MATTER, SPACE, AND TIME 249 



corresponding to the visible lines of hydrogen 

 known as Balmer's series. Another group, 

 obtained from one-ninth of 109700, was found in 

 the infra-red by Paschen. 



These relations were discovered by making 

 experiments, and then guessing at arithmetical 

 rules till one was found to fit the facts. They are 

 purely empirical. But Bohr saw how to explain 

 them all by applying Planck's quantum theory to 

 the atom. 



Bohr pointed out that, if ''action " is absorbed 

 only in units, of all conceivable orbits in which 

 the hydrogen electron might revolve, only a certain 

 limited number would be possible. In the smallest 

 orbit, the action would be one unit or h^ in the 

 next orbit 2/^, and so on. Mathematical investiga- 

 tion shows that the energy of motion in the second 

 orbit is a quarter that in the first, in the third 

 orbit one-ninth, and in the fourth one-sixteenth. 

 As an electron falls in from an outer to an 

 inner orbit, it loses energy of position and gains 

 energy of motion. It may be shown that the total 

 loss of energy is equal to the gain in energy of 

 motion. Hence, if e be the energy of motion in 

 the first or smallest orbit, it follows that, in passing 

 from the second orbit to the first, the loss of energy 



is - e, in passing from the third to the second, 



8 T T e 



- e, and from the third to the first, - — or -^ e. 



9 , ' 4 9 36 



It will be seen that this series of numbers Is the 

 same as that found experimentally in the vibration 

 numbers of the hydrogen spectrum. 



On this evidence Bohr founded his theory 

 of the hydrogen atom. He supposes that the 



