276 Dr. L. Silberstein on Fluorescent Vapours 



2 

 equations (20), the value of Ic=~ would be found. And 



T 



since t)t can be measured on the fundamental line, we should 

 have 7] as well as t. 



To illustrate (20) a little further, take the first line of the 

 resonance-spectrum, n=pN. Let T be the fundamental 

 period of oscillation, and r the extinction-time, as before. 

 Then 6 = 6 1 is given by 



tanfl^ n 2p . T (21) 



7r(l— p~) T 



For the second line we have only to replace p by 2p— 1, 

 and for the third line, by 3p — 2, etc. Thus 



tan , 2 _ 2(2„- 1) T 



7T[l-(2p-l) 2 ] 



toft- 2 ^- 2 ) 



. . (21') 



. . (21") 



and so on. Thus in the case of the iodine series A, for 

 which/? =0-9889, 



tan #! = 28-51^; tan'0, = 14\L8-; tan 6> 3 = 9'396-, 



T T T 



and so on. Now, T/t is certainly a small fraction, so that 

 6i is a small angle, 6 2 nearly one-half of #i, and so on. 

 Thus, by (20), the angles £\, f 2 ? e tc, become, apart from the 

 sign, ^i 2 , 1# 2 2 , and so on, i. e. of the order 10 3 (T/t) 2 , 

 3.10 2 (T/t) 2 , etc. 

 written 



And as for the ratio b/a, this can now be 

 6 



t. e. 



*' =14-26^ 

 a x t 



b/a-- 

 a 2 ~ 



2 = -tan#, 



7-09 -; °i=4-70i, etc., 



T £to T 



(22) 



and may, if t does not greatly exceed 10 3 T, be just detectable. 

 The decision must be left to the experimental physicist. 

 At any rate, b/a would be for the second line only about 

 one-half, and for the third line one-third of what it is for 

 the first line, and so on. 



It will be remembered that (20), and therefore also (21), 

 (22) are valid for H = H C , as defined above, and this field is, 

 as we shall see in the next section, very likely equal to about 

 10 4 gauss. For other field intensities of this order the 

 behaviour of the lines n l} n 2 , etc., will be very much the same. 

 For any field we have the rigorous equations (1.8), (19) with 

 (16), determining completely the u character " of each line 

 of the resonance-spectrum. 



