Three massive double cantilevers join across 2.5km: 54,000 tonnes of steel held together by 6.5 million rivets, the final one gold-plated and hammered home by Edward, Prince of Wales. At the peak of construction, 4000 men were working on the bridge, and 98 lost their lives - but they were doing something that had never been done before, and doing it so well that, more than a century later, the bridge is still the main railway crossing of the firth.
The coming of the railway (thanks to James Watt perfecting the steam engine) required not just new bridges: Scotland's lumpy landscape needed some straightening too, and one of the grandest results is the Glenfinnan Viaduct near Loch Shiel, in the west.
Harry Potter fans will recognise it instantly, especially when The Jacobite tourist train is puffing across its graceful curve, steam billowing from the black-and-brass engine pulling maroon carriages filled, in the Potter movies, with young witches and wizards off for a new year at Hogwarts. Standing 30m above the valley floor, the viaduct was finished in 1901 and earned contractor Robert McAlpine - still a familiar name in construction - the moniker "concrete Bob". It was the biggest project ever made of concrete, and although its 21 arches are unreinforced, it's still safe, and beautiful, more than a century later.
While rail inspired some engineering icons, it was the death knell for the canal system: until then transport was all about barges stuttering along the waterways. How clever then of Hugh Baird to devise the Union Canal, using aqueducts and tunnels so that it followed the same contour for 50km from the heart of Edinburgh to Falkirk. And what a shame that only 20 years after this "mathematical river" was finished in 1822, it became redundant.
But all was not lost: in 2002 Scottish inspiration and engineering resurrected it, thanks to the astonishing Falkirk Wheel which uses the power of eight boiling kettles to lift 600 tonnes of barge and water 35m straight up, connecting the Union Canal with the Forth and Clyde Canal. It's all about cogwheels and counter-balance, Archimedes and wrist action: its 15,000 bolts were all hand-tightened. A fantastic sight, the Wheel ensures that today's boaties can be on their way in just 15 minutes, instead of the half day it used to take to go through 11 locks.
The canal leads to Glasgow, where the river lends its name to a cast-iron guarantee of engineering quality: from the Industrial Revolution till around 1960, "Clydebuilt" was the benchmark of excellence.
If it was big and made of steel, Glasgow would build it for you, and a trip "doon the watter" goes past the sorry remains of dozens of once-noisy shipyards. A couple still remain constructing car ferries and merchant navy ships, but the glory days - when John Brown's Shipyard alone produced the Lusitania, HMS Hood, and the first three Cunard ocean liner Queens - are well over; however, four of the huge Titan cranes remain with one of them restored as a heritage attraction. Looming high over the river, it could lift 200 tonnes into the great ships that were launched here.
One of the best-known is now moored at Leith, near Edinburgh. The Royal Yacht Britannia was decommissioned in 1997 after 44 years' service during which she travelled more than 1.5 million kilometres.
"Britannia is the one place where I can truly relax," said the Queen, which explains her sad face in the photo taken at the end of an era that started with the first royal yacht in 1660.
A tour of the ship's five decks - from the drawing room with its fireplace and baby grand piano to the engine-room's gleaming copper and chrome - is a glimpse into royal foibles.
It has the only non-historic royal bedrooms open to public view, including the Queen's single bed with sheets recycled from Victoria's time, and the guest cabin's double bed that's shrouded in ill-fortune (each of the four honeymoons celebrated there ended in divorce).
But there's more to discover that's fascinating and amusing: apparently shouting was forbidden; the crew communicated with hand-signals and were obliged to freeze like statues if a royal personage hove into view; and it took three hours to set the 56 places for a state banquet with porcelain, crystal and silver - which didn't include fish knives.
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Getting there: Cathay Pacific offers a daily one-stop service from Auckland to London, with convenient connections and special fares to Edinburgh and Glasgow.
Where to stay:
In Edinburgh: The Scotsman Hotel - the Forth Rail Bridge and Leith are short drives away.
At Glenfinnan: Glenfinnan House - the viaduct is within walking distance.
In Glasgow: The Malmaison Hotel - take a trip down the river with Clyde Cruises and up the Titan.
Falkirk is midway between Edinburgh and Glasgow.
Further information: See cometoscotland.co.nz.
Pamela Wade travelled to Scotland as a guest of VisitBritain and flew courtesy of Cathay Pacific. Read Wade's blog here.
