In his lecture ‘Computing methods’ (J.S.S. Vol. VIII, pp. 76-7), D. H. Sadler describes a method of inverse interpolation invented by Dr Comrie. This note shows how the method may be used to solve for i the equation = K. The solution of this equation to a sufficient degree of accuracy is a minor but troublesome problem of office practice, and the writer hopes that the method here described will be of practical value. In addition to its simplicity and directness it has the considerable merit that it makes full use of what a calculating machine can do, and, in consequence, requires from the computer very little calculation. It will be seen that, apart from the making of a short difference table, the whole of the work is done on the machine.

Students of the subjects of compound interest and life contingencies are usually baffled by the type of problem in which the value of a premium, say P, can only be ascertained when one knows the number of years, say n, after which there is some definite change in the conditions of the problem. Such is, for example, the valuation of a variable annuity-certain subject to different remunerative and reproductive rates of interest when, in the beginning, the payments under the annuity are too small to meet requisite interest payments. In Chapter IV, article 16, of Todhunter, the student is advised that in such cases the value must in general be sought by trial and error. Similar exhortations perplex the student's mind when he turns to the subject of life contingencies, in which he is frequently required to evaluate the premium for a complicated assurance in which the death benefit is defined by different expressions before and after a period of time which is itself unknown.