442 Dr. J. W. Nicholson on the Damping of the 



We apply the results in the first place to the model 

 atom used by Lamb to illustrate selective absorption. In 

 that model, it is found that in order to obtain a fundamental 

 vibration which shall fall in the ultra-violet, with a sphere of 

 atomic dimensions, k must be of order 10 6 . The actual 

 values taken by Lamb are k=5A0% a = l*3.10~ 8 , in C.G.vS. 

 units. In this case, it is found from the above formula (3) 

 that k l = l'D, which is not small, and the fundamental vibration 

 is decreased in a ratio 1/e in 2/3 of a second. The vibrations 

 are therefore not very permanent. With the uncorrected 

 formula of the decrement given by Walker, the ensuing 

 value of Jx\ is of order 10 ~ 12 , leading to great permanence. 

 The difference in the results is therefore considerable. But 

 the comparatively rapid dissipation of the free vibrations 

 is perhaps not sufficiently rapid to impair the efficiency of 

 Lamb's suggested model of a gas exhibiting selective 

 absorption. 



The positive particle may be supposed to be of atomic size. 

 Moreover, we may write for this particle, m = 10~ 24 , e/c= 10~ 20 

 as approximate values, where e is its charge. Its electro- 

 magnetic mass for small motions is therefore ??/ = 2e 2 /3ac 2 or 

 5 . 10 " 33 , so that m'/m = 5 . 10 ~ 9 . Thus with k= 5 . 10 6 , the value 

 required to bring its vibration also within the visible spectrum, 

 it is possible, with p equal to 5 approximately for the funda- 

 mental free vibration, to ignore m'/m altogether in the 

 expression (m' ■+ ??i/3 2 / /c )/( w H- w oi (10). Accordingly, the 

 decrement may be given its value for the uncharged fixed 

 sphere of atomic size, and is again k = l'5. This is the 

 decrement of the fundamental free vibration of the positive 

 particle if it can be regarded as a superficially charged 

 dielectric of constant form and of such a character that this 

 vibration comes within the visible spectrum. 



The decrement of the higher vibrations is of course greater 

 on account of p. The second root of tanh /e^=/e*A.is given by 

 /ci\= + 7*725i, and m'lm being negligible more and more in 

 the higher vibrations, the decrement is proportional to p 4 , 

 and becomes A;' = 13*1. For the third vibration. p = 10*904, 

 leading to A/ / =52 , 2. The increase in k is therefore rapid. 



Proceeding to the case with which we are at present more 

 immediately concerned, of a hypothetical spherical electron 

 without deformation, we may write, in accordance with 

 current estimates of approximate size, a = 10 ~ 13 . As Walker 

 has remarked, in order that a vibration from a sphere of this 

 size shall appear in the visible spectrum, the dielectric con- 

 stant must be of order 10 16 . This appears at once from the ex- 

 pression for the period as 27r(a/vc)^, where iv is the imaginary 



