Page:PoyntingTransfer.djvu/5

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(5)

where P', Q', R' are put for the parts of P, Q, R which do not contain the velocities.

Then

where X, Y, Z are the components of the electromagnetic force per unit of volume (Maxwell, vol. ii, p. 227).

Now substituting in (4) and putting for their values in terms of the magnetic force (Maxwell, vol. ii, p. 233) and transposing we obtain

[Integrating each term by parts)]

(The double integral being taken over the surface)

(6)

where are the directioncosines of the normal to the surface outwards.