160 



Tlie mnltmoniial Theorem has been generally expanded in 

 the following form, viz. 



w 2 *" S 



r" r" 



1.2 1.2.3 



+>^ R« +g.("— l) .y^ "QR3+&C. 

 1x1 



+;'x7 Sz +&C. 



+ &C- 



Now, in this expression, the first quantity that is expanded 

 is :v4-Qzl?, and then " X 5TQz^"~ x (Rz + Sz+&c.), and af- 

 terwards J^^£—0- ;^7q^?-^x (Rz+SzV&c.f' and so on. 



1 . 2 

 But the arrangement which would follow from the Demonstra- 

 tion which I have given, would be the following, viz. 



2 3 Ttl 



(.r + Q2 + Rz + Sz-l-&c.)^ = 

 + ^.(«_l)x-F "(Qz + Rsj + Sz + iScc.) 



i. 2 



+ ^.(?— 1).(^— 2>7- ^(Q2+R2 + Sz+ &c.)' 

 1. 2. 3 



1. 2. 3. 4 -r -r / ^ 



+ &c. . According 



