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Rh small dimensions, intended to be held in the hand. Tycho remarks that the instruments of the ancients were of solid metal, and as they had to be very large to allow spaces of 10′ to be marked on them, they must have been very cumbersome; and it is deserving of particular notice that he has an open eye to the importance of perfect symmetry in the instrument. He points out that the poles of the ecliptic at different times occupy different positions with regard to the meridian, and that the instrument therefore must be subject to severe strains, which would seriously affect the accuracy of the observations, even if the circles are of moderate dimensions and not too heavy. For the same reasons he rejected the clumsy "Torquetum" of Regiomontanus, which had never been much used.

Although Tycho possessed a zodiacal instrument which had the advantage of consisting only of four circles, he chiefly made use of equatorial armillæ, which instruments represent a great step forward, on account of their comparative simplicity and perfect symmetry. He constructed three instruments of this kind, which are all figured in his Mechanica. The first one, which was mounted in the small northern observatory of Uraniborg, consisted of three circles of steel, of which the meridian and the equator were firmly joined together, and both the equator and the movable declination circle were furnished with sights (made of brass), which could be moved along the circles, and to which the observer applied his eye, while a small cylinder in the centre of, and perpendicular to, the polar axis served as objective sight. The second instrument was placed in the small southern observatory, and only differed