(1) The purpose of this paper is to describe the results of further investigations into the possibilities of trigonometrical representation of actuarial functions. The authors’ previous paper (J.I.A. Vol. LIX, p. 256) was concerned mainly with the use of Fourier’s Series, and the simplicity of that series in practice invites its use in any work of this nature. To a large extent Fourier’s Series, or a modification thereof, is employed in the present work, but the authors do not insist that the final formulae suitable for use in practice should be Fourier’s Series.