The Eev. J. H. Jellett on the Properties of Inextmsible Surfaces. 345 



passage of a molecule, or pliysical point, from one geometrical point of space 

 to another. Then, since the curve of which ds is an element, is by the assumed 

 definition inextensible, we must have 



Ids^O; 

 or, putting for ds its value, 



V{dx- + dif + dz') ; 



and performing the operations indicated by c, 



dxdcx + di/diy + dzdcz = ; (A) 



recollecting that c is a commutative symbol. But since the displacements 

 £.r, By, iz, refer to a point on the surface, we must have 



,„ dcx , dcx , 

 dcx = — — dx -\ — ;- ay, 

 dx dy 



,, dcz , dcz , 

 dcz = -Y~ dx + ^- dj/; 

 dx dy 



X, y, being the independent variables. 



Let dz — pdx + qdy, 



be the equation of the surface. 



Substituting for dcx, dly, dlz, dz, in equation (A), we have 



^dix dlz\ , , fd?y dZx dlz dcz\ , , , fdcy dcz\ 



jij-'Pii:^)'''-\ii+ii^+^d^'-P7iyr'''\di-''^)'' '■ 



But since the condition expressed in this equation is supposed to hold for 

 every curve traced upon the surface, it must be true for all values of 



dy 



dx' 

 We have, therefore, 



dcx dcz _ 



dx ^ dx ' 

 dh/ dcx dlz dcz . .■n\ 



dly dcz „ 

 dy ^ dy 



