312 



LIPKA. 



dFi. 



the coefficient of in the second sum, we have from (33) 



dp 



dUk i=2pl dUk dUr 



i = 2PldUr' 



hence, 



dFi fdP. dfi dPi dfi 



dp2\durduk dUk du 

 and 



^dFi/dP2 dfi dP2dj\\_ 



i dp2 \dUr dUk dUk dUr 

 dFi P2 dFi 

 _dp2 pidp2 



_ » Pi dFr fdP^ dfi dPi dfi 



i=2 p\ d p2 \ du r duk d 2ik du r 



n 

 t = 2 



dFi PidF^ 



dP. dfi dPt dfi 

 dpo pidpij \duT dUk diikdur 

 dFi PidF, 

 dp2 Pidp2 

 dP2dfi_ _ dP^dfi, 



dUr dUk dUk dUr 



(dP2df2_dP2df2\_^^ 



\duTdUk duk durj t=3 



Similarly, we may eliminate the coefficient of — ^^^ in the 7?ith 



sum in (71), and thus find 

 (72) ^dF\(^Mi_^Mi 



i dpm \dUr dUk dUk dUr 



dFi 



dF„ 



dp„ 



Pm dFm-1 



dpm Pm-1 dp„ 



dPm dfm 

 dUr dUk 



_ dPmdfm\ 

 dUk dUr) 



+ 



Pi dF 



HI.— I 



dpm Pm-\ dp„ 



dPm dfi dPm dfi 



dUr dUk dUk dUr 



We may consider this as a typical term, letting m assume all values 

 from 1 to n cyclically, or m = 1-^ 2— >. . . . -^n. Substituting in (71) 

 and noting that the coefficients 



dPm dfm dPm dfm 



dUr dUk dUk dUr 



are still related by the identity (34), whereby 



dJ\d_f^_dPndfr^ 

 dUr dUk dUk dUr 



n— 1 



dPi dfi 



i=l \dUrdUk 



dPidf 



dUk dUr 



