248 PHYSICAL SCIENCE 



then, should emit radiations of all frequencies of 

 vibration, that is, should give a continuous 

 spectrum. 



Hence we see that the existence of line 

 spectra, not from hydrogen merely but from 

 many other elements, again leads us to contem- 

 plate the difficulties of Newtonian dynamics 

 applied to electro-magnetic atoms, and once more 

 brings us to some form of quantum theory. 



The application of these conceptions to the 

 problems of atomic structure was first made by 

 Niels Bohr of Copenhagen, then working in 

 Rutherford's laboratory at Manchester. 



Certain regularities in the complex spectrum 

 of hydrogen become apparent if we consider not 

 the wave-lengths of its luminous lines but the 

 number of waves in a centimetre — a quantity 

 which may be called the vibration number. It 

 is found that the vibration numbers of all the 

 lines may be expressed as the difference between 

 two terms. There is first a fundamental term, 

 called Rydberg's constant, after its discoverer ; 

 its number is about 109700 waves per centimetre. 

 Other terms are obtained from it by dividing it 

 by four (2 x 2), nine (3 x 3), sixteen (4 x 4), and 

 so on. If we subtract these terms from R, 

 Rydberg's constant, we get vibration numbers, 



R 5 "DO 



R — — = ^R, R =-R, etc., and these numbers 



4 4 9 9.. 



correspond to hydrogen lines in the ultra-violet. 



If we begin with the first derived term, that is 



one-fourth of 109700 or 27425, and subtract the 



higher derived terms from it, we get another 



. , R R (9-4)R 5p . 

 series ot numbers, — = ^— — ^ — = ^K, etc., 



4 9 36 36 



