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The life of James Clerk Maxwell

Part 1 — CHAPTER XII. CAMBRIDGE—1871 TO 1879.

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THE Chair of Experimental Physics in the University of Cambridge was founded by a Grace of the Senate on the 9th of February 1871.

In October 1870 the Duke of Devonshire, who was Chancellor of the University, had signified his desire to build and furnish a Physical Laboratory for Cambridge. In acting as a member of the Royal Commission on Scientific Education, he had perceived how useful such an institution might be made. It was in connection with the acceptance of this munificent offer that the new professorship was established by the Senate.

The question, who should be the first professor? was for some time attended with anxiety. It was understood that Sir William Thomson had declined to stand, and it was thought uncertain whether Clerk Maxwell could be persuaded to leave the retirement of his country-seat. After some hesitation, arising chiefly from genuine diffidence, he was induced to become a candidate, on the understanding that he might retire at the end of a year, if he wished to do so. His candidature was announced on the 24th of February.[217] There was no opposition, and he was appointed on the 8th of March.

The following letters indicate the part taken by various persons in bringing about this result:—

From the Hon. J. W. Strutt (Lord Rayleigh).

Cambridge, 14th February 1871.

When I came here last Friday I found every one talking about the new professorship, and hoping that you would come. Thomson, it seems, has definitely declined.... There is no one here in the least fit for the post. What is wanted by most who know anything about it is not so much a lecturer as a mathematician who has actual experience in experimenting, and who might direct the energies of the younger Fellows and bachelors into a proper channel. There must be many who would be willing to work under a competent man, and who, while learning themselves, would materially assist him.... I hope you may be induced to come; if not, I don’t know who it is to be. Do not trouble to answer me about this, as I believe others have written to you about it.

From the Rev. E. W. Blore, M.A. (now Vice-Master of Trinity).

14th February 1871.

Many residents of influence are desirous that you should occupy the post, hoping that in your hands this University would hold a leading place in this department. It has, I believe, been ascertained that Sir W. Thomson would not accept the professorship. I mention this lest you should wish to avoid the possibility of coming into the field against him.

Maxwells usual modesty is apparent in the draft of his reply to this letter:—

Glenlair, Dalbeattie, 15th February 1871.

My dear Blore—Though I feel much interest in the proposed Chair of Experimental Physics, I had no intention of applying for it when I got your letter, and I have none now, unless I come to see that I can do some good by it.

... I am sorry Sir W. Thomson has declined to stand. He has had practical experience in teaching experimental work, and his experimental corps have turned out very good work. I have no experience of this kind, and I have seen very little of the somewhat similar arrangements of a class of real practical chemistry. The class of Physical Investigations, which might be undertaken with the help of men of Cambridge education, and which would be creditable to the University, demand, in general, a considerable amount of dull labour which may or may not be attractive to the pupils.

In the Grace of Senate of 9th February, it had been enacted that it should be “the principal duty of the professor to teach and illustrate the laws of Heat, Electricity, and Magnetism; to apply himself to the advancement of the knowledge of such subjects; and to promote their study in the University.”

For some time after his appointment, Maxwell’s principal work was that of designing and superintending the erection of the Cavendish Laboratory.

He inspected the Physical Laboratories of Sir William Thomson at Glasgow and of Professor Clifton at Oxford, in order to embody in the new structure the best features of both of these institutions. But many of the most important arrangements were of his own invention. An account of the Laboratory itself will be found in Nature (vol. X. p. 139); it is sufficient here to say that it would be difficult to imagine a building better adapted to its purpose, or one in the construction of which more provision should be made for possible requirements. In no case was convenience sacrificed to architectural effect, but in both respects the building is a decided success. The architect was Mr. W. M. Fawcett of Cambridge, who appears to have fully appreciated and thoroughly carried out all Professor Maxwell’s suggestions. The contract was given to Mr. Loveday of Kibworth, his tender being recommended by the report of the Syndicate appointed to superintend the building, dated 1st March 1872.

The work of arranging and furnishing the Cavendish Laboratory occupied a considerable time. It was not completed until the spring of 1874, when the practical work of experimenting commenced, and on the 16th of June in that year, the Chancellor formally presented his gift to the University. Sir Charles Lyell and the French astronomer Leverrier were among those who visited the Laboratory and received the honorary degree of LL.D. from the University on that occasion.

The following draft of a letter from Maxwell to the Vice-Chancellor in the previous year affords an interesting illustration of the thorough and business-like manner in which he had addressed himself to these preliminary labours.

To the Vice-Chancellor, Cambridge.

(Draft of a Letter.)

Glenlair, 5th July 1878.

I enclose a provisional list of fixtures and apparatus required for the Laboratory.

At present I am not able to estimate the prices of many of the articles.

Some of them are in the market, and have simply to be ordered; others require to be constructed specially for the Laboratory.

I have begun with a list arranged according to the places and rooms in the Laboratory, but, of course, all small things must be kept in cases, either in the apparatus room, or in the special rooms.

The special duty of the professor of experimental physics is to teach the sciences of heat and electricity, and also to encourage physical research. The Laboratory must therefore contain apparatus for the illustration of heat and electricity, and also for whatever physical research seems most important or most promising.

The special researches connected with heat which I think most deserving of our efforts at the present time are those relating to the elasticity of bodies, and in general those which throw light on their molecular constitution; and the most important electrical research is the determination of the magnitude of certain electric quantities, and their relations to each other.

These are the principles on which I have been planning the arrangement of the Laboratory. But if in the course of years the course of scientific research should he deflected, the plans of work must vary too, and the rooms must be allotted differently.

I agree with you that the income of the Museums must be largely increased in order to meet the demands of this and other new buildings, and I am glad that the University is able to increase it.

It is impossible to procure many of the instruments, as they are not kept in stock, and have to be made to order. Some of the most important will require a considerable amount of supervision during their construction, for their whole value depends on their fulfilling conditions which can as yet be determined only by trial, so that it may be some time before everything is in working order.

Even in 1874, however, there were still manifold desiderata, and the Duke expressed his wish to furnish the Laboratory completely with the necessary apparatus. To carry out this wish was again a work of time, for the Professor would never order an important instrument until he was satisfied that its design and construction were the best that could be obtained. In his annual report to the University in 1877 Professor Maxwell announced that the Chancellor had now “completed his gift to the University, by furnishing the Cavendish Laboratory with apparatus suited to the present state of science;” but at the same time he wrote to the Vice-Chancellor stating that he should reserve to himself the privilege of presenting to the Laboratory such apparatus as the advancement of science might render it desirable for the University to possess. And during the short remainder of his tenure of the professorship he expended many hundreds of pounds in this manner. And already, in the spring of 1874, he had presented to the Laboratory all the apparatus in his own possession. The apparatus provided by the British Association for their Committee on Electrical Standards (see p. 316), was also deposited in the Laboratory, in accordance with a resolution passed at the Edinburgh Meeting of 1871—the apparatus remaining the property of the Association, and subject to the control of the Committee.

While the Laboratory was thus gradually made available, the other work of the professorship went on uninterruptedly from the first. Maxwell gave annual courses of lectures on the subjects prescribed in his commission,[218] commencing with October 1871, when he delivered his inaugural lecture. This and the lecture “On Colour Vision,” given at the Royal Institution shortly after his appointment in the preceding spring, are perhaps the happiest of his literary efforts. Philosophic grasp, scientific clearness, and poetic imagination could hardly be more successfully combined.

The Cambridge lecture (October 1871) sets forth in luminous outline the meaning and tendency of the moment in the evolution of the University of Cambridge, which was marked by the institution of the course of Experimental Physics, and the erection of the Devonshire Laboratory.

The following passage is especially characteristic:—

Science appears to us with a very different aspect after we have found out that it is not in lecture-rooms only, and by means of the electric light projected on a screen, that we may witness physical phenomena, but that we may find illustrations of the highest doctrines of science in games and gymnastics, in travelling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion.

This habit of recognising principles amid the endless variety of their action can never degrade our sense of the sublimity of nature, or mar our enjoyment of its beauty. On the contrary, it tends to rescue our scientific ideas from that vague condition in which we too often leave them, buried among the other products of a lazy credulity, and to raise them into their proper position among the doctrines in which our faith is so assured that we are ready at all times to act on them. Experiments of illustration may be of very different kinds. Some may be adaptations of the commonest operations of ordinary life; others may be carefully arranged exhibitions of some phenomenon which occurs only under peculiar conditions. They all, however, agree in this, that their aim is to present some phenomenon to the senses of the student in such a way that he may associate with it some appropriate scientific idea. When he has grasped this idea, the experiment which illustrates it has served its purpose.

In an experiment of research, on the other hand, this is not the principal aim.... Experiments of this class—those in which measurement of some kind is involved—are the proper work of a physical laboratory. In every experiment we have first to make our senses familiar with the phenomenon; but we must not stop here,—we must find out which of its features are capable of measurement, and what measurements are required in order to make a complete specification of the phenomenon. We must, then, make these measurements, and deduce from them the result which we require to find.

This characteristic of modern experiments—that they consist principally of measurements—is so prominent that the opinion seems to have got abroad that, in a few years, all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry these measurements to another place of decimals.

If this is really the state of things to which we are approaching, our Laboratory may perhaps become celebrated as a place of conscientious labour and consummate skill; but it will be out of place in the University, and ought rather to be classed with the other great workshops of our country, where equal ability is directed to more useful ends.

But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continually be poured.... The history of science shows that even during that phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers.

The movement which was now to receive so great an impulse may be roughly dated from Sir William Thomsons first appearance as a Public Examiner in Cambridge; and Maxwell's own influence, as Examiner and Moderator, had been mainly instrumental in promoting it. The nature of the change has been described as follows by one whose University experience reaches back into the previous time:—

The style of mathematics which was popular in Cambridge for some time before was, to say the least, one-sided, and one-sided in a somewhat unproductive direction. There were many complaints that Cambridge was behind the rest of the scientific world, and that, whereas the students of so many other Universities were introduced to the splendid discoveries of such subjects as Electricity and Heat, the Wranglers of Cambridge spent their time upon mathematical trifles and problems, so-called, barren alike of practical results and scientific interest. Maxwell’s questions (as Moderator in 1866) infused fresh life into the Cambridge Tripos, and, therefore, into the University studies, by the number of original ideas and new lines of thought opened up by them, thus preparing for the change of system in 1873, when so many interesting subjects were added to the Examination.

Sir William Thomson gives the following important testimony to the same effect:—

The University, Glasgow, 21st January 1882.

The influence of Maxwell at Cambridge had undoubtedly a great effect in directing mathematical studies into more fruitful channels than those in which they had been running for many years. His published scientific papers and books, his action as an examiner at Cambridge, and his professorial lectures, all contributed to this effect; but above all, his work in planning and carrying out the arrangements of the Cavendish Laboratory. There is, indeed, nothing short of a revival of Physical Science at Cambridge within the last fifteen years, and this is largely due to Maxwell’s influence.

Evidence might easily be multiplied, but it is enough to quote the weighty words of Lord Rayleigh at a recent public meeting at Cambridge in support of the proposed Devonshire Memorial:—

It was no little thing to have had Professor Maxwell so closely connected with Cambridge, for by his genius effects were produced which could hardly have been produced in any other way. Before coming there to occupy the position he then held, he (Lord Rayleigh) had not given any particular attention to electricity, but he found Cambridge to be so saturated with the subject that he quickly came to the conclusion that it would be best to make it his particular study. All this was owing to the influence of Maxwell.[219]

While speaking of his work in lecturing, it may be well briefly to advert to the famous “Discourse on Molecules,” delivered before the British Association at Bradford in September 1873, which has been more often quoted than, perhaps, any other of his writings. This address was extremely rich in scientific matter, but its chief interest lay in the concluding paragraphs, which may be said to indicate more clearly than any other of Maxwell’s writings the position of his mind towards certain doctrines maintained by scientific men:—

In the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time.

Each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the temple of Karnac.

No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction.

None of the processes of Nature, since the time when Nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to any of the causes which we call natural.

On the other hand, the exact equality of each molecule to all others of the same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article, and precludes the idea of its being eternal and self-existent.

Thus we have been led, along a strictly scientific path, very near to the point at which Science must stop,—not that Science is debarred from studying the internal mechanism of a molecule which she cannot take to pieces, any more than from investigating an organism which she cannot put together. But in tracing back the history of matter, Science is arrested when she assures herself, on the one hand, that the molecule has been made, and, on the other, that it has not been made by any of the processes we call natural.

Science is incompetent to reason upon the creation of matter itself out of nothing. We have reached the utmost limits of our thinking faculties when we have admitted that because matter cannot be eternal and self-existent it must have been created.

It is only when we contemplate, not matter in itself, but the form in which it actually exists, that our mind finds something on which it can lay hold.

That matter, as such, should have certain fundamental properties,—that it should exist in space and be capable of motion,—that its motion should be persistent, and so on,—are truths which may, for anything we know, be of the kind which metaphysicians call necessary. We may use our knowledge of such truths for purposes of deduction, but we have no data for speculating as to their origin.

But that there should be exactly so much matter and no more in every molecule of hydrogen is a fact of a very different order. We have here a particular distribution of matter—a collocation—to use the expression of Dr. Chalmers, of things which we have no difficulty in imagining to have been arranged otherwise.

The form and dimensions of the orbits of the planets, for instance, are not determined by any law of nature, but depend upon a particular collocation of matter. The same is the case with respect to the size of the earth, from which the standard of what is called the metrical system has been derived. But these astronomical and terrestrial magnitudes are far inferior in scientific importance to that most fundamental of all standards which forms the base of the molecular system. Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built—the foundation-stones of the material universe—remain unbroken and unworn. They continue this day as they were created—perfect in number and measure and weight; and from the ineffaceable characters impressed on them we may learn that those aspirations after accuracy in measurement, and justice in action, which we reckon among our noblest attributes as men, are ours because they are essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials of which heaven and earth consist.

In 1875 he read before the Chemical Society a paper “On the Dynamical Evidence of the Molecular Constitution of Bodies.”

The lecture on Thermodynamics at the Loan Exhibition of Scientific Apparatus in London in 1876 (to which he had contributed his real-image Stereoscope, etc.), was illustrated by his own model of the Thermodynamic Surface.[220]

The last of his public lectures was the Rede Lecture “On the Telephone,” delivered at Cambridge in 1878, and illustrated with the aid of Mr. Gower’s Telephonic Harp.

After pointing out the extreme simplicity as well as the absolute novelty of the invention, he made it the text of a discourse which is remarkable both for suggestiveness and discursiveness.

I shall ... consider the telephone as a material symbol of the widely separated departments of human knowledge, the cultivation of which has led, by as many converging paths, to the invention of this instrument by Professor Graham Bell.

... In a University we are especially bound to recognise not only the unity of Science itself, but the communion of the workers of Science. We are too apt to suppose that we are congregated here merely to be within reach of certain appliances of study, such as museums and laboratories, libraries and lectures, so that each of us may study what he prefers. I suppose that when the bees crowd round the flowers it is for the sake of the honey that they do so, never thinking that it is the dust which they are carrying from flower to flower which is to render possible a more splendid array of flowers and a busier crowd of bees in the years to come.

We cannot therefore do better than improve the shining hour in helping forward the cross-fertilisation of the Sciences.

One great beauty of Professor Bell's invention is that the instruments at the two ends of the line are precisely alike.... The perfect symmetry of the whole apparatus—the wire in the middle, the two telephones at the ends of the wire, and the two gossips at the ends of the telephones, may be very fascinating to a mere mathematician, but it would not satisfy the evolutionist of the Spenserian type, who would consider anything with both ends alike, such as the Amphisbæna, or Mr. Bright’s terrier, or Mr. Bell’s telephone, to be an organism of a very low type, which must have its functions differentiated before any satisfactory integration can take place.

Accordingly many attempts have been made, by differentiating the function of the transmitter from that of the receiver, to overcome the principal limitation of the power of the telephone. As long as the human voice is the sole motive power of the apparatus, it is manifest that what is heard at one end must be fainter than what is spoken at the other. But if the vibration set up at one end is used no longer as the source of energy, but merely as a means of modulating the strength of a current supplied by a voltaic battery, then there will be no necessary limitation of the intensity of the resulting sound, so that what is whispered to the transmitter may be proclaimed ore rotundo by the receiver.

He then briefly referred to Edison's loud-speaking telephone, and went on to exhibit and explain the microphone of Professor Hughes.

I have said the telephone is an instance of the benefit to be derived from the cross-fertilisation of the sciences. ... Professor Graham Bell ... is the son of a very remarkable man, Alexander Melville Bell, author of a book called Visible Speech, and of other works relating to pronunciation. In fact his whole life has been employed in teaching people to speak. He brought the art to such perfection that, though a Scotchman, he taught himself in six months to speak English, and I regret extremely that when I had the opportunity in Edinburgh I did not take lessons from him.[221] Mr. Melville Bell has made a complete analysis and classification of all the sounds capable of being uttered by the human voice, from the Zulu clicks to coughing and sneezing; and he has embodied his results in a system of symbols, the elements of which are not taken from any existing alphabet, but are founded on the different configurations of the organs of speech.

... Helmholtz, by a series of daring strides, has effected a passage for himself over that untrodden wild between acoustics and music—that Serbonian bog where whole armies of scientific musicians and musical men of science have sunk without filling it up.

We may not be able even yet to plant our feet in his tracks and follow him right across—that would require the seven league boots of the German Colossus; but to help us in Cambridge we have the Board of Musical Studies vindicating for music its ancient place in a liberal education. On the physical side we have Lord Rayleigh laying our foundation deep and strong in his Theory of Sound. On the æsthetic 3side we have the University Musical Society doing the practical work, and, in the space between, those conferences of Mr. Sedley Taylor, where the wail of the Siren draws musician and mathematician together down into the depths of their sensational being, and where the gorgeous hues of the Phoneidoscope are seen to seethe and twine and coil like the

Dragon boughts and elvish emblemings

on the gates of that city, where

An ye heard a music, like enow They are building still, seeing the city is built To music, therefore never built at all And therefore built for ever.

The special educational value of this combined study of music and acoustics is that more than almost any other study it involves a continual appeal to what we must observe for ourselves.

The facts are things which must be felt; they cannot be learned from any description of them.

All this has been said more than 200 years ago by one of our own prophets, William Harvey of Gonville and Caius College:—“For whosoever they be that read authors, and do not, by the aid of their own senses, abstract true representations of the things themselves (comprehended in the author’s expressions) they do not represent true ideas, but deceitful idols and phantasmas; by which means they frame to themselves certaine shadows and chimaeras, and all their theory and contemplation (which they call science) represents nothing but waking men’s dreams and sick men’s phrensies.”

After the opening of the Cavendish Laboratory in 1874, the most continuous, as well as the most important, work of the Chair was the superintendence of various courses of experiments, undertaken by young aspirants for scientific distinction. With characteristic loyalty and humility, Maxwell seems often to have taken more pride in their researches than in his own. To enumerate the men who were thus favoured would be to name many who are now amongst the most efficient teachers of science in the United Kingdom. But there can be nothing invidious in making particular mention of those who are named by Maxwell himself in his correspondence, although the omission of other names may be accidental. Besides Mr. W. Garnett, who was his demonstrator in the Laboratory from first to last, he refers with especial satisfaction to the work of Mr. George Chrystal, now Professor of Mathematics in Edinburgh, and to that of Mr. W. D. Niven.

Mr. Chrystal was encouraged by him to undertake a series of experiments for verifying Ohm’s Law respecting the relation between the current and the electro-motive force in a wire, on which some doubt had been thrown by Weber’s theories, and, in an opposite direction, by a series of experiments reported to the British Association by Dr. Schuster in 1874.

In consequence of these doubts a committee was appointed by the British Association consisting of Professor Maxwell, Professor Everitt, and Dr. Schuster, and the report of this committee was presented to the Association at their annual meeting in Glasgow in 1876. The report consists mainly of an account of two experimental investigations planned by Professor Maxwell and carried out in the Cavendish Laboratory by Mr. Chrystal. To this report Mr. Chrystal added a brief account of his experiments on the unilateral and bilateral deflection of a galvanometer, affording a possible explanation of Dr. Schuster’s result. The investigation proved that when a unit current passes through a conductor of a square centimetre section, its resistance does not differ from its value for indefinitely small currents by 0·000,000,001 per cent.

1873-9.

The scene of these congenial labours was surrounded with manifold associations, which his love for Cambridge intensified. He had pleasant intercourse with many persons there, and after a while resumed the habit of occasional essay writing. Under the name of Erănus (or picnic) a club of older men was formed, differing little apparently from the “Apostles,” except in the greater seriousness of the discussions. Dr. Lightfoot (now Bishop of Durham) and Professors Hort and Westcott were members of this little circle of congenial spirits. Maxwell’s contributions, containing his matured thoughts on various speculative questions, will be found in Chapter XIII. It may be remarked generally that the most marked feature of his later life was an ever-increasing soberness of spirit, and a deepening inward repose, which took nothing from the brightness of his companionship, but rather kept fresh the inexhaustible springs of cheerfulness and humorous mirth in him. The beginnings of such “life in earnest” may be traced far back, but are most obviously perceptible in his third year at Cambridge (1853),[222] in the summer of 1856, after his father’s death, and in the crisis of his life at Aberdeen (1857-8).

This graver tone by no means checked the playful impulses that burst forth from time to time in sparkling jeux d'esprits. It rather fledged his arrows, while it loaded them, giving them a steadier aim, so that his lightest effusions carried an unsuspected weight of meaning. His wit was never more brilliant, more incisive, or (it may be added) more perfectly good-humoured, than in the verses on Professor Cayley’s portrait, and the “Notes of the President’s Address.” He found time also to indulge his old taste for reading and writing in cypher, and thus, on one occasion, considerably disconcerted a contributor to the second column of the Times.

His outward appearance in these later years has been well described by one who saw him first in 1866:—

A man of middle height, with frame strongly knit, and a certain spring and elasticity in his gait; dressed for comfortable ease rather than elegance; a face expressive at once of sagacity and good humour, but overlaid with a deep shade of thoughtfulness; features boldly but pleasingly marked; eyes dark and glowing; hair and beard perfectly black, and forming a strong contrast to the pallor of his complexion.... He might have been taken, by a careless observer, for a country gentleman, or rather, to be more accurate, for a north country laird. A keener eye would have seen, however, that the man must be a student of some sort, and one of more than ordinary intelligence.

In later years his hair had turned to iron gray, but until a few years before his death he retained his elasticity of step.

The picture of Maxwell, as he appeared in 1866, became afterwards perfectly familiar to residents in Cambridge. They will remember his thoughtful face as he walked in the street, revolving some of the many problems that engaged him, Toby lagging behind, till his master would suddenly turn, as if starting from a reverie, and begin calling the dog.

The same authority continues—

... He had a strong sense of humour, and a keen relish for witty or jocose repartee, but rarely betrayed enjoyment by outright laughter. The outward sign and conspicuous manifestation of his enjoyment was a peculiar twinkle and brightness of the eyes. There was, indeed, nothing explosive in his mental composition, and as his mirth was never boisterous, so neither was he fretful or irascible. Of a serenely placid temper, genial and temperate in his enjoyments, and infinitely patient when others would have been vexed or annoyed, he at all times opposed a solid calm of nature to the vicissitudes of life.

In performing his private experiments at the laboratory, Maxwell was very neat-handed and expeditious. When working thus, or when thinking out a problem, he had a habit of whistling, not loudly, but in a half-subdued manner, no particular tune discernible, but a sort of running accompaniment to his inward thoughts.... He could carry the full strength of his mental faculties rapidly from one subject to another, and could pursue his studies under distractions which most students would find intolerable, such as a loud conversation in the room where he was at work. On these occasions he used, in a manner, to take his dog into his confidence, and would say softly, “Tobi, Tobi,” at intervals, and after thinking and working for a time, would at last say (for example), “It must be so: Plato (i.e. Plateau), thou reasonest well.” He would then join in the conversation.

... His acquaintance with the literature of his own country, and especially with English poetry, was remarkable alike for its extent, its exactness, and the wide range of his sympathies. His critical taste, founded as it was on his native sagacity, and a keen appreciation of literary beauty, was so true and discriminating that his judgment was, in such matters, quite as valuable as on mathematical writings. ... As he read with great rapidity, and had a retentive memory, his mind was stored with many a choice fragment which had caught his fancy. He was fond of reading aloud at home from his favourite authors, particularly from Shakspeare, and of repeating such passages as gave him the greatest pleasure.[223]

Maxwell wag rarely seen walking without a dog accompanying him, and, when visiting the Laboratory for a short time, Toby or Coonie, or both, would always attend him. Toby (II. or III.) came to Cambridge with Professor Maxwell in 1871, and was thoroughly conversant with the details of the Laboratory and some of its apparatus. He always betrayed signs of uneasiness when he heard electric sparks, but when summoned to his post he would sit down between his master’s feet and allow the electrophorus to be excited upon his back, growling all the time in a peculiar manner, as though to relieve his mind, but not evidencing any signs of real discomfort. On one occasion Toby sat quietly on an insulating support, and allowed himself to be rubbed with a cat’s skin, when it was found that the dog became positively electrified, contrary to the general belief that a cat’s skin is positive to everything; whereupon Professor Maxwell remarked that “a live dog is better than a dead lion.” It remains for a future physicist to determine the electric relations of a live cat and dog.

One great charm of Maxwell’s society was his readiness to converse on almost any topic with those whom he was accustomed to meet, although he always showed a certain degree of shyness when introduced to strangers. He would never tire of talking with boyish glee about the d——l on two sticks and similar topics, and no one ever conversed with him for five minutes without having some perfectly new ideas set before him; sometimes so startling as to utterly confound the listener, but always such as to well repay a thoughtful examination. Men have often asked, after listening to a conversation on some scientific question, whether Maxwell were in earnest or joking.[224] The charm of his conversation rendered it very difficult to carry on any independent work when he was present, but his suggestions for future work far more than compensated for the time thus spent.

On one occasion, after removing a large amount of calcareous deposit which had accumulated in a curiously oolitic form in a boiler, Maxwell sent it to the Professor of Geology with a request that he would identify the formation. This he did at once, vindicating his science from the aspersion which his brother professor would playfully have cast on it.

Maxwell still found occasional recreation in riding at Cambridge as well as more frequently at Glenlair, where he resided as much as he could consistently with his professional duties.[225] He always arranged to leave Cambridge at the end of the Easter term in time to officiate at the midsummer communion in the kirk at Parton, where he was an elder. His liberality in his own neighbourhood was very great. Besides the endowment of the church, and building of the manse at Corsock, he had planned a large contribution to the cause of primary education. When the School Board was instituted in the district, Maxwell was very anxious to keep up the school established in the reign of George III. at Merkland, in the immediate neighbourhood of the village of Kirkpatrick-Durham, in addition to the Board school at Corsock, five miles away. When this offer was refused, he set apart a site and had plans made for a school to be erected and supported at his own expense upon his estate, but failing health prevented the accomplishment of his purpose.

The last few years of Maxwell’s life were saddened by the serious and protracted illness of Mrs. Maxwell. Notwithstanding the inexhaustible freshness of his spirit, his work could not but be somewhat modified by a cause so grave. He was an excellent sick-nurse, and we have already seen how he attended upon Pomeroy when attacked with fever in college, how he devoted himself to his father during his illness, and how he cared for his brother-in-law when in London. On one occasion during Mrs. Maxwell’s illness he did not sleep in a bed for three weeks, but conducted his lectures and other work at the Laboratory as usual. While attending on his wife he would continue working at his manuscripts, or would arrange a series of experiments to be carried out by one of the workers at the Cavendish Laboratory; but the time which he could personally devote to his own experiments was very limited. The same cause prevented his attendance at meetings in London and at the British Association, for which, however, he retained his affection. His wonderful devotion to his wife, and the almost mystical manner in which he regarded the marriage tie, are sufficiently apparent from his letters.

The meeting of the British Association, held at Belfast in 1874 when Professor Tyndall was President, was the last which Maxwell attended. Before Section A he read a note “On the Application of Kirchhoff’s Rules for Electric Circuits to the Solution of a Geometrical Problem;” but his attendance at this meeting will be remembered chiefly on account of his paraphrase of the President’s address, which was published in Blackwood’s Magazine, and, together with the late Mr. Shilleto’s Greek translation of it, will be found reprinted in Part III. His verses on the Red Lions, a social club consisting of members of the Association, were also written at this meeting.

In university politics Maxwell was regarded as a Conservative, and, as such, in November 1876, he was elected a member of the Council of the Senate of the University. His views respecting various questions of university reform are sufficiently indicated by his letters, especially those addressed to Mr. Monro (see p. 269). He was also a member of the Mathematical Studies and Examinations Syndicate, which was appointed on 17th May 1877, and which sat every week during term for a whole year for the purpose of reorganising the Mathematical Tripos.

In 1873 and 1874 Professor Maxwell was one of the examiners for the Natural Sciences Tripos, and in 1873 he was the first “Additional Examiner” in the Mathematical Tripos under the new regulations which then came into force. This was the fifth time that he had examined in the Mathematical Tripos in the course of seven years. He was president of the Cambridge Philosophical Society during the session 1876-7.[226]

Besides many contributions to Nature and other similar publications during his residence in Cambridge, Maxwell wrote several articles for the Ninth Edition of the Encyclopœdia Britannica. The last scientific paper he ever wrote was the very brief article on Harmonic Analysis, the proof of which was sent for correction when its author was too weak to read it.

Although the publication of the Treatise on Heat and of the Electricity and Magnetism falls within this period, they were mainly written during the time of his retirement at Glenlair. The “small book on a great subject,” entitled Matter and Motion, was merely the concise expression of his most habitual thoughts. But his chief literary work during the last seven years of his life was the editing of the Electrical Researches of the Hon. Henry Cavendish, F.R.S.

Henry Cavendish was son of Lord Charles Cavendish and great uncle to the present Duke of Devonshire. He published only two papers relating to electricity—“An Attempt to Explain some of the Phenomena of Electricity by means of an Elastic Fluid” (Phil. Trans. 1771) and “An Account of some Attempts to Imitate the Effects of the Torpedo by Electricity” (Phil. Trans. 1776). He had prepared, however, some twenty packets of manuscript on Mathematical and Experimental Electricity. These, after his death, were placed by the then Earl of Burlington, now Duke of Devonshire, in the hands of the late Sir William Snow Harris, who appears to have made an abstract of them, with a commentary of great value on their contents. Of this abstract and commentary Professor Maxwell was unable to gain possession, but the Cavendish Manuscripts were placed in his hands by the Duke of Devonshire in 1874. The manner in which the contents of these manuscripts were investigated by Professor Maxwell, and the series of experiments he conducted in order to test Cavendish’s results, will be referred to in Part II. The final proof-sheets were returned to press during the summer of 1879, and the book was published in October of the same year. The letters on this subject, which will be found below, are types of very many that were written by Maxwell respecting the Cavendish papers.

The title of the book as published in October 1879 (one thick volume, 8vo) is An Account of the Electrical Researches of the Honourable Henry Cavendish, F.R.S., between 1771 and 1781. Few or none could have performed that task as he has performed it. And yet some may wish that these precious years had been given rather to the unimpeded prosecution of his own original researches.[227]

At my last meeting with him,—it was in his house at Cambridge, in the year 1877,—in the midst of some discursive talk, he took the MS. of this book out of a cabinet, and began showing it to me and discoursing about it in the old eager, playful, affectionate way, just as with the magic discs in boyhood, or the register of the colour-box observations at a later time, in the little study at Glenlair. “And what,” I said, “of your own investigations in various ways?” “I have to give up so many things,” he answered, with a sad look, which till then I had never seen in his eyes. Even before this, as it now appears, he had felt the first symptoms of the inexorable malady, which in the spring of 1879 assumed a dangerous aspect, and killed him in the autumn of that year.

Letters, 1871 to 1879—ÆT.. 39-48.

From C. J. Monro, Esq.

Hadley, Barnet, 3d March 1871.

The Hon. J. W. Strutt, son of Lord Rayleigh, and senior wrangler in 1865, has been meddling with your colours, and has given occasion also to me to do so again. I send a selection of Natures containing him and me, and my old contributions of last year, which, or one of which, you say met Mr. Benson’s approval. Strutt’s last letter ends with a sentence which obliged me to write to him personally; and I could not help saying, with regard to the sentence which begins it, p. 264, that I thought you would object to inferences founded on comparison by contrast, and that the proper way was to compare by matching recognised browns with a compound.

Listing’s paper, mentioned in p. 102, was to me rather a paradox,—I had got to regard the subdivisions of the colour-scale which are assumed in language, as something so arbitrary. If you cared to see it, I have that number of Poggendorff; I think he would hardly agree with your J. J. Müller. I wish you or Benson could eradicate the insane trick of reasoning about colours as identified by their names. People seem to think that blue is blue, and one blue as good as another. Benson’s book I have seen (since I heard of it from you), but not read. His way of mixing by means of a prism is very happy.... I wish, with your new set up box, you would just put the prism observations into relation with the disk ones. It would be very easy. White we have got; and it would only be strictly necessary to determine two other standard colours, such as vermilion or emerald, by reference to the spectrum primaries. You don’t say whether your dwellers in Mesopotamia and elsewhere agree on the whole better or worse than “J” and “K,” who, I suppose, agree for better and for worse. To judge by their case, the discrepancy would be a little diminished by taking as units of colour co-ordinates for any given pair of eyes, not the intensities of the primaries as they appear in the spectrum, but their intensities as they appear in the combination which to that pair of eyes makes (say) white. This amounts to transforming from trilinear to Hamilton’s anharmonic co-ordinates with white for the fourth point,— in the language of “scientific metaphor.” On the other hand, ought not all your co-ordinates to be cooked by multiplying by ?

You know where I learnt scientific metaphor. I have read the address in Section A more than once with much pleasure, and, I hope, profit in proportion. The pleasure, I confess, was with me, as I found it was with Litchfield, partly that of recognising an old well-remembered style, and reflecting that here at least was something which might be “thought to be beyond the reach of change.”... By the way, Boole is “one of the profoundest mathematicians of our time;” but how about “thinkers”? Certainly his expositions of the principle of a piece of mathematics are beautiful up to and, I don’t doubt, beyond my appreciating. But that last chapter of the Laws, etc., from which you quote, with Empedocles and Pseudo-Origen and the rest of them, always seems to me to render a sound as of a largish internal cavity; and the whole book, taken together with his B.S.E. paper on testimony and least squares, presents, I think, too many instances of a particular class of fallacy—I know I am speaking blasphemies, but there would be a strike among the postmen if I put in all the necessary qualifications—too many instances to be got over, not in absolute number if they were of different kinds, for anybody may make mistakes, but too many of one kind. The kind is insufficient interpretation, i.e. letting your equations lead you by the nose. The most serious example,—I maintain it is an example,—is his insisting that his theory of logic is not founded on quantity, so that it furnishes (he holds) an independent foundation for probabilities, independent of the usual quantitative foundation. That this is a fallacy, and that in particular it is an example of the fallacy of insufficient interpretation, is evident surely when you find that, even in the higher case of “secondary” propositions, the elective symbols represent in his own opinion quantities of “time” after all. With regard to the sentence you quote, I am always suspicious of any inclination I may feel to find a question too easy; and, independently of that, your quoting it is itself a staggerer. But the difficulty I confess does strike me as a rather artificial one. There is nothing, scarcely, in which I think Mill is so right and the Hamiltonians so wrong as that question about logic being the laws of thought. Hamilton says as thought, Mill says as valid, and so does Boole and so do you; but if Mill is right, where is the difficulty? Why should the conditions of thinking correctly he inviolable in the sense of not preventing you from thinking incorrectly, provided they are inviolable in the sense of ensuring that you take the consequences if you do? The laws of projection in geometry are inviolable, but nobody ever thought it a paradox that it is possible for a picture to be out of drawing in spite of them, nor is it a paradox that in unfamiliar classes of cases a rigorously accurate piece of perspective looks out of drawing. Perhaps you meant, for I suppose the report in Nature is incomplete, that it was a difficulty to say in what sense mathematical propositions could be said to be certain, considering that one may make mistakes about them. Perhaps something else, which for the above reason or others, is hidden from me.

... By the way, I hope it is true that you are to profess experimental physics at Cambridge, or what I hope comes to the same thing, that you are a candidate.

To C. J. Monro, Esq.

Glenlair, Dalbeattie, 15th March 1871.

I have been so busy writing a sermon on Colour, and Tyndalising my imagination up to the lecture point, that along with other business I have had no leisure to write to any one.

I think a good deal may be learned from the names of colours, not about colours, of course, but about names; and I think it is remarkable that the rhematic instinct has been so much more active, at least in modern times, on the less refrangible side of primary green (.

I am not up in ancient colours, but my recollection of the interpretations of the lexicographers is of considerable confusion of hues between red and yellow, and rather more discrimination on the blue side. Qu. If this is true, has the red sensation become better developed since those days? Benson has a new book, Chapman & Hall, 1871, called Manual of Colour. I think it is a great improvement on the Quarto, both in size and quality. It is the size of this paper I write on.

I have not asked you if you wish to go to sermon on Colour, for I do not think the P. I.[228] a good place to go to of nights, even for strong men. I have, however, some tickets to spare.

The peculiarity of our space is that of its three dimensions none is before or after another. As is , so is and so is .

If you have 4 dimensions this becomes a puzzle, for—first, if three of them are in our space, then which three? Also, if we lived in space of dimensions, but were only capable of thinking of them, then 1st, Which ? 2d, If so, things would happen requiring the rest to explain them, and so we should either be stultified or made wiser.

I am quite sure that the kind of continuity which has four dimensions all co-equal is not to be discovered by merely generalising Cartesian space equations. (I don’t mean by Cartesian space that which Spinoza worked from Extension the one essential property of matter, and Quiet the best glue to stick bodies together). I think it was Jacob Steiner who considered the final cause of space to be the suggestion of new forms of continuity.

I hope you will continue to trail clouds of glory after you, and tropical air, and be as it were a climate to yourself. I am glad to see you occasionally in Nature. I shall be in London for a few days next week,—address Athenæum Club.

I think Strutt on sky-blue is very good. It settles Clausius’s vesicular theory,

“for, putting all his words together. ’tis 3 blue beans in 1 blue bladder.”—Mat. Prior.

The Exp. Phys. at Cambridge is not built yet, but we are going to try.

The desideratum is to set a Don and a Freshman to observe and register (say) the vibrations of a magnet together, or the Don to turn a winch, and the Freshman to observe and govern him.

From Professor Tyndall.

Monday.

My dear Maxwell—Why ... did you run away so rapidly. I wished to shake your hand before parting.—Yours ever,

John Tyndall.

To Mrs. Maxwell.

20th March 1871.

There are two parties about the professorship. One wants popular lectures, and the other cares more for experimental work. I think there should be a gradation—popular lectures and rough experiments for the masses; real experiments for real students; and laborious experiments for first-rate men like Trotter and Stuart and Strutt.

From C. J. Monro, Esq.

Hadley, 21st March 1871.

... I never observed before that ancient colour-nomenclature was more discriminate than ours for the more “violently” refracted tints as compared with the less; but I think there must be something in it. But I have always suspected that they referred colour to a positively distinct set of co-ordinates from ours. Gladstone says something of this sort in Homer; who put it into his head I can’t think; if he made it out for himself I should be very sorry to agree with a man who does not believe in spectrum analysis, and does believe that Leto is the Virgin Mary. Such queer applications of words of colour one does find. You know the “pale” horse of the Apocalypse (vi. 8); well, that is which is usually “green,” you know. General Daumas says the Arabs call “vert” what the French call “louvet” in horses; and louvet, in Littré, “Se dit, chez le cheval, d’une robe caractérisé par la présence de la nuance jaune et du noir, qui lui donne une certaine ressemblance avec le poil du loup.... Substantivement,” he continues, “Le louvet n’est, à proprement parler, qu’un isabelle charbonné.” The Arabic for green, and (I have no doubt) the word Daumas speaks of, is akhdár, kh as ch in Scotch, and the dot marking a modification which, it happens, is imitated by interpolating an L in Spanish and Portuguese; so may have been supposed to have something to do with the Semitic word. However, according to dictionaries, “the three greens” in Arabic are “gold, wine, and meat,” which beats the green horse. I suppose the Revisionists will leave “pale,” and certainly δέος? is the Homeric for a blue funk. But , and akhdár, too, are certainly the colour of chlorophyll, and Daumas’s remark is a note on a line in a translation from a poet, which runs “Ces chevaux verts comme le roseau qui croit au bord des fleuves.”

I am glad you are going to preach, and I should like to sit under you, but as you assume, it would not do. Thanks all the same.

To Mrs. Maxwell.

Athenæum, 22d March 1871.

I also got a first-rate letter from Monro about colour, and the Arab words for it (I suppose he studied them in Algeria). They call horses of a smutty yellow colour “green.” The “pale” horse in Revelation is generally transcribed green elsewhere, the word being applied to grass, etc. But the three green things in the Arabic dictionary are “gold, wine, and meat,” which is a very hard saying.

From C. J. Monro, Esq.

Hadley, Barnet, 10th September 1871.

... Of your own things, the Classification of Quantities and the Hills and Dales, are all I have read to much purpose. Nor them either, you may say, if I go on to ask why you say that “in the pure theory of surfaces there is no method of determining a line of water-shed or water-course, except as therein is excepted, that is in page 6? Why does not this determine them? to wit— Or if this does determine them, how does it resolve itself into “first finding,” etc.?

I am glad you like Strutt on sky-blue. You see he sees his way now to a new theory of double refraction. Looking at your old letter again, I don’t quite see the force of either of your objections to space of more than three dimensions. First, you ask if we can think some of the dimensions and not others, then which? Surely one might answer, that depends—depends namely on your circumstances—on circumstances which in your circumstances you cannot expect to judge of.

“I can easily believe,” as Darwin would say, that before we were tidal ascidians we were a slimy sheet of cells floating on the surface of the sea. Well, in those days, the missing dimension, and the two forthcoming ones respectively, kept changing with the rotation of the earth,—we now know how, but could not guess then. So, now, the missing dimension or dimensions, if any, might be determined by circumstances which we could not tell unless we knew all about the said dimension or dimensions.

To Professor Lewis Campbell.

Glenlair, Dalbeattie, 19th October 1872.

... Lectures begin 24th. Laboratory rising, I hear, but I have no place to erect my chair, but move about like the cuckoo, depositing my notions in the chemical lecture-room 1st term; in the Botanical in Lent, and in Comparative Anatomy in Easter.

I am continually engaged in stirring up the Clarendon Press, but they have been tolerably regular for two months. I find nine sheets in thirteen weeks is their average. Tait gives me great help in detecting absurdities. I am getting converted to Quaternions, and have put some in my book, in a heretical form, however, for as the Greek alphabet was used up, I have used German capitals from to to stand for Vectors, and, of course, occurs continually. This letter is called “Nabla,”[229] and the investigation a Nablody. You will be glad to hear that the theory of gases is being experimented on by Profs. Loschmidt and Stefan of Vienna, and that the conductivity of air and hydrogen are within 2 per cent of the value calculated from my experiments on friction of gases, though the diffusion of one gas into another is “in erglanzender ubereinstimmung mit schen Theorie.”

To Professor W. G. Adams.

Natural Science Tripos, 3d December 1873.

I got Professor Guthrie’s circular some time ago. I do not approve of the plan of a physical society considered as an instrument for the improvement of natural knowledge. If it is to publish papers on physical subjects which would not find their place in the transactions of existing societies, or in scientific journals, I think the progress towards dissolution will be very rapid. But if there is sufficient liveliness and leisure among persons interested in experiments to maintain a series of stated meetings to show experiments, and talk about them as some of the Ray Club do here, then I wish them all joy; only the manners and customs of London, and the distances at which people live from any convenient centre, are very much against the vitality of such sociability.

To make the meeting a dinner supplies that solid ground to which the formers of societies must trust if they would build for aye. A dinner has the advantage over mere scientific communications, that it can always be had when certain conditions are satisfied, and that no one can doubt its existence. On the other hand, it completely excludes any scientific matter which cannot be expressed in the form of conversation with your two chance neighbours, or else by a formal speech on your legs; and during its whole continuance it reduces the Society to the form of a closed curve, the elements of which are incapable of changing their relative position.

For the evolution of science by societies the main requisite is the perfect freedom of communication between each member and any one of the others who may act as a reagent.

The gaseous condition is exemplified in the soiree, where the members rush about confusedly, and the only communication is during a collision, which in some instances may be prolonged by button-holing.

The opposite condition, the crystalline, is shown in the lecture, where the members sit in rows, while science flows in an uninterrupted stream from a source which we take as the origin. This is radiation of science.

Conduction takes place along the series of members seated round a dinner table, and fixed there for several hours, with flowers in the middle to prevent any cross currents.

The condition most favourable to life is an intermediate plastic or colloidal condition, where the order of business is (1) Greetings and confused talk; (2) A short communication from one who has something to say and to show; (3) Remarks on the communication addressed to the Chair, introducing matters irrelevant to the communication but interesting to the members; (4) This lets each member see who is interested in his special hobby, and who is likely to help him; and’ leads to (5) Confused conversation and examination of objects on the table.

I have not indicated how this programme is to be combined with eating. It is more easily carried out in a small town than in London, and more easily in Faraday’s young days (see his life by B. Jones) than now. It might answer in some London district where there happen to be several clubbable senior men who could attract the juniors from a distance.

To Professor Lewis Campbell.

Glenlair, Dalbeattie, 3d April 1873.

The roof of the Devonshire Laboratory is being put on, and we hope to have some floors in by May, and the contractors cleared out by October. We are busy electing School Boards here. The religious difficulty is unknown here. The chief party is that which insists on keeping down the rates; no other platform will do. All candidates must show the retrenchment ticket.

The Cambridge Philosophical Society have been entertained by Mr. Paley on Solar Myths, Odusseus as the Setting Sun, etc. Your Trachiniæ is rather in that style, but I think Middlemarch is not a mere unconscious myth, as the Odyssey was to its author, but an elaborately conscious one, in which all the characters are intended to be astronomical or meteorological.

Rosamond is evidently the Dawn. By her fascinations she draws up into her embrace the rising sun, represented as the Healer from one point of view, and the Opener of Mysteries from another; his name, Lyd Gate, being compounded of two nouns, both of which signify something which opens, as the eye-lids of the morn, and the gates of day. But as the sun-god ascends, the same clouds which emblazoned his rising, absorb all his beams, and put a stop to the early promise of enlightenment, so that he, the ascending sun, disappears from the heavens. But the Rosa Munda of the dawn (see Vision of Sin) reappears as the Rosa Mundi in the evening, along with her daughters and , in the chariot of the setting sun, who is also a healer, but not an enlightener.

Dorothea, on the other hand, the goddess of gifts, represents the other half of the revolution. She is at first attracted by and united to the fading glories of the days that are no more, but after passing, as the title of the last book expressly tells us, “from sunset to sunrise,” we find her in union with the pioneer of the coming age, the editor.

Her sister Celia, the Hollow One, represents the vault of the midnight sky, and the nothingness of things.

There is no need to refer to Nicolas Bulstrode, who evidently represents the Mithraic mystery, or to the kindly family of Garth, representing the work of nature under the rays of the sun, or to the various clergymen and doctors, who are all planets. The whole thing is, and is intended to be, a solar myth from beginning to end.

To Mrs. Maxwell.

December 1873.

I am always with you in spirit, but there is One who is nearer to you and to me than we ever can be to each other, and it is only through Him and in Him that we can ever really get to know each other. Let us try to realise the great mystery in Ephesians V., and then we shall be in our right position with respect to the world outside, the men and women whom Christ came to save from their sins.

To Professor Lewis Campbell.

11 Scroope Terrace, Cambridge, 26th February 1874.

Jackson has sent me a MS. of yours about the mechanism of the heavens.[230] After the interpretation of είλλομένην, about which Greek appears to meet Greek as to whether it expresses motion or only configuration, the main point seems to be, What is the motion and function of τὸν διὰ παντὸς πόλον?

() Is it in one piece with the sphere of the stars? or () with that of the sun or () is it fixed in the earth?

It is evidently a good stout axle, not a mere geometrical line, and it has some stiff work to do.

What is this work?

If the earth is fixed, and the great shafts has its bearings in a hole in the earth, then she (the earth) may, in virtue of her dignity and office, cause the axle to revolve, carrying with it the stars according to , or the sun according to . Thus the earth may be the cause of the motion of the Same without moving herself, as a spinster is the cause of the whirling of the spindle, though she does not herself pirouette.

Or we may suppose the earth to act as one who twirls an expanded umbrella over his head about its stick as an axis, the holes in the same representing the stars. The objection to this view (which seems to me to be Jowett’s) is that in stating the relation between the earth and the axis, the earth is said to be related to the axis (packed or whirling as the case may be), and not the axis to the earth. Now, I suppose that without all contradiction the less is related to the better. Here the earth is like a ball of clay packed round a graft on the branch of a tree, rather than like a field in which, by means of a rotatory boring tool, men bore for water.

But the business of the earth is not so much to keep the stars in motion as to effect the changes of night and day. This she may do either by rotating herself from W. to E., or by controlling the motion of the sun, by the help of the great shaft.

Now, if you always observe at the same time of night (a common practice), you find the eastern stars higher every day, and the western lower. All have the same motion, which carries them round from E. to W. in a year.

Mars, Jupiter, and Saturn, in spite of their wanderings go on the whole in the same direction, but slower. Venus and Mercury oscillate about the sun, and the moon goes the opposite way—from W. to E.

That this way of viewing the matter was really prevalent at one time is plain, from the expression the rising of such a star to denote not a time of night but a time of year. It means either (1) the day when the star rises, just before it is lost in the brightness of the sun who follows it, or (2) the day when the star is rising, when it just becomes visible after sunset.

Virgil, who speaks of stars rising, evidently had no practical knowledge of what he meant. Plato, if he sometimes gets hazy, is far clearer than Virgil. Grote would place him far below Mr. Jellinger Symons, who denied the rotation of the moon, because Grote makes Plato say that both the heavens and the earth rotate both in the same direction, and with the same angular velocity.

I think I understand you to make Plato make the earth sit still and preside over the heavenly motions, and so become the artificer of day and night, like a policeman who swings his bull’s-eye round to his back. But his words are capable of being used by the movers of the earth, as Milton says,

If earth, industrious of herself, fetch day Travelling east.

I hope you will let me know whether I have not misunderstood both you, Plato, and the Truth. I have never thanked you for your Œdipus, etc., which I have enjoyed. But at present I am all day at the Laboratory, which is emerging from chaos, but is not yet cleared of gas-men, who are the laziest and most permanent of all the gods who have been hatched under heaven.[231]

Mrs. Maxwell joins me in kind regards to Mrs. Campbell and yourself.—Your afft. friend.

To W. Garnett, Esq.

Glenlair, 8th July 1874.

... In the MS. he [Cavendish] appears to be familiar with the theory of divided currents, and also of conductors in series, but some reference to his printed paper [on the Torpedo] is required to throw light on what he says. He made a most extensive series of experiments on the conductivity of saline solutions in tubes compared with wires of different metals, and it seems as if more marks were wanted for him if he cut out G. S. Ohm long before constant currents were invented. His measurements of capacity will give us some work at the Cavendish Lab., before we work up to the point where he left it. His only defect is not having Thomson’s electrometer. He found out inductive capacity of glass, resin, wax, etc.

To Professor Lewis Campbell.

Glenlair, Dalbeattie, 26th September 1874.

Æt. 43.

Yours of the 29th instant is to hand. Whether your devotion to Michael Angelo has urged you to anticipate his day, or whether Time gallops with those who sit to view Necessity, with her weary pund o’ tow massed round her rock, being all the remains of the stane o’ lint with which she was originally endowed, those who may be set to construe this sentence will be apt to lose much time.

With regard to atoms, I am preparing a hash of them for Baynes of the Britannica. The easiest way of showing what atoms can’t do is to get some sort of notion of what they can do. If atoms are finite in number, each of them being of a certain weight, then it becomes impossible that the germ from which a man is developed should contain (actually, of course, not potentially, for potentiality is nonsense in materialism unless it is expressed as configuration and motion) gemmules of everything which the man is to inherit, and by which he is differentiated from other animals and men,—his father’s temper, his mother’s memory, his grand-father’s way of blowing his nose, his arboreal ancestor’s arrangement of hair on his arms, and his more remote littoral ancestor’s devotion to the tide-swaying moon. Francis Galton, whose mission it seems to be to ride other men’s hobbies to death, has invented the felicitous expression “structureless germs.” Now, if a germ, or anything else, contains in itself a power of development into some distinct thing, and if this power is purely physical, arising from the configuration and motion of parts of the germ, it is nonsense to call it structureless because the microscope does not show the structure; the germ of a rat must contain more separable parts and organs than there are drops in the sea. But if we are sure that there are not more than a few million molecules in it, each molecule being composed of component molecules, identical with those of carbon, oxygen, nitrogen, hydrogen, etc., there is no room left for the sort of structure which is required for pangenesis on purely physical principles. Again, suppose that a great many individual atoms take part in a disturbance in my brain, to whom does this signify anything? As for the atoms, they have been in far worse rows before they became naturalised in my brain, but they forget the days before, etc.[232] At any rate the atoms are a very tough lot, and can stand a great deal of knocking about, and it is strange to find a number of them combining to form a man of feeling.

In your letter you apply the word imponderable to a molecule. Don’t do that again. It may also be worth knowing that the æther cannot be molecular. If it were, it would be a gas, and a pint of it would have the same properties as regards heat, etc., as a pint of air, except that it would not be so heavy.

Under what form (right or light) can an atom be imagined? Bezonian! speak or die! Now I must go to post with two dogs in the rain.—Your afft. friend.

To the Same.

11 Scroope Terrace, Cambridge, 4th March 1876.

Æt. 44.

Aias arrived here about a week ago. I read him with pleasure. He recalled the year 1851, when I got him up. The outline of the play seems very bare and unpromising compared with some others, but this is relieved by other features which are not in the “argument,” as e.g. the loyalty of the chorus and of Tecmessa to Aias under all circumstances (for the chorus in general veers about, and backs occasionally, according as the wind blows or the cat jumps).

This contrasts favourably with the character of Athena, who is but so, only not so comic as the Atreidæ.

But why do Ulysses and Aias not name each other in the same language? I suppose the last syllable of Odysseus, pronounced Anglicé, is somewhat unpleasant in verse, and Ajax, though familiarised by Pope, has lost the interjectional sound of your hero’s name.

Two Aberdonians, Chrystal and Mollison, are working at the Cavendish Laboratory. I think Chrystal’s work is of a kind not comparable with that done in “a third-class German university,” which was the charitable hope of Nature as to what we might aspire to in ten years' time. He has worked steadily at the testing of Ohm's Law since October, and Ohm has come out triumphant, though in some experiments the wire was kept bright red-hot by the current.—Your afft. friend.

From the Right Rev. C. J. Ellicott, D.D., Lord Bishop of Gloucester and Bristol.

Palace, Gloucester, 21st Nov. 1876.

My dear Sir—Will you kindly pardon a great liberty? I have quoted in a forthcoming charge a remarkable expression of yours that atoms are “manufactured articles.” Could you in your kindness give me the proper title and reference to the paper and the page? I am now, alas, far from libraries, and have, in matters scientific especially, to ask the aid of others. Will you excuse me asking this further question?

Are you, as a scientific man, able to accept the statement that is often made on the theological side, viz. that the creation of the sun posterior to fight involves no serious difficulty,—the creation of light being the establishment of the primal vibrations, generally; the creation of the sun, the primal formation of an origin, whence vibrations would be propagated earthward?

My own mind,—far from a scientific one,—is not clear on this point. I surmise, then, that the scientific mind might not only not be clear as to the explanation, but equitably bound to say that it was no explanation at all. Excuse the trouble I am giving you, for the truth’s sake, and believe me, very faithfully yours,

C. J. Gloucester and Bristol.

Maxwell replied as follows by return of post:—

11 Scroope Terrace, Cambridge, Nov. 1876.

My Lord Bishop—The comparison of atoms or of molecules to “manufactured articles,” was originally made by Sir J. F. D. Herschel in his “Preliminary Discourse on the Study of Natural Philosophy,” Art. 28, p. 38 (ed. 1851, Longmans).

I send you by book post several papers in which I have directed attention to certain kinds of equality among all molecules of the same substance, and to the bearing of this fact on speculations as to their origin.

The comparison to “manufactured articles” was criticised (I think in a letter to Nature) by Mr. C. J. Monro [Nature, X. 481, 15th October 1874], and the latter part of the Encyc. Brit., Article “Atom,” is intended to meet this criticism, which points out that in some cases the uniformity among manufactured articles is evidence of want of power in the manufacturer to adapt each article to its special use.

What I thought of was not so much that uniformity of result which is due to uniformity in the process of formation, as a uniformity intended and accomplished by the same wisdom and power of which uniformity, accuracy, symmetry, consistency, and continuity of plan are as important attributes as the contrivance of the special utility of each individual thing.

With respect to your second question, there is a statement printed in most commentaries that the fact of light being created before the sun is in striking agreement with the last results of science (I quote from memory).

I have often wished to ascertain the date of the original appearance of this statement, as this would be the only way of finding what “last result of science” it referred to. It is certainly older than the time when any notions of the undulatory theory became prevalent among men of science or commentators.

If it were necessary to provide an interpretation of the text in accordance with the science of 1876 (which may not agree with that of 1896), it would be very tempting to say that the light of the first day means the all-embracing æther, the vehicle of radiation, and not actual light, whether from the sun or from any other source. But I cannot suppose that this was the very idea meant to be conveyed by the original author of the book to those for whom he was writing. He tells us of a previous darkness. Both light and darkness imply a being who can see if there is light, but not if it is dark, and the words are always understood so. That light and darkness are terms relative to the creature only is recognised in Ps. CXXXIX. 12.

As a mere matter of conjectural cosmogony, however, we naturally suppose those things most primeval which we find least subject to change.

Now the æther or material substance which fills all the interspace between world and world, without a gap or flaw of anywhere, and which probably penetrates through all grosser matters, is the largest, most uniform and apparently most permanent object we know, and we are therefore inclined to suppose that it existed before the formation of the systems of gross matter which now exist within it, just as we suppose the sea older than the individual fishes in it.

But I should be very sorry if an interpretation founded on almost conjectural scientific hypothesis were to get fastened to the text in Genesis, even if by so doing it got rid of the old statement of the commentators which has long ceased to be intelligible. The rate of change of scientific hypothesis is naturally much more rapid than that of Biblical interpretations, so that if an interpretation is founded on such an hypothesis, it may help to keep the hypothesis above ground long after it ought to be buried and forgotten.

At the same time I think that each individual man should do all he can to impress his own mind with the extent, the order, and the unity of the universe, and should carry these ideas with him as he reads such passages as the 1st Chap, of the Ep. to Colossians (see Lightfoot on Colossians, p. 182), just as enlarged conceptions of the extent and unity of the world of life may be of service to us in reading Psalm viii.; Heb. II. 6, etc. Believe me, yours faithfully,

J. Clerk Maxwell.

From the Bishop of Gloucester and Bristol.

Palace, Gloucester, 24th Nov. 1876.

Dear Professor Clerk Maxwell—Allow me not to lose a post in thanking you most warmly for your most kind letter and for the packet of pamphlets,—for which I hardly know how enough to express my gratitude. They are exactly what I needed,—yet I fear I may be taking from your stock more than I ought to take. I have already read a good deal of the Encyc. Brit. article on atoms; so pray, if you are short of copies, don’t hesitate to drop me a line. The paper on attraction was also most welcome. I am ashamed to own (for bishops should not enter into these pleasures) that I have of late been speculating a good deal on the physical explanation of gravitation. I seem to feel it must be in the Ether,—and yet how, I see not. In the case of a body near the earth, I can conceive a vast amount of elastic ether behind it, and possibly urging it on, while a small quantity is under it, being excluded by the earth.

I seem also to see how this might be applied to the case of the heavy bodies that fell nearer to the steep side of Schehallion than they ought to have done by calculation; but then, when I attempt to go farther, I find the theory break down.

It seems to me that we want for several things, e.g. light, the conception of an ether-beach all round the visible universe from which waves might be reflexively started, and at which the particles might be more closely packed; but then again I see not what it is that keeps up the beach.

But I am really ashamed of troubling you, a scientific man, with such wanderings. It will only show that your kindness is thoroughly appreciated.

I cordially agree with you as to the light question. Theologians are a great deal too fond of using up the last scientific hypothesis they can get hold of. The Christian Knowledge Society are publishing my charge. When it is published I shall ask you to do me the favour to accept a copy. You will then see that the best note in the little volume is due to your kindness and aid. I remain, with all good wishes, and sincere thanks, very faithfully yours,

C. J. Gloucester and Bristol.

(P.S.)—If you are in London in the spring and near the Athenæum, do me the kindness of looking in on me, as I shall be very glad to make your personal acquaintance. I am commonly in town regularly after Easter.

To Professor Lewis Campbell.

Glenlair, Dalbeattie, Christmas 1876.

Æt. 45.

... I hope that when this severe weather is past you will be able to derive benefit from a moderate use of Plato and Sophocles.

We intended to have gone round by Edinburgh, to pay Aunt Jane a visit; but we both had such bad colds that we came home to nurse them, and are now snowed up, and enjoying the artificial heat of coals, peats, and sticks judiciously intermingled.

The demonstrator at the Cavendish Laboratory has been out of sorts all this term, and has had to go home about a month ago, so we have not been in full force there. I hope he will be well in February, to absorb the energy of the new B.A.’s set free from the Tripos and its attendant anxieties.

As we get richer in apparatus, mathematical lectures give way to experimental, and the black board to the lamp and scale. I have had a pupil quite innocent of mathematics who has learned to measure focal lengths of lenses, and has found the electro-motive force from the water-pipes to the gas-pipes, and from either set of pipes to the lightning-conductor.

I have been making a mechanical model of an induction coil, in which the primary and secondary currents are represented by the motion of wheels, and in which I can symbolise all the effects of putting in more or less of the iron core, or more or less resistance and Leyden jars in either circuit.

I have also been making a clay model of Prof. W. Gibb’s thermodynamic surface, representing the relations of the solid liquid and gaseous states, and the different paths by which a body may get from the one to the other.—Your afft. friend,

J. Clerk Maxwell.

To W. Garnett, Esq.[233]

Glenlair, 4th January 1877.

By all means take the Groves and coils for your lecture. Are you aware that the electric flash is entirely due to the resinous particles of electricity? This is well known on the stage, where they blow the particles through a tube over a candle to make stage lightning. The vitreous electricity has nothing to do with it, as you may prove by using pounded glass.

In a letter to Mr. Garnett, dated Glenlair, 9th July 1877, Professor Maxwell gave the following suggestions respecting a projected article on Dynamics, and the letter, like those which follow it, is a good illustration of the help he was constantly rendering to his students and others who asked his advice:—

I think it a pity that the old historical word Dynamics should, for mere considerations of time, be split up into Kinematics, Kinetics, and Statics. With respect to the divisions of the subject, I think they fall thus:—

1. Early attempts at founding the science, ancient Kinematics (mechanical description of curves, etc.) generally correct.

Ancient Statics.—Archimedes.

Modern Dynamics.—Galileo, first founder. Descartes, good up to Kinematics and Statics, failed in Kinetics.

Promoters—

Wren, Wallis, Huygens, Hooke.

Laws of collision established, and motion in a circle.

Newton.

Three laws of motion. Form suggested by the laws of Descartes. Meaning established by Newton’s own copious and complete examples of using them.

Second statement of Newton’s third Law.

My notions on the three laws are in “Matter and Motion.”

Newtonians.

Cambridge School. Popularisers. Scotch School.

Roger Cotes. D. Gregory. Colin Maclaurin.[234]

Robert Smith, etc. Desaguliers. James Gregory.

Attwood. Mme. du Chatelet J. Playfair.

Whewell. and Voltaire. Ivory.

Leibniz and the Vis Viva Controversy.

Methods of dealing with connected systems.

Example of correct methods by Newton and others before D’Alembert.

D’Alembert’s enunciation.—Its historical importance.

Euler. The Bernoullis, etc. Laplace, the flower of this stage of development.

Lagrange and Virtual Velocity.

This is the germ of the method of energy which was fully developed in mathematical form in the Mecanique Analytique, but very little appreciated outside the inner circle of mathematicians till the physical theory of energy became generally known.

Mathematical development of higher dynamics. (See Cayley’s Brit. Ass. Report, 1857 and 1862? specially Hamilton and Jacobi.)

Effect of T and T' since 1867. Kirchoffs notions in beginning of Vorlesungen (not equal to Lagrange, but worth noticing).

I also think that Clausius’ equation and definition of “Virial” is important.

The dynamics of other varieties of space than our own requires very brief notice indeed.—Yours truly,

J. Clerk Maxwell.

To W. Garnett, Esq.

Glenlair, Dalbeattie, 24th July 1877.

... There is a great slur over the word mechanics since a few poets and biologists have misused it. Pratt thought it a fine word.

The result of motion without reference to time I call Displacement. Kinematics must involve the idea of time if it treats of continuous displacements, velocities, and accelerations, though it does not contain within itself materials for comparing different intervals of time. For this we must go to the science which deals with matter; call it Kinetics, Dynamics, or Mechanics.

But I consider that Statics also deserves a place on the same level as Kinematics, as it deals with the equivalence of different systems of forces. But I do not agree with Whewell that Statics is more elementary than Kinematics....

To the Same.

Glenlair, 11th August 1877.

Your experiments on electrified paraffin oil are excellent, and may lead to increase of knowledge.

If the fluid dielectric and also the air are perfect insulators, nothing can get electrified, but the equation at the surface, instead of being . will be (excluding capillary action) where is the resultant electric force normal to the surface and just outside it. This causes the surface to rise wherever the normal force is great, or close to the electrodes.

The science of displacements is in Euc. I. 4, etc., and wherever one figure is placed upon another. It belongs to the method of contemplating the relations of two figures which may be supposed to co-exist, though we may also suppose that they are copies of the same figure in different positions.

But just as we assume that distance is a continuous quantity capable of measurement, though all our attempts at measurement are made with instruments made of non-rigid and discontinuous matter, so we may assume that time is a continuously flowing quantity capable of measurement, though we have not yet found out any accurate method of comparing distant intervals of time.

Now Kinematics requires no more than this notion of time, as the common independent variable . If we suppose that is that (unknown) which flows uniformly, then for kinematical purposes it is enough that is a function of ; but when we come to Kinetics proper we must have very small.

Have you read Julius in Nature, about the beginning of June? [14th June].

The most constant things we know are the properties of bodies. For instance, water in equilibrium with ice and vapour gives us a good deal.

I. A unit of density (not the orthodox one) .

II. A unit of pressure (too small for practical use) .

III. A unit of time (namely, the time of revolution of a satellite just grazing a sphere of water) =.

These three quantities being independent of each other give , and .

gives a which could also be got from the of the vapour (a different one).

Then this gives also a standard temperature; all that we want is to get pure water.

To the Same.

Glenlair, 23d August 1877.

I have been copying Cavendish on the resistance of electrolytes. If there is any one who would try a few of them roughly in the U tube, it might be interesting to compare with Cavendish’s results. For weak solutions Kohlrausch may be referred to.

Sea Salt (Chloride of Sodium.)

Experiments in January 1781.

Watered to 1 of Salt. Resistance. Resistance quantity of Salt.

Saturated sol.

12

30

70

143

1000

20,000

Salt in 20,000 conducts about 7 times better than distilled water.

Salt in 69 of water conducts 1·97 times better at than at .

If Professor Liveing is in Cambridge, could you ask him to put me in the way of finding the best book on chemistry for the year 1777, so as to obtain the equivalents and the names of salts used by Cavendish?

The numbers in the first columns are the quantities which were equivalent to the “acid” in solution of 1 of salt in 29 of water. Sal Sylvii (potassium chloride). Sal Amm. (ammonium chloride). Calc. S.S.A. (?) Calcined Glauber's Salt (sodium sulphate). Quadrangular Nitre (sodium nitrate). Salt D. (?)

The solutions were 3, 10, 12.

I am going to try if this is Troy or Apothecaries’ weight.

Saturated solution (1 in 3·78) of common salt has 437,000 the resistance of iron wire. New distilled water has more resistance than distilled water kept a year.

All these results and many more were got by comparison of the strength of shocks taken through Cavendish’s body. I think this series of experiments is the most wonderful of them all, and well worth verification.

Cavendish is the first verifier of Ohm’s Law, for he finds by successive series of experiments that the resistance is as the following power of the velocity, 1·08, 1·03, ·980, and concludes that it is as the first power. All this by the physiological galvanometer.

... Can you solve the equation

is a solution. Find the general ditto.

To Professor Lewis Campbell.

11 Scroope Terrace, Cambridge, 5th January 1878.

Æt. 46.

It is more than a month that I have had your letter lying by me. I am glad you like Chrystal. His departure is a great loss to the laboratory, as it is difficult to find any one to take up heavy work. W. D. Niven (brother of the competitor) is going in for a heavy piece of work on conduction of heat in gases. I am no judge of Greek plays, but I think that your success in choruses is fully equal to that in dialogue, considering the greater difficulty, not only in the interpretation, but in guessing the kind of effect, musical, rhythmical, rhetorical, poetical, and pictorial, which was aimed at in the delivery of the chorus.

We have all been conversing on the telephone. Garnett recognised the voice of a man who called by chance. But the phonograph will preserve to posterity the voices of our best speakers and singers. See Nature of Jan. 3d.

To W. Garnett, Esq.

Glenlair, 20th September 1878.

... Cavendish would speak of the pressure of a voltaic battery (only he hadn’t one), but we require to be educated up to his mark.

To the Librarian of the Royal Society.

Glenlair, Dalbeattie, 23d June 1879.

Dear Sir—Your information about FF.R.S. has been so useful to me that I now ask about Dr. G. Knight, F.R.S., librarian to the British Museum.

(1.) Is his name Gowan, Gowen, Gowin, or Godwin, for I find all four spellings current?

(2.) Who is the author of the paper in Phil. Trans. for 1776 (near the end of the vol.) describing his great magazines of magnets?

(3.) Are the magazines [sketch shown] mounted like great guns still in the possession of the R.S.?

(4.) Is the portrait of Gowin Knight, by Benjamin Wilson, F.R.S., among the pictures of the R.S.?

I have got from the Meteorological Office some Cavendish MSS. on Magnetism which prompt these enquiries and also this—

When the R.S. was at Crane Court had it a garden adjoining? Also, where was Crane Court?

Henry Cavendish and his father Lord Charles worked together at observations of the variation compass and dipping needle in the R.S. room and garden. Are the variation compass and dipping needle still in the R.S. collection?

Cavendish wrote out directions for using the dipping needle for Captain Pickersgill, Captain Bayley, Dalrymple.

Notes in this chapter

Note 1 · On 23d February, Professor Stokes (who had been urgent in pressing Maxwell to stand) wrote to him:—“I am glad you have decided to come forwaNote 2 · Throughout the tenure of his Cambridge Chair Maxwell annually delivered a course of lectures on Heat and the Constitution of Bodies during tNote 3 · Professor Westcott’s utterance on the same occasion, though less immediately relevant, ought not to be omitted:—“It was impossible to think Note 4 · See Part II. In the official handbook to the collection, the articles entitled “General considerations respecting Scientific Apparatus” and Note 5 · Maxwell had profited not a little by his own studies in this direction. But the Gallowegian tones are hard to modify, and even in his verse Note 6 · How readily his thoughts took a serious turn, even in the earlier undergraduate days, may be seen in a letter (not given above) of 26th MarcNote 7 · There was found amongst his papers a scrap on which he had written, in pencil, the whole of Shelley’s “Ode to the West Wind,” in all probabiNote 8 · For an instance of tumorous mystification, see the letter to Mr. Garnett of 4th January 1877.Note 9 · He kept up the old habit of regulating the clocks at Glenlair by the sun, which, when on the meridian, threw the shadow of a stick upon a noNote 10 · An account of the last years of Maxwell’s life would not be complete without a reference to his acquaintance with Professor H. A. Rowland, fNote 11 · An unfinished fragment of a new work on Electricity, in which he treads more closely than ever in the steps of Faraday, has been edited sincNote 12 · Royal Institution.Note 13 · The name of an Assyrian harp of the shape .Note 14 · See the Cambridge Journal of Philology, vol. V., No. 10, pp. 206, foll.Note 15 · Alluding to the passage of Plato’s Timœus, p. 40, which had given rise to the previous discussion.Note 16 · Tennyson’s In Memoriam.Note 17 · See p. 370.Note 18 · Introduces etc. See Maclaurin’s Fluxions.
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