182, 183] 



Adiabatic Model 



183 



this value of (p Q <r)/p , so that the critical value derived from the terms 

 actually calculated may be expected to be tolerably near to the true value. 



Putting (p cr)/p Q = 1, the critical value of 7 derived from the first two 

 terms of the equation is seen to be 



7 = 2-0509 .............................. (497), 



while if all the terms written down are used, the value is found to be 



7 = 21521 .............................. (498). 



We cannot state with great accuracy the value of 7 to which these values 

 are converging, but there is not likely to be any very great error in taking 

 it to be 7 = 2*2. Assuming this value, it appears that a mass of gas for 

 which 7 = 2'2 will begin to lose matter equatorially at precisely the moment 

 at which the pseudo-spheroidal form becomes unstable and gives place to 

 the pseudo-ellipsoidal form. 



183. The value of So> 2 has already been obtained in 181. From this 

 we find that equation (488) extended as far as the second order of small 

 quantities becomes 



= 0-18712 + 0-06827 + [0-01602 + 0*07098 (7 - 2)] - 



2-7T/3 



When 7 = 2'2, this becomes 



= = 018712 + 0-06827 



(499). 



+ 0-03022 



...(500). 



The general series of which the first- three terms are here written down is 

 probably convergent right up to the limiting value (p <r)/p = 1, but it 

 is not easy to determine the value to which it converges. At a guess the 

 value of &) 2 /27rp appears to converge to about 0'3 1. 



The critical figure for 7 = 2'2 is shewn in fig. 36, but it is not possible to 

 draw the figure with much accuracy in the neighbourhood of the sharp edge. 

 The interior curves are equipotentials and so are also surfaces of constant 

 density and temperature. 



Fig. 36. 



