4 INFLUENCE OF A MAGNETIC FIELD UPON THE SPARK SPECTRA OF IRON AND TITANIUM. 



there is always a great diversity for the lines of the same element. As this point will receive a good deal 

 of attention in the consideration of the results for the spectra of iron and titanium, it may be well to go 

 briefly into this portion of the theory. 



If the Zeeman phenomenon were in full accord with the simplest form of the electron theory as given 

 by Lorentz, all lines would show the separation of the "normal triplet," in which the distance of each 

 side component from the central Hne would be given by the relation 



.- e HX= 

 AX = 



m 4irv 



where e/m is the ratio of charge to mass of the electron, H the field-strength, and v the velocity of light. 

 This is derived (2) from the fact that the change of period of the light producing one side com- 

 ponent is eH/2m in 27r seconds, or eR/^-Kni vibrations in one second. The number of vibrations per 

 second is n = v/\. The change of frequency is then 



, _vdX_ eH 

 X' 47rw 

 from which 



^^ e HX' 

 AX = 



m ^TTV 



If I' be expressed in centimeters per second, the change in frequency per cm length is 



AX _ e H 

 X^ m 47rii 



The factor e/m is here expressed in electro-magnetic units. This value of AX/X^ for a given field deter- 

 mines the separation of the side, components of the "normal triplet" from the central line, and a con- 

 siderable number of lines in a spectrum will usually give a value of e/m in close agreement with that 

 obtained for cathode rays. The separation of the majority of triplets, however, differs from the normal 

 type, though sometimes by even multiples. This means either that there are real differences in the values 

 of e/m for different negative electrons, or that the relation derived from the elementary theory is not 

 sufficiently general. Lorentz inclines to the latter view (4a). In discussing this question, Voigt (3a) 

 observes that it is by no means certain that the field acting upon a given electron is the same as that 

 which we measure by one of our regular methods. The field due to the movement of charged parts of 

 the molecule itself must be recognized as possibly superposed on the external field due to the magnet. 



The elementary theory does not provide for the more complicated types of separation, nor does any 

 extension so far worked out cover them satisfactorily. However, an examination of the results of Runge 

 and Paschen (18) (24) for several elements and of Lohmann (27) for the spectrum of neon (with the 

 echelon spectroscope) enabled Runge (29) to enunciate the following: 



Die bisher beobachteten komplizierten Zerlegungen von Spektrallinien im magnetischen Felde zeigen die folgende Eigentiim- 

 lichkeit: Die Abstande der Komponenten von der Mitte sind Vielfache eines aliquoten Teil des normalen Abstandes 



X'- m ^nv 

 Sicher beobachtet sind bisher die Teile a/2, a/j,, a/4, a/^, 0/6, 0/7, a/ii, a/12. 



This work of Runge is regarded by Voigt as showing that the internal field acting on the electron can 

 have little effect, that the electrons within the molecule have the same value of e/m as that of cathode rays. 



Such a relation between the separation for individual fines and that of the normal triplet is of high 

 interest when appHed to spectra containing many lines. It has been examined by Moore (28) for the spectra 

 of barium, yttrium, zirconium, osmium, and thorium, and relations similar to those observed by Runge 

 have been obtained. The objection can be raised to this method that, by choosing small fractions of the 

 interval a and correspondingly large multiples, the difference between the calculated and observed values 



