﻿Cubic Crystals with Theoretical Atoms. 773 



in centimetres. A rough approximation to it was given in 

 the former paper, but a more accurate way is to derive it 

 from the hydrogen spectrum, assuming that (59) gives the 

 vibration frequency of the fundamental term in Balmer's 

 series. This may be written 



i(t)'« (67) 



"along q3 



All the quantities in the right member of this are known 

 except a*. Hence, by equating the frequency to '823 x 10 15 , 

 the constant in Banner's series, we find a*, 



a*=-207xl0- 12 cm. 



&=^*= -00103 (68) 



and a*co% 



The value of this unit in the former paper, determined in a 

 different way, was *285 x 10 -12 cm. From (63) and (68) 

 the universal constant angular moment of momentum of 

 every electron is seen to be 



mo>a 2 = -564xlQ- 32 , (69) 



185,000 times smaller than the value of this constant given 

 by Bohr's theory* of the central nucleus atom. 



If we assume that the electrons are distributed in a 

 chlorine atom according to the scheme shown in fig. 3 of the 

 former paperf, having rings of 16, 12, 6, and 1 electrons, 

 and also that the positive charge has a spherical shape, its 



radius is 2'4x 10 -12 cm., or — — = 11*6 a* units. Taking 



w =ll, n 1 = 7'5, n 2 = 5, and n 3 negligible, we find Sn 2 = 2800 



approximately. The electrons in the sodium atom are not 

 shown in the figure referred to, but the radius of the positive 

 charge is 2*09 x 10~ 12 cm., =10*ltt* units. An estimate of 

 the positions of the electrons in three rings 13, 8, and 2, 

 gives about 1500 as the value of £m 2 for sodium. The 



23 



theoretical value is, therefore, approximately 



N /^t 2 S^ = 2050, (70) 



23 35 



which is to be compared with 2895 in (GG). It is needless 

 to say that these figures are in agreement within the limits 



* N. Bohr, Phil. Mug. July 1913, vol. xxvi. p, 1& 

 f Loc. cit. p. 323. 



