204 The Evolution of Rotating Nebulae [CH. ix 



In the chapter preceding this we found that an actual mass of gas would 

 not arrange itself in adiabatic equilibrium while contracting under its own 

 gravitation. In adiabatic equilibrium the quantity denoted by k is everywhere 

 constant ; in an actual contracting mass, we found that k, defined by the 

 equation p = kpi, would increase continually from the centre to the edge. 

 Except possibly in a comparatively shallow surface layer, there is no con- 

 vection, and the result of this must be that the heavier elements tend to 

 congregate at and near the centre, while the lighter elements form a sur- 

 rounding atmosphere. That this actually occurs is made probable by the 

 results of spectroscopic examination of nebulous masses. Campbell* found 

 that in a number of nebulae the different gases are not uniformly distributed 

 throughout the nebular structure. In some, as for example the Orion and 

 Trifid nebulae, the hydrogen is definitely found to extend further out than 

 the other chemical elements. Wright has found that in the planetary nebulae 

 the helium always favours the central nucleus more than the hydrogen and 

 nebulium do ; in some cases the helium is entirely confined to the central 

 nucleus. Campbell again has found that in a slitless spectrum of the small 

 planetary nebula N.G.C. 418 2 , the Hp line of hydrogen forms a circle of 

 14" diameter, while the first and second green nebulium lines form circles of 

 diameters only 11" and 9" respectively. 



Thus both theory and observation agree in suggesting that the "adiabatic" 

 model does not altogether give a faithful representation of actual conditions. 

 The quantity k is not constant throughout the mass but increases from centre 

 to edge, while the different chemical constituents are not thoroughly mixed 

 up ; the heavier elements have sunk towards the centre. 



We are accordingly led to inquire to what extent the theoretical results 

 which were obtained from a study of the " adiabatic " model may be expected 

 to require modification for an actual mass of gas. 



204. In our study of the adiabatic model, p and p were supposed con- 

 nected by the relation 



p = kpi, 



and k and 7 were supposed constant throughout the mass, but it was nowhere 

 found necessary to attach any special physical meanings to k and 7. Frorr, 

 this general relation we readily find that 



(532), 



since k was supposed kept constant. Thus 7 might have been regarded 

 merely as a symbol for d log p/d log p. 



* Science, 45 (1917), 11(59, p. 538. 



