insight into such space relations as strains, twists, spins and rotational or irrotational movements in general. Maxwell, who once declared that he had been striving all his life to be freed from the yoke of the Cartesian coordinates, had already found such an instrument in the Hamiltonian quaternions, the application of which he brilliantly demonstrated in his great treatise on electricity and magnetism. Quaternions are elegant, consistent, concise and uniquely adapted to Euclidean space, but physicists have latterly found them artificial and unnatural to their science, because the square of the quaternionic vector becomes a negative quantity.[1] The Gibbsian vectors obviate this difficulty, and while seemingly uncouth, furnish' a mode of attack more simple and direct and adaptable to space of any dimensions. Their capacity for interpreting space relations was amply tested by Gibbs in his five papers on the electromagnetic theory of light and his application of vectors to the calculation of orbits, since incorporated in recent German treatises on astronomy. The fact that vectors tend to displace the quaternionic analysis of Sir William Rowan Hamilton involved our author in a lengthy controversy with Hamilton's best interpreter, the ingenious and versatile Tait,[2] who looked upon Gibbs as "one of the retarders of quaternionic progress," defining his system as "a sort of hermaphrodite monster compounded of the notations of Hamilton and Grassmann." But Gibbs did not regard his method as strictly original; he was only concerned with its application in the task of teaching students; and when, after testing it by twenty years' experience in the class-room, he reluctantly consented to the publication of his lectures in full, the task was confided to one of his pupils, our author declining, with a characteristic touch of conscience, to have the work appear under his name or even to read the proof. In the controversy with Tait there is, as in most controversies, an amusing element of human nature. The name of Hamilton is undoubtedly one of the most illustrious in the history of science, and Tait and his adherents seemed to regard it as an impertinence and a desecration of his memory that any other
- ↑ "I have the highest admiration for the notion of a quaternion; but. . . as I consider the full moon far more beautiful than any moonlit view, so I regard the notion of a quaternion as far more beautiful than any of its applications. . . . I compare a quaternion formula to a pocket-map—a capital thing to put in one's pocket, but which for use must be unfolded: The formula, to be understood, must be translated into coordinates," Arthur Cayley, Proc. Roy. Soc. Edinb., 1892-5, XX., 271. At the Southport meeting of the British Association in 1903, Professor Larmor, while admitting the extreme usefulness of the different methods of vector analysis, argued that their slow progress in physics was due to the lack of uniformity in definitions and notations, requiring that each system must be mastered separately before it can be applied. To which Professor Boltzmann not inaptly replied that the confusion might have been avoided, if Hamilton had adopted the notations of Grassmann in the first instance.
- ↑ Nature, 1891-3, passim.
