LAPLACE. 489 



value, the law of facility of a single error being any what- 

 ever. 



Pages 390 — 397 of the memoir are spent in demonstrat- 

 ing the formula marked [q] which occurs at the top of page 170 

 of the Theorie...des Prob. The remaining pages of the memoir 

 amount to demonstrating the formula marked fp) on page 168 of 

 the Theor{e...des Proh., which is again discussed in pages 475 — 482 

 of the Theorie...des Prob. The methods of the memoir are very 

 laborious and inferior to those of the Th^orie...des Prob. 



918. The supplement to the memoir consists of the matter 

 Avhich is reproduced in pages 333 — 335 and 340 — 342 of the 

 TJieorie...des Prob. In his supplement Laplace refers to his 

 memoir of 1778; see Art. 901: the reference is not preserved 

 in the Theorie...des Prob. He names Daniel Bernoulli, Euler, 

 and Gauss; in the corresponding passage on page 335 of the 

 Theorie...des Prob., he simply says, des geomUres celebres. 



919. Laplace's next memoir is entitled, Me moire sur les Inte- 

 grates Definies, et leur ajyj^Ucatiori aux Probabilites, et specialement 

 a la recherche dii milieu quil faut choisir entre les residtats des 

 observations. This memoir is published in the Memoires ...de 

 rinstitut for 1810; the date of publication is 1811 : the memoir 

 occupies pages 279 — 347 of the volume. 



920. Laplace refers to his former memoirs on Generating 

 Functions and on Approximations ; he speaks of the approaching 

 publication of his work on Probabilities. In his former memoirs 

 he had obtained the values of some definite integrals by the 

 passage from real to imaginary values ; but he implies that such a 

 method should be considered one of invention rather than of 

 demonstration. Laplace says that Poisson had demonstrated several 

 of these results in the Bidletiii de la Societe Philoinatique for March 

 1811 ; Laplace now proposes to give direct investigations. 



921. The first investigation is^that which is reproduced in 

 pages 482 — 484 of the Theorie...des Prob. Then follow those 

 which are reproduced in pages 97 — 99 of the Theorie...des Prob. 

 Next we have the problem of the Duration of Play, when the 



