75 



where u and v are co-ordinates of points on the pseudo-sphere and u' and 

 \' co-ordinates of points on S. The equations of transformation from S to 

 tlie plane are 



v = x 

 — u 



"d 

 c e =y 



The real part of the surface being 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 the helix surface may be conveniently expressed in 

 surface co-ordinates, thus : 



x=;rcosu = fi (ru) 



y = r sin u = fa (ru) 

 z = — r=f3(ru) 

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



