376 INDUCTION. 



Generalizing the result, we may say that if A occurs in a larger propor- 

 tion 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, be- 

 tween 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 generalization 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 empirical 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, pro- 

 ducing an effect which is successively modified by a series of variable 

 causes. Thus, as summer advances, the approach 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 vari- 

 able 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 con- 

 stant cause is always accompanied and disguised by effects of variable 

 causes, it is impossible to ascertain the law of the constant cause in the or- 

 dinary 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 stead- 

 ily by the same cause or causes, but by different causes at different times, 

 and when these are so frequent, or so indeterminate, that we can not pos- 

 sibly exclude all of them from any experiment, though we may vary them ; 

 our resource is, to endeavor to ascertain what is the effect of all the vari- 

 able causes taken together. In order to do this, we make as many trials 

 as possible, preserving A invariable. The results 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 contraiy, to oscillate about a certain point, one experiment giv- 

 ing 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 experi- 

 ments (taken in as great a variety of circumstances as possible) yield the 

 same mean, provided only they be suflUciently 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 average is struck does not materially 

 alter the average. 



