OUTLINE OF SCHRODINGER'S THEORY 215 



sub-aethereal waves are limited to a particular discrete 

 series of frequencies. Remembering that a frequency 

 in the sub-aether means an energy in gross experience, 

 the atom will accordingly have a discrete series of pos- 

 sible energies. It is found that this series of energies 

 is precisely the same as that assigned by Bohr from his 

 rules of quantisation (p. 191). It is a considerable 

 advance to have determined Jiese energies by a wave- 

 theory instead of by an inexplicable mathematical rule. 

 Further, when applied to more complex atoms Schro- 

 dinger's theory succeeds on those points where the Bohr 

 model breaks down; it always gives the right number of 

 energies or "orbits" to provide one orbit jump for each 

 observed spectral line. 



It is, however, an advantage not to pass from wave- 

 frequency to classical energy at this stage, but to follow 

 the course of events in the sub-aether a little farther. 

 It would be difficult to think of the electron as having 

 two energies (i.e. being in two Bohr orbits) simultane- 

 ously; but there is nothing to prevent waves of two dif- 

 ferent frequencies being simultaneously present in the 

 sub-aether. Thus the wave-theory allows us easily to 

 picture a condition which the classical theory could only 

 describe in paradoxical terms. Suppose that two sets 

 of waves are present. If the difference of frequency is 

 not very great the two systems of waves will produce 

 "beats". If two broadcasting stations are transmitting 

 on wave-lengths near together we hear a musical note 

 or shriek resulting from the beats of the two carrier 

 waves; the individual oscillations are too rapid to affect 

 the ear, but they combine to give beats which are slow 

 enough to affect the ear. In the same way the individual 

 wave-systems in the sub-aether are composed of oscilla- 

 tions too rapid to affect our gross senses ; but their beats 



