AND THE NEBULAR HYPOTHESIS. 459 



solution, and it may as well be stated at once that it does not. All I have been able 

 to do is to grope after general principles by solving a problem here and a problem 

 there as seemed needful to illuminate a possible path towards a general theory, and 

 the present paper is confined to a very few of the special problems I have considered, 

 but I have selected those which seemed to have most bearing on the general question 

 in hand. 



v 



Medium in which the Pressure is a Function <>f ///' 7>c//.v/V//. 



3. In the most general astronomical medium the pressure is, of course, not a 

 function of the density. The relation between pressure and density varies from 

 point to point, partly on account of inequalities of temperature and partly on account 

 of variations of chemical constitution. But no general theory can l>e expected to 

 apply to the most general heterogeneous mass of matter possible, and before any 

 general theory can be deduced we must have material from which to deduce it. 



4. The simple system from which we shall start will be a system in which the 

 matter is homogeneous as regards its properties, so that at all points the pressure 

 and density will be connected by the same relation. It will be seen later ( 1 5) how 

 it is possible, in at least one important respect, to escape from this limitation. 



For the present we assume the pressure and density to be connected by the 

 relation 



0) 



at every point. We take the centre of gravity of the rotating mass to be the origin, 

 and the axis of rotation to be the axis of z. The equations of equilibrium are 



= + i( f 



r 



in which V is the potential of the whole gravitational field of force. In virtue of 

 relation (l), these equations have the common integral 



......... ( 2 ) 





in which > stands for *+* and ,(,) for j<fe, which is by hypothesis a function of 



3 N 2 



