102 PETER GUTHRIE TAIT 



In a post card to Thomson of date Nov. 5, 1871, Maxwell, after referring 

 to some proof sheets of his book which he had sent to Thomson to revise, 

 remarked : 



" Laplace has a clear view of the Biaxal harmonic. T' has an excellent discussion 

 of Qi and ^ w and their relations deduced from their definitions and not from their 

 expansions as Murphy does. Murphy is very clever, but not easily appreciated by 

 the beginner." 



This post card found its way finally to Tait and was duly filed along with 

 the other correspondence. The whole correspondence shows the free inter- 

 change of thought which went on between Maxwell and Tait and the subtle 

 manner in which each helped the other. We can in many cases infer the 

 nature of Tail's letters which Maxwell was obviously replying to ; but the 

 characteristic language in which these must have been expressed is unfortunately 

 irrecoverable. 



For anything of Hamilton's Tait had a profound respect ; and in the 

 " beautiful invention of the Hodograph " he found on more than one occasion 

 a source of inspiration. His hodograph note communicated to the Royal 

 Society of Edinburgh in 1867 contains an elegant geometrical construction in 

 which the equiangular spiral is used with effect to represent motion in a 

 resisting medium. Maxwell practically introduces the whole investigation 

 into the second volume of his Electricity and Magnetism, when he is dis- 

 cussing the theory of damped vibrations of a swinging magnetic needle. 



The powerful quaternion papers on the rotation of a rigid body and on 

 Green's theorem were communicated to the Royal Society in 1868 and 1870 

 respectively. They will be most suitably discussed in the following chapter on 

 quaternions. To this period also belongs a quaternion investigation into the 

 motion of a pendulum when the rotation of the earth is taken into account. 

 This is reproduced in the second edition of his Quaternions. The paper is 

 called an " Abstract " in the Proceedings ; and the closing sentences epitomising 

 other developments imply that Tait had every intention of publishing a complete 

 and elaborate discussion as a Transactions paper. For this however he never 

 found leisure. This habit of printing an abstract, indicating the lines of 

 development in a projected large memoir which never saw the light, was one 

 which grew with the progress of the years. 



During the early seventies, when the experiments in thermo-electricity 

 were in full swing, nothing very serious was taken up on the mathematical 

 side ; but the game of golf suggested this curious and by no means easy 



