Kinematical Analysis of B aimer s Formula. 23 



mental standing wave of length \.ttc in the atom, which 

 becomes lircY/v or \ in free aether. This gives an important 

 relation between a linear dimension of the atom and the 

 wave-length of its light. We can test this relation in the 

 following way. We have 



v = (W/p)i= (2tt/3)* (es/(2a) z pi) = (2w/3)* (M 2 //B 2 p)i 



Now in the non-metals we have B = 10~ 5 (M 2 /)2 nearly, and 

 p of the same order of magnitude as 27r/3, so that v is of the 

 order 10 5 , and Y/v is of the order 3 x 10 5 . In the visible 

 part of the spectrum X is of the order 6 x 10~ 5 and c at its 

 maximum will be R, but R is of the order 8x 10~ 9 , so that 

 \/47rR is of the order 600. To make Xjkirc of the same 

 order as Y/v we should need to take c to be only about 1/500 

 of R. In the combined metals of the Li family we have 



t>= (27t/3)H1'270-65 3 (2, 3, 4, 5, 6)M}», 



with a value whose order ranges from 10 6 for Li to 10 5 for 

 Cs, so that c in Li would need to be about 1/50 of R, and 

 for Cs it would need to be about 1/500 of R. If further 

 investigation bears out this view of the kinematical origin of 

 Balmer's formula there will be special interest in seeking for 

 the simplest kinematical conditions that will lead to Rydberg's 

 law of the relations between the principal and usual series in 

 the spectra of the alkalies. 



4. Summary. 



The central cause of the spectrum of an atom is a special 

 pair of electrons situated within the atom on its electric axis. 

 The atom is electrized, or electrically polarized, because it is 

 formed of constitutive pairs of electrons which have their 

 electric axes similarly directed so as to give the atom electric 

 properties analogous to the magnetic ones of a uniformly 

 magnetized sphere. The internal electric field of the atom 

 corresponds with the external field which produces cohesion, 

 and has been investigated in several papers on the laws of 

 molecular attraction. The special electron pair consists of 

 a positive electron which acts as though uniformly distributed 

 through a sphere of radius R = 0'795 x 10" 8 , which is the 

 same for all atoms. This action may be due to the rapid 

 random motion of a small positive electron through this 

 sphere of constant size. The negative electron is situated at 

 distance r along the electric axis of the atom from the centre 

 of the sphere of radius R. As regards outside action the 

 positive electron may be supposed altogether at the centre of 



