( 301 ) 



(t'o).,, for the vulume ocoupiofl bv a molecular quantity at 0", the 

 characteristic equation is 



[p + "- Po ^] ['—''- (^'oV] = Po (^'c)' (Ho.) {l-h.) i\ +a t) , 



from which we deduce that the conditions that in ] cM^. the same 

 number of molecules be found are, that we have different mix- 

 tures with the same value for v, the same value for t and that we 

 have that value of p, for which the first member and therefore also 

 the second, is the same. The simple result is that the quantity of 

 the different mixtures is to be chosen in such a way that 

 {*'oV (1 + "') (1 — ^'^) has the same value for them all. 



As T^o ('^'o^^- (1 + ^•') (^ ~ M (1 + " is the limiting value of the 

 product pv, the preceding condition is also fulfilled, when this limiting 

 value is the same for the different mixtures. 



In the two preceding proceedings of the Academy Mr. J. Ver- 

 sciiAFFELT has published observations about mixtures of carbonic 

 acid and hydrogen. In order to determine the volumes, which contain 

 an equal number of molecules, the observer has followed a course 

 which agrees with the determination of (cq)^ (I + o^) (1 — M- He 

 is of opinion that the investigation of the limiting value of po would 

 not serve the purpose. I think that this conclusion must be drawn 

 from his remark p. 332. „From the point of view" etc. 



Be this as it may, I shall prove that both ways may be followed. 

 At the same time I shall investigate, in how far his observations 

 agree with my characteristic equation. But first a remark about the 

 accurate form of the characteristic equation, or rather about the 

 value of the quantities c^ and b^. 



I have always taken for them the following expressions: 



cij. = O] (1 — .c/ + 2 rtj.i X (!—.'■) + «2 -f^" 

 and b^ — b^ (1 —.if + 2 bj^ x ( I —•>•) f 63 j" . 



It is easy to see that if we want to be perfectly accurate we 

 must put : 



0.r ("0)^ = "1 ("o)ï (!—•'■)- + 2 «12 (l'u)l (('0)2 '*• (I— «•) + «3 ("0)2 ■>■'" 



and b, (.g. =. b, (r„)i (l_.r)3 + 2 b,, ^(^öhT^h^ (I--'') + b, (v,), x^ . 

 If we were allowed to equate {vi^\ , {t\^.2 and (i'o)j-, there would 



