THE INTERNAL CONSTITUTION OF BODIES. 463 
—ar 
4 e 
(1u1)" G=%+ 55297, + f4)82 |: 
where the sums = are to be extended to all the molecules, including the 
first. 
_ This last equation determines what the density of the zther must be 
at each point x y z, in order that it may be in equilibrium when it is 
submitted to the action of the spherical molecules of matter. The value 
of this density consists of different terms, each of which is due to a par- 
ticular molecule, and represents its proper atmosphere. As the quan- 
tity of ether diffused through the immensity of space may be considered 
as infinite, the atmosphere formed by each molecule for itself is always 
the same, and its density is only superadded to that which the zther in 
the same places owes to other causes. According to the nature of the 
sf should 
be considered as very great: hence it follows that the dite of each 
atmosphere will be incomparably greater when quite near or in con- 
taet with the molecule, and will decrease very rapidly as its distance 
from the molecule increases. This circumstance enables us to deter- 
mine with ease, by approximation, the value of q,, or the density of the 
ather at the surface of any molecule whatsoever, on the supposition 
that the molecules are not too near each other. If, for instance, we 
make 7 = @ in the term answering to the first molecule, and r, = r,, 
T,=T,--.7, =r, in the other terms, all these will be very small 
in comparison with the first, and by neglecting them we shall have 
very nearly 
molecular actions, the value of the coefficient a = whee ae 
4 , 
G=gt s(gatfa)& 
whence we derive 
te Iz ® 
(6) =e moe 
6. We are now in a condition to consider the equilibrium of any 
molecule whatever, such as it is given by the equations (II). 
The quantity e under the double integral in these equations must be 
replaced by } 49°. Let us represent the coordinates 2, y, z, so far as 
they belong to the points in contact with the surface of the molecule, 
byx+4,y+n.2+¢; x,y,z being the coordinates of its centre: 
by developing the expression for g, and stopping, because of the small- 
ness of the molecule, at the first terms, we shall be able to take 
dq e E42 9 dq 
dq 
+2 : 
dx “Vay” ee 
ae i A We 
