It has frequently been remarked, that however varied and uncertain may be the occurrence of the events to which the life of a single individual is exposed, the average return in a large mass of persons is so regular, as to be predicted with confidence within very small limits of error. On the uniform happening of these events under similar circumstances, or the discovery of the laws by which they are governed, the actuary depends for the application of the theories of probabilities to the many useful purposes for which they may be rendered available.