THE LA W OF ERROR. 447 



parison, the larger errors being less frequent than theory 

 would indicate. 



We may also regard the experiments enumerated in 

 the chapter on Probabilities (p. 238), as forming an em- 

 pirical verification of the theory of error. 



Remarks on the General Law of Error. 



The mere fact that the Law of Error allows of the 

 possible existence of errors of every assignable amount 

 shows that it is only approximately true. We may fairly 

 say that in measuring a mile it would be impossible to 

 commit an error of a hundred miles, and the length of life 

 would never allow of our committing an error of one 

 million miles. Nevertheless the general Law of Error 

 would assign a probability for an error of that amount or 

 more, but so small a probability as to be utterly incon- 

 siderable, and almost inconceivable. All that can, or in fact 

 need, be said in defence of the law is, that it may be made 

 to represent the errors in any special case to a very close 

 approximation, and that the probability of large and prac- 

 tically impossible errors, as given by the law, will be so 

 small as to be entirely inconsiderable. And as we are 

 dealing with error itself, and our results pretend to no- 

 thing more than approximation and probability, an in- 

 definitely small error in our process of approximation is 

 of no importance whatever. 



The Probable Mean Result as defined ~by the Law 

 of Error. 



One immediate result of the Law of Error, as thus stated, 

 is that the mean result is the most probable one ; and 

 when there is only a single variable this mean is found by 

 the familiar arithmetical process. An unfortunate error 



