502
PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD.
The equations of electric currents (C) remain as before.
The equations of electric elasticity (E) will be
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(82)
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where , , and are the values of for the axes of .
Combining these equations with (A) and (D), we get equations of the form
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(83)
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(104) If are the directions-cosines of the wave, and V its velocity, and if
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(84)
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then F, G, H, and will be functions of w, and if we put F', G', H', for the second differentials of these quantities with respect to , the equations will be
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(85)
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If we now put
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(86)
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and shall find
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(87)
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with two similar equations for G' and H'. Hence either
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(88)
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(89)
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or
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(90)
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The third supposition indicates that the resultant of F', G', H' is in the direction normal to the plane of the wave; but the equations do not indicate that such a disturbance, if possible, could be propagated, as we have no other relation between and F, G', H'.
The solution refers to a case in which there is no propagation.
The solution gives two values for corresponding to values of F, G', H', which