280 Froceedings of Royal Society of Edinburgh. [sess. 
continued (if only partial) recognition Avas indispensable to the 
reception of his method by a world steeped in Cartesianism ! 
Through the whole compass of each of his tremendous volumes 
one can find traces of his desire to avoid even an allusion to h ; 
and, along with them, his sorrowful conviction that, should he do 
so, he would be left without a single reader. There can be little 
doubt that, by thus taking a course Avhich he felt to be far beneath 
the ideal which he had attained, he secured for Quaternions at 
least the temporary attention of mathematicians. But there seems 
to me to be just as little doubt that in so doing he led the vast 
majority of them to take what is still Professor Cayley’s point of 
view j and thus, to regard Quaternions as (apparently at least) 
obnoxious to his criticisms. And I further believe that, to this 
cause alone, Quaternions owe the scant favour with which they 
have hitherto been regarded. 
[I am quite aware that, in making such statements, I inferentially 
condemn (to some extent, at least) the course followed in my own 
book. But, since my relations with Hamilton in the matter have 
been alluded to more than once, and alike incompletely and incor- 
rectly, by Hamilton’s biographer, I may take this opportunity of 
making a slight explanation, not perhaps altogether uncalled for. 
That Hamilton can altogether have forgotten the permission (limited 
as it was) which he had given me, when, a little later, I proposed 
to avail myself of it {strictly within the limits imposed) seems in- 
credible. Mr Graves should either have let the matter alone, or have 
gone into much greater detail about it. As it stands, he virtually 
represents Hamilton as being unaccountably capricious. The fol- 
lowing extract from the letter (of date July 10, 1859) in which 
Hamilton gave his sanction to my writing a book on the subject, 
speaks for itself. I had, of course, no rights in the matter : — and I 
cheerfully submitted to the restrictions he imposed on me ; especially 
as I understood that he expressly (and most justly) desired to be the 
first to give to the world his system in its vastly improved form. 
“ [2] If I shall go on to speak of my views, wishes, or feelings, on the 
subject of future publication, I request you beforehand to give to any 
such expression of mine your most indulgent construction ; and not to 
attribute to me any jealousy of you, or any wish to interfere, in any 
way, with your freedom, as Author and as Critic. 
