The Genesis of the Law of Error. 347 



spectrum seems to fall into line. A further linearity is 

 indicated for the helium column. 



It is found that Runge and Precht's logarithmic law is 

 not an essential improvement. The required correction is 

 apparently necessitated on Relativity grounds. 



It is shown that in two ol the columns of the table there 

 is a two-fold linearity, the lines branching definitely at one of 

 the elements. 



The Physical Laboratory, 



The University of Michigan, 

 June 1918. 



XXXVII. The Genesis of the Law of Error. 

 By Prof. R. A. Sampson*. 



IN the issue of this Journal for May of the present year, 

 Prof. F. Y. Edgevvorth does me the honour to criticise 

 a paper on the law of distribution of errors which I con- 

 tributed to the Fifth International Congress of Mathe- 

 maticians in 1912 and have published in their Proceedings, 

 vol. ii. p. 163. In the course of his remarks he points to an 

 error in one of my formulae, for which I desire to thank him. 

 My excuse must be that the formula in question was thrown 

 out collaterally and was unnecessary to support the point 

 which I wished to make. Therefore it escaped, I suppose, suf- 

 ficient examination. Apart from this, — and in itself it hardly 

 seems sufficient reason, — after reading Prof. Edgeworth's 

 paper somewhat carefully, I am a little at a loss to know 

 why it was written ; for while it certainly shows little 

 agreement between us, the points of difference appear to me 

 equally unsubstantial. The basis which he dubs my " peculiar 

 notion of the nature of an error of observation " seems to me 

 identically the same thing as he refers to earlier under the 

 name of " some instructive remarks on the nature of errors 

 in astronomical observations'" by Morgan Crofton, in Phil. 

 Trans. 1870; while for a text for the whole of my paper 

 I might have taken, had I chosen, a sentence from his own 

 article on " Probability " in Enc. Brit. 11th edition, p. 376 — 

 " the paths struck out by Laplace and Gauss have hardly 

 yet been completed and made quite secure," — and indeed 

 would prefer this to his present statement that my " attack 

 on the proof given by Poisson after Laplace strikes at all the 



* Communicated by the Author. 

 2 A2 



