( 476 ) 
differences of density which pr Heen observed in carbon dioxide. 
Small admixtures of the same kind as those by which pr HreN'’s 
experiments can be explained, may, until we have a proof to the 
contrary, also be assumed in the carbon tetrachloride with which 
TricHNer experimented. I therefore hold that Tricuyer’s researches, 
which from an experimental point of view leave less to be desired 
than those of pe HeEN's, must be explained in the same way. 
They are now being repeated at the Leiden laboratory with carbon 
dioxide of the greatest possible purity, while in order to omit all 
- doubts of temperature equilibrium 9, thermoelements are sealed in 
the tube. 
§ 2. Difference in density between two phases with slightly differing 
proportions of admixture, when equilibrium of pressure and of tem- 
perature exists. We imagine that in a tube, at a temperature Te 
which differs only little from the critical 7) of the pure substance, 
there are two layers of which the one contains per gramme molecule 
x, mol. of the admixture, the other z, mol; the pressure is supposed 
to be the same’), i.e. equal to p, and also to differ little from the 
critical pressure p, of the pure substance. In order to determine the 
density of a mixture with an (infinitely small) composition z, we 
may proceed as follows. The quantities a, 3, and y = «—@ determine 
the critical elements Tir, per, Von Of the point which for the mixture 
corresponds to the critical point of the pure substance, in first 
approximation (Comm. N°. 81 equation (14)) by the equations : 
Ta= T, (+62), par = pe + 82), viz =m +72): 
Hence to the temperature of observation 7’, i.e. the temperature 
of the mixture, a temperature 7” of the pure substance corresponds 
El 7 
: k : : 
in such a way that = =F. and we may therefore write in first 
xk 
approximation: 7” = T'(A — aw). In the same way the pressure 
p =p(1— ge) of the pure substance corresponds to the observed 
pressure p (pressure of the mixture). Suppose that at the temperature 
T’ and the pressure p’ the pure substance occupies the molecular 
volume v’, a volume which may be derived from the empirical equation 
of state or which may be read on a diagram of isothermals, then, 
under the circumstances observed (7, p), we have for the molecular 
volume of the mixture considered v =v’ (1+ y2). 
1) Cf. Vizarp, C. R. 118 and Comm. N°. 68 (April ’01). 
2) Doing so, we neglect the influence of gravitation, which is much smaller than 
at of the admixtures, and moreover increases the differences of density. 
