CHANCE, AND ITS ELIMINATION. 57 



This kind of elimination, in which we do not eliminate 

 any one assignable cause, but the multitude of floating un- 

 assignable 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 different results, to get rid of the 

 effects of the unavoidable errors of each individual experiment. 

 When there is no permanent cause such as would produce 

 a tendency to error peculiarly in one direction, we are war- 

 ranted by experience in assuming that the errors on one side 

 will, in a certain number of experiments, about balance the 

 errors on the contrary side. We therefore repeat the experi- 

 ment, until any change which is produced in the average of 

 the whole by further repetition, falls within limits of error 

 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 uncertainty, and the object of the 

 eliminating process was only to ascertain how much is attri- 

 butable to that cause ; what is its exact law. Cases, however, 

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

 pared with that of some of the changeable causes with which 



* In the preceding discussion, the mean is spoken of as if it were exactly 

 the same thing with the average. But the mean for purposes of inductive 

 inquiry, is not the average, or arithmetical mean, though in a familiar illustra- 

 tion of the theory the difference may be disregarded. If the deviations on one 

 side of the average are much more numerous than those on the other (these last 

 being fewer but greater), the effect due to the invariable cause, as distinct from 

 the variable ones, will not coincide with the average, but will be either below or 

 above the average, whichever be the side on which the greatest number of the 

 instances are found. This follows from a truth, ascertained both inductively 

 and deductively, that small deviations from the true central point are greatly 

 more frequent than large ones. The mathematical law is, "that the most 

 probable determination of one or more invariable elements from observation is 

 that in which the sum of the squares of the individual aberrations," or devia- 

 tions, " shall be the least possible." See this principle stated, and its grounds 

 popularly explained, by Sir John Herschel, in his review of Quetelet on Proba- 

 bilities, Essays, pp. 395 et seq. 



