120 



SCIENTIFIC THOUGHT. 



connected with it the doctrine of averages and the mathe- 

 matical theory of probabilities. 1 The same great mind 



1 The beginnings of the science 

 and theory of probabilities are net 

 subject to controversy, as were 

 those of the infinitesimal calculus. 

 Pascal and Fennat about the middle 

 of the seventeenth century entered 

 into a correspondence relative to a 

 question in a game of chance, pro- 

 pounded by the Chevalier de Mere", 

 a noted gambler. They agreed in 

 their answer, but could not con- 

 vince their friend, who moreover 

 made this the occasion of denounc- 

 ing the results of science and arith- 

 metic. But this comparatively in- 

 significant problem so different 

 from the great cosmical problems 

 which led to the invention of the 

 infinitesimal calculus about the 

 same time was the origin of a 

 series of investigations and discus- 

 sions in which the greatest mathe- 

 maticians, such as Huygens, James 

 and Daniel Bernoulli, De Moivre, 

 D'Alembert, and Condorcet joined. 

 Most of them did not escape the 

 errors and misstatements which 

 creep in an insidious manner into 

 the discussion and vitiate the conclu- 

 sions. In fact, the science advanced 

 through the influence of those who 

 depreciated it like D'Alembert, and 

 those who exaggerated its import- 

 ance like Condorcet. At length, 

 under the hands of Laplace, who 

 defined it as common-sense put into 

 figures and attributed to it a high 

 educational value, it assumed a state 

 wellnigh approaching to that per- 

 fection which Euclid gave to geo- 

 metry and Aristotle to logic. Since 

 the publication of Laplace's cele- 

 brated ' Theorie analytique des Pro- 

 babiliteV (Paris, 1812) writers on 

 the subject have found ample oc- 

 cupation in commenting on the 

 theorems or recasting the proofs 

 given in that work, which holds a 

 similar position to that occupied in 



! another department of mathematics 

 by the 'Disquisitiones Arithmetics? ' 

 of Gauss (1801). Up to the pres- 



; ent day there exist differences of 

 opinion as to the value of the 

 science, the two opposite views be- 

 ing represented in this country by 

 Mill ('Logic,' 5th ed., vol. ii. p." 62) 

 and Jevons (' Principles of Science,' 

 vol. i. ), the latter summing up his 

 opinion as follows : " In spite of its 

 immense difficulties of application, 

 and the aspersions which have been 

 mistakenly cast upon it, the theory 

 of probabilities is the noblest, as it 

 will in course of time prove perhaps 

 the most fruitful, branch of mathe- 

 matical science. It is the very 

 guide of life, and hardly can we 

 take a step or make a decision of 

 any kind without correctly or in- 

 correctly making an estimation of 

 probability" (1st ed., p. 248). A 

 similar opinion seems to have been 

 held by James Clerk Maxwell (see 

 Life by Campbell and Garnett, p. 

 143), who called the calculus of 

 probabilities " Mathematics for 

 practical men." In this country 

 A. de Morgan and Todhunter, the 

 former in a popular essay in the 

 1 Cabinet Cyclopaedia ' and in a 

 profound treatise in the ' Encyclo- 

 paedia Metro politana,' the latter in 

 his well - known History (London 

 and Cambridge, 1865), have done 

 a great deal to make this subject 

 better understood. The applica- 

 tions of the theory have gradually 

 increased through numerous mor- 

 tality and insurance calculations ; 

 as also in the estimations of error 

 in astronomical and physical ob- 

 servations, where the well-known 

 method of least squares (first em- 

 ployed by Gau.*s in 1795, see Gauss, 

 Werke, vol. vii. p. 242 ; first pub- 

 lished by Legendre in 1806, and then 

 proved by Laplace in his ' Theorie,' 



