The Modern Clock / A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair

by Ward L. Goodrich

The earth revolves about its axis with a circular motion; it revolves about the sun with an elliptical motion. This means that the earth will move through a greater angular distance, measured from the sun’s center, in a given time at some portions of its journey than it will do at others; at times the sun describes an arc of 57 minutes of the ecliptic; at other times an arc of 61 minutes in a day; hence the sun will be directly over a given meridian of the earth (noon) a little sooner at some periods than at others. Now the time at which the sun is directly over the given meridian is apparent noon, or solar noon. As before stated, this is irregular, while the motion of our clocks is regular, consequently the sun crosses the meridian a little before or a little after twelve by the clock each day, varying from 15 minutes before twelve to 15 minutes after twelve by the clock. The best we can do under these circumstances is to divide these differences of gaining or losing, take the average or mean of them and regulate the clock to keep mean time. Here then we have two times—the irregular apparent time and the regular mean apparent time. The amount to be added to or subtracted from the mean in order to get the solar or actual apparent time is called the equation of time and this is shown by the equation hand on an astronomical or perpetual calendar clock.

The moon revolves on its axis with a circular motion and it revolves about the earth with an elliptical motion, the earth being at one focus of the ellipse; as this course does not agree with that of the sun, but is shorter, it keeps gaining so that the lunar months do not agree with the solar.

Certain stars are so far away that they apparently have no motion of their own and are called fixed; hence in observing them the only motion we can discern is the circular motion of the earth. We can set our clocks by watching such stars and a complete revolution of the earth, measured by such a star, is called an astronomical or sidereal day. This is the one used in computing all our time. It is shorter than the mean solar day by 3 minutes 56 seconds.

A year is defined as the period of one complete revolution of the earth about the sun, returning to the same starting point in the heavens. By taking different starting points we are led to different kinds of years. The point generally taken is the vernal equinoctial point, and when measured thus it is called the tropical year, which gives us the seasons. It is 20 minutes shorter than the siderial year.

A siderial year is the period of a complete revolution of the earth about the sun. This period is very approximately 365 days, 6 hours, 9 minutes, 9.5 seconds of mean time. Here we see an important difference between the siderial and the civil year of 365 days, and it is this difference, which must be accounted for somehow, that causes the irregularities in our calendar work.

For ordinary and business purposes the public demands that the year shall contain an exact number of days and that it should bear a simple relation to the recurrence of the seasons. For this reason the civil year has been introduced. The Roman emperor, Julius Caesar, ordered that three successive years should have 365 days each and the fourth year should have 366 days.

The fourth year, containing 366 days, is called a leap year, because it leaps over, or gains, the difference between the civil and siderial time of the preceding three years. For convenience the leap year was designated as any year whose number is exactly divisible by 4. This is called the Julian calendar.

But as a siderial year is 365 days, 6 hours, 9 minutes, 9.5 seconds of mean time, the addition of one day of twenty-four hours would not exactly balance the two calendars; therefore Pope Gregory XIII., in 1582, ordered that every year whose number is a multiple of 100 shall be a year of 365 days, unless the number of the year is divisible by 400, when it shall be a leap year of 366 days.

The calendar constructed in this way is called the Gregorian calendar, and is the one in common use. Its error is very small and will amount to only 1 day, 5 hours, 30 minutes in 4,000 years.

The revolution of the moon around the earth in relation to the stars, takes place in 27 days, 7 hours and 43 minutes this is called a siderial month. But during this period the earth has advanced along the plane of its path about the sun and the moon must make up this distance in order to return to the same point in relation to the sun. This period is called a synodic month. Its average length is 29 days, 12 hours, 44 minutes, 2.9 seconds.