Periodic changes of D and B may be called "electric" and "magnetic
vibrations." Properly choosing the units, the axes of coordinates (in
the first proposition also the positive direction of s and n), and
denoting components of vectors by suitable indices, we can express in
the following way the fundamental propositions of the theory.
(a) Let s be a closed line, [sigma] a surface bounded by it, n the
normal to [sigma]. Then, for all bodies,
_ _ _ _
/ 1 / / 1 d /
| H_s ds = --- | C_n d[sigma], | E_s ds = - --- --- | B_n d[sigma],
_/ c _/ _/ c dt _/
where the constant c means the ratio between the electro-magnet and
the electrostatic unit of electricity.
From these equations we can deduce:
([alpha]) For the interior of a body, the equations
[dP]H_z [dP]H_y 1
------- - ------- = --- C_x,
[dP]y [dP]z c
[dP]H_x [dP]H_z 1
------- - ------- = --- C_y,
[dP]z [dP]x c
[dP]H_y [dP]H_x 1
------- - ------- = --- C_z (12)
[dP]x [dP]y c
[dP]E_z [dP]E_y 1 [dP]B_x
------- - ------- = - --- -------,
[dP]y [dP]z c [dP]t
[dP]E_x [dP]E_z 1 [dP]B_y
------- - ------- = - --- -------,
[dP]z [dP]x c [dP]t
[dP]E_y [dP]E_x 1 [dP]B_z
------- - ------- = - --- -------; (13)
[dP]x [dP]y c [dP]t
(ß) For a surface of separation, the continuity of the tangential
components of E and H;
([gamma]) The solenoidal distribution of C and B, and in a dielectric
that of D. A solenoidal distribution of a vector is one corresponding
to that of the velocity in an incompressible fluid. It involves the
continuity, at a surface, of the normal component of the vector.
(b) The relation between the electric force and the dielectric
displacement is expressed by