Every student of actuarial literature can call to mind the writings of leading experts that deal with the methods to be employed in order to ascertain what pecuniary profit or loss has resulted from the mortality experienced by a life assurance company. In this path of knowledge, Mr. C. D. Higham may be said to have been, if not the first to tread the soil, at least the earliest to write, for the benefit of the community, a record of his travels. Certain it is that since his paper on the “Value of the Death-Strain” (J.I.A., xx, 153), the importance of considering the true amount rather than the nominal amount at risk in such investigations as I have referred to, has been freely recognized and acted upon; and the death-strain as a function in actuarial matters has been much written and talked about.

In a paper by the late Mr. Samuel Brown “On the Rate of Mortality and Marriage among Europeans in India” (J.I.A., xi, 1), reference is made to a method used by Griffith Davies to deduce rates of mortality from the records of the Madras Military Fund. It appears that Davies ascertained the average age of the lives in each of certain groups into which the experience naturally divided itself, and obtained the ratios which the actual deaths in the several groups bore to the corresponding number expected according to the Northampton Table at the average age. These ratios were then set out as ordinates corresponding to abscissae representing years of age, and a continuous curve was drawn in the usual way, by reading off which the graduated ratios for each age were obtained, and from these the graduated rates of mortality were at once formed.

I shall, in the following remarks, mainly confine myself to some considerations connected with the rise and the development of life assurance business in Australasia—a development which, considering the limited population of these colonies, is probably quite as phenomenal as that which has attended its progress in the United States of America with their teeming millions. To such an extent, in fact, has this been the case, that in no part of the world, so far as I am aware, has the amount assured per head of the population reached so high a figure as in Australasia. The figures are approximately as follows: Australasia, £19; Canada, £9; United Kingdom, £12; United States, £10.

In the Journal for July and October 1891 (J.I.A., xxix, 242 and 444), Mr. William Matthew Makeham published two papers “On the Theory of Inverse Probabilities.” In the first he obtained a new formula, and in the second he pointed out some applications of the formula. I desire to present some considerations which I think will show that this formula is not suitable for any application.