606 PHILOSOPHICAL TRANSACTIONS. [aNNOI/IO. 



An Argument for Divine Providence, taken from the Constant Regularity ob- 

 served in the Births of both Sexes, By Dr. John Arbuthnot,* Physician 

 in Ordinary to her Majesty, and F. R. S. N'* 328, p. 186. 



Among innumerable evidences of Divine Providence to be found in the works 

 of nature, there is a very remarkable one in the exact balance maintained be- 

 tween 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 proportionable age. This equality of males and females is not the 

 effect of chance, but Divine Providence, working for a good end, which I thus 

 demonstrate. 



Let there be a die of two sides, m and f, which denote cross and pile. Now 

 to find all the chances of any determinate number of such dice, let the binomial 

 M -[- p be raised to the power whose exponent is the number of dice given ; 

 then the coefficients of the terms will show all the chances sought. For 

 example, in two dice of two sides, m + p, the chances are m^ + 2mf -|- p'^ ; 



* Dr. John Arbuthnot is well known as a satirical writer, and as the associate of Pope, Swift, 

 Gay, and other wits, who flourished during the reign of Q. Anne ; a reign eminently distinguished 

 In the annals of polite literature. But in this place we are to consider this author in the character of 

 a physician, not that of a critic or satirist. 



Dr. A. was a native of Scotland, and took his degree of M. D. at Aberdeen. For some time 

 after he settled in London, his practice produced so little emolument, that he found it necessary, fof 

 his support, to teach the mathematics. Like many others of the medical profession, he was indebted 

 to a circumstance wholly fortuitous for his first elevation. Prince George of Denmark was suddenly 

 taken ill at Epsom, at the time Dr. A. happened to be there ; he was accordingly called in j the 

 Prince recovered; and he was ever afterwards employed by him as his physician. In 1709 he was 

 appointed physician in ordinaiy to Q. Anne. Some years before, he had been elected a fellow of 

 the R. S. J and now he had another honour conferred upon him, that of being admitted a fellow of the 

 college of physicians. He died in 1735, after long and severe suflFering from an asthma. Besides 

 his satirical and other literary compositions, he wrote An Examination of Woodward's Account of 

 the Deluge ; A Treatise on the Usefulness of Mathematical Learning ; Tables of Ancient Coins, 

 Weights and Measures ; An Essay on the Nature and Choice of Aliments ; and an Essay on the 

 Effects of Air on Human Bodies. The subjects of both these medical essays are, it must be ac- 

 knowledged, of great importance; but they have not been discussed by Dr. A. in the manner they 

 should have been. His book on Aliments is too much incumbered with useless disquisitions relative 

 to the humoural pathology, and he appears to have had very inaccurate views of some parts of the 

 animal economy. Thus, he compares digestion to putrefaction, and supposes the gall to be the prin- 

 cipal solvent of the food, &c. &c. With regard to his Essay on the Effects of Air on Human 

 Bodies, it contains less theory, and more matter of fact, than his other medical treatise 3 but as 

 pneumatic chemistry was then only in its infancy, we shall in vain look in that work for a clear and 

 just account of the phaenomena which take place in the process of respiration. Nevertheless many 

 useful hints may be derived from the practical aphorisms with which that Essay is concluded. 



