﻿194 Dr. J. W. Nicholson on the 



first place, that this conclusion requires modification when 

 the path extends to infinity. The hyperbolic orbits of 

 Epstein, which have been used extensively in the inter- 

 pretation of certain groups of 7 rays associated with many 

 of the chemical atoms, constitute an instance, and we shall 

 show that they rest on a mathematical error, and that in fact 

 it is not possible to preserve finite phase-integrals in the 

 process of quantizing the momenta. In fact, it appears that 

 the whole process is only applicable to finite paths, and gives 

 no clue to the phenomena taking place during the binding 

 of an electron which comes from a considerable distance. 



In another form, the question we propose is as to whether 

 a hyperbolic path is possible in the same way as an elliptic 

 one. Such would, of course, be characterized by a positive 

 energy W. Certain available evidence of a simple kind, 

 apparently not hitherto noticed, is in existence. For the 

 existence of such paths involves the existence of parabolic 

 paths, with W = 0. In passage from a stationary state of 

 energy Wi (negative) to a parabolic path taking the electron 

 outside the atom altogether, a quantity of energy Wi should 

 be involved. Spectral lines given by 



hv = W 



Hi 



where W n corresponds to any one of the stationary states, 

 should thus exist. In other words, the ' limits ' of spectral 

 series should themselves be spectral lines. But there are 

 two reasons why evidence on these lines cannot be decisive, 

 especially when it is negative evidence. For in the first 

 place, the values of W n determining the limits of series are 

 of such magnitude that only for two or three, in any case, 

 can the corresponding lines come into the visible spectrum, 

 and with only hydrogen atoms and charged helium atoms 

 to test, and enormous band spectra for both elements, the 

 test cannot readily be applied. Moreover, the probability of 

 an electron entering the atom in a parabolic rather than a 

 hyperbolic path is so small that any resulting lines could 

 hardly be expected to be of visible intensity under ordinary 

 conditions. We consider, therefore, that the question 

 whether limits of series are themselves spectral lines, on 

 the principles of the quantum theory, cannot, at least at this 

 juncture, be examined in the light of experiment, and 

 that it must remain a matter of deduction from other 

 phenomena. 



We find it necessary, as stated, to disagree with the 

 hypothesis, explicitly indicated several times by Sommerfeld 

 and others, and implicitly assumed at least by the remaining 



