TERMINOLOGY AND NOMENCLATURE. 253 



to it on any former occasion, is to us a new phenomenon ; 

 it is of importance that this new conception, or this new 

 result of ahstraction, 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 geometrical 

 demonstrations, if wherever the word circle is used, the 

 definition of a circle were inserted instead of it In mathe 

 matics and its applications, where the nature of the processes 

 demands that the attention should be strongly concentrated, 

 but does not require that it should be widely diffused, the 

 importance 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 algebraical opera 

 tions, he substitutes for (a m + l n ) * , or for- + + - + c., the 



q bed 



single letter P, Q, or S ; not solely to shorten his symbolical 

 expressions, but to simplify the purely intellectual part of his 

 operations, by enabling the mind to give its exclusive atten 

 tion to the relation between the quantity S and the other 

 quantities which enter into the equation, without being dis 

 tracted by thinking unnecessarily of the parts of which S 

 is itself composed. 



But there is another reason, in addition to that of pro 

 moting perspicuity, for giving a brief and compact name to 

 each of the more considerable results of abstraction which 

 are obtained in the course of our intellectual phenomena. 

 By naming them, we fix our attention upon them ; we keep 

 them more constantly before the mind. The names are 

 remembered, and being remembered, suggest their definition ; 

 while if instead of specific and characteristic names, the 



