TERMINOLOGY AND NOMENCLATURE. 283 



comparison of a set of phenomena leads to the recog- 

 nition in them of some common circumstance, which, 

 our attention not having been directed to it on any 

 former occasion, is to us anew phenomenon; it is of 

 importance that this new conception, or this new 

 result of abstraction, should have a name appropriated 

 to it ; especially if the circumstance it involves be one 

 which leads to many consequences, or which is likely 

 to be found also in other classes of phenomena. No 

 doubt, in most cases of the kind, the meaning might 

 be conveyed by joining together several words already 

 in use. But when a thing has to be often spoken of, 

 there are more reasons than the saving of time and 

 space, for speaking of it in the most concise manner 

 possible. What darkness would be spread over geo- 

 metrical demonstration, if wherever the word circle is 

 used, the definition of a circle were inserted instead 

 of it. In mathematics and its applications, where 

 the nature of the processes demands that the atten- 

 tion should be strongly concentrated, but does not 

 require that it should be widely diffused, the import- 

 ance of concentration also in the expressions has 

 always been duly felt ; and a mathematician no sooner 

 finds that he shall often have occasion to speak of the 

 same two things together, than he at once creates a term 



to express them whenever combined: just as, in his 



P 

 algebraical operations, he substitutes for (a + 5 n ) q 



or for - + - + - + &c.. the single letter P, Q, or S; 

 b c d 



not solely to shorten his symbolical expressions, but 

 to simplify the purely intellectual part of his opera- 

 tions, by enabling the mind to give its exclusive 

 attention to the relation between the quantity S and 

 the other quantities which enter into the equation, 



