On the Interpolation of Logarithmic Series

Abstract

In this paper Mr. Meikle states it to be his object to simplify and popularize what has been written by Mr. Gompertz and Mr. Farren on the subject in question. He says, “In the construction of tables of mortality, the results arising out of the statistics, viz. the logarithms of the number alive at the beginning of each year, or the logarithms of the probability of living one year, generally proceed so irregularly from age to age that it is deemed expedient to graduate and reduce them to a more consistent and harmonious form. For this purpose it is thought that the characteristic features of the table which is being developed will be as equally retained in any set of equidistant terms of the series as they are now exhibited in the rough and irregular items of the table. Selecting, therefore, the terms of the series at ages 10, 20, 30, &c., or at ages 10, 20, 40, &c., and making these the fixed points of a new series, it is required to interpolate for the values at the intermediate ages.”