LAPLACE. 497 



been almost a satire to have repeated it when the tyrant of Europe 

 had become the mock sovereign of Elba or the exile of St Helena : 

 the fault was in the original publication, and not in the final sup- 

 pression. 



932. We have said that some pages of the original impression 

 were cancelled, and others substituted ; the following are the pages : 

 25, 26, 27, 28, 37, 38, 147, 148, 303, 304, 359, 360, 391, 392; we 

 note them because a student of the first edition will find some 

 embarrassing errata in them. 



933. The introduction to the Theorie...des Proh. was pub- 

 lished separately in octavo under the title of Essai pkilosophique 

 sur les Prohahilites; we shall however refer to the introduction 

 by the pages of the third edition of the Theorie...des P7'ob. 



934. On pages I — xvi. of the introduction we have some gene- 

 ral remarks on Probability, and a statement of the first principles 

 of the mathematical theory ; the language is simple and the 

 illustrations are clear, but there is hardly enough space allotted to 

 the subject to constitute a good elementary exposition for be- 

 ginners. 



935. On pages xvi — xxxvii. we have a section entitled Des 

 mModes analytiques dii Calcul des Probahilites ; it is principally 

 devoted to an account of the Theory of Generating Functions, the 

 account being given in words with a very sparing use of symbols. 

 This section may be regarded as a complete waste of space ; it 

 would not be intelligible to a reader unless he were able to master 

 the mathematical theory delivered in its appropriate symbolical 

 language, and in that case the section would be entirely super- 

 fluous. 



This section differs in the two editions ; Laplace probably 

 thought he improved in his treatment of the difficult task he had 

 undertaken, namely to explain abstruse mathematical processes in 

 ordinary language. We will notice two of the changes. Laplace 

 gives on pages xxiiL and xxiv. some account of De Moivre's 

 treatment of Recurring Series; this account is transferred fi'om page 

 CI. of the second edition of the introduction : a student however 



32 



