. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. tS be some celestial body. The geocentric parallax of the bodyIs the angle CSL. Let S be the same body in the angle LSG is the parallax of the body for that position,and is called its horizontal parallax. If we denote this hori-zontal parallax by P, the earths radius by i?,and the distance ofthe body from the earths centre by d, we have, by Trigonometry, sin P = a To find the parallax for any other position, as at 8, we repre-sent the angle LSGhj p, and the apparent zenith distance ofthe bod
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. tS be some celestial body. The geocentric parallax of the bodyIs the angle CSL. Let S be the same body in the angle LSG is the parallax of the body for that position,and is called its horizontal parallax. If we denote this hori-zontal parallax by P, the earths radius by i?,and the distance ofthe body from the earths centre by d, we have, by Trigonometry, sin P = a To find the parallax for any other position, as at 8, we repre-sent the angle LSGhj p, and the apparent zenith distance ofthe body, or the angle ZLS, by z, the sine of which is equalto the sine of its supplement SL G. We have from the tri-angle LSG, since the sides of a plane triangle are proportionalto the sines of their opposite angles, sin p __ R9 sin z ~~ d Combining this equation with the preceding, we have, sin p = sin P sin P and p are small angles, we may consider them pro-portional to their sines, and thus have, finally,p — P sir* z* The parallax, then, is proportional to the sine of the zenith. 56 PARALLAX. distance, and may be found for any altitnae when the hori-zontal parallax is known. It evidently decreases as the alti-tude increases, and in the zenith becomes zero. 55. Application of Parallax.—In order that observationsmade at different points of the earths surface may be com-pared, they must be reduced to some common point. Geo-centric parallax is applied to reduce any altitude observed atany place to what it would have been had it been observed atthe earths centre. We see from Fig. 21 that parallax acts ina vertical plane, and that the zenith distance of the body asobserved from the earths centre, or the angle ZOS, is less thanthe observed zenith distance ZLS, by the parallax OSL. Par-allax, then, is always subtractive from the observed zenith dis-tance, and additive to the observed altitude. The parallax above described is, strictly speaking, the paral-lax in altitude. Ther
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