A mortality table shows the number living at each age x, and the number dying in the following year; and the ratio of the latter to the former, is the probability of dying in a year, and is called the rate of mortality at age x. This function varies from age to age by finite steps; but it is not to be supposed that the actual intensity of mortality remains constant throughout each year and changes suddenly at the end of each completed year of life. On the contrary, it is a function which varies by an indefinitely small amount with each indefinitely small interval of time; and the measure of its value at any instant, like that of any other varying rate, is the change that would be produced in a unit of time if the rate were to remain constant throughout that unit, and equal to its value at the instant in question. For example, when we speak of a railway train travelling at the rate of 60 miles an hour, we do not mean that it has travelled 60 miles in the past hour, or that it will travel 60 miles in the next; but that, if its rate were to remain the same for an hour, it would travel 60 miles in that time, the unit of time in this case being one hour. Similarly, the intensity of mortality at any instant among a large number of persons, is not measured by the number who actually die in the following year (the unit of time in the case of a mortality table being one year), but by the number who would die in that year if all the conditions remained unchanged throughout the year; that is to say, it is measured by the number who would die if they did not deteriorate in any way with their increasing age or otherwise, and if the number of persons under observation remained unaltered, the places of those who died being constantly filled by fresh lives subject to the same intensity of mortality.