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.