[ '59 ] 



Hence collecting the co-efficients it readily appears by con- 

 fidering the general value of the fum of u producls ftated above, 



2 n — 2 m 



that the coefficient of the term x the fame as the coeff. o£ 



-^ J. 2 3 - - ' m J 



or reducing thefe fradions to a common denominator the nume« 

 rator becomes « X into the expreffion in the Lemma vphich there- 

 fore = o hence 



an n 



PO^XPO'^X&C. =x— 2X+ I or POxPO'x &c. = *ot i. 

 Q; E. D. 



2. Because POxPSxPO' x PS'x&c. = « co i and POx 

 P0'x&c. = ^w3 I .-.PSxps'x&c. = x+ I. Q-E. D. 



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