498 LAPLACE. 



who wished to understand the treatment would have to consult 

 the original work, namely De Moivre's Miscellanea Analytical 

 pages 28 — 83. Also some slight historical reference to Wallis and 

 others is introduced on pages xxxv— xxxvn. ; this is merely an 

 abridgement of the pages 3 — 8 of the Theorie . . .des Proh. 



936. We have next some brief remarks on games, and then 

 some reference to the unknown inequalities which may exist in 

 chances supposed to be equal, such as would arise from a want of 

 symmetry in a coin or die ; see Arts. 877, 881, 891. 



937. We have next a section on the laws of probability, which 

 result from an indefinite multiplication of events ; that is the 

 section is devoted to the consideration of James Bernoulli's theorem 

 and its consequences. Some reflexions here seem aimed at the 

 fallen emperor to whom the first edition of the work was dedicated ; 

 we give two sentences from page XLiii. 



Voyez au contraire, dans quel abime de mallieurs, les peuples ont 

 ete souvent precipites par I'ambition et par la perfidie de leurs chefs. 

 Toutes les fois qu'une grande puissance enivree de I'amonr des conquetes, 

 aspire h la dominatiou universelle; le sentiment de I'mdependance pro- 

 duit entre les nations menacees, une coalition dont elle devient presque 

 toiijours la victinie. 



The section under consideration occurs in the second edition, 

 but it occupies a different position there, Laplace having made 

 some changes in the arrangement of the matter in the third 

 edition. 



We may notice at the end of this section an example of the 

 absurdity of attempting to force mathematical expressions into 

 unmathematical language. Laplace gives a description of a certain 

 probability in these words : 



La theorie des fonctions generatrices donne une expression tres 

 simple de cette probabilite, que Ton obtient en integrant le produit de 

 la differentielle de la quantite dont le resultat deduit d'un grand nombre 

 d' observations s'ecarte de la verite, par une coustante moindre que 

 I'unite, dependante de la nature du probleriie, et elevee a une puissance 

 dont I'exposant est le rapport du carre de cet ccart, au nombre des 

 observations. L'integrale prise entre des limites donnces, et divisee 



