APPLICABLE TO MATHEMATICS, &C. 351 



If we suppose that the intensity of each indivi- 

 dual ray of force emanating from the centre of the 

 material particle, to vary as any function of the dis- 

 tance, namely f(.i), where .r is the distance of the 

 attracting particle from the attracted : and also the 

 repelling force to vary by the same law. Then 



we shall have ^J"^^ for the attracting force at 

 oCy and ^ j' for the repelling force at x ; where 



mf(l) is the attractive force at a unit of distance 

 and m' f(l) is the repelling force at a unit of 

 distance. We shall have for the effective force 

 of one particle on the other, 



To determine the point C where the two forces 

 are equal we must substitute AC z: p, for x in the 

 eqation m f(^) zr m' {{x) c 

 from which we have, ^ " b 



m f(j9) = m' f(;>) 



.-. (m-m^)f(p) =:0 



orf(^)=0 (1) 



To find the motion of two bodies subject to 

 forces varying by means of the above law. 



