168-no] Adiabatic Model 



Using relation (429) we find 



V,(q)df+ 



169 



...(443), 



where q is the x value of q at the point x, y, 2 at which the potential is being 

 evaluated. The sum of the two integrals in square brackets is found, on 

 integrating by parts, to become 



4- 



Since Vi (q') = V (q), the sum of the first two terms in this expression 

 reduces at once to Vi(l), so that equation (443) can be put in the. form 



where 



The first term on the right hand of equation (444) is the internal 

 potential of a homogeneous solid of uniform density p Q ; the second term 

 accordingly represents the effect of the falling off of density from p at the 

 centre to cr at the boundary. 



The value of V (q), as given by equation (441) is a function of q and 

 also of X', which is connected with q by equation (442). Thus 



dV cTPo ax' 



dq* 



In this equation we have 



d\' 



and this vanishes from the definition of X' (equation (442)). We accordingly 

 have, from equations (441) and (439), 





r^_^^ 



Jv V dq 2 ) A' 



while similarly by direct differentiation, 



d 5<2>. ,*, r (!_?*>). 



dq 9 Jo V dq* ] A 



Thus the value of E given by equation (445) becomes 



(446). 



