How to use a sextantA principle of optics states that the angle between the first and last directions of a ray of light that has suffered two reflections in the same plane is equal to twice the angle that the two reflecting surfaces make with each other. The sextant is based on this principle. The plane of reflection of the ray of light is the vertical plane through the line of sight. The two reflecting surfaces are the index mirror and the mirror half of the horizon glass. When the sextant is held vertically, it is in the plane of reflection, and the two mirrors, being perpendicular to this plane, insure that the ray of light is reflected in this plane. In Fig. 1002, let the sextant be held vertically, with the index arm so adjusted that the index mirror is parallel to the horizon glass, at which position the index mark coincides with the zero of the limb. A ray of light from the horizon will be reflected from the index mirror to the mirror half of the horizon glass, and from that mirror through the telescope to the observer's eye. The ray has now undergone two reflections in the same plane, and its final direction is inclined to its original direction by twice the angle between the two reflecting surfaces. But the reflecting surfaces are parallel: their inclination is zero. Therefore, the final and original rays are parallel. The reflected ray from the mirror half of the horizon glass therefore agrees with the ray seen direct through the clear part of the horizon glass. The reflected image of the horizon as seen in the horizon glass mirror should therefore be a continuation of the horizon as seen direct, as illustrated in Fig. 1003. When the sextant is set at zero, if the image is not a continuation of the horizon as seen direct, the horizon glass is not parallel to the index mirror and may be adjusted by means of adjusting screws. If the index arm of the sextant is set for an angle other than zero, say 5 degrees, then the index mirror will reflect a portion of the sky onto the mirror half of the horizon glass. The observer will see the horizon in the clear part of the horizon glass, and a reflection of the sky in the mirror half, as illustrated in Fig. 1004. Now suppose that it is desired to measure the angle between the horizon and some celestial body, such as the sun. The sextant angle observed, called hs, is illustrated in FIG. 1005 In Fig. 1007 this is the angle SMH. The observer, holding the sextant vertically, looks through the clear part of the horizon glass at the horizon, and then slowly moves the index arm from its zero position until the image of the sun is seen in the horizon mirror, and is tangent to the line of the horizon as seen through the clear glass, as illustrated in Fig. 1006. Refer to Fig. 1007. The ray of light, S, from the sun, is reflected in the line SABM, so that the image of S is seen in the horizon mirror tangent to the horizon. The final direction of the ray of light from S is BM, and the angle between its first and last directions is SMB = SMH. But, according to the law of optics previously stated, this angle is equal to twice the angle ACB, the angle between the two reflecting surfaces. Or, putting it another way, the angle ACB is equal to half the angle SMH. When the index arm was set at zero (Fig. 1002), the angle between the two mirrors was zero. The angle ACB between the two mirrors (Fig. 1007) is equal to the angular movement of the index arm along the arc, indicated by hs. But, since this angle is equal to one half the sextant altitude, the limb is graduated so that 0 degrees.5 of arc reads 1 degree. This graduation of the arc is carried out along its whole length, so that the are of 90 degrees on the limb is graduated to read 180 degrees. Therefore, although the angle measured, ACB, is equal to half of SMH, the limb is graduated so that we may read directly therefrom the value of the angle SMH, or the altitude of the body above the visible horizon. |
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