( 551 ) 



Total curvature = 



EG- F' 4 F* 



1 ö / 2 èF\ 1 ()Hlf\ 



{TX) 



2iFd7i yiF d^J F d^dr] 



(We notice moreover that, as is directly to be seen, 



2 _ 1 1 

 F r, r^ ' 



where i\ and }\ are the principal radii of curvature). 



Let us novk^ deduce from {VI) the value of F, we then find 



2 ^u öu 



F z= 



or : 



8 dw Ö?; 



F — 



H\v~uy ' örj ' dg ' 



We substitute this value of F into {IX) by means of the following 

 calculations. Out of {VII) follows 



1 ai^_ö^ 2 ÖM 



This must be equal to 



4 F {v — uy ÖTi d^ ^ dic dv 



and so we find : 



drj'd^ 



H' 'A i^) 'A (V) ' {v-^^)' ^ddri^ dg . drj 

 du dv de, du v — u' 



dri d§ dri 



The second member can be once more reduced by means of (VII), 

 and we find : 



H'fA^)fAn)iv-^^)' ^ 2 d_v d_u 



du dv (v — m)* dtj' d^' 



dri'd^ 



38 

 Proceedings Royal Acad. Amsterdam. Vol. X. 



