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.

It has frequently been insisted upon that in the financial management of a life assurance company the scales of premiums, the method of valuation, and the mode of distribution of surplus should be considered together, and not independently of one another. Many instances could be given of unfairness in the treatment of the members of different classes and ages due to a want of recognition of this principle. It is, of course, impossible, in the practical management of a life office, that abstract justice should be administered as between the various policyholders; but as the system of charging uniform premiums for all ages at entry has given way to that of graduating the premiums according to the age of the life assured, so it may be possible and politic from time to time to find means of making the payments of the assured still more accurately conform to the exact value of the benefits they are to receive.

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.