58 INDUCTION. 



it is liable to be casually conjoined, that of itself it escapes 

 notice, and the very existence of any effect arising from a 

 constant cause is first learnt, by the process which in general 

 serves only for ascertaining the quantity of that effect. This 

 case of induction may be characterized as follows. A given 

 effect is known to be chiefly, and not known not to be wholly, 

 determined by changeable causes. If it be wholly so pro- 

 duced, then if the aggregate be taken of a sufficient number of 

 instances, the effects of these different causes will cancel one 

 another. If, therefore, we do not find this to be the case, but, 

 on the contrary, after such a number of trials has been made 

 that no further increase alters the average result, we find that 

 average to be, not zero, but some other quantity, about which, 

 though small in comparison with the total effect, the effect 

 nevertheless oscillates, and which is the middle point in its 

 oscillation ; we may conclude this to be the effect of some 

 constant cause : which cause, by some of the methods already 

 treated of, we may hope to detect. This may be called the 

 discovery of a residual phenomenon by eliminating the effects 

 of chance. 



It is in this manner, for example, that loaded dice may 

 be discovered. Of course no dice are so clumsily loaded that 

 they must always throw certain numbers ; otherwise the fraud 

 would be instantly detected. The loading, a constant cause, 

 mingles with the changeable causes which determine what 

 cast will be thrown in each individual instance. If the dice 

 were not loaded, and the throw were left to depend entirely 

 on the changeable causes, these in a sufficient number of in- 

 stances would balance one another, and there would be no 

 preponderant number of throws of any one kind. If, there- 

 fore, after such a number of trials that no further increase of 

 their number has any material effect upon the average, we find 

 a preponderance in favour of a particular throw ; we may con- 

 clude with assurance that there is some constant cause acting 

 in favour of that throw, or in other words, that the dice are 

 not fair; and the exact amount of the unfairness. In a 

 similar manner, what is called the diurnal variation of the 

 barometer, which is very small compared with the variations 



