g(J ON THE CONSTRUCTION OP THE HEAVENS. 



Obfervations fyftem will be equally permanent when they defcribe fimilar 

 refpeahreAe e ^ip^ es about the common center of gravity, which will alio be 

 nature of the the common focus of the four ellipfes. In Fig. 10. the ftars 

 ^governed" a b c d > evolving in ellipfes that are fimilar, will always de- 

 by an attra&ive fcribe, at the fame time, equal angles in each ellipfis about the 

 f oTc n t ie6led centre of hypothetical attra&ion ; and, when they are removed 

 from abed to a b' c' d f , they will ftill be fituated in a ftraight 

 line, and at the fame proportionate diftances from each other as 

 before. By this it appears, as we have already obferved, that 

 the abfolute hypothetical force in the fituation a' b ' d d', com- 

 pared to what it was when the ftars were at a b c d, is inverfely 

 as the fquares of the diftances ; but that its comparative exer- 

 tion on the flars, in their prefent fituation, is ftill in a direct 

 ratio of their diftances from the centre o, juft as it was when 

 they were at abed; or, to exprefs the fame perhaps more 

 clearly, the force exerted on a', is to that which was exerted 



11 



on a as . ■ — ; • — z . But the force exerted on a is to 



ao\ ao\ 



that exerted on c, in our prefent inftance, as a o = 1 to c o 

 = 3 ; and ftill remains in the fame ratio when the ftars are at 

 a f and c ' ; for the exertion will here be likewife as a o =; 1 

 to c'o = 3. 



Fig. 1 1 reprefents four ftars in one circular orbit ; and its 

 calculation is fo fimple, that, after what has been faid of Fig. 5, 

 I need only remark that the ftars may be of any fize, provided 

 iheir mattes of matter are equal to each other. 



It is alfo evident, that the projectile motion of four equal 

 ftars is not confined to that particular adjuftment which will 

 make them revolve in a circle. It will be fufticient, in order 

 to produce a permanent fyftem, if the ftars abed, in Fig. 12, 

 are imprefled with fuch projectile forces as will make them 

 defcribe equal ellipfes round the common centre o. And, as 

 the fame method of calculation which has been explained with 

 Figs. 6 and 1 may here be ufed, it will not be neceflary to 

 enter into particulars. 



Fig. 13 reprefents four ftars, placed fo that, with properly 

 adjufted projcclHe forces, they may revolve in equal times, and 

 in two different circles, round their common centre of gravity 

 *. If ao = bo = 4, co = do =z 5, and c = d = 1, then 

 will the mafs of matter in a = b t required for the purpofe, be 



