CHAPTER XX. 



LAPLACE. 



860. Laplace was born in 1749, and died in 1827. He wrote 

 elaborate memoirs on our subject, which he afterwards embodied 

 in his great work the Theorie analytique des ProhabiliUs, and on 

 the whole the Theory of Probability is more indebted to him than 

 to any other mathematician. We shall give in the first place a 

 brief account of Laplace's memoirs, and then consider more fully 

 the work in which they are reproduced. 



861. Two memoirs by Laplace on our subject are contained in 

 the Memoir es...pa7^ divers Savans, Vol. vi. 1774. A brief notice 

 of the memoirs is given in pages 17 — 19 of the preface to the 

 volume which concludes thus : 



Ces deux Memoires de M. de la Place, ont ete choisis parmi un 

 tres-grand nombre qu'il a presentes depuis trois ans, a I'Academie, oii il 

 remplit actuellement une place de Geometre. Cette Compagnie qui s'est 

 empressee de recorapenser ses travaux et ses talens, n'avoit encore vu 

 personne aussi jeune, lui presenter en si peu de temps, tant de Memoires 

 importans, et sur des matieres si diverses et si difficiles. 



862. The first memoir is entitled Memoir e sur les suites re- 

 ciirro-recurrentes et sur leurs usages dans la theorie des hasards. It 

 occupies pages 353 — 371 of the volume. 



A recurring series is connected with the solution of an equation 

 in Finite Differences where there is one independent variable ; see 

 Art. 318. A recurro-recurrent series is similarly connected with 

 the solution of an equation in Finite Differences where there are 

 two independent variables. Laplace here first introduces the term 



