128 ASTRONOMY. 
part of his light will be reflected from the atmosphere to the surface of the 
earth. Thus, in fig. 22, let MGBD be the earth, and G a point on its sur- 
face for which the sun is just about to rise. It is now evident that the 
horizon HGR, of the point G, receives light from every part of the heavens, 
whether direct or reflected ; consequently the point A, for which the sun has 
not yet risen, has above its horizon the indirectly illuminated part, KLR, 
of the heavens. The morning redness is more brilliant at K, becoming 
vradually feebler towards R. The point B, on the contrary, has no light at 
all, and it is there midnight. The cause of evening twilight may be 
explained in the same manner, and it will be perceived that for the point D, 
where the sun is just setting, the whole horizon is still bright ; while for the 
point C, the part TNX of the heavens is only indirectly illuminated. A 
circle in the heavens, parallel to the horizon, and at a distance of 18° below 
it, is called the crepuscular circle, or circle of twilight. 
Let the point M (fig. 22) represent Leipzig, and the time be exactly 
noon; for the place G, situated 90° west, it will be past 6 o’clock A.M. ; for 
the place Y, 45° west, it will be 9 o’clock A.M.; and to this latter the sun, 
on account of refraction, will appear at J. It will moreover be seen that 
for a place III., situated 45° east, the sun will appear at i, and that it will 
there be already 3 o’clock P.M. Finally, it will be readily understood, that 
while the earth moves about its axis, whose north pole is P, from west to 
east, or in the direction of the arrows, it must seem as if the sun, in an 
inverse order, attained successively the points F, J,S, EK, U. Mig. 22 has 
been drawn to represent the time of the equinox, when the sun appears to 
describe the equator. . 
The morning and evening dawn or twilight is, in conclusion, not only 
more or less different in the same place at different seasons, but also different 
at places of different latitudes for the same season. 
The Tides. 
49. Another very remarkable phenomenon, produced by the attraction 
of the sun and moon upon the surface of the earth, is the ebb and flow of 
the tide, that well-known and generally regular motion of the sea, which 
results in a considerable variation of its height twice every day. On the 
coast of a great and open sea, as the North Sea, the phenomena of ebb and 
flow will take place in the following manner :—At the time when the water 
is highest, or at high tide, no change will be perceptible for some minutes. 
Gradually the water begins to run off westward, slowly at first, then with a 
continually increasing velocity, which reaches its maximum in about three 
hours. After this the fall continues for three hours with decreasing 
velocity, so that in a little more than six hours from the time of highest 
tide, low tide takes place. The sea, after remaining at this stage for some 
minutes, again begins to rise for six hours, and indeed in the same manner 
as it fell, so that in a little more than six hours from low tide, high tide 
again prevails. The rise of the water is called the flow of the tide, and 
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