Spectra and Planck'' s Lair. 429 



the expression for the frequency 



would be different for electrons lying on different radii 

 drawn from the centre of the atoms, the limiting frequency 

 of electrons lying along these radii would be different, and 

 the lines of the pair would not close up as the wave-length 

 diminished. 



Again, the directions in which the electrons giving the 

 principal series bulged out, and along which the vibrations 

 had the smaller frequency, would be the directions where 

 the magnetic boundary bulged out in the atoms giving the 

 first subordinate series. The directions where the magnetic 

 boundary bulges out correspond to places where the constant 

 term inside the bracket is a maximum and therefore to 

 directions along which the frequency is a maximum. 



The line of longer wave-length in a pair in the principal 

 series is thus analogous to that of shorter wave-length in 

 one in the first subordinate series. This is in accordance 

 with the behavour of the* pairs in the spectra of the alkali 

 metals, for when the more refrangible line of a pair is the 

 stronger in the principal series, in the first subordinate series 

 the more refrangible line is the weaker, while the Zeeman 

 effect for the more refrangible lines in the principal series 

 is analogous to that of the less refrangible one in the first 

 subordinate series. 



In the spectra of the alkali metals the terms l/(n-f fi)'\ 

 l/(m-4-/i) 2 , which occur in the expression for the series 

 approximate to l/(n + -|) 2 in some cases and to 1/n 2 in others 

 where n is an integer. This would occur if the positions 

 where the electrons are in equilibrium were given by the 

 equation sin 2x — rather than by sin# = 0, for then the 

 solution of the equation would be < 2x=pir, where p is an 

 integer. If p is an even integer this may be written x=ri7r, 

 and if jo is an odd one x={n + ^)7r where n is an integer. 

 Thus, if we call the former the " S " solutions and the latter 

 the"C" ones and suppose that the magnetic boundary of 

 the atom may coincide with either a C or an S solution, we 

 can have the following types of series. I call the constant 

 term inside the bracket in Rydberg's expression the limit of 

 the series, and denote it by L s or L c according as it corresponds 

 to an 8 or C solution ; the steps, the variable part, will be 

 denoted by S 5 or S r according as the electrons giving out the 

 vibrations are in the position of equilibrium corresponding 

 to the S or C solution respectively. 



