452 MOSSOTTI ON THE FORCES WHICH REGULATE 
ANALYSIS. 
3. If several material molecules. which mutually repel each other, 
are plunged into an elastic fluid, the atoms of which also mutually repel 
each other, but are at the same time attracted by the material mole- 
cules, and if these attractive and repulsive forces are all directly as the 
masses, and inversely as the square of the distance, it is proposed to 
determine whether the actions resulting from these forces are sufficient 
to bring the molecules into equilibrium, and keep them fixed in that 
state. The object of this inquiry, as may be perceived, is to complete 
the deductions from the hypothesis of Franklin and AZpinus. It is al- 
ready known that the conditions of equilibrium which it furnishes, in 
reference to questions of statical electricity, are in accordance with the 
phenomena: it remains to be ascertained, whether the molecular ac- 
tions which result from it are also in accordance with those which de- 
termine the interior constitution of bodies. An agreement of this 
kind would add greatly to the probability that the hypothesis in ques- 
tion is well founded, and afford us a glimpse of the means by which we 
should be enabled to consider all physical phenomena in one and the 
same point of view. 
Let f be the accelerative force of repulsion existing among the atoms 
of the ther at a distance taken as unity; g the density at a point z yz, 
and ¢ the measure of the elastic force or pressure at the same point, 
referred to the superficial unit. Let g be the accelerative force of at- 
traction between the atoms of the ether and the matter of the molecules 
at a distance equal to unity, and @ the density at the point £y {of a 
molecule which we suppose to be possessed of a certain though very 
small extension. 
By putting 
tq dz' dy' dz! 
Ff] (ey tG yt a 
w, gudedydt 
, MN (E—w)? + (y—y) 2+(8—2)2}* 
the triple integral #’ being extended to the whole space from 2’, y/, 2', 
equal to — o, as far as a’, y’, 2’, equal to = «© (the small parts occu- 
pied by the molecules being excepted), and the triple integral G being 
extended to all the values of §, y, ¢, that answer to the points occupied 
by the molecule, we shall have for the equilibrium of the ether the 
equations 
dle DEE MAGA NDB LODE dG 
da= Vda t+de + de +U- dg 7 +4 G #ete. 
