L. Page — Relativity and the Ether. ITT 



Two types of field are of especial interest on account of 



their simplicity. If the charged particle has been moving 



with constant velocity for an infinite time, (T) gives the 

 iamiliar expression 



E=^^^ (0) 



47r>- 3 (l-/3 2 sin 2 a)2 



where E is the ether strain at P at the same instant as that at 

 which the charge is at 0. r being the vector OP and a being 

 the angle between r and V. The tubes of strain are straight 

 lines diverging from the charged particle. 



The second case of interest is the field of a charged particle 

 which for an infinite time Has had a constant acceleration (j> 

 relative to its own system and which has zero velocity relative 

 to the observer in K at the instant considered. This is the 

 type of motion a charged particle would assume in a uniform 

 field. For this case (T) reduces to 



4*r° /, <j>-r 4?> 



1+ V ' 4o< 



.2 \ 3 

 2 



4-/ >3 





(10) 



where E is the ether strain at P at the same instant as that at 

 which the charge is at rest at 0, and r is the vector OP. The 

 tubes of strain are circles having their centers in a plane per- 

 pendicular to <j> at a distance from the charged particle equal 



c 2 ... 



to — -, a 4>. To an observer in motion relative to the charge 



the ether strain can be obtained from (1-0) by means of the 

 transformation equations (16) subsequently derived. This 

 field, * on account of its importance, will be discussed more 

 in detail later. 



(b) Equations of the Ether Strain. 



First we shall derive the equations of the ether strain due 

 to a single charged particle. Then, since the total ether strain 

 is the vector sum of the strains due to all the particles whose 

 fields extend to the point in question, the general equations 

 will follow at once. 



* Compare G-. A. Schott, Electromagnetic Radiation, p. 63 et seq. 



