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



135 



(m-l) (m-2) 

 e, (m — 1) d, c, 



e, (in — 1) of, 



Q - 1) Qi» - 2) 

 /, (m — l)e, g- -f/, 



= 0. 



/, O - 1) «f • 



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

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



e = 0,f=0. 



The next consecutive generator has for its equations, 



e + 8t . d= 

 f+8t.e=0 



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



whose equations are 



e = 0, /= 0, d= 0. 



This F n ^ 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) d, 



(m — 1) (m - 2) d, 

 (m — 1) e, 



f, 



= 0. 



is not generally satisfied when the equations of the i^,_3 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. 



