ON THE STATISTICAL VIEW OP NATURE. 569 



in appalling mystery. 1 There is, however, no doubt that 

 the Theory of Probability increasingly pervades scientific 

 as well as statistical work in our age, and that in the 



1 In spite of the encomium on 

 the theory of probabilities quoted 

 in vol. i. p. 123, Sir John Herschel 

 gave only a qualified adherence to 

 one of its principal applications 

 (see ' Brit. Assoc. Rep.,' vol. i. p. 

 165). The two foremost adverse 

 critics of the theory were Auguste 

 Comte in France and John Stuart 

 Mill in England. In the second 

 volume of the ' Philosophic Posi- 

 tive' (1st ed., 1835, p. 371) the 

 former explains why he omitted 

 to deal with so important a sub- 

 ject in his mathematical philosophy. 

 " Le calcul des probabilite"s ne me 

 semble avoir e"t reellement, pour 

 ses illustres inventeurs, qu'un texte 

 commode a d'inge'nieux et difficiles 

 problemes nume'riques, qui n'en con- 

 servent pas moins toute leur valeur 

 abstraite, comme les theories ana- 

 lytiques dont il a e'te' ensuite 1'occa- 

 sion, ou, si 1'on veut, 1'origine. 

 Quant a la conception philoso- 

 phique sur laquelle repose une telle 

 doctrine, je la crois radicalement 

 fausse et susceptible de conduire 

 aux plus absurdes consequences. 

 Je ne parle pas seulement de 

 1'application eVidemment illusoire 

 qu'on a souvent tente" d'en faire 

 au pre"tendu perfectionnment des 

 sciences sociales : ces essais, ndces- 

 sairement chime'riques, seront car- 

 acterises dans la derni6re partie de 

 cet ouvrage " : and in the fourth 

 volume (1839, p. 512), "La seule 

 aberration de ce genre . . . c'est 

 la vaine pre"tention d'un grand 

 nombre de ge"ometres a rendre 

 positives les etudes sociales d'apres 

 une subordination chime"rique a 

 1' illusoire the"orie mathe'matique 

 des chances. . . . Quelque gros- 

 siere que soit eVidemment une 

 telle illusion, elle dtait neanmoins 



essentiellement excusable, quand 

 1'esprit eminemment philosophique 

 de 1'illustre Jacques Bernoulli 

 con9ut, le premier, cette pense'e 

 generate, dont la production, a une 

 telle e"poque, constituait reellement 

 le precieux et irrecusable symptome 

 du besoin prdmaturts pour ce temps, 

 mais qui n'y pouvait etre eprouve^ 

 meme ainsi que par une intelligence 

 vraiment supeYieure." John Stuart 

 Mill, in the second volume of his 

 ' Logic,' has devoted a whole chapter 

 to the subject, in which he corrects 

 a statement made by him in the 

 first edition of his book, attributing 

 a " fundamental fallacy " to the 

 arguments of Laplace and other 

 mathematicians, but nevertheless 

 takes an unfavourable view of the 

 usefulness of the calculus. In 

 more recent times the subject has 

 been exhaustively treated from a 

 logical point of view by Mr John 

 Venn in his work, 'The Logic of 

 Chance' (3rd ed., London, 1888), 

 and by Stanley Jevons in ' The 

 Principles of Science' (vol. i. ch. x.) 

 The doubts with which Mill, and 

 still more Comte, regarded the 

 subject, seem to have been dis- 

 pelled in works on Logic ; and the 

 increasing use to which the methods 

 for the correction of error have 

 been put in many branches of 

 science have convinced mathema- 

 ticians of its applicability. The 

 ninth edition of the 'Ency. Brit.' 

 contains an excellent article on 

 " Probabilities " by M. W. Crofton. 

 Among the clearest and safest 

 guides in this intricate subject 

 must be counted the late Prof. 

 Augustus de Morgan, whose pro- 

 found treatise in the ' Ency. 

 Metrop.' (vol. ii.), as well as his 

 ' Essay on Probabilities ' (London, 



