194 
ON SKEW SURFACES, OTHERWISE SCROLLS. 
[339 
The plexus in question is the square +1 system, 
A U, A *17, . . 
AU,.. 
= 0, 
A7, A 2 F, . . 
AF,.. 
p + q — 3 columns, (q — 2) + (p — 2) = (p + q — 4) lines ; or representing the terms accord 
ing to their order and weight, that is, degree in (x, y, z, w) and (x\ y\ z\ w') 
respectively (the order and weight of the evanescent terms being fixed so as that 
they may form a regular series with the other terms), the system is 
P + q - 3 columns. 
. 
XJ1 
0) 
(p-l)„ (p — 2). 2 , ... 
£ 
1 
. ’'¡S 
O 
1 
1—i 
1 
f (q - i)i> (? - 2) 3 , 
?o , (q - IX, 
1 
a. 
so that 
a,@,..=p- 1, p, ... p + q-4s, q-1, q, ... p + q-% 
a',/3',..= 1, 0,.. -q + 4>, 1,0,.. -p + 4, 
A , B,.. = -1,-2, ..-(p + q-4>), 
A', B', .. = 1, 2, p + q- 4 , 
or, as regards the first two lines, 
a, /3, 
a', /S', 
. =p -2 + 6, q — 2 + cf>] 
2-6, 2-<f>) 
6=1 to q — 2, and <£ = 1 to p — 2. 
We then find 
2c = (j-2)(p-2) + i(}-2)(g-l) + 0>-2)(}-2) + i(j>-2)(j>-l), 
2 a' = 2(3 — 2) — i(i~ 2)<g — l) + 2(p-2)-i0> — 2)(p — 1), 
1A = -SA' = -$(p + q-4:)(p + q-3), 
2aa' = 2( i >-2)(3-2)-( i ,-4).i(3-2)(3-l)-i(3-2)(3-l)(2 i -3) 
+ 2(3-2) (p-2)-( i -4).i(y-2)0,-l)-*( i >-2)( i ,-l)(2p-3), 
SAA’ = -%(p + q-i)(p + q- 3)(2p + 2q- 7),