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The ancients called the places occupied by the sun when highest and lowest the Solstices, and the intermediate positions the Equinoxes. The first instrument made was for the determination of the sun’s altitude in order to fix the solstices. This instrument was called the Gnomon. It consisted of an upright rod, sharp at the end and raised perpendicularly on a horizontal plane, and its shadow could be measured in the plane of the meridian by a north and south line on the ground. Whenever the shadow was longest the sun was naturally lowest down at the winter solstice, and vice versâ for the summer solstice.

Here then we leave observations on the horizon and come to those made on the meridian.

The Gnomon is said to have been known to the Chinese in the time of the Emperor Yao’s reign (2300 B.C.), but it was not used by the Greeks^[4] till the time of Thales, about 585 B.C., who fixed the dates of the solstices and equinoxes, and the length of the tropical year—that is, the time taken by the sun to travel from the vernal equinoctial point round to the same point again.

The next problem was to discover the inclination of the ecliptic, or, what is the same thing, the amount that the earth’s equator is inclined to the ecliptic plane (represented by the surface of the water in our tub).

Now in order to ascertain this, the angular distance between the positions occupied by the sun when at the solstices must be measured; or, since one solstice is just as much below the equinoctial line as the other is above it, we might take half the angle between the solstices as being the obliquity required.

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.

The instrument in question was probably the invention of Eratosthenes. It consisted of two circles of nearly the same size crossing each other at right angles, (Fig. 6); one circle represented the equator and the other the meridian, and it was employed as follows:—

The circle A was fixed perfectly upright in the meridian, so that the greatest altitude of the sun each day could be observed; the circle B was then placed exactly in the plane of the earth’s equator by adjusting the line joining C and D to the part of the heavens between the Bears, about which the stars appear to revolve. This done, the occurrence of the equinox was waited for, at which time the shadow of the part of the circle E must fall upon the part marked F, so as exactly to cover it.

Fig. 7.—The First Instrument Graduated into 360° (West Side).

We now come to the time when the circle began to be divided into 360 divisions or degrees—about the time of Hipparchus (160 B.C.). There are two instruments described by Ptolemy for measuring the altitude of the sun in degrees instead of in fractions of a circle. They, like the gnomon, were used for determining the altitude of the sun. The first, Fig. 7, consisted of two circles of copper, one, C D, larger than the other, having the smaller one, B, so fitted inside it as to turn round while the larger remained fixed. The larger was divided into 360°, and the smaller one carried two pointers. This instrument was placed perfectly upright and in the plane of the meridian, and with a fixed point, C, always at the top by means of a plumb-line hanging from C over a mark, D. On this small circle are two square knobs projecting on the side, E and F. When the sun was on the meridian the small circle was turned so as to bring the shadow of the knob E over the knob F, and then the degree to which the pointer pointed was read off on the larger circle. And of course, as the position of the knobs had to be changed as the sun moved in altitude, the angle through which the sun moved was measured, and the circle being fixed, the sun’s altitude could always be obtained.

The other instrument consisted of a block of wood or stone, one side of which was placed in the plane of the meridian; and on the top corner of this side was fixed a stud; and round it as a centre a quarter of a circle was described, divided into 90°. Below this stud was another, and by means of a plumb-line one stud could always be brought over the other; so that the instrument could always be placed in a true position. At midday then, when the sun was shining, the shadow of the upper stud would fall across the scale of degrees, and at once give the altitude of the sun.

Ptolemy, who used this instrument, found that the arc included between the tropics was 47⅔°.

The result of all these accurate determinations of the solstices and equinoxes was the fixing of the length of the year.

We have so far dealt with the methods of observation which depend upon the use of the horizon and of the meridian; we will now turn our attention to extra-meridional observations, or those made in any part of the sky.

Before we discuss them, let us consider the principles on which we depend for fixing the position of a place on a globe. On a terrestrial globe there are lines drawn from pole to pole, called meridians of longitude; and if a place is on any one meridian it is said to be in so many degrees of longitude, east or west of a certain fixed meridian, as there are degrees intercepted between this meridian and the one on which the place is situated. There are also circles at right angles to the above and parallel to the equator; these are circles of latitude, and a place is said to have so many degrees N. or S. latitude as the circle which passes through it intercepts on a meridian between itself and the equator, so that the latitude of a place is its angular distance from the equator, and the longitude is its angular distance E. or W. of a fixed meridian—that of Greenwich being the one used for English calculation; and each large country takes the meridian of its central observatory for its starting-point. The distance round the equator is sometimes expressed in hours instead of degrees; for as the earth turns round in twenty-four hours, so the equator can be divided into hours, minutes, and seconds. So that if a star be just over the meridian of Greenwich, which is 0° 0´ 0˝, or 0^h 0^m 0^s longitude at a certain time, in an hour after it will be over a meridian 15° or one hour west of Greenwich, and so on, till at the end of twenty-four hours it would be over Greenwich again.

Now let us turn to the celestial globe.

What we call latitude and longitude on a terrestrial globe is called declination and right ascension on the celestial globe, because in the heavens there is a latitude and longitude which does not correspond to our latitude and longitude on the earth. If we imagine the lines of latitude and longitude on the earth to be projected, say as shadows thrown on the heavens by a light in the centre of the earth, the lines of right ascension (generally written R.A.) and declination (written Dec. or D.) will be perfectly depicted.

But there is another method of co-ordinating the stars, in which we have the words latitude and longitude used also, as we have said, for the heavens; meaning the distance of a star from the ecliptic instead of the equator, and its distance east or west measured by meridians at right angles to the ecliptic.

This premised, we are in a position to see the enormous advance rendered possible by the methods of observation introduced by Hipparchus and Ptolemy.

4. This instrument is also reported to have been used by the Chaldeans in 850 B.C.; the invention of it being attributed to Anaximander. This philosopher, says Diogenes Laertes, observed the revolution of the sun, that is to say, the solstices, with a gnomon; and probably he measured the obliquity of the ecliptic to the equator, which his master had already discovered.

5. 28,279 miles.