56 Dr. P. Zeeman on Doublets and Triplets in the 



positions, we might conclude also that the line will be simply 

 widened in a strong field. I take the liberty of stating briefly 

 to the readers of the ' Philosophical Magazine ' the preliminary 

 results I have obtained in regard to these questions. 



2. In § 18 of the cited paper, the motion of an ion in a 

 magnetic field was treated according to Lorentz's theory. The 

 system of coordinates was chosen in such a manner that the 

 axis of z was parallel to the magnetic force, the plane of (x, y) 

 being perpendicular to it. Referring for the rest to the 

 cited paper, I recapitulate that the considered motions of the 

 ions, existing before the putting on of the magnetic force, were 

 resolved into a rectilinear harmonic motion parallel to the axis 

 of z and two circular (right-handed and left-handed) motions 

 in the plane of (a?, y). 



The first remains unchanged under the influence of the 

 magnetic force, the periods of the last are changed. 



3. Using the rule given by Lorentz, therefore, we see that 

 in the direction of the lines of force, right-handed and left- 

 handed circularly polarized light of changed period must be 

 propagated. The ions vibrating parallel to the lines of force 

 of course do not cause any disturbance in the aether equivalent 

 to light in that direction. 



In a direction perpendicular to the lines of force, those 

 motions of the ions which have a component parallel to the 

 plane of {x, y) give plane-polarized light vibrating in a 

 vertical plane and with changed period (I suppose the axis of 

 «ina horizontal plane). The ions, however, moving parallel 

 to the axis of z give electrical vibrations in a horizontal 

 direction with unchanged period. 



4. Magnetic Doublets. — Hence with every value of the 

 magnetic force, an infinitely narrow spectral line breaks up 

 into two lines, the light being emitted in the direction of the 

 lines of force. However, for lines of finite width the mag- 

 netic change of the period must exceed somewhat that corres- 

 ponding to half the width of the original line in order that 

 the doublet may be seen. One of the components then must 

 be over the whole width left-handed, the other right-handed 

 circularly polarized. 



5. Magnetic Triplets. — With finite width of the spectral 

 line and observing in a direction perpendicular to the lines of 

 force, the line is broken up into a triplet if the magnetic 

 change of the period corresponds to the whole width of the 

 original spectral line. Hence the magnetic force necessary to 

 produce a triplet is equal to twice the value necessary for 

 a doublet. 



6. Intermediate Forms of Magnetic Doublets and of Triplets 

 — With magnetic forces less than the ones supposed in § § 4 



