The late Mr. William Morgan, in the second edition of his Principles and Doctrine of Assurances and Annuities on Lives, published in the year 1821, has, in the 7th Problem of that work, investigated “the method of determining the amount of an annuity forborn and improved at compound interest during the continuance of a given life.” This problem he has subsequently discussed in an algebraical form, in Note V., page 154; and he has moreover given a table (Table VII.) showing the sum to which an annuity for-born and improved at 4 per cent, compound interest will amount, on the extinction of a given life, computed according to the foregoing method, from the Northampton Table of Observations.

Another mode of easily appreciating the regularity and the analogies of different tables is, to construct a diagram, in the form of a curve, of which the absciss represents the age, and the ordinates the corresponding decrements of life (see opposite). The inspection of such a diagram is sufficient to convince us of the great irregularity of the Carlisle Tables of Mortality, which must obviously have been formed, as they confessedly were, from observations on a very limited number of individuals, so that they exhibit a succession of different climacterics, after which the mortality is diminished; while about the age of 74 the curve that represents them towers to an incredible height, affording an expectation of longevity which some of the strongest advocates of those tables have abandoned in their practical applications, since they take their estimate of life, in advanced age, even lower than it is represented in the Northampton Tables.

It was intended that the short essay descriptive of the existing system of settlements of claims under average fire policies, which appeared in this Journal as far back as No. X. (January, 1853), should have been promptly followed by some remarks on the most obvious defects of the system, with a few practical suggestions for their remedy. It is not necessary to explain here the reasons for the delay which has taken place in the fulfilment of that intention; but it is satisfactory to know that the postponement has not been without its use. Many valuable hints have been offered; and although some marked differences of opinion exist as to any proposed remedies, the explanations given of the existing rules are, without any exception, admitted to be correct.

Since the establishment of the Statistical Society of London, so great an impetus has been given in this country to the study of statistics, that probably in no branch of knowledge have more important results been produced in the same time. This arises in a great measure from the very nature of statistics, and from the universality of their application. Every science, the facts of which can be expressed in a tabular form, comes within their range; and the great object of those who desire to elevate the character of statistics in the mind of the philosopher or the man of science is, to show how, by a correct and methodical classification of facts of every kind, the boundaries of knowledge are enlarged, new laws developed, and new theories suggested.