IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 313 
Take two active liquids which can mingle with one another 
without appreciable chemical reaction, at least for a short space 
of time; for example, essential oil of turpentine and essential 
oil of lemon. Let 8), 8, be their densities at the ordinary and 
constant temperature at which the experiment is performed. 
_ The deviations which these liquids produce on the type ray in 
tubes of known lengths are successively observed, and these 
results reduced to the same thickness L by the law of propor- 
tionality. Let «,, «, be the corresponding deviations thus de- 
duced. If we call [«],, [#], the rotatory powers peculiar to the 
two liquids, we shall have by these observations 
Fl= pp [h= Le 
Now let us take a weight P, of the first liquid, a weight P, of 
the second, then mix them, and the result is a mixed liquid 
whose density is 8. What will be the deviation « produced on 
the type ray by this system, when observed through a tube of 
the length J? 
I first find the ponderable proportions ¢,, ¢, of the two liquids 
in the mixture formed under these conditions. They will evi- 
dently be faa i PEE: 
nk A ene 
then, this mixture having the density 3, when observed through 
the length /, each of the two liquids will there produce indivi- 
dually the partial deviation peculiar to its nature and to its pon- 
derable proportion. This will give, for the first, [a], ¢,/3; for 
the second, [a],,/2. The sum of these two quantities then 
will compose the total deviation which should be observed under 
these circumstances; and since we designate it by a, we should 
have [a], 2,20 + [a],e le =a. 
Putting for [«],, ¢,, []o, ¢o, their expressions previously formed, 
and transferring the common factors into the second member, 
_ this equation becomes 
P, Po — , (Pit P) L 
ay a + ae, =a ENE RIT 
As a special application, let us propose to form the mixture in 
such proportions that the resulting deviation « may be exactly 
null for the type ray. The condition of this result will evidently 
be Ue BR 
