CHAPTEE XXII. 



QUANTITATIVE INDUCTION. 



LET it be observed that we have not yet formally con 

 sidered any processes of reasoning which have for their 

 object to disclose general laws of nature expressed in 

 quantitative formulae or equations. We have been in 

 quiring 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 rlso considered the precau 

 tions to be taken in the performance of observations and 

 experiments in order that we may know what phenomena 

 we really do measure and record. In treating of the 

 approximate character of all observations, we have par 

 tially entered upon the subject of Quantitative Induction 

 proper, but we must remember that no number of facts 

 and observations can by themselves constitute science or 

 general knowledge. Numerical facts, like other facts, 

 are but the raw materials of knowledge, upon which our 

 reasoning faculties must be exerted in order to draw 



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

 process of reasoning that we can alone discover the mathe 

 matical laws to which varying quantities conform. By well- 

 conducted experiments we gain a series of values oi 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 :- 



