There are, however, three different ways of reckoning time, or, as it is usually said, three kinds of time. One is sidereal time, which is indicated by the passage of stars across the meridian, and which measures the true period of the earth's rotation; another is apparent solar time, which is indicated by the passage of the sun across the meridian; and a third is mean solar time, which is indicated by a carefully regulated clock, whose errors are corrected by star observations. This last kind of time is that which is universally used in ordinary life (the use of sidereal time being confined to astronomy), so it is necessary to explain what it is and how it differs from apparent solar time.
Fig. 9. Sidereal and Solar Time.
C is the centre of the earth, and O the place of an observer on the earth's surface.
Suppose the sun at A to be in conjunction with the star S. Then, at the end of twenty-four sidereal hours, when the earth has made one turn on its axis and the place O has again come into conjunction with the star, the sun, in consequence of its yearly motion in the ecliptic, will have advanced to B, and the earth will have to turn through the angle A C B before O will overtake the sun and complete a solar day; wherefore the solar day is longer than the sidereal.
In the first place, the reason why sidereal time is not universally and exclusively used is because, although it measures the true period of the earth's rotation by the apparent motion of the stars, it does not exactly accord with the apparent motion of the sun; and, naturally, the sun, since it is the source of light for the earth, and the cause of the difference between day and night, is taken for all ordinary purposes, as the standard indicator of the progress of the hours. The fact that it is mid-day, or noon, at any place when the sun crosses the meridian of that place, is a fact of common knowledge, which cannot be ignored. On the other hand, the vernal equinox, which is the “noon mark” for sidereal time, is independent of the alternation of day and night, and may be on the meridian as well at midnight as at mid-day. Before clocks and watches were perfected, the moment of the sun's passage over the meridian was determined by means of a gnomon, which shows the instant of noon by the length of a shadow cast by an upright rod. Since the apparent course of the sun through the sky is a curve, rising from the eastern horizon, attaining its greatest elevation where it meets the meridian, and thence declining to the western horizon, it is evident that the length of the shadow must be least when the sun is on the meridian, or at its maximum altitude. The gnomon, or the sun-dial, gives us apparent solar time. But this differs from sidereal time because, as we saw in Part I, the sun, in consequence of the earth's motion round it, moves about one degree eastward every twenty-four hours, and, since one degree is equal to four minutes of time, the sun rises about four minutes later, with reference to the stars, every morning. Consequently it comes four minutes later to the meridian day after day. Or, to put it in another way, suppose that the sun and a certain star are upon the meridian at the same instant. The star is fixed in its place in the sky, but the sun is not fixed; on the contrary it moves about one degree eastward (the same direction as that of the earth's rotation) in twenty-four hours. Then, when the rotation of the earth has brought the star back to the meridian at the end of twenty-four sidereal hours, the sun, in consequence of its motion, will still be one degree east of the meridian, and the earth must turn through the space of another degree, which will take four minutes, before it can have the sun again upon the meridian. The true distance moved by the sun in twenty-four hours is a little less than one degree, and the exact time required for the meridian to overtake it is 3 min. 56.555 sec. Thus, the sidereal day (period of 24 hours) is nearly four minutes shorter than the solar day.
It would seem, then, that by taking the sun for a guide, and dividing the period between two of its successive passages over the meridian into twenty-four hours, we should have a perfect measure of time, without regard to the stars; in other words, that apparent solar time would be entirely satisfactory for ordinary use. But, unfortunately, the apparent eastward motion of the sun is not regular. It is sometimes greater than the average and sometimes less. This variation is due almost entirely: first, to the fact that its orbit not being a perfect circle the earth moves faster when it is near perihelion, and slower when it is near aphelion; and, second, to the effects of the inclination of the ecliptic to the equator. In consequence, another measure of solar time is used, called mean solar time, in which, by imagining a fictitious sun, moving with perfect regularity through the ecliptic, the discrepancies are avoided. All ordinary clocks are set to follow this fictitious, or mean, sun. The result is that clock time does not agree exactly with sun-dial time, or, what is the same thing, apparent solar time. The clock is ahead of the real sun at some times of the year, and behind it at other times. This difference is called the equation of time. Four times in the year the equation is zero, i.e., there is no difference between the clock and the sun. These times are April 15, June 14, Sept. 1, and Dec. 24. At four other times of the year the difference is at a maximum, viz. Feb. 11, sun 14 min. 27 sec. behind clock; May 14, sun 3 min. 49 sec. ahead of clock; July 26, sun 6 min. 16 sec. behind clock; Nov. 2, sun 16 min. 18 sec. ahead of clock. These dates and differences vary very slightly from year to year.
But, whatever measures of time we may use, it is observation of the stars that furnishes the means of correcting them.
Morehouse's Comet, October 15, 1908
Photographed at the Yerkes Observatory by E. E. Barnard with the ten-inch Bruce telescope. Exposure one hour and a half.
Note the detached portions which appeared to separate from the head and retreat up the line of the tail at enormous velocity.
Morehouse's Comet, November 15, 1908
Photographed at the Yerkes Observatory by E. E. Barnard, with the ten-inch Bruce telescope. Exposure forty minutes.