On the Simplification of Mathematical Analyses. 177 
tioned by the terms Thermometer and Photometer now in com- 
mon use.’’ I shall only remark respecting Mr. Walker’s ‘‘ Pho- 
iogen,”’ that in the language of the Greeks (from whence the 
two words composing this term are derived) the literal inter- 
pretation is to generate dight. How this applies to “the im- 
ponderable element of combustibles,” Ihave to learn. In page 24, 
Mr. Walker observes “that light and head are produced in the 
electric discharge. J observe none sufficient to affect our most 
delicate thermometers. 1 have by this means suffered metallie 
‘amine to be fused on the back and ether inflamed in the hollow 
of the hand, by a spark taken throughit, by means of a person 
uninsulated ; and surely, if sensible heat had been excited, I must 
have felt it. Ifnone other more competent to the task than my- 
self takes up the subject, I shall endeavour shortly to point out 
some inadyertencies into which I conceive Mr. Walker has fallen. 
I am, with much respect, gentlemen, 
Your obliged obedient servant, 
J. Murray, 
Messrs. Nicholson and Tilloch. 
= _...__.__.__.._______ 
XXXIV. On the Simplification of Mathematical Analyses :— 
a Paper read to the Liverpool Philosophical Society, By 
Mr. Egerton Smiru Eyres. 
< 
qT, all inventive sciences, it happens that particular methods for 
determining every possible proposition cannot be laid down; for 
the science would in that case be no longer an inventive, but 
barely a substitutive one. But although we experience the im- 
practicability of discerning rules so universal as to include every 
known case of the branch of knowledge with which they are con- 
nected, yet it is very possible, by proper explanations and con- 
cise methods, much to facilitate the operations and assist the in- 
vention; for the whole art of solution consists in reducing com- 
plex matter to a more simple form ; and therefore, if we can de-~ 
termine wherein the complexity of problems consists, as opposed 
to their simplicity, we may know, not only when we have re- 
duced a complex to a simpler problem, but also in some measure 
obtain rules concerning the method to be pursued in such re- 
ductichs, 
I think we may assume it as an axiom,’ that complexity in- 
creases with the number of data or things to be considered; that 
is, complexity is as the number of data directly; and, therefore, 
one division of the method of reduction will consist in diminish- 
ing the number of data from a greater to a lower number, till 
we arrive at the simplest possible conclusion, and that will be 
Vol. 43, No, 191. March 1814, M the 
