The values which it has been heretofore customary to tabulate for actuarial purposes, in connection with specified rates of mortality and interest, are those of annuities on single and joint lives at all ages; and from these, by operations more or less complex, and with the aid of subsidiary tables, the actuary has had to form such other values as might be required in the solution of any particular problem in hand. Of the values thus requiring to be formed, those of the single and annual premiums for assurance occur perhaps more frequently than any others; and hence the desirableness of simplifying as much as possible the operations by which these are deduced from the corresponding annuities. To effect this simplification was the object of Mr. Orchard's work, in which, as will be admitted by all competent to form an opinion on the subject, the author has been completely successful. The arithmetical operation heretofore necessary has been entirely superseded, and the required values are found simply by inspection.

In this paper Mr. Meikle states it to be his object to simplify and popularize what has been written by Mr. Gompertz and Mr. Farren on the subject in question. He says, “In the construction of tables of mortality, the results arising out of the statistics, viz. the logarithms of the number alive at the beginning of each year, or the logarithms of the probability of living one year, generally proceed so irregularly from age to age that it is deemed expedient to graduate and reduce them to a more consistent and harmonious form. For this purpose it is thought that the characteristic features of the table which is being developed will be as equally retained in any set of equidistant terms of the series as they are now exhibited in the rough and irregular items of the table. Selecting, therefore, the terms of the series at ages 10, 20, 30, &c., or at ages 10, 20, 40, &c., and making these the fixed points of a new series, it is required to interpolate for the values at the intermediate ages.”

A Specific Policy is one which insures stated sums on particular risks, and guarantees the assured against any loss thereon within the limits of the amounts insured. It differs from anAverage or Floating Policy in several respects—the latter, amongst other privileges, having only to bear a share of any loss compared with the whole loss, similar to the proportion which the amount it insures bears to the whole value of the property insured at the time of the fire.

Take first the case in which. A has not a life interest, but one for n years, remainder to B. Let P be a sum of consols, 100–δ the present price of consols; consequently, P consols sells for

cash, which may be called M; A's and B's shares of it being M1 and M2.

B has a right to a sum of P consols n years hence: it matters not to him how this sum arises, provided it be ready for him in n years’ time. Suppose such a sum now appropriated to accumulate for n years as will produce P, B will be in the same position as if A enjoyed the sum intermediately; and if such sum be now handed over to B he will neither gain nor lose. Supposing M2 to be this sum, M2 invested to accumulate for n years = P consols.