﻿202 Dr. J. W. Nicholson on the 



With the value of dr, the phase-integral 



n 3 h=\ dr( Pl -{p,)J 

 Je=o 



breaks into three parts, thus 



Jo . (cos </>- cost;) 2 ^J„ Y 



T 271 " sin (ft (sin </> + sin nMcfr 

 J 27r _„ (cos</>- cost;) 2 



Jo (cos</>~ cost;) 2 ^J „ 



by a simple transformation. 



Finally, the only accurate phase-integral is 



f' sin»(»in»-Bi n ^)^ 



,.J (cos 9— cost;)"' 

 while Epstein gives, in our notation, 



nji 



— 28 f "" sm< ^ f s i K< fr~ sin?;) 

 ~ J (cos <j>— cost;) 2 



the part of his range from r/ to it involving a meaningless 

 negative value of r, and violating p 1 = (p 1 ) x though the 

 moving electron is at infinity. The principal value of 

 Epstein's integral is, using the indefinite integral for the 

 function in the form, readily obtained by parts, 



J sin $ (sin ff>— sin 7;) 

 (cos <£-- cost;) 2 ™ 



sm 0— sin 7} , , , 1 2 



= 7 '- —6+ COt T) . lOge S T 



cos </> — cos t; r n I . rj+(p 



of the type 



^ = 2^1-1^—1—1 

 I 7rsmT;J 



or 2 _ (wi + rc 2 + rc 3 ) 



7r sin rj n 1 -\-n 2 ' 



and ultimately 



2 meV J 1 



w= 



^ 7J "" / . . \2 / 



— (Tl! + W 2 + %) - (^1 + W ? / 



— generalized from his value which relates only to a plane 



