HAMILTON'S APPRECIATION OF THECORRESPONDENCE 131 



might perhaps be called a ' Manual of Quaternions.' In it I suppress (decidedly) 

 more than half of the existing Book ; not that I am ashamed of it, but because 

 I conceive that it has served its purpose : and that what we may call a working 

 volume is wanted now. 



" I fear that No. XVI of the series of MS will never be completed, or will be 

 brought abruptly to a termination 1 : but I don't think that you require my word, 

 for you have perhaps already indications enough, that I possess a number of 

 uncommunicated results, respecting the function <j> for instance, which will yet 

 throw additional light on the treatment by quaternions of surfaces of the second 



order 



"[72] January 31, 1859. I see that the enclosed sheet, though not yet sent off, 

 was written ten days ago. I have not even thought about the Wave Surface since, 

 much less written a line about it ; but I by no means abandon the project of 

 publishing some such short paper as I described to you in a former sheet ; leaving 

 it to you to develope, in whatever form you choose, your own independent investiga- 

 tions and results. It really seems to me that there would be some impertinence in 

 my having the air of examining whether your formulae on that subject are correct. 

 You are quite as well able as myself to decide any such point : especially since you 

 have got into the way of making transformations and of multiplying them. I trust 

 however that it is not an impertinence in me to confess that I think (or at all 

 events, hope) that this correspondence has been useful to you, in some degree ; 

 chiefly by causing you to feel a greater degree of confidence in your own powers ; 

 as applied to a new subject ; and as evincing that whatever obscurity may have 

 been allowed to remain in parts of my printed Lectures, from want of skill of an 

 artistic kind in the author, it has not been fatal to a comprehension of the Book, 

 by such a Reader as yourself; although the particular obscurity (about dp), which 

 led to our correspondence, has not (in my opinion) been at all sufficiently yet 

 removed, by my Letters V and X. 



" [73] As to myself I cheerfully confess, that I consider myself to have, in 

 several respects, derived advantage, as well as pleasure, from the Correspondence. 

 It was useful to me, for example, to have had my attention recalled to the whole 

 subject of the Quaternions, which I had been almost trying to forget; partly under 

 the impression that nobody cared, or would soon care, about them. The result 

 seems likely to be, that I shall go on to write some such ' Manual,' not necessarily 

 a very short one, as that alluded to in a recent paragraph. 



"[74] In fact, after pretty nearly filling two books, A. 1858 and T. 1858 with 

 matters relating to the 'Tait Correspondence' [for 'A' had happened to be 

 reserved, although 'B,' ' C,' 'D,' and 'E' (at least) had been stuffed with things 

 connected with De Morgan, and with Definite Integrals &c. and after a few more 

 letters of the alphabet having been pressed into the service, I used ' Alliteration's 

 artful aid' and made a sudden bound, in honour of you, to 'T'] I have lately 



1 No. xvi was begun on Dec. 14, 1858, but the greater part was written on Jan. u, 

 1859. It was abruptly finished off on Feb. 4, 1859, after a few paragraphs on surfaces of the 

 second order had been put together. 



17 2 



