Note on the Possibility of the Division of the Law of Mortality into Geometrical Series

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.