592- LAPLACE. 



1021. Laplace's sixth Chapter is entitled De la prohahilite des 

 causes et des Mnemens futurs, tiree des evenemens observes: it 

 occupies pages 363 — 401. 



The subject of this Chapter had engaged Laplace's attention 

 from an early period, and to him we must principally ascribe 

 the merit of the important extension thus given to the Theory of 

 Probability, due honour being at the same time reserved for his 

 predecessor Bayes. See Arts. 851, 868, 870, 903, 909. 



Let X denote the chance, supposed unknown, of a certain 

 simple event ; let y denote the chance of a certain compound 

 event depending in an assigned manner on this simple event : 

 then y will be a known function of x. Suppose that this com- 

 pound event has been observed ; then the probability that the 

 chance of the simple event lies between a and ^ is 



I y dx 



\ y dx 



Jo ' 



This is the main formula of the present Chapter: Laplace 

 applies it to examples, and in so doing he evaluates the integrals 

 by his method of approximation. 



In like manner if the compound event depends on two inde- 

 pendent simple events, the probability that the chance of one lies 

 between a and fi and the chance of the other between a! and ^' is 



y dx dx 



ny dx dx 

 



1022. The examples in the present Chapter of Laplace's work 

 exhibit in a striking way the advantage of his method of approxi- 

 mation ; but as they present no novelty nor difficulty of principle 

 we do not consider it necessary to reproduce any of them in detail. 



1023. Laplace makes a remark on his page 366 which may 

 deserve a brief examination. He says that if we have to take the 



integral I e-^' dt between the limits — r and r we may for an ap- 



