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User:Peter Mercator/Draft for Kirkhill

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The pillar

The Kirkhill Astronomical Pillar was constructed in 1776 by David Stewart Erskine, 11th Earl of Buchan[a] and erected in the grounds of his estate at Kirkhill House, near Broxburn. The pillar fell into disrepair and eventually collapsed in the 1970's but fortunately the stones were preserved and the pillar was reconstructed (1988) in Almondell Country Park on land once owned by the Erskine family.[b] The pillar records the details of an adjacent scale model of the solar system constructed by Erskine following the measurements of the size of the solar system deduced from the observations of the Transits of Venus in 1761 and 1769. The model, centred on a sun of stone six feet in diameter with planets at distances and sizes to scale, has long since disappeared, only the pillar remains.

Erskine and science

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David Erskine, the 11th Earl of Buchan
Main article: David Erskine, 11th Earl of Buchan

As a young child Erskine was taught at home by his parents, both of whom had studied (and met each other) in the classes of the famous mathematician Colin Maclaurin at Edinburgh University.[1] They also employed a private tutor, James Buchanan, a graduate of Glasgow university, well versed in mathematics and languages.[2] Under the guidance of this trio he developed a life long love for mathematics and astronomy.

At the age of 13, Erskine entered St. Andrews University (1755-59) and then continued to Edinburgh University (1760-62) and finally Glasgow University (1762-63).[3] Although Erskine's later intellectual activities were dominated by his investigation of Scottish antiquities, he remained interested in science and mathematics. He was honoured by election to the Royal Society of London in 1765.[c] At that time he was living in London and at meetings of the society he would have heard much of the following topical astronomical problem.

How far is the sun?

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Main article: Transit of Venus
Venus in transit over the face of the sun

By the beginning of the eighteenth century the Copernican model of a heliocentric solar system was well established and astronomers such as Tycho Brahe and Johannes Kepler were able to describe the motions of the planets with ever greater precision.[4] However, no one knew the absolute size in miles (or any other units) of the solar system although the solar distances of the planets could all be expressed as definite ratios of the Earth-Sun distance by using Kepler's laws. This fundamental distance is termed the Astronomical Unit (AU).[d]

The breakthrough came in 1639 when Jeremiah Horrocks made the first scientific observation of a transit of Venus and used his results to estimate an approximation for the AU.[5][6] A second method, proposed in 1663 by the Scottish mathematician James Gregory,[7] was promoted by Edmond Halley in a paper published in 1691 (revised 1716).[8] He demonstrated how the AU could be measured very accurately by comparing the duration of the Venus transit across the face of the sun as measured by two observers spaced at latitudes a few thousand kilometres apart.[e]

The next opportunities of observing such a transit were in 1761 and 1769 but Halley had died in 1642 and it was left to others to organise observations in the first ever major international scientific collaboration. The event of 1761 produced sparse results because travel overseas was greatly hindered by the Seven Years' War but in 1769 many observers were again despatched all over the world, amongst them being Captain James Cook on behalf of the Royal Society of London. Various pairs of observation results were input into Halley's calculations giving many slightly different values and a mean value of the AU was published shortly afterwards in the Philosophical Transactions of the Royal Society.[9]. The result was 93,726,900 miles, within one per cent of the presently accepted value is 92,955,807 miles.

In Scotland, both transits were observed by Erskine's friend and neighbour, Reverend Alexander Bryce,[f][10][11] minister of the church at Kirknewton, only 3 miles from Kirkhill. Bryce was a competent mathematician and he calculated[g] the AU and the other distance parameters of the solar system: it is these values that Erskine used to create his scale model of the solar system.

The epitome

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The table as printed in the Uphall account.[12]
A portion of the badly eroded table inscribed on the pillar

In his 'Account of the Parish of Uphall', Erskine writes:[12]

"In the year 1776, I caused a representation to be made of the solar system, on a scale of 12,283 miles and 28/100 to an inch; the table of which epitome[h] is engraved on a belfray which stands in the middle of my garden, and of which I shall insert a transcript below."

The scale appears unusual but it followed simply from Bryce's calculation of the diameter of the sun as 884,396 miles and Erskine's arbitrary choice of a representation of the sun by a freestone spheroid 6 feet, or 72 inches, in diameter. Dividing 884,396 by 72 gives 12,283.28 miles to one inch, or 778,268,621:1. Of the six planets known in the eighteenth century Jupiter and Saturn were modelled in stone, the latter having an iron band, and the smaller planets were made of bronze: all were mounted on plinths or pillars in the grounds of the Kirkhill estate at the correct scaled distance from the sun. Primrose, writing in 1898, says that only a few of the plinths remained in his day.[13].

The table giving the dimensions of his representation is carved into the east face of the stone pillar, or belfry; it is barely legible now, but the details are preserved in the Uphall account.[14]. Planet diameters and distances on the pillar are reproduced here, along with the values obtained by scaling inches up to miles, by a factor of 12,283.28. Modern values are shown for comparison. Details for the moons of Jupiter and Saturn have been omitted.

Diameter Mean distance
model1(in) scaled2(mi) actual3(mi) model1(ft) scaled2(mi) actual3 (mi)
Sol Sun 72 D=884,396 864337 -- -- --
Mercury Mercury 0.402 4938 3032 249.06 36,711,285 36,000,000
Venus Venus 0.750 9212 7521 466.05 68,695,472 67,200,000
Earth
Earth
 Earth 0.646 7935 7926 645.0 AU=95,072,587 93,000,000
First quarter moon Moon 0.178 2186 2159 1.6154 238,050 4 239,0004
Mars Mars 0.422 5184 4221 982.06 144,755,752 141,600,000
Jupiter Jupiter 7.710 94704 88846 3354.05 494,384,823 438,800,000
Saturn Saturn 6.448 79203 74897 6153.03 906,952,684 890,400,000
Rings5 14.50 c.178108 170,0005 0.41 60,434 57,2006
1 Feet(F), Inches(I), decimal(D) part of inches converted to decimal inches/feet for diameters/distances.
2 Scaled figures in miles by multiplying inches by 12283.23 and feet by 12*12283.23
3 Average present day values are taken from NASA factsheets for planets and sun.
4 Moon distance is from Earth. Moons of Jupiter and Saturn omitted from this table.
5 Erskine's sign for the rings is the same as that for the constellation of Aquarius.
6 Typical data for the width and inner radius of the Rings of Saturn.

Calculation of the values in the table starts from the new value of the AU calculated by Bryce. Kepler's Laws then give the solar distance (in miles) for every planet and therefore, given the actual dimensions of the orbits, it is straightforward to calculate the distance of any planet from Earth at the time of any observation. Then, using the observed angular sizes of the sun and the planets he could deduce their diameters in miles.[15]

To fit the data on the table Bryce's must have calculated the value for the AU to be 95,072,587 miles. This value is greater than the modern (average) value of 93,000,000 miles. This largely accounts for the discrepancies in Erskine's data for distances and diameters.

The third, fourth and fifth columns of the pillar are reproduced in a second table below. It shows that the eccentricities of the planets and their inclinations to the ecliptic were quite well known at the time. (In the table Erskine's eccentricity value 80)387( is simply the fraction 80/387 and this has been replaced by decimal 0.207 etc.). Eccentricity and inclination are the essential parameters for working out the motions of the planets. No values are given for the orbit inclinations to the ecliptic for Mars and Jupiter, the space on the table having been utilised for a comment on the moons of Jupiter. The last pair of columns refer to to what Erskine terms the inclination the planet rotation axis to the plane of the orbit. Nowadays the term axial tilt is used by astronomers: it defines the angle between the rotation axis and the normal to the plane of the orbit and it is equal to 90 degrees minus Erskine's inclination. The values for Mercury and Venus are omitted on the pillar.

Obliquity1 Eccentricity Inclination2
pillar actual pillar actual pillar 90°− tilt
Mercury Mercury 6°59′20″ 7° 00′ 0.21 0.2 -- 0°2′
Venus Venus 3°23′05″ 3°24′ 0.007 0.007 -- 2°36′
Earth
Earth
 Earth 0° 0° 0.017 0.017 66° 32′ 66°36′
First quarter moon Moon 5° 5°06′ 0.053 0.055 90° 83°18′
Mars Mars -- 1°54′ 0.093 0.094 ≈90° 64°48′
Jupiter Jupiter -- 1°18′ 0.048 0.049 ≈90° 86°54′
Saturn Saturn 2°33′30″ 2°30′ 0.057 0.057 ≈90° 63°18′
Rings 2°33′ 31°0′3 -- -- -- --
1 Erskine's 'obliquity' now termed Orbital inclination
2 Erskine's inclination of the axis is the complement of the modern axial tilt; (90° minus axial tilt).
3 The rings are perpendicular to the axis of saturn.

The final column on the pillar is a prediction of where the planets will be on May 20th 2255. The heliocentric places within the zodiac constellations define an angle now termed the heliocentric ecliptic longitude. Both are measured from the point in the sky where Aries begins. Each constellation covers 30 degrees whereas the longitude covers the whole 360 degrees spanned by all 12 constellations. The order of zodiac constellations is Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. Therefore 9°40′ in Sagittarius for Mercury becomes a (decimal) longitude of 249.667° etc.

  Heliocentric place (pillar) JPL prediction1
planet zodiac long. 20/05/2255 9/06/22552
Mercury Mercury   9°40′ Sagittarius 249.67° 343.75° 94.90°
Venus Venus 25°50′ Libra 205.83° 222.30° 254.19°
 Earth  Earth 29°30' Scorpio 239.50° 235.08° 254.30°
Mars Mars 27°42' Sagittarius 267.70° 264.86° 276.28
Jupiter Jupiter 17°40' Scorpio 227.67° not given3
Saturn Saturn 19°16' Capricorn 289.27° not given3
1 Data for planets from Jet Propulsion Laboratory (JPL). The data is given at 0 hours U.T. on the day in question.
2 Date of transit as given in JPL data
3 JPL data for Jupiter and Saturn are not available after 2200.

The significance for the year 2255 specified in the prediction is that it is a year in which a transit of Venus occurs; the eighth after that of 1769. During such a transit the Earth, Venus and the sun must be closely aligned, in other words the heliocentric[i] places (longitude) of the planets must very close, as shown by the predictions for the actual transit on 9th June, 2255. Therefore, since Erskine gives heliocentric places for Venus and Earth differing by about 35°, he was clearly not predicting a transit for the 20th May. There is no astronomical phenomenon associated with that day but it must have had some significance for Erskine, as yet unexplained.

Other inscriptions on the pillar

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There are inscriptions on the four sides of the pillar but they are now difficult to read. Fortunately some are recorded in Erskine's history of Uphall[16] and others in the account of the same parish by James Primrose.[17] Most are in Latin, often abbreviated, but translations have been given by James Primrose in his chapter on Kirkhill.

East Face

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This face has the table described in the previous section. Above the table is the quotation given at the beginning of the previous section where Erskine (Buchan) describes his construction and its scale.

West Face

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An inscription in Latin:
Jacobo Buchanano, Matheseos P. Glasg. Adolefcentiae meae Custod. incorruptissicno has Amoenitates Academicas Manibus propriis dedicavi, inscripsi, sacraque esse volui. Anno ab ejus excessu XV. et a Christo natu MDCCLXXVII. Ille ego qui quondam patriae perculsus amore, Civibus oppressis, libertati succurrere aussim, Nunc Arva paterna colo, fugioque liruina regum.

Primrose gives the translation:
To James Buchanan, Professor of Mathematics at Glasgow,[j] the most incorruptible guardian of my youth, have I dedicated, inscribed with my own hands, these Academic Amenities, and I wish them to be sacred. On the 15th year of his death and from the birth of Christ 1771, I who formerly animated by love of country, dared to succour liberty and oppressed citizens, now cultivate my paternal fields and shun the threshold of Kings.

This a very touching dedication of his epitome to James Buchanan, the tutor and mentor of his early years. He died in 1761.

South Face

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A quotation from Vergil's Georgics: DIGNA MANET DIVINA GLORIA RURIS which may be translated as "Pay homage to the heavenly sent land" or "The worthy glory of the Divine Country is abiding"[13] Underneath the inscription is a large bow and arrow the significance of which is unknown.

North Face

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A long inscription gives abbreviated details of the location of the pillar and other points. Erskine gives a fuller version in his account of Uphall Parish.[18]

"The latitude of Kirkhill is 55°56'17" north, the west longitude in time from Greenwich Observatory is 13′ 59′′10′′′.[k] The variation of the compass 1778 in June was 22°, the dip of the north end of the needle at the same time was 71°33'. The elevation above high water mark at Lieth (sic) when there is 12 feet of water in the harbour 273 feet; it is lower than the top of Arthurs Seat, 546 feet, lower than the Observatory on Calton Hill 83, than the top of the Castle Rock 290. West longitude in time from Edinburgh Observatory, 1°8"; east longitude in time from Glasgow Observatory, 3′11′′50′′′ - distance from Kirknewton Manse in Midlothian, 20,108 feet; north from Kirknewton Manse, 17,005 feet or 2′47′′ (arc); west from Kirknewton Manse, 10,680 feet or 12′′30′′′ in time."

The mention of Kirknewton Manse links this inscription to its resident, Alexander Bryce, who provided the details of the epitome table. The latitude is in a conventional notation but the longitudes are defined in terms of time: 15 degrees of longitude corresponding to one hour. The Greenwich time separation from Kirkhill given as 13′ 59′′ 10′′′ (minutes, seconds, sixtieths) corresponds to longitude 3.496°W: the modern value is 3.46°W. Similarly time displacements of the observatories at Edinburgh and Glasgow should be read as 1′8′′ (not 1°8") and 3′11′′50′′′ respectively, corresponding to 17 and 48 arc minutes of longitude, or 11 and 31 miles. The distances from Kirknewton Manse to the pillar are direct, north and west: the latitude difference is 2′47″ (arc) and the longitude difference in time is 12′′30′′′ corresponding to 3.12 arc minutes of longitude. The height differences between the pillar and locations in Edinburgh are an interesting by-product of Bryce's survey of a canal from the city, past Kirkhill and on to Falkirk.[10] Since there were to be no locks between the city and Broxburn the height of the pillar was easily related to that of the canal terminus and hence other known Edinburgh locations.

Other inscriptions

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There are a number of other inscriptions which were close to the pillar. The globe representing the sun was engraved, in large Hebrew letters, with the question "What is man?" A plinth showing the Moon orbiting the Earth was inscribed "Newtono Magno". A small building near the pillar was inscribed "Keplero Felici". The approach to Kirkhill was guarded by pillars inscribed "Libertate quietate". On a triangular equilateral stone in Erskine's garden, was the inscription, "Great are thy works, Jehovah, infinite thy power!"

The model re-imagined

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In the years leading up to the 2012 transit a group of Scottish artists collaborated on an artistic realisation of the solar system model of Erskine. The Kirkhill Pillar Project was commissioned under the auspices of Artlink Edinburgh.[19] The sun is represented by a light box on the top of Broxburn academy, within a few hundred metres of the Erskine's own house. The artefacts representing the nine planets are distributed around the county of West Lothian at distances given by Erskine's scale. Mars and Jupiter are represented by small spheres mounted on plinths. Mercury is represented by a cast iron replica of the cratered surface of the predominantly iron planet. Venus is represented by a schematic version of its transit over the face of the sun. Earth, inspired by the blue and white image seen on early space missions, is represented by two planters containing blue and white flowers. Mars is a distinctive red sculpture in community woodland. A cast acrylic clear block houses a painted model of the planet Jupiter. Saturn is represented by a technical image used by James Clerk Maxwell in his explanation of the structure and stability of the rings.[20] Uranus is represented by a band suspended from two trees: it houses seven opaque apertures which allow the light to shine through. Neptune is captured as a blue orb in a lantern above the doors of Kingscavil church. Pluto is carved into black polished granite placed in Beecraigs Country Park. Images, further details and a map of locations may be found at may be found on the website of the Kirkhill project.[19]

Sun
Mercury
Neptune
Saturn's ring stability
Artistic installations representing the Sun, Mercury, Neptune and Saturn.

References

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Notes

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  1. ^ Erskine's second given name is spelled either Stewart or Steuart. The latter, a French version originating in the time of Mary, Queen of Scots, was that adopted by his mother's father (James Steuart). See also Encyclopaedia Britannica (2020).
  2. ^ The present location of the pillar is about 2.5 miles from Kirkhill House, close to the location of the home built by his younger brother Henry Erskine.
  3. ^ List of fellows of the Royal Society D, E, F
  4. ^ In the 18th and 19th centuries astronomers did not refer to the astronomical unit, instead they referred to the solar parallax, the angle subtended by the known radius of the earth at the distance of the sun. The definitions are equivalent.
  5. ^ Halley's method, as described in his 1716 paper, is fairly inscrutable for modern readers with one simple figure and no equations in sight. The method is of historic interest only. Simplified modern discussions are Odenwald (2012) are Odenwald and DePontieu (2012) Nowadays the scale of the solar system is measured by radar ranging to Venus and and inter-planetry space probes.
  6. ^ Bryce, described as an eminent geometrician in the Dictionary of Eminent Scotsmen (BDES (1857)), and as an applied mathematician in the Dictionary of National Biography (ODNB Bryce (2004)), continued with his mathematical studies and for a while took over the lectures of Maclaurin during the latter's closing illness.
  7. ^ It is not known which distant observation was used by Bryce in his calculation of the AU.
  8. ^ Erskine is using the word 'epitome' in the sense of a summary of knowledge but he would have been aware that Kepler's Epitome Astronomiae Copernicanae was the standard astronomy text book for the seventeenth century.
  9. ^ The actual heliocentric longitudes are given by the Jet Propulsion Laboratory ephemerides
  10. ^ Erskine describes Buchanan as a professor of mathematics at Glasgow but, although nominated, he died before the faculty could proceed. He was a professor of oriental languages at that time.
  11. ^ Erskine uses a Sexagesimal notation for divisions of an hour with one, two and three primes denoting minutes, seconds and sixtieths of seconds.

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Citations

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  1. ^ Cant 1981, p. 3.
  2. ^ Buchanan.
  3. ^ Cant 1981, p. 4.
  4. ^ Kepler 1995.
  5. ^ Chapman 1990.
  6. ^ ODNB Horrocks 2004.
  7. ^ Gregory 2006.
  8. ^ Halley 1716.
  9. ^ Hornsby 1769.
  10. ^ a b BDES 1857.
  11. ^ ODNB Bryce 2004.
  12. ^ a b Buchan, p. 152.
  13. ^ a b Primrose 1898.
  14. ^ Buchan, p. 153.
  15. ^ Smart 1977, p. 98.
  16. ^ Buchan 1793.
  17. ^ Primrose 1898, pp. 79–83.
  18. ^ Buchan 1793, p. 142.
  19. ^ a b Kirkhill Pillar Project.
  20. ^ Maxwell 1859.

Sources

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Lee, Sidney, ed. (1885–1900). Dictionary of National Biography. London: Smith, Elder & Co. David Steuart Erskine]. {{cite book}}: External link in |postscript= (help)CS1 maint: postscript (link)

Category: Solar System

Category: Solar System models

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