224 DANIEL BERNOULLI. 



397. We shall find hereafter that D' Alembert did not admit 

 that there was any value in Daniel Bernoulli's calculations. 



Laplace proposes to find the probability that the sum of all the 

 inclinations should not exceed an assigned quantity ; see Theorie... 

 des Prob. page 257. The principle of Daniel Bernoulli's attempt 

 seems more natural, because it takes more explicit account of the 

 fact that each inclination is small. 



398. The next memoir by Daniel Bernoulli is entitled Essai 

 dune nouvelle analyse de la mortalite causee par la petite Verole, 

 et des avantages de V Inocidation pour la prevenir. 



This memoir is contained in the Hist de FA cad. ... Paris, for 

 1760 ; the date of publication of the volume is 1766 : the memoir 

 occupies pages 1 — 45 of the part devoted to memoirs. 



399. The reading of the memoir commenced on April 30th, 

 1760, as we learn from its seventh page. Before the memoir 

 was printed, a criticism on it appeared, which Daniel Bernoulli 

 ascribes to a grand mathematicien ; see his pages 4 and 18. 

 In consequence of this, an introduction apologetique was written 

 on April 16th, 1765, and now forms the first six pages of the 

 whole. 



The critic was D'Alembert; see Montucla, page 426, and 

 our Chapter xiii. 



400. Daniel Bernoulli's main object is to determine the mor- 

 tality caused by the small-pox at various stages of age. This of 

 course could have been determined if a long series of observations 

 had been made ; but at that time such observations had not been 

 made. Tables of mortality had been formed, but they gave the 

 total number of deaths at various ages without distinguishing 

 the causes of death. Thus it required calculation to determine 

 the result which Daniel Bernoulli was seeking. 



401. Daniel Bernoulli made two assumptions : that in a year 

 on an average 1 person out of 8 of all those who had not pre- 

 viously taken the disease, would be attacked by small-pox, and 

 that 1 out of every 8 attacked would die. These assumptions he 

 supported by appeal to observation ; but they might not be uni- 



