CHANCE, AND ITS ELIMINATION, 317 



of variable causes. Thus, as summer advances, the approach of the 

 sun to a vertical position tends to produce a constant increase of tem- 

 perature ; but with this efl'ect of a constant cause, there are blended 

 the effects of many variable causes, winds, clouds, evaporation, elec- 

 tric agencies, and the like, so that the temperature on any given day 

 depends in part upon these fleeting causes, and only in part upon the 

 constant cause. If the effect of die constant cause is always accom- 

 panied and disguised by effects of variable causes, it is impossible to 

 ascertain the law of the constant cause in the ordinary manner, by 

 separating it from all other causes and observing it apart. Hence 

 ai-ises 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 differ- 

 ent times, and when these are so frequent, or so indeterminate, that 

 we camiot possibly exclude all of them from any experiment, although 

 we may vary them ; our resource is, to endeavor 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 invariable. The 

 results of these diffi>rent trials will naturally be different, since the 

 indeterminate modifying causes are different in each : if, then, we do 

 not flud 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 

 under as great a variety of circumstances as possible) yield the same 

 mean, provided only they be sufficiently 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 coexistence 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. 



This kind of elimination, in which we do not eliminate any one 

 assignable cause, but the multitude of floating unassignable ones, may 

 be termed the Elimination of Chance. We afford an example of it 

 when we repeat an experiment, in order, by taking the mean of differ- 

 ent results, to get rid of the effects of the unavoidable eri'ors of each 

 individual experiment. Wlien tliere is no permanent cause such as 

 would produce a tendency to error peculiarly in one direction, we are 

 wananted by experience in assuming that the errors on one side will, 

 in a ceitain number of experiments, about balance the errors on the 

 contrary side. We have, therefore, to repeat the experiment, until 

 any change which is produced in the avetage of the wliole by further 

 repetition, f;iJls within limits of eiTor consistent with the degree of 

 accuracy required by the purpose we have in view. 



§ 4. In the supposition hitherto made, the effect of the constant cause 

 A has been assumed to form so great and conspicuous a part of the 

 general result, that its existence never could be a matter of uncer- 

 tainty, and the object of the eliminating process was only to ascertain 

 how much is attributable to that cause ; what is its exact law. Cases, 



