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Clock errors and the regulation, rating and comparison of Flamsteed's clocks (1676-1719)

 

page under construction

 

As far as can be discerned, no detailed analysis of Flamsteed's methods of observing, recording and reducing his observations has been made since Francis Baily's partial study in the 1830s. This culminated in 1835 with the publication of his book An account of the Revd. John Flamsteed, the first Astronomer Royal. Baily did not however pay much attention to the clocks and how they were used and regulated.

Later, in the early 1970s, Derek Howse at the Old Royal Observatory, carried out a detailed study of the clocks from a horological perspective. This was published in Antiquarian Horology and subsequently reissued as an off-print under the title The Tompion Clocks at Greenwich and the dead-beat escapement. It is recommended reading and often available at a reasonable price through AbeBooks.

What follows is the first study of how the clocks were used in practice. It is very much a preliminary study.

Flamsteed tells us very little about the clocks and next to nothing about the way he used them. It has required much detective work and cross-referencing particularly as much of the material has not been transcribed, and much of what has, is not available in a digital format.

 

The sources

What follows draws primarily on the following sources: 

• The published observations (Historiae Coelestis Libri Duo 1712 & Historia Coelestis Britannica (1725)
• The English translation of the prefaces to the two Historias published by the National Maritime Museum in 1982 under the title The preface to John Flamsteed's Historia Coelestis Britannica (Maritime Monographs and Reports, No.52) 
• The original observing books, the multiple copies that were made from them and the reductions that were subsequently made (all preserved in the Observatory Archives (RGO1)
• The published correspondence of Flamsteed (over 1500 letters)
• Baily's book and Howse's study of Flamsteed's clocks

It is not known how complete the records in the archive are. It is known for certain that some of the original observations are lost and some things that might be expected to be there are missing. No fully detailed catalogue ever been produced, perhaps in part because there are many records whose meaning and structure would probably have been obvious to Flamsteed but are not necessarily obvious to us. 

Three different versions of the catalogue are readily available.

1. Baily's catalogue from the 1830s
2. The old digital catalogue (the Janus version, now archived)
3. The current on line version of the catalogue (ArchiveSearch)

Although Baily's catalogue is regarded as obsolete, it does contain information that was presumably considered  inappropriate for a modern catalogue, but is none the less very useful. 

The old Janus catalogue was based on a revised catalogue produced by Francis Wilmoth during 1979-80 and later revised and edited by Lesley Murdin and Adam Perkins. It remained in use until the 2010s. In the preamble at the start the general arrangement and is described:

'During the 1830s, the collection was arranged and catalogued by the stockbroker and astronomer Francis Baily (1774-1844). Baily examined a rough catalogue of the papers that had been compiled in or soon after 1771, and concluded that while the overall composition of the collection had been retained since Flamsteed's death, the papers had become disordered through neglect. He undertook a reorganisation of the collection, giving prominence to the dispute connected with the Prince Consort's sponsorship of the publication of Flamsteed's stellar catalogue. He separated letters relating to this dispute from the bulk of Flamsteed's correspondence, and created a related series containing Flamsteed's correspondence with his friend and assistant Abraham Sharp. The remaining letters were arranged in alphabetical order of writer. The completed catalogue was published in 1835 as a prefix to Baily's 'Account of the Revd. John Flamsteed'. The modern catalogue essentially retains the order established by Baily, with the addition of the later accessions, RGO 1/72-76.'

The current catalogue contains one additional item RGO1/77 which was added in 2022, The description of the general arrangement that accompanies it has been updated to reflect this. The actual content is the same as the earlier version. The older version is preferred by some researchers as unlike the current catalogue the whole of it can be viewed on a single webpage making a word-search much quicker to perform. The current version requires a new page for each section viewed.

What is apparent from both the manuscript and the published observations is a lack of consistency in the way that the data is presented. Numerous examples are mentioned below. What it shows is that although Flamsteed had a broad plan about his observations would be published, he did not have a plan that would provide for consistency from the start. This is very obvious in the published observations and was probably made worse by the fact that  printing began before all the sheets of data had been prepared for the press. One practical consequence of this variation is that word or phrase searches could easily lead to things being missed.

 

The publication of the two Historias

Flamsteed's observations were published in Latin in two editions. The first, Historiae Coelestis Libri Duo, appeared in 1712. The story of how it came to be published is both complex, and acrimonious and resulted in Flamsteed having a lifelong feud with both Halley and Newton. Flamsteed thoroughly disapproved of it. Following the death of  Queen Anne in 1714 and Newton’s patron, the Earl of Halifax, in 1715, he was able to acquire 300 of the 400 copies that had been printed. After extracting those pages of which he approved for reuse in a new edition (those that had been printed before the end of 1707), apart from a few copies, he burnt the rest. 

The second edition was published posthumously in three volumes in 1725: 

Historia Coelestis Britannica Volume 1
Historia Coelestis Britannica Volume 2
Historia Coelestis Britannica Volume 3

The pages extracted pages from the 1712 edition make up the bulk of Volume 1 which covers the years 1676-1689, whilst the observations in Volume 2 cover the period 1689-1719. Volume 3, amongst other things, contains his star catalogue as well as a lengthy preface that runs to some 164 pages of text. It was originally intended to be rather longer, but following Flamsteed's death at the end of 1719, his widow and assistants decided that the section berating Newton and Halley should be supressed. 

The 1712 edition also had a preface, but this one was very much shorter and was written by Halley. 

 

Flamsteed's observing Instruments

The Observations from which Flamsteed compiled his star catalogue were made with just a handful of instruments:

1. The Small Quadrants which were used to measure the Sun's altitude from which Flamsteed was able to deduce the time
2. The 7-foot Equatorial Sextant, which was his main instrument until 1689
3. His Mural Arc, which was the main observing instrument from 1689 until his death in 1719

Other important instruments he made use of were the Sirius Telescopewhich was set up in 1677 and the 'Slight' Mural Arc which was the precursor of the later Mural Arc.

In addition to these, Flamsteed had a number of long refractors that were used for observing eclipses and the satellites of Jupiter. He also had two telescopes that turned out to be useless: Hooke's 10-foot Mural Quadrant and theWell Telescope both of which were first tried out in 1676. 

 

Introduction

Flamsteed made the great majority of his published observations in three distinct locations: the Octagon Room (1676-1719), the Sextant House where the Equatorial Sextant was installed (1676-1690), and the Quadrant/Arc House (1689-1719) which is where he installed the Mural Arc in 1689. He may also have made a small number of observations of solar eclipses in the eastern Summer House (and possibly the western one). He also made a few attempts to observe from the bottom of the Well Telescope (not published) and with his long refractors from the roof of Flamsteed House and from the garden. The Octagon Room, the Sextant House and the Quadrant (Arc) House were each equipped with their own clock or clocks in the case of the Octagon Room. Flamsteed also had a portable clock.

Until the introduction of atomic time in 1967, the rotating Earth and the length of the day were the basis of our timekeeping system. When the Observatory was founded precision timekeeping was still very much in its infancy. It had long been known that natural days varied slightly in length and that the difference between apparent and mean solar time varied during the course of the year. The difference between apparent and mean solar time is today known as the equation of time. In Flamsteed's era, it was sometimes referred to as the equation(s) of natural(l) day(e)s. In 1672, three years before he became Astronomer Royal and before he even owned a clock, Flamsteed wrote a paper on the equation of time –  De temporio aequatione diatriba. It first appeared in 1673 as an appendix to John Wallis's Jeremiae Horrocci opera poshuma (which was reprinted in a different order in 1678).

Many astronomers also believed that the Earth was rotating at a steady rate (i.e, that it was isochronal) – but nobody had yet be able to show it, not least because prior to the invention of the pendulum clock by Christiaan Huygens in 1656, nobody had a sufficiently accurate timekeeper to do so.

In 1721, the Observatory acquired its first Transit Telescope – a telescope mounted between two piers in such a way that it could only point higher of lower in the plane of the meridian. By 1750 and until 1871, the Transit Clock (i.e. the one used with the Transit Telescope) was the Observatory's de facto sidereal standard – the clock to which all others (including those set to mean solar time) were ultimately referred. The transit clock itself was checked by comparing it with the rate of the Earth's rotation using the telescope. Certain of the brighter stars, whose positions had been refined by repeated observation over a long period of years, were used as ‘clock stars’ to determine the errors of the Observatory’s clocks and hence the local time at Greenwich. In 1851 for example, some 67 clock stars were kept under observation for this purpose. With the help of a good clock, astronomers were able to reverse the process and determine the right ascensions of stars from their times of meridian transit.

When Flamsteed became Astronomer Royal in 1675, he considered the best available star catalogue to be that produced by Tyco in 1598 long before telescopes, pendulum clocks, logarithms and the micrometer screw had been invented. Even if Flamsteed had had a transit telescope, it would not have been much use for determining accurate clock times as the star positions in the catalogue were not of sufficiently accuracy ... and it was, after all, partly to improve this catalogue, that the Observatory had been founded. Given the absence of any established 'clock stars', Flamsteed needed to find a different way of compiling his catalogue to that used by his successors. 

 

Treading in Tycho's footsteps

In 1669, Flamsteed started corresponding with various fellows at the Royal Soicety (the president, Lord Bruckner; the secretary,  Henry Oldenburg; and John Collins, who oversaw the financial accounts. In a letter to Oldenberg sent in April 1673, Flamsteed wrote:

'had the latitudes of the fixed star of Tychoes constitution beene exact and coherent, wee should easily have determined the praecise quantity of this inclination [the Eclipick], and those regular inequalityes wee find in this and in all the other planets which are found irrepresentable by numbers, onely by reason of some latent errors in the places and latitudes of the fixed:  wee can expect no great effect from Hevelius his endeavors since hee uses no glasses. It would be a takske deserveing the paines and accuracy of Cassinus, and of all others, worthy the French observatory, to endeavor the restoreing of these fixed stars especiall those which lie neare the ecliptick.  had I onely a large 7 foot Wall quadrant, a Sextans or octans of the same radius, a convenient place for observeing, one good pendulum clock and a ready assistant“, I should not doubt in a few nights. to rectifie a many of Tychos errors and add some stars to his cataloge as well visible to the bare eye, yet omitted, as Telescopicall: but this apparatus being beyond my facultys, I can onely, as it were, dreame of, and wonder that amongst so many ingenious persons of large estates there should be none that dares adventure at so small charges, as this provision requires, to undertake this worke whereby hee may raise him a selfe a name greater then Tychos, and a monument with posterity - aere perrenius:'

As an aside, it is worth comparing the manuscript copy of the letter with the edited version that appeared in Philosphical Transactions, where amongst other cuts, the derogatory comment about Hevelius has been removed (Phil Trans R.Soc. 1673, Vol 8, 6033-36).

At this point in time, it would appear that Flamsteed's planned to measure the positions of the fixed stars in much the same way is Tycho, i.e to measure declination with the wall quadrant fixed in the plane of the meridian and to triangulate his way around the sky by measuring the angular distance between pairs of stars with the Sextant.

When he became Astronomer Royal, these were the instruments together with a pair of clocks that he was provided with by his patron Jonas Moore. There is no indication that he planned to use the Mural Quadrant with a clock to measure right ascensions.  In the preface to the 1725 Historia he merely states 'I asked that a quadrant or arc be made first, for measuring the meridonial altitudes or distances of the fixed stars from the vertex: and this was promised to me' (Chapman 1982 p.118). No record has yet been found that suggests that the the deviation of the Quadrant from the meridian at different points was ever measured as part of a calibration process – something that would have been essential if the instrument was to be used for finding right ascensions with the help of a clock. Having said that, since it rapidly became apparent that the Quadrant was not fit for purpose, Flamsteed may have thought it not worth is while to calibrate it and by 1678 seems to have stopped wasting any more time with it. With no immediate prospect of a replacement instrument, found a way of measuring a number of 'meridonial distances of the stars' from the vertex with the Sextant (Chapman 1982 p.119). None of this of course precludes the fact that Flamsteed may have had it in mind from the beginning that there was a possibility that the quadrant might prove suitable for measuring right ascensions as well as declinations.

By 1678, Flamsteed had satisfied himself that the Earth was isochronal and this opened up the possibility of measuring relative right ascensions with the help of a clock with a proven record of consistent timekeeping and a suitably rectified and calibrated mural instrument. This was possibly on his mind in early 1680 when in a letter to Seth Ward written at the end of January he wrote: 

'If you ask me what are the Right Ascentions of the aforementioned stars, I must needs confess I have not yet absolutelye determin'd, nor can I for want of a good Meridionall fixed Quadrant, but by such Observations as I have made with the Sextans, I find that if the Right Ascention of the bright * of Aries be stated 27°.18'.20". to the beginninge of this Year 1680, it will answer the Suns Meridionall heights, as near as I can expect, the Right Ascensions of the rest may be easilye made by the addition of the first difference to this, and the followinge to the Summs, and thier Places thence easilye computed in Longitude, and Latitude, supposeinge the obliquity of the Ecliptick onely 23°.29'.00" which is the most my observations will warrant.'

 

Rectifying the Mural Arc

Int the seventeenth and eighteenth centuries it was impossible to make a mural quadrant or arc where all points along it were exactly in the plane of the Meridian. As a result, some stars would transit just before they reached the true meridian and some after. Knowing that this would be the case, Flamsteed calibrated his Mural Arc to take this into account. In the preface to the Historia (p.132-3) he described how this was done. A rough translation is given below: 

'The wall on which the Mural Arc was placed was built on the Meridian Plane, by the help of Observations of the Polar Star in the year 1675: but the instrument was not attached to it before the year 1689; after which I discovered that the southern part of the Wall subsided every year, and the Errors of the Instrument increased a little every year. I have hitherto shown the method of finding the Error, the size of which is noted in the Observations which were taken with this instrument [at the top of the last column on each page of observations in Volume 2 of the 1725 Historia].

Though, the Errors of the Mural Arc, in the Distances of the Stars from the Vertex, may be easily discovered and determined in this way; but the Errors of the Plane were not so easily manifested and established. These may arise either from the Wall on which the instrument was placed (if, of course, it is not exactly in the Meridian Plane) or from the Pole of the Telescopic Glass, if the Cell in which it lies is not placed precisely in the Center.

And therefore, that the effects of these two angles might be found together, on the 8th and 110th of April, 1690, in the morning, by the aid of a good iron quadrant, the radius of which was 4 plus feet, in which were telescopic diopters and a rim carefully divided (by my own hand and the hand of Mr. Sharp) by which a fourth, or rather a smaller, part of a minute could be perceived; with this, I say, I took the altitudes and times of the solar transits, along the lines of the wall arc, at noon; and repeating my observations of the altitude of the sun on the same day after noon, I noted the times when the rim, observed in the morning, had reached the same altitudes after noon, in which I had observed it in the morning. With these aids, I found out the time by the clock when the center of the sun was in the meridian; and comparing this with the time in which the Sun's Center passed the Southern Thread, measuring it, I found that at 40 degrees from the Vertex, the Sun, or STAR, passed the Southern Thread in a decapitated manner about 33" of fruitful time, before it had passed the true Meridian. I frequently afterwards renewed this examination of mine up to the Autumnal Equinox, and from thence discovered the Plane Errors in the whole Arc between the Equinoctial and the Tropic of Mars. That the Error might be discovered below the Equator, and between the Tropic and the Polar Star, I computed the Differences between the Right Ascensions of certain eminent Fixed Points, interjacent to the Equator and the Tropic of Mars, and the Right Ascensions of others which are between the Equator and the Southern Tropic, from the mutual, namely, their Distances, observed by the Sextant, and their Distances from the Pole, determined by the help of the Mural Arc: For from the Comparison of these with the Differences between the Times of Transits through, or Moreover, the Vertical Thread of the South in the Telescopic Index, the Error of the Arc in the Degree, which any Star traversed, became very sharp. And of these Errors I completed the Table, which I used in the Year 1690 to find the Right Ascensions of the Stars: but here it is to be noted that this Table is not needed when the Stars traverse the Meridian, at the same nearly the same Distance from the Vertex; for in the same Degree, or near the same Degree, the Errors are almost the same, or at least differ insensibly.' (from Google Translate with modifications)

Flamsteed does not appear to have published the table he produced in 1690. Nor is it specifically mentioned in any of the catalogues of the Flamsteed Archive (RGO1).  Baily however located an undated copy at the start of ROG1/39 (RGO1/39/8). The table as published by Baily is reproduced below:

	Zen.dist.o	Add (s)	Zen.disto	Add (s)	Zen.dist.o	Add (s)
	6	32s	40	33	56	25
	18	37	42	32	58	24
	28	39	44	31	60	23
	30	38	46	30	61	22
	32	37	48	29	68	22
	34	36	50	28	75	22
	36	35	52	27	80	17
	38	34	54	26	85	15

Baily found no evidence that it had been 'verified or altered as any subsequent period' and concluded that the same table was used by Flamsteed in all his reductions. It does not seem to have occurred to him to check what figures had been applied when the observations had been reduced, especially as on p.371 of his book (reproduced below)he reproduced a table from RGO 1/24/21 containing over 20 stars in which both the clock times and the adjusted times are shown. Such an examination would have shown that the values applied were not consitent with the above table. Indeed, he would have also have found a star with an observed zenith distance of 20^o46'20" had a time correction of + 42 seconds. The obvious conclusion, is not only that the above table is incomplete, but that it was also updated or had been updated at some point.

A comparison of the corrections applied to the zenith distances for the effects of refraction with the tables of refraction published in the 1725 Historia (right) also reveals unexplained discrepancies. Amongst these is why the star with a the star with a zenith distance of 34^o51'5" has a correction of 35", whilst another with the similar value of 34^o56'40" has had a correction of 40" applied. It is also unclear why all the applied corrections have seemingly been rounded to the nearest 5".

Halley appears to have been somewhat sceptical about Flamsteed's use of time differences to measure right ascensions. After moaning in the preface to the 1712 Historia about the fact that all the data that he had access to for 1689 onwards been lumped together in chronological order he continued: 

'Hence another labor of extracting the Observations of the Planets, and of differentiating them into their classes, and of deducing the right inclinations and declinations from them. Not all the Observations which we find, however, can be printed, namely, the transits of the Stars, whose declinations differ farther from each other, because the perfect plane of the Instrument, and the same perfect fit in the plane of the Meridian is assumed, so that from the time intervals the true differences of the right ascensions are obtained, which seems a daring Hypothesis. Therefore, only those of the Planets in which this difference of declinations was as small as possible have been selected.' (a rough translation derived from Google Translate)

Following this, Halley went on to say that all the lunar observations had been printed because of their importance to navigators.

Based on what Halley said, we can probably assume that not only was he unaware of how Flamsteed had calibrated the instrument, he was also unaware of just how Flamsteed planned to use the data to determine right ascensions.

 

Demonstrating that both the swing of a clock pendulum and the spinning Earth are isocochronal

One of Flamsteed's first investigations at Greenwich was to check if the swing of the pendulums of the two clocks in the Octagon Room was isochronal, and if this was the case, to use them to establish if the spinning Earth was tool. By 1678, with the help of a fixed telescope with which to observe the dog star Sirius that he had set up in 1677 and rhe Octgagon Room clocks, he had been able to satisfy himself that it was. Somewhat surprisingly Flamsteed did not publish a paper announcing his findings. From the time of the Observatory's founding in 1675 until his death in 1719, Flamsteed used mean solar time and/or apparent solar time for all his observations including those that he made with his mural instruments – a practice that was discontinued by his successors.

 

A brief history of the clocks owned by Flamsteed

The preface to the 1725 Historia includes an extensive description of Flamsteed's major instruments as well as the means by which he calibrated them (p.101-113). Of the clocks he says virtually nothing. The only ones he mentions are the three that he had when he entered the Observatory in 1676 ( p.103) and of these, he only tells us their going times ('duobus pendulis Oscilatoriis annuis' & 'Pendulo hebdomadario'). None of the other four are mentioned, nor does he state where where any of the clocks were deployed. 

The Sextant House Clock (where Flamsteed made most of his observations prior to the arrival of his Mural Arc in 1689) was made by Thomas Tompion in 1675. Prior to being placed in the Sextant House, it was used for a few months in the Octagon Room while the clocks for that room were under construction. The first recorded observations made there were related to the eclipse of 1676, June 11 (June 1 old style civil, May 31 old style astronomical). Details of the clock are scanty. It had a one-second pendulum, but possibly no maintaining power (this is based on a record in Flamsteed's observing Book RGO1/1 that it lost 8 seconds when it was wound on 9 October 1676).

Two year going clocks made by Tompion with 13-foot (four-metre) two-second pendulums (the Great Clocks) were installed in the Octagon Room in the summer of 1676 (probably on 7 July) and were in proper working order for the first time by 24 September. They can be seen to the left of the door in the etching below. Although at first sight, the clocks appear identical, a key difference was in the way the pendulums were suspended. The one closest to the window was suspended from a spring  whilst that nearest the door was pivoted on a knife edge. Both were set to show mean solar time, with one presumably acting as a check on the other. One thing we don't know is to what extent they may have interfered with one another (something that Huygens had previously observed in his own clocks and written about in 1673 in his book Horologium Oscillatorium). However, as Flamsteed's pendulums were long and the arc through which they swung was small, any such interference was likely to be undetectable. A third clock with a shorter pendulum (and seemingly designed to show sidereal time) was also planned for the Octagon Room though there are no obvious records of it having been used in practice.

In 1690, Flamsteed bought a new clock for use with the Mural Arc which first came into use at the end of 1689 and was mounted in the former Quadrant House. From September 1689 until the arrival of the new clock on 31 October 1690, the Sextant House Clock was used instead. Like the Sextant House Clock it replaced, the new clock had a seconds pendulum, but little else is known about it. It was probably made by Tompion.

As well as the clocks already mentioned, Flamsteed had a clock made by Tompion in 1691 with a 2/3 second pendulum that was designed to show sidereal time in terms of degrees minutes and seconds rather than in terms of hours minutes and seconds. Now referred to as the Degree Clock, there appear to be virtually no manuscript records (and no published records) of this clock ever being used.

We also know that Flamsteed had a portable clock or horologium ambulatorium. Little is know about the clock, but it does appear in one of the Francis Place etchings of the Observatory produced in about 1677. There, it is shown in the eastern summerhouse where it would presumably have been used to time solar eclipses. It was presumably also used when timings were required with one of the outside telescopes. Presumably spring driven It was probably only wound when needed for observing and would most likely have been set by comparing it to one of the clocks in the Octagon Room. There are sporadic references to it by name in the original observing books (RGO1/1-8).

There are also occasional references in the observing books to a 'horologium suprá' and a 'horologium infrá' which were presumably alternative names Flamsteed used for two of the clocks already mentioned (one of the Great Room Clocks and the Sextant House Clock?). An example can be found in the observing book (RGO1/3) under the date of 2 October 1685 where Flamsteed has recorded:

19.28.00 Horologium Suprá
19.28.19 Horologium infrá

The Octagon Room Clock was also referred to as the 'Horologium in Camera Superiore'. There are several references to it in both the observing books and the published observations during November and December 1689 it's time was being compared with that of the Sextant House Clock while the Mural Arc was still undergoing the calibration process.

Of the seven clocks owned by Flamsteed, only three survive: the two great clocks (both of which have been modified from their original form and the Degree Clock.

 

Flamsteed's observing books

Rather than each location at the Observatory having its own observing book, all the observations were recorded chronologically into a single volume, new volumes being started as and when needed. Some of the observations and notes are recorded in English and some in Latin. Not all of the observing books survive. There is no book of the original entries from 17 November 1702 to 2 January 1712 exclusive. The surviving volumes have the class marks RGO1/1-8. The missing entries would have been preceded by the entries in RGO1/7 and followed by those in RGO1/8. We know from Flamsteed's preface to the 1725 Historia that these First Night Notes (as he referred to them) 'were wrote in 4^to Volumes & from them were commonly transcribed correctly into large folios next morning from which the [later] Copies were taken.' (Newton Project RGO1/32C & Baily's Flamsteed, p.80). Those made from the observations made between 1689-1719 (RGO21/4-8) appear to have been transcribed into the volumes that now carry the classmarks RGO1/15-17 and are described by Flamsteed as 'Apographa' and in the current catalogue as 'exact copies'. This is not entirely true as some data that is key to the present investigation was omitted (more on this later). Although he did not comment on this particular omission, when he catalogued the papers in the 1830s. Francis Baily did write:

'In the preceding volume [RGO1/15], and in the present one [RGO1/16] as far as the end of 1698, the zenith distances are copied from the originals with the correction of the instrument applied; which does not always accord with that which Flamsteed ultimately adopted. I would also remark that I have occasionally met with entries of observations which are not to be found in the original MSS: so that it will be necessary to examine these copies as well as the originals, in case of any revision of the observations.'

There is also at least one incidence of a whole day's observations being omitted, for example those that took place on 24 July 1690, seemingly after some issue with the clock at the start of the day's observing.

There is nothing in the archive catalogue to suggest that the earlier observations were copied in the same way. What may have happened is that they were transcribed into a variety of different places depending on the type of observation. Further research is required to properly understand how RGO1/1-3 were processed.

The clock times in both the 1712 and 1725 Historias are given in terms of the astronomical day, with each day beginning and ending at midday (rather than the civil day which ran from midnight to midnight and started 12 hours earlier). It is important to note too that all Flamsteed's clocks (apart from the unsuccessful Degree Clock) were set to mean solar time rather than sidereal time. Despite the fact that the observations as published in the Historias were given based on the astronomical day, Flamsteed only started using astronomical time in the observing books when the mural arc came into use in 1689 (RGO1/4-8). The times recorded in Flamsteed's first three observing books (RGO1/1-3) were recorded in terms of the civil day using a 12 hour rather than 24 hour notation. Civil time was also the time system used for eclipse observations in Philosophical Transactions where some of Flamsteed's observations were also published. 

Despite the fact that Flamsteed was using astronomical time in the observing books used with the mural arcs, there was an anomaly, at least to start with (and until at least 1693), about the way in which he recorded the times of the Sun's transit, Those observations that were made at the end of the astronomical day were recorded with the following day's observations but the time was given using a 12 hour nomenclature for example 11.55.46 on 18 April 1690. When transferred to the apocrapha this was recorded as A.M. 4.14, by which Flamsteed meant 4 minutes 14 seconds before 0h, 0', 0" astronomical time. In the published observations, it was recorded under 17 April as 23.55.46.

There are also a number of anomolies where in the published observations where both the civil date and the astronomical date are given. For example, the first two days worth of published observations are given as 1689, 'Sept.11 vel 12 mane' and 'Sept.12 vel 13 mane'. There are eight other occurancies, with the last one being on 1690 Feb 4 vel mane 5.

Although he recorded the time of each observation, Flamsteed did not record where in the Observatory the observation was made or the clock used. When he came to publish his observations, those from different locations remained lumped together in chronological order, again without any mention of clock or location. Although other factors mean that it is often possible to distinguish observations made in the Octagon Room from those made elsewhere this is not always possible. Nor is it possible to discern from which of the two Octagon Room clocks the recorded time was taken though this would not matter if Flamsteed always took the time from the same one if they were syncronised (which seems unlikely). Flamsteed seems to have 'corrected' (ie deduced the errors) of the clock he was using in the Octagon Room from measurements of the Sun's altitudes (more on this later). Similar observations of the Sun's altitude were also made in the Quadrant house during the commissioning of the Mural Arc and possibly later. Likewise, the published observations and correspondence show that Flamsteed used a projection screen to view a solar eclipse on at least six occasions but there is no explicit record of whether these observations were made in the Octagon Room or in one of the Summer Houses. For more information on this see: Solar eclipses observed at Greenwich during the time of Flamsteed (1675–1719).

 

The recording adjustments made to the clocks

Unlike the published observations from Bradley's time onwards, those of Flamsteed do not record the adjustments made to the time shown by the clock once the cumulative error had exceeded an acceptable value. An examination of the observing books show that by the time he was using the Mural Arc (if not before) such alterations were recorded in the observing book and transcribed into the apographas (RGO1/15-17). 

On 10 February 1690, in both the observing book and the apocrapha , this was flagged not only with a comment, but also by the drawing of a pointing hand alongside it. On this occasion, Flamsteed put the clock forward by 25 seconds which was also recorded in the 1725 Historia. Further research is required to see if Flamsteed always commented in the observing book and if this was always transcribed.

Other comments can certainly be found in the 1725  Historia, In the entry for 30 October 1690, Flamsteed records 'purgato prius horologio' (after having first cleaned the clock). The following day, in the Observing book, Flamsteed recorded in Latin 'I have put the new clock next the old one in the Arc House, and have set the hands at the same time, 9.39.00.a.m.' This was not transferred to the apocapha nor is there any mention of a change of clock in the published observations. However, a note in the observing book made a few days later on 4 November about Abraham Sharp leaving to teach mathematics was transferred across to the apocrapha.

.....

 

From observing books to publication - the organisation of the times recorded in the Historias

Things are not straight forward. The first of the 1725 volumes contains observation made between 1676 and 1689 when the equatorial sextant was the main observing instrument. The second contains those made between 1689 and 1720 when with the Mural Arc was the main instrument. However, the way in which Flamsteed presents his observations changes between the two volumes. In Volume 2, the observations are published in the order that they appear in the observing books. In Volume 1, they are divided into six categories (which makes comparison with the observing books a lot more time consuming). They are numbered from two to seven.

No explanation is given for the change in presentation between the two volumes. Nor does Flamsteed explicitly explain how he rated his clocks or deduced their errors. Nor did he publish tables of their rate or error, though it is possible (though unlikely) that such tables exist and are waiting to be discovered in the archives.

Not all the manuscript observations appear in the printed Historias. One example of those omitted are the observations of Sirius made with with the Sirius Telescope in the late 1670s. Another example is the third set of observations of the Sun's altitude that he took for correcting the clock at the time of the solar eclipse of 1676 (the three sets of observations having been taken on 31 May and the 1 June). It should be noted here that there is also an unexplained discrepancy in these particular sets of altitude observations in the observing book and those subsequently published in the Historia and Philosophical Transactions, which also differ from one another. Other examples of observations of the sun's altitude being omitted from the Historia have also been found.

 

The column headings relating to time in the two Historias 

The following column headings relating to the clock were used in the two editions of the Historia:

	Latin term used	Translation
1	Temp. App. / Temp. Ap.	Apparent time
2	Tempora per Horologium Oscillatorium/Tempora per Horolog. Oscillat.	Time by the pendulum clock
3	Tempora ex Altitud. Correcta	Times corrected by altitude(s) [of the Sun]
4	Tempora ab Observationibus Correcta	Times corrected by observations
5	Tempora Correcta	Corrected times
6	Tempora (inde) ab Observationibus Correcta	Times corrected (from) observations
7	Tempora vera Apparentia	True apparent times
8	Tempora vera & correcta	The true and correct time
9	Tempora juxta Horolog. Oscillatorium	Times according to the pendulum clock
10	Transituum tempora per horologium Oscillatorium	Time of transit by the pendulum clock

 

The grouping of observations and the times as published in volumes 1 & 2 of the
1725 Historia and books 1 & 2 of the 1712 Historia

	Section from 1712 book 1 & 1725 Vol.1		Times given
2	Distances of fixed stars taken with the sextant (1676–1689)4		Temp. App.1
3	Observations of comets & primary planets made with the sextant (1676–1689)5		Temp. App.1
4	Observations of the Moon's approach to fixed stars made with the sextant and other instruments (1676–1689)		Tempora per Horologium Oscillatorium & Tempora ex Altitud. Correcta
5	Observations of the configurations & eclipses of the Jovian comets (1676–1689)		Tempora per Horologium Oscillatorium & Tempora ab Observationibus Correcta
6	Observations of sunspots (1676–1689)		Tempora Correcta
7	Observations of altitudes & distances of the sun from the vertical quadrants and the distances of Venus from the sun made with the sextant for investigating celestial refraction (1678–1681)		Tempora per Horologium Oscillatorium & Tempora (inde) ab Observationibus Correcta2
	Sections from Book 2 (1712 edition)
1	Observations of the primary planets made with the Mural Arc (1689-1705)		Tempora juxta Horolog. Oscillatorium2 & Transituum tempora per horologium Oscillatorium & Tempora vera & correcta1
2	Observations made of the Sun and Moon with the Mural Arc (1689-1705)		Tempora per Horolog.Oscillat. & Tempora juxta Horolog. Oscillatorium & Tempora vera & correcta
3	Observations of eclipses of Jupiter (1689-1705 [1702])		Tempora juxta Horolog. Oscillatorium & Tempora vera & correcta
	Sections from Vol 2 (1725 edition)
1	Observations of the fixed stars & planets (and the moon and sun) made with the Mural Arc and other instruments (1689–1720 [1719])		Tempora per Horologium Oscillatorium & Tempora vera Apparentia & Tempora vera & correcta3

1. Times given to nearest minute only
2. Only applies to some observations
3. This heading probably used incorrectly on pages 3-36 (out of a total of 573) instead of Tempora vera Apparentia
4. The distances of the fixed stars are further rearranged in chronological order by constellation.
5. The observations of Comets and primary planets are also arranged chronologically in the following order: comets, Saturn, Jupiter, Mars, Venus, Mercury.  

 

The Sextant House Quadrant / Arc House clock conundrum

Until 1690, Flamsteed had only one clock available for use in both the Sextant House and the Quadrant House (later referred to as the Arc House). The first? recorded observation made with the Sextant was made on 14 September 1676 and the first? published observation a few days later on 19 September 1676. Meanwhile, in July 1676, Hooke's Mural Quadrant had been mounted in the adjacent Quadrant House. With only one clock, Flamsteed would not have been able to make timed observations in both locations.

It is interesting to note, that the set of Francis Place etchings (that date from about 1677 and were originally probably intended to be included in the Historia) includes images of both Hooke's Mural Quadrant and the Equatorial Sextant with a clock clearly in view alongside the latter. There was no clock in the Quadrant House until it was moved for use with the Mural Arc.

The last published observations in the Sextant House were made on September 3 and the first recorded and published observation in the Arc House (the former Quadrant House) on 12 September 1689 (RGO1/4)

 

......

 

Explicit comparisons of the Arc House Clock with the Octagon Room Clock included by Flamsteed in Volume 2 of the 1725 Historia

In Flamsteed's time, the Octagon Room was known as the Camera Stellata. Fourteen explicit references have been found that compare the time on the clock there with the time on the clock in the Arc House. They all date from the period 1689-1690 while the Mural Arc was undergoing calibration and the Sextant House Clock was being used with it. They are entered under the following dates:

	Page	Date	Phrase used	Arc House Clock	Octagon Room Clock	A - O
	6	1689, Nov 16	Per Horologium in Camera Superiore	05h29'19"	05h29'00"	+19"
	8	1689, Nov 23	Supra in Camera Observ	00h31'33"	00h31'00"	+33"
	9	1689, Nov 28	"	10h36'07"	10h36'00"	+7"
		1689, Nov 30	in camera	00h13'00"	00h12'00"	+60"
	10	1689, Dec 01	in camera supra	19h45'48"	19h44'00"	+108"
		1689, Dec 02	"	00h13'54"	00h12'00"	+114"
		1689, Dec 09	"	05h53'00	00h53'00"	+0"
	11	"	"	15h38'15"	15h38'00"	+15"
		"	"	23h57'32"	23h57'00"	+32"
	12	1689, Dec 12	Supra in Camera	09h05'20"	09h02'00"	+220"
		"	"	09h30'20"	09h30'00"	+20"
		1689, Dec 13	"	05h42'31"	05h38'00"	+271"
		"	"	10h06'48"	10h02'00"	+288"
	18	1690 Jan 13	"	07h51'51"	07h52'00"	-9"

The figures are all over the shop making alarm bells start to ring such as why the comparisons were stopped before the rates had stabilised. A reasonable explanation for the figures being all over the shop is that one or other of the clocks was undergoing adjustment. However, there is no mention of any such adjustments in the published observations, the apographa or the observation book. It is interesting to note too that Flamsteed used five different phrases for the same thing. However, it should also be noted that with just one exception (p.9), the same phrase was used for all the entries on any particular page.

 

Determining the true time from observations of the Sun's altitude

 

Interpreting the observations

All this presents a problem when trying to work out how Flamsteed obtained the rate and hence the errors of his clocks. There are occasional references to comparisons between the the Sextant House and Octagon Room Clock in the first volume of Flamsteed's observing book (RGO1/1). How they were made is not stated but it was presumably by means of his portable clock or a watch.

We can be pretty sure that to start with at least, Flamsteed determined the errors and rate of the clocks used in the Octagon Room clocks by making equal altitude observations of the Sun. By 1678 however he also had the means to determine their error and rate from observations made with the Sirius Telescope, but no evidience has been uncovered to suggest that he did?

Likewise, the errors and rate of the mural arc clock could easily have been determined from observations of selected stars as they crossed the meridian. But an examination of the observations shows that he probably determined them by applying the equation of time to timings of the Sun as it crossed the meridian.

Hypothesis:

In volume 2 of the Historia, timings made in the Octagon Room were converted into the equivalent time shown by the Quadrant (Arc) House at the same moment, the comparison being made with the help of the horologium ambulatorium

Possible evidence (1).

The timings of the observations of Jupiter's satellites on 20 September 1702 recorded in the Observation Book (RGO1/7) differ from those published in the Historia, in one key respect. Each of the clock times is preceded by another that is 7minutes 27 seconds ahead. It is therefore surmised that the first time is the time by the Octagon Room Clock and the second (the one that was eventually published), the equivalent time on the Quadrant (Arc) House clock.

Possible evidence (2).

A similar state of affairs occurs with the recording of the observations of Jupiter's satellites made on 3 February 1691. In this case, the Octagon Room Clock would appear to be 5 minutes 20 seconds slow compared to the Quadrant (Arc) House Clock.

Given that relatively few observations were made in the Octagon Room after 1689, this raises the question: were all the post 1689 Octagon Room timings converted to the equivalent time on the Quadrant (Arc) Room Clock?

Volume 1 of the Historia contains numerous off meridian measurements of the Sun's altitude, all of which appear to relate to the Octagon Room Clocks. There is a dearth of off equivalent measurements in Volume 2 and most of these took place between 8 April and 21 September 1690 in conjunction with the calibration of the Mural Arc. This could be explained by the hypothesis above.

Further Research?

Investigate the recording of all the eclipses of the Sun, the Moon and Jupiter's satellites to see how many of these are recorded in a similar way.

Little in-depth research has been done into Flamsteed's methods of recording and structuring his observations since Francis Baily's investigations of the 1830s and those more limited ones by Derek Howse in the 1960s and early 1970s. Since that time, all the known correspondence of Flamsteed has been published and many resources digitised. A serious, systematic in-depth investigation of how Flamsteed operated is now long overdue, but beyond the scope of this website. It would be a major undertaking for any research group.

 

Misunderstandings

In her book Under Newton's shadow: astronomical practices in the seventeenth century (1985), Lesley Murdin incorrectly wrote (p.129):

'To find the error of his clocks, Flamsteed attached two 5-foot telescopes to a wall so that he could take the times of well observed stars crossing the Meridian'

 

In his book John Flamsteed (1999), John Birks writes p.60:

'In addition to the two Great Clocks in the Octagon Room, which were the standard reference clocks kept accurate by stellar sightings, Flamsteed had another pendulum clock to use in his work. In the Sextant and Quadrant House he had a secondary standard clock to use in his recordings of transit times, ... The first clock in the "Arc House" ... was replaced in 1690 by another clock'.

 

Further reading

Pierre Barbier