APPLICATIONS OF ELLIPTIC FUNCTIONS TO PROBLEMS OF CLOSURE 133 



The loxodromics of a torus which turn once about the axis and 

 07i,ce about the axial circle are the circles cut out hy the double- 

 tangent plaries of the torus. 



Pig. 14 



The numbers of the orthogonal loxodromic are v/=3, iii==\. and 

 its projection is a curve of the 6th order, as is shown in Fig. 14. 

 I71 general if m=l, then the projected loxodroinic is of the 2nth 

 order ^ and the loxodromic itself of the 4nth order. 



A proof of this theorem will appear in the December number of 

 the American Mathematical Monthly. 



September, 1902. 



