694 MOORE. 



and therefore the path curves all lie in a variety Vp of order 2^. The 

 parameters equations of this variety are 



.Ti = OiCOS Wi, .T2 = oisin Vi, 



a»3 = c/ocos 112, ^'i = 02sin U2, 



.T2p-1 = OpCOS lip, X2p = ttpSm tip. 



The element of arc then is 



ds^ = a^diii + a-^dii^ +. . . Mpdu^ 



which shows that Vp can be developed on a plane space of p dimen- 

 sions. A linear relation among the ?7i's gives a variety of jj-l dimen- 

 sions immersed in Vp and it is easily shown that this is also developable. 

 The path curves are geodesies on both varieties. 



For each point of Vp there is a curvature p-point and these js-points 



all cut -p fixed circles, one lying in each of the invariant planes Mi. 



