222 PROCEEDINGS OF THE AMERICAN ACADEMY. 



A pseudo geodesic curvature of a curve can be defined as for the plane 

 and will be found to be, 



du d 2 v dv d 2 u 

 ds ds 2 ds ds 2 



where the curve is defined parametrically on terms of arc length. 

 The pseudo geodesic circle of constant radius will be, 



au -f- bv = 1, 

 And the pseudo geodesic circle of constant curvature will be 



Aw 2 + 2Buv + Cv 2 = 1, 

 and the curvature is, 



T , AC - B 2 



