Cause of the Structure of Spectra. 271 



complicated effects that are now known to constitute the whole 

 phenomenon. 



The equation (13) shows that, when we compare different 

 elements, co the angular velocity of the electron must be of 

 the form A/(l +/a), where A is an absolute constant of nature. 

 Thus co is derived from A in exactly the same way as our 

 angular velocity ft>/(l + At) was derived from co. To account 

 for this we must reconsider the motions of our two electrons 

 of opposite sign. We gave each of these a circular motion 

 round the centre of the atom, compounded with another 

 circular motion. Now on account of these second circular 

 motions of periods (1 + fiij'2irj(o and (l + /^ 2 )27r/ft), the centre 

 of inertia of the positive and negative electrons together will 

 have not only a fundamental circular motion, but a variation 

 involving two coexistent motions of periodicities (l + /i 1 )27r/o> 

 and (1 -f fi 2 ) 27r/ft>. Thus then we should start with the motion of 

 this centre of inertia R, and represent it as caused by the 

 revolution of OP with angular velocity A, of PQ 

 with velocity A/(l + /j^) and of QR with velocity r 



A/(l + A4). 



Now on account of the circular motion of 



period (l + ^ 1 )27r/A possessed by the centre of 



inertia of the two electrons, and the motion 



of, say, the negative electron relative to the 



centre of inertia, we have to consider a nearly 



circular motion of the negative electron, which, 



in the manner just shown, may be considered to 



consist of a motion of a vector ORi with 



angular velocity A/Cl + z-ij) round 0, and of a 



vector RiHg with velocity A/(l+ /a,) 2 round R l5 



where R 2 represents the negative electron. For 



the negative electron we can also in the same way get derived 



circular motions of velocities 



A/(l + / x 1 )(2 + /. l ) A/(l + ^)(^ + A*i) 



and also of velocities 



A/(1+ M „)(l+ / * 1 ) A/(l+^)(m+^). 



Similarly for the positive electron we get velocities 



A/(l + /* 2 )(l+/* 2 ) A/(l+/* 2 )(m+^) 



A/(l + / x 1 )(l+/^ 2 ) A/(l+/*i)(m + /a 3 ). 



The Principal and Sharp series in the Alkalis are caused by 

 the relative motion due to the motion of the negative electron 



