:- 



PROBABILITY. 



TROBLEM. 



7-1 



of ill subjects, UMT* is no one in which writers of every grade have 

 o frequently or so strangely made mistake* of mere inadvertence. 

 One was pointed out about twenty years ago (' Camb. Phil. Trans.') 

 into which both Laplace and Poisson had fatten, one after the other; 

 bat the discoverer of their alip proved himself signally 1UM. t<> 

 mater ooei a very tittle while after. (' Cab. Cyclop. : Probability and 



:-- 



We ahall conclude by a brief account of the historical progress of 

 thia branch of nienoe ; referring the reader for more detail to Mon- 

 toda, and to the Treatise ' On Probability,' in the ' Library of Useful 

 Knowledge.' Than who cultivated game* of chance most at all times 

 bare had a general notion of oombinatiuni which were more probable 

 than others, and must hare seen that those cases of which there were 

 uioat to happen, always did in reality happen moat often. They could 

 nut fail to know, by reckoning on their fingers, that out of, for instance, 

 all the throws of a pair of dice, there are only aix doublets, and thirty 

 other equally possible cases ; nor could they have missed knowing that 

 Uu> must be tie reason why doublets occur seldom in comparison with 

 other throws. Notwithstanding this, the mathematical history of the 

 subject usually dates from a fragment by Galileo, which merely shows 

 why 10 can lx- oftener thrown on three dice than 9, and two problems 

 proposed by Chevalier de M<M to Pascal, in 1(354, concerning certain 

 I>inU connected with games of chance. 



That the history of correct investigation dates from this period 

 there can bo little <! >ubt. I nit the subject had been previously considered 

 by Cardan, in a work, ' De Ludo Alex,' published from his manuscript 

 in the first volume of the collected edition of his works, and never 

 separately ; and also so badly printed as to be almost unintelligible ; 

 circumstances both of wlii. 'i have probably contributed to keep it, as 

 it has been kept, totally out of view. Cardan's theory is perfectly 

 false : he supposes, for example, that since there are six faces to a die, 

 it will happen in the long run that each face will come up once in six 

 throws, which is true when many collections of six throws are 

 averaged ; but from this he draws the false conclusion that it is an 

 even chance that any one face comes up in three throws. His 

 numerical reasoning is therefore totally incorrect ; but his notions on 

 the general subject of probability are reasonably sound. Fortune, 

 according to him, does not decide the general average of the play, but 

 only the deviations on one aide and the other which a small number of 

 cases present ; and experiment would, he says, prove that the long run 

 would agree with the predictions of theory ; it were to be wished that 

 he had tried it on his own theory. This treatise was written about 

 1564, and published in 1663. But before this, in 1657, the tract of 

 Huyghens, De Katiociniis in Ludo Aletc,' was published as an appendix 

 to ochooten's ' Exercitationes Geometricic,' being not only the first 

 regular treatise, but the first which applies the theory to chances of 

 loss or gain. It was translated into English, with additions, in 1692, 

 the reputed translator being Motte, the secretary of the Royal Society. 

 Then followed the ' Analyse des Jeux de Haeord,' by Monttnort (first 

 edition 1708, second, enlarged, 1713), a work of higher mathematical 

 pretensions. The ' Ars Conjectandi,' of James Bernoulli, posthu- 

 mously published by his nephew Nicolas, in 1713 (and which, it may 

 be worth noting, is not contained in the.collection of James Bernoulli's 

 works), gives the first glimpse of the more difficult class of problems 

 in which processes containing very large numbers are abbreviated by 

 mathematical analysis. This was carried still further by De Moivre, 

 whose first work, a paper, ' De Mensura Sortis ' (' Phil. Trans.,' 1711), 

 was expanded into his celebrated treatise on the doctrine of chances, 

 first edition 1718 (not 1716, as frequently stated), second edition 1738, 

 third edition, with his 'Treatise on Life Annuities,' 1756. The next 

 top was made by Bayes (' Phil. Trans.,' 1763 and 1764), who first 

 considered the probability of hypotheses as deduced from observed 

 n -- 



The great work of Laplace (first edition 1812, third 1820) had in 

 great part appeared at various previous times in the ' Memoirs' of the 

 Academy of Sciences. It is remarkable, first by the extension of 

 methods which it furnishes ; secondly, by its giving at one view the 

 whole state of the science and its applications ; thirdly, by the particular 

 attention given to the application of the theory to the results of obser- 

 vation. [MCA*; LEAST SQUARES.] The next step in the history in 

 Poisson's ' Itecherches sur lea Probabilities des Jugemens,' 1837, which 

 gives the grand results of Laplace by a somewhat different analysis, 

 and applies them particularly to the decisions of courts of law. This 

 species of application had been before considered by Condoroet, in his 

 ' Essai sur 1' Application de r Analyse a la Probability des Decision/I,' 

 Paris, 1785. It may also be worth while to mention the ' Traitc 1 do 

 Calcul Conjectural/ of Parisot, Paris, 1810, a work which deals largely 

 in the theory of simple combinations. The elementary work of longest 

 standing, which exhibits some view of the higher mathematical appli- 



s is the Trait*! Elementaire du CalcuTdes ProbabilitcV by M. 

 Lacroix (second edition, 1822). The ' Essai Philosophiquc' of Laplace, 

 which is an introduction to the third edition of bis theory, contains no 

 mathematics, and may be usefully read with any elementary treatise. 



Instructions Popiilaires sur le Calcul des Probability' by M. 



t, lirusscla, 1828, contains the most elementary view of the 

 : uWject, and uses only simple arithmetic. 



1 :ngland, since the publication of Simpson's Laws of Chance,' 

 Mo, and the 'Laws of Chance,' by Samuel Clark, 1758, little was 



written on the mathematical theory except so far as it had reference to 

 life annuities and assurance, until a very recent period. About 1830 

 Messrs. Lubbook and Drinkwater (Bethuue) published a tract 

 I'robability,' in the ' Library of Useful Knowledge,' giving more general 

 methods of applying modern algebraical investigation than had before 

 appeared in thu country : by a binder's mistake this work is often attri- 

 buted to Mr. De Morgan. In 1837, the article ' Theory of ProbaU'lities,' 

 in the ' Encyclopaedia Metropolitana,' written by Mr. De Morgan, gave 

 the results and methods of Laplace on moat of the great questions of 

 the theory. The ' Essay on Probabilities, and on their Application to 

 Life Contingencies and Insurance Offices,' published by the same 

 writer in the ' Cabinet Cyclopaedia/ 1838, exhibits the principles with- 

 out mathematical investigation, and the results arranged in n. 

 use. The article on ' Probability ' in the new edition of the I 

 clopudia Metropolitana,' by Mr. Galloway, gives the mathematical 

 investigation of the higher parts of the theory, following the methods 

 of Poisson. This treatise is published separately. 



On subject* connected with this article, ew UAMINO; RISK; WAGER; 

 MEAN; LEAST SQOABKS; OBSERVATION AND EXPERIMENT; WEIUUT or 

 OIISKBVATIONB; AsMcrr r ; MORTALITY ; REVERSION, &c. 



I'KtUlATK. [\ViLL.] 



PROBATE, COURT UK. The grant of letters of administration of the 

 effects of persons dying intestate, and of probate of the wills of testa- 

 tors, which wore formerly the prerogative of the Ecclesiastical Court* 

 [ECCLESIASTICAL COURTS], have been recently (20 & 21 Viet. c. 77) 

 vested in a newly established court, called the Court of Probate. 

 The functions of this court ore confined entirely to deciding upon the 

 authenticity of wills, and upon the proper persons to whom administra- 

 tion is to be committed, when no will exists. With the distribution of 

 the property of deceased persons, and the rights of the various parties 

 who claim it beneficially, the court has nothing to do. These matters 

 must be decided by the courts of law and equity, as before the passing 

 of the Act. The duties of executors and administrators remain the 

 same as formerly. A central registry of wills and administration is 

 established in London, and district registrars are established in forty 

 of the principal towns of England. The office or registry in which 

 probate or a grant of administration is to be sought, is no longer to be 

 determined by the locality of the astelt of the deceased person, but by 

 the place where the deceased had a fixed abode at the time of death. 

 Should the testator or intestate have a permanent place of residence 

 in one of the registry districts at the time of his decease, probate or 

 grant of administration may be obtained there ; but the executors or 

 parties claiming administration may, if they think fit, apply to tho 

 principal or metropolitan registry, and this may in some cases tie 

 found more convenient. Original wills proved in the country will 

 be preserved in the district registries; but copies of them will bo 

 transmitted to the principal registry in London, so that iu future the 

 metropolitan registry will be tho most convenient office of scorch for 

 any will whatsoever. 



The practice of ithe Court of Probate has been thrown open to the 

 whole legal profession, so that the close monopoly of t 

 business formerly enjoyed by advocates and proctors is at an end. 

 The court is presided over by a single judge, who sits at Westminster. 

 An appeal lies from his decision direct to the House of Lords. 



In coses where a person dies in one of the forty districts, 1. 

 personal property under 2002., tho judge of tho County Court of the 

 district has jurisdiction should any contention arise, but from his 

 decision an appeal, which is final, lies to the Court of Probate. 



One principal advantage of the new system lies in the removal of all 

 difficulty as to the question where a will ought to bi- in-nveil, and tho 

 old question of lona notabilia, on which tho necessity of obtaining 

 prerogative probate or administration was founded. Tho rules of 

 evidence in the Court of Probate ore to be the same as those iu courts 

 of law and equity, while its proceedings are likewise assimilated to 

 those of the courts of common law. 



The duties raised in the Probate Court yielded in the year ending 

 March 31, 1860, the sum of 3,463,226?., including the succession < 1 

 The legacy duty is charged on legacies of tho value of '201. and upwards 

 out of personal estate or charged upon real estate, and upon every share 

 of residue. Legacy to a husband or wife is exempt from duty. To a 

 child, the husband of a child, a parent, or any lineal descendant or 

 ancestor of the deceased, the duty is 11. per. cent. ; to a brother or 

 sister or then* descendants, St. per cent. ; to an uncle or aunt or their 

 descendants, St. per cent. ; to a great uncle or great aunt or their 

 descendants, 6V. per cent. ; to any other relation or any stranger in 

 blood, 101. per cent The probate duty is payable on the total sura 

 left by the deceased. For sums above 20i and not exceeding 1001. the 

 duty is 10*. if there is a will ; and if there is no will the duty of 10. 

 is chargeable on sums of 201. and not exceeding 501. The duties con- 

 tinue to increase according to a certain scale. The succession 

 on real estate have the same scale, and the valuation is made according 

 to the worth as an annuity. 



PROBLEM (p<f/3A7)^a) means simply a thing put forward or pro- 

 posed. In mathematical language it is anything which is requi 

 be done, and in the earlier writers is distinguished from a theoi 

 assertion to be proved, iu that the latter does not require any >] 

 iibj-i-t to bo effected. Thus, " all tho angles of a triangle are together 

 equal to two right angles " is to be shown or made evident, and is a 





