490 OPERATIONS SUBSIDIARY TO INDUCTION. 



" Other characters, as well as form, are conveyed with the like precision'. 



Color by means of a classified scale of colors This was done with 



most precision by Werner, and his scale of colors is still the most usual 

 standard of naturalists. Werner also introduced a more exact terminology 

 with regard to otlier characters which are important in mineralogy, as lustre, 

 hardness. But Mohs improved upon this step by giving a numerical scale 



of hardness, in which talc is 1 , gypsum 2, calc spar 3, and so on Some 



properties, as specific gravity, by their definition give at once a numerical 

 measure ; and others, as crystalline form, require a very considerable array 

 of mathematical calculation and reasoning, to point out their relations and 

 gradations." 



§ 3. Thus far of Descriptive Terminology, or of the language requisite 

 for placing on record our observation of individual instances. But when 

 we proceed from this to Induction, or rather to that comparison of ob- 

 served instances which is the preparatory step toward it, we stand in need 

 of an additional and a different sort of general names. 



Whenever, for purposes of Induction, we find it necessary to introduce 

 (in Dr. Whewell's phraseology) some new general conception ; that is, 

 whenever the comparison of a set of plienomena leads to the recognition 

 in them of some common circumstance, which, our attention not having 

 been directed 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 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 

 geometrical demonstrations, if wherever the word circle is used, the defini- 

 tion of a circle were inserted instead of it. In mathematics and its appli- 

 cations, 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 operations, he substitutes for (a"" 4- 6") ^, or for j-J — \—^-\- etc., 



' <i oca 



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

 pressions, but to simplify the purely intellectual part of his operations, 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, 

 without being distracted by thinking unnecessarily of the parts of which 

 S is itself composed. 



But there is another reason, in addition to that of promoting perspicui- 

 ty, 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 



