95. Statistics. Their Relation to Induction. -- Scientific induction concludes with certainty to the existence of a definite law of nature. Now we are often brought face to face with facts evidently governed by laws, the intricacy of which the mind does not fathom. We then have recourse, provisionally, to the registration of these facts and their coincidences. This constitutes the object of statistics.

Statistics are an inventory of numerous facts in which their relative frequency and their coincidences are noted, with the view of discovering indications of natural causes.

It is beyond doubt that there must be a sufficient cause, in the very nature of things, for this constant recurrence of events, but we do not know, or even guess, with what natural properties this law is connected.^{1} just as soon as the observer guesses, out of all this heap of facts, what invariable conditions (method of agreement), which are also exclusive (method of difference) and correlative in point of intensity (method of concomitant variations), are antecedent to the event to be explained, so soon will he enter upon a science. A scientific hypothesis will have emerged. The verification of the hypothesis will be the work of induction.

{1} There are cases where the facts sbow neither the. regularity nor the constancy which indicate a law, e. g., a homogeneous die, with one of the numbers from 1 to 6 on each of its faces, is thrown. In 12 throws, the numbers 3 and 5 have each turned up three times; the 2 and the 4, twice; the 1 and the 6 only once. The probability of contingent events may be submitted to calculation and affords opportunity for interesting applications. For the theory of probabilities and its logical value, Bernouilli's theorem, and Poisson's law of higher numbers, see Higher Conrse, vol. I, pp. 352 sqq.