IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 355 
without any appreciable contraction or dilatation occurring 
among the liquid systems, whose mixture determines such great 
reactions. 
This is seen by the numbers given at page 379 of the memoir 
cited, in the table mentioned above in No. 13*, They relate to 
acertain combination of tartaric acid, alumina and water, which, 
by simple additions of this liquid, passed progressively from left- 
handed to right-handed rotation, with a progressively increasing 
energy, and afterwards resumed its left-handed power by the 
abstraction of water. Now, in all these considerable changes of 
chemical constitution, the primitive system is associated with 
water as in the case of a simple mixture, without appreciable 
contraction or dilatation. 
This is another application of the equation (2.), § 39, in which 
we must make 3, = 1, since the inactive liquid progressively 
added is pure distilled water. Thus, calling <, the ponderable pro- 
portion of the primitive system which enters, with the density 
8,, into each of those deduced from it, the resulting density 8 cal- 
culated on the supposition of a simple mixture will be, as in 
§ 42, 
MAR TSE 2 
Sarasa Gg A ee (2. 
the value of 8, is given in the table cited, and that of «, is also 
mentioned there for each of the successive systems. We have 
then all the necessary elements for calculating the resulting den- 
sities 8, which I compare with those which have been really ob- 
served. Such is the object of the following table. 
* I avail myself of the opportunity here offered to rectify a typographical 
error in column 9 of the table cited. It is entitled actual specific rotatory power 
of the liquid for 100™™, and = is added as the sign of this power: but it should 
be 33 for the numbers which the column contains are calculated according 
to this expression. I must add moreover that they apply to observations made 
with the naked eye, without the intervention of red glass. The last number, 
— 18-992, is the only one which corresponds to the quantity = and it was 
requisite, in fact, to calculate it thus, because the liquid observed being the 
product of a concentration of all the united residues of the preceding ones, the 
quantities were unknown. 
