80. _Inequality in the Length of Solar Days._--The sidereal days are all of the same length; but the solar days differ somewhat in length. This difference is due to the fact that the sun's apparent position moves eastward, or _away from the meridian_, at a variable rate. There are three reasons why this rate is variable:-- (1) The sun's eastward motion is due to the revolution of the earth in its orbit. Now, the earth's orbital motion is _not uniform_, being fastest when the earth is at perihelion, and slowest when the earth is at aphelion: hence, other things being equal, solar days will be longest when the earth is at perihelion, and shortest when the earth is at aphelion. [Illustration: Fig. 92.] [Illustration: Fig. 93.] (2) The sun's eastward motion is along the ecliptic. Now, from Figs. 92 and 93, it will be seen, that, when the sun is at one of the equinoxes, it will be moving away from the meridian _obliquely_; and, from Figs. 94 and 95, that, when the sun is at one of the solstices, it will be moving away from the meridian _perpendicularly_: hence, other things being equal, the sun would move away from the meridian _fastest_, and the days be _longest_, when the sun is at the _solstices_; while it would move away from the meridian _slowest_, and the days be _shortest_, when the sun is at the _equinoxes_. That a body moving along the ecliptic must be moving at a variable angle to the meridian becomes very evident on turning a celestial globe so as to bring each portion of the ecliptic under the meridian in turn. [Illustration: Fig. 94.] [Illustration: Fig. 95.] (3) The sun, moving along the ecliptic, always moves _in a great circle_, while the point of the meridian which is to overtake the sun moves in a diurnal circle, which is _sometimes a great circle_ and _sometimes a small circle_. When the sun is at the equinoxes, the point of the meridian which is to overtake it moves in a great circle. As the sun passes from the equinoxes to the solstices, the point of the meridian which is to overtake it moves on a smaller and smaller circle: hence, as we pass away from the celestial equator, the points of the meridian move slower and slower. Therefore, other things being equal, the meridian will gain upon the sun _most rapidly_, and the days be _shortest_, when the sun is at the _equinoxes_; while it will gain on the sun _least rapidly_, and the days will be _longest_, when the sun is at the _solstices_. The ordinary or _civil day_ is the mean of all the solar days in a year.