Occasional allusions to copyhold tenure are met with in works upon actuarial science, and in exercises for students; and the admirably lucid paper by Mr. Peter Gray upon the Theory of Successive Lives, which appeared in the second volume of the Journal, is likely to be remembered as having a bearing upon the subject. A brief account of the intricacies which beset this tenure, and of the attempts which have been made to cope with the arithmetical difficulties to which these intricacies give rise upon proceeding to convert the tenure into freehold, may not be without interest for some of the readers of the Journal.

In valuing interests that involv the probabilitys ov marryge and ov leaving issue, we require to hav the means ov ansering such questions as the folloing among others. What is the probability that a bachelor ov a givn age wil (1) marry, or (2) die unmarryd, in an asignd year from the present time? or (3) be alive and stil unmarryd after the laps ov a givn number ov years ? In ordinary life contingency calculations, the corresponding questions as to the probabilitys ov life and deth ar anserd by means ov the figurs containd in the familiar mortality tabl (formerly cald a tabl ov mortality, but by Dr. Farr a life tabl); and the great practical convenience ov that tabl sugests that, when we hav to deal with chances ov marryge as wel as ov deth, we shoud at the outset construct on analogos principls a combined marryge and mortality tabl.

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.