1. It has always been known that, while some sets of events invariably happen together, other sets generally happen together. That experience shows one thing, while not always a sign of another, to be a usual or probable sign of it, must have been one of the earliest and most primitive forms of knowledge. If a dog is generally given scraps at table, that is sufficient for him to judge it reasonable to be there. But this kind of knowledge was slow to be made precise. Numerous experiments must be carefully recorded before we can know at all accurately how usual the association is. It would take a dog a long time to find out that he was given scraps except on fast days, and that there was the same number of these in every year.

The necessary kind of knowledge began to be accumulated during the seventeenth and eighteenth centuries by the early statisticians. Halley and others began to construct mortality tables; the proportion of the births of each sex were tabulated; and so forth. These investigations brought to light a new fact which had not been suspected previously—namely, that in certain cases of partial association the degree of association, i.e. the proportion of instances in which it existed, shows a very surprising regularity, and that this regularity becomes more marked the greater the number of the instances under consideration.