295 



If E^ should denote the average value of ^^ throughout the sphere 

 we have with a good approximation E^=:. E because the usual 

 treatment of polarized media may be applied to E and the result 

 is E^ if the powder is fine. 



Let a certain volume be occupied by the powder and put in an 

 external field 'i". Then E^ ^ ^ on account of the charges of polari- 

 zation on the outer surface of the volume. It is for this fact that 

 the correction has been made by Prof. H. Kamerlingh Onnes. We 

 shall suppose in what follows that this or an equivalent correction 

 is made in the final interpretation of the experiment. In order to 

 make such a correction however one must first obtain the effective 

 dielectric constant and then operate with this constant just as one 

 would in the case of a homogeneous medium. Thus e.g. it may be 

 shown ') that the force on a sphere of radius a placed in a field 

 of force given by E^ -\- Bz parallel to the OZ a,x\s of a rectangular 

 system of coordinates having its origin at the centre of the sphere 



and along the radius q perpendicular to the axis of z is 



F=a* n^Eg where E^, B are constants and s is the dielectric 



constant. Hence 



1 — ^/a» BE, 



Preliminary approximate solutions. 



(a) A space lattice of spheres. 



Consider a space lattice of spheres the density of packing being 

 not too great. We can get very easil}' an approximate solution for 

 this case. Let us suppose that each sphere has its boundary removed 

 80 far from the surface of the adjacent spheres that the field acting 



1 



1) Using equation (6) (to be derived presently) we find that the density of the 

 fictitious distribution of charge is (using polar coordinates with OZ as axis) 



1 1 



Hence the force 

 F =zj-l [E, + Ba P, {cos 6)] 



cos 6^ — 1 



3(6—1) 5(€— 1) „ „ , 



-^'-^E.PAcos6) + ^-^BaPAcos6) 



3(6-1) 



5(6—1 



+ -^—^ Ba P, {cos 6) 

 ^ 2g + 3 '^ 



6—1 



d {cos 6) = a' E, B. 



19* 



