49 s Dr. Hersche-l’s Catalogue 
line, and at the same proportionate distances from each other as 
before. By this it appears, as we have already observed, that 
the absolute hypothetical force in the situation a'b'c'd', com- 
pared to what it was when the stars were at a b c d, is inversely 
as the squares of the distances ; but that its comparative exertion 
on the stars, in their present situation, is still in a direct ratio of 
their distances from the centre o, just as it was when they were 
at a bed; or, to express the same perhaps more clearly, the 
force exerted on a', is to that which was exerted on a as 
But the force exerted on a is to that exerted 
a o 
a 0 ]* 
on c, in our present instance, as ao — 1 to co = g; and still 
remains in tl?e same ratio when the stars are at a' and c' ; for 
the exertion will here be likewise as a'o — 1 to c'o = 3. 
Fig. 11 represents four stars in one circular orbit ; and its 
calculation is so simple, that, after what has been said of Fig. 5, 
I need only remark that the stars may be of any size, provided 
their masses of matter are equal to each other. 
It is also evident, that the projectile motion of four equal stars 
is not confined to that particular adjustment which will make 
them revolve in a circle. It will be sufficient, in order to pro- 
duce a permanent system, if the stars abed, in Fig. 1 2, are 
impressed with such projectile forces as will make them describe 
equal ellipses round the common centre 0. And, as the same 
method of calculation which has been explained with Figs. 6 
and 10 may here be used, it will not be necessary to enter into 
particulars. 
Fig. 13 represents four stars, placed so that, with properly 
adjusted projectile forces, they may revolve in equal times, and 
in two different circles, round their common centre of gravity 0 . 
