235 
of Edinburgh, Session 1870 - 71 . 
In alluding to the award of this prize, it is only right to men- 
tion the high estimation in which, as I have reason to know, 
this paper and other mathematical papers by the same author 
are held by men of science. These papers are examples of the 
application and use of a new and wonderful instrument of ana- 
lysis invented by the late Sir William Hamilton of Dublin, one 
of the profoundest philosophers of his day, known by the name of 
“ Quaternions .” I am told that there are as yet few mathematicians 
who can work with it. But Professor Tait has been able, both to 
work with it, and to improve upon it; and has applied it to the 
solution of many important physical questions not easily solved 
by ordinary analysis. 
To show that these remarks rest on better testimony than my own, 
I beg to refer to the high appreciation of Professor Tait’s applica- 
tion of “Quaternions,” as expressed by the distinguished inventor 
himself, in a work published shortly after his death. Sir William 
Hamilton’s “ Elements of Quaternions” (page 755) contains the 
following passage : — 
“ Professor Tait, who has already published tracts on other applications of 
Quaternions, mathematical and physical, including some on Electro-dynamics, 
appears to the writer eminently fitted to carry on, happily and usefully, this 
new branch of mathematical science, and likely to become in it, if the ex- 
pression may be allowed, one of the chief successors to its inventor.” 
To these gracious words of Hamilton, may be added the testimony 
of Professor Sir William Thomson of Glasgow, himself a mathe- 
matician and physicist second to none in Europe, contained in a 
letter to our General Secretary, from which I am allowed to quote : — ■ 
“ My Dear Balfour, — The marked appreciation by Sir William Hamilton 
of Tait’s work in quaternions, is about the highest possible testimonial to its 
excellence. His book on the subject will constitute, I believe, a permanent 
monument of the most marvellously ingenious generalisation ever made in 
mathematical science. It has already done much to render the new instru- 
ment available for researches in Natural Philosophy, and I can see signs 
(witness the two most transcendent and practical naturalists of the age, 
Helmholtz and Clerk Maxwell) of quaternions becoming, through its teach- 
ing, a useful implement, though many years may pass before fruits resulting 
from quaternionic husbandry can be gathered.” 
Besides the ordinary business of the Society for the past year 
