464 MOSSOTT1I ON THE FORCES WHICH REGULATE 
If this expression for g? be put in the integral 4 kf dn dé, and 
the limits extended to the whole surface of the molecule, it is easy to 
see that it is reduced wha Th [[ednae, But f [dn dé ex- 
presses the volume v of the molecule, which is equal to e 63; the 
term on the right in the first of the equations (II) will therefore be 
simply represented by k vq ee It is proper to remark, that in the 
value of q f we are not to include the term which, in the expression 
for g marked (III)" is due to the molecule whose equilibrium we are 
considering, because this term undergoes a change of sign at the two 
opposite sides of the surface of the molecule, and vanishes within the 
limits between which the integral is extended. 
The inspection of the triple integral which gives the value @ is suffi- 
cient to show that this integral must be given by the same function 
that represents F, in which f, x, y, z may be replaced by g, & 7,6. If, 
because of the smallness of the dimensions of the molecule, we consi- 
der in the differential oP the coordinates £, n, Z, which answer to any 
point of the surface as being constant, and substitute for them x, y, z 
which answer to the centre, then, it being observed that (7; didn 
d& represents the volume v of the molecule, the first integral of the 
second member of the first of the equations (II) may be represented 
by av ae : 
dx 
The value of @ being deduced from the expression for F’, such as it 
is given by the equation (IV)’, will contain, as we have already ob- 
served, a surplus of action, due to the ether which is supposed to oceupy 
the place of the molecules also. It will therefore be necessary to make 
a compensation here also, by adding to the contrary action of the 
molecules an equal quantity ; that is to say, by changing in the triple 
integral represented by I,, the mass y@y into the mass y @y +g q» 
If we conceive this change made, the expression for Ty will be of the 
same form as that for G marked (V)', except that 2,y,z andga + fq 
will be replaced by & n, Z, and yay + gq», and x, y, z by X» Y» Z» Let 
us then, by approximation, introduce into the differential on instead 
of the coordinates (& y, £) of the surface, the coordinates (x, y, z) of 
the centre considered as constant; if we perform the integration, which 
