Genesis of the Law of Error. 153 



at variance with those of Professor Sampson as seemed before 

 his conciliatory explanations. There was, however, and, 

 indeed, still is, an appearance of difference which may excuse 

 my previous expressions of dissent. It may be of! more 

 than personal interest to exhibit the seeming difference'. 



II. A. Wishing to "discard as far as possible the language 

 of probabilities" (Congress*, p. 163), Professor Sampson 

 runs the risk of obscuring the conceptions proper to the 

 science (1)|- I do not recognize the doctrines of Proba- 

 bilities in the following description of the Laplace-Poisson 

 theory of error : - " It is a theorem of convergence and must 

 be judged so. It is either true or false. Such phrases as 

 '« tres peu pres' are not in the first place admissible. If 

 they are required to help the demonstration out, that means 

 the theorem is false ; for Poissonin particular seems to have 

 held that no conditions were necessary to impose upon the 

 frequencies of the elementary contributing errors Hafonction 

 aura telle forme que Von voudra 9 "%. But if the view above pre- 

 sented — (6) and (7) — is correct, the conditions for Hie genesis 

 of thn la.w-of-error are, in general, only fulfilled approximately ; 

 the phrase of Laplace "a tres peu tres" is generally, not to 

 say, universally § appropriate. On the same view the words- 

 of Poisson are perfectly correct; convergence towards the 

 normal law will set im whatever the frequency-function of 

 the contributory elements — with one exception, indeed, formed 

 by the fourth condition (8), an exception which proves the 

 rule as it has no concrete existence (9) and (10). 



Discarding the language of Probabilities, Prof. Samp-on 

 writes (Congress, p. 168) : — " The term accidental error has 

 come to carry with it an undefined suggestion of a peculiar 

 quality, but there seems no reason to treat an error otherwise 

 than as a disregarded unknown "... It appears to me that 

 in accounting for the presence of the law of error we cannot 

 discard the peculiar quality of accident or Probability (1) 

 and (2). It is the attempt to get rid of that peculiarity 

 which I described as Professor Sampson's " peculiar notion 



* The reference is to Professor Sampson's paper on the "Law of Distri- 

 bution of Errors " read before the 5th Congress of Mathematicians ( 1912; 

 at a joint meeting of the sections on Astronomy and Statistics; published 

 in the ' Proceedings of the Congress,' vol. ii. p. 163. 



t The numerals in Section II. refer to passages numbered in Section I. 



X Phil. Mag. p. 349. The references hereinafter thus made are to 

 Prof. Sampson's article on the " Genesis of the Law of Error " in the 

 Philosophical Magazine for October 1918, vol. xxxvi. 



§ Even in games of chance perfect independence is probably only an 

 ideal (6) ; also the number of trials being finite, there can only be an 

 •approximation, e. g. (3) to the normal law of frequency. 



