364 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
at which these experiments are usually made, it is scarcely pos- 
sible to obtain stable tartaric solutions, that is to say. which re- 
main in the liquid state when proportions of water e are employed 
less than 0°4; neither can we suppose e to have become, by 
dilution, greater than 1, since at this last limit the correspond- 
ing proportion 1 — e of acid would necessarily be null or infi- 
nitely small, so that we could perceive the deviations only through 
tubes of an infinite length. For this reason it is requisite to 
restrict the dilution to values of e considerably less than 1, in 
order to avoid very long tubes. But, fortunately, towards this 
second limit of e, the values of [«] experience only such slight 
changes, that they evidently tend towards a constant and not 
distant limit. I thus made the observations up to «= 0°95, 
and always observed the rectilinear form of [«] maintained. 
Now, when physical phenomena present laws of simple pro- 
portionality, relatively to the values of one of their elements, of 
which the observable phases of variation are comprised within 
such narrow limits, it may always be suspected that this pro- 
portionality expresses only the first term of the development of 
the complete laws ; so that the straight line representing it is 
really nothing more than the initial tangent of the curve which 
expresses these laws. But although both modes of construc- 
tion are then equivalent for the numerical representation of the 
observed results, they are far from being so as regards the de- 
termination of the physical analogies which it is so important to 
establish among the phznomena in which they exist. For the 
simple proportionality which suffices as an approximation for 
some of them, would evidently render these analogies misun- 
derstood if it were supposed rigorous. 
52. The necessity of applying these considerations to the tar- 
taric solutions appeared manifest, when, in a subsequent investi- 
gation, I followed the varied properties which they present in 
their combinations with other bodies, particularly with boracic 
acid; and I then indicated the curvilinear law which it seemed 
to me should be substituted for the law of simple proportionality. 
(Mém. de l’ Académie, vol. xvi. p. 259.) I proceed to establish 
here this generalization. 
It consists in replacing the rectilinear law of the [a] by a hy- 
perbolic law, expressed under the following form, 
