929] 
231 
929. 
NOTE ON THE SKEW SURFACES APPLICABLE UPON A GIVEN 
SKEW SURFACE. 
[From the Proceedings of the London Mathematical Society, vol. xxm. (1892), 
pp. 217—225.] 
The question was considered by Bonnet, in § 7 of his “ Mémoire sur la théorie 
générale des surfaces,” Jour. École Polyt., Cah. 32 (1848); I resume it here, making 
a greater use of the line of striction. 
We may construct a skew surface, inextensible but flexible about its generating 
lines, as follows : Imagine a flexible extensible plane, and in it the rigid parallel 
lines L, L 1} L 2 , L 3 , &c., connected each with the following one by the rigid lines 
V J 
h J 
J 2 * 
- 
4k 
P 2 
Pi 
Q 2 
p 
Q i 
» 
PQi, PiQi, P- 2 Q 3 , &c., where PQ 1 cuts L, L u PiQ 2 cuts L lt L 2 , &c., at right angles; 
the angles LPP 1} L 1 P 1 P 2 , L 2 P 2 P 3 , &c., are taken to be a>, to lt co 2 , &c., respectively. 
Keeping the line L fixed, we may twist the whole plane L X L 3 L 3 ... round PQ l , so 
that the line L x becomes inclined at a small angle to L, these lines now having 
PQi for their shortest distance, and the lines L 2 , L 3 , &c., remaining parallel to L x 
in As new position; the foregoing twisting implies an extension (increasing with the