$815.) Royal Institute of France. 464 
that of the Mecanique Analytique. They are much more general, 
but they are at the same time more complicated. 
~The flexible surface presents, in a particular case, a result 
worthy of being remarked. If we suppose all the points of it 
essed upon by a heavy fluid, we obtain for equation that which 
NM. Laplace has found for a capillary surface, concave or convex. 
Hence it results that when a liquid rises or falls in a capillary tube, 
it takes the same form as a flexible and impermeable piece of linen 
filled with a gravitating fluid. yep sf 
After having found the equation of equilibrium of a flexible sur- 
face, all the points of which are pressed upon by any forces, nothing 
more is wanting to determine the equation of an elastic surface than 
to' comprehend among the number of forces those which proceed 
from elasticity. The determination of this species of force forms 
the object of the second part of the memoir. 
Whatever be the cause of the elasticity of bodies, it is certain 
that it must consist in a tendency of their molecules to repel each 
other, and that this tendency may be ascribed to a repulsive force 
which they exercise according to a certain function of their dis= 
tances. It is natural to think that this force, as well as all the other 
actions of the molecules, is only sensible at imperceptible distances. 
The function which expresses its law must be considered as null as 
soon as the variable quantity which represents the distance is not 
exceedingly small. We know that such functions generally disap- 
pear in the calculus, and only leave in the definitive results total 
integrals or arbitrary constant quantities, which are the data of ‘the 
observation. This happens in the theory ef refractions, and still 
better in the theory of capillary action, which the author ‘of the 
memoir considers as one of the most beautiful applications of mathe- 
matics to natural philosophy. ‘The same thing holds in the present 
question. Elence we can express the forces proceeding from the 
elasticity of the surface by quantities depending ‘solely on’ the 
figure, as the principal radii of curvature and. their partial differ- 
ences. In this way M. Poisson obtains an equation of the’ elastic 
surface, the object of his research. It is not possible to give these 
formulas here, nor the details of calculations on which they are 
founded ; we are obliged to refer to the memoir. 
The principal equation supposes the ‘thickness constant, and 
agrees only with an elastic surface nearly plane. lt neither com- 
prehends bells, nor other surfaces which are naturally curved. The 
author comes to them in another manner, which he draws from the 
principle of virtual velocities. This manner is even more simple 
than the first; but it leads to a more complicated equation, the 
identity of which with the former it has been impossible to verify, 
except by a particular artifice. But in so difficult a case, jit is an 
additional security to have two different methods which lead to the 
same result, iot 
“After having considered the problem as a question'in general 
a 
