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A transit-circle is the main instrument used for that. It is a telescope mounted on an east-west axis so that it moves only in the meridian plane. Stars and other objects cross the meridian and when they do that they move across the field of view of the telescope. The time at which they do that indicates their right ascension, and the angle of the telescope indicates their declination. So the astronomer sits at the transit circle with a stopwatch and when the star goes across the centre of the field of view the time is noted on the stopwatch.

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