450 
Dr. Herschei/s Catalogue 
their motion in opposite directions, and begin to approach to 
their common centre of gravity o, in which they will meet a 
second time. It is evident that the orbit of the two large stars 
will suffer considerable perturbations, not only in its plane, but 
also in its curvature, which will not remain strictly circular; 
the construction of the system, however, is such as to contain a 
sufficient compensation for every disturbing force, and will con- 
sequently be in its nature permanent. 
In order to add an oscillating star, it is not necessary that the 
two large stars should be so situated as to move in a circular 
orbit, without the oscillating star. In Fig. 8, the stars a and b 
may have such projectile forces given them as would cause them 
to describe equal ellipses, of any degree of excentricity. If now 
the small star c be added, the perturbations will undoubtedly 
affect not only the plane of the orbits of the stars, but also their 
figures, which will become irregular moveable ovals. The extent 
also of the oscillations of the star c will be affected ; and will 
sometimes exceed the limits c d , and sometimes fall short of 
them. All these varieties may easily be deduced from what has 
been already said, when Fig. 7 was considered. It is however 
very evident, that this system also must be permanent; since 
not only the centre of gravity 0 will always be at rest, but a 0 , 
whatever may be the perturbations arising from the situation of 
r, will still remain equal to b 0. 
It should be remarked, that the vibratory motion of the star c 
will differ much from a cometary orbit, even though the latter 
should be compressed into an evanescent ellipsis. For, while the 
former extends itself over the diameter of a globe in which it 
may be supposed to be inscribed, the hypothetical attractive 
force being supposed to be placed in its centre, the cometary 
