1899-1900.] Prof. Tait on a Claim made for Gauss. 
17 
On the Claim recently made for Gauss to the Invention 
(not the Discovery ) of Quaternions. By Prof. Tait. 
(Read December 18, 1899.) 
It is only within a few months that my attention has been (at 
first accidentally) called to this matter. For, though I owe to the 
kindness of Prof. Klein a copy of his and Sommerf eld’s Tlieorie des 
Kreisels , I had passed over, in reading the work, the “ Digression 
on Quaternions” which it contains. But Prof. C. N. Little, in the 
course of correspondence about his remarkable paper on Knots 
(whose passage through the press I was looking after), referred me 
for a numerical detail to an article by Prof. Klein on the progress 
of publication of Gauss’ Gesammelte Werke. Shortly afterwards 
Prof. Joly called my attention to the same article from another 
point of view. These references have led me to write the present 
paper ; whose somewhat puzzling title is explained in the first 
section below. 
1 . 
In 1894 a paper by Prof. Cayley was read before the Society, 
under the title “ Coordinates versus Quaternions In this paper 
the gain in compactness and expressiveness secured by the use of 
the quaternion method was allowed ; but the concession was 
virtually nullified by the implication that, to be of any use, these 
simple expressions must be degraded into the vile elements of 
x, y, 2 or i , j, k , which were looked upon as their necessary basis. 
In reply, I allowed that this statement was to a certain extent 
warranted, provided the quaternion were regarded as Hamilton’s 
brilliant Invention of 1843 : — a splendid system of imaginaries ; but 
insisted that it had no application whatever to the quaternion of 
the latter half of the century : — a Discovery of the highest order, in 
which the Real took everywhere the place of the Imaginary. 
From that point of view, of course, the discovery was the great 
thing, the invention merely an exceedingly elegant trifle. Still 
both were regarded as due exclusively to Hamilton. 
These two papers were printed in our Proceedings , vol. xx. 
VOL. XXIII. B 
