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Rh get their heads too close together, there was for that purpose a second cylinder on one of the end-radii (F), and a removable sight on the arc (G), placed so that the line through them was parallel to a line from the centre to the middle of the arc. One observer then sighted along these, and the other along the movable arm as usual.

For measuring small distances (less than 30°) Tycho also constructed an "arcus bipartitus," consisting of a rod 5$1⁄2$ feet long, with a cross-bar at one end, having at each extremity a small cylinder, and two arcs of 30° at the other end, of which the cylinders occupied the centres. With this instrument, which was placed in the great northern observatory, the distances of the principal stars of Cassiopea inter se were measured in order to fix the position of the new star by the measures taken in 1572–73.

The size of these various instruments, as well as their solid construction, would not have been sufficient to ensure the accuracy in the observations which Tycho actually attained, and which so much exceeded that reached by previous observers, if he had not added special contrivances for that purpose. Before Tycho's time there was only one way of making small fractions of a degree distinguishable—by making the instrument as large as possible. In addition to Al Chogandi's 60-foot sextant, a quadrant of 21 feet radius is said to have been constructed by Al Sagani (about the year 1000), and the value which the Arabs were obliged to attach to large instruments was expressed in the remark of Ibn Carfa, that if he were able to build a circle which was supported on one side by the Pyramids and on the other by the Mocattam mountain, he would do it.