Spectra of the Elements, and Structure of the Atom. 547 



since the outer is practically under the influence of a nucleus 

 N— n or in. Thus 



and a and h must be comparable in all cases, in contradiction 

 to the fundamental assumption. 



The above relates, of course, to rings moving with the 

 same angular velocity, for which case a somewhat cursory 

 treatment is possible. When they have different angular 

 velocities, the electrons of the two rings are not in the same 

 configuration relatively to each other at two successive 

 instants, and their orbits cannot in such circumstances 

 remain circular. Before proceeding further with such a case, 

 therefore, we must make a definite choice between the older 

 electrodynamics and a non-mechanistic theory such as that 

 of Bohr, at variance with ordinary electrodynamics, and the 

 method of argument adopted must depend on this choice. 



Let us choose, in the first. place, the ordinary electro- 

 dynamics. We are then compelled to suppose that an electron 

 in accelerated motion must radiate energy, and an atom 

 containing a system of circulating electrons would rapidly 

 lose its internal energy unless the radiations from all the 

 electrons could be arranged so as to interfere. Schott has 

 proved conclusively that this condition requires all the 

 electrons to be arranged at every specified instant on circles 

 with a common axis, though their orbits are not necessarily 

 circular, the circles on which they are arranged being- 

 capable of varying from one instant to another. A set of 

 orbits satisfying this condition, which at the same time are 

 not circular orbits, is mentioned later in this paper, and 

 other sets exist, illustrated, for example, by the remarkable 

 epitrochoidal orbits discussed by Schott*, which could, so 

 far as the necessary interference of radiation is concerned, 

 almost be described as the steady motion in an atom, under 

 the influence of a nucleus, though the interference is in this 

 case probably too imperfect. 



" Steady motion " is a term normally applied to dynamical 

 systems, all of whose component parts move with constant 

 velocities. But such a term can be applied to the motions in 

 an atom, if they are really periodic, and if they involve no 

 radiation of energy, — if in fact, on the older electrodynamics, 

 Larmor's condition, that the vector sum of the accelerations of 

 all the electrons is permanently zero, is fulfilled. As we have 

 seen, the non-mechanistic theory of Bohr uses ordinary dy- 

 namics to obtain the condition of steady motion or dynamical 

 * ' Electromagnetic Radiation,' Camb. Univ. Press, 1911. 



