LAPLACE. 60o 



like that given in Art. 993. The result is that there is approxi- 

 mately the probability 



that the number of unbroken couples will lie between 



fia'-T\f2fia'{l-d') and /J^d" + t ^/2y.a'' {1- a!'). 



This substantially agrees with Laplace, observing that in the 

 third line of his page 418 the equation ought to be simplified by 

 the consideration that p' has been assumed very great ; so that 

 the equation becomes 



271 f (1 - (j^') ' 



See Art. 148 of the Theory of Prohahilities in the Encyclopcedia 

 Metropolitana. 



There is still another way in which the problem may be solved. 

 We may take it as a result of observation that out of fi^ man-iages 

 of persons aged A years there remained v^ unbroken couples at 

 the end of T years, and we require the consequent probability 

 that out of fji marriages now contracted between persons aged 

 A years v unbroken couples will remain at the end of T years. 

 Then as in Art. 1030 we obtain 



P = 





\1 \f: — ^ I ic"! (1 - a?)'*i-»'i dx 



J 



The result will be like that which we have found by the 



second method, having — instead of al Practically -^ may be 



nearly equal to a^, but tliey must not be confounded in theory, 

 being obtained from ^Ufferent data. The last mode is simpler in 

 theory than the second, but it assumes that we have from observa- 

 tion data which bear more immediately on the problem. 



1037. Laplace's ninth Chapter is entitled Des benefices depen- 

 dans de la prohabiliU des Svenemens futiirs: it occupies pages 

 419—481. 



