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Bourne Eau rises in The Wellhead, otherwise known as St Peter's Pool, in the town of Bourne, Lincolnshire. The Wellhead is a natural artesian spring which once formed the source of the water defences of Bourne Castle as well as the power for the town's mills. On entering Bourne North Fen it follows an artificial course which it was given, probably, in the first half of the thirteenth century when the south Lincolnshire Fens were disafforested. Hitherto, it had flowed (latterly rather badly) in the channel known as the Old Ea which was of Roman date, most likely second century. The present course enters the River Glen at Tongue End, a name which derives from the low tongue of land within the enclosing banks of the rivers. In some countries, the river banks would be called levees.

Apart from the spring, most of the water of the river is collected by the Car Dyke, which, near Bourne, is arranged to act as a catchwater drain, gathering the surface water of the upland and feeding it via the Bourne Eau and River Glen to the sea, without its entering The Fens. Thus the need for pumping this water is avoided (but see Soak dike).

The use of the French-seeming Eau as the name of a Fenland river is not unique. It appears to have arisen in the eighteenth century. The earlier term was Ea, which arises from an Anglo-Danish word for river. Compare the Danish aa, nowadays written å. This Danish, one-letter word is pronounced as a French o but shortened by a glottal stop or as a curt English aw as a pure vowel rather than a diphthong. The eighteenth century engineers and map-makers seem to have been more familiar with French than with Danish.

The following is extracted from the Wikipedia article on Aachen. "The Romans named the hot sulphur springs there, Aquis-Granum. For the origin of the Granus several theories were developed, but it is now widely accepted that it derives from the Celtic god of water and health. And since Roman times, the hot springs have been channeled into baths (which are still in use). [The element] ‘’âh’’- is an Old German cognate with Latin ‘’aqua’’, both meaning "water". In French-speaking areas of the former Empire the word ‘’aquas’’ was turned into ‘’aix’’, hence Aix-en-Provence is an old Roman spa in Provence." Thus, the use of the French word for water, eau is not after all, so inappropriate.

A bourne is a stream flowing from a spring. Thus, although the town in which it rises is called Bourne and this apparently gives rise to the river's name, the Bourne Eau is clearly the bourne in question. Bourne is the southern English cognate of the burn of northern English. However, in later use, each has begun to lose its association with the spring, burn the more so.

• Aa River