460 Mr. J. Prescott on Convective Equilibrium 



likewise doubled ; hence the resultant attraction would be 

 quadrupled. And since, before the alteration in density, the 

 pressures and attraction balanced, it follows that the attraction 

 under the new conditions would be preponderant everywhere 

 and each element would move nearer the centre of the sphere. 

 Thus the larger mass, starting from the same initial con- 

 ditions as the smaller mass, will occupy the smaller volume. 

 In the preceding argument there is no assumption concerning 

 the variation of temperature throughout the mass ; and there- 

 fore the conclusion is true however the temperature may 

 vary from point to point. 



The consideration that the smaller the mass the larger is 

 the sphere occupied by a gas led me to suspect that there 

 might be a critical mass of gas which, starting with a given 

 amount of internal energy per unit mass, would just diffuse 

 to infinity. In the case of convective equilibrium, however, 

 I find that this surmise is not correct. Although the bounding 

 sphere may become very great for small masses yet it never 

 becomes infinite. But practically a small mass of gas could 

 not be held together by its own gravitation in the neighbour- 

 hood of other bodies ; for the attraction on the outer portions 

 of the mass would be so small that the slightest attraction, 

 even from distant external bodies, would suck some of 

 it away, and this process would go on until nothing was 

 left. 



Now I propose to obtain the relation between the density 

 p and the distance from the centre r in a mass of gas in 

 convective equilibrium. 



The equation expressing the condition of equilibrium is 



t=-f*> « 



where p is the pressure, and F is the attraction on unit mass 

 at a distance r. Thus 





F=- 2 \ fAm^dr, (2) 



K being the constant of gravitation. 

 Hence 



J = -$J>^ • • • • (3) 



Assuming convective equilibrium we have 



p = cp*. 



