The idea came from the economist Johann Heinrich Gottlob von Justi, who in 1758 recommended that the Danish crown develop the Jutland heath. King Frederik V of Denmark-Norway made the invitation and made it generous: farmland with livestock and equipment, money to start with, twenty years free of tax, and exemption from military service. For families in Hesse and the Palatinate - and some from Austria - living in territories worn down by war, that was a serious offer.

They came in waves from 1759. Craftsmen, mostly. Many had trades rather than farming experience, and very few of them were farmers, and none of them had farmed anything remotely like a Jutland heath. Nobody in Copenhagen appears to have considered this a problem worth solving before the ships sailed.

Alheden lies in the southernmost part of Fjends and the northernmost part of Lysgård, covering the ground where Frederiks, Grønhøj, Havredal and Karup stand today. The soil was thin, acidic, and matted with heather roots. Working it required first burning the heather off, then fighting the sand underneath.

The crown's promises proved hard to fulfil, and the discontent was considerable. Drought came. Livestock sickened. Around 88 colonist families were settled on Alheden in the villages of Grønhøj and Havredal, and the colony began shedding people almost immediately. An official assessment in 1763 judged many families unsuitable, and what followed was a mix of expulsion and departure - some families were sent away, some went home to Germany, and some accepted a second recruitment offer and left for Russia. Fewer than sixty families remained. By 1768 there were 49 households on Alheden, 241 people in all, out of the 965 who had come.

The potato is the reason the survivors survived. Once the heather was burned off, the sandy ground turned out to suit potatoes rather well, and the Germans knew how to grow and eat them. Their Danish neighbours, at the time, largely did not - the potato was regarded as something between a curiosity and a weed.

So the name was a description before it was anything else: those Germans, the ones who grow the potatoes. It hardened into a label, then into an identity, and eventually into something the descendants claim for themselves. It is worth noticing which way the joke ran in the end. The crop the neighbours dismissed became a staple of the Danish table, and the families who had been laughed at for eating it had simply been right first.

What is striking is how long the colony stayed itself. The state built Frederiks Church in 1766, set between the settlements of Frederikshøj - now Grønhøj - and Frederikshede, now Havredal, to serve the German community. Sermons there were preached in German until 1870. The colony schools taught exclusively in German until 1845.

That is more than a hundred years of holding a language in a country that did not speak it, in villages a day's ride from anywhere. Part of it was pride, part of it was isolation, and part of it was the plain fact that a community which had been treated as outsiders had little incentive to hurry into assimilation. They kept their own church, their own school, and their own churchyard, and passed the heath farms down inside the colony.

The clearest surviving trace is in the phone book. Agricola, Betzer, Bitsch, Bräuner, Bärthel, Cramer, Dickes, Dürr, Frank, Gantzhorn, Harritz, Herbel-Schmidt, Hermann, Herold, Jung, Keller, Krath, Kriegbaum, Lajer, Lauth, Marcher, Marquard, Maul, Morratz, Philbert, Rost, Schönheider, Wacher, Wendel, Winkler, Woller, Würtz. Rare across Denmark as a whole; unremarkable around Alheden.

The colony is commemorated in three modest places. A memorial stone raised in 1959 in Frederiks churchyard, southwest of Viborg, carries thirty of the family names. A sculpture by Ole Herold called Kartoffelpigen - the Potato Girl - was unveiled in 1984. And at Grønhøj there is a small museum housed in the last surviving original colonist barn: a low building of the kind 965 hopeful people were handed in place of the farms they had been promised.