I have not found it easy to select a proper title for this paper; and I am very conscious of the difficulty of explaining my reasons for instituting the somewhat laborious experiments of which I am now to state the results. Perhaps, indeed, I ought to apologize for offering to the Institute of Actuaries a communication which some of its members, who are conversant with the leading treatises on the doctrine of probabilities, may know to have been anticipated and rendered unnecessary by the labours of men much better qualified than I can pretend to be, to do justice to so profound a subject. I have some reason, however, to believe that the experiments I am about to describe are new; inasmuch as, though I have consulted one or two works which are likely to have contained some reference to such experiments, had they been already made, and have questioned more than one eminent member of your Society upon the subject, I have not been able to learn that any such experiments are upon record.