Professor Tait was appointed to the Chair of Natural Philosophy in the University of Edinburgh in 1860, and came almost immediately into frequent contact with Thomson. Both were Peterhouse men, trained by the same private tutor—William Hopkins—both were enthusiastic investigators in mathematical as well as in experimental physics, they taught in the sister universities of Edinburgh and Glasgow, and had much the same kind of classes to deal with and the same educational problems to solve. Tait was an Edinburgh man—an old school-fellow of Clerk Maxwell at the Edinburgh Academy—and had therefore been exposed to that contact, in play and in work, with compeers of like age and capabilities, which is one of the best preparations for the larger school and more serious struggles of life. Thomson's early education, under his father's anxious care, had no doubt certain advantages, and his early entrance into college classes gave him to a great extent that intercourse with others for which such advantages are never complete compensation. The two men had much community of thought and experience, and the literary partnership into which they entered was hailed as one likely to do much for the progress of science.
In some ways, however, Thomson and Tait were very different personalities. Thomson troubled himself little with metaphysical subtleties, his conceptions were like those of Newton, absolutely clear so far as they went; he never, in his teaching at least, showed any disposition to discuss the "foundations of dynamics," or the conception of motion in a straight line. These were taken for granted like the fundamental ideas in a book on geometry; and the student was left to do what every true dynamical student must do for himself sooner or later—to compare the abstractions of dynamics with the products of his experience in the world of matter and force. Perhaps a little guidance now and then in the difficulties about conceptions, which beset every beginner, might not have been amiss: but Thomson was so intent on the concrete example in hand—pendulum or gyrostat, or what not—that he left each man to form or correct his own ideas by the lessons which such examples afford to every one who carefully examines them.
Tait, on the other hand, though he continually denounced metaphysical discussion, was in reality much more metaphysical than Thomson, and seemed to take pleasure in the somewhat transcendental arguments with regard to matters of analysis which were put forward, especially in the Elements of Quaternions, by Sir William Rowan Hamilton, of Dublin, a master whom he much revered. But there is metaphysics and metaphysics! and the pronouncements of professed metaphysicians were often characterised as non-scientific and fruitless, which no doubt they were from the physical point of view.
Then Tait was strongly convinced of the importance for physics of the quaternion analysis: Thomson was not, to say the least; and this was probably the main reason why the vectorial treatment of displacement, velocities, and other directed quantities, has no place in the joint writings of the two Scottish professors. In controversy Tait was a formidable antagonist: when war was declared he gave no quarter and asked for none, though he never fought an unchivalric battle. He admired foreign investigators—and especially von Helmholtz—but he was always ready to put on his armour and place lance in rest for the cause of British science. Thomson was much less of a combatant, though he also could bravely splinter a spear with an opponent on occasion, as in the memorable discussion with Huxley on the Age of the Earth.
Tait's professorial lectures were always models of clear and logical arrangement. Every statement bore on the business in hand; the experimental illustrations, always carefully prepared beforehand, were called for at the proper time and were invariably successful. With Thomson it was otherwise: his digressions, though sometimes inspired and inspiring, were fatal to the success of the utmost efforts of his assistants to make his lectures successful systematic expositions of the facts and principles of elementary physics.
As has been stated in Chapter IV, two books were announced in 1863 as in course of preparation for the ensuing session of College. These were not published until 1867 and 1873; the first issued was the famous Treatise on Natural Philosophy, the second was entitled Elements of Natural Philosophy, and consisted in the main of part of the non-mathematical or large type portions of the Treatise. The scheme of the latter was that of an articulated skeleton of statements of principles and results, printed in ordinary type, with the mathematical deductions and proofs in smaller type. As was to be expected, the Elements, to a student whose mathematical reading was wide enough to tackle the Treatise, was the more difficult book of the two to completely master. But the continued large print narrative, as it may be called, is extremely valuable. It is a memorial of a habit of mind which was characteristic of both authors. They kept before them always the idea or thing rather than its symbol; and thus the edifice which they built up seemed never obscured by the scaffolding and machinery used in its erection. And as far as possible in processes of deduction the ideas are emphasised throughout; there is no mere putting in at one end and taking out at the other; the result is examined and described at every stage. As in all else of Thomson's work, physical interpretation is kept in view at every step, and made available for correction and avoidance of errors, and the suggestion of new inquiries.
The book as it stands consists of "Division I, Preliminary" and part of "Division II, Abstract Dynamics." Division I includes the chapter on Kinematics already referred to, a chapter on Dynamical Laws and Principles, chapters on Experience and Measures and Instruments. Division II is represented only by Chapter V, Introductory; Chapter VI, Statics of a Particle and Attractions; and Chapter VII, Statics of Solids and Fluids. Thus Abstract Dynamics is without the more complete treatment of Kinetics to which, as well as to Statics, the discussion of Dynamical Laws and Principles was intended to be an introduction. But to a considerable extent, as we shall see, Kinetics is treated in this introductory chapter: indeed, the discussion of the general theorems of dynamics and their applications to kinetics is remarkably complete.
In Volume II it was intended to include chapters on the kinetics of a particle and of solid and fluid bodies, on the vibrations of solid bodies, and on wave-motion in general. It was expected also to contain a chapter much referred to in Volume I, on "Properties of Matter." That the work was not completed is a matter of keen regret to all physicists, regret, however, now tempered by the fact that many of the subjects of the unfulfilled programme are represented by such works as Lord Rayleigh's Theory of Sound, Lamb's Hydrodynamics, and Routh's Dynamics of a System of Rigid Bodies. But all deeply lament the loss of the "Properties of Matter." No one can ever write it as Thomson would have written it. His students obtained in his lectures glimpses of the things it might have contained, and it was most eagerly looked for. If that chapter only had been given, the loss caused by the discontinuance of the book would not have been so irreparable.
The first edition of the book was published by the Clarendon Press, Oxford. It was printed by Messrs. Constable, of Edinburgh, and is a beautiful specimen of mathematical typography. In some ways the first edition is exceedingly interesting, for it is not too much to say that its issue had an influence on dynamical science, and its exposition in this country, only second to that due to Newton's Principia. Three other works, perhaps, have had the same degree and kind of influence on mathematical thought—Laplace's Mécanique Céleste, Lagrange's Mécanique Analytique, and Fourier's Théorie Analytique de la Chaleur.
The second edition was issued by the Cambridge University Press as Parts I and II in 1878 and 1883. Various younger mathematicians now of eminence—Professor Chrystal, of Edinburgh, and Professor Burnside, of Greenwich, may be mentioned—read the proofs, and it is on the whole remarkably free from typographical and other errors. With the issue of Part II, the continuation was definitely abandoned.