Szdereal System called the Milky Way. 87 
whole annular space, crossing it in its path alternately towards 
the outer and the inner edge, thus describing a wavy line and 
revolving in an infinite number of revolutions, all limited within 
that space. What wehave said of one star is equally appli- 
Fig. 1. 
—me =e 
-- - 
Orbit 
of 
a Star. 
cable to all of them, even though they were moving ina given 
annular space with given velocities*. The countless stars of 
* I have not entered into any calculations, since the want of suffi- 
cient data at present would render them too hypothetical. It needs, how- 
ever, but little reflection to see that the velocity of a star will be least when 
it approaches the external edge of the ring at the moment of changing its 
direction. If then we conceive several stars distributed along the orbit 
described by one of them, all proceeding in the same direction, they will ap- 
proach each other more closely towards the outer edge than they will to-. 
wards the inner edge. This greater crowding of stars towards the external 
edge being the same all round the ring, will make the attraction there vary 
more rapidly, and hence a star will be sooner retarded in its motion, and 
made to recede, when it is proceeding from the centre of the annular space 
towards the exterior edge, than when it is moving from that centre towards 
the interior edge. The stars therefore in their course will go further from 
the circumference of equilibrium, that is, from the circumference in which 
the radial force is zero, towards the interior than towards the exterior 
edge: thus the centrifugal force which tends to carry the stars from the 
centre of equilibrium will be counteracted, and the ring will preserve its di- 
mensions permanently. 
If weconsider the symmetry of anannularsystem, andapply to it the general 
formule of the principles of vis viva and of the conservation of areas, in the 
forms given by Lagrange in the volume of the Memoirs of the Academy of 
Berlin for 1777, we shall easily see that there are many cases in which the 
velocities of all bodies must be confined within certain limits, and hence that 
a system of attracting bodies in the shape of a ring can preserve a perma- 
nent form, or at most will be subject merely to a tremulous motion. 
