| tan E = | μ | cos lat = | T cos lat | , or E = | T cos lat | , |
| μ1 | 86400 | 8π |
(4)
if E is expressed in minutes, taking μ = 2π/86400; thus making the true latitude E nautical miles to the south of that given by the top (Revue maritime, 1890; Comptes rendus, 1896).
This can be seen by elementary consideration of the theory above, for the velocity of the vector OC′ of the top due to the rotation of the earth is
μ·OC′ cos lat = gMh sin E = μ1·OC′ sin E,
| sin E = | μ | cos lat, E = | T cos lat | , |
| μ1 | 8π |
(5)
| Fig. 11. |
in which 8π can be replaced by 25, in practice; so that the Fleuriais gyroscopic horizon is an illustration of the influence of the rotation of the earth and of the need for its allowance.
7. In the ordinary treatment of the general theory of the gyroscope, the motion is referred to two sets of rectangular axes; the Euler’s coordinate angles. one Ox, Oy, Oz fixed in space, with Oz vertically upward and the other OX, OY, OZ fixed in the rotating wheel with OZ in the axis of figure OC.