Of course our usual practical resource in such cases is to make appeal to our previous knowledge of the subject in question, which enables us to reject as absurd a great number of hypotheses which can nevertheless make a fair show when they are allowed to rest upon a limited amount of adroitly selected instances. But it must be remembered that if any theory chooses to appeal to statistics, to statistics it must be suffered to go for judgment. Even the boat race theory could be established (if sound) on this ground alone. That is, if it really could be shown that experience in the long run confirmed the preponderance of successes on one side or the other according to the relative frequency of the sun-spots, we should have to accept the fact that the two classes of events were not really independent. One of the two, whichever it may be, must be suspected of causing or influencing the other; or both must be caused or influenced by some common circumstances. 10. (III.) The fallacy described at the commencement of this chapter arose from determining to judge of an observed or reported event by the rules of Probability, but employing a wrong set of statistics in the process of judging. Another fallacy, closely connected with this, arises from the practice of taking some only of the characteristics of such an event, and arbitrarily confining to these the appeal to Probability. Suppose I toss up twelve pence and find that eleven of them give heads. Many persons on witnessing such an occurrence would experience a feeling which they would express by the remark, How near that was to getting all heads! And if any thing very important were staked on the throw they would be much excited at the occurrence. But in what sense were we near to twelve? There is a not uncommon error, I apprehend, which consists in unconsciously regarding the eleven heads as a thing which is already somehow secured, so that one might as it were keep them, and then take our chance for securing the remaining one. The eleven are mentally set aside, looked upon as certain (for they have already happened), and we then introduce the notion of chance merely for the twelfth. But this twelfth, having also happened, has no better claim to such a distinction than any of the others. If we will introduce the notion of chance in the case of the one that gave tail we must do the same in the case of all the others as well. In other words, if the tosser be dissatisfied at the appearance of the one tail, and wish to cancel it and try his luck again, he must toss up the whole lot of pence again fairly together. In this case, of course, so far from his having a better prospect for the next throw he may think himself in very good luck if he makes again as good a throw as the one he rejected. What he is doing is confounding this case with that in which the throws are really _successive_. If eleven heads have been tossed up in turn, we are of course within an even chance of getting a