The Quadrans Vetus - Museum of the History of Science : Museum of the History of Science

Spring, 1995

The ‘quadrans vetus’ or ‘old quadrant’ is one of the most ingenious of medieval instruments and it is also extremely rare. The Museum has a single example (accession number F10), dated to around 1300 A.D.

The principal face of the quadrans vetus is used for calculating the time from the altitude of the sun. The apparent position of the sun in the sky is related to time, but it also varies with the time of the year and the latitude of the observer; a sun-based universal time-teller must somehow take account of these variables.

A common horizontal sundial deals with the date variable in the equation by having its ‘style’ or ‘gnomon’ pointed to the celestial pole, so that it is always positioned at right angles to the daily apparent circle made by the sun across the sky, regardless of the time of year. But this means that the horizontal dial can deal with the latitude variable only by standing still; in other words, it will only work in one latitude.

The old quadrant is more subtle. Simply to take the altitude of the sun, the instrument is held in the vertical plane, the pair of sights mounted on one edge trained on the sun, and the position of the plumb line read off the degree scale along the curved rim. However, the desired measurement is not the solar altitude but the time, and for this allowance must be made for both latitude and date. This is done by setting up the instrument so that the noon reading is correct: the scales allow this to be done without observation. Provided the hour lines are correctly drawn, all measurements of time for a particular latitude and date will then follow from observation.

On any day, the sun appears to cross the eastern horizon (altitude zero), rise to a maximum altitude at noon when due south (for an observer in the northern hemisphere), and descend to the western horizon. When the sun is overhead at the equator (on the date of either equinox) this apparent path identifies the celestial equator. With the sun due south (when the angles of latitude and solar altitude are in the same plane) this maximum altitude is simply 90° minus the observer’s latitude (the complement of the latitude). Consequently, at the equinox, the noon position of the plumb line can be found by placing the thread across the value of the complement of the latitude on the degree scale.

However, in its yearly cycle of seasonal change, the sun is sometimes above and sometimes below the equator: the plate sliding in the groove of the quadrans vetus is there to adjust for this. Its centre can be moved to the complement of the latitude (and thus adjusted for latitude) and the thread then set to the angle on the plate equal to the sun’s angle above or below the equator (and thus adjusted for date). Since this is the position for noon, the bead on the thread, which will indicate the time, must then be slid to the noon line on the pattern of arcs in the central area of the quadrant, which are the hour lines. The quadrant’s sights are trained on the sun and the actual time is indicated by the position of the bead among these lines.

One further complication concerns the hour lines themselves. The time they yield is in the old system of ‘unequal hours’, where the day-time was divided into twelve hours, with zero at sunrise, six at noon and twelve at sunset. The length of an hour therefore varied throughout the year and, except at the equinoxes, daytime and night-time hours were different.

We tend to assume that life was simpler and less sophisticated in former times. The old quadrant, however, demonstrates that medieval time-telling was certainly much more challenging than its modern counterpart, and in so doing may well provide us with good reasons to reconsider this and similar assumptions.