Theory of Matter and on Radiation. 191 



a previous communication*; it is there shown that, if the 

 electron be supposed to expand, and n such electrons be moving 

 in a circle at equal distances apart, any one of them is subject 

 to two force? along the tangent to its orbit : (1) the reaction 

 which the aether exerts on it in consequence of radiation ; 

 (2) a pull which the rest of the riug exerts on it as a result 

 of the expansion. According as either force is in excess the 

 electron is retarded or accelerated until its velocity reaches 

 a perfectly definite equilibrium value; this value depends 

 mainlj' on n ; changes in the field of force in which the ring 

 moves, in its radius, in the mass of the electron, in its rate 

 of expansion, produce no appreciable effect, uuless they 

 involve a change in the order of magnitude of the quantity 

 which is changed. 



V>e shall assume that the structure of the system is rendered 

 definite by this cause. 



§ 3. The following notation will be used : — 

 Charge of the electron = e electrostatic units, 



Mass = m, velocity=i>, velocity of light = C, p=/3, radius 

 of curvature of the orbit = p. 



Occasionally we shall use a moving system of axes of 

 (%7) £) the origin being at the electron, Of along the tangent 

 to the orbit, Orj towards the centre of curvature, Of along the 

 binormal. The components of the mechanical force on the 

 electron in these directions will be denoted by T, P, S. 



The energy radiated per second will be denoted by R, for 

 a single electron or for a group of electrons. 



The following numerical values will be useful : — 

 e = 3-4: x 10- 10 (J. J. Thomson). 



— — = l'88xi0 7 for a slowly moving negative electron 

 %jm (Kaufmann). 



|O = 10 -8 cm., or thereabouts. 

 Kinetic energy of a particle of radium = 5*9 x lO - ^ erg 



(Rutherford). 

 Kinetic energy of ft particle of radium — 7 x 10 -8 erg 



(Rutherford), 

 both of course average estimates. 



Limits of the spectrum between which series lines have 

 been observed: X = 10~ 5 cm. and X = S x 10 -5 cm. 



With a time of revolution equal to the period of these 

 extreme rays in a circle of atomic radius, a body has velocities 

 given by /3 = '0063 and fi = '000-8 respectively. 

 * Phil. Mag-. [6] vol. xii. p. 21. 



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