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Decoding Flamsteed: Flamsteed's modus operandi and the methods used to compare, regulate, rate and determine the errors of his clocks (1676-1719)

This page is very much a work in progress and may undergo significant restructioning.
Some sections contain only notes at present.

Others remain to be added.

John Flamsteed. Line engraving by G. Vertue, 1721, after T. Gibson, 1712. Image courtesy of the Wellcome Collection (see below)

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 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, compared and regulated.

Over a hundred years later, Derek Howse at the Old Royal Observatory, carried out a detailed study of the clocks from a horological perspective. This was published in two parts in Antiquarian Horology in 1970 & 1971 and subsequently reissued as an off-print under the title The Tompion Clocks at Greenwich and the dead-beat escapement.

What follows is thought to be the first study of how the clocks were used in practice and how the observations were recorded and subsequently published. It is very much a preliminary study.

Introduction

Flamsteed made the great majority of his published observations in three distinct locations: the Octagon Room (1676–1719), the Sextant House (1676–1690), and the Arc House (1689–1719). Each was equipped with its 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 the early 1690s, Ole Rømer was the first to design and use what has since become known as a transit telescope. In 1721, a year after Flamsteed's death, the Observatory acquired its first such instrument. Its key role was to delineate a meridian and maintain it as a standard of adjustment for the other instruments, most notably the 8-foot Iron Mural Quadrant by George Graham, installed in 1725. Like the later transit instruments it was also used for the determination of time.

Transit Instruments consist of a telescope mounted between two piers in such a way that it can 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 Tycho in 1598 long before telescopes, pendulum clocks, logarithms and the micrometer screw had been invented. Even if transit telescopes had existed, when Flamsteed started work at Greenwich, they would not have been much use for determining accurate clock times as the star positions in the existing catalogues were not of sufficiently accuracy ... and it was, after all, partly to improve these catalogues, 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. The methods he used built on those of Tycho and were the precursor of those used by his successors.

Treading in Tycho's footsteps

Back in 1669, Flamsteed began corresponding with the Royal Society, writing to:

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 [taske] 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 [more enduring than bronze]:'

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, Flamsteed 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.'

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. Edited by Allan Chapman, it was 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 (both of which are fully referenced above)

The archive catalogue

Three different versions of the catalogue are readily available.

Although Baily's catalogue has been deemed obsolete, it does contain information that is now considered to be more appropriate for a commentary and therefore inappropriate for a modern catalogue. The commentary element most definitely remains useful for modern researchers.

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 is described as follows:

'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 or phrase search much quicker to perform. The current version requires a new page for each section viewed.

No fully detailed catalogue ever been produced, perhaps in part because there are records that it is not known what they relate to.

One of the big unknowns is how complete the archive is. Some of the original observations are lost and some things that might be expected to be there are missing.

Some documents are written in Latin and others in English. None of the archive has been digitised, though some parts such as Flamsteed's Gresham Lectures (RGO1/38) have been both transcribed and published (though mostly not in a digital format).

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.

Some of the problems when trying to analyse the published observations is the lack of consistency in the layout, the numerous transcription and typographical errors errors and the use of unexplained phrases such as "reducto pondere" which appears over 180 times in Volume 2 of the 1725 edition and appears to be a reference to the index (alidade) of the mural arc rather than anything to do with the arc house clock.

Indeed, Halley ended the preface of the 1712 edition with this warning to its readers:

'Yet in view of the great bounty of the gift [i.e. the published volume], the odd blemish should not cause offence nor the fact that so many printing errors are found in the first book, hardly excused by the haste of the toiling press ...'

Each of the two editions has an extensive errata. It is suspected that very few copies have had the offending pages corrected by their users. If anyone knows of copies that have, please contact the website though the link in the copyright notice in the footer at the bottom of the page.

Flamsteed's observing Instruments

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

The Small Quadrants which were used to measure the Sun's altitude from which Flamsteed was able to deduce the time
The 7-foot Equatorial Sextant, which was his main instrument until 1689
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 the Well Telescope both of which were first tried out in 1676. He may also have made a small number of observations of solar eclipses in the eastern Summer House (and possibly the western one).

A brief history of the clocks owned by Flamsteed

From the time of the Observatory's founding in 1675 until his death in 1719, Flamsteed used mean solar time when making his observations including those that he made with his mural instruments – a practice that was discontinued by his successors.

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, but we do know that it had a one-second pendulum. Howse speculated that it possibly had no maintaining power following his discovery in Flamsteed's observing Book that it lost 8 seconds when it was wound on 9 October 1676 (RGO1/1). However, no similar entries have have yet been found.

Two year going clocks made by Tompion with 13-foot (four-metre) two-second pendulums (which are usually referred to as the Great Clocks, the Tompion Clocks or the Octagon Room Clocks) were delivered to the Octagon Room in the summer of 1676 (probably on 7 July). It is not known how long they took to install (which was not straight forward) and adjust, but what we do know is that they only clocks in the Octagon Room by 14 September which is the date that the first recorded observation was made in the Sextant House. The two clocks can be seen to the left of the door in the etching below. Although at first sight, they appear to be 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. A third clock with a shorter pendulum of 72 1/2 inches was also planned for the Octagon Room. There are no obvious records of it having been used in practice, but there is evidence to suggest that at the very least, preparations were made to install it to the right of the door.

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 of it ever being used. There is certainly no mention of it in the Historia.

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 may only have been 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) as well as an entry under the date of 16 February 1686 in Volume 1 of the Historia (p.333), which states: 'Tempora notata fuere ab Horologio ambulatorio quibus propterea haud nimium fidas certa sunt ad minutum temporis vix proprius.' which translates roughly as 'The times were noted by an ambulatory clock, which, therefore, is not very reliable, being accurate to the minute of time.) As the observations to which it refers were made in the Sextant House, the Sextant House Clock presumably being out of order. Despite what Flamsteed wrote, all the timings are given to the nearest 10 seconds.

As well as the horologium ambulatorium, Flamsteed also mentions a pocket watch (which appears to have had both an hour and a minute hand) which he used while observing in May 1675 (RGO1/10/19&20). Nothing is known about its construction of when Flamsteed acquired it. Assumingi that he did compare them, it is entirely possible that he sometimes used it when comparing the Octagon Room and Sextant House Clocks (more on this below).

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. There are no records of his watch surviving.

The Great Clock enigma

in 1673 in his book Horologium Oscillatorium, Huygens wrote how two identical pendulum clocks, weakly coupled through a heavy beam, soon synchronized with the same period and amplitude but with the two pendula swinging in opposite directions. Given that the pendulums of the two Great Clocks in the Octagon Room were the same length and attached to the same wooden beam, it is important to establish whether they too became syncronised. the question has to be asked: did they become syncronised? It's not easy to answer. Not only that, there are many other things that remain unclear about the two clocks.

The Historias themselves provide no answers, but there are some clues in the observing books and amongst Flamsteed's correspondence. By using these, Howse compiled a table to illustrate the performance of the two clocks between their arrival in July 1676 and February 1678 which he included in his account of the clocks. Useful as it is, it is it fails to give the full picture which is unfortunate.

Flamsteed's letter to Towneley dated 11 December 1676 is worthy of study as it gives the difference in time shown by the two clocks on a roughly daily basis between 20 October and 8 December as well as the absolute error as obtained from altitude observations on six of those dates. What is quite clear is that during this very early period at least, the clocks did not become syncronised and showed no sign that they were ever going to do so. The following table is based on what Flamsteed wrote:

Pivot	slower	Pivot	slower	Pivot	slower
20 Oct	0.06	17	0.52	1 Dec	0.06
21	0.10	19	0.46	2	0.00
22	0.12	20	0.40	Pivot	swifter
25	0.20	22	0.44	3	0.04
29	0.28	23	0.44	4	0.06
31	0.38	24	0.44	5	0.22
4 Nov	0.30	25	0.44	6	0.40
6	0.36	26	0.46	7	0.50
13	0.52	27	0.45	8	1.00
14	0.52	28	0.34
15	0.52	29	0.30
16	0.52	30	0.18

What is also interesting is that in the letter Flamsteed records that altitude observation were taken on 22, 25 & 29 October, 5, 16, 17, 23 & 27 November and 3, 5 & 8 December (Civil dates?). During this period, the only altitude observations that were published were made on 30 October, 10 November and 2 & 5 December (astronomical dates). These are also the only dates where altitude observations are recorded in the observing book and what's more, the 10 November altitude measurements were not amongst those mentioned by Flamsteed in his letter. All this strongly implies that additional records on the clocks' performance must have been kept. The most likely scenario is that they are now lost, thought there remains the possibility that they are somewhere waiting to be discovered in the archive.

What is also odd is that the published figures for 5 December are at odds with those in the observing book in that although the altitude observations appear to correspond, the clock times and the clock errors recorded are all 50 seconds less than those that were published, suggesting that the recorded time may have come from one clock and the published time from the other, though there is no record of the difference in the clock times in the observing book. Nor can the figure of 50 seconds be reconciled with what Flamsteed recorded in his letter where he states the difference between the two clocks as 6, 22, 40, 50 and 60 seconds on 4, 5, 6, 7 and 8 December respectively.

A table of comparisons has also been found amongst notes at the end of RGO1/2/167, from which the following has been adapted:

1682 Jan.17. Clocks both cleaned & set together at 9^h.00' then:

Date	Spring pendulum window	Pivot pendulum door	Difference (s)
	h m s	h m s
17 Jan 1682	9. 00. 00	9. 00. 02	+2
18 Jan	6. 25. 36	6. 25. 32	- 4
21 Jan	10. 21. 14	10. 21. 00	- 14
24 Jan	9. 07. 01	9. 07. 00	- 1
26 Jan	6. 46. 00	6. 46. 07	+7
28 Jan	10. 03. man.	10. 03. 09	+9
30 Jan	11. 24. man.	11. 24. 08	+8
31 Jan	8. 24. m.	8. 24. 07	+7
5 Feb	11. 40. 50	11. 40. 00	+50
10 Feb	3. 50. 04	3. 48. 15	+109

When Flamsteed was observing in the Octagon Room, he did not record the time from both clocks. So how do we know which clock the recorded clock times were taken from? At the moment, the answer seems to be we don't. It does seems probable that in the long run at least, they were always taken from the same clock ... but if they were, then what happened if that clock was temporarily out of use and how and where was this information recorded?

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.

Amongst the observations in the published Historias are some made at the Observatory in 1678 by Edmond Halley that do not appear in the observing books. For example, those made on 27 July (in the observing books the the observations made on 23 July are immediately followed by those made on 2 August). None of the observations made between1 September and 14 October are there either, but there is a note dated 31 August 31 that states (in Latin), 1678, that Flamsteed went to Derby for about a month, on account of a dangerous illness with which he was seized: and that during his absence Dr. Halley had made some observations which Flamsteed says are described in another little book, of a few pages; and for the insertion of which, blank pages were left in the observing book. Baily however was unable to 'discover either the little book, or the observations' though some appear on the pages of the Historia that follow those made on 27 July, whilst others appear elsewhere in the volume. There are also ones that were made with the Equatorial Sextant during August that do not appear in the observing book. Another example of missing observations are those of Jupiter's satellites that were made on 12 April 1684 (p.357). Further research is required to fine other omissions.

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 apographa 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 is also a curious entry in the apographa under the date 30 April 1706 where Civil time has been used and the entry appears under 1 May. It appears under the correct date in the published observations. What was recorded in the observing book is unknown as this volume is missing.

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).

Evolving a house style and the use of standardised expressions

What is apparent from both the manuscript and the published observations is a lack of consistency in the way that data is presented. This not only makes it more difficult to carry out research, but more importantly, it makes it much more difficult to generalise with confidence. It would seem that although Flamsteed had a broad plan about the way his observations would appear in print, he had not fully thought though the some of the details in order to have a plan that would provide for consistency from the start. Things were probably made worse by the fact that printing began before all the sheets had been prepared for the press which resulted in inconsistencies in the presentation and abbreviations used. A further issue that arises because some sheets were corrected during the printing process. As a result some pages vary slightly from copy to copy. No evidence has been found to suggest that these changes are anything but minor and don't appear to affect the meaning; but one practical consequence is that it can hamper the effectiveness of a word or phrase search could easily lead to things being missed. For example, in some of the pages of some copies, 'err.' has been printed as 'err' without the full stop.

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

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)⁶	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

Times given to nearest minute only.
Only applies to some observations.
This heading was used in the second column on pages 3-36 (out of a total of 573), the remainder being headed Tempora vera Apparentia. Those on pages 1-2 in the published observations were labeled Tempora vera & correcta or Tempora correcta in the apographa. They were the last in the first volume of the apographa (RGO1/15) to have the headings written in. The headings in the second volume were also left blank (RGO1/16). However, those in the third volume of the apograph are marked 'Tempora Correct(a). There is no mention of anything about the headings being wrong in the erata. Further research is required to establish which heading(s) are correct. To do this 'accurately' requires the tables for the equation of time that were originally used to be identified. In a letter to Newton dated 18 January 1695 Flamsteed stated 'The Tables in Parkers allmanack are those I have hitherto used'. These would appear to have been published as Mercuriouse Anglicannus between 1690 to 1698 and An Ephemeris of the Coelestiall Motions from 1695 to 1699 and a Double Ephemeris from 1700.
The distances of the fixed stars are further rearranged in chronological order by constellation.
The observations of Comets and primary planets are also arranged chronologically in the following order: comets, Saturn, Jupiter, Mars, Venus, Mercury.
Includes observations made from the Queen's House from 11 February 1676 onwards.

Determining the true time from observations of the altitude of the sun and other stars, 1676–1689

Until 3 September 1689, Flamsteed found the error of the clocks by measuring the altitude of either the sun or one of a number of stars selected for the purpose. When making such an observation, Flamsteed would typically take three to five readings (sometimes more) over a period of about five minutes (or so). As far as can be ascertained, all such measurements were made in the Octagon Room with the help of a small quadrant, and published with the Lunar observations in Volume 1 of the 1725 Historia. It is important to note:

they appear only in the Lunar section which covers the period 11 February 1676 and 3 September 1689
not all the sets of observations were published

It is clearly helpful to have a feel for how frequently Flamsteed checked the clock. The table below gives the number of sets of altitude observations published in each year. It is lower than the actual number of sets recorded in the observing books. The figures given in brackets for the years 1684 & 1689 are the actual number of sets that were made. They should not be extrapolated for other years. Further study is required to establish both the number taken each year and why particular sets were excluded from publication.

Year	Sets published	Year	Sets published
1676^a	27	1683	30
1677	27^c	1684	26^c,f (at least 50 sets in obs. book)
1678	19^d	1685	15^g
1679	36	1686	18
1680	52^e	1687	15^h
1681	36^c	1688	9^j
1682	46	1689^b	10^k (30 sets in obs. book)

	a: 11 Feb - 31 Dec		b: 1 Jan - 3 Sep
	c: one set not reduced		d: two sets not reduced
	e: four sets not reduced		f: last set dated 19 Oct
	g: first set dated 27 mar		h: last set dated 9 Sep
	j : last set Sep 29 & first set missing altitudes		k: refers to a set in Aug that was not published (see below)

Flamsteed was well aware that his altitude observations were affected by refraction and discussed the problem with various people including Towneley and Newton who on 17 November 1694 sent him a refraction table with different values computed for summer, spring/autumn and winter. Flamsteed never took seasonal of temperature variations into account in his tables, but when he wanted more certainty in his time determinations, he took sets of observations before and after noon when the sun was at the same altitude, presumably because he supposed that the amount of refraction would be the same. These are now referred to as equal altitude observations and, because Flamsteed was using astronomical time the two sets of observations appear under two dates rather than one in the Historia. Sometimes Flamsteed took equal altitude observations that were 24 hours or more apart. Other times, a single set of observations seems to have sufficed. What cannot be known is how often the second of a planned pair of equal altitude observations was lost because of the weather. One important thing to note about Flamsteed's equal altitude observations is that although the morning and afternoon altitudes were almost the same, in practice they were very rarely exactly the same. It should also be noted that Flamsteed was only able to use this method because he had previously determined the Observatory's latitude, and if a star rather than the Sun was being used, the declination of the star as well.

In his writings, Flamsteed briefly described the instruments that he used to measure the altitudes. The following transcript was made and published by Baily and is thought to be taken from RGO1/41 (but this requires checking).

'My pendulum clocks were the work of Mr. Tompion: the pendulums,13 feet long, make each single vibration in two seconds of time; and their weights need only to be drawn up once in twelve months. For rectifying these, I had provided a quadrant of about 3 feet radius, which I brought with me from Derby. It was no very good contrivance; but with it, however, I could take the sun's or a star's height so exactly that the differences betwixt the errors of the clock, collected from 4, 5, and sometimes 6 several heights of the sun or a star, was scarcely more than 10"; but commonly much less. This quadrant I employed till June, 1678; when, Sir Jonas Moore having procured me a neater that belonged to the Royal Society, I divided and employed it till October, 1679, when the ill-nature of Mr. Hook forced it out of my hands. Yet I lost nothing by it; for it was so ill contrived by him that I could not make it perform better than my first. And now he obliged me to think of fitting up one of my own, of 50 inches radius [the 50-inch Voluble Quadrant], wherein by peculiar contrivances I had avoided all the inconveniences I had met with in his. This gives an observed height to half a minute: and now, by it, I am sure of the observed times to three seconds; which I could not have expected from either of my other instruments.'

In 1678, Flamsteed stopped using the term altitude when recording the observations for correcting the clock and started using the term Dist. a Vert. instead. The last published set to use the term Altitud. was made on 22 February and the first to use Dist. a Vert. on 16 June. Although no reason for the change was given in the published observations, we know from the above and from a letter dated 4 July 1678 that Flamsteed sent to Towneley that it coincided with a switch of instruments. The first published observation made with the 50-inch Voluble Quadrant was made on 20 October 1679. A record come be found in the Historia where in the middle of the day's observations the following appears: 'Quadrante deindè proprio pedum plus quam 4 Radio, diftantiae à Vertice obfervatae.' which roughly translates to 'Then, in the proper quadrant, the radius is more than 4 feet, the distances from the vertex are observed.'

When the published figures are compared with those in the observing books, there are discrepancies. The four dates mentioned immediately below were sampled fairly at random from the earlier observations.The published figures for 5 May 1676 differ from those in the observing book as do those for 31 May and 1 June 1776 and 28 January 1677, where some sort of correction for refraction appears to have been applied to the published figures of altitude though the corrections applied do not seem to tally with those published in the refraction table above. Those published for 28 January 1677 are all 6" of arc lower than those initially recorded in the observing book (RGO1/1), though the clock error is the same (on this occasion, the 6" correction also appears in the observing book). This is in contrast to the observing book record for 1 June 1776 (RGO1/1) where neither the altitude, corrected times or clock errors agree with what was later published.

Moving on to a randomly selected later observation made on 16 June 1684, we find much the same discrepancies between the observing book and the published observations with the published Dist. a Vert. figures differing (RGO1/3) but with the figures for the clock errors agreeing (RGO1/3).

Over a period of several years there is a mismatch between the altitudes / zenith distances recorded in the observing book and those subsequently published. In the example below, this is clearly not a correction being applied for refraction as the published correction for refraction for a ZD of 62^o is 1'31" and for 61^o is 1'27".

		23 Jan	1681
		Published		Obs. Book

1	Clock time	8^h06'10"		8^h06'10"
	Zenith Dist	62^o21'50"	[+2'40"]	62^o20'40" 62^o23'20"
	Corrected time	8^h04'41"		8^h04'41"
	Error of clock	-1'29		+1'29

2	Clock time	8^h08'24"		8^h08'24"
	Zenith Dist	62^o00'50"	[+2'40"]	61^o59'40" 62^o02'20"
	Corrected time	8^h06'56"		8^h06'56"
	Error of clock	-1'28"		+1'28"

3	Clock time	8^h10'30"		8^h10'30"
	Zenith Dist	61^o41'30"	[+2'40"]	61^o40'20" 61^o43'00"
	Corrected time	8^h09'00"		8^h09'00"
	Error of clock	-1'30"		+1'30"

4	Clock time	8^h13'06"		8^h13'06"
	Zenith Dist	61^o17'10"	[+2'40"]	61^o16'00" 61^o18'40"
	Corrected time	8^h11'35"		8^h11'35"
	Error of clock	-1'31"		+1'31"

In the above example, all the published zenith distances are all 1'10" higher than the first in the observing book which is itself 2'40" less than the second. So how does this compare with other sets? Selecting some at random, the same pattern occurs for the observations made on 13 Feb 1688. However on 25 Nov 1685, although the published zenith distances are all 1'10" higher than the first recorded observation, the second entry in the observing book is only 2'30" higher. The figures for the set of three measurement made on 5 Oct 1684 are 1'10" and 2'24, 2'23" and 2'22".

Going back further in time to 27 November 1680 we find that the published ZD is 1'10" higher, whilst the second figure in the observing book is and 2'30" higher. The ZD figure is still 1'10" higher on 1 June and 30 April 1680, but 1'20" higher on 12 April. The figures for 17 April were not published, but in the observing book there is a semi-legible note containing the figures 2'20" and 1'20" (RGO1/2/31). The ZD figure is 2'20" higher on 28 March 1680, but the second figure in the observing book is 12'10" lower.

What is important to note, is that in all the examples given, the published figures for the clock time and the error of the clock are the same in the observing books

But moving forward to 15 Feb 1689, we find that that Flamsteed's recorded and published ZDs are the same, but the second figures given in the observing book is 1'10" less the first. The last set to be published before 15 Feb 1689 were taken on 29 Sep 1688, when the pubished and recorded ZDs are the same, but the second figure in the observing book is 1'40" more (rather than less) than the first. However, on the set before that which is dated 14 Sep 1688 and contained five observations, the pubished and recorded ZDs are the same, but the second figures in the observing book 13'60", 13'23", 13'24", 13'29" & 13'22" lower than the first. The published ZD for 30 March 1688 is 1'10" greater than that in the observing book. However, the top of the column containg the second ZD figures is headed add 1'10" .

It would seem therfore, that the published observations from some time around the middle of 1680 have been corrected for a systematic error of 1'10". However, if this is the case, then the variations that seem to have occured in 1688 need some sort of explanation.

Clearly, many more sets of observations need to be compared if we are to get a full understanding of how Flamsteed processed this class of observation and any instrumental adjustments that he made.

There are several examples in Volume 1 of the 1725 Historia where Flamsteed has shown his workings to determine the rate of the clock. A search using the term 'error' will locate them. The table below shows his workings to determine the rate of the clock prior to observing a partial eclipse of the Sun on 3 September 1689. It appears on p.350 of Volume 1.

	Latin text		Translation
	Die 27Augufti mane Horologii error erat + 3' 35" Sept. 3.00h p. m. + 6h 23' Ergo Diebus 6 2/3 retardaverat 2'46" & Quotidiè ferè 30" ut hora 4 fiet 6'27" ♂ Septembris 3. Eclipsis Solis coelo valde sereno Obfervavi		On the morning of August 27th the clock was + 3' 35" Sept. 3.00h p. m. + 6h 23' Therefore, on the 6 2/3 rd day, it had slowed down by 2' 46" & every day by about 30" so that the 4th hour would be 6'27" Tuesday September 3rd I observed the eclipse of the Sun 30th in a very clear sky

An examination of the volume however shows no observations under the date 27 August 1689. Not only that, the last published set prior to 3 September are dated 10 June. From the reader's perspective, the text above is therefore not overly helpful as it is impossible to check the data on which it relies. However, an examination of Flamsteed's observing book (RGO1/3) reveals that he made measurements to determine the clock's error on 7, 13, 22 & 29 July and 16, 22 & 27 August. Why he chose not to publish any of them is not known.

Recording adjustments made to the Octagon Room Clocks

By 1679/80, the Octagon Room clocks seem to have been adjusted so that in general they always had a gaining rate. Every now and again the hands would be put back. The smallest adjustment so far identified is 6 minutes and the largest 1hour & 10 minutes. Not every alteration to the clocks was published which makes those that were of limited value. This leads one to wonder about Flamsteed's own thinking not only about the importance of the clocks but also of how he thought his observations would be useful to his readers.

Those published in the Historia were generally recorded in italics from 1681 onwards. Nine of the entries contain the term 'reduxi'.

table under construction

Date	Entry in volume 1 of the Historia	page
1678, Jul 12	Indices minutorum utriusq; Horologii promovi 6', & ad eosdem scrupulos composui, eo concilio ut tempora quam proximè media in posterum ostendant (I have advanced the minute indices of both clocks to 6', and have composed them to the same scruples, with the intention that they should show the times which are approximately half in the future.) translation t.b.c. RGO1/1/123 states: 'July 12 at 9 1/2 xxx of indices of both put 6 minutes forward & set together'	230
1678, Jul 27	NB There is no entry in the observing book for the period 24 Jul to 1 Aug inclusive. This appears to be an observation made by Halley (at Greenwich or elsewhere?)	231
1679, Mar 17	Quod in omnibus hucusque Observationibus in Obfervatorio habitis, Tempora per Horologium Axiculare numerata fuerint: In Sequentibus Laminari utar (That in all the Observations hitherto made in the Observatory, the Times have been numbered by the Axillary Clock: In the Following I will use the Laminar). What does this mean? This is the only reference to the Horologium Axiculare in the volumes of the Historia. In the observing book there under 19 May 1679 there are two mentions of the aord Laminar, one of which appears to say Horologÿ Laminar. Horologÿ Axiculare mentioned on 27 March 1679 and on 23 Feb 1681	241
1679, Aug 12?	Die sequente retraxi Indicem minutorum 40', quem à Kalendis Januarii raecedentis, nunquàm attigeram, nèc mutaveram (The following day I took back the Index of Minutes 40', which I had never touched or changed since the first day of the month of January preceding.) There is no entry for 1 Jan in the Historia, but in the observing book Flamsteed has recorded: that there was a 20' adjustment and that he altered the length of the pendulum by 2/3 of a revolution (RGO1/1/137)	251
1680, Feb 19		253
1680, Nov 23	both clocks put back by 24 minutes (Reduxi Indices Horologiorum 24' deinde pro Errore inveftigando diftantias a Vertice cepi)	272
1681, May 17	?? probably not	278
1681, Jul 20	Aequatio Dierum est 5' 49" quae subducta Errori Horologii manent. 12′ 50″. Reduxi Minutorum Indicem 13'. Undefit Error Horologii in fequentibus hujus Vesperae Observatis 5' 40". (The equation of the days is 5' 49", which, after subtracting the error of the clock, remain 12' 50". I have reduced the index of the minutes to 13'. Hence the error of the clock in the following observations of this evening is 5' 40".)	280
1682, Jan 17	Clock cleaned (purgatis)	287
1682, May 20		290
1682, Oct 21		301
1683, Jan 2		305
1683, Dec 3		317
1684, Feb 12	On Wedneday 13th, the clock's index was reduced by 6 minutes ¹	318
1684, Oct 8&9	Clock cleaned (purgatis)	328
1686, Mar 7		335
1686, May 17		336
1687. Mar 12	Stetere Horologia propter Ventum Vehementissimum. (The clock stopped because of very strong wind). There is no such entry under this date in the observing book (RGO1/3/51), but there is an entry for March 14 which states: 'Ye same day both clocks had stood it being a strong wind[.] clocks set together after [,] at 12^h '	340
1689, May 15		349

Amongst the changes not published were those made on:

30 May 1687, when the hands were put back 25 minutes
4/5 Jan 1684, 1^h10'

17 Apr 1684 adjsutment to pendulum as well in observing book only 'horologium hoc tempora 47 secunda tardid ra longiori Pendulo numerabat' ('This clock counted the time 47 seconds slower than the longer pendulum') seems to be a reference to a comparison between the Octagon Room and sextant house clocks.

p333? 1686, feb16: 'Tempora notata fuere ab Horologio ambulatorio quibus propterea haud nimium fidas certa sunt ad minutum temporis vix proprius,' (The times were noted by an ambulatory clock, which, therefore, is not very reliable, being accurate to the minute of time.) The Sextant house clock was presumably out of order. Times given to the nearest 10 seconds only.See also p.142 for a second reference to the same clock. There are other references that were not published e.g. 14 March, 1687 (RGO1/3/

p.273, hands put back by 30 minutes RGO1/2/71 on 13 Jan 1681, , but this info not published on p.273

20 October 1679, RGO1/1/191&2: '4.35.29 {illegible} 4.36.00 {j like symbol} horologium majus in Camera [illeg] in observatlr and '12.37.20 in Camera superiori {j like symbol} horologium lam. 1.38.00' . None of this appears in the published observations

12 April 1684: Tempora haec 1'22" tardiora horologijis suprá

There are also occasional references (just one?) in the first three observing books to a 'horologium suprá' and a 'horologium infrá' which were presumably alternative names Flamsteed used for the Octagon Room Clock(s) 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

In the published observations (p.330) he wrote: 'Aufer utriusque temporibus 0'19" ' (subtract 19 seconds from both times [from these sextant observations]). No other similar entry has been located in Volume 1 of the Historia.

Notes:

1) In the satellite of Jupiter section (p.357), the clock error is recorded as being 1^h1'10" fast on 3 Jan 1684. Five days later on 8 Jan it is recorded as being 3'38" behind suggesting a significant reset of the Octagon Room Clock(s) had taken place. There is no record of this amongst the lunar observations, but in the observing book (RGO1/2/162) a figure of 1h10' is mentioned on 4 (or possibly 5) January, the rest of the comment not being properly legible.

Observations of Jupiter's Satellites 1676-1689

Although the lunar observations are accompanied by measurements of the altitude of the Sun or a star that were taken to measure the error of the clock, the observations of Jupiter's satellites have no such accompanying reference. Instead, the reader has either to take Flamsteed's word for what the clock error was or refer back to those altitude observations that Flamsteed chose to publish to accompany the lunar observations. How much more helpful it might have been if only Flamsteed had published a section of the Historia with just the altitude observations.

Having said that, the corrected times given by Flamsteed in the section on Jupiter's satellites does give us an easy way of seeing something of what was going on with the Octagon Room clocks and how the error fluctuated over time. The first published observation was made on 6 June 1677 when the error was -6'30". By 8 September 1677 it was -21'50". Just over a month later on 24 October it was -15'00" and a few weeks later on 13 November was -11'32". Moving on to 1682, we find that on 25 Nov it was just +20". On 3 January 1684 it was + 1^h1'13", but a few days later on 8 January it was -3'38" suggesting that some adjustment had been made to the clock between those two dates. There is no record of such an alteration having been made at that time amongst the lunar observations. However in his observing book Flamsteed recorded that he had put the clock back by 1^h10', marking the entry with a pointing hand in the left-hand margin (recheck the original (RGO1/2) for the form of words Flamsteed used).

Comparison of the Octagon Roon and Sextant House Clocks

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 observations in the Sextant House that were published in Volume 1 of the 1725 Historia were made on September 3 and the first recorded observation in the Arc House (the former Quadrant House) on 12 September 1689 (RGO1/4). It was the first of the observations to be published in Volume 2 of the 1725 Historia. A search for the term sext in this volume throws up about several sets of observations prior to the start of August 1690 where the word sextante (or an abrivieation of it) appears (about 50 in total) with just a few ooccurances after that date up to 1698. Most of these were made prior to the Sextant House Clock being released from duty in the Arc house at some point on or after 31 October 1890

???Those that were made with the Sextant prior to the arrival of the new Arc House clock were presumably made using the horologium ambulatorium. Unlike the sextant observations in Volume 1 which are given to the nearest minute, those that were recorded in Volume 2 are given to the nearest second. The question therefore arises: when Flamsteed began using the new clock he had commissioned for the Arc House, did he place the Sextant House Clock back in the Sextant House?

......

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. Fifteen explicit references have been found in Volume 2 of the 1725 Historia that compare the time on the clock there with the time on the clock in the Arc House. 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	05^h29'19"	05^h29'00"	+19"
8	1689, Nov 23	Supra in Camera Observ	00^h31'33"	00^h31'00"	+33"
"	1689, Nov 28	Horologiis ad idem moment.comp.	05h21'00"	-	65"
9	1689, Nov 28	"	10^h36'07"	10^h36'00"	+7"
"	1689, Nov 30	in camera	00^h13'00"	00^h12'00"	+60"
10	1689, Dec 01	in camera supra	19^h45'48"	19^h44'00"	+108"
"	1689, Dec 02	"	00^h13'54"	00^h12'00"	+114"
"	1689, Dec 09	"	05^h53'00	00^h53'00"	+0"
11	"	"	15^h38'15"	15^h38'00"	+15"
"	"	"	23^h57'32"	23^h57'00"	+32"
12	1689, Dec 12	Supra in Camera	09^h05'20"	09^h02'00"	+220"
"	"	"	09^h30'20"	09^h30'00"	+20"
"	1689, Dec 13	"	05^h42'31"	05^h38'00"	+271"
"	"	"	10^h06'48"	10^h02'00"	+288"
18	1690 Jan 13	"	07^h51'51"	07^h52'00"	-9"

Instead of the time difference between the clock increasing or decreasing in a uniform way, the figures are all over the shop causing alarm bells to start to ring, especially as the comparisons were seemingly stopped before the rates had stabilised. A possible explanation is that one or other or both of the clocks was undergoing adjustment. However, there is no mention of this in the published observations, the apographa or the observation book. In the circumstances, the inclusion of the comparisons in the Historia does little to inspire confidence.

Also of interest is the fact that not only did Flamsteed use five different phrases for the same thing, but also, with just one exception (p.9), all the entries on any one page are all the same.

Although these are the only explicit references, there are many more in the observing books that have historically been overlooked as they have not been labeled as such. These are explored in a later section.

An apparent mismatch between timings given by Halley in Book 2 of the 1712 Historia and those published by Flamsteed in Volume 2 of the 1725 Historia

When comparing the same observations made with the Sextant in book 2 of the 1712 Historia with those in the 1725 edition some timings are different. This is not because they were transcribed incorrectly but because Flamsteed usually repeated the observation immediately after the first had been taken. In the 1725 Historia both sets of observations are reproduced. In the 1712 edition, Halley took the average of the two readings and published this instead. Given that the column heading in the 1712 edition for the timings is Tempora juxta Horrologium Oscillat. or equivalent (Times according to the pendulum clock), it would be natural to think that what had been put into print was the actual observation.

Check. Examples required. Does not seem to be true of all observations.

Newton's demands and a flirtation with sidereal time

Normally, there is no physical distinction between a clock set to mean solar time and one set to sidereal time except for a small difference in the effective length of the pendulum. Most clocks could be adjusted to accomodate both systems. In 1691, Flamsteed came up with the design for a sidereal clock that today is known as his 'Degree Clock' that would show sidereal time in degrees, minutes and seconds rather than hours minutes and seconds. As such, it had an unusual length pendulum and gearing.

On 15 January 1695 in a letter to Flamsteed, Newton asked him if he would stop using Tempus Apparens and start using sidereal time instead.

' I desire you would ....'

Correspondence " p.555 & 551

https://cudl.lib.cam.ac.uk/view/MS-ADD-03979/79

Time determination with the Mural Arc

When the Mural Arc came into use, Flamsteed took regular observations of the Sun at local noon as it transited the meridian. Looking at the published record, it would seem, other things being equal, that to start with, he probably made them on every day that the weather permitted. In June 1690 for example there are 14 sets of observations. In March 1702 there are 13. By 1712, Flamsteed was taking very few observations of anything. During the whole of 1712 just six sets of observations of the Sun's transit appear in the Historia. In 1713, there are five and in 1714 just three with the first being occurring on 26 September with no observations of anything being recorded between 16 March and 4 September inclusive. A check against Flamsteed's Observing book (RGO1/8) indicates that all the observations made in 1714 were published.

Search for possible examples of clock being corrected from star transits

Rectifying the Mural Arc

In 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 in the 1725 Historia or elsewhere. This is particularly unfortunate as in the published observations Flamsteed only gave the clock time of when the observations were made despite the fact that he could easily have had a second column showing the clock time adjusted for the error in azimuth. Had a table of the errors been published, this would not have been too much of a problem. What is particularly galling is that for each observation Flamsteed published not only the zenith distance, but also a corrected value to take into account the subsidence of the wall on which the instrument was mounted. Given that a user of the Historia had no means of knowing the errors due to the misalignment of the instrument, the value of much of what was published in Volume 2 has to be questioned.

Not only was Flamsteed's table of errors never published, 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.dist^o	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 consistent 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.

Pages 371 & 372 from Baily's Flamsteed. The table is taken from RGO1/24/21, whilst the page on the right (where references to the clock have been highlighted) explains its structure and how the figures were derived. It is recommended that the pages that follow are also consulted

$Flamsteed's Refraction-Table$

Flamsteed's Refraction Table from Volume 1 of the 1725 Historia. It was published in Volume 2, but without the date of 1698 at the top

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.

Sun & other star altitude observations made with a quadrant in the Octagon Room to determine the errors of the Arc House clock during the rectification of the Mural Arc

There is evidence in the observation books that these measurements were made in the Octagon Room rather than the arc house and the times converted to the equivalent of the arc house using either the horologium ambulatorium or some other means. See RGO1/4 for observations made on 13 & 14, 16, 17 Jun 1690. Also of interest is that unlike most of those in Volume 1 of the Histroria, the zenith distances in the observing book are the same as those that have been published.

Year	Month	Date (Astronomical)
1689	Sep	18(x2)
	Oct	Oct 4, 8, 17*
	Nov	9, 16, 22, 30
	Dec	9, 13
1690	Apr	8, 9, 11(x2), 12, 13, 14(x2), 15
	May	14, 15, 22, 23, 25, 26?
	Jun	6, 7, 13, 14, 16, 17
	Jul	25, 26,
	Aug	24, 25, 27(x2), 31
	Sep	1**, 15, 16, 19, 20
1699	May	19, 20
	Sep	11, 12
1712	Jan	12*^a
1713	Jun	15, 16
1718	Aug	28, 29

* = arietis or other star

** different column order

a= incorrect hour recorded in published vol 8^h11'18 instead of 10^h11'18". Also has a column with corrections for refraction

Recording adjustments made to the Arc House clock

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 apographa , 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 minutes which was also recorded in the 1725 Historia. This is the only occasion in Volume 2 of the Historia where such an adjustment is recorded. Further research is required to see if Flamsteed recorded other occasions in the Observing books.

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.' Although a note in the observing book made on 4 November about Abraham Sharp leaving to teach mathematics was transferred across to the apographa, the earlier note about the new clock was not ... and because this was the volume that Flamsteed ultimately referred to when preparing the text for the Historia, it was also omitted from the published observations .

In Volume 2 of the 1725 Historia, there are just ten references to the clock being cleaned where the word purgato is used. Flamsteed also recorded 25 occassions when the clock stopped (Stetit Horolgium).

But there are other relevant entries for further research ( word search Indices (10 Feb 1690) but do not confuse with adjustments made to the mural arc

Year	Stopped	Cleaned
1689	–	Oct 30
1690	July 22	–
1691	Aug 31 (x2), Sep 11	–
1692	Apr 10	Feb 2, Feb 12, Apr 16
1693	–	–
1694	Jan 20, Feb 25, Nov 11	Dec 13
1695	–	–
1696	–	Apr 2
1697	–	–
1698	Apr 12, Jun 16, Jul 25, Aug 15, Dec 11	Jan 12
1699	–	–
1700	Feb 6, Jun 18, Aug 13, Nov 6	Nov 7
1701	May 3	Sep 11
1702	–	–
1703	Jul 13, Aug 13	–
1704	Apr 2, Apr 10, Oct 24	–
1705	Mar 1, Mar 5	–
1706	–	–
1707	–	Apr 4
1708-19	–	–

In Volume 1 of the 1725 Historia Flamsteed uses the term purgatis rather than purgato when referring to the clocks presumably those in the Octagon Room) being cleaned. Just two references have been found, They occur on 17 Jan 1682 and 8–9 Oct 1684. On both occasions both of the Octagon Room Clocks appear to have been cleaned. The volume does not appear to tell us anything about adjustments made to the Sextant House clock. There are no references to the clocks being stopped. We do know however from Howse's research that there were a considerable number of interventions between 1676 and 1678.

1689: Towards a unified time scale: the arc house clock becomes something approximating to the Observatory's standard clock

In volume 2 of the Historia, timings made in the Octagon Room appear to have been converted into the equivalent time shown by the Quadrant (Arc) House at the same moment.

As an example of what was recorded, 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 Arc House clock.

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.

The same is also true of the ZD observations of the Sun taken in the Octagon Room on 14 May 1690 where the Octagon Room clock seemed to be 1 minute 25 seconds behind and roughly nine hours later on 15 May 1690 when it was 1 minute 27 seconds behind.

There are a small number of sets of observations where the conversion is less clear. One example are the solar eclipse observations made on 21 April 1715 when Flamsteed was very infirm and his writing very spidery where there is an extra column, but the layout is in a different pattern. However the original pattern of recording was resumed for solar eclipse of 18 February 1718 where the record shows not only that the Octagon Room clock was 10 seconds behind the Arc House clock, but the times recorded in the Octagon Room are actually labelled as such (in Camera Supra).

Unfortunately, it is not possible to check how observations made between 17 November 1702 and 2 January 1712 were treated as the original observations are lost and when the apographa was compiled (RGO1/15–17), only the converted data was included.

We don't know how the Octagon Room times were transmitted to the Arc House, but there are a number of possibilities including:

Using the horologium ambulatorium
Using a speaking tube that ran between the buildings (though there is no evidence that such a thing existed
Shouting the times from the Octagon Room window

Although it seems pretty clear is that from the end of 1789, Flamsteed used a standardised time system based on the Arc House Clock, it is less clear what he did before that. The following points need to be reconciled

the observing books record all the observations in chronological order irrespective of where the observation was taken
In the observing books, times recorded in the Sextant House are given to the nearest second, but in some, sections of the published observations, they are only given to the nearest minute
Only a very small number of direct comparisons between the Octagon Room Clock and Sextant House Clock have been identified
Although there are lots of observations used to determine the error of the Octagon Room Clock(s), no such observations have been found for the Sextant House Clock
In the observations of the Moon's approach to fixed stars made with the sextant and other instruments (Vol 1, part 4), there does seem to be a discrepancy between the times recorded alongside the sextant observations and those that were published. For example, the published times for 8 Feb 1677 are 28 seconds ahead of those in the observing book (there is also a typographical error), but on that day, Flamsteed records that the error of the Octagon Room Clock is 12 minutes 40 seconds which is the correction then applied to the Sextant House Clock.
But on 14 Jan 1681, no correction appears to have been applied to the published clock time (Tempora per Horologium Oscillatorium), though the figure in the column Tempora ex Altitud.Correcta has been corrected by roughly the error detmined by altitudes in the Octagon Room roughly 141.5 hours earlier.
On 23 July 1683 a similar situation arises,

So was Flamsteed using a standardised time system based on the Octagon Room Clocks? If it was, the challenge is to find something in the observing books (or elsewhere) that shows how and when the Sextant House clock was compared with those in the Octagon Room.

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

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 too. By 1678, seemingly with the help of a fixed telescope set up in 1677 with which to observe the dog star Sirius and the Octagon Room clocks, he was satisfied that it was. Somewhat surprisingly Flamsteed did not publish a paper announcing his findings.

Also of some concern is that to date, the evidence on which he based his conclusions has not been found.

Flamsteed described the Sirius telescope and his use of it in a letter written to Richard Townley on 24 March 1677:

‘…I have now fixed a payre of convex glasses of six foot focus in brasse cells upon an Iron Ruler to one of our Walls and three or 4 times observed the transits of Sirius over it. my last note was the 21th instant when hee passed it 3 min before 5 a clock at which time the sun was more than 10 degrees high and yet I saw the star as plainely as you usually see the planet♀ [Venus] upon the sun rise in winter with your bare eyes…'

Although a record on this and three earlier observations made on 23 & 27 February and 19 March have been located in RGO1/1, a preliminary search has so far failed to find any later ones. The question therefore arises: Did Flamsteed abandon the Sirius Telescope or did he keep a record of the observations in a book on loose sheets now lost. Much the same seems true for the comparisons between the great clocks in the Octagon Room. Logic would have expected these to be recorded or transferred in a separate volume. Again, no such record has yet been found, although Howse did manage to reconstruct some of their early history from a combination of his correspondence and the observing books

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'.

FLAMSTEED’S LUNAR DATA, 1692-95, SENT TO NEWTON , Journal for History of Astronomy, xxvi (1995), 237-246. NICHOLAS KOLLERSTROM, University College London, and BERNARD D. YALLOP, Royal Greenwich Observatory, Cambridge

'This displacement concurred with times given for stellar meridian transits in the [1725] Historia’s Book II: thus, six stellar transits for 1691 averaged 5’ ± 2’ due east of south, while for 1695 the figure was 8’ ± 2’. Such a displacement would make all his meridian readings half a minute too early. Forbes claimed that Flamsteed corrected for this: “[Flamsteed] determined that the transit on the tropic occurred 38 seconds earlier than it should have done, indicating that the alignment of the instrument was then 92’ west of the true meridian” (26). For a south-facing instrument, a too-early transit implies a deviation to the east! We found no indication that Flamsteed had made such an adjustment.'

As can be seen from RGO1/23&24, Flamsteed did correct his transit time for the misalignment of the Mural Arc when computing his star catalogue. What he did not do is publish the corrected figures with the observations, but he did mention how he deterrmined the errors in the preface to the volume (see section on Rectifying the Mural Arc above).

…where east meets west

Decoding Flamsteed: Flamsteed's modus operandi and the methods used to compare, regulate, rate and determine the errors of his clocks (1676-1719)

This page is very much a work in progress and may undergo significant restructioning.Some sections contain only notes at present.

Others remain to be added.

Introduction

Treading in Tycho's footsteps

Sources

The archive catalogue

The publication of the two Historias

Flamsteed's observing Instruments

A brief history of the clocks owned by Flamsteed

The Great Clock enigma

1682 Jan.17. Clocks both cleaned & set together at 9h.00' then:

Date

Spring pendulum window

Pivot pendulum door

Difference (s)

Flamsteed's observing books

Evolving a house style and the use of standardised expressions

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

The column headings relating to time in the two Historias

Latin term used

Translation

The grouping of observations and the times as published in volumes 1 & 2 of the1725 Historia and books 1 & 2 of the 1712 Historia

Section from 1712 book 1 & 1725 Vol.1

Times given

Sections from Book 2 (1712 edition)

Sections from Vol 2 (1725 edition)

Determining the true time from observations of the altitude of the sun and other stars, 1676–1689

Year

Sets published

Year

Sets published

23 Jan

1681

Published

Obs. Book

Latin text

Translation

Recording adjustments made to the Octagon Room Clocks

Date

Entry in volume 1 of the Historia

page

Observations of Jupiter's Satellites 1676-1689

Comparison of the Octagon Roon and Sextant House Clocks

The Sextant House Quadrant / Arc House clock conundrum

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

Page

Date

Phrase used

Arc House

Clock

OctagonRoom Clock

A - O

An apparent mismatch between timings given by Halley in Book 2 of the 1712 Historia and those published by Flamsteed in Volume 2 of the 1725 Historia

Newton's demands and a flirtation with sidereal time

Time determination with the Mural Arc

Rectifying the Mural Arc

Zen.dist.o

Add (s)

Zen.disto

Add (s)

Zen.dist.o

Add (s)

Sun & other star altitude observations made with a quadrant in the Octagon Room to determine the errors of the Arc House clock during the rectification of the Mural Arc

Year

Month

Date (Astronomical)

Recording adjustments made to the Arc House clock

Year

Stopped

Cleaned

1689: Towards a unified time scale: the arc house clock becomes something approximating to the Observatory's standard clock

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

Misunderstandings

Further reading

This page is very much a work in progress and may undergo significant restructioning.
Some sections contain only notes at present.

1682 Jan.17. Clocks both cleaned & set together at 9^h.00' then:

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

Octagon
Room Clock

Zen.dist.^o

Zen.dist^o

Zen.dist.^o