Mass, Energy, and Radiation. 081 



of surface of one of the spheres, and N the number of lines of 

 force passing through unit area of the sphere. Since the 



•charge is given, \ N d$ is fixed, and when this is so, i*N 2 ^S 

 will be least when N is uniformly distributed over S, and 

 for other cases the excess over the minimum value will 

 increase with the amount by which the lines of force are 

 concentrated in definite directions. The greater the velocity 

 of the electron the greater is this concentration and there- 

 fore the greater the value of \X 2 <iS, i. e. the greater the 



value of the mass in the region close to the electron. Tims 

 the movino; electron has more mass in its immediate neioh- 

 bourhood than an electron at rest, and as each unit of mass 

 possesses, since the mass is moving with the velocity of light, 

 a definite amount of energy, the energy of the moving 

 •electron will be greater than that of an electron at re>t. 

 This increase in energy is what is usually called the Kinetic 

 Energy of the movino- electron. It is necessary to say a few 

 words about the definition and measurement of kinetic 

 energy. When, as in ordinary dynamics, the kinetic energy 

 of a body is defined by the expression |mrl it depends 

 essentially upon the axes with respect to which the velocity 

 is measured, the kinetic energy of the same body may be 

 increasing when measured with reference to one set of axes 

 and decreasing when measured with reference to another. 

 The changes, however, of the total kinetic energy in a self- 

 contained system, i. e. one which is not acted upon by any 

 external forces, will, if action and reaction are equal and 

 opposite, be independent of the axes used. What may be 

 called the localization of energy, i. e. the assignment of a 

 certain amount of energy to each member of a dynamical 

 system, is a problem which, as far as rigid dynamics goes, 

 has an unlimited number of solutions ; any one of these 

 solutions will give the same changes in the configuration of 

 the system as any other, so that the localization of energy 

 could not be deduced without ambiguity from observations 

 of the configuration of the system. 



On the method considered in this paper, the energy 

 associated with an electron, for example, could be determined 

 independently of any axes of reference if we had the power 

 of counting the individual mass particles in its vicinity. We 

 know, however, of no physical phenomenon which will 

 enable us to do this, all that with our present knowledge of 

 physics we are able to do is to compare the number of mass 

 ^particles in one region with that in another, and this will 



Phil. Mag. S. 6\ Vol. 39. No. 2U. June 1920. 2 Y 



