462 MOSSOTTI ON THE FORCES WHICH HEGULATE 



The expression for F will then be reduced to 

 (5)' F=^'nf-~l {Toe + VoC ) r' dr' 



+ 4 7r// {Toe + Voe )dr' 



All the quantities T^^ and F,^ being null, except T^ and V^, the values 

 of Q will also be null, except that of Q^ : the formula (2)' will then 



_ Toe'' + Voe-'' 

 give q-qo= -^ ^ 



When r = 00 we must have q = q^; we must then also have T^ = o, 



K -"r 

 and there will remain only q = q^+ ~^e 



By performing the integrations of the formula (5)' within the limits 

 indicated, and observing that To = o, we shall obtain 



F=-kY^{e-'' -1); 

 r 



As, in the differential expression for F, we may change a-' into a;' — x, 

 and X into a; — 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 formulas, to put 



7-= \f{x - x)2 -r (y - y)^ + (2 - z)^ 



or, generally, r, = ^(a; - x J« + (y - y, )"- + (z - z^ y. 



Now if, by placing the origin of the coordinates in the centre of each 

 molecule respectively, we substitute these expressions of F and q, and 

 that previously found (or G in the equation (HI)', and take successively 

 for Vo as many constants as there are molecules, we shall find that the 

 equation 



— ar — ar 



(.)e ' (Oe "-1 ^^Ci/^. +/qv) V 

 S A Fo — — = S A Fo + 2 ^^ 



'v ■> ► 



will be satisfied by taking for each molecule 



By substituting for Vq the value just found, we shall finally have 



— ar 

 (IV)' i^ = - -^ 2 (5r tzr, + / q,) \^ ,. ~ 



