( 547 ) 



The equations (!) and (II) give back for 11=0 the problem of 

 the minimal surfaces. 



rr 



For ; we shall introduce for brevity the symbol Q. 



§ 2. To satisfy beforehand (II) we put 



d.v . dy dz dcv ,dy dz] 



dx ,dy 1 dz dx ,dy ldz\ 



d§ d§ u d§ dï^ dr, v dr] 



(III) 



where u and v are functions to be determined of ^ and r]. 



When we substitute the equations (III) into (I) we find the equations 



d^ dx dy dy 



which u and v must satisfy, whilst moreover t^; » ^ ? t^ and ^, 



-^ d^ dri dS, dt] 



derived from (III) must obey the conditions of integrability. 



The latter furnish 



{IV) 



dx dx dy dy , 



If we now also substitute the values of ^r^ , t" ' ^^ ^^^ ^ ^^^^ the 

 . • o§ Oi] 05 Ori 



H 

 equations (I) whilst we put Q = ; we find : 



/du I du\dz / ]\d'z _Q/ ^ I 1 \dz dz 



\di] u' dy\) d% \ 21 Jd^di] i \ u v yö§ * dt] 



1 rdu 1 du\ dz 1 / l\d'z/ 1 1 \dz dz 



A ^A-h:- + -^r + -W = ^^ ^^ + - A-C-A-' 



d>j u^ di]J 0^ i\ u Joi,oi] \ V ujdi, dt] 



d'z Q/ u v\dz dz 

 d%dri 2i\ V u J d^' dti 



