1. The object of the following investigation is to show how the probabilities of an individual living any given number of years are to be deduced from any table of mortality. All writers (with the exception of Laplace) have considered the probability of an individual dying at any age to be the number of deaths at that age recorded in the table, divided by the sum of the deaths recorded at all ages. This would be the case if the observations on which the table is founded were infinite; but the supposition differs the more widely from the truth the less extended are the observations, and cannot, I think, be admitted where the recorded deaths do not altogether exceed a few thousand, as is the case in the tables used in England. The number of deaths on which the Northampton Tables are founded is 4,689 (Price, vol. i. p. 357). The tables of Halley are founded upon the deaths which took place at Breslau, in Silesia, during five years, and which amounted to 5,869.