( 97 ) 



= 0. 



If we develop this (leterminaut, all ferms, -which have an odd 

 number of factors er.s l-, are excluded by (2). Hence the equation 

 may be written 



(^2 + k«)^ + ^ (Z2 -f k2)« + 5=0, (6) 



where A contains terms with 2 factors er.s I, and 7? terms witli 4 

 factors of this kind. In all these factors l^ may be replaced by 

 — k^. Consequently, A and B can be found, and A is now propor- 

 tional to the square and B proportional to the fourth power of the 

 intensity of the field. 



From (6) we get two values of {l'^ + k^)^, which are both real and 

 positive, because, as was already remarked, real values must be 

 found for /^ Hence the solution of (6j may be represented by 



and 



(fi 4- k2)2 = «2, 



(/2 + k2)2 = /?^ 



(7) 



(8) 



where cc and /i are known, say positive, quantities. By reason of 

 what has been remarked about A and B, the values of « and /i 

 will be proportional to the intensity of the field. 



Finally from (7) and (8) the following four values of P are 

 obtained : 



Z2 = — k2 + a, 



-«, -k2 + /?, -kS-/?, 



so that in fact there must be seen a quadruplet in the spectrum. In 

 order that the four lines of this quadruplet may be perfectly sharp, 

 it is however necessary, that in a given magnetic field the quantities 

 a and f:t are independent of the direction into which the molecule 

 is turned, or, what comes to the same thing, that, for a given po- 

 sition of the molecule, a and /i are independent of the direction of 

 the magnetic force. 



Mr. Pannekoek has also remarked, that a similar reasoning ap- 

 plies when an arbitrary number, e. g. jj, frequencies k are equal. 

 In this case we come to the conclusion that, for a given position of the 



