 dedication and preface to passages from the life of a philosopher this is a LibriVox recording or LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org passages from the life of a philosopher by Charles Babbage dedication and preface dedication to Victor Immanuel II King of Italy 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 choices sons to the King your father I am indebted for the first public and official acknowledgement of this invention I am happy in that's expressing my deep sense of that obligation to his son the sovereign of united Italy the country of Archimedes and of Galileo I am Sire with the highest respect your Majesty's faithful servant Charles Babbage preface some men write their lives to save themselves from ennui careless of the amount they inflict on their readers others write their personal history less some kind friend should survive them and ensuring 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 e-log 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 while several of them furnish interesting illustrations of human character end of dedication and preface section one of passages from the life of a philosopher this is a LibriVox recording or LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org passages from the life of a philosopher by Charles Babbage section one my ancestors traced his descent through ages dark from cats that catawalled in Noah's Ark Salma Gandhi quarter 1793 What is there in a name? It is merely an empty basket until you put something into it. My earliest visits 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. The truth I never found more fully appreciated nor more admirably expressed than in a conversation with the son of Philangieri, the author of the celebrated treaties 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 mortgage 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 a 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 away 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. Footnote, on the remains of human art mixed with the bones of extinct races of animals. Proceedings of the Royal Society, 26th of May, 1859. End footnote. Descent from Flint workers. 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 arrowheads 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. 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 linearly 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. Not through Cain. I possess no evidence that I am descended from Cain. If any heralds 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 Bab. As we have in the west of England, Bab Taw, Babacum, etc. 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. Mérouvenant à nos moutants. How my blood was transmitted to me through more modern races is quite immaterial, seeing the admitted antiquity of the Flint workers. Sad omission. 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 role 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 Bab 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 to have been that of a goldsmith, although several are believed to have practised less dignified trades. In the time of Henry VIII one of my ancestors, together with a hundred men, were taken prisoners at the Siege of Calais. When William III landed in Torbay, another ancestor of mine, a yeoman possessing some small estate, undertook to distribute his proclamations. From 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, and 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 Berthog, an intimate friend and correspondent of John Locke. A wild ancestor. 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 his 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 air-in-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 Bamfield 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. 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. Act of Parliament In the year 1773 it became necessary to sell a portion of this property for the purpose of building a church at Ashbrunton. A private act of Parliament was passed for that purpose, in which the rights of the true heir were reserved. End of chapter one. Section two of Passages from the Life of a Philosopher This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Passages from the Life of a Philosopher by Charles Babbage. Chapter two, Childhood The Prince of Darkness is a Gentleman. Hamlet From my earliest years I had a great desire to inquire into the causes of all those little things and events which astonished 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 into my inquiries from any fear of the conclusions to which they might lead. As it may be interesting to some of those who will here after 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 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 afterward so much disgusted me in my youthful years. My invariable question on receiving any new toy was mama 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. Earliest recollections. 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 Tule Street where I remained watching the passing vehicles in order to find a safe opportunity of crossing that very busy street. In the meantime 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 the door of the linen draper shop on the opposite corner of Tule Street when the gold-laced crier was making proclamations 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 linen draper 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 Tule Street were being pulled down I believed 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 was thrown from the roof of one of the houses and penetrated into the earth close to my feet. Footnote there exists an aristocracy even among slates perhaps from their occupying the most elevated position in every house. Small ones are called ladies the larger size countesses and the biggest of all are duchesses and footnote. The other event which I believed happened sometime 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. 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 the 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 savior 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 10 by violent fevers from which I was with difficulty saved I was sent into Tevincher and placed under the care of a clergyman who kept a school at Elfington 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 among 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 of 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, 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 a rabbit, an owl, a black cat very frequently, a raven, a man with a cloven foot also frequent. After long thinking over the subject although checked by a belief that the inquiry was wicked my curiosity at length overbalanced 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. 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 center 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 center 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-position 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 first few 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 over him I remained long awake and very unhappy. I thought that this forgetfulness was a punishment inflicted 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 a 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 presumed 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 by my native air. My mind however receiving but little instruction began I imagine to pray upon itself. Such at least I inferred 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 headache. 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 headache 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 tram weight which had escaped from the box of a pair of medical scales. This little incident had an important effect upon my afterlife. I reflected upon the extraordinary fact that my headache 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 headache 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 toothache not acute though previously wearing I often had records to a volume of darn purity 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 Daakris the son of Admiral Richard Daakris. 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 assured I saw him frequently. He was in a ship of 80 guns at the passage of the Dardanelles under the command of Sir Thomas Duckworth. Ultimately he was sent home in charge of a price 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 18. 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 set up until after midnight and evering 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 and I had studied the forms of the furniture lest they should in 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 sound which disturbed the intense silence of that anxious night. End of section 2. Section 3 of Passages from the Life of a Philosopher This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org Passages from the Life of a Philosopher by Charles Babbage. Chapter 3. Boyhood 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 12 inches high. One of these walked or rather glided along a space of about four feet when she turned around and went back to her original place. She used an eyeglass occasionally and bowed frequently as if recognizing her acquaintances. The motions of her limbs were singularly graceful. The other silver figure was an admirable dance use with a bird on the forefinger of her right hand which wagged its tail, flapped its wing and opened its beak. This lady attitudinized in a most fascinating manner. Her eyes were full of imagination and irresistible. These silver figures were the Shedavra of the artist. They had cost him years of unburied labor and were not even then finished. After I left Devonshire I was placed at a school in the neighborhood of London in which there were about 30 boys. My first experience was unfortunate and probably gave an unfavorable 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 playground 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 humored it. We now returned all together towards the playground when we met our master who immediately pronounced that we were each fine one chilling 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 demonstrate and explain the case. But all the remote strengths was vain and we were accordingly fine. I never forgot that injustice. The school room adjoined the house but was not directly connected with it. It contained a library of about 300 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 Mathematicians 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 12 month 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 afterlife. 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 Marriott made the same request but not with the same motive footnote afterwards captain Marriott and footnote. 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 Marriott told me he was determined to get up and would do it whether I liked it or not. Marriott slept in the same room as myself. It contained five beds our room opened up 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 bedroom 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 bedroom I found Marriott'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 awakening him and went as usual to my work. This occurred two or three nights successively. One night however I found a piece of packed thread tied to the door lock which I traced to Marriott's bed and concluded that 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 Marriott's bed. This defeated my efforts for that night and I retired to my own bed. The next night I was provided with a pair of pliers and unbent one of the links leaving the two portions attached to Marriott'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 packed thread. As soon as I heard by his breathing that Marriott was asleep I crept over to the door drew one end of my ball of packed thread through a link of the two powerful chain and bringing it back with me to bed. Gave it a sudden jerk by pulling both hands of the packed thread passing through the link of the chain. Marriott jumped up put out his hand to the door and 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 Marriott 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 Marriott joined our party and as I had anticipated no work was done. We all got to play we let off fireworks in the playground 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 their pallid contenances 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 practiced the system of turning night in today. 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 parlor boarder had I believe expatiated to Marriott 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 Treyacle. This thought was unanimously adopted and a subscription made to purchase the Treyacle. 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 extemporized 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 Treyacle 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. Many boys rose up from their knees but some fell down again. Some turned around several times and then fell. Some turned around 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 Salmody 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 Mystery Echel whom all the boys knew and loved and who lodged at the grocers in the neighboring 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 the school I was for a few years under the care of an excellent clergyman in the neighborhood 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 Reverend 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 copper smith 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. 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 rose an awful explosion which I declined to paint. I did however learn something at this school for I observed a striking illustration of the economy of manufacturers. 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. End of chapter 3. Section 4 of passages from the life of a philosopher this is the labor box recording all labor box recordings are in the public domain for more information or to volunteer please visit laborbox.org passages from the life of a philosopher by Charles Babbage. Section 4 Cambridge 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 neighboring watering place Tynmouth he dined with us frequently the advice of the Reverend 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 super intend 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 order so as to find as in a dictionary the meaning of each one wanted it was only after I had been sometime 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 words 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 flexions of which I could make nothing madam Agnesi's analytical institutions from which I acquired some knowledge wood houses principles of analytical calculation from which I learned the notation of Leibniz and Lagrange's Theore de Functions I possessed also the flexions 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 Leibniz or the dashes of Lagrange I had however met with many difficulties and look 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 purchased the work of LeCroy in 1811 during the war it was very difficult to procure foreign books I had heard of the great work of LeCroy 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 bookseller de l'eau 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 difficulties not answered 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 Pittsburgh, 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 Leibniz at an earlier period probably at the commencement of the second year of my residence at Cambridge a friend of mine Michael Slag 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 results of Bible society 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 Slag 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 La Croix on the differential and integral La Croix it proposed that we should have periodical meetings for the propagation of and consigned to perdition all who supported the heresy of dots it maintained that the work of La Croix was so perfect that any comment was unnecessary on Slag'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 a footnote afterwards Sir Edward F. French Bromhead Baronette the author of an interesting paper in the transactions of the royal society and footnote the next day Slag 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 analytical society the next day Bromhead called on me we talked the subject over and agreed to hold a meeting at his lodgings 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 footnote the only son of madam D'Arblay and footnote Ryan footnote now the right honor bolster Edward Ryan and footnote Robinson footnote the Reverend Dr. Robinson master of the temple and footnote Frederick Mowley footnote a younger brother of the late Mr. Justice Mowley and footnote and several others we constituted ourselves the analytical society hired a meeting room open daily held meetings read papers and discuss them of course we were much ridiculed by the dawns 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 deism in opposition to the dotage of the university footnote Leibniz indicated flexions by a D Newton by a dot and footnote elected leukasian professor and thus reviving this wicked pun I ought at the same time to record an instance of forgiveness unparalleled in history 14 years after being then at Rome I accidentally read in Gallaght nanny's newspaper the following paragraph dated Cambridge yesterday the bells of St. Mary rang on the election of Mr. Babbage as leukasian professor of mathematics 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 honor they had done me but to decline it the sketch of a letter was hardly dry when two of my intimate friends the Reverend Mr. Lun and Mr. Bailby Thompson footnote afterwards Lord Winnlock and footnote 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 believe 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 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 number one 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 labor 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 first examination in January 1829 I visited Cambridge to fulfill one of the first duties of my new office the examination of Dr. Smith's prizes these two prizes of twenty five pounds each exercise a very curious and important to 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 the others the second and third etc Wranglers all the young men who have just taken their degree whether with or without honors 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 court of appeal 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 consequences 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 approve those decisions without implying any censure on the officers of the university informing 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 set 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 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 remarkable agreement on our meeting at the vice chancellors 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 lacks 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 was that a professor lacks 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 honor the university conferred upon me the only honor I ever received in my own country footnote this professorship is not in the gift of the government the electors are the masters of the various colleges it was founded in 1663 by Henry Lucas MP for the university and was endowed by him with a small estate in Bedfordshire during my tenure of that office my net receipts were between 80 pounds and 90 pounds a year I'm glad to find that the estate is now improved and that the university have added an annual salary to the chair of Newton and footnote 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 live 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 ghost club extractors 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 whereas follows first every member shall communicate his address to the secretary once in six months second if this communication is delayed beyond 12 months it shall be taken for granted that his relatives had shut him up as insane third every effort legal and illegal shall be made to get him out of the madhouse hence the name of the club the extractors fourth every candidate for admission as a member shall produce six certificates three that he is saying and three others that he is insane 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 afterlife he would have induced the fact of membership of the club of extractors as an indication of sanity or of insanity shyness chess during the first part of my residence at Cambridge I played a chess very frequently often with the our plans with several other good players there was at that period a fellow commoner at Trinity named brand 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 friends rooms I found a note informing me that he had gone to new market and had left coffee and the chess men for us I was myself tormented by great China's and my yet unseen adversary was I understood equally diffident I was sitting before the chess board when brand entered I rose he advanced sat down and took a white and black pond 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 brand uttered the first word another to this I a nodded ascent how that game was decided I do not now remember but the first sentence pronounced by either of us was a remark by brand that he had lost the first game by a certain move of his white bishop to this I replied that I thought he was mistaken and that the real cause of his losing the game arose from the use I had made of my night to moves previously to his white bishops move we then immediately began to replace them in on the board in the positions they occupied at that particular point of the game when the white bishops 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 night brand 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 traveled abroad took lessons from every celebrated teacher and played with all the most imminent 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 brand possessed and had read almost every book upon the subject six penny wist another site which I frequently joined were addicted to six penny wist it consisted of Higman afterwards tutor of Trinity Follett afterwards attorney general I've learned it 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 of the morning chapel bell again called us to our religious duties I mixed occasionally with a different set of wist 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 expeditions to the fins totally different in character was another set in which I mixed I was very fond of boating not of the manual labor 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 the illy into the fins 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 caliber as my friends of the ghost club they were 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 agrotat 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 mead pie a couple of fouls etc these were packed in a hamper with three or four bottles of wine and one of noi we sailed when the wind was fair and rode when there was none widdle sea mirror was a very favorite resort for sailing fishing and shooting sometimes we reached lin after various adventures in 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 chemistry during my residence at Cambridge smithson tenant was the professor of chemistry and I attended his lectures having a spare room I turned it into a kind of laboratory in which her shell 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 Bulo across a drawbridge at Bologna the bolt having been displaced smithson tenant 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 translation of Lacroix my views respecting the notation of lupinitz now 1812 received confirmation from an extensive course of reading I became convinced that the notation of flexions 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 lupinitz into an elementary work this opinion naturally 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 LeCroy was published for several years after the progress of the notation of Leibniz at Cambridge was low it is true that the tutors of the two largest colleges had adopted it but it was taught at none of the other colleges collection of examples 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 propose 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 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 in 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 on trampled by a limited and imperfect system of signs entered on equal terms into competition with their continental rivals end of section four section five of passages from the life of a philosopher this is a LibriVox recording all LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org passages from the life of a philosopher by Charles Babbage section five difference engine number one part one oh no we never mention it its name is never heard difference engine number one first idea at Cambridge 1812 plan for dividing astronomical instruments idea of a machine to calculate tables by differences illustration by piles of cannonballs 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 operations without any mental attention when once given the 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 or 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 or 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 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 origin of difference engine the earliest idea that I can trace in my own mind of calculating arithmetical tables by machinery rose in this manner one evening I was sitting in the rooms of the analytical society at Cambridge my head leading 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 Reverend Dr. Robinson the master of the temple for this anecdote the event must have happened either 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 the time in speculating about making machinery to compute arithmetical tables one morning I called upon the late Dr. Walliston 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 Descholne in the memoirs of the French Academy of Sciences about 50 or 60 years before I then mentioned my other idea of computing tables by machinery which Dr. Walliston thought a more promising subject I considered that a machine to execute the mere isolated operations over 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 addition and carriage 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 ensure 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 mold 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 particular form cut upon these 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 by instructions leaving with him a drawing as his guide unexpected difficulty explained 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 that they were quite unfit for their task I examined the shape of the 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 readings 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 the precise number which I had required he therefore had asked me whether another number which is 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 movable type I proposed to make metal boxes each containing three thousand types of one of the ten digits these types were to be made to pass out one by one from the bottom of their boxes when required by the computing part of the machine verification of type but here a new difficulty arose the attendant who put the types into the boxes might by a mistake put a wrong type into 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 has 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 movable types thus interlocked could never have any of their figures drawn out by the adhesion of 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 is rather roughly used as a plating by my children one such box was finished and delivered its type satisfactorily another plan for printing the table 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 impressed this mold was formed of a mixture of plaster of paris with other materials so as to become hard in the course of a few hours molds and copper plate the first difficulty arose from the impression of one tabular number on the mold 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 shape 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 stereo type molds 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 coordinate machine because it moved the copper plate and steel punches in the direction of three rectangular coordinates this machine was afterwards found very useful for many other purposes it was in fact a general shaping machine upon which many of the 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 by means of a certain system called the method of differences which is the object of this sketch to explain the first difference engine with which i am acquainted comprised a few figures and it 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 20 places of figures and also that it should print the tables that compute it a small portion of it which was placed in the international exhibition of 1862 was put together nearly 30 years ago it was accompanied by various parts intended to enable it to print the results of calculated either as a single copy on paper or by putting together movable types or by stereotype plates taken from molds 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 the copper and of stereotype molds were exhibited in a glass case adjacent to the engine Edenberg review in 1834 Dr. Lardner published in the Edenberg review 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 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. Deakin Mr. Schweitz Mr. Deakin of Buford 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. Schweitz 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 sometime 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 Esquire an exact copy of this machine was made by Mr. Duncan and Company 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 explanation of the difference engine 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 arithmetical tables 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 one to a hundred pounds of butchers meat at various prices per pound let us examine one of those tables that is the price of meat five pence per pound we find a table where the first column is the number of pounds and the second column is the price the number of pounds being one the first row the price is five pence the second row two pounds ten pence three pounds one shelling three pence four pounds one shelling eight pence five pounds two shillings one pence there are two ways of computing this table first we might have multiplied the number of pounds in each line by five the price per pound and have put down the result in pound shelling pence as in the second column or second we might have put down the price of one pound which is five pence and have added five pence for each succeeding pound let us now examine the relative advantages of each plan we shall find that if we had multiplied each number of pounds in the table by five 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 differences 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 that is that when the table has been so computed if we calculate its last term directly and if it agreed with the last term found by the continual addition of five 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'd express it in pence it becomes a table where the first row first column is five and the second column is the first difference of five and the second row first column is ten and the first difference in the second column is five the third row first column fifteen the first difference is a difference of five in the second column the fourth row first column twenty with a difference of five in the second column the fifth row is twenty five 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 groups of marbles 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 our solid air board the boy may place a row of his marbles on the sand at equal distances from each other he might then beginning with the second place two other marbles under each 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 each 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 one three six ten fifteen twenty one he might also want to know how many marbles the thirteenth 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 we tell him that it was nonsense that it was useless that nobody knew the number and so forth but 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 of knowledge in as much as he possesses the consciousness that he does not know and he has the moral courage to avow it footnote the most remarkable instance i have ever met with one of distinctness with which any individual perceived the exact boundary of his own knowledge was that of the late dr walliston end of footnote if papa failed to inform him let him go to mama who will not fail to find means to satisfy her darlings curiosity in the meantime the author of this sketch will endeavor 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 second difference constant in the case of the table of the price of butcher's 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 a table of three columns the first column is the number of marbles in each group the second column is the first difference the difference between the number of marbles in each group and that in the next the third column is the second difference first row number of the group is one number of marbles in each group is one the difference between the number of marbles in each group and that in the next is one and the second difference is one the second row the number of the group is two the number of marbles in each group is three the difference between the number of marbles in each group and that in the next is two. The second difference is one. The third row, the number of marbles in each group is six. The difference between the number of marbles in each group and that in the next is three. The second difference is one. The fourth group contains ten marbles. The difference is four. The second difference is one. The fifth group, fifteen marbles. Difference of five. Second difference, one. The sixth group, twenty-one marbles. The first difference, six. The seventh group, twenty-eight marbles. The difference, seven. It is usual to call the third column, thus formed, the column of 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 one as the first number of the table. The number one as the first difference and also the number one 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. Take the number of the group, five. Add one to this number. It becomes six. Multiply these numbers together, thirty. Divide the product by two, fifteen. This gives fifteen the number of marbles in the fifth group. 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 butcher's 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. End of part one, end of section five.