CHAP. XXI.] PROBABILITY OF JUDGMENTS. 389 



With this understanding we shall have, by the general Rule 

 (XVII. 17), 



Prob. t 



1 ) *, 7 8 . .?.!..+ (XX m . i)?! ..T m .2t m .i 



V = X m ?! . . 7 W _, + X x *i 7 a t-i . . + X*.! 7i . . T OT _2 * w -i (10) 



whence the relations determining #1, . . # B > 'u -i will be of 

 the following type (z varying from 1 to ri), 



(xj X m ) % . . ?., + (a< Xjj *! 7, . . 7,.! . . + (^ X^.Q 7 X . . T m _ 2 ^ 



t\ 



tl-F. (11) 



From the above system we shall next eliminate the symbols 



tl, ..*-! 



We have 



t\ t% . . ^jn-i = v 5 #1 . . ^wt-2 t-m-i ~^r? (12) 



A! Am-1 



Substituting these values in (10), we find 



V= XmT, . . Tm-i + a,V . . + ttm.iV. 



Hence, 



(1 -...- a,..) P 



fi . . fcm-l -- V= - 

 ^m 



Now let 



m= 1 -i - flm-i (13) 



then we have 



< 



OT 



(14) 



Now reducing, by means of (12) and (14), the equation (9), 

 and the equation formed by equating the first line of (11) to the 

 symbol V\ writing also Prob. X for Prob. t, we have 



wherein X OT and a m are given by (7) and (13). 



