75 



wliere u and v are co-ordiuates of points on the pseudo-sphere and u' and 

 v^ co-ordinates of points on S. The equations of transformation from S to 

 the plane are 



v = x 

 — u 



"d 



c e =y 



The real part of the surface heing represented on the strip included 

 between y = c and y^c, e. 



Comparison of Gauss' and Cayley's Proofs of the Existence 



Theorem. 



O. E. Glenn. 

 [By title. ] 



Motion of a Bicycle on a Helix Track. 

 O. E. Glenn. 



The equation of tlie helix surface may be conveniently expressed in 

 surface co-ordinates, thus: 



X = r cos u = fi (ru) 



y = r sin u = f-i (ru) 

 z^-- — f3(ru) 

 in which r represents the distance of a point from the z axis, and u the 



