128 NEWTON S PRINCIPIA. 



that the several resulting forces are not directed towards 

 the several centres. But this departure will be less con 

 siderable in proportion as the body in the centre of any 

 system, or in the common centre of any number of sys 

 tems, is of a magnitude exceeding that of the revolving 

 bodies, or systems of bodies, because this will prevent 

 the central body moving far from its place, or much out of 

 a straight line; and also the departure will be less in 

 proportion as the bodies, or systems revolving, are at a 

 great distance from the centres or from the common centre, 

 because the diminution of this distance increases the 

 inclination of the lines in which the disturbing forces act, 

 and thus disturbs the motions of the bodies among them 

 selves. Again, if the law of the attraction varies from the 

 inverse square of the distance in some, and not in others, 

 the disturbing effect will be increased. So that we may 

 infer the universality of the law and also the small amount 

 of the disturbing force, and its acting in nearly parallel 

 lines, if we find the ellipticity of the orbits not much de 

 ranged, and the proportions of the areas to the times not 

 greatly interrupted. 



Newton proceeds to examine more minutely the disturb 



ances caused in a system of Three Bodies, of which two 

 smaller ones move round a third larger one, and all attract 

 one another by forces inversely as the squares of the dis- 



