234 Intelligence and Miscellaneous Articles. 



On the contrary, assuming Betti's formula (2), 



Jc' = —^-=-Jc(l+4:irk) (4) 



d log x 



Both formulas (3) and (4) give for the magnetizing number Jc, 

 or for the dielectric constant K=l + 47r^, a decrease as the volume 

 increases. 



Both give for feebly magnetic or dielectrically polarizable sub- 

 stances, neglecting terms of higher order, 



fc '=sr^-=-*' ( 5 > 



ologv 



but otherwise Jc' as a quadratic function of Jc, and therefore 

 agreeing in the order of magnitude. 



From the experimental results on the dependence of Jc on the 

 increase of volume a decision is possible, whether Poisson's or 

 Betti's formula is in accordance with facts. 



The only direct experimental results on this view are in the case 

 of gases. 



The measurements of Boltzmann show that the dielectric 

 constant increases directly with the pressure. If with Boltzmann 

 we make the further assumption that the proportionality of the 

 increase of the dielectric constant with increase of pressure holds 

 up to complete exhaustion, his results maybe embraced within two 

 formulas propounded by him, the first of which is the dielectric 

 constant for the normal pressure of an atmosphere, 



K^l + X, (6 a) 



while the other fixes its dependence on the pressure p by 



K=(l+Xp) (G) 



Prom (6) we have 



dlogp 



Now for a gas ^=const., and accordingly d\ogp= — dhg v ; 

 hence 



dK fcK 



log ^ d log v 



= 4:7rJc'=— 4?rl\ 



from which we get the formula (5) deduced from Poisson's and 

 Betti's formula, 



7c'=-Jc. 



There are no direct experimental results as to the change of Jc 

 with the volume except in the case of gases. 



From the theory of Helmholtz and Kirchhoff as to the change 

 of shape of magnetic or dielectric polarized bodies, the magnitude 

 of Jc' together with Jc is decisive as to the change of volume 



