102 ASTRONOMY. 
produces an eclipse of the sun, whose extent, as in the case of the lunar 
eclipses, is given in digits (12 digits = diameter of the sun’s disk). Hence 
it follows that the limits of possible occurrence of eclipses are much more 
extended in the case of the sun than in that of the moon. Consequently it 
follows that, for the whole surface of the earth, the former are much more 
frequent than the latter, for on an average there may happen within 18 
years 41 eclipses of the sun and only about 29 of the moon. At least two 
eclipses of the sun must occur annually, because the sun every six months 
comes in the neighborhood of the moon’s ascending or descending node; 
while eclipses of the moon may be wanting for an entire year. But for any 
particular place on the surface of the earth, as, for instance, Leipzig. the 
visible eclipses of the moon are thrice as numerous as those of the sun. It 
may be assumed that every part of the earth’s surface may expect a partial 
eclipse of the sun within every two years, and a total within 200. Some- 
times, though but rarely, the number of solar and lunar eclipses for the 
entire earth may amount to seven in a year, occurring then in January, 
July, aad December. 
By the actual observation of a solar eclipse, its beginning and end can be 
determined much more accurately than the same circumstances of a lunar 
eclipse. For this reason observations on the former are much more certain 
assistants in determining geographical longitude. 
The course and extent of the moon’s shadow over the surface of the 
earth during a total or annular eclipse of the sun is shown by jig. 56, pl. 14. 
it represents also the manner in which the principal circumstances of such 
a phenomenon are usually delineated on a map. 
The Planetary Systems of Ptolemy, Copernicus, Tycho, and the Egyptians. 
Tabular Exhibition of the Most Important Features of our Planetary 
System. 
23. By a planetary system, the ancients understood the disposition and 
course of seven planets with respect to our earth. Since the time of 
Copernicus, however, by the solar system, in the ordinary acceptance of the 
term, is meant the disposition and mutual arrangement of 14 primary and 
19 secondary planets about our sun, which system is commonly termed the 
Copernican. By a solar system, taken generally, is understood any fixed 
star of the heavens, as a sun, with the spheres revolving about it as planets. 
Since astronomy has been pursued as a science, four planetary systems 
have had the greatest share of attention, being, in order of time, that of 
Ptolemy, the Egyptians, Copernicus, and Tycho. 
According to Ptolemy (an astronomer of Alexandria, living about a.p. 
150), the earth (pl. 7, fig. 1) stands immovably in the centre of 12 circles. 
From the earth outwards the seven first circles represent the paths of the 
following bodies as planets, and in the following order :—the Moon; Mer- 
cury; Venus; the Sun; Mars; Jupiter: and Saturn. The eighth circle, 
e, represents the path of the fixed stars; the ninth, d, and tenth, c, called 
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