On Christmas Eve 1872, the Ottoman Empire opened one hundred kilometres of single-track railway extending to Dobrljin, the northernmost point of the Empire in central Europe. Starting in Banja Luka, a fortress-town in Bosnia, the track was meant to be the penultimate leg of a great railway connecting Istanbul to Vienna. But Dobrljin is forgotten now.

The Ottomans laid railways to modernise their Empire and to connect their citizens and their neighbours. In the same year that the Dobrljin line was opened, German engineers, invited to Istanbul to build a new train station on land excavated from the eastern shore of the Bosphorus, opened the great Haydarpaşa terminal, like a Bavarian castle sitting at the head of the Asian stretch of the Berlin-Baghdad railway.

By then, however, the Ottoman Empire was already on the long decline that would see its defeat in the Balkan Wars and the Great War, the abdication of the Sultan and the final dismantling of the Empire into independent states. Only six years after opening the Dobrljin line, the Ottomans retreated from Bosnia and the Austrian Empire took their place. Austrian soldiers crossed over the border and headed through Banja Luka, pushing the limits of the Empire southwards. Almost overnight, this railway lost its symbolic meaning and became a poor branch line in a forgotten corner of the Austrian Empire.

For a while, the Austrians built new train stations on the railway, helping to smooth the slow march of modernity into northern Bosnia; but in the end, they left too. The grand railway stations along the Dobrljin line fell into disrepair. Postcards once depicted the iconic stations: tinted lithographs of ladies in carriages, pretty flower boxes hung from lampposts and along the station's windows. Today some of the old buildings have been turned into museums or municipal offices or replaced by square Yugoslav stations with concrete pillars; others still stand there, especially the smaller stations, lonely and cold, their white walls patched up with concrete but streaked brown by dampness. A far cry from the Dobrljin line that the Ottomans had dreamed of.

You can still take a train to Dobrljin: international trains from Zagreb stop there on their way to Sarajevo. So, I set out in search of this old Ottoman railway on a northbound train from Mostar, a southern town in Hercegovina famous for the Old Bridge over the river Neretva, built in 1566, destroyed by artillery fire in 1993 and rebuilt in 2004. Mostar is a most Ottoman of European towns: once a seat of Islamic learning, the city and its Old Bridge - an exemplar of sixteenth-century Islamic European architecture - are still eagerly visited by Turkish schoolchildren and tourists. Indeed, Bosnia can still feel like the outpost of the Ottoman Empire it once was, a reminder that the Sultan's writ ran here, deep into Europe, further north than Madrid, or Rome, or Marseille.

At Mostar's station they told me that I could go as far as Sarajevo, and no further. The northbound trains stopped running to Dobrljin a while ago. Nobody could tell me precisely when. In fact, the woman at the ticket desk said that trains did still head to Banja Luka and beyond, only not today or tomorrow. Soon. It was all to do with the bad weather and the flooding, the risk of landslides, the poor tracks and the new trains from abroad with the wrong gauge wheels. Another reason, people mutter, is the division of Bosnia between its two autonomous regions: the Banja Luka-Dobrljin line is in the Republika Srpska in the north, inhabited by Bosnian Serbs; the Mostar-Sarajevo line is in the Federation in the centre of the country, inhabited by Bosniaks and Croats. A railway divided: this was an un-Ottoman fate.

And so my journey from Mostar in search of the Dobrljin railway ended in Sarajevo. I boarded a train that evening in the crumbling Mostar station, among Roma and Mostaris who prefer not to drive. Heading out of town, the railway skirts the banks of the Neretva and cuts into the cliffside, running through tunnels and across viaducts in a long arc to the north. That evening, the waters of the Neretva, still and deep behind the dams near Jablanica, shone brightly in the twilight.

After Mostar, if the train stopped at all, a lonely warden held up a lantern, touched his red railwayman's cap and blew his whistle; nobody climbed on or off. It was a quiet, slow run-down train - a gift from Sweden, with the warning signs on the carriage windows still written in Swedish. The compartments in the carriages were quiet too: young people heading back to Sarajevo after a day by the river; farmers going to the market; grandparents on their way to see their families. A steward in a white short-sleeved shirt carried a tray with bottled water and beer - nobody bought anything.

Yet, for all the melancholy of the train, it was a remarkably informative trip. When in Bosnia, one often looks for signs of the last war: the pock-marked walls, the "Remember" signs, the retiring, keep-to-yourself glances at the ground. The houses have been rebuilt and the worst scars covered up, although the bright, white headstones in the new graveyards always catch the eye. Travelling by evening, however, it was too dark to see all that. The setting sun, and then the full moon cast gloomy shadows across the countryside. But their pale light also picked out the remains of an older Ottoman age, just beyond the carriage window: the rusty tap on an ablution fountain by a mosque; the brass star and the crescent moon on top of a minaret; the pewter džezva and thimble-like cups, full of thick Bosnian coffee, in a station café where old men played backgammon and smoked cigarettes under the dull station light.

Something of the enduring Ottoman influence on Bosnian culture might have gleamed through the darkness that night; but what of the strong bonds of Empire, crossing ethnic and religious divisions, that the Ottomans must have hoped this once-grand railway would have forged? Sitting in my quiet carriage, I looked across at the man on the seat next to me. He was dozing, with an unlit cigarette between his lips, his head leaning against the window. His dark hair had been shaved almost to the scalp, and he wore khaki trousers, a black jumper and well-polished, black boots. By his feet was a khaki rucksack. He looked like a soldier, or maybe someone from the state security, or perhaps he was just a tough with military airs. But it was the label on his rucksack that caught my eye: a flag with horizontal red, white and blue stripes (the flag of the Republika Srpska), angrily crossed out. No matter to him that the train stopped in Sarajevo - he would not be travelling to Dobrljin anytime soon.