The stars were observed through a hole in a wall and through an eyehole, sliding on a fixed arc. The number of degrees marked at the eyehole on the arc at once gave the altitude of the heavenly bodies as seen through that hole. If a star was very high, it would be necessary for an observer to place his eye low down to be able to see it. If it were near the horizon, he would have to travel up to the top of this circle to determine its altitude, and having done that, and knowing the latitude of the place of observation, the observer will be able to determine the position of the star with reference to the celestial equator. The actual moment at which the star was seen was noted by the clock, and the time that the sun had passed the hole being also previously noted, the length of time between the transits was known; and as the stars appear to transit or pass the meridian every twenty-four hours, it was at once known what part of the heavens was intercepted between the sun and the star in degrees, or, as is usually the case, the right ascension of the star was left expressed in hours and minutes instead of degrees; thus he had a means of determining the two co-ordinates of any celestial body. The places of the comet of 1677, which Tycho discovered, and of many stars, were determined with absolute certainty; but astronomers began to be ambitious. It was necessary in using this instrument to wait till a celestial body got to the meridian. If it was missed, then they had to wait till the next day; and further, they had no opportunity whatever of observing bodies which set in the evening. [Illustration: FIG. 18.—The Quadrans Maximus reproduced from Tycho’s plate. ] Seeing, therefore, that clocks were improving, it was suggested by one of Tycho’s compeers, the Landgrave of Hesse-Cassel, that by an instrument arranged something like Fig. 18, it would be possible to determine the exact position of any body in the heavens when examined out of the meridian, and so they got again to extra-meridional observations.