Chemistry and Physics. 71 



In the first place, if the law of electric force had the form 

 r" 2 (l — c^- 1 ) (1 — CoT- 1 ) (1 — c^r- 1 ), where c 1} c 2 , c 3 are of the 

 order of atomic distances, and r is the distance from the positive 

 nnclens, there wonld be no lack of accord with the inverse square 

 law for actual experimental distances, which are always enor- 

 mous in comparison with atomic magnitudes, 10~ 8 cm. On the 

 other hand, the force would change from attraction to repulsion 

 when r assumed any one of the values c ± , c 2 , c 3 . Since the law 

 of force within the atom is not known there is no objection to 

 assuming the alternation of sign involved in the above expres- 

 sion. Instead of using the preceding multiplier of r -2 , Thomson 

 prefers the factor (sin cu)/cu, where u = 1/r. Inside the atom, 

 if atomic dimensions are comparable with c, there will be a series 

 of positions of equilibrium for an electron determined by 

 cu = n-rr where n is an integer. Thus even if there is only one 

 positive charge and one electron (hydrogen) there may be a 

 singly infinite series of atoms with the electron at distances from 

 the center represented by r = c/n-ir. The times of vibration of 

 the electrons about these positions would be different, so that 

 a collection of such atoms could give rise to an infinite number 

 of lines both in the absorption and emission spectra. Among 

 other things, this conception accounts qualitatively for the 

 observed decrease in the intensity of spectral lines of a given 

 series as the term number of the line increases. 



Further progress is made by supposing that magnetic instead 

 of electric forces are predominant in determining the electronic 

 vibrations. In this case it is convenient to assume that the value 

 of the magnetic induction, at a point of equilibrium at a distance 

 r from the center, is given by n(a? — r 2 ). This distribution of 

 magnetic force is not a priori improbable as it is that inside a 

 sphere uniformly electrified and rotating like a rigid body. It 

 is then shown that the frequencies in these positions would be 



proportional to -»( — i)> which expression represents a 



series of the Balmer type. If, in addition, the place r = a, 



where the magnetic force vanishes, is also a place where the elec- 



c 

 trie force vanishes, — =m7r where m is an integer, and the 



expression for the frequency becomes C( — — ^), where C is a 



constant. The type of atom which is required to satisfy the 

 assumptions made in the analysis is described as follows. ' ' This 

 atom consists of a field of electric force which may be regarded 

 as made up of a series of shells of attractive and repulsive force 

 following one another alternately, the radii of the boundary of 

 these shells, which are places where an electron would be in 

 equilibrium, being in harmonical progression. Superposed on 

 the field of electric force is a field of magnetic force, also 



