PREVOST AND LHUILIER. 457 



Art. 843. The coincidence of the results obtained on the two dif- 

 ferent hypotheses is remarkable. 



848. Suppose that r = 1 and 5 = in the result of Art. 843 ; 

 we thus obtain 



p-hl 



Again suppose ?^ = 2 and 5 = 0; we thus obtain 



The factor -^ is, as we have just seen, the probability 



of drawing another white ball after drawing p white balls and 



p + 2 



q black balls ; the factor — expresses in like manner the 



^ 7^ + ^ + 3 ^ 



probability of drawing another white ball after drawing^ + 1 white 



balls and q black balls : thus the formula makes the probability 



of drawing two white balls in succession equal to the product of 



the probability of drawing the first into the probability of drawing 



the second, as should be the case. This property of the formula 



holds generally. 



849. The memoir which we have now examined contains the 

 first discussion of the problem to which it relates, namely, the 

 problem in which the balls are not replaced. A particular case of 

 the problem is considered by Bishop Terrot in the Transactions of 

 the Royal Society of Edinburgh, Vol. xx. 



850. The other two memoirs to which we have referred in 

 Art. 841 are less distinctly mathematical, and they are accordingly 

 printed in the portion of the volume which is devoted to speculative 

 philosophy. The second memoir occupies pages 3 — 24, and the 

 third memoir pages 25 — 41. A note relating to a passage of the 

 third memoir, by the authors of the memoir, is given in the volume 

 for 1797 of the Memoires de V Acad.... Berlin, page 152. 



851. The second memoir is entitled 8ur Vart d'estimer la 

 prohabilite des causes par les effets. It consists of two sections. 

 The first section discusses the general principle by which the 



