By Sir John Frederick William Herschel
This Elibron Classics booklet is a facsimile reprint of a 1833 version by way of Longman, Rees, Orme, Brown, eco-friendly, & Longmans; and John Taylor, London. the cupboard Cyclopaedia.
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Extra resources for A treatise on astronomy
So the alternative solution can be ruled out “by inspection” in this case. As a rule, however, the other quadrant solution cannot be dismissed without further calculation. 5); the actual value need not even be calculated (although a numerical check is always a good idea) because the sign of cos H alone can resolve the ambiguity. The cosine function is double valued because, cos Q = cos(360 - Q) = cos(-Q), where Q is a given angle, but examination of sin Q resolves the ambiguity. The sine function is non-negative in both the ﬁrst (0° to 90°) and the second (90° to 180°) quadrants, whereas the cosine function is nonnegative in quadrants one and four (270° - 360°).
Note that no altitude can exceed 90° or be less than -90°, and that the azimuth may take any value between 0° and 360°. The azimuth coordinate may be considered in any of three ways: 7 An alternative convention is to measure the azimuth from the South point of the horizon westward. (1) The angle subtended at the center of the celestial sphere between the North point of the horizon and the intersection of the vertical circle through the object and the horizon (2) The arc length along the horizon subtended by the angle at the center (the observer) 16 2.
At the equinoxes, where (and when) it crosses the celestial equator, the Sun rises at the east point of the horizon, and sets at the west point. The azimuth of rise (or set) of the Sun on any given day depends both on its declination and on the observer’s latitude. Solving Eqn. 6) and on the horizon,12 h = 0, so that cos Arise set = sin d . 7) At d = 0°, cos A = 0, so that A = 90° and 270°, the azimuths of the east and west points of the horizon, respectively. Beginning at (Northern Hemisphere) winter solstice, the Sun rises further to the North each day, with decreasing azimuth, until it reaches summer solstice.
A treatise on astronomy by Sir John Frederick William Herschel