412 MOORE AND PHILLIPS. 



Any four points not lying in a plane can be taken as antecedents or as 

 consequents. 



As an operator on planes the dyadic gives a correlation which trans- 

 forms each plane ^ into a point 



X = B{C4) = BriC^) + B,{C,^) + B,{a) + B,{C,^). 



If ^ is the plane [C2C3C4], 



■ (5o|) = (B^i) = (B,^) = 0, 

 and 



X = Bi{C\C2CzCi). 



If then the consequents do not lie in a plane, the correlation transforms 

 the planes of the tetrahedron Ci Co C? C4 into the points By, Bo, B3, B^. 

 Since the antecedents and consequents of the one-one dyadic are 

 extensive quantities of the same dimension it can be expressed as the 

 sum of a self-conjugate and an anti-self-conjugate dyadic. 



$ = !(* + $,) + i($ - *c). ■ (34) 



We therefore consider these two types of dyadics first. 



A self-conjugate one-one dyadic can be expressed in the form 



BB = ByBi + 52^2 -f £3^3 + BiBi. (35) 



To show this, express the antecedents and consequents in terms of 

 four points, Ai, A2, A3, Ai, not lying in a plane. The dyadic will then 

 take the form 



i:\ikAiAu, i, k = 1, 2, 3, 4. 



Since the dyadic is self conjugate 



'L'KikA.Ak = ^XikAkAi. 



Hence 



(A) 



(B) 



(C) 

 (D) 



