230 DANIEL BERNOULLI. 



413. Suppose 500 men of a given age, as for example 20 years, 

 to marry 500 women of the same age. The tables of mortality 

 will shew at what rate these 1000 individuals gradually diminish 

 annually until all are dead. But these tables do not distinguish 

 the married from the unmarried, so that we cannot learn from them 

 the number of unbroken couples after the lapse of a given number 

 of years. Daniel Bernoulli applies the result of Art. 410 ; the pairs 

 of cards correspond to the married couples. From that article 

 knowing- the number of cards which remain undrawn we infer the 

 probable number of pairs. The number of cards remaining un- 

 drawn corresponds to the number of persons remaining alive at a 

 given age ; this is taken from the tables of mortality, and by the 

 formula the probable number of unbroken couples is calculated. 

 Daniel Bernoulli calculates such a table for the numbers we have 

 supposed above. 



414. Daniel Bernoulli then proceeds to the case in which the 

 husband and wife are supposed of different ages ; this requires the 

 extended problem to which we have referred in Art. 411. Daniel 

 Bernoulli calculates a table for the case in which 500 men aged 

 40 years marry 500 women aged 20 years. 



Daniel Bernoulli allows that his results must not claim im- 

 plicit confidence. He has taken the same laws of mortality for 

 both men and women, though of course he was aware that on an 

 average women live longer than men. With respect to this fact he 

 says, page 100, ...neque id diversse vivendi rationi tribui potest, 

 quia ista sequioris sexus praerogativa a primis incunabilis constan- 

 tissime manifestatur atque per totam vitam in illo manet. 



Daniel Bernoulli's process is criticised by Trembley in the 

 M^moires de V Acad.... Berlin, 1799, 1800. 



The problem respecting the mean duration of marriages is con- 

 sidered by Laplace, Theorie...des Proh. page 415. 



415. The memoir which we have noticed in Arts. 412 — 414 

 bears a close analogy to the memoir which we have noticed in 

 Arts. 398 — 406. In both cases theory is employed to supply the 

 lack of observations, in both cases the questions discussed are of the 

 same kind, and in both cases the use of the Differential Calculus is 

 illustrated. 



