53 



^-,(7^,)./r,(r<T,)} I 



and J 

 respec'lively, where 



;,^./ri-n(rrT,)./r,-M(r^j} (113) 



/( - 'î| ^ n., — /I , , 



(114) 



«2 + "3 



'2 



^23 = 



n 



If one of the quantities /![ and n.^, say n.,, l)ecomes equal to zero the expressi- 

 ons for the aniphtudes become much simpler. The character of the motion in the 

 corresponding stales of the atom has been considered in detail in § 3 on page 2ö, 

 where it was seen that the motion of the electron in these states may he resolved 

 in a number of linear vibrations of frequencies z■^ to^ parallel to the field and a 

 number of circular harmonic rotations of frequencies z^(Oy-\- w.^ perpendicular to 

 the field, so that the amplitudes will be equal to zero unless r.^ = 0. For the ex- 

 pressions for the relative amplitudes of the vibrations of frequencies ZyW^ and 

 Ti^j + ^ü.;, we find from (72) and (110) 



In the formulae (113) and (116) holding for the relative amplitudes of Ihe 

 circular rotations, -, is considered to be equal to 1. In the case where -, ^ — 1, 

 however, i. e. for transitions during which the angular momentum of the electron 

 round the axis of the system increases by h-)-, w-e may obviously apply the same 

 formulae if only we reverse the sign in the values for z^ and r.^. For the relative 

 amplitudes of the linear vibrations we have both in (112) and in (115) given two 

 exjjressions, the former of which is more symmetrical, while the laller lends itscll 

 better to numerical calculations as long as no tables of tlio functions ./),(/>) are 

 at hand. 



The ciglh and ninlh columns in the tables contain llie scpiares of R' and R'\ 

 which (puintities, according to the considerations in 5, should l)e expected to 

 atîord an estimate for the relative inlensilies of the dilTorenl components. Here it 



where 



RiZyCO,) = lt,Jr(rt,) = (,/r- i(,rf,) — ./r+i(n,)}, 

 = \ '1^' , r = -, -L -g, ,( = „j 4- II,, (n, - -2 



0). 



(115) 



(110) 



