Chap. XXL] THE HEAVENS. 271 



PEOPOSITION XXXV. 



Problem. — To determine the motion of a body in space 

 under the action of revolving forces proceeding 

 from different centres of rotation. 



1. If a body in space be acted on equally by equal 

 forces proceeding from two different centres of rota- 

 tion, and tending to carry it in the same direction, it 

 is evident that as it proceeds, and the directions of 

 rotation diverge, it must take an intermediate course 

 between the two, and therefore be equally carried 

 away from both centres of rotation. 



As it recedes it must, at some point equidistant 

 from both centres, be brought into equilibrium as 

 regards the centripetal and centrifugal forces : be- 

 cause it is carried off from both centres in conse- 

 quence of the force of astral gravitation acting from 

 them increasing as the square of the velocity (Propo- 

 sition VIII.) is increased by the combined action ot 

 the two revolving forces ; but, whilst carried off 

 along a line forming a tangent to both of the orbits, 

 the centripetal forces decrease as the square of the 

 distance increases, whilst the centrifugal forces of 

 astral gravitation which carry it off along that tan- 

 gent (because in it they equally retard it from the 

 positions on each side to which the revolving forces 



