 section 36 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 recording by William Jones in Benita Springs, Florida. Passages from the Life of a Philosopher by Charles Babbage section 36 The Author's Further Contributions to Human Knowledge Part 1 of Glaciers Much has been written upon the subject of glaciers. The view which I took of the question on my first acquaintance with him still seems to me to afford a sufficient explanation of the phenomena. It is probable that I may have been anticipated in it by an associate and others, but having no time to inquire into its history I shall give a very brief statement of those views. The greater part of the material which ultimately constitutes a glacier arises from the rain falling and the snow deposited in the higher portions of mountain ranges, which naturally first fill up the ravines and valleys and rest on the tops of the mountains covering them to various depths. The chief facts to be explained are, first, the causes of the descent of those glaciers into the plains, second, the causes of the transformation of the opaque consolidated snow at the sources of the glacier into pure transparent ice at its termination. The glaciers usually lying in valleys having a steep descent, gravity must obviously have a powerful influence, but its action is considerably increased by another cause. The heat of the earth, and that derived from the friction of the glacier and its broken fragments against the rock on which it rests, as well as from the friction of its own fragments, slowly melts the ice and thus diminishing the amount of its support, the ice above cracks and falls down upon the earth, again to be melted and again to be broken. But as the ice is upon an inclined plane, the pressure from above on the upper side of the fragment will be greater than that on the lower. Consequently, at every fall the fallen mass will descend by a very small quantity further into the valley. Another consequence of the melting of the lower part of the center of the glacier will be that the center will advance faster than the sides, and its termination will form a curved convex toward the valley. The above was, I believe, the common explanation of the formation of glaciers. The following part explains my own views of the causes of the transformation of condensed snow into transparent ice. It is a well-known fact that water, rapidly frozen, retains all the air it held in solution and is opaque. It is also known that water freezing very slowly is transparent. Whenever, by the melting of the lower portion of any part of a glacier, a piece of it cracks and falls to a lower level, the friction of the broken sides will produce heat and melt a small portion of water. This water trickling down very slowly will form a thin layer on the broken surface and a portion will be retained in the narrowest part of the crack. But since the temperature of a glacier is very near the freezing point, that water will freeze very slowly. It will therefore become transparent ice and will, as it were, solder together the two adjacent surfaces by a thin layer of transparent ice. But the transparent ice is much stronger and more difficult to break than opaque ice. Consequently, the next time the soldered fragments are again broken, they will not break in the strongest part, which is the transparent ice, but the next fracture will occur in the opaque ice as it was at first. Thus, by the continued breaking and falling downward of the fragments of the glacier, as it proceeds down the valley, a series of vertical, rudely parallel veins of transparent ice will be formed. As these masses descend the valley, fresh vertical layers of transparent ice will be interposed between those already existing until the hole takes that beautiful, transparent cerulean tent, which we so frequently see at the lower termination of a glacier. Another effect of this vertical fracture at the surfaces of least resistance will be alternate vertical layers of opaque and transparent ice shading into each other. This would, in some of its stages, give a kind of ribboned appearance to the ice. Probably traces of it would still be exhibited even in the most transparent ice. Speaking roughly, this ribboned structure ought to be closer together than near the piece examined is to the end of the glacier. It ought also to be more apparent towards the other glacier than toward the sides. The effect of this progress downward is to produce a very powerful friction between the masses of ice and the earth over which they are pushed and consequently a continual accession to that stream of water which is found issuing from all glaciers. The result of this continual breaking up is to cause all the water melted by the friction of the blocks of ice, which is not retained by the glaciers to fall toward the lowest part of the descending valley and thus increase the stream and so take away more and more of the support of the central part of the glacier. Hence the advance of the surface of the glacier will be much quicker toward its middle than near the sides. Cracks in glaciers perpendicular. The consequence of these actions is that cracks in the ice will occur generally in planes perpendicular to its surface. The rain which falls upon the glacier, the water produced from its surface by the sun's rays and by the effect of the temperature of the atmosphere as well as the water produced by the friction of its descending fragments, will penetrate through these cracks and be retained by capillary action on the surfaces. The distance of the adjacent surfaces is very small. The rest of this unfrozen water will reach the rocky bottom of the glacier and give up some of its heat to the bed over which it passes to be again employed in melting away the lowest support of the glacier ice. Although the temperature of the glacier should differ but by a very small quantity from that of the freezing point of water, yet these films will only freeze the more slowly and therefore become more solid and transparent ice. Their very thinness will enable the air to be more readily extricated by freezing. The question of the regulation of pounded ice, if by that term is meant anything more than welding ice by heat or of joining its parts by a process analogous to that which is called burning together, two separate portions of a bronze statue has always appeared to me unsatisfactory. Burning Together Bronze The process of burning together is as follows. Two portions of a large statue which have been cast separately are placed in a trough of sand with their corresponding ends near to each other. A channel is made in the sand leading through the juncture of the parts to be united. A stream of melted bronze is now allowed to run out from the furnace through the channel between the contiguous ends which it is proposed to unite. The first effect of this is to heat the ends of the two fragments. After the stream of melted metal has continued some time the ends of these fragments themselves begin to melt. When a small quantity of each is completely melted the further flow of the melted metal is stopped and as soon as the pool of melted metal connects the two ends of the pieces to be united begins to consolidate. The pool is covered up with sand and allowed to cool gradually. When cold the unnecessary metal is cut away and the fragments are as perfectly united as if they had been originally cast in one piece. The sudden consolidation by physical force of pounded ice or snow appears to me to arise from the first effect of the structure producing heat which melts a small portion into water and brings the particles of ice or snow nearer to each other. The portion of water thus produced then having its heat abstracted by the ice connects the particles of the latter more firmly together by freezing. If two flat surfaces of clear ice had a heated plate of metal put between them very thin layers of water would be formed between the ice and the heated plate. If the hot plate were suddenly withdrawn and the two pieces of ice pressed together they would then be frozen together. This would be equivalent to welding. In all these cases the temperature of the ice must be a very little lower than the freezing point. The more nearly it approached that point the slower the process of freezing would be for the more transparent the ice thus formed. Ice frozen in the exhibition 1862. In the exhibition of 1862 there were two different processes by which ice was produced in abundance even in the heat of the machinery annex in which they were placed. In both the water was quickly converted into ice and in both cases the ice was opaque. In one of them the ice was produced in the shape of long hollow cylinders. These were quite opaque and were piled up in stacks. The temperature of the place caused the ice to melt slowly. Consequently the interstices where the cylinders rested upon each other received and retained a small portion of the water which trickling down was detained by capillary attraction. Here it was very slowly frozen and formed at the junction of the cylinders a thin film of transparent ice. This gradually increased as the upper cylinders of the ice melted away and after several hours exposure I have seen clear transparent ice a quarter of an inch thick where at the commencement there had not been even a trace of translucency. On inquiring of the operator why the original cylinders were opaque he told me because they were frozen quickly. I then pointed out to him the small portions of transparent ice which I have described and asked him the cause. He immediately said because they had been frozen slowly. It appears to be an axiom derived from his own experience that water quickly frozen is always opaque and water slowly frozen always transparent. I pointed out this practical illustration to many of the friends I accompanied in their examination of the machinery of the annex. It would follow from this explanation the glaciers on lofty mountains and in high latitudes may by their own action keep the surface of the earth on which they rest at a higher temperature than it would otherwise attain. Book and Parcel Post When my friend the late General Colby was preparing the materials and instruments for the intended Irish survey he generally visited me about once a week to discuss and talk over with me his various plans. We had both of us turned our attention to the post office and had both considered and advocated the question of a uniform rate of postage. The ground of that opinion was that the actual transport of a letter formed but a small item in the expense of transmitting it to its destination. While the heaviest part of the cost arose from the collection and distribution and was therefore almost independent of the length of the journey. I got some returns of the weight of the Bristol Mailbag for each night during one week with a view to ascertain the possibility of a more rapid transmission. General Colby arrived at the conclusion that supposing every letter paid six pence and that the same number of letters were posted then the revenue would remain the same. I believe when an official comparison was subsequently made it was found that the equivalent sum was five pence half pinning. I then devised a means for transmitting letters enclosed in small cylinder along wires suspended from posts and from towers or from church steeples. I made a little model of such an apparatus and this transmitted notes from my front drawing room through the house into my workshop which was in a room above my stables. The date of these experiments I do not exactly recollect but it was certainly earlier than 1827. Cost of verification I had also at a still earlier period arrived at the remarkable economical principle that one element in the price of every article is the cost of its verification. It arose thus. In 1815 I became possessed of a house in London and commenced my residence in Devonshire Street, Portland Place in which I resided until 1827. A kind relative of mine sent up a constant supply of game but although the game cost nothing the expense charged for its carriage was so great that it really was more expensive than the butcher's meat. I endeavored to get redress for the constant overcharges but as the game was transferred from one coach to another I found it practically impossible to discover where the overcharge arose and thus to remedy the evil. These efforts however led me to the fact that verification which in this instance constituted a considerable part of the price of the article must form a portion of its price in every case. Acting upon this I suggested that if the government were to become through the means of the post office parcel carriers they would derive a greater profit from it than any private trader because the whole price of verification would be saved by the public. I therefore recommended the enlargement of the duties of the post office by employing it for the conveyance of books and parcels. I mentioned these facts with no wish to disparage the subsequent exertions of Sir Roland Hill. His devotion to the subject is unwirried industry and his long and last successful efforts to overcome the notorious official friction of that department required all the enduring energy he so constantly bestowed upon the subject. The benefit conferred upon the country by the improvement he introduced is as yet scarcely sufficiently estimated. These principles were established in the economy of manufactures. See 1st edition 8th June 1832 2nd edition 22 November 1832 See chapter on the influence of verification on price page 134 and conveyance of letters page 273 Submarine Navigation Of this it is not necessary to do more and refer for the detail to the chapter on experience by water and also to the article Diving Bell in the Encyclopedia Metropolitana. I have only to add my opinion that in open inverted vessels it may be probably be found under certain circumstances of important use. Difference Engine Enough has already been said about that unfortunate discovery in the previous part of this volume. The first and great cause of its discontinuance was the inordinately extravagant demands of the person whom I had employed to construct it for the government. Even this might perhaps by great exertions and sacrifices have been surmounted. There is, however, a limit beyond which human endurance cannot go. If I survive some few years longer the analytical engine will exist and its works will afterwards be spread over the world. If it is the will of that being who gave me the endowments which led to that discovery that I should not survive to complete my work I bow to that decision with intense gratitude for those gifts, conscious that through life I have never hesitated to make the severest sacrifices of fortune and even of feelings in order to accomplish my imagined mission. The great principles on which the analytical engine rests have been examined, admitted, recorded and demonstrated. The mechanism itself has now been reduced to unexpected simplicity. Half a century may probably elapse before anyone without those aids which I leave behind me will attempt so unpromising a task. If, unwarranted by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means I have no fear of leaving the rotation in his charge for he alone will be fully able to appreciate the nature of my efforts and the value of their results. Explanation of the Cause of Magnetic and Electric Rotations In 1824, Aragot published his experiments on the magnetism manifested by various substances during rotation. I was much struck with the announcement and immediately set up some apparatus in my own workshop in order to witness the facts thus announced. My friend Herschel who assisted at some of the earliest experiments joined with me in repeating and varying those of Aragot. The results were given in a joint paper on that subject published in the Transaction of the Royal Society in 1825. I had previously made some magnetic experiments on a large magnet which would under peculiar management sustain about 32 and a half pounds. It was necessary to commence with a weight of about 28 pounds and then to add at successive intervals additional weights but each less and less than the former on electric rotations. This led me to an explanation of the cause of those rotations which I still venture to think is the true cause although it is not so recognized by English philosophers. The history is a curious one and whether the cause which I assigned is right or wrong the train of thought by which I was led to it is valuable as an illustration of the mode in which the human mind works in its progress towards new discoveries. The first experiment showing that the weight suspended might be increased at successive intervals of time was stated in most treatises on magnetism. But the visible fact impressed strongly on my mind the conclusion that the production and discharge of magnetism is not instantaneous but requires time for its complete action. It appeared therefore to me that this principle was sufficient for the explanation of the rotations observed by Erigo. In the following year it occurred to me that electricity possessed the same property namely that of requiring time for its communication. I then instituted a new series of experiments and succeeded, as I had anticipated in producing electric rotations. But a new fact now presented itself. In certain cases the electric needle moved back in the contrary direction to that indicated by the influences to which it was subjected. Whenever this occurred the retrograde motion was always very slow. After eliminating successively by experiment every cause which I could imagine the fact remained was that in certain cases there occurred a motion in the direction opposite to that which was expected. But whenever such a motion occurred it was always very slow. Upon further reflection I conjectured that it might arise from the screen interposed between the electric and the needle itself becoming electrified possibly in the opposite direction. New experiments confirmed this view and proved that the original cause was sufficient for the production of all the observed effects. These experiments and their explanation were printed in the Trans 1826 but they met with so little acceptance in England that I had ceased to contend for them against more popular doctrines and was too deeply occupied with other inquiries to enter on their defense. Several years after during a visit to Berlin taking a morning walk with Mitterlich I asked what explanation he adopted of the magnetic equations of Eregel. He instantly replied there can be no doubt that yours is the true one. It will be a curious circumstance in the history of science if an erroneous explanation of new and singular experiments in one department should have led to the provision of another similar set of facts in a different department and even to the explanation of new facts at first but ultimately contradicting it. Mechanical Notation This also has been described in a former chapter. I look upon it as one of the most important additions I have made to human knowledge. It has placed the construction of machinery in the rank of a demonstrative science. The day will arrive when no school of mechanical drawing will be thought complete without teaching it. Occulting Lights The great object of all my inquiries has ever been to endeavor to ascertain those laws of thought by which man makes discoveries. It was by following out one of the principles which I had arrived at that I was led to the system of occulting numerical lights for distinguishing lighthouses and for night signals at sea which I published twelve years ago. The principle I allude to is this principle of invention. Whenever we meet with any defect in the means we are contriving for the accomplishing of a given object that defect should be noted and reserved for future consideration and inquiries should be made whether that which is a defect as regards the object in view may not be the source of advantage in some totally different subject. I had for a long series of years been watching the progress of electric, magnetic and other lights of that order with the view of using them for domestic purposes but their want of uniformity seemed to render them hopeless for that object. Returning from a brilliant exhibition of voltaic light I thought of applying the above rule. The accidental interruptions might by breaking the circuit be made to recur at any required intervals. This remark suggested their adaptation to a system of signals but it was immediately followed by another namely that the interruptions were equally applicable to all lights and might be affected by a simple mechanism. Unexpected difficulty I then by means of a small piece of clockwork and an Argan lamp made a numerical system of occultation by which any number might be transmitted to all those within sight of this source of light. Having placed this in a window of my house I walked down the street to the distance of about 250 yards. On turning around I perceived the number 32 clearly indicated by its occultations. There was however a small defect in the apparatus. After each occultation there was a kind of semi-occultation. This arose from the arm which carried the shade rebounding from the stop on which it fell. Aware that this defect could easily be remedied I continued my onward course for about 250 yards more with my back towards the light. On turning around I was much surprised to observe that the signal 32 was repeatedly distinctly without the slightest trace of any semi-occultation or blink. I was very much astonished at this change and on returning towards my house had the light constantly in view. After advancing a short distance I thought I perceived a very faint trace of the blink. At 30 or 40 paces near it was clearly visible and at the halfway point it was again perfectly distinct. I knew that the remedy was easy but I was puzzled as to the cause. After a little reflection I concluded that it arose from the circumstance that the small hole through which the light passed was just large enough to be visible at 500 yards yet that when that same hole was partially covered by the rebound there did not remain sufficient light to be seen at the full distance of 500 yards. Thus prepared I again applied the principle I had commenced with and proceeded to examine whether this defect might not be converted into an advantage. Occulting Signals I soon perceived that a lighthouse whose number was continually repeated with a blink obscuring just half its light would be seen without any blink at distances beyond half its range but that at all distances within its half range that fact would be indicated by a blink. Thus with two blinks properly adjusted the distance of a vessel from a first class light would be distinguished from 20 to 30 miles by occultations indicating its number without any blink between 10 and 20 miles by an occupation with one blink and within 10 miles by an occultation with two blinks. Another advantage was also suggested by this effect if the opaque cylinder which intercepts the light consists of two cylinders A and B connected together by rods thus if the compound cylinder descends to A and then rise again there will be a single occultation. If the compound cylinder descends to B and then rise again there would be a double occultation. If the compound cylinder descends to C and then rise again there would be a triple occultation. Such occultations are very distinct and are especially applicable to lighthouses. In the year 1851 during the Great Exhibition the light I have described was exhibited from an upper window of my house in Dorset Street during many weeks. It had not passed unnoticed by foreigners who frequently reminded me that they had passed my door when I was asleep by writing upon their card the number exhibited by the occulting light and dropping it into my letterbox. About five or six weeks after its first appearance I received a letter from a friend of mine in the United States expressing great interest about it and inquiring whether its construction was a secret. My answer was that I made no secret of it and would prepare and send him a short description of it. I then prepared a description of which I had very few copies printed. I sent twelve of these to the proper authorities of the Great Maritime Countries. Most of them were accompanied by a private note of my own to some person of influence with whom I happened to be acquainted. One of these was addressed to the present emperor of the French then a member of their representative chamber. It was dated 30th November 1852. Three days after I read in the newspapers the account of the coup of December 2nd and smiled at the inopportune time at which my letter had accidentally been forwarded. However, three days after I received from Mr. M. Mokard the prettiest note saying that he was commended by the prince president to thank me for the communication and to assure me that the prince was as much attached as ever to science and should always continue to promote its cultivation. End of section 36 the author's further contributions to human knowledge part 1 section 37 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 recording by William Jones in Benita Springs, Florida section 37 the author's further contributions to human knowledge part 2 experiments in America the letter which was sent to the United States was placed in the hands of the Coast Survey. The plan was highly approved and Congress made a grant of $5,000 in order to try it experimentally. After a long series of experiments in which its merits were severely tested a report was made to Congress strongly recommending its adoption. I then received a very pressing invitation to visit the United States for the purpose of assisting to put it in action. It was conveyed to me by an amiable and highly cultivated person the late Mr. Reed Professor of English Literature at Philadelphia who on his arrival in London proposed that I should accompany him on his return in October the best season for the voyage and in the finest vessel of their mercantile Navy. I had long had a great wish for the continent but I did not think it worth crossing the Atlantic unless I could have spent a 12 month in America. Finding this impossible under the then circumstances about a month before the time arrived I resigned with great reluctance to the pleasure of accompanying my friend to his own country. The authors escape it was most fortunate that I was thus prevented from embarking on board the Arctic steamer of the largest class steaming at the rate of 13 knots an hour over the banks of Newfoundland during a dense fog the Arctic was run into by a steamer of about half its size moving at the rate of 7 knots. The concussion was in this circumstance fatal to the larger vessel. This sad catastrophe was thus described by the brother of my lost friend quote of September 1854 Mr. Reed with his sister embarked at Liverpool for New York in the United States steamship Arctic. Seven days afterward at noon on the 27th when almost in sight of his native land a fatal collision occurred and before sundown every human being left upon the ship had sunk under the waves of the ocean. The only survivor who personally acquainted with my brother saw him about two o'clock p.m. after the collision and not very long before the ship sank sitting with his sister in the small passage aft of the dining room. They were tranquil and silent though their faces were the look of painful anxiety. They probably afterwards left this position and repaired to the promenade deck for a selfish struggle for life with a helpless companion dependent upon him with a physical frame unsuited for such a strife and above all with a sentiment of religious resignation which taught him in that hour of agony even with the memory of his wife and children thronging in his mind to bow his head in submission to the will of God. For such a struggle he was fully unsuited and his is the praise that he perished with the women and children close quote In 1853 I spent some weeks at Brussels during my residence in that city a congress of naval officers from all the maritime nations assembled to discuss and agree upon certain rules and observations to be arranged for the common benefit of all. One evening I had the great pleasure of receiving the whole party at my house for the purpose of witnessing my occulting lights. The portable occulting light that had brought with me was placed in the veranda on the first floor and then we went along the boulevard to see its effect at different distances and with various numerical symbols. On our return several papers relating to this subject were lined upon the table. The Russian representative Mr. Blank took up one of the original printed descriptions and was much interested in it. On taking leave he asked with some hesitation whether I would lend it to him for a few hours. I told him at once that if I possessed another copy I would willingly give it to him. But that not being the case I could only offer to lend it. Mr. Blank therefore took it home with him and when I sat down to breakfast the next morning I found it upon my table. In the course of the day I met my Russian friend in the park. I expressed my hope that he had been interested by the little track he had so speedily returned. He replied that it had interested him so much that he had set up all night and copied the whole of it and that his transcript and dispatch upon the subject was now on its way by the post to his own government. Several years after I was informed that occulting solar lights were used by the Russians during the siege of Sebastopol. Night Signals The system of occulting lights applies with remarkable facility to night signals either on shore or at sea. If it is used numerically it applies to all the great dictionaries of the various maritime nations. I may here remark that there exists the means by which all such signals may, if necessary, be communicated in cipher. Sun Signals The distance at which such signals can be rendered visible exceeds that of any other class of signals by means of light. During the Irish Trigonometrical Survey a mountain in Scotland was observed with an angular instrument from a field in Ireland at the distance of 108 miles. This was accomplished by stationing a party on the summit of the mountain in Scotland with a looking glass of about a foot square directing the sun's image to the opposite station. No occultations were used, but if the mirror had been larger and occultation employed the messages might have been sent and the time of resonance upon the mountain considerably diminished. When I was occupied with occulting signals I made this widely known. I afterwards communicated the plan during a visit to Paris to many of my friends in that capital and by request to the Minister of Marine. I have observed in the Comte-Grandeux that the system has to a certain extent been since used in the south of Algeria where, during eight months of the year the sun is generally unobscured by clouds as long as it is above the horizon. I have not, however, noticed in those communications to the institute any reference to my own previous publication. Xenothalite signals another form of signal although not capable of use at very great distances may, however, be employed with considerable advantage under certain circumstances. Universality and economy are its great advantages. It consists of a looking glass making an angle of 45 degrees with the horizon placed just behind and opening in a vertical board this being stuck into the earth. The light of the sky in Xenoth which is usually the brightest will be projected horizontally through the opening in whatever direction the person to be communicated with may be placed. The person who makes the signals must stand on one side in front of the instrument and by passing his hat slowly before the aperture any number of times may thus express each unit's figure of his signal. He must then leaving the light visible pause while he deliberately counts himself ten. He must then with his hat make a number of occultations equal to the ten's figure he wishes to express. This must be continued for each figure in the number of the signal always pausing between each during the time of counting ten. When the end of the signal is terminated he must count sixty in the same manner and if the signal he gave has not been acknowledged has been observed. The same simple telegraph may be used in a dark night by substituting a lantern for the looking glass. The whole apparatus is simple and cheap and can be easily carried even by a small boy. I was led to this contrivance many years ago by reading an account of a vessel stranded within thirty yards of the shore. Its crew consisted of thirteen people, one got into the boat leaving the master who thought himself safer in the ship with two others of the crew. The boat put off from the ship keeping as much out of the breakers as it could and looking out for a favorable place for landing. The people on shore followed the boat for several miles urging them not to attempt landing but not a single word was audible by the boat's crew who after rowing several miles were the first favorable law. They did so. The boat was knocked to pieces and the whole crew were drowned. If the people on the shore could at that moment have communicated with the boat's crew they could have informed them that by continuing their course for half a mile further they might turn into a cove and land almost dry. I was much impressed by the want of easy communication between stranded vessels on shore who might rescue them. Shipwreck signals I can even now scarcely believe it credible that the very simple means I'm about to mention has not been adopted years ago. A list of about a hundred questions relating to directions and inquiries required to be communicated between the crew of a stranded ship and those on shore who wish to aid it would I am told be amply sufficient for such purposes. Now if such a list of inquiries were prepared and printed by competent authority any system of signals by which a number of two places of figures can be expressed might be used. This list of inquiries and answers ought to be printed on cards and nailed up on several parts of every vessel. It would be still better by conference with other maritime nations to adopt the same system of signs and to have them printed in each language. A looking glass, a board with a hole in it and a lantern would be all the apparatus required the lantern might be used for night and the looking glass for day signals. These simple and inexpensive signals might be occasionally found useful for various social purposes. Short distance signals two neighbors in the country whose houses though reciprocally visible are separated by an interval of several miles might occasionally telegraph to each other. If the looking glass were of large size its light and its occultation might be seen perhaps from 6 to 10 miles and thus become by daylight a cheap guiding light through the channels and into harbors. It may also become a question whether it might not in some cases save the expense of booing certain channels. For railway signals during the daylight it might in some cases be of great advantage by saving the erection of very lofty poles carrying dark frames through which the light of the sky is emitted. Amongst my early experiments I made an occulting handle lantern with a shade for occulting by the pressure of the thumb and with two other shades of red and green glass. This might be made available for military purposes by the police. Greenwich time signals It has been thought very desirable that a signal to indicate Greenwich time should be placed on the start point, the last spot with ships going down the channel on distant voyages usually sight. The advantage of such an arrangement arises from this, that chronometers having had their rates ascertained on shore may have them somewhat altered by the motions through which they are submitted at sea. If therefore after a run of above 200 miles they can be informed of the exact Greenwich time the sea rate of their chronometers will be obtained. Of course no other difficulty than that of expense occurs in transmitting Greenwich time by electricity to any points on our coast. The real difficulty is to convey it to the passing vessels. The firing of a cannon at certain fixed hours has been proposed but this plan is encumbered by requiring the knowledge of the distance of the vessel from the gun and also from the variation of the velocity of the transmission of sound under various circumstances. During the night the flash arising from ignited gunpowder might be employed but this in the case of rain or other atmospheric circumstances might be impeded. The best plan for night signals would be to have an occulting light which might be that of the lighthouse itself or other specially reserved for the purpose. During the day and when the sun is shining the time might be transmitted by the occultations of reflected solar light which would be seen at any distance the curvature of the earth admitted. The application of my zenith light might perhaps fulfill all the required conditions in daylight. I have found that even in the atmosphere of London an opening only 5 inches square can be distinctly seen and its occultations counted by the naked eye at the distance of a quarter mile. If the side of the opening were double the former then the light transmitted to the eye would be four times as great and the occultations might be observed at the distance of one mile. The first part of the asteroid must have its side nearly in the proportion of three to two so that one of five feet by seven and a half ought to be seen at the distance of about eight or nine miles. Geological theory of isothermal surfaces. During one portion of my resident at Navel's my attention was concentrated upon what in my opinion is the most remarkable building upon the face of the Temple of Serapis at Putsul. In this inquiry I profited from the assistance of Mr. Head, now the right Honourable Sir Edmund Head Bart K.C.B., late Governor General of Canada. An abstract of my own observations was printed in the Abstracts of Proceedings of the Geological Society Volume 2, page 72. My friend's historical views were printed in the Transactions of the Antiquarian Society. Temple of Serapis It was obviously built at or above the level of the Mediterranean in order to profit by a hot spring which supplied its numerous baths. There is unmistakable evidence that it has subsided below the present level of the sea at least 25 feet that it must have remained there for many years that it then rose gradually up probably to its former level and that during the last 20 years it has been again slowly subsiding. The results of this survey led me in the following year to explain the various elevations and depressions on portions of the Earth's surface at different periods of time by a theory which I have called the theory of the Earth's isothermal surfaces. I do not think the importance of that theory has been well understood by geologists who are not always sufficiently acquainted with physical science. The late Sir Henry Delabesh perceived at an early period the great light of those sciences might throw upon his own favorite pursuit and was himself always anxious to bring them to bear upon geology. I am still more confirmed in my opinion of the importance of the theory of isothermal surfaces from the fact that a few years afterwards my friend Sir John Herschel arrived independently at precisely the same theory. I have stated this at length in the notes to the Ninth Bridgewater Treatise. Games of Skill A considerable time after the translation of Menebarae's memoir had been published and after I had made many drawings of the analytical engine and all its parts I began to meditate upon the intellectual means by which I had reached to such an advanced and even to such unexpected results. I reviewed in my mind the various principles which I had touched upon in my published and unpublished papers, and dwelt with satisfaction upon the power of which I possessed over the mechanism through the aid of a mechanical notation. I felt, however, that it would be the minds of others and even in some measure to my own that I should try the power of such principles as I had laid down by assuming some question of an entirely new kind and endeavouring to solve it by the aid of those principles which had so successfully guided me in other cases. Games of Skill can be played by an automaton. After much consideration I selected for my test the ability of a machine that should be able to play a game of purely intellectual skill successfully such as tit-tat-toe, drafts, chess, etc. I endeavored to ascertain the opinions of persons in every class of life and of all ages whether they thought it required human reason to play Games of Skill. The most constant answer was in the affirmative. Some supported this view of the case by observing that if there were otherwise an anautomaton could play such Games. A few of those who had considerable acquaintance with mathematical science allow the possibility of machinery being capable of such work but they most statly deny the possibility of contriving such machinery on account of the myriads of combinations which even the simplest Games included. On the first part of my inquiry I soon arrived at a demonstration that every Game of Skill is susceptible of being played by anautomaton. Further consideration showed that if any position of the men upon the board were assumed whether that position were possible or impossible then if the automaton could make the first move rightly he must be able to win the game. Always supposing that under the given position of the men that conclusion were possible. Whatever move the automaton made another move would be made by his adversary. Now this altered state of the board is one amongst the many positions of the men in which by the previous paragraph the automaton was supposed capable of acting. Hence the question is reduced to that of making the best move under any possible combinations of positions of the men. Now several questions the automaton has to consider are of this nature. 1. Is the position of the men as placed before him on the board a possible position that is one which is consistent with the rules of the game? 2. If so has automaton himself already lost the game? 3. If not then has automaton won the game? 4. If not can he win it at the next move? If so make that move. 5. If not could his adversary if he had the move win the game? If so automaton must prevent him if possible. 7. If his adversary cannot win the game at his next move automaton must examine whether he can make such a move that if he were allowed to have two moves in succession he could at the next move have two different ways of winning the game and each of these cases failing automaton must look forward to three or more successive moves. Now I have already stated that in the analytical engine I had devised mechanical means equivalent to memory also that I had provided other means equivalent to foresight and that the engine itself could act upon this foresight. 8. In consequence of this the whole question of making an automaton play any game depended upon the possibility of the machine being able to represent all the merits of combinations relating to it allowing 100 moves on each side for the longest game of chess I found that the combinations involved in the analytical engine enormously surpassed any required even by the game of chess 9. Game of tit-tat-toe As soon as I had arrived at this conclusion I commenced an examination of a game called tit-tat-toe usually played by little children it is the simplest game with which I am acquainted each player has five counters one set marked with a plus the other with a zero the board consists of a square divided into nine smaller squares and the object of each player is to get three of his own men in a straight line one man is put on the board by each player alternately in practice no board is used but the children drop on a bit of paper or on their slate they figure likely any of the following the successive moves of the two players may be represented as follow and here a diagram is presented in this case the next step I made was to ascertain what number of combinations were required for all the possible variety of moves and situations I found this to be comparatively insignificant I therefore easily sketched out mechanism by which such an automaton might be guided here the two I had considered only a philosophical view of this subject but a new idea now entered my head which seemed to offer some chance of enabling me to acquire the funds necessary to complete the analytical engine it occurred to me that if an automaton were made to play this game it might be surrounded with such attractive circumstances that a very popular and profitable exhibition might be produced I imagined that the machine might consist of the figures of two children playing against each other accompanied by a lamb and a cock who won the game might clap his hands whilst the cock was crowing that the child who was beaten might cry and ring his hands whilst the lamb began bleeding I then proceeded to sketch various mechanical means by which every action could be produced these when compared with those I had employed for the analytical engine were remarkably simple a difficulty however a rose of a novel kind it will have been observed by the calculation I gave of the analytical engine that cases arose in which it became necessary on the occurrence of certain conditions that the machine itself should select one out of two or more distinct modes of calculation the particular one to be adopted could only be known when those calculations on which the selection depended had been already made difficulty arising from choice the new difficulty consisted in this that when the automaton had to move it might occur that there were two different moves each equally conducive to his winning the game in this case no reason existed within the machine to direct his choice unless also some provision were made that the machine could attempt two contradictory motions the first remedy I devised for this defect was to make the machine keep a record of the number of games it had won from the commencement of its existence whenever two moves which we may call A and B were equally conducive to winning the game the automaton was made to consult the record of the number of games it had won if that number happened to be even he was directed to take the course A if it were odd he was to take course B if there were three moves equally possible the automaton was directed to divide the number of games he had won by three in this case the number zero one or two might be the remainder and the machine was directed to take the course A, B, or C accordingly it is obvious that any number of conditions might be thus provided for an inquiring spectator who observed the games played by the automaton might watch a long time before he discovered the principle upon which it acted it is also worthy of remark how admirably this illustrates the best definitions of chance by the philosopher and the poet quote exhibition of automaton having fully satisfied myself of the power of making such an automaton the next step was to ascertain whether there was any probability if it were exhibited to the public of its producing any moderate time such as some of money as would enable me to construct the analytical engine a friend to whom I had at an early period communicated the idea entertained great hopes of his pecuniary success when it became known that an automaton could beat not merely children but even papa and mama at a child's game it seemed not unreasonable to expect that every child who heard of it would expect mama to see it on the other hand every mama and some few papa's who heard of it would doubtless take their children to so singular and interesting a side I resolved on my return to London to make inquiries as to the relative productiveness of the various exhibitions of recent years and also to obtain some rough estimate of the probable time it would take to construct the automaton as well as some approximation of the expense it occurred to me that if half a dozen were made they might be exhibited in three different places at the same time each exhibitor might then have an automaton in reserve in case of accidental injury on my return to town I made the inquiries I alluded to and found that the English machine for making Latin verses the German talking machine as well as several others was a pecuniary point of view I also found that the most profitable exhibition which had occurred for many years was that of the little dwarf General Tom Thumb on considering the whole question I arrived at the conclusion that to conduct the affair to a successful issue it would occupy so much of my own time to contrive and execute the machinery and then to superintend the working out of the plan that even if successful of pecuniary profit it would be too late to avail myself of the money that's acquired to complete the analytical engine problem of the three magnetic bodies the problem of the three magnetic bodies which has caused such unworried labor to so many of the highest intellects of this and the past age is simple compared with another which is opening upon us we now possess a very extensive series of well-recorded observations of the positions of the magnetic needle in various parts of our globe during about 30 years causes of magnetic changes certain periods of changes of about 10 or 11 years are said to be indicated as connected with changes in the amount of solar spots but the inductive evidence scarcely rest upon three periods and it seems more probable that these effects arise from some common cause one, it has been long known that the earth has at least two if not more magnetic poles two, it is probable therefore that the sun and moon also have several magnetic poles three, in 1826 I proved that when a magnet is brought into proximity to a piece of matter capable of becoming magnetic the magnetism communicated by it requires time for its full development in the body magnetized also that when the influence of the magnet is removed the magnetized body requires time to regain its former state this being the case it is required having assumed certain positions for the poles of these various magnetic bodies to calculate the reciprocal influences in changing the positions of the poles on other bodies the development of the equations representing these forces will indicate cycles which really belong to the nature of the subject the comparisons of a long series of observations with recorded facts will ultimately enable us to determine both the number and position of those poles upon each body electric changes electricity possesses an analogous property with respect to time being required for its full action if the bodies of our system influence each other electrically other developments will be required and other cycles discovered when the equations resulting from the actions of these causes are formed and means of developing them are arranged the whole of the rest of the work becomes under the domain of machinery end of section 37 the author's further contributions to human knowledge part 2 section 38 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 recorded by Thomas Trask near Tucson, Arizona passages from the life of a philosopher by Charles Babbage section 38 results of science chapter 35 results of science at the commencement of life I had hoped that whilst I indulged in the pursuits of science I might derive from it some advantages for my family or at least that it might enable me to replace a small portion of the large expenditure without which one of my most important discoveries could not be practically worked out. I shall now mention briefly several of those appointments for which I had the vanity to suppose myself qualified and the simplicity to believe that fitness for the office was of the slightest use without interest to get the appointment. 1 In the early part of 1816 the professorship of mathematics at the East India College in Hallibur became vacant. The salary I believe was 500 pound a year I became a candidate and had strong recommendations from Ivory and Playfair. I was informed as usual for candidates to call on the directors. I did so. One of them was an honest man for he was kind enough to tell me the truth. He said, if you have interest you will get it. If not you will not succeed. 2 In 1819 the professorship of mathematics at Edinburgh became vacant by the death of Playfair and the succession of Professor Leslie to his chair. I immediately became a candidate and received testimony of my fitness from La Croy, Boyd and Laplace. These communications though gratifying to myself were useless for the object. Not being a Scott I was rejected at Edinburgh. That visit however led to a very agreeable incident. I spent a delightful week in Canal with Dougal Stewart, the second volume of his philosophy of the human mind had fortunately fallen into my hands at an earlier period during my residence at Cambridge and I had derived much instruction from that valuable work. Board of Longitude 3 About this time in a conversation with Sir Joseph Banks I mentioned my wish to have a seat at the Board of Longitude, an office to which a salary of one hundred pounds a year was attached. Although not then appointed, hopes were held out by Sir Joseph that at some future occasion I might be more successful. In 1820 another vacancy occurred to ask his influence with the Admiralty. This he declined, alleging as a reason for withholding it the part I had taken in the institution of the Astronomical Society. I was one of its founders and had been one of its first honorary secretaries and had taken an active part in that committee by which the nautical almanac was remodeled. 4 In 1824 an opportunity unexpectedly presented itself. I was invited to take the entire organization and management of an office for the assurance of lives then about to be established. It is sufficient to state that amongst our officers were the late Marquis of Landsdown and the late Lord Ambercrombie the present master of the roles and the present judge of the Admiralty court and that our direction included some of the first merchants in the city, two or three directors of the Bank of England and about an equal number of India directors. Life Assurance Office The proposition made to me was that I should have the entire management of the concern as director and actuary with a salary of 1,500 pounds a year and an apartment in the establishment with liberty to practice as an actuary. On consulting my friend the late Francis Bailey FRS who had himself practiced as an actuary he strongly advised me to accept the office. He assured me that the profit arising from private practice could scarcely be less than 1,000 pounds a year and would probably be much more. Under these circumstances I accepted the proposition. On examining the materials which existed for a table for the values of lives I found in one of the addresses for Mr. Morgan, the actuary of the equitable materials with which to construct by the aid of various calculations a very tolerable table of the actual mortality in that society. Upon this basis I calculated the tables of our new institution. After three months labor, when the whole of the arrangement had been completed and the day of our opening had been fixed circumstances occurred which induced us to give up the plan. After the experience I had now had of the amount of time occupied by such an office I was unwilling to renew the engagement with other parties. I hoped by great exertions to complete the difference engine after the lapse of a few years and that I should not be allowed to become a serious loser by that course. The institution was therefore given up and we each contributed about 100 pounds to discharge the expenses incurred. Within the subsequent 12 month an application to take the management of another life assurance society was made to me which I declined. That office is still in existence. The information and experience I had thus gained led me to think that the public were not sufficiently informed respecting the nature of assurances on lives and that a small, popular work on the subject might be useful. I prepared such a work, as intervals of leisure admitted and early in 1826 published it under the title a comparative view of the various institutions of the assurance of lives. This little volume was soon translated into German and became the groundwork upon which the great life assurance society of Elsa was founded. Every year since that event I have received a copy of the report of the state of the institution a gratifying attention which I am happy to have this opportunity of acknowledging. The wish expressed by my translator in his preface has always been fulfilled by the establishment of many other excellent life assurance offices founded on similar principles. Footnote 64 May this book soon give rise to many flourishing life assurance companies in our beloved fatherland by which proportionate wealth and happiness may be promoted amongst us and at the same time prepare for the decline of lotteries, German translation of Babbage on Life Assurance German Assurance Companies In Germany alone there were in 1860 24 life assurance companies in which about 260,000 persons were assured to the amount of upwards of 40 million sterling. The oldest and most successful of these institutions have adopted my table of the equitable experience and I am informed that it agrees very well with the results of their own experiences up to about the 57th year. After this the deaths are rather more frequent than those of the equitable. Another still more gratifying result arose. My father, whose acquaintance with mercantile affairs was very extensive was so pleased with the little book that during the last two years of his life he read it through three times. Mastership of the Mint 5. In 1846 the Mastership of the Mint became vacant. In former days it was held by Newton. I had pointed it out in the decline of science as one of those offices to which men of science might reasonably aspire. A complete acquaintance with the most advanced state of mechanical science which the demands of my own machinery had compelled me to improve added to a knowledge of the internal economies of manufactures appeared to me to constitute fair claims on that office. In the event of my succeeding I had proposed to let the whole of my salaries accumulate so that at the end of 10 or 12 years I might retire from the office and be enabled with 20,000 pounds thus earned to construct the analytical engine. I wrote to Lord Melbourne on the subject but I did not mention that circumstance even to my most intimate friends. It came, however, to the knowledge of one of them who took a very warm interest in my success and I believe that at first I had a very fair chance. The appointment remained for a short time in abeyance but it was found necessary to detach shale from O'Connell and the appointment was therefore given to shale. Some years after when shale was appointed our minister at the court of Tuscany he asked me to give him a letter of introduction to the Grand Duke Leopold II. Of course I treated the application as a joke but shale assured me that he was quite serious and that he knew it would be of use to him. I therefore gave him a letter of introduction to a sovereign from whom both before and subsequently I have been honored by many gratifying attentions. Six In 1849 on the promotion of shale the Mastership of the Mint again became vacant. I thought my own claim sufficiently known to the public but I had no political interest. My friend Sir John Herschel was more fortunate and he received the appointment. Seven. After a few years the office again became vacant by the resignation of Sir John Herschel. The government had now for the third time an opportunity of partial repairing its former neglect. I had however no political party to support me and the present Master the Mint, Mr Graham then received the appointment. Registrar General of Births, Deaths, etc. In 1835 a new office was created that of Registrar General of Births, Deaths, and Marriages. Mr Francis Bailey and others then suggested to me that being known to the public as qualified for this situation by my previous publications I had a fair claim to the appointment. Having made inquiries on this subject I found that it would be useless to make any application as the place was intended for the brother-in-law of the Secretary of State. Nine. On the death of Mr Lister a few years after the same office again became vacant when other friends then made a suggestion. On making preliminary inquiries I found as before that all applications would be useless as the appointment was intended for a military officer Major Graham, the brother of another Secretary of State commissioners of railways. Ten. Some years ago the alarm created by accidents occurring upon railways induced the government to consider about the appointment of a commission to examine into their causes the rules for the guidance of the companies in the prevention of those dangers. In 1846 an act of parliament was passed appointing commissioners for the supervision of railways. Having myself thought much upon the subject and having had personally some experience on railways I had the vanity to think that the mechanical knowledge of the author of the economy of manufacturers would justify his appointment as one of those commissioners applying under such circumstances as the commissionership of the railway board I expected that I should find few competitors with higher claims but I had no interest. A military engineer was appointed who already held a civil appointment and who died in less than two years after. Eleven. On the occurrence of this vacancy another military officer was appointed I was again passed over under circumstances which at the time I thought must have caused deep regret in the mind of the minister who made the appointment. After an experience of a few years public opinion was so strongly expressed against the railway commission that it was dissolved. I'm satisfied that in each of these cases the appointment was entirely due to family or political influence. I have in the course of my experience frequently heard of appointments made in the most flattering and unexpected manner of titles offered in fact in such a way that it was impossible to decline them. I myself seen a good deal behind the scenes of the drama of life I have repeatedly found that those unsolicited honors have been obtained by the most persevering applicants and by the most servile flattering. Indeed, to the great scandal of public life success has in some instances been obtained by a man condescending for a time to oppose his own party and as some observer has wittily remarked of attempting to break into the shop for the purpose of serving behind the counter. Reflections on patronage It cannot be doubted that patronage entrusted to the disposition of a minister often proves an onerous and ungrateful trust demanding powers of discrimination and forbearance not always found in public men. Whilst a careful observation of the manner in which patronage is usually dispensed does not lead to the conclusion that its exercise is always free from the influence of corrupt motives. Even in the cases in which such impure motives seem absent it too frequently happens that other influences besides a just and honest discrimination appear to have taken a part in regulating the distribution of public favor. It would be invidious to speculate on the motives or discuss the merits of the appointments to which I have had occasion to refer with their propriety or otherwise I have individually no concern of the positive motives which induce them I have no knowledge at least not sufficient to justify me in condemning them on that score but I cannot help thinking that such appointments have not always been made without some degree of pain or misgiving and perhaps a conscientious scruple on the part of the minister. Indeed I have sometimes indulged a suspicion that a little firmness to resist external pressure would occasionally secure more fairness to candidates for public employment and tend to retain the services of more efficient agents of the public well. The weight of nepotism although mankind may differ among one another individual at infinitum they possess certain moral elements which are common to the race such belong to the animal and are never obliterated though they may occasionally be concealed in the office or the robe of state. Self interest is the great lever of society and though the patriot profess to sacrifice it for the public good or the cynic effect to despise its influence as opposed to his philosophy both these may claim our respect but neither should be permitted to deceive us. A minister who professes to cast off the attributes of humanity is either a victim of delusion created in deceiving himself or a nave who is bent upon deceiving others. He may spurn the temptation of a bribe because his wants do not lie in that direction and notwithstanding his generous pretensions he will never discern merit unless accompanied by popular suffrage or political influence. In his balance one gain of nepotism will weigh down all the honesty he has in his disposal. End of section 38 recorded by Thomas Trask near Tucson, Arizona June 2019 Section 39 Agreeable Recollections From 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 Recording by Dale Grossman In the course of this volume I have mentioned under other heads many agreeable circumstances and many others remain unwritten. I shall now confine myself to two. On one occasion when I was engaged in my workshop in arranging some machinery for experiments on a difficult part of the analytic engine an intimate friend called and I went into the library to see it an unopened letter lying on the table he asked whether I usually treat my letters in that way I looked at the letter which appeared to be a printed one when my friend had left me I opened it and found that it professed to be from the Institute of France announcing my nomination as a corresponding member of that distinguished body on looking at the conclusion for the well-known signature of my friend I found another name which I could not read I therefore concluded that some wag had played me a trick I, however, doubted whether the joke was intended to hit me or the Academy of Sciences having left the paper on my table I returned to my experiments after dinner I took up the neglected document and then for the first time perceived that it professed to be from the Academy of Moral Sciences on reexamining the signature I found it to be that of its eminent secretary M. and Y. and that it was an official announcement of my election as a corresponding member of that Academy now the first impression on my mind was one of sincere regret I felt for a moment that the Academy might have thus honored me not solely for my labors in their own but in other departments of science this painful feeling was, however only momentary then it occurred to me that I had written the economy of manufacturers which related to political economy one section and the Ninth Bridgewater Treatise which related to philosophy another section of the Academy of Moral Sciences I now felt a real pleasure which amply compensated me for the transitory regret and I am sure no member of the many academies who have honored me by enrolling my name on their list will reproach me for stating the fact that no other nomination ever gave me greater satisfaction than the one to which I have now adverted some years ago my eldest son Mr. B. Herschelbedd was employed by the government of South Australia to explore and survey part of the northwest portion of that colony after an absence of about six months a considerable portion of which time he spent in a desert he reached a small station at the head of Spencer's Gulf intending to wait there until the arrival of a steamer from Adelaide which was expected in about a week to carry back the wool of the distant and scattered colonists it so happened that a few days before a Swedish merchant vessel commanded by Captain Orling a part owner of the ship afraid of wool Captain Orling, on going ashore heard of the arrival at the settlement of a stranger from the interior and on inquiring found that he bore my name he immediately went in search of my son and having found him said I am not personally acquainted with your father but I am well acquainted with his name he has shown such kindness to a countryman of mine that every swede would be proud to acknowledge it the steamer for which you are waiting cannot arrive until a week hence there is no accommodation in this station not even a public house I entreat you to come on board my ship and be my guest until the steamer arrives and is ready to take you to Adelaide it had been my good fortune to have an opportunity to render justice to the merits of Mr. Schützer and inventor of the Swedish difference engine my son who during the six previous months has slept under no canopy but that of heaven accepted this delightful invitation and enjoyed during the week the society of a very agreeable and highly informed gentleman I have received many marks of attention of various kinds from the natives of Sweden paragraphs translated from Swedish newspapers which were particularly interesting to me engravings and printed volumes I have been honored with these attentions by persons in various classes of society up to the highest and I am confident that the enlightened and accomplished prince to whom I elude will not think be ungrateful when I avow that the most gratifying of all of these attentions to a father whose name in his own country has been useless to himself and to his children was to hear from England's antipodes of the grateful swede welcoming and giving hospitality on the part of his countrymen to my son for the sake of the name he bore conclusion I will now conclude as I began by invoking the attention of my reader to a subject which if he is young may be of importance to him in afterlife he may reasonably ask what peculiarities of mind enabled me to accomplish what even the most instructed in their own senses deemed impossible I have always carefully watched the exercise of my own facilities and I have also endeavored to collect from the light reflected by other minds some explanation of the question I think one of the most important guiding principles has been this that every moment of my waking hours has always been occupied by some train of inquiry in far the largest number of instances the subject might be simple or even trivial but still work of inquiry of some kind or other was always going on the difficulty consists in adapting the work to the state of the body the necessary training was difficult whenever at night I found myself sleepless and wished to sleep I took a subject for examination that required little mental effort and which also had little influence on worldly affairs by a success or a failure on the other hand when I wanted to concentrate my whole mind upon an important subject I studied during the day all the minor accessories and after two o'clock in the morning I found that repose which the nuisances of the London streets only allowed from that hour until six in the morning at first I had many sleepless nights before I could thus train myself I believe my early perception in the immense power of signs in aiding the reasoning facility contributed much to whatever success I may have had probably a still more important element was the intimate conviction I possessed that the highest object a reasonable being could pursue was to endeavor to discover those laws of mind by which man's intellect passes from the known to the discovery of the unknown this feeling was ever present to my mind and I endeavored to trace its principles in the minds of all around me as well as in the works of my predecessors the end of section 39