690 BELL SYSTEM TECHNICAL JOURNAL 



transition between two States, Ez and R^ for instance, is thus resolved 

 into a set of lines lying close together. These individual " Stark-efifect 

 components" testify to the individual existence of the several distinct 

 modes of vibration which, when there is no impressed electric field, 

 should share a common energy-value £„ and be indistinguishable 

 from one another. '^^ 



In the closing section w^e shall consider another aspect of these 

 Stark-effect components. At this point I wish only to allude to a 

 quaint little paradox which may already have disconcerted the reader. 

 I have just said that the imaginary "fluid" executes stationary 

 vibrations in which it is divided into compartments by nodal planes 

 and nodal paraboloids, even when the impressed field F is made equal 

 to zero; but earlier I said that the "fluid" representing the unper- 

 turbed hydrogen atom executes vibrations in which it is divided into 

 compartments by nodal planes, nodal double-cones and nodal spheres. 

 There is no actual contradiction between these two assertions; for a 

 mode of vibration of the one kind can be obtained by superposing two 

 or more modes of vibration of the other kind, with a proper distribu- 

 tion of relative amplitudes. Take the specific case of the "first 

 excited state" of the hydrogen atom, n = 2. By the earlier process, 

 we find three wave-patterns: (a) with one nodal sphere, (b) with one 

 nodal double-cone, (c) with one nodal plane. By the later process, we 

 find three wave-patterns; (a) with one nodal paraboloid facing one 

 way; (/S) with one nodal paraboloid facing the other way; (7) with 

 one nodal plane. The wave-patterns (c) and (7) are evidently the 

 same, while either (a) or (/3) can be reproduced by superposing (a), 

 (b) and (c) with the proper relative amplitudes.^^ If the field 7^ acting 

 upon a hydrogen atom in the first excited state were to be gradually 

 reduced to zero, it would leave the atom, or to speak more carefully 

 the "imaginary fluid," vibrating in a manner which would be one of 

 the modes (a), (/3) or (7), hence a cleverly adjusted superposition of 

 the three modes (a), (b) and (c). Suppose however that a very small 

 field F were to be applied to a hitherto unperturbed atom ; why should 

 it necessarily find ready for it a vibration with precisely the proper 

 relative adjustment of the modes (a), (b) and (c)? or if it did not, if 

 it should find the atom vibrating say in mode (a), how would it per- 

 suade the "fluid" to change over into the manner of vibration suitable 

 for its own operations to begin P-^ 



^" A couple of "contour maps" of the wave-patterns for two of these paraboloidal 

 modes of vibration are given by F. G. Slack (Ann. d. Pliys., 82, pp. 576-584; 1927). 



21 I have not actually proved this, but believe that it must follow from Schroe- 

 dinger's general theorem. 



^^ This same curious thing occurs in a somewhat different guise when the electron- 

 orbit theory is adopted. 



