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its name of la Maison de Bain: above ffairs are the fame number of rooms; each of them fitted up in the most elegant manner. The King received us in the faloon with wonderful affability: : his brother and two of his nephews were prefent, and a few of the nobility of both fexes, who generally compofe his private parties. There were two tables for whift, and thofe who were not engaged at cards walked about, or stood at different fides of the room, while the King, who feldom plays, converfed occafionally with every one. At about half an hour after nine, fupper being announced, we followed the King into an adjoining apartment, where was a fmall round table with eight covers: the fupper confifted of one courfe and a deffert. His Majefty fat down, but eat nothing; he talked a great deal without wholly engroffing the converfation. After fupper we repaired to the faloon, part of the company returned to their cards, while we, out of refpect to the King, continued standing, until his Majefty was pleafed to propofe fitting down, adding "we fhall be more at our eafe chatting round a table." We accordingly feated ourfelves, and the converfation lafted without interruption, and with perfect eafe, till midnight, when the King retired. Before he withdrew, he gave a general order to a nobleman of the party, that we should be conducted to fee every object in Warsaw worthy of a ftranger's curiofity. This extraordinary degree of attention penetrated us with gratitude,

and proved a prelude to ftill greater honours.

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Auguft 5. We had the honour of dining with his Majefty at the fame villa, and experienced the fame eafe and affability of reception as before. His Majefty had hitherto talked French, but he now did me the honour to converfe with me in English, which he fpeaks remarkably well. He expreffed a great predilection for our nation: he farprifed me by his extraordinary knowledge of our conftitution, laws, and hiftory, which was fo circumftantial and exact, that he could not have acquired it without infinite application: all his remarks were pertinent, just, and rational. He is familiarly acquainted with our beft authors; and his enthufiaftic admiration of Shakfpeare gave me the moft convincing proofs of his intimate acquaintance with our language, and his tafte for the beauties of genuine poetry. He inquired much about the state of arts and fciences in England, and fpoke with raptures upon the protection and encouragement which our fovereign gives to the liberal arts, and to every fpecies of literature. After we had taken our leave, we drove round the wood to feveral other villas, in which the King occafionally refides. They are all conftructed in different ftyles with great tafte and elegance. His Majefty is very fond of architecture, and draws himfelf all the plans for the buildings, and even the defigns for the interior decorations of the feveral apartments."

(To be continued.)

ART. CI. The Principles of the Doctrine of Life-Annuities; explained in a familiar Manner, fo as to be intelligible to Perfons not acquainted with the Doctrine of Chances; and accompanied with a Variety of new Tables of the Values of fuch Annuities, at feveral different Rates of Intereft, both for fingle Lives and for two joint Lives, accurately computed from Obfervations. By Francis Maferes, Efq. F. R. S. Curfitor Baron of his Majefty's Court of Exchequer. 4to. 2 Vols. l. 11s. 6d. boards. White.

WE have here a very extenfive, rational, and perfpicuous work, on the fubject of Life Annuities, comprehending not only what concerns private perfons, but alfo an account of the most important public or national con

cerns, to which, in the prefent ftate of affairs, the doctrine may poffibly be applicable. The author feems to be actuated by the pureft motives of true patriotifm; and though, in one or two inftances, we may differ in opinion from

him, we, on the whole, highly applaud his undertaking, and fincerely with it may obtain its deferved fuccefs.

The hints which the author has given may be highly ufeful to the ftatesmen of this nation, if the happy period be at length arrived, when, intead of perfifting in a fyftem big with ruin, and of accumulating debts and taxes without measure and without end, as if they meant to tire out the patience of the people, and drive them to acts of defperation, they fhall ferioufly think of adopting fome certain, efficacious, and permanent plan, to pay off fuch a part of the prefent enormous debt as may be judged expedient. If fuch a scheme were once adopted, and all poffible fecurity given that it would be faithfully purfued till the defired end should be attained, and fo as to put it out of the power of any corrupt miniftry hereafter to pervert and abuse it, as they have done by the finking fund, we fhould foon fee the happy effects of fuch a wife and prudent meafure; and returning confidence and credit at home would become fuch a bulwark of profperity as could not eafily be fhaken. It is a moft melancholy reflection; to think how much the nation groans under grievous taxes, and that, during the very time that the debt has been contracting, we have, or might have, been poffeffed of the means of fo lightening them, that the neceffary ones would now fcarcely have been felt. What then does the memory of the firft perverters of the finking fund deferve from their injured countrymen! And what will not be due to him, who fhall firft ftep forward to refcue pofterity from the evils with which they are threatened!

The author tells us, that his work is fo much longer than he at first intended, that he has thought it neceffary, in his preface, to give an account of it, fo as to enable his readers to diftinguish between the different parts, and to felect thofe which fhall be thought moft deferving of their perufal. The principles of the whole doctrine are contained in the first ninety pages; and are the fame with thofe before made ufe of by the most approved LOND. MAG. Jan. 1785.

writers on the fubject, Halley, De Moivre, Simpson, Price, &c. but given much in detail, for the benefit of ordinary readers. The grounds on which it is built, are firft, the decrease of the prefent value of a fum of money to be paid in future, arifing from the mere diftance of the time at which it is to be paid; and, fecondly, the chance which the grantor of the annuity has of efcaping payment by the death of the perfon before it becomes due; in order to determine which chance, it is neceffary to have recourfe to tables of the feveral probabilities of the duration of human life, at every different year of age, which have been formed from obfervations of the numbers of perfons who died, every year, in the course of a long feries of years, at different ages, in divers cities and parishes, and among other numerous bodies of men.

"The doctrine of life-annuities (fays our author) is by no means of fo ab ftrufe and difficult a nature as many people are apt to imagine. A moderate fhare of common fenfe, or capacity to reafon juftly, and a knowledge of common arithmetic, are all the qualities that are neceffary to a right understanding of the principles on which it is founded; even fo far as to be able to compute the value of any proposed annuity for any given life, or number of lives, if a perfon is difpofed to undergo the labour of performing all the neceffary arithmetical operations that arife in fuch a computation. To explain thefe principles in an eafy and familiar manner, fo as to make them intelligible to as many readers as poffible, without having recourfe to Algebra, or the books written on the doctrine of chances, is the defign of the following pages: which, as the fubject of life-annuities is a matter of very general concern, will, I flatter myfelf, be confidered by the public as an useful and commendable undertaking.

"As to the degree of probability that a perfon of a given age will, or will not, live to any other given age, or till the fum of money granted to him becomes due, it is obviously in many cafes a matter of very great un

I

certainty,

prolongation of human life to more than 100 years are fo unfrequent, that they are not thought to be worth attending to in forming any general rules upon this fubject.

"The most exact tables of this kind that have hitherto been publifhed seem to be thofe of Mr. Kerffeboom, and Monfieur de Parcieux; which are to be inferted in the Appendix to M. De Moivre's treatife on the valuation of annuities. The former were published in an effay of the aforefaid Mr. Kerffeboom on the number of people in the provinces of Holland and West Friesland, written in the Dutch language, about the year 1738 (of which an account is given in the ninth volume of the Abridgment of the Philofophical Tranfactions, page 326) and is faid to have been formed from certain tables of affignable annuities for lives in Holland, which had been kept there for 125 years, and in which the ages of the feveral perfons dying in that period had been truly entered. And M. de Parcieux's table was made, by a like ufe of the lifts of the French Tontines or long annuities; and the numbers of it were verified by the necrologies, or mortuary regifters, of feveral religious houfes of both fexes. Thefe feem to be the moft folid and authentic grounds upon which it is poffible to form any tables of this kind: whereas, there are fome circumftances of doubt and uncertainty in the methods of forming all the other tables of the probable duration of hu

certainty, and will be often very different in different perfons of the fame age. The chance which a man of thirty years of age, who is in good health, and leads a temperate and quiet life in the country, has to live twenty years, or till he is fifty years of age, is evidently much greater than that of another man of the fame age of thirty years, and of the fame degree of health and vigour of body, who is going into a hot and unhealthy climate, to which he has never been accuftomed, as, for example, to Senegal in Africa: and it is likewife greater than that of another man of thirty years of age, and of the fame degree of health and vigour, but who lives in a capital city, and in fcenes of pleasure and debauchery; and fill more evidently it is greater than that of another man of thirty, who is of a weakly and unhealthy conftitution of body, or who by his daily occupation is expofed to many dangers of his life, from which the generality of mankind are exempt, as is the cafe with foldiers and failors in time of war. But thefe are circumftances out of the reach of calculation, and must be left to be confidered by the perfons who grant and purchafe life-annuities, according to their own judgement and difcretion, in the particular cafe in which they occur. All that can be done by any general rules upon this fubject, is to eftimate the degree of probability with which it may reafonably be expected that a perfon of any given age will live to any other given age, upon a fuppo-man life, which prevent them from fition that he has neither a better nor a worfe chance of doing so than the majority of other perfons of the fame age. And this medium, or average chance of living, is determined by tables that exhibit the numbers of perfons which, out of a certain pretty large number of children of one, or two, or three years of age (which is ufually not lefs than 1000) all living at the fame time, are found (by methods of reafoning that are grounded on long feriefes of obfervations) to be living at the end of every fubfequent year of human life to its extreme period, which fome of the tables carry to 86, and others to more than 90 years. The inftances of the

being entirely fatisfactory. And, therefore, I conceive these two tables to be more exact and fit to be adopted in computing the values of life-annuities, than any other tables I have feen; and particularly in computing the values of any annuities for lives which the government of this kingdom may at any time think fit to grant, if that method of raising money fhould hereafter be adopted (as is the cafe at this time in Ireland) or it fhould be thought expedient to discharge a part of the national debt in that way, by converting a part of the perpetual three per cent. annuities payable at the Bank into annuities for the lives of their refpective pro

prietors,

prietors, or for a term certain of 20 or 30 years and further for their lives." He then gives these two tables, with their explication, and a comparison of their different refults; both of them reprefent the probability of the duration of human life as greater than it appears to be by any other tables, as thofe promifcuously formed from the bills of mortality of Breflaw, London, &c. until towards the age of 70 years, yet they do not entirely agree with each other; but the French table reprefents that probability as ftill greater than the Dutch one, till towards this advanced age of 70 years, and from that time fomewhat lefs. But our author prefers the French with respect to tables of life-annuities to be calculated for the ufe of Englishmen; because the foil and temperature of the air in England bear a greater refemblance to thofe in the northern parts of France, than to thofe of Holland, which is fo full of moift vapours arifing from the waters among which it is fituated, that the Dutch are in general reckoned to be fhorter-lived than either the French or the English.

Our author having, in the first ninety pages, delivered the fundamentals of his doctrine, proceeds to give short and general expreffions or theorems for the values of annuities, by recapitulating the fubftance of his former conclufions; and this, with its application to general and particular examples, with their proofs or corroborations by other different methods, the neceffary tables and their uses, take up the following 188 pages. At p. 278 he comes to the fubject of remote life-annuities, that are to commence at the diftance of thirty years, or whereof the firft payments are to be made at the end of thirty-one years; which feem to him more interefting than any others, and that it would be a very ufeful and convenient meafure, both for the public, and the individuals whom it would concern, if parliament were to establish fuch annuities as the people fhould be at liberty to purchafe at their full and proper values, according to the feveral ages of the purchasers. For, as the parliament has, within thefe few years pait, thought

fit to establish annuities for a term of thirty years certain, it seems reasonable to fuppofe that it would be a great fatisfaction to the younger part of the proprietors of thofe annuities to be able, for a moderate fum of money (fuch as about two years annuity) to purchafe an additional intereft in them for their own lives, and thereby to rid themfelves of the uneafy apprehenfion of outliving the income that fupports them.

To remove the only difficulty that attends this, our author has procured four tables of the values of such remote life-annuities, to be computed according to M. de Parcieux's table of probabilities, at the feveral rates of 5,4, 4, and 3 per cent. and given them with the method of computation.

At page 288 he begins his obfervations on that moft interefting subject the payment of the national debt; he gives two different methods of employing one million per annum for this purpofe; and fhews, that, in a term of fixty years, more than the whole of the prefent debt may be extinguished by either of them; and observes, that this very great operation of only one million a year, when strictly applied without any interruption, ought, one would think, to induce the parliament to appropriate that fum out of the Sinking Fund to this important purpofe in the ftricteft manner that can be devised, for the space of fifty or fixty years, and to forbear to interrupt its operation during that period upon any account, or occafion, however urgent: and it seems the more reasonable to expect that fuch a measure will foon be adopted, because the finking fund has of late years produced no lefs a fum than three millions of pounds fterling per annum: and our minifters of ftate, as well as the owners of property in the public funds, ought to recollect that the whole of the faid fund, as its name imports, was once appropriated by parliament to this very purpofe, of finking, or diminishing, the national debt, in the manner now recommended for one third of it. To thefe he has added five other methods of difcharging the national debt, and given complete examples, illuftrations,

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and obfervations on every one of them; but for thefe we muft refer to the book itfelf, not doubting but they will give full fatisfaction to every unprejudiced mind.

He concludes the first volume, which contains 389 pages, with fome account of a pamphlet, intitled, "An Effay on the Public Debts of the Kingdom, pubfifhed about the year 1726, by Sir Nathaniel Gould as it is fuppofed;" and which, he fays, in Dr. Price's opinion (and we may add, furely, in the opinion of all friends to this country) deferves to be put into every hand in the kingdom. He begins his fecond volume with a republication of this pamphlet, entire; and he has alfo printed off a number of them, to be difpofed of feparately.

The latter part of the work before us, which is taken up with tables and directions for finding the values of an

ART. CII. Elegiac Sonnets, and other Park, in Sufex. 4to. 2s. Dodfley.

THE poetefs apologizes, in her preface, that her fonnets are not of the legitimate kind. We cannot, however, agree with her. That recurrence of the rhyme which, in conformity to the Italian model, fome writers fo fcrupulously obferve, is by no means effential to this fpecies of compofition, and it is frequently as inconvenient as it is unneceffary. The English language can boaft of few good fonnets. They are in general harth, formal, and uncouth: faults entirely owing to the pedantic and childish affectation of interchanging the rhymes, after the manner of the Italians. The flightest attention to the peculiarities of the refpective languages might evince the propriety of the copy, in this point, deviating from the original.

Plaintive tendernefs and fimplicity characterife the fonnets before us. The introductory one is as follows:

"The partial Mufe has from my earliest hours,
Smil'd on the rugged path I'm doom'd to tread,
And till Wfportive hand has fnatch'd wild flowers,
To weave fantaftic garlands for my head:
But far, far happier is the lot of thofe

Who never learn'd her dear delufive art,
Which, while it decks the head with many a rofe,
Referves the thorn-to fefter in the heart.

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nuities at different rates of intereft for two and three joint lives, and for the furvivor or furvivors of them, is, like the foregoing part, very full and explicit; and has coft the author no fmall pains. To this is added (at p. 605.1 an Appendix, containing an exact copy of the bill to encourage the poor to induftry and frugality, by accommodating them with a fafe and convenient method of laying out what little money they could fave out of the earnings of their labour; which was brought into the Houfe of Commons by the late Mr. Dowdefwell, in 1773, and paffed that Houfe; alfo a copy of the tables of the values of remote life-annuities, for the ufe of parishes in London and the country, which the late Sir George Savile procured to be computed under the infpection of Dr. Price, for the purposes of the faid bill, and which were confidered as a part of it.

Effays. By Charlotte Smith, of Bignor1784.

For till fhe bids foft Pity's melting eye

Stream o'er the ills fhe knows not to remove, Points every pang, and deepens every ligh

Of mourning friendship, or unhappy love, Ah! then, how dear the Mufe's favours coft, If thofe paint forrow belt who feel it moft!"

The following beautiful poem is as fprightly and elegant as the fonnets aré plaintive and tender:

The ORIGIN of FLATTERY.

Bid artful VULCAN give PANDORA birth,
"When Jove, in anger to the fons of earth,

And fent the fatal gift, which fpread below
O'er all the wretched race contagious woe,

Unhappy man, by vice and folly toft,
Found in the storms of life his quiet loft,
While Envy, Av'rice, and Ambition hurl'd
Difcord and death around the warring world;
Then the bleft peafant left his fields and fold,
And barter'd love and peace for power and gold
Left his calm cottage, and his native plain,

In fearch of wealth, to tempt the faithless main ;

Or, braving danger, in the battle stood,
And bath'd his favage hands in human blood:
No longer then, his woodland walks among
The fhepherd lad his genuine paffion fung,
Or fought at early morn his foul's delight,
Or grav'd her name upon the bark at night;
To deck her flowing hair no more he wove
The fimple wreath, or with ambitious love
Bound his own brow with myrtle or with bay,
But broke his oaten pipe and threw his crook
away.

The nymphs forfaken, other pleasures fought;
Then firit for gold their venal hearts were bought,

And

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