ON THE CONSTRUCTION OF THE HEAVENS. 87 



1,5136. This arrangement, remarkable as it may appear, Ob/ervatlons 



cannot be made in all fixations ; for inftance, if the ,diftance ^^^ 



ao =zbo were aflumcd equal to 1, that of co = do being 2, nature of the 



it would be impoffible to find fuch quantities of matter in a P. ofliUe revo,u - 

 1 n . _ tions governed 



and b as would unite the four ftars into one fyftem. by an attractive 



As we have fhewn how the arrangement in Fig. 10. may be fo^> d reeled 

 derived from that of Fig. 9, fo it will equally appear, (hat four 

 ftars may revolve in difFerent but fimilar ellipfes round their 

 common centre, as in Fig. 14. For here the four (tars, when 

 placed at abed, are exactly in the fituation reprefented in 

 Fig. 13; but, on account of difFerent projeclile forces, they 

 revolve, not as before in concentric circles, but in fimilar el- 

 liptical orbiis. 



Fig. 15 reprefents three ftars, a be, in the fituation of Fig. 5, 

 to which a fmall ofcillating ftar, d, is added. The addition of 

 fuch a liar to Fig. 1, has been fufficiently explained in Fig. 7 ; 

 and, what has been remarked there, may eafily be applied to 

 our prefent figure. As the fictitious body m t in Fig. 7, was 

 made to reprefent the ftars a and b } it will now ftand for the 

 three ftars a b and c. If we fuppofe thefe liars to be of an 

 equal magnitude in both figures, the centre of gravity o, of the 

 three liars, will not be fo far from m and n as in Fig. 7 ; and 

 the perturbations will be proportionally lelTened. 



Fig. 16 gives the fituation of three Itars, a be, moviilg in 

 equal elliptical orbits about their common focus o, while the 

 ftar d performs ofcillations between d and e. What has been 

 faid in explaining Fig. 8, will be fufficient to fhew, that the 

 prefent arrangement is equally to be admitted among the con- 

 ftruclions of fidereal fyftems that may be permanent. 



We have before remarked, that any appearance of treble 

 ftars might be explained, by admitting the combinations 

 pointed out in Figs. 5, 6, 7, and 8 ; and it muff be equally 

 obvious, that quadruple fyftems, under what fiiape foever they 

 may mow themfelves, whether in ftraight lines, fquares, tra- 

 pezia, or any other feemingly the moft irregular configurations, 

 will readily find a folution from one or other of the arrange- 

 ments of the eight lafl figures. 



More numerous combinations of ftars may ftill fake place, 

 by admitting fimple and regular perturbations ; for then all 

 forts of erratic orbits of multiple flexures may have a perrrta- 

 nent exiftence. But, as it would lead me too far, to apply cal- 

 culation to them, I forbear entering upo* the fubjeel at prefent. 



Before 



