7(ï5 



t!ie first integral is to be extended over the volume of tlie first 

 sphere, the second over the volume of the second, and the third 

 over the whole space outside both spheres. P^j must be calculated 

 at a point near dS^ ; in the same way Q^ near dS and /?„ near 

 dS^. r in each expression represents tlie distance from the point, 

 at which y„ is to be calculated, to the point near which the element 

 of volume is situated. 



§ 3. From (7) we are able to calculate the function y,, for all 

 values of a and r. For the motion of a particle in tlie field of tlic 

 two centres only y^^ is to be calculated if no terms of higher ordei 

 than the second are required. For this reason we will finish only 

 the calculation of y,, ; at tlie same time we introduce the suppo- 

 sition i\^ = 0, which, in connexion with the supposition already 

 used of both centres remaining spherical under each other's influence, 

 comes to the same thing as exclusion of any variation of shape and 

 volume. We then find 



(1) 1-2. 



where /, denotes the distance from dS^ to the centre of the second 

 sphere, and /( the distance from dS^ to that of the first. In case the 

 mutual distance / of tlie centres or the distances i\ and r, of these 

 centres from the point, in wliich y^, is required, is large with 

 respect to R^ and R^ tlie value of the first integral wil! be 4.t/;/: 3r,/ 

 and of the second 4:t/?3' : "irj. In this case we have 



— to, to, / 5 1 1 \ 



r..=^7^ -~ + 7- + 7- (8) 



For the calculation of the quantity y^^ itself it is sufficient now 

 to know y^y^ and y,/'-^. From the equation 







occurring on p. 1006 of iny former communication, quoted above, 

 it follows that 



y, 11) = 1 -H \ and y.S'> ;= 1 A -\ 



and from this and (8), in connexion with (1), 



