114? MONTMORT. 



as these passages have been modified or corrected in accordance 

 with the criticisms contained in the letters, it is not always ob- 

 vious what the original reading was. 



196. The first letter is from John Bernoulli ; it occupies 

 pages 283 — 298 ; the letter is also reprinted in the collected 

 edition of John Bernoulli's works, in four volumes, Lausanne and 

 Geneva, 1742 ; see Vol. I. page 453. 



John Bernoulli gives a series of remarks on Montmort's first 

 edition, correcting some errors and suggesting some improvements. 

 He shews that Montmort did not present his discussion relating 

 to Pharaon in the simplest form ; Montmort however did not 

 modify this part of his work. John Bernoulli gave a general 

 formula for the advantage of the Banker, and this Montmort did 

 adopt, as we have seen in Art. 155. 



197. John Bernoulli points out a curious mistake made 

 by Montmort twice in his first edition ; see his pages 288, 296. 

 Montmort had considered it practically impossible to find the 

 numerical value of a certain number of terms of a geometrical 

 progression ; it would seem that he had forgotten or never known 

 the common Algebraical formula which gives the sum. The 

 passages cited by John Bernoulli are from pages 35 and 181 of 

 the first edition ; but in the only copy which I have seen of the 

 first edition the text does not correspond with John Bernoulli's 

 quotations : it appears however that in each place the original page 

 has been cancelled and replaced by another in order to correct 

 the mistake. 



After noticing the mistake, John Bernoulli proceeds thus in 

 his letter : 



...mais pour le reste, vous faites bien d'employer les logarithm es, 

 je m'en suis servi utilement dans une parcille occasion il y a bien 

 douze ans, ou il s'agissoit de determiner combien il restoit de vin et 

 d'eau mele ensemble dans un tonneau, lequel etant an commencement 

 tout plein de vin, on en tireroit tons les jours pendant une amice 

 une certaine mesure, en le remplissant incontinent apres cliaque ex- 

 traction avec de I'eau pure. Vous trouveres la solution de cette ques- 

 tion qui est asses curieuse dans ma dissertation De Nutritlone, que Mr 

 Varignon vous pourra communiquer. Jc fis cette question pour faire 



