184
MR. W. B. MORTON ON THE
(x y ζ) on the surface, are
.
This force acts in the normal to the surface, and is proportional to the surface-density at (x y ζ), which we shall call σ'. Therefore
But
;
therefore, denoting differentiation with respect to x y z by subscripts 1 2 3,
.
Now let σ be the surface-density at (x y z) on the moving conductor F(x y z)=C, then equating σ to the normal component of (f g h),
,
or putting in the values we have found for (f g h) in terms of φ
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.
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Now the perpendicular from the origin on the tangent plane to F(x y z)=C at the point (x y z) is
,
and the perpendicular from the origin on the tangent plane to F(x, y, kζ)=C at (x y ζ) is