258 Prof. a. A. Schott on Bohr's Hypothesis 



as regards converge rice, so that we conclude that the error 

 committed in using (24) as a first approximation is relatively 

 only of the order ajp. 



18. Returning to the consideration of our main problem 

 we must insist particularly on the fact that the contradiction 

 we have found subsists between hypothesis A in the form 

 adopted by Bohr on the one hand, and the four electro- 

 dynamic equations of Maxwell and Hertz for space at a 

 distance from all electric charges, together with the 

 Poynting energy flux, that is to say, not merely with the 

 fundamental equations of the modern electron theory, but 

 with those of the classical electromagnetic theory for the 

 free aether, formulated by Maxwell and established by 

 the experiments of Hertz and all the experience of wire- 

 less telegraphy. Doubtless no one will be willing to 

 renounce so useful a theory as this is until much stronger 

 reasons are forthcoming ; hence there only remains the 

 choice between the Poynting energy flux, together with 

 the classical expressions for the electric and magnetic 

 energies and the electromagnetic momentum which it im- 

 plies, and Hypothesis A in its present form. Although the 

 position as regards the Poynting flux is not so clear as that 

 respecting the theory of Maxwell, yet, as we have seen 

 above, there are very strong reasons for retaining the 

 Poynting flux, so that it becomes necessary to consider 

 the possibility of modifying Bohr's hypothesis A. After 

 mature consideration the following wording has suggested 

 itself to me as one which is sufficient for our purpose and at 

 the same time satisfies the requirements of Bohr's theory in 

 all essential respects : — 



A. An atomic system possesses a number of states in which 

 its electromagnetic energy continues unchanged, even if the 

 particles are in motion and an emission of energy radiation 

 is to be expected on ordinary electrodynamics. The states 

 are denoted as the states of stationary motion of the system 

 under consideration. 



19. It will be seen that here the stress is laid on the con- 

 stancy of the electromagnetic energy in spite of radiation, 

 instead of on the total absence of emission of energy radia- 

 tion. The emission of energy radiation in consequence of 

 acceleration is supposed to take place continuously, not in 

 quanta, and this may be objected to as contradicting the 

 quantum hypothesis assumed by Bohr for the series spectrum 

 emission in his hypothesis B. In reply, it may be urged that 

 the original form of the quantum theory, in which all energy 

 was assumed to occur only in quanta, has been abandoned 



