﻿1-40 Dr. H. Stanley Allen on the Series Spectrum of 



^measured. The assumption of a large free path to compensate 

 a small number leads to contradictions with the optical pro- 

 perties of metals. It is suggested that the free electrons in a 

 metal form a space-lattice, which corresponds to a crystal at 

 a very low temperature, as the small mass of the electrons 

 leads to a high frequency. The point of view from which 

 this theory would explain the various metallic phenomena is 

 indicated. Although it explains the exceptional behaviour 

 of alloys and the general outlines of the photoelectric effect, 

 special assumptions are needed to arrive at the law of 

 "\Viedemann-Franz. The contradictions entailed by the old 

 theory, more especially the one mentioned above, do not 

 arise. 



Sidmouth, Dec. 3rd, 1914. 



XIII. The Series Spectrum of Hydrogen and the Structure of 

 the Atom. By H. Stanley Allen, M.A., D.Sc. * 



THE series spectrum of hydrogen can be represented with 

 considerable accuracy by the formula of Balmer, which 

 may be written 



-*(i-i\ (1) 



where n is the number of wave-lengths per centimetre, X is 

 the series constant, and m = 3, 4, 5 . . . . 



In a recent investigation by W. E. Curtis | the wave- 

 lengths of the first six lines of the series have been deter- 

 mined with an accuracy of 0*001 A.U. It was found that 

 Balmer's formula was inexact. This was shown by the fact 

 that the values of N calculated by the above expression for 

 the different lines are not the same. (See Table I., which is 

 reproduced from the paper referred to.) Curtis found that 

 the results could be better represented by the Rydberg 

 formula, 



N X 



W = (2T^"(^+^? (2) 



By putting ;> = 0. ^=+0'0 5 69, and N=109,679"22 the 

 formula gives a fit quite within the limits of experimental 

 error. Very little improvement is obtained by introducing 

 ;i third constant p. If this be done the values of the 

 constants are 



p=z +0-0 7 8, /fc-=-r(M) 5 70, N= 109,679-23. 



* Communicated bv the Author. 



t W. E. Curtis, Proc. Roy. Soc. vol. xc. p. 605 (1914). 



