It is not my intention in this paper to travel over the same ground as that followed by Mr. Sprague in his paper in the 7th vol. of the Journal, p. 61, “On Certain Methods of Dividing the Surplus among the Assured in a Life Assurance Company; and on the Rates of Premium that should be Charged to Render them Equitable”, and that by Mr. Tucker, in the 9th vol., p. 245, “On the Rates of Premiums Required to Provide certain Periodical Returns to the Assured”, although the changes which have been introduced into the methods described by both writers, and the increased knowledge we possess of life assurance mortality statistics, would fully justify a revision and extension of their labours. Such a work, if undertaken, would fully repay the time spent upon it, and would prove a valuable addition to the information we already possess upon a very important subject.

Both the above-mentioned gentlemen enlarged upon what “H. A. S.”, in the 8th vol. of the Journal, p. 167, describes as “The incongruity existing between the rates of premium charged at certain ages and the benefits accruing therefrom”; and they have shown that when the net cost of the assurances and bonuses is calculated upon a certain basis, the figures differ, often very materially, from those of the premiums charged.