It is commonly known that in calculating an annuity on three joint lives, two of the lives are made to count as one life of the same annuity value; and that the result is approximately true. Twenty years ago (Phil. Mag., Nov., 1839), I showed that if the law of mortality explained by Mr. Gompertz were accurately true for the whole of life, this substitution of one life instead of two would also be accurately true. I now repeat the same proposition in a more general form.