280 
ON CERTAIN DEVELOPABLE SURFACES. 
[344 
HP- LM 
= 4 x 
FG-CH 
= 16 x 
GP-LN 
= 4 x 
Il F - BG 
= 16 X 
cPde' + 2 
cfîbâré* — 15 
a?b 3 e 3 + 54 
a We- 12 
ab 4 de* — 252 
(did 4 - 2 
Fdle - 18 
a?be 4 + 2 
d'ds'é 2 — 36 
aWde 3 + 3 
a?bd 4 e + 9 
ab 3 d?e 2 + 33 
cdrd? +864 
b 4 d 3 e + 16 
a 4 be 3 + 2 
a 4 d 3 e — 36 
a 3 b 2 de 2 — 15 
a s bd 4 +144 
d 2 b :i d 2 e — 12 
a5 5 e 2 + 36 
ab 4 d 3 +322 
5 s de + 18 
a :! c/e 4 + 2 
a?bd 2 e 3 + 3 
a 2 d 5 e — 18 
a& 3 e 4 — 54 
ab' 2 d 3 e 2 — 453 
aôd 6 —576 
&W - 27 
5 :! d 4 e + 16 
- 243 +891 +459 -1107 
where, by way of verification, I have annexed to each column the sum of the coefficients. 
29. Forming from these the seven component terms of the determinant, and 
collecting, the result divides by 5, and we have 
a 8 e 8 
+ 
1 
+ 
5 
olbde 7 
+ 
4 
4- 
16 
16 
— 
44 
+ 
16 
+ 
16 
a 7 d 4 e 5 
— 
135 
- 
432 
+ 
432 
— 
99 
_ 
288 
_ 
288 
a 6 b 2 d 2 e 6 
— 
722 
— 
96 
— 
96 
— 
3226 
■ — 
96 
— 
96 
a 6 bd 5 e 4 
+ 
432 
+ 
3312 
— 
1368 
— 
2592 
+ 
2232 
+ 
576 
aide 2 
+ 
2916 
— 
7776 
— 
972 
+ 
20736 
+ 
2592 
cdb 4 d 
— 
135 
— 
288 
— 
288 
— 
99 
+ 
432 
— 
432 
a 5 b 3 d?e 5 
+ 
6784 
+ 
3876 
— 
7788 
+ 
41744 
— 
7788 
+ 
3876 
a 5 b 2 d 6 e 3 + 
21492 
+ 
4788 
+ 
3960 
+ 
27180 
+ 
8100 
+ 
63432 
a 5 bd 9 e 
+ 
11664 
— 
7776 
— 
27216 
+ 
20736 
+ 
72576 
a 4 b 5 de G 
+ 
432 
! + 
576 
+ 
2232 
— 
2592 
— 
1368 
+ 
3312 
a 4 b 4 d, 4 e 4 
352 
s + 
2524 
+ 
36220 
- 
117200 
+ 
41472 
+ 
36220 
+ 
2524 
a 4 b 3 d 7 e 2 
— 
26352 
_ 
133272 
— 
30024 
— 
61920 
373248 
— 
51984 
— 
227808 
adrd 10 
— 
40824 
! — 
1944 
+ 
124416 
+ 
5184 
— 
331776 
a 3 b 6 d 2 e 5 
+ 
21492 
| + 
63432 
+ 
8100 
+ 
27180 
+ 
3960 
+ 
4788 
d 3 b 4 d 3 ë 3 
+ 
50944 
I + 
6504 
+ 
177576 
— 
154912 
+ 
41472 
+ 
177576 
+ 
6504 
a 3 b 4 d 8 e 
+ 
11232 
— 
65088 
— 
18504 
— 
19008 
+ 
186624 
— 
41544 
+ 
13680 
a 2 b 8 e G 
+ 
2916 
+ 
2592 
— 
972 
+ 
20736 
- 
7776 
cdbW 
- 
26352 
— 
227808 
— 
51984 
— 
61920 
+ 
373248 
— 
30024 
— 
133272 
cdbW 
— 
140624 
— 
668472 
— 
872592 
+ 
689024 
+ 
1689984 
- 
872592 
— 
668472 
a?b 5 d 9 
— 
131328 
+ 
1152 
— 
1152 
+ 
92160 
— 
6912 
_ 
741888 
ab 9 de 5 
+ 
11664 
4“ 
72576 
— 
27216 
+ 
20736 
_ 
7776 
ab 8 d 4 e 3 
+ 
11232 
•f* 
13680 
— 
41544 
— 
19008 
+ 
186624 
— 
18504 
— 
65088 
ab 7 d 7 e 
- 
25088 
— 
20864 
— 
62336 
+ 
40960 
_ 
62336 
— 
20864 
b 10 d 2 e 4 
— 
40824 
— 
331776 
+ 
124416 
+ 
5184 
_ 
1944 
¡Idle 2 
— 
131328 
— 
741888 
— 
6912 
+ 
92160 
— 
1152 
+ 
1152 
b 8 d 8 
- 
81920 
- 
409600 
+ 492075 
_ 
2032452 
866052 
+ 
350649 
4- 
2985984 
866052 
2032452 
where the first column is the Hessian.