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228 F. Y. EDGEWORTH: content with a mere guess as to the value of a constant ; for instance, the weight to be assigned to an observation. Func- tions evaluated only to the third or fourth term of develop- ment are employed. Nay we may reason about functions without knowing even approximately their form. I have else- where attempted to illustrate this characteristic of mathe- matical reasoning, superfluously indeed, for, as a reviewer observes, the person who supposes that the higher mathe- matics are but a complicated sort of double rule of three is not worth arguing with. So far then as the imperfections of our reasonings are of the kind that is familiar in mathematical physics, no par- ticular apology is required. Even Mr. Venn, while he points out the imperfection of our statistical data, yet allows a reasonable license in treating them as if they were perfect. Even that precisian, M. Block, for whom ' point de nombres point de statistique,' is obliged to admit a certain element of approximation. Nor is there any particular difficulty in extending the statistical method to unnumerical quantities, as Professor Jevons has pointed out. 1 There is no difficulty about handling those constants which, as Boole and Donkin point out, are generally introduced by problems in inverse probability ; provided that we have some quantitative datum about the constant, as that it is not very great or not very small. This is admirably shown by Donkin in his pro- found essays on Probability in the Philosophical Magazine, 1850-1. Donkin puts the problem : A person who under- stands the game of chess sees a certain number of pieces placed in a particular situation. " What is to him the pro- bability that the situation was actually produced by a game?" This inverse problem introduces the a priori probability that a game would be played, and other con- stants. If w r e know something about the ways of the house, we may know that this probability is not very small, and thus from the mathematical formula deduce a substantial though not a numerical conclusion. Similarly the much decried method of Bayes may be employed to deduce from the frequently experienced occurrence of a phe- nomenon the large probability of its recurrence. There is not required a precise a priori knowledge, as of variously constituted bags of balls, which Mr. Venn postulates (ch. 5). Almost any a priori knowledge, as Cournot 2 has well shown, is sufficient to deduce an overwhelmingly large, 1 Report of the British Association, 1870. 2 TMorie des Chances, 95, p. 169.