ON THE CONSTRUCTION OE THE HEAVENS, §3 



In Figures 2 and 4, when the flars a and b are unequal, and Observations 

 their diftances from o alfo unequal, let o a = ra, and ob z=.m ; re fn e &in? the 

 and let the mafs of matter in a = w, and inb =zn. Then the nature bf the 



, pofiible revolu- 



attra&ion of b on a = , will be to the attraction of a on b tion s governed 



# £ 4 by an attractive 



force, directed 

 = — -, 2nn:mi which is again directiy as«o:5o. t0 a center. 



1 proceed now to explain a combination of three bodies, Figure of orbits, 

 moving round a centre of hypothetical attraction. Fig. 5 con- 

 tains a tingle orbit, wherein three equal bodies a b c, placed 



at equal diflances, may revolve permanently. For, the real 



attraction of b on a will be exprefled by — ; but this, reduced i 



ab x 



to the direction of, will be only ., ' - 7 A; for, the attraction 



ab 3 



in the direction & a is to that in the direction by, parallel to a o, 



b b .by 

 as ^7a ^Tt" The attraction alfo of c on a is equal to that 



of b on a; therefore the whole attraction on a, in a direction 



towards o, will be exprefled by w ' I. In the fame manner 



ab 3 



we prove, that the attraction of a and c on b, in the direction 



h o, is «__J — £ ; and that of a and b on c, in the direction c o, 

 ab 3 



2 c b v 



is — 1-^-. Hence, a b and c being equal, the attractions in 

 ab 3 



the directions ao b o and c o will alfo be equal ; and, confe- 

 quently, in the direcl: ratio of thefe diflances. Or rather, the 

 hypothetical attractions being equal, it proves that, in order to 

 revolve permanently, a b and c muft be equal to each other. 



Inftead of moving in one circular orbit, the three flars may 

 revolve in three equal ellipfes, round their common centre of 

 gravity, as in Fig. 6. And here we mould remark, that this 

 centre of gravity will be (ituated in the common focus o, of the 

 three ellipfes ; and that the abfolute attraction towards that 

 focus, will vary in the inverfe ratio of the fquares of the dis- 

 tances of any one of the flars from that centre, while the rela- 

 tive attractions remain in the direcl: ratio of their feverai dif- 

 tances from the fame centre. This will be more fully ex- 

 plained, when we come to confider the motion of four flars. 

 . G 2 A very 



