148 
ON THE MECHANICAL DESCRIPTION OF A CUBIC CURVE. 
[506 
2 Square ACD, and connected with it by a pin at D, rod DG. 
3. Square ECF ; the two squares being connected by a pin at G. 
4. Rod IJ. 
F .T 
The rod OH rotates about a pin at 0; taking HA = HI, there is a pin at A 
connecting a fixed point of this rod with the extremity A of the square ACD: the 
fixed point B of this square moves along the line Ox. There is a pin at I connecting 
the extremities of the rods HI, IJ; and this slides along the leg AG of the square 
ACD, the rod IJ being always at right angles thereto: finally the legs of the square 
ECF are always parallel to Ox, Oy, and the rod DG at right angles to EC. I have 
omitted from the description the parallel-motion rods or other arrangements necessary 
for giving these fixed directions to the rod IJ, the square ECF, and the rod DG. 
It will be seen that the angles A OB, ABO are variable angles connected by an 
equation of the form above referred to; and that the lines IJ, CF determine by their 
intersection the point P; and the lines CE, DG determine by their intersection the 
point Q; the curve about to be considered is that determined by the relative motion 
of P in regard to Q; or say the curve the coordinates of a point of which are 
x = QC, y = CP. 
I write 
ZA0B = 6, zAB0 = cf>, 
OA = a, AB = b, AC = c, CD — d, 
AH = HI = \h.