The city of Sheffield is said to be built on seven hills, just like Rome. This has been repeated for at least ninety years.¹ The earliest written reference anyone has produced is from 1936, in George Orwell’s diary.² But even Orwell put it in brackets and hedged it. No two independent lists agree, and J. G. Harston’s survey, the most careful local attempt to count them, arrives at five, or perhaps eight.

The town is very hilly (said to be built on seven hills, like Rome)

George Orwell, diary, 3–4 March 1936

Here we show that Sheffield has exactly seven hills. (Although they’re not quite the ones popularly named.)

1. Counting hills

Hills have hills. A bump on the side of a bigger hill still looks like a hill, and any rule loose enough to count it will also count the step outside your front door. So how many hills depends on how much of a rise counts as a hill.

The usual way to decide what counts as a hill is topographic prominence, which British hill lists call a summit’s drop: stand on the top and walk to any higher ground, by whatever route keeps you as high as possible. The lowest point you are forced down to, subtracted from the summit, is its prominence.

A high bump on a plateau has very little prominence, because the ground barely dips before it climbs again, while a modest hill standing on its own has a great deal. Prominence measures how much of a hill something is, rather than how high it is.

Britain already counts hills this way, and publishes the bar: a Marilyn drops at least 150 m, a HuMP at least 100 m, and a Tump at least 30 m. So “how many hills” already has several correct answers — one for each bar.

2. The Geoff

Every bar gives a different count. So instead of counting Sheffield’s hills, we will declare how many it has and let the declaration fix the bar.

Definition 1For a drop d > 0, let H_Sheff(d) be the number of hills inside the Sheffield city boundary, as drawn on a stated date, whose drop is at least d.

H_Sheff falls as d rises: demand more of a hill and fewer qualify. Somewhere on the way down from “every bump” to “nothing at all” it passes through seven. Not every city’s does — see §9.

Axiom 1Sheffield has exactly seven hills.

Definition 2One Geoff is the largest drop d at which H_Sheff(d) is exactly seven.

The largest drop d at which the city holds seven hills and not eight. With ≥ 7 a tie would leave the set inhabited and the Geoff would outlive its own failure condition; this way it is empty exactly when the seventh and eighth drops meet.

Alternatively, line the city’s hills up by how far they drop, and one Geoff is the seventh-biggest drop.

Proposition 1Let d₇ and d₈ be Sheffield’s seventh- and eighth-largest drops. If d₇ > d₈ then Axiom 1 can be met, the Geoff exists, it is unique, and it is d₇.

Which is the proof as well as the statement: the thresholds at which Sheffield has exactly seven hills are the interval in (3), and (2) takes its largest member, which the interval contains.

The axiom is a constraint, not a gift. Had the seventh and eighth hills been tied, that interval would be empty — H_Sheff would step from six straight to eight and never rest on seven — and no threshold would give the city seven hills, so there would be no Geoff to define. They are 40 m and 38 m (§4), which is the whole of what Sheffield contributes here: Sheffield is entitled to the convention.

The inequality is the contribution, not the margin. Any two drops separate if you measure them finely enough — except that sometimes they do not, and §12 watches that expectation fail on the better of two instruments. A tie is usually the instrument talking; whether it is only the instrument talking is a thing to measure. What Sheffield has today is 2 clear metres on a surveyed list, and that is an ordinary margin, not a wide one: among the 133 UK authorities whose seventh and eighth hills can be told apart at all, the median gap is 4 m and Sheffield’s beats 26% of them. Nor is having a gap at all the scarce part — only 8 of the 141 authorities whose lists run deep enough to ask are tied there. What is scarce is having seven hills to sort in the first place.

Every city could do this. Bradford could mint a Brian at 41 m and have exactly seven hills by the same construction, and the construction would be just as valid. Three things make it Sheffield’s anyway: the tradition already exists here and wants testing; the failure condition is real, and §12 watches it fire in Sheffield itself while the city clears it today on a surveyed list where §9’s Bristol cannot; and a unit is a convention, which means the question is not who is entitled but who went first. This is that.

Definition 3A Geoff is a hill whose drop is at least one Geoff.

British hill classifications already work this way — a Marilyn is a summit with 150 m of drop, a Tump one with 30 m. The Geoff is only the first whose threshold is fixed by the count rather than the count by the threshold.

3. What the unit is pinned to

Corollary. Sheffield has seven Geoffs, and cannot have any other number of them.

That is Axiom 1 arriving back, recovered from the definitions. It is true by construction and carries no information about Sheffield. The content is in what happens when the boundary moves. The Geoff is fixed to Sheffield as drawn on a given date. Sheffield’s boundaries have changed and will change again; when they do, its summits change, its prominences change, the seventh-biggest drop changes, and a new Geoff is defined. Sheffield still has seven — provided the new seventh and eighth keep missing each other, which is the one thing §2 does not give for free.

Corollary. Everywhere else does not. A region has however many summits clear one Geoff, which may be more than seven, fewer, or none — and since the unit is Sheffield’s, redrawing Sheffield’s boundary changes the number of hills in Rome.

A metre was once the distance between two scratches on a bar in Sèvres, and every length on earth was defined by it. The Geoff differs only in being pinned to a city council’s boundary review.

4. The current value

The Database of British and Irish Hills gives every hill it lists its drop,³ which is prominence under the name Britain uses, and the ONS publishes the boundaries. Taking Sheffield as currently drawn:

1 Geoff = 40 metres

Lodge Moor here is the moor, not the suburb: the summit is 6.6 km west-north-west of the houses that share its name.

Height has nothing to do with it. The seven range from 173 m to 550 m above sea level, and three of the five highest points in Sheffield are not among them:

Sheffield’s second-highest ground is not one of its seven hills. Margery Hill, Outer Edge and Horse Stone Naze are bumps on the same Dark Peak plateau — high, but they barely fall before the ground rises again, so they are not separate hills. They are lumps on one hill. Parkwood Springs stands alone above the Don and drops fifty metres on every side, so it is. That is section 1 in a table: hills have hills, and the question is only ever how far down you have to go.

The seventh-biggest drop is 40 m⁴ and the eighth is 38 m, so there is no tie and Sheffield has exactly seven Geoffs. The database is complete to 30 m of drop and the unit sits above that, so nothing is hidden beneath its floor.

The boundary is not a formality. Sheffield’s two largest hills sit on the line — each within a few tens of metres of it, on a rendering other sources disagree with by about as much — while Wharncliffe Chase, with more prominence than every hill in the city but one, lies 700 m outside. Moving the border a few hundred metres moves the unit and nothing else:

5. The traditional hills

One list that circulates locally is Stannington, Netherthorpe, Upperthorpe, Heeley, Norton, Wincobank and Crookesmoor. Others swap in Walkley, Crookes, Park Hill or Meersbrook, and Harston’s survey finds eight ridgelines and seven at no point in the city’s history. There is no authoritative version, which is the point — but a list has to be measured against something, so this one is. Only one of the names is in the hill database, because a hill and the district on it are rarely called the same thing, so each is measured to the nearest summit instead:

One of them is a Geoff. Backmoor and Norton are 380 m apart: the same high ground, the one with the water tower, visible from most of Sheffield. Sheffield’s seventh hill is a traditional hill under a name almost nobody uses for it.

One misses by two metres. Wincobank is a real summit, 430 m from where the tradition puts it, with 38 m of prominence against a unit of 40. It is the eighth hill in Sheffield: the first non-Geoff. Losing any one of the seven would let it in, and §7 argues about which one that should be.

The other five are summits, but only just. The database stops at 30 m, so they were swept from the satellite model instead: Stannington 4 m of drop, Heeley 7 m, and Upperthorpe, Netherthorpe and Crookesmoor sharing a single 14 m rise between the three of them. A tenth of a Geoff to a third of one, and in a built-up valley some of it will be roof rather than ground. The tradition was pointing at something.

Not at Parkwood Springs, though, which is a mile or two off and a Geoff: the Don runs between at about 55 m, which is 67 m below the col that gives Parkwood Springs its prominence in the first place. The three are on the far bank, on the rise that climbs west out of the city towards Crookes and, eventually, Lodge Moor. The tradition names neighbourhoods on high ground rather than the tops of it, which is what you would expect of a list made by people who lived on the hills.

And it knew which high ground was one hill. The same survey puts Walkley, Crookes, Broomhill, Fulwood and the city centre on a single ridge. Swept for drop, Crookes, Broomhill and Fulwood are 10 m, 5 m and 3 m; Crookes stands about 250 m above the sea, higher than two of the seven, and is still not a hill, because the ground barely falls before it climbs again towards Redmires. That is §4’s argument about Margery Hill, run on a ridge covered in houses instead of on open moor.

Two methods with nothing in common, one tracing water and one measuring drops, putting the same places on the same hill. The tradition is wrong about which rises are hills. It is not wrong about the shape of the ground.

6. Other UK cities

Held against Sheffield’s 40 m, the 361 local authorities of the United Kingdom come out as follows: 95 have more than seven Geoffs, 150 have between one and six, 108 have none at all, and 8 have exactly seven.

But a local authority is not a city. The Highland authority has 2,899 Geoffs and is not a town or city. Restricting it to 47 places that actually are cities, and whose council covers roughly the city rather than half a county:

Cities level on Geoffs are ordered by how many summits they hold, and then by name. Nothing in the ordering knows whose unit it is.

Sheffield is 5th of 47. Four cities are built on more hills than Sheffield — Swansea, Edinburgh, Wrexham, Newport — and not one of them has ever mentioned it, which is either oversight or restraint, but probably oversight. Sheffield shares its seven with Bradford (§7), and with five places that are not cities: Barnsley, the Isles of Scilly, Pendle, Renfrewshire and Stafford — and with Winchester, which is a city, but whose district is mostly rural Hampshire.

Twenty of the 47 cities have no Geoffs at all: Portsmouth, Bristol, Kingston upon Hull, Southend-on-Sea, Wolverhampton, Birmingham, Colchester, Nottingham, Salford, Coventry, Derby, Leicester, Manchester, Peterborough, Southampton, York, Cambridge, Norwich, Oxford, St Albans.

Among English cities Sheffield is 1st of 38:

Somewhere else:

7. The Bradford problem and a proposal

Sheffield currently ties with Bradford, and sits above it only on the tie-break: sixteen summits to ten. On the count the paper is about they are level. Bradford’s seventh hill has 41 m of prominence, so any unit above 41 m puts Bradford below seven.

The Geoff cannot simply be raised. One Geoff is the largest threshold at which Sheffield has seven hills, so any threshold above 40 m is one at which Sheffield has fewer than seven — and is therefore not a Geoff. The seven is fixed by the definition, the unit by Sheffield’s terrain, and the only free variable in the whole apparatus is where the line goes. It moves up only one way: taking in a hill bigger than the seventh Sheffield already has.

It moves the other way too, and that is what keeps Wincobank out. Take the largest drop away — High Neb — and every hill gains a place: one Geoff falls to 38 m and the traditional hill that missed by two metres in §5 clears it. Annexing raises the unit and pushes everything down a place; losing one lowers it and pulls everything up. The seventh-largest drop depends on the first.

High Neb is the least hill-like of the seven, seen from Sheffield. It is the highest point of Stanage Edge, thirteen kilometres from the city centre, and from the city side you reach it by gaining about 25 m over two kilometres of moor; the 78 m in a kilometre that makes it a hill is on the far side, falling into Derbyshire, where the nearest houses are — Bamford, 2.7 km off, in another county. Sheffield’s biggest hill is a plateau you walk on to and a cliff you look off. Prominence measures how much of a hill something is, not how much it looks like one from town.

To state the obvious: Sheffield does not need another hill. It does, however, need a bigger one, and it needs to annex it.

The nearest hill outside the city is Wharncliffe Chase — 102.6 m of prominence measured nationally, as everything here is measured and as the method note defines it; measured within boundaries there is no shortfall to correct and nothing to annex. 318.9 m high, and 700 m beyond the line, in Barnsley. Taking it in pushes every hill down a place, so the seventh-biggest drop becomes what was the sixth, and one Geoff becomes 49 m, and the standing of every city in England is revised accordingly:

This puts Sheffield in first place outright, and Bradford’s seven falls to three.

The cost falls on Barnsley: Barnsley is today one of the eight authorities with exactly seven Geoffs, and the transfer takes it to three — losing the hill itself, and then facing the higher bar the hill creates. That is a real loss to a neighbour, incurred so that Sheffield need not share first place. This does not seem unreasonable.

Note that Barnsley holds 18 summits to Sheffield’s 16, and that the tie at the top of §6’s table of English cities is broken on summits. Were Barnsley a city it would be first and Sheffield second. It is not one, so it does not appear at all — which means the hill is to be taken from the only neighbour that would win the league it is barred from entering.

8. The neighbours

Leeds has two Geoffs. It holds eight summits, but only The Chevin and Tinshill Moor clear the unit; the rest fall between 37 m and one metre. Leeds is therefore two sevenths of Sheffield. Its best hope is §4: losing High Neb and Back Tor would drop the unit to 34 m and promote Leeds to five sevenths, at the price of Sheffield’s two largest hills.

Manchester has no Geoffs, from one summit. Nothing in this paper can be said about Manchester, and that is a result, not an omission.

9. Bristol

Bristol also claims to be built on seven hills, and so, more insistently than anyone, does Edinburgh — which has run a race over its seven most years since 1980. Edinburgh needs no help from this paper: it holds eighteen Geoffs from 27 summits, so its tradition undercounts rather than overreaches, and a city with that many does not have to argue about which seven. Bristol is the harder case.

Bristol has no Geoffs, from three summits.

Sheffield’s seven was borrowed rather than counted — a companion piece asks where it was borrowed from, and finds no English town that reached seven by counting — and the counts that were attempted came back with five, or with eight. Bristol’s cannot be met at all — and not for the reason the summit count suggests.

Lower the bar and Bristol’s hills multiply like anywhere else’s. But the count never passes through seven. At 22 m Bristol has six; at 21 m three of its summits tie and it steps straight to nine. H_Bristol takes the value seven at no threshold whatever, which is Proposition 1’s failure condition happening to a real city: Bristol cannot adopt Axiom 1 even as a convention — at the resolution this sweep can see. Drops computed from a satellite model arrive in whole metres, and three of them landing on the same one says as much about the instrument as about Bristol; a finer survey would probably split them, and the count would pass through seven on its way down.

At Sheffield’s bar Bristol has no Geoffs. And 21 m, the bar where its count steps over seven, is one that gives Sheffield twenty-two.

On the count. The database stops listing below 30 m of drop, so it cannot say how many either city has at 21 m; those counts come from the satellite model instead, swept the same way for both. At one Geoff that sweep gives Sheffield seven, agreeing with the database exactly — and gives Bristol one, where the database gives none. That extra one is the surface model reading a roof; the figure above is the database’s, not the sweep’s. Those four counts are the only figures on this page not read from a file in the repository: that sweep’s output was never committed, so nothing re-checks them when the data moves, and they should be read as reported rather than as derived. Everything else here is computed from the committed sweeps at build time, and a test fails when the prose and the data part company.

10. Rome

Rome is the comparison we started with. The database stops at the English Channel, so Rome has to be computed, and it has now been computed twice. The first pass used a satellite radar model, and is what earlier revisions of this paper reported. The second used Rome’s own survey: Regione Lazio’s 1:5,000 mapping — five-metre contours and ground spot heights, thirteen sheets of it — triangulated to a ten-metre surface and swept by the same definition as everything above.

Both answers are five. Only two of the hills are the same.

Roma quinque Galfridos habet.

Of the five the radar found, two are where the survey puts them. Two are not there at all: the nearest summit of even 30 metres’ drop is 4.36 km from one and 8.49 km from the other, where the radar had reported 43 m. The fifth is a real hill that falls 36.4 metres and so is no longer one. In their place the survey finds three the radar missed. The count survived the change of instrument; the list did not, and that is the more useful fact about both.

Only one of the five carries a hill’s name at its summit — Monte Loreto, which falls 44.1 metres. The rest are known, if at all, by the suburbs on them: Colle Salario, Serpentara, San Vittorino, and a hill above Polline whose summit no map troubles to name, though it puts Monte Santa Caterina on the knoll below it. Rome’s real hills are anonymous, and its famous ones are not hills.

And none of the five is Monte Mario, the highest ground overlooking the old city: a ridge running north off the right bank of the Tiber, which falls 25.8 metres before the ground rises again, so it does not clear one Geoff. It was already excluded from the canonical seven for standing outside the ancient walls; it is excluded from the five as well, which leaves the one hill in Rome a visitor might be able to name on no list of Rome’s hills at all. The comune’s highest summit is not in the city: it is the one above Polline, in the detached northern piece, and it stands more than twice as tall.

On the instrument. The radar model sees rooftops and trees, and the survey sees the ground, which is why the lists differ; where they disagree the survey is believed. Britain’s figures come from a curated database of surveyed hills and Rome’s from a sweep of surveyed ground, so the two are not the same kind of measurement even now — but §4 sweeps Sheffield the same way the survey sweeps Rome, and gets the same seven hills in the same order as the database. The comparison is between instruments that have been checked against each other, which is the most that can be said for it.

11. Could Rome have had seven?

Rome’s boundary has moved more than Sheffield’s, and outwards at every step that could matter: the substantial losses — Pomezia’s farmland in 1938, Fiumicino’s coastal plain in 1992 — hold no summits to take. So the question has a direction: every historical Rome held no more high ground than today’s, and a smaller region holds fewer summits. Approximating each historical Rome by a circle of equal area about the Capitoline, and setting the modern comune beside them as it is, all at today’s 40 m:

No historical Rome had a Geoff at today’s bar. Ancient Rome — the Rome of the Seven Hills, the Rome the comparison invokes — has none. The canonical seven are spurs of one plateau divided by shallow valleys, and the most prominent of them, the Capitoline, falls 26.4 metres before the ground rises again: 13.6 metres short of being a hill at all. The nearest ground to the Capitoline that clears the bar is 8.5 kilometres away. Under the unit that exists because of them, they are not hills, and nothing near them is.

That is at today’s bar, and the bar moves. A Geoff is Sheffield’s seventh drop, and §12 sweeps a Sheffield that had a smaller one — the city as it stood before it took in the moors. That section refuses to put a single number on it, because neither of its instruments can separate that city’s seventh drop from its eighth. What they do fix is a range: 22.8 to 25.47 m. The argument here needs nothing better. Everywhere in that range two of the canonical seven clear the bar — the Capitoline and the Palatine — and the next canonical hill down, the Aventine, falls 21.4 m and clears no part of it. The only other thing inside the Aurelian Walls that clears it is Monte Testaccio, at 33.8 m, which is a heap of broken amphorae and not a hill at all — so the count inside the walls is three, and a third of it is rubbish. That is a lower bound rather than a total: the Rome sweep emitted summits from 25 m and its drops were corrected upward afterwards, so at a bar this low a summit could have been missed. It cannot cost the argument anything, which needs only that the canonical two clear the bar and the third does not. The count holds without the bar being pinned, which is the only form in which it can now be stated. The tradition was not describing nothing. It was describing hills that a bar set in another country has since risen past: Rome’s list was not broken by anything Rome did, but by a boundary review in South Yorkshire. Only one of the two cities got to move the bar afterwards.

And the ground itself has moved, though not all one way. Rome’s valleys hold metres of the city’s own debris. Albert Ammerman’s cores beside Sant’Omobono, reported in Antiquity in 2018, were taken from the base of a trench dug below the modern street. They recovered dark anthropic soil horizons between 3.2 and 6 m above the sea, with radiocarbon dates reaching the end of the Bronze Age. The earlier excavations there could not dig below the water table, which sits high in that valley. Ammerman is careful about what those horizons are, and this paper will be too: he calls their being in place an open question, and thinks it likely most of the material has moved down the slope. What is not in doubt is the depth, which is all this argument uses. Fill of that kind raises a col and shortens the hill above it. But of the three canonical hills that have a col of their own — the Capitoline, the Palatine and the Aventine — only the Aventine’s lies in a valley at all.

The other two sit where a ridge was taken away. The Capitoline’s col is at Piazza Venezia, on the saddle to the Quirinal that Trajan’s builders cut through; the column they left there carries an inscription usually read as saying it stands to show how high the ground had been, and it is about one Geoff tall. The Palatine’s col is the stump of the Velia, the ridge levelled in 1932 to drive the Via dei Fori Imperiali past it. Those two hills are more prominent now than they were, not less, and the tradition named them long before either cut was made.

What survives all of it is structural. Three of the seven have a col of their own, however since altered. The other four do not: their cols are saddles on the plateau the four of them share, and no reworking of the valleys, by Trajan or anyone after him, separates a spur from its own ridge. Rome made the same distinction and then ignored it: the Septimontium, the archaic festival whose name means seven mounts, counted two divisions of the Palatine and three of the Esquiline as separate hills — and Festus’s version of its list runs to eight, of which Platner and Ashby write that “one of these eight names must obviously be omitted”.

Rome’s seven are three hills and four spurs. Two millennia of digging changed their size. It has not changed their kind.⁵

The most prominent summit inside the ancient walls is not on the list either, and it is not natural. It is Monte Testaccio, which falls 33.8 metres, and which is a tip: a mound of broken amphorae stacked by the Romans themselves over about two hundred and fifty years, and the only summit inside the walls with more drop than the Capitoline. Sheffield has nothing of the kind. Parkwood Springs carries a tip, but it stops below that hill’s own summit; and the one Sheffield reading that is not ground, Backmoor’s (note 3), is a water tank rather than a hill. Rome’s was never anything but rubbish, and it out-drops the Capitoline.

And the modern comune is two hills short. Both of them are on the Baccano crater rim, in Campagnano di Roma, and both are within eighty metres of Rome’s own boundary: one of 100 metres, whose summit falls 3.4 metres the wrong side of the line, and one of 64.2 metres beside it. Annex a sliver of the crater rim eight hundred metres across and Rome has seven.

Rome is two hills short of seven, and they are next door. Two is a convention rather than a count.⁶

Sheffield, in §7, annexes to move the unit, which moves every city’s count including this one’s. Rome can only annex to move its own, because the unit is not Rome’s to touch — which is §3’s corollary seen from the other end, and the only kind of annexation available to anybody but Sheffield. It seems inappropriate to suggest it of another city, let alone the capital of another country. We will, however, note that Rome has previous form in this regard.

12. Orwell’s Sheffield

Sheffield’s present boundary was set in 1974, when the county borough took in Stocksbridge and the Wortley Rural District parishes of Bradfield and Ecclesfield. All but one of the hills the moors contribute arrived that year. Of the 16 summits the city holds today, ten were somebody else’s when the sentence at the top of this page was written — including the second, third, fourth and sixth Geoffs.

The old county borough needs no historical map. It is exactly the part of Sheffield that is unparished today, because the parishes are the parts that were added, and the ONS publishes both. Sweeping inside it, and setting aside the one summit whose ground was still Derbyshire in 1936:

And the first one out: Burbage Moor, 23.81 m. Those two decimals are the model’s and not the hill’s. On three of the seven the bare-earth survey finds ground below the point the radar calls the summit — by 5.15 to 9.57 m, worst at Norton Lees. On three it finds ground the radar missed, and at Wincobank Hill the two return the same height. Where both are looking at open ground the heights part by at most 2.1 m and the drops by 1.26, which is how one can tell the excess is roofs and trees rather than the model’s mood — and how little room a floor of 1 m leaves.

Run the same sweep on the Environment Agency’s bare-earth survey — the source note 3 sweeps the modern city on at 10 m and §4 reads single summits off at 1, here at 5 m because the 1936 city is a smaller window and a finer grid fits in it — and the table does not survive it. Beauchief, fifth on the surface model, is not on the survey’s list at all, and Manor Top becomes the first one out. Neither summit was ground: both stand on built hillsides where the radar returns roofs and garden trees rather than the slope beneath them. One rise the 30 m grid never resolved comes in, Banner Cross; the Norton ridge keeps its place with its summit moved 843 m along it, to Backmoor, which is the one relocation this paper can check against a third instrument, because §4’s LiDAR audit measures that summit directly. Burbage Moor was the radar’s own first one out and is promoted rather than discovered. Every change runs the way a surface-to-terrain correction predicts, and on the open ground above the two never part by more than 1.26 m of drop.

Nor does the answer. On the better instrument the seventh and eighth drops are 23.04 m at Banner Cross and 22.8 m at Manor Top: 0.24 m apart, on ground interpolated under buildings at both summits, where these two instruments differ by more than that on bare moor. It is not a gap. It is two readings of the same height.

1 Geoff, in 1936, does not exist⁷

Which is Proposition 1’s failure condition, arriving at home. §9 declines Bristol its seven because Bristol’s seventh and eighth drops cannot be told apart. Sheffield’s, in 1936, cannot either.

One hill in seven from the moors instead of five, and at today’s 1 Geoff the city of 1936 had three hills, not seven.

On the boundary. The line drawn above is the county borough’s as it stood in 1974, because that is the one there is data for: it is exactly the part of Sheffield that is unparished today. Reading it as 1936 rests on one thing, and the register of the borough’s boundary changes supplies it — between the day Orwell wrote and the review of 1967, Sheffield’s boundary moved by one acre. So the 1974 line minus the 1967 additions is not an estimate of the 1936 city; it is the 1936 city, give or take that acre.

Those 1967 additions took 2,079 acres out of Chesterfield Rural District — parts of Beighton, Eckington, Holmesfield and Killamarsh, Derbyshire until then. Frecheville was in Beighton parish and under Chesterfield RD, so the one summit inside the drawn line that is not Orwell’s is the Frecheville rise, 26.07 m, which would otherwise be the seventh. It is ringed on the map and left out of the table. Note too that the satellite sweep puts the Norton ridge’s summit at Norton Lees where the database in §4 puts it at Backmoor, 844 m east. The bare-earth survey settles that disagreement. On terrain the summit is at Backmoor, at the height §4’s own audit measures there to the decimetre. The database was right; the radar was reading the wood.

The rest was the city’s when he wrote, though some of it barely. Beauchief came with the extension that took Norton Lees, or with the abolition of Norton Rural District on 1 April 1934, and this paper cannot say which: Beauchief was split, part going to Sheffield in 1901 and the remainder in 1933, with the civil parish abolished the following April. Harston’s border series lists Beauchief among the additions of 1900; the register of parish abolitions puts it in 1934. Which transfer took the ground this summit stands on is not established here. High Neb, Parkwood Springs, Manor Top and Wincobank Hill sit inside the boundary Harston’s 1918 map describes, which already ran west to Stanage Edge and took in Concord Park, Manor Top and Abbeydale; Waverley was the borough’s before Orwell wrote, though which extension brought it is not established. So when the sentence was written down, six of Sheffield’s seven hills had been the city’s for a generation, and the seventh had been either thirty-five years or twenty-three months, depending on which transfer took it.

But look at what the seven were. Wincobank is on the traditional list, and Norton Lees is a stone’s throw from Norton, which is too. Manor Top, Beauchief and Waverley are the kind of ground the other names on it point at — ridges between the rivers, with houses on them. Take the moors away and Sheffield’s hills stop being places nobody lives and start being places people are from.

The tradition was not wrong about the terrain. It was right about a different city — and it is the 1974 boundary review, not the tradition, that made its list look mistaken.

On the boundary’s age. The 1934 additions took Dore, the oldest part of all this. The city’s line with Derbyshire once divided Mercia from Northumbria — the Limb Brook, the Sheaf, the Meers Brook — and both names describe it. Sheffield is the open ground at the Sheaf, whose name is sceāth, a boundary; Dore is dor, the gate through it. Ecgbert of Wessex took Northumbria’s submission there in 829, and the stone on the green says he became the first overlord of all England — at the gate, because that is what the place was. In 1934 the city annexed the doorway.

13. Conclusion

Sheffield has, and for as long as the sentence has existed has had, exactly seven hills^*.

Seven is fixed by definition and 40 metres is measured. Sheffield contributes one fact — that its seventh and eighth hills differ, and on the database’s figures by two metres — and the rest follows from it: the unit, the count, the standing of every city in England, and a justifiable case for annexing part of Barnsley.

The traditional hills come out of this better than they went in. Two of them clear every bar the city of the 1930s could have had: Wincobank, and the rise above Norton wherever the instruments put its summit. That is two more than a list picked for the view has any right to, though the other five clear none of them. And the survey that counts Sheffield’s hills by drawing its rivers puts the same places on the same rise as the one that counts by drops.

Rome has five Geoffs, and not one of them is a hill anyone has heard of. The seven it is famous for are not hills at this bar, though §11 finds two of them were at every bar §12 leaves open for the city that borrowed the phrase; the most prominent thing inside the walls is a heap of Roman rubbish.

Rome’s count has only ever fallen, because Sheffield’s boundary only ever grew: at least twenty-four hills when Orwell wrote, at least twenty-two after 1967, five since 1974. The first two are floors, because the sweep stops at 25 m and those bars sit around it.

And the number the comparison wants is the one that never happened. The unit went from the twenties to 40 in a single year — loosely on purpose, because §12 can no longer sharpen it — and Rome’s count fell from twenty-two to five without passing through seven. It did not need to be sharp: exactly seven needs a unit between 33.8 and 35.1 m, and no unit Sheffield has ever had comes within 4.9 m of it. Going back further only lowers the bar, and a lower bar gives Rome more hills, not fewer. At every boundary either city has actually had, the sentence is true of exactly one of them — and it is not the one with the famous hills.

Roma septem Galfridos numquam habuit.

* For as long as its seventh and eighth drops keep missing each other, which today they do by two surveyed metres and which nothing guarantees — and which, at the two earlier boundaries §12 can sweep, they do not do at all. The note on always below says what that costs.

Notes

Method and sources