424 OPERATIONS SUBSIDIARY TO INDUCTION. 



and extent of the divisions of the leaf with the divisions of its outHne, 

 In some cases, arbiti-ary numerical relations are introduced into the 

 definition : thus, a leaf is called bilobate, when it is divided into two 

 parts by a notch ; but if the notch go to the middle of its length, it is 

 bijid; if it go near the base of the leaf, it is bipartite; if to the base, 

 it is bisect. Thus, too, a pod of a cruciferous plant is a silica, if it is 

 four times as long as it is broad, but if it be shorter than this it is a 

 silicula. Such terms being established, the form of the very complex 

 leaf or frond of a fern* is exactly conveyed by the following phrase : — 

 'fronds rigid pinnate, pinnae recurved subunilateral pinnatifid, the seg- 

 ments linear undivided or bifid spinuloso-serrate.' 



"Other characters, as well as form, are conveyed with the like pre- 

 cision: Color by means of a classified scale of colors. ... This was 

 done with most precisionby Werner, and his scale of colors is still the 

 most usual standard of naturalists. Werner also introduced a more 

 exact terminology with regard to other characters which are impor- 

 tant 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 



gi'avity, by their definition give at once a numerical measure ; and 

 others, as crystaline form, require a very considerable array of math- 

 ematical calculation and reasoning, to point out their relations and 

 gradations." 



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

 requisite for placing upon record our observation of individual in- 

 stances. But when we proceed from this to Induction, or rather to 

 that comparison of observed instances which is the preparatory step 

 towards it, we stand in need of an additional and a difierent sort of 

 general names. 



Whenever, for purposes of Induction, we find it necessary to intro- 

 duce (in Mr. Whewell's phraseology) some new general conception; 

 that is, whenever the comparison of a set of phenomena leads to the 

 recognition in them of some common circumstance, which, our atten- 

 tion 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 

 demonstration, if wherever the word circle is used, the definition of a 

 circle were inserted histead of it. In mathematics 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 importancd of concentration also in the expressions has 

 always been duly felt ; and a mathematician no sooner finds that he 

 ahall often have occasion to speak of the same two things together, 



* " Hymeiiovhyllum WihonV 



