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.