Stargazing: Past and Present

by Sir Norman Lockyer

The first method of measuring the angle was to measure the length of the sun’s shadow at each solstice, and so, by comparison of the length of the shadow with the height of the gnomon, calculate the difference in altitude, the half of which was the angle sought. And this was probably the method of the Chinese, who obtained a result of 23° 38´ 11˝ in the time of Yao; and also of Anaximander in his early days, who obtained a result of 24°. But before trigonometrical tables, the first of which seem to have been constructed by Hipparchus and Ptolemy, were known, in order to find this angle it was constructed geometrically, and then what aliquot part of the circumference it was, or how much of the circumference it contained was determined; for the division of the circle into 360° is subsequent to the first beginning of astronomy—and hence it was that Eratosthenes said that the distance from the tropics was 11
83 of the circumference, and not that it was 47° 46´ 26˝.

The gnomon is, without exception, of all instruments the one with which the ancients were able to make the best observations of the sun’s altitude. But they did not give sufficient attention to it to enable it to be used with accuracy. The shadow projected by a point when the sun is shining is not well defined, so that they could not be quite certain of its extremity, and it would seem that the ancient observations of the height of the sun made in this manner ought to be corrected by about half the apparent diameter of the sun; for it is probable that the ancients took the strong shadow for the true shadow; and so they had only the height of the upper part of the sun and not that of the centre. There is no proof that they did not make this correction, at least in the later observations.

In order to obviate this inconvenience, they subsequently terminated the gnomon by a bowl or disc, the centre of which answered to the summit; so that, taking the centre of the shadow of this bowl, they had the height of the centre of the sun. Such was the form of the one that Manlius the mathematician erected at Rome under the auspices of Augustus.

But in comparatively modern times astronomers have remedied this defect in a still more happy manner, by using a vertical or horizontal plate pierced with a circular hole which allows the rays of the sun to enter into a dark place, and in fact to form a true image of the sun on a floor or other convenient receptacle, as we find is the case in many continental churches.

Of course at this early period the reference of any particular phenomenon to true time was out of the question. The ancients at the period we are considering used twelve hours to represent a day, irrespective of the time of the year—the day always being reckoned as the time between sunrise and sunset. So that in summer the hours were long and in winter they were short. The idea of equal hours did not occur to them till later; but no observations are closer than an hour, and the smallest division of space of which they took notice was something like equal to a quarter or half of the moon’s diameter.

When we come down, however, to three centuries before Christ, we find that a different state of things is coming about. The magnificent museum at Alexandria was beginning to be built, and astronomical observations were among the most important things to be done in that vast establishment. The first astronomical workers there seem to have been Timocharis and Aristillus, who began about 295 B.C., and worked for twenty-six years. We are told that they made a catalogue of stars, giving their positions with reference to the sun’s path or ecliptic.

It was soon after this that the gnomon gave way to the invention of the Scarphie. It is really a little gnomon on the summit of which is a spherical segment. An arc of a circle passing out of the foot of the style was divided into parts, and we thus had the angle which the solar ray formed with the vertical. Nevertheless the scarphie was subject to the same inconveniences, and it required the same corrections, as the gnomon; in short, it was less accurate than it. That did not, however, hinder Eratosthenes from making use of it to measure the size of the earth and the inclination of the ecliptic to the equator. The method Eratosthenes followed in ascertaining the size of the earth was to measure the arc between Syene and Alexandria by observing the altitude of the sun at each place. He found it to be 1
50 of the circumference and 5,000 stadia, so that if 1
50 of the circumference of the earth is 5,000 stadia, the whole circumference must be 50 times 5,000, or 250,000 stadia.[^[5]]

Fig. 6.—The First Meridian Circle.

And now still another instrument is introduced, and we begin to find the horizon altogether disregarded in favour of observations made on the meridian.