American Horological Journal, Vol. I, No. 1, July 1869: Devoted to Pratical Horology

by Unknown

Nothing can be more interesting in the study of astronomy than its chronological value. La Place says: “Whole nations have been swept from the earth, with their languages, arts, and sciences, leaving but confused masses of ruins to mark the place where mighty cities stood; their history, with but the exception of a few doubtful traditions, has perished; but the perfection of their astronomical observations marks their high antiquity, fixes the periods of their existence, and proves that even at that early time they must have made considerable progress in science.”

The earth revolving around the sun in an ellipse, the position of the major axis of the orbit would indicate something in regard to eras in astronomy extending not only beyond the historical period, but so far back in the past that imagination is almost at fault. The position of the major axis of the orbit depends on the direct motion of the perigee and the precession of the equinoxes conjointly, the annual motions respectively being 11´´.8 and 50´´.1, the two combined motions being 61´´.9 annually. A tropical revolution is made in 209.84 years. This being a constant quantity, we may ascertain when the line of the major axis coincided with the line of the equinoxes. This occurrence took place about 4,000 or 4,090 years before the year 0. In the year 6,483 the major axis will again coincide with the line of the equinoxes, but then the solar perigee will coincide with the vernal equinox. So, it will be seen that the period of revolution is 20,966 years. But in the progress of this revolution there must have been a time when the major axis was perpendicular to the line of the equinoxes. A simple calculation will show that the eventful year was 1250; and so important is this event considered, that La Place, the immortal author of the Méchanique Céleste, proposed to make the vernal equinox of this year the initial day of the year 1 of our era. Again, at the solstices the sun is at the greatest distance from the equator; consequently the declination of the sun is equal to the obliquity of the ecliptic. The length of a shadow cast at noonday from the stile of an ordinary sun-dial would accurately determine the precise time on which this position occurs.

Though wanting in accuracy, such a measurement is of interest, from the fact that there are recorded observations of this kind that were taken in the city of Layang, in China, 1100 years before our present era is dated. This observation gives the zenith distance of the sun at the moment of the observation. Half the sum of the zenith distances gives the latitude, and half their difference gives the obliquity of the ecliptic at the period. Now the law of the variation of the ecliptic is well known, and modern computation has verified both the moment of taking the observation and the latitude of the place. Eclipses were the foundation of the whole of Chinese chronology, and recorded observations prove the civilization of that strange race for 4700 years.

Horology, with astronomy, was not neglected even as early as 3102 years before Christ, as the following will show.

The cycles of Jupiter and Saturn are very unequal, the latter being a period of 918 years; the mean motion of the two planets was determined by the Indians in that part of the respective orbits where Saturn’s motion was the slowest and Jupiter’s the most rapid. This observed event must have been 3102 years before, and 1491 after the year 0; but the record shows that the observation was taken before the last-named date.

Since both solar and sidereal time is estimated from the passage of the sun and the equinoctial point across the meridian of the place of observation, the time will vary in different places by as much as the passage precedes each. It being obvious that when the sun is in the meridian at any one place, it is midnight at a point on the earth’s surface diametrically opposite; so an observation taken at different places at the same moment of absolute time, will be recorded as having happened at different times. Therefore when a comparison of these different observations is to be made, it becomes necessary to reduce them by computation to what the result would have been had they been taken under the same meridian at the same moment of absolute time. Sir John Herschel proposed to employ mean equinoctial time, which is the same for all the world. It is the time elapsed from the moment the mean sun enters the mean vernal equinox, and is reckoned in mean solar days and parts of days. This difference in time is really the angular motion of the earth, and by measuring it the longitude of any place on the surface of the earth can be determined, provided we have a standard point of departure, and an instrument capable of accurately dividing the time into small quantities during its transit from the meridian on which it was rated.

As will be hereafter shown, the axis of the earth’s rotation is invariable. Were the position of the major axis of the earth’s orbit as immutable, an observation of any star on the meridian taken at any place would always be the same. Again, the form of the earth has an important effect; the equatorial diameter exceeds the polar, thus giving a large excess of matter at the equator. Now the attraction of an external body not only draws another to it in its whole mass, but, as the force of attraction is inversely as the square of the distance, it follows that the attracted body would be revolved on its own centre of gravity until its major diameter was in a straight line with the attracting body.

The sun and moon are both attracting bodies for the earth; the plane of the equator is at an angle to the plane of the ecliptic of 23° 27´ 34´´.69, and the plane of the moon’s orbit is inclined to it 5° 8´ 47´´.9 Now from the oblate form of the earth, the sun and moon, acting obliquely and unequally, urge the plane of the equator from its own position from east to west, thus changing the equinoctial points to the extent of 50´´.41 annually.

This action, were it not compensated by another force, would in time alter the angle of the ecliptic until the equatorial plane and the ecliptic coincided. There are few but have seen the philosophical toy called the Gyrascope. This toy, on a miniature scale, gives a fine illustration of the force brought in to correct the combined action of the sun and moon on the obliquity of the equator. The rotation of the earth is held in its own plane by its own revolution, the same as the gyrascope seems to overcome the laws of gravitation by its force of revolution.

But not only do the sun and moon disturb the plane of the ecliptic, but the action of other planets on the earth and sun is to be taken into account. A very slow variation in the position of the plane of the ecliptic, in relation to the plane of the equator, is observed from these influences. It must be remembered that a very slight deviation in the angle can and would be detected by observation with modern instruments. We do find that this attraction affects the inclination of the ecliptic to the equator of 0´´.31 annually.