If the witness, wishing to deceive, has some interest in choosing number 79 among the numbers not drawn,—if he judges, for example, that having placed upon this number a considerable stake, the announcement of its drawing will increase his credit, the probability that he will choose this number will no longer be as at first, 1/999, it will then be ½, ⅓, etc., according to the interest that he will have in announcing its drawing. Supposing it to be 1/9, it will be necessary to multiply by this fraction the probability 999/1000 in order to get in the hypothesis of the falsehood the probability of the event observed, which it is necessary still to multiply by 1/10, which gives 111/10000 for the probability of the event in the second hypothesis. Then the probability of the first hypothesis, or of the drawing of number 79, is reduced by the preceding rule to 9/120. It is then very much decreased by the consideration of the interest which the witness may have in announcing the drawing of number 79. In truth this same interest increases the probability 9/10 that the witness will speak the truth if number 79 is drawn. But this probability cannot exceed unity or 10/10; thus the probability of the drawing of number 79 will not surpass 10/121. Common sense tells us that this interest ought to inspire distrust, but calculus appreciates the influence of it. The probability _à priori_ of the number announced by the witness is unity divided by the number of the numbers in the urn; it is changed by virtue of the proof into the veracity itself of the witness; it may then be decreased by the proof. If, for example, the urn contains only two numbers, which gives ½ for the probability _à priori_ of the drawing of number 1, and if the veracity of a witness who announces it is 4/10, this drawing becomes less probable. Indeed it is apparent, since the witness has then more inclination towards a falsehood than towards the truth, that his testimony ought to decrease the probability of the fact attested every time that this probability equals or surpasses ½. But if there are three numbers in the urn the probability _à priori_ of the drawing of number 1 is increased by the affirmation of a witness whose veracity surpasses ⅓.