480 LAPLACE. 



Lb X Lb 



^ = -7^-^.+ . -7-- + 



dz 

 Hence we see that z and -^ both increase with x so long 



as X is less than : this establishes the required proposition. 



See also Art. 767. 



896. Laplace then takes the following problem. In 26 years 

 it was observed in Paris that 251527 boys were born and 241945 

 girls : required the probability that the j^ossibility of the birth 



of a boy is greater than -^ . The probability is found to differ 



from unity by less than a fraction having for its numerator 1*1521 

 and for its denominator the seventh power of a million. 



This problem is reproduced in the Theorie...des Pi^oh. pages 

 877 — 380, the data being the numbers of births during 40 years 

 instead of during 26 years. 



897. Taking the same data as in the preceding Article, La- 

 place investigates the probability that in a given year the number 

 of boys born shall not exceed the number of girls born. He 



1 



finds the probability to be a little less .than ^—^ . The 



result of a similar calculation from data furnished by observations 



in London is a little less than t^^tzti . In pa<?es 397 — 401 of the 



12410 ^ ° 



Theorie...des Prob. we have a more difficult problem, namely to 

 find the probability that during a century the annual births of 

 boys shall never be less than that of girls. The treatment of 

 the simpler problem in the memoir differs from that of the 

 more difficult problem in the Theorie...des Froh. In the memoir 

 Laplace obtains an equation in Finite Differences 



hence he deduces 



%m= constant -f ?/,„.^,„_, |l - A^^,„_2 + A {z,,,_^i^z^,,_^ 



