148 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



u than u 2 , then not only do the former definitions give different results, but also we 

 are not justified in attempting to form any equation of motion at all or draw any 

 conclusion about the inertia. 



The method of investigation by means of the Poynting vector of energy flux 

 (ABRAHAM, 'Ann. d. Physik,' 10, 1903), although possessing some elegant features, 

 is open to many objections. In addition to those raised by SOMMERFELD (loc. cit., 

 p. 368) we must add that of MACDONALD already mentioned. Further, the satis- 

 faction of surface conditions become very difficult. The method is very suitable for 

 determining the field due to rigidly electrified systems moving in a prescribed way, 

 but does not reveal the manner in which the prescribed motion is established. The 

 systems to be considered are not rigidly electrified, and our problem is the deter- 

 mination of the motion, and the way in which it is produced, subject to the necessary 

 surface conditions. 



To give a definite instance, it will be shown that a uniformly accelerated motion of 

 a charged sphere is established by aid of a rapidly damped harmonic train of waves. 

 Knowing this to be the case, we might use the method to verify the result, but the 

 method itself does not suggest the occurrence of this damped harmonic train. Thus 

 as a means of discovery it lacks an essential element. 



Although these considerations had not been definitely formulated when I attacked 

 the problem of accelerated motion, I had a very distinct impression that the 

 Newtonian method of investigation would prove the most effective. The measure of 

 success of the following investigations confirms a growing belief that Newtonian 

 methods give a more direct correspondence with physical phenomena than any other 

 process that has been devised. 



2. Fundamental Equation*. It is now generally accepted that the electromagnetic 

 equations of the free stagnant tether are unaffected by the motion of electrified bodies. 

 Thus while such motion gives rise to electric and magnetic actions they must conform 

 to the equations for the stagnant sether. 



Hence, if X, Y, Z are the components of electric force, a, ft, y are the components 

 of magnetic force, and C the velocity of radiation, the equations referred to a right- 

 handed system of fixed axes are 



*\ *"\ n ^ -N ^ O ^ \ T / ^"V" "Mi 7" ft \ r 7 



cy op COL cy vp ca. \ 1 AoA oY oZ 



~ ~ ~ 



h Sy' 2x oz' dy 2xJ C\dt ' ot ' ?/' 

 dx oy oz 

 ox oy 82 



