Mar. 1911.
of Relativity on Gravitational Astronomy.
391
Further, we put
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The modulus of the transformation is
. We also introduce
. If
is a small quantity of the first order, then
is of the second order. The cosines of the angles which the axis of the transformation makes with the axes of
are denoted by
so that
.
The transformation-formulæ are then—
|
(1)
|
We find easily
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(2)
|
and similarly for
and
.
Further,
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In these formulæ
and
are the projections of
and
on the axis of transformation:—
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If we put
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we can easily verify that the transformation-formulas for
are the same as those for
, viz.—
|
(3)
|