198 'SGKAVESANDE. 



It appears from page 237; that when Nicolas Bernoulli travelled 

 in Holland he met 'sGravesande. 



In this discussion we have first a memoir by 'sGravesande. 

 This memoir contains a brief statement of some of the elements 

 of the theory of probability. The following result is then obtained. 

 Assume that the chance is even for a male or female birth, and 

 find the chance that out of 11429 births the males shall lie 

 between 5745 and 6128. By a laborious arithmetical calculation 



1 



this is found to be about -r . Then the chance that this should 



4 



happen for 82 years in succession will be j^ . 



4 



But in fact the event for which the chance is so small had 

 happened in London. Hence it is inferred that it is not an even 

 chance that a male or female should be born. 



It appears that 'sGravesande wrote to Nicolas Bernoulli on 

 the subject; the reply of Nicolas Bernoulli is given. This reply 

 contains a jDroof of the famous theorem of James Bernoulli ; 

 the proof is substantially the same as that given by Nicolas Ber- 

 noulli to Montmort, and published by the latter in pages 389 — 393 

 of his book. 



Then 'sGravesande wrote a letter giving a very clear account 

 of his views, and, as his editor remarks, the letter seems to have 

 impressed Nicolas Bernoulli, judging from the reply which the 

 latter made. 



Nicolas Bernoulli thus sums up the controversy : 



Mr. Arhutlmot fait consister son argument en deux cliosesj 1°. en 

 ce que, supposee une egalite de naissance entre les filles et les gargons, 

 il y a peu de probahilite que le n ombre des garyons et des filles se trouve 

 dans des limites fort proches de I'egalite: S''. qu'il y a peu de proba- 

 hilite que le nombre des gargous surpassera un grand nombre de fois de 

 suite le nombre des filles. C'est la premiere partie que je refute, et non 

 pas la seconde. 



But this does not fairly represent Arbuthnot's argument. 

 Nicolas Bernoulli seems to have imagined, without any adequate 

 reason, that the theorem known by his uncle's name was in some 

 way contradicted by Arbuthnot. 



348. Two memoirs on our subject are published in Vol. 



