208 Mr. F. Y. Edgeworth on 



inmate constants introduced by Boole and Donkin into the 

 expression for a posteriori probabilities do not refuse a quan- 

 titative though not numerical conclusion ; provided that we 

 know something of those a priori probabilities : that they are 

 not extremely great or small*. Since, indeed, these constants 

 are of a somewhat fainiant character, and have at most a veto 

 on the conclusion, there seems a good deal to be said (beyond 

 what has been said by Boole and Donkinf ) in favour of the prac- 

 tice of Laplace and Herschel and other high authorities, who 

 omit these constants in their estimate of a posteriori probability. 

 Only it must be remembered that such measures are not of 

 the exacter species contemplated by Herschel % and DeMorgan§, 

 but rather like economic measures of utility, not proportional 

 to the thing measured, but increasing with its increase and 

 decreasing with its decrease in general and in the absence of 

 extraordinary circumstances. 



(2) If greater precision is desiderated, may we postulate that 

 the measurables in our first two paragraphs and the constants 

 representing probability in our third paragraph do as often 

 have one value as another (of all the values which they can 

 possibly have, or at least over a certain range of those values). 

 Such a postulate is based by the present writer || upon a sort 

 of unconscious induction; like that upon the strength of which 

 it has been believed (correctly, as more definite experience 

 shows) that one digit in general recurs as often as another. 

 This position is not exposed to Boole's remark^ upon apriori 

 probability, which Mrs. Bryant** has lately reinforced. They 

 seem to fire altogether above our humble empirical ground. 

 But it may be well to show that, as we are not aimed at, so 

 neither are we hit, Boole, objecting to the assumption that 

 a priori one value of a probability-constant is as likely as 

 another, propounds a counter hypothesis according to which 

 a priori probabilities are no longer evenly distributed, but 

 crowded together in the neighbourhood of the value J. The 

 reply is tt that the hypothesis does not agree with fact, that 

 experience (e. g. the Registrar-General's returns) presents a 

 great variety of statistical ratios, and no decided preponder- 

 ance of the ratio \. Mrs. Bryant follows, objecting " that if 

 all frequencies of the event Y are equally probable, the fre- 

 quencies of the event which consists in a Y following a Y are 



* See Phil. Mag. 4th series, vol. i. p. 360, vol. ii. p. 99; Cf. 'Mind,' 

 April 1884, the Philosophy of Chance 



t Phil. Mag. 4th ser. vol. i. p. 462, vol. ii. p. 98. 

 % 'Essays/ p. 369. § 'Formal Logic/ chapter on Probability. 



|| ' Mind/ April 1884 ; ' Hermathena/ May 1884. 

 11 ' Laws of Thought/ p. 370. ** Phil. Mag. June 1884. 



tt Cf ' Mind/ loc. cit. 



