TREMELEY. 415 



— ^^- 6, lie obtains as the numerator of the required probability, 



approximately 



\p + <t ) \p + q ) L pq + {p + qf S' 



\ p \q 

 The denominator would be ' ,, . 



Trembley refers to two places in which Laplace had given this 

 result; they are the Hist de T Acad.... Par is for 1778, page 270, 

 and for 1783 page 445. In the Theorie...des Frob. Laplace does 

 not reproduce the general formula ; he confines himself to suppos- 



.7) X 



ing —^ — —0 = -- see pao^e 379 of the work. 



Trembley's methods are laborious, and like many other at- 

 tempts to bring high mathematical investigations into more 

 elementary forms, would probably cost a student more trouble 

 than if he were to set to work to enlarge his mathematical know- 

 ledge and then study the original methods. 



7G8. Trembley follows Laplace in a numerical application 

 relating to the births of boys and girls at Vitteaux in Bourgogne. 

 Laplace first gave this in the Hist, de V A cad.... Paris for 1783, 

 page 448; it is in the Theorie . . . des Proh. page 380. It appears 

 that at Vitteaux in five years 212 girls were born to 203 boys. 

 It is curious that Laplace gives no information in the latter work 

 of a more recent date than he gave in the Hist, de V Acad.... Paris 

 for 1783 ; it would have been interesting to know if the anomaly 

 still continued in the births at Vitteaux. 



769. We may observe that Laplace treats the problem of 

 births as analogous to that of drawing black and white balls from a 

 bag. So he arrives at this result ; if we draw 212 black balls to 203 

 white balls out of a bag, the chance is about '67 that the black 

 balls in the bag are more numerous than the white. It is not 

 very easy to express this result in words relating to births ; Laplace 

 says in the Hist, de V Acad.... Par is, la difference "670198 sera la 



