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Fig. 8.—Astrolabe (Armillæ Æquatoriæ of Tycho Brahe) similar to the one contrived by Hipparchus.

In this manner, then, Hipparchus could point to any part of the heavens and observe, on either side of the meridian, the sun, moon, planets or any of the stars, and obtain their distance from the equatorial plane; but another fixed plane was required; and Hipparchus, no longer content with being limited to measuring distances from the equator, thought it might be possible to get another starting-point for distances along the equator. It was the determination of this plane, or starting-point from which to reckon right ascension, that was one of the difficulties Hipparchus had to encounter. This point he decided should be the place in the heavens where the sun crosses the equator at the spring equinox. But the stars could not be seen when the sun was shining; how, then, was he to fix that point so that he could measure from it at night?

Fig. 9.—Ecliptic Astrolabe (the Armillæ Zodiacales of Tycho Brahe), similar to the one used by Hipparchus.

He found it at first a tremendous problem, and at last hit upon this happy way of solving it. He reasoned in this way: “As an eclipse of the moon is caused by the earth’s shadow being thrown by the sun on the moon, if this happen near the equinox, the sun and moon must then be very near the equator, and very near the ecliptic—in fact, near the intersection of the two fundamental planes which are supposed to cross each other. If I can observe the distance, measured along the equator, between the moon and a star, I shall have obtained the star’s actual place, because, of course, if the moon is exactly opposite the sun, the sun will be 180 degrees of right ascension from the moon, and the right ascension of the sun being known it will give me the position of the star.” This method of observation was an extremely good one for the time, but it could only have been used during an eclipse of the moon, and when the sun was so near the equator that its distance from the equinoctial point along the ecliptic, as calculated by the time elapsed since the equinox, differed little from the same distance measured along the equator, or its right ascension, so that the right ascension of the sun was very nearly correct. Hipparchus hit upon a very happy alteration of the same instrument to enable him to measure latitude and longitude instead of declination and right ascension—in fact, to measure along the ecliptic instead of the equator. Instead of having the axis of the inner rings parallel to the axis of the earth, as in Fig. 9, he so arranged matters that the axis of this system was separated from the earth’s axis to the extent of the obliquity of the ecliptic, the circle R, Q, N, therefore instead of being in the plane of the equator, was in that of the ecliptic. Then it was plain to Hipparchus that he would, instead of being limited to observe during eclipses of the moon, be able to reckon from the sun at all times; because the sun moves always along the ecliptic and the latitude of the sun is nothing.

We will now describe the details of the instrument. There is first a large circle, E, B, C, Fig. 9 (which is taken from a drawing of this kind of instrument as constructed subsequently by Tycho Brahe), fixed in the plane of the meridian, having its poles, D, C, pointing to the poles of the heavens; inside this there is another circle, F, I, H, turning on the pivots D, C, and carrying fixed to it the circle, O, P, arranged in a plane at right angles to the points I, K, which are placed at a distance from C and D equal to the obliquity of the ecliptic; so that I and K represent the poles of the ecliptic, and the circle, O, P, the ecliptic itself. There is then another circle, R, M, turning on the pivots I and K, representing a meridian of latitude, and along which it is measured.

Then, as the sun is on that part of the ecliptic nearest the north pole, in summer, its position is represented by the point F on the ecliptic, and by N at the winter solstice; so, knowing the time of the year, the sight Q can be placed the same number of degrees from F as the sun is from the solstice, or in a similar position on the circle O P as the sun occupies on the ecliptic.

The circle can then be turned round the axis C, D, till the sight Q, and the sight opposite to it, Q´, are in line with the sun. The circle, O, R, will then be in the plane of the ecliptic, or of the path of the earth round the sun. The circle, R, M, is then turned on its axis, I, K, and the sights, R, R, moved until they point to the moon. The distance Q, L, measured along O, P, will then be the difference in longitude of the moon and sun, and its latitude, L, R, measured along the circle R, M.

But why should he use the moon? His object was to determine the longitude of the stars, but his only method was to refer to the motion of the sun, which could be laid down in tables, so that its longitude or distance from the vernal equinox was always known. But we do not see the stars and the sun at the same time; therefore in the day time, while the moon was above the horizon, he determined the difference of longitude between the sun and the moon, the longitude of the sun or its distance from the vernal equinox being known by the time of the year; and after the sun had set he determined the difference of longitude between the moon and any particular star; and so he got a fair representation of the longitude of the stars, and succeeded in tabulating the position of 1,022 of them.

It is to the use of this instrument that we owe the discovery of the precession of the equinoxes.

Fig. 10.—Diagram Illustrating the Precession of the Equinoxes.

After Hipparchus had fixed the position of a number of stars, he found that on comparing the place amongst them of the sun at the equinoxes in his day with its place in the time of Aristillus that the positions differed—that the sun got to the equinox, or point where it crossed the equator, a short time before it got to the place amongst the stars where it crossed in the time of Aristillus; in fact, he found that the equinoctial points retrograded along the equator, and Ptolemy (B.C. 135) appears to have established the fact that the whole heavens had a slow motion of one degree in a century which accounted for the motion of the equinoxes.

Fig. 11.—Revolution of the Pole of the Equator round the Pole of the Ecliptic caused by the Precession of the Equinoxes.

Let us see what we have learned from the observation of this motion, for motion there is, and the ancients must be looked on with reverence for their skill in determining it with their comparatively rude instruments. In Fig. 10, A represents the earth at the vernal equinox, and at this time the sun appears near a certain star, S, which was fixed by Aristillus; but in the time of Hipparchus the equinox happened when the sun was near a star, S´, and before it got to S. Now we know that the sun has no motion round the earth, and that the equinox simply depends on the position of the earth’s equator in reference to the ecliptic; so that in order to produce the equinox when the earth is at E and before it get to A, its usual place, all we have to do is to turn the pole of the earth through a small arc of the dotted circle, and so alter its position to that shown at F, when its equator and poles will have the same position as regards the sun as they have at A, so the equinox will happen when the earth is at E, and before it reaches A. This may be practically represented by taking an orange and putting a knitting-needle through it, and drawing a line representing the equator round it, and half immersing it in a tub of water, the surface of which represents the ecliptic. We are then able to examine these motions by moving the orange round the tub to represent the earth’s annual motion, and at the same time making the orange slowly whobble like a spinning-top just before it falls, by moving the top of the knitting-needle through a small arc of a circle in the same direction as the hands of a clock at every revolution of the orange round the centre of the tub.

The points where the equator is cut by the surface of the water (or ecliptic) will then change, as the orange whobbles, and the line joining them, will rotate, and as the equinox happens when this line passes through the sun, it will be seen that this will take place earlier at each revolution of the orange round the tub.

The equinox will therefore appear to happen earlier each year, so that the tropical year, or the time from equinox to equinox, is a little shorter than the sidereal year, or the time that the earth takes to travel from a certain place in its orbit to the same again; for if the earth start from an equinoctial point, the equinox will happen before it gets to the same place where the equinoctial point was at starting.

This is called the precession of the equinoxes.

Fig. 12.—The Vernal Equinox among the Constellations, B.C. 2170.

Fig. 13.—Showing how the Vernal Equinox has now passed from Taurus and Aries.

This discovery must be regarded as the greatest triumph obtained by the early stargazers, and there is much evidence to show that when the zodiac was first marked out among the central zone of stars, the Bull and not the Ram was the first of the train. Even the Ram, owing to precession, is no longer the leader, for the sign Aries is now in the constellation Pisces. The two accompanying drawings by Professor Piazzi Smyth of the position of the vernal equinox among the stars in the years 2170 B.C. and 1883 A.D. will show how precession has brought about celestial changes which have not been unaccompanied by changes of religious ideas and observances in origin connected with the stars.

Fig. 14.—Instrument for Measuring Altitudes.

We now come to Ptolemy. There was another instrument used by Ptolemy, and described by him, which we may mention here; it was called the Parallactic Rules, so named perhaps because that ancient astronomer used it first for the observation of the parallax of the moon. It consists of three rods, D E, D F, E F, Fig. 14, two of which formed equal sides of an isosceles triangle; and the third, which had divisions on it, made the one at the base, or was the chord of the angle at the summit. One of the equal sides, D F, was furnished with pointers, over which a person observed the star, whilst the other, D E, was placed vertically, so that they read off the divisions on E F, and then, by means of a table of chords, the angle was found; this angle was the distance of the star from the zenith. Ptolemy, wishing to observe with great accuracy the position of the moon, made himself an instrument of this kind of a considerable size; for the equal rulers were four cubits long, so that its divisions might be more obvious. He rectified its position by means of a plumb-line. Purbach, Regiomontanus, and Walther, astronomers of the fifteenth century, employed this manner of observing, which, considering the youth of astronomy, was by no means to be despised. This instrument, constructed with great care, would have sufficiently been useful as far as concerns certain measurements and would have furnished results sufficiently exact; but the part of ancient astronomy that failed was the way of measuring time with any precision.

There were astronomers who proposed clepsydras for this purpose; but Ptolemy rejected them as very likely to introduce errors; and indeed this method is subject to much inconvenience and to irregularities difficult to prevent. However, as the measurement of time is the soul of astronomy, Ptolemy had recourse to another expedient which was very ingenious. It consisted in observing the height of the sun if it were day, or of a fixed star if it were night, at the instant of a phenomenon of which he wished to know the time of occurrence, for the place of the sun or star being known to some minutes of declination and right ascension as also was the latitude of the place, he was able to calculate the hour; thus when they observed, for example, an eclipse of the moon, it was only necessary to take care to get the height of some remarkable star at each phase of the eclipse, say at the commencement and at the end, in order to be able to conclude the true time at which it took place. This was the method adopted by astronomers until the introduction of the pendulum.