544 The Genesis of Double Stars 
position is a stable one, the second is unstable. But this case is too 
simple to illustrate all that is implied by stability, and we must 
consider cases of stable and of unstable motion. Imagine a satellite 
and its planet, and consider each of them to be of indefinitely small 
size, in fact particles ; then the satellite revolves round its planet in 
an ellipse. A small disturbance imparted to the satellite will only 
change the ellipse to a small amount, and so the motion is said to be 
stable. If, on the other hand, the disturbance were to make the 
satellite depart from its initial elliptic orbit in ever widening circuits, 
the motion would be unstable. This case affords an example of stable 
motion, but I have adduced it principally with the object of illustrating 
another point not immediately connected with stability, but important 
to a proper comprehension of the theory of stability. 
The motion of a satellite about its planet is one of revolution or 
rotation. When the satellite moves in an ellipse of any given degree 
of eccentricity, there is a certain amount of rotation in the system, 
technically called rotational momentum, and it is always the same at 
every part of the orbit. 
Now if we consider all the possible elliptic orbits OF a satellite 
about its planet which have the same amount of “rotational 
momentum,” we find that the major axis of the ellipse described will 
be different according to the amount of flattening (or the eccentricity) 
of the ellipse described. Fig. 1 illustrates for a given planet and 
satellite all such orbits with constant rotational momentum, and with 
all the major axes in the same direction. It will be observed that 
there is a continuous transformation from one orbit to the next, and 
that the whole forms a consecutive group, called by mathematicians 
“a family” of orbits. In this case the rotational momentum is 
constant and the position of any orbit in the family is determined by 
the length of the major axis of the ellipse; the classification is 
according to the major axis, but it might have been made according 
to anything else which would cause the orbit to be exactly deter- 
minate. 
I shall come later to the classification of all possible forms of 
ideal liquid stars, which have the same amount of rotational momentum, 
and the classification will then be made according to their densities, 
but the idea of orderly arrangement in a “family” is just the same. 
We thus arrive at the conception of a definite type of motion, 
with a constant amount of rotational momentum, and a classification 
of all members of the family, formed by all possible motions of that 
type, according to the value of some measurable quantity (this will 
1 Moment of momentum or rotational momentum is measured by the momentum of 
the satellite multiplied by the perpendicular from the planet on to the direction of 
the path of the satellite at any instant. 
