250 PHYSICAL SCIENCE 



hydrogen electron has four possible stable orbits, 

 corresponding to successive units of action. Here 

 we leave Newtonian dynamics. A planet can 

 revolve round the sun in any one of an infinite 

 number of orbits, the actual path being adjusted 

 to its velocity. But an electron can only move in 

 one of a few paths, each of which corresponds to 

 an integral number of units of action. If it leaves 

 one such path, it must jump instantaneously to 

 another, apparently without passing over the 

 intervening space. Perhaps there is no inter- 

 vening space : perhaps space, perhaps even time, 

 is discontinuous. But that is another story. 



When the electron leaps from one stable path 

 to another it radiates energy hv^ the action of 

 which is h, and the frequency of vibration v. The 

 energies lost in the changes described above are 



- e, - e, — ^ 6, etc. Hence, smce k is constant, the 

 4 ' 9 ' i6 



frequencies v^, v^^ v^, etc., must be in the ratios 



-, -, ^, etc., and we get the known series of lines 

 4' 9' 1 6 ' ^ 



in the hydrogen spectrum. It is possible, further- 

 more, to calculate the numerical value of the 

 fundamental term corresponding to Rydberg's 

 constant, and to reach the amazing result that it 

 agrees with the figure on page 248, as obtained by 

 observation. Even more complex phenomena 

 of the hydrogen spectrum are fully explained by 

 Bohr's theory as developed by Sommerfeld, and 

 it is impossible to doubt that we are on the right 

 road. Hydrogen atoms must be something like 

 Bohr's picture of them. Heavier atoms with 

 more planetary electrons give problems beyond 

 the present power of mathematical analysis. But 



