460 MOSSOTTI ON THE FORCES WHICH REGULATE 
of the formula (5) from = o to 6! = g, from p' = o to )! = 27, and 
from r = 0 tor = &. 
Let us begin with performing the integrations of the ahs (V). 
In consequence of the quantity ga + fq being considered as constant, 
and as the spherical form of the molecules renders p independent of w 
and ¢, all the terms of the second and third line of this formula will 
vanish, and it being observed that we always have 
2 
fife "IL, snwdwdg =o, 
0.57, 0 
unless in the case of [I° = 1, which gives 
r 29 
fi of II], sinwdwdg=4m; 
o o 
an (gu+fq)® 
3 
the expression for G will become G = . 
, 0 repre- 
senting the semidiameter of the molecule. 
This integral has been obtained under the supposition that the origin 
of the coordinates is in the centre of the molecule; but the origin may 
be transferred to any point whatever, by restoring, instead of 7, its 
general expression, and writing 
an (ga + fq)® 
3{(w — x)? + (y—y)? + (e—2zpP}? 
where x, y, z represent the coordinates of the centre of the molecule. 
Before we proceed to the expression for F’, we had better clearly define 
the signification of the term g which it contains. We must consider this 
quantity (q) such as it is given by the equation (III), not as the entire 
value of the density of the ether, but as the value only of its excess or 
deficiency above or below the sensibly uniform density which the ether 
diffused in equilibrium is supposed to have in that part of space. If we 
represent the latter density by go, the equations (III) and (VI), while 
we suppress the terms due to the quantities G, G,, G., &c., must be 
satisfied by the substitution of g = g,: and that, in order that the 
ether may remain in equilibrium spontaneously, or in consequence of 
the action of the forces not expressed, whose centres must be supposed 
to be at a very great distance. If, therefore, we take the difference be- 
tween the equations resulting from this substitution and the original 
equations themselves, we shall have 
(Vy G= 
(IIT)’ k(q-—Q@)=—-F+G+G6,+G, of dpe. + G+ &e. 
a (g—q) , @(G— GQ) , (9 — %) 
Agate) 4 EG I) , T=) _ sa p(y — qe) 
provided that, in #, we substitute for g the value of g — qp resulting 
a Pe 
