130 NEWTON S PRINCIPIA. 



proportion of S L = ^r^ J, the nearer S N is to unity, 



the mean force upon M ; and the nearer the forces exerted 

 by S on M and on E approach to equality, the less will 

 the elliptical orbit be disturbed, and the more nearly will 

 the areas be described proportionally to the times. If the 

 disturbing force of S acts in a plane different from that in 

 which M and E are, M will be deflected from the plane 



of its orbit; because the force SN - 2 will not pass 



through E; consequently this deflection will be greater or 

 less in proportion as this difference is greater or less, and 



will be least when ^^ ^ s nearly equal to the mean force 



of S upon M. 



We have hitherto been supposing S, the greater body 

 round which M and E revolve, to be at rest while they 

 revolve round each other (the case of the earth and of 

 other planets having satellites). If we now suppose E to be 

 the greater and central body, and that M and S both move 

 round E (the case of the planets round the sun), a similar 

 proposition may be demonstrated with respect to the dis 

 turbances : And it is further clear in this case that if S 

 moves round G, the centre of gravity of M and E, the 

 orbit of S will be less drawn from the elliptical form, and 

 its radius vector will describe areas more nearly proportional 

 to the times than if it moved round E. This appears 

 clearly from observing that the direction of the centripetal 

 force towards G, that is S G, must be nearer E than M ; 

 that the attractive forces by which S is drawn are as 



- ~~ ~^ tnat their resu l tin force lies in tne line 



S G ; and also that S M varies, while S E remains the 

 same, or nearly so. 



