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



du' , . 



ay ax 



^^ - u-'t = 0. 

 ay 



Hence it is plain, that the displacements of a siirf;icc which is but slightly 

 extensible will differ from those of an inextensible surface, by quantities which 

 are of the same order of magnitude as tlie extensibility of the surface. From this 

 it is easy to infer, that all the theorems which are rigorously true for an inex- 

 tensible surface are approximately true for a surface possessed of an indefinitely 

 small amount of extensibility. 



Let us now consider the coefficients of the quantities 



dx dn dy dn dn- 

 d?dJ" dl'd^" d7- 



These coefficients give the equations 



dlx' dlz' dhx' , dly' dlz' . , 



an •* an dx dx dx 



diy' dhz' dlx' dly' dlz' .„ ,^„, 



dlx dly' dlz' _ 



dn dn dn 



A,B, C being of the same order as Ix', ly', Iz'. Since a, |3, 7 are independent 

 of 72, the tliird of these equations may be integrated at once. Performing the 

 integration, and supposing the integrals to begin when 



x' = X, y' = y, z' = z, 

 we have 



acx' + foy' + ^cz' = alx + /3?_y + jlz + i [" Cdn. (0') 



Now it is evident that 



alx' + ply' + 7?.^' = c«, 

 alx + ^ly + '^Iz = {ln)o, 



