¹ “Short-term Capital Movement and the Flexible Canadian Exchange Rate, 1953–1961,” this Journal, XXX, no. 1, Feb., 1964, 76–94.

² This is proved in Harry C. Eastman and Stefan Stykolt, “Exchange Stabilization Once Again,” ibid., XXIV, no. 2, May, 1958, 268.

³ Let A = A₀ sin x

B = B₀ sin x

Then C = B ₀ sin(x −6), since the maximum value of C is B₀; and if this occurs where the curve for C intersects the curve for A, then

θ = (π/2) −sin⁻¹(B ⁰/A ₀)

D = A − B = (A ₀ − B ₀ ) sin x = D sin x

E = A − C = A₀ sin x − B₀ sin (x − θ) = E₀ sin (x + ψ).

Substituting for θ in the equation for E, and combining the two sine functions into one gives and ψ = sin⁻¹ (B₀/A₀).

The ratio of the areas under the half cycles of two sine curves of the same period is the ratio of their amplitudes. Therefore the ratio of the area under a half cycle of E to that under a half cycle of D is

I am indebted for the solution of this problem to my versatile colleague, Professor W. E. Grasham.

⁴ Harry C. Eastman and Stefan Stykolt, “Exchange Stabilization in Canada, 1950–4”, this Journal, XXII, no. 2, May, 1956.