596 



NATURE 



[October i8, 1900 



the electric force. For reasons which are stated, how- 

 ever, in a crystal, this third vector, the electric current, 

 is taken to represent the light vector. The consequences 

 of this theory are then worked out fully. The general 

 equations of the electromagnetic field are obtained from 

 the two laws (i) that the work done in carrying a 

 unit magnetic pole once round an electric current i is 

 4 TT/ ; and (2) that the work done in carrying a unit 

 quantity of electricity once round a magnetic current j is 



The phrase magnetic current is perhaps not a very 

 common one, though some English writers have used it. 

 The magnetic current multiplied by 4 tt is equal to the 

 rate of change of magnetic induction ; thus the second 

 law is merely Faraday's law of induction of electric 

 currents. 



In forming the equations care must be taken to 

 measure throughout in the same units, electrostatic or 

 electromagnetic, as the case may be. Prof. Drude 

 assumes that electric inductive capacity and permeability 

 have no dimensions and introduces a quantity, which 

 he tells us is of the dimensions of a velocity and equal to 

 thevelocity of light, as representing the ratio of the units. 

 The same result would have been reached more simply 

 by introducing two symbols, k^^ ^q, of unknown dimen- 

 sions to represent the inductive capacity and permeability 

 of a vacuum, and then showing that i/(»fo/xo)^ was of the 

 dimensions of a velocity. 



From the equations thus found, together with the 

 known electromagnetic laws expressing the action which 

 takes place at the common surface of two media, the 

 laws of transmission, reflexion and refraction in isotropic 

 and crystalline transparent bodies can, as is well known, 

 be deduced so long at least as we avoid phenomena of 

 dispersion. They lead to Fresnel's sine and tangent 

 laws for reflexion, and these in reality are not accurately 

 satisfied ; but it is shown that the small amount 

 of elliptic polarisation observed can be accounted 

 for by the supposition that the transition across 

 the interface is not sudden. On this point a refer- 

 ence to a paper in the PAt7. Trans, for 1894, Part ii., 

 by G, A. Schott, would not have been misplaced. In 

 fact, we may say that so long as the difference between 

 the properties of a refracting body and those of the ether 

 can be completely expressed by a change in the inductive 

 capacity, the simple equations of the electromagnetic 

 field suffice for the co-ordination of optical effects ; but 

 when this is no longer the case, when the supposition of 

 a mere change in refractive index is not sufficient to express 

 the action of the matter upon ether, modifications in the 

 equations which can not be entirely justified by reference 

 to known electromagnetic laws become necessary. 

 Absorption and dispersion, aberration and the action 

 of magnetism on light require further hypotheses for 

 their explanation, and the part of the book in which Prof 

 Drude deals with these and cognate phenomena is of 

 great interest. 



The phenomena of absorption and of metallic reflexion 

 are explained by the hypothesis that absorbing media are 

 conductors like the metals. 



The total current in such media is composed of two 

 parts, that of displacement or polarisation depending on 

 the rate of change of the electric force, and that of con- 

 NO. 1616, VOL. 62] 



duction proportional to the force. From this it follows 

 that in the equation for a component of the electric force, 

 X, for example, a term in aX/(i/ appears ; we have a 

 viscous as well as an elastic resistance to the motion. 

 Prof Drude points out, as Lord Rayleigh had done 

 nearly thirty years before (PAi7. Mag.^ 1872), that the 

 numerical results derived from experiments on the metals 

 cannot be reconciled with such a simple theory ; it needs 

 modification, and the direction of the requisite change is 

 indicated by the theory of dispersion which is discussed 

 next. 



Up to this point the theory has not been mechanical. 

 We know from purely electrical observations the laws of 

 electromagnetic force without needing to know the 

 mechanism, aitherial or material, to which that force is 

 due. Changes in the electric force give rise in a dielectric, 

 to an electric current. Maxwell's displacement current, and 

 the laws obeyed by this current in transparent bodies are 

 exactly those of light. 



The light vector may be electric displacement, or it 

 may be some periodic change in the ether, e.g^. a twist or 

 a displacement of the ether particles, which obeys exactly 

 the same laws as electric displacement ; we do not 

 know, and, so far as the theory is concerned, we do not 

 need to know, which of these hypotheses is true. 



When we are dealing with the action of matter, how- 

 ever, it becomes necessary to introduce some mechanical 

 conceptions. Thus Prof Drude, following von Helmholtz, 

 supposes that the molecules of a dielectric are composed 

 of charged ions which are set in motion by the electric 

 force when a train of light waves traverse the medium. 

 The current in this case across any section is made up 

 of the displacement current, together with the convection 

 current due to the displacement of the ions ; thus a new 

 variable, expressing the displacement of the matter, is 

 brought into Maxwell's simple equations. In conse- 

 quence a new set of equations, determining the motion of 

 the ions, become necessary. 



Now, the external force on an ion will be proportional 

 to its charge and to the electric force. Drude supposes 

 that, in addition, its motion is retarded by a force pro- 

 portional to its displacement, and by a frictional force. 

 Of course, since we are dealing only with harmonic 

 motion, this is merely equivalent to saying that the force 

 of restitution can be expressed by a series of harmonic 

 functions. In this way equations are obtained similar to 

 those given by Sellmeyer's mechanical theory — a theory, 

 as Lord Rayleigh has recently shown, originally due to 

 Maxwell — from which the phenomena of dispersion can 

 be deduced. The same hypotheses serve to overcome 

 the difficulties of a theory of metallic reflexion based on 

 conductivity. 



Fairly obvious modifications of the equations of motion 

 of the ions lead to explanations of the rotatory polarisa- 

 tion of sugar and quartz. The action of magnetism on 

 light is more complex ; it is deduced from an hypothesis 

 of molecular vortices. The ionic charges are supposed 

 to be in a state of rotation about the lines of magnetic 

 force, and the consequences of this on the equations of 

 motion are examined. This leads to a rational explana- 

 tion of the magnetic rotation of the plane of polarisation, 

 and of the Hall effect, while in another section the 

 Zeemann effect is touched on. The last chapter of the 



