The Rev. J. H. Jellett on the Properties of Inextensihle Surfaces. 35 1 



dy = mdx, 



be the equation of the projection of the given curve upon the plane of xy. 

 Then since ti, v, w, vanish for a continuous portion of tliis curve, we must have 



du du 



dx dy 



dv dv ^ ,^ , 



dw dio 



ax ay 



But if we make 



w = 



in the first and third of equations (C), we shall have 



Hence and from equations (L) we have 



Differentiating these equations upon the same principle, we have 



d'u d^u _ d'u d'u 



da^ dxdy ~ ' dxdy dy- ~ ' 



d^v d'v _ d-v d'^v _ 



da^ dxdy ' dxdy dy'^ ~ 



(M) 



Hence it is easily seen that the equations (D) and (E), p. 346, become for this 

 curve 



(7- + 2sm + tm') ^ = 0, 



axay ^^^ 



(r + 2sm + tm-) -j—.- = Q. 

 ^ dxdy 



Hitherto the reasoning employed has been perfectly general, embracing 

 surfaces of every class. But in our subsequent investigations we must discuss 



