380 PROBABILITY OF JUDGMENTS. [CHAP. XXI. 



mined by direct observation. We can only presume that they 

 must both in general exceed the value ; that the former, #, must 



increase with the progress of public intelligence ; while the latter, 

 k, must depend much upon those preliminary steps in the ad- 

 ministration of the law by which persons suspected of crime are 

 brought before the tribunal of their country. It has been re- 

 marked by Poisson, that in periods of revolution, as during the 

 Reign of Terror in France, the value of k may fall, if account be 



taken of political offences, far below the limit - . The history of 



Europe in days nearer to our own would probably confirm this 

 observation, and would show that it is not from the wild license 

 of democracy alone, that the accusation of innocence is to be 

 apprehended. 



Laplace makes the assumption, that all values of x from 



*=-, to x = 1, 



are equally probable. He thus excludes the supposition that a 

 juryman is more likely to be deceived than not, but assumes that 

 within the limits to which the probabilities of individual cor- 

 rectness of judgment are confined, we have no reason to give 

 preference to one value of x over another. This hypothesis is 

 entirely arbitrary, and it would be unavailing here to examine 

 into its consequences. 



Poisson seems first to have endeavoured to deduce the values 

 of x and &, inferentially, from experience. In the six years from 

 1825 to 1830 inclusively, the number of individuals accused of 

 crimes against the person before the tribunals of France was 

 11016, and the number of persons condemned was 5286. The 

 juries consisted each of 12 persons, and the decision was pro- 

 nounced by a simple majority. Assuming the above numbers 

 to be sufficiently large for the estimation of probabilities, there 



would therefore be a probability measured by the fraction ,, * 



or .4782 that an accused person would be condemned by a simple 

 majority. We should have the equation 



XT+XI..+ X u = .4782, (5) 



