ON THE DOCTRINES OF CHANCE. 



than h, and c greater than d, the denominators a c-{-b c and 



a c-\-a d to the common numerator a c will be each of them 



greater than a c-\-b d and consequently the value of the frac- 



a c 

 tions less than — , ; ", , viz. the probability ofa circumstance 



being true in the relation of which two persons agree, who are 

 each in the habit of relating more truth than falsehoods, will 

 he greater than when related by either of them separately. 



a c 



Cor. 3. If a be less than b and c less than d, then tTI Cor. 3» 



' ac-\'ba 



a c 



will be less than either — TT" or "■., ■ /: viz. the probability 

 a-\-b c-\-d ' ' ^ 



of the truth of a circumstance in liie relation of which two 



persons agree, Avho are each in the habit of relating fewer 



truths than falsehoods, will be less than when related by either 



of them separately. 



Cor. 4. If a be either greater or less than b, and c—d. Cor, 4. 



a c a c a 



then will r-r-/ = TT' — — Tl'> viz. the probability 



ac^bd ac+hc a + b * -^ 



of the truth of a circumstance in the relation of which two 



persons agree, the one of whom is in the habit of relating an 



equal number of truths and falsehoods, and the other any 



number of truths with any other number of falsehoods, will 



be the same as if related by that other onli;, 



a c a c 

 Cor. 5. If c? — 0, then rrH — — ^ or certainty, r^. e 



viz. the probability of the truth of a circumstance in the 

 relation of which two person? agree, the one of whom uni- 

 formly relates truth, and the other any number of truths with 

 any number of falsehoods, will always amount to certainly: 

 as is evident from reflection also, for, in this case, to agree 

 they must both speak truth. 



Cor. 6. Hence also it appears, that the corroborating tes- q ^ 

 timony of a second person or witness is not always an addi- 

 tional evidence in favour of the truth of a circumstance re- 

 lated by the first, for if d be greater than c,b d will be greater 



a c / (i \ 



than b c, and consequently •-; ^ or its equal - . ■ - \ 



Vol. XXI.— Nov. 1808. P will 



2U;» 



