MAGNUS80N — AN0MAL0U8 DISPERSION OF CYANIN. 267 



In the energy equation Helmholtz takes account of electro- 

 static, magnetic, electro-magnetic, and mechanical forces and de- 

 rives equations representing each. Finally, he applies the Prin- 

 ciple of Least Action considering variations to be present in 

 f, g, h„ f, g, li, and f, g., h, and derives an expression for the re- 

 fractive index. 



Heaviside 1 criticizes several points, especially the term elec- 

 tro-magnetic energy, and the application of the Principle of 

 Least Action. 



Ketteler 2 has shown that the dispersion formula developed by 

 Helmholtz, from the electro-magnetic theory, and the one pub- 

 lished by himself, based on the elastic solid theory, can be ex- 

 pressed by the same equation. 



, y, ^ ^ DA» a' -*.'„) 

 Mo - * - 1 =-2 (A3 _ A2m)a + g2 A 2 (29a). 



D g A 3 



2 Mo X = 2 (As _ A3m)2 +g 2 A 3 (29b). 



Where /* equals refractive index for wave length A. at perpen- 

 dicular incidence. 



Where X equals extinction index for wave length at perpen- 

 dicular incidence. 



Where A^ equals wave length in free ether of rays absorbed. 



Where D equals a constant depending, in the elestic theory, upon 

 the refractive index of infinitely long waves, and, in the 

 electro-magnetic theory, upon the dielectric constant of the 

 medium. These equations are usually termed the Ket- 

 teler-Helmholtz dispersion formula, and were tested by 

 Pfliiger 3 as described in the first part of this paper. 



i Heaviside, L. E. Vol. XXXVII., p. 470. 



a Ketteler, Wied. Ann. XL1X., p. 382 ; LIII., p. 823. 



a PflUger.Ibid., LXV., pp. 173, 225. 



