28(> d'alembeut, 



justness of his objections. Nevertheless he gives his reasons for 

 regarding Inoculation as a useful practice. 



526. The seventh and eighth volume of the Opuscules were 

 published in 1780. D'Alembert says in an Advertisement pre- 

 fixed to the seventh volume, ''... Ce seront vraisemblablement, ^ 

 peu de chose pr^s, mes derniers Ouvrages Mathematiques, ma tete, 

 fatiguee par quarante-cinq annees de travail en ce genre, n'etant 

 plus gu^re capable des profondes recherches qu'il exige." D'Alem- 

 bert died in 1788. It would seem according to his biographers 

 that he suffered more from a broken heart than an exhausted 

 brain during the last few years of his life. 



527. The seventh volume of the Opuscules contains a memoir 

 Sur le calcul des Prohahilites, which occupies pages 39 — 60. We 

 shall see that D'Alembert still retained his objections to the 

 ordinary theory. He begins thus : 



Je demande pardon aux Geometres de revenir encore sur ce sujet. 

 Mais j'avoue que j)lus j'y ai pense, plus je me suis confirme dans mes 

 <k>utes sur les principes de la theorie ordinaire; je desire qu' on eclaircisse 

 ces doutes, et que cette tlieorie, soit qu'on y change quelques principes, 

 soit qu'on la conserve telle qu'elle est, soit du moins exposee desormais 

 de maniere a ne plus laisser aucuii nnage. 



528. We will not delay on some repetition of the old remarks ; 

 but merely notice what is new. We find on page 42 an error which 

 D'Alembert has not exhibited elsewhere, except in the article 

 Cartes in the Encyclopedie Methodique, which we shall notice 



hereafter. He says that taking two throws there is a chance ^ of 



1 -^ 



head at the first throw, and a chance - of head at the second 



2 



throw ; and thus he infers that the chance that head will arrive at 



least once is - +-^ or 1. He says then, Or je demande si cela est 



vrai, ou du moins si un pareil r^sultat, fonde sur de pareils prin- 

 cipes, est bien propre a satisfaire I'esprit, The answer is that the 

 result is false, being erroneously deduced : the error is exposed in 

 elementary works on the subject. 



529. The memoir is chiefly devoted to the Petersburg Problem. 

 D'Alembert refers to the memoir in Yol. vi. of the Memoires...par 



