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Consider two fixed points A, B where AB = 2c. The locus of a point P which moves so that AP-BP = b2, a positive constant, is a curve called an oval of Cassini. When i> » c, the curve is a closed convex oval. As b decreases the curve ceases to be convex, developing a "waist", and finally, when b = c, becomes a figure of 8 known as Bernoulli's Lemniscate. If b < c the locus splits into two closed curves, one within each loop of the lemniscate, and finally degenerates into the two points A and B when 6 = 0. We shall be concerned here only with the case b > c. Taking A and B to be the points z = —c and z = c, z = x + iy, these curves are given by £ = a, where a is a constant parameter, in the net

Potential flow when a uniform stream of inviscid liquid is disturbed by an oval of Cassini