The studies of an actuary depend so much for their success on the accurate and full collection of statistics, that we cannot but feel a deep interest in every effort that is made to improve the method of and to lay down sound principles for obtaining them. Hitherto we have been more especially concerned with the laws of population, vitality, and disease, because they form the basis of the vast extension of life assurance in this and other countries. But in the course of the last few years the progress of social science has brought forward many questions tq. which the doctrine of probability as to the recurrence of events may be applied, which, though not strictly within the limits of our professional pursuits, afford many opportunities for the use and extension of our science.

Let there be letters x, y, z,…each of which has values, choices, or drawings. Let their number be σ, and let, ξ, η, ζ,…be their several numbers of drawings : x1, x2,…xξ the drawings of x; and so on. Let Σx, Σy,…be the sums of the drawings of x, y, &c.; and Σ:x, Σ:y, the average drawings: so that , and so on.

My second example is the Austrian Loan of 1865. The conditions are as follows:—

734,694 Bonds, each of £19. 17s. 0d., issued at £13. 14s. 4d., that is, at a discount of £6. 2s. 8d. each.

Subscribers will be at liberty to pay their Scrip in full on any one of the above dates, under discount at 6 per cent per annum.

The interest with which I have perused Mr. Gray's very able paper in the last number of the Journal, has led me to give some consideration to the general theory of varying Annuities; and as the results of the investigation appear to me somewhat striking, I am induced to think that a brief paper on the subject may not be unacceptable to that section of the scientific world to which this Journal more particularly addresses itself.

There has been no more valuable improvement in the science of Assurance calculations than that effected by the invention of the Commutation or D and N System of calculation;—a method which, as is now universally known through the writings of Baily, Professor De Morgan and Mr. Gray, we owe, in this country, to the genius of Mr. George Barrett, of Petworth, Sussex. It appeared at first in an incomplete and rather inconvenient form, but various important modifications and extensions of the principle of the method were some time afterwards made; and it was practically applied to the calculation of Life Contingencies by the late eminent actuary Mr. Griffith Davies, with whose name it is now generally associated.

In this paper, Mr. Henry describes an instrument by the aid of which he has actually obtained the values (to four figures) of many thousand products, being the D values in the various tables he has published. The principle of the instrument, which he claims as entirely his own invention, may be briefly described as follows:—

Let ABC be a right-angled triangle, of which AB is the base and AC the hypothenuse, and from any point D in the hypothenuse let fall DE perpendicular to AB; then from the similar triangles ADE, ABC, we have

Although the general principles upon which the business of Insurance is based, must be the same wherever it is carried on; yet its particular developments must of necessity vary in countries under different laws, and with a public opinion differently educated. An investigation therefore of the book before us, with the view of pointing out those points wherein the practice of our Trans-Atlantic Brethren differs from ours, may not be without advantage to the interests of Insurance in this country.