1904.] 



BROOKS — ORTHIC CURVES. 



299 



if 



If the two pencils are given, it is only necessary to pair off lines 

 and curves according to the relation 



and to mark intersections. These will be points of the curve. 



A very simple instrument for drawing the equilateral hyperbolas 

 required in the construction is made in the following way : Two 

 toothed wheels of equal diameters are attached beneath the drawing 



Figure 



A unipartite orthic cubic which has three real inflections, one of 

 which is at infinity. 



board in such a way that their teeth engage. The axles are perpen- 

 dicular to the board and come through it at /5 and y. The axles, 

 which turn with the wheels, carry long hands or pointers which 

 sweep over the board. On account of the cogs, the wheels can turn 

 only through equal and opposite angles. As a consequence, .r, the 



