198 
ON SKEW SURFACES, OTHERWISE SCROLLS. 
[339 
2a' = ß + ^a 2 — ^a + 18, 
2aa' = ß (- |a) - i a 3 + f a 2 — ip a + 58, 
2aV = ß* (- f) + ß (- fa 2 + 9a - if»-) + £ a 4 - § a 3 + if»- a 2 - 119a +198, 
2^. 2 = - 2AA' = i a 3 - | a 2 + ifi a - 30, 
2,A 3 = - 2A 2 A' = l a 4 - f a 3 + i|i a2 _ go« + 100, 
2AB 
2ABC= 
we then find 
ZA + 2a = ß — 8, 
2-4' + 2a = ß — 3a -f- 8, 
2AB -Zaß = /3 2 (— |) + /3 (fa 2 — 5a + p) — 4a 2 + 36a — 1.26, 
2 A A' - 2aa' =ß (-fa) + 9a-28, 
2J.5C+2a/37 = /3 2 (i)+/3 3 (- i a 2 + J^a-^) + /3(fa 4 -fa 3 + ^a 2 -ipa + pp) 
- a 4 + ^ a 3 - 162a 2 + a - 1210, 
2A 2 A' + 2a 2 a' = ß 2 (-£) + £(-§ a 2 + 9a - ifL) - 29a + 98; 
and then also 
2a(2J.+2a) = /3 2 +/3(— |a 2 +1 a— 26)+ 4a 2 —36a+144, 
(2^45—2a/3)+2a(2^4 +2a) =/3 2 (f) +/3( -fa- f ) + 18, 
{(2^5-2a/3)+2a(2A+2a)}(24'+2a')= 
+ 18, 
- (2^ + 2a)(2^U'-2aa / ) 
/3 3 (J) + /3 2 (-2a+i)+/3( fa 2 +4fa- 10) -54a+144, 
= /3 2 ( |a )+£( — 13a+ 28) + 72a-224, 
and 
2A*A' + 2a-a! = (ut supra) /3 2 ( —f) + /3(—§a 2 + 9a—ip) —29a+ 98; 
whence, adding the last three expressions, we find 
Weight = /3 3 (f ) + /3 2 (-fa+f)+£ (f a 2 + f a - p) - 11 a + 18; 
and for the order we have 
(2a) 2 - 2a/3 = /3 2 (|) + ß (— 1 a 2 + 4a — ff) + i a 4 - ff a 3 + if & a 2 - a +133 ;