# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                3 Propagation of Electromagnetic Disturbances
in a Crystallised Medium

[(1]02) Let us now calculate the conditions of propagation of a
plane wave in a medium for which the values of k and [mu]
are different in different directions. As we do not propose to
give a complete investigation of the question in the present
imperfect state of the theory as extended to disturbances of short
period, we shall assume that the axes of magnetic induction
coincide in direction with those of electric elasticity. <s> and that
(as in the case of an isotropic medium) the terms including [psi] have
nothing to do with the result.<\s>

(103) Let the values of the magnetic coefficient for the three axes be [lambda], [mu], [nu],
then the equations of magnetic force (b) become
[lambda][alpha] = dH/dy - dG/dz
[mu][beta] = dF/dz - dH/dx
[nu][gamma] = dG/dx - dF/dy }(81)

The equations of electric currents (C) remain as before
The equations of electric elasticity (E) will be
P = 4[pi]a<sup>2<\sup>f
Q = 4[pi]b<sup>2<\sup>y
R = e[pi]c<sup>2<\sup>h } (82)
where 4[pi]a<sup>2<\sup>, 4[pi]b<sup>2<\sup>, 4[pi]c<sup>2<\sup> are the values of k for the <s>different<\s> axes of x, y, z
Combining these equations with (A) and (D) we get equations of the form
1/[mu][nu]([lambda] d<sup>2<\sup>F/dx<sup>2<\sup> + [mu]d<sup>2<\sup>F/dy<sup>2<\sup> + [nu]d<sup>2<\sup>F/dz<sup>2<\sup>) - 1/[mu][nu] d/dx([lambda] dF/dx + [mu]dG/dy + [nu]dH/dz) = 1/d<sup>2<\sup> (d<sup>2<\sup>F/dt<sup>2<\sup> + d<sup>2<\sup>[psi]/dxdt) (83)

(104) If l m n are the direction - cosines of the wave and V its velocity
and if lk + my + nz - Vt = w (84)
then F G H & [psi] will be functions of w and if we put F' G' H' [psi]' for
the second differentials of these quantities with respect to w, <s>then<\s> the equations
will be

```
images

## Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
IIIF (What's this?)
This is a link to the IIIF web URL for this item. You can drag and drop the IIIF image link into other compatible viewers

## Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7