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Lucan's manifestoes against tyrants. It is probable, however, that the benefit accruing from this hopeful source, was about as great as that from the expedient suggested by the sapience of the royal father, of getting together a party of the most erudite men of the age, to talk their best on high matters of literature and science, in the presence, and for the advan· tage, of a boy who was probably meditating on the philosophy of frolics one half of the time, and literally dreaming of them the other. The time came at last for this royal receivergeneral of wisilom to be a man, and to be married, for the good of the nation; and then, it should seem by Huet's own confession, that, along with the governor and preceptors, he kicked away all the classics with a prodigious good will,

When the official employment, in which Huet had been enabled to render such inestimable benefits to the public, was approaching toward a close, there appears to have occurred to his mind an idea that he should be never the worse for an improvemeiit of his income; and obviously now was the time for securing some permanent source, But the precise form in which this suggestion came to his mind was altogether unprecedented, and a similar instance can scarcely have happened since. It came in the form of a divine call to the ministry of the church. He prepares us by several hints to expect the ultimate occurrence of this solemn event; noticing, in the course of the history, several periods of his life at which he felt, in a certain degree, the promptings of divine grace to enter into the service of Christ.' 'But the fascinalions of literature and the world had still withheld him, till summoned by this last decisive and irresistible call, which occurred in his forty-sixth year. The church was, of course, most ready to receive him; and there is a delectable account of divers solemn deliberations and consultations held some time before concerning the change of his dress, as preparatory to his induction. He had previously taken another preparae tory step, but short of becoming a down-right priest. From this previous step he was enabled, by favour of the pope, to leap at once into the very midst of the church,

I had been initiated into the lesser orders by the bishop of Bayeux, to whose diocese Caen belongs. I therefore obtained an indulgence from the pope, allowing me to be promoted to holy orders without the abseira vance of those intervals and stated times which the church enjoined. In consequence, after the proper pious exercises, the business was com. pleted in three successive days by the administration of Claude Auvri, bishop of Coutances, I then employed a whole month in learning the sacred rițes; and when I thought myself sufficiently versed in them. from practice, I first officiated at the tomb of St. Genevieve (for which the Parisians have a singular veneration) in a subterraneous crypt i hoping



p. 197.

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that, through the patronage of this holy virgin, my newly conferred priesthood would conduce to the glory of God and my own salvation. For 1 had long been excited by a pious ardour to the worship of this saint ; nor from this time did I omit any year to perform my adorations at her shrine on her anniversary, while the state of my health permitted ; but this being debilitated, first by a severe disease, and then by the infirmity of old age, I have latterly intermitted the practice. But that the Almighty has suffered me to survive to the present day; that I still live, after recovery from that dreadful disorder under the attacks of which a few years ago I lay almost at the last gasp; I entirely ascribe to the protection and guardianship of my excellent patroness, which I humbly implored in my greatest danger and obtained by no merit of

my own. Vol. II.

It is bat melancholy, to be sure, thus to see a man return from making the circuit of universal learning, as desperately befooled, with superstition as the most degraded boor that could not spell the title-pages of his learned writinys. So profound a scholar, however, being so excellent a catholic, had beer worth more than loads of gold to the church, if he had really been zealous for its interests; but he was not, as appears from his taking so slight a polemic share in its defence. And as to the grand object for which every established church professes to be instituted, the instruction of the people, he seems really never to have recollected any thing of the kind. There are various indications of the utmost contempt of the vulgar; and we observed one remarkable passage in which he deplores, in the following terms, the fate of a person who had been expected to obtain honourable distinction by producing a 'copious commentary on the Periegesis of Dionysius;'

• But it was his fortune to be banished to a rustic and ignoble re. tirement, for the purpose of instructing the inhabitants in religion, where he grew old without fulfilling any of the expectations which he had excited, Vol. I. p. 247.

Our author was first made abbot of Aulnai, and afterward nominated bishop of Soissons, which see he exchanged with the bishop of Avranches. But after holding the episcopal station some time, he became so intolerably tired of its routine, and of its troublesome duties relative to the vindication and disposition of ecclesiastical property, that he abdicated the bishopric, well content with the abbacy of Fontenai, as a pecuniary succedaneum.

In whatever station or residence, his ardour in literary purasuits continued unabated to the very evening of his life, which closed at Paris, in 1721, at the age of ninety-one-Dr.

Aikin has added a catalogue of his works, extended to the Jimits of a brief analysis.'

Art. II. The Doctrine of Life Annuities and Assurances analytically in

vestigated and explained. Together with several useful Tables connected with the Subject: and a variety of Practical Rules for the Illustration of the Same. By Francis Baily, of the Stock Exchange. 8vo.

pp. xli. 622. Price 11. 48. bds. Richardson. 1810. THE mortality of mankind is a subject of interesting con

templation, not only to the moralist and divine, but to the politician and the philosopher. The physical and political uses of this kind of speculation have, indeed, been long since pointed out by Sir William Petty in his “ Natural and Political Observations on the Bills of Mortality of London," But the inquiry has, moreover, led to the creation of a distinct branch of analytical science,-that, we mean, which relates to the valuation of Life Annuities and Assurances. This species of mathematical investigation is perfectly modern, and, in fact, may be called new; for we find scarce. ly any traces of it before the commencement of the last century. Van Hudden was the first who attempled the developè. ment of a rational theory; and this was still farther expanded by the celebrated pensionary John de Witt, in a tract printed at the Hague in 1671, under the title “De vardye van de Lif-renten na proportie van de Losrenten." Nothing, howerer, to which a reader of the present times could recur with advantage, was produced till 1692—3 ; when Dr. Halley, whose labours so greatly enriched almost every department of mathematical knowledge, gave, in the Philosophical Transactions, “ An Estimate of the Degrees of Mortality of Mankind, drawn from curious tables of the births and funerals at the city of Breslaw ; with an attempt to ascertajn the price of annuities of lives.” In this paper Dr. Halley presented a very perspi. cuous view of the principles on which an accurate theory of assurances and annuities must rest, and from the application of these principles to the Breslaw observations, deduced the first correct table of the value of Life Annuities. De Moivre. took

up the subject where Halley left it, and in 1724 published the first edition of his « Annuities on Lives." In this very ingenious and valuable work, he started the hypothesis, that the decrements of life are equal and uniform, from birth to the utmost extremity of human life;" an hypothesis wbich, though it much simplifies computation, and furnishes a very elegant theory, considered merely in relation to its an. alytical symmetry, and facility of practice, yet when applied to such cases as actually occur, often leads to results tremely erroneous, unless it be subjected to the checks furnished by other theories. In 1742 another excellent mathematician, Mr. T. Simpson of the Woolwich academy, in a car


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rious little treatise "On the Doctrine of Annuities and Re. versions,” clearly explained the method of computing the values of annuities, &c. from the real observations of life,an improvement certainly of great importance-and prosecuted the subject still farther in his “ Select Exercises,” published in 1752. In 1753 and 1755 Mr. James Dodson published the 2d and 3d volumes of bis “ Mathematical Repository,” in which he has given the most extensive collection. extant of probleins purely algebraical, and solved an immense variety of questions relative to annuities, reversions, survivorships, and assurances; though, unfortunately, he has throughout adopted the hypothesis of his friend M. De Moivre.

We cannot pursue this bistory better than in the language of Mr. Baily :

The science,' says he remained in this state, without much im. provenient, till the publication of the first edition of Dr. Price's celebrated treatise' in 1769. This work, entitled Observations on Reversionary Payments, &c., was first published with a view to oppose and destroy the injurious effects and evil intentions of a class of men (unfortunately to be found in every stage of society, who, under pretence of establishing Societies for the berefit of Old Age, and of Widows, were only forming schemes to allure and to defeat the hopes of the ignorant and the distressed. His efforts were eventually crowned with success : and those bubble societies have long since met with the fate which he so truly predicted.

• In this laudable pursuit, Dr. Price saw the necessity of more accurate observations on the mortality of human life; in order to determine with more correctness the value of Life-Annuities, and to show more forcibly the futility and extravagance of the schemes that were issued by those societies* By the assistance of some public.spirited individuals, he obtained correct registers of the rate of mortality at Northampton, Norwich, Chester, and other places in England. But, still, the computation of the values of annuities, according to these observations, was a work so tedious and unpleasant, that little hopes were entertained of profiting by those researches : and Dr. Price suffered three several editions of his - treatise to pass over without affording any additional information on this

subject. At length the fourth edition appeared (1783) enriched with several valuable tables of Annuities on Single and Joint Lives, at different rates of interest, deduced not only from the probabilities of living as ob

•* Any person, who will take the trouble to go through the Examples 'inserted in Dr. Price's treatise, will readily observe how inaccurately he was obliged to proceed in this infant state of the science. In calculating the value of deferred annuities, (a case of frequent occurrence, 1 he was obliged to take the value of the annuity from M. De Moivre's tables, but, the probabilities of life he deduced from Dr. Halley's table of observations at Breslaw. A practice which gives an air of imperfection to the work at the present day; and which ought to have been removed, after the publication of the late valuable tables,

served at Northampton, but also from the probabilities of living as observed in the kingdom of Sweden at large*.

T'he great addition which Dr. Price has made to our means of information respecting this science, and the assiduity with which he thus promoted some of the best interests of mankind, deserve the highest commendation : and his labours on this subject entitle him to our warmest praise. The primary object, which he had in view, has been fully answered; and his treatise was admirably adapted to that end. In every other respect, however, it is far from being complete : and the reader will look in vain for the most common cases that occur in practice. Indeed, those subjects, which are to be met with, do not readily present themselves ; owing to the loose ard irregular manner in which they are treated. Dr. Price's object was not so much to insert what was new, as to illustrate (by some striking examples) a few of the leading problems, with a view to oppose the pernicious schemes that disgraced the age in which he lived. But, those schemes having long since vanished, his observations may now be considered rather as a beacon to posterityt.

• The dext treatise on this subject is that by Mr. Morgan, entitled The Doctrine of Annuities and Assurances, which appeared in 1779. This author sets out with the vain attempt to render the principles of the science intelligible to persons unacquainted with matherriatics : but, after a fruitless effort for this purpose, he ultimately leaves his readers to pursue their inquiries by the common and only useful method of analysis. Besides some valuable observations “ on the different methods of determining the state of a Society, whose business consists in making Assurances on Lives,” that work will be found to contain a variety of problems treated, for the most part, in a plain, easy and familiar manner; and adapted to the state of the science at that period. But, out of the fortytwo problems which that treatise contains about thir:y of them, chiefly relating to contingent annuities and assurances, are owing to more accurate observations and a more improved analysis) now rendered totally unfit for general use. Mr. Morgan himself, however, has been the principal cause of this revolution in the science : but of the merit of his improve. ments on this subject I shall speak hereafterţ.

6* These tables are inserted at the end of the present work ; being Tables XIV to XLIV. Their publication forms a new era in the science; and has, in a great measure, rendered obsolete and useless the preceding works of De Moivre, Dodson, Simpson and Morgan. This latter treatise had been published about four years before this period; as will be mentioned in the sequel.

* † Any person, the least acquainted with the subject of the present work, must be aware that any additional Tables of the value of Life-Annuities, or any Observations on the best method of forming them, will add greatly to our means of information. It will therefore readily be seen that my remarks do not allude to this part of his treatise, which I consider invaluar ble, and of constant utility. My observations, in the present instance, apply more particularly to any improvement in the analysis of the science; and its application to any practical cases,

In Mr. Morgan's Doctrine of Annuities, &c. we find three new tables of the value of Life. Annuities, deduced from the probabilities of life an

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