206 



FIGURE OF THE EARTH. 



[11 



TT 



and again, Attraction on M' of shell with centre M'= , op' . QS\ 



_ . , p' p' + op' Sp' a r' /r' 



out we have seen - - sr- = -sr = - = = A./ . 



p p + op op r a v r 



Hence 



Attraction of former shell on M : attraction of latter shell on M' 



- 



a 



and it is immediately clear that the attractions of the whole sphere are 

 in the same ratio*. 



4. Attraction of a segment of a sphere upon a particle in the axis 

 of the segment. 



First^, let the particle M lie at the centre of the sphere, and let a 

 shell be described in the segment, M being the common centre of its internal 

 and external surfaces, and MK, Mk the radii of these surfaces ; call MK, Mk 

 respectively p, p + op. Then the attraction of this shell upon M 



where c stands for MS; and the value of this integrated from p = c to 

 p = r gives the attraction of the whole segment. 



Secondly^, let the point M lie anywhere on the axis. 



With M as centre describe a spherical segment QB. The attraction 

 of such a segment we have just found. To find the attraction of the 



* Compare Principia, Prop. LXXXII. 

 J Compare Principia, Prop. LXXXIV. 



t Compare Principia, Prop. LXXXIII. 



