MAGNUSSON — ANOMALOUS DISPERSION OF CTANIN. 265 



number of papers, in which dispersion is discussed from several 

 points of view. To briefly state his views would be impossible, 

 still, the main idea in his works on dispersion seems to be this : 

 the mutual reactions between ether and matter, that is, the A' 

 and A forces, are unknown, and, hence, they should be elimi- 

 nated from equations. The total work done per unit of time 

 on the whole system is equated to the rate of change of kinetic 

 energy, and in this the mutual reactions do not appear. 1 Thus, 

 he obtains the f ollowing equation : 



m 



d 2 u d 2 U 



^T du + m' -^r dU = e V 2 u du - K U d U. (25). 



Where u, U are displacements and e the rigidity of ether in free 

 space. The notation is changed so as to make it uniform 

 throughout this paper. Those equations he combines with a 

 "second equation relating to the special mode of action of the 

 matter particles which can be no other than the renowned funda- 

 mental equation of Bessel's theory of the pendulum." This 2 he 

 writes : 



d 2 u d 2 U 



m dt 2 " c + m ' dt 2 " = — K u - (26). 



These equations would apply for transparent media, and when 

 absorption takes place terms are added for the reaction of the 

 matter on the ether. The fundamental equations then become 3 



d £ u d*U d 2 u dU 



m dt 2 "- m 'dF C==e d^" + bm ' U + cm '"dT (27a). 



d*u d 8 u dU 



■dF C + dt 2 ~ = - K ' U -g'-dt (27b). 



i Ketteler, Wied. Ann., XXI., p 201. 



a Ketteler, ibid. XXI., p. 201 ; XVIII., p. 413. 



* Ketteler, " Theoretische Optik," pp. 93-95. 



2 



