﻿328 Dr. A. C. Crehore on the 



angle 6 such that the potential energy of the one atom is 

 represented by 



and of the other by 



iau^ b {g), 



|<u' 2 + 



<M 2 



'■>(§)'■ 



where a and b are constants. Then if the gyroscopic con- 

 nexion between the atoms gives rise to a term ^ . ^ in 



qu ot QU 



the kinetic potential, the equations of motion are 



If, now, u and v are assumed to be simple periodic functions 

 given by the equations 



u = A sin (lit + m0), 

 r = ~B cos {nt-\-m6)j 



where m denotes an integer and n gives the frequency, the 

 solution of these equations gives 



(a + m 2 b)A = m 2 nB, 



(a + ?>i 2 6)B = m 2 n A ; 



whence eliminating A and B, we obtain Balmer's equation 

 for the frequency as in (21) above, 



. a 

 m~ 



The low-frequency vibrations and the long wave-lengths 

 due to the vibration of the positive electron in (20) and (21) 

 may be considered as heat rather than light. When the 

 energy of these vibrations becomes excessive the whole atom 

 may depart so far from the equilibrium position that it will 

 not return to it and the substance becomes volatilized by 

 excessive heating. 



Photo-Electric Phenomena. 



There are certain experimental facts connected with the 

 photo-electric effect which are not easily explained on any 

 atomic theory. It seems as if this theory contains elements 

 which will eventually lead to a more complete understanding 



