166 PETER GUTHRIE TAIT 



thought in quantics and coordinates ; Tail laid hold of each physical 

 quantity as an entity for which the quaternion notation supplied the 

 complete mental image. To Cayley the quaternion of Hamilton was an 

 algebraic complex which he and Sylvester regarded as a matrix of the 

 second order. For Tait the quaternion was a quantity obeying certain 

 laws, and yielding by its transformations endless physical interpretations. 

 These interpretations were of little interest to Cayley ; just as the general 

 solution of the linear matrix equation had small attractions for Tait. 



It is a misfortune that in this remarkable correspondence on things 

 quaternion Tail's letters to Maxwell have not been preserved. Towards 

 Hamilton Tait was the loyal disciple, eager to have the master's help at 

 all stages, and always ready to give him the fullest credit as the prime 

 source of every luminous thought. This deep loyalty no doubt prompted 

 Tait to destroy certain of Hamilton's later letters, which did not show the 

 great man at his best. To Cayley Tait turned as to the embodiment of 

 mathematical wisdom and knowledge. In spite of their fundamental difference 

 of outlook on quaternion fields a difference which gradually emerged as 

 they corresponded on the subject Tait had the greatest confidence in 

 Cayley's mathematical intuitions. Once when questioned as to his opinion 

 of Cayley's discoveries in pure mathematics, he remarked: "Cayley is 

 forging the weapons for future generations of physicists." But for Maxwell 

 Tait had not only unstinted admiration as a man of science ; he had for 

 him a deep strong love which had its roots in common school life and grew, 

 strengthened and ripened with the years. He understood to the full 

 Maxwell's intellectual oddities, his peculiar playful humour, his nobility of 

 character, and the deeper thoughts which moved his mind but rarely 

 found expression. Maxwell's letters, which Tait preserved with the greatest 

 care, imply an equivalence of correspondence on Tail's side, the general 

 nature of which may in certain cases be guessed, but the exact terms of 

 which are no longer accessible. Just as Tait placed implicit confidence in 

 Maxwell's physical intuitions, so Maxwell accepted the leadership of Tait 

 in quaternion symbolism and interpretation. He once playfully remarked 

 that he envied Tait the authorship of the quaternion paper on Green's 

 Theorem ; and the extracts given above indicate how much he was influenced 

 by Tait when preparing his great work on Electricity and Magnetism. 

 Tail's quaternion work was indeed the necessary precursor of the qualernion 

 symbolism and nomenclature which Maxwell inlroduced inlo his book. 



