gg ON TfiE CONSTRUCTION O*' THE- HEAVENS. 



fome perturbations arifing from the proper motion of neigh-* 

 bouring liars or fyftems, than (o be placed to the account of 

 a periodical revolution round fome imaginary diftant centre. 



III. Of more complicated Jidereal Syftems, or treble, quadruplet 

 quintuple, and multiple Stars. 



3. Complicated Thofe who have admitted our arguments for the exiftence of 

 fidcreal l fyftems : rea i double liars, will eafily advance a ftep farther, and allow 



or treble, qua- J r 



druple, &c that three itars may be connected in one mutual fyftem of re- 

 ftars * ciprocal attraction. And, as we have from theory pointed out, 



in figures 1, 2, 3, and 4-j how two liars may be maintained in 

 a binary fytiem, we mail here mew that three ftars may like- 

 wife be preferved in a permanent connection, by revolving in 

 proper orbits about a common centre of motion. 

 Obfervations In all cafes where ftars are fuppofed to move round an empty 



and inferences centre, in equal periodical times, it may be proved that an 

 nature of the imaginary attractive force may be- fuppofed to be lodged in 

 poflible revolu- that centre, which increafes in a direct ratio of the difiances. 

 by an attractive ^ or ^ lnce > m different circles, by the law of centripetal forces, 

 force, directed the fquares of the periodical times are as the radii divided by 

 the central attractive forces, it follows, that when thefe perio- 

 dical times are equal, the forces will be as the radii. Hence 

 we conclude, that in any fyftem of bodies, where the attractive 

 forces of all the reft upon any one of them, when reduced to a 

 direction as coming from the empty centre, can be (hewn to 

 be in a direct ratio of the diftance oi' that body from the centre, 

 the fyftem may revolve together without perturbation, and re- 

 main permanently connected without a central body. 



Hence may be proved, as has teen mentioned before, that 

 two ftars will move round a hypothetical centre of attraction. 

 For let it be fuppofed that the empty centre o, in Fig. 1 and 3, 

 is poifeiled of an attractive force, increafing in the direct ratio 

 of the difiances oa : ob. Then, ftnee here ao and bo are 

 equal, the hypothetical attractions will be equal, and the bo- 

 dies will revolve in equal times. That this agrees with the 

 general law of attraction, is proved thus. The real attraction 



of b upon a is ; and that of a uoon b is JL. ; and, fince- 



b zz a, it will be : : : ao ; bo; which was required. 



ab z ub' 2 - ^ 



* In 



to a center. 



