138 



Note. These, together with the simplified Gauss and Godazzi equations, should 

 grive by integration the required surfaces. In the attempt to perform the integration, the 

 following geometric solution was reached. I hope to complete the solution by integration 

 later. 



The c-curvL's make principal sections. 



The equation of principal normal to the surface is 

 5 — X //— y : — z 



d^x d2y d2z 



ds^ ds- ds^ 



dx dx 



— := - along v-curve 



ds dSv 



dx _ 



= — , since dSv := |/E du = du 

 du 



const. 



X y z 



which is the normal to the surface at (x, y, z). 



