Journal & Proceedings of the Asiatic Society of Bengal November 1908

He calls the line OT in its ultimate position the axis of deviation and takes.61118 as the measure of the rate of deviation of the curve from circular fo m or of the second affection of curvature. [...] The conic of four-pointic contact at any point (x y) of a given curve has the first second and third differentials of x and y the same as with the given curve but the fourth and higher differentials arbitrary and in general different from those with the given curve. [...] Equation (66) gives the diameter through the point of contact and as it is independent of A it represents the locus of centres of all conics of four-pointic contact at the given point. [...] The co-ordinates of the point where the normal at the point of contact meets the equilateral hyperbola again are found to be X + 2P dy (77) V— Y 2Pdx But the co-ordinates of the centre of curvature are (11) P dy P dx X=x-- Q x=y+-- Therefore the osculating equilateral hyperbola meets the normal again towards the convex side of the curve at a distance from t Ile point of contact equal to twice [...] To these appointments was added a gift of thirty lakhs of rupees payable from the Bengal treasure remittance to replace the expenditure on his army and the defence of the fort together with a jewelled turban ornament a special dress of honour and an elephant from the emperor.