130 MONTMORT. 



Montmort refers on his page 364 to a letter dated June 8*^ 

 1710, which does not appear to have been preserved. 



223. The next letter is from Nicolas Bernoulli to Montmort ; 

 it occupies pages 871 — 375. Nicolas Bernoulli demonstrates a 

 property of De Beaune's curve ; he also gives a geometrical recti- 

 fication of the logarithmic curve ; but his results are very in- 

 correct. He then remarks on a subject which he says had been 

 brought to his notice in Holland, and on which a memoir had been 

 inserted in the Philosophical Transactions. The subject is the 

 argument for Divine Providence taken from the constant regu- 

 larity observed in the births of both sexes. The memoir to which 

 Bernoulli refers is by Dr John Arbuthnot ; it is in Vol. XXVII. of 

 the Philosophical Transactions, and was published in 1710. Nicolas 

 Bernoulli had discussed the subject in Holland with 's Gravesande. 



Nicolas Bernoulli says that he was obliged to refute the argu- 

 ment. What he supposes to be a refutation amounts to this ; he 

 examined the registers of births in London for the years from 1629 

 to 1710 inclusive; he found that on the average 18 males were 

 born for 17 females. The greatest variations from this ratio were 

 in 1661, when 4748 males and 4100 females were born, and in 

 1703, when 7765 males and 7683 females were born. He says 

 then that we may bet 800 to 1 that out of 14,000 infants the ratio 

 of the males to the females will fall within these limits ; we shall 

 see in Art. 225 the method by which he obtained this result. 



224. The next letter is also from Nicolas Bernoulli to Mont- 

 mort ; it occupies pages 875 — 887. It contains some remarks on 

 the game of Her, and some remarks in reply to those made by 

 Montmort on De Moivre's memoir De Mensura Soi'tis. The most 

 impoj'tant part of the letter is an elaborate discussion of Walde- 

 grave's problem ; we have already said enough on this problem, 

 and so need only add that Nicolas Bernoulli speaks of this discus- 

 sion as that which he preferred to every thing else which he had 

 produced on the subject; see page 881. The approbation which 

 he thus bestows on his own work seems well deserved. 



225. Thie next letter is also from Nicolas Bernoulli to Mont- 

 mort ; it occupies pages 388 — 893. It is entirely occupied with 



