MORENO. — ON RULED LOCI IN W-FOLD SPACE. 



135 



^^ ^ (m-l) (m-2) 

 e, (m — 1) rf, ,r Cj . . . . = 0. 



e, (m - 1) 



., ,, (m - 1) {m - 2) 

 /, (m - 1) e, ^ ^, 



y; (m — 1) e, 



where there are 2 (m — 2) rows and 2 m — 2 columns 

 For < = we have the particular (n — 2)-flat 



The next consecutive generator has for its equations, 



e + S« . rf=: 

 /+ 8^. e = 



The intersection of the two consecutive generators is the (n — 3)-flat 



whose equations are 



e = 0, f= 0, d=^. 



This i''„_3 does not generally lie on the total triple spread for one of the 

 equations of that system, namely 



(m — 1) (m — 2) c 



(m — 1) c?, 



(m - 1) (m - 2) (/, 

 (/w — 1) e, 



= 0. 



is not generally satisfied when the equations of the F^_^ are satisfied. 



The points that satisfy both these systems of equations are evidently 

 points on two consecutive generators and at the same time points on 

 three generators. 



