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a better conductor in consequence 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 subverfive of those produced by Mr. Wilson; the Author does not make any particular application to these Jalt, but intends very soon to give to the world a direct refutation of the conclufion's drawn' from Mr. Wilson's experiments. We learn with pleasure, too, that the experiments and observations that he has lately made upon Leyden jars, &c. will be the subject of some future publication.- We shall only add that, as the Author does not write to Tyros, but to proficients in the science of electricity, we think that, by aiming at too great precision, he has in the present work fallen into verbosity and repetition; by which his meaning is frequently rather obscured than illustrated ; and the bulk, and consequently price, of the work unnecessarily increased.

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ART. V. The Doctrine of Annuities and Asurances on Lives and Survi.

vorfpips, flated and explained. By William Morgan, A&tuary to the Society for equitable Asurances on Lives and Survivorships. To which is added, an Introduction, addrefled to the Society. Also an Effay on the present State of Population in England and Wales. By the Reverend Dr. Price. 8vo. 55. fewed. Cadell.

1779. 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 assu. rances on lives and survivor!hips; together with a particular account of the society for making such assurances, and of the methods which have been taken to determine how far it has been hitherto a gainer by the business it has transacted.

The second 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-anouities, which must, I think, be very acceptable to all who have ever en ployed themselves in making such calculations.'

In these two chapters Mr. Morgan has rendered the subjects of which he treats as intelligible, to persons who are unac. quainted 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 perspicuity which we do not remember to have seen elsewhere.

· The third chapter contains a complete account of the rules for folving all quetions concerning the values (in fingle and annual pay. bents) of all annuities, whether in pofleflion or expectation; and of

all

all reverfionary interests depending on any one, two, or three lives, or on any survivorships among them, either for terms or for perpetuity, Several of these questions are incapable of being answered without entering into the abstruselt parts of mathematics. Most of them have never been before answered ; and yet there arises, in many cases, a necessity of answering them, in order to determine correctly the value of reversionary interests depending on survivorships ; and some of them are often occurring in practice, at the office whose business Mr. Morgan transacts. The solutions in this chapter also are given in words at length, with suitable 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 demonstrations in the Appendix, must admire Mr. Morgan's attention and skill; and see 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 society in whole business Mr. M. is engaged.

• First,” says Dr. Price, in the course of the traffic of this kingdom, and particularly the law transactions of it, such questions as are contained in this work are continually occurring; and, in numberless cases, it is imposible to give right decisions, or to make an equitable diftribution of property, according to the real value of the different claims and intereits, without obtaining accurate answers to them. The experience of many years has taught me, that there are great mistakes committed in answering these questions, by which means many persons are injured in their property. It feems, there. fore, that it may be of particular use to the public to be informed where they may apply for solutions that may be depended on; and, at the same time, to be furnished with such an account of the rules and principles of calculation, mathematically demonstrated, as may remove every doubt, and be a sufficient direction to all who may chuse to employ themselves in business of this kind.'

But this reason 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 transacting the business of the society, which assures all kinds of reverfionary annuities, and contingent interests, dependent on the continuance of any lives, or any survivorships of any lives beyond other lives. In carrying on this bufinels the society profesies to regulate its demands by calculations founded on strict mathematical principles. There is not any other society now existing of the same kind; and its business has been, for some years, increasing so fast, that it is already become an object of vast importance to the public, and is likely foon to become of much more importance.

It seems therefore necesiary that the Public should be fully in2

formed

formed of its state, the security it offers, the principles on which it proceeds, and the method in which it makes its calculations : and the great design of this publication is to give that information-an information which is rendered the more necessary by the multitude of bubble societies which were some time ago established, and some of which are still existing in this kingdom.

The Doctor then proceeds to inform us, that in consequence of some propositions which he made to the society 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 society has ever since been enabled to keep constantly under its eye the true state of its affairs, the expences of management it can afford, the progress 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 first eftablishment.

In 1776, a particular inquiry was made into the state of the fociety, by the nethod which had been proposed by the Doctor, when it appeared that a much smaller proportion of the perfons affured had died than the calculations supposed ; and that the fociety poffefied 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 2400 l. per annum, nearly, and a surplus of Itock equal to 30,000 l. In these circumftances, the society, not willing to continue any exorbitant profits, determined to reduce all the payments for assurances on single lives one tenth. They likewise resolved at the same 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 admission. Equitable as this latter measure appears, Dr. Price seems to think that a repetition of it might have a very pernicious tendency with respect to the affairs of the society, and ought not to be adopted on any similar future occafion, let the state of the society be ever so flourishing. We are however given to understand, that what is here said relates only to future opportunities of making reductions in the terms of admission. The annual profits of the society considerably 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 excess of the surplus stock above 30,000 l, which sum, together with the succeeding annual profits, the society have placed out on interest, as a fund to secure it from any contingencies which may hereafter arise from seasons of extraordinary mortality, which would bring on the society extraordinary expences. This stock, fo placed out, the 5

Doctor

Doctor allows, must give full security to the Public, and make the society a permanent benefit to it.-Dr. Price adds, "When I speak of full security, I must be understood to mean all the security that property in the public funds can give. It is earnestly to be wished, that this was greater than it is; but though greater might be obtained, yet in an undertaking of this kind it is scarcely reasonable to aim at it. The failure of the Public funds will be the commence. ment of a new æra 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 so near as perhaps it is, there would be an end of most of the business and traffic of the nation.'

While we reverence the great learning and extensive abilities of Dr. Price, we cannot help lamenting, in some degree, that foreboding spirit which so frequently leads him to turn the dark side of our national affairs to public view. It has been asked, “ What purpose can such fentiments, and such affertions, serve? 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 such a manner as would render that dreadful calamity inevitable. Can Dr. Price reflect on the almost numberless families which that tremendous period muft reduce, in an instant, from ease and affluence to the utmost extreme of penury and distress, without trembling at the thought that he may have been the means of plunging them into it some

years before it would otherwise bave happened, and possibly, in some meafure, the cause why it ever happened at all *?". In truth, weighty as we acknowledge the Doctor's opinion will be with many persons, and is, in many cases, with ourselves, we can by no means subscribe to the inference which he draws in this ina ftance; and we think that many substantial reasons may be urged why a' national bankruptcy (which we fincerely with and hope is at a very great distance), though it would undoubte edly 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 same 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, so 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.”—Thole who do not totally diffent from the Doctor's political principles, and who do not form estimates of a different and opposite kind, will candidly allow to this apology its due weight.

who

who now enjoy happiness and independence, to poverty and dirtress, would not bring with it the consequence which he prediets; namely, the destruction of trade. On the contrary, we are inclined to think, that in this would consist 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 situation and consequence. It must moreover be considered, that the hand which annihilates the principal, wipes off the intereft allo : the taxes, therefore, which have been levied to pay that interest must cease of course; the necessaries of life which pay those taxes would return, in fome measure, 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 consequences of a national bankruptcy to trade : what its effects would be in respect to arts and sciences,-on our consequence as a nation,

and, above all, in the calamities and miseries 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 fume obfervations which particularly respect the society in whose business Mr. Morgan is engaged, many of which may also be very interesting to the public at large. And, first, it appears, that the tables which the society use at present in making their calculations, are founded on the rate of mortality which happened amongst the inhabitants of London, taken in the gross, 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 since the plague in 1665. In consequence of this, the values of affurances on lives are given in thele tables somewhat 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 reasons for the society's beginning with fuch tables; but he thinks, and in our opinion with great reafon, that as it is now established in some degree of security, and has better grounds to go upon, it would be right to calculate and use new tables, founded on observations which will give the value of life-affurances, not among the bulk of people in London, where life is particularly thort; but among mankind in general. And in order to this, he observes, that the decrements of life at every age, as deduced by Dr. Halley from observations at Breslaw in Silesia, or those deduced by himself from the Bills of Mortality at Northampton

and

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