( 392 ) 



bo no difference between the two values of Oj. and 6^; and at any 

 rate the difference will be scarcely noticeable, if the observations 

 on the mixtures do not reach the highest degree of accuracy. But 

 to know the accurate form is necessary in the first place for the 

 sake of perfect accuracy of the theoretical considerations, and in the 

 second place in his observations Mr. Verschaffelt seems to have 

 aimed at and perhaps reached that high degree of accuracy, at 

 which differences between the two sets of values of a.^ and bj, might 

 be of influence. 



Let us now proceed to investigate in how far Mr. Verschaffelt 

 has succeeded in determining the volumes which contain an equal 

 number of molecules under a pressure of 1 atmosphere. 



He puts for this : 



ij = 0,99931 + 0,000 {1—xf . 



From this formula we obtain the value 0,99931 for hydrogen 

 (iP =z 1)^ the value 1,0053 for carbonic acid (x = 0) and the value 

 1,00081 for iT = i. By means of these three values, taken from 

 observations, he has calculated his formula, assuming that y might 

 be put under the form a -\- hu' -\- cx^. 



According to the theory the factor, with which {vq)x is to be 

 multiplied in order to obtain (he volume, which contains the same 

 number of molecules, must be equal to: 



(1 +a^) (1 _;,,)— 1 + a, _^,^. 



If we take the latter form, viz {1 ~\- a^- — ^x), we make already 

 use of an approximation. But even with this approximation we find : 



r öi(l-*)^ a-(l-a;) x^ "l 



= \-\-{li-0:,-b:t'n-— -- + 2fl,2 -— — -j-j r^ + «2 7n T^ 



L(l+«l-^l)-' (l+fll-^l)(l+«3-M (l+«2-^2)-l 



L 14-ai-/'i 1/(1 +«1-61X1+02-^^2) l-|-«2-^2 J 



so that we must make use of another approximation to get a form 

 like »/ = o + b.v + cx\ All this may cause deviations, but the error 

 which is committed by assuming this form, will remain butiusigni- 

 ficant. My objection to the formula: 



y = 0,99931 + 0,000 (1— ,tf 



