Cotton explored on horseback, but modern adventurers can get by with public transport mixed with gentle hiking. All the wonders lie on the battered slab of limestone known as the White Peak. Over the centuries it has been crushed, excavated and trampled upon. From medieval packhorse routes to drystone walls, the traces of man are everywhere.
A vast cave, which the old people say
One Poole an out-law made his residence
The western edge of Buxton has long been residential, but these days the locals live in detached houses rather than caves. Derbyshire is riddled with holes. Huge caverns were created when water sought a path through faults in the limestone.
Poole's Cavern, the size of an aircraft hangar, is one of the most spectacular. The constant 7C temperature gave ancient Britons shelter and security. The cave is named for a 15th-century rogue; loot from his robberies is said to be somewhere inside, but no one has found it.
'So deep, and black, the very thought does make my brain turn giddy,' was Cotton's description of the cave. The Victorians installed gas lamps to illuminate its features, such as the 'frozen waterfall', a curtain of delicate stalactites.
The most spectacular formations, however, are due to past ecological outrages. Most people snigger at what the guide calls the 'poached egg chamber'. The cylindrical stalagmites look just like stone penises. There are further giggles when the guide says they are growing by one inch every 10 years. This strange phenomenon is caused by the lingering effects of the lime-burning that took place above the cave for 200 years. Ash was dumped in heaps on the hillside. When it rains, calcite-rich water seeps through to augment the phallic forest.
St Ann's Well, Buxton
Six hundred paces hence, and northward still
A crystal fountain springs in healing streams
Oh no, it doesn't. St Ann's Well is a sad little fountain. Tepid water trickles out of this stumpy monument in the middle of Buxton. The classiest thing about it is the billing: 'a well of living waters'.
The Romans came to Buxton for the water, and among the Elizabethans the supposed therapeutic powers of the minerals gave the town a second burst of popularity. The Pump Room has now been taken over by the tourist office, but you can still see the source once claimed to be 'most efficacious for gout, rheumatism, sciatica and lumbago'. (Compared with a brewery tour, say, it is dull and unrewarding.)
Half the people of England, it is claimed, live within 60 miles of Buxton. Most are probably glad they don't actually live there. Even the boundary of the Peak National Park makes an improbable bend to exclude Buxton; 1,000ft (328m) above sea level, it is a bleak and chilly town that seems to be falling apart. The Crescent, a semicircular sweep of shops, restaurants and assembly rooms, was the glorious centrepiece of Buxton for two centuries. It was intended to make Buxton the Bath of the North, but today the Crescent is boarded up and fenced off.
A few steps away, a one-eyed crustacean called Cyclops bounds across the field of vision. At 90 times normal size, this revolting creature and its monocular pals hop around alarmingly as visitors track them by microscope. Buxton Micrarium is an exhibition that stops mercifully short of being hands on. Visitors are given self- drive microscopes and can examine specimens from wasps to worms in all-too-great detail.
Two new wonders have emerged since Cotton's tour. Europe's largest unsupported dome, a span of slate with a diameter of 154ft (50m), tops the Devonshire Royal Hospital. Opposite is the Opera House, an implausibly grand Edwardian auditorium for a small Derbyshire town. It is the main venue for the Buxton International Festival, which begins on Wednesday.
North-east from hence three Peakish miles
Peakish miles are at least 50 per cent longer than regular ones. I lost another hour searching for the tidal well that gives the village its name. Cotton tells of a natural siphon that caused a well to ebb, flow and sometimes spout violently. He visited it 10 times without catching a performance: 'Whether this a Wonder be or no, 'Twill be one, Reader, if thou seest it flow.' By the end of the 18th century, the fickle porous limestone had swallowed up the unpredictable waters for good.
The village is pretty, though dishevelled after centuries of commerce. Narrow lanes burrow off into the banks of the valley in which Tideswell lies. Some end in 'rakes' - the shallow shafts dug into the hillsides by lead miners.
The miners have a footnote in history. Much renowned for their strength and resilience, they were regarded as ideal soldiers. It was a platoon of Tideswell men which caused George III to remark: 'I don't know what effect these men will have on the enemy, but good God they frighten me.'
Tideswell's present-day wonder is the church of St John the Baptist, better known as the Cathedral of the Peak. In the 14th century the local squire ploughed his profits from the wool trade into a spectacular church.
Hence two miles east does a fourth wonder lye,
Worthy the greatest curiosity
Eldon's Hole is the original bottomless pit, a terrible open wound on the southern slope of the Old Moor. This vast natural chasm is all the more strange because of the idyllic surroundings. From foreground to infinity, the scenery is splendid. The hillside is dressed in tiny golden and porcelain petals entwined with sombre twists of purple thistle. Sheep graze affably, a crow flickers listlessly across the afternoon sun, the emerald hills tumble away towards the horizon. And down there, somewhere, is the centre of the earth.
Unfortunately, a huge limestone quarry sits on the hilltop like a scab. The name Old Moor is appropriate: you need an almanac to find a way across it. Eventually you stumble upon a footpath across the plateau, leading to a lovely dale.
Cave Dale - an unPeakish mile long - offers the ideal walk for the unenthusiastic hiker. As Cotton writes, it 'falls with so easie a descent, as nere could trouble the most Southern Traveller'. Brusque moorlands soften gradually into a gentle valley, complete with babbling brook and the ruins of Peveril Castle towering overhead. The dale narrows dramatically, then expels hikers amid the cottages of Castleton.
A new strange thing, a village under ground
Peak Cavern, the operators boast, is the Only True Cave in Castleton; the other three - Blue John, Speedwell and Treak Cliff - are man-made wonders. When Cotton visited it, Peak Cavern also housed a complete village. Given the protection of the cave, cottages did not need to be particularly hardy. Peak Cavern is also a perfect natural workshop and, for a time, was a rope-making factory.
Today it is devoted to the tourist industry. The guides point out imaginary figures in the rock formations, such as Father Christmas next to Mary and Jesus (convincing) and the 'Peak Cavern Streaker' (a vivid imagination or a hallucinogen would help).
The cave intrudes one-third of a mile into the limestone plateau. A constriction just inside the entrance impeded early tourists, who had to lie flat on a raft and be pushed under an arch to reach the next gargantuan chamber. Victoria herself tried it as a princess; when she returned in 1842, she ordered a tunnel to be hewn through the rock.
Other thrills awaited the early tourists. For a consideration, the village choir would perch on a ledge high up in the cavern and perform a ghostly rendition of hymns. The surviving stalactites are pathetic stumps; previous visitors, including Byron, collected all the best ones. The Victorians also left graffiti engraved on the cave wall. Byron's signature is clearly visible. He would have chosen a much more flowery description of the cavern than Cotton's: 'The intestinum rectum of the Fiend'.
Enough of Hell] From hence you forward ride
Or walk, to the 1,695ft (556m) summit of Mam Tor. The name is derived from 'mammary', on account of its breast-like profile. The eastern slope has been gouged out into a huge shale precipice, a raw exposed face that crumbles after frost or rain.
A howling gale greets those who climb to the Bronze Age fort at the top. So does the finest panorama in the Peak, high ground giving way to the fair Edale Vale. This raft of green farmland divides the White Peak of the south from the Dark Peak of the north.
The sturdy village of Edale concludes the wonder tour. It also marks the start of the Pennine Way - the long-distance footpath which ends across the Scottish border 250 miles north. The southern terminus is the Old Nag's Head, a pub bristling with the owners of serious boots.
You can tick off the first six wonders at about one an hour. Derbyshire's greatest marvel is Chatsworth, way downstream.
So singularly rare, as does indeed amount to miracle
It is wise to get there early in the day: not before the crowds, for that is never possible, but before the stampede. You enter through a vast hall with inlaid marble floor, flanked by 18 or 20 hall chairs and a matching sofa below an ugly painting of two stout, naked children kissing, watched by an old crone.
The public is shepherded through the Great Hall, with heads tipped back to view the painted ceiling yards above them. The tourists perch cine-cameras on their shoulders and shoot away. People seem impressed without exactly liking what they see. It is undoubtedly large and old and splendid; perhaps that's all it takes. It is also, in most rooms, too dimly lit to see properly, the pictures hung too high for detail, the furniture too far away to be able to observe the craftsmanship.
Chatsworth retainers stand in corners, their faces masks of silent boredom, ready to interpose their bodies between any object and a visitor unwise enough to want a closer look. Consequently, the overwhelming impression is of size, swags and buckles and bows; gilt and velvet, loops and scrolls, carved, painted, chiselled and then dusted and polished by generations of housemaids; an overwhelming abundance of pattern and ornament.
The main treasures do not disappoint. The crowd cranes towards the famous trompe-l'oeil violin (a safe six yards away on the other side of the restraining rope) and people gasp. It's a good joke that can still astonish people two centuries later.
But mostly the visitors are made uncomfortably aware of their own ignorance and poverty by comparison with this flamboyant and shameless wealth. On payment of pounds 4.25 they have the right to gawp at these bloated and otherwise useless rooms.
Chatsworth has some surprises left. In a corner of the west staircase, a bleak Lucian Freud portrait shows the present duke's mother seated in a dark chair wearing a black dress, while behind her on a bed lies one of the artist's anguished skeletal nudes. In the dining-room, a visitor says, 'Doris: I've seen something I want at last]' and points to the wine glasses, four to each place setting. I prefer the handsome Regency chairs; but I would not need 36.
If you love the style of Chatsworth, you will love the Cavendish (0246 582311). This hotel is owned by the Duke and Duchess of Devonshire and furnished with Chatsworth cast-offs. But before the cost ( pounds 89 for a double room without breakfast) drives you to a B & B, it must be said that prices on the menu can be halved by eating in the conservatory ('The Garden Room') rather than the dining-room; - and the bedroom views are incomparable.
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