305 



we get on neglecting terms of higher order than the second in g, — 1 



= ^ 



[ 



1 -\ ^ — 9 



(16) 



Thus owing to the interaction among the particles of the powder 

 the force on a ball made of the powder can no longer be considered 

 as the snm of the foi'ces on the individual particles independently. 

 The increase of the force to within terms in {e^ — 1)* is given by 



(«0—1)* 



the factor 1 -| q'. For the maximum possible value of q for 



o 



the model considered q' = 0.065 and the correction factor becomes 



1 + ^^^^ -. If the quantity — — of Suppl. N". Ua is 0.09 for 



46 3 H 



gadolinium sulphate at 2° K. then since d was taken as |- of the 



actual density the quantity e^ — 1 becomes 0.36 and the correction 



factor is 1.0028. Thus the etfect discussed must be taken into account 



if the measurements of the force are made to within O.379. If such 



a correction is made it should be also borne in mind that even the 



simple formula (1") involves terms of the second order in the apparent 



\^s — 1) if it is solved for a, as may be seen in the following way. 



For small values of e^ — 1 we have q{s^ — 1) z= xF where jP is 



the force and x is a constant of the apparatus. For larger values 



of E — 1 this is not true but it is convenient to call the quantity 



Sa — 1 defined by the above equation: "the apparent f — 1". If the 



sample is spherical and if the powder may be considered as tlie 



cubical lattice just discussed 



s.-l 



1 



f, + 2^ jB.-iy 



"it fa 1 



3 ^3 



Hence 



ëa — 1 



3 ^3^ ' 



1+ 



fa-l 



r I' ^^'-'^^ 



(««-!) (17) 



q' ,1 



Thus — occurs here together with the larger term — . 

 3 q 



If the demagnetizing field is negligible as in the case of a thin 

 long tube s — l = itF=q{sa — 1) where s is the effective suscepti- 

 bility. Hence by (14") 



fa — 1 



^-1= ——, .... (17') 



i-|(««-i)-f|(««-ir 



