On the The Aberrancy Curve

The origin is an undulation on the curve y=px+qx²/2!+… if q = r = o. The point on the aberrancy curve corresponding to the origin is x = -3qr/P,y = 3q(3q²-Pr)/P, where P=3qs-5r². When q = r=o, Lt.dP/dθ = 3qt-7rs = o and Lt. d²P/dθ² = -7s². The limiting values of x and y at the origin are respectively, given by - 3r. Lt. q/P = -3r. Lt. r/dp/dθ = -3r. Lt. S/d²p/dθ² = 3r/7s = o, and 3(3q²-pr). Lt- q/P = 0, i.e. x = o, y = o on the aberrancy curve. So the origin also lies on the aberrancy curve.