ca 
IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 365 
A, B, C being three constant coefficients for all the observations 
made at the same temperature, whatever be the proportion of 
water designated by e. The geometrical locus of e and [«] 
then becomes an equilateral hyperbola, having its asymp- 
totes respectively parallel to the axes of the rectangular co- 
ordinates of e, [a], and the general disposition of which is re- 
presented in fig. 2, for the case in which the coefficient A is 
negative, in order to assimilate it to the analogous case which 
we have supposed in the construction of the rectilinear locus. 
The centre C of this hyperbola is situated at the point whose 
algebraic abscissa O X would be e = — C, and the ordinate C X, 
[«]= A+B. Its summit S corresponds to the abscissa O H, 
in which e = —C + “BC: andit has for its ordinate HS, where 
[2]=A+B— BC. The point D, taken on the curve, for the 
abscissa e = 0, answers to the case in which the system con- 
tains no water associated with the acid, which gives [«] = A; 
and it has been constructed, like the right line of fig. 1, for the 
case in which the coefficient A is negative. It is therefore on 
starting from this point D that the hyperbolic relation com- 
mences at most to be realized by experiment, and only for posi- 
tive values of e. Again, its physical application does not extend 
indefinitely to all these values, because, from the nature of the 
problem, e representing the proportion by weight of the water 
associated with the acid, it should always remain less than 
unit, which is its extreme limit. The ordinate [«]=A+ me 
which corresponds to the abscissa e = 1, expresses therefore 
the greatest physical value which [a] can attain; and as the 
coefficient C has always a positive numerical value sufficiently 
considerable, as we shall presently see, this extreme [a] is 
always much less than the asymptotic ordinate [#] = A + B, 
and even than the ordinate of the summit S,[a] =A+B— “BC. 
So that the hyperbola can only be realized in a very small por- 
tion of its geometric course, from the point D to a point far 
below the summit S; and for this reason it can scarcely be distin- 
guished from a straight line in this limited arc. 
_ I shall explain at the end of this memoir the process of cal- 
culation most convenient in order to adapt this hyperbolic law 
to observations, and to deduce thence the numerical values of the 
coefficients A, B, C. In the present case, in order not to inter- 
