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LXXXIII. The Quantum-Theory of Radiation and Line 

 Spectra, By William Wilson, Ph.D., University of 

 London, .King's College *. 



IN his able report on Radiation and the Quantum-Theory 

 Prof. Jeans f, dealing with theories of line spectra, 

 remarks that Bohr's assumption is "not inconsistent with 

 the quantum-theory and is closely related to it/' The 

 possibility therefore of deducing the results of Planck and 

 Bohr from a single form of quantum-theory naturally suggests 

 itself. Such a theory is developed in the present paper, and 

 it will be seen that it contains that of Planck (in one of its 

 forms) as a special case and, while formally distinct from 

 Bohr's theory, leads to the same results when applied to the 

 Rutherford type of atom in which an electron travels in a 

 circular orbit round a positively charged nucleus. 

 This theory is based on the following hypotheses : — 



(1) Interchanges of energy between dynamical systems 

 and the aether, or between one dynamical system and another, 

 are "catastrophic'"' or discontinuous in character. That is 

 to say, each system behaves as a conservative one during 

 certain intervals, and between these intervals are relatively 

 very short ones during which definite amounts of energy 

 may be emitted or absorbed. 



(2) The motion of a system in the intervals between such 

 discontinuous energy exchanges is determined by Hamil- 

 tonian dynamics as applied to conservative systems. It will 

 be convenient to speak of a system, during such an interval, 

 as being in one of its steady states. 



(3) Let q lz q 2 , . pi, p 2 , ... be the Hamiltonian positional 

 and impulse coordinates of a system in one of its steady 

 states, and let L be its kinetic energy, expressed as a function 

 °£ Vi? <]2, ••• and q u q 2 ,.... This function is homogeneous 

 and of the second degree in q u q 2 ,.... If L contains 

 products q r q s (r=fcs), we shall suppose them to have been 

 removed by a substitution of the form : 



2V=« lr qi -j- a 2 r <72 f + • • • + «nf 2»'j 

 and we have therefore 



L=iA 1 g 1 2 +iA a g 2 2 + ... + iA n q n \ 



* Communicated by Prof. J. W. Nicholson. 



t J. H. Jeans, Phys. Soc. Report on Radiation and the Quantum- 

 Theory, p. 51 (1914). " 



