QUANTITATIVE INDUCTION. 127 



laboured on the subject without exhausting it, and Brink- 

 ley and Ivory have since treated it. A closely connected 

 problem, that regarding the relation between the pressure 

 and elevation in different strata of the atmosphere, has 

 received the attention of a long succession of physicists 

 and was most carefully investigated by Laplace. Yet no 

 invariable and general law has been detected. The same 

 may be said concerning the law of human mortality ; 

 abundant statistics on this subject are available, and many 

 hypotheses more or less satisfactory have been put for- 

 ward as to the general form of the curve of mortality, 

 but it seems to be impossible to discover more than an 

 approximate law. 



It may perhaps be urged that in such subjects no single 

 invariable law can be expected. The atmosphere may be 

 divided into several variable strata which by their uncon- 

 nected changes frustrate the exact calculations of astro- 

 nomers. Human life may be subject at different ages to 

 a succession of different influences incapable of reduction 

 under any one law. The results observed may in fact be 

 aggregates of an immense number of separate results each 

 governed by their own separate laws, so that the subjects 

 may be complicated beyond the possibility of complete 

 resolution by empirical methods. This is certainly true 

 of the mathematical functions which must some time or 

 other be introduced into the science of political economy. 



Simple Proportional Variation. 



When we first treat numerical results in any novel kind 

 of investigation, our impression will probably be that one 

 quantity varies in simple proportion to another, so as 

 to obey the law y = mx + n. We must learn to distinguish 

 carefully between the cases where this proportionality is 

 really, and where it is only apparently true. When con- 



