a better conductor in confequence of that circumstance, and is thus enabled to convey the stroke to a greater distance.

Though the experiments and principles contained in this work are totally fubverfive of thofe produced by Mr. Wilfon; the Author does not make any particular application to these laft, but intends very foon to give to the world a direct refutation of the conclufions drawn' from Mr. Wilfon's experiments. We learn with pleafure, too, that the experiments and obfervations that he has lately made upon Leyden jars, &c. will be the subject of fome future publication. We fhall only add that, as the Author does not write to Tyros, but to proficients in the fcience of electricity, we think that, by aiming at too great precifion, he has in the prefent work fallen into verbofity and repetition; by which his meaning is frequently rather obfcured than illuftrated; and the bulk, and confequently price, of the work unneceffarily increased.

ART. V. The Doctrine of Annuities and Affurances on Lives and Survivorfhips, flated and explained. By William Morgan, Actuary to the Society for equitable Afferances on Lives and Survivorships. To which is added, an Introduction, addressed to the Society. Alfo an Effay on the prefent State of Population in England and Wales. By the Reverend Dr. Price. 8vo. 5 s. fewed. Cadell. 1779.

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THIS very ingenious performance is divided into three chapters, of the contents of which, and the Author's motives for publication, we cannot give a better account than that we meet with in a very curious Introduction by the truly learned and ingenious Dr. Price.

The first chapter contains an explanation of the nature of affurances on lives and furvivorships; together with a particular account of the fociety for making fuch affurances, and of the methods which have been taken to determine how far it has been hitherto a gainer by the bufinefs it has tranfa&ted.

The fecond chapter contains an explanation of the doctrine of life-annuities in general, and of the principles on which their values are calculated. At the end of this chapter, an account is given of a method of expediting all calculations of the values of life-annuities, which muft, I think, be very acceptable to all who have ever employed themfelves in making fuch calculations.'

In these two chapters Mr. Morgan has rendered the fubjects of which he treats as intelligible, to perfons who are unacquainted with mathematics, as the nature of them will admit. The whole is delivered in a manner independent of algebra, and, in general, in words at length, with a clearness and perfpicuity which we do not remember to have feen elsewhere.

The third chapter contains a complete account of the rules for folving all questions concerning the values (in fingle and annual payments) of all annuities, whether in poffeffion or expectation; and of

all

all reverfionary interefts depending on any one, two, or three lives, or on any furvivorships among them, either for terms or for perpetuity. Several of thefe queftions are incapable of being answered without entering into the abftrufeft parts of mathematics. Most of them have never been before anfwered; and yet there arifes, in many cafes, a neceffity of anfwering them, in order to determine correctly the value of reverfionary interefts depending on furvivorships; and fome of them are often occurring in practice, at the office whose bufinefs Mr. Morgan tranfacts. The folutions in this chapter alfo are given in words at length, with fuitable examples; but the mathematical investigations have been thrown together into an Appendix; where every rule or direction, about which any doubt can be entertained, is particularly demonstrated. Every competent judge who will examine this chapter, and compare it with the demonftrations in the Appendix, muft admire Mr. Morgan's attention and skill; and fee that it contains a valuable addition to this part of science.'

Mr. Morgan's motives for this publication are next affigned. They appear to be partly of a public, and partly of a private nature, in as much as they relate more particularly to the affairs of the fociety in whofe bufinefs Mr. M. is engaged.

Firft,' fays Dr. Price, in the course of the traffic of this kingdom, and particularly the law tranfactions of it, fuch questions as are contained in this work are continually occurring; and, in numberlefs cafes, it is impoffible to give right decifions, or to make an equitable diftribution of property, according to the real value of the different claims and interefts, without obtaining accurate answers to them. The experience of many years has taught me, that there are great mistakes committed in anfwering thefe queftions, by which means many perfons are injured in their property. It feems, therefore, that it may be of particular ufe to the public to be informed where they may apply for folutions that may be depended on; and, at the fame time, to be furnished with fuch an account of the rules and principles of calculation, mathematically demonftrated, as may remove every doubt, and be a fufficient direction to all who may chufe to employ themfelves in business of this kind.'

But this reafon alone, the Doctor tells us, might not have been fufficient to induce Mr. Morgan to undertake this laborious work. There was another, which, though of a more private nature, more immediately and more forcibly influenced him. It was his employment in tranfacting the bufinefs of the fociety, which affures all kinds of reverfionary annuities, and contingent interefts, dependent on the continuance of any lives, or any furvivorships of any lives beyond other lives. In carrying on this bufinefs the fociety profeffes to regulate its demands by calculations founded on ftrict mathematical principles. There is not any other fociety now exifting of the fame kind; and its business has been, for fome years, increafing fo faft, that it is already become an object of vaft importance to the public, and is likely foon to become of much more importance. It feems therefore necefiary that the Public fhould be fully informed

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formed of its ftate, the fecurity it offers, the principles on which it proceeds, and the method in which it makes its calculations and the great defign of this publication is to give that information-an information which is rendered the more neceffary by the multitude of bubble societies which were fome time ago established, and some of which are still exifting in this kingdom.

The Doctor then proceeds to inform us, that in confequence of fome propofitions which he made to the fociety about four years ago concerning the methods by which they then kept their accounts, and determined annually their profits; a more ftrict and determinate mode of doing each was adopted, by which means the fociety has ever fince been enabled to keep conftantly under its eye the true ftate of its affairs, the expences of management it can afford, the progrefs of the balance in its favour from year to year, and the clear amount remaining on hand of all the profits it has made from the time of its firft eftablishment.

In 1776, a particular inquiry was made into the state of the fociety, by the method which had been propofed by the Doctor, when it appeared that a much fmaller proportion of the perfons affured had died than the calculations fuppofed; and that the fociety poffeffed then a furplus of income (or an income more than was neceflary to enable it to make good its engagements, and to bear the expences of management) equal to 2400l. per annum, nearly, and a furplus of stock equal to 30,000 l. In thefe circumftances, the fociety, not willing to continue any exorbitant profits, determined to reduce all the payments for affurances on single lives one tenth. They likewife refolved at the fame time to return the whole overplus of the payments which had been made by the members, over and above those which they would have made had this reduction taken place at the time of their admiffion. Equitable as this latter measure appears, Dr. Price feems to think that a repetition of it might have a very pernicious tendency with refpect to the affairs of the fociety, and ought not to be adopted on any fimilar future occafion, let the ftate of the fociety be ever fo flourishing. We are however given to understand, that what is here faid relates only to future opportunities of making reductions in the terms of admiffion. The annual profits of the fociety confiderably exceeded the reduction, together with all the expences of management; and the fums which have been returned to the different members are short of the excefs of the furplus stock above 30,000l. which fum, together with the fucceeding annual profits, the fociety have placed out on intereft, as a fund to fecure it from any contingencies which may hereafter arife from feafons of extraordinary mortality, which would bring on the fociety extraordinary expences. This ftock, fo placed out, the Doctor

Doctor allows, must give full fecurity to the Public, and make the fociety a permanent benefit to it.-Dr. Price adds, When I fpeak of full fecurity, I must be understood to mean all the fecurity that property in the public funds can give. It is earnestly to be wifhed, that this was greater than it is; but though greater might be obtained, yet in an undertaking of this kind it is fcarcely reasonable to aim at it. The failure of the Public funds WILL be the commence. ment of a new era in this kingdom, of which, like the end of the world, we can now form no conception; and were every one to act with a view to its being fo near as perhaps it is, there would be an end of most of the bufinefs and traffic of the nation.'

While we reverence the great learning and extenfive abilities of Dr. Price, we cannot help lamenting, in fome degree, that foreboding fpirit which fo frequently leads him to turn the dark fide of our national affairs to public view. It has been asked, "What purpose can fuch fentiments, and fuch affertions, ferve? If the failure of our public funds be as certain as the Doctor seems to think it, they can answer no purpose whatever but that of bringing our ruin fafter on; and even if it be not, they may, by alarming the people more immediately concerned, induce them to act in fuch a manner as would render that dreadful calamity inevitable. Can Dr. Price reflect on the almoft numberlefs families which that tremendous period muft reduce, in an instant, from ease and affluence to the utmost extreme of penury and diftrefs, without trembling at the thought that he may have been the means of plunging them into it fome years before it would otherwise have happened, and poffibly, in fome measure, the cause why it ever happened at all?" In truth, weighty as we acknowledge the Doctor's opinion will be with many perfons, and is, in many cafes, with ourselves, we can by no means subscribe to the inference which he draws in this inftance; and we think that many fubftantial reasons may be urged why a national bankruptcy (which we fincerely with and hope is at a very great diftance), though it would undoubtedly lay many affluent families in ruins, and reduce numbers,

To this objection, however, Dr. Price may, perhaps, with great appearance of justice reply, "That he has not endeavoured to excite the apprehenfions of his countrymen, without having the most falutary ends in view; that he has, at the fame time that he warned us of our danger, pointed out the means of avoiding it, viz. by a timely reformation of our impolitic and ruinous public measures:" and he may add, "That, fo far, he has acted as did the good prophets of old, who, when they denounced the wrath to come againit a wicked people, exhorted them to avert the Divine judgments by REPENTANCE, and the amendment of their wICKED WAYS."-Thofe who do not totally diffent from the Doctor's political principles, and who do not form eftimates of a different and oppofite kind, will candidly allow to this apology its due weight.

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who now enjoy happiness and independence, to poverty and dif trefs, would not bring with it the confequence which he predicts; namely, the deftruction of trade. On the contrary, we are inclined to think, that in this would confift the only bright part of the picture. A calamity of the kind we are speaking of muft undoubtedly throw many adventurers into that track, who before were above it, as the only way in which they could hope to employ the ruins of their fortune in earning a livelihood, or in endeavouring to regain their former fituation and confequence. It must moreover be confidered, that the hand which annihilates the principal, wipes off the intereft alfo: the taxes, therefore, which have been levied to pay that intereft muft cease of course; the neceffaries of life which pay thofe taxes would return, in fome meafure, to their original value; the manufacturer could afford to work at a lower rate, and we should be enabled, by our misfortunes, to underfell our more wealthy neighbours; and who is it that does not fly to the cheapest market? Such, it seems reasonable to conclude, would be the confequences of a national bankruptcy to trade: what its effects would be in respect to arts and fciences,-on our confequence as a nation, -and, above all, in the calamities and miferies in which it would involve individuals, it is the duty of every good man (like Dr. Price) to pray that we may never know them.

The Doctor proceeds to make fome obfervations which particularly refpect the fociety in whofe bufinefs Mr. Morgan is engaged, many of which may alfo be very interefting to the public at large. And, firft, it appears, that the tables which the fociety ufe at prefent in making their calculations, are founded on the rate of mortality which happened amongst the inhabitants of London, taken in the grofs, during 23 years, from 1728 to 1750: a period of time which included two years, namely 1740 and 1741, of greater mortality than has ever been known in London fince the plague in 1665. In confequence of this, the values of affurances on lives are given in these tables fomewhat too high for the inhabitants at large even of London itself, and much too high for the better part of the inhabitants, The Doctor allows, that there were good reafons for the fociety's beginning with fuch tables; but he thinks, and in our opinion with great reafon, that as it is now eftablished in fome degree of fecurity, and has better grounds to go upon, it would be right to calculate and ufe new tables, founded on obfervations which will give the value of life-affurances, not among the bulk of people in London, where life is particularly fhort; but among mankind in general. And in order to this, he obferves, that the decrements of life at every age, as deduced by Dr. Halley from obfervations at Breflaw in Silefia, or thofe deduced by himself from the Bills of Mortality at Northampton

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