Page:DeSitterGravitation.djvu/23

410 The orbit thus remains fixed and plane after the transformation. Since

we find easily

If $$\mathrm{L}$$ and $$\mathrm{B}$$ are the longitude and latitude of the positive half of the axis of the transformation we have—

If the plane to be transformed is the plane of ($$x, y$$) itself, we have in the system ($$x, y, z, t$$) $$i_{0}=0$$. The transformed position of the plane is then defined by

or

Let the plane of ($$x, y$$) be the ecliptic, and consider another plane of which the inclination and node in the system ($$x, y, z, t$$) are $$i$$ and $$\Omega$$. In the system ($$x', y', z', t'$$) its inclination and node on the plane of ($$x', y'$$) are $$i + di$$ and $$\Omega + d\Omega$$, as given by the formulæ (40). Let its inclination on the transformed ecliptic be $$i + \Delta i, \Omega + \Delta \Omega$$. Taking unity for the denominator of $$\tan i'_0$$ in (41) we find easily—

or

If the transformed plane be the equator, we have—