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
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
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Cite as
J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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