245 



A Family of Warped Surfaces. 



O. A. Waldo. 



Derivation of the general equation of all warped surfaces having two 

 distinct rectilinear directrices and its application to a few special cases. 



Fig. 1. 



Let the surface be detined by the three directrices 



X ^ O, z =r p, 



y = O, z = q, 



f (s'y') = O, z = 0. 



The curve f (x'y') = O lies in the plane z = O, the A' and Faxes are 

 parallel to the rectilinear directrices; the Z axis includes the common per- 

 p3ndicular to the rectilinear directrices, unless otherwise specified. 



In the diagram Fig. 1, let X' X'^ be one straight line directrix at the 

 distance q above the plane z ^ o, Y' Y" the other at p above z = o. Their 

 horizontal projections will be the X and Y axes of reference. 



