Note on Prof. Pell's Paper on the Institute of Actuaries Life Tables

Extract

As the formulas obtained by Prof. Pell differ from those generally in use among actuaries, it seems desirable for the sake of future students of the subject to point out that he has inadvertently fallen into an error which will necessitate considerable alteration in the reasoning on pages 142 to 144 of his paper. He uses k to denote what he calls “the absolute rate of mortality at the exact age x”, and k′ for the same at age x + 1; evidently meaning the same quantity that British actuaries now by common consent call the force of mortality. This term is embodied in the Scheme of Notation appended to the “Institute of Actuaries Life Tables”, regarding which the Council of the Institute say in the preface to the volume, that they strongly recommend the notation for general adoption, in the expectation that its use will contribute materially to advance the study of life contingencies, by promoting exactness of thought and expression. It would always be convenient, and occasionally save much trouble and confusion to readers, if all the writers in this Journal would invariably adhere to the recognized notation, so far as they can make it answer their purpose for the time being.