»'=7C' -tn' 



27S D ALEMBEllT. 



D'Alembert as he supposed they were meant for him. He refers 

 to them in the Opuscules, Vol. IV. pages IX, 99, 100 ; and he 

 seems with ostentatious deference to speak of Daniel Bernoulli 

 as ce grand Geometre; see pages 99, 101, 315, 821, 323 of the 

 volume, 



507. D'Alembert objects to the hypotheses on which Daniel 

 Bernoulli had based his calculation ; see Art. 401. D'Alembert 

 brings forward another objection which is quite fallacious, and 

 which seems to shew that his vexation had disturbed his judg- 

 ment. Daniel Bernoulli had found that the average life of all 

 who die of small-pox is 6^^ years ; and that if small-pox were 

 extinguished the average human life would be 29^^ years. More- 

 over the average human life subject to small-pox is 26^^ years. 

 Also Daniel Bernoulli admitted that the deaths by small-pox 



were — ^^ ^^^ ^^® deaths, 



J-O 



Hence D'Alembert affirms that the folloAving relation ought 



to hold; 



1 12 



but the relation does not hold; for the terms on the left hand side 

 will give 27{^ nearly instead of 263^. D'Alembert here makes the 

 mistake which 1 have pointed out in Art. 487 ; when that Article 

 was written, I had not read the remarks by D'Alembert which 

 are now under discussion, but it appeared to me that D'Alembert 

 was not clear on the point, and the mistake which he now makes 

 confirms my suspicion. 



To make the above equation correct we must remove 29^, 

 and j)ut in its place the average duration of those who die of 

 other diseases while small-pox still prevails ; this number will be 

 smaller than 29j^2' 



508. We pass on to the pages 283—341 of the fourth volume 

 of the Opuscules. Here we have two sections, one Sur le Calcul 

 des probahilites, the other Sur les Calculs relatifs a I' Inoculation, 



609. The first section consists of little more than a repetition 



