IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 347 
last equations, and substituting them in the relation to which 
they are subjected, there evidently results 
Lr niin RR ater i 1 P, 
Fe Pe ae 
8 8) eS gh 0 (P, + P,) ( ) 
the second member is entirely composed of observable quantities. 
: - . 1 
Its calculated numerical value will give therefore >: and conse- 
quently 6; that is to say, the resulting density in the hypothesis 
under consideration. 
1 
The coefficients of 5 
] 
portions of the two liquids contained in each unity of weight of 
the mixed system. As their intervention is most usually indi- 
cated under this form in the tables of experiments which I shall 
use, I will introduce them explicitly, making for abbreviation, 
i wa ees uaa 
1 a ry rs 2 Pj ae Ee 
whence will result 
and of + express respectively the pro- 
2 
1 
7a phen e ° . . . ° (2.) 
to which must be added 
4 t+e,=1. 
If one of the liquids, for instance that to which the sign 2 is ap- 
plied, is distilled water, in that case 6, = 1, which supposes that 
the primitive density 0, and the resulting density ¢ are taken, 
comparatively with water, at a common temperature, in which 
the mixture formed has become stable. This community of 
temperature should also be supposed to occur, in the general 
case, for all the operations by which the three densities ¢,, 2, 4 
are evaluated, of which the equation (1.) expresses the mutual 
relations, whether measured relatively to distilled water, or to 
any other liquid taken as atype. The identity of temperature 
thus established allows of the formula being applied to each 
given case, and the result compared with experiment without 
any knowledge of the dilatations. 
40. The expression of 8 may even be applied to the case in 
which the element P, of the mixture is a solid body, provided 
that we know the density 8, which should be attributed to this 
body, when it is in a state of disaggregation immediately pre- 
2c2 
