Imágenes de páginas

In 1601 was enacted the Stat. 43 Eliz. c. 12, under which was estab. the Policies of Ins. Court, appointing special commissioners to hear and determine disputes under pol. of ins. The preamble of this Act set forth that the said commissioners "shall meet weekly at the office of ins. on the west side of the Royal Exchange, for the execution of their commissions, without fee or reward,"-thus proving the continued existence of the Chamber of Ins., and adding another link to its usefulness. [POLICIES OF INS. COURT.]

In the year following that of the Great Fire of Lond. an Act was passed containing provisions for the rebuilding of the City, and in that Act it was provided, that all moneys which ought to be paid to the late Assu. Office in the late Royal Exchange, might be made "to the present Assu. Office in Gresham House."

Molloy [De Jure Maritimo] writes in 1682 :

Assurances are either publick or private. Publick when they are made and entered in a certain office or court, commonly called the Office of Assu., on the Royal Exchange in Lond.; and the same are called publick, for that it is free for any man to resort and see what another hath assu, upon his adventure. Private is when an assu. is made, but the insured keeps the same secret, not deeming it fit that any should see or know their cargo or adventure, or what premio they have given, or assu. they have made: and the same being never entered in the Office is known by the name of a Private Assu. By the Common Law they are both of the same validity, as in reference to obtain satisfaction from the insurers, if loss or damage should happen to the adventure. But by the proceedings erected by Statute of 43 Eliz. cap. 12, only those that are entered in the Office of that Court can be sued or determined there.

The same writer summarized the advantages of an "Office pol." as follows:-1. If the pol. was lost, the entry thereof in the regis. of the Office was sufficient evidence, both at Common Law, and in the same Court; but a private pol. lost is like a deed burnt, unless there be a copy thereof or some other very strong evidence; so that then there will remain nothing but an equitable relief in Chancery for the satisfaction of the party. 2. The commissioners may, in case of any dispute between the assurers and assured, examine them upon oath, and determine the matter according to law and the custom of merchants; but this cannot be done at Common Law, and relief can be had only in a Court of Equity, where the party has not sufficient evidence at Law. 3. It was a Court of Equity as well as a Court of Law; and they could decree against twenty assurers at the same time; but at Law they must be sued severally. 4. They could proceed out of term as well as in term, and they might finish a cause in a fortnight's time or less. 5. The judgments there given were generally upon mature deliberation, and by persons well skilled in marine affairs; and if their sentence was thought unreasonable, the Lord Chancellor or Lord Keeper might, on appeal, examine and determine the same. 6. The Legislature had such respect for the judgments delivered in this Court, that no appeal lay from thence until the whole money decreed was deposited, and full costs paid to the appellee; and though this Court could not compel the defendant to put in bail, yet the sentence there being so expeditious was esteemed very convenient to the assurers as well as the assured. [POLICIES OF INS. COURT.]

Leybourne [Panarithmologia, 1693] says:

Suppose you ship £300 of goods for Jamaica; you being unwilling to run so great a hazard yourself, you go to the Assu. Office behind the Royal Exchange, in Lond., and there acquaint the clerk you will insure for £200 or £250, or, if you will, the whole £300 (for you may insure the whole or any part), upon such ship for so much goods as you have on board.

This must not be read to imply that the Chamber, or Office, undertook the ins. Underwriters assembled there for the purpose of undertaking any manner of ins. risk which offered.

In the London Gazette for Feb. 2-6, 1720, there appeared the following:

Publick Assu. Office on the Royal Exchange, Feb. 6, 1719 [old style]: Whereas information has been given that there have been illegal and fraudulent practices committed to the prejudice of this Office, Notice is hereby given to all persons who can make any such discoveries, that they shall meet with suitable encouragement from the Office.

It appears that the Chamber began to lessen in its attractions to insurers early in the 18th century. It has been supposed that the granting of charters to the two great Ins. Corporations in 1720, which charters expressly provided that all actions on their pol. were to be brought in the Courts at Westminster, had an influence in this direction. We are more disposed to believe that the estab. of Lloyd's Coffee House in 1710, which became the resort of a large number of underwriters, and has eventuated into the world-renowned Lloyds of the present day [LLOYDS], was the real reason of the sudden decline of the Chamber of Ins. The constitution of the Chamber of Ins. was defective, insomuch as it appeared to have no control over the underwriters who frequented it, and undertook risks apparently under the shadow of its authority. Lloyds, on the other hand, instituted in process of time a system of membership, and so obtained at least some control over the action of its members.

The final decline of the Chambers will be treated under POLICIES OF INS. COURT. CHAMBERS, T., AND G. TATTERSALL, pub. in 1845, Laws relative to Buildings, comprising the Metropolitan Buildings Act, Fixtures, Ins. against Fire, etc. CHAMPION ASSURANCE CO. FOR LIFE, FIRE, AND GUARANTEES.-This project was set on foot in 1853, but with what especial end in view, unless to insure the successive Champions of England [Sir John Dymoke is the present Champion of the Queen of

England], or the Champions of the Ring [we do not know the name of the present holder of the belt], we cannot say. CHAMPION LIFE ASSU., ÁNNU., AND REVERSIONARY INT. Co., projected in 1848 by Mr. Edward Power, Barrister-at-Law. He seems to have been content with securing the title, for no steps were taken towards complete regis.

CHANCE.—If we can see no reason why an event is more likely to happen than not to happen, we say it is a chance whether the event will happen or not; or if it may happen in more ways than one, and we have no reason for supposing it will happen in any one of these ways rather than in another, we say it is a chance whether it will happen in any assigned way or in any other. Suppose, for example, an unknown number of balls of different colours to be placed in an urn, from which a ball is about to be extracted by a person blindfold. Here we have no reason for supposing that the ball about to be drawn will be of one colour rather than another, that it will be white rather than black, or red; and accordingly we say it is a chance whether the ball will come out of a particular colour, or a different. In this instance then the term chance denotes simply the absence of a known cause. If, however, we are made acquainted with the number of balls in the urn, and the number there are of each of the different colours, the term is used in a definite sense. For instance, suppose the urn to contain ten balls, of which nine are white, and the remaining one black; we say there are nine chances in favour of drawing a white ball, and one chance only in favour of drawing the black ball. Chance in this sense denotes a way of happening, or a particular case or combination that may arise out of a number of other possible cases or combinations; and an event becomes probable or improbable according as the number of chances in its favour is greater or less than the number against it. Chance and presumption are also frequently used synonymously with probability.— Galloway. CHANCE OF DYING.-A healthy man stands about 8 chances out of 1000 of dying within one year, at the age of 27; about 9 out of 1000 at 33; about 10 out of 1000 at 39; about 11 out of 1000 at 43; 12 at 45; 13 at 47; 14 at 48; 15 at 49; 16 at 50; 17 at 51; 18 at 52; 30 at 60; 44 at 65; 65 at 70; etc. Hence it costs eight times as much to ins. a given sum for one year at 70 as at 27.-Prof. E. Wright. CHANCES, DOCTRINE AND LAWS OF.-Laplace, no mean authority, declared "chance" to be "but the expression of man's ignorance." Pope clothed the same idea in the language of poetry:

"All chance-decrees not understood."

It certainly is not a little remarkable that out of a contemplation of the Doctrine of Chances should have become developed the theory of Life Contingencies-now regarded, and properly so, as among the most certain things with which we are familiar. Whether among the numerous writers who have treated of this subject the majority have been induced to do so, either by the love of scientific speculation; the desire for gain at play; or, as seems more prob., from an intuitive perception of a deeper philosophy than appeared upon the surface, it is not our present purpose to determine. We propose briefly to trace the direction of their inquiries, so far as it has any bearing upon ins. topics.

Poisson remarks that a problem relative to games of chance, proposed to an austere Jansenist by a man of the world, was the origin of a branch of science, now one of the most important in its effects on society.

Mr. W. T. Thomson [Proof-sheets, 1856] remarks: It is curious to observe that L. assu., which is eminently calculated to afford protection against risks adverse to our individual pecuniary interests, by combination and union, which has so favourable a bearing on our social and moral welfare, and which may be considered one of the most valuable discoveries of modern times, may be said to have originated from the study of the laws of chance, as observed in the experience of the gambler. It will be remarked, however, that the one is the very antithesis of the other. In L. assu. the individual is freed from risk by union for mutual protection with his fellow-men. The gambler takes the single risk upon himself, and his average, if he obtain it, can only arise from the duration of his play. In fact, the man who has the opportunity of assu. his life, and does not do it, is the gambler, taking the single risk upon himself.

In 1606 Kepler pub. his work, De Stella Nova in pede Serpentarii, which related mainly to the appearance of a new star two years previously: the discussions relating to the appearance of which caused him to bestow some consideration to the subject of chance. He shows in his work that even such events as throws of dice do not happen without a


Galileo also turned his attention to chance, as is shown by his treatise, Considerazione sopra il Giuco dei Dadi, the date of which is unknown. It was first pub. in 1718. [Galileo died in 1642.] It appears that a friend had consulted this learned man on the following difficulty: with three dice the number 9 and the number 10 can each be produced by six different combinations, and yet experience shows that the number 10 is oftener thrown than the number 9. Galileo made a careful and accurate analysis of all the cases which can occur, and he showed that out of 216 possible causes 27 were favourable to the appearance of the number 10, and 25 were favourable to the appearance of the number 9.

But Galileo's attention was called to the subject of Chance in another form. From his letters we learn that in his day the Florentine gentlemen, instead of employing their time in attention to ladies, or in the stables, or in excessive gaming, were accustomed to improve themselves by learned conversation in cultivated society. In one of their meetings the following question was proposed: a horse is really worth a 100 crowns; one person estimated it at io crowns, another at a 1000-which of the two made the more extravagant estimate? Among the persons who were consulted was Galileo; he pronounced the two estimates to be equally extravagant, because the ratio of a 1000 to a 100 is the same as the ratio of 100 to 10. On the other hand, a priest named Nozzolini, who was also consulted, pronounced the higher estimate to be more extravagant than the other, because the excess of a 1000 above a 100 is greater than that of a 100 above 10. It appears that Galileo had the same notion as Nozzolini when the question was first proposed to him, but afterwards changed his mind.

It was in 1654 that the subject was destined to receive a greater development. The Chevalier de Méré applied to Pascal for a solution of two problems, for which he was unable to find answers. The one was to ascertain in how many throws one might bet with advantage that two sixes would be thrown with two dice; the other to find a rule for dividing the stakes between two players-who were desirous of breaking off an unfinished game-in exact proportion to their relative fortune at the time, and to their chances of winning the remaining stakes. Pascal considered all the possible combinations that could be formed by the simultaneous throw of two dice, and of all the possible changes that might occur in a game of cards, interrupted at any point, and what number of them were in favour of the event for which his solution was required. He then computed the number of cases in which two sixes could be thrown with two dice, and the number of changes which in the actual state of the game of cards would secure to each player, separately, the whole or any part of the stakes, and thus arrived by proportion at the required result. Simple as this method seems (continues Mr. Samuel Brown), it was the first attempt to employ mathematics in such subjects; at least the first that, being closely followed up, led directly to the great discoveries that ensued. Boole, in his Laws of Thought, says this was the first of a long series of problems destined to call into existence new methods in mathematical analysis, and to render valuable service to the practical concerns of life.

Fermat, a magistrate of the Parl. of Toulouse, a mathematician of great repute in his day, was a friend of Pascal, one with whom he corresponded daily on the subject of his studies, and to whom he freely communicated his doubts and his discoveries. He forwarded to him the solution he had arrived at. The original correspondence is now lost; but it appears clear that in his solution he had merely replied to the questions put to him; and however ingenious and minute the investigation, it did not lead to ready solutions of other questions of a similar kind. Copies of the correspondence will be found in the works of the respective authors.

It was Fermat who generalized the solution, and found a rule not merely for ascertaining the value of each player's expectation in the particular case referred to, but at any moment of interrupting the game between any number of players. This was the next step, and by far the most important one, in the science of Prob. Without it the attempt of Pascal might have remained, like some previous problems and speculations by Galileo and Cardan, in obscurity till a much later period.

The correspondence of Pascal and Fermat was not generally made known at this time, though Pascal (as is shown by a letter to one of the learned societies in Paris in 1654) appears to have entertained the thought of introducing his discovery to the world. He evidently appreciated the importance of it; but about this time he met with the accident which led him to retire altogether from his scientific studies, and devote himself to those religious pursuits of which his celebrated Provincial Letters were the fruit. Fermat appears to have been indifferent to his discovery, and but little progress was made for nearly half a century.

Huygens, a celebrated geometrician, on the mere rumour of the questions submitted to Pascal, wrote a treatise in Dutch, which was afterwards translated into Latin by Schootens, and pub. by the latter in a work which appeared in 1658. This was the first systematic treatise which appeared on the Doctrine of Chances. It contained an analysis of the various questions which had been solved by Pascal and Fermat, and at the end five new questions were proposed; the solutions of which, simple as they may now appear, were then attended with considerable difficulty. The analysis of two of them was in fact given for the first time by Montmort half a century after their pub.-Galloway.

In the treatment of the subject these great men had already in effect passed beyond the immediate range of the original inquiry, and were rapidly developing the Theory of Probabilities. Prof. Todhunter indeed remarks: "The practice of games of chance must at all times have directed attention to some of the elementary considerations of the Theory of Prob." A still further stage of progress was near at hand. [1671.]

In 1663 was pub. a treatise De Ludo Alea by Cardan. This was included in the collected works of that author, then for the first time pub. [Cardan died in 1576]. It contains much miscellaneous matter connected with gambling, such as descriptions of 32



games, and an account of the precautions necessary to be employed in order to guard against adversaries disposed to cheat. The discussions relating to Chance form but a small portion of the treatise, which may be best described as the Gambler's Manual.—Todhunter.

In 1671 the Grand Pensionary De Wit came upon the scene. This great man, celebrated alike as a statesman and a mathematician of the highest repute, who had already pub., in 1650, a work on Curves, to which Condorcet refers in terms of eulogy, conceived the design of applying the doctrines of probabilities to the valuation of human life in the question of Government annuities. The result of his labours we have already given in some detail in our hist. of ANNU. ON LIVES.

We must confine ourselves in the remainder of the present art. as much as possible to the Doctrine and Laws of Chance. The Theory of Prob. as developed from the same will be treated of in detail under PROBABILITY; while the application of the Science of Prob. to the contingencies of human life will be treated of under LIFE CONTINGENCIES. In 1692 John Arbuthnot, M.D., pub. a work, Of the Laws of Chance; or, a Method of Calculating the Hazards of Game Plainly Demonstrated. This was prob. the first work pub. in England on the subject. In the same year there appeared a trans. of Huygens' tract into English, accompanied by an Essay on the Laws of Chance, which is supposed by some to have been written by Motte, stated to have been the then Sec. of the Royal So.; but Prof. Todhunter attributes it to Arbuthnot. In this essay are some remarks relative to the advantage of the banker in the game of Pharaon. [See 1738.]

We have shown in our account of the BRESLAU TABLE OF MORT., pub. 1693, how Dr. Halley applied the Doctrine of Chance to the solution of the problems first presented to him by the study of his newly-formed T.

In 1693 there was also pub. in vol. xvii. of Phil. Trans., An Arithmetical Paradox Concerning the Chances of Lotteries, by the Hon. Francis Roberts, F.R.S. [LOTTERIES.] In 1699 John Craig, a Scotch mathematician, pub. a remarkable tract, of which we shall have to speak more at large hereafter. Its main feature was the application of mathematical calculations to the credibility of Gospel history; and he predicted the termination of the Christian religion at a date determined by the Doctrine of Chances! About this date Nicolas Bernouilli pub. a thesis, De Arte Conjectandi in Jure, of which we do not find any detailed account. It is mentioned by Montmort.

In 1708 Pierre Redmond de Montmort pub. his Essai d'Analyse sur les Jeux de Hazards, of which we shall have to speak more at large under date 1714, when the 2nd ed. appeared. Todhunter says of this work of 1708 that, "with the courage of Columbus, he revealed a new world to mathematicians." He adds that much which Montmort had included in his chapter on Combinations would now be considered to belong rather to the chapter on Chances. There were numerous examples about drawing cards and throwing dice.

In 1709 M. Barbeyrac pub., Traité du feu, one of the objects of which appears to have been to show that religion and morality do not prohibit the use of games in general, or of games of chance in particular. Montmort refers to this book, which he says he had lately received from Paris. He said it was un livre de morale. He praises the author, but considers him to be wrong sometimes in his calculations, and gives an example. Nicolas Bernouilli, in reply, says that the author of the book is M. Barbeyrac; he agrees with Montmort in his general opinion respecting the book; but in the example in question he thinks Barbeyrac right, and Montmort wrong.

In 1710 De Moivre submitted to the Royal So. a paper, On the Doctrine of Chances, and the same was pub. in the Phil. Trans. for that year. This paper was afterwards expanded, and pub. in book form. [See 1718.]

In 1713 the Ars Conjectandi of James Bernouilli was pub. under the circumstances we have already explained. [BERNOUILLI, JAMES.] The author solved four out of the five problems which Huygens had placed at the end of his treatise. The last of the five problems which Huygens left to be solved was the most remarkable of all. It is the first example on the Duration of Play, a subject which afterwards exercised the highest powers of De Moivre, Lagrange, and Laplace. James Bernouilli solved the problem, and added, without a demonstration, the result for a more general problem, of which that of Huygens was a particular case. Perhaps (says Todhunter) the most valuable contribution to the subject which this part of the work contains, is a method of solving problems in chance which James Bernouilli speaks of as his own, and which he frequently uses." Finally, "We may observe that Bernouilli seems to have found-as most who have studied the subject of chances have also found that it was extremely easy to fall into mistakes, especially by attempting to reason without strict calculation."

[ocr errors]

In 1714 the 2nd ed. of Montmort's essay appeared [1st ed., 1708]. It was much more bulky than the first ed. He makes some judicious obs. on the foolish and superstitious notions which were prevalent among persons devoted to games of chance, and proposes to check these by showing, not only to such persons, but to men in general, that there are rules in chance, and that for want of knowing these rules mistakes are made which entail adverse results; and these results men impute to destiny instead of their own ignorance. The work is divided into four parts. The 1st contains the theory of combinations; the 2nd discusses certain games of chance depending on cards; the 3rd discusses certain games of chance depending on dice; the 4th part contains the solution

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.'

[ocr errors]

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 Aleæ ; 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 [1658], 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., 1755 (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-quarante, et que l'on nomme à Florence le trente-et-un.

« AnteriorContinuar »