166-168] Adiabatic Model 167 



Then it is readily seen that the potential of the whole heterogeneous 

 mass whose density is given by equation (427), and whose boundary is 

 given by p = a, will be 



F = erF (l)+ rV.(q)dp ................... ..._,.. .(431), 



(432), 



the first formula giving the potential at a point outside the mass, and the 

 second formula giving the potential at an internal point at which the 

 density is p'. 



168. As in 77, let us suppose that P is put in the form 



y z 



Introduce new coordinates f, rf , f such that 



y- x etc 

 ' * 



and let 



so that P reduces to P when /j, = 0. 



Suppose further that /and D are given by 



_ 



(fa? 



-I- /i) 7; /2 + (g 2 c 2 + ft) ^ 2 - 1 ...... (433), 



2 (434) 

 /2 



Let ^> (g) be given by our former equation (200), namely 

 < (q) = e [P - IfDP + I 



- ie 2 [DP 2 - 



- - -] etc .......... (435), 



in which y and Z) are now supposed defined by equations (433) and (434). 

 When yit = the equation /=0 represents an ellipsoid of semi-axes qa> 

 qb, qc. Moreover, when //, = 0, D reduces to zero and P to P , so that <f>(q) 

 reduces to eP , and 



