QUANTITATIVE INDUCTION. 125 



trace of every change which a substance could undergo 

 under unattainable circumstances. By observing, for in- 

 stance, the tension of aqueous vapour between o and 

 1 00 C., we ought theoretically to be able to infer its 

 tension at every other temperature ; but this is out of 

 the question because we cannot really ascertain the law 

 precisely between those temperatures. 



Many instances might be given to show that laws 

 which appear to represent correctly the results of experi- 

 ments within certain limits altogether fail beyond those 

 limits. The experiments of Koscoe and Dittmar, on the 

 absorption of gases in water r afford many interesting 

 illustrations, especially in the case of hydrochloric acid, 

 the quantity of which dissolved in water under different 

 pressures follows very closely a linear law of variation, 

 from which however it diverges very widely at low pres- 

 sures 8 . Sir J. Herschel having deduced from various 

 recorded observations of the double star 7 Virginis, an 

 elliptic orbit for the motion of one component round the 

 centre of gravity of both, found that for a certain time the 

 motion of the star agreed very well with this orbit. 

 Nevertheless a divergence began to appear by degrees, 

 and after a time became so great that an entirely new 

 orbit, of more than double the linear dimensions of the 

 old one, had ultimately to be adopted*. 



Illustrations of Empirical Quantitative Laws. 



Although our chief object in every quantitative inquiry 

 must be to discover the exact or rational formulae, express- 

 ing the general laws of nature applying to the subject, 

 it is instructive to observe in how many important branches 



r Watts's 'Dictionary of Chemistry,' vol. ii. p. 790. 



8 'Quarterly Journal of the Chemical Society,' vol. viii. p. 15. 



* 'Kesults of Observations at the Cape of Good Hope,' p. 293. 



