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a siugle line in the middle, whose intensity would be 3. If in this 

 case, for one reason or another, this line -C, 3, and the lines A^ 1 

 and B, 2 were to disappear or to become imperceptible, we should 

 only see A^2 and -S, 1 and this would bo a quartet as has been 

 observed by CoRKU. 



The case n'^ = Vs '*'i (§ 9) is likewise of some interest. i>, 1 and 

 B,2 would then form a single pair, each of whose components would 

 have the intensity -^2- The distance of these strong lines would be 

 half that of the lines A^ 2, and, if it were not for A, 1 and -B, 3 we 

 should have a quartet, the outer components of which would be 

 polarized perpendicularly to, and the inner components in the direc- 

 tion of the lines of force. Quartets of this kind have been really 

 observed. 



§ IG. The following remarks remain to be made. 



1. Since the frequency of the secondary vibrations is wholly 

 determined by that of the primary ones, we need not trouble our- 

 selves about a direct ZEEMAN-effect in these secondary vibrations. 



2. Any explanation of the spectral lines must account for their re- 

 versibility. Consequently, the foregoing theory, which attributes some 

 lines to derived vibrations, will hold only, if a system can be made 

 to vibrate by the action of forces, whose period corresponds not to 

 a primary, but to a secondary vibration of the system. I believe 

 this to be really possible, but for want of space, I shall not now 

 insist on this point. 



3. If one wishes to apply the above considerations to vibrations of 

 an order, higher than the second, one soon perceives that it is 

 impossible to obtain a motion of the first order by combining these 

 higher modes with vibrations of the first order. 



Vibrations that are capable of radiating may however be derived 

 from two vibrations whose order diifers by unity. If now the priraai'y 

 motions showed the peculiarity that has been mentioned in § 10 

 and has been observed in the series of spectral lines, this peculiarity 

 would also present itself in those derived vibrations whose frequency 

 is the sum of the frequencies of the primaries ; it would not exist 

 in the secondary vibrations corresponding to the difference of these 

 frequencies. I must acknowledge however that this conception of 

 the series of spectral lines seems hardly reconcilable to the fact of 

 so large a number of lines becoming simple triplets in the magnetic 

 field. 



(March 32tü, 1899.) 



