When we consider in a table of mortality the consecutive terms which express the number living at each age, we remark that the differences between those numbers are almost constant in the middle ages of life; they change afterwards, remaining however uniform for another series of terms; so that the table can be considered as a series of decreasing arithmetical progressions. Let c be the difference between lx and lx+1; and let us suppose this difference constant for n years. We shall then have for the value of the life annuity during that time.