148 Mr. TOZER, ON THE FORCE OF TESTIMONY 



that the accused is innocent ; and tlie analyst therefore assigns unity as a measure of the probability 

 of his innocence, though it may merely represent the confidence which the state reposes in the 

 inteority of its individual members. The claim to the property in waste lands beside a road is 

 advanced by the owner of the adjoining freehold, with a probability in favour of its justice measured 

 by unity, which must be reduced below one half by any claimant who would deprive him of 

 the benefit of the presumption. The consequences attached by the statutes of limitation to the ex- 

 piration of the periods which they assign, cause 1 or to be employed as the measures of pro- 

 babilities imperceptibly near in value to those to which by the non-expiration of the periods or 1 

 would be immediately before assigned. Some legal presumptions have, however, the effect of 

 modifying the probability, that the inference which they establish is a just one; it is perhaps 

 immaterial whether that raised by the production of a subsequent receipt in favour of the payment 

 of previous rent be absolute or capable of being rebutted. If it were absolute, and generally 

 known to be such, the knowledge that a conclusive presumption existed would diminish the proba- 

 bility of such a receipt being given when any previous rent was unpaid. In the presumptions 

 raised in criminal cases against the innocence of a prisoner, the probability that the inference is 

 just can never be less than that which justifies conviction. 



The presumption of guilt in the case of stolen property of which the possession by an accused 

 party is unaccounted for is defined by decisions on actual cases, and becomes more accurately so 

 as the number of these decisions is increased: the test of consistency among these appears to be simply 

 this, that for each case the probability that the guilt of the accused is the cause of the unaccounted- 

 for possession of the property should have the same numerical measure. 



Proceeding to the investigation of the reasoning processes by the algebraic solution of an example. 

 In a case of alleged poisoning by arsenic, to determine from the testimony of the witnesses the 

 probability of the presence of the poison. 



Let there be n witnesses, who respectively allege, with a greater or less degree of confidence, that 

 they discovered As ; and m others that they were unable to do so ; and suppose there is no doubt 

 about the veracity of any of them. 



An ordinary jury is not competent, from a detail of the processes of experiment, to decide on the 

 success with which they have been conducted. The phenomenon, therefore, which they witness is 

 the delivery of the testimony by a number of witnesses, whose respective abilities to judge it is a 

 part of their duty to estimate. 



In the case where As is present: 



Let p,...p„ be the probabilities that the first n witnesses would elicit from its presence 

 such appearances as to induce them to allege its presence. 

 §',...<]'„, that the m latter ones would do so. 

 Then 1 - p, 1 — g would be the probabilities that they would not succeed in doing so. 



Where As is not present : 



Let r,, r^,..r„ be the probabilities that some other substance has caused the appearances 

 in the case of the first n witnesses. 

 «i, S2...s^ in the case of the latter m witnesses. 

 Then 1 - r, 1 - s are the probabilities that appearances causing the testimony to be given would 



not be exhibited by any other substance than As. 

 Then if P be the probability that As was present, 



p ^ Pi---f)„-(l -q^) (1 -gj 



V\---Pn • (1 - ?l)-"0 - 9") + n...'>'„ (1 - «,)...(! - Sj ' 



If the jury were capable of judging of tlie evidence as furnished l)y the immediate result 

 of the experiments, selecting among the various causes of appearances which might be mis- 

 taken for those produced by As, would be performed by its members instead of by the witnesses. 



