We have, then, next to consider the difference between the clock used for the transit, or the sidereal clock, and an ordinary solar clock, or between a solar and a sidereal day. Let S, Fig. 122, represent the sun, and the arc a part of the orbit of the earth, the earth going in the direction of the arrow. Let 2 represent the position of the earth one day, and let 1 represent the position of the earth on the day before. A line drawn from the sun through the earth’s centre will give us the places _a_, _b_, on the earth at which it is midday on the side turned towards the sun, and midnight on the side turned from the sun. Now when a revolution of the earth with reference to the stars has been accomplished the earth comes to the second position, 2; and _c_ is the point of midday; and there is a certain angle here between _a_ and _c_, through which the earth must turn before it is noon at _a_, due to the change of position of the earth, or to the apparent motion of the sun among the stars, by which the sun comes to the meridian rather later than the stars each day. Now let us suppose that, while one observer in England is observing the sun at midday, another is observing the stars at the antipodes at midnight, the star is seen in the direction ⁎. We are aware that the stars are so far away, that from any point of the earth’s orbit they seem to be in absolutely the same place—they do not change their positions in the same way as the sun appears to do amongst them—an observer at _b_ therefore sees on his meridian the star ⁎ while the observer at _a_ sees the sun on his meridian; supposing _b_ to represent the same observer, on the second day, he will see the star due south before the other observer at _a_ sees the sun due south. The result of that is, that the sidereal day is shorter than the solar day, and the sun appears to lose on the stars. If we wish to have a clock to show 12 o’clock when the sun is southing, we shall want it to go slower by nearly four minutes a day than one which is regulated by the stars and is at 12 o’clock when our starting-point of right ascension—which is the intersection of those two fundamental planes, the equator and the ecliptic—passes over the meridian. One of the uses of the clock showing sidereal time in connection with the convenient fiction of the “Mean Sun,” is to give to the outside world a constant flow of mean time regulated to the average southing of the sun _in the middle of the period for which the sun is above the horizon each day in the year_.