d'alembeet. 285 



we gave in Art. 402. D'Alembert's method is too arbitrary in 

 its hypotheses to be of any value. 



522. D'Alembert proposes to develop his refutation of the 

 Savant Geometre whom we introduced in Art. 487. He shews 

 decisively that this person was wrong ; but it does not seem to 

 me that he shews distinctly Jiow he was wrong. 



523. D'Alembert devotes the last ten pages of the memoir 

 to the development of his own theory of the mode of comparing 

 the risk of an individual if he undergoes Inoculation with his 

 risk if he declines it. We have already given in Art. 482, a hint 

 of DAlembert's views ; his remarks in the present memoir are 

 ingenious and interesting, but as may be supposed, his h}^otheses 

 are too arbitrary to allow any practical value to his investiga- 

 tions. 



524. Two remarks which he makes on the curve of mortality 

 may be reproduced ; see his page 840. It appears from Buffon''s 

 tables that the mean duration of life for persons aged n years 



1 



is always less than ^ (100 — n). Hence, taking 100 years as the 



extreme duration of human life, it will follow that the curve of 

 mortality cannot be always concave to the axis of abscissse. Also 

 from the tables of Buffon it follows that the pivhahle duration 

 of life is almost always greater than the mean duration. D'Alem- 

 bert applies this to shew that the curve of mortality cannot be 

 always convex to the axis of abscissae. 



525. The fifth volume of the Opuscules was published in 

 1768. It contains two brief articles with which we are con- 

 cerned. 



Pages 228 — 231 are Bur les Tables de mortalite. The numeri- 

 cal results are given which served for the foundation of the two 

 remarks noticed in Art. 524. 



Pages 508 — 510 are Sur les calculs relatifs d V inoculation.,. 

 These remarks form an addition to the memoir in pages 283 — 341 

 of the fourth volume of the Opuscules. D'Alembert notices a reply 

 which had been offered to one of his objections, and enforces the 



