﻿1090 Mr. R. Hargreaves on Atomic Systems 



column gives in the case of Barium (n = 56) <z = *99 X 10"*" 9 ,. 

 Aa 3 = l-33xl0- 25 . 



The corresponding series of periods of type P^ is not 

 limited to a narrow range; its shortest periods are about 

 50 times those of the shortest period above (7) or about 

 43 times those of the other extreme («). The table in 

 Sommerfeld's Atombau gives no data in which the elements 

 of K and M series overlap, but the above factors are somewhat 

 in excess of values I get by comparison of M figures with 

 extrapolated values of the K series. 



There is also a special ionic period, due to the axial 

 oscillation of a central ion, of much greater duration than 

 those enumerated above. When n is great, the factor con- 

 necting it with the shortest period above is about 32n 2 /9. 

 The numerical value \ = 3*73xl0~ 5 then corresponds to 

 *388 x 10 ~ 8 in the K(«) series for Barium in the above 

 interpretation. 



§ 23. Consider now the period of revolution of satellites. 

 When corrections due to the rings are ignored, the motion 

 of a single satellite is given b}^ m 2 nV 3 = e 2 . If the period 

 27r/I2 is identified with A/V, the numerical connexion of r 

 and A is given by (r x 10 8 ) 3 x 1*405 = (A x 10 5 ) 2 . For an 

 external satellite, A will be of order 10 " 5 if r isof order 10~ 8 . 

 Thus a period in the range of light corresponds with such a 

 value of r as appears in Chemistry in the role of radius 

 of activity. Also the influence of the rings is negligible 

 if a is of the order suggested in the last paragraph,, 

 viz. a/r is then small ; but corrections can be applied by use 

 of (23). 



For an internal satellite the same equation is (rXlO 10 ) 3 

 x 1*405 = (Ax 10 8 ) 2 . Identification with the L series 

 would here make r of the order 10~ 10 , and the correction for 

 the rings would be negligible as rja is small. 



A value of the ratio r/a near to 1 would involve a serious 

 perturbation in the mutual action of satellite and rings, 

 which may be the reason for the strong action of ultra-violet 



li « ht - 



If the axial oscillation of satellites has a period 27r/qfl, 

 then for 5=1, 2, 3 I find q=l, 1*155, 152 ; also I find 

 axial instability for 5 = 4. For the cases of 2 and 3 satellites, 

 m 2 n 2 r 3 /e 2 = *75 and *423 respectively. These cases show 

 radial and tangential instability. Of the more complicated 

 orbits to which this instability points, the elliptic is the more 

 permanent form, liable, however, to a stronger perturbation 

 from the double ring than would attach to the circular orbit.. 



