[339 
ON SKEW SURFACES, OTHERWISE SCROLLS. 
197 
339] 
he form 
so that we have 
w) as weight 
yz + 8w) b □ is 
6, = (Weight 
z, w) of the 
it is easy to 
or, as regards the first two lilies, 
We then find 
2a = 2(q — 3)—%(q — 3)(q — 2) + 2(p — 3) — %(p—3)(p — 2), 
= (i>-2)(?-3) + i(?-3)(2-2)+(2-2)(^-3) + |(^-3)Q?-2), 
2a 2 = 4>(q-3)-4.%(q-3)(q-2) + £(q-3)(q-2)(2q-5) 
+ 4(p-3)-4.±(p-3)(p-2) + ±(p-3)(p-2) (2\p - 5), 
2a* = 8(2-3) —12.i(<?-3)(<? - 2) + 6 . % (q-3) (q - 2) (2q - 5) - ± (q - 3)>(q - 2)> 
+ 8(p-3)-12.^(p-3)(p-2) + 6.i(p-S)(p-2)(2p-5)-l(p-3) 2 (p - 2) 2 , 
2aa' = 2(p — 2)(q — 3) — {p—4t).^{q — 3) (q — 2) — ^ (q — 3) (q — 2) (2q — 5) 
+ 2(q-2)(p-3)-(q - 4) . | (p - 3) (p - 2) - ±(p - 3) (p - 2) (2p - 5), 
2a 2 a' = 4{p-2){q-3)-4{p-3).^(q-3\q-2)+{p-Q).^{q-3){q-2){2q-h) + l(q-3f(q-2)\ 
+ 4(q-2)(p-3)-4(q-3)±(p-3)(p-2)+(q-6)±(p-3)(p-2)(2p-o)+l(p-3)Xp-2)\ 
ZA = i (p + q - 5 ) (p + 9. - 4 )> 
the terms by 
O, y, z, w), 
and weight 
2^. 2 = — 2AA' = i (p 4- q - 5) (p + q - 4) (2p + 2q - 9), 
2.4 3 = — tA 2 A' = i (p + q — 5) 2 (p + q — 4) 2 > 
which, putting therein p + q = a, pq = /3, and from the reduced expressions obtaining the 
values of 2a/3, &c., give 
2a = /3 — | a 2 + | a —18, 
2a 2 = /3 (— a + 9) + £ a 3 — § a 2 + i|i a — 58, 
“ A “ 6 + U a 5 - ^1r a4 + -fi 1 « 3 ~ m 2 - “ 2 + 1071a - 1560,