318 INDUCTION. 



however, occur in which the effect of a constant cause is so small, 

 compared with that of some of the changeable causes with which 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 produced, then 

 if the aggregate be taken of a sufiicient 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, around 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 con- 

 stant 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 

 plienomenon by elmiinating the effect of chance. 



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

 Of course no dice are so climisily 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 

 upon the changeable causes, these in a sufiicient number of instances 

 would balance one another, and there would be no preponderant 

 number of throws of any one kind. If, therefore, 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 favor of a partic- 

 ular throw; we may conclude with assurance that there is some constant 

 cause acting in favor of that throw, or in other words, that the dice 

 are not fair ; and moreover 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 arising from the 

 irregular changes in the state of the ' atmosphere, was discovered by 

 comparing the average height of the barometer at different hours of 

 the day. When this comparison was made, it was found that there 

 was a small difference, which on the average was constant, however 

 the absolute quantities might vary, and which difference, therefore, 

 must be the effect of a constant cause. This cause was afterwards 

 asceitained, deductively, to be the rarefaction of the air, occasioned 

 by the increase of temperature as the day advances. 



§ 5. After these general remarks on the nature of chance, we are 

 prepared to consider in what manner assurance may be obtained that 

 a conjunction between two phenomena, which has been obseiTed a 

 certain number of times, is not casual, but a result of causation, and 

 to be received therefore as one of the uniformities in nature, although 

 (until accounted for a priori) only as an empirical law. 



We will suppose the strongest case, namely, that the phenomenon B 

 has never been observed except in conjunction with A. Even then, 

 the probability that they are connected is not measured by the total 



