468 MOSSOTTI ON THE FORCES WHICH REGULATE 
tion of this equation, that the molecules attract each other most 
forcibly. 
Recapitulating these results, we shall say then, that the action of two 
spherical molecules on each other is repulsive, from their point of con- 
tact to a distance given by the equation (4). At this distance the two 
molecules are in a state of fixed equilibrium, and as it were linked 
together; at a greater distance their action is attractive, and the 
attraction continues to increase until they are at the distance r, fur- 
nished by the equation (¢), which distance is still very inconsiderable 
because of the magnitude of @ in the exponential term e_ “1 From 
this point the force remains always attractive, and, when the distance 
has acquired a sensible value, follows the inverse ratio of the square of 
the distance. All these properties of molecular action flow as neces- 
sary consequences from Franklin’s hypothesis respecting statical elec- 
tricity, and appear perfectly conformable to those indicated by the 
phzenomena. 
Let us suppose four homogeneous and equal molecules placed at the 
points of a regular tetrahedron. If we assume as the origin of the co- 
ordinates the ‘place occupied by the molecule whose equilibrium it is 
proposed to consider, and as the plane of the x y, a plane parallel to 
that in which the three others are found, the coordinates of these 
molecules will be given by the formule 
x)=! 0 y=o 710 
r Te 2 
= — Cos es — sin Zz, = Se 
x; 5 B y 5 B 1 \/ 
r 29 F st 27 2 
re + —— = sin = =r a 
Mera a (8 3 ) a tiahy (° Fs Bag ied V2 
r 4% Pea: 40 
X= Tz 008 (e+) = 73 sin (6+ Ta : 
where r denotes the mutual distance of the molecules, which is the same 
for all; ( the angle which is formed in the plane of x y with the axis 
of the 2, by the projection of the straight line drawn from the molecule 
placed at the origin of the coordinates to the first of the three others; 
and # the semicircumference. 
If these values be substituted in the three equations (A), and it is 
observed that we always have, whatever may be the value of 6, 
cos § + cos (8 + ==) + cos (2 + =) =o, sing + sin(6+2 
+ sin (6+% = 0; 
it will beseen that the two first are verified by themselves, and that 
