152 The Rev. S. Haveuton on the Equilibrium and 
ing that the sum of the moments (as defined by Lagrange) of the external forces 
is equal to the sum of the moments of the internal forces; hence the general 
equation of the system is 
SSS (x8E ++ vox + zeQ)dm = SY bvdadydz, (1) 
where , y, z are the coordinates of the position of rest of any molecule (m), and 
r+& y+ 2+, are the coordinates of the same molecule when displaced ; 
and the function v depends on the medium in such a manner that év is the sum 
of the moments of internal forces acting at any point of the medium; and 
§§§ évdadydz represents the sum of all the moments arising from internal forces. 
It appears, therefore, that in investigating the laws of any medium, it is necessary 
to know the form of the function v; being given the form of v, the laws of the 
medium and of the actions of its molecules on each other are known, and vice 
versd, if we know the nature of the medium, we can determine the form of v. 
Hither of two methods may, therefore, be followed, in discussing the conditions 
of a system such as a solid or fluid body; the form of the function v may be 
assumed, and the truth of the assumption afterwards verified,—or the form of the 
function v may be determined from whatever assumption we make, as to the mode 
of action of the molecules of the system on each other: the latter method is used in 
this paper. The assumed definition of solid and fluid bodies is the following: that 
they consist of molecules, which act on each other only in the line joining them ; 
i. e. the whole of the action of one molecule on another is a force in the 
line joining the molecules, and none at all in a direction perpendicular to 
that line. This force is also assumed to be a function of the distance of 
the molecules, and in the case of crystalline structure also of the direction of 
the line joining them. All solid and fluid bodies are either homogeneous or 
heterogeneous in their structure: in homogeneous bodies the molecular forces 
will, ceteris paribus, be the same at all points of the body, but in heterogeneous 
bodies they will vary from point to point of the body, and become functions 
of (wv, y, 2). A crystalline structure is different, and consists in this, that 
the action of the molecules surrounding any molecule (m), depends upon the 
direction in which they lie, and not merely on their distance from (m). In order 
to avoid misconception, it is necessary to state that the molecular forces alone are 
included in the internal forces; the mutual gravitations of the particles towards 
each other, although they might with propriety be called internal forces, are 
