185-187] Summary of Results 187 



* 



finally jets of matter stream out from these cones, just as they streamed off 

 at the equator in the rotational problem. 



On the chain G of generalised Roche's models, we have found that the 

 former method of break-up gives place to the latter when s, the_ratio of the 

 volume of the atmosphere to that of the central mass, has a value approxi- 

 mately equal to T \j. The chain D of adiabatic models has not been studied 

 in detail, but it seems safe to suppose that at some point on this chain the 

 one method of break-up gives place to the other. Assuming this, the results 

 obtained for the tidal problem are those exhibited diagrammatically in fig. 39 ; 

 the region to the left of the broken line represents configurations in which 

 the mass, when broken up tidally, divides into a number of masses of com- 

 parable size, while the region on the right represents configurations in which 

 one or two jets of matter will be thrown off from the mass. 



CT? / JUT f \ -1. -\ 

 The figures in brackets denote the values of ( ) . I 

 r o \ M / J 



The Double-star Problem 



187. The results obtained for the double-star problem are so similar to 

 those obtained for the tidal problem that it is hardly worth recapitulating 

 them in detail. In the double-star problem, as in the tidal problem, there 

 are two masses concerned, and we have been studying the mutual gravi- 

 tational action of these two bodies on one another. From the mathematical 

 point of view the double-star problem is little more than the tidal problem 

 with a rotation set up just adequate to keep the masses permanently at a 

 given distance from one another, and this explains the general similarity of 

 the mathematical results obtained. 



We proceed now to apply the abstract results obtained to actual problems 

 of astronomy and cosmogony. 



