( 252 ) 
(43). | (24) | (play NEA (19, 34) 
(49) (BIj ANB) (12, 34) 
(8-4) | (18) (18, 24) (23) | (41) 
(Q—1), | (4—3) (13, 24) | (l—4) | (3—2) 
as 28) 43) |A) |B) | @-4) 
(14, 23) | (2—1) | (3—4) | (49) (8) 
This table shows that so far there is regularity in the irregularity, 
that each conjugate quintuple as to this irregularity corresponds 
with the quintuple of the lines a; 
Before we pass to an entirely regular form of the equations of 
the fifteen lines, we determine, also to show the fitness of the 
system of equations, the locus of the planes cutting the four lines 
a given originally. For this we search for the conditions, under 
which the space 
Po =P) A + Po A2 + ps %3 + Pa Ta + Ps 7 = O 
contains such a plane. The number of planes cutting four lines 
given arbitrarily in S, being twofold infinite, this investigation must 
lead us to a homogeneous equation f(p)=0 in the five spacial 
coordinates pi, the tangential equation of the curved space enveloped 
by the spaces p, — 0. 
The coordinates of the points of intersection of the space px = 0 
with the four lines a), a, as, a, are the elements of the four rows 
of the matrix 
P3 — Ps: 0 soa for) 0 ad 7 
Oe: Pa — Ps» OF thee Pe) Pa + Pal 
0 a PaP) Pa — Pos aes eee | 
(pa t+ 25), eae es Dit Pee Pit Pk 
