018 APPENDIX. 



Thubeuf. EMmens et principes de la royale Arithm^tique 

 aux jettons, etc. 12mo. Paris, 1661. 



Marpurg, F. W., Die Kunst, sein Gliick spielend zu maclien. 

 Hamburg, 1765. 4to. 



Fenn, (I.) Calculations and formulae for determining the Ad- 

 vantages or Disadvantages of Gamesters,... 1772. 4to. 



Frommichen Ueber Lelire d. Wahrsclieinl. Braunscbw. 1 773 . 4 to. 



1061. I had overlooked a passage in Montucla which bears 

 on the point noticed in Art. 990; see Montucla, page 421. It 

 seems that a mode of election suggested by Condorcet was for 

 some time adopted at Geneva. The defects of the mode were 

 indicated in a work by Lhuilier entitled, Examen dii mode d'elec- 

 tion propose en fevrier 1793, a la Convention nationale de France^ 

 et adopts d Geneve (1794, en 8^). 



1062. A very curious application of the Theory of Proba- 

 bility was stated by Waring; see his Meditotiones Algehraicce, 

 3rd Edition, 1782, pages xi, 69, 73. For example, he gives a rule for 

 ascertaining the number of imaginary roots in an equation, and 

 says : Haec methodus in quadraticis sequationibus verum prgebet 

 numerum impossibilium radicum : in cubicis autem ejus proba- 

 bilitas inveniendi impossibiles radices non videtur majorem habere 

 rationem ad probabilitatem fallendi quam 2:1. 



I owe this reference to the kindness of Professor Sylvester in 

 sending me a copy of his remarkable memoir in the Philosophical 

 Transactions for 1864, on the Real and Imaginary roots of Alge- 

 hi'aical Equations. Professor Sylvester had independently made 

 the same kind of application ; see page 580 of the volume, where 

 he says : " Like myself, too, in the body of the memoir Waring 

 has given theorems of probability in connexion with rules of this 

 kind, but without any clue to his method of arriving at them. 

 Their correctness may legitimately be doubted." 



