( 341 ) 



tots, tlu! iiiiKM' lUid Diitcr lines have inlcrcliaiincil tlicii' oiiliiiary 

 states of polarization. Finally Miciiklson, Pueston ') and otlior 

 physicists bavo seen a division of some lines into ,">, (! or oven more 

 oomponents. 



I shall examine in this paper, to what extent such multiple lines 

 may be explained by appropriate assumptions concerning the way in 

 which light is emitted. Of course I am perfectly aware of the possi- 

 bility that my interpretation of the facts will have to be replaced 

 by u more adequate one. Tiie special form of my hvpothescs has 

 the less value, as in the only case in which I have endeavoured 

 to account for all the peculiarities of the phenomena, I have suc- 

 ceeded but poorly, at the best. 



§ 2. Since the components, into which a line is broken up bv 

 the magnetic force, are in many cases as sharp as the original line 

 itself, it must be admitted that the periods of all the luminous par- 

 ticles of the source i>f light are modified in the same way. This is 

 only possible in two ways. P^ither, in the magnetic field, all the 

 particles must take the same direction, or the modification of the 

 periods must remain unchanged, into whatever position the particles 

 may be turned. The firet assumption leads however to some diffi- 

 culties '-). I shall therefore suppose the luminous particles to be 

 spherical bodies, having the same pioperties in all directions. This 

 may be true, even though the chemical atoms be of a much less 

 simple structure; indeed, the vibrating spherical ion may very well 

 be only a part, perhaps a very small part, of the whole atom "'). 



It has been shown in a former paper +) that a triplet may be obser- 

 ved if, among the principal modes of vibration of the sysiem, there 

 be three, for wliich, outside the magnetic field, the time of vibration 

 is the same, or, as we may say, if the system have throve equiva- 

 lent degrees of freedom. Afterwards Mr. Pannkkoek "') remarked 

 that a quartet may appear if there be, in the same sense, four equi- 

 valent degrees of liberty, and in genei'al, a ?(-fold line, if n df the 

 principal modes have ecjual periods. 



Now, spherical systems, vibrating in one of their higher modes, 

 have indeed more than three cfjuivalent degrees of freedom. 



') MlCHELSON, Phil. Mag,, ^'ol. 15, 1). 348. PkesTon, ibidem, p. 525, 



") See LoEENTZ, Versing der Verg, Akiid, van VVeteiistdi. V [, p. l',)7, iind Arch, 

 iirerl., Sér. 2, T. 2, p, .5, 



■') See LoHENT/,, Vershig der Verg. Akiidemie van Weteiischnppeu Yl, p. .514. 



■*) Wied. Ann. Bd. 63, p. 27s. 



') Yershig der Verg. Akademie van Wetensehappeii VII, p. 120, Procpedings lidv.d 

 Acad. Vol. I, p. 'JO 



