Fig. 30.—The equation of time.
53. Mean solar time.—To remedy these inconveniences there has been invented and brought into common use what is called mean solar time, which is perfectly uniform in its lapse and which, by comparison with sidereal time, loses exactly one day per year. "The time" in this system never differs much from true solar time, and the difference between the two for any particular day may be found in any good almanac, or may be read from the curve in [Fig. 30], in which the part of the curve above the line marked 0m shows how many minutes mean solar time is faster than true solar time. The correct name for this difference between the two kinds of solar time is the equation of time, but in the almanacs it is frequently marked "sun fast" or "sun slow." In sidereal time and true solar time the distinction between A. M. hours (ante meridiem = before the sun reaches the meridian) and P. M. hours (post meridiem = after the sun has passed the meridian) is not observed, "the time" being counted from 0 hours to 24 hours, commencing when the sun or vernal equinox is on the meridian. Occasionally the attempt is made to introduce into common use this mode of reckoning the hours, beginning the day (date) at midnight and counting the hours consecutively up to 24, when the next date is reached and a new start made. Such a system would simplify railway time tables and similar publications; but the American public is slow to adopt it, although the system has come into practical use in Canada and Spain.
54. To find (approximately) the sidereal time at any moment.—Rule I. When the mean solar time is known. Let W represent the time shown by an ordinary watch, and represent by S the corresponding sidereal time and by D the number of days that have elapsed from March 23d to the date in question. Then
S = W + 69/70 × D × 4.
The last term is expressed in minutes, and should be reduced to hours and minutes. Thus at 4 P. M. on July 4th—
| D | = | 103 days. |
| 69/70 × D × 4 | = | 406m. |
| = | 6h. 46m. | |
| W | = | 4h. 0m. |
| S | = | 10h. 46m. |
The daily gain of sidereal upon mean solar time is 69/70 of 4 minutes, and March 23d is the date on which sidereal and mean solar time are together, taking the average of one year with another, but it varies a little from year to year on account of the extra day introduced in leap years.
Rule II. When the stars in the northern sky can be seen. Find β Cassiopeiæ, and imagine a line drawn from it to Polaris, and another line from Polaris to the zenith. The sidereal time is equal to the angle between these lines, provided that that angle must be measured from the zenith toward the west. Turn the angle from degrees into hours by dividing by 15.
55. The earth's rotation.—We are familiar with the fact that a watch may run faster at one time than at another, and it is worth while to inquire if the same is not true of our chief timepiece—the earth. It is assumed in the sections upon the measurement of time that the earth turns about its axis with absolute uniformity, so that mean solar time never gains or loses even the smallest fraction of a second. Whether this be absolutely true or not, no one has ever succeeded in finding convincing proof of a variation large enough to be measured, although it has recently been shown that the axis about which it rotates is not perfectly fixed within the body of the earth. The solid body of the earth wriggles about this axis like a fish upon a hook, so that the position of the north pole upon the earth's surface changes within a year to the extent of 40 or 50 feet (15 meters) without ever getting more than this distance away from its average position. This is probably caused by the periodical shifting of masses of air and water from one part of the earth to another as the seasons change, and it seems probable that these changes will produce some small effect upon the rotation of the earth. But in spite of these, for any such moderate interval of time as a year or a century, so far as present knowledge goes, we may regard the earth's rotation as uniform and undisturbed. For longer intervals—e. g., 1,000,000 or 10,000,000 years—the question is a very different one, and we shall have to meet it again in another connection.