84 ON THE CONSTRUCTION OF THE HEAVfiNfJ 



A ftmight-lined -A very lingular ftraight-lincd orbit, if fo it may be called, 

 orbit or ofciih- mayaifo exift in the following manner. It' a and b, Fig. 7, 

 tory motion. J 6 , 



are two large equal ftars, which are connected together by 



their mutual gravitation towards each other, and have fuch 

 projectile motions as would caufe them to move in a circular 

 orbit about their common center of gravity, then may a third 

 fmall ftar c, fituated in a line drawn through o, and at rectan- 

 gles to the plane defcribed by the ftars a b, fall freely from reft, 

 with a gradually acquired motion to o; then, palling through 

 the plane of the orbit of the two ftars, it will proceed, but with 

 a gradually retarded motion, to a fecond point of reft d; and, 

 in this manner, the ftar c may continue to ofcillate between e 

 and d, in a ftraight line, palling from c, through the centre o, 

 to d, and back again to c. ^ 



In order to fee the poffibility and permanency of this con- 

 nection the better, let o be the centre of gravity of the three 

 bodies, when the ofcillating body is at c ; then, fuppofing the 

 bodies a and b to be at that moment in the plane p I, and ad- 

 mitting m to reprefent a body equal in mafs to the two bodies 

 a b t o will be the common centre of gravity of m and c. Then, 

 by the force of attraction, the body c and the fictitious body wt 

 will meet in o ; that is to fay, the plane p /, of the bodies a b, 

 will now be at p' I'. The fictitious body m may then be con- 

 ceived to move on till it comes to n, while the body c goes to 

 d; or, which is the fame, the plane of the bodies a b will novr 

 be in the pofition p" i" , as much beyond the centre of gravity o, 

 as it was on the oppofite fide m. By this time, both the ficti- 

 tious body m, now at n, and the real body c, now at d, have loft 

 their motion in oppofite directions, and begin to approach to 

 their common centre of gravity o, in which they will meet a 

 fecond time. It is evident that the orbit of the two large ftars 

 will fuffer confiderable perturbations, not only in its plane, but 

 alfo in its curvature, which will not remain ftrictly circular ; 

 the conftruction of the fyftem, however, is fuch as to contain a 

 fuflicic-nt compenfation for every difturbing force, and will con- 

 fequently be in its nature permanent. 



Iii order to add an ofcillating ftar, it is not neceflary that the 

 two large ftars (hOuld be fo fituated as to move in a circular 

 orbit, without the ofcillating ftar. In Fig. 8, the ftars a and b 

 may have fuch projectile forces given them as would caufe 

 tliem todefcribe equal ellipfes, of any degree of excentricity. 



If 



