258 Mr. W. Sutherland on the 



and then from (5) and (9) 



VB 



(« (1 ^)- • • (IB) 



So Rydberg's chief law amounts to this, that the principal 

 and the Sharp series in the spectra of the alkalis result 

 respectively from the fundamental motion of the reFerence- 



vector with the motions of velocities l-\~. p fi, 2+ p /ul m + p/j, 



of the disturbance-vector, and from the fundamental motion 

 of the disturbance-vector with the motions of velocities 1 -f u fi, 



2 + u (i m + ufi of the reference-vector. 



The study of Rydberg's Laws will be resumed in Section 8. 



5. Two Supplementary Principles. 

 Rydberg has connected the differences v, v u and v 2 in the 

 usual series with the square of the atomic weight of the 

 elements in each natural group ; but the true law of these 

 spectral parameters can be seen by a study of the data for 

 Zn, Cd, and Hg, namely, for v x 386*4, 1159-4, 4633*3. Three 

 times the value for Zn gives 1159*2 the value for Cd, and 

 twelve times the value for Zn gives 4636*8, which is within 

 one part in 1000 of the value for Hg. This example makes it 

 clear that the relations between the values of v in a group of 

 elements are purely numerical, and have no direct relation to 

 atomic weight. The point is of some importance, because a 

 direct relation between v and atomic weight would indicate 

 that v depended on dynamical conditions, whereas a numerical 

 relation such as that just proved points to the control of v 

 resting with kinematical conditions. 



This kinematical relation of v in different elements such as 

 Zn, Cd, and Hg, seems to me strong evidence that in the 

 atoms of different elements we have practically the same 

 electrical apparatus engaged in emitting the radiations. It is 

 therefore worth while to investigate the law of v in other 

 natural groups of elements. 



In the Li group the value for Li itself is too small for 

 measurement so far, but for the others we have the values 

 given in the first row of the next little table, while the second 

 row gives the values of 1, 3, 12, and 28 times 19*6 with 2 

 subtracted. 



Na. K. Rb. Cs. 



v 17*2 b6'8 234*4 545*0 



17*6 56*8 233*2 546*8 



Here again is clear evidence of a numerical law for v, and 

 we have the series 1, 3, 12 of the Zn family repeated with 

 the addition of the next member, namely 28, and these are 

 the first four terms of the mathematical series whose general 



