126 PETER GUTHRIE TAIT 



with all its deficiencies is the best I could make out of the subject before today 

 when a new idea suggested itself that of avoiding the fearful eliminations which 

 my method would seem to require in obtaining the equation of Fresnel's Wave 

 Surface. The idea, which I have easjjy satisfied myself is correct, is to show that 

 surfaces derived from reciprocal ellipsoids are themselves reciprocal. 



Meanwhile on December 3 Hamilton began his letter xv on the Wave 

 Surface and dispatched the early sheets of it along with some pages of 

 letter xiv, in which he acknowledged receipt of Tail's 



"...note No. 13 together with its very valuable enclosure of two sheets entitled 

 ' Quaternion Proofs of some Theorems connected with the Wave Surface in Biaxal 

 Crystals.'... I have read the first sheet of your Quaternion Proofs, and must say 

 that they appear to me to be wonderfully elegant and to exhibit a very remarkable 

 degree of mastery (so far) over the calculus of Quaternions, used as an instrument 

 of expression and of investigation. 



" It would interest me much to know, whether (previous to our present cor- 

 respondence) you had received ANY assistance from any other student of that 

 calculus. Or did you learn all that you had acquired from the BOOK itself, 

 combined (no doubt) with your own private exercises of various sorts? If the 

 ' Lectures on Quaternions ' have been your ONLY teacher, I must consider the 

 result of such a state of things to be not merely creditable to your own talents and 

 diligence, but also complimentary to, and evidence of, some (scarcely hoped for) 

 didactic capabilities of my volume ; which ought to tend to console me, under my 

 artistic consciousness (as an author) of so many faults of execution, that if I could 

 afford the expense of bringing out a New Edition I should be more likely to make 

 it a New Work... My old friend John T. Graves called my attention about a year 

 ago to a highly favourable, and very eloquent, article in the North American Review 

 for July, 1857, on the subject of the Quaternions, and of my Book. But a 

 conscientious Author wishes rather to be read, than to be praised, and therefore I 

 should like to be informed, what drew your attention to my Book, and whether 

 you had any personal assistance in studying it." 



To this request Tait replied in his letter 14 of date December 7, 1858 : 



With regard to my study of Quaternions I may affirm with some certainty that 

 when I ordered your book, on account of an advertisement in the Athenaeum, I 

 had NO IDEA what it was about. The startling title caught my eye in August '53, 

 and as I was just going off to shooting quarters I took it and some scribbling paper 



with me to beguile the time However, as I told you in my first letter I got 



easily enough through the first six Lectures and I have still a good many notes 

 I made at that time from which it now seems to me that I had not fully appreciated 

 the simplicity of the method but had used quaternions generally in the shape 



