QUANTITATIVE INDUCTION. 



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 ouo-ht 

 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. 7 



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 Eoscoe and Dittmar on the 

 tbsorption of gases in water 1 afford interesting illustration, 

 especially in the case of hydrochloric acid, the quaSHf 

 which dissolved in water under different pressures follows 

 very closely a linear law of variation, from which howeve? 

 it diverges widely at low pressures.' Herschel, havin- 

 deduced from observations of the double star 7 Vir*in 

 an elliptic orbit for the motion of one component rSund 

 e 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 

 adopted 3 6 dimenS1 nS f the old one > h *d ultimately to be 



Illustrations of Empirical Quantitative Laws. 



Although our object in quantitative inquiry is to discover 



ne exact or rational formulas, expressing the laws which 



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



Arago, Magnus, and Kegnaulfc-and by the last mentioned 

 the measurements were conducted with extraordinary care 



1 Watts' Dictionary of Chemistry, vol. ii. p. 790. 



2 Quarterly Journal of the Chemical Society, vol. vm p jr 

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



K K 2 ' 



