LAPLACE. 487 



The problem is reproduced in tlie Theorie...des Proh. pages 

 391 — 39-i. The necessary observations were made by the Frencb 

 government at Laplace's request ; the population of the district 

 selected was a little more than two millions. 



The solutions of the problem in the memoir and in the 

 Theorie. . .des Proh. are substantially the same. 



912. In the Lecons de Mathematiques donnees a Tecole normale, 

 en 1795, par M. Laplace, we have one le^on devoted to the subject 

 of probabilities. The legons are given in the Journal de VEcole 

 Poly technique y vii^ et viii® cahiers, 1812; but we may infer from 

 page 164 that there had been an earlier publication. The lecon 

 on probabilities occupies pages 140 — 172. It is a popular state- 

 ment of some of the results which had been obtained in the 

 subject, and was expanded by Laplace into the Introduction 

 which appeared with the second edition of the Theorie.,. des Proh., 

 as he himself states at the beginning of the Introduction. 



913. With the exception of the unimportant matter noticed 

 in the preceding Ai'ticle, Laplace seems to have left the Theory 

 of Probability untouched for more than twenty-five'^years. His 

 attention was probably fully engaged in embodying his own re- 

 searches and those of other astronomers in his Mecanique Celeste, 

 the first four volumes of which appeared between 1798 and 1805. 



914. Laplace's next memoir connected with the Theory of 

 Probability is entitled Memoire sur les approximations des for- 

 mules qui sont fonctions de tres-grands nomhres, et sur leur ap- 

 plication aux prohoMlites. This memoir is published in the 

 Memoires...de VInstitut for 1809; the date of publication is 1810 ; 

 the memoir occupies pages 353 — 415 of the volume, and a supj^le- 

 ment occupies pages 559 — oQo. 



915. The first subject which is discussed is the problem re- 

 lating to the inclination of the orbits of the planets and comets 

 which is given in the Theorie... des Proh. pages 253 — 261; see 

 also Art. 888. The mode of discussion is nearly the same. [There 

 is however some difference in the jDrocess relating to i\iQ planets, 

 for in the memoir Laplace takes two right angles as the extreme 



