The origin and progress of the principles of insurance are subjects, which not only call for the endeavour to elicit and clear from seeming contradictions such records of the insurer’s calling as are blended with the remote history of mercantile customs and laws, but which likewise particularly suggest the necessity of some essay to connect those rude outlines with the more advanced stage of the theory, in its immediate alliance with the sciences of applied probabilities and political or social arithmetic.

My object in the following paper is to give, in a few leading problems, a general and somewhat elementary view of the Theory of Probabilities, exhibiting the immediate dependence of the doctrine of Life Contingencies on the laws of probability and combination, and showing how apparently complicated problems, involving two and three lives, can be deduced directly from their very simplest and most elementary forms of expression.

This subject has been so ably treated by Mr. Sang, in the paper transferred by Mr. Thomson’s permission to the pages of this Magazine, that it might seem almost superfluous to revert to it. Nevertheless, there are considerations connected with it which I believe to be of some importance, and which that gentleman has not adverted to; and I am therefore induced to submit the following remarks, by way of pendant to his observations :—

The Council of the Institute of Actuaries are making a laudable attempt to collect such data as the Assurance Offices possess, with a view to determine the mean duration of human life in different parts of the Globe; and thence to ascertain the proper rate of premium to be charged in the several localities to which persons whose lives are assured may be desirous of proceeding. The almost entire absence of any authentic information upon this subject renders such a proceeding of the greatest importance and interest; since it is only by such means we can hope to be able to substitute, for the present uncertain and arbitrary charges, rates which are based upon actual experience, and which are justified by the circumstances of each particular case.