IN laying down the following considerations, I think it right to state most explicitly, that I intend no direct reflection upon any office now in existence, or whose establishment is contemplated. In a set of societies so numerous and varied as those in question, there must be details in one and another, of which any individual, who turns his attention to the subject, must disapprove ; but the studied exclusion of the name of every office whatwill, I hope, be taken as earnest of my desire to confine myself to the enabling other persons to discover the grounds of censure, without directing their attention to the quarter in which they are to be found. I have not much fear that any part of this chapter could have been misconstrued into allusion ; and perhaps even the present disclaimer may have no other effect than to make some imagine that there must be more meaning some-where than is openly expressed. Leaving such lovers of mystery to their search, I proceed to the subject be-fore me.

The avowed levellers in politics, a rare and scanty sect among educated persons, would have an argument of some force, from considerations of general expediency, if it could not be shown that any attempt to equalise property would be attended with a vast diminution of the fund itself, so that the great majority *

The only great alteration of property which is likely to be agitated, is the question of the national debt, the entire abolition of which is not with-out its advocates. This enormous sum, as it appears, is really little more than one year's income of the country, and perhaps not so much, if all the colonies be considered. The honesty of a sponge not being considered, there would still remain this question :—Would the ultimate loss occasioned by the subversion of such a debt, amount to a year's income of the country ? If so, there would be nu gain arising from the abolition of the debt.

would really have even less than they now possess, and also less facilities of increasing their stock. The differences of talent and of life would still remain, constantly working towards a restoration of the ancient inequalities, in which they would almost instantaneously show their power. A division of property, to be permanent, must be accompanied by a division of intellect, a division of manual skill, and a division of life; nor would the sum of the parts make up the whole in anyone of the four, except the last. A law which should tax the property of all who live beyond a certain time of life, to provide an addition to the maintenance of the widows and children of those who die before it, would not be so utterly imnor so pernicious, as an attempt at equalizaof fortune, intellect, or skill. Such a law would, however, fail in its operation, by the mere difficulty of arranging its enormous details, the frauds to which it would give rise, and the temptation to idleness which it would hold out to the young. A small community, consisting of members of known honesty, living under a government in which they reposed entire confidence, and possessing sufficient inducements not to relax in their exertions, by the certainty of a provision for their families, might live under such a law : and such comactually do exist, under the name of insurance companies.
If a large number of persons, all of the same income and prospects, and all certain of the same duration of life, were to choose a common bank in which to de-posit their savings, each laying by a given proportion of his income, it is obvious that each would receive the same sum as the rest at his decease ; but, if the lives were of unequal and uncertain duration, this result would no longer be produced. It might, however, be attained by a covenant, that all sums paid in should remain till all were dead, and then be equally divided among the executors of the parties. Such a bank might be called an equalization office, and it would present

the first approximation towards an insurance office such as those which at present exist.
As yet we have not mentioned the interest of money. Suppose the equalization office to pay no interest ; and suppose all the lives to be 20 years of age, such as are described in the Carlisle tables, the average duration of which is 41 years. If, then, every person pay 11. per annum, each will ultimately receive 41;1., which is the mere compensation of the inequality of life. Such per-sons would enter into a mutual covenant, by which those who live beyond the average term would divide the surplus of their savings among those who fall short of it.
Probably, if the following question were put to all those whose lives are now insured, What is the advantage which you derive from investing your surplus income in an insurance office ? more than half would reply, The certainty of my executors receiving a sum at my death, were that to take place to-morrow. This is buc half an answer ; for not only does the office undertake the equalization of life, as above described, but also the return of the sums invested, with compound interest.
No one can form an accurate idea of such an estawho does not consider it as a savings bank, yielding interest, and interest upon interest. This is the reason why an office which charges for its insurance more than it is worth, as an insurance, may nevertheless put its contributors in a better position than they could have held if there had been no such institution. To make this clear, let us consider the working of a simple investment office. A large number of individuals sub-scribe a sum, which they intrust to an individual or a company to employ., yielding them the return at some fixed, but distant, period. Let each share be 1001. The best thing which an individual could do with such a small sum, so as to have perfect security for its return, would be to invest it in the funds, at 3 per cent. He might also invest the interest, and thus obtain compound interest : but it is not easy for an individual to

do this. Unless he provide an agent to draw the dividends immediately on their becoming due, various circumstances will happen to prevent the immediate incuvestment of the interest. It is not at all an unfair calculation to suppose that, upon each half yearly dividend a month will be lost, so that nominal compound interest for 42 years will only be really for 35 years. A single pound, therefore, laid up by a man of 20 and improved for the average term of his life, at 31, per cent., would only become 3Al. ; while, in the hands of a person who lost no time, it would become 411., or nearly a pound more. On the other hand, a company, or a skilful individual who can command large sums of money, can always make the best interest which the market will afford. The funds, from the security of their tenure, and the conveniences which they offer, will always, in ordinary times, represent the lowest rate of interest which money will yield. Other investments, which offer better interest, are generally only accessible to those who can command considerable sums, and are frequently attended with risk; so that it requires know-ledge to distinguish between the sound and the unsound. A company, employing the whole time of a person or persons skilled in money matters, and having continual large investments to make, can realise not only more interest, but so much more, that there shall remain a surplus worth considering, after the skill employed has been paid for. It is not assuming too much to say that, all expenses paid, they can command 3— per cent. compound interest. More than this, they can obtain such interest without any delay in investing the interest. The process is extremely simple : it is not difficult to ascertain what sum should lie permanently at the banker^{'s, in order to meet current expenses, so that the banker has general directions to buy stock as soon as the balance in his hands exceeds that sum ; and all cash received is paid into the bank at the close of each day. Suppose it should happen that ten individuals paid lOW. into the office on account of life insurance premiums, in}

the same hour in which the executors of a deceased contributor received a claim of 1001. The hundred pounds, which, in the theory of the process, should be sold out, or otherwise set free, to meet the claim, is in its practice supplied by the new premiums, so that the premiums of those contributorsare making interest from the hour in which they are paid. But there is always an unemployed sum lying at the banker^{'s. This is true; but the interest of that sum is the salary of an officer of the institution, namely, the banker himself. Al] such expaid, I believe it may be stated, with correctness, that an investment office can net 3 per cent. compound interest. Hence 11., improved during the average life of an individual aged 20 years, would become 411.
The institution we have hitherto described is simply an office for the investment of premiums and the equalof results : it becomes an insurance office when it undertakes to pay a fixed sum for a fixed premium, at the end of a given time after the decease of the party. It then begins to incur a risk of a twofold character: in the first place, the lives which it undertakes to insure may not die, one with another, in or near the same manner as those from which the tables were constructed ; in the second place, the rate of interest, upon which it calculates the premiums, may be higher than it is after-wards able to obtain. According to the Carlisle table, the premium which should now be paid to insure 1001. upon the life of an individual aged 20, is one pound seven shillings, or 1.321., at four per cent. According to the Northampton table, and at three per cent., the same premium should be 2.21. Taking the first preand assuming its table, the office will not be sure of avoiding loss, until the party has lived 35 years; by which time the premiums, with their accumulated interest, will have passed 1001. It is a little more than 2 to 1 that a life of such an age shall live beyond 32 years after the contract. Taking the premium of the Northampton table, the party must live 28 years before the office can gain by him ; and it is about 10 to}

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7 that he will outlive this term. We have now to ask, What are the principles which should guide the office in the determination of its premiums, it being remembered that there is an absolute security required, and that the remote chance of bankruptcy, which is almost essential to the ordinary run of commercial affairs, is not to be encountered ?
The basis of the tables is the observation of the lives of a comparatively small number of individuals; it being well known that the value of life varies considerably in passing from one class of society to another. Now, we have seen (page 91.) that we cannot depend upon a law of probability, derived from a limited number of instances, with the same degree of confidence, as upon one which we know to exist a priori. If we were sure beforehand that the great average of life in England was according to the Northampton, or any other table, we might rely upon such a document as being extremely likely to exhibit, with small fluctuations, the future course of the lives of the two thousand or ten thousand persons insured in any given office. Let such a table be assumed, and let the premiums be so calculated, that it shall be a thousand to one against any ruinous amount of fluctuation, taking the law of the tables as that which will certainly prevail in the long run. Then return from the hypothesis to the truth, and, taking the numof lives from which the table was actually formed, say 5000, suppose another 5000 persons to have commenced an insurance office. The degree of fluctuation within which it was 1000 to 1 that the future results should be contained, is now larger than before, in the proportion of the square root of 2 to 1, or in that of 14 to 10, nearly. Larger premiums would then be required to make ruinous fluctuation as unlikely as upon the preceding supposition. These considerations, which may easily be reduced to calculation by the rules in chapters IV. and V., will serve to show that there may be danger in the assumption of any table formed from experience; and they ought to operate powerfully

as a caution against lightly admitting a change of preon the authority of any small number of facts. But more particularly should they be attended to in the formation of new varieties of contingency offices, the chances of which have not yet stood the test of excuperience.
But there are reasons why the premiums of an inoffice need not be so high as the very limited number of data in their tables might seem to require. If the fluctuations from the average, which are within the most cautious definition of reasonable probability, were all to be encountered at once, or might be en-countered at once, it is difficult to say what premiums should be considered as too high. But this cannot be the case, unless, indeed, a pestilence should single out time members of an insurance office, or an earthquake should, by one extraordinary event, swallow them all up in the place where, by a most remarkable coincidence, they were all assembled together. Such extreme cases are not worth consideration ; and we may take the chances of life and death as distributed over a large number of years. In the meanwhile the surplus fund increases at compound interest; and the problem is, not whether a given number of lives will, on the whole, drop so much before the predicted time that a given fund will be destroyed, but whether this can happen so fast, that it will outrun the increase of the fund at compound interest. If, indeed, there were compound mortality to set against compound interest ; that is, if the number of deaths must become larger from year to year, or if the rate of mortality were increasing, the fear of such a result might be entertained ; but^{. all experience is on the other side, and tends to show that the value of life is increasing, instead of decreasing.
' The tables of an insurance office must be considered as collections of limited data, the premiums deduced from which are increased by a percentage, to meet the possible fluctuations of mortality. As soon as these tables are formed, and the directors have published}

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their proposals, an insurance office is created, with all these fundamental characters already described, and which are but ill represented by the term. The word insurance or assurance has given rise to some wrong notions, and it will be worth while to examine the nature of the contract.
A and Co. engage with B that, in consideration of 11. a year, paid by him during his life, they will pay 201. to his representatives as soon as he shall be dead. Both parties run a risk ; A and Co. that of having to pay B more than they receive ; B, that of paying more than will at his death produce 201. But the risk of the office is of immediate loss, and that of B, of deferred loss : that of the former is also continually lessening, and that of the latter increasing ; until, should B live long enough, both risks become certainties. If the inbe only for a term of years, B runs the risk of losing his premiums altogether.
The office does not inquire what reason B may have for insuring his own life or that of another person, nor do any possible contingencies, except those of life, affect the office calculations. We cannot, therefore, be too much surprised at the ignorance shown by that judge* who declared that life insurance  was of its own nature a contract of indemnity ; that is to say, if, by any lucky chance, B can be proved to have accomplished the object for which he insured by other means, he has no claim upon the office. The circumstances are as follows ; and the absurd conclusion is law, and would be practice, if the insurance offices had not re-fused to acknowledge the decision, or protect themselves by the precedent. A and Co. covenanted with B to pay 5001., if C should die within the term of seven years next ensuing, in consideration of the usual preC did die within the term; and A and Co., in
Godsall' ^{v. Boldero.- See the report of the case in Mr. Babbage's Comparitive View of Institutions for the Assurance of Lives."
t He might have said that the law would refuse to consider an assurance in any other light ; but he was palpably wrong in asserting that the con-tract, as understood by the parties, was merely one of indemnity.}

answer to a claim of 5001., replied, that the intention of B in insuring the life of C, was to obtain security for the payment of a debt of 5001., due by C to B, which debt had been already paid by C^{'s executors : consequently they owed nothing to B. An action was brought by B, and defended by A and Co. on the above plea; and a special case being made, the point was decided by the court of King's Bench against the plaintiffs ; thereby establishing the principle, that life insurance is a thing similar to fire or ship insurance ; namely, a contract of indemnity, to be fulfilled with allowance for salvage.
The defendants' case rested upon the asserted nature of the contract, and the statute 14 Geo. III. c. 48., which enacts, that " no greater sum shall he recovered from the insurers than the amount or value of the interest of the insured in such life." The act does not state at what time this interest is to be reckoned, but the plaintiffs contended that the time of death was the meaning of the statute ; the defendants averred, and the court decided, that the time of bringing the action was to be understood. The plaintiffs contended that the debt was not the object of insurance, but the life of the insured ; the court decided, that " This action is, in point of law, founded upon a supposed damnification of the plaintiffs, occasioned by the death, existing and continuing to exist at the time of the action brought ; and, being so founded, it follows, of course, that if, before the action was brought, the damage which was at first supposed likely to result to the creditor were wholly obviated and prevented by the payment of his debt, the foundation of any action on his part, on the ground of such insurance, fails." This sentence contains nothing but very good sense, and, no doubt, very good law: but the application of it was accompanied by a mistake as to the nature of the damnification which the plaintiffs had sustained. The counsel on both sides, the court, the insurance office, and the plaintiffs themselves, showed a very partial knowledge}

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of the nature of the contract ; and I make no doubt, that almost every person who heard it agreed with the court, however much they might impugn the decision on other grounds, that the damage* to the creditor " was wholly obviated and prevented by the payment of his debt.^"

In order to show that such was not the case, we must suppose that an exactly similar transaction had taken place before any insurance office existed. How this could have been may not be apparent, if we take the notion which the law formerly entertained of such an office ; namely, that it is a species of gambling house : but if we prefer to consider it as a savings bank, with an equalization system (page 238.), which is unquestionably the correct notion, we may return to the circumstances which the case would have presented had there been no insurance. C, a person whose credit has become doubtful, is indebted to B to an amount which B could not afford to lose ; consequently, B, knowing that his chance of payment is precarious, resolves to diminish his expenses, hoping by economy to restore to his family the sum which he may have lost by his engagements with C. He collects, accordingly, a small fund, which he places with his banker, avowing the purpose of its collection. In the mean time C dies, and some friends pay off his debts, and that due to B among the rest. The latter having now no further occasion for such economy, draws upon his banker for the amount, and is answered, that, since the purpose of the saving was fulfilled by the payment of C's debt, he, B, has no further claim upon his own money. An action is brought, and the courts decide that the banker is right, and that B, having really attained his object in one way, has no right of property in the proceeds of another attempt to serve the same purpose.

The defendants paid into court a sum somewhat less than the amount of the premiums they had received from the plaintiffs, doubtless as a pre-caution, in case the court or jury should think the premiums ought to have been returned.

The only distinction between the case just put and that which actually occurred is, that the banker was a person who gained his profits by receiving such savings during a contingent term, and guaranteeing a fixed sum ; standing the loss, if there were any, and paying himself for it out of the gain which would accrue in another instance: the premium having been calculated so as to insure a moral certainty of profit upon the average of similar cases. It is not pretended, on either side, that the chance of indemnification at the hands of C^{'s executors was made to lessen the consideration paid by B for the guarantee; and the legal iniquity of the decision may, I think, be made clear, as follows : —}

It will hardly be disputed, firstly, that the legislature is the judge of what shall constitute valuable consideration ; and, secondly, that a consideration which is exallowed to be good in a statute, should be admitted as such in the decisions of the courts. Now, the contract of insurance, be it gambling, or be it not, rests entirely upon the permission given by the law to consider a high chance of a small sum as good consideration for a low chance of' a large sum. If I now pay 21. of premium for 1001., in case I should die in a year, and if my executors can maintain an action for 1001., it must he because the law sanctions the notion that 21., nearly certain, may, with consent of parties, be considered as an actual equivalent for a distant chance of 1001., as much so as one weight of silver for another of bread, or food, clothing, and wages for personal service. It is true that the same law, fearing certain reputed immoral practices, to which the power of making a particular bargain offers temptations, may limit the circumstances under which it will permit such bargains to be made ; but this is equally true in regard to the other sort of contracts mentioned : indeed, there is no sort of bargain which is not under regulation. The law, then, allows risks, and permits unequal chances to be compensated by giving odds ; the courts declare that, after the cast shall have

been made, and one of the parties shall have stood his risk, which turns out in his favour, the other party shall receive an ex post facto release from the conditions of his bargain, because circumstances afterwards arise, which, had they existed* at the time of making the bargain, would have made it illegal. The several principles on which the decision was founded, well carried out, as they say in parliament, would require that the previous contracts of a man who becomes insane should be null and void ; that the meat which a man buys for his dinner should be returnable to the butcher under the cost', if a friend should invite him in the mean time ; and, in the case before us, supposing that C should have outlived the term, and his debt were paid, as before, then B might have brought his action against the office, for the return of the premiums; alleging that, as it turned out, the office would have been indemnified, and, therefore, should be considered as having run no risk.
But, said the judge, the damage was "wholly " obviated and prevented by the payment of the debt. To try this point, let us make a debtor and creditor account of the whole transaction. The following is the way in which it will stand.

Certain small premiums Those same premiums re-paid to an insurance office, turned by the office, instead with imminent risk of their of 1500.

This is admitting more than is absolutely necessary ; for, unless there were mathematical certainty that a third party would step in and pay C^{ls debts, it is difficult to see how B's insurable interest would cease.}

ON THE NATURE OF INSURANCE.    249
The advantage of the moral security which a contract of insurance gives is obvious in the transaction which led to this decision; namely, the insurance of the life of a creditor by a debtor at his own expense. Commercially speaking, such a transaction is literally this: C owes 5001. to B, who, doubting his chance of payment if the debtor should die, buys 5001. from a third person, and makes believe that it is the 5001. which C owes him. Morally speaking, it is the determination of B to retrench his own expenditure, as soon as he finds that a part of his property consists in bad debts. This the office enables him to do in a manner which will make the retrenchment proportional to the necessity for it. In the mean time, it is much to be wished that the law of life insurance were settled upon a fixed basis, which should proceed upon such a definition of the contract as has been here explained, and not on the notions which have been drawn from a supposed analogy between It and the insurance of a ship or a house. The effect of the present state of the law is, that the offices have no law except that of honour, which, though it more than suffices for the protection of the insured, yet may at any time involve the offices in the necessity of paying really questionable policies, without having the means of submitting to open examination the point on which they wish to resist. Policies of insurance are sold daily to persons who have no interest in the lives of the insured parties, on the faith of the good conduct of the offices. If an office were to resist the payment of a policy so transferred, say on the ground of fraudulent representation, the parties so resisted might give out that the opposition of the office arose out of an intention to cover themselves by the present letter of the law. Neither could such a case be carried into court without proof that the plaintiffs possessed that insurable interest in the life of the deceased which the law requires.
The nature of the contract, both in law and usage, having been laid down, we must next ask what are the means which the offices employ to reduce the risk so as

to render themselves safe against fluctuation. The state of opinion upon this matter is somewhat unsettled; one party advocating the practice of approaching near to the line which separates security from insecurity ; another insisting upon what appears to the first a most superdegree of caution. Without expressing an opinion, I will describe the various risks, and the method of avoiding them which has usually prevailed.
1. The insecurity of data, that is, of existing tables of mortality. This divides itself into two parts ; that relating to the young and middle aged, and that relating to old lives. With regard to the first, the data might probably be obtained in sufficient numbers to justify a considerable degree of confidence in them as to the chances of a single life, or even of a considerable number ; but when the number of lives is to be as great as the number of persons who may choose to offer themselves, the considerations in Chapter IV., again adverted to in page 242, present themselves in force. I am not aware that any writer on the subject in this country has formally taken into consideration the uncertainty of tables, arising from their limited numbers, except Mr. Lubbock, who has made use of (Cambridge Phil. Trans., and Treatise on Probability Lib. Usef. Know.) the correction which the probability of living a given number of years should receive on that account. But, considering the probable errors of the data, this correction is small, and the question how far an office proceeding upon such data can deal with the public to any amount is yet in its infancy, though the necessity for its consideration is approaching, and it is one of vital importance to the interests of the middle and lower classes.
The constructor of tables of mortality draws a number of balls from an urn which contains an infinite number and, having sorted them into red, blue, black, &c. presents them to the world as a necessary representation (or very nearly so) of the proportions in which those colours are scattered throughout the whole urn. He commits an error which is in all probability very small,

and which has hitherto been carefully guarded in the deduction of office results. But there is a much more important question behind. Suppose the calculator had undoubtedly succeeded in exhibiting the real law of mortality, and that it were quite certain the next hundred million inhabitants of Great Britain would die in the manner pointed out in a table. In such a case, many will say, the office may charge the real premiums deduced from the table, with a very slight addition for expenses of management. They may leave the fluctuations to take care of themselves, and trust in the long run. This assertion I now proceed to discuss.
If the banker of a gaming_table were to follow the same plan, that is, if he were to stake against all comers with only just enough of advantage to cover expenses, he would infallibly be ruined at last. It might not be in this year nor the next, nor in this century nor the next; but ruined at some time or other he must be (see page 110, and also Appendix I.). If the case of the office managers were precisely analogous to that of the bankers of the gaming_table, I would repeat with as much confidence of the former what I have said of the latter. But, in the first place, the fluctuations of mortality are not, by very much, so great as those which take place in the assortment of cards, nor even so great as those which take place in harvests, in the price of provisions, &c. This is much in favour of the insurance office; but who can say how much?
In the second place, the fluctuations of mortality have of themselves a tendency to create opposite flucThus, a very sickly season carries off the weak, and deprives the succeeding years of those who were most likely to have died; causing, therefore, a season of remarkable health. This is a very important item in the theory of the fluctuations of mortality, and there is nothing similar to it in the case of the gaming house. It reduces annual fluctuation itself to a species of reguand is, perhaps, the sufficient reason for the slightof the total fluctuations.

In the third place, with a merchant or a banker, the liability to a demand and the demand itself come so nearly upon one another, that real insolvency and bankruptcy are never far asunder. When credit cannot be sustained by monthly, and even daily, proofs of substance, it takes its departure altogether : but it is not necessarily so with an insurance office, of whose existence it is the essence to be always receiving consideration for bills which, one with another, have a long time to run. Such an establishment, as will presently more distinctly appear, may be in reality insolvent many years before the symptoms of bankruptcy come on. As no large concern of the kind has hitherto failed, it is difficult to say how they would finally come on : but this much is certain, that an insurance office which could really pay only ten shillings in the pound might, by introducing a better system, or by mere force of circumstances, not only recover its ground, but ultimately become exceedingly profitable. But I throw this part of the argument (though it shows a strong principle of vitality inherent in the constitution of such offices) out of the question ; for, surely, no sane and honest person would trifle with important matters so far as to assert that the possibility of temporary insolvency, to be redeemed by the chapter of accidents, or prudence, when it was wanted, should enter into the deliberate calculations on which men should be invited to stake the subsistence of their children.
If the last contingency be rejected, that is, if it he held absolutely necessary to calculate on permanent solvency, both real and apparent, then I assert that there is not sufficient ground to gainsay the conclusion, that any insurance office charging only real* premiums (increased for expenses of management) must inevitably have its phases of solvency and insolvency, at the very best. Begin by considering the office as identical in principles with the gaming house, and beat down the

* By real premiums I mean those which only cover the risks of life.

certainty of ruin which is thus known to exist, if they play upon equality of chance, by allowing for the first two of the three preceding considerations. There must still remain more risk than it is safe to face of insolvency, either temporary or permanent. And though, in con-sequence of the smallness of the portion which the office risks upon one hazard, a very small mathematical ad-vantage might be sufficient, yet, so long as the necessity for such an advantage exists, and its absolute amount is unknown, so long must an office guard itself by requiring, in the first instance, a sensible addition to the real premiums.
With regard to the old lives, there is an additional ground of insecurity. Not only are the probable errors of the tables exceedingly large with respect to them, but, from the smallness of the number which will enter an office, there will be a liability to great flucin the results of transactions with them. The first circumstance would prevent the second from becoming ruinous, but at a risk of loss to the capital invested by younger lives : it is usual, therefore, to exclude all lives above a certain age from entering the office, upon the principle that no risks are to be taken of which the numerical amount is not well understood, and of which the number is not large enough to secure an average. But, since the tables of old lives are only a very unsatisfactory approximation, and since the premiums payable by young lives depend in part on the chances of those lives becoming very old, how does it happen that the insecurity of the latter part of the tables does not affect the premiums throughout? It does affect them, but not sensibly, for the following reason. If, assuming the Northampton table, we sup-pose a person aged 40 to insure his life, we see that the portion of the present value of his insurance which depends upon his dying in his 85th year is very small, on two accounts : firstly, because the chance of his living to the age of 84 is very small; and, secondly, because the present value of a sum to be received

45 years hence is small, compared with that of a sum now due, or receivable soon. This last consideration works as follows:—When a percentage comes to be added to the whole present value or to the premium deducible from it, for the security of the office, that percentage being made upon a much larger sum than the present value just mentioned, a very trifling deduction from the whole additional sum will cover a very serious mistake in the mortality of the older years. For ex-ample, in the Northampton tables, the chance of 40 living to 85 is about ,^I_o, and the present value of 11. due in 45 years is about 5s. at 3 per cent. From this it follows that 1001., to be paid if a person aged 40 dies after 85, cannot be worth so much as 1^{.251. But the present value of the whole insurance is 53.81. ; and if this be the real value, and 10 per cent. be added for security, then 5'381. is added ; so that if 1.251. were considered as added solely for the chances after 85 years, it follows that we might consider ourselves' as having allowed for not being able to calculate the chances on old lives within one half, and as having added 8 per cent. to the whole present value besides. Thus, it apthat our comparatively little knowledge of old life, though not unimportant, yet can be made to be of less importance than might have been expected by one who has not considered the matter. Of course, the preceding reasoning must be considered only as addressed to a person to whom, for any thing he sees to the contrary, it is of as much consequence to know the entire law of mortality in the insurance of young lives as of old ones.
There is one use of the table of old lives, by which an insurance office might make its existence very proto use a gentle term ; namely, by inverting the order of security, and selling guaranteed* benefits, which are to increase with the age of the party, and to be accumulated solely out of his premiums. To take}

an extreme case, suppose an office should name a prefor which it would undertake to pay 1001., if the party dies in the subsequent year ; 2001. if he dies in the second subsequent year ; 3001. if he dies in the third ; and so on. In this case, every fluctuation which bears the appearance of lengthened life, were it only to amount to deferring one death for a single year, would be a new claim of 1001. upon the office. The flucwhich are observable in the very old lives, would become matters of extreme importance ; and though, assuming a given table fairly to represent the average, premiums might be calculated which should be sufficient in the long run, yet there is no possibility of saying what capital might become necessary to meet the flucof half a century. Such an attempt as the preceding can be compared to nothing but gambling, and its stability to nothing but that of a ship running before the wind, with all the heavy cargo lashed to the topgallant mast. Other cases might be mentioned, which should partake of the same species of danger in a less degree; but every attempt to guarantee increased benefits with increasing life should be looked at with caution, as being of its own nature the addition of risks in which the errors of the unsafe part of the tables are, or may be, multiplied into importance. There is an opposite plan, which I am not aware has been tried, but which I should strongly recommend to any new insurance office, as being of a safe character, and also meeting the views under which many insure their lives. It is that of insuring decreasing sums, upon either fixed or decreasing premiums. Many persons are so situated, that they will be able to provide for their families if they live a few years. To provide for the hazardous period, they are under the necessity either of insuring for their whole lives, that is, of buying more insurance than they want; or of insuring for a fixed term of years, which does not meet several con; or of making complicated survivorship inBut, if a person so circumstanced found, by
256    ESSAY ON PROBABILITIES.
estimation of his income, that he should want 50001. if he died in one year, 48001. if he died in the second, and so on, it would be desirable that he should be able to insure for these several sums, contingently upon his dying in any of the several years to which they are made to belong. Various modifications of this scheme might be proposed, all having this difference from the usual plans, in that the lattcr enable a person to make a provision for his family, while the former would only supply the deficiencies which his death would leave in the proceeds derived from other sources. In an appendix (on the value of increasing annuities) will be found the method of calculating the present values of such insurances.
2. The possible fluctuations of the rate of interest. These may be either general and national fluctuations, or alterations in the value of the property held by the office. The former cannot be guarded against or predicted ; and, as the rate of interest has been slowly falling for centuries, there is some reason to suppose that this depreciation of money may continue. But this gradual sinking of the rate of interest may be only partly dependent upon the fall of profits, and part may be due to the increase of security. I question whether the political economist has found the historical materials for determining this most important element; namely, the extremes of interest at which loans were contracted in the different periods of our history. The legal maximum of interest, at the beginning of the reign of James I., was 10 per cent., and at the end of the cen6 per cent. But, at the beginning of the century, land was commonly bought at 20 years^{' purchase, and never at less than 16 years' purchase ; while at the end of the century it was still at 20 years' purchase. No method of proving such a point is better than the examination of the works on interest which appeared during the century. If, then, we suppose, with Adam Smith, and I believe with most others, that the changes in the legal maximum of interest followed, and did not
ON THE NATURE OF INSURANCE.    257
precede, those of the market, there is good ground for imagining that the diminution of the rate of interest between borrower and lender (from 10 to 4 per cent.) has arisen more from the increase of security than from any other cause. If such be the case, there is strong presumption that the fall is near its end. But, if the preceding surmise should not be well founded, and if (as was the case in Holland during a part of the last century) the rate of interest should fall until gocan borrow at 2 per cent., and others at 3 per cent., the change may happen in a manner which will seriously affect the insurance offices, unless it should come about so gradually that they will have time to introduce new premiums for incomers, and surplus to meet the claims of those to whom they are already engaged. It is, in the meanwhile, a question well worth the attention of those connected with them, what the causes have been which have determined the rate of interest, and the rapidity and amount of its variations.
The offices depend for the existence of their present system upon the national debt; and they are differently situated from the government which owes the debt, in that the engagements of the latter are all maxima, while theirs are minima. If the rate of interest should really fall, the government will have the means of reducing the interest of the debt, never to rise again ; while the offices have, in fact, guaranteed to their excustomers a rate per cent., which is never to fall during their lives. The rate assumed by the offices should, therefore, never be above that at which the government can borrow.
With respect to the second reason for a variation in the rate of interest, as experienced by the office, namely, a depreciation in its own property, such an establishnot being allowed to run the usual risks of mercantile life, should not deal in any but the most secure investments, and those which depend on the personal security of others should be altogether avoided. The only point which it is incumbent to mention, in}

addition to general cautions, is a mistake to which such offices are subject in the valuation of their property ; namely, the estimation of different items by their reputed worth, or by the price which was given for them, instead of the actual income which they produce. We shall see the effect of such a mistake in considering the proper method of inquiring into the state of their affairs.
The precedent are the contingent risks to which an office is subject : its certain expenses are the ordinary charges of management, including rent, salaries, interest of sums lying at the banker^{'s, &c., advertisements, and the commission, as it is called, which most of the offices pay to those who bring them business.
Commission, in general, means either a per centage paid to a factor for the transaction of business, or a voluntary relinquishment in favour of the person who brings business of a part of the profit which the said person, being honourably free to choose between one competitor and another, has brought to the trader who, there-fore, allows the commission. It answers to the profit which the retail dealer is allowed by the wholesale merfrom whom he buys. But, when an insurance office announces to the solicitor, attorney, or agent of a party desiring to insure, that they will allow him a liberal commission, the term has a different meaning. As between one office and another, the attorney is in a judicial capacity ; and, as regards his client, he is already the paid protector of the interests of another per-son. He has, therefore, no liberty of choice between one office and another, but is already bound to choose that which he judges best for his client. All who have written on the subject of late years have attacked this bribe, for such it is ; but they have directed all their cenagainst the offices, as if they were the only parties to blame. If, indeed, the bribe had been offered to the needy and ignorant only, this partial distribution of blame might have been allowed; but when the parties who receive the bribe are men of education, and moving
ON THE NaTURE OF INSURANCE.    259
in those professions which bring the successful to afflu_ ence, I do not see the justice of allowing them to escape. I have little doubt that an increasing sense of right and wrong will banish this unworthy practice, either by failure of givers or receivers. A barrister cannot offer an attorney commission on the briefs which he brings, nor can a physician pay an apothecary for his recommendation ; a jury never receives a hint that the plaintiff will give commission on the damages which they award ; and the time will come when the offer of money to a person whose unbiassed opinion is already the property of another, will be deemed to be what it really is, namely, bribery and corruption. It is one among many proofs how low is the standard of collective morality ; and how easy it is for honourable individuals to do in concert that from which they would separately shrink.
It appears, then, from all which precedes, that the ordinary risks of an insurance office are alterations of, and mistakes in determining, the rate of mortality, and reduction of the rate of interest : which are guarded against by assuming a rate of mortality beyond all question greater than exists, and a rate of interest below that which the funds will yield. At the peace of 1815, every insurance office used the Northampton table at 3 per cent. This was at a time when the real rate of interest was higher than at present, and the offices must have made considerable profit. It was well known that they did so ; and, accordingly, new offices were formed, and have continued to be formed up to the present time, some upon lower premiums than others, and most of them returning all or part of the profits to the insured. At the same time, an opinion has become very prevalent, that it is possible for such offices to maintain their ground at much lower rates of premium than those in use ; a notion which I proceed to examine.
Mr. Finlaison, whose experience in such matters is well known to the public, and for whose opinion I ena high respect, stands foremost among those who contend for low rates of premium, having pub-.}

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lished a table, which he certifies to be " abundantly safe and practicable,^{" and Q° so high as to insure, beyond all doubt, a surplus of profit ;" which table charges preat the ages in which most insurances are made, falling short of those actually in use about 15 per cent. These premiums are supposed not chargeable with the management of the office, and at a rate of interest of 3,'1 per cent. I take Mr. Finlaison's proposition as a modified one, for there are some which go beyond it.
On the other hand, the late Mr. Morgan could never be persuaded that it was safe to abandon the Northtable ; and considered that the superior vitality of the members of the Equitable was altogether a con-sequence of their being select lives. He seems to have thought that, whatever run of success an office might have, it should always be on the look out for reverses; and that even the enormous accumulations of his office were no more than the seven good harvests, a provision for other seven of a different character.
In holding an opinion which comes between that of these two authorities, I form it on a ground on which neither would have rested the truth or falsehood of his own. I consider the fluctuations of mortality as very little to be feared, compared with those of the rate of interest. It has long been matter of observation, that the phenomena of the natural state of man vary but little compared with those of his social condition. The price of provisions swings to and fro like a pendulum ; the variations of mortality which follow its changes, though sensible, bear no proportion to the magnitude of their cause. The rate of interest has been halved within the memory of man, and a heavy war might double it again. That same war, with all its casualties, direct and indirect, included, would not alter the morof the country by any serious amount. I consider it, then, as next to certain, that the insurance offices have more to look for, whether as matter of hope or fear, from the fluctuations of the rate of interest, than from those of mortality. If the interest of money
ON THE NATURe OF INSURANCE.    261
could be made as stable as the duration of human life, I could then see no objection to an immediate and considerable reduction of the premiums charged, to an amount at least equal to that proposed by Mr. FinlaiBut here lies the difficulty; that these tables, at 31 per cent., already involve a rate of interest which the office cannot much exceed, if at all ; so that the secu_ rity which the precautions, nominally made against morreally afforded against fluctuations of interest, is partially or wholly destroyed, while no safeguard is introduced to supply its place.
An office raises its premiums either because its prenotions of existing mortality were wrong. or be-cause it finds that it had calculated upon too high a rate of interest. A mistake on either of these points might be compensated by a contrary mistake as to the other. Now, though the offices which existed during the war have demonstrated that the mortality and rate of interest together yielded a large profit, it by no means follows that one of those causes of profit may be fully corrected, while the other has been correcting itself. To make both perfectly accurate, would bring the office to the very line which divides security from insecurity ; a position which it would not be safe to endeavour to maintain. We are already in a very different position as to the rate of interest, which has been gradually falling since the war. The opinion as to the extent to which tables of mortality may be safely corrected, is formed upon arguments which dwell on the favourable rate of mortality, without sufficiently considering the counterpoise (for, as far as it goes, it is a counterpoise) existing in the alteration of the value of money.
Assuming the necessity of calculating upon a rate of interest something less than that which can actually be attained, I should think that no office would be justified in supposing more than 3 per cent., with tables which are sufficiently high to come any ways near to the actual experience of mortality. With regard to one}

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262    eSSAY ON PROBABILITIES.

point, and that of fundamental importance, namely, the possibility of a still further fall in the rate of interest, it may even be doubted whether, with such tables, a still lower rate of interest should not be allowed. But I am not here advocating one result or another, but only the necessity of taking into consideration all the possources of danger. To those who would use tables of greater vitality, I concede that, so far as mortality alone is concerned, the alteration is admissible; and for this reason, that experience shows human life to be of a higher value than formerly ; but the concession is accompanied by the requisition of a lower rate of interest, and for the selfsame reason, that experience shows the value of money to be less than it was.

The preceding conclusion is reinforced by the consideration, that the worst is to be made of every circumstance in our previous calculations. When moris diminishing, the whole diminution is not to be allowed ; but when it is increasing, a larger increase is to be contemplated. A person who would walk dry_ shod on the sea shore, must not advance so fast as the

. ebb, and must retreat faster than the flow. Upon this consideration, the necessity of providing for a further fall in the interest of money is increased ; or, which amounts to the same thing, the amount by which the favourable alteration in the rate of mortality may be allowed to affect the premiums is less than it would be it .t were certain that the value of money would remain unaltered.

A very common security or guarantee to the public is the announcement of a large subscribed capital, either paid up in whole or part, or liable to be called for. This is equivalent to the personal security of a number of shareholders, collectively making themselves answerable for the engagements of the office up to a certain amount. Such a provision in itself is an obvious good; but, it being remembered that this security must be paid for, it becomes a question how much it is worth, and whether it may not be bought at too high a price. It is easily