«3 



367 



/ • _ ^ 



^ wit:' K'e ' 



wlu'ic K- r is livDKi KG s coiislanl. I nking K c.^ 1,097 • 10 ' and using Mili.ikan .s value 

 lor c {e 4,77 • 10 "'i, we liiHi 



k =-- (),()() IH.). (125) 

 Tlu' expressions lor llie relative amplitudes may now he written in Ihi- form 



/,'(T— 2^0, -T-2<«2 l = -s'l(3£' 2) -r£'(5 3s'-)) (re) + (1 - £')(;(1 -c')(:W4-2) -i- 7£X5-3£-)/r+l(rs)j. 



/>'tr,«,-,«, + ^3) = g{(3 + 5rfl-f£V/))/r_l(r£)-f-(;{-5r(l--£>'J)Jr-fl(«i;. 



«(7=2r«, ) =^^''l^"-' 2) r£'(5-3£"^))J__j(")-t-(l s ((1 £')(3£' + 2)- r3'(5 as"^)) (rsjj^ 



/;(r+2«;i 3«.2 + w,) = '^Jr,v'{(l '-''(a £')(3e'+2)-r£'(5-3£'-'l)J^_j(re)-(l-£')((l^e')(3e' 2)-^r£'(5 3£'-'))/.^^(re)}, 



(1L>6) 



where the (|uantities z\ t, ;i! and // are lunctions of the ns which according to 

 (94) and (124) are expressed by means of the formulae 



t' — , c = ^ V n' — nr; , n! " , n ^ ^ \/n\ — n, (n = n, 4-/i,). 

 n n - n., n - i . 



In case of circular orbits (;' = !, ; = (), = Ü) the formulae (12fi> accord- 

 in;; to (97) assume the sim[)le form 



H{oj,i-w,) - ^, , (127) 



«(— 3fü2 J ru..) = ^, ^ — . 



The appearance of the factor n'ni in the formulae indicates that the intensities 

 of the perturbed components will, for the same intensity of the electric field, 

 increase very fast if the quantity li characterising the initial state increases, so that 

 lor instance in the Balmer series the higher members will be mucli more influenced 

 by an electric field than the first members. Further the appearance of AT ' in the 

 denominator indicates that for a hydrogen line (iV = 1) the influence of an electric 

 Held will again be much stronger than for one of the analogous helium lines [N — 2) 

 in the same part of the spectrum, in agreement with what might be directly 

 expected from the fact that for the latter lines the frequency differences of the 

 fine structure components are much smaller than for the former lines, whih- the 

 frequency ditîerences for the com[)i)nents of the Stark etTecl are larger. 



47* 



