It may not unfairly be said that the earliest approximate valuation method—Woolhouse's—was born out of its time. Presented as it was nearly fifty years ago to a world whose views on such matters were rather different from our own, it attracted but little attention, and appears to have given rise to no subsequent developments. Indeed, the author himself seems to have thought rather slightly of the suggestion, and in the brief discussion which followed the reading of his paper, emphasised distinctly that he regarded the method merely as an auxiliary check. The truth is, the idea was altogether too simple, and so has suffered half-a-century of neglect whilst other methods (some of which have received impressive algebraic treatment and given rise to a quite extensive literature), dating from independent investigations made many years after Woolhouse's, have been devised, tested, acclaimed and have passed into current use. And so we come to the latest pronouncement on Woolhouse's method, the almost ex cathedra sentence passed by Mr. Lochhead in “Valuation and Surplus“ (page 52) that the “method is extremely simple, but is not very powerful.”

The object of this paper is to draw attention to a process of checking the accuracy of the valuation results of any financial year from the preceding year's valuation results (the attained ages as at valuation date increasing by one year) by means of the elements which connect both valuations. These elements are the interest required to maintain the reserves, the net premiums, the reserves of the policies coming in and going out during the financial year, and the expected death strain. In the appendix to this paper the checking process has been applied to the revenue account for the year ending 31st December, 1921, given in Appendix B of Mr. C. Carpmael's paper in J.S.S. Vol. II, No. 2. The determination of the profit or loss from each source has been made on two different assumptions—namely, the one adopted by Mr. Carpmael, that the income and outgo are uniformly distributed over the year allowing half-a-year's interest at valuation rate and the other adopted in the North American gain and loss exhibit of the convention edition by which no allowance is made for half-a-year's interest for the two cases in which the policies are assumed to come in and go out at the beginning of the valuation year as done by Mr. Carpmael in his paper, and in the middle of the valuation year.

Everyone has, theoretically, the choice, or option of being or declining to be assured. In order to prevent discrimination being exercised against him it is usual for the assurer to demand some evidence of health before issuing an assurance at his advertised rate of premium, and this method of preventing discrimination by rejecting proposals below a certain standard results in the phenomenon of temporary selection. That the assurer is not primarily concerned with equity may be seen by considering group assurance. The assurance is of different value to the different members of the group but as they have no option, or a very restricted one, this does not militate to the disadvantage of the assurer.

The definition of the term “probability” is almost as illusive as that of the term “electricity.” Much as the average person knows that the effect of an electric current is to produce certain phenomena with which he is familiar, so he understands in a general manner what is implied by the words “the probability that an event will take place.” The term is employed colloquially in many instances in which the quantitative idea is missing. “ Kain is probable today”; “He will probably be late”; and so on. Frequently, however, some measure of probability is implicit. For example, if the odds against a specified horse are quoted as being longer than the odds against another horse, it is understood that the chances in favour of the second horse are greater than those in favour of the first. It is to be supposed that it is more probable that the second horse will win than will the first, and a certain amount of arithmetical work has been necessary in order to obtain the figures for the odds.