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.