300 



Varia b Ie suscep tib ility . 



To within I lie approximations made so far the case of variable 

 susceptibility ofTers no difficulty. Thus in the case (<•/) it was assumed 

 that tlie field acting on each particle of the powder is uniform. 

 Whether the susceptibility of this particle depends on the field or 

 not its polarization is uniform and is such that the electric intensity 

 E inside the particle is 



3 



E: 



^ {E) + 2 



where F is the iritensity of the field acting on the particle and 



sJ^E) is the value of the dielectric constant of the material of the 



— — 4^ 



particle corresponding to E. If the mean field is E, F = E -\- — F 



o 



( TP\ "1 



and P=q ^— E. Hence E and ?„ are the result of solving the 



simultaneous equations 



3 A 3 — 



f,+ l]E = -E 



P J ^ { 



^ = ^0 {E) ' 



The solution may be obtained graphically or otherwise. 

 In the calculations that follow the correction for variable suscep- 

 tibility is more complex and will not be considered. 



The distribution of potential in a rectangular space lattice of 



dielectric spheres. 



In order to investigate the errors involved in the approximations 

 we shall look for an exact solution in the case of a space lattice 

 of dielectric spheres. The following notation will be employed; 



li = distance between centres of adjacent spheres. 



g, =i: dielectric constant of the material of the spheres. 



(r, 'V, (/)) = polar coordinates of a point referred to centre of sphere 

 placed at the origin. The polar axis is chosen along one of the 

 rectangular axes of the lattice. 



(y\, 1^1, (fJ■^) = polar coordinates of a point referred to centre of 

 sphere whose Cartesian coordinates are: 



{oCi,yi,Zi) and whose polar coordinates are: 



The radius of each sphere is taken to be 1. The mean field is 

 also supposed to be 1 and directed along the polar axis. 



