(Cathedrals as solar observatories)

By J.L. Heilbron

Harvard University Press, 1999. 366 pages, $35

Quoting from the Introduction:

The Roman Catholic Church gave more financial and social support to the study of astronomy over six centuries…than any other, and, probably, all other, institutions. Those who infer the Church's attitude from its persecution of Galileo may be reassured to know the basis of its generosity to astronomy was not a love of science but a problem in administration. The problem was establishing and promulgating the date of Easter. The old theologians, that is those who lived before and up to the Council of Nicea (325 AD), decreed that Easter should fall on the first Sunday after the first full moon after the vernal equinox.1 Since Passover was supposed to fall on the full moon after the equinox (except for the frequent leap-months of the Jewish calendar) this definition of Easter was consistent with Jesus Christ's having celebrated His Passover seder on the day He was crucified (please remember that in the Jewish calendar the day begins at sunset). But this definition was inadequate for a number of reasons.

First one had to observe the equinox and then wait for the next full moon, declaring Easter to be the following Sunday. But this hardly left enough time to prepare properly for Easter. For example, Lent was supposed to be observed starting with Ash Wednesday, 46 days prior to Easter,2 and basing the date of Easter on an observation of the equinox would introduce an unacceptable a posteriori element into such an important penitential season.

Furthermore, the equinox and the full moon fall on different dates at different places on the earth, and it was decreed, with some rationality, that Easter should be celebrated on the same day everywhere. To take an extreme example, if the equinoctial full moon fell on a Sunday in China and a Saturday in the United States, then Chinese Easter would be a week later than the American Easter.3

The actual full moon was difficult for the ancients to determine, so initially the calendar was based on the first sighting of the new moon, which then became the first day of the month. Then Passover (Pesach) fell on the fourteenth day of the month (Nissan).4 But as the Jewish civilization spread it became impossible to disseminate the fact of the new-moon sighting sufficiently rapidly, and the Jews switched to tabulated moons. The Catholic Church also adopted tabulated moons in order to avoid the difficulties mentioned above.

Since the Roman world and hence the Catholic Church had adopted the solar Julian calendar, the problem arose of making the Jewish lunar calendar compatible with the solar calendar. If this could be done then from a given Easter the dates of Easter for a number of years in advance could be determined. The problem is the incommensurability of the lunar and solar years. The lunar month (time between successive full moons, not the sidereal month) is 29.53059 days long, while the solar year consists of 365.2422 days (rounded off to 365.25 in the Julian calendar, a source of second-order problems). A little arithmetic produces the (approximate) 19-year cycle of the full moon, that is 19 solar years contain 561.081 lunar months. This cycle permits the extrapolation of the date of Easter far into the future from 19 original data points. This Metonic cycle was discovered in Alexandria (by Meton, a Greek mathematician) and was used throughout the fifth and sixth centuries.

Following the lead of Council of Nicea, in the sixth century the definition was changed in that "vernal equinox" became "March 21" where it remains today. (Cf. footnote 1.) The importance of this choice is demonstrated by the author in Chapter 5. (Cf. below).

The first chapter of The Sun in the Church gives a detailed history of the struggle to determine the date of Easter, including the reformation of the calendar sponsored by Pope Gregory XIII in 1582 to account for the fact that the Julian year was abut 11 minutes too long.5 While this doesn't seem like much, by 1582 it amounted to ten days, meaning that the Easter was moving backwards. After sufficient time had elapsed, Easter would come before Christmas setting the Crucifixion before the Nativity, an obvious logical impossibility. By now everyone should know that whereas in the Julian calendar every year whose number was divisible by four was declared to be a leap year, according to the Gregorian scheme even century dates were not leap years unless they were also divisible by 400. Although Catholic countries adopted the new calendar in 1582, the Protestant world only adopted it in the middle 1700's, the Greek Orthodox Church in the 1900's and the Russian Orthodox Church never!6 The Russian government adopted the Gregorian calendar only after the revolution, explaining why the October revolution is (was) celebrated in November.

All of the above is numerology, but fascinating. However, the final seven chapters of the book describe actual astronomical measurements carried out before accurate instruments were available, the main purpose being to determine the date of the equinox and the length of the equinoctial year.7 Chapter 2 describes, through ample diagrams, the geometry of the earth-centered universe (still useful--even essential--today to those interested in the motions of the stars, the planets and the luminaries). It then gives a detailed explanation, with pictures, of the instrument constructed in 1574 on the facade of Firenze's Santa Maria Novella to determine the precise time of the equinox, the length of the year and the inclination ? of the earth's axis to the ecliptic (the so-called obliquity). That instrument is still there today! Then the merdiane are described. These are lines constructed on the floor of various large churches and cathedrals on which the sun's image falls exactly at noon (through a window high in the wall of the church. The Church becomes in effect a huge pinhole camera). By measuring the length of time it took the sun's image to return to a given point, the length of the (equinoctial) year could be determined.

The laying out of the meridiane obviously required careful engineering, as they had to be straight and level. Chapter 3 discusses this problem, and also the questions of solar parallax, determination of latitude (an essential parameter, the author points out, in laying out the meridian line) and the "eccentricity" of the sun's "orbit" (under the Ptolemaic model, of course). This long and abundant chapter even goes into Kepler's model of the solar system, and introduces a fascinating concept I had never heard of, namely the "eccentric anomaly." See page 115.

Chapter 4 goes into more detail on the amazingly precise measurements of solar parallax and atmospheric refraction, the obliquity of the ecliptic and the earth's radius.

Chapter 5 returns, inter alia, to the question of Easter with the following fascinating example. In 1665 the vernal equinox fell on Friday, March 19, with the full moon coming a few hours later. Thus, Easter would fall on March 21 according to the canonical scheme. But the Nicean equinox of March 21 would lead to the next full moon's falling on Sunday April 18, and hence Easter would be on April 25. This, as far as I know, is the latest date possible for Easter, which did indeed fall on April 25 in 1944 and will again in 2038.8 Further problems arose with the Easters of 1700, 1701, 1703, and 1704, and as a result the Protestant world at last decided to adopt the Gregorian calendar despite the belief in some circles that it was a "Popish plot." The chapter then goes on to describe the improvements in the meridiane fostered by Pope Clement XI in order to improve the measurements on which the date of Easter was based. Very accurate values were obtained for the solar year, the lunation (i.e. the length of the average lunar month) and for the equinoctial precession. This corresponds to 50'' of arc per year, easily observable with the improved instruments (it's about a 20 minute change in the length of the equinoctial year).

Chapter 6 deals with the problems created by the fact that the "cathedral observations" actually supported the heliocentric model, a model which had been condemned by the Church, and the Church's attempts to cope with this problem. These attempts included book banning, censorship and, for example, the persecution of Galileo.

Chapter 7 describes the "modern" cathedral observatories, i.e. those of the 18th and 19th centuries which made amazingly accurate measurements. For example, the obliquity of the ecliptic was measured in 1756 to be within 1'08'' of arc to today's value. It goes on to discuss the construction of telescopes in those days (which were often constructed very long, with huge lenses) and alternative devices such as quadrants attached to walls. The two devices, telescopes and quadrants, essentially put the meridiane out of business.

The last chapter discusses "time" and how the cathedral observatories were used to determine precisely the times of local noon, taking into account the fact that the speed of the sun on the ecliptic is not uniform (since that path is not circular). This leads to esoteric concepts such as the "true" and "mock" suns and a strange-looking curve called "the equation of time" and the geometrical device used to measure it, namely the analemma. (See page 282 for a picture and Appendix B for the math,)

Although this book requires nothing more than a (profound) knowledge of high-school geometry (and some trigonometry) it is Tough!9 I found it to be highly enjoyable and rewarding, although in the process of working through all of the proofs and derivations I thought I found a couple of errors. I say "thought" since I was not completely sure of my grasp of high-school essentials.

In any event I highly recommend this book to anyone10 who appreciates the wonders of astronomy, especially he or she who believes, as I do, that the unraveling of the mysteries of the heavens represents the supreme achievement of the human intellect. And for her/him who thinks she/he already knows all that stuff, I've compiled a list of terms for you to define. If you can't, then you don't already "know all that stuff."


  1. Meridiane*
  2. Metonic cycle*
  3. Line of absides
  4. Obliquity of the ecliptic*
  5. Armillary sphere
  6. Acta eruditorium
  7. Epact
  8. Saltus
  9. De temporum ratio
  10. Equinoctial colure
  11. Solstitial colure
  12. Radio latino
  13. Almagestum novum
  14. Ephemeris of Jupiter's moons
  15. Urbanoctarians
  16. Solar eccentricity
  17. Eccentric anomaly*
  18. Equant
  19. The spot on the floor
  20. Analemma*
Well, I could go on virtually forever, but perhaps I've written enough to convince the reader that he/she has something to learn from the book. Starred items on the list above have been mentioned earlier in the review.


  1. Today the rule is the first Sunday after the first full moon on or after March 21 (rather than the vernal equinox).
  2. Readers who think that Lent is 40 days long should be advised, especially if they give up some pleasure such as sex or alcohol during that season, that Sundays are not part of Lent.
  3. That is, if Easter were celebrated in China.
  1. This explains why days begin at sundown in civilizations which adhere to lunar calendars. In fact, the Muslim world still uses the sighting of the new moon to determine the first day of Ramadan (according to press reports).
  1. This is the second-order problem mentioned earlier.
  2. So the Russians celebrate Christmas on January 6, the Feast of the Epiphany in the rest of the Christian world.
  3. The equinoctial year differs from the solar year due to the precession of the equinoxes.
  4. In 2000, Easter fell on April 23, the latest date (except for 1944) of the 190 listed in The Book of Common Prayer except for the two April 25’s noted in the text, April 24 (2011) and additional April 23’s (1905, 1916 and 2079).
  5. That is, tough with a capital "T."
  6. Anyone with sufficient technical background, for example, which certainly includes all of the readership of this journal.

Paul F. Zweifel