340 KEPORT— 1893. 



Mathematical Representations tested hy VerdeVs Experiments on 

 Magnetic Dispersion. 



5. The use of the term of type k^ to explain magnetic rotation was 

 arrived at by Maxwell ' by the help of a provisional theory of molecular 

 vortices, in which it occurs as standing for the reaction of a vortical 

 motion of the medium representing its magnetisation, when that motion 

 is disturbed by the light- vibrations passing through it. 



A very full examination has been made by Verdet ^ of the manner in 

 which the constant of magnetic rotation (hence called Verdet's constant) 

 depends on the direction of the ray with regard to the magnetic force, on 

 the refractive power of the medium, on the dispersive power of the 

 medium, and in the same medium on the wave-length of the light. The 

 rotation comes out, as has since been verified in detail by Du Bois, to be 

 proportional simply to the component of the magnetic force along the 

 ray. Media of great refractive power have in general high magnetic 

 rotatory power. For the same medium the product of the rotatory 

 power and the square of the wave-length is nearly constant, but always 

 increases slightly with the index of refraction ; media of great dispersive 

 power have in general also high rotatory dispersion. 



Verdet's most important piece of work is, however, a precise comparison 

 of his experimental numbers for different wave-lengths with the results of 

 a mathematical formula adapted to express both ordinary dispersion and 

 the magnetic rotation according to Maxwell's theory. He assumes 

 Cauchy's form of the ordinary dispersion terms, and so obtains equations 

 equivalent to 



from which is derived (Maxwell, 'Treatise,' §§ 828-830) the formula 

 connecting 0, the rotation, with m, a specific constant for the medium ; 

 y, the magnetic force resolved along the ray ; c, the length of path of the 

 ray on the medium ; X, the wave-length of the light in air ; and i, the 

 index of refraction of the medium. This formula is 



d=mcy — ; I i-X ---]. 



l=:mcy -^ I * • 



dXj 



The comparison with experiment leads to agreement within the possible 

 errors of observation (Maxwell, loc. cit.) for the case of bisulphide of 

 carbon, but for the ordinary creosote of commerce the agreement is not 

 so good. The fact that creosote is a chemically complex substance, or 

 rather a mixture of diSerent substances, may be of influence here. 



A coefficient of the type k2 leads also to the general law of proportion- 

 ality to the inverse square of the wave-length, but does not correspond 

 nearly so well in detail as k, ; a coefficient of the type k-^ (C. Neumann's) 

 must be rejected altogether. 



It is to be borne in mind that it is only in substances with regular 

 dispersion that Cauchy's dispersive terms can be taken to represent the 

 facts ; whereas the />2 rotatory term is, as we have seen, related to a free 

 period of some kind in the system, and therefore to abnormal dispersion. 



' J. C. Maxwell, Phil. Mag., 1861 ; Treatise, § 822, scq. 



^ E. Verdet, Comptes Bendvs, 1863 ; Annales de Chimie (.S), Ixix. ; in (Euvres, vol. i. 

 p. 265. 



