( 543 ) 



five cells Cg, CiB, C'ie, C'\e, C^^ by giving the coordinates of the 

 points £, K, F, R belonging to these concentric cells with respect 

 to two systems of axes of coordinates with the common centre of 

 the cells as origin, the systems {OXi) of the four axes ORg and the 

 system (OYi) of the four axes OE\g (fig. 2) between which the relations 



hi = -^'l + •'^'s + -^'3 + '^4 



2y» = '^'l — ^^', — -^'b + '^'4 



hi = — '^'l + '^'ï — ^i + '^'4 



2y, = — .V, — .r, -f .^3 + .V, 



exist, ^"i 



Fig. 2. 



1) We selected this transformation T, because it causes the octuples of vertices of C^g 

 and C'ls to pass into each other and those of C'V, into itself. It satisfies the condition 

 T* = — l, so that first T^ gives unity. We find that T^ is a rectangular double- 

 rotation round by which (Xy^x^) passes into (— a;^, iCi) and (Xj, ^Cg) into (— a^, a;<j). 



