In the former paper, it was laid down, as the basis of any improvements I might be able to suggest as to life contingency calculation, that, in place of premises of a specific nature leading to special conclusions, we should rather, from the very commencement, recognise the variable nature of the results we might have to encounter, and accordingly construct a system of limits rather than one of particular values.

Among the numerous classes of risks now undertaken by Insurance Companies, those against the contingency of leaving issue are beginning, from their increasing numbers, to assume a position of greater importance than heretofore. Nothing has hitherto, to my knowledge, been written upon the subject, and the premiums for insurances of this nature have been left to the judgment of the actuary as each individual case has come before him, there being no recognized and accurate formula for the calculation of the risk. Under these circumstances, and as a considerable amount of material exists from which approximate results may be deduced, I venture to submit to the Institute a few considerations upon the subject, but confined principally to the probabilities of marriage so far as they affect the calculation of such premiums.

Dr. Farr. in the 12th Report of the Registrar-General, has given the value of annuities and the expectation of life, as deduced from the male English Life Table.

Observing a very uniform difference between the results thus obtained and those from the Carlisle Table of Mortality, it appeared to me probable that a simple hypothesis might be constructed which would produce a close approximation to the expectation of life between certain ages, but somewhat less favourable than the hypothesis. I proposed in 1857 for the expectation of life according to the Carlisle Table of Mortality.

According to present practice, when property is insured, both by average and by specific policies, the latter have to bear the whole of any loss which may occur, unless it exceed the total amounts which they insure; and, in that case, the excess of loss over the amounts they insure is covered by the average policies, and is subject to average at the settlement of the claim.

A note of alarm has been sounded at the present mode of adjusting fire losses under average policies; and it will be well, though for other reasons, hereafter to be explained, than those to which it owes its origin, that it be not allowed to die away without some effort to gain additional vantage-ground towards the substitution of a comprehensive and reasonable scheme of apportionment for the mischievous and unsound practice which now exists.

The Great Exhibition of 1851, however fruitful it was in direct results beneficial to the trade and commerce of this country, has indirectly produced greater consequences still, by leading to the discussion of questions in which the common interests of all the nations of Europe are concerned.