250 



of whicli lies in a square two sides of wliicli converge in the angle in ques- 

 tion, or one of the two terms lies in a square bounded above and to the 

 right by one of the lines converging at the angle, the other in a square 



Fig. 2. 



bounded above and to the left by the other line making the angle. Thus 

 below one of the points marked 5 is found the term x''y2. This term joined 

 with any or all others lying between the lines converging at that particu- 

 lar 5, will yield a scroll of the otii order. 



So also we will have a scroll of the 5th order if we select x^y^ on one 

 side and x^ on the other side of the space bounded by the lines converging 

 at the same point 5. 



At the middle point of the whole of Fig. 2 is a vertex marked 4. The 

 following groups can be arranged for the equation of the curvilinear 

 directrix, but in every case the resulting scroll will be of the ith order. 



1. x*y2 and c present, xy present or absent, 



2. x^y- and c present, and other terms present besides xy, 



