142 PETER GUTHRIE TAIT 



merely write to say that I shall be most happy if you will persevere in your intention 

 of publishing an elementary volume on the subject. In fact the papers I have sent 

 you contain nearly the whole of my researches in the elementary part of the theory. 

 I have an immense store of work in MSS relating to its higher applications but 

 unfit for an elementary treatise. 



Since I projected the treatise I have ceased to be a Professor of Mathematics ; 

 and with private experiments and the ordinary preparation for the work of my class, 

 I feel that I have barely time enough to contribute my fair share to the " Treatise 

 on Natural Philosophy " which Thomson and I have undertaken. And, as this Treatise 

 is certain to extend to three volumes at least, of which (after two years work) not 

 even one is yet published, I feel that it may be years before I shall be in a position 

 to write on Quaternions in a carefully considered popular style. I am sure that 

 my old friend Macmillan would be delighted to have the chance of substituting your 

 name for mine in the advertisement, which he has been hopelessly repeating for 

 some years. 



But the consent of Sir W. R. Hamilton is absolutely necessary to anyone 

 undertaking the work. 



Believe me, my dear Sir, 



Yours very truly 



P. GUTHRIE TAIT. 

 Sir J. F. W. Herschel, Bart. 



It is certainly remarkable that Herschel at the age of 72 should have 

 thought of such a project. 



Only a careful comparison of the pages of Hamilton's and Tail's works 

 could establish to what extent Tail's contribulions were essenlially original. 

 Their melhods were markedly different Hamillon revelled in geomelrical 

 development of all kinds, ihe fertility of his malhemalical imagination 

 lending al limes lo make him discursive and almosl prolix. Tail's endeavour 

 in all his really original quaternion work was lo grapple wilh physical and 

 dynamical problems. Compare for example ihe Hamillonian development of 

 ihe properlies of ihe linear vector funclion wilh ihe chapler on slrains which 

 Tail conlribuled lo Kelland and Tail's Introduction to Quaternions each 

 mode of irealmenl admirable in ils way. 



The linear veclor funclion conlinued lo absorb much of Tail's allenlion 

 up to ihe very lasl day of his life. He made important contribulions lo 

 ihe iheory as well as many inleresling applications of ils power. See for 

 example papers xv, xxi, xxvi, cxiv, cxx, cxxi, cxxn, cxxiv in ihe Scientific 

 Papers, Vols. i and n especially ihe firsl-named, lhal on ihe Rolalion of a 

 Rigid Solid. 



Unqueslionably, however, Tail's greal work was his developmenl of 



