rxn.] QUANTITATIVE INDUCTION. 499 



change which a substance could undergo under unattain- 

 able circumstances. By observing, for instance, the ten- 

 sion of aqueous vapour between o and 100 C., we ought 

 theoretically to be able to infer its tension at every other 

 temperature ; but this is out of the question practically 

 because we cannot really ascertain the law precisely be- 

 tween 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 1 afford 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 widely at low pressures. 2 Herschel, having 

 deduced from 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 time 

 the motion of the star agreed very well with this orbit. 

 Nevertheless divergence began to appear and after a time 

 became so great that an entirely new orbit, of more than 

 double the dimensions of the old one, had ultimately to be 

 adopted. 3 



Illustrations of Empirical Quantitative Laws. 



Although our object in quantitative inquiry is to discover 

 the exact or rational formulae, expressing the laws which 

 apply to the subject, it is instructive to observe in how 

 many important branches of science, no precise laws have 

 yet been detected. The tension of aqueous vapour at 

 different temperatures has been determined by a succession 

 of eminent experimentalists Dalton, Kaemtz, Dulong, 

 Arago, Magnus, and Eegnault and by the last mentioned 

 the measurements were conducted with extraordinary care. 



1 Watts' Dictionary of Chemistry, >ol. ii. p. 790. 



2 Quarterly Journal of the Chemical Society, vol. vni. p. 15. 

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



K ': 2 



