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therefore, to expect that his Comparative View' would throw considerable light on an obscure and complicated subject, and were prepared indeed for close mathematical reasoning, deep research, and new algebraic formula for facilitating the various calculations required to obtain correct results in all things relating to Assurances on Lives. Nothing of the kind, however, appears in the book now before us; but in lieu of all this, a plain statement of facts, most of which, as the author observes, had been already, in some shape or other, before the public. In short, Mr. Babbage avows himself to have been induced to bring forward the subject in a popular form, from having had occasion to observe how very imperfectly the merits of the numerous and complicated institutions for the assurance of lives were understood, even by persons otherwise wellinformed. The design is, without question, entitled to praise ; and not less so, on the whole, the manner in which Mr. B. has executed his task, though it is neither free from the occurrence of mistakes, nor from the charge of omissions. The style is plain, and his statements sufficiently clear and intelligible to the commonest reader. The book is, in fact, well calculated to convey important information on a subject in which vast numbers are interested. It requires only to be generally known to become generally useful,-if it were but that it must give rise to further inquiries; and, in aid of this view, we shall embrace the opportunity to draw up a brief and popular sketch of the system and practice of assuring lives at the various offices for conducting that business.
Few of our readers, in all probability, can need to be told, that an Assurance on Life is the assurance that a certain sum of money will be paid on the event of the death of a certain person named, either within a specified number of years, or (as is more generally the case,) immediately after his decease, in consideration of paying at once, or annually, a certain sum; the party contracting to make such payment being called the assurer, the payment the premium, and the instrument binding the contract the policy of assurance. It will be evident, that the amount of the annual payment, or premium, must be proportionate to the age of the assurer, and the sum to be assured to his executors.
The uncertainty of the duration of human life, proverbial as regards an individual, is not applicable to an aggregated multitude of individuals. If, for example, we take the population of a large city, or of a whole kingdom, the uniformity in the number
singular and most ingenious contrivance. These machines not only make the calculations for which they are set, but are so framed, that "they themselves shall take, from several boxes containing type, the number which they calculate, and place them side by side; thus becoming at the same time a substitute for the compositor and the computer; by which means all error in copying, as well as printing, is removed."
of deaths among the inhabitants is such, that the excess or diminution in any one year, above or below the average number, seldom exceeds a small fractional part of the whole; say, from one-thirteenth to one-fifteenth part-this deviation from the average will be less, in proportion as the aggregate multitude is greater; and if from this multitude be excluded the aged, the infants, and those portions of the population which are most exposed to the casual effects of disease and want, the variations from the mean number of deaths will be still less.
Thanks to long experience and attentive observation, it is now no longer a difficult problem to find the probability of the duration of human existence, at any given period of age; and hence to calculate what sum of money, paid annually, by a person of such an age, during life, will be equivalent to a certain sum to be assured to his executors after death. Various tables have been constructed to shew this, by inspection; but that which is formed from observations on the duration of human life among the inhabitants of Northampton, has for many years been the basis of the premiums taken by most of the Assurance Companies; some few of them have employed, with certain modifications, the observations on the mortality among the inhabitants of Carlisle; while others have constructed for themselves tables, of which it is difficult to say from what source they are taken. 'Many offices,' says Mr. Babbage, seem to have arbitrarily altered those of the Equitable (the Northampton) according to their own fancy. For several of these it would be difficult to find any table of mortality which should represent their premiums; but the University Assurance Society stand unrivalled in their ingenuity, and have succeeded in manufacturing tables which it is impossible to derive from any rates of mortality, real or imaginary.' This is not the only slur which Mr. Babbage has taken occasion to throw on this learned Assurance Company, which must necessarily boast, among its members, so many senior wranglers and optimists: but daily experience shews that, in conducting worldly affairs, mere abstract mathematicians are not among the wisest of mankind. The theorem of De Moivre, which makes the probability of human existence, at any given age, equal to half the complement of that age to 86, answers within a fraction to the Northampton table, excepting at the higher ages; and this simple rule is easy of application and well worthy of recollection.
Seeing, therefore, that the average mortality among a whole population will necessarily be much greater than that among a selection from it, composed of the middle and higher ranks of society, from which infancy, old age, poverty, and disease, are excluded (and such is the selection at all the Assurance Offices),
it follows, that the actual rate of mortality among assurers is much below that which appears by tables constructed for the whole population; and consequently, that the annual premiums required to be paid by the offices are very much higher than they ought to be in most of them the excess is about 30 per cent., or one-third nearly. It is from this overcharge,-from the calculations of the tables being made at three per cent., while the money received by the offices is lent out at four or five per cent.,from the interest derived from an accumulating capital,-forfeiture of policies, and some other petty sources,-that the profits of some of the Assurance Companies have become so enormous as they are. How these profits are disposed of we shall presently see. The Northampton tables,' says Mr. Babbage, are, of any which possess the slightest reputation, those least calculated to represent the probable rate of mortality among a body of insurers; they are tables which an experience of thirty years has proved to be (for this purpose) erroneous throughout a large part, in the proportion of two to one?' Yet fourteen of the Assurance Offices use these tables, so highly favourable to their gains, and so much the reverse to the assurers. Mr. Babbage, in lieu of them, would recommend the substitution of a table, actually constructed from the deaths occurring among a large body of persons of a selected class, such as is above mentioned. He observes that the records of the Equitable Society, which has been established above sixty years, and the Amicable, which has existed above a century, might of themselves furnish authentic materials for such a table. We doubt, indeed, whether, if an honest table of this kind were constructed, any of the Societies would make use of it, though a body of men, as those of the legal, clerical, or medical professions, officers of the army or navy, &c., mutually assuring each other, might employ such a table to much advantage to themselves, by reason of the great diminution of the premiums that would in that case be required. By the following illustration, the immense difference may be seen between making an assurance by such a table and by those at present in use:
The system of a mutual assurance society, in one of its simplest forms, may be illustrated by supposing it to consist of one thousand persons, each aged twenty, and in good health, and with such certificates of a good constitution as the Equitable Society would admit. Each individual should pay 17. 9s. 6d. to receive 100l. on his death. The premiums at the end of the first year, increased by the interest on them, would amount to 1468l; and the payments to be made on account of six deaths being deducted, would leave 868l. At the commencement of the second year the 994 payments of 17. 9s. 6d. each, added to the SGSI., would produce 2334/., which at the end of the year
would amount to 24041.; from this the claims due from the average number of deaths being substracted would leave 18041. The 988 payments of the next year added to this sum, would at the end of the third year, after deducting six claims, produce 27591. The capital of the society at the end of the first, second, and third years, would be as follows:'At the end of the 1st year 8681. after paying 600l. claims.
2d year 18041.
For many years this capital would continue to increase, until the sum arising from the diminished number of contributors would exactly pay the number of the annual claimants. After this, the annual income arising from the premiums being insufficient to pay the annual claims, a portion of the accumulated capital must each year be taken to make up the sum required for that purpose, until after about eighty years; when the remains of this fund, together with the premium paid at the beginning of the last year, will be just sufficient to pay the last claim.'-pp. xxii-xxiv.
'If we now suppose that the sum annually paid by each of the thousand assurers had been one-third larger, or 11. 19s. 4d. each, which is less than many Assurance Companies at present charge, (the Equitable is 21. 3s. 7d.) then, besides the sums already mentioned, the society would possess
At the end of the 1st year
2d year 3d year
The annual payments, before the additional third was taken, were sufficient to form a fund which would exactly pay all the policies as they became claims, and itself be exhausted on the payment of the last. If, therefore, the deaths took place in the manner supposed, no further sum of money would be required to meet all the demands, and these additional sums would be really profit; and, unlike the former, they will continue to increase until the last claim is paid.
At the termination of this society of mutual assurers there will, therefore, remain a large unappropriated capital.'-pp. xxvii-xxviii.
With such premiums, therefore, as are now demanded, a large excess of capital beyond the amount of the claims must, necessarily, in a very few years, accrue; and the practice of most of the Companies is to distribute a certain portion, or the whole, of the surplus beyond what may be necessary to satisfy the claims, at certain periodical intervals, among the assurers. The portion thus distributed is usually called a bonus, a term which is well understood, from the Chancellor of the Exchequer to the broker of 'Changealley, to mean a good thing,-so very good, we suppose, that it has been thought entitled to the honour of appearing in the most worthy gender.' This bonus is, however, strictly speaking, a return
of the surplus premiums with interest derived from them, and there→ fore belongs of right to the assurers. If the assurer was always certain of getting his just proportion of this good thing, either to be added to the amount of his policy, or applied to the reduction of his annual premium, it would be a matter of little moment at what office he assured his life; but as this is very far from being the case, we might almost say in any of them, it is of some importance that he should be in possession of circumstances, on which he may found his judgment in the selection of an office, wherein to make his assurance on the most favourable terms.
The following are the Companies for the assurance for lives, and insurance against fires, losses by shipwreck, &c. enumerated by Mr. Babbage: but the list is not complete.
These Companies may be considered as constituted on three different plans. The first is, where all the assurers for the whole term of life are mutually responsible. They participate in the profits, and are subject to calls to replace any loss or deficiency in the funds. This responsibility, however, is merely nominal, as