. Astronomy for students and general readers . e precedingsections. (I). At the poles = 90°,tan 0 = infinity, and therefore cos h = infinity. But the cosine ofan angle can never be greater than unity; there is therefore no valueof h which fulfils the condition. Hence, a star at the pole canneither rise nor set. (2). At the earths equator * = 0°, tan ^ = 0, whence cos A = 0,h = 90°, and 2 A = 180°, whatever be 6. This being a semicircum-ference all the heavenly bodies are half the time above the horizon toan observer on the equator. (3). If (5 = 0° (that is, if the star is on the celestial equa
. Astronomy for students and general readers . e precedingsections. (I). At the poles = 90°,tan 0 = infinity, and therefore cos h = infinity. But the cosine ofan angle can never be greater than unity; there is therefore no valueof h which fulfils the condition. Hence, a star at the pole canneither rise nor set. (2). At the earths equator * = 0°, tan ^ = 0, whence cos A = 0,h = 90°, and 2 A = 180°, whatever be 6. This being a semicircum-ference all the heavenly bodies are half the time above the horizon toan observer on the equator. (3). If (5 = 0° (that is, if the star is on the celestial equator), thentan (! = 0, and cos A = 0, A = 90°, 2 ^ = 180°, so that all stars onthe equator are half the time above the horizon, whatever be the lati-tude of the observer. Here we except the pole, where, in this case,tan 9 tan (5 = a X 0, an indeterminate quantity. In fact, a star onthe celestial equator will, at the pole of the earth, seem to move roundin the horizon. (4). The above value of cos h may be expressed in the form:. Fig. 15.—upper and lower Drmi- NAL ARCS. cos A = — tan <5cot l/) tan 6 tan (90° — This shows that when S lies outside the limits + (90° — 0) and_ (90° — ^\ cos Ti will lie without the limits — 1 and + 1, andthere will be no value of h to correspond. Hence, in this case, thestars neither rise nor set. These limits correspond to those of per-petual apparition and perpetual disappearance. (5). In the northern hemisphere ^ and tan. ^ are positive.^ w^lwhen 90°, 2 A > 180. With 46 ABTRONOMT. negative i, cos A is positive, h < 90°, 2 A. < 180°. Hence, in north-ern latitudes, a northern star is more than half of the time ahove thehorizon, and a southern star less. In the southern hemisphere, ^ andtan (p are negative, and the case is reversed. (6). If, in the preceding case, the declination of a body is supposedconstant and north, then the greater we make (p the greater the nega-tive value of cos A and the greater
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