100 MOLECULAR MOTION AND ITS ENERGY 43 



observations on the compressibility of carbonic acid with 

 great exactness ; since it gives a maximum value for p, 

 this occurring for v = %B, it suffices also to represent 

 Eegnault's determinations of the maximum pressure of 

 the gas as a function of the temperature. It thereby appears 

 what deserves to be mentioned as especially important 

 that the saturated vapour of carbonic acid has the same 

 thermal coefficient of expansion as the permanent gases. 



This is, however, not an incontestable proof of the exact- 

 ness of the hypothesis from which the formula was deduced. 

 For exactly the same formula comes also from the different 

 assumption that in condensable gases a part of the mole- 

 cules are bound together in pairs, since with this hypothesis 

 we have to take into account a diminution of the number 

 of colliding molecules, which diminution is to be assumed 

 the greater the oftener the molecules collide together, that 

 is, the more particles there are in unit volume. 



44. Hirn's and van der "Waals's Correction of 

 Boyle's Law 



For the same reason a more general theory, which we 

 owe to Hjm^and to van der Waals, 2 leads also to .the 

 same result, without its appearing necessary to specialise 

 the hypothesis so exactly. 



This theory not only considers the force of cohesion, 

 which alone up to the present has been mentioned as a 

 cause of the deviations from Boyle's law, but also takes 

 into account, as a second cause, the circumstance that has 

 been mentioned before ( 8), viz. that the dimensions of 

 the molecules are of disturbing influence on the exactness 

 of the law. This necessitates a twofold change in the 

 theoretical formula 



p = NmG 2 , 



1 Th&orie Mtcanigue de la Chaleur, ii. 1864, p. 215 ; Ann. Chim. Phys. [4] 

 xi. 1867, p. 47. 



2 ' Over de continuiteit van den gas- en vloeistof-toestand,' Academisch 

 Proefschrift, Leiden 1873. Translated into German by F. Both, Leipsig 

 1881 [and thence into English for the Physical Society of London]. Abstracted 

 in Fogg. Beibl i. 1877, p. 10. 



