iz8 PETER GUTHRIE TAIT 



by reading this subject than the facility of making problems and transformations 

 for Examination papers (especially in Trigonometry) and so saving an immense 

 amount of time and trouble, I sh(61d have considered myself amply rewarded, but 

 I hope in time to be able to apply it to perfectly original work (if anything can 

 be quite original in these days).... 



In the portion of letter xiv which containing his reply to this letter 

 from Tait Hamilton suggested publishing in the Philosophical Magazine 

 his own investigations on the Wave Surface, and referred in particular to 

 certain sections of his letter xv which might form the substance of this 

 note. He said : 



"(54) It seems to me that some such sketch..., instead of forestalling your own 

 communication, which appears likely to be of weight enough to deserve ampler 

 space than the pages of a Magazine could afford, might, on the contrary, serve as 

 a not ungraceful introduction to whatever you were disposed to publish afterwards. 

 But let me know. ..what your FEELINGS in the matter are. I am quite aware 

 that I can implicitly rely on your allowing me at least as much credit as you may 

 be of opinion that I deserve ; and I think that you have really made the subject 

 your own by your laborious and (so far as I yet know) successful investigations." 



To this Tait replied : 



Q. C. BELFAST, 



7/1/59- 

 My dear Sir William Hamilton 



Many thanks for your very kind letter containing XIV pp. 57-60 & xv 

 pp. 93, 94, which I received this morning... 



I had been casting about as to how I should ask you to do the very thing 

 you have just proposed as I have, as you will see when you look at the recent 

 sheets of my Quat. Proofs, found one or two things which I believe were given by 

 you for the first time but which I had either not received from you or not read 

 until my own investigations were advanced beyond that point. For instance, 

 I consider that I am not directly indebted to you for the quaternion form of the 

 equation 1 to the wave in i, K, though of course you had it years before I knew of 

 such a thing as quaternions at all. But then, knowing as I do the date of your 

 discovery of that formula, I could not have published my own investigation without 

 specially mentioning that you had communicated it to me, and the latter course it 

 was impossible to follow, as I consider your letters private. 



You see then that I was in a difficulty and I should probably have tried at 

 some other matter for a paper to publish, but for your last. I am delighted at the 

 idea of being introduced to the Phil. Mag. (in which I have never written) in 

 connection with "quaternions by you, especially when the subject as well as the 



1 This is equation 13 in Tail's paper published in the Quarterly Journal of Mathematics, 

 May 1859 (Set. Pap. Vol. i, page 7), namely, 



(K" - i*) = \S (f - K') p}' + ( Wp + TV'pf. 



