CHAPTER XXXIII. THE AUTHOR’S CONTRIBUTIONS TO HUMAN KNOWLEDGE.

Scientific Societies — Analytical Society — Astronomical Society — Grand Duke of Tuscany, Leopold II. — Scientific Meeting at Florence — Also at Berlin — At Edinburgh — At Cambridge — Origin of the Statistical Society — Statistical Congress at Brussels — Calculus of Functions — Division of Labour — Verification part of Cost — Principles of Taxation — Extension to Elections — The two Pumps — Monopoly — Miracles.

Of the part taken by the Author in the formation of various Scientific Societies.

THE origin of the Analytical Society has been already explained in the fourth chapter. In the year 1820 the Author of this volume, joining with several eminent men attached to astronomical pursuits, instituted the Royal Astronomical Society. At the present time only three of the original founders survive. The meetings, and still more the publications of that society, have contributed largely to extend the taste for astronomy.

In 1827 I visited Italy, and during my residence at Florence had many opportunities of observing the strong feeling of the reigning Grand Duke Leopold II., not only for the fine arts, but for the progress of science, and for its application to the advancement of the arts of life.

〈THE GRAND DUKE OF TUSCANY.〉

After a long tour in Italy, I found myself in the following year again in Florence, and again I was received with a kindness and consideration which I can never forget. The Grand {431} Duke was anxious to know my opinion respecting the state of science in Italy. At one of the many interviews with which I was honoured, he asked me whether I could point out any way in which he could assist its progress.

The question was unexpected; but it immediately recalled to me a recent circumstance, which I then mentioned, namely, that in three of the great cities of Italy I had been consulted confidentially by three distinguished men of science upon the same subject, on which each was separately engaged without being aware of the fact that the other two were employed on the same inquiry. The result, I remarked, would probably be that Italy would thus make one step in science, and that the discovery might probably be accompanied by painful discussions respecting priority; whilst with better means of intercommunication amongst its men of science Italy might have made three steps in advance. The idea of a periodical meeting of men engaged in scientific pursuits naturally arose out of these remarks. At parting, the Grand Duke requested me to draw up a minute of the conversation. I therefore drew up a note on the subject, in which I shadowed out an annual meeting of learned men in the various cities of Italy.

On finally taking leave, previous to my visit to Germany, the Grand Duke assured me that he had read the minute of our conversation with much attention, that he saw the evils pointed out, and agreed with me as to the remedy. He then observed that “the time for such a meeting had not yet arrived; but,” added the Grand Duke, “when it does arrive, you may depend upon me.”

Eleven years after, in 1839, I was honoured by an invitation from the Grand Duke of Tuscany to meet the men of science of Italy, then about to assemble at Florence. In this communication it was observed, that “the time had now arrived.” {432}

In the autumn of 1828 I reached Berlin, and unexpectedly found, from M. Humboldt, that in the course of a few weeks the phi­los­o­phers of Germany were to hold a meeting in that capital.

I then learnt for the first time that, some years before, Dr. Oken had proposed and organized an annual congress of German naturalists, meeting in each succeeding year in some great town.

I remained to witness the enlarged meeting at Berlin, which was very successful, and wrote an account of it to Sir D. Brewster, who published the description of it in “The Edinburgh Journal of Science.”[58] This was, I believe, the first communication to the English public of the existence of the German Society.

〈BRITISH ASSOCIATION: ITS ORIGIN.〉

A few years after, Sir David Brewster, Sir John Robison, Secretary of the Royal Society of Edinburgh, and the Rev. William Vernon Harcourt, undertook the foundation of a similar periodical and itinerant society in our own country.

It appeared to me that the original organization of the British Association, as developed at York and at Oxford, was defective,—that its basis was not sufficiently extended. In fact, that other sciences besides the physical were wanting for the harmony and success of the whole. There was no section to interest the landed proprietors or those members of their families who sat in either house of parliament. Nor was there much to attract the man­u­fac­turer or the retail dealer. A purely accidental circumstance enabled me to remedy one of these defects.[59] {433}

[58] Vol. x., p. 225. 1829.

[59] I afterwards succeeded in getting the British Association to adopt the plan of having an exhibition of specimens of the various man­u­fac­tures and commercial products of the districts it successively visited. This commenced at Newcastle in 1838, and was carried to a much greater extent in the following year at Birmingham. I am not aware that this fact was ever referred to by those who got up the Exhibition of 1851.

〈THE STATISTICAL SOCIETY: ITS ORIGIN.〉

At the Third Meeting of the British Association at Cambridge in 1833, I happened, one afternoon, to call on my old and valued friend the Rev. Richard Jones, Professor of Political Economy at Haileybury, who was then residing in apartments at Trinity College. He informed me that he had just had a long conversation with our mutual friend M. Quételet, who had been sent officially by the Belgian Government to attend the meeting of the British Association. That M. Quételet had brought with him a budget of statistical facts, and that as there was no place for it in any section, he (Professor Jones) had asked M. Quételet to come to him that evening, and had invited Sir Charles Lemon, Professor Malthus, Mr. Drinkwater (afterwards Mr. Bethune),[60] and one or two others interested in the subject, to meet him, at the same time requesting me to join the party. I gladly accepted this invitation and departed. I had not, however, reached the gate of Trinity College before it occurred to me that there was now an opportunity of doing good service to the British Association. I returned to the apartments of my friend, explained to him my views, in which he fully coincided, and I suggested the formation of a Statistical Section. We both agreed that unless some unusual course were taken, it would be impossible to get such a Section organized until the meeting in the following year. I therefore proposed that when we met in the evening we should consider the question of constituting ourselves provisionally a Statistical Section, and afterwards, at the general meeting in the Senate House, that I should explain the circumstance which had arisen, and the {434} great advantage to the British Association of rendering such a Section a permanent branch of its institution. After further explanations its utility was fully admitted; certain rather stringent rules were laid down in order to confine its inquiries to collections of facts. The sanction of the General Meeting was then given to the establishment of the Statistical Section, and before the termination of the Congress, a larger audience was collected in its meeting-room than in those of any of its sister sciences.

[60] I have reason to believe, from the Note Book of Mr. Drinkwater (Bethune), that this meeting was held on Wednesday, 26th June, 1833.

The interest of our discussions, and the mass of materials which now began to open upon our view, naturally indicated the necessity of forming a more permanent society for their collection. The British Association approved of the appointment of a permanent committee of this section. I was requested to act as chairman, and Mr. Drinkwater as secretary. On the 15th March, 1834, at a public meeting held in London, the Marquis of Lansdowne in the Chair, it was resolved to establish the Statistical Society of London.

The Committee of the British Association, in reporting this fact to the Council, observe that “though the want of such a society has been long felt and acknowledged, the successful establishment of it, after every previous attempt had failed, has been due altogether to the impulse given by the last meeting of the Association. The distinguished foreigner (M. Quételet) who contributed so materially to the formation of the Statistical Section, was attracted to England principally with a view of attending that meeting; and the Committee hail this as a signal instance of the beneficial results to be expected from that personal intercourse among the enlightened men of all countries, which it is a principal object of the British Association to encourage and facilitate.”

M. Quételet, on his return to his own country, continued to {435} direct by his counsel, and to advance, by his own indefatigable industry, those statistical inquiries of which the Belgian Government so well appreciated the advantage.

At length the conviction of the importance of the value of Statistical Science becoming widely extended in other countries, M. Quételet saw that a fit time had arrived for summoning a European Congress. The results of such meetings are invaluable to all sciences, but more peculiarly to statistics, in which names have to be defined, signs to be invented, methods of ob­ser­va­tion to be compared and rendered uniform; thus enhancing the value of all future ob­ser­va­tions by making them more comparable as well as more expeditiously collected.

The proposal was adopted by the Belgian Government, and the first International Statistical Congress was held at Brussels in September, 1853.

The result was most successful; all the cultivators of Statistical Science are deeply indebted to M. Quételet for the unwearied pains he took to insure its success. He was assisted in this arduous task by the ministers of the crown, and supported by the high approbation of an enlightened sovereign.

Calculus of Functions.

This was my earliest step, and is still one to which I would willingly recur if other demands on my time permitted. Many years ago I recorded, in a small MS. volume, the facts, and also extracts of letters from Herschel, Bromhead, and Maule, in which I believe I have done justice to my friends if not to myself. It is very remarkable that the Analytical Engine adapts itself with singular facility to the development and numerical working out of this vast department of analysis.

In the list of my printed papers, at the end of this volume, will be found my various cont­ri­bu­tions to that subject.

{436}

POLITICAL ECONOMY.

My cont­ri­bu­tions to Political Economy are chiefly to be found in “The Economy of Machinery and Man­u­fac­tures,” which consists of illustrations and developments of the principles regulating a very large section of that important subject.

Division of Labour.

It is singular that in the analysis of the division of labour, given by Adam Smith in “The Wealth of Nations,” the most efficient cause of its advantage is entirely omitted. The three causes assigned in that work are—

These are undoubtedly true causes, but the most important cause is entirely omitted.

The most effective cause of the cheapness produced by the division of labour is this—

By dividing the work to be executed into different processes, each requiring different degrees of skill, or of force, the master man­u­fac­turer can purchase exactly that precise quantity of both which is necessary for each process. Whereas if the whole work were executed by one workman, that person must possess sufficient skill to perform the most difficult, and sufficient strength to execute the most laborious, of those operations into which the art is divided.

Needle-making is perhaps the best illustration of the overpowering effect of this cause. The operatives in this {437} man­u­fac­ture consist of children, women, and men, earning wages varying from three or four shillings up to five pounds per week. Those who point the needles gain about two pounds. The man who hardens and tempers the needles earns from five to six pounds per week. It ought also to be observed that one man is sufficient to temper the needles for a large factory; consequently the time spent on each needle by the most expensive operative is excessively small.

But if a man­u­fac­turer insist on employing one man to make the whole needle, he must pay at the rate of five pounds a week for every portion of the labour bestowed upon it.[61]

[61] See “Economy of Man­u­fac­tures.”

Cost of any Article.

Besides the usual elements which contribute to constitute the price of any thing, there exists another which varies greatly in different articles. It is this—

This is in some cases very small; but in many instances it is scarcely possible for the purchaser to verify the genuineness of certain articles. In these cases the public pay a larger price than they otherwise would do to those tradesmen whose character and integrity are well established.

Principles of Taxation.

In a pamphlet printed in 1848, I published my views of taxation, especially with reference to an Income Tax.

The principle there supported was entertained and examined by the French Minister of Finance, M. Passy. The pamphlet itself was sub­se­quent­ly translated into Italian and published at Turin, under the auspices of the Sardinian Finance Minister. {438}

〈THE PRINCIPLE OF REPRESENTATION.〉

The principle there maintained admits, I think, of an extension to the election of rep­re­sen­ta­tives.

In that case, each person would have one vote on the ground of his personality, and other votes in proportion to his income. Whenever any further extension of our rep­re­sen­ta­tive system becomes necessary, the dangers arising from the extension of the personal suffrage may fairly be counterbalanced by giving a plurality of votes to property. Such a course would have a powerful tendency to good, by supporting the national credit and by preventing the destructive waste of capital by war, and it might even make us a highly conservative people.

As the subject of political economy will be considered rather dry by most readers, I will endeavour to enliven it by an extract from that pamphlet, which singularly illustrates the question of direct and indirect taxation. I had mentioned the productive pump of my Italian friend to the late Lord Lansdowne, who supplied me with the counterpart in the unproductive pump erected by the late William Edgeworth, at Edgeworth Town, in Ireland.

That proprietor, whose country residence was much frequented by beggars, resolved to establish a test for discriminating between the idle and the industrious, and also to obtain some small return for the alms he was in the habit of bestowing. He accordingly added to the pump by which the upper part of his house was supplied with water, a piece of mechanism so contrived that, at the end of a certain number of strokes of the pump-handle, a penny fell out from an aperture to repay the labourer for his work. This was so arranged, that labourers who continued at the work, obtained very nearly the usual daily wages of labour in that part of the country. The idlest of the vagabonds of course refused this new labour test: but the greater part of the beggars, whose {439} constant tale was that ‘they could not earn a fair day’s wages for a fair days work,’ after earning a few pence, usually went away cursing the hardness of their taskmaster.

〈STORY OF THE TWO PUMPS.〉

An Italian gentleman, with greater sagacity, devised a more productive pump, and kept it in action at far less expense. The garden wall of his villa adjoined the great high road leading from one of the capitals of northern Italy[62], from which it was distant but a few miles. Possessing within his garden a fine spring of water, he erected on the outside of the wall a pump for public use, and chaining to it a small iron ladle, he placed near it some rude seats for the weary traveller, and by a slight roof of climbing plants protected the whole from the mid-day sun. In this delightful shade the tired and thirsty travellers on that well-beaten road ever and anon reposed and refreshed themselves, and did not fail to put in requisition the service of the pump so opportunely presented to them. From morning till night many a dusty and wayworn pilgrim plied the handle, and went on his way, blessing the liberal proprietor for his kind consideration of the passing stranger.

[62] Turin.

But the owner of the villa was deeply acquainted with human nature. He knew in that sultry climate that the liquid would be more valued from its scarcity, and from the difficulty of acquiring it. He therefore, to enhance the value of the gift, wisely arranged the pump, so that its spout was of rather contracted dimensions, and the handle required a moderate application of force to work it. Under these circumstances the pump raised far more water than could pass through its spout; and, to prevent its being wasted, the surplus was conveyed by an invisible channel to a large reservoir judiciously placed for watering the proprietor’s own house, stables, and garden,—into which about five pints were poured for every spoonful passing out of the spout for the {440} benefit of the weary traveller. Even this latter portion was not entirely neglected, for the waste-pipe conveyed the part which ran over from the ladle to some delicious strawberry beds at a lower level. Perhaps, by a small addition to this ingenious arrangement, some kind-hearted travellers might be enabled to indulge their mules and asses with a taste of the same cool and refreshing fluid; thus paying an additional tribute to the skill and sagacity of the benevolent proprietor. My accomplished friend would doubtless make a most popular Chancellor of the Exchequer, should his Sardinian Majesty require his services in that department of administration.

Monopoly.

In the course of my examination of this question I arrived at what I conceive to be a demonstration of the following principle:—

I devoted a chapter to this subject in an edition which I prepared several years ago for a new Italian translation of the “Economy of Man­u­fac­tures;” but I am not aware whether it has yet been published.

Miracles.

The explanation which I gave of the nature of miracles in “The Ninth Bridgewater Treatise,” published in May, 1837, has now stood the test of more than a quarter of a century, during which it has been examined by some of the deepest thinkers in many countries. Its adoption by those writers who have referred to it has, as far as my information goes, been unanimous.

CHAPTER XXXIV. THE AUTHOR’S FURTHER CONTRIBUTIONS TO HUMAN KNOWLEDGE.

Glaciers — Uniform Postage — Weight of the Bristol Bags — Parcel Post — Plan for trans­mit­ting Letters along Aërial Wires — Cost of Verification is part of Price — Sir Rowland Hill — Submarine Navigation — Difference Engine — Analytical Engine — Cause of Magnetic and Electric Rotations — Mechanical Notation — Occulting Lights — Semi-oc­cul­ta­tion may determine Distances — Distinction of Lighthouses numerically — Application from the United States — Proposed Voyage — Loss of the Ship and Mr. Reid — Congress of Naval Officers at Brussels in 1853 — My Portable Occulting Light exhibited — Night Signals — Sun Signals — Solar Occulting Lights — Afterwards used at Sebastopol — Numerical Signals applicable to all Dictionaries — Zenith Light Signals — Telegraph for Ships on Shore — Greenwich Time Signals — Theory of Isothermal Surfaces to account for the Geological Facts of the successive Uprising and Depression of various parts of the Earth’s Surface — Games of Skill — Tit-tat-to — Exhibitions — Problem of the Three Magnetic Bodies.

Of Glaciers.

MUCH has been written upon the subject of glaciers. The view which I took of the question on my first acquaintance with them still seems to me to afford a sufficient explanation of the phenomena. It is probable that I may have been anticipated in it by Saussure 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 {442} naturally first fill up the ravines and valleys, and rests 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 these 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 centre of the glacier will be that the centre will advance faster than the sides, and its termination will form a curve convex towards 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. {443}

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 whole takes that beautiful transparent cerulean tint 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 the nearer the piece examined is to the end of the glacier. It {444} ought also to be more apparent towards the centre of the glacier than towards 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 in the interstices to fall towards 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 towards 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, and still more where 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 all the air to be more readily extricated by freezing.

The question of the regelation of pounded ice, if by that {445} 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 junction 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 those fragments themselves begin to melt. When a small quantity of each end 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 whole 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 pressure 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, two very thin layers of water would be formed between the ice and the heated plate. If the hot {446} plate were suddenly withdrawn, and the two plates 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, and therefore 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 appeared to be an axiom, derived from his own experience, that water quickly frozen is always opaque, and water {447} 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, that 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; whilst the heaviest part of the cost arose from the collection and distribution, and was, therefore, almost independent of the length of its journey. I got some returns of the weight of the Bristol mail-bag 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 sixpence, 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 fivepence halfpenny. I then devised means for trans­mit­ting letters enclosed in small cylinders, along wires suspended from posts, and from towers, or from church steeples. I made a little model of such an apparatus, and thus trans­mit­ted notes from my front drawing-room, through the house, {448} 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 butchers’ meat. I endeavoured 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 mention these facts with no wish to disparage the subsequent exertions of Sir Rowland Hill. His devotion to the subject, his unwearied industry, and his long and at 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 {449} conferred upon the country by the improvements he introduced is as yet scarcely sufficiently estimated.

These principles were published afterwards in the “Economy of Man­u­fac­tures.”—See First Edition, 8th June, 1832; Second Edition, 22nd November, 1832. See chap. on the “Influence of Verification on Price,” p. 134, and “Conveyance of Letters,” p. 273.

Submarine Navigation.

Of this it is not necessary to do more than mention the title and refer for the detail to the chapter on Experience by Water: and also to the article Diving Bell in the “Encyclopædia Metropolitana.”

I have only to add my opinion that in open inverted vessels it may 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 {450} 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 any one without those aids which I leave behind me, will attempt so unpromising a task. If, unwarned 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 my reputation 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 Arago 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 Arago. The results were given in a joint paper on that subject, published in the “Transactions of the Royal Society” in 1825.

I had previously made some magnetic experiments on a large magnet which would, under peculiar management, sustain about 32½ lbs. It was necessary to commence with a weight of about 28 lbs., and then to add at successive intervals additional weights, but each less and less than the former. {451}

〈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 Arago.

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 which 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 {452} that the original cause was sufficient for the production of all the observed effects.

These experiments and their explanation were printed in the “Phil. 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 defence. Several years after, during a visit to Berlin, taking a morning walk with Mitscherlich, I asked what explanation he adopted of the magnetic rotations of Arago. 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 prevision of another similar set of facts in a different department, and even to the explanation of new facts at first apparently 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.

〈PRINCIPLE OF INVENTION.〉

The great object of all my inquiries has ever been to endeavour 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 {453} and for night signals at sea, which I published about twelve years ago. The principle I allude to is this:—

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 effected by simple mechanism.

〈UNEXPECTED DIFFICULTY.〉

I then, by means of a small piece of clock-work and an argand lamp, made a numerical system of oc­cul­ta­tion, by which any number might be trans­mit­ted to all those within sight of the 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 round 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 be easily remedied, I {454} continued my onward course for about 250 yards more, with my back towards the light. On turning round I was much surprised to observe that the signal 32 was repeated 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 thirty or forty paces nearer it was clearly visible, and at the half-way 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 five hundred yards, yet that when the same hole was partially covered by the rebound there did not remain sufficient light to be seen at the full distance of five hundred 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 all 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 at from twenty to thirty miles by oc­cul­ta­tions indicating its number without any blink; between ten and twenty miles by an occultation with one blink, and within ten miles by an oc­cul­ta­tion with two blinks.

But another advantage was also suggested by this defect. {455} If the opaque cylinder which intercepts the light consists of two cylinders, A and B, connected together by rods: thus—

Such oc­cul­ta­tions are very distinct, and are specially 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 letter-box.

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 {456} secret of it, and would prepare and send him a short description of it.

I then prepared a description, of which I had a 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 the 30th November, 1852. Three days after I read in the newspapers the account of the coup of December 2, and smiled at the inopportune time at which my letter had accidentally been forwarded. However, three days after I received from M. Mocquard the prettiest note, saying that he was commanded 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.

〈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 dollars, 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 to visit the American continent, but I did {457} not think it worth crossing the Atlantic, unless I could have spent a twelvemonth in America. Finding this impossible under the then circumstances, about a month before the time arrived I resigned with great reluctance the pleasure of accompanying my friend to his own country.

〈THE AUTHOR’S ESCAPE.〉

It was most fortunate that I was thus prevented from embarking on board the Arctic, a steamer of the largest class.

Steaming at the rate of thirteen 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 seven knots. The concussion was in this instance fatal to the larger vessel.

This sad catastrophe was thus described by the brother of my lost friend:—

“On the 20th of September, 1854, Mr. Reed, with his sister, embarked at Liverpool for New York, in the United States steamship Arctic. Seven days afterwards, 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-saloon. They were tranquil and silent, though their faces wore 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 {458} submission to the will of God,—for such a struggle he was wholly unsuited; and his is the praise, that he perished with the women and children.”

〈OCCULTING LIGHT AT BRUSSELS.〉

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 which I had brought with me was placed in the verandah on the first floor, and we then went along the Boulevards to see its effect at different distances and with various numerical signals. On our return several papers relating to the subject were lying upon the table. The Russian rep­re­sen­ta­tive, M. ———, 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. M. ——— 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 tract he had so speedily returned. He replied that it had interested him so much that he had sat up all night, had copied the whole of it, and that his transcript and a despatch 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 {459} were used by the Russians during the siege of Sebastopol.

Night Signals.

The system of occulting light 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 exist 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 station 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, messages might have been sent, and the time of residence 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 “Comptes Rendus” 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.

{460}

Zenith-light 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° with the horizon, placed just behind an opening in a vertical board. This being stuck into the earth, the light of the sky in the zenith, 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 whilst he deliberately counts to himself ten.

He must then with his hat make a number of oc­cul­ta­tions equal to the tens 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, he should repeat it until it 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. {461} Its crew consisted of thirteen people, ten of whom 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 favourable 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, resolved to take advantage of the first favourable lull. 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 and those on shore who might rescue them.

〈SHIPWRECK SIGNALS.〉

I can even now scarcely believe it credible that the very simple means I am 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 {462} 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 neighbours 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 six to ten miles, and thus become by daylight a cheap guiding light through channels and into harbours.

It may also become a question whether it might not in some cases save the expense of buoying certain channels.

For railway signals during 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 admitted.

Amongst my early experiments, I made an occulting hand-lantern, with a shade for occulting by the pressure of the thumb, and with two other shades of red and of green glass. This might be made available for military purposes, or for 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 which 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 to {463} which they are submitted at sea. If, therefore, after a run of above two hundred 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 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 another 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 fulfil all the required conditions during daylight.

I have found that, even in the atmosphere of London, an opening only five inches square can be distinctly seen, and its oc­cul­ta­tions counted by the naked eye at the distance of a quarter of a 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 looking-glass employed must have its side nearly in {464} 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 residence at Naples my attention was con­cen­trat­ed upon what in my opinion is the most remarkable building upon the face of the earth, the Temple of Serapis, at Puzzuoli.[63]

[63] In this inquiry I profited by the assistance of Mr. Head, now the Right Hon. 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, vol. ii. p. 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 twenty-five feet; that it must have remained there during many years; that it then rose gradually up, probably to its former level, and that during the last twenty 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 of 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 De la Beche perceived at an early period the great light those sciences might throw upon his own favourite pursuit, and {465} 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 in Geology” 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 Menabrea’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 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 which I possessed over mechanism through the aid of the Mechanical Notation. I felt, however, that it would be more sat­is­fac­tory to 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 contrivance of a machine that should be able to play a game of purely in­tel­lec­tual skill successfully; such as tit-tat-to, drafts, chess, &c.

I endeavoured 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 almost constant {466} answer was in the affirmative. Some supported this view of the case by observing, that if it were otherwise, then an automaton could play such games. A few of those who had considerable acquaintance with math­e­mat­i­cal science allowed the possibility of machinery being capable of such work; but they most stoutly denied 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 an automaton.

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 the several questions the automaton has to consider are of this nature:—

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 on this foresight.

〈NUMBER OF THE COMBINATIONS.〉

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 myriads of combinations relating to it. Allowing one hundred moves on each side for the longest game at chess, I found that the combinations involved in the Analytical Engine enormously surpassed any required, even by the game of chess.

〈GAME OF TIT-TAT-TO.〉

As soon as I had arrived at this conclusion I commenced an examination of a game called “tit-tat-to,” 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 +, the other set with an 0. 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 {468} line. One man is put on the board by each player alternately. In practice no board is used, but the children draw upon a bit of paper, or on their slate, a figure like any of the following.

The successive moves of the two players may be represented as follow:—

In this case + wins at the seventh move.

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. Hitherto I had considered only the philosophical view of the 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. That the child who won the game might clap his hands whilst the cock was crowing, after which, that the child who was beaten might cry and wring his hands whilst the lamb began bleating.

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, {469} were remarkably simple. A difficulty, however, arose of a novel kind. It will have been observed, in the explanation 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, the machine would 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 the games he 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 the 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 numbers 0, 1, or 2 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 {470} the best definitions of chance by the phi­los­o­pher and the poet:—

“Chance is but the expression of man’s ignorance.”—LAPLACE.

“All chance, design ill understood.”—POPE.

〈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, in a moderate time, such a sum 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 its pecuniary success. When it became known that an automaton could beat not merely children but even papa and mamma at a child’s game, it seemed not unreasonable to expect that every child who heard of it would ask mamma to see it. On the other hand, every mamma, and some few papas, who heard of it would doubtless take their children to so singular and interesting a sight. 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 to 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, were entire failures in 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. {471}

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 in point of pecuniary profit, it would be too late to avail myself of the money thus acquired to complete the Analytical Engine.

Problem of the Three Magnetic Bodies.

The problem of the three bodies, which has cost such unwearied labour 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 thirty years.

〈CAUSES OF MAGNETIC CHANGES.〉

Certain periods of changes of about ten or eleven years are said to be indicated as connected with changes in the amount of solar spots; but the inductive evidence scarcely rests upon three periods, and it seems more probable that these effects arise from some common cause.

This being the case, it is required, having assumed certain positions for the poles of these various magnetic bodies, to calculate their reciprocal influences in changing the positions of those poles on the 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 arranged, the whole of the rest of the work comes under the domain of machinery.