DEPRESSION or DIP OF THE HORIZON is the angle through which the sea-horizon ap pears depressed in consequence of the elevation of the spectator.
Let A be a point on the surface of the earth, B a point situated in a vertical line from A. Let BH be a tangent to the earth's surface drawn from B, Bit a line in the same ver tical plane perpendicular to AB. The angle hBII is the true dip of the horizon to a spectator at B.
The true dip measured in minutes is equal to the distance in nautical miles of the visible horizon. Let C. be the center of curvature of the surface; then, since CHB is a right angle, the angle AIM = HCA; and the minutes in this angle are the nautical miles in the arc AIT. To find this angle in minutes or nautical miles, the rule is: Multiply the square root of the height in feet by 1.063.
The true dip of the horizon, however, is not exactly the same as its apparent. depression. The apparent sea-horizon is raised above its true place by refraction through an angle, which varies according to the state of the atmosphere and the relative temperatures of the air and water, the variation ranging from one third to one twenty-third of the amount of the true dip. The rule
commonly employed is to diminish the true dip by about one fourteenth of its amount, to find the apparent dip.
If S be a star or the sun in the same vertical plane with ABII, and an observation of the altitude above the sea-horizon be made by means of a sextant from the point B (as from the deck of a vessel), the apparent dip of the horizon must be subtracted from the observed angle, in order to find the altitude of the sun. Owing to the uncertainty of the amount of refraction, the nearest minute to the dip given in the tables is usually taken. The following table gives a sample of the amount of the apparent dip under ordinary state of the atmosphere and equal temperature of air and water. See Raper's Practice of Navigation.
Height. Dip. Height. Dip.
Feet. m. s. "eet. xn. 4.
0 0 0 8 2 50 1 1 0 9 3 0 2 1 20 10.... 3 10 3 140 20 4 20 4 2 0 30.... 5 20 5 2 10 40.... 6 10 6 2 20 '50 7 0 7 2 40 100 9 50