It must be allowed that the hypothesis adopted by Laplace is in some degree arbitrary, so that there was some opening for the doubt which Boole has cast upon it.[168] But it may be replied, (1) that the supposition of an infinite number of balls treated in the manner of Laplace is less arbitrary and more comprehensive than any other that can be suggested. (2) The result does not differ much from that which would be obtained on the hypothesis of any large finite number of balls. (3) The supposition leads to a series of simple formulas which can be applied with ease in many cases, and which bear all the appearance of truth so far as it can be independently judged by a sound and practiced understanding. [168] *Laws of Thought*, pp. 368–375. *Rules of the Inverse Method.* By the solution of the problem, as described in the last section, we obtain the following series of simple rules. 1. *To find the probability that an event which has not hitherto been observed to fail will happen once more, divide the number of times the event has been observed increased by one, by the same number increased by two.* If there have been *m* occasions on which a certain event might have been observed to happen, and it has happened on all those occasions, then the probability that it will happen on the next occasion of the same kind (*m* + 1)/(*m* + 2). For instance, we may say that there are nine places in the planetary system where planets might exist obeying Bode’s law of distance, and in every place there is a planet obeying the law more or less exactly, although no reason is known for the coincidence. Hence the probability that the next planet beyond Neptune will conform to the law is 10/11. 2. *To find the, probability that an event which has not hitherto failed will not fail for a certain number of new occasions, divide the number of times the event has happened increased by one, by the same number increased by one and the number of times it is to happen.* An event having happened *m* times without fail, the probability that it will happen *n* more times is (*m* + 1)/(*m* + *n* + 1). Thus the probability that three new planets would obey Bode’s law is 10/13; but it must be allowed that this, as well as the previous result, would be much weakened by the fact that Neptune can barely be said to obey the law. *3. An event having happened and failed a certain number of times, to find the probability that it will happen the next time, divide the number of times the event has happened increased by one, by the whole number of times the event has happened or failed increased by two.*