There is nothing immutable in this world, and certainly life companies are no exception to the general rule; for in them, from year to year, we find fluctuations of every kind—in amount of new assurances—in expenses of management—in value of assets—in realized interest—in the death claims—in fact, in every branch and item of their business. Of all these variations there is none so important as that concerning the mortality experienced. The fluctuations in the other elements of a life office's affairs are trifling as compared with this, and can without difficulty be prepared for. But in the perturbations of the death claims from year to year, we are dealing with a matter that cannot be calculated on in advance —an element which, if violent, may endanger the safety of the company itself; and, even when this is not the case, will often prove a serious inconvenience to it. I have called violent mortality fluctuations inconvenient to a life office. To men acquainted with the practical as well as the theoretical side of assurance, the word will not seem exaggerated. They, at least, know how important it is that the bonus to policyholders and the dividend to shareholders, do not retrograde. The moment the bonus tide begins to ebb, there is an outcry; and variations in the mortality may thus create disgust in those already connected with an office, and at the same time add another difficulty to the already sufficiently difficult task of its agents and canvassers.

We are so accustomed, even when we do not aim at scientific exactness, to regard every phenomenon as produced by causes,—as the resultant of forces,—that we cannot help looking on what we call “life” as the effect of certain definite forces, and on death as the consequence of the extinction of those forces. But when we thus contrast life and death, we must always bear in mind not only that what we call “life” is a condition which presents itself under circumstances of unexhaustable variety, but that in all probability quite as many differences in its manifestation entirely elude our observation. Given the effect, we reason as to the cause; when the effects are different, we infer that either the causes are different, or the conditions on which the effect depends. But if the differences are so numerous that we can scarcely find two cases exactly alike, we can draw no conclusion either as to the causes or as to the conditions. Since in no single case can we recognize the various conditions under which the cause of life works, we cannot hope to decide how the effect is connected with the conditions and how with the causes. Death too is a phenomenon as to which we have not the least idea why it happens; whether because the vital force in the individual has sunk below a certain degree which is necessary for the maintenance of life, or whether as a result of wholly different forces. On this point we scarcely know more than that the possibility of organic life depends upon certain conditions, that it can exist so long as these conditions remain within limits more or less wide, and that a transgression of the limits causes death. We do not, however, know exactly what these conditions are, and still less do we know the limits within which human life can exist; and if we reflect how complicated are the circumstances to be taken into account, we can scarcely hope to see these relations settled for some time to come. It is further to be observed that life, being regarded as the effect of a force, and death as its extinction, there must be a gradual transition from the one to the other.

Problem VIII—To construct a table for the formation of Survivorship Assurances.

A survivorship assurance on (x) against (y) is an assurance payable at the end of the year in which the combination (x. y) is dissolved, provided the dissolution is caused by the death of (x).

The question with which I have headed this paper is one that may seem startling enough. It has been so widely taken for granted that a large new business must be an unmixed good to all concerned in a life company, that to debate whether it be so or no, will seem in the eyes of many to be a very idle thing. And yet, though I have been considering the subject for a long time, I cannot answer the question unhesitatingly in the affirmative. In saying this, it ought to be pointed out, that the matter is regarded from a purely practical point of view. The problem is not ought a large new business to benefit policyholders? but, as a matter of fact, does it? Even if the question were answered in the negative, it would not follow that no new business, or an insufficient quantity of it, would better suit the interests of the policyholders. Waste must be supplied, and a certain degree of magnitude maintained in life companies.

I have somewhere read that the experience of life assurance companies furnishes the only certain means of ascertaining the law of mortality, since by this means only is it possible to keep in view through a lengthened period and trace up to death, each of a selected number of persons. As far as the possibility is concerned, we may admit that the law of mortality of the members may be deduced in this manner by proper methods. It is important, however, to bear in mind that, in the case of assurances, we have to deal with selected lives; and the influence of this selection, though it may be disregarded in the later years of assurance, is of considerable importance in the earlier years, so that, unless special precautions be taken, the mortality of the general population cannot be correctly obtained. The mortality may be more nearly determined if an account be kept of the rejected proposals, as is done in England, and the deaths noted which happen among those cases. This, I certainly think, should be done universally, as it must be of practical use to the companies to know how far the rules by which they are guided in accepting or rejecting proposals are justified. No such account is kept, as far as I know, either in Germany or Austria. We may otherwise eliminate the influence of selection, by omitting from the calculation the earlier years of assurance, during which this influence is felt.

A correct knowledge of the rate of mortality among mankind is of such importance for answering many interesting questions, that we might hav expected it would hav been diligently studied from the earliest times. This, however, appears not to hav been the case, the reason probably being that questions as to the expectation of life arise in the first instance with reference to particular persons, and not to men in general. The proverbial uncertainty of human life—so often seen in the occurrence of death when least expected—is unfavourable to the notion of a general law of mortality, but naturally suggests the search after a means of predicting the duration of individual life. As thus understood, the question of the duration of life has at all times attracted great attention. Soothsayers and magicians claimd to hav the power of discerning from signs and omens of many kinds every event of life, its termination not excepted, and astrologers pretended to read in the stars the precise hour of each man's death.

The only treatise of any value on this subject that I am acquainted with is a paper by Mr. Peter Gray, in vol. xiv of the Journal of the Institute of Actuaries. Considering the magnitude of the pecuniary interests frequently involved in transactions of the nature referred to, it is somewhat surprising that Mr. Gray's valuable labours have not, ere this, been followed up by contributions from other writers on the doctrine of Interest and Annuities. This, I think, is much to be regretted,—and must form my apology for the following attempt to add something to what Mr. Gray has given us.