Semi-diameter of the sun is obtained readily from the Nautical Almanac for each ten-day period, for it must be remembered that the sun is continually changing its distance from the earth, and consequently the diameter of the former is increased and lessened slightly at different times of the year. For instance: On January 2d, when the earth is near perihelion and we are at our nearest point to the sun, the semi-diameter is 16´ 17´´.90, while on July 2d, when we are in the remote parts of the orbit, the semi-diameter is only 15´ 45´´.69, making a difference of over 32´´.
The moon being such a near neighbor of ours gives more trouble in determining her diameter. Besides being greatly affected by her rapidly changing distance from the earth, a further correction is occasioned by the fact that our position on the surface is nearer the moon at times than is the center of the earth. That is, when the moon is in the zenith we are 4000 miles, the earth’s radius, nearer that body than when she is in our horizon. It is evident that the direction of the moon in our sensible horizon is at right angles to a perpendicular erected at our place of observation and passing through the earth’s center, and this again makes it evident that the moon is about equally distant from the earth’s center and our position on the surface; but as she ascends the heavens she comes nearer our position until in the zenith the distance has been reduced by 4000 miles and the diameter appears correspondingly larger. Draw a diagram and see for yourself. This Augmentation of the Semi-diameter, due to the altitude, is found tabulated in Bowditch, Table 18.
The semi-diameter becomes too small to consider in ordinary navigation when observing any of the planets, and of course fixed stars are beyond its scope.
Refraction
Everyone knows that the blade of an oar when dipped in the water appears to be bent in a remarkable manner at the surface. This is a clear case of refraction. Should the oar, however, be held under everywhere at an equal depth, a square look downward at it would fail to show any refraction. So it becomes evident that refraction is caused by the rays of light passing obliquely from a rarer to a denser medium or vice versa. A ray of light coming from a heavenly body to the earth passes through a medium of gradually increasing density, from the thin outer air to the denser atmosphere at the surface of the earth. The ray of light consequently becomes curved downward and reaches the earth at a point nearer the heavenly body than would be the case if the light ray traveled in a straight line. The effect of this to the observer is that the body appears higher than it really is. The difference between the actual direction of the ray of light unaffected by the air, and our line of vision as we see the body, is the refraction.
The amount of refraction ordinarily affecting an observed altitude depends upon the distance of the body above the horizon. At the zenith, the rays of light, entering our atmosphere perpendicularly, are not deflected and refraction is nil. But, on the other hand, when the body is near the horizon, the rays of light pass through the atmosphere at a sharp angle and are consequently subject to the greatest bending, thus giving us our maximum refraction. In fact, this element becomes so unreliable in low altitudes that it is not advisable to observe a body when less than 10° or 13° above the horizon. This in no way concerns bearings taken of bodies in the horizon for amplitude, as refraction affects the altitude and not the azimuth of a body.
Dip
It is a well-known fact to every seaman that by going aloft, he can pick up a light sooner than on deck; that is, the higher his elevation the wider his horizon becomes. The horizon of a man in a small boat is only about 3 miles away, but, if he climbs to the bridge of a steamer some 60 feet above the water, he finds that the horizon has receded until he has a range of about 9 miles.
The fact that the horizon can be altered by changing the altitude should appeal to every navigator as a possible means of getting a horizon in foggy weather, by going aloft or getting as low as possible, provided the fog bank is lying above or close to the water.
The altitude of a body is measured to the visible horizon, yet the measurement must be adjusted to the sensible horizon before the true altitude can be obtained. This correction is accomplished by applying to the observed altitude the amount of the angle formed at the observers eye by the planes of the sensible and visible horizons. The angle is known as the dip of the horizon. It is readily seen that this angle always makes the observed altitude too large, for the eye if located at the exact surface of the sea, theoretically sees the sensible and visible horizons in one, while at every elevation above the surface it depresses the visible horizon correspondingly. It is, therefore, always necessary to apply the dip as found in Table 14, Bowditch, with a minus (-) sign.