536 



Oil (lie curve (5) we have cos =z 0. With the -exception of 

 quantities of the order /' the tangent space (7) behaves along the 

 curve (5) as the euclidian s|»ace (8). Hence we need only trace the 

 movement of the geodesicaliy moving system in (8) along the curve 

 corresponding to (5). As the coordinates '/ and 8 have obtained a 

 factor cos 'ji according to (9j, (8) can be realized by ihe part of the 

 euclidian space a' y u that remains, when a rotation-cone having for 

 axis the ?/-axis and a top-angle of 2.t (1 — cos y^) is taken away, 

 (fig. 2). ' 



U 



Fig. 2. 



The part of the circle : 



x' + V' = 



W 



^^* X ....... . (11) 



situated within (his space viz. the part extending in fig. 2 from A 

 via a point in the iiegati\ e part of the y-axis to B, will then corre- 

 spond with the entire cuive (5). 



This result may also be obtained by replacing (he cone (6) by 

 its unfolded mantle, laid down in the y:c plane symmetrically 

 to the y axis, being a sector with an angle 2% cosy. The curve (5) 

 will (hen coincide with (11). During the revolution about the yz 



