It has often been asserted that Thomson appealed to his assistant for information contained in the multiplication-table, and could not perform the ordinary operations of arithmetic. His active mind, working on ahead of the statements he was making at the moment, often could not be brought back to the consideration of the value of 9 times 6, and the like; but it was quite untrue that he was incapable of making calculations. His memory was good, and though he never could be, for example, sure whether the aqueous humour was before or behind the crystalline in the eye, he was generally able at once to tell when a misstatement had been made as to any numerical question regarding the subject under discussion.
In the higher mathematical class, to which he lectured on Wednesdays, at noon, Thomson was exceedingly interesting. There he seemed to work at the subject as he lectured; new points to be investigated continually presented themselves, and the students were encouraged to work them out in the week-long intervals between his lectures. Always the physical interpretation of results was aimed at, even intermediate steps were discussed. Thus the meaning of the mathematical processes was ever kept in view, and the men who could follow were made to think while they worked, and to regard the mathematical analysis as merely an aid, not an end in itself. "A little expenditure of chalk is a saving of brains;" "the art of reading mathematical books is judicious skipping," were remarks he sometimes made, and illustrate his view of the relative importance of mathematical work when he regarded it as the handmaid of the physical thinker. Yet he valued mathematics for its own sake, and was keenly alive to elegance of form and method, as readers of such great mathematical discussions as the "Appendix on Spherical Harmonics," in Thomson and Tait, will observe. He spoke with unqualified admiration of the work of Green and Stokes, of Cauchy's great memoir on Waves, and of Hamilton's papers on Dynamics. But no form of vector-analysis, neither the Quaternions of Hamilton nor the Vectors of Willard Gibbs and Heaviside, appealed to him, and the example of his friend and co-worker, Tait, had no effect in modifying his adverse verdict regarding this department of mathematics, a verdict which in later years became only more emphatic.
One session he began the first lecture of the higher class by writing dx ⁄ dt in the middle of the blackboard, and demanding of each of the ten or a dozen students present, some of them distinguished graduates, what it meant! One student described it as the limiting value of the ratio of the increment of the dependent variable x to the increment of the independent variable t, when the latter increment is made indefinitely small. He retorted, "That's what Todhunter would say!" The others gave various slightly different versions of the same definition. At last he impatiently remarked, "Does nobody know that dx ⁄ dt means velocity?" Here the physical idea as a whole was before his mind; and he did not reflect that if t denoted time and x distance in any direction, the explanation given by the student did describe velocity with fair accuracy.
An embarrassing peculiarity of his mathematical discussions was his tendency, when a difficulty of symbolisation occurred, to completely change the notation. Also he was not uniformly accurate in analytical work; but he more than made up for this by the faculty he had of devising a test of the accuracy of the result and of divining the error which had crept in, if the test was not satisfied.
The subjects he treated were always such great branches of mathematics as the theory of the tides—he discussed the tidal phenomena of the English Channel in one course—the general theory of vibrations, Fourier analysis, the theory of waves in water, etc., etc. A very good idea of the manner and matter of his mathematical prelections can be obtained from a perusal of the Baltimore Lectures.
In the physical laboratory he was both inspiring and distracting. He continually thought of new things to be tried, and interrupted the course of the work with interpolated experiments which often robbed the preceding sequence of operations of their final result. His ideas were on the whole better worked out by a really good corps of students when he was from home, and could only communicate by letter his views on the work set forth in the daily reports which were forwarded to him.
He insisted with emphasis that a student who found that a quadrant electrometer would not work well should take it to pieces to ascertain what was the matter. This of course generally resulted in the return of the instrument to White's shop to be put together again and adjusted. But, as he said, there was a cause for every trouble of that kind, and the great thing was to find out at once what it was.
Thomson's concentration on the work in hand, and his power of simply taking possession of men, even mere spectators, and converting them into assistants, was often shown in the laboratory. Several men who have since become eminent were among the assistants enrolled from the laboratory students. Professor W. E. Ayrton and, later, Professor John Perry, were students at Glasgow for a time, and rendered the most able and willing help in the researches which were then proceeding. This power was, no doubt, the secret of his success in gathering round him an enthusiastic corps of laboratory workers in the early years of his professorship, and it was shown also by the ease with which he annexed the Blackstone examination-room and, later, various spaces in the new University buildings. There, after a time, the Natural Philosophy rooms were found by the senatus to include not only the original class-room, laboratory, etc., but also all the spare attics and corridors in the neighbourhood, and even the University tower itself! One of his colleagues, who venerated him highly, remarked recently, "He had a great faculty for annexation!"
The incident referred to occurred while he was preparing the article on Heat for the ninth edition of the Encyclopædia Britannica. It seemed at first a pity that Thomson should undertake to write such articles; but in the course of their preparation he came upon so many points on which experimental information was wanting, and instituted so many researches to answer his questions, that the essays took very much the character of original papers. In the article on Heat (he also wrote Elasticity), will be found a long account of "Steam Thermometry," that is, of thermometers in which the indicating substance was to be the saturated vapours of different substances, water, sulphurous acid, etc., etc., for he did not limit the term "steam" to water-vapour. For some time every one in the laboratory was employed in making sulphurous acid, by heating copper in sulphuric acid in the usual way, and condensing the gas in tubes immersed in freezing mixtures; and the atmosphere of the room was of a sort which, however noxious to germs of different kinds, it was a little difficult to breathe. One morning, when all were thus occupied, an eminent chemist, who had just come home from the south for a vacation, called to pay his respects. After a word or two of inquiry as to how his young friend was prospering in his new post, Thomson said, "We are all very busy brewing liquid sulphurous acid, for use in sulphurous acid steam thermometers; we want a large quantity of the liquid; would you mind helping us?" So, desiring an assistant to find a flask and materials, he enrolled this new and excellent recruit on the spot; and what was intended to be a mere call, was prolonged into a long day of ungrudging work at an elementary chemical exercise!