IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 379 
in order to obtain, as a verification and proof of continuity, the 
agreement of the constant A with the value of [«] proper to 
the pure tartaric solution. The exactitude of this agreement 
will be seen by the tables themselves. 
64. If we consider generally [«] as the ordinate of a pline 
curve of which the abscissa is 8, the relation here found between 
these two variables is constructed by an equilateral hyperbola, 
whose asymptotes are respectively parallel to the axes of the co- 
ordinates [a] and 8, as is represented in Plate V. fig. 5. The 
centre C of this hyperbola is placed at the point whose ab- 
scissa OX is B= —C, and the ordinate CX [4] =A +B; its sum- 
mit S corresponds to the abscissa OH where 8 = —C+ / BC; 
and it has for its ordinate HS, where [24] =A+B— WBC. The 
point D, taken on the curve, for the abscissa 8 = 0, answers to 
the case in which the system contains no boracic acid; and 
thus the ordinate which corresponds to it is [«] = A, that is 
to say, the primitive value of [«] for the pure tartaric solu- 
tion. It is then, starting from this point D, that the hyper- 
bolic relation begins to be realized by experiment, and only 
for positive values of 8. Its physical application does not how- 
ever extend indefinitely to all these values, because, from the 
nature of the problem, f, representing the ponderable proportion 
of boracic acid existing in the mixed system, should always re- 
main less than unit, which is its extreme limit. The ordinate 
[aJ=A+t ae which answers to the abscissa 6 = 1, ex- 
presses therefore the greatest physical value which [«] can at- 
tain; and as the coefficient C is always a very small fraction, 
as will be seen in the tables, it is a little inferior to the final 
asymptotic ordinate [«] = A + B, which is the geometrical limit 
of [«]. But the slight solubility of the boracie acid, even under 
the influence of the tartaric acid, creates another material obsta- 
‘cle which renders the system of the three bodies impossible in 
the liquid state, for values of 8 much below the numerical limit 
f=1. For, with far less values, at temperatures at which these 
experiments can be practically made, the proportions of the bo- 
racic solution which it would be requisite to introduce would 
precipitate their acid in the solid state, which interrupts abruptly 
the physical continuity of the results. It is for this reason that 
I have never been able to realize the hyperbola up to its summit 
S, so that only a very limited arc beyond the point D, corre- 
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