224 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1913. 



and Searle and later and fundamentally by J. J. Thomson (1881), 

 a theory which has passed through many successive developments.^ 



(1) An electron moving Avith a uniform velocity, or at least a 

 velocity only slowly variable (quasi-stationary), carries invariably 

 tied to it an electromagnetic field the form of which can be com- 

 pletely deduced from the Maxwell-Lorentz equations. This moving 

 field has been called the " velocity wave." 



(2) If the electron suffers an acceleration, a wave is immediately 

 propagated from it having all the characteristics of a luminous wave 

 (transverse vibrations, rectangular electric and magnetic fields). 

 This disturbance has been called an " acceleration wave." At great 

 distances from the electron the latter wave alone exists because its 

 amplitude varies inversely as the distance from the electron and not 

 as the inverse square as does that of the othfir wave. This shows us 

 the probable origin of luminous radiations and the root of the expla- 

 nation of the Zeeman effect. Here also we find the explanation of 

 X-rays which are electromagnetic pulses ^ due to the abrupt stoppage 

 of cathode corpuscles at the anticathode and the resulting negative 

 acceleration. 



(3) In order to give an electron a quasi-stationary movement 

 there must be communicated to it energy which is stored up in its 

 field as electric and magnetic energy. The necessarj'' calculations 

 for this field are relatively simple where the ratio (^) of the veloc- 

 ity (v) of the particle to the velocity of light, V) is small. They 

 become more complicated where ^ approaches unity and were first 

 made completely by Max Abraham ^ in 1903 upon the hypothesis of 

 a rigid, spherical electron carrying a charge uniformly distributed 

 throughout its volume. Then the magnetic energy of the field can 



mv^ 

 always be expressed in the form of kinetic energy, ^k"* ^^ ^^ 



quite natural to speak of the coefficient m as the electromagnetic 

 mass of the electron. This mass may be superposed upon the ordi- 

 nary mass, at least it does not wholly take its place. This leads to 

 an electromagnetic interpretation of mechanics. In this new me- 

 chanics, the mass m does not maintain a constant value mo except 

 at very small velocities. For a velocity comparable with that of 

 light (P near 1) the mass becomes a function of ^ and increases 

 indefinitely as ^ approaches unity. Further it is necessary to dis- 

 tinguish between a longitudinal and a transverse mass according 



1 See the referonccp cited further on. 



- We have not sufficient space to describe the curious theory of Bragg according to 

 which the X-rays and the r rays of radium are uncharged particles of matter. More- 

 over this theory appears to be contradicted by the recent beautiful experiments of Lane 

 and his pupils upon the diffraction of X-rays by crystals. (Bragg, Phil. Mag., Oct., 

 1907 ; Chem. News, vol. 97, p. 1G2, 1908 ; Radium, p. 213, 1908. See also article? by 

 Brunet in this Revue for Feb. 15, 1913.) 



' See Ions, electrons and corpuscles, vol. 1. 



