Talk about Hutton

Without Professor Robin Johnson there would be no ‘centre piece’ map in the exhibition, Robin was able to enlighten and elucidate on the maths Charles Hutton used in inventing lines of equal altitude. As Nevil Maskelyne – the Astronomer Royal – needed Hutton, so I have needed the Professor to help me re-create Hutton’s missing map (and 3d model).3d model hutton

Last night to a packed hall, Robin gave a talk: Charles Hutton: scientist, mathematician and the density of the Earth (a copy of it is available through this link: Charles Hutton)

Hutton would not have recognised the title “British inventor of contour lines“. Mathematician, scientist even natural philosopher are descriptions he would have understood. Robin talked us through his humble origins in the mining community of Newcastle, through the ‘accident’ that led to his schooling, his mentors, and the range of mathematical conundrums he was involved in. It was both fascinating and remarkable how much material Robin uncovered that I had missed.hutton talk 2

One of the many joys of this project has been encountering professionals both curious enough and generous with their time; they have enhanced the research and opened new avenues in both breadth and depth. And it was great to see so many of them at the Opening.

Next up is a ‘fantasy maps’ free drop-in at the Lit and Phil this Saturday 10 till noon, if you have young children interested in creative thinking and making things do call by.

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The Exhibition

The Exhibition opens tomorrow with Preview & meet the artist: 5.30 to 6.30pm (FYI Library closes at 7). The Lit & Phil, Newcastle, NE1 1SE

Alongside 4ft map, models and drawings will be material held by the Lit & Phil pertaining to Charles Hutton: inventor of contour lines.

Plus, Monday 6th June, 6.00pm. ‘Charles Hutton: scientist, mathematician and the density of the Earth’, talk by Prof. Robin Johnson.

And Saturday 11th June, 10am till noon ‘Fantasy Maps’ FREE creative drop-in for families.

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Shape of a Mountain

A photo of Schiehallion is an impressive thing, with great hunk with spine aloft, the mountain rises magnificently out of its surroundings. But before photography – and prior to contours – depicting a mountain and suggesting its elevation had quite a history. According to Ainslie’s map of 1783 Schiehallion was but a heap of absently poured salt on a flat, flat table top. Each Scottish peak appears as a little salt pile drawn in profile, each the same size. Rivers are dispensed with so ‘Tumel Bridge’ is simply a mile marker. As the ‘road atlas’ of its day this can be forgiven. shape of mountain copy What I find harder to understand is his revised map just 6 years later. Although rivers are now present – a useful guide to travellers – and mountains are no longer in relief, it’s painful to behold; the hachuring gives the whole land surface the appearance of angry teenage acne.shape of mountain 1A lot depends on who you are drawing a map for; Lempriere’s from 1731 has a more contemporary feel, probably due to its function which was to describe: “…the situation of the several clans and the number of men able to bear arms, as also ye forts lately erected and roads of communication and military ways carried on by his majesty’s commands…” Here, if the map was a table-cloth it is un-ironed, the highlands of Scotland appear foreboding; ‘Chechalian’ dominates surrounding hills.shape of mountain 2I’m on the splendid NLS online map service darting across a century of map making, comparing depictions of Schiehallion. This quest has led to a series of drawings that will be on show (alongside the 4ft map, models and other materials) in the exhibition later this week.

After Lempriere comes Roys’ Military map, this is incredible, detailed, exquisite  map-making for its day, not least because it looks so modern, ‘google earth’ rendered in pen and ink. All these maps are pre Maskelyne’s experiment, pre Hutton; none gives an indication of altitude. The first post Hutton map I find is Arrowsmith’s in 1807, here the hachuring is more refined, like the whorls of a thumb print, rivers run like veins, all very expressive compared to his perfunctory treatment of roads and place names. And there is a ‘spot height’, only one: Schiehallion. He has sheared off the whole mountain top, almost as though creating a plinth for his magnificent text:

‘Schiehallion, 2000Ft. above the Valley, 3550 above the Level of the Sea’

The text curves slightly and ‘sea’ is beginning to slip down the mountainside. Not until Carrington’s map in 1846 is another ‘spot height’ added, (he includes Ben Lawers at 4015ft and has also raised ‘Schichallion’ to 3564).shape of mountain 3As the need for military maps receded so those giving the geology grew, some like MacCulloch in 1840 simply added colours to pre-existing maps. Others started again, flattening the land as though the mountains have lost all importance. Necker in 1808 squeezes in as many place names as he can, and in between slots chains of hills, unlike Ainslie’s little salt heaps 25 years earlier, Necker’s at least are ‘hill shape’… though Schiehallion is not shown at all.

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Map Mark Making

The look of a mountain.Crucially – with neither faint (contour) lines nor numbered heights – we have illustration IX. It probably represents the stage before the invention, on it are marked the perimeter stations – where a theodolite would have been positioned – joined together with bold straight lines.Prof hutton spots

Giving this illustration its strange target like quality are a series of radial lines and evenly spaced concentric circles which, I imagine outline his ‘columns’.

The mass of wee dots represent a position in which a pole-bearer stood while traversing a – usually – straight line up the mountain. Some are obvious ascents; between A (Creag  an Eara) and N (the summit) are 13 dots, thirteen times that poor lad set down his load to hold up a pole while the distant and static surveyor took readings. Cloud rolls in so fast and low, one wonders how often his slow ascents were rendered redundant. In 4 months, those climbs for the summit were successful on just 4 occasions from: A D G and F’.map mark making

Where my maths fails me is understanding the epicentre or bulls-eye of the concentric circles, which is not the summit (N), but rather the Northern Observatory (P), suggesting a second map with the Southern Observatory as bulls-eye.  I am omitting the circles from my recreation of Hutton’s map on the grounds I would need two sets: two stones sending out ripples on the pond.Hutton worked everything out from negative figures – the summit of Schiehallion was marked as ‘zero’ (this long before the invention of mean sea level), I have read of a French cartographer who used the same method for estimating the elevation of a fort in Minorca in 1761, but the source is not reliable (according to Josef Konvitz, Hutton is a naturalist, Ancelin is not French, and Marsigli drew 2 isobaths, not one). So as intriguing as Cartography in France 1660 to 1848 is, until I get to Paris to see the map with my own eyes, I am with Hutton on this innovation.

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Scaling the Mountain

Journey north: A1, A9; spent pondering scales for drawings: A3, A5? No need to curse the ‘badnef of the weather’ this time, heading for the camp site I see Schiehallion’s Western Edge for the first time; a cool pinnacle glistening in low sun, so other to the brooding hulk in most photos. The next morning Liz Auty from the John Muir Trust guides us around the eastern skirts and up to the site of Nevil Maskelyne’s Southern Observatory: his ‘home’ half way up a mountain. It’s taken much less time than we thought and feels wrong to be breaking into lunch boxes at 11.

I pose for a photo ‘sleeping’ in Nevil’s ‘bothy’.







But here’s the thing. What I hadn’t expected was such a clear picture of Hutton’s map to be laid out before (and above) me. With clarity, the random seeming ‘delta‘ symbol north (& a little west) of the site appears to be a tall, probably natural  (or augmented) cairn on the sky line, it would certainly have been used for bearings and will now be added to his/my contour map (when I finally get to the studio this afternoon).

Looking downwards the whole of the southern base line is visible, Nevil would literally have ‘overseen’ the work of the surveyors and pole bearers inching their way around each triangulation point below, perhaps even scorning their stumbling slowness like an angry god.Invites to the exhibition are going out on Monday, if you are a ‘follower’ but not on my mailing list, do drop me a line and I will add your email address:

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Great lines, Faint lines

It’s not even a page in length; there is just one paragraph that makes clear Hutton is inventing a new type of line: “This method was the connecting together by a faint line all the points which were of the same relative altitude… the relative altitude of all the parts being known; and as every base or little place had several of them passing through it, I was thereby able to determine the altitude belonging to each space with much ease and accuracy.”

I imagined him pencil and ruler to hand slowly joining the dots that made up his spot height bases, and that with the help of Prof. Robin Johnson I could now follow his method and replicate the missing map. I prepared my stout piece of paper: “four feet long by four feet broad”  placed upon it all the points for which heights had been calculated, reversing two number sequences that ‘read the wrong way’: I doubt it was Robin’s mistake, with so many hands in play – the surveyors, the astronomer royal and Hutton himself – it would be easy for a set to be copied in the wrong order from one notebook to another.

It seemed easy enough to mark lines at 100ft elevation, and in plenty of places those for 50ft but I think either he didn’t publish everything or it was really a boast too far when in the next sentence he states: “In this estimation I could generally be pretty sure of the altitude to within ten feet and often within five feet”.Even with the multitude of spot heights at my disposal interpolation was not straight forward, there were a number of places where the ‘either/or’ of bifurcation tempted, though I chose not to (come to the Lit and Phil and I’ll explain). But am not so sure Hutton wouldn’t have employed the occasional branching line. It’s strange how full it looks, but even  OS maps 70 years later had much less data to play with. Hutton’s surveyors  provided a wealth of material to work from (unlike the French ha ha! I will come onto them… eventually).

With this map near complete, I have begun work on ‘compare and contrast’ models: Schiehallion in contours á la Hutton versus modern OS. But now, today, weather permitting (this time), it’s back to the mountain, and with the aid of the John Muir Trust, a mission to find the sites of the astronomer royal’s observatories.

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Cooking with Columns (and tables)

Once Hutton had conceived his columns: “it is evident that the plan must be divided into a great number of parts, perhaps not less than a thousand for each observatory… forming about two thousand such pillars of matter…” Prof hutton spotsWith his pillars planned it became apparent that not each one had a spot height within it:

Prof hutton calcs“numerous as these points are, there are evidently many bases in which none at all are contained, nor even near them. The circumstance at first gave me much trouble and dissatisfaction, till I fell upon the following method…”

These snippets appear within the 100 plus pages of Hutton’s calculations, where even the title seems inordinately long and tedious: “An Account of the Calculations made from the Survey and Meafures taken at  Schehallien, in order to afcertain the mean Denfity of the Earth”.  Prof hutton calcs1

Over half the pages are devoted to mathematical tables I struggle to follow, with each reading though I began to see the shape at least of each necessary calculation.

My way of tackling it, is to conceive of it as a cookery book: all the ‘ingredients’ needed to recreate the missing (first contour line) map are there, just I don’t possess the skills to follow the recipe.

However through very good fortune I found my ‘Master Chef’; the head librarian at the Lit and Phil put me in touch with Emeritus Professor of Mathematics Robin Johnson who skilfully number-crunched Hutton’s calculations into a visual format I could follow. Work has begun on recreating the missing map which hopefully will be ready for unveiling at the Great Lines exhibition next month.

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