ARBUTHNOT, 1Q7 



taken from the constant Regularity ohservd in the Births of both 

 Sexes. By Br John Arbuthnott, Physitian in Ordinary to Her 

 Majesty, and Felloiu of the College of Physitians and the Royal 

 Society. 



This memoir is published in Vol. xxvii. of the Philosophical 

 Transactions; it is the volume for 1710, 1711 and 1712 : the 

 memoir occupies pages 186 — 190. 



844. The memoir begins thus : 



Among innumerable Footsteps of Divine Providence to be found in 

 the Works of Nature, there is a very remarkable one to be observed in 

 the exact Ballance that is maintained, between the Numbers of Men and 

 Women; for by this means it is provided, that the Species may never fail, 

 nor perish, since every Male may have its Female, and of a proportion- 

 able Age. This Equality of Males and Females is not the Effect of 

 Chance but Divine Providence, working for a good End, which J thus 

 demonstrate : 



845. The registers of births in London for 82 years are given ; 

 these shew that in every year more males were born than females- 

 There is very little relating to the theory of probability in the 

 memoir. The principal point is the following. Assume that 

 it is an even chance whether a male or female be born ; then 

 the chance that in a given year there will be more males than 



females is ^ ; and the chance that this will happen for 82 years in 



succession is ^ . This chance is so small that we may conclude 

 that it is not an even chance whether a male or female be born. 



846. The memoir attracted the attention of Nicolas Bernoulli, 

 who in his correspondence with Montmort expressed his dissent 

 from Ai'buthnot's argument ; see Art. 223. There is also a letter 

 from Nicolas Bernoulli to Leibnitz on the subject ; see page 989 of 

 the work cited in Art. 59. De Moivre replied to Nicolas Bernoulli, 

 as we have already intimated in Art. 835. 



847. The subject is also discussed in the Oemres Philo- 

 sophiques et Mathematiques of 's Gravesande, published at Amster- 

 dam, 1774, 2 vols. 4to. The discussion occupies pages 221—248 

 of the second volume. 



