( ^79 ) 



root of whicli is fouixl in Iho way inoiilioncd of' the first sub- 

 ordinate sei'ies '). Tlie first subordinate series, howevei-, not iiaving 

 been measured accurately, the root of Bergmann's series can also 

 only be determined by approximation by tins method. The fact that 

 this series consists of doublets is in connection with the satellites, 

 which accompany the I S.S. "). 



For this line Hicks ') calculates the constants in Rydbkro's formula 

 and in the empiric formula given by me. The errors of ob.servation 

 in these lines are too great to allow us to decide which formula is 

 to be preferred. It has appeared to me that a change within the 

 possible error of observation of the lines on which the calculation 

 was based, has a considerable influence on these constants, and also 

 on the calculated deviations of the other lines. 



The first two lines of the above series give again a differential 

 vibration, Moll's line 3,97 /^ ; the difference of the observed lines 

 gives 3,89. 



Hydrogen. Balmer's formula for a hydrogen series may be written 



109675 109675 

 thus : n=z --— (1), w = 1,2,... 



It is remarkable that the root of this series amounts to exactly V4 

 of the universal constant. This phenomenon is accounted for when 

 w^e consider this observed series as a differential series which corre- 

 sponds to that discovered by Lenard and others in the spectrum of 



109675 

 Na. If we assume the formula n = A (II), ?/? = 1, 2, . . . 



for the principal series of H, which lies in the ultra-violet, formula 

 (I) represents the lines whose frequencies are equal to the differences 

 of the frequencies of the first line of formula (II) with each of the 

 following ones. The root of the differential series is ??» — 7i^ = A — n^ 

 and this is the root at which we arrive for a subordinate series 



^) Randall's measuremeiils (Ann. d Fiiys. Vol. 33, IDIO, p. 743) are more 

 accurate. 



-) W. RiTZ, I.e. p. 52:2, case 5. 



■') W. M. Hicks, A critical study of si ectral series, Phil, Transact, of the R.S. 

 Loudon, Ser. A, Vol. 210, p. 85, 191U. Hicks assumes the formula 



A' 



71 ^ A 



b 



m -\- a -\ 



m 



Probably Prof. HicKS is not acquainted with the Proceedings of the Meeting of 

 Nov. 27. 1906 of this Academy. An abstract of this paper and of my Thesis for the 

 doctorate Amsterdam appeared in the Beibl. 1907. HiCKs does not mention that 

 this formula has been treated already elsewhere. 



