into the kitchen to {196} coun­ter­mand it, the half hundred of eggs would have assuredly been simmering over the fire.

A few days after our arrival in Paris, we dined with Laplace, where we met a large party, most of whom were members of the Institut. The story had already arrived at at Paris, having rapidly passed through several editions.

To my great amusement, one of the party told the company that, a few days before, two young Englishman being at Abbeville, had ordered fifty-two eggs to be boiled for their breakfast, and that they ate up every one of them, as well as a large pie which was put before them.

My next neighbour at dinner asked me if I thought it probable. I replied, that there was no absurdity a young Englishman would not oc­ca­sion­al­ly commit.

One morning Herschel and I called on Laplace, who spoke to us of various English works on math­e­mat­i­cal subjects. Amongst others, he mentioned with approbation, “Un ouvrage de vous deux.” We were both quite at a loss to know to what work he referred. Herschel and I had not written any joint work, although we had together translated the work of Lacroix. The volume of the “Memoirs of the Analytical Society,” though really our joint production, was not known to be such, and it was also clear that Laplace did not refer to that work. Perceiving that we did not recognise the name of the author to whom he referred, Laplace varied the pronunciation by calling him vous deux; the first word being pronounced as the French word “vous,” and the second as the English word “deuce.”

Upon further explanation, it turned out that Laplace meant to speak of a work published by Woodhouse, whose name is in the pronunciation of the French so very like vous deux. {197}

Poisson, Fourier, and Biot were amongst my earliest friends in Paris. Fourier, then Secretary of the Institute, had accompanied the first Napoleon in his expedition to Egypt. His profound acquaintance with analysis remains recorded in his works. His unaffected and genial manner, the vast extent of his acquirements, and his admirable taste conspicuous even in the apartments he inhabited, were most felt by those who were honoured by his friendship.

With M. Biot I became acquainted in early life; he was then surrounded by a happy family. In my occasional visits to Paris I never omitted an opportunity of paying my respects to him: when deprived of those supports and advanced in life, he still earnestly occupied himself in carrying out the investigations of his earlier years.

His son, M. Biot, a profound oriental scholar, who did me the honour of translating ‘The Economy of Man­u­fac­tures,’ died many years before his father.

In one of my visits to Paris, at a period when beards had become fashionable amongst a certain class of my countrymen, I met Biot. After our first greeting, looking me full in the face, he said, “My dear friend, you are the best shaved man in Europe.”

At a later period I took with me to Paris the complete drawings of Difference Engine No. 2. As soon as I had hung them up round my own apartments to explain them to my friends I went to the College de France, where M. Biot resided. I mentioned to him the fact, and said that if it was a subject in which he was interested, and had leisure to look at these drawings, I should have great pleasure in bringing them to him, and giving him any explanation that he might desire. I told him, however, that I was fully aware how much the time of every man who really adds to science must be {198} occupied, and that I made this proposal rather to satisfy my own mind that I had not neglected one of my oldest friends than in the expectation that he had time for the examination of this new subject.

The answer of my friend was remarkable. After thanking me in the warmest terms for this mark of friendship, he explained to me that the effect of age upon his own mind was to render the pursuit of any new inquiry a matter of slow and painful effort; but that in following out the studies of his youth he was not so much impeded. He added that in those subjects he could still study with sat­is­fac­tion, and even make advances in them, assisted in the working out of his views experimentally by the aid of his younger friends.

I was much gratified by this unreserved expression of the state of the case, and I am sure those younger men who so kindly assisted the aged phi­los­o­pher will be glad to know that their assistance was duly appreciated.

The last time during M. Biot’s life that I visited Paris I went, as usual, to the College de France. I inquired of the servant who opened the door after the state of M. Biot’s health, which was admitted to be feeble. I then asked whether he was well enough to see an old friend. Biot himself had heard the latter part of this conversation. Coming into the passage he seized my hand and said “My dear friend, I would see you even if I were dying.”

One of the most remarkable char­ac­ter­is­tics of Humboldt’s mind was, that he not merely loved and pursued science for its own sake, but that he derived pleasure from assisting with his information and advice any other inquirer, however humble, who might need it. {199}

In one of my visits to Paris, Humboldt was sitting with me when a friend of mine, an English clergyman, who had just arrived in Paris, and had only two days to spare for it, called upon me to ask my assistance about getting access to certain MSS. Putting into Humboldt’s hand a tract lying on my table, I asked him to excuse me for a few minutes whilst I gave what advice I could to my countryman.

My friend told me that he wanted to examine a MS., which he was informed was in a certain library in a certain street in Paris: that he knew nobody in the city to help him in his mission.

Humboldt having heard this statement, came over to us and said, “If you will introduce me to your friend, I can put him in the way of seeing the MSS. he is in search of.” He then explained that the MSS. had been removed to another library in Paris, and proposed to give my friend a note of introduction to the librarian, and mentioned other MSS. and other libraries in which he would find information upon the same subject.

Many years after, being at Vienna, I heard that Humboldt was at Töplitz, a circumstance which induced me to visit that town. On my arrival I found he had left it a few days before on his return to Berlin. In the course of a few days, I followed him to that city, and having arrived in the middle of the day, I took apartments in the Linden Walk, and got all my travelling apparatus in order; I then went out to call on Humboldt. Finding that he had gone to dine with his brother William, who resided at a short distance from Berlin, I therefore merely left my card.

The next morning at seven o’clock, before I was out of bed, I received a very kind note from Humboldt, to ask me to breakfast with him at nine. In a postscript he added, “What {200} are the moving molecules of Robert Brown?” These atoms of dead matter in rapid motion, when examined under the microscope, were then exciting great attention amongst phi­los­o­phers.

I met at breakfast several of Humboldt’s friends, with whose names and reputation I was well acquainted.

Humboldt himself expressed great pleasure that I should have visited Berlin to attend the great meeting of German phi­los­o­phers, who in a few weeks were going to assemble in that capital. I assured him that I was quite unaware of the intended meeting, and had directed my steps to Berlin merely to enjoy the pleasure of his society. I soon perceived that this meeting of phi­los­o­phers on a very large scale, supported by the King and by all the science of Germany, might itself have a powerful influence upon the future progress of human knowledge. Amongst my companions at the breakfast-table were Derichlet and Magnus. In the course of the morning Humboldt mentioned to me that his own duties required his attendance on the King every day at three o’clock, and having also in his hands the organization of the great meeting of phi­los­o­phers, it would not be in his power to accompany me as much as he wished in seeing the various institutions in Berlin. He said that, under these circumstances, he had asked his two young friends, Derichlet and Magnus, to supply his place. During many weeks of my residence in Berlin, I felt the daily advantage of this thoughtful kindness of Humboldt. Accompanied by one or other, and frequently by both, of my young friends, I saw everything to the best advantage, and derived an amount of information and in­struc­tion which under less favourable circumstances it would have been impossible to have obtained.

The next morning, I again breakfasted with Humboldt. {201} On the previous day I had mentioned that I was making a collection of the signs employed in map-making. I now met Von Buch and General Ruhl, both of whom were profoundly acquainted with that subject. I had searched in vain for any specimen of a map shaded upon the principle of lines of equal elevation. Von Buch the next morning gave me an engraving of a small map upon that principle, which was, I believe, at that time the only one existing.

After breakfast we went into Humboldt’s study to look at something he wished to show us. In turning over his papers, which, like my own, were lying apparently in great disorder upon the table, he picked up the cover of a letter on which was written a number of names in different parallel columns. “That,” he observed incidentally, “is for you.” After he had shown us the object of our visit to his sanctum, he reverted to the envelop which he put into my hands, explaining that he had grouped roughly together for my use all the remarkable men then in Berlin, and several of those who were expected.

These he had arranged in classes:—Men of science, men of letters, sculptors, painters, and artists generally, instrument-makers, &c. This list I found very convenient for reference.

When the time of the great meeting approached, it became necessary to prepare the arrangements for the convenience of the assembled science of Europe. One of the first things, of course, was the important question, how they were to dine? A committee was therefore appointed to make experiment by dining successively at each of the three or four hotels competing for the honour of providing a table d’hôte for the savans.

Humboldt put me on that committee, remarking, that an Englishman always appreciates a good dinner. The committee performed their agreeable duty in a manner quite {202} sat­is­fac­tory to themselves, and I hope, also, to the digestions of the Naturforschers.

During the meeting much gaiety was going on at Berlin. One evening previous to our parties, I was walking in the Linden Walk with Humboldt, discussing the singularities of several of our learned acquaintance. My companion made many acute and very amusing remarks; some of these were a little caustic, but not one was ill-natured. I had contributed a very small and much less brilliant share to this conversation, when the clock striking, warned us that the hour for our visits had arrived. I never shall forget the expression of archness which lightened up Humboldt’s countenance when shaking my hand he said, in English, “My dear friend, I think it may be as well that we should not speak of each other until we meet again.” We then each kept our respective engagements, and met again at the most recherché of all, a concert at Mendelssohn’s.

From my father’s house on the coast, near Teignmouth, we could, with a telescope, see every ship which entered Torbay. When the “Bellerophon” anchored, the news was rapidly spread that Napoleon was on board. On hearing the rumour, I put a small telescope into my pocket, and, mounting my horse, rode over to Torbay. A crowd of boats surrounded the ship, then six miles distant; but, by the aid of my glass, I saw upon the quarter-deck that extraordinary man, with many members of whose family I sub­se­quent­ly became acquainted. Of those who are no more I may without impropriety say a few words.

My first acquaintance with several branches of the family {203} of Napoleon Buonaparte arose under the following circumstances:—

When his elder brother Lucien, to avoid the necessity of accepting a kingdom, fled from his imperial brother, and took refuge in England, his position was either not well understood, or, perhaps, was entirely mistaken. Lucien seems to have been looked upon with suspicion by our Government, and was placed in the middle of England under a species of espionage.

Political parties then ran high, and he did not meet with those attentions which his varied and highly-cultivated tastes, especially in the fine arts, entitled him to receive, as a stranger in a foreign land.

A family connection of mine, residing in Worcestershire, was in the habit of visiting Lucien Buonaparte. Thus, in my occasional visits to my brother-in-law’s place, I became acquainted with the Prince of Canino. In after-years, when he oc­ca­sion­al­ly visited London, I had generally the pleasure of seeing him.

In 1828 I met at Rome the eldest son of Lucien, who introduced me to his sisters, Lady Dudley Stuart and the Princess Gabrielli.

In the same year I became acquainted, at Bologna, with the Princess d’Ercolano, another daughter of Lucien, whom I afterwards met at Florence, at the palace of her uncle Louis, the former king of Holland. During a residence of several months in that city I was a frequent guest at the family table of the Compte St. Leu. One of his sons had married the Princess Charlotte, the second daughter of the King of Spain, a most accomplished, excellent, and charming person. They reminded me much of a sensible English couple, in the best class of English society. Both had great taste in the fine {204} arts. The prince had a workshop at the top of the palace, in which he had a variety of tools and a lithographic printing press. Oc­ca­sion­al­ly, in the course of their morning drives, some picturesque scene, in that beautiful country, would arrest their attention. Stopping the carriage, they would select a favourable spot, and the princess would then make a sketch of it.

At other times they would spend the evening, the prince in extemporizing an imaginary scene, which he described to his wife, who, with admirable skill, embodied upon paper the tasteful conceptions of her husband. These sketches then passed up to the workshop of the Prince, were transferred to stone, and in a few days lithographic impressions descended to the drawing-room. I fortunately possess some of these impressions, which I value highly, not only as the productions of an amiable and most accomplished lady, but of one who did not shrink from the severer duties of life, and died in fulfilling them.

After the melancholy loss of her husband, the Princess Charlotte remained with her father, who resided at one period in the Regent’s Park, where I from time to time paid my respects to them. Oc­ca­sion­al­ly I received them at my own house. One summer letters from Florence reached them, announcing the dangerous illness of the Comte de St. Leu. The daughter of Joseph immediately set out alone for Florence to minister to the comfort of her uncle and father-in-law. On her return from Italy she was attacked by cholera and died in the south of France.

THE grounds surrounding my father’s house, near Teignmouth, extended to the sea. The cliffs, though lofty, admitted at one point of a descent to the beach, of which I very frequently availed myself for the purpose of bathing. One Christmas when I was about sixteen I determined to see if I could manage a gun. I accordingly took my father’s fowling-piece, and climbing with it down to the beach, I began to look about for the large sea-birds which I thought I might have a chance of hitting.

I fired several charges in vain. At last, however, I was fortunate enough to hit a sea-bird called a diver; but it fell at some distance into the sea: I had no dog to get it out for me; the sea was rough, and no boat was within reach; also it was snowing.

So I took advantage of a slight recess in the rock to protect my clothes from the snow, undressed, and swam out after my game, which I succeeded in capturing. The next day, having got the cook to roast it, I tried to eat it; but this was by no means an agreeable task, so for the future I left the sea-birds to the quiet possession of their own dominion. {206}

Shortly after this, whilst residing on the beautiful banks of the Dart, I constantly indulged in swimming in its waters. One day an idea struck me, that it was possible, by the aid of some simple mechanism, to walk upon the water, or at least to keep in a vertical position, and have head, shoulders, and arms above water.

My plan was to attach to each foot two boards closely connected together by hinges themselves fixed to the sole of the shoe. My theory was, that in lifting up my leg, as in the act of walking, the two boards would close up towards each other; whilst on pushing down my foot, the water would rush between the boards, cause them to open out into a flat surface, and thus offer greater resistance to my sinking in the water.

I took a pair of boots for my experiment, and cutting up a couple of old useless volumes with very thick binding, I fixed the boards by hinges in the way I proposed. I placed some obstacle between the two flaps of each book to prevent them from approaching too nearly to each other so as to impede their opening by the pressure of the water.

I now went down to the river, and thus prepared, walked into the water. I then struck out to swim as usual, and found little difficulty. Only it seemed necessary to keep the feet farther apart. I now tried the grand experiment. For a time, by active exertion of my legs, I kept my head and shoulders above water and sometimes also my arms. I was now floating down the river with the receding tide, sustained in a vertical position with a very slight exertion of force.

But unfortunately one pair of my hinges got out of order, and refused to perform its share of the propulsion. The result was that I became lop-sided. I was therefore obliged to swim, which I now did with considerable exertion; but another difficulty soon occurred,—the instrument on the {207} disabled side refused to do its share in propelling me. The tide was rapidly carrying me down the river; my own exertions alone would have made me revolve in a small circle, consequently I was obliged to swim in a spiral. It was very difficult to calculate the curve I was describing upon the surface of the water, and still more so to know at what point, if at any, I might hope to reach its banks again. I became very much fatigued by my efforts, and endeavoured to relieve myself for a time by resuming the vertical position.

After floating, or rather struggling for some time, my feet at last touched the bottom. With some difficulty and much exertion I now gained the bank, on which I lay down in a state of great exhaustion.

This experiment satisfied me of the danger as well as of the practicability of my plan, and ever after, when in the water, I preferred trusting to my own unassisted powers.

At the close of the year 1827, as I anticipated a long absence from England, I paid a visit to the Thames Tunnel, in the construction of which I took a great interest. My eldest son, then about twelve years of age, accompanied me in this visit. I fortunately found the younger Brunel at the works, who kindly took us with him into the workings.

We stood upon a timber platform, distant about fifty feet from the shield, which was full of busy workmen, each actively employed in his own cell. As we were conversing together, I observed some commotion in the upper cell on the right hand side. From its higher corner there entered a considerable stream of liquid mud. Brunel ran directly to the shield a line of workmen was instantly formed, and whatever tools or timber was required was immediately conveyed to the spot.

I observed the progress with some anxiety, since but a short time before a similar occurrence had been the prelude {208} to the inundation of the whole tunnel. I remained watching the fit time, if necessary, to run away; but also noticing what effect the apparent danger had on my son. After a short time it was clear that the ingress of liquid mud had been checked, and in a few minutes more Brunel returned to me, having this time succeeded in stopping up the breach. I then inquired what was really the nature of the danger we had escaped. Brunel told me that unless himself or Gravatt had been present, the whole tunnel would in less than ten minutes have been full of water. The next day I embarked for Holland, and in about a week after I read in Galignani’s newspaper, that the Thames had again broken into the tunnel; that five or six of the workmen had been drowned, and that Brunel himself had escaped with great difficulty by swimming.

In 1818, during a visit to Plymouth, I had an opportunity of going down in a diving-bell: I was accompanied by two friends and the usual director of that machine.

The diving-bell in which I descended was a cast-iron vessel about six feet long by four feet and a half wide, and five feet eight inches high. In the top of the bell there were twelve circular apertures, each about six inches in diameter, filled by thick plate-glass fixed by water-tight cement. Exactly in the centre there were a number of small holes through which the air was continually pumped in from above.

At the ends of the bell are two seats, placed at such a height, that the top of the head is but a few inches below the top of the bell; these will conveniently hold two persons each. Exactly in the middle of the bell, and about six inches above its lower edge, is placed a narrow board, on which the feet of the divers rest. On one side, nearly on a level with the shoulders, is a small shelf, with a ledge to {209} contain a few tools, chalk for writing messages, and a ring to which a small rope is tied. A board is connected with this rope; and after writing any orders on the board with a piece of chalk, on giving it a pull, the superintendent above, round whose arm the other end of the rope is fastened, will draw it up to the surface, and, if necessary, return an answer by the same conveyance.

In order to enter the bell, it is raised about three or four feet above the surface of the water; and the boat, in which the persons who propose descending are seated, is brought immediately under it; the bell is then lowered, so as to enable them to step upon the foot-board within it; and having taken their seats, the boat is removed, and the bell gradually descends to the water.

On touching the surface, and thus cutting off the communication with the external air, a peculiar sensation is perceived in the ears; it is not, however, painful. The attention is soon directed to another object. The air rushing in through the valve at the top of the bell overflows, and escapes with a considerable bubbling noise under the sides. The motion of the bell proceeds slowly, and almost imperceptibly; and, on looking at the glass lenses close to the head, when the top of the machine just reaches the surface of the water, it may be perceived, by means of the little impurities which float about in it, flowing into the recesses containing the glasses. A pain now begins to be felt in the ears, arising from the increased external pressure; this may sometimes be removed by the act of yawning, or by closing the nostrils and mouth, and attempting to force air through the ears. As soon as the equilibrium is established the pain ceases, but recommences almost immediately by the continuance of the descent. On returning, the same sensation of {210} pain is felt in the ears; but it now arises from the dense air which had filled them endeavouring, as the pressure is removed, to force its way out.

If the water is clear, and not much disturbed, the light in the bell is very considerable; and, even at the depth of twenty feet, was more than is usual in many sitting-rooms. Within the distance of eight or ten feet, the stones at the bottom began to be visible. The pain in the ears still continues to occur at intervals, until the descent of the bell terminates by its resting on the ground. The light is sufficient, after passing through twenty feet of sea water, even for delicate experiments; and a far less quantity is enough for the work which is usually performed in those situations.

The temperatures of the hand and of the mouth, under the tongue, were measured by a thermometer, but they did not seem to differ from those which had been determined by the same instrument previous to the descent; at least, the difference did not amount to one-sixth of a degree of Fahrenheit’s scale. The pulse was more frequent.

A small magnetic needle did not appear to have entirely lost its directive power, when placed on the footboard in the middle of the bell; but its direction was not the same as that which it indicated on shore. This was determined by directing, by means of signals, the workmen above to move the bell in the direction of one of the co-ordinates; a stick then being pressed against the bottom drew a line parallel to that co-ordinate, its direction by compass was ascertained in the bell, and the direction of the co-ordinate was determined on returning to the surface after leaving the bell.

Signals are communicated by the workmen in the bell to those above, by striking against the side of the bell with a hammer. Those most frequently wanted are indicated by {211} the fewest number of blows; thus a single stroke is to require more air. The sound is heard very distinctly by those above; but, it must be confessed, that to persons unaccustomed to it, the force with which a weighty hammer is driven against so brittle a material as cast iron is a little alarming.

After ascending a few inches from the bottom, the air in the bell became slightly obscured. At the distance of a few feet this appearance increased. Before it had half reached the surface, it was evident that the whole atmosphere it contained was filled with a mist or cloud, which at last began to condense in large drops on the whole of the internal surface.

The explanation of this phenomenon seems to be, that on the rising of the bell the pressure on the air within being diminished by a weight equal to several feet of water, it began to expand; and some portion of it escaping under the edges of the bell, reduced the temperature of that which remained so much, that it was unable to retain, in the state of invisible vapour, the water which it had previously held in solution. Thus the same principle which constantly produces clouds in the atmosphere filled the diving-bell with mist.

This first led me to consider the much more extensive question of submarine navigation. I was aware that Fulton had already descended in a diving-vessel, and remained under water during several hours. He also carried down a copper sphere containing one cubic foot of space into which he had forced two hundred atmospheres. With these means he remained under water and moved about at pleasure during four hours.

But a closed vessel is obviously of little use for the most important purposes to which submarine navigation would be applied in case of war. In the article Diving Bell, published in 1826, in the ‘Encyclopedia Metropolitana,’ I gave a {212} description and drawings of an open submarine vessel which would contain sufficient air for the consumption of four persons during more than two days. A few years ago, I understand, experiments were made in the Seine at Paris, on a similar kind of open diving-vessel. Such a vessel could be propelled by a screw, and might enter, without being suspected, any harbour, and place any amount of explosive matter under the bottoms of ships at anchor.

Such means of attack would render even iron and iron-clad ships unsafe when blockading a port. For though chains were kept constantly passing under their keels, it would yet be possible to moor explosive magazines at some distance below, which would effectually destroy them.

CALLING one morning upon Chantrey, I met Captain Kater and the late Sir Thomas Lawrence, the President of the Royal Academy. Chantrey was engaged at that period in casting a large bronze statue. An oven of considerable size had been built for the purpose of drying the moulds. I made several inquiries about it, and Chantrey kindly offered to let me pay it a visit, and thus ascertain by my own feelings the effects of high temperature on the human body.

I willingly accepted the proposal, and Captain Kater offered to accom­pany me. Sir Thomas Lawrence, who was suffering from indis­po­si­tion, did not think it prudent to join our party. In fact, he died on the second or third day after our exper­i­ment.

The iron folding-doors of the small room or oven were {214} opened. Captain Kater and myself entered, and they were then closed upon us. The further corner of the room, which was paved with squared stones, was visibly of a dull-red heat. The thermometer marked, if I recollect rightly, 265°. The pulse was quickened, and I ought to have counted but did not count the number of inspirations per minute. Perspiration commenced immediately and was very copious. We remained, I believe, about five or six minutes without very great discomfort, and I experienced no subsequent inconvenience from the result of the experiment.

I have never been so fortunate as to be conscious of having experienced the least shock of an earthquake, although, when a town had been destroyed in Ischia I hastened on from Rome in the hope of getting a slight shake. My passion was disappointed, so I consoled myself by a flirtation with a volcano.

The situation of my apartments during my residence at Naples enabled me constantly to see the cone of Vesuvius, and the continual projections of matter from its crater. Amongst these were oc­ca­sion­al­ly certain globes of air, or of some gas, which, being shot upwards to a great height above the cone, spread out into huge coronets of smoke, having a singular motion amongst their particles.

A similar phenomenon sometimes occurs on a small scale during the firing of heavy ordnance. I have frequently seen such at Plymouth and elsewhere; but I was not satisfied about the cause of this phenomenon. I was told that it occurred more frequently if the muzzle of the gun were rubbed with grease; but this did not always succeed.

Soon after my return to London I made a kind of drum, by {215} stretching wet parchment over a large tin funnel. On directing the point of the funnel at a candle placed a few feet distant, and giving a smart blow upon the parchment, it is observed that the candle is immediately extinguished.

This arises from what is called an air shot. In fact, the air in the tubular part is projected bodily forward, and so blows out the candle. The statements about persons being killed by cannon balls passing close to but not touching them, if true, are probably the results of air shots.

Wishing to trace the motions of such air shots, I added two small tubes towards the large end of the tin funnel, in order that I might fill it with smoke, and thus trace more distinctly the progress of the ball of air.

To my great delight the first blow produced a beautiful coronet of smoke, exactly resembling, on a small scale, the explosions from cannon or the still more attractive ones from Vesuvius.

If phosphoretted hydrogen or any other gas, which takes fire in air, were thus projected upwards, a very singular kind of fire-work would be produced.

It is possible in dark nights or in fogs that by such means signals might be made to communicate news or to warn vessels of danger.

Vesuvius was then in a state of moderate activity. It had a huge cone of ashes on its summit, surrounding an extensive crater of great depth. In one corner of this was a smaller crater, quite on a diminutive scale, which from time to time ejected red-hot fragments of lava oc­ca­sion­al­ly to the height of from a thousand to fifteen hundred feet above the summit of the mountain.

I had taken apartments in the Chiaja, just opposite the volcano, in order that I might watch it with a telescope. In fact, {216} as I lay in my bed I had an excellent view of the mountain. My next step was to consult with Salvatori, the most experienced of the guides, from whom I had purchased a good many minerals, as to the possibility of getting a peep down the volcano’s throat.

Salvatori undertook to report to me from time to time the state of the mountain, round the base of which I made frequent excursions. After about a fortnight, the explosions were more regular and uniform, and Salvatori assured me that all the usual known indications led him to think that it was a fit time for my expedition. As I wished to see as much as possible, I made arrangements to economize my strength by using horses or mules to carry me wherever they could go. Where they could not carry me, as for instance, up the steep slope of the cone of ashes, I employed men to convey me in a chair.

By these means, I saw in the afternoon and evening of one day a good deal of the upper part of the mountain, then took a few hours’ repose in a hut, and reached the summit of the cone long before sunrise.

It was still almost dark: we stood upon the irregular edge of a vast gulf spread out below at the depth of about five hundred feet. The plain at the bottom would have been invisible but for an irregular network of bright-red cracks spread over the whole of its surface. Now and then the silence was broken by a rush upwards of a flight of red-hot scoria from the diminutive crater within the large one. These missiles, however, although projected high above the summit of the cone, never extended themselves much beyond the small cavity from which they issued.

Those who have seen the blood-vessels of their own eye by the aid of artificial light, will have seen on a small scale a {217} perfect resemblance of the plain which at that time formed the bottom of the great crater of Vesuvius.

As the morning advanced the light increased, and some time before sunrise we had completed the tour of the top of the great crater. Then followed that glorious sight—the sun when seen rising from the top of some lofty mountain.

I now began to speculate upon the means of getting a nearer view of the little miniature volcano in action at one corner of the gulf beneath us. We had brought ropes with us, and I had observed, in our tour round the crater, every dike of congealed lava by which the massive cone was split. These presented buttresses with frequent ledges or huge steps by which I hoped, with the aid of ropes, to descend into the Tartarus below.

Having consulted with our chief guide Salvatori, I found that he was unwilling to accompany us, and proposed remaining with the other guides on the upper edge of the crater. Upon the whole, I was not discontented with the arrangement, because it left a responsible person to keep the other guides in order, and also sufficient force to lift us up bodily by the ropes if that should become necessary.

The abruptness of the rocky buttresses compelled us to use ropes, but the attempt to traverse the steep inclines of light ashes and of fine sand would have been more dangerous from the risk of being engulfed in them.

Having well examined the several disadvantages of these rough-hewn irregular Titanic stairs, I selected one which seemed the most promising for facilitating our descent into the crater. I was encumbered with one of Troughton’s heavy barometers, strapped to my back, looking much like Cupid’s quiver, though probably rather heavier. In my pocket I had an excellent box sextant, and in a rough kind of basket {218} two or three thermometers, a measuring tape, and a glass bottle enclosed in a leather case, commonly called a pocket-pistol, accompanied by a few biscuits.

We began our descent by the aid of two ropes, each supported above by two guides. I proceeded, trusting to my rope to step wherever I could, and then cautiously holding on by the rope to spring down to the next ledge. In this manner we descended until we arrived at the last projecting ledge of the dike. Nothing then remained for us but to slide down a steep and lengthened incline of fine sand. Fortunately, the sand itself was not very deep, and was supported by some solid material beneath it. I soon found that it was impossible to stand, so I sat down upon this moving mass, which evidently intended to accompany us in our journey. At first, to my great dismay, I was relieved from the care of my barometer, of which the runaway sand immediately took charge. I then found myself getting deeper and deeper in the sand, and still accelerating my downward velocity.

Gravity had at last done its work and became powerless. I soon dug myself out of my sandy couch, and rushed to my faithful barometer lying at some distance from me with its head just unburied. Fortunately, it was uninjured. My companion, with more skill or good fortune, or with less incumbrances, had safely alighted on the burning plain we now stood upon.

The area of this plain, for it was perfectly flat, was in shape somewhat elliptical. The surface consisted of a black scoriacious rock, reticulated with ditches from one to three feet wide, intersecting each other in every direction. From some of these, fumes not of the most agreeable odour were issuing. All those above two feet deep showed that at that depth below us everything was of a dull-red heat. It was {219} these ditches with red-hot bottoms which, in the darkness of the night, had presented the singular spectacle I described as having witnessed on the evening before.

At one extremity of this oval plain there was a small cone, from which the eruptions before described appeared to issue.

My first step, after examining the few instruments I had brought with me, was to select a spot upon which to measure a base for ascertaining the depth of the crater from its upper edge.

Having decided upon my base line, I took with my sextant the angle of elevation of the rim of the crater above a remarkable spot on a level with my eye. Then fixing my walking-stick into a little crack in the scoria, I proceeded to measure with a tape a base line of 340 feet. Arrived at this point, I again took the angle of elevation of the same part of the rim from the same remarkable spot on a level with the eye. Then, by way of verification, I remeasured my base line and found it only differed from the former measure by somewhat less than one foot. But my walking-stick, which had not penetrated the crack more than a few inches, was actually in flames.

Having noted down these facts, including the state of the thermometer and barometer, in my pocket-book, I took first a survey and then a tour about my fiery domain. I afterwards found, from the result of this measurement, that our base line was 570 feet below one of the lowest points of the edge of the crater. Having collected a few mineral specimens, I applied myself to observe and register the eruptions of the little embryo volcano at the further extremity of the elliptical plain.

These periodical eruptions interested me very much. I proceeded to observe and register them, and found they occurred {220} at tolerably regular intervals. At first, I performed this operation at a respectful distance and out of the reach of the projected red-hot scoria. But as I acquired confidence in their general regularity, I approached from time to time more nearly to the little cone of scoria produced by its own eruptions.

I now perceived an opening in this little cone close to the perpendicular rock of the interior of the great crater. I was very anxious to see real fluid lava; so immediately after an eruption, I rushed to the opening and thus got within the subsidiary crater. But my curiosity was not gratified, for I observed, about forty or fifty feet below me, a huge projecting rock, which being somewhat in advance, effectively prevented me from seeing the lava lake, if any such existed. I then retreated to a respectful distance from this infant volcano to wait for the next explosion.

I continued to note the intervals of time between these jets of red-hot matter, and found that from ten to fifteen minutes was the range of the intervals of repose. Having once more reconnoitred the descent into the little volcano, I seized the opportunity of the termination of one of the most considerable of its eruptions to run towards the gap and cautiously to pick my way down to the rock which hid from me, as I supposed, the liquid lava. I was armed with two phials, one of common smelling salts, and the other containing a solution of ammonia. On reaching the rock, I found it projected over a lake which was really filled by liquid fiery lava. I immediately laid myself down, and looking over its edge, saw, with great delight, lava actually in a state of fusion.

Presently I observed a small bubble swelling up on the surface of the fluid lava: it became gradually larger and larger, but did not burst. I had some vague suspicion that {221} this indicated a coming eruption; but on looking at my watch, I was assured that only one minute had elapsed since the termination of the last. I therefore watched its progress; after a time the bubble slowly subsided without breaking.

I now found the heat of the rock on which I was reposing, and the radiation from the fluid lava, almost insupportable, whilst the sulphurous effluvium painfully affected my lungs. On looking around, I fortunately observed a spot a few feet above me, from which I could, in a standing position, get a better view of the lake, and perhaps suffer less inconvenience from its vapours. Having reached this spot, I continued to observe the slow formation and absorption of these vesicles of lava. One of them soon appeared. Another soon followed at a different part of the fiery lake, but, like its predecessor, it disappeared as quietly.

Another swelling now arose about half way distant from the centre of the cauldron, which enlarged much beyond its predecessors in point of size. It attained a diameter of about three feet, and then burst, but not with any explosion. The waves it propagated in the fiery fluid passed on to the sides, and were thence reflected back just as would have happened in a lake of water of the same dimensions.

This phenomenon reappeared several times, some of the bubbles being considerably larger in size, and making proportionally greater disturbance in the liquid of this miniature crater. I would gladly have remained a longer time, but the excessive heat, the noxious vapours, and the warning of my chronometer forbade it. I climbed back through the gap by which I had descended, and rushed as fast as I could to a safe distance from the coming eruption.

I was much exhausted by the heat, although I suffered still greater inconvenience from the vapours. From my {222} ob­ser­va­tions of the eruptions before my descent into this little crater, I had estimated that I might safely allow myself six minutes, but not more than eight, if I descended into the crater immediately after an eruption.

If my memory does not fail me, I passed about six minutes in examining it, and the next explosion occurred ten minutes after the former one. On my return to Naples I found that a pair of thick boots I had worn on this expedition were entirely destroyed by the heat, and fell to pieces in my attempt to take them off.

On my return from the pit of burning fire, I sat down with my companion to refresh myself with a few biscuits contained in our basket. Cold water would have been the most refreshing fluid we could have desired, but we had none, and my impatient friend cried out, “I wish I had a glass of whisky!” It immediately occurred to me to feel in my own basket for a certain glass bottle preserved in a tight leather case, which fortunately being found, I presented to my astonished friend, with the remark that it contained half a pint of the finest Irish whisky. This piece of good luck for my fellow-traveller arose not from my love but from my dislike of whisky. Shortly before my Italian tour I had been travelling in the north of Ireland, and having exhausted my brandy, was unable to replace it by anything but whisky, a drink which I can only tolerate under very exceptional circumstances.

During my residence at Naples in 1828, the government appointed a commission of members of the Royal Academy of Naples to visit Ischia and make a report upon the hot springs in that island. Being a foreign member of the Academy, they {223} did me the honour of placing my name upon that commission. The weather was very favourable, the party was most agreeable, and during three or four days I enjoyed the society of my colleagues, the delightful scenery, and the highly interesting natural phenomena of that singular island.

None of the hot springs were deep: in several we made excavations which, in all cases, gave increased heat to the water. In one or two, I believe if we had excavated to a small depth or bored a few feet, we might have met with boiling water.

I took the opportunity of this visit to view the devastations made by the recent earthquake in the small town which had been destroyed.

The greater part of the town consisted of narrow streets formed by small houses built of squared stone. In some of these streets the houses on one side were thrown down, whilst those a few feet distant, on the opposite side, although severely damaged, had their walls left standing.

The landlord of the hotel at which we took up our quarters assured me the effects of the recent earthquake were entirely confined to a small portion of the island which he pointed out from the front of his hotel, and added that it was scarcely felt in other parts.

At the commencement of this chapter I mentioned that I had never been consciously sensible of the occurrence of an earthquake. I think it may perhaps be useful to state that on a recent occasion I really perceived the effects of an earthquake, although at the time I assigned them to a different cause.

On the 6th of last October, about half-past three, a.m., {224} most of the inhabitants of London who were awake at that hour perceived several shocks of an earthquake. I also was awake, although not conscious of the shocks of an earthquake.

As soon as I read of the event in the morning papers, I was forcibly struck by its coincidence with my own ob­ser­va­tions, although I had attributed to them an entirely different cause. In order to explain this, it is necessary to premise that I had on a former occasion instituted some experiments for the purpose of ascertaining how far off the passing of a cart or carriage would affect the steadiness of a star observed by reflection. Amongst other methods, I had fixed a looking-glass of about 12 by 16 inches, by a pair of hinges, to the front wall of my bedroom. It was usually so placed that, as I lay in bed, at the distance of about 10 or 12 feet, I could see by reflection a small gas-light burner, which was placed on my left hand.

By this arrangement any tremors propagated through the earth from passing carriages would be communicated to the looking-glass by means of the front wall of the house, which rose about 40 feet from the surface. The image of the small gas-burner reflected in the looking-glass would be proportionally disturbed. In this state of things, at about half-past three o’clock of the morning in question, I observed the reflected image of the gas-light move downwards and upwards two or three times. I then listened attentively, expecting to hear the sound of a distant carriage or cart. Hearing nothing of the kind, I concluded that the earth wave had travelled beyond the limit of the sound wave, arising from the carriage which produced it. Presently the image of the gaslight again vibrated up and down, and then suddenly fell about four or five inches lower down in the glass, where it remained fixed for a time. Still thinking the ob­ser­va­tion of no consequence, {225} I shut my eyes, and after perhaps another minute, again saw the image in its lower position. It then rose to its former position, vibrated, and shortly again descended: it remained down for some time and then resumed its first position.

An opportunity presented itself several years after my examination of Vesuvius of witnessing another form under which fire oc­ca­sion­al­ly exerts its formidable power.

I was visiting a friend37 at Merthyr Tydfil, who possessed very extensive coal-mines. I inquired of my host whether any fire-damp existed in them. On receiving an affirmative answer, I expressed a wish to become personally acquainted with the miner’s invisible but most dangerous enemy. Arrangements were therefore made for my visit to the subterranean world on the following day. Professor Moll of Utrecht, who was also a guest, expressed a wish to accompany me.

The entrance to the mine is situated in the side of a mountain. Its chief manager conducted our expedition to visit the ‘fire-king.’

We found a coal-waggon drawn by a horse, and filled with clean straw, standing on the railway which led into the workings.

The manager, Professor Moll, and myself, together with two or three assistants, with candles, lanterns, and Davy-lamps, got into this vehicle, which immediately entered the adit of the mine. We advanced at a good pace, passing at intervals doors which opened on our approach and then instantly closed. Each door had an attendant boy, whose duty was confined to the regulation of his own door. {226}

Many were the doors we passed before we arrived at the termination of the tram-road. After travelling about a mile and a half, our carriage stopped and we alighted. We now proceeded on foot, each carrying his own candle, until we reached a kind of chamber where one of our attendants was left with the candles.

We, each holding a Davy-lamp in our hand, advanced towards a small opening in the side of this chamber, which was so low that we were compelled to crawl, one after another, on our hands and knees. A powerful current of air rushed through this small passage. On reaching the end of it, we found ourselves in a much larger chamber from which the coal had been excavated. At a little distance opposite to the path by which we entered was a continuation of the same narrow hole which had led us to the waste in which we now stood. From this opening issued the powerful stream of air which seemed to pass in a direct course from one opening to the other.

On our right hand the large chamber we had entered appeared to spread to a very considerable distance, its termination being lost in darkness. The floor was covered with fragments which had fallen from the roof; so that, besides the risk from explosion, there was also a minor one arising from the possible fall of some huge mass of slate from the roof of the excavation beneath which we stood: an accident which I had already witnessed in the waste of another coal-mine. As we advanced over this flaky flooring it was evident that we were making a considerable ascent. We, in fact, now occupied a vast cavern, which had been originally formed by the extraction of the coal, and then partially filled up by the falling in from time to time of portions of the slaty roof.

As we advanced cautiously with our Davy-lamps beyond {227} the current of air which had hitherto accompanied us, it was evident that a change had taken place in their light: for the flames became much enlarged. Professor Moll and myself mounted a huge heap of these fragments, and thus came into contact with air highly charged with carburetted hydrogen. At this point there was a very sensible difference in the atmosphere, even by a change of three feet in the elevation of the lamp.

Holding up the lamp at the level of my head, I could not see the wick of the lamp, but a general flame seemed to fill the inside of its wire-covering. On lowering it to the height of my knee, the wick resumed its large nebulous appearance.

My companion, Professor Moll, was very much delighted with this experiment. He told me he had often at his lectures explained these effects to his pupils, but that this was the first exhibition of them he had ever witnessed in their natural home.

Although well acquainted with the miniature explosions of the experimentalist, I found it very difficult to realize in my own mind the effects which might result from an explosion under the circumstances in which we were then placed. I inquired of the manager, who stood by my side, what would probably be the effect, if an explosion were to take place? Pointing to the vast heap of shale from which I had just descended, he said the whole of that would be blown through the narrow channel by which we entered, and every door we had passed through would be blown down.

We now retraced our steps, and crawling back through the narrow passage, rejoined our carriage, and were rapidly conveyed to the light of day.

DURING one of my visits to Leeds, combinations and trades-unions were very prevalent. A medical friend of mine, who was going to Bradford on a pro­fes­sion­al visit, very kindly offered to take me over in his carriage and bring me back again in the evening. He had in that town a friend engaged in the manufactories of the place, to whom he proposed to introduce me, and who would willingly give me every assistance. Unfortunately, on our arrival we found that this gentleman was absent on a tour.

My medical friend was much vexed; but I assured him that I was never at a loss in a manufacturing town, and we agreed to meet at our hotel for dinner. I then went into the town to pick up what information I might be able to meet with.

Passing a small manufactory, I think it was of door-mats, I inquired whether a stranger might be permitted to see it. The answer being in the affirmative, one of the men accompanied me round the works. Of course I asked him many questions which he answered as far as he could; but several of them {229} puzzled him, and he very good-humouredly tried to supply the information I wanted by asking several of his fellow-workmen. One question about which I was anxious to be informed, puzzled them all. At last one of the men to whom he applied said, “Why don’t you go and ask Sam Brown?” My guide immediately went in search of his learned friend, who gave me full information on the subjects of my inquiry.

Much pleased by the intelligence and acuteness of this man, I thought it possible he might have read the “Economy of Man­u­fac­tures.” On mentioning that work, I found he was well acquainted with it, and he asked my opinion of its merits. I told him that, having myself written the book, I was not an impartial judge. On hearing that I was its author, his delight was unbounded; he held out his brawny hand, which I cordially grasped. The most gratifying remark to me, however, amongst the many things in it to which he referred with approbation, was the expression he applied to it as a whole. “Sir,” said my new friend, “that book made me think.” To make a man think for himself is doing him far higher service than giving him much in­struc­tion.

I now told my new friend that I had studied a little the effects of combinations, and also the results of co-operative shops, and that I was very anxious to add to my stock of information upon both subjects, but par­tic­u­lar­ly on the latter. Knowing that there existed a co-operative shop in Bradford, I asked whether it would be possible to see it and make some inquiries as to its state and prospects. He said if he could get permission for half an hour’s absence he would accompany me to it, and give me whatever information I wished as to its operation.