of 500 new Nebulcs , and Clusters of Stars . 491 
orbit will only describe a radius of the same globe, on account 
of its requiring a solid attractive centre. 
After what has been said, it will hardly be necessary to add, 
that with the assistance of any proper one of the combinations 
pointed out in the four last figures, the appearance of every 
treble star may be completely explained; especially when the 
different inclinations of the orbits of the stars, to the line of sight, 
are taken into consideration. 
If we admit of treble stars, we can have no reason to oppose 
more complicated connections ; and, in order to form an idea 
how the laws of gravitation may easily support such systems, I 
have joined some additional delineations. A very short expla- 
nation of them will be sufficient. 
Fig. 9 (Plate XVII.) represents four stars, a b c and d, arranged 
in a line; a being equal to b , and c equal to d. Then, if ao = 
bo, and co — do, the centre of gravity will be in 0 ; and, with a 
proper adjustment of projectile forces, the four stars will revolve in 
two circular orbits round their common centre. By calculating 
in the manner already pointed out, it will be found, that when, 
for instance, ao = 1, co = 3, and c — d — 1, then the mass of 
matter in a = b, will be required to be equal to 1,3492. 
It is not necessary that the projectile force of the four stars 
should be such as will occasion them to revolve in circles. The 
system will be equally permanent when they describe similar 
ellipses about the common centre of gravity, which will also be 
the common focus of the four ellipses. In Fig. 10, the stars 
abed, revolving in ellipses that are similar, will always 
describe, at the same time, equal angles in each ellipsis about the 
centre of hypothetical attraction ; and, when they are removed 
from abed to a'b' c' d they will still be situated in a straight 
