A CTUARIAL SCIENCE, at least as the term is used in the English speaking countries, differs radically from some other sciences in that great amounts of practical material are included. For this reason, a survey of the field, such as we customarily attempt at the turn of centuries and half centuries, is most effectively made in two articles, one on theory, one on practice. Conceive, if you please, that botany, horticulture, and greenhouse operation were all lumped together under the heading Plant Science, and you would have something of the same situation. Here we are concerned with theoretical developments and it is just here that we come up against the first problem. While it is true that no sharp line of demarcation exists between theory and practice, it is not too difficult to make a rough separation of the material on empirical grounds. This, however, does not provide a categorical answer to the question of just what, fundamentally, constitutes a theoretical development of Actuarial Science. Before attempting to answer this question, a brief review of the subject matter is useful in order to provide a point of departure. There is probably no better method of summarizing the content of actuarial theory than to list and comment on the subjects studied by beginners in the profession in the order that they are taken up in their course of study. After passing tests to assure himself of the adequacy of his formal mathematical equipment, which includes some training in finite differences and the theory of probability and mathematical statistics, the student at once plunges into the basic insurance mathematics generally known by the term "life contingencies." This subject presupposes the existence of a mortality table, which might be thought of as sprung fully computed from the head of Jove; it has been defined by the famous English actuary, George King, as "the instrument by means of which are measured the probabilities of life and the probabilities of death." From this table are derived the net premiums and reserves for the various forms of life insurance policies as well as the expectation of life and the solution to population problems. The student is then led into the intricacies of working with multiple decrement tables, which enable him to handle the effect of sickness, withdrawal,