QUANTITATIVE INDUCTION. 115 



a closed one, or whether it has infinite branches ; 

 vhether such branches are asymptotic, that is, approach 

 ndefinitely towards straight lines ; whether it is loga- 

 ithmic in character, or trigonometric. This indeed we 

 jan only do if we remember the results of previous in- 

 estigations. The process is still inversely deductive, and 

 consists in noting what laws gave particular curves, and 

 hen inferring inversely that such curves belong to such 

 aws. If we can in this way discover the class of func- 

 ions to which the required law belongs, our chances of 

 complete success are much increased, because our hap- 

 lazard trials are now reduced within a narrower sphere. 

 3ut, unless we have almost the whole curve before us, the 

 dentification of its character must be a matter of great 

 incertaiuty ; and if, as in most physical investigations, 

 have a mere fragment of the curve, the assistance 

 riven would be quite illusory. Curves of almost any 

 character can be made to approximate to each other for a 

 imited extent, so that it is only by a kind of divination 

 ;hat we can fall upon the actual function, unless we have 

 ;heoretical knowledge of the kind of function applicable 

 to the case. 



When we have once obtained what we believe to be the 

 correct form of function, the remainder of the work is 

 nere mathematical computation to be performed infallibly 

 iccording to fixed rules 1 , which include those employed 

 n the determination of empirical formulas (vol. ii. p. no). 

 jThe function will involve two or three or more unknown 

 ponstants, the values of which we need to determine by 

 . )ur experimental results. Selecting some of our results 

 ; kidely apart and nearly equidistant, we must form by 

 . neans of them as many equations as there are constant 

 quantities to be determined. The solution of these equa- 

 ions will then give us the constants required, and having 



1 See Jamin, ' Cours de Physique,' vol. ii. p. 50. 

 ' I 2 



