482 LAPLACE. 



Then, as ,,., "" .,, = ^ , Laplace infers that 



r r dxch _'TT f' dx 



Bat this is wrono^ ; for the limits of x are and 7 , and 



° (1 - £y 



not and 1, as Laplace says ; and so the process fails. 



Laplace makes the same mistake again immediately after- 

 wards ; he puts -jj^ -^ — z\ and thus deduces 



I 



dxdz [^ dx [^ dz 



J„ (1 _ ^^ _ ^^)i J, (1 _ x^)k!, (1 _ ^-)t • 



But the upper limit for z should be -j-Fx — ~T\ > ^^^ ^^^ ^ ^^ 



'Y ( X X j 



Laplace assumes ; and so the process fails. 



901. -Laplace applies his method to evaluate approximately 



I a?^ (1 — xY dx ; and he finds an opportunity for demonstrating 



•J 



Stirling's Theorem. See Art. 333. 



902. Laplace discusses in pages 304 — 313 of the memoir the 

 following problem. Observation shews that the ratio of the num- 

 ber of births of boys to that of girls is sensibly greater at London 

 than at Paris ; this seems to indicate a greater facility for the birth 

 of a boy at London than at Paris : required to determine the 

 amount of probability. See Art. 773. 



Let w be the probability of the birth of a boy at Paris, p the 

 number of births of boys observed there, and q the number of births 

 of girls ; let z^ — ic be the possibility of the birth of a boy at Lon- 

 don, p the number of births of boys observed there, and q the 

 number of births of girls. If P denote the probability that the 

 birth of a boy is less possible at London than at Paris, we have 



{U (1 _ uy {u - xY (1-U + xY du dx 



P = 



\ie (1 - uY {u - xY (1 - M + xY die dx 



