344] 
ON CERTAIN DEVELOPABLE SURFACES. 
281 
30. This divides, as it should do, by 
a 3 e 3 
J- 1 
a 2 bde 2 
- 12 
a 2 d 4 
- 27 
ab 2 d 2 e 
- 6 
b 4 e 2 
- 27 
b 3 d 3 
- 64 
-135 
and the other factor, which is the Prohessian, is 
al'e;' 
+ 
1 
a 4 bde 4 
+ 
16 
a 4 d 4 e 2 
— 
108 
a 3 b 2 d 2 e 3 
— 
524 
a 3 bd B e 
_ 
432 
a 2 b 4 e 4 
— 
108 
a 2 b 3 d 3 e 2 
+ 
656 
a 2 b 2 d e 
+ 
1512 
alfdd' 
— 
432 
ab 4 d 4 e 
+ 
272 
b e <Pe 2 
+ 
1512 
b 5 æ 
4- 
1280 
+ 3645. 
31. To simplify this, I first collect the six terms 
— 108 are- (a 2 d 4 +b 4 e 2 ) 
— 432 abde (a 2 d 4 + b 4 e 2 ) 
+ 1512 b 2 d 2 (a 2 d 4 + b 4 e 2 ), 
and then putting a 2 d 4 + b 4 e 2 = (ad 2 + b 2 e) 2 — 2ab 2 d 2 e, we have the terms 
+ 216 a 3 b 2 d 2 e 3 
+ 864 a 2 b 3 d 3 e 2 
— 3024 ab 4 d 4 e, 
which combined with the remaining terms give 
+ 1 a 5 e 5 
+ 16 a 4 bde 4 
— 308 a 3 b 2 d 2 e s 
+ 1520 a 2 b 3 d 3 e 2 
— 2752 ab 4 d 4 e 
+ 1280 b 5 d 5 ; 
C. V. 
36