210 THE ROYAL SOCIETY OF CANADA 



The alternative possibility is: |-X — =0. 



dx dy 



This is Lagrange's linear equation; its solution is: 



(12) y^\x+f{\). 



From (12) and the first of (9) we derive: 



This equation shows that the curves cut from an integral surface of (B) 

 by the planes (12) are asymptotic lines on the surface. The surface 

 must therefore be ruled. 



