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 elhptic 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 orbits 



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 gi'oup, 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. 



I 



