Cause of the Structure of Spectra. 251 



hydrogen lines of Balmer's formula /jl = 0. Rydberg takes 

 Pickering's series by itself and calculates from it the most 

 probable values of n and jju that will bring it under his for- 

 mula. The result is that n has the same value as for the 

 Balmer series in hydrogen, while /j, has the value '500737.. 

 Rydberg then makes a brilliant application of his principles, 

 as will be explained later on, to demonstrate that there ought 

 to be another series of hydrogen lines, the principal series, 

 most of which are of so short a wave-length as to be 

 absorbed in passing through our atmosphere, but the chief 

 one ought to have a wave-length 4687*88. As Maury and 

 Pickering in the spectra of stars of their fifth type give a 

 line of wave-length 4688 of much greater intensity than any 

 of the known hydrogen lines in spectra of that type, it is 

 certain that Rydberg by his reasonings has found the most 

 important of all the hydrogen lines in these star-spectra. The 

 most significant point about this discovery in the present 

 connexion is that Rydberg finds the length 4687*88 when he 

 uses the value *5 for ja, whereas if he uses '500737 the 

 length is altered to 461)8*43. Thus, then, we may take it 

 as proved cumulatively that \5 is the value of the fraction 

 under discussion, and that for some unknown reason much 

 larger variations in value occur with the values of r + l/s 

 than with the purely integral form r, as, for instance, in our 

 series 4*518, 5*525, and so on. 



Returning now to the other nodal series in our table, we 

 have under the form ?' + l/3 the incomplete series of numbers 



4-331 4*679 5*636 8*366 



where the departures range from — *031 to +*033, to be 

 compared with the *025 in 5*525 : under the form r+ 1/4 



3-76 ... 4*249 6*247 6*748 7*273 ... 8*273 



in which the greatest departure from the strict nodal position 

 is by *023. Under the form r+1/6 we have the values 

 3*830, 6*841, and 9*842 with a maximum departure of *009 y 

 and under r±l/S the values 3*872, 4*129, and 6*880, with a 

 maximum departure of *005. 



The strongest lines in the ordinary hydrogen spectrum are 

 F and G' for which m=4 and 5, and it is in the neighbour- 

 hood of 4 and 5 that we have the values 4 + 3/7, 5 — 2/5, 

 5_2/7, 5 + 5/11, 5 + 6/13, 6 — 2/5 corresponding to the more 

 general form r + q[s. 



In the next section we get further evidence for the ex- 

 istence of harmonics in connexion with atomic vibrations. 



