Fig. 8 shows the instrument called the “armillæ equatoriæ,” which he constructed, and which was based upon the principle of that which Hipparchus had used. Here the axis of motion, C, D, of these circles is so arranged that it is absolutely parallel to the axis of the earth; but instead of the circle R, Q, N, representing the equator, being fixed, it revolved in its own plane while held by the circle G, H, I, making its use probably more easy, but leaving the principles unaltered. Tycho Brahe also used another similar instrument of much larger size for the same purposes as the one we have just considered. It consisted of a large circle, which was seven cubits in diameter, corresponding to the circle K, L, M, Fig. 8; and carrying the sights in the same manner, it was placed in a circular pit in the ground, with its diameter pointing towards the pole. This was used for measuring declinations. The circle R, Q, N, Fig. 9, was represented by a fixed circle carried on pillars surrounding the pit, and along which the right ascension of the star was measured. This instrument, therefore, was more simple than the smaller one, and probably much more accurate. Tycho was not one of those who was aware of the true system of the universe; he thought the earth fixed, as Ptolemy and others did; but whether we suppose the earth to be movable in the middle of the vault of stars or stationary, in either case that position is absolutely immaterial in ascertaining the right ascension of stars. If one takes the terrestrial globe, and looks upon the meridians, it is at once clear that the distance from meridian to meridian remains unaltered, whether the globe is still or turning round: so the stars maintain their relative positions to each other, whether we consider the earth in motion or the sphere in which the stars are placed to revolve round it. [Illustration: FIG. 17.—Tycho Brahe’s System. ] The introduction of clocks gave Tycho the invention of the next instrument, which was the transit circle. At this time the pendulum had not been invented; but it struck him and others that there was no necessity for having two or more circles rotating about an axis parallel to the earth’s axis, as in the astrolabes or armillæ, but only to have one circle in the plane of the meridian of the place. So that, by the diurnal movement of the earth round its own axis, all the stars in the heavens would gradually and seriatim be brought to be visible along the arc of the circle, so he arranged matters in the following way.