40 PLATEAU ON THE FIGURE OF A LIQUID MASS 
or accidental causes have still no part in them. I have repeated 
a great number of times the experiments detailed above, and 
the effects have always been identically the same for the same 
velocities. 
After having seen the stable figures which the mass takes in 
these circumstances, we cannot help making a comparison be- 
tween these figures and the ellipsoids of three axes of MM. 
Jacobi and Liouville ($ 15),—ellipsoids which are also always, 
as the latter of these geometricians has shown, figures of stable 
equilibrium. Would the identity of the phenomena in the case 
of universal gravitation and in that of molecular attraction hold 
good so far? Doubtless the singular figures which we have just 
described are not ellipsoids; but their aspect admits of our 
attributing the difference to the resistance of the ambient liquid, 
which on one side determines the flexures of which we have 
spoken, and on the other maintains a permanent inequality of 
angular velocity between the portions adjoining the disc and the 
more distant portions. Calculation alone could inform us up to 
what point the above comparison is well founded; the complete 
solution of the problem, for the case of molecular attraction, 
would perhaps not present difficulties so insurmountable as for 
that of universal attraction. 
24. In all the experiments which I have described in this 
memoir, I have supposed that the oil and the alcoholic mixture 
were rendered chemically inert with regard to each other, and I 
have said (§ 6) that it was easy in a short space of time to ob- 
tain two such liquids. I proceed now to detail the process by 
means of which this object is attained. 
We begin by making a mixture of alcohol and distilled water, 
containing a certain excess of alcohol, so that when submitted 
to the trial of the test tube (§ 3) it lets the small sphere of oil 
fall to the bottom rather rapidly. After having formed the mix- 
ture in quantity more than sufficient to fill the vessel which is to 
serve for the experiments, we introduce into this same mixture 
a quantity of oil about double what is considered necessary for 
these experiments *. Ifa flask is not at hand large enough to 
contain the whole, we divide the masses among several separate 
flasks: but care must then be taken that each one may contain 
* It is indispensable to have the two liquids thus in excess, on account of 
the quantities which are necessarily lost during the different operations which 
we shall describe, and in the preparation of the experiments. 
