iG'l' IMOSSOTTl ON THE FORCES WHICH REGULATE 



If this expression for q"- be put in the integral \ k Iq'^ d j] di^, and 

 the limits extended to the whole surface of the molecule, it is easy to 

 see that it is reduced to ^ q J /Vl dr) d'C- But I fidj] dt, ex- 

 presses the volume v of the molecule, which is equal to —P; the 

 tenu on the right in the first of the equations (II) will therefore be 

 simply represented by ^ v q --9. It is proper to remark, that in the 



valueof q J, we are not to include the term which, in the expression 



for q marked (HI)" is due to the molecule whose equilibrium we are 

 considering, because this term undergoes a change of sign at the two 

 opposite sides of the surface of the molecule, and vanishes within the 

 limits between which the integral is extended. 



The inspection of the triple integral which gives the value # is suffi- 

 cient to show that this integral must be given by the same function 

 that represents F, in which /J x, y, z may be replaced by g, I, r}, ^. If, 

 because of the smallness of the dimensions of the molecule, we consi- 

 der in the diflFerential — , the coordinates ^, rj, ^, which answer to any 

 dt, 



point of the surface as being constant, and substitute for them x, y, z 

 which answer to the centre, then, it being observed that / / / d^ d-q 



d I, represents the volume v of the molecule, the first integral of the 

 second member of the first of the equations (II) may be represented 



, di 



by ra- V — — . 

 "' t?x 



The value of * being deduced from the expression for F., such as it 

 is given by the equation (IV)', will contain, as we have already ob- 

 served, a surplus of action, due to the asther which is supposed to occupy 

 the place of the molecules also. It will therefore be necessary to make 

 a compensation here also, by adding to the contrary action of the 

 molecules an equal quantity ; that is to say, by changing in the triple 

 integral represented by r„ the mass y OTv into the mass y^v-\- g q». 

 If we conceive this change made, the expression for r» will be of the 

 same fonn as that for G marked (V)', except that x, y, z and g tss +fq 

 will be replaced by ^, t], C, and yar, -j- g q„ and x, y, z by x„ yv, Zv. Let 



dr 



us then, by approximation, introduce into the differential — :.*, instead 



di, 



of the coordinates (|, jj, ^) of the surface, the coordinates (x, y, z) of 



the centre considered as constant ; if we perform the integration, which 



