﻿318 Dr. A. C. Crehore on the 



the frequency of revolution of each electron in its orbit, 

 then co = 2tts. 



Any disturbance of the uniform state of motion due to 

 outside causes will in general disturb the planes of the 

 orbits of the electrons as well as their eccentricities, and 

 thereby give rise to motions similar to those of gyroscopes 

 but more complex. It is suggested that the resulting rapid 

 nutations, both natural and forced, cause the high fre- 

 quencies of the X-rays, and that the slow p recessional 

 motions cause the light spectra. The difficulties of any 

 complete investigation compel me to resort to the analogy 

 of the gyroscope, the investigation of which is known. In 

 the case of a simple gyroscope with a rigid wheel, acted 

 upon by an external moment of force M, the frequency of 

 the resulting nutations is given by the expression 



2^rA' 



« 



where a> is the angular velocity of the wheel, and C its 

 moment of inertia about the principal axis, and A its 

 moment of inertia about an axis in the plane of th^ wheel. 

 If Ave now conceive of the mass of a single electron as 

 uniformly distributed like a ring throughout its entire orbit, 

 then the moment of inertia G about the principal axis is 

 double A, the moment about an axis in the plane of the 

 ring. Hence, 0/A — 2, and 



v = 2s (5) 



That is to say, the frequency of nutation of the electron in 

 the single electron atom is twice its frequency of revolution. 

 Moreover, this frequency is independent of the external dis- 

 turbing force, though the energy is not, and is dependent 

 only upon the constitution of the atom itself. This shows 

 that the order of magnitude of X-ray frequencies, if due to 

 this cause, is not different from the frequency of revolution 

 of the electron in its orbit. 



When the number of electrons in a ring is more than one, 

 the analogy to the rigid wheel can hardly be u^ed to give 

 even an approximation to the principal nutation frequencies. 

 We shall make the assumption that the frequency of the 

 nutations occurring in a ring of n electrons is proportional 

 to the number of electrons, n, in the ring and is equal to 



v = k 2 n (6) 



