100 ASTRONOMY. 
equation of the orbit, and is one of the most essential elements in the theory 
of the planetary motions. For, knowing the equation of the orbit, the sum 
of the mean anomaly and the equation of the orbit gives the true anomaly, 
and consequently the true—-that is, the elliptic longitude of a planet in its 
orbit. In conclusion, P is the perihelion and A the aphelion of the planet, 
in which points it will be respectively at its least and greatest distances from 
the sun. 
ficlipses of the Sun and Moon. 
22. We come now to eclipses of the sun and moon (pi. 6, fig. 18). The 
full moon at times loses gradually its light in a manner just as if a blackish 
grey disk were drawn slowly over its face, moving from left to right, and 
passing off on the opposite side. An eclipse of the moon is then said to 
take place, which, as it only occurs when the moon is full, and, indeed, 
when the full moon is in or near the straight line connecting the centres of 
the sun and earth, is of easy explanation. The earth, as an opake globe 
illuminated by the sun, must throw a shadow into space on the side oppo- 
site to the sun, this shadow being conical, and longer than the distance of 
the mvon from the earth. The moon must also, as a body likewise illu- 
minated by the sun, lose partly or entirely her light by passing partly or 
entirely into the shadow of the earth. If the moon’s orbit lay in the plane 
of the ecliptic, it is clear that an eclipse would occur at every full moon, 
which experience shows not to be the case. We learn above, section 8, 
that the path of the moon is inclined 5° 8’ 48” to the ecliptic ; the full moon 
passes for the most part, therefore, above or below the earth’s shadow, and 
it is only when the full moon happens in or near one of the moon’s nodes, 
that the moon can encounter the earth’s shadow. As the moon’s nodes do 
not remain in the same part of the ecliptic, it is very evident that the 
eclipses of the moon (and sun) must take place in different years and 
months, so that definite periods arise, after whose lapse the eclipses again 
occur in the same months. 
Astronomy teaches the conditions necessary for the occurrence of an 
eclipse. Should the full moon be situated at a distance from one of its 
nodes of less than 123°, the moon may be partially eclipsed. Should the 
distance be less than 93°, and greater than 53°, a partial eclipse must take 
place. The eclipse will be total, that is, the moon will be entirely obscured, 
when the full moon takes place at less than 54° from one of the nodes. A 
merely partial eclipse of the moon cannot last more than 2 hours and 18 
minutes ; the time of a partial, and at the same time total eclipse, may 
amount to 4 hours and 24 minutes. Astronomers are accustomed to deter- 
mine beforehand the particular circumstances of an eclipse of the moon, as 
the beginning, the middle, and the end of the obscuration, the countries in 
which it will be visible, as well as the size of the eclipsed portion. The 
latter is given in digits (1 digit = ;, of the diameter of the disk). Unfor- 
tunately, however, the period of beginning and ending of an eclipse cannot 
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