CHAP. XXI.] PROBABILITY OF JUDGMENTS. 397 



correct judgment for a member of the court, and the general pro- 

 bability k of guilt in an accused person. 



The solution of this problem differs in but a slight degree 

 from that of the last, and may be referred to the same general 

 formulae, (4) and (5), or (7). It is to be observed, that as there 

 are two elements, c and A, to be determined, it is necessary to 

 reserve two of the functions Xi 9 X% 9 . . X m _i 9 let us suppose X\ 

 and Xm-i, for final comparison, employing either the remaining 

 m - 3 functions in the expression of the data, or the two respec- 

 tive sets X 29 X Z9 . . X m .v and X X 29 . . . X m _ 2 . In either case 

 it is supposed that there must be at least two original indepen- 

 dent data. If the equation (7) be alone employed, it would in 

 the present instance furnish two equations, which may thus be 

 written : 



q.QA-0 a,(xX t ) a m (xX m ) 



v ~~v ' + Y ' ^ ' 



^\i .A.2 j\. m 



.(**.) , .(*.*.) . -(**.) _ , m 



~xT ~xT ~sr~ 



These equations are to be employed in the following manner : 

 Let a? 19 # 2 , . . x n represent those events which consist in the for- 

 mation of a correct opinion by the members of the court respec- 

 tively. Let also w represent that event which consists in the 

 guilt of the accused member. By the aid of these symbols we 

 can logically express the functions X 19 X 29 . . X m _i 9 whose proba- 

 bilities are given, as also the function X m . Then from the func- 

 tion Xi select those constituents which contain, as a factor, any 

 particular symbol of the set x i9 a? z , . .x n9 and also those consti- 

 tuents which contain as a factor w. In both results change 

 Xi 9 # 2 ) #n severally into x 9 and w into k. The above results 

 will give (xXi) and (kXi). Effecting the same transformations 

 throughout, the system (1), (2) will, upon the particular hypo- 

 thesis involved, determine x and k. 



14. We may collect from the above investigations the fol- 

 lowing facts and conclusions : 



1st. That from the mere records of agreement and disagree- 

 ment in the opinions of any body of men, no definite numerical 

 conclusions can be drawn respecting either the probability of cor- 



