of 500 new Nebula, and Clusters of Stars. 489 
from the same centre. This will be more fully explained, when 
we come to consider the motion of four stars. 
A very singular straight-lined orbit, if so it may be called, 
may also exist in the following manner. If a and b, Fig. 7, are 
two large equal stars, which are connected together by their 
mutual gravitation towards each other, and have such projectile 
motions as would cause them to move in a circular orbit about 
their common centre of gravity, then may a third small star c, 
situated in a line drawn through 0, and at rectangles to the plane 
described by the stars a b, fall freely from rest, with a gradually 
acquired motion to 0; then, passing through the plane of the 
orbit of the two stars, it will proceed, but with a gradually re- 
tarded motion, to a second point of rest d ; and, in this manner, 
the star c may continue to oscillate between c and d , in a straight 
line, passing from c, through, the centre o> to d, and back again 
to c. 
In order to see the possibility and permanency of this con- 
c 
nection the better, let 0 be the centre of gravity of the three 
bodies, when the oscillating body is at c ; then, supposing the 
bodies a and b to be at that moment in the plane p l, and ad- 
mitting m to represent a body equal in mass to the two bodies 
a b, 0 will be the common centre of gravity of m and c. Then, 
by the force of attraction, the body c and the fictitious body m 
will meet in 0 ; that is to say, the plane p l , of the bodies a b , 
will now be at p' V . 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 same, the plane of the bodies a b will now 
be in the position p" l ", as much beyond the centre of gravity 0, 
as it was on the opposite side m. By this time, both the ficti- 
tious body m, now at n , and the real body c, now at d, have lost 
