302 Lord Kelvin on the Application of Sellmeier's Dynamical 

 The minimum reflected amplitude is got when 



ffl = # 2 = \/ — 



V a 



The reflexion-factor is then — , and the phase-difference 



s/ab + h 



is ^-. When #=0 we have complete reflexion with unaltered 



phase; with # = co, or the circuit open, we have complete 

 reflexion with reversed phase. The simultaneous alteration 

 of amplitude and phase difference brings it about that we 

 appear to pass continuously from amplitude +1 (x = 0) to 

 amplitude —1 (<^ = oo ) without passing through amplitude zero. 

 This apparent anomaly was pointed out to me by Dr. Barton. 

 Putting in the values of a, a, A, and substituting for va and 

 v/3 approximate values from (11), (12), we And that the 

 minimum value of the reflexion-factor s/f 2 -\-g l is 



4:{p 2 + q 2 )\ 

 and that the corresponding value of x is 



1 _ q{p-(r) 



neglecting higher terms in pa. 



Numerical Values, — Again using Dr. Barton's numbers we 

 get for the minimum reflexion-factor the value *0004, and 

 for the corresponding terminal resistance Lv(\ + '00009). 

 If, therefore, the terminal resistance be adjusted until the 

 reflected wave is a minimum, we may, without sensible error, 

 take this resistance to be Lv, and ignore the reflected train 

 altogether. 



Queen's College, Belfast, 

 13th October, 1898. 



XXIII. Application of Sellmeier's Dynamical Theory to the 

 Dark Lines D l3 D 2 produced by Sodium- Vapour, By 

 Lord Kelvin, G, C. V. 0„ P.R.S.K* 



§ 1. T^OR a perfectly definite mechanical representation of 

 J? Sellmeier's theory, imagine for each molecule of 

 sodium-vapour a spherical hollow in ether, lined with a thin 

 rigid spherical shell, of mass equal to the mass of homo- 

 geneous ether which would fill the hollow. This rigid lining 



* Communicated by the Author, having been read before the Eoval 

 Society of Edinburgh on Feb. 6, 1899. J 



