^{page 94 note *} H. Baron Collot d'Escury,—Hollands roem in Kunsten en Wetenschappen. 'S Hage en Amsterdam, gebr. v. Cleef. 1835.

^{page 94 note †} From the most remote times the Egyptians, Jews, Greeks, and Romans bestowed a scrupulous attention upon the births and deaths of mankind, although with the two latter people the principal object was to learn the number of men fit for war; the early Christians doing the same, with the design of knowing the number of neophytes (nieuwbekeerden), baptized persons, apostates, and ecclesiastical elders. It is true that the practice was continued subsequently on the spur of other circumstances; but the keeping of better established registers of births and deaths does not generally extend back beyond the commencement of the seventeenth century, as has been the case in this respect in our country. However, at the time of De Wit, a great enough advance had not yet been made in this subject to warrant congratulation on the possession of sufficient observations and calculations upon the proportion of deaths to births; and it was not until the last half of the eighteenth century that the laborious Sussmilch came forward in a voluminous work (which we are acquainted with in our country under the title of De Goddelyke Orde, heersehende in de veranderingen van het menschelyke geslacht), with the express view of providing against the want of such calculations; and hardly had this want been remarked, before the author had numerous imitators amongst his compatriots, which imitators have written in the like spirit. With us we had, in the same century, Kersseboom, Nicholas Struyck, and Houttuyn, who all applied themselves to this work. Struyck very modestly calls his treatise, which appeared in his Introduction to Universal Geography, ‘Gissingen’—i.e., conjectures—on account, says he, of the uncertainty of his researches; he constantly, however, expresses a hope that further astonishing things will be discovered therein. As regards the rest of this subject, read especially what relates to it in the Historical Introduction to the Essay to establish Mortuary Registers, & c. on the most appropriate footing (Geschiedkundige inleiding van het Onderzoek naar de doelmatigste inrigting van Sterflysten enz.), for which Professor Suringar, of Amsterdam, obtained a prize of honour.—(C. d'E.)

^{page 95 note *} “Jan de Witt en zyn Tyd.”

^{page 96 note *} C. d'E. Hollands Roem, &c, 6th part, section 1, p. 100.

^{page 97 note *} See the Commentaries of Van Schooten. The letters which the latter published under the title Jo. Huddenii de Reductions Æquationum et de Maximis et Minimis. Letter II. And Montuela, Histoire des Maihématiques, torn, ii., page 149, etseq.—(C.d'E.) The reader should also refer to Professor De Morgan's paper in the Companion to the Almanac for 1853, pages 12 and 13.–(F. H.)

^{page 97 note †} The resolution is of the 24th February, 1678, and the report was rendered to the Assembly of Holland of the twenty-fifth November following. The proposition, the resolution, and the report, are to be found in the Statements and Memoirs upon the Finances of Holland, published in 1797 by Messieurs Tan Herzeele and Goldberg.—(C. d'E.)

^{page 97 note ‡} As remarks Professor van Lennep, in his Memoirs (Memorabilia) of the AthenæBum of Amsterdam, page 106, where we read [Huddenus]—Joannes Hudde, anno 1667 Civitatis Amstelodamensis Scabinus, anno 1668 Senator, et circa idem tempus etiam Athenæi curator factus, mox effecit, ut Rauis Philosophise Professor Amstelodamum Leida vocaretur, qua de re d'Orvillius infra dicit, p. 41. Consul factus est demum Huddenus in illa rei publicæ conversione, anno 1672. Inde autem vicies fungens eomunere semper promovendis Athenæi commodis intentus fuit; et erat ipse vir, doctissimus, præsertim mathematicis, neque indignus, qai Archimedes nostras diceretur Francio in Oratione xxiii., p. 308, et hinc d'Orvillio, l. c. Juvenis scripta ediderat mathematica, de Reductione Æquationum et de Maximis et Minimis; atqne eum multa in mathematicis primum inyenisse ipse testatus est Leitmitzius, qui anno 1674 Hollandiam invisens familiaritatem cum eo contraxerat. Illam autem scientiam suam Huddenus sæpe in utilitatem urbis patriæ adhibuit, ut in defæcendo per annum 1671,et seq. Amstela, quam operam ejus Francius celebravit dicta oratione et poematum, p. 243. Diem suum obiit 15th Aprilis, 1704, relictis plurimis scriptis mathematicis, quæ quominus absolveret ac vulgaret publica eum negotia prohibuerant. Scripta illa certum habeo adhuc alicubi condita servari, unde optandum est, ut aliquando in lucem proferautnr.”—(C. d'E.)

^{page 101 note *} There is a marginal note in De Wit's handwriting against the first part of this Memoir, with the computations checked by rule of three in each case two or three times over, by different abbreviations. The substance of the note is to observe that “Upon 100,000 florins there being paid annually to the broker 1 per mille, or the sum of 100 florins, consequently 2,400 florins for 24 years, which being reduced to present value (in the proportion first referred to, i.e. as to doubling of capital) gives 1,200 florins (200 : 100 :: 2400 : 1200): for 20 years, 176 : 100 : : 2000 : florins; for 17 years, 162 : 100 :: 1700 : florins; and so on, for each term oi years mentioned in the body of the Memoir.

^{page 102 note *} Oudt Schepen—Gallicè, Ancien Echevin. Query—Ex-Treasurer?

^{page 103 note *} The note referred to is not copied in the minute.

The above short letter affords the most conclusive of proofs that De Wit's and Hudde's studies respecting annuities were entered upon consentaneously with or rather immediately consequent upon their attention “being directed to the discoveries of the laws of chance or probability, exemplified in the then unpublished but already celebrated labours of Pascal and Fermat, on those laws applied to games of hazard; and which were the more familiar to De Wit and Hudde through the treatise of their countryman Huyghens (De Ratiociniis in Ludo Aleæ).

We may be sure it would have rejoiced the great Hanoverian Philosopher (whose words I quoted in my former paper) if he could have seen this direct illustration by De Wit of the truth of that favorite theory of his to which those words advert.

An explanation of the problem of the game of Quinque Novem will be found in the work of Remond de Montmort, p, 173.

^{page 104 note *} Sic.

^{page 105 note *} Affsterven—deaths, decrements of life.

^{page 107 note *} N.B.—The calculations referred to are wanting.

^{page 109 note *} That is to say, for each life separately; therefore, if 2, 3, or even several lives have survived the same number of years, one must also arrange the number of their years twice, thrice, or more times, one beneath the other.—(De W.)

^{page 111 note *} Add to the first item of the first column, the second item; to the second item, the third item; and so on,to the seventh.

^{page 111 note †} This sum includes 7 times the first item, 6 times the second, 5 times the third, 4 times the fourth, 3 times the fifth, twice the sixth, and once the seventh; ergo, according to the rule, let it be divided by 28, and it gives the value of the annuity upon two lives; viz., 20 florins stuyvers.‡

^{page 111 note ‡} The above two notes are from De Wit.

^{page 112 note *} I. Vertoogh, en Calculatie, waer mede, klaer en blijckelijck wort vertoont, en aengewesen, de Beneficien en voordeelen, die uyt dese Lyf-Renten by Overlevingh, in diervoegen, als by de Stadt Kampen werden opgenomen, soo wel voor de Opnemers, als voor de Gevers, staen getrocken en genooten te werden. Gestelt in vergelijckinge met Los-Renten tegens 4 ten hondert, en ordinaris Lijf-renten tegens 8 ten hondert. Small 4to. Amsterdam, 1670. 8 pp.

II. Naerder Conditien en Voorwaerden waer naer de Heeren Burgermeesteren, Schepenen en Raedt der Stadt Kampen hebben geresolveert op te nemen een somme van hondert duysent guldens op Lijfrenten by Overlevingh. Te weten; op een Collegie of Compagnie van 400 Persoonen, tegens 4 per cento's Jaers : Oock de versekeringh die voor de prompte betahnge sal werden gegeven; als mede de ordre die in't admimstreren, en betalen van de Lijf-renten sal werden geobserveert. Small 4to. Amesterdam, 1670. 8 pp.

III. Lyste van het Collegie ofte de namen der Persoonen, op wiens leven de Heeren Regeerders der Stadt Campen, hebben opgenomen ten behoeve ende tot laste van haer gemelte Stadt, door t' Administratie van Jacob van Dael, gesworen Makelaer der Stadt Amsterdam, hondert duysent Caroli guldens, ofte veertigh duysent Rijcxdaelders, op lijfrenten by Overlevingh, Gesloten den primo November Ouden, ofte den elfden dito Nieuwen—stijl, Anno 1670. De Gecommitteerde van't Collegie, Adriaen van Loon, Isaac Jan Nys, Joost de Smith, Johan van Beuningen. Small 4to. Amsterdam, 1671. pp. 16.

IV. Conditien en Voorwaerden waer naer de Heeren Burgermeesteren ende Raedt tot Middelburg in Zeelandt, hebben geresolveert, te doen verhandelen, &c. Een Capitael van hondert twintigh dnysent guldens “by Overlevinge tegens 4½ per cento in't Jaer. Ende dat op het Leven van een Collegie of Compagnie van 240 Persoonen. Small 4to. Amsterdam, 1671. pp. 8.

V. Conditien en Voorwaerden waer naer de Heeren Burgermeesteren en Raedt in Groningen hebben geresolveert, te doen negotieren, &c. Een Capitael tegens 4 per cento van vijf dnysent ses hondert en vijf-en-twnrtigh guldens jaerlijcksche Lijfrenten by Overlevingh. En dat op het Leven van een Collegie ofte Compagnie van 500 Persoonen, alle van ongelimiteerden Oaderdorn. Small 4to. Amsterdam, 1670. 8 pp.

VI. Vertoogh en Uytrekeningh, waer mede Klaer en duydelijck wort betoont en aengewesen, dat de Lijf-renten by Overlevingh, invoegen als onlanghs voor de Stadt Campen, ende nu noch tegenwoordigh voor de Stadt Groningen, en andere Steden zijn ende werden genegotieert; voor de Contribuanten ofte Inleggers, better en voordeeliger zijn, als ordinaris Lijf-renten tegen 8, ja selfs tegen 10 ten hondert. Als mede, Dat die te prefereren zijn voor de Collegien, die hare Capitalen aenleggen in Actie op de Oost-Indische Compagnie. Small 4to. Amsterdam, 1671. pp. 20.

VII. Conditien en Voorwaerden Waer naer de Heeren Burgermeesteren en Raedt in Groningen noch hebben geresolveert, te doen negotieren en opnemen, &c. Een Capitael van hondert en tien duysent guldens, op Lijfrenten by Overlevingh, tegens 5 per cento's Jaers En dat op het Leven van een Collegie ofte Compagnie van 200 Persoonen, alle van den Ouderdom van 25 Jaren en daer boven. Small 4to. Amsterdam 1671. pp. 10.

^{page 116 note *} We need not, of course, take this statement of the Tontine projectors as to their calculations, except with the “grain of salt,” with which experience tells us we must season our belief in worldly matters; but nevertheless the fact of the remark existing in a paper getting on for two centuries old is worth some notice.

I should also mention, in passing, that in the pamphlet respecting the Groningen plan (see No. VI. in last note) the credit of the invention is honestly and properly given to the “sagacious,” or more literally “sharp-witted” Italians, and the statement is further made of its having been but recently introduced into Holland (“eerst by de Scherp-sinnige Italianen uytgevonden, ende nu onlanghs door ons op de Hollandtsche wijse geschickt en in't werck gestelt”).

N.B. It would be desirable to ascertain whether previous Tontine annuity schemes, as, for instance, those instituted by Tonti, in France or elsewhere, and prior in date to 1670, include any tables assimilating to that quoted in this paper.

^{page 118 note *} This sufficiently accounts for the rareness of the work in its separate form as a Report or Treatise. The members of the Council of State were few in number, and we are not aware that they had any incentives for preserving a paper which to them possessed only a passing interest. Should a copy ever be met with, it will be well to look to the paging, as it may either be complete in itself or run on consecutively with the paging of the other Resolutions. The Printer was Jacobus Scheltus, typographer in ordinary to the States.