PHYSICAL ASTRONOMY. 127 
at A. Since the curve described by the refracted ray has its concavity 
tnferior, the tangent line As must lie above the unbroken ray AS; conse- 
quently the star S will, by means of the refracting atmosphere, appear 
higher above the horizon AH than it would were there no such atmosphere. 
Moreover, since the direction of the strata of air is the same in every 
direction about A, the ray cannot deviate laterally, but must always remain 
in the same vertical plane, SAC’, passing through the eye, the star, and the 
centre of the earth. 
From what precedes it is evident that refraction causes all the heavenly 
bodies to appear higher than they really are. Therefore, a star actually 
below the horizon may, by refraction, be raised above it, and become 
visible, which could not occur without the refracting atmosphere. Thus. 
for example, the sun, when actually at P, below the horizon AH of the 
observer, may be rendered visible by the curved line PgrA, of which Ap 
is the tangent, so as to be referred top. The amount of the astronomical 
refraction (to be distinguished from terrestrial refraction), for any given 
altitude in the heavens, depends mainly upon the character, density, tem- 
perature, and moisture of the atmosphere; and for this reason the accurate 
determination of refraction for al] heights, particularly for moderate ones, is 
one of the most difficult problems of physical astronomy. The following 
general considerations alone can here be mentioned: In the zenith there 
is no refraction, that is, it is equal to Zero; consequently, a star directly 
overhead will be seen in its true direction, or as if no refracting atmosphere 
surrounded the earth. The astronomical refraction increases from the 
zenith to the horizon, at first very slightly, afterwards more decidedly, so 
that a star situated near the horizon wili appear more distant from its true 
place than one at a greater altitude. The mean amount of refraction for a 
celestial body, midway between the zenith and horizon, or at an altitude of 
45°, is only 57 seconds, an amount scarcely sensible to the naked eye; but 
in the horizon, where refraction is greatest, it amounts to 83 minutes, which 
is more than the greatest apparent diameter of the sun or moon. 
48. A prominent consequence of the refraction and deviation of the rays 
of light is the morning and evening twilight. Night, as is well known, does 
not immediately follow the day, nor the day night; after the setting of the 
sun, his rays still penetrate the higher regions of the atmosphere, losing 
themselves in space. The night thus comes on gradually. This prolon- 
gation of day is known commonly as twilight, produced partly by reflection, 
partly by refraction. Let SO (jig. 22, pl. 6) be a ray of sunlight entering 
the atmosphere at O; then, instead of following the original direction, and 
leaving the atmosphere at M, it will be diverted from its course or become 
broken. This deviation will be the greater the further the ray penetrates 
into the lower strata, which are denser as they are situated nearer the earth, 
so that the ray will describe the curve OG. In like manner, the ray SZ 
will become a curve from Z to D. Since, as has already been shown in pi. 
6, fig. 16, this refraction is most considerable in the horizon, the sun appears 
to rise earlier and set later than is actually the case, by which means the 
day is lengthened and the night shortened. Before the rising of the sun, a 
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