CHAPTER XL 



DANIEL BERNOULLI. 



376. Daxiel Beexoulli was the son of the John Bernoulli 

 to whom we have often referred ; Daniel was born in 1700, and 

 died in 1782 : he is the author of some important memoirs on 

 our subject, remarkable for their boldness and originality, which 

 we shall now proceed to examine. 



377. Tlie first memoir which we have to notice is entitled 

 Specimen TJieornce Xovcb de Mensura Sortis. This memoir is 

 contained in the Commentarii Acad. ...Petrop. Vol. v., which is 

 the volume for the years 1730 and 1731 ; the date of publication 

 of the volume is 1738 : the memoir occupies pages 175 — 192. 



378. This memoir contains the theory of Moral expectation 

 proposed by Daniel Bernoulli, which he considered would give 

 results more in accordance with our ordinary notions than the 

 theory of Mathematical expectation. Laplace has devoted to this 

 subject pages 432 — 415 of his Theorie...des Proh., in which he 

 reproduces and developes the hypothesis of Daniel Bernoulli. 



379. Mathematical expectation is estimated by the product 

 of the chance of obtaining a sum of money into that sum. But 

 we cannot in practice suppose that a given sum of money is of 

 equal importance to every man ; a shilling is a matter of small 

 moment to a person who possesses a thousand pounds, but it is 

 of great moment to a person who only possesses a few shillings. 

 Various hj^otheses may be proposed for taking into account the 



