In a note by Goodey on the combined use of the WKB solution and Rayleigh's principle to estimate the lowest eigenvalue of a second-order linear differential equation, a numerical error concealed an interesting aspect of the result. The exact value λ = 2·062 corresponds to 0·6564π; and not 0·654π as stated. The approximate value 0·6559π is therefore lower than the exact value.

The possibility of approximate evaluation of the integral in a variational expression affecting the direction of approach to the exact value was pointed out by the author in a recent paper on the application of quadrature by differentiation. The application of the method described there to the example considered by Goodey may be of some interest as it gives the eigenvalue to within 1/2 per cent by the solution of a quadratic equation.