684 Sir J. J. Thomson on 



We regard magnetic force as clue to the motion of the 

 lines of electric force past the observer who is .measuring 

 the magnetic force. The relation between the electric and 

 magnetic force when all the lines of electric force at P are 

 moving with the same velocity is given by the equations 



ot = 4:7r(gw — hv) ; /3 = 4c7i'(hu — fw) ; ^ — ^{fv—gu) ; 



when u, v, w are the components of the velocity of the lines 

 of electric force relative to axes fixed with reference to the 

 observer of the magnetic force. 



From this equation combined with the expressions for 

 the energy per unit volume, we see that P, Q, R, the com- 

 ponents of the momentum per unit volume at' P are given 

 by the equations 



P=--jL(Zj8-YTr)- Q=i(X 7 ^Z«) ; R=l(Y«-X/3); 



where X, Y 3 Z are the components of the electric force. 



We can also, by the principle of varying action, deduce 

 from the expression for the value of the energy the 

 Maxwellian expressions for the stresses in the electric and 

 magnetic fields which reproduce the mechanical forces 

 existing in those fields. 



From the expression for the energy in the electric field, 

 we see that the mass particles are concentrated in the places 

 where the electric field is strongest. Thus when the electric 

 charges are electrons or positively charged units of exceed- 

 ingly small dimensions — when, in consequence, the electric 

 force is exceedingly strong close to the charge — by far the 

 greater part of the mass will be quite close to the charge. 

 Thus, for example, if the radius of an electron is 10" 13 cm., 

 only one thousandth part of its mass will be at a distance 

 from the electron greater than 10 " 10 cm. Thus, though the 

 mass particles are present wherever there is an electric field 

 an enormous majority of them cluster close round the 

 electrons and positive charges. 



The mass particles perform the functions both of aether 

 and matter. They perform the function of matter by en- 

 dowing the electrons and positive charges found in the atoms 

 of the chemical elements with mass, and when they are 

 moving through space and carrying energy with them with 

 the velocity of light they are performing functions usually 

 ascribed to the aether. 



By themselves the particles are not the whole, either of 

 matter or of aether, for lines of electric force are an integral 

 part both of aether and matter. We only get matter when we 



