IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 349 
To adapt the formula to these circumstances, without a new 
calculation, let us consider 4, as representing the density of the 
disaggregated sugar, supposed simply mixed with water in each 
solution. If 3, was known, ¢ would express the absolute density 
which this solution ought to have for the ponderable proportion 
e,- Designating then, by one or two accents, the various ele- 
ments of two solutions made at the same temperature, but dif- 
ferent in densities as well as in proportions, we have the follow- 
ing equations, in which ®, is common :— 
1 él 
eas, + (1—))3 
pie NG ; (2.) 
y= a b= D5 
then, on eliminating 8, between them, there remains 
ee 
Eq 
> == 7 + a — ais ath ant Mt Si es (3.) 
By means of this relation the density 8” may be concluded from 
8, according to the ponderable proportions ¢,, <’, of solid sugar 
entering into the two solutions under comparison ; at least when 
it is admitted, as we do, that they are effected by simple mixture 
and at a common temperature, these two conditions being neces- 
sary for the constancy of 8,. Reciprocally, in this same hypo- 
thesis, the value of 8, may be directly arrived at by the equations 
(2.) for each solution observed ; and this value ought to be found 
constant, from whatever solution deduced, if they are associated 
by simple mixture. 
The following table presents the application of these formulz 
to the four solutions of cane-sugar above-mentioned. In the 
calculation of the successive densities I have derived the three 
last solutions from the first, in which the proportion of solid 
sugar was most considerable. Lastly, I have inserted in the 
last column the value of the density 8, of the disaggregated solid 
sugar, which would be concluded from each solution from its 
observed density and quantity, in the hypothesis of a simple 
mixture by diffusion. 
