462 MOSSOTTI-ON THE FORCES WHICH REGULATE 
The expression for F will then be reduced to 
1 r ar’ —ar’ 
(5) Foanfh fe (Toe eee Meese) ar" 
=) ar’ —ar’ 
+ anf f (Tyé.ipe Woes dr! 
Tr 
All the quantities 7’, and V,, being null, except 7’, and V,, the values 
of Q, will also be null, except that of Q,: the formula (2)’ will then 
Tee £ re. ental 
give g — Y= = 
When r= © we must haveg = 3 we must then also have F = 0, 
Vi-—a 
and there will remain only g = 7, + ——e 
By performing the integrations of the formula (5)! within the limits 
indicated, and observing that T, = o, we shall obtain 
F=—k # (e~*” —1); 
As, in the differential expression for 7, we may change 2’ into 2! — x, 
and x into z — x, without any change taking place in its value, and as 
a similar change may be made in respect to the other coordinates, it 
follows that, by taking the point x, y, z, as the origin of the coordinates, 
we shall be able, in the two preceding formule, to put 
r= V(e—3P+y—yP t+ @— 4 
or, generally, 7, = al (@—x,)?+(y—y,)2 + (@—z,) 
Now if, by placing the origin of the coordinates in the centre of each 
molecule respectively, we substitute these expressions of # and g, and 
that previously found for G in the equation (IIT)’, and take successively 
for V, as many constants as there are molecules, we shall find that the 
equation 
—ear —ar 
() , () ee 40 (ga,+fq,) 3 
AT ve Oe eae ee 
id a 3 ’, 
z 
will be satisfied by taking for each molecule 
(») 4. 
| Meas aa 5 3, 
Sk (9 z,+f4,) 4, 
(») 
By substituting for V, the value just found, we shall finally have 
—er 
4a Ee ‘ce 
(Iv)’ ce ae: a fia 
r, 
