348 Prof. R. A. Sampson on tlie 



applications of the law." T have, I feel^ failed to convey 

 my point to Prof. Edgeworth. Within ten minutes of the 

 delivery of the paper at the Congress he had banned every 

 detail of it, and now six years afterwards he puts into print 

 his matured objections. I am not able to write more clearly 

 than that paper is written; but in the hope that I may succeed 

 better with those who view the subject with a less magisterial 

 eye, I shall take the occasion to make a few supplementary 

 remarks. 



What is an Error, and why is an Error, of all things, 

 subject to a Law ? Has our notion of the nature of an 

 error a definable character from which such a law may be 

 deduced, or must we accept the existence of the law as a fact 

 or as an axiom, without attempting to derive it as implicitly 

 contained in an adopted definition of an error ? There can 

 hardly be a doubt as to the right answer to this question. 

 The law is an approximation, and must follow as such, from 

 some rough and ready, tacitly accepted, notion of what con- 

 stitutes an error, — however difficult it may prove to assign 

 the least restricting notions from which it can be shown to 

 arise. The trouble is that proofs are in existence that seem 

 to dispense, more or less completely, with any definition of 

 an error, and which therefore derive without anterior con- 

 ditions the conclusion that unconditioned errors occur 

 according to a law of frequency of definite form. One 

 must not hesitate to put such proofs aside, including any 

 which begin by postulating the existence of an error function. 

 Among these, to mention no more, are Gauss's original 

 proof in the Theoria JMotus, HerscheFs proof from the distri- 

 bution of shots on a target, and Morgan Crofton's proof by 

 means of differential equations. The question is a logical one 

 of the hio-hest moment and well deserves a few sentences to 

 make it clear. 



If we postulate the existence of a law of frequency ruling 

 the unknown and unknowable domain of errors, we so far 

 limit Reality. We add to our view of the Nature of Things 

 a new restriction. An exact analogue may be found in the 

 domain of geometry. If we accept as an ascertained fact 

 the twelfth of Euclid's "common notions,"" we make an affir- 

 mation as to the nature of real space, which in the same 

 way has the character of a limitation of Reality, for we 

 know that as a logical axiom it need not exist. This obstacle 

 has been visible from the beginning. It did not escape the 



