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This and other scientific work involving fine measurement, with the correlative investigations into the theory of probable error, seem to have been a decisive influence in the development of Peirce’s philosophy of chance. Philosophers inexperienced in actual scientific measurement may naïvely accept as absolute truth such statements as “every particle of matter attracts every other particle directly as the product of their masses and inversely as the square of the distance,” or “when hydrogen and oxygen combine to form water the ratio of their weights is 1 : 8.” But to those who are actually engaged in measuring natural phenomena with instruments of precision, nature shows no such absolute constancy or simplicity. As every laboratory worker knows, no two observers, and no one observer in successive experiments, get absolutely identical results. To the men of the heroic period of science this was no difficulty. They held unquestioningly the Platonic faith that nature was created on simple geometric lines, and all the minute variations were attributable to the fault of the observer or the crudity of his instruments. This heroic faith was, and still is, a most powerful stimulus to scientific research and a protection against the incursions of supernaturalism. But few would defend it to-day in its explicit form, and there is little empirical evidence to show that while the observer and his instruments are always varying, the objects which he measures never deviate in the slightest from the simple law. Doubtless, as one becomes more expert in the manipulation of physical instruments, there is a noticeable diminution of the range of the personal “error,” but no amount of skill and no refinement of our instruments have ever succeeded in eliminating irregular, though small, variations. “Try to verify any law of nature and you will find that the more precise your observations, the more certain they will be to show irregular departure from the law.”^[2] There is certainly nothing in our empirical information to prevent us from saying that all the so-called constants of nature are merely instances of variation between limits so near each other that their differences may be neglected for certain purposes. Moreover, the approach to constancy is observed only in mass phenomena, when we are dealing with very large numbers of particles; but social statistics also approach constant ratios when the numbers are very large. Hence, without denying discrepancies due solely to errors of observation, Peirce contends that “we must suppose far more minute discrepancies to exist owing to the imperfect cogency of the law itself, to a certain swerving of the facts from any definite formula.”^[3]