U6 Mr. TOZER, on THE FORCE OF TESTIMONY 



The phenomenon then actually witnessed is that of a witness alleging that, from appearances 

 which his experiments have produced, he infers the existence of a certain fact, and the object is to 

 determine the probability of tiiat fact being true. First then we consider, for each separate experi- 

 ment, on the hypothesis that the fact is true, what is the probability that it would have produced 

 appearances sufficient to convince the mind of the witness, and induce him to give the testi- 

 mony he has given. We then take each of the known possible causes of such appearances, and 

 similarly calculate the probabilities that each one of those severally would, if it existed, have pro- 

 duced them in such a way as to have impelled the giving of tlie testimony. And, lastly, the pro- 

 bability of some unknown cause having so acted. The probability of the hypothesis that the 

 alleo-ed fact is the true cause, is then determined by the known processes of the science. If the 

 operations have been conducted in symbolical language, no step has thus far been taken without the 

 sanction of rigid demonstration ; the effect has been to resolve the probability whose value is sought 

 into tiie elementary probabilities of which it is composed. To the next step therefore, which is that 

 of assigning numerical values to the symbols in which the result is expressed, has been given all the 

 facility of which it is capable. In the particular case of persons accused of crime, the minimum 

 value of the probabilities which favour the accusation alone are required, the precise numerical 

 value of their measures never need therefore be assigned. The values which in our judgments those 

 which favour the hypothesis cannot fall short of, and which those that favour any other hypothesis 

 cannot exceed, are all that are necessary to be decided; the result is a number which is not greater 

 than the numerical value of the measure of the probability whose value is sought: and as far as this 

 particular fact is concerned, conviction or acquittal must follow, as this measure does or does not 

 exceed the standard which justifies decision. The actual measure of the value of the probability 

 is left indefinite in magnitude; its least possible value alone is defined, but the assigning of accurate 

 values to the elementary probabilities, and thus defining the actual measure, will not in the slightest 

 degree affect the result. 



The next formula applies to allegations of facts the truth of which cannot be tested by experi- 

 ment ; the consideration of the credibility of the witness is also introduced; the modification by 

 which it is made to differ slightly from that given by Poisson, does not affect the principle by which 

 it is obtained. The hypothesis that the fact alleged is true will account for its being alleged, 

 first, when the witness is neither deceived, nor intending to deceive ; and secondly, when both the 

 one and the other, provided that among the various allegations which he may make for the purpose 

 of deceiving, he should chance to make that which is in fact true. The various ways in which he 

 may be deceived without intending to deceive, endeavour to deceive without being himself deceived, 

 and being himself deceived also endeavour to deceive without alleging the fact which did occur; all 

 suggest hypotheses which will or may, with some degree of probability, account for the testimony 

 being given, though the fact which it alleges is not true. The probability that the hypothesis 

 which assumes the fact alleged to be true is the correct one, is then as before given by the scientific 

 process, and this whether its truth be alleged by one or more witnesses, or alleged by some and denied 

 by others. The antecedent probability, of the fact alleged having occurred, is also taken account of 

 in the formula. 



The same process applies to ascertaining the probability that a fact is true which is alleged, 

 but which is not material to the issue, of which an example also occurs. We then have a witness 

 alleging a fact the probability of whose truth we have measured ; and also other facts, the probability 

 of whose truth we wish to measure ; and the former modifies the values of the probabilities, that 

 the witness deceives, or is deceived, which are involved in the equations which express the latter. 



When the measures of the probabilities of those facts which must be proved to sustain the 

 accusation have been ascertained, their product will measure the probability of a series of facts 

 being true, from which the truth of the accusation is an inference; the probability of the accusa- 

 tion being true will therefore be this product, or this product multiplied by the fraction which 

 expresses the probability of the inference being true, on the assumption that all the facts of the 



