( 331 ) 



(lüuble volume uiiilei' ii pressure of 1.0014 atiu. Let « bc the nuiubei' 

 of molecules which one Yolume of a perfect gas would contain at 

 0° and 1 atm., so that 0,99931 n is the number of molecules of 

 hydrogen and 1,0053 n the number of molecules of carbonic acid, 

 then it is easy to see that one volume of the mixture at 0° and 

 1 atm. must contain 1,0009 n mol. And so in order to find the theo- 

 retically normal volume of a mixture consisting of an equal number 

 of molecules of hydrogen and carbonic acid w^e must multiply the 

 volume at 0° and 1 atm. by 1,0009. 



Let, as in v. d. Waals's paper, x be the proportion of tlie number 

 of hydrogen-molecules to the whole number of molecules, tlien avo 

 can represent the deviation from Avogadro's law by the numbers: 

 1,0053 for x = <d, 1,0009 for a; = 0,5, and 0,99931 for *=1. The 

 deviation for intermediate mixtures can be found with sufficient ap- 

 proximation by applying a parabolic formula of the form ?/ =: a -j- ^.r-j-cr^j 

 and then we find that the deviation may be represented by 



I/ — 0,99931 + O.OOGO {\—xf . 



According to this formula the influence of small admixtures of 

 carbonic acid with the hydrogen is very small, a fact to which the 

 attenticm will be drawn later on. 



For the reduction to 0° C. we had to use the coefficients of 

 expansion of the mixtures. As a first approximation I might have 

 calculated the coefficients of expansion with the aid of a linear 

 formula from the coefficients of expansion of the pure substances: 

 0,00366 for Hj, 0,00371 for COa- But led by the previous result 

 regarding the deviations from Avogadro's law I thought it probable 

 that the dependence of the coefficient of expansion on the compo- 

 sition it would show the same characteristics; and so I was obliged 

 to put it thus : 



0^ = 0,00366 + 0,00005 (1— ,r)2 . 



\\\ determining the theoretically normal volume of hydrogen it was 

 mentioned that by starting from different experimental data we 

 arrive at diÖerent deviations from Avogadro's law. 



This is even more so in the case of carbonic acid. If by the side 

 of the number 0,99950 for hydrogen formerly accepted by Kamerlingii 

 Onnes we alst) borrow from v. D. Waals's Continuïteit (p. 76) the 

 number 1,00646 for carbonic acid (deduced from Regnaült's iso- 

 thermal lines) and if wo substitute this for Regnault's determination 



