374 The Eev. J. H. Jellett on the Properties of Inextensible Surfaces. 



forces which are supposed to be applied to the membrane are incapable of ex- 

 tending it. And in such a case all the foregoing theorems will hold, if we sub- 

 stitute for " all possible displacements," " all displacements which can be 

 eifected by any amount of force which is supposed to be present." 



Some interesting practical conclusions follow from this discussion. Thus, 

 if we desire to take advantage of the very slight extensibility of many species 

 of laminffi, to enable them to resist flexure, it appears, from p. 359, that we 

 must be careful to form the lamina originally, while in a soft, semi-fluid, or 

 otherwise extensible state, into a surface whose curvatures are similar, other- 

 wise it will always be liable to bend along a curve of flexure. If sulficient 

 force be used to make the lamina bend along any other curve or in any 

 way violate the conditions which have been established, it will be found 

 that there is always produced a crease, in other words a curve, along which 

 the separation between one molecule and the next is not indefinitely small. 

 In such a case there will in general be a permanent alteration in the sub- 

 stance of the lamina. Thus, for example, it is easy to fold a sheet of paper 

 into the form of a cone, without breaking or in any way injuring it. Let the 

 base of this cone be rendered rigid by being attached to a ring, and it will be 

 found that any further attempt to bend the paper will produce a crease, or 

 curve of permanent alteration in its substance. 



Again, from the discussion of p. 361, we may deduce the practical conclu- 

 sion, that the strength by which a surface of dissimilar curvatures resists flexure 

 may be greatly increased, if it be traversed by a rigid rod attached to its sub- 

 stance, along any curve not a curve of flexure. 



