348 The Rev. J. H. Jellett on the Properties of Inextensihle Surfaces. 

 in the equations (C) we shall find without difficulty the solution : 



Ix = cy — az + e\ 



ly = hz — ex -V e". 

 Hence we infer that — 



If the movement of an inextensihle surface., parallel to any one line., he that of 

 a rigid body, the entire movement is that of a rigid body. 



4. Variations of the Differential Coefficients. — If we denote by h' the variation, 

 properly so called, i. e., the change which the function receives in consequence 

 of a change of form, it is evident that 



iz =pl.x + qly + iz', 



^ dx dy dx dx dy "^ dx 



_dlz _ dBx__ % (^) 



~ dx " dx " dx ^ 



Eliminating 



_diz dlx dly 



'^~ dy ~'^ dy ~ '^ dy ' 



dix dly 

 1^' d^' 



from these equations, by means of the first and third of equations (B), we have 



., „ „, dlz [dcy dcz 



'^p = (^^^f-^i')-rx-i[-d'^^Tx 



/, •> ■>\dhz fdlx , dlz 



In the same way we find, 



_ dip dlx dly 

 ~ dx dx dx ' 



dlj) dlx dly dlq dlx ^ dly 



ls = ~ — T —, s -r^=-r^-s-T ^-j-) 



dy dy dy dx dx dx 



_ dlq dlx dly 



~ dy dy dy ' 



