34^ 



INDUOTIOI^. 



that if A occurs in a larger proportion 

 of the cases where B is than of the 

 cases where B is not, then will B 

 also occur in a larger proportion of 

 the cases where A is than of the cases 

 where A is not, and there is some 

 connection through causation between 

 A and B. If we could ascend to the 

 causes of the two phenomena, we 

 should find, at some stage, either 

 proximate or remote, some cause or 

 causes common to both ; and if we 

 could ascertain what these are, we 

 could frame a generalisation which 

 would be true without restriction of 

 place or time ; but until we can do 

 so, the fact of a connection between 

 the two phenomena remains an em- 

 pirical law. 



§ 3. Having considered in what 

 manner it may be determined whether 

 any given conjunction of phenomena 

 is casual or the result of some law, 

 to complete the theory of chance it 

 is necessary that we should now con- 

 sider those effects which are partly 

 the result of chance and partly of 

 law, or, in other words, in which the 

 effects of casual conjunctions of causes 

 are habitually blended in one result 

 with the effects of a constant cause. 



This is a case of Composition of 

 Causes ; and the peculiarity of it is, 

 that instead of two or more causes 

 intermixing their effects in a regular 

 manner with those of one another, we 

 have now one constant cause, produc- 

 ing an effect which is successively 

 modified by a series of variable causes. 

 Thus, as summer advances, the ap- 

 proach of the sun to a vertical position 

 tends to produce a constant increase 

 of temperature ; but with this effect 

 of a constant cause there are blended 

 the effects of many variable causes, 

 winds, clouds, evaporation, electric 

 agencies and the like, so that the 

 temperature of any given day depends 

 in part on these fleeting causes, and 

 only in part on the constant cause. 

 If the effect of the constant cause is 

 always accompanied and disguised by 

 effects of variable causes, it is impos- 



sible to ascertain the law of the con- 

 stant cause in the ordinary manner, 

 by separating it from all other causes 

 and observing it apart. Hence arises 

 the necessity of an additional rule of 

 experimental inquiry. 



When the action of a cause A is 

 liable to be interfered with, not steadily 

 by the same cause or causes, but by 

 different causes at different times, 

 and when these are so frequent, or so 

 indeterminate, that we cannot pos- 

 sibly exclude all of them from any 

 experiment, though we may vary 

 them, our resource is, to endeavour 

 to ascertain what is the effect of all 

 the variable causes taken together. 

 In order to do this, we make as many 

 trials as possible, preserving A invari- 

 able. The result of these different 

 trials will naturally be different, since 

 the indeterminate modifying causes 

 are different in each ; if, then, we do 

 not find these results to be progressive, 

 but, on the contrary, to oscillate about 

 a certain point, one experiment giving 

 a result a little greater, another a 

 little less, one a result tending a little 

 more in one direction, another a little 

 more in the contrary direction ; while 

 the average or middle point does not 

 vary, but different sets of experiments 

 (taken in as great a variety of cir- 

 cumstances as possible) yield the same 

 mean, provided only they be suffi- 

 ciently numerous ; then that mean or 

 average result is the part in each 

 experiment which is due to the cause 

 A, and is the effect which would have 

 been obtained if A could have acted 

 alone : the variable remainder is the 

 effect of chance, that is, of causes the 

 co-existence of which with the cause 

 A was merely casual. The test of 

 the sufficiency of the induction in this 

 case is, when any increase of the 

 number of trials from which the aver- 

 age is struck does not materially alter 

 the average. 



This kind of elimination, in which 

 we do not eliminate any one assign- 

 able cause, but the multitude of float- 

 ing unassignable ones, may be termed 

 the Elimination of Chance. We 



