In Römer’s “Observatorium Tusculaneum,” near Copenhagen, built in 1704, there was not only a transit circle in the meridian of course, but a transit instrument in the prime vertical, _i.e._ swinging in a vertical plane at right angles to the former one, so that while the optical axis of one always lies in a N.S. plane, that of the other lies in an E.W. one. Römer did not use this instrument much; it remained for the great Bessel to point out its value in determinations of latitude. This instrument is, so to speak, self-correcting, because between the transit of a star over its wires while pointing to the east of the meridian, and that while pointing to the west its telescope can be reversed in its =Y=s, or one position may be taken for one night’s observations, and the other for the next, and so on. In Struve’s form of this instrument the transit of stars can be observed at an interval of one minute and twenty seconds, this time only being required to raise it from the =Y=s, to rotate it through 180°, and lower it again. This rapid reversal, and consequent elimination of instrumental imperfections, enable observations of the most extreme precision to be made in such delicate matters as the slight differences of declination of stars due to aberration, nutation, and the like. The intersection of the meridian with the prime vertical marks the zenith. To determine this:—first, there is the zenith sector, invented by Hooke; it consists of a telescope, carried by an axis on one side of the tube, and at right angles to it, so that the telescope swings exactly as a transit does, and it is provided with cross wires in the same manner; instead, however, of having a whole circle, it has only two segments of a circle; and as it is never required to swing the telescope far from its vertical position, there is a diagonal reflector at the eyepiece, so that the observer can look sideways, instead of upwards, in an awkward position. Its use is to determine the zenith distance of stars as they pass near that point. These distances are read off on the parts of the circle by verniers or microscopes, as in the transit circle. The zenith telescope, chiefly designed by Talcott, is the modern equivalent of the sector, and both instruments are more used in geodetical operations than in fixed observatories. At Greenwich, however, there is an instrument for determining zenith distances of very special construction. This is called the reflex zenith tube, shown in Fig. 131. It is a sectional drawing of one of those instruments showing the path of the rays of light. A, B, is an object-glass, fixed horizontally, and below it is a trough of mercury, C, the surface of which is always of course horizontal. The light from a star near the zenith is allowed to fall through the object-glass, which converges the rays just so much that they come to a focus at F, after having been reflected from the surface of the mercury, and also by the diagonal