CHAP. XXI.] PROBABILITY OF JUDGMENTS. 381 



the general expression for Xi being given by (3) after making 

 therein n = 12. In the year 1831 the law, having received alte- 

 ration, required a majority of at least four persons for condemna- 

 tion, and the number of persons tried for crimes against the 

 person during that year being 2046, and the number condemned 

 743, the probability of the condemnation of an individual by the 



743 

 above majority was oTZ"' or .3631. Hence we should have 



(6) 



Assuming that the values of k and x were the same for the 

 year 1831 as for the previous six years, the two equations (5) and 

 (6) enable us to determine approximately their values. Poisson 

 thus found, 



k = .5354, x = .6786. 



For crimes against property during the same periods, he 

 found by a similar analysis, 



= .6744, a? = .7771. 



The solution of the system (5) (6) conducts in each case to 

 two values of k, and to two values of x, the one value in each 



pair being? greater, and the other less, than - . It was assumed, 



2i 



that in each case the larger value should be preferred, it being 

 conceived more probable that a party accused ; should be guilty 

 than innocent, and more probable that a juryman should form 

 a correct than an erroneous opinion upon the evidence* 



5. The data employed by Poisson, especially those which were 

 furnished by the year 1831, are evidently too imperfect to permit 

 us to attach much confidence to the above determinations of # and 

 k ; and it is chiefly for the sake of the method that they are here 

 introduced. It would have been possible to record during the 

 six years, 1825-30, or during any similar period, the number of 

 condemnations pronounced with each possible majority of voices. 

 The values of the several elements X 8 , X 9 , . . X W9 were there 

 no reasons of policy to forbid, might have been accurately ascer- 

 tained. Here then the conception of the general problem, of 

 which Poisson's is a particular case, arises. How shall we, from 



