NEWSON: REAL COLLINEATIONS. 47 



exp. i 6, and that r and s are both real. The cross-ratios along the six 

 edges of the tetrahedron (ABCD) are written thus: 



AB : k = exp. i 6, 



BC : k-^=exp. ri 6, 



CD : k^-^^ = exp. rsi 0, 



DB : k'-''*=exp.(r— rs)i ^, 



AC : ki-' = exp.(l— r)i^, 



AD : ki-^+'-^^exp. (1— r + rs)i 6. 



It is now evident that every transformation in eeGs (ABCD) is to 

 be found in some one of its one-parameter subgroups. The grouj) 

 eeGs (ABCD) contains two real subgroups of type VIII, both elliptic, 

 and one of type X, which is common to the two of type VIII. 



4-K.U.Qr. A-x2 



