SECT. 11.] Arrangement and Formation of the Series. 39 



draw a similar conclusion from this deductive line of argu 

 ment as from the direct appeal to statistics. The same 

 general result seems to be established ; namely, that approxi 

 mately, with sufficient accuracy for all practical purposes, we 

 may say that an examination of the causes by which the 

 deflections are generally brought about shows that they are 

 mostly of such a character as would result in giving us the 

 commonly accepted c Law of Error, as it is termed 1 . The 

 two lines of enquiry, therefore, within the limits assigned, 

 afford each other a decided mutual confirmation. 



11 (III.). There still remains a third, indirect and 

 mathematical line of proof, which might be offered to esta 

 blish the conclusion that the Law of Error is always one and 

 the same. It may be maintained that the recognized and 

 universal employment of one and the same method, that 

 known to mathematicians and astronomers as the Method of 

 Least Squares, in all manner of different cases with very 

 satisfactory results, is compatible only with the supposition 

 that the errors to which that method is applied must be 

 grouped according to one invariable law. If all laws of 

 error were not of one and the same type, that is, if the 

 relative frequency of large and small divergences (such as we 

 have been speaking of) were not arranged according to one 

 pattern, how could one method or rule equally suit them all ? 



In order to preserve a continuity of treatment, some 

 notice must be taken of this enquiry here, though, as in the 

 case of the last argument, any thorough discussion of the 



1 Law of Error is the usual tioned in 4, but by a convenient 



technical term for what has been generalization it is equally applied 



elsewhere spoken of above as a Law to the other two ; so that we term 



of Divergence from a mean. It is in the amount of the divergence from 



strictness only appropriate in the the mean an error in every case, 



case of one, namely the third, of the however it may have been brought 



three classes of phenomena men- about. 



