297 



to tlie density of packing but should be corrected by the factor 

 1 



1 +P ^3 



It is worth noting that (1) may be written as 



9 — -^ (1 ) 



64-2 ^f. + 2 



which means that if the powder is moulded in a sphere then the 



force on that sphere is a q^^ part of the force which would be 



exerted on a solid sphere of the same radius. In other words each 



individual particle of the powder may be considered as acted on 



only by the external force. (I have seen a very direct and simple 



proof of this fact from Prof. Ehrenfest). 



We see therefore that to within the approximations made so far 



I 



the factor ■ used by Prof. H. Kamerlingh Onnes should be 



4::töd '^ 



1 H 



3 H 



used with the value of the density in the solid — not the powdered 



form. 



(b) A space lattice of spherical holes'^). 



The case considered above may be expected to give a good ap- 

 proximation if the powder is packed loosely. If it is packed closely 

 a better approximation must be expected from a space lattice of holes. 



It is not necessary to treat this case independently because use 

 can be made of formula (1) if it is remembered that in (1) e is the 

 ratio of the effective dielectric constant to the dielectric constant of 

 the space between the spheres of the lattice. Denoting by q as before 

 the proportion of the volume occupied by the substance (i.e. the 

 ratio to the total volume of total volume minus the volume of the 

 holes) and leaving (l^i) unchanged we arrive at 



8-1 1 



^(«0— ^) ^ , P(^ 



(2) 



3 + 2d 

 which may be also shown to be equivalent to 



(2') 



1 + 26, ^ 



1) The possibilities of this case have been pointed out to me by Prof. H. 

 Kamerlingh Onnes and Dr. H. R. Woltjer. 



