IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 307 
expression of the deviation, under such circumstances, is [a] / @. 
Since then it was found by observation equal to a, we ought to 
a eat ie. 
This is only a reversed application of equation (1.). The essence 
is now heated and raised to the temperature ¢', when its density 
becomes 2’; it is then observed again through the same tube, 
which I suppose to be of glass, so that we may neglect its longi- 
tudinal dilatation, which can be easily taken account of in cases 
where the experiment is made with sufficient exactness to ren- 
der it necessary *. Ifthe molecular power of the essence has 
not changed, the new deviation should be [a] /8’. Thus, denoting 
it by !, we should have 
a = lad Loe 
this second equation, combined with the preceding one, gives, 
on eliminating [a], which is common, 
epee 
==> 
a 
or a’—a —8 
FES ae ae 
The first equation shows that the deviations should be propor- 
tional to the corresponding densities; the second denotes that 
the variations of these two elements should be expressed by the 
same fraction. 
Let us apply this to our experiment. We had at first the 
primitive deviation « equal to 55° towards the left, then the de- 
viation a! was found 2° less in the same direction. Thus the re- 
al —a 
F 2 : Mihi 
is here —— or that is to say, the deviation 
: 1 
lation 55 9753 
- Now the elevation ¢’ — ¢ of its tem- 
* Let be the length of the tube at the primitive temperature ¢, and /’ its 
length at the subsequent temperature ¢'; 7’ will be known in function of / by 
the linear dilatation which the substance of the tube experiences for the differ- 
ence of temperature i/—¢; then, in order to reduce the two observations to one 
and the same thickness, the primitive deviation « should be increased by a 
has diminished about 
. * . Y 
which it might be employed concurrently with the deviation «!, as if they had 
been both observed in the same tube /! of constant length under the respective 
densities 3 and 3. 
quantity proportional to //—J, which would change it into a( 1+ Ries y after 
