. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. oes not materially differ from the arcitself, hence, the preceding equation becomes the following, withoutany essential error. That is, x=p cos. altitude. Or, in words, tlie parallax in altitude is equal to the horizontalparallax multiplied into the cosine of the apparent altitude ( radiusbeing unity ). EXAMPLES. 1. The apparent altitude of the moons center after being correctedfor dip and refraction was 31° 25; and its horizontal parallax atthat time, taken from a
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. oes not materially differ from the arcitself, hence, the preceding equation becomes the following, withoutany essential error. That is, x=p cos. altitude. Or, in words, tlie parallax in altitude is equal to the horizontalparallax multiplied into the cosine of the apparent altitude ( radiusbeing unity ). EXAMPLES. 1. The apparent altitude of the moons center after being correctedfor dip and refraction was 31° 25; and its horizontal parallax atthat time, taken from a nautical almanac, was 57 37; what was thecorrection for parallax, and what was the true altitude as seen fromthe center of the earth ? p=5T 37=3457 log. - - ° 25cos. - - x=49 10=2950 log. - - . Ans. Cor. for parallax 49 10True altitude 32° 13 102. The apparent altitude of the moons center on a certain occa-sion was 42° 17; and its horizontal parallax at the same time was58 12; what was the parallax in altitude, and what was the moonstrue altitude? Ans. Parallax in alt. 43 4 True alt. 43° 0 4. 202 CELESTIAL OBSERVATIONS. No other examples of this kind are necessary, as they will inciden-tally occur in several places further on. It now remains to describe the instrument used for taking anglesat sea. We, therefore, give the following illustrations on the QUADRANT AND SEXTANT. The quadrant and sextant are essentially the same instrument,and the following is an explanation of the principle on which theyare constructed. Let ABC be a section of a reflecting sur-face, FB a ray of light falling upon it, andreflected again in the direction BE, and BDa perpendicular at the point of impact; thenit is a well known optical fact, that the anglesFB C and EBA are equal, and that FB, DB, and EB are in thesame plane. Again, if A C were a reflecting surface,and a ray of light, SB, from any celestialobject S, were reflected to an eye at E, theimage of the object wou
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