284 
Proceedings of Royal Society of Edinhurgh. [sess. 
As to the necessity, in modern mathematical physics, for some 
substitute for what I must (with all deference to Prof. Cayley) call 
the cumbersome, unnatural, and unwieldy mechanism of co-ordi- 
nates, I have elsewhere fully expressed my own opinion, and 
need not repeat it. 
Of course it will be obvious from what precedes that I adhere to 
every word of the first extract which Professor Cayley has made 
from my original Preface. 
The phrase which he afterwards extracts for comment : — “ such 
elegant trifles as Trilinear Co-ordinates ” : — seems somewhat too 
sweeping, and I should certainly hesitate to use it without quali- 
fication. But the context shows that, in my Preface^ it was used 
to characterize the so-called “Abridged hTotation ” which had then 
been for some years introduced into Cambridge reading and 
examinations, not at all because of its superiority in completeness 
to the ordinary y system : — and therefore not on scientific 
grounds: — but mainly for the purpose of “aggravating” students, 
whether in the lecture-room or in the Senate House, at very small 
additional labour on the part of the lecturer or the examiner. But 
I made no reference whatever to Quadriplanar Co-ordinates ; for 
which I feel all due respect, not altogether free from an admixture 
of wholesome awe ! 
