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. [Illustration: FIG. 12.—The Vernal Equinox among the Constellations, B.C. 2170. ] [Illustration: 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. [Illustration: 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.