His mechanical skill was very great, and in his workmanship he was satisfied with nothing but the best. He recognised the importance of rigidity in the instruments, and, whereas these had generally been made of wood, he designed them in metal. His instruments included armillae like those which had been used in Alexandria, and other armillae designed by himself--sextants, mural quadrants, large celestial globes and various instruments for special purposes. He lived before the days of telescopes and accurate clocks. He invented the method of sub-dividing the degrees on the arc of an instrument by transversals somewhat in the way that Pedro Nunez had proposed.
He originated the true system of observation and reduction of observations, recognising the fact that the best instrument in the world is not perfect; and with each of his instruments he set to work to find out the errors of graduation and the errors of mounting, the necessary correction being applied to each observation.
When he wanted to point his instrument exactly to a star he was confronted with precisely the same difficulty as is met in gunnery and rifle-shooting. The sights and the object aimed at cannot be in focus together, and a great deal depends on the form of sight. Tycho Brahe invented, and applied to the pointers of his instruments, an aperture-sight of variable area, like the iris diaphragm used now in photography. This enabled him to get the best result with stars of different brightness. The telescope not having been invented, he could not use a telescopic-sight as we now do in gunnery. This not only removes the difficulty of focussing, but makes the minimum visible angle smaller. Helmholtz has defined the minimum angle measurable with the naked eye as being one minute of arc. In view of this it is simply marvellous that, when the positions of Tycho's standard stars are compared with the best modern catalogues, his probable error in right ascension is only ± 24", 1, and in declination only ± 25", 9.
Clocks of a sort had been made, but Tycho Brahe found them so unreliable that he seldom used them, and many of his position-measurements were made by measuring the angular distances from known stars.