Some apology is needed, perhaps, for proposing to rediscuss a subject which has been handled so often, and by so many distinguished actuaries. But I am probably addressing gentlemen who have not had occasion to become familiar with all that has been written or said on the subject, and others to whom it may usefully be presented from a fresh point of view; and there are some important practical questions too on which the profession seem scarcely yet agreed, which will admit of further consideration. I shall not attempt to notice the various papers which from time to time have been contributed by actuaries towards the solution of the questions I am to consider. For many of the views I am to express I am necessarily indebted to those who have preceded me; and the aim of this paper is less to introduce what is new, than to enforce, and illustrate if possible, sound and correct opinions. I am anxious to set the subject in a light which will make it intelligible to others than actuaries, and to discuss principles rather than formulas.