1. When we proceed to obtain the equation of the join of points on the ellipse x2/a2 + y2/b2 = 1 whose eccentric angles are θ and ϕ, we find that cos ½ (θ − ϕ) is a factor of each term, and similarly a common factor is found to exist for any other case of parameters. We may therefore suspect the existence of a common factor when we find the equation of the secant in the general case. It is proposed to find this common factor and to apply the simplified equation to the solution of a well-known problem.