Page:A Dynamical Theory of the Electromagnetic Field.pdf/42

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If we determine from the equation


and F', G', H' from the equations




and the equations in (94) become of the form


Differentiating the three equations with respect to , and , and adding, we find that


and that


Hence the disturbances indicated by F', G', H' are propagated with the velocity through the field: and since

the resultant of these disturbances is in the plane of the wave.

(99) The remaining part of the total disturbances F, G, H being the part depending on is subject to no condition except that expressed in the equation

If we perform the operation on this equation, it becomes


Since the medium is a perfect insulator, , the free electricity, is immoveable, and therefore is a function of , and the value of J is either constant or zero, or uniformly increasing or diminishing with the time; so that no disturbance depending on J can be propagated as a wave.

(100) The equations of the electromagnetic field, deduced from purely experimental evidence, show that transversal vibrations only can be propagated. If we were to go beyond our experimental knowledge and to assign a definite density to a substance which