A spectator at the north pole has the pole of the heavens coincident with his zenith; and there, all declination circles are also vertical circles; and there, the equator coincides with the horizon; whereby the whole effect of the rotation of the earth there (15deg hourly) may be conceived to be given to the _horizon_: whilst, at the equator, the horizon is perpendicular to the equator, which therefore gives no such rotation at all to the horizon. Simple inspection of a celestial globe will illustrate this. Considering the matter thus, at the pole the rotation of the _horizon_ is 15deg hourly, and at the equator is 0, or nothing. But the sine of the latitude (=90deg) at the pole is unity, or 1; and the sine of the latitude (=0deg) at the equator is 0. Therefore, at these two extremes, the expression 15deg x sin. lat. actually does give the amount of _hourly apparent rotation of the horizon_; namely, 15deg at one place, and 0deg at the other. Now, as I understand the experiment, as given in the public prints, it is asserted that the same expression of 15deg x sin. lat. will give the _rotation of the horizon_ in intermediate latitudes; of which rotation I subjoin a table calculated for the purpose. +-----------+-------------+-----------------------+---------------------+ | | | Value of | Apparent | | | Natural | 15deg x Sin. Lat., | corresponding | | Degrees | Values of | or apparent | Times of _Horizon_, | | of | Sine of the | _hourly_ Amount of | performing | | Latitude. | Latitude. | Rotation of | one Rotation | | | | _Horizon_, in Degrees | of 360deg, in Hours | | | | and Decimals. | and Decimals. | +-----------+-------------+-----------------------+---------------------+ | deg | | deg | h | | 0 | 0.000 | 0.00 | Infinite time. | | 1 | 0.017 | 0.26 | 1371.0 | | 2 | 0.035 | 0.53 | 682.1 | | 3 | 0.053 | 0.79 | 458.5 | | 4 | 0.070 | 1.05 | 342.6 | | 5 | 0.087 | 1.31 | 255.4 | | 6 | 0.104 | 1.57 | 229.6 | | 7 | 0.122 | 1.83 | 169.9 | | 8 | 0.139 | 2.09 | 172.5 | | 9 | 0.156 | 2.35 | 153.4 | | 10 | 0.173 | 2.60 | 138.1 | | 20 | 0.342 | 5.13 | 70.2 | | 30 | 0.500 | 7.50 | 48.0 |