406 MOORE AND PHILLIPS. 



If the consequents of <l> are complementary to the antecedents of 

 an idemfactor /, 



^I = <!>. 



For, if 



$= A,Br-\- A2B2 -{-.... -{-AnBn 



by the definition of an idemfactor 



BJ = Bi, 

 and so 



$7 = AiBJ + A2B2I + ....+ AnBnl 



= AlBi + A2B2 + . . . .AnBn = $. 



Similarly if the consequents of / are complementary to the antecedents 

 of <!>, 



7$ = $. 



If there exists a dyadic ^ such that 



'l>^ = 7 

 or 



^$ = 7 



$ and ^ are said to be inverse dyadics. In many cases these two 

 relations of ^ and $ will be equivalent, but there are some cases in 

 which they are not. 



10. Symbolic Notation. If we write a dyadic as 

 (A)* AiBi + A2B2 + ....+ y4„5„ = 2.4 ,5 i, 



the products of the dyadic with an extensive quantity X are 



(B) Ai[BiZ] + A-ABoX] +....+ An[BnX] = i:Ai[BiX], 



(C) [XA,]B, + [XA2]B2 + ....+ [X^n]5„ = 7:[XAi]Bi. 



Similarly if 



(D) CDy + C2P2 + . . . . + CnDn = ^C^A' 



is a second dyadic, the products of the two dyadics are 



(E) i:ikAi[BiCu\Dk, ^ikCi[DiAu]Bk. 



