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XX] II. Intelligence and Miscellaneous Articles. 



OX A CONSEQUENCE OF THE POISSON-MOSSOTTI THEORY. 

 BY GOTTLIEB ADLER. 



T>01SSOX'S theory of magnetic induction gives the magnetizing 

 constant Jc as depending in a very simple manner on the ratio g 

 of the space e actually occupied by the molecules of magnetic 

 substance to the whole volume v. 



h = a n V where ,y = - (1) 



The same equation holds also, as Mossotti has shown, for di- 

 electric polarization, the magnitudes e, v, and g having the same 

 significance, except that Jc=(K — 1)4tt, where K is the dielectric 

 constant of the substance. 



As the ratio for iron was found to be #=134/135, and therefore 

 the space occupied by the molecules was so great as to be incon- 

 sistent with the idea of equal spherical molecules, Betti (LeJirbuch 

 der Potenticdiheorie, pp. 377, 378) was led to modify Poisson's funda- 

 mental assumption, and he thereby arrived at the expression 



*-5^. • ■■•; • • •(*> 



which gave for iron g= 134/403; thus the objection mentioned 

 above, and first pointed out by Maxwell (' Electricity,' vol. ii. 

 § 430; see also Mascart and Joubert's ' Electricity,' English 

 translation, vol. i. p. 151), is removed. 



In describing the phenomena of magnetic or dielectric polariza- 

 tion, since these are based on the magnitude Jc itself, it is quite 

 immaterial whether we regard Jc as defined by the expressions (1) 

 or by (2), or whether it is simply taken as an empirical constant. A 

 decision is, however, in so far important, since formula (1) is taken 

 by some authors as starting-point for a determination of the size 

 of the molecules from the value g. 



It is now perhaps remarkable, that when Jc is taken as defined 

 by the formula (1), or by the function of g as defined by (2), at 

 the same time we can deal with a second constant introduced by 

 Helmholtz and Kirchhoff (Helmholtz, Wied. Ann. vol. xiii. p. 397, 

 1881 ; Kirchhoff, "Wied. Ann. vol. xxiv. p. 55, 1885), and used for 

 describing the pressures occurring in magnetic or dielectric polarized 

 bodies: %k 



d iogv 



For k ,_ U- _ d& dr/ ( bJc 

 dlogv d(/ dlogv - d# ' 





; easily follows from (1). 





Assuming Poisson's formula (1) we get 





*-^-~*(i+n?> • 



. . . (-3) 



Phil Mag. S. 5. Vol. 33. No. 201. Feb. 1892. 



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