QUATERNIONS EXCLUDED 185 



It is now clear that there is no hope of the small book appearing 

 first. 



The references in these letters to Quaternions show that there was in the 

 early days an intention to have an appendix on quaternionic treatment of 

 physical problems. There were obvious practical difficulties in the way of 

 introducing a mathematical method which in spirit and notation was so unlike 

 that in ordinary use. It could not have been done without a preliminary 

 statement of the purely mathematical laws of combination and transforma- 

 tion. Then again Thomson was not merely not interested but emphatically 

 antagonistic. In a letter to Cayley in 1872, quoted above (p. 152), Tait 

 mentioned incidentally that Thomson " objects utterly to Quaternions " ; and 

 Kelvin in 1901 in a letter to Chrystal wrote regarding Tait : 



" We have had a thirty-eight year war over quaternions. He had been captured 

 by the originality and extraordinary beauty of Hamilton's genius in this respect ; 

 and had accepted I believe definitely from Hamilton to take charge of quaternions 

 after his death, which he has most loyally executed. Times without number I offered 

 to let quaternions into Thomson and Tait if he could only show that in any case our 

 work would be helped by their use. You will see that from beginning to end they 

 were never introduced." 



The implication here is that Tait was unable to show that the use of 

 quaternions would be of any advantage. It should be remembered, however, 

 that Tail's own most important applications and developments were of later 

 date than the years preceding 1867 when "T and T"' was published; and 

 that, although Tait was himself fully convinced of the value of quaternions as 

 an instrument of research, it was a very different matter to get Thomson to 

 look at the matter from his point of view. Rather than risk the collapse 

 of the whole enterprise Tait relinquished what must have been at one 

 time a keen desire. 



Meanwhile the book grew like an organism. With the exception of 

 appendices and parts introduced bodily from Thomson's published papers, 

 the manuscript first supplied to the printer was largely contributed by Tait. 

 Then, in proof, certain paragraphs, whose subject matter seized the mind of 

 Thomson, developed in a wonderful way. New sections and extensions of 

 old sections were added, and were altered, pruned and expanded by both 

 writers, until it was difficult to say how much was due to each. 



When the Treatise finally appeared in 1867, after six years' preparation, 

 it was at once seen to be a great work ; and within two years the edition was 



T. 24 



