356 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
Centi- rnc 
grade | Densit culated |: 
‘i y Dxcess as 
Ponderable| tem observed, |¢ clay of observed | Direction of 
Name of the pen Ptie-erd that of | |" he density | the deviation 
obseryed system. as the we me - distilled |}, ee th os over the produced on 
fin = water ypornesis | calculated | polarized light. 
system A.| density ne ofa : 
“53 eing 1 simple density. 
observed, mixture. 
£} fy. 
Primitive tartro- ° : 
ini = : 14 ATT Oo ivcees evoe very consi- 
ected sy 1:00000; + 114771 x 8 an 
B deduced from 
A by addition || 050261] +14 | 1-06990) 1-06916)+0-00074 | /* feeble. 
of water ...... 
C deduced from 
B by sition 025195} +15 | 1:03467| 103351 |+-0-00116 < increasing. 
of water ...... 
D deduced from 
C by sion 0:13064| +13 | 1-01803} 1:01710 +0-00093 Pa increasing. 
of water ...... | | | 
Norr.—We have not comprised in these comparisons the system E mentioned 
in the printed table, and the dilution of which was still greater, because we had 
accidentally omitted to observe its density. But as it should differ very little from 
the unit, we were contented to derive it from D by the hypothesis of a simple 
mixture. The temperatures of the weighings given in the third column are those 
which I have found in my note-book. 
The differences between the densities observed and those de- 
duced from the hypothesis of a simple mixture are here too 
small to be relied upon ; and we must conclude that, within the 
limits of precision which my processes for obtaining the specific 
gravity allowed, these systems which experienced such con- 
siderable molecular changes that the direction of their rotation 
changed and always increased specifically, are nevertheless de- 
rived from one another by addition of water, with no changes 
of volumes, or excessively slight ones. 
46. I now come to the aqueous solutions of tartaric acid. For 
these, if we compare their densities for various proportions, and 
at one and the same temperature, it is found that they are con- 
nected with one another by a hyperbolic law, the precision of 
which is such that it may be substituted for the quantities by 
weight without any errors resulting which could be noticed in 
the usual processes of taking the densities. I have established 
this fact in a memoir inserted among those of the Institute, t. xv. 
pp- 124 et seg. Since I have been aware of the fact, I have 
made numerous applications of it, which have all confirmed its 
truth. I shall admit it therefore in what follows. The follow- 
ing is the statement which I then gave. Let y be the proportion 
