Having read with much pleasure and profit the several articles upon this subject, chiefly in the Assurance Magazine, from such able contributors as Messrs. De Morgan, Jellicoe, Brown, Sprague, Pattison and others, whose names are known and honoured on this side the Atlantic as well as at home, I have thought that, in return, a brief account of the method adopted in the recent distribution of the surplus of our largest American Life Company might be acceptable to the members of the Institute of Actuaries.

If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavour to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use such arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others—I should feel quite at my ease.

If the series of the numbers living which constitute the law of mortality could be approximately derived, by collecting together the corresponding terms of a limited number of geometrical progressions, it is evident that the mathematical formula involving any combination of life contingencies and of the interest of money would expand into a certain number of geometrical series, the summation of each of which might be easily expressed. Such a result, as a general principle, would not appear to be attainable, so far as can be judged by an example I have been induced to test with the Carlisle table.

The investigation of the different causes that tend to influence the health of the community, either injuriously or otherwise, is one of great public importance, particularly in a high-pressure age like the present—an age in which it is too much the custom to sacrifice all considerations of health and safety to a determined and eager desire to do in a few hours what our ancestors were content to do in as many days.