The law adopted by the German Reichstag on the 23rd of May 1889 for insurance against invalidity and old age must demand careful attention as one of the most daring social and economic experiments in modern history.

Its many varied aspects solicit and repay the sedulous thought of the philosopher, as a contribution to one of the deepest problems in the evolution of man: of the statesman, as a signal tentative experiment in the compacting of a nation into an intimate and interdependent unity: of the economist, as a bold departure from principles of social condition which had generally prevailed, and as a practical criticism upon the doctrine of laissez faire: of the historian, as a problem in the mode of development of nations: of the moralist, as a contribution to practical social ethics: and of the actuary, as affording him a question which peculiarly is fitted to engage the disciplined thought and experience in which he has been trained.

In response to the suggestion of our President, in his inaugural address for the present session, I commenced to put together some notes which seemed suitable for a paper to be read before one of the provincial institutes. In this I proposed to deal with some practical legal questions which are encountered by officials engaged in various positions outside the head offices of life insurance companies.

When I agreed to prepare a paper for the consideration of the Institute of Actuaries, on the Life Assurance Companies Acts, 1870–72, I did not do so with a light heart. The task in any case would have been onerous, and events which have since transpired have not tended to increase my confidence. It has become a matter of public knowledge that the Council of the Institute had under consideration the laws relating to life offices, and that it was intended to take an early opportunity to debate the question. Moreover, it has been surmised that Government had in contemplation to take action in the matter, and, possibly in next session of Parliament, to bring in a Bill for the amendment of the law. I, therefore, cannot help feeling that a great responsibility rests upon me in opening a discussion of such importance, but I am emboldened to proceed, because, even if I fail to produce anything new or important, there are many here of far riper experience than myself, and a debate in such an assembly cannot but be instructive and useful.

The subject of Life Assurance Investments does not seem to have been discussed for a long time at the meetings of the Institute. Two valuable and instructive papers, bearing the honoured names of Mr. Samuel Brown and Mr. Arthur H. Bailey, were read to the Institute respectively on 25 January 1858 (J.I.A., vii, 241) and 24 February 1862 (J.I.A., x, 142), but they appear to be the only contributions of importance, dealing with the question in its entirety, to be found in the Journal. Notwithstanding the lapse of time which has taken place since the latter date, the principles of investment as defined by these two distinguished authorities are still very generally applicable to present needs; and the articles themselves have lost none of their charm for the student of life assurance finance, characterized as they are by soundness of judgment and by felicity of expression.

My first impressions on considering the magnitude and pretensions of the investigation which I now present to the Institute were that it would perhaps be more suitable for a communication to the Journal, or that at any rate it would scarcely provide sufficient matter to occupy the attention of the meeting for a whole evening. This impression was strengthened when I considered the importance and wide scope of the researches which have been presented as food for our reflection at many of the meetings held in recent years. But, on further consideration, it appeared the subject I had chosen was one likely to give rise to useful discussion. Also I feel that, from a good number of the members of the Institute, at any rate, on whose time and attention the cares of business are continually making greater and greater demands, I may hope for forgiveness if I place before them a somewhat lighter paper than usual.

Before proceeding to describe the mortality experiences made use of in this investigation, I will first of all discuss the various materials that have been used in investigations into the mortality among assured lives, the methods of arranging those materials in order to deduce the rate of mortality, and the method of graduation best adapted for the adjustment of the rate of mortality among recently-selected lives, pointing out the advantages and disadvantages of each, and stating which I have adopted. This will necessarily partake more or less of the nature of an historical sketch; but I think it will conduce to clearness, and will, I trust, prove interesting as well as instructive. I have also thought it desirable to state somewhat fully the information on which I have based my conclusions, in order that my readers may be in a position to exercise an independent judgment.

In his great work, the Théorie Analytique des Probabilités (which may he supposed to embody the author's latest and most matured views respecting that abstruse and difficult subject), Laplace reduces the fundamental principles of the whole doctrine of probabilities (both direct and inverse) to four comprehensive propositions. The four “Principes” of Laplace are extremely well adapted to show how important is the part, in that doctrine, which belongs to the indirect or inverse branch of it; and I know of no means better calculated to throw light upon the subject of this article than the course which I propose in the present section to follow, namely, to illustrate each “Principe” by an example relating to a coin falling head a certain number of times in succession.

Another investigation into the mortality experience of life assurance companies by the Institute of Actuaries will, in all probability, take place at no very distant period; and I think it is extremely desirable that this subject should previously be ventilated in the pages of the Journal. A very elementary acquaintance of that branch of the doctrine of probabilities which treats of the law of “Errors of Observation” will suffice to enable anyone to follow my reasoning in the following pages, and to form his own opinion as to whether the conclusions which I have arrived at are right or wrong.