410 Dr. H. Bateman on some 



velocity of light if L touches the sphere because then L' also 

 touches the sphere. 



It should be noticed that there are relations of the form 



qx o® c ot c Qt 



for two points on the line L' can be derived from the 

 functions X and Y, just as two points on L were derived 

 from V and T. 



§ 4. The Electromagnetic Potentials. — The fundamental 

 equations 



r ° tH= K^ + /9V )' divE = ^' 



rotE = - 1 !? divH = 0, 



c ot 



are usually solved by writing 



H = rotA, E=--|p-gradtf> J . . . (7) 

 where the vector A and the scalar <E> satisfy the equation 



divA+l|f=0 (8) 



c ot 



In the present case we can obtain the expressions (5) 

 for E and H by assuming 



ilx_ *ox P o^ c ot c dt' 



where a and /3 are functions of V and T such that 



oj3_o*_' 

 oY 3T 



A second relation must also be satisfied in order that (8) 

 may hold. 



§ 5. Equations of motion of an electrified particle in an 

 electromagnetic field when there is permanent incidence between 

 the particle and a line of electric force. — Let us now suppose 

 that the volume distribution of electricity is negligibly small 

 in some regions of space, so that the present type of electro- 

 magnetic field may resemble an electromagnetic field in the 

 aether for these regions. Let a particle of electricity be 

 introduced into one of these regions : the problem is to find 

 out how it will move. 



