IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 353 
rately determined proportions, I introduced a certain quantity 
of an aqueous sulphuric acid, the quantity of acid in which was 
known, and I observed the rotatory power of the mixed system 
which resulted. I then calculated the total proportions of water 
and of anhydrous sulphuric acid present ; after which I formed 
another system of these two bodies only, in which they were as- 
sociated in the same proportion, and I employed it to dilute 
progressively the first mixed system, by quantities the weights 
of which were determined. Now, whether it be from a special 
consequence of the relations thus established between the three 
elements of these systems, or by a more general property result- 
ing from the constancy of the relation which is maintained be- 
tween the sulphuric acid and the water, the characteristic function 
a(P+E) 
Pr 
fractions, for which I cannot answer. And (which I did not 
then remark) the densities of the successive systems are likewise 
derived from one another, conformably to the law of simple 
mixture, as I am about to prove. 
This is an application of the equation (2.) of § 39, taken in 
its most general form. If we call 0, the density of the primitive 
tartaro-sulphuric system, ¢, its proportion in each of the systems 
deduced from it, and 3, the density of the constant system oc, 
composed of anhydrous sulphuric acid and water, by the addi- 
tion of which the successive dilutions are effected, the density 
8 of each mixed system thus formed will be, in the hypothesis 
of a simple mixture, determined by the following formula, 
Ey (i=«) 
3, 8, . . . . . (2.) 
presented in all the same value, within very small 
ae 
>= 
Not having then had this application in view, I did not think 
of measuring the density %, of the system «; but it may be de- 
termined from the quantities, the proportions of which I have 
given in my memoir (Académie des Sciences, tome xvi. p. 287), 
by applying to it the tables of densities given in the Traité de 
Chimie of M. Berzelius, the accuracy of which I had occasion 
to confirm for mixtures of water and sulphuric acid varying little 
from that in proportion. I thus found 
8,=1:2015, 
a result which every one can verify. 
Now, according to the quantities of the mixture o progres- 
