648 Professor A. Fowler [March 31, 



first line of the Diffuse series (see fig. 2). The chief relations are 

 embodied in the following formnla? given by Rydberg : 



Principal series : P (»^) = N 

 Sharp series : S (m) = N 

 Diffuse series : D(w) = Ni,, ^., ,^^^ 



where jt?, s, and d are the values of /jl for the respective series. The 

 main point I wish you to observe is that the Principal and Sharp 

 series are so related that if one of them be known the other can be 

 immediately calculated from it by a mere transposition of terms. 

 More accurate formulae have since been employed, but the formulas 

 of Rydberg are the simplest and are sufficiently accurate for our 

 present purpose. 



Coming now to the spectrum of helium, it was found by Rnnge 

 and Paschen that the lines could be included in six series : a 

 Principal, Sharp, and Diffuse series of very close doublets (including 

 the yellow line D3 at A 5876), and a similar set of series of single 

 lines. A portion of the spectrum is shown in Fig. 3. 



The existence of two complete sets of series, with no recognized 

 connexion between them, was for some time thought to be an indica- 

 tion that helium was a mixture of two gases, and the supposed element 

 giving the family of single-hne series was even named " parhelium." 

 This idea was not wholly dependent on spectroscopic observations, 

 but was apparently strengthened by the fact that either of the two 

 systems could be developed with greater intensity than the other by 

 varying the conditions of discharge. Thus, one of the tubes exhibited 

 glows with a pale green light and shows the single line series most 

 strongly, while the other shines with a yellow light and specially 

 emphasises the doublet series. Helium, however, is not unique in 

 showing such variations, or in giving more than one family of series, 

 and the view that it might be a mixture of gases has long been 

 abandoned. 



Helium, like hydrogen, has also a very complex secondary spectrum, 

 though it escaped notice for many years. It was missed, I think, 

 because those who made helium-tubes in the early days were too 

 sparing of the gas. It was discovered independently at the Imperial 

 College and by Goldstein, and may be obtained quite brilliantly in 

 the wider parts of a tube containing helium of sufficient density, if a 

 small condenser and spark-gap be included in the circuit. This 

 spectrum is definitely banded, but although each band is built up 

 on the standard pattern for bands, some of them are arranged in 

 accordance with the law of line series. In this respect helium is 



