Reading the Dial in Old Court

queens' college dialThis is an idealised diagram of the Dial in Old Court: the lines of the Dial are shown as they ought to be, if perfectly computed. The actual Dial only approximates to this form.

You may also view the history of the Dial.

To read the Dial, first identify the gnomon: a metal rod projecting from the centre of the Sun in his Glory at the top of the Dial (other rods are just supports for the gnomon). Information can be read from the Dial as follows.

Time of day

Reading the TimeLook for the shadow of the gnomon among the straight black lines radiating from the Sun in his Glory to the roman numerals in the blue border. The roman numerals give the hour of day in Cambridge apparent solar time, and the minutes between the hours can be estimated (the quarter-hours are marked).

For a discussion of the corrections to be taken into account when comparing sundial time with time as shown by clocks and watches, see Correcting sundial time below.

The Nodus (gold ball)

A gold-coloured ball is attached to the gnomon, level with the line marked HORIZON. This ball is the Nodus of the Dial. To extract further information from the Dial, you need to locate the shadow of this ball among the pattern of curves and lines on the Dial plane behind, as detailed further in the following sections.

Time of year (Sign of Zodiac)

Telling the ZodiacLook for the shadow of the ball amongst the green hyperbolic curves. The straight sloping line is a member of this family of curves, but is coloured black on the Dial itself. Then:

  • when after midwinter and before midsummer, look to the right-hand ends of the green curves; or
  • when after midsummer and before midwinter, look to the left-hand ends of the green curves.

The two green lines that the ball’s shadow lies between will enclose the current sign of the zodiac (except that the signs immediately before and after the winter solstice have moved above the solstice line, owing to lack of space). The sign of the zodiac is drawn as a full representation, accompanied by its own symbol and the symbol of its astrological ruling planet, according to the scheme in the following table:

Zodiac Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricorn Aquarius Pisces
Picture Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image Zodiac image
Informal Ram Bull Twins Crab Lion Maiden Scales Scorpion Archer Goat Water-bearer Fish

The green hyperbolic curves are formally known as lines of constant declination. During the passage of one day, the shadow of the ball follows a line of constant declination, particular to the time of year. The lines of constant declination depicted on the Dial are those which are the twelve zodiac period boundaries, which include the solstices and equinoxes. The lowest green line on the Dial represents the summer solstice (when the sun is highest, so its shadow lowest), the lower border of the gold band represents the winter solstice, and the sloping straight line represents the equinoxes, both spring and autumn.

Time (in the form of Hour-angle) and Declination together define the position of the sun in the Equatorial Coordinate System, based on the earth’s equatorial plane.

Month of year, and estimated Date

Telling the DateIn columns outside the signs of the zodiac are the names of the months written in Latin, with the breaks between the months marked. The names of the months at the two solstices are split between the left and right columns: DECEM-BER and JU-NIUS. By interpolating the position of the ball’s shadow between two green lines, and extending that interpolation to the column of month names, you can tell the month of the year, and by interpolation estimate the date within the month. The Dial itself was drawn before Britain adopted the current Gregorian calendar in 1752, so the month breaks shown are probably those of the old Julian calendar: you should add 11 days to the estimated date. The diagrams on this page are drawn on the basis of the Gregorian calendar, and the month breaks re-positioned accordingly.

Time of Sunrise

Telling the time of sunriseNote the position of the ball’s shadow between the green lines, and extend that relationship to the column on the left labelled ORTUS SOLIS. Times of sunrise are marked for each green line, and you may interpolate between the given times to find the local apparent solar time of sunrise. To derive the clock time for sunrise, see Correcting sundial time below.

Length of Daylight Hours

Note the position of the ball’s shadow between the green lines, and extend that relationship to the column on the right marked LONGITUDO. The length of daylight is given in hours and minutes for each green line, and you may interpolate between the given figures to find the current length of day. On the Dial itself, the punctuation separator between the hour and minute figures has been omitted.

Azimuth (Bearing) of the Sun

Telling the AzimuthNote the position of the ball’s shadow amongst the straight vertical black lines. Each vertical line is labelled with an azimuth in the form of a Point of the Compass. The 12 o’clock time line serves also as the line indicating azimuth due South. The vertical lines are separated by 11¼º of azimuth.

Altitude of the Sun above the Horizon

Telling the AltitudeNote the position of the ball’s shadow amongst the red hyperbolic curves. Each red line is marked with altitude in degrees above the horizon, at intervals of ten degrees: the HORIZON line can be considered to be a member of this family of curves, corresponding to altitude zero. You may interpolate between the red curves to estimate the altitude to the nearest degree.

Azimuth and Altitude together define the position of celestial objects in the Horizontal Coordinate System, based on the horizon at the observer’s location.

Temporary, or Unequal, Hours

Telling the Unequal HoursA set of black lines (radiating from the gold band under HORIZON, and apparently straight, but actually slightly curved) subdivides daylight into twelve equal parts, whatever the time of year: these are the Temporary, or Unequal, Hours. This was once a common method of measuring working hours during daylight. In the idealised diagrams on this page, the Unequal Hour lines coincide with the solar time lines (the ones projecting to the roman numerals) at the equinoxes (the straight sloping line). On the actual Dial, the agreement is not so good. The HORIZON line may be considered as a double member of the set of unequal hour lines: the HORI side representing sunrise (unequal hour zero), and the ZON side representing sunset (unequal hour 12).

Correcting sundial time

All sundials, most of the time, give readings for time of day which differ from that shown by clocks and watches. The factors to take into account are as follows:

1. Longitude

Sundials display the apparent solar time appropriate to the geographic longitude of their location, such that, when the sun there is overhead due South, the sundial reads 12 o’clock midday. Clocks and watches in Britain are set (during winter) to a mean time based on time at the Greenwich Meridian (longitude 0°), called Greenwich Mean Time. The time correction required on account of longitude amounts to 4 minutes of time per degree of longitude, with sundials further east being faster. The longitude of Cambridge is close enough to that of the Greenwich Meridian for time in Cambridge to be almost the same as time at Greenwich, so no correction on account of longitude is required when reading sundials in Cambridge, including this Dial. [The precise calculation is that, since Queens’ College is at longitude 00° 07′ East, a sundial in Queens’ will be 28 seconds faster than a sundial on the Greenwich meridian: this is less than the precision with which a sundial of our design can be read].

2. Daylight Saving Time

Between the last Sunday of March and the day before the last Sunday of October, clocks and watches are set to British Summer Time, which is one hour ahead of Greenwich Mean Time, and therefore about one hour ahead of local mean time in Cambridge. So do not be surprised if the Dial shows 1 p.m. when the clock shows 2 p.m.

3. Equation of Time

Apparent solar time (as given by a sundial) may differ from local mean time (as shown by clocks and watches, after correction for longitude) by up to 16 minutes in either direction, according to the time of year. This divergence is given by the Equation of Time. The lengths of solar days are not exactly 24 hours of synthetic mean time. This arises because of two factors:

EoT graphObliquity

The earth’s axis of rotation is not perpendicular to the plane of the earth’s orbit around the sun. This obliquity is responsible for the seasons of the year. It also causes apparent solar time (as given by sundials) to differ from local mean time according to season. The divergence arising from this factor taken alone (blue curve) is zero at four times in the year: the solstices (around June 20/21 and December 21/22) and the equinoxes (around March 20 and September 22/23).


The earth’s orbit around the sun is elliptical rather than perfectly circular, so the earth’s angular velocity around the sun is variable. A solar day consists of one absolute rotation of the earth plus a little bit extra to make up for one day’s worth of progression of the earth around the sun, and the little bit extra varies according to the earth’s angular velocity about the sun at that time of year. This eccentricity causes another variation to the length of solar day, and therefore a second divergence between apparent solar time and local mean time. The divergence arising from this factor taken alone (green curve) is zero twice a year: at aphelion (sometime in the first week of July) and perihelion (sometime in the first week of January).

When the two factors are combined (red curve), the Equation of Time yields zero divergence around April 16, June 15, September 1, and December 25. Around these dates, sundials should show a time very close to the local mean time (as given by clocks and watches after correction for longitude). Sundials are at their most slow (14·3 mins) around February 12, and at their most fast (16·4 mins) around November 4.

4. Errors of sundial implementation

The last time the Queens’ Dial was repainted, the pattern on the wall was located several inches too far to the left. If painted correctly, the vertical line representing midday should, if projected, pass through the intersection of the line of the gnomon with the plane of the wall. Instead, the artist appears to have aligned the midday line with a strut supporting the gnomon. This error will cause the Queens’ Dial to read time about 10 minutes fast in the middle of the day.


Underneath the Dial is a table of numbers in three rows, shown here with some visual cues added:

Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0·48 1·36 2·24 3·12 4·0  4·48 5·36 6·24 7·12 8·0  8·48 9·36 10·24 11·12 12·0 
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image Moon image

You are required to already know the age of the lunar month in days (1–30) since the last New Moon. For instance, Full Moon is day 15, and the next New Moon is day 30. To ascertain the age of the lunar month, you can either (a) look up the dates of New Moons in a pocket diary or online database, or (b) use the visible shape of the moon, as shown above, to estimate the age. Locate the current age of the lunar month on the top or bottom line, then read off a time from the centre line, in hours and minutes. That time gives the offset which needs to be added to the apparent lunar time, as indicated by the shadow of the gnomon cast by moonlight, in order to yield an estimate of the time of night. With the offset changing at 48 minutes per day, the calculated result might be subject to considerable error. On the night of the New Moon, the correction offset is zero, but you are advised not to attempt this exercise on that night.

Here is a worked example: Suppose the lunar month is 10 days old, and the shadow of the gnomon in moonlight indicates 3 o’clock on the dial. The table shows, on day 10, that 8 hours needs to be added to any moonlight time. 3 plus 8 yields 11: so the time of night is 11 p.m. If the result of the addition exceeds 12 hours, then deduct 12 hours.

A purist might argue that the lunar month is not 30 days long: it is closer to 29½. But the errors introduced by assuming a 30-day month are smaller than the errors arising from attempting to estimate the age of the lunar month from the moon’s shape, or quantising the age of the lunar month into whole numbers of days. Even this 29½ figure is only a long-term average: the lengths of individual lunar months, because of the irregularity of the moon’s motion, can vary between 29·18 and 29·93 days. For this, and other, reasons, there is little point in trying to improve the accuracy of the estimates of time given by moon-dials much beyond what can be achieved by simple readings taken from the table above.

Tables like this one could also be used as tide predictors (although this was unlikely to be a need felt in Cambridge). For any given location, a high-tide usually follows the moon being due south by a fixed amount of time each day, an amount which would be local knowledge. Knowing the age of the lunar month, one could use the table to look up the time at which the moon would be due south, then add the known local tide delay, to derive the expected time of high-tide. There would be another high-tide just over 12 hours later.

Text by , 1997 April 15, revised 1998 May 19, 2014 August 31, 2015 at the Summer Solstice, 2016 February 14, 2016 August 19, 2016 December 29, .

With thanks and acknowledgements to Dr Frank King, who made computations for the diagram at the head of this page. Scalable graphics of the zodiac figures by Raingoose Design, 2016.


Further reading

1886: The Architectural History of the University of Cambridge, by Robert Willis and John Willis Clark, Volume 2, p. 51. (OCLC 6104300)

1912: The Dial, by Eric Harold Neville, in The Dial, [magazine] Vol. 3: No. 13, Lent 1912, pp. 25–​28; No. 14, Easter 1912, pp. 91–​94; No. 16, Lent 1913, pp. 196–​200. (OCLC 265448755)
1933: reprinted, with some editorial changes, in The Dial, No. 73, Lent 1933, pp. 6–​11; No. 74, Easter 1933, pp. 5–​9.

1948: The Dial, by Geoffrey Colin Shephard, in The Dial, [magazine] No.  97, Easter 1948, pp. 40–​48; (OCLC 265448755)
1948: Queens’ College Dial, reprinted from “THE DIAL”, May, 1948 (OCLC 57297303) [offprint of above]
1957: Second edition, revised, as: Queens’ College Dial: a short description of the Sun-dial in Queens’ College, Cambridge; (OCLC 19863415)
1972: Third edition. (OCLC 16244615, ISBN 978-0-9503358-0-3) [unchanged reprint of 1957 edition]

1957: About Sundials and Moondials, by Hermann Egger, in Sky and Telescope, Vol. XVI, No. 10, August 1957, pp. 480–​1. (ISSN 0037-6604)

1965: Les Cadrans solaires : Traité de gnomonique théorique et appliquée, by René Rodolphe Joseph Rohr (10 chapters); (OCLC 4673165)
1970: Sundials : History, Theory, and Practice, translation of 1965 edition into English by Gabriel Godin, pp. 121–​2, plate 9, and pp. 107–​8 on Moondials; (ISBN 978-0-8020-1567-9)
1982: Die Sonnenuhr : Geschichte, Theorie, Funktion, translation of 1965 edition into German with extra material (12 chapters); (ISBN 978-3-7667-0610-2)
1986: Cadrans solaires : histoire, théorie, pratique : traité de gnomonique, expanded version in French, incorporating extra material of 1982 German edition (12 chapters), pp. 190–​2, frontispiece, and pp. 184–​5 on Moondials; (ISBN 978-2-85369-052-2)
1988: Meridiane : Storia, teoria, pratica, translation into Italian (12 chapters); (ISBN 978-88-414-3002-6)
1996: reprint of 1970 English edition (10 chapters only). (ISBN 978-0-486-29139-0)

1988: The Dial in Old Court, Queens’ College Cambridge : its background, history and use, by Maurice Meynell Scarr (1914–​2005). (OCLC 84705218) [re-working of material from Shephard’s pamphlet of 1957/72] 

1991: Cambridge Sundials, by Alexis Michael Panther Brookes (1913–​2002) and Margaret Stanier (1919–​2007). (OCLC 40223537)

1994: The Queens’ College Dial, Cambridge, by Charles Kenneth Aked (1921–​1998), in the Bulletin of the British Sundial Society, Vol. 94.3 October 1994, pp. 2–​6; (ISSN 0958-4315) [reproduced by kind permission of the BSS]
1997: Queens’ College Sundial (follow-up): ibid., Vol. 97.2 April 1997, pp. 51–​2.

2005: Moondials and the Moon, by Michael Lowne, in the Bulletin of the British Sundial Society, Vol. 17(i), March 2005, pp. 3–​12. (ISSN 0958-4315)

2006: The Queens’ Dial : Refurbishment Considerations, by Dr Frank H. King.

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