WHERE better to test a "theory of navigation" than on a river some 25 miles from the sea? And who better to test it than the village schoolmaster?

So William Emerson launched some kind of vessel, bearing himself and a number of his pupils, into the Tees at Hurworth, on the Durham bank of the river near Darlington. Their voyage was short for, as an old account puts it, "the whole crew soon got swampt". Of the readers of his treatise, which was published despite the watery setback, Emerson remarked ruefully: "They must not do as I do, but as I say."

But this advice didn't typify the man. Or the mathematician. For it was as a wizard in that taxing branch of learning that Emerson, born in Hurworth in 1701, rose to eminence. The 1910 edition of Encyclopaedia Britannica - and perhaps others - noted: "He never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model."

Thus, Emerson's home was littered with what a contemporary report described as "all kinds of mechanical instruments, together or disjointed". His wife, niece of Hurworth's rector, spun all the household's linen by an elaborate spinning wheel of Emerson's own design - so novel that he incorporated a drawing of it in his book Mechanics, or the Doctrine of Motion. Published in 1769, it was one of more than a score of works by Emerson. In his General Biographical Dictionary of 1814, A Chalmers hailed them as "all good treatises, although the style and manner of some is rough and unpolished".

But it is as an eccentric that Emerson has endured in Hurworth history. He wore his shirt back to front, displaying much of it since his coat - his only coat - was never fully buttoned. His flaxen wig was much plainer than most. And his cap - his only cap - protected ever less of it, since he repeatedly shortened the cap's side flaps as they became worn.

Though Emerson often led a horse carrying provisions he would never ride one. Or get in a carriage. He walked to London with his manuscripts.

When fishing in the Tees, he invariably stood up to his waist in water, which he insisted was good for his gout. Chalmers says: "He used to study incessantly for some time, and then for relaxation take a ramble to any pot ale-house where he could get anybody to drink with and talk to."

AT present, a Newcastle University student, Stephen Erskine, is researching Emerson's life with the aim of producing a biography of him. The attention once paid to Emerson makes it surprising than none has appeared so far. The Dictionary of National Biography used to feature him, and as late as 1966 he appeared in a book entitled The Mathematical Practioners of Hanoverian England. Author G E R Taylor remarked: "He was widely known and his books highly esteemed."

All sources agree that Emerson received his grounding in maths from his father, who preceded him as village schoolmaster. Though sent away to schools at Newcastle and York, he also learned languages from a curate who lodged at his boyhood home.

Chalmers says: "His manners and appearance were that of a rude and rather boorish countryman. He was of very plain conversation, commonly mixing oaths in his sentences. He could discourse sensibly on any subject, but was always positive i.e. dogmatic and impatient of any contradiction."

Published in 1748, it was a mathematical study entitled The Doctrine of Fluxions that brought Emerson to academic notice. No shrinking violet, Emerson later said of its publication: "I stepped forth like a giant in all his might." But maths' scholars agree that Emerson was not an originator. His reputation came from his amazing grasp of mathematical knowledge and practice up to that point, and his skill in communicating it.

Once, a party of distinguished mathematicians turned up at Emerson's door to seek advice on some knotty problem.

"Is the great Mr Emerson within?" one of the worthies asked the dishevelled figure who answered the door. "Great or little, I am the man," replied Emerson. He thought so little of their query that he bawled it up, for a solution, to a workman on the roof. Whether the answer came from there or not, Emerson chalked the vital formula on the brim of a hat.

Emerson was offered membership of the Royal Society. Declining, he complained: "It's a damned hard thing that a man should burn so many farthing candles as I have and then have to pay so much a year for the honour of FRS after his name." He huffed again: "When a man becomes eminent he has to pay quarterly for it. This is the way ingenuity is rewarded in England."

As a teacher, Emerson lacked patience and soon gave it up. In Hurworth folklore, his navigation experiment ranks with his action when the rector, Dr John Johnson, failed to pay a promised dowry of £500 on Emerson's marriage to his niece. Emerson sent his wife's trousseau round to the rector on a barrow, with the message that he would "scorn to be beholden to such a fellow for a single rag".

Other Hurworthians prized Emerson for such skills as clock mending and harpsichord tuning. With a keen ear for music and wide knowledge of its theory, he made a violin with a double first string, said to be more melodious than the conventional instrument. He also added half tones to a spinnet, though the result, intended to bring tuning to a new pitch of perfection, did not please him.

"It was a foolish thing to be vexed with," he remarked.

Fascinated by time, Emerson set up several sundials around the village. At least two, one adorning a house on The Green, the other on the Bay Horse Inn, still survive.

Emerson died in 1782. In 1909, a number of stained glass windows honouring him were inserted at the Emerson Arms, near the Bay Horse. Recording the year of his birth, the one window that remains also bears an anagram of his name, Merones, that he adopted as a pen-name for magazine articles - some of which appeared in The Ladies' Diary. Another pseudonym was the longest in history: Philofluentimechanalgegeomastrolongo. Yes, that's right. Probably it was another anagram. Can anyone unravel it?

Perhaps it was also in 1909 that Emerson's present table-top tombstone was erected in Hurworth churchyard. A barely-decipherable inscription at its base reveals that the stone's epitaph was copied from Emerson's original headstone. Taken from Ecclesiastes and written in Hebrew, it nevertheless seems very Emersonian:

"Then said I in my heart, as it happeneth to the fool, so it happeneth even to me."

Death claims all. If Stephen Erskine can tell us more of this intriguing but now little-known luminary, he will put us all in his debt.