CHAPTER XXI I 



QUANTITATIVE INDUCTION. 



WE have not yet formally considered any processes 

 of reasoning which have for their object to disclose laws 

 of nature expressed in quantitative equations. We liave 

 been inquiring into the modes by which a phenomenon 

 may be measured, and, if it be a composite phenomenon, 

 may be resolved, by the aid of several measurements, into 

 its component parts. We have also considered the pre- 

 cautions to be taken in the performance of observations 

 and experiments in order that we may know what pheno- 

 mena we really do measure, but we must remember that 

 no number of facts and observations can by themselves 

 constitute science. Numerical facts, like other facts, are 

 but the raw materials of knowledge, upon which our 

 reasoning faculties must be exerted in order to draw 

 forth the principles of nature. It is by an inverse process 

 of reasoning that we can alone discover the mathematical 

 laws to which varying quantities conform. By well- 

 conducted experiments we gain a series of values of a 

 variable, and a corresponding series of values of a variant, 

 and we now want to know what mathematical function 

 the variant is as regards the variable. In the usual pro- 

 gress of a science three questions will have to be answered 

 as regards every important quantitative phenomenon : 



(1) Is there any constant relation between a variable 

 and a variant ? 



(2) What is the empirical formula expressing this relation? 



(3) What is the rational formula expressing the law of 

 nature involved ? 



