140 PETER GUTHRIE TAIT 



with examples the other, the examples alone. I went on to say that even the first 

 of these " could not in the least interfere with your (then projected) new work, as it 

 would treat only of the practice of the method, and not at all of the principles." And 

 I added, " I have not the least intention of publishing a volume on the subject 

 without your approval." When (in XXVIl) you wrote in answer to the above " I should 

 prefer the establishment of PRINCIPLES being left, at least for some time longer, 

 say even 2 or 3 years in my own hands ; and I think you may be content to deduce 

 the Associative Law from the rules of i, j, k, etc." I fancied that you meant me to 

 give these deductions in print beginning from i"-=j* = k* = ijk = i as something 

 established in your Lectures and Manual. When some months or so later, I wrote 

 to you that I had asked Macmillan to advertize for me " An Elementary Treatise 

 on Quaternions, with numerous examples" I had no idea whatever that I was 



giving you any annoyance 



But (as I have already quoted from 38) I am most desirous to avoid the 

 slightest suspicion of interference with your intentions and I therefore particularly 

 request you to give me a perfectly distinct idea of your desire in the matter and 

 my advertisement and form of treatment shall be at once adapted to it. But 

 I regret you did not tell me of this, at once, more than a year ago, when I enclosed 

 a printed copy of Macmillan's advertisement 



Hamilton's reply to this was evidently very satisfactory, for on 

 December n, 1860, Tait wrote: 



I am glad to find that my explanation has been sufficient, for I assure you 

 that I had attributed the slackness of our correspondence of the last year to your 

 having been bored and tired with my continued questions about various old and 

 new points in Quaternions, and had no idea whatever that I had annoyed you in 

 any way by the publication of my unlucky advertisement. 



In letter 46, January 14, 1861, Tait acknowledged receipt of proof 

 sheets of the Elements, and made further references to his electrodynamic 

 work. 



Here the correspondence practically ended. We learn from Tail's 

 preface to his Treatise that Hamilton shortly before his death in 1865 urged 

 Tait to push on with his book, as his own was almost ready for publica- 

 tion. 



It is pleasing to know that the misconception of the situation which 

 had fretted the mind of the master was entirely removed by the straight- 

 forward honest dealing of the disciple. 



Broadly speaking the subject-matter of the Hamilton-Tait correspondence 

 may be grouped under five heads. 



(i) Quaternion differentials. These are discussed at length in 

 Hamilton's letters v and x, the former of 45 pages having been written 

 between the dates of Oct. 1 1 and 1 6, and the latter of 48 pages between 



