Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/447

is proportional to ±εU, and the fictitious charge on the surfaces of the dielectric is proportional to $\mp (\epsilon -1)U$. It is evident from this that if a plane condenser is charged to a given difference of potential, and is rotated in its own plane, the magnetic field produced is proportional to ε if (as in Rowland's experiment^[1]) the coatings are rotated while the dielectric remains at rest, but is in the opposite direction, and is proportional to (ε - 1) if (as in Röntgen's experiment) the dielectric is rotated while the coatings remain at rest. If the coatings and dielectric are rotated together, the magnetic action (being the sum of these) should be independent of ε—a conclusion which was verified later by Eichenwald.^[2]

Hitherto we have taken no account of the possible magnetization of the ponderable body. This would modify the equations in the usual manner,^[3] so that they finally take the form

${\begin{matrix}{\text{div }}&\mathbf {D} &=&\rho ,\qquad \qquad (I)\\{\text{div }}&\mathbf {B} &=&0,\qquad \qquad (II)\\{\text{curl }}&\mathbf {H} &=&4\pi \mathbf {S} ,\qquad \qquad (III)\\-{\text{curl }}&\mathbf {E} &=&\mathbf {\dot {B}} ,\qquad \qquad (IV),\end{matrix}}$

where S denotes the total current formed of the displacementcurrent, the convection-current, the conduction-current, and the current of dielectric convection. Moreover, since

$\mathbf {S} ={\bar {\rho \mathbf {v} }}+\mathbf {\dot {d}} /4\pi c^{2}$,

we have

${\begin{matrix}{\text{div }}\mathbf {S} &=&{\text{div }}{\bar {\rho \mathbf {v} }}&+&(1/4\pi c^{2}){\text{div }}(\partial \mathbf {\bar {d}} /\partial t)\\{\text{div }}\ &=&{\text{div }}{\bar {\rho \mathbf {v} }}&+&\partial {\bar {\rho }}/\partial t\end{matrix}}$,

1. Cf. p. 339.
2. Ann. d. Phys. xi (1903), p. 421; xiii (1904), p. 919. Eichenwald performed other experiments of a similar character, e.g. he observed the magnetic field due to the changes of polarization in a dielectric which was moved in a non-homogeneous electric field.
3. It is possible to construct a purely electronic theory of magnetization, a magnetic molecule being supposed to contain electrons in orbital revolution. It then appears that the vector which represents the average value of h is not H, but B.