Very — On a Possible Limit to Gravitation. 39 



is an exceedingly elongated ellipse, subject to these per- 

 turbations: (1) Decrease of amplitude; (2) diminution of 

 periodic time; (3) slow apsidal motion opposite to the 

 orbital revolution of the electron; (4) a slight fluttering 

 motion like nutation; (5) a further slight secular change 

 in the form of the ellipse. As to whether the spiral is 

 the primary motion and the elliptic relations a concomi- 

 tant resultant of perturbations, or vice versa, may not 

 be easy to determine from the mathematics. The suppo- 

 sition as thus stated by Stoney is somewhat vague, and 

 in spite of appearances of spiral relations in the wave- 

 lengths of a series of lines forming a group, or band in 

 the spectrum, it is not easy to see how such definite wave- 

 lengths can result from a perpetually and gradually 

 modified series of spiral circulations. Besides this, the 

 oxygen series relates to atoms in molecular combination, 

 and not to dissociated atoms which give quite a different 

 and much simpler spectrum. 



A more reasonable supposition is that of Bohr, of 

 which a slight modification is described by Millikan in 

 Science? where it is shown that certain orbits whose radii 

 are in the ratio of the squares of the ordinal numbers 

 are stable, but all intermediate orbits are unstable. 

 When, therefore, the position of an electron is disturbed, 

 it passes explosively to the next stable orbit and may 

 repeat the process several times in succession, each 

 transfer giving rise to an electromagnetic vibration in 

 the period of the new orbit. The number of transfers 

 depends upon the thermal energy available. Under the 

 moderate thermal conditions of our laboratories, often 

 only five members of the Balmer hydrogen series are pro- 

 duced and at most twelve ; but in the hottest stars over 

 thirty appear. 



In any case, the fact of internal orbital revolution of 

 certain electrons in an atom, presumably the satellite or 

 characteristic electrons, is demonstrated by the Zeeman 

 effect, and by the wonderful agreement in the quantita- 

 tive values which Millikan has deduced from Moseley's 

 measurements {op. cit.). The radiation equation VU 

 (mv 2 )=hv, where m is the mass of an electron, v its 

 orbital velocity, h = Planck's radiation energy factor, 

 and v = the vibrational frequency, represents the energy 

 expended in reversing the electric sign, that is, in over- 



3 Kadiation and Atomic Structure, — Science, N. S., vol. 45, p. 321, April 

 6, 1917. 



