DOUBLE STARS 149 



with the known laws of mechanics, and, if it is in accord- 

 ance with these laws, to trace the manner in which it may 

 be effected. Unfortunately, however, the difficulties pre- 

 sented by the problem are so great that it has so far defied 

 the power of modern mathematics. Recently, however, 

 certain remarkable investigations have been made upon 

 the behaviour of rotating masses of gravitating fluid, 

 which, while not supplying an actual solution of the 

 problem, do undoubtedly appear to throw some light 

 upon it. The results of these investigations appear to 

 me to be so interesting, and so suggestive in their astro- 

 nomical application, that I propose to consider them in 

 some detail. 



Let us imagine a mass of fluid of any form to exist in 

 celestial space, and to be so far removed from other bodies 

 as not to be appreciably affected by their gravitational 

 attraction. Let us further assume that the fluid is incom- 

 pressible, and that it is of uniform density throughout. 

 By the law of gravitation each portion of it will attract 

 every other portion with a force that is inversely propor- 

 tional to the square of the distance between them. Under 

 the influence of these attractions between its parts the 

 mass will tend to acquire the form of a sphere. If, at the 

 instant at which our attention is first directed to it, every 

 part is at rest, the mass will in fact ultimately assume a 

 spherical form, in which all its parts are at rest. The 

 sphere is therefore regarded as a figure of equilibrium 

 for the gravitating fluid. Further, if the spherical mass 

 is subjected to any accidental disturbance, if for instance, 

 it were drawn out of form by the tidal action of a passing 

 planet, it would, when the disturbing influence has ceased, 

 reassume the spherical form. For this reason the figure 

 is regarded as one of stable equilibrium. 



Next, let us suppose that a motion of rotation is imparted 



