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The subsidence of Flamsteed's Mural Arc

 

page under construction

Construction of Flamsteed's Mural Arc began in the spring of 1688. Over fourteen months later, in September 1689, it was ready for use (though apparently not 'completely finished' until October (Baily p.55). Not long after, on checking his observations, with those made with the instrument while it was still under construction, he became aware of a discrepancy. Flamsteed decided to monitor the situation in order to establish their cause. His conclusion was that the 'southern end' of the wall on which the Mural Arc was mounted was subsiding. He also appears to have decided that it was sinking vertically rather than sinking and simultaneously tilting sideways or twisting to one side, both of which would have had an impact on the errors in azimuth.

The error at any point in time could easily be calculated from the apparent change in ZD of certain selected stars and the ZDs of the other observations corrected accordingly. The size of the corrections he applied to the observed zenith distances were published in the Historia and increased in steps ranging from 5" to 40"  from 0' 45" in 1689 to 16' 0" in 1719. Other things being equal, this means that during the 30 years that the Mural Arc was in use, the southern end of the wall (whose length was about 25 feet), must have dropped by about 1⅓ inches (3⅓ cm) relative to the northern end, the exact amount being dependent on the length of the wall.

 

The wall on which the Mural Arc was mounted

Although Flamsteed wrote a fair bit about the Mural Arc, he never seems to have unambiguously stated exactly where it was mounted. This has led to some confusion amongst those who have subsequently had an interested in its history. 

Given that Flamsteed made the instrument himself, the most obvious place to mount it would have been on the eastern wall of the Quadrant House where Hooke's Mural Quadrant had been mounted. However, in order to have been mounted there it would have needed to be a mirror image of the engraving above. So was it actually a mirror image? A second image painted by Sir James Thornhill on the ceiling of the Painted Hall in the Old Royal Naval College between 1707 and 1712 confirms that it was not.

What is apparent from both images is that the Mural Arc must have been mounted on an east facing meridian wall. Flamsteed had two such walls at his disposal: the west wall of the Quadrant House and the west wall of the Sextant House (i.e. the back of the wall on which the Mural Quadrant had been mounted). Although the sixth Astronomer Royal George Airy was under the impression that it was mounted on the latter, other evidence suggests it was actually the former (more on this below).

It can be seen from the adjacent plan and the two etchings below that the Quadrant House had  windows in both the southern and western walls. Although one might imagine that Flamsteed would at the very least have bricked up the window in the western wall before mounting the Mural Arc, no one seems to have found any evidence that he did.

Although we don't know why Flamsteed decided to mount the instrument on the western wall of the Quadrant House rather than the Western Wall of the Sextant House, we do know from the etchings of the Mural Quadrant and the Equatorial Sextant (immediately below) that the two rooms had very different floor levels. Had the Mural Arc been placed in the Sextant House, at the very least the floor would have needed to be reconfigured. 

From September 1689 (the date of the first published observation) until October 1690, Flamsteed only had one clock to share between the Sextant House and the Quadrant House (which by then was known as the Arc House). A search for  the term sext in in Volume 2 of the 1725 Historia throws up about several sets of observations prior to the start of August 1690 where the word sextante (or an abbreviation of it) appears (about 50 in total) with just a few occurrences 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. Given that to start with both instruments were in use, having them both in the same room would have been a definite advantage.

Another thing we don't know is why Flamsteed didn't design the Mural Arc to go on the wall where the Mural Quadrant had been mounted? One possible answer is that may well have been the plan when he first attempted to make a Mural Arc back in 1683 (now known as the Slight Mural Arc). When this instrument was abandoned, logic would suggest that Flamsteed might have decided to reuse the brass arc, by turning it over and remarking the graduations on the other side – something that would have required it to be mounted on an east facing wall. It seems however that this was not the case as in an unsent letter to Newton dated 20 February 1691/2 (RGO1/35/6–8) Flamsteed wrote:

'But after the decease of my good father in the spring of the yeare 1688. findeing I could spare some monys I resolved to Make my Arch Anew and very solid. and therefore added about 150^li of Iron in Bars to strengthen it and a new limbe of solid brasse halfe an Inche thick  the Index I caused to be made all of Iron which was before onely Wood covered with a broad brasse plate. and hired a servant [Abraham Sharp] that Was the fittest for my purpose. that could be a curious Mechanick and An excellent Geometrician. who screwd the limbe. wrought the Index and after I had fixed the point for the beginning of the divisions inscribed them and engraved the Numbers both for the diagonalls and revolves so curiously that I thinke I may say it without vanity or ostentation. tis the neatest limbe that ever was made of the same bignesse being 150 degrees in the Arch and 6 foot 9 Inches Radius.

It was wrought into a true plane after it was fixed on the Wall where it stands by a peculiar contrivance with no lesse then 4 moneths labor. but in all I am confident we bestowed not lesse then 10 moneths paines upon it and it lies me by a very moderate account in no lesse then 100^li forth of my owne pocket.'

If it really was an entirely new instrument, it is entirely possible that the old one was mounted in place of the Mural Quadrant and remained in place at least for a while after the new instrument was mounted. 

 

The evidence for and against the Mural Arc having been mounted on the western wall of the Quadrant House and for subsidence affecting both the Quadrant House and the Sextant House

1692:
Extract from an unsent letter from Flamsteed to Newton, 20 February 1691/2 (RGO1/35/6–8)

'Some that see it and are desirous to show their witt in findeing falts with what they understand not will hint the wall to which tis fastened is too weake. I find no such thing. the other that was 3 foot thick was not drie in the Middle tho It has stood above 16 yeares. this is but 2½ brick. and I doubt not is, and has sunke all it is likely it can I am sure I find no alterations in this Instrument since I began to use it first in Sept. 89 but what proceeded from the other causes and if the Wall should any ways sinke never so little it would Imediately and easily be perceived.'

What Flamsteed appears to be saying is that the Quadrant Wall was 3 feet thick, but the wall on which the Mural Arc was mounted was only the width of 2½ bricks thick (ie about 20 to 24 inches depending on the size of the bricks).

1714:
Draft of a letter to the Office of Ordinance read at a meeting of the Royal Society 18 February 1713/14

'….That in the Garden, there being a shed with a sextant a wall quadrant and a clock therein, the shed should be removed six or eight yards further from the brow of the hill that the ground may not sink under it; And the western wall should be thick and firm, with a broad foundation that it may not warp because the wall quadrant is to be fixed on it. The sextant is grown rusty, and should be cleaned, and there should be a new wall Quadrant made, the old one being much wore by long usage, and belonging as we hear to Mr. Flamsteed. The clock is also said to be Mr. Flamsteed’s, and a better clock would be useful. (RGO6/21/11 & Baily p.307)'

1720:
Feb 9, Edmond Hally appointed as the new Astronomer Royal following the death of Flamsteed on 31 Dec 1719.

1721: 
Correspondence between two of Flamsteed’s assistants relating to the Quadrant and Sextant House as published in An account of the Revd. John Flamsteed, Francis Baily(1835) p343 & 346. and The Life and Correspondence of Abraham Sharp (1889), Cudworth p.140, (first letter only).

   Jun 1: Letter from Joseph Crosthwait to Abraham Sharp:

'Dr. Halley makes no overtures for the mural arc, nay is he so far from thinking of that instrument, that he has pulled down part of the meridonial wall upon which it was fixed.' (Baily)

'Dr. Halley makes no overtures for obtaining the mural arc; nay, he is so far from thinking of that instrument that he has pulled down the meridonial wall upon which it was fixed.' (Cudworth)

Note: Baily's transcription states part of the wall was pulled down. Cudworth's implies that it was the whole wall that was pulled down. Baily's original transcripts of the originals are at the Royal Astronomical Society and need to be consulted (RAS MSS Baily 11). The location of the originals is unknown.

   Dec 28: Letter from Joseph Crosthwait to Abraham Sharp:

'Mr Molineux has not purchased the instruments; and Dr Halley has converted the sextant and quadrant houses into a pigeon-house'

1724
  Aug 1: Letter from Joseph Crosthwait to Abraham Sharp (Baily p.356)

'Dr. Halley has lately built a new meridian wall of stone; and, as I am informed, has a new quadrant a making, of the same radius with Mr. Flamsteed's arc. I presume his building this wall of stone is in order to find fault with Mr. Flamsteed for having one of brick, which was more liable to warp; and its being built so near the precipice of the hill caused it to sink, the hill being washed from it. Yet, for both these accidents, you know Mr. Flamsteed has made annually proper allowances.'

This is the only reference to structural damage in the wall on which the Mural Arc was mounted. The nature of the warping is unknown, but Crosthwait's comment suggests that it may have distorted the Arc. Given that it was always going to be impossible to construct an arc that was exactly aligned to the Meridian, back in 1690, Flamsteed determined the errors in its alignment from observations of the Sun when it transited the Meridian (read more about this here). There is no evidence that he ever redetermined the errors in later years using the same technique. However, the corrections applied to his observation (RGO1/23) are not consistent with the table of errors that was constructed in 1690. A full analysis of the corrections in azimuth that were applied is beyond the scope of this article.

On the issue of subsidence, the underlying ground structure on which the Observatory is built is compacted sand and pebbles (the Blackheath beds). Based on the plan and images above, it seems unlikely that material would have been washed out from under the wall(s) (unless that is, it they had absolutely no foundations). Photos taken in the 1960s (more on this below) suggest that earlier structures from Greenwich Castle sit beneath the Quadrant & Sextant Houses. Given the fact that the south walls are considerably below the ground level inside the building, part of the structure may have been built on made up ground.

It seems highly likely that Flamsteed knew exactly what lay beneath the Arc house and the Sextant House as he took a deep interest in the Observatory's construction which took place when he was living at the bottom of the hill in the Queen's House. Neither Crosthwait nor Sharp had such knowledge, Crosthwait not having arrived until 1708 whilst Sharp first appeared on the scene in 1684.

 

1725:
The preface to Flamsteed's Historia (1725) states:

'The wall upon which the mural Arc is placed was originally orientated to the plane of the meridian from observations of the Pole Star made in 1675, but the instrument was not fixed to it until 1689.'

Although it was important for the Quadrant Wall to be exactly orrientated to the plane of the meridian, back in 1675 there was no reason for the western wall of the Quadrant House to be aligned in the same manner. It would seem more likely that it was simply been built so that it was parallel to the Quadrant Wall.

1764/5 – 1773:
Halley was succeeded as Astronomer Royal by James Bradley. Following Bradley’s death on 13 July 1762, he was succeeded by Nathaniel Bliss. The Minutes of the Observatory’s Board of visitors for 3 Sep 1762 record:

'And, as a further improvement of the said observatory for the advantage of Astronomy & Navigation, they do likewise recommend it, that the Rooms which is usually called Mr Flamstead’s Sextant Rooms be fitted up with a stone Floor, & a circular versatile Roof, for the receptions of the forty inch moveable Quadrant, there being at present no place, where it can be properly used.' (RGO6/21/49)

An inventory taken on 16 March 1765 (RS MS600/8–9) indicates that by that date the conversion had been completed. It can be seen on an undated plan by John Evelegh (RGO101/2/22) showing the Observatory as it was between about 1764 and 1773. Amongst other things it shows a repositioned window in the south wall of the Sextant house and the addition of new windows in the east and west walls.

1779
In 1779, the Sextant House was altered for a second time, this time by raising its north wall and placing above the room a steep wooden roof with sliding shutters sloping down to the south. The room was referred to both as the Enlarged Room South of the Quadrant Room and as the Advanced Building on account of it being ‘advanced to the south of the Quadrant Room’ (RS MS600/59). It is at this time that the former Sextant House became linked to, and accessible from the Bradley Observatory.

1844:
In 1844, the seventh Astronomer Royal George Airy designed a tower with a dome on the top (the South Dome) to be built on the existing brick walls of the Advanced Building (i.e. on the walls of Flamsteed’s Sextant House) in order to house a new Altazimuth Telescope. Prior to work commencing, in March 1844 he made five detailed sectional drawings of the Advanced Building (RGO6/45). These, together with his plans for the tower are preserved in RGO6/45. The sectional drawings show that the lower part of the walls of the Advanced Building walls were made of solid brick whilst the upper parts were of timber.  On the plans for the tower (RGO6/45), Airy wrote:

'The [brick] walls exist to a height of 6 feet, & the windows must be partly cut out of them.'

In his 1844 Report to the Board of Visitors, he wrote:

'The walls have accordingly been erected on the walls of the Advanced Buildings, and the structure, though not yet complete, is in such a state of forwardness that the Visitors can examine the arrangement of every part. … I may mention here that in stripping the walls of the Advanced Building, traces were found of windows or doors in each of its three sides (the fourth side being that which joins to the observing buildings). These windows are not represented in Flamsteed’s plans: it seems very unlikely that they were opened since his time; and on the whole I suppose that they were walls of some outbuilding of the old Greenwich Castle. It is to be remarked, however, that the western wall, which contains one of these unexplained windows, ranges due north and south (the others being inclined to the cardinal points); but as Flamsteed’s arc was attached to its outside surface, and as the window does not pass through the whole thickness, which is 28 inches, it seems certainly anterior to Flamsteed’s time. It can hardly be conjectured that it was made for anything like a meridian line ... In the center of the building, under the paved floor, was a pier of later [earlier] date, covered with a massive block of stone.'

In other words, the openings made in the walls in the 1760s for Bliss had been bricked up when the Advanced Building was constructed for Maskelyne.

At this point, Airy seems to have been unaware of the history of the building between Flamsteed's death and the constuction of the Advanced building. He also seems to have been believed that the Mural Arc was fixed on the west facing wall of the Quadrant House, which for reasons discussed above was incorrect.

 

Structural damage to the building

Given the amount of subsidence to the wall on which the Mural Arc was mounted, it is pertinent to ask the following questions.

• Were there any cracks in either the Arc House or the adjoining Sextant House prior to 1689?
• Did any cracks appear in either the Arc House or the adjoining Sextant House after 1689?
• Was the subsidence confined solely to the wall with the Mural Arc given that Bradley, Maskelyne and Airy all subsequently raised structures on the existing walls of the Sextant House?

If cracks did occur, then it would appear that either Flamsteed kept the information to himself, or he shared it with others but that information is either lost or has not yet been located.

It subsidence had occurred in the Sextant House, it seems most unlikely that Flamsteed's successors would have built up structures on the existing walls.

 

Sources of information about the amount of subsidence and how it was calculated

There are 5 related sources of data that shed light on the issue.

1. The published observations (Historia Coelestis Britannica Volume 2)
2. The raw data in the observing books from which the subsidence was calculated (incomplete record)
3. Flamsteed's draft letter to Newton dated 18 June 1700 (RGO1/39/68-86)
4. The preface to the Historia (Historia Coelestis Britannica Volume 3)
5. A Manuscript table for the period Jan 1691 to Aug 1694 in one of the observing books whose origin and purpose is not obvious (RGO1/5/4)

The observing books contain raw data for the periods: 1691-1700 and 1712-1719. They are located as follows:

• 1691 Jan 17 to 1693 Dec 05 (RGO1/5)
• 1694 Jan 20 to 1698 Mar 16 (RGO1/6)
• 1698 Mar 22 to 1700 Dec 14 (RGO1/7)
• 1712 to 1719 to Dec 27 (RGO1/8)

The volumes also contain aggregated figures that cover a slightly longer period.

The key thing to note is that the errors published in volume 2 of the Historia do not reconcile with the figures elsewhere. How Flamsteed went from the raw data to his final figure remains to be established. If the published figures are to be believed, the wall would appear to:

• have undergone a number of sudden shifts
• Subsided more in the winter months than the summer ones

In the preface to the Historia (p.132–3) Flamsteed spoke about the wall subsiding. A rough translation from the Latin is given below: 

'When the instrument was thus complete the first task was to see whether it had undergone any alterations since its adjustment in the previous July ... (p111)

'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].(p.132–3)

 

 

Data extracted from Historia Coelestis Britannica volume 2
 

			Date	Subsidence	increment	xx
	1	1689	11 Sep	00'45"	-
	2(*)		17 Oct	00'55"	10"
	3		28 Nov	01'05"	10"
	4		15 Dec	01'10"	05"
	5	1690	02 Feb	01'20"	10"
	6		08 Feb	01'25"	05"
	7		14 Feb	01'30"	05"
	82	1691	02 Jan	02'10"	40"	Novis filis
	9		01 Feb	02'15"	05"
	10		02 Mar	02'20"	05"
	11*		07 Oct	02'30"	10"
	12	1692	10 Jan	02'40"	10"
	13*		07 Mar	02'50"	10"
	14		02 May	03'00"	10"
	15		11 Jun	03'10"	10"
	16		11 Jul	03'20"	10"
	17		04 Dec	03'30"	10"
	18*	1693	03 Feb	03'40"	10"
	191		22 Sep	04'00"	20"	Novis filis
	20		06 Oct	04'10"	10"
	21		05 Dec	04'20"	10"
	22	1694	01 Mar	04'25"	05"
	23*		04 May	04'30"	05"
	24		18 Aug	04'35"	05"
	25	1695	08 Jan	05'00"	25"
	26		11 Jan	05'30"	30"
	27		02 Oct	05'40"	10"
	28		03 Dec	05'45"	05"
	29*	1696	04 Jan	05'55"	10"
	30		19 Jan	06'00"	05"
	31		25 Sep	06'10"	10"
	32		29 Sep	06'30"	20"
	33		21 Nov	06'45"	15"
	34		02 Dec	06'50"	05"
	35	1697	11 Jan	07'00"	10"
	36		11 Dec	07'20"	20"
	37		16 Dec	07'30"	10"
	38	1698	07 Sep	07'40"	10"
	39		01 Oct	08'00"	20"
	40		13 Oct	08'10"	10"
	41		30 Nov	08'20"	10"
	42	1699	01 Feb	08'30"	10"
	43		05 Dec	08'40"	10"
	44	1700	05 Feb	08'50"	10"
	45		16 Oct	09'00"	10"
	46*		30 Oct	09'10"	10"
	47	1701	02 Feb	09'20"	10"
	48		04 Jun	09'30"	10"
	49		02 Sep	09'40"	10"
	50		12 Dec	09'45"	05"
	51	1702	27 Jan	09'50"	05"
	52		25 Apr	10'00"	05"
	53	1703	05 Jan	10'10"	10"
	54		06 Apr	10'20"	10"
	55(*)		31 Jul	10'30"	10"
	56	1704	1 Sep	10'40"	10"
	57*		27 Nov	10'50"	10"
	58	1705	21 Jan	11'00"	10"
	59*		25 May	11'10"	10"
	60(*)	1706	07 Mar	11'20"	10"
	61		24 Mar	11'30"	10"
	62		10 Apr	11'40"	10"
	63		03 Jun	11'50"	10"
	64	1707	21 Jan	12'00"	10"
	65	1708	19 Jan	12'40"	40"
	66	1709	18 Jan	12'50"	10"
	67		24 Dec	13'10"	20"
	68	1711	05 Jan	13'30"	20"
	69	1712	06 Mar	13'35"	05"
	70		19 Sep	13'40"	05"
	71	1713	18 Jan	14'00"	20"
	72*		07 Nov	14'10"	10"
	73	1714	10 Sep	14'20"	10"
	74*		04 Nov	14'30"	10"
	75*		07 Dec	14'40"	10"
	76	1715	07 Nov	14'50"	10"
	77		07 Dec	15'00	10"
	78	1716	06 Mar	15'10"	10"
	79*		09 Dec	15'20"	10"
	80*	1717	07 Jul	15'30"	10"
	81*		29 Dec	15'35"	05"
	82	1718	12 Feb	15'40"	05"
	83*		09 Mar	15'35"	05" (-)	misprint?
	84*		18 Apr	15'40"	05"
	85*		28 Aug	16'00"	20"
	86	1719	27 Dec	16'00"	-

*   Indicates that value changed during the day's observing (20 in total) including during observations of the Moon

1. The observing book indicates that the amount increased to 03'50" on or about 16 May 1693

2. Recorded in observing book as 02'20" on 2 Jan, (at the end of RGO1/4) but as 02'10" on 17 January (at the start of RGO1/5 which also contains a similar table for the dates 1691 Jan to 1694 Aug (RGO1/5/5). In the observing book RGO1/4, the amount to add is generally recorded at the top of every page until 25 March 1690 after which it is absent until 16 Dec 1690 where it is recorded as still being 01'30" (was it recorded mid-page instead - if so, it is not immediately obvious where). Note, the ZDs for the observations of Sagittaria made on 14 May 1690 are different between the observing book, the apographa and the published observations

Tables showing (1) the number of increases by month and
(2) the number of times each increment appears

	Month	Number of occurrences		Size of increment (")	Number of occurences
	January	15		5	20
	February	9		10	51
	March	8		15	1
	April	4		20	8
	May	3		25	1
	June	3		30	1
	July	3		35	0
	August	2		40	2
	September	8
	October	8
	November	7
	December	14

 

Table constructed by Flamsteed at the start of the observing book RGO1/5 (under construction as original difficult to decipher)

	Year	Months	Error
	1691		2'10"
			2'15"
			2'20"
			2'30"
			2'40"
	1692	Jan: Feb	2'40"
		Mar-Apr	2'50"
		May	3'00"
		June	3'10"
		July Aug Sep Oct Nov	3'20"
			3'30"
	1693		3'30"
			3'40"
		Sept 22	4'00"
		Octob 6	4'10"
		Der 5	4'20"
	1694	Jan & Feb	4'20"
		Mar Ap M	4'25"/4'30"
			4'35"

 

Acknowledgements and Image licensing

The two images from the British Museum are reproduced under an Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license, courtesy of the The Trustees of the British Museum. Both have been cropped and recompressed for this website. 

Museum number: 1865,0610.947.
Museum number: 1865,0610.951.