346 



MEMOIRS OF THE AMERICAN ACADEMY. 



Since 



a 



b 



a,b -fe- etc. , 



a,b -j? e tc. , 



we have 



la 



Ih 



^(a,b -fc etc.) = /(a,b) -^ J(etc.) , 

 /(a,b -(7 etc.) = /(a,b) -^ £(etc.) . 



Multiplying these two equations commutatively we have 



(/a),(/b) = /(a,b)-( r etc. 



or 



(104.) 



OT 



nv. 



Now 



(h) 



w 



Hence, 

 (105.) 



ls w 



(fc)W' -fr W" + W" +■ etc 

 frW + W" 4r r + etc. 



IT (fr ) 



w 



117* W, 



m'sw 



fr w 



W w , 



or every lover of a servant of all women stands to every woman in the 

 lover of a servant of hers. 



to 



From (102) we have 



(106.) 



By (95) and (96) we have 



of 



/ S W 



fr w 



/*W 



*(W -J- W" -k- W" etc.) = *W -J- *W" -t *W" + etc 



pw -|_>w -fcT'W'" 4. etc. 



Now 



s w 



5 W 4 W" -|r W" + etc. 



«w,,W"^w'" etc. 



So that by (94) 

 Hence by (92) 



s w 



*W* 



sW. 



?w- 



£ w , 



?w 



// 



£ w , 



£ W 



// 



l* w . 



Adding, 



(sW _j_. IsW" _|_ | s f" 



£ w ; 



or 



(107.) 



I s w 



^• w . 



That is, every lover of every servant of any particular 

 servant of all women. 

 By (102) we have 



woman is a lover of every 



(108.) 



Thus we have 



Isvr 



l*vr . 



Aw 



^W 



/* w 



ls w 



(Is) 



W 



Isw 







