493 
of $ o° new Nebula, and Clusters of Stars. 
If ao = bo = ^, co = do — 5, and c — d — i, then will the 
mass of matter in a — b, required for the purpose, be 1,5136. 
This arrangement, remarkable as it may appear, cannot be 
made in all situations ; for instance, if the distance ao — bo were 
assumed equal- to 1, that of co — do being 2, it would be im- 
possible to find such quantities of matter in a and b as would 
unite the four stars into one system. 
As we have shewn how the arrangement in Fig. 10 may be 
derived from that of Fig. 9, so it will equally appear, that four 
stars may revolve in different but similar ellipses round their 
common centre, as in Fig. 14. For here the four stars, when 
placed at abed, are exactly in the situation represented in 
Fig. 13; but, on account of different projectile forces, they re- 
volve, not as before in concentric circles, but in similar elliptical 
orbits. 
Fig. 15 represents three stars, a b c, in the situation of Fig. 5, 
to which a small oscillating star, d, is added. The addition of 
such a star to Fig. 1, has been sufficiently explained in Fig. 7; 
and, what has been remarked there, may easily be applied to 
our present figure. As the fictitious body m, in Fig. 7, was made 
to represent the stars a and b, it will now stand for the three 
stars a b and c. If we suppose these stars to be of an equal 
magnitude in both figures, the centre of gravity 0, of the three 
stars, will not be so far from m and n as in Fig. 7; and the 
perturbations will be proportionally lessened. 
Fig. 1 6 gives the situation of three stars, a b c, moving in 
equal elliptical orbits about their common focus 0, while the 
star J performs oscillations between d and e. What has been 
said in explaining Fig, 8, will be sufficient to shew, that the 
mdcccii. g S 
