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? [Illustration: 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