On the Inequitable Operation of the Property and Income Tax Enactment as regards Life and other Interests; and on the Principles by which Direct Taxation should be regulated

The mode in which the Property and Income Tax of this country is levied, has created so much dissatisfaction, and is so universally acknowledged to be inequitable, that I am induced to call the attention of the Members of this Institute to the subject, with a view to arrive at some elucidation of the principles upon which direct taxation should be based: being satisfied that there is no tribunal before which the consideration of such a matter could be more properly brought, or where its peculiar features could be more thoroughly and efficiently investigated.

On the Value of Selection as exercised by the Policy-holder against the Company

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.

On a general method of approximation to the Values of Annuities and Assurances, for long terms of years, depending on One or Two Lives

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 cases, 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.

On the Value of Selection Among Assured Lives, and its Effect Upon the Adjustment of a Scale of Premiums, as Between Persons Assuring at Different Ages

I cannot better introduce the subject of this paper than by a quotation from Mr. Morgan's Preface to his Tables of the experience of the Equitable Society. He writes as follows, viz.:—“In a body of lives of the same age, all selected as healthy from the general mass of mankind, it is obvious that the rate of mortality must be considerably less for the first ten or twenty years after selection, than amongst those from whom they are thus chosen. As, however, these selected lives advance in age, their general health and the rate of mortality amongst them will naturally approximate to the common standard.

On Methods of Approximation

To discover in the doctrine of life contingencies, convenient, and at the same time nearly true approximations, to be employed in determining the values of Survivorships, instead of the long and complex formulæ at present required for their solution, is an inquiry of no small importance to the practical actuary, more especially when it is remembered, that, even if the exact formulæ be employed, the results will in the greater number of cases be themselves mere approximations, in consequence of the defective nature of some of the elementary values employed in the solution

On the proper Allowance to be made for the Surrender of Policies of Assurance

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.Now, the annual amount required by any such Company to meet its engagements, will entirely depend upon the particular rates which happen to obtain in it; and hence it becomes a question of the utmost importance to such bodies, to determine as nearly as possible how they are situated in this respect.

On the Values of Annuities, which are to pay Certain given Rates of Interest on the Purchase Money During the Whole Term of Their Continuance, and to replace their Original Values, on their Expiration, at Certain other given Rates

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.It is not unfrequently imagined by a buyer, that if he purchase a leasehold property or a temporary Annuity at a price corresponding with the value of an Annuity at a given rate of interest, (say 5 per cent.,) that he has made a purchase which will pay him 5 per cent., or which, in other words, will enable him to spend 5 per cent, per annum on his outlay, and at the same time replace his capital undiminished at the expiration of the term.

On the Rates of Premium to be charged for Assurances on the Lives of Military Officers serving in Bengal

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 climate, extent of cultivation, modes of life, state of public morals, each and all of them have a tendency to affect the longevity of the human race, and will not fail to make their influence felt in proportion as their good or evil energies are called into existence.

The Practice and Experience of the Clerical, Medical, and General Life Assurance Society, chiefly with reference to Invalid Lives

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. In the absence of any trustworthy data which might serve as a guide, the projector considered that the object in view could be accomplished, with safety, only by the aid of more extended and diversified medical knowledge than was obtainable by Offices dependent on the unassisted judgment of one or two Medical Examiners. In forming the Board of Directors, therefore, he expressly provided, that of the 17 gentlemen of whom it was composed, 8 at least should be members of the Medical Profession.

On a New Method of Constructing a Table of the Probabilities of Survivorship between Two Lives for every Combination of Ages, and also a Table of the Present Value of Survivorship Assurances of £1 on (x) against (y)

The present paper was undertaken on happening to peruse very lately Messrs. Gray, Smith, and Orchard's laborious and useful work, entitled Assurance and Annuity Tables, according to the Carlisle rate of Mortality, at 3 per Cent. In the introductory section of that work, when referring to the larger Tables V. and VI., containing the single and annual premiums for survivorship assurances, it is there very justly remarked, “Considering the frequency with which occasion arises for the functions here tabulated, and the tedious nature of the operations requisite when their values have to be formed from other tables, it may, at first sight, seem.