45S 



OPERATIONS SUBSIDIARY TO INDUCTION. 



numerous and distinct. Thus leaves 

 may be called pinnatifid, pinnatipar- 

 tite, pinnatisect, pinnatilobate, palma- 

 tifid, palmatipartitef &c., and each of 

 these words designates different com- 

 binations of the modes and extent 

 of the divisions of the leaf with the 

 divisions of its outline. In some cases, 

 arbitrary numerical relations are in- 

 troduced into the definition : thus, a 

 leaf is called hilobate when it is divided 

 into two parts by a notch ; but if the 

 notch go to the middle of its length, 

 it is bifid ; 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 cruci- 

 ferous plant is a slliqua, if it is four 

 times as long as it is broad, but if it 

 be shorter than this it is a silicvla. 

 Such terms being established, the form 

 of the very complex leaf or frond of 

 a fern (Hymenophyllum Wilsoni) is 

 exactly conveyed by the following 

 phrase : — 'Fronds rigid pinnate, pinnae 

 recurved subunilateral pinnatifid, the 

 segments linear undivided or bifid, 

 spinulososerrate. ' 



" Other characters, as well as form, 

 are conveyed with the like precision : 

 colour by means of a classified scale 

 of colours. . . . This was done with 

 most precision by Werner, and his 

 scale of colours is still the most usual 

 standard of naturalists. Werner also 

 introduced a more exact terminology 

 with regard to other 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 i, gyp- 

 sum 2, calc spar 3, and so on. . . . 

 Some properties as specific gravity, by 

 their definition give at once a mimeri- 

 cal measure ; and others, as crystal- 

 line form, require a very considerable 

 array of mathematical calculation and 

 reasoning to point out their^relations 

 and gradations." 



§ 3. Thus far of Descriptive Ter- 

 minology, 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 observed 

 instances which is the preparatory 

 step towards it, we stand in need of 

 an additional and a different sort of 

 general names. 



Whenever, for purposes of Induc- 

 tion, we find it necessary to introduce 

 (in Dr. 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 circum- 

 stance, which, our attention not hav- 

 ing been directed to it on any former 

 occasion, is to us a new phenomenon — 

 it is of importance that this new con- 

 ception, or this new result of abstrac- 

 tion, 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 pheno- 

 mena. No doubt, in most cases of 

 the kind, the meaning might be con- 

 veyed 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 pos- 

 sible. What darkness would be spread 

 over geometrical demonstrations, if 

 wherever the word cirde is used, the 

 definition of a circle were inserted in- 

 stead 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 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 substi- 

 tutes for (a™ + 6°)|, or forl + ^ + ^-f- 

 fcc, the single letter P, Q, or S ; not 

 solely to shorten his sjrmbolical ex- 

 pressions, but to simplify the purely 

 intellectual part of his operations, by 



