196 ON SKEW SURFACES, OTHERWISE SCROLLS. [339 
of an arbitrary plane, and then eliminating (x', y', z r , to'), the result is of the form 
(ax + ¡3y + ryz + Bw) 6 □ = 0, 
where □ is a function of (x, y, z, w) only; and considering (x, y, z, w) as weight 
variables, 6 = Order of Plexus. But degree in (x, y, z, w) of (ax + ¡3y + 7z + Bio) e □ is 
= Weight of Plexus, and therefore Degree of □ is = Weight of Plexus — 9, = (Weight 
— Order) of Plexus. 
o 
The equations U=0, F= 0, □ = 0 then give the coordinates (x, y, z, w) of the 
points through which may be drawn a line G (m 4 ); viz. they give (as it is easy to 
see) these points four times over. And we therefore have 
G (m 4 ) = \ Order of (U = 0, F= 0, □ = 0) A 
= J Deg. U. Deg. F Deg. □ 3 
= 4 /3 x (Weight — Order) of Plexus. x 
The Plexus is here the square + 2 system “ 
A U, 
A*U, ... 
• 
A U, 
AF, 
A 2 F, 
• 
A F, 
(p + q — 4 columns, (q — 3) + (p — 3) = p + q — 6 lines). Or representing the terms by 
their order and weight (the weight variables being in the present case (x, y, z, w), 
and the order variables (x', y', z, tv')), and attributing as before an order and weight 
to the evanescent terms, the system is 
p + q- 3 columns. 
co 
I 
a* 
03 
I 
( 
■j 
I5—15 
0, , 
2 9 - 2 , 
I9-1» 
2 
5 
2 
2 
2 
2 
\v 
Vi 
2 
2 
2 
2 
2