786 Dr. L. Silberstein on Radiation from 



Poisson's formula * in its approximate form, which is known 

 as Mossotti's formula, i. e. 



where « is the volume of the spheres per unit volume of 

 gas. Consequently, remembering that K is in our case 

 but slightly greater than unity, 



a, = (K -l)/(K + 2) = J-(K -l). 



Here K -l = 2-fi4 . 10" 4 , and therefore 



<w = O88.10- 4 . 



Let us suppose for the moment that each spherical source 

 contains more than one molecule of hydrogen, say, a? mole- 

 cules. Then, the number of molecules (or atoms, if the gas 

 be dissociated) per cubic centimetre being 2*76 . 10 9 , we 

 should have 



o> = 2-76 . lO 9 ^ 3 =0-88 . 10" 4 , 

 a? 3 



whence, in round figures, 



a/<r=9-13.10- 9 cm. 



Now the molecules or atoms being distributed homogeneously, 

 it is obvious that if each sphere a contained (on the average) 

 more than a single atom, the spheres would practically 

 occupy all the volume of the gas, or would even overlap 

 with one another. But if such were the case, its macro- 

 scopic permittivity K would, instead of being but slightly 

 greater than unity, be practically as great as K itself. We 

 must conclude, therefore, that # = 1, and consequently 



a = 9'13.10- 9 cm (30) 



Thus the source shrinks to molecular or atomic dimensions f . 



Using this result, it will be seen at once that the corre- 

 sponding value of permittivity of the spherical source in 

 the case of line spectra is enormous. Take, for example, 

 the value of & =47r 2 a 2 K as required by Table III. for the 



K„ = 



2+K +2a,(K -l) 



n ' ° ' / " -,/ , cf. Maxwell's ' Treatise. 



2+K — w(K -l) J 



+ The values of the radius of a hydrogen molecule calculated from 

 the deviations from Boyle's law, and from the coefficients of viscosity, of 

 thermic conduction, and of diffusion are 1*025, 1*024, 0'995, and 

 l'Ol . 10 -8 cm., respectively. cy., for instance, J. H. Jeans's 'Dyna- 

 mical Theory of Gases,' Cambridge, 1904, p. 340. 



