Professor WILLIAM THOMSONProfessor WILLIAM THOMSON, 1846
Professor WILLIAM THOMSON, 1846
The subject chosen had reference no doubt to thepapers on the theory of heat which Mr. Thomson had already published. The thesis was presented to the Faculty on the day appointed, and approved, and Mr. Thomson having produced a certificate of his having taken the oaths to government, and promised to subscribe the formula of the Church of Scotland as required by law, on the first convenient opportunity, "the following oath was then administered to him, which he took and subscribed:Ego, Gulielmus Thomson, B.A., physicus professor in hac Academia designatus, promitto sancteque polliceor me in munere mihi demandato studiose fideliterque versaturum." Professor Thomson was then "solemnly admitted and received by all the Members present, and took his seat as a Member of Faculty."
No translation of this essay was ever published, but its substance was contained in various papers which appeared later. The following reference to it is made in an introduction attached to Article XI of hisMathematical and Physical Papers(vol. i, 1882).
"An application to Terrestrial Temperature, of the principle set forth in the first part of this paper relating to the age of thermal distributions, was made the subject of the author's Inaugural Dissertation on the occasion of his induction to the professorship of Natural Philosophy in the University of Glasgow, in October 1846, 'De Motu Caloris per Terræ Corpus'11: which, more fully developed afterwards, gave a very decisive limitation to the possible age of the earth as a habitation for living creatures; and proved the untenability of the enormous claims for TIME which, uncurbedby physical science, geologists and biologists had begun to make and to regard as unchallengeable. See 'Secular Cooling of the Earth, Geological Time,' and several other Articles below." Some statement of the argument for this limitation will be given later. [See Chap.XIV.]
Thomson thus entered at the age of twenty-five on what was to be his life work as a teacher, investigator, and inventor. For he continued in office fifty-three years, so that the united tenures of his predecessor and himself amounted to only four years less than a century! He took up his duties at the opening of the college session in November, and promptly called the attention of the Faculty to the deficiencies of the equipment of apparatus, which had been allowed to fall behind the times, and required to have added to it many new instruments. A committee was appointed to consider the question and report, and as a result of the representations of this committee a sum of £100 was placed at Professor Thomson's disposal to supply his most pressing needs. In the following years repeated applications for further grants were made and various sums were voted—not amounting to more than £500 or £600 in all—which were apparently regarded as (and no doubt were, considering the times and the funds at the disposal of the Faculty) a liberal provision for the teaching of physical science. A minute of the Faculty, of date Nov. 26, 1847, is interesting.
After "emphatically deprecating" all idea that such large annual expenditure for any one department was to be regularly contemplated, the committee refer in their report to the "inadequate condition of the department in question," and express their satisfaction "with the reasonable manner in which the Professor of NaturalPhilosophy has on all occasions readily modified his demands in accordance with the economical suggestions of the committee." They conclude by saying that they "view his ardour and anxiety in the prosecution of his profession with the greatest pleasure," and "heartily concur in those anticipations of his future celebrity which Monsr. Serville,12the French mathematician, has recently thought fit to publish to the scientific world."
Again, in April 1852, the Faculty agree to pay a sum of £137 6s.1½d.as the price of purchases of philosophical apparatus already made, and approve of a suggestion of the committee that the expenditure on this behalf during the next year should not exceed £50, and "they desire that the purchases shall be made so far as is possible with the previously obtained concurrence of the committee." It is easy to imagine that the ardent young Professor of Natural Philosophy found the leisurely methods of his older colleagues much too slow, and in his enthusiasm anticipated consent to his demands by ordering his new instruments without waiting for committees and meetings and reports.
In an address at the opening of the Physical and Chemical Laboratories of the University College of North Wales, on February 2, 1885, Sir William Thomson (as he was then) referred to his early equipment and work as follows: "When I entered upon the professorship of Natural Philosophy at Glasgow, I found apparatus of a very old-fashioned kind. Much of it was more than a hundred years old, little of it less than fifty years old, and most of it was worm-eaten. Still, with such appliances, yearafter year, students of natural philosophy had been brought together and taught as well as possible. The principles of dynamics and electricity had been well illustrated and well taught, as well taught as lectures and so imperfect apparatus—but apparatus merely of the lecture-illustration kind—could teach. But there was absolutely no provision of any kind for experimental investigation, still less idea, even, for anything like students' practical work. Students' laboratories for physical science were not then thought of."13
It appears that the class of Natural Philosophy (there was then as a rule only one class in any subject, though supplementary work was done in various ways) met for systematic lectures at 9 a.m., which is the hour still adhered to, and for what was called "Experimental Physics" at 8 p.m.!
TheUniversity Calendarfor 1863-4 states that "the Natural Philosophy Class meets two hours daily, 9 a.m. and 11 a.m. The first hour is chiefly spent in statements of Principles, description of Results of Observation, and Experimental Illustrations. The second hour is devoted to Mathematical Demonstrations and Exercises, and Examinations on all parts of the Course.
"The Text Books to be used are: 'Elements of Dynamics' (first part now ready), Printed by George Richardson, University Printer. 'Elements of Natural Philosophy,' by Professors W. Thomson and P. G. Tait (Two Treatises to be published before November. Macmillan.14)
"The shorter of the last mentioned Treatises will be used for the work required of all students of Natural Philosophy in the regular curriculum. The whole or specified parts of the larger Treatise will be prescribed in connection with voluntary examinations and exercises in the Class, and for candidates for the degree of M.A. with honours. Students who desire to undertake these higher parts of the business of the class, ought to be well prepared on all the subjects of the Senior Mathematical Class.
"The Laboratory in connection with the class is open daily from 9 a.m. to 4 p.m. for Experimental Exercises and Investigations, under the direction of the Professor and his official assistant."
In 1847 the meetings for experimental physics were changed to 11 a.m. The hour 9 a.m. is still (1908) retained for the regular meetings of the ordinary class, and 11 a.m. for meetings held twice a week for exercises and tutorial work, attendance at which is optional.
[A second graduating class has now been instituted and is very largely attended. Each student attends three lectures and spends four hours in the laboratory each week. A higher class, in two divisions, is also held.]
At an early date in his career as a professor Thomson called in the aid of his students for experimental research. In many directions the properties of matter still lay unexplored, and it was necessary to obtain exact data for the perfecting of the theories of elasticity, electricity and heat, which had been based on the researches of the first half of the nineteenth century. To the authors of these theories—Gauss, Green, Cauchy and others—he was a fit successor. Not knowing all that had been done by these men of genius,he reinvented, as we have seen, some of their great theorems, and in somewhat later work, notably in electricity and magnetism, set the theories on a new basis cleared of all extraneous and unnecessary matter, and reduced the hypotheses and assumptions to the smallest possible number, stated with the most careful precautions against misunderstanding. As this work was gradually accomplished the need for further experiment became more and more clearly apparent. Accordingly he established at the old College in the High Street, what he has justly claimed was the first physical laboratory for students.15An old wine-cellar in the basement adjoining the Natural Philosophy Class-room was first annexed, and was the scene of early researches, which were to lead to much of the best work of the present time. To this was added a little later the Blackstone Examination-room, which, disused and "left unprotected," was added to the wine-cellar, and gave space for the increasing corps of enthusiastic workers who came under the influence of the new teacher, and were eager to be associated with his work. A good many of the researches which were carried out in this meagre accommodation in the old College will be mentioned in what follows.
INNER COURT OF THE OLD COLLEGEINNER COURT OF THE OLD COLLEGEShowing Natural Philosophy Rooms
INNER COURT OF THE OLD COLLEGEShowing Natural Philosophy Rooms
[In the view of the inner court of the Old College given opposite, the windows on the ground-floor tothe right of the turret in front, are those of the Blackstone Examination-room, which formed a large part of the new Physical Laboratory. The windows above these, on the second floor, are those of the Apparatus-room of the Natural Philosophy Department. Between the turret on the right of the picture and the angle of the court are the windows of the Natural Philosophy Class-room. The attic above the Apparatus-room was at a later time occupied by the Engineering Department, under Professor Macquorn Rankine.]
Here again we may quote from the Bangor address:
"Soon after I entered my present chair in the University of Glasgow in 1846 I had occasion to undertake some investigations of electrodynamic qualities of matter, to answer questions suggested by the results of mathematical theory, questions which could only be answered by direct experiment. The labour of observing proved too heavy, much of it could scarcely be carried on without two or more persons, working together. I therefore invited students to aid in the work. They willingly accepted the invitation, and lent me most cheerful and able help. Soon after, other students, hearing that their class-fellows had got experimental work to do, came to me and volunteered to assist in the investigation. I could not give them all work in the particular investigation with which I had commenced—'the electric convection of heat'—for want of means and time and possibilities of arrangement, but I did all in my power to find work for them on allied subjects (Electrodynamic Properties of Metals, Moduluses of Elasticity of Metals, Elastic Fatigue, Atmospheric Electricity, etc.). I then had an ordinary class of a hundredstudents, of whom some attended lectures in natural philosophy two hours a day, and had nothing more to do from morning till night. These were the balmy days of natural philosophy in the University of Glasgow—the pre-Commissional days. But the majority of the class really had very hard work, and many of them worked after class-hours for self-support. Some were engaged in teaching, some were city-missionaries, intending to go into the Established Church of Scotland or some other religious denomination of Scotland, or some of the denominations of Wales, for I always had many Welsh students. In those days, as now, in the Scottish Universities all intending theological students took a 'philosophical curriculum'—'zuerst collegium logicum,' then moral philosophy, and (generally last) natural philosophy. Three-fourths of my volunteer experimentalists used to be students who entered the theological classes immediately after the completion of the philosophical curriculum. I well remember the surprise of a great German professor when he heard of this rule and usage: 'What! do the theologians learn physics?' I said, 'Yes, they all do; and many of them have made capital experiments. I believe they do not find that their theology suffers at all from (their) having learned something of mathematics and dynamics and experimental physics before they enter upon it.'"
This statement, besides throwing an interesting light on the conditions of university work sixty years ago, gives an illustration of the wide interpretation in Scotland of the termArts. Here it has meant, since the Chair of Natural Philosophy was founded in 1577, and held by one of the Regents of the University,Artes Liberalesinthe widest sense, that is, the study ofLitteræ Humaniores(including mental and moral philosophy) and physical and mathematical science. These were all deemed necessary for a liberal education at that time: in the scientific age in which we live it is more imperative than ever that neither should be excluded from the Arts curriculum of our Universities. The common distinction between Arts and Science is a false one, and the product of a narrow idea which is alien to the traditions of our northern Universities.
It is to be noted, however, that the laboratory thus founded was essentially a research laboratory; it was not designed for the systematic instruction of students in methods of experimenting. Laboratories for this purpose came later, and as a natural consequence. But for the best students, ill prepared as, no doubt, some of them were for the work of research, the experience gained in such a laboratory was very valuable. They learned—and, indeed, had to learn—in an incidental manner how to determine physical constants, such as specific gravities, thermal capacities, electric resistances, and so forth. For, apart from theRelations des Expériencesof Regnault, and the magnetic and electric work of Gauss and Weber, there was no systematised body of information available for the guidance of students. Good students could branch out from the main line of inquiry, so as to acquire skill in subsidiary determinations of this kind; to the more easily daunted student such difficulties proved formidable, and often absolutely deterrent.
It is not easy for a physicist of the present day to realise the state of knowledge of the time, and so he often fails to recognise the full importance ofThomson's work. The want of precise knowledge of physical constants was to a considerable extent a consequence of the want of exact definitions of quantities to be determined, and in a much greater degree of the lack of any system of units of measurement. The study of phenomena was in the main merely qualitative; where an attempt had been made to obtain quantitative determinations, the units employed were arbitrary and dependent on apparatus in the possession of the experimenter, and therefore unavailable to others. In the department of heat, as has been said, a great beginning had been made by Regnault, in whose hands the exact determination of physical constants had become a fine art.
In electricity and magnetism there were already the rudiments of quantitative measurement. But it was only long after, when the actions of magnets and of electric currents had been much further studied, that the British Association entered on its great work of setting up a system of absolute units for the measurement of such actions. Up till then the resistance, for example, of a piece of wire, to the passage of an electric current along it, was expressed by some such specification as that it was equal to the resistance of a certain piece of copper wire in the experimenter's possession. It was therefore practically impossible for experimenters elsewhere to profit by the information. And so in other cases. An example from Thomson's papers on the "Dynamical Theory of Heat" may be cited here, though it refers to a time (1851) when some progress towards obtaining a system of absolute units had been made. In § 118 (Art. XLVIII) he states that the electromotive force of a thermoelectric couple of copperand bismuth, at temperatures 0° C. and 100° C. of its functions, might be estimated from a comparison made by Pouillet of the strength of the current sent by this electromotive force through a copper wire 20 metres long and 1 millimetre in diameter, with the strength of a current decomposing water at a certain rate, were it not that the specific resistances of different specimens of copper are found to differ considerably from one another. Hence, though an estimate is made, it is stated that, without experiments on the actual wire used by Pouillet, it was impossible to arrive at an accurate result. Now if it had been in Pouillet's power to determine accurately the resistance of his circuit in absolute units, there would have been no difficulty in the matter, and his result would have been immediately available for the estimate required.
When submarine cables came to be manufactured and laid all this had to be changed. For they were expensive; an Atlantic cable, for example, cost half a million sterling. The state of the cable had to be ascertained at short intervals during manufacture; a similar watch had to be kept upon it during the process of laying, and afterwards during its life of telegraphic use. The observations made by one observer had therefore to be made available to all, so that, with other instruments and at another place, equivalent observations could be made and their results quantitatively compared with those of the former. To set up a system of measurement for such purposes as these involved much theoretical discussion and an enormous amount of experimental investigation. This was undertaken by a special committee of the Association, and a principal part in furnishing discussions of theoryand in devising experimental methods was taken by Thomson. The committee's investigations took place at a date somewhat later in Thomson's career than that with which we are here dealing, and some account of them will be given in a later chapter; but much work, preparatory for and leading up to the determination of electrical standards, was done by the volunteer laboratory corps in the transformed wine-cellar of the old College.
The selection and realisation of electrical standards was a work of extraordinary importance to the world from every point of view—political, commercial, and social. It not only rendered applications of electricity possible in the arts and industries, but by relieving experimental results from the vagueness of the specifications formerly in use, made the further progress of pure electrical science a matter in which every step forward, taken by an individual worker, facilitated the advance of all. But like other toilsome services, the nature of which is not clear to the general public, it has never received proper acknowledgment from those who have profited by it. If Thomson had done nothing more than the work he did in this connection, first with his students and later with the British Association Committee, he would have deserved well of his fellow-countrymen.
When Professor Thomson was entering on the duties of his chair, and calling his students to his aid, the discoveries of Faraday on the induction of currents by the motion of magnets in the neighbourhood of closed circuits of wire, or, what comes to the same thing, the motion of such circuits in the "fields" of magnets, had not been long given to the world, andwere being pondered deeply by natural philosophers. The time was ripe for a quantitative investigation of current induction, like that furnished by the genius of Ampère after the discovery by Oersted of the deflection of a magnet by an electric current. Such an investigation was immensely facilitated by Faraday's conception of lines of magnetic force, the cutting of which by the wire of the circuit gave rise to the induced current. Indeed, the mathematical ideas involved were indicated, and not obscurely, by Faraday himself. But to render the mathematical theory explicit, and to investigate and test its consequences, required the highest genius. This work was accomplished in great measure by Thomson, whose presentation of electrodynamic theory helped Maxwell to the view that light was an affair of the propagation of electric and magnetic vibrations in an insulating medium, the light-carrying ether.
Another investigation on which he had already entered in 1847 was of great importance, not only for pure science but for the development and proper economy of all industrial operations. The foundations on which a dynamical theory of heat was to be raised had been partly laid by Carnot and were being completed on the experimental side by James Prescott Joule, whom Thomson met in 1847 at the meeting of the British Association at Oxford. The meeting at Oxford in 1860 is memorable to the public at large, mainly on account of the discussion which took place on the Darwinian theory, and the famous dialectic encounter between Bishop Wilberforce and Professor Huxley; the Oxford meeting of 1894 will always be associated with the announcement of the discovery ofargon by Lord Rayleigh and Sir William Ramsay: the meeting of 1847 might quite as worthily be remembered as that at which Joule laid down, with numerical exactitude, the first law of thermodynamics. Joule brought his experimental results before the Mathematical and Physical Section at that meeting; and it appears probable that they would have received scant attention had not their importance been forcibly pointed out by Thomson. Communications thereafter passed frequently between the two young physicists, and there soon began a collaboration of great value to science, and a friendship which lasted till the death of Joule in 1884. [See p.88below.]
We shall devote the next few chapters to an account, as free from technicalities as possible, of these great divisions of Thomson's earlier original work as professor at Glasgow.
Duringhis residence at Cambridge Thomson gained the friendship of George Gabriel Stokes, who had graduated as Senior Wrangler and First Smith's Prizeman in 1841. They discussed mathematical questions together and contributed articles on various topics to theCambridge Mathematical Journal. In 1846 "Cambridge and Dublin" was substituted for "Cambridge" in the title of theJournal, and a new series was begun under the editorship of Thomson. A feature of the earlier volumes of the new issue was a series of Notes on Hydrodynamics written by agreement between Thomson and Stokes, and printed in vols. ii, iii, and v. The first, second, and fifth of the series were written by Thomson, the others by Stokes. The matter of these Notes was not altogether novel; but many points were put in a new and more truly physical light, and the series was no doubt of much service to students, for whose use the articles were intended. Some account of these Notes will be given in a later chapter on Thomson's hydrodynamical papers.
For the mathematical power and sure physical instinct of Stokes Thomson had always the greatest admiration. When asked on one occasion who wasthe most outstanding worker in physical science on the continent, he replied, "I do not know, but whoever he is, I am certain that Stokes is a match for him." In a report of an address which he delivered in June 1897, at the celebration of the Jubilee of Sir George Stokes as Lucasian Professor of Mathematics, Lord Kelvin referred to their early intercourse at Cambridge in terms which were reported as follows: "When he reflected on his own early progress, he was led to recall the great kindness shown to himself, and the great value which his intercourse with Sir George Stokes had been to him through life. Whenever a mathematical difficulty occurred he used to say to himself, 'Ask Stokes what he thinks of it.' He got an answer if answer was possible; he was told, at all events, if it was unanswerable. He felt that in his undergraduate days, and he felt it more now."
After the death of Stokes in February 1902, Lord Kelvin again referred, in an enthusiastic tribute inNaturefor February 12, to these early discussions. "Stokes's scientific work and scientific thought is but partially represented by his published writings. He gave generously and freely of his treasures to all who were fortunate enough to have an opportunity of receiving from him. His teaching me the principles of solar and stellar chemistry when we were walking about among the colleges sometime prior to 1852 (when I vacated my Peterhouse Fellowship to be no more in Cambridge for many years) is but one example."
The interchange of ideas between Stokes and Thomson which began in those early days went on constantly and seems to have been stimulating to both.The two men were in a sense complementary in nature and temperament. Both had great power and great insight, but while Stokes was uniformly calm, reflective, and judicial, Thomson's enthusiasm was more outspokenly fervid, and he was apt to be at times vehement and impetuous in his eagerness to push on an investigation; and though, as became his nationality, he was cautious in committing himself to conclusions, he exercised perhaps less reserve in placing his results before the public of science.
A characteristic instance of Thomson's vehement pursuit of experimental results may be given here, although the incidents occurred at a much later date in his career than that with which we are at present concerned. In 1880 the invention of the Faure Secondary Battery attracted his attention. M. Faure brought from Paris some cells made up and ready charged, and showed in the Physical Laboratory at Glasgow the very powerful currents which, in consequence of their very low internal resistance, they were capable of producing in a thick piece of copper wire. The cells were of the original form, constructed by coating strips of sheet lead on both sides with a paste of minium moistened with dilute sulphuric acid, swathing them in woollen cloth sewed round them, and then rolling two together to form the pair of plates for one cell.
A supply of sheet lead, minium, and woollen cloth was at once obtained, and the whole laboratory corps of students and staff was set to work to manufacture secondary batteries. A small Siemens-Halske dynamo was telegraphed for to charge the cells, and the ventilating steam-engine of the University was requisitionedto drive the dynamo during the night. Thus the University stokers and engineer were put on double shifts; the cells were charged during the night and the charging current and battery-potential measured at intervals.
Then the cells were run down during the day, and their output measured in the same way. Just as this began, Thomson was laid up with an ailment which confined him to bed for a couple of weeks or so; but this led to no cessation of the laboratory activity. On the contrary, the laboratory corps was divided into two squads, one for the night, the other for the day, and the work of charging and discharging, and of measurement of expenditure and return of energy went on without intermission. The results obtained during the day were taken to Thomson's bedside in the evening, and early in the morning he was ready to review those which had been obtained during the night, and to suggest further questions to be answered without delay. This mode of working could not go on indefinitely, but it continued until his assistants (some of whom had to take both shifts!), to say nothing of the stokers and students, were fairly well exhausted.
On other occasions, when he was from home, he found the post too slow to convey his directions to his laboratory workers, and telegraphed from day to day questions and instructions regarding the work on hand. Thus one important result (anticipated, however, by Villari) of the series of researches on the effects of stress on magnetisation which forms Part VII of hisElectrodynamic Qualities of Metals—the fact that up to a certain magnetising force the effect of pull, applied to a wire of soft iron, is to increase themagnetisation produced, and for higher magnetising forces to diminish it—was telegraphed to him on the night on which the paper was read to the Royal Society.
It will thus be seen that Thomson, whether confined to his room or on holiday, kept his mind fixed upon his scientific or practical work, and was almost impatient for its progress. Stokes worked mainly by himself; but even if he had had a corps of workers and assistants, it is improbable that such disturbances of hours of attendance and laboratory and workshop routine would have occurred, as were not infrequent at Glasgow when Thomson's work was, in the 'sixties and 'seventies, at its intensest.
Stokes and Thomson were in succession presidents of the Royal Society, Stokes from 1885 to 1890, and Thomson (from 1892 as Lord Kelvin) from 1890 to 1895. This is the highest distinction which any scientific man in this country can achieve, and it is very remarkable that there should have been in recent times two presidents in succession whose modes of thought and mathematical power are so directly comparable with those of the great founder of modern natural philosophy. Stokes had the additional distinction of being the lineal successor of Newton as Lucasian Professor of Mathematics at Cambridge. But it was reserved for Thomson to do much by the publication of Thomson and Tait'sNatural Philosophyto bring back the current of teaching and thought in dynamical science to the ideas of thePrincipia, and to show how completely the fundamental laws, as laid down in that great classic, avail for the inclusion of the modern theory of energy, in all its transformations,within the category of dynamical action between material systems.
An exceedingly eminent politician, now deceased, said some years ago that the present age was singularly deficient in minds of the first quality. So far as scientific genius is concerned, the dictum was singularly false: we have here a striking proof of the contrary. But then few politicians know anything of science; indeed some of those who guide, or aspire to guide, the destinies of the most scientific and industrial empire the world has ever seen are almost boastful of their ignorance. There are, of course, honourable exceptions.
It is convenient to refer here to the share which Stokes and Thomson took in the physical explanation of the dark lines of the solar spectrum, and to their prediction of the possibility of determining the constitution of the stars and of terrestrial substances by what is now known as spectrum analysis. Thomson used to give the physical theory of these lines in his lectures, and say that he obtained the idea from Stokes in a conversation which they had in the garden of Pembroke at Cambridge, "some time prior to 1852" (see the quotation from hisNaturearticle quoted above, p.80, and theBaltimore Lectures, p.101). This is confirmed by a student's note-book, of date 1854, which is now in the Natural Philosophy Department. The statements therein recorded are perfectly definite and clear, and show that at that early date the whole affair of spectrum analysis was in his hands, and only required confirmation by experiments on the reversal of the lines of terrestrial substances by an atmosphere of the substance which produced the lines, and acomparison of the positions of the bright lines of terrestrial substances with those of the dark lines of the solar spectrum. Why Thomson did not carry out all these experiments it would be difficult to say. Some of them he did make, for Professor John Ferguson, who was a student of Natural Philosophy in 1859-60, has recently told how he witnessed Thomson make the experiment of reversing the lines of sodium by passing the light from the salted flame of a spirit lamp through vapour of sodium produced by heating the metal in an iron spoon. A few days later, says Professor Ferguson, Thomson read a letter to his class announcing Bunsen and Kirchhoff's discovery.
A letter of Stokes to Sir John Lubbock, printed in theScientific Correspondence of Sir George Gabriel Stokes, states his recollection of the matter, and gives Thomson the credit of having inferred the method of spectrum analysis, a method to which Stokes himself makes no claim. He says, "I know, I think, what Sir William Thomson was alluding to. I knew well, what was generally known, and is mentioned by Herschel in his treatise on Light, that the bright D seen in flames is specially produced when a salt of soda is introduced. I connected it in my own mind with the presence of sodium, and I suppose others did so too. The coincidence in position of the bright and dark D is too striking to allow us to regard it as fortuitous. In conversation with Thomson I explained the connection of the dark and bright line by the analogy of a set of piano strings tuned to the same note, which, if struck, would give out that note, and also would be ready to sound it, to take it up, in fact, if it were sounded in air. This would imply absorption of the aërial vibrations, asotherwise there would be a creation of energy. Accordingly I accounted for the presence of the dark D in the solar spectrum by supposing that there was sodium in the atmosphere, capable of absorbing light of that particular refrangibility. He asked me if there were any other instances of such coincidences of bright and dark lines, and I said I thought there was one mentioned by Brewster. He was much struck with this, and jumped to the conclusion that to find out what substances were in the stars we must compare the positions of the dark lines seen in their spectra with the spectra of metals, etc....
"I should have said that I thought Thomson was going too fast ahead, for my notion at the time was that, though a few of the dark lines might be traced to elementary substances, sodium for one, probably potassium for another, yet the great bulk of them were probably due to compound vapours, which, like peroxide of nitrogen and some other known compound gases, have the character of selective absorption."
It will be remembered that the experimental establishment of the method of spectrum analysis was published towards the end of 1859 by Bunsen and Kirchhoff, to whom, therefore, the full credit of discoverers must be given.
Lord Kelvin in the later years of his life used to tell the story of his first meeting with Joule at Oxford, and of their second meeting a fortnight later in Switzerland. He did so also in his address delivered on the occasion of the unveiling of a statue of Joule, in Manchester Town Hall, on December 7, 1893, and we quote the narrative on account of its scientific and personal interest. "I can never forget the BritishAssociation at Oxford in 1847, when in one of the sections I heard a paper read by a very unassuming young man, who betrayed no consciousness in his manner that he had a great idea to unfold. I was tremendously struck with the paper. I at first thought it could not be true, because it was different from Carnot's theory, and immediately after the reading of the paper I had a few words with the author, James Joule, which was the beginning of our forty years' acquaintance and friendship. On the evening of the same day, that very valuable institution of the British Association, its conversazione, gave us opportunity for a good hour's talk and discussion over all that either of us knew of thermodynamics. I gained ideas which had never entered my mind before, and I thought I, too, suggested something worthy of Joule's consideration when I told him of Carnot's theory. Then and there in the Radcliffe Library, Oxford, we parted, both of us, I am sure, feeling that we had much more to say to one another and much matter for reflection in what we had talked over that evening. But ... a fortnight later, when walking down the valley of Chamounix, I saw in the distance a young man walking up the road towards me, and carrying in his hand something which looked like a stick, but which he was using neither as an alpenstock nor as a walking-stick. It was Joule with a long thermometer in his hand, which he would not trust by itself in thechar-à-banc, coming slowly up the hill behind him, lest it should get broken. But there, comfortably and safely seated in thechar-à-banc, was his bride—the sympathetic companion and sharer in his work of after years. He had not told me in Section A, or in theRadcliffe Library, that he was going to be married in three days, but now in the valley of Chamounix he introduced me to his young wife. We appointed to meet again a fortnight later at Martigny to make experiments on the heat of a waterfall (Sallanches) with that thermometer: and afterwards we met again and again, and from that time, indeed, remained close friends till the end of Joule's life. I had the great pleasure and satisfaction for many years, beginning just forty years ago, of making experiments along with Joule which led to some important results in respect to the theory of thermodynamics. This is one of the most valuable recollections of my life, and is indeed as valuable a recollection as I can conceive in the possession of any man interested in science."
At the beginning of his course of lectures each session, Professor Thomson read, or rather attempted to read, an introductory address on the scope and methods of physical science, which he had prepared for his first session in 1846. It set forth the fact that in science there were two stages of progress—a natural history stage and a natural philosophy stage. In the first the discoverer or teacher is occupied with the collection of facts, and their arrangement in classes according to their nature; in the second he is concerned with the relations of facts already discovered and classified, and endeavours to bring them within the scope of general principles or causes. Once the philosophical stage is reached, its methods and results are connected and enlarged by continued research after facts, controlled and directed by the conclusions of general theory. Thus the method is at first purely inductive, but becomes in the second stage bothinductive and deductive; the general theory predicts by its deductions, and the verification of these by experiment and observation give a validity to the theory which no mere induction could afford. These stages of scientific investigation are well illustrated by the laws of Kepler arrived at by mere comparison of the motions of the planets, and the deduction of these laws, with the remarkable correction of the third law, given by the theory of universal gravitation. The prediction of the existence and place of the planet Neptune from the perturbations of Uranus is an excellent example of the predictive quality of a true philosophical theory.
The lecture then proceeded to state the province of dynamics, to define its different parts, and to insist on the importance of kinematics, which was described as a purely geometrical subject, the geometry of motion, considerations from which entered into every dynamical problem. This distinction between dynamical and kinematical considerations—between those in which force is concerned and those into which enter only the idea of displacement in space and in time—is emphasised in Thomson and Tait'sNatural Philosophy, which commences with a long chapter devoted entirely to kinematics.
Whether Professor Thomson read the whole of the Introductory Lecture on the first occasion is uncertain—Clerk Maxwell is said to have asserted that it was closely adhered to, for that one time only, and finished in much less than the hour allotted to it. In later years he had never read more than a couple of pages when some new illustration, or new fact of science, which bore on his subject, led him to digress from themanuscript, which was hardly ever returned to, and after a few minutes was mechanically laid aside and forgotten. Once on beginning the session he humorously informed the assembled class that he did not think he had ever succeeded in reading the lecture through before, and added that he had determined that they should hear the whole of it! But again occurred the inevitable digression, in the professor's absorption in the new topic the promise was forgotten, and the written lecture fared as before! These digressions were exceedingly interesting to the best students: whether they compensated for the want of a carefully prepared presentation of the elements of the subject, suited to the wants of the mass of the members of the class, is a matter which need not here be discussed. All through his elementary lectures—introductory or not—new ideas and new problems continually presented themselves. An eminent physicist once remarked that Thomson was perhaps the only living man who made discoveries while lecturing. That was hardly true; in the glow of action and stress of expression the mind of every intense thinker often sees new relations, and finds new points of view, which amount to discoveries. But fecundity of mind has, of course, its disadvantages: the unexpected cannot happen without causing distractions to all concerned. A mind which can see a theory of the physical universe in a smoke-ring is likely, unless kept under extraordinary and hampering restraint, to be tempted to digress from what is strictly the subject in hand, to the world of matters which that subject suggests. Professor Thomson was, it must be admitted, too discursive for the ordinary student, and perhaps did notstudy the art of boiling down physical theories to the form most easily digestible. His eagerness of mind and width of mental outlook gave his lectures a special value to the advanced student, so that there was a compensating advantage.
The teacher of natural philosophy is really placed in a position of extraordinary difficulty. The fabric of nature is woven without seam, and to take it to pieces is in a manner to destroy it. It must, after examination in detail, be reconstructed and considered as a whole, or its meaning escapes us. And here lies the difficulty: every bit of matter stands in relation to everything else, and both sides of every relation must be considered. In other words, in the explanation of any one phenomenon the explanation of all others is more or less involved. This does not mean that investigation or exposition is impossible, or that we cannot proceed step by step; but it shows the foolishness of that criticism of science and scientific method which asks for complete or ultimate knowledge, and of the popular demand for a simple form of words to express what is in reality infinitely complex.
In the earlier years of his professorship Professor Thomson taught his class entirely himself, and gathered round him, as he has told us in the Bangor address, an enthusiastic band of workers who aided him in the researches which he began on the electrodynamic qualities of metals, the elastic properties of substances, the thermal and electrical conductivities of metals, and at a later date in the electric and magnetic work which he undertook as a member of the British Association Committee on Electrical Standards. The class met, as has been stated, twice a day, first for lectures, thenfor exercises and oral examination. The changes which took place later in the curriculum, and especially the introduction of honours classes in the different subjects, rendered it difficult, if not impossible, for two hours' attendance to be given daily on all subjects, and students were at first excused attendance at the second hour, and finally such attendance became practically optional. But so long as the old traditional curriculum in Arts—of Humanity, Greek, Logic, Mathematics, Moral Philosophy and Natural Philosophy—endured, a large number of students found it profitable to attend at both hours, and it was possible to give a large amount of excellent tutorial instruction by the working of examples and oral examination.
Thomson always held that his commission included the subject of physical astronomy, and though his lectures on that subject were, as a rule, confined to a statement of Kepler's laws and Newton's deductions from them, he took care that the written and oral examinations included astronomical questions, for which the students were enjoined to prepare by reading Herschel'sOutlines, or some similar text-book. This injunction not infrequently was disregarded, and discomfiture of the student followed as a matter of course, if he was called on to answer. Nor were the questions always easy to prepare for by reading. A man might have a fair knowledge of elementary astronomy, and be unable to answer offhand such a question as, "Why is the ecliptic called the ecliptic?" or to say, when the lectures on Kepler had been omitted, short and tersely just what was Newton's deduction from the third law of the planetary motions.
Home exercises were not prescribed as part of theregular work except from time to time in the "Higher Mathematical Class" which for thirty years or more of Thomson's tenure of office was held in the department. But the whole ordinary class met every Monday morning and spent the usual lecture hour in answering a paper of dynamical and physical questions. As many as ten, and sometimes eleven, questions were set in these papers, some of them fairly difficult and involving novel ideas, and by this weekly paper of problems the best students, a dozen or more perhaps, were helped to acquire a faculty of prompt and brief expression. It was not uncommon for a good man to score 80 or 90 or even 100 per cent. in the paper, no small feat to accomplish in a single hour. But to a considerable majority of the class, it is doubtful whether the weekly examination was of much advantage: they attempted one or two of the more descriptive questions perhaps, but a good many did next to nothing. The examinations came every week, and so the preparation for one after another was neglected, and as much procrastination of work ensued as there would have been if only four or five papers a session had been prescribed. Then the work of looking over so many papers was a heavy task to the professor's assistant, a task which became impossible when, for a few years in the early 'eighties, the students in the ordinary class numbered about 250.
The subject of natural philosophy had become so extensive in 1846 that Professor J. P. Nichol called attention to the necessity for special arrangements for its adequate teaching. What would he say if he could survey its dimensions at the present time! To give even a brief outline of the principal topics in dynamics,heat, acoustics, light, magnetism, and electricity is more than can be accomplished in any course of university lectures; and the only way to teach well and economically the large numbers of students16who now throng the physics classes is to give each week, say, three lectures as well considered and arranged as possible, without any interruption from oral examination, and assemble the students in smaller classes two or three times a week for exercises and oral examination.
Thomson stated his views as to examinations and lectures in the Bangor address. "The object of a university is teaching, not testing, ... in respect to the teaching of a university the object of examination is to promote the teaching. The examination should be, in the first place, daily. No professor should meet his class without talking to them. He should talk to them and they to him. The French call a lecture aconférence, and I admire that idea. Every lecture should be a conference of teachers and students. It is the true ideal of a professorial lecture. I have found that many students are afflicted when they come up to college with the disease called 'aphasia.' They will not answer when questioned, even when the very words of the answer are put in their mouths, or when the answer is simply 'yes' or 'no.' That disease wears off in a few weeks, but the great cure for it is in repeated and careful and very free interchange of question and answer between teacher and student.... Written examinations are very important, as training the student to express withclearness and accuracy the knowledge he has gained, but they should be once a week to be beneficial."
The great difficulty now, when both classes and subject have grown enormously, is to have free conversation between professor and student, and yet give an adequate account of the subject. To examine orally in a thorough way two students in each class-hour is about as much as can be done if there is to be any systematic exposition by lecture at all; and thus the conference between teacher and individual student can occur only twice a year at most. Nevertheless Lord Kelvin was undoubtedly right: oral examination and the training of individual students in the art of clear and ready expression are very desirable. The real difficulties of the subject are those which occur to the best students, and a discussion of them in the presence of others is good for all. This is difficult nowadays, for large classes cannot afford to wait while two or three backward students grope after answers to questions—which in many cases must be on points which are sufficiently plain to the majority—to say nothing of the temptation to disorder which the display of personal peculiarities or oddities of expression generally affords to an assembly of students. But time will be economised and many advantages added, if large classes are split up into sections for tutorial work, to supplement the careful presentation of the subject made in the systematic lectures delivered to the whole class in each case. The introduction of a tutorial system will, however, do far more harm than good, unless the method of instruction is such as to foster the self-reliance of the student, who must not be, so to speak, spoon-fed: such a method, and the advantagesof the weekly examination on paper may be secured, by setting the tutorial class to work out on the spot exercises prescribed by the lecturer. But the danger, which is a very real one, can only be fully avoided by the precautions of a skilful teacher, who in those small classes will draw out and direct the ideas of his students, rather than impart knowledge directly.
After a few years Thomson found it necessary to appoint an assistant, and Mr. Donald McFarlane, who had distinguished himself in the Mathematics and Natural Philosophy classes, was chosen. Mr. McFarlane was originally a block-printer, and seems to have been an apprentice at Alexandria in the Vale of Leven, at the time of the passing of the first Reform Bill. After some time spent in the cotton industry of the district, he became a teacher in a village school in the Vale of Leven, and afterwards entered the University as a student. He discharged his duties in the most faithful and self-abnegating manner until his retirement in 1880, when he had become advanced in years. He had charge of the instruments of the department, got ready the lecture illustrations and attended during lecture to assist in the experiments and supply numerical data when required, prepared the weekly class examination paper and read the answers handed in, and assisted in the original investigations which the professor was always enthusiastically pursuing. A kind of universal physical genius was McFarlane; an expert calculator and an exact and careful experimentalist. Many a long and involved arithmetical research he carried out, much apparatus he made in a homely way, and much he repaired and adjusted. Then, always when the professor was out of the wayand calm had descended on the apparatus-room, if not on the laboratory, McFarlane sat down to reduce his pile of examination papers, lest Monday should arrive with a new deluge of crude answers and queer mistakes, ere the former had disappeared. On Friday afternoons at 3 o'clock he gave solutions of the previous Monday's questions to any members of the class who cared to attend; and his clear and deliberate explanations were much appreciated. An unfailing tribute was rendered to him every year by the students, and often took the form of a valuable gift for which one and all had subscribed. A recluse he was in his way, hardly anybody knew where he lived—the professor certainly did not—and a man of the highest ability and of the most absolute unselfishness. An hour in the evening with one or two special friends, and the study of German, were the only recreations of McFarlane's solitary life. He was full of humour, and told with keen enjoyment stories of the University worthies of a bygone age. For thirty years he worked on for a meagre salary, for during the earlier part of that time no provision for assistants was made in the Government grant to the Scottish Universities. By an ordinance issued in 1861 by the University Commissioners, appointed under the Act of 1858, a grant of £100 a year was made from the Consolidated Fund for an assistant in each of the departments of Humanity, Greek, Mathematics, and Natural Philosophy, and for two in the department of Chemistry; and McFarlane's position was somewhat improved. His veneration for Thomson was such as few students or assistants have had for a master: his devotion resembled that of the oldfamulusrather than the muchmore measured respect paid by modern assistants to their chiefs.
After his retirement McFarlane lived on in Glasgow, and amused himself reading out-of-the-way Latin literature and with the calculation of eclipses! He finally returned to Alexandria, where he died in February 1897. "Old McFarlane" will be held in affectionate remembrance so long as students of the Natural Philosophy Class in the 'fifties and 'sixties and 'seventies, now, alas! a fast vanishing band, survive.
Soon after taking his degree of B.A. at Cambridge in 1845, Thomson had been elected a Fellow of St. Peter's College. In 1852 he vacated his Fellowship on his marriage to Miss Margaret Crum, daughter of Mr. Walter Crum of Thornliebank, near Glasgow, but was re-elected in 1871, and remained thereafter a Fellow of Peterhouse throughout his life.
Themeeting of Thomson and Joule at Oxford in 1847 was fraught with important results to the theory of heat. Thomson had previously become acquainted with Carnot's essay, most probably through Clapeyron's account of it in theJournal de l'École Polytechnique, 1834, and had adopted Carnot's view that when work was done by a heat engine heat was merely let down from a body at one temperature to a body at a lower temperature. Joule apparently knew nothing of Carnot's theory, and had therefore come to the consideration of the subject without any preconceived opinions. He had thus been led to form a clear notion of heat as something which could be transformed into work, andvice versa. This was the root idea of his attempt to find the dynamical equivalent of heat. It was obvious that a heat engine took heat from a source and gave heat to a refrigerator, and Joule naturally concluded that the appearance of the work done by the engine must be accompanied by the disappearance of a quantity of heat of which the work done was the equivalent. He carried this idea consistently through all his work upon energy-changes, not merely in heat engines but in what might be called electric engines.For he pointed out that the heat produced in the circuit of a voltaic battery was the equivalent of the energy-changes within the battery, and that, moreover, when an electromagnetic engine was driven by the current, or when electrochemical decomposition was effected in a voltameter in the circuit, the heat evolved in the circuit for a given expenditure of the materials of the battery was less than it would otherwise have been, by the equivalent of the work done by the engine, or of the chemical changes effected in the voltameter. Thus Joule was in possession at an earlier date than Thomson of the fundamental notion upon which the true dynamical theory of heat engines is founded. Thomson, on the other hand, as soon as he had received this idea, was able to add to it the conception, derived from Carnot, of a reversible engine as the engine of greatest efficiency, and to deduce in a highly original manner all the consequences of these doctrines which go to make up the ordinary thermodynamics even of the present time. Though Clausius was the first, as we shall see, to deduce various important theorems, yet Thomson's discussion of the question had a quality peculiarly its own. It was marked by that freedom from unstated assumptions, from extraneous considerations, from vagueness of statement and of thought, which characterises all his applications of mathematics to physics. The physical ideas are always set forth clearly and in such a manner that their quantitative representation is immediate: we shall have an example of this in the doctrine of absolute temperature. In most of the thermodynamical discussions which take the great memoir of Clausius as their starting point, temperature is supposed to be given by a hypotheticalsomething which is called a perfect gas, and it is very difficult, if not impossible, to gather a precise notion of the properties of such a gas and of the temperature scale thereon founded. Thomson's scale enables a perfect gas to be defined, and the deviations of the properties of ordinary gases from those of such a gas to be observed and measured.
The idea, then, which Joule had communicated to Section A, when Thomson interposed to call attention to its importance, was that work spent in overcoming friction had its equivalent in the heat produced, that, in fact, the amount of heat generated in such a case was proportional to the work spent, quite irrespective of the materials used in the process, provided no change of the internal energy of any of them took place so as to affect the resulting quantity of heat. This forced upon physicists the view pointed to by the doctrine of the immateriality of heat, established by the experiments of Rumford and Davy, that heat itself was a form of energy; and thus the principle of conservation of energy was freed from its one defect, its apparent failure when work was done against friction.
Rumford had noted the very great evolution of heat when gun-metal was rubbed by a blunt borer, and had come to the reasonable conclusion that what was evolved in apparently unlimited quantity by the abrasion or cutting down of a negligible quantity of materials could not be a material substance. He had also made a rough estimate of the relation between the work spent in driving the borer by horse-power and the heat generated. Joule's method of determining the work-equivalent of heat was a refinement of Rumford's, but differed in the all-important respect that accuratemeans were employed for measuring the expenditure of work and the gain of heat. He stirred a liquid, such as water or mercury, in a kind of churn driven by a falling weight. The range of descent of the weight enabled the work consumed to be exactly estimated, and a sensitive thermometer in the liquid measured the rise of temperature; thus the heat produced was accurately determined. The rise of temperature was very slight, and the change of state of the liquid, and therefore any possible change in its internal energy, was infinitesimal. The experiments were carried out with great care, and included very exact measurements of the various corrections—for example, the amount of work spent at pulleys and pivots without affecting the liquid, and the loss of heat by radiation. The experiments proved that the work spent on the liquid and the heat produced were in direct proportion to one another. He found, finally, in 1850, that 772 foot-pounds of work at Manchester generated one British thermal unit, that is, as much heat as sufficed to raise a pound of water from 60° F. to 61° F. An approximation to this conclusion was contained in the paper which he communicated to the British Association at Oxford in 1847.
The results of a later determination made with an improved apparatus, and completed in 1878, gave a very slightly higher result. When corrected to the corresponding Fahrenheit degree on the air thermometer it must be increased by somewhat less than one per cent. The exact relation has been the subject during the last twenty years of much refined experimental work, but without any serious alteration of the number indicated above.
It is probable that in consequence of the conference which he had with Joule at Oxford Thomson had his thoughts turned for some time almost exclusively to the dynamical theory of heat engines. He worked at the subject almost continuously for a long time, sending paper after paper to the Edinburgh Royal Society. As we have seen, he had given Joule a description of Carnot's essay on the Motive Power of Heat and the conclusions, or some of them, therein contained. Joule's result, and the thermodynamic law which it established, gave the key to the correction of Carnot's theory necessary to bring it into line with a complete doctrine of energy, which should take account of work done against frictional resistances.
Mayer of Heilbronn had endeavoured to determine the dynamical equivalent of heat in 1842, by calculating from the knowledge available at the time of the two specific heats of air—the specific heat at constant pressure and the specific heat at constant volume—the heat value of the work spent in compressing air from a given volume to a smaller one. The principle of this determination is easily understood, but it involves an assumption that is not always clearly perceived. Let the air be imagined confined in a cylinder closed by a frictionless piston, which is kept from moving out under the air pressure by force applied from without. Let heat be given to the air so as to raise its temperature, while the piston moves out so as to keep the pressure constant. If the pressure bepand the increase of volume bedv, the work done against the external force ispdv. Let the rise of temperature be one degree of the Centigrade scale, and the mass of air be one gramme, the heat given to the gasis the specific heatCpof the gas at constant pressure, for there is only slight variation of specific heat with temperature. But if the piston had been fixed the heat required for the same rise of temperature would have beenCv, the specific heat at constant volume. Now Mayer assumed that the excess of the specific heatCpaboveCvwas the thermal equivalent of the workpdvdone in the former case. Thus he obtained the equationJ(Cp−Cv) =pdv, whereJdenotes the dynamical equivalent of heat andCp,Cvare taken in thermal units. But if a be the coefficient of expansion of the air under constant pressure (that is 1 ⁄ 273), andv0be the volume of the air at 0° C., we have dv = av0, so thatJ(Cp−Cv) =apv0. Now ifpbe one atmosphere, say 1.014 × 106dynes per square centimetre, and the temperature be the freezing point of water, the volume of a gramme of air is 1 ⁄ .001293 in cubic centimetres. Hence