JO SI AH WILLARD GIBBS 201 



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 Carte- 

 sian coordinates, had already found such an instrument in the Hamil- 

 tonian quaternions, the application of which he brilliantly demon- 

 strated in his great treatise on electricity and magnetism. Quater- 

 nions 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. 153 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, 154 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 orig- 

 inal ; 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 



153 " 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 appli- 

 cations. ... 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 Asso- 

 ciation 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, requir- 

 ing 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. 



154 'Nature, 1891-3, passim. 



