The Rev. J. H. Jellett on the Properties of Inextensible Surfaces. 377 



If we now follow the same reasoning as in p. 352 we shall readily see that aU the diffe- 

 rential coeiEcients of w will vanish at the equator, and therefore that we must have 



generally 



w -0. 



Hence, and from p. 347, it is evident that the displacements represented by Ax, Ay, A^, 



are those of a rigid body. Since then ^x, S'y, ^z are by hypothesis the displacements of a 

 rigid body, it is evident that the differences between these quantities, ^x - Sx, Ay - 8y, 

 A« - ^z, or S«, 8y, Sz, are so likewise. We infer, therefore, that — 



The most general displacement which a closed, oval, inextensible surface admits of, is thai of 

 a rigid body. 



Such a surface is therefore inflexible. 



