516 
Proceedings of the Royal Irish Academy. 
Third Experiment. 
A solution of quinia is acidulated with such an amount of hydro- 
chloric acid, that the quantity of the base which remains uncombined 
shall bear to the acid the same ratio as exists in the foregoing mix- 
ture between the uncombined quinia and the quantity x. A solution 
of brucia is similarly acidulated so as to preserve the ratio of the 
uncombined brucia io a - x. It is plain then that in these acidulated 
solutions respectively the ratios of to Sx, and of ^2 to >S^2 are the same 
as in the case of equilibrium. The rotations caused by these fluids 
being and R-z respectively, let them be mixed in any proportion, 
and let the rotation caused by the mixture be observed. Then, if the 
proportion in which they have been mixed be m:n^ it is found that 
the rotation caused by the mixture is 
It is easily inferred then as before, that there is no rupture of 
equilibrium in this mixture, whatever be the ratio m : n. Hence it is 
evident that if the ratios £1 : >S'i and £2 : S2 have the values proper for 
equilibrium, this latter will be preserved, however the ratio ^1 : 
may vary. Hence, in mathematical language 
A mixture of solutions of quinia and brucia is made, in which 
these bases have to each other the same ratio as the uncombined bases 
in the second experiment. A second mixture is made of the same 
solutions, in which the bases have the same ratio as the combined 
bases in the second experiment, and a sufficient quantity of hydro- 
chloric acid is added to the second mixture to convert the whole of 
both bases into salts. Hence it is evident that the ratios Bi : B^ and 
Si : S.2 in these mixtures, respectively, have the values required for 
equilibrium. If now, as before, these two mixtures be added to each 
other in the proportion m : n, it is found that the rotation caused by 
the mixture is 
mRi + nR^ 
Fourth Experiment. 
mRx + nR^ 
m + n 
Ri, R2, being the rotations caused by each of the added fluids separately. 
We infer then in the same way as before that 
