Jakuaby 12, 1906.] 



SCIENCE. 



53 



the distance r from the center of the sphere 

 whose charge is e, has the direction of r 

 and the magnitude e/r-. 



If the sphere is in motion it carries its 

 field along almost unaltered, provided the 

 velocity v of the sphere be small in com- 

 parison with the velocity of light. But it 

 excites a magnetic field, the magnetic force, 

 or intensity, being H =; E X v ; i. e., the 

 magnitude of the force at P is = ev sin 

 (E, v)/r-, its direction is at right angles to 

 E and v, and its sense is such that the 

 three vectors E, v, H form a right-handed 

 set. The lines of magnetic force are, there- 

 fore, coaxial circles about the direction of 

 motion. 



According to the electromagnetic theory, 

 the energy of the magnetic field is distrib- 

 uted throughout the field, with volume 

 density (1/8t);u,H^, where ix is the mag- 

 netic permeability of the medium. The 

 energy of the whole field is readily obtained 

 by integrating over the space outside the 

 sphere; it is found ^^^^^jxe^v-fa, where a is 

 the radius of the sphere. This magnetic 

 energy, being due to the motion of the 

 charge, is analogous to kinetic energy. 



If the charged sphere consists of an ordi- 

 nary mass m carrying the charge e so that 

 its ordinary kinetic energy is \mv-, the 

 total kinetic energy due to the motion of 

 m and e with the velocity v is 



T = l(^n + lii^^^v\ 



that is, the same as if the mass m of the 

 sphere were increased by the amount 

 %lt.e-/a. 



The result, then, is similar to that known 

 in hydrodynamics for a sphere of mass m 

 moving through a frictionless liquid. In 

 moving, the sphere sets the surrounding 

 liquid in motion; to move the sphere we 

 have to set in motion not only the mass 

 m, but also that of the liquid around it. 

 Thus the sphere moves in the liquid just 

 as a sphere of greater mass would move 



in vacuo. In the ease of a sphere the mass 

 is increased by one half of that of the 

 liquid displaced. But in the case of a 

 body whose mass is not distributed as sym- 

 metrically as in the case of the sphere the 

 mass to be added depends on the direction 

 of motion. 



As the apparent mass of the charged 

 sphere in motion, owing to the presence of 

 the charge e, exceeds the ordinary mass 

 m by l/xe^/a, the apparent momentum ex- 

 ceeds the ordinary momentum mv by 

 %ixe-v/a; and this additional momentum 

 must be regarded as residing not in the 

 sphere but in the surrounding field. This 

 momentum possessed by the field is what 

 Faraday and Maxwell used to call the elec- 

 trotonic state. 



In the ease of the free electron we have 

 m = ; hence the total mass, momentum, 

 kinetic energy, is magnetic and is distrib- 

 uted throughout the field. Moreover, if 

 the velocity of the electron be comparable 

 with the velocity of light, the apparent 

 mass will depend not only on the direction, 

 but also on the magnitude of this velocity. 



Any variation in the velocity of the 

 charged sphere, or of the electron, produces 

 a variation in the momentum of the field, 

 which is propagated as a pulse through the 

 field with the velocity of light. If such a 

 pulse strikes a charged body at rest, the 

 body acqiiires velocity and momentum, the 

 momentum acquired being equal to that 

 lost by the pulse. As the pulse resides in 

 the ether, the law of the equality of action 

 and reaction would make it necessary to 

 assume an action exerted on the ether it- 

 self. In the electron theory of Lorentz 

 which does not admit such actions on the 

 ether Newton's third law of motion is vio- 

 lated in as much as action and reaction 

 take place neither at the same place nor at 

 the same time. 



These very brief and incomplete indica- 

 tions will perhaps suffice to call to mind 



