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 advantages of 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 way and 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 old famulus rather than the much more 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.
CHAPTER VII
THE "ACCOUNT OF CARNOT'S THEORY OF THE MOTIVE POWER OF HEAT"—TRANSITION TO THE DYNAMICAL THEORY OF HEAT
The meeting 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 the Journal 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, and vice 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 hypothetical something 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.