Physics. — ''Calculations of the effective permeability and dielectric 

 constant of a powder." Bj G. Breit, National Research 

 Fellow U.S.A. (Supplement N". 46 to the Communications 

 from the Physical Laboratory at Leiden. (Communicated by 

 Prof. H. Kamerlingh Onnes). 



(Communicated at the meeting of October 28, 1922). 



Introductory. 



The pure samples of some rare substances are available only in 

 powdered form and show particularly interesting magnetic properties. 

 For this reason it is desirable to know the relation between the 

 measured and the true permeability of a powdered substance. 



If the susceptibility is small the effects of the demagnetizing field 

 are negligible and the magnetization of any individual particle of 

 the powder is the same as it would be if the particle were part of 

 a solid block. Supposing that the particles are ciystalline, the measured 

 specific susceptibility is the mean specific susceptibility of a crystal 

 provided in taking the mean equal weights are given to all orien- 

 tations of the crystal. 



In the case of gadolinium sulphate at 2° K. tlie magnetization is 

 considerable and the above approximation does not suffice. This fact 

 has been realized by Piof. H. Kamerlingh Onnes and a correction 

 has been made by him ^). Prof. Kamerlingh Onnes expressed his desire 

 to the author to see a more accurate correction. This forms the 

 subject of the following pages. 



Approximations and statement of problem. 



In view of the random distribution of the principal directions of 

 the individual crystalline particles the difference between suscepti- 

 bilities in different directions will be neglected. This probably intro- 

 duces an error in the calculations which however is likely to be 

 small. 



It will be supposed that the applied field is so small that the 

 magnetization is proportional to the field. Some of the results of 

 the calculation are independent of this assumption as will be brought 

 out later. 



1) Leiden Comra. Suppl. N». 44a p. 10. 



19 

 Proceedings Royal Acad. Amsterdam. Vol. XXV. 



