UKQUISITES OV LANGtTAGE. 



44t 



in (lelining momentum. It was al- 

 ready' a received doctrine, that when 

 two objects impinge upon one an- 

 other, the momentum lost by the one 

 is equal to that gained by the other. 

 This proposition it was deemed neces- 

 sary to preserve, not from the motive 

 (which operates in many other cases) 

 that it was firmly fi.xed in a popular 

 belief, for the proposition in question 

 had never been heard of by any but 

 the scientifically instructed ; but it 

 was felt to contain a trutii : even a 

 superficial observation of the pheno- 

 mena left no doubt that in the pro- 

 pagation of motion from one b<xly to 

 another there was something of which 

 the one body gained precisely what 

 the other lost ; and the word momen- 

 tum had been invented to express 

 this unknown something. The settle- 

 ment, therefore, of the definition of 

 momentum involved the determina- 

 tion of the question. What is that of 

 which a body, when it sets another 

 body in motion, loses exactly as much 

 as it communicates ? And when ex- 

 periment had shown that this somc- 

 th in;/ was the product of the velocity 

 of the body by its mass, or quantity 

 of matter, this became the definition 

 of momentum. 



The following remarks,* therefore, 

 arc perfectly just : " The business of 

 definition is part of the business of 

 discovery. ... To define, so that our 

 definition shall have any scientific 

 value, requires no small portion of 

 that sagacity by which truth is de- 

 tected. . . . When it has been clearly 

 seen what ought to be our definition, 

 it must be pi*etty well known what 

 truth we have to state. The defini- 

 tion, as well as the discovery, sup- 

 poses a decided step in our knowledge 

 to have been made. The writers on 

 Logic in the Middle Ages made Defi- 

 nition the last stage in the progress of 

 knowledge ; and in this arrangement 

 at least, the history of science, and 

 the philosophy derived from the his- 

 tory, confirm their speculative views." 

 For in order to judge finally how the 

 * Nov. Onj. Iknov., p. 39-40. 



name which denotes a class may best 

 be defined, we nuist kntnv all the pro- 

 perties common to the class, and all 

 the relations of causation or depen- 

 dence among those properties. 



If the properties which are fittest 

 to be selected as marks of other com- 

 mon properties are also obvious and 

 familiar, and especially if they bear a 

 great part in producing that general 

 air of resemblance which was the ori- 

 ginal inducement to the formation of 

 the class, the definition will then be 

 most felicitous. But it is often neces- 

 sary to define the class by some pro- 

 perty not familiarly known, provided 

 that property be the best mark of 

 those which are known. M. de Blain- 

 ville, for instance, founded his defini- 

 ti«)n of life on the process of decom- 

 position and recomposition which in- 

 cessantly takes place in every living 

 body, so that the particles composing 

 it are never for two instants the same. 

 This is by no means one of the most 

 obvious properties of living bodies ; it 

 might escape altogether the notice of 

 an unscientific observer. Yet great 

 authorities (independently of M. de 

 Blainville, who is himself a first-rato 

 authority) have thought that no other 

 property so well answers the condi- 

 tions required for the definition. 



§ 5. Having laid down the prin- 

 ciples which ought for the most part 

 to be observed in attempting ti) give 

 a precise connotation to a term in use, 

 I must now add that it is not always 

 practicable to adhere to those prin- 

 ciples, and that even when practicable 

 it is occasionally not desirable. 



Cases in which it is impossible to 

 comply with all the conditions of a 

 precise definition of a name in agree- 

 ment with usage occur very frequently. 

 There is often no one connotation 

 capable of being given to a word, so that 

 it shall still denote everything it is ac- 

 customed todenote ; or that allthepro- 

 positions into which it is accustomed to 

 enter, and which have any foundation 

 in truth, shall remain true. Indepcn- 

 dentlv of accidental ambiiruities, in 



