TREMBLEY. 4*29 



grange with all tlie misprints or errors which it involves; see 

 Art. 567. 



798. The last memoir by Trembley is entitled Observations 

 sur le calcul cVun Jeu de hasard. 



This memoir is published in the volume for 1802 of the 

 Memoir es de V Acad. ... Berlin ; the date of publication is 180-i : 

 the memoir occupies pages 86 — 102 of the mathematical portion 

 of the volume. 



799. The game considered is that of Her, which gave rise to 

 a dispute between Nicolas Bernoulli and others ; see Art. 187. 

 Trembley refers to the dispute. 



Trembley investigates fully the chance of Paul for every case 

 that can occur, and more briefly the chance of Peter. He states 

 his conclusion thus : 



...M. de Montmort et ses amis concluoient de la centre Nicolas 

 Bernoulli, que ce cas 6toit insoluble, car disoient-ils, si Paul sait que 

 Pierre se tient au huit, il cliangera an sept, mais Pierre venant k savoir 

 que Paul change au sept, changera au huit, ce qui fait un cercle vicieux. 

 Mais il resulte seulement de la que chacun sera perjDetuellement dans 

 I'incertitude sur la maniere de jouer de son adversaire; des lors il con- 

 viendra a Paul de changer au sept dans un coup donne, mais il ne 

 pourroit suivre constamment ce sjsteme plusieurs coups de suite. II 

 conviendra de meme a Pierre de changer au huit dans un coup donn6, 

 sans pouvoir le faire plusieurs coups de suite, ce qui s'accorde avec les 

 conclusions de M. Nicolas Bernoulli contre celles de M. de Montmort. 



800. It is hardly correct to say that the conclusion here 

 obtained agrees with that of Nicolas Bernoulli against that of 

 Montmort. The opponents of Nicolas Bernoulli seem only to 

 have asserted that it was impossible to say on which rule Paul 

 should uniformly act, and this Trembley allows. 



801. In Trembley's investigation of the chance of Peter, he 

 considers this chance at the epoch before Paul has made his choice 

 ivhether he will exchange or not. But this is of little value for 

 Peter himself ; Peter would want to know how to act under cer- 

 tain circumstances, and before he acted he would know whether 

 Paul retained the card he obtained at first or compelled an ex- 



