28 Frederick C. Ferry. 



m' 4- m' -|- m' -f- ra' — 1 -|- m' =; 5 m' — 1 distinct species of 

 curve for m' >2. 



p -|- q here has the values 3m' , 3m' — 1, , 2m' — 3, 



2m' — 2, which are in number m'-|-3; hence any surface S 

 as defined above cuts from 2 curves (p , q) of m' -|- 3 different 

 orders. 



If q = 1 , a plane through the double director will meet 

 the curve in only one point elsewhere; such a curve is uni- 

 cursal, and the surface S as defined cuts from 2 three species 

 of unicursal curves, viz., (2m' , 1), (2m' — 1,1) and (2m' — 2, 1), 

 of orders 2m' -j- 1 , 2m', and 2m' — 1 respectively, if m'>2.. 



The following table contains all cases as far as m' = 5,, 

 class I' ; the species under class II are in most cases 

 repeated under class II' since the conditions put upon S 

 are different there. 



