( 96 ) 



where the sum is to be extended to all combinations of unequal 

 indices r and .s. 



I inferred from this equation, that a triplet can only be observed, 

 if three of tlie values k are equal, or, in other words, if the system 

 has three equivalent degrees of freedom. This will also be clear 

 when it is considered, that by a continuous decrease of the magnetic 

 field, the three components of the triplet may be made to coincide, 

 so that the simple spectral line, as seen out of the field, may be 

 considered as consisting of three coinciding lines. Applying the same 

 argument to Cornu's quadruplet, it seems natural to suppose that the 

 lines, which are apt to undergo this modification, consist already, 

 under ordinary circumstances, of four coinciding lines, or otherwise, 

 that now we have four equivalent degrees of freedom, or four equal 

 values le. 



Yet, the origin of a quadruplet cannot be explained by equation (4). 

 Indeed, if /ti, ^3, ^3, k^ are the frequencies having the same value k, 

 there are in each term of (4) at least two factors P + k^. Hence, 

 the equation must still have two equal roots — k^, and besides only 

 two roots, diifering very little from — k^. 



§ 7. It was however brought to the notice of the autiior by 

 Mr. A. Panxekoek that in this case equation (4) is incomplete, 

 because some of the terms neglected are of the same order of mag- 

 nitude as those retained, and that, by returning to equation (3), an 

 explanation of the quadruplet may be arrived at. 



If k^~ ^ h^ =z k^^ = ^/ =r k^, certainly four roots of equation (3), 

 if not = — k^, will differ only very little from this value. 



If l^ is one of these values (we need not occupy ourselves with 

 the other values of l^}, then the four quantities l^ -\- ^1^, l^ + V» 

 p ^_ /tgZ^ 12 ^_ ^.^2 yf[\\ \yQ small. On the other hand, the quantities 



Z2 + V. i' + h^ . . . P + k,? .... (5) 



will have values, which by no means become small. Since all the 

 quantities el are likewise small, the elements (5) of the determinant 

 will exceed by far all other elements, and we shall obtain a suffi- 

 cient approximation, when we take in the development of the 

 determinant only those terms, which contain all the quantities (5). 

 Evidently, the equation serving for the determination of the values 

 of I-, which differ only slightly from — k^, will therefore be 



