The study of statistics is so peculiarly connected with the vocation and intellectual pursuits of the actuary, that I feel convinced there is no member of the Institute who will not be interested in a full report of the very important meeting recently held at Brussels. I apprehend that the real business of the actuary is the reasoning on all events to which the mathematics of probability can be applied, and reducing the conclusions to a form in which they can be practically used for the public benefit. His study is the doctrine of averages; and though his functions have been hitherto confined in a great measure to subjects relating to the assurance of human life, there are evidently many other topics to which, in time, his attention ought to be directed. The discovery of the mathematical laws of events will eventually be recognized as the sole means of bringing uncertainty to certainty, and out of irregularity deducing order.

In the paper I shall have the honour of reading to you this evening, upon some points connected with the education of an actuary, I shall endeavour to describe some of the more important duties and responsibilities of that office—to offer some observations to the student, as to his preparation for the profession of an actuary—and to suggest to the Council of the Institute some reasons for enlarging the sphere of the examinations that they may think proper to prescribe.

I shall not detain you with any account of the ordinary duties of an actuary, which are of course well understood in this room, but shall at once proceed to the consideration of the foundation of all actuarial knowledge—mathematics.