272 



ATTRACTION OP BODIES. 



sum of the whole bodies A, B, C ; and the attracted body will 

 revolve in an ellipse with a force directed towards its centre 

 as if all the attracting bodies were formed into one globe and 

 placed in that centre. 



But if we would find the attraction of bodies whose particles 

 act according to any power n of the distance, we must, to 

 simplify the question, suppose these to be symmetrical, that 

 is, formed by the revolution of some plane upon its axis. 

 Let A M C H G be the solid, M G the diameter of its extreme 

 circle of revolution next to the particle P ; draw P M and p m 

 to any part of the circle, and infinitely near each other, and 

 take P D = P M, and P o = P m ; D d will be equal to o M (dn 

 being infinitely near D N), and the ring formed by the revo- 

 lution of M m round A B will be as the rectangle A M x M m, 



or (because of the triangles A P M, m o M, being similar, and 

 D d = om) P M x D d, or P D x D d. Let D N be taken = y 

 = force with which any particle attracts at the distance 

 P D = P M = x, that is as x n ; and if A P = b, the force of any 



b tj 

 particle of the ring is as , and the attraction of the ring, 



1} V 



described by M m, is as X D d x 



X 



. or as I y dx, and the 



