540 THE ROYAL SOCIETY OF CANADA 



transaction from the books of the bank and from the inspector's 

 knowledge, and he asked for no specific receipt because the merchant 

 had also entrusted him with the signed note without cash or a written 

 receipt. These two explanations are not only equally probable 

 but very plausible. Oh the basis of probability, therefore, the same 

 material features of evidence can give rise to two plausible interpre- 

 tations and conclusions, each with substantially the same degree of 

 probability, and either of which explodes the other. 



d. The Balancing of probabilities. Probable conclusions of the 

 inferior measure rest ordinarily on a variety of opposing reasons of 

 different values, and the respective groups of favorable and unfavor- 

 able reasons as a whole are weighed or balanced against each other 

 in order to strike what historians call a "balance of probability" 

 for or against the conclusion. In historical conclusions of this de- 

 scription a weight of favorable reasons twice as great as the unfavor- 

 able would be regarded as very strong. As a rule the margin or 

 balance either way is so small that even impartial persons will differ 

 as to the side on which the greater weight seems to lie. Case 12 in 

 the present test illustrated the peculiar weakness of these conclusions 

 having only a narrow margin either way, but further light is thrown 

 on their exact scientific status by a feature in Case 11. It was found 

 there, according to comprehensive statistics, that there is a regular 

 excess of male births over female of about 6 per cent. Thus, in Ger- 

 many, for every 100 girls born in the years 1872-1888, the number of 

 boys was 106-2. If then it be placed in evidence that a child has been 

 born to John Doe, there is a moderate but definite and stable balance 

 of probability of the superior measure (in Germany 106 -2/206 -2 or 

 106 -2:100) that this child is a son, and this conclusion has more 

 scientific value than a balanced probable conclusion resting on a 

 variety of opposing reasons, with a margin either way so slight that 

 impartial judges will differ as to the side on which the margin lies. 

 In reaching such a balanced conclusion a person must first decide for 

 himself which of the opposing groups he will select as the weightier; 

 and then follows the final inference in favor of the conclusion supported 

 by the group selected. The final inference is as real a step toward the 

 conclusion as was the first selection, because in all probable conclu- 

 sions, even where the weight of probability is strongly in favor, there 

 are always chances that the actual facts lie on the contrary or weaker 

 side; and where the favorable margin or balance of probability is 

 small, these contrary chances are correspondingly great. In a balanced 

 conclusion of this description both the first selection and the final 

 inference are made according to probability of the inferior, con- 

 ceptualistic measure.'^a^On the other hand, in the conclusion that 



