184 Compressible and Non- Homogeneous Masses [en. vn 



SUMMARY OF RESULTS 



184. Let us now recapitulate and summarise the results which have been 

 obtained in the present and preceding chapters. We have been attempting 

 to obtain an idea of the configurations which will be assumed by astro- 

 nomical matter under the influence of its own rotation and under the action 

 of tidal forces. Some results have been obtained which are applicable to 

 all matter, but in general the investigation has had to be limited to certain 

 simplified model masses. The models we have had under consideration 

 have been four in number : 



(A) The incompressible model, consisting of a mass of homogeneous 

 incompressible matter of uniform density. 



(B) Roche's model, consisting of a point nucleus of very great density, 

 surrounded by an atmosphere of negligible density. 



(C) The generalised Roche's model, consisting of a homogeneous in- 

 compressible mass of finite size and of finite density, surrounded by an 

 atmosphere of negligible density. 



(D) The adiabatic model, consisting of a mass of gas in adiabatic equi- 

 librium, so that the pressure and density are connected at every point by 

 the relation p = /ep*, where K and 7 retain the same values throughout the 

 mass. 



Of these four models A and B are limiting cases of the more general 

 models C and D. If s denote the ratio of the volume of the atmosphere to 

 that of the nucleus in the generalised Roche's model C, then model C de- 

 generates into model A when s = 0, and degenerates into model B when 

 s = oo . Similarly the adiabatic model D degenerates into model A when 

 7= oo and into model B when 7 = 1| (cf. 149). The relation between the 

 four models is represented diagram matically in fig. 37. 



C 



,A 

 (Incompressible* = (Roches model) 







Fig. 37. 



Independently of the study of any particular model, we have seen that 

 an increase of rotation to a certain amount will tend to break up the 

 original mass, while the same is true of tidal forces of sufficient intensity. 



Generalised Roche's mode 



