486 LAPLACE. 



of the memoir are not reproduced in the Theorie , . .des Proh.; 

 they depend partly on those pages of the memoir of 1782 which 

 are erroneous, as we saw in Art. 907. 



Laplace in this memoir applies his formulae of approxima- 

 tion to the solution of questions in probability. See Arts. 767, 769. 

 He takes the problem which we have noticed in Art. 896, and 

 arrives at a result practically coincident with the former. He takes 

 the problem which we have noticed in Art. 902, gives a much 

 better investigation, and arrives at a result practically coincident 

 with the former. He solves the problem about the births during a 

 century to which we have referred in Art. 897, using the smaller 

 values of j9 and q which we have given in Art. 902; he finds 

 the required probability to be "664. In the Theorie...des Proh. 

 page 401 he uses the larger values of j) and q which we have 

 given in Art. 902, and obtains for the required probability "782. 



910. This memoir also contains a calculation respecting a 

 lottery which is reproduced in the Theo7'ie...des Proh. page 195. 

 See Arts. 455, 864. 



Laplace suggests on page 433 of the memoir that it would 



be useful to form a table of the value of \e~^'dt for successive 

 limits of the integration : such a table we now possess. 



911. In the same volume there is another memoir by La- 

 place which is entitled, Sur les naissances, les mcwiages et les 

 marts d Paris.... This memoir occupies pages 693 — 702 of the 

 volume. 



The following problem is solved. Suppose we know for a 

 large country like France the number of births in a year ; and 

 suppose that for a certain district we know both the population 

 and the number of births. If we assume that the ratio of the 

 population to the number of births in a year is the same for the 

 whole country as it is for the district, we can determine the popu- 

 lation of the whole country. Laplace investigates the probability 

 that the error in the result will not exceed an assiofned amount. 

 He concludes from his result that the district ouo'ht to contain 

 not less than a million of people in order to obtain a sufficient 

 accuracy in the number of the population of France. 



