( 546 ) 



As independent coordinates on the surface we choose those which 



are invariable along the lines with length zero and we represent 



them by § and n- So we tind. 



D' 

 H— — 2~, whilst E—G=0. 



Let us multiply both members of the first equation by A' (cosine 

 of the angle of the normal with the Z-axis) ; we then find : 



FHX — — 2D'X . 



But 



and moreover*) 



FX = 



D'X =r 



dy dz 



MM 



dy dz 



d%di] 



1 



i 



y 2 



where x, y, z represent the Cartesian coordinates of the surface with 

 respect to a rectangular system of axes. 

 So we find 





— — 2 



d\x 



or : 



0'^ H ( y z 



{I) 



{II) 



1) BiANCHi, Vorlesungen über Differential-Geometrie, translation into German by 

 Max Lukat, page 89. 



2) 1. c. page 86. 



