VIIL—On the Equilibrium and Motion of Solid and Fluid Bodies. By the Rev. 
Samuet Haventon, F. T. C. D. 
Read May 25, 1846. 
THE object of the present paper is to deduce from simple physical considerations 
the laws of equilibrium and motion of elastic solid and fluid bodies, by the 
method followed in the Mecanique Analytique of Lagrange, which possesses the 
remarkable advantage of giving, by the same analysis, the general equations of 
any system, together with the particular conditions to be fulfilled at the limits. 
This method is particularly valuable in such cases as the present, where the 
problem is, to determine the conditions of equilibrium or motion of an indefinite 
number of material points, situated indefinitely near each other, and acting 
according to certain laws; although it may be admitted that the ordinary methods 
usual in mechanics are preferable to Lagrange’s method, in cases where the 
points of application of the forces of the system are definite in number, and 
situated at finite distances from each other. The first application of Lagrange’s 
method to the problem of elastic solids was made by Navier (Mem. de l Institut. 
Tom. VII.), who discussed the laws of equilibrium of a homogeneous uncrystal- 
line solid, but does not appear to have ever undertaken the general problem, or 
to have obtained any dynamical results. The present paper is an attempt to 
apply the same method of Lagrange to the general case of material substances, 
whether fluid or solid, homogeneous or heterogeneous, and whether possessed of 
a crystalline structure or not; and more particularly to investigate the general 
dynamical laws of solid elastic bodies, and the conditions at the limiting surfaces 
which bound the solid. 
In the method of Lagrange the forces in action in such a system as a con- 
tinuous body must be divided into two parts—the external and the internal forces 
of the system; and the general equation of equilibrium is determined by express- 
VOL. XXI. Y 
