raonumr < .".:.; 



?' be the mass of any attracting particle which U 

 !ig bj hypothesis external to S. 



igh P draw any ri-ht lin<- L rutting 8, and produce it 



a one direct i lie line L will in 



general cut N in two , tt it' tin- mfnnci ff ho if tnlTMSjl 



is, a closed surface which may be cut by a tangent plant), 



h may rut it in four, six, or anj even number of points. 



Denote the points of section, tal. . &c., 



lies nearest to P. \ 

 describe about tii<> line L a conical surface containing a 



ly small solid angle measured by the area a which the 



B cuts out from a sphere of radius ui Kb the 



Tertex of the cone as its en I denote by A. t A^ ... the 



areas which the conical surface cuts out from 8 about the 



< P,, P t , ...... Let ^., 0., be the angles whit ! 



mals drawn outwards at i make with tl 



taken in the . . the attrac- 



tions of m :i .resolved along 



he distances of P |f P f ,... /''. It i- r\ 



he angles lt t , ...... >vill i>o alternately acute and obtuse. 



Thru we have 



N. ,.(- tf 



i r t 



ave also in the limit, 



4-r t 'a6C0 t , ^-ar.'sec^-^J, - 



^J.-ctm', ^ t --am', A^-am', 1 

 and tlu-rofori', since tlu- number of points P lf P t ,... is even, 



>^^+^, + A;^...-m f - f +cB'-i'...-a 



Now the whole solid angle contained within a conical 

 surface described v, -rtcx, so aa to circumscribe 8, 



may be divided into an infinite number of elementary solid 

 angles, to each of which the preceding reasoning will aj 

 that the whole suruce 8 will thus t> 

 hausted. We have, therefore, 



lii: J-0 



