A good deal of misconception prevails, on the part of many interested in the science of life contingencies, in regard to the expressions usually assigned as the measures of the probabilities of the different orders of survivorship among two or more lives. It seems to be supposed that these expressions are little better than rude approximations, adopted from convenience or necessity, depending on no definite principles, and consequently giving results but little entitled to confidence.

Notwithstanding the very large amount of leasehold property, which in the course of every year is bought and sold in this country, and notwithstanding the extensive transactions—of almost hourly occurrence—in the public market, in Government and other temporary Annuities, the subject of the rate of interest which any given purchase will yield the buyer is very imperfectly understood, even by those most deeply interested in the inquiry, unless they happen to be at the same time well versed in actuarial computations.

In the year 1823 a plan was projected, by the late Dr. George Pinckard, for establishing an Assurance Office which should undertake, as its leading feature, to grant policies on lives deviating so much from the common standard of health as to render them wholly inadmissible at any Office then existing. In pursuance of this plan, the Clerical, Medical, and General Life Assurance Office was established early in 1824.

As nearly all those readers whom the subject-matter of the following pages is likely to interest, are already fully acquainted with the nature and acknowledged utility of the Commutation Method, or arrangement of the preparatory Tables for Annuity and Assurance calculations into certain forms called the D,N,S,M, and R columns; it will, therefore, be unnecessary to enlarge on those points; and the facts to be presently adduced will have reference simply to the early history of that system of computation, or, more strictly, to the date when, and the person by whom, it was first really promulgated. In bringing such facts forward, it is requisite to disclaim the remotest intention of urging that full merit is not likewise due to those English writers who have either foreshadowed or extended the method in this country, and who, although not its first discoverers, were undoubtedly its improvers.

Since the loss occasioned by the reassurance varies with the mode of operation, it becomes interesting to inquire in which way the loss may be made the least possible. B is in the situation of a merchant who possesses a commodity not quite in a marketable state, and who seeks to bring it into a condition for sale at the least expense. A little reflection will show that the longer the borrowing is deferred, the less loss will B sustain, on account of the difference at interest; hence we must seek to diminish as much as possible the early payments, and to throw the weight of the premiums to a distant time—a scale of ascending premiums is thus the more advantageous for B.

In any Company or Society for the assurance of lives—let it be constituted in whatever manner it may—it is evident that certain rates of mortality and interest are always prevailing; and that such rates are more or less constant throughout any given period. as the causes on which they depend are more or less stationary.

The discovery of some general Law of Mortality, by means of which the values of the contingencies, depending upon human life, might be expressed in some simple formulæ, without the necessity of performing the numerous calculations which are required even for the chances of a single life, and still more in the various eases, in which two or more lives are involved, has occupied the attention and labours of many scientific men. But the result has not hitherto been satisfactory, in spite of the skill with which their investigations have been conducted, and the unwearied patience which they have brought to the task. The failure has probably arisen from the want of a sufficient number of observations, the authenticity of which could be relied upon; or for want of that accuracy in the data, without which it is in vain to attempt to find the traces of a regular law, disturbed as it must be by the peculiar circumstances under which the observations were made, or by the ignorance, and, in some cases it may be, by the wilful errors of those who have been employed to collect the facts.

Let be the given function, then, by a well known theorem

the integral of which, since u0, δu0, δ2u0, &c., are constants, and

will be

which differs from (A) only by the coefficients of δu0, δ2u0, &c, being shifted each one place to the left.

Having been favoured by Mr. W. T. Thomson with a copy of his large Table, “Carlisle 3 Per Cent.,” and believing that the insertion of a notice of such laborious and useful computations as are brought together in that extensive work is in accordance with the objects of the Assurance Magazine, I beg to offer a brief explanation of some of the most important features of the Table; and such notice will afford an opportunity of referring to particulars which it appears desirable to annex to those submitted in my former paper.

The term scholar, as current in the English language, has two extreme acceptations, tyro and proficient; or what the later Greeks fancifully termed the alpha and omega of acquirement. If we attempt to trace the steps by which even the adult student of any especial branch of professional or literary knowledge has fairly passed the boundary defined by the one meaning in passing on to that position denoted by the other, it will commonly be found, that in place of that lucid order, that straight line from point to point, which theory and resolve generally premise, the real order of acquirement has been desultory—the real line of progression, circuitous and uncertain.

Having, in our preceding Number, endeavoured to lay down what appears to us to be a correct method of procedure with reference to the determination and division of surplus, we now proceed to consider the modes usually adopted for the return of it to the contributors.

The third question proposed to Mr. Sang is as follows :—

B, aged 30, requires an advance of £100 ; and in consideration thereof, offers to pay to the lender an annuity during his life after A’s death. Required the annuity to be demanded, and the sum to be assured.

The point here proposed for consideration is not the mere amount of the annuity to be charged, the computation for which is sufficiently simple, but the nature and amount of the assurance.

That the mean duration of life amongst the indigenous inhabitants of one part of the globe differs more or less from that which obtains amongst those of other parts, there is every reason to believe. It is probable that a difference exists even when comparing the most civilized nations of Europe one with another; and still more may we look for discrepancies when we carry our investigations amongst the natives of more remote and less civilized lands.

The question as to the liabilities arising upon the destruction of property by a fire which has originated through negligence, is one of considerable importance, both to the public and to Insurance Offices; and as it appears that the vulgar notions afloat upon it, by no means tally with the law, and have, nevertheless, their origin in no less an authority than that of Sir William Blackstone, it may be a matter of interest to the readers of this magazine to investigate the subject.

In laying before the members of the Institute of Actuaries this hasty sketch of the Progress of the Assurance of Life and Property on the Continent, I beg to offer a few words of explanation on what induced me to attempt it.

Understanding that several actuaries and managers of Foreign Assurance Companies were likely to be in England at this time, without any general acquaintance with, or means of introduction to, those who are engaged in similar pursuits and studies in this country, the council of the Institute were led to propose a general meeting and conference, and to offer to them the hospitality and attentions which, all classes and professions are vying with each other in paying to our distinguished foreign visitors.

We have been favoured by Mr. Thomson, the Actuary of the Standard Life Assurance Company, and one of the Vice-Presidents of the Institute, with a copy of certain cases submitted to Mr. Edward Sang, and of his opinion in reference thereto. The matters to which they relate are of so much practical importance, and the learning and ability of Mr. Sang are so well known, that we gladly avail ourselves of Mr. Thomson’s kind permission to publish them, and feel we need offer DO apology to our readers for giving them entire.

In the present paper it is intended to investigate the nature of mortality from Suicide, with a view to assist statists in estimating the value of life, and society in its endeavours to remedy so frightful an evil.

It is usual with Assurance Offices to make void policies which have lapsed from the above cause; and it was not until a very recent period that the justice of this proceeding was called into question,—especially when it is borne in mind that these risks are invariably calculated in the premiums.

In making this contribution to the spirit of advance which is characteristic of our age, the writer is fully aware of the danger of reforms. He remembers “the grace which antiquity can lend” even “to error;” and that by an almost universal instinct the Past is consecrated in the eyes of the Present. Thus, the half-lights and imperfections of our forefathers are clung to with a generous pertinacity. We endeavour to manage with the customs and remedies which sufficed for an early state of society, rather than frame new ones to suit the exigencies of our altered condition. In fact, to speak with Scaliger, we had rather eat acorns with our ancestors than bread with the men of our own generation.

Considering the undeniable importance of a conformity to correct principles in carrying out the processes which must he resorted to for the purposes above mentioned, it is not a little remarkable that no work exclusively on the subject has hitherto appeared. If we except Mr. De Morgan’s and Mr. Sang’s Essays and the Observations scattered through the writings of Mr. Babbage, Mr. David Jones, Mr. Samuel Brown, and one or two others, we believe it may be truly said that scarcely any allusion to it is to be found.

During the last session of the Institute of Actuaries, I had the honour to read a paper on the Value of the Principle of Selection as exercised by the Offices in granting Assurances upon Lives, and to submit some calculations which I had made with reference to that subject, in which calculations the lives admitted at particular ages were kept apart from others during their subsequent existence. I have now to offer to the Institute an extended set of Tables of a similar character; and, after stating the course which I have followed in constructing them, I shall make a few observations on the value of selection as exercised by the policy-holder against the Company.