1893 - 94 .] Prof. Tait on the Quaternion Method. 
281 
[3.] If we were altogether strangers, I could have no right to address 
you on such a subject at all. [Here follow, as an example, some allusions 
(which need not he quoted) to a then recent pamphlet of Mobius, dealing 
with the Associative Principle in Quaternion Multiplication.] But 
between you and me, the case is perhaps not exactly similar ; as we 
have so freely corresjDonded, and as you are an Author in the same 
language, and of the same country ; — England, Scotland, and Ireland, 
being here held to have their sons compatriots. 
[4.] To Mobius’s excellent Pamphlet, it is likely that I may return. 
Meanwhile I trust that it cannot be offensive to you, if I confess, — 
what indeed your No. 38 encourages me to state, — that in any such 
future publication on the Quaternions as you do me the honour to 
meditate, I should prefer the establishment of ‘ Principles ’ being left, for 
some time longer, — say even 2 or 3 years, — in my own hands. Open to im- 
jDrovement as my treatment of them confessedly is, I wish that improve- 
ment, at least to some extent, to be made and published by myself. 
Briefly, I should like (I own it) that no book, so much more attractive to 
the mathematical public than any work of mine, as a book of yours is 
likely to be, should have the apj)earance of laying a ‘Foundation’ : 
although the richer the ‘ Superstructure,’ on a previously laid founda- 
tion, may be, the better shall I be pleased. I think, therefore, that you 
may be content to deduce the Associative Law, from the rules of -i, j, h ; 
leaving it to me to consider and to discuss whether it might not have been 
a fatal objection to these rules^ if they had been found to be inconsistent 
with that Principle. 
[7.] For calculation, you know, the rules of f, j, Jc are a sufficient basis, 
although of course we have continual need for transformations, such as 
YyYPa = aSfiy - ^Sya, 
which may at last be reduced to consequences of those rules ; and also 
require some Notation, such as S,V,K,T,U, which I have been glad to 
find that you are willing, at least for the present, to retain and to employ. 
But my peculiar turn of mind makes me dissatisfied without seeking to 
go deeper into the philosophy of the whole subject, although I am 
conscious that it will be imprudent to attempt to gain any lengthened 
hearing for my reflections. In fact I hope to get much more rapidly on 
to rules and operations, in the Manual than in the Lectures ; although 
I cannot consent to neglect the occasion of developing more fully my 
conception of the Multiplication of Vectors, and of seeking to establish 
such mult[iplication] as a much less arbitrary process, than it may seem to 
most readers of my former book to be.” 
I do not now think that Hamilton, with the “ peculiar turn of 
mind ” of which he speaks, could ever, in a hook, have conveyed 
