( 472 ) 



vibrating- sysU'iu of some oscillations of so great an aniplitiide that 

 the law of the simple pendnlnm that the force which repels the 

 vibrating particle (system) to its state of equilibrium is equal to the 

 deviation, does not hold for them. This force now depends also on 

 higher powers of the deviation. If as Hei.mholtz did for the combinational 

 tones, we assume also in this case that the force which causes the 

 motion, also depends on the square of the amplitude, a new system 

 of combinational vibrations may be expected from two sucli vibrations. 



Of all the series known up to uow (principal series, first and 

 second subordinate series) the first lines have the ijreatest intensity; 

 these lines occur, as will appear from what follows, in combinations, 

 and it is clear tliat the above remarks apply to these vibrations. 



When in wdiat follows we speak of the difference or the sum of 

 tw^o lines, the difference resp. the sum of the frequencies is meant 

 corresponding to these lines. 



Lithium: In a paper on a new empirical spectrum formula') 

 a number of lines of this element is mentioned as third subordinate 

 series. We have here to do with a differential series, the terms of 

 which represent the differences in frequency between the 1^^ li,,^. qj 

 the principal series and each of the following ones. In the subjoined 

 table the first column contains the observed wave-lengths of the 

 principal series in A- U. 'j, the second gives the difference of the 

 frequencies, the third the wave-length 'h calculated from it, the 

 fourth the observed wave-length ;.„• • After this the observer's initials 

 are given with the possihle erroi' of observation given by him. It is 

 clear that Xi. must be followed by a ± A, as this wave-length has 

 been calculated from observed lines, in which an error of observation 

 is vei'y probable. 



3) 



^) E. E. Mogendorff: On a new empiric spectral formula. These Proc. Vol. IX 

 p. 434. Cf Thesis for the doctorate, Amsterdam 1906. 



2) These lines are the intensest of the ij-spectrum. Kayser and Runge, Handb. 

 der Spectr. Vol. II. p. 517. 



3) S = Saunders, E. H. is Exner and Haschek (3921,8 has been observed in the 

 spark spectrum). 



