sextant clamped in the interval between two observations, to make sure that no change had taken place in the instrument in the meantime. The star being circumpolar for his latitude, he was able to follow it right round the pole, and he took advantage of this circumstance to observe its altitude at the lower culmination by the sextant, as he did not at that time possess a quadrant. He placed it in the plane of the meridian with the one arm, which we may call the fixed one, and to which he had now attached an arc of 60°, resting horizontally on a window-sill and a short column inside the room.[1] To ensure the horizontal position of the arm, it was moved until a plumb-line suspended from the end of the graduated arc touched a mark exactly at the middle of the arm,[2] and as the instrument might happen to be slightly moved while the observation was being made, a short graduated arc was traced at the middle of the arm, on which the plumb-line would immediately mark the small correction to be applied to the observed altitude. This simple but neat contrivance is highly characteristic of Tycho; we recognise here the modern principle of acknowledging an instrument to be faulty, and applying corrections for its imperfections to the results determined by it, a principle which we shall see he followed in the construction of all his instruments. From repeated observations he found the smallest altitude of the new star to be 27° 45′, and consequently, as he assumed the latitude of Heridsvad to be 55° 58′, the declination of the star was 61° 47′. He remarks that the declination was as constant as the distances from the neighbouring stars, and that the
- ↑ The sextant in this position is figured in Progymnasmata, p. 348; Mechanica, fol. E. 3 verso.
- ↑ Tycho considers it necessary to quote Euclid iv. 15 and i. 12 in explanation of this (Progymn., p. 349). Euclid was apparently still considered an author with whose work but few were familiar (see H. Hankel, Zur Geschichte der Mathematik im Alterthum und Mittelalter, p. 355).
