155-157] 



Roche's Model 



155 



156. In illustration of this the equipotentials when M' = 2M are shewn 

 in fig. 30. The values of x for which 9ft/9# vanishes are found to be 

 x = -457 R and x = "85 R, while the critical values of O are Hj = kStfM/R 

 and H 2 = 3*96 M/R. The last entirely closed equipotential is the curve 

 1 = 4>'95*7M/R which is drawn thick in the figure. From~a Tough quad- 

 rature it is found that the whole volume of this equipotential is equal to 

 that of a sphere of radius "3487?. 



Fig. 30. 



157. As a second illustration, the equipotentials when M'/M is infinite 

 are shewn in fig. 31. The value of H is now given by equation (406), in 

 which M' and R are both infinite. Thus 



or, replacing the infinite constant M'/R by 0, 



Fig. 31. 



