If we refer again to Fig. 18, we see the method by which Tycho tried to get the two co-ordinates. On the horizontal circle there are the graduations for azimuth, or the measurement from the south along the horizon, and on the vertical quadrant are the graduations for altitude. Now let us turn to the modern equivalent of that instrument. Fig. 133 shows this in a portable form. The upper part of the instrument is, as one sees, nothing more than a transit circle exactly equivalent to the one described. We have a telescope carried on a horizontal axis, supported by a pillar; we have the reading microscopes, and the like; but the support of the horizontal axis, instead of being on the solid ground, as it is in the transit circle, rests on a movable horizontal circle, which is also read by microscopes arranged round it, so that all errors may be eliminated. With this instrument we can get the altitude of an object at any distance from the meridian, and at the same time measure its distance east and west of it. The arrangements designed by the Astronomer Royal for observations of the moon at Greenwich are more elaborate. In the Greenwich alt-azimuth, the telescope is swung on pivots between two piers, just as in the case of the transit, these piers being fixed to the horizontal circle. The great advantage of this instrument is that the true place of a heavenly body can be determined whenever it is above the horizon; we have neither to wait for a transit over the meridian nor over the prime vertical. Nevertheless its use is not general in fixed observatories. Reduce the dimensions of the horizontal circle and increase those of the vertical one, and we have the _vertical circle_ designed by Ertel, and largely used in foreign observatories. BOOK V. _THE EQUATORIAL._ CHAPTER XX. VARIOUS METHODS OF MOUNTING LARGE TELESCOPES. We have already gone somewhat in detail into the construction of the transit circle, which is almost the most important of modern astronomical instruments. We then referred to the alt-azimuth, in which, instead of dealing with those meridional measurements which we had touched upon in the case of the transit circle, we left, as it were, the meridian for other parts of the sphere and worked with other great circles, passing not through the pole of the heavens, but through the zenith. We now pass to the “optick tube,” as used in the physical branch of astronomy, and we have first to trace the passage from the alt-azimuth to the Equatorial, as the most convenient mounting is called.