162 THE ROYAL SOCIETY OF CANADA 
“n1” represent the statement that the agent purchased it for 
£1,000, 
“m2” represent the statement that the duke purchased it for 
£2,000, and 
“n2” represent the statement that the agent purchased it for 
£2,000, 
then the chances of B contradicting himself at various times in state- 
ments concerning the purchaser and price combined are six in number, 
as follows:— 
Bm1 v. Bn1; Bm1 v. Bm2; Bm1 v. Bn2; 
Bn1i v. Bm2; Bnl v. Bn2; Bm2 v. Bn2. 
The chances of self-contradiction by C and D are identical with 
those of B, therefore the total chances of self-contradiction by B, C, 
and D in combined statements concerning purchaser and price are three 
times six, or in all eighteen. The chances of B contradicting C in such 
combined statements are twelve in number, as follows:— 
Bm1 v. Cn1; Bm1 v. Cm2; Bm1 v. Cn2; 
Bni v. Cm2; Bni v. Cn 2; Bm2 v. Cn2; 
Cm1 v. Bn1; Cml v. Bm2; Cm1 v. Bn2; 
Cnl1 v. Bm2; Cnl v. Bn 2; Cm2 v. Bn2. 
The chances of B contradicting D, and of C contradicting D, are 
identical with those of B contradicting C, therefore the total number 
of chances of contradiction between B, C, and D in combined statements 
concerning purchaser and price are three times twelve, or in all thirty- 
six. Summarized, the chances of contradictory statements of all sorts 
in the single transaction stated in Case 11 are seventy-two in number, 
as follows:— 
(1) Statements concerning purchaser alone............. 9 
(2) Statements concerning price alone.................. 9 
(3) Statements concerning purchaser and price combined. : 
(a) Sef- contradictory by’ BY C, D 200 4022.2... 18 
(b) Contiadictory. Gelveen BD 0 "D: 700,2, ae 36 
COG TAG Si UG SHE CCR eae SOs AR A ew Lead, TE 72 
In calculating the above chances in Cases 6, 7 and 11, only persons 
directly sharing or interested in the respective transactions have been 
considered. Many other persons might have, or obtain, acquaintance 
with the circumstances and make the same legitimately discrepant 
statements as the principals in the transaction. The addition of even 
