The opinions exprest at several recent meetings ov the Institute ov Actuaries apear to indicate that ther is a general agreement among practical actuaries, that the Institute Tabl HM(5) represents very faithfully the mortality among insured lives after the first benefit ov selection has worn of,—say, after the laps ov five years from the date ov insurance;—and that therefore life office valuations shoud, in the case ov policies ov five or more years' standing, be to a great extent based upon that tabl. When we consider to what extent it shoud be uzed, we see at once that we shoud calculate by means ov it the values ov the sums payabl by the offis and ov the sums receivabl, that is, ov the gross premiums; we shoud also, ov cours, uze it in converting the divisibl surplus into reversionary bonuses. But it is not a suitabl tabl for the calculation ov the net premiums; and net-premium valuations therefore cannot with propriety be made by means ov it alone. The mortality during the first five years being considerably less than that shoen by the tabl in question, the true initial anuities (or anuities at the date ov asurance) wil be greater than those givn by it for the same age, and the net premiums consequently less. It folios then that, if we wer to value the HM(5) net premiums, we shoud hav too large a credit, and the liability bro't out woud be too smal.

The calculations which I have made respecting the rates of mortality in New South Wales are founded upon the returns of the Registrar-General for the years 1860-75, and upon two censuses taken in the years 1861 and 1871. There is every reason to believe that the returns of births and deaths are as accurate as can be expected in any case, and that the results of the censuses are as trustworthy as is usually the case. The returns for the year 1876 were not published when I commenced the calculations; and I have not gone farther back than 1860, because during the year before, Queensland with a considerable population was separated from New South Wales, producing of course an awkward break in the registrations.

It is one of the fundamental theorems of the Doctrine of Probability that, “If a compound event consists in the concurrence of two or more independent simple events, that is, events the happening or failing of any of which has no influence on the happening or failing of any of the others, the probability of the compound event is equal to the product of the probabilities of the simple events.”