5

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themselves to primitive man, it has become precious to every civilized grocer and butcher. The Arabians began to find it valuable shortly after A. D. 800; the less advanced Europeans four centuries later. A far more logical method, first developed in a more complete constitution of society, is the doctrine of chances. In our days, familiarity with this calculus may be of vital service to many an individual, although it is those corporations which in the modern world have transactions with millions of parties, like insurance companies, that the logic of probability chiefly concerns.

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Still, I repeat it, it is not in questions closely concerning a man's business that he can with any semblance of fairness look to finding the theory of reasoning helpful. Such help is rather to be expected in extraordinary and unusual problems,--especially in those of a speculative character, where conclusions are not readily checked