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of various problems in chances, including five problems proposed by Huygens. Todhunter concludes an exhaustive criticism of this ed. as follows:
Montmort's work, on the whole, must be considered highly creditable to his acuteness, perseverance, and energy. The courage is to be commended which led him to labour in a field hitherto so little cultivated, and his example served to stimulate his more distinguished successor. De Moivre was certainly far superior in mathematical power to Montmort, and enjoyed the great advantage of a long life, extending to more than twice the duration of that of his predecessor; on the other hand, the fortunate circumstances of Montmort's position gave him that abundant leisure which De Moivre in exile and poverty must have found it impossible to secure.
De Moivre spoke in very high terms of Montmort's work, and said that therein he had given "many proofs of his singular genius and extraordinary capacity."
In 1714 also M. Barbeyrac pub. in Amsterdam a discourse, Sur la Nature du Sort. In the same year Nicolas Bernouilli transmitted to the Royal So. a problem in the doctrine of chances, which was pub. in the Phil. Trans.
In 1714 also appeared a work, Christiani Hugenii Libellus de Ratiociniis in Ludo Alea; or, the Value of all Chances in Games of Fortune; Cards, Dice, Wagers, Lotteries, etc., Mathematically Demonstrated. Lond.: Printed by S. Keimer for T. Woodward, near the Temple Gate, in Fleet St., 1714. This was a trans. of Huygens' treatise , by W. Browne. In his adv. to the reader, Browne refers to a trans. of Huygens' treatise which had been made by Arbuthnot; he also notices the labours of Montmort and De Moivre. In 1718 De Moivre pub., in book form, The Doctrine of Chances; or, a Method of Calculating the Prob. of Events at Play. This, as we have said, was an expansion of his paper of 1710. A 2nd ed. of this work was pub. in 1738; 3rd ed., 1756 (after the author's death). The author says in his preface:
'Tis now about 7 years since I gave a specimen in the Phil. Trans. of what I now more largely treat of in this book. The occasion of my then undertaking this subject was chiefly owing to the desire and encouragement of the Hon. Francis Robartes, Esq. (now Earl of Radnor), who, upon occasion of a French tract, called L'Analyse des Jeux de Hazards, which had lately been pub., was pleased to propose to me some problems of much greater difficulty than any he had found in that book; which having solved to his satisfaction, he engaged me to methodize those problems, and to lay down the rules which had led me to their solution. After I had proceeded thus far, it was enjoined me by the Royal So. to communicate to them what I had discovered on this subject; and thereupon it was ordered to be put in the Trans., not so much as a matter relating to play, but as containing some general speculations not unworthy to be considered by the lovers of truth.
Many important results were here first pub. by De Moivre, although it is true that these results already existed in manuscript in the Ars Conjectandi, and the correspondence between Montmort and the Bernouillis.-Todhunter.
In the Hist. of the Academy of Paris for 1728 [pub. 1730], there is a notice respecting some results obtained by Mairan-Sur le Jeu de Pair ou Non. The art. is not by Mairan. In the 9th vol. of Actorum Eruditorum . . Supplementa, pub. in Leipzig in 1729, there is a memoir: Johannis Rizzetti Ludorum Scientia, sive Artis Conjectandi elementa ad alias applicata, from which it appears that Daniel Bernouilli had a controversy with Rizzetti and Riccati relating to some problems in chances. It led to nothing new, and chiefly turned upon the proper definition of " expectation."
In the Hist. of the Academy of Paris for 1730 [pub. 1732], there is a memoir by M. Nicole, entitled: Examen et Résolution de quelques Questions sur les feux. In the same vol. is another memoir by Nicole. But, in each case, Montmort and De Moivre had already covered the same ground.
In the St. Petersburg Memoirs (vol. 5) for 1730-31, there is an interesting paper by Daniel Bernouilli on the relative values of the expectations of individuals who engage in play, or stake sums on contingent benefits, when regard is had to the difference of their fortunes; a consideration which in many cases it is necessary to take into account; for it is obvious that the value of a sum of money to an individual depends not merely on its absolute amount, but also on his previous wealth. On this principle Bernouilli has founded a theory of moral expectation, which admits of numerous and important applications to the ordinary affairs of life.-Galloway.
In 1733 the Compte de Buffon communicated to the Academy of Sciences in Paris the solution of some problems in chances. [See 1777.]
In 1738 there was pub. another ed. of the trans. of Huygens, spoken of under date 1692, with the following title: Of the Laws of Chance; or, a Method of Calculation of the Hazards of Game, plainly demonstrated, and applied to Games at present most in use; which may be easily extended to the most intricate cases of Chance imaginable. The 4th ed. revis'd by John Ham. By whom is added a Demonstration of the Gain of the Banker in any circumstance of the Game call'd Pharaon; and how to determine the Odds at the Ace of Hearts, or Fair Chance; with the Arithmetical Solution of some Questions relating to Lotteries; and a few Remarks upon Hazard and Backgammon. London: Printed for B. Motte and C. Bathurst, at the Middle Temple Gate in Fleet-street, M. DCC. XXXVIII. This second part, which is here attributed to John Ham, Todhunter believes to have been taken in greater part from De Moivre, who however is not named in the work.
In 1738 also there was pub. 2nd ed. of De Moivre's Doctrine of Chances, "fuller, clearer, and more correct than the first," by admission of the author. [See 1718.]
In 1739 there was pub. in Florence, "Par Mr. D. M.," a work, Calcul du feu appellé par les François le trente-et-quaranté, et que l'on nomme à Florence le trente-et-un.
The problem is solved by examining all cases which can occur, and counting up the number of ways. The operation is most laborious, and the work is perhaps the most conspicuous example of misdirected industry which the literature of games of chance can furnish.-Todhunter.
In 1740 Mr. Thomas Simpson pub., The Nature and Laws of Chance, containing among other Particulars [see below]. The whole after a New, General, and Conspicuous Manner, and Illustrated with a great variety of Examples. The part of the title just
omitted is as follows:
(1) The solutions of several abstruse and important problems. (2) The doctrine of combinations and permutations clearly deduced. (3) A new and comprehensive problem of great use in discovering the advantage or loss in lotteries, raffles, etc. (4) A curious and extensive problem on the duration of play. (5) Problems for determining the prob, of winning at bowls, coits, cards, etc. (6) A problem for finding the trials wherein it may be undertaken that a proposed event shall happen or fail a given number of times. (7) A problem to find the chance for a given number of points on a given number of dice. (8) Full and clear investigations of two problems, added at the end of Mr. De Moivre's last ed., one of them allowed by that great man to be the most useful on the subject, but their demonstrations there omitted. (9) Two new methods for summing of series.
This work engaged some attention. Simpson implies in his preface that his design was to produce an introduction to the subject less expensive and less abstruse than De Moivre's work; and in fact Simpson's work may be considered as an abridgment of De Moivre's. Simpson's problems are nearly all taken from De Moivre, and the mode of treatment is substantially the same. The very small amount of new matter which is contributed by a writer of such high power as Simpson shows how closely De Moivre had examined the subject, as far as it was accessible to the mathematical resources of the period.-Todhunter. In the Hist. of the Berlin Academy for 1751 [pub. 1753] there appeared Euler's first memoir, entitled Calcul de la Probabilité dans le Jeu de Rencontre. The problem discussed is that which is called the game of Treize, which had previously been treated of by Montmort and Nicolas Bernouilli, and more simple results than those now given had been obtained by the latter. [See also 1764.]
In the 2nd vol. of Dodson's Mathematical Repository, dated 1753, there are some problems on Chances, which, however, present nothing new or important.
In 1754 Edmund Hoyle pub. An Essay towards making the Doctrine of Chances easy, to those who understand Vulgar Arithmetic only, &c., &c., &c. The preface says:
In order to put play upon the most equal foot, in this treatise you have practical rules and examples, plainly expressed in words at length, whereby all various cases and the odds of games of any kind, may be easily resolved, without any knowledge of algebra or logarithms; by which the most unskilful person in betting his money is put upon an equal foot with those who have applied themselves to this study for many years.
He also gave: "A short table of the powers of two, showing the odds of winning or losing any number of games upon an equality of chance."
In 1754 D'Alembert contributed to the Encyclopédie [Paris] an art., Croix ou Pile, wherein he proposes to find the chance of throwing head in the course of two throws with a coin. He deals with questions of play also. [See 1761.]
The result of all De Moivre's laboured and continuous investigation of the subject was embodied in this proposition-which we believe only appeared in the last ed. of his work, 1756, revised just before and pub. after his death" That although chance produces irregularities, still the odds will be infinitely great, that in process of time, those irregularities will bear no proportion to the recurrency of that order which naturally results from ORIGINAL DESIGN."
In 1757 there was pub. in Padua a quarto vol., Dell' Azione del Caso nelle Invenzioni, e dell' influsso degli Astri ne' Corpi Terrestri Dissertazioni due. The first dissertation is on the influence of Chance in inventions. It recognizes this influence, and gives various examples. The second is on the influence of the celestial bodies on men, animals, and plants; and is intended to show that there is no influence produced in the sense in which astrologers understand such influence. The author expressed more belief in the squaring of the circle than in the Newtonian theory of gravitation then recently propounded.
In 1758 Mr. Samuel Clark pub., The Laws of Chance; a Mathematical Investigation of the Prob. arising from any proposed Circumstances of Play, applied to the Solution of a great variety of Problems relating to Cards, Bowls, Dice, Lotteries, etc. The work is written in a very plain and simple style. It is almost entirely based upon De Moivre and Simpson; but it does not contain anything new or important.
In the 2nd vol. of his Opuscules Mathématiques, pub. 1761, D'Alembert says, in reference to chance and probability, that we must distinguish between what is metaphysically possible and what is physically possible. In the first class are included all those things of which the existence is not absurd; in the second are included only those things not too extraordinary to occur in the ordinary course of events. It is metaphysically possible to throw two sixes with two dice a hundred times running; but it is physically impossible, because it never has happened, and never will happen. He applied this principle in various forms.
In vol. v. of the Acta Helvetica, 1762, there is a memoir by M. Mallet, entitled, Recherches sur les avantages de trois Jeueurs qui font entr'eux une Poule au trictrac ou à un autre Feu quelconque. The problem had been treated by De Moivre, but was now extended by Mallet.
In the Phil. Trans. for 1763 [pub. 1764] there is the following memoir: An Essay towards solving a Problem in the Doctrine of Chances. By the late Rev. Mr. Bayes, F.R.S., communicated by Mr. Price in a Letter to John Canton, A.M., F.R.S. This letter commences: "Dear Sir,-I now send you an essay which I have found among the papers of our deceased friend Mr. Bayes, and which, in my opinion, has great merit, and well deserves to be preserved." The essay of Bayes follows the introductory letter. It begins with a brief demonstration of the general laws of the Theory of Prob., and then establishes his theorem. Dr. Price added: An Appendix containing an application of the foregoing rules to some particular case.
The Phil. Trans. for 1764 [pub. 1765] contains a memoir: A Demonstration of the second Rule in the Essay towards the solution of a Problem in the Doctrine of Chances, pub. in the Phil. Trans., vol. liii., communicated by the Rev. Mr. Richard Price in a Letter to Mr. John Canton, M.A., F.R.S. This memoir contains Bayes' demonstration of his principal rule for approximation; and some investigations by Dr. Price which also relate to the subject of approximation.
In the Hist. of the Berlin Academy for 1764 [pub. 1766] was a further memoir by Euler: Sur l'avantage du Banquier au Jeu de Pharaon. Euler here merely solves the problems which had been already solved by Montmort and N. Bernouilli, to whom, however, he makes no reference [see 1751]. In the same vol. were two other memoirs on the same problem by Beguelin.
In the Hist. of the Berlin Academy for 1768 [pub. 1770] there is a contribution from John Bernouilli: Mémoire sur un Problème de la Doctrine du Hazard. It requires no special comment here. [MARRIAGE.]
In 1772 Mr. Fenn. pub. Calculations and Formula for determining the advantages or disadvantages of Gamesters.
In the Mémoires par divers Savans [vol. vi.], 1774, there are two memoirs by Laplace. The first: Mémoire sur les suites récurro-récurrentes et sur leurs usages dans la théorie des hazards. The author considers three problems. The first is the problem of the duration of play, supposing two players of unequal skill and unequal capital. Todhunter says that Laplace rather shows how the problem may be solved than actually solves it. He begins with the case of equal skill and equal capital, and then passes on to the case of unequal skill. He does not actually discuss the case of unequal cap., but intimates that there will be no obstacle except the length of the process. The second memoir is on Prob. [PROBABILITIES.]
In the Select Memoirs of the Academy of Berlin for 1775 [pub. 1777] there is a paper by Lagrange which treats of the Theory of Chances. The 5th problem therein relates to the duration of play in the case in which one player has unlimited capital. This subject had been previously treated by De Moivre.
In 1776 was pub. anon. Reflections on Gaming, Annuities, and Usurious Contracts; and in the same year some Essays on Mathematical Subjects, by W. Emerson, including one on the Laws of Chance. "Emerson's work would be most dangerous for a beginner, and quite useless for a more advanced student."-Todhunter.
In 1777 Buffon pub. his Essai d'Arithmétique Morale. Struck by the remarkable speculations of Daniel Bernouilli, on the subject of the relative gain or loss at play on the private fortunes of the players, he commenced to write in 1760, and pub. in 1777, that most eloquent and impressive attack on the immorality, the danger, and the vicious principle of government gaming tables, and contributed perhaps more than any other to their gradual extinction in some countries, and the disrepute to which they have justly fallen in others. "The Doctrine of Chances (says Mr. Brown) has seldom been converted to a more honourable or benevolent purpose, and never with greater eloquence and force." The following is one of Buffon's ingenious arguments: He supposes two players of equal fortune, and that each stakes half of his fortune. He says that the player who wins will increase his fortune by a third, and the player who loses will diminish his by a half; and as half is greater than a third, there is more to fear from loss than to hope from gain. Other writers, as we have seen, have touched upon this same consideration. [MATHEMATICAL EXPECTATION.] [MONEY.]
In the Select Berlin Memoirs for 1780 [pub. 1782], there is one by Herr Prevost, Sur les principes de la Théorie des gains fortuits. This simply consists of an attempted criticism of the elementary principles laid down by James Bernouilli, Huygens, and De Moivre. In the Select Memoirs of the Berlin Academy for 1784 [pub. 1786] there is one by D'Anieres, entitled Réflexions sur les Jeux de Hazard. The memoir is not mathematical; it alludes to the fact that games of hazard are prohibited by governments, and shows that there are different kinds of such games, namely, those in which a man may ruin his fortune, and those which cannot produce more than a trifling loss in any case.-2 - Todhunter. In 1787 W. Painter pub., Guide to the Lottery; or, the Laws of Chance. In the same year John Johnson pub., A Complete Abridgment of the Laws respecting Gaming and Usury, with Adjudged Cases.
In 1792 there was pub. in Paris, in connexion with the Encyclopédie Méthodique, a special vol. entitled Dictionnaire des Jeux, faisant suite au Tome III. des Mathématiques. There are no mathematical investigations, but in several cases the numerical values of the chances are given. The work does not appear to have been completed.
In the Commentaries of the Royal Scientific So. of Gottingen (vol. xii.) for the year 1793-4 [pub. 1796] there is a memoir by Herr Trembley: Disquisitio Elementaris circa Calculum Probabilium, wherein are discussed nine problems in Chance, most of which had been dealt with by De Moivre. [See 1802.]
In 1795 the Baron Maseres pub. a translation into English of the famous Ars Conjectandi of James Bernouilli; also an English trans. of Wallis's Algebra. These were included in a vol. of reprints, under the title of The Doctrine of Permutations and Combinations, being an essential and fundamental part of the Doctrine of Chances; as it is delivered by Mr. James Bernouilli in his excellent Treatise on the Doctrine of Chances, intitled Ars Conjectandi, and by the celebrated Dr. John Wallis, of Oxford, in a tract intitled from the subject, and published at the end of his Treatise on Algebra: In the former of which Treatise is contained a Demonstration of Sir Isaac Newton's famous Binomial Theorem, in the cases of Integral powers, and of the Reciprocals of Integral powers; together with some other useful mathematical tracts.
In the Memoirs of the Berlin Academy for 1802 [pub. 1804] is a further paper by Herr Trembley: Observations sur le calcul d'un Jeu de Hazard. The game considered is that of Hez, which had been previously considered by N. Bernouilli and others.
In 1808 an article appeared in Nicholson's Journal (xxi. p. 204) by William Saint: Remarks on the Doctrines of Chance, in answer to Optimath.
In 1812 was pub. in Paris: Essais Métaphysiques et Mathématiques sur le Hazard, by Francis Corbaux.
In 1814 Mr. Wm. Rouse pub. The Doctrine of Chances; or, the Theory of Gaming; and a few years later [prob. about 1820] he pub., The Doctrine of Chances; or, the Theory of Gaming made easy to every person acquainted with common Arithmetic: so as to enable them to calculate the prob. of events in Lotteries, Cards, Horse-racing, Dice, etc.; with Tables on Chance never before pub., which from mere inspection will solve a great variety of questions. As we cannot fix the precise date of the pub. of the last-named work, which is evidently only an enlargement of the former one, we shall review its contents at this point. The uses of a knowledge of the Doctrine of Chances are explained by Mr. Rouse as follows: If, for a moment, such an imaginary being as luck is allowed to influence the actions of men (as it seems generally amusing to believe), yet it will follow to be equally useful to know the laws of chance, as they teach a man how to secure to himself more ways of this said luck than his neighbour or opponent, who may know nothing of these laws or rules: and it cannot be denied by the advocates for luck that if one man has five ways to win a game, and another only two, the first man is more likely to be lucky than the second.
Now the laws of chance are nothing more than rules to teach a person how many different ways there are to obtain an object; and if he finds there are fifteen ways, divided into two unequal parts, as 10 and 5, has he not a great advantage over his opponent, who, if he is ignorant of such rules, is as likely to choose one part as another? If a man is acquainted with the laws of chance, he will not be compelled to take that side which has most chances to win unless he likes it; for if he thinks he shall be more lucky with the 5 chances, he can take them, and leave the 10 chances for his opponent, which few adversaries will object to. Therefore, whether luck, or no luck, it must be greatly useful to know the laws of chance, as they enable a person to measure his advantage or disadvantage in any event, and teach him to estimate the comparison between chance and design.
Again, advancing upon the subject:
Although chance is generally considered to be effect without design, yet throughout universal nature all events appear to be governed by immutable laws, which have existed from the beginning of time, whatever partial irregularities may arise; and the utmost stretch of the human mind has been only able to discover a few of those laws or rules by which the phenomena of nature appear to be governed; but the great first cause that produced those laws is unknown to us.
The existence of our species and the near equality of the sexes, which have continued for near six thousand years, cannot be called effect without design; and yet this is as much an object of the doctrine of chances as any event depending on the cast of a die or the combinations of cards; for if we suppose an equality of chance, whether the next child to be born will be a boy or a girl, the chances are 3 to 1 against the first two children being boys: as there may be born either boy and boy, girl and girl, boy and girl, or girl and boy, being four ways, and only one of them for boy and boy; therefore 3 chances to 1 against the event happening: the same as throwing a die or a counter with two faces, a red and a black one; the chances are 3 to 1 against two red faces coming up in two throws; and upon the same supposition of equality it can be demonstrated that the odds are 772 to 252 that in 20 births there will not be exactly 10 boys and 10 girls; yet (although partial inequalities may and do arise in any assignable number of births, and which seem to imply chance), it must be admitted it was originally designed that the whole should be governed by this ratio of equality, or nearly so, ages before men began to think of the philosophy of causes, or had discovered any of those laws or rules of nature, all of which existed from the beginning, and will remain through time, whether the mind of man has discovered them or not. pp. vii. and viii.
In 1819 an art. on Chance appeared in Rees' Cyclo. This was written by Mr. W. Morgan. In 1824 Mr. Francis Corbaux pub. An Inquiry into the National Debt, and into the Means and Prospects of its Redemption; with an Appendix on State Lotteries, and new Illustrations of the Doctrine of Chances.
In 1828 Mr. [now Sir] John Wm. Lubbock read before the Cambridge Philosophical So. a paper: On the Calculation of Annu., and on some questions in the Theory of Chances. The paper was printed in the Trans. of that So., and has been reprinted in the Assu. Mag. [vol. v., p. 197]. It is of a purely scientific character; but we have had occasion to quote from it in these pages.
In 1853 there was was pub. in Paris: Traité du Trente-quarante, contenant des analyses et des faits pratiques du plus haut intérêt suivis d'une collection de plus de 40,000 coups de Banque. Chaque operation donne le dessin des figures appliquées et l'importance des résul
Par G. Gregoire, Membre de plusieurs sociétés, Auteur du Manuel théorique et pratique du Feu de Dames à la Polonaise.
In 1855 Dr. W. A. Guy read before the Inst. of Act. a paper: The analogy existing between the aggregate effects of the operations of the Human Will, and the Results commonly attributed to Chance. This paper is printed in the Assu. Mag. [vol. v. p. 315], and will be more particularly spoken of under HUMAN WILL.
In 1856 there appeared in the Quarterly Journal of Science a paper: On the Application of the Doctrine of Chances as it regards the subdivision of risks. This paper printed in the Assu. Mag. [vol. vi. p. 287]. It will be referred to more particularly under RISKS, THEORY OF.
In 1865 was pub. by Prof. Todhunter, A Hist. of the Mathematical Theory of Prob. from the time of Pascal to that of Laplace. It is from this work that we have frequently quoted in the present art.
As we have already said, it was out of the earlier investigations of the Law of Chances, that the Theory of Prob. was enunciated. The teachings of this latter theory were soon applied, with the greatest advantage, to the development of the Science of Life Contingencies; hence, in our art. upon LIFE CONTINGENCIES, and upon PROBABILITIES, many of the writers whose works have been here mentioned will be met with again. CHANDLER, S. C., JUN., Act. of Continental L., N.Y. In 1872 he contributed to the Spectator Ins. Journal of N. Y. a paper, On the Law of the Ages at which L. Ins. are Effected. This paper [reprinted in Assu. Mag. vol. xvii. p. 56] possesses very considerable interest; and we shall speak of it more particularly. [INSURED LIFE.] CHANGE OF NAME.-See NAME, CHANGE OF.
CHANGE OF VENUE.-In the case of McLaughlin v. Royal Exchange Assu. Corp., which came before the Irish Courts in 1844, motion was made for a Change of Venue to the county where the fire occurred. The motion was supported by an affidavit setting forth : "That to enable the defendants to bring their defence fairly and fully before a jury, it will be necessary that the said jury, or some of them, should have an opportunity of viewing the shop in which the said fire took place," etc. The affidavit was held insufficient, inasmuch as it did not state why such a view was necessary to the defence.
In a previous case, Mc Donnel v. Carr (1832), on a similar affidavit, the venue was changed. CHANGE OF VOYAGE.—A Change of Voyage takes place when, either before or after sailing, the assured definitively abandons all thought of proceeding to the port of destination set down in the pol.-Casaregis.
The great distinction between a deviation and a change or abandonment of voyage is, that in the former the orig. voyage, as described in the pol., is not given up or lost sight of, while in the latter it is.
A Deviation, says Chancellor Kent, is not a change of the voyage, but of the proper and usual course of performing it.
The effect of a Change of Voyage is to discharge from all liability on the pol. from the moment the purpose of so changing the voyage is definitively formed. Hence if the purpose of changing the voyage be fixed before the commencement of the risk, the pol. is void ab initio, and the risk never attaches; or, if it be not formed till after the ship has sailed, the underwriter is discharged from all liability for losses which may accrue subsequently to its having been formed, although such loss may take place while the ship is on the track common both to the voyage ins. and to that which is substituted for it.-Arnould. The Marine Ins. Ordin. of France provides to the same effect.
CHAPLIN, FREDERICK, Sec. Lond. branch of Edinburgh L., which position he has occupied since 1851. He was at first associated with Mr. Stainforth, the Resident Director of the Co. in Lond.
CHARGE. To lay a duty upon any one; to acquaint any with the nature of their duty-as a judge charging a jury. An act done, binding on the party who does it-as a borrower "charging" his lands by way of security; hence, when the advance is repaid, a "discharge" becomes necessary.
CHARGES [a term used in Marine Ins.].-These are expenses applicable to a particular interest, as to the ship alone, or the cargo alone. They are incidental to "total loss," and to "average"; and the liability of the underwriter to contribute to them is properly dependent upon his liability for the loss which has occasioned them, or to avoid which they have been incurred. This, on the general rule that "the accessory follows its principal."-McArthur.
CHARITABLE PURPOSES.-Life Ins. has often been propounded as a means of aiding Charitable and Benevolent objects. The earliest instance of this character we have met with is by way of appendix to the Proposal for Estab. a Perpetual Assu. Office, pub. early in the 18th century, and is as follows:
A Charitable Proposal for the augmentation of small Vicarages and for Erecting of Publick Libraries and Free Schools for the Education of Poor Children in all the Counties of England, or for any other Charitable Use.
That any number of persons may join in their contributions and pay £6 a year, jointly, during the life of any man or woman they shall name, provided the person named be not above 55 years of age; and when the person dies upon whose life they paid the money, the said Contributors shall be entitled to an equal dividend of £10,000, together with other advantages, besides £3 out of every £6 which they shall have paid into the office.