OF CENTRAL FORCES. 29 



is in any part of its orbit (as suppose at K) a smaller LECT. 

 body as L, within the sphere of attraction of the body ^^^^^ 

 K, be projected in the right line L M, with a force duly 

 adjusted, and perpendicular to the line of attraction LK; ^ 

 then, the small body L will revolve about the large body 

 K in the orbit N O, and accompany it in its whole course 

 round the yet larger body 5. But then, the body K will 

 no longer move in the circle A T W; for that circle will 

 now be described by the common center of gravity be- 

 tween K and L, Nay, even the great body S will not 

 keep in the center ; for it will be the common center of 

 gravity between all the three bodies 5, K, and L, that 

 will remain immoveable there. So, if we suppose S and 

 K connected by a wire P that has no weight, and K and 

 L connected by a wire q that has no weight, the com- 

 mon center of gravity of all these three bodies will be a 

 point in the wire P near S ; which point being support- 

 ed, the bodies will be all in equilibria as they move 

 round it. Though indeed, strictly speaking, the com- 

 mon center of gravity of all the three bodies will not be 

 in the wire P but when these bodies are all in a right 

 line. Here, S may represent the sun, K the earth, and 

 L the moon. 



In order to form an idea of the curves described by 

 two bodies revolving about their common center of gra- 

 vity, whilst they themselves < with a third body are in 

 motion round the common center of gravity of all the 

 three ; let us first suppose E (p. 30.) to be the sun, and e 

 the earth going round him without any moon ; and their 

 moving forces regulated as above. In this case, 

 whilst the earth goes round the sun in the dotted circle The c ." n ", C)l 

 R T U W X, &c. the sun will go round the circle by bodies 

 A B D, whose center C is the common center of gravity ^mlt thfir 

 between the sun and earth : the right line /38 represent- common 

 ing the mutual attraction between them, by which " 



are as firmly connected as if they were fixed at the two 



