while thus employed; according to another he borrowed books from his brother, an excise officer. He soon acquired sufficient knowledge to become an itinerant schoolmaster, staying two or three months at a time at a farmhouse, and teaching the children of the neighbourhood. In 1756 three young men went to read with him during the summer before they entered the university of Cambridge. One of these was Richard Sedgwick, afterwards vicar of Dent, and father of Professor Adam Sedgwick; another was John Haygarth, afterwards a physician at Leeds. Sedgwick always spoke of this summer spent in Garsdale as one of very great happiness and profit.
Soon after this Dawson went as assistant to Mr. Bracken, an eminent surgeon of Lancaster, where he obtained sufficient knowledge of surgery and medicine to enable him to set up for himself at Sedbergh, though without any regular license. As soon as he had saved 100l., he set out on foot, with his capital, to use his own words, ‘stitched in the lining of his waistcoat,’ and walked to Edinburgh. There, living with the sternest self-denial, he went through a course of medical instruction, and probably of mathematical reading also, until the exhaustion of his funds compelled him to trudge home again. But the medical knowledge obtained at Edinburgh stood him in good stead, and his practice increased so largely that before long he had saved about 300l. With this sum he went to London, partly on foot, partly in a wagon, and stayed long enough to obtain a diploma, and to make the personal acquaintance of several leading mathematicians. Having become a regular member of the medical profession, he returned to Sedbergh as a surgeon and general practitioner. Before long he had an extensive practice in the neighbouring dales, and occasionally was sent for to great distances beyond them.
Meanwhile, however, his favourite study of mathematics was not neglected. It was said that he could solve a problem better in the saddle than at a desk. He kept abreast of the mathematical knowledge of the day, took part in various controversies, but always with modesty and self-restraint, and gradually acquired so great a reputation as a teacher that pupils flocked to him from all parts of England. His charge for instruction was only five shillings per week, for which sum he would teach for as many hours as his pupils would work.
Through the connection of the grammar school at Sedbergh with St. John's College, Cambridge, Dawson's instruction was specially sought by Cambridge men, and between 1781 and 1794 he counted eight senior wranglers among his pupils. It is now impossible to identify all of these, but we may safely claim for him: John Bell [q. v.] of Trinity, the distinguished leader at the chancery bar (1786); John Palmer of St. John's, professor of Arabic on Sir T. Adams's foundation (1792); Thomas Harrison of Queens' (1793); George Butler [q. v.] of Sidney (1794). To this list four senior wranglers of later years may be added: John Hudson of Trinity (1797); Thomas Sowerby of Trinity (1798); James Inman of St. John's (1800); Henry Gipps of St. John's (1807); and a host of pupils who took less conspicuous degrees. Among these the Rev. Adam Sedgwick [q. v.] should be specially commemorated. He greatly admired Dawson, and has left the following account of his personal characteristics: ‘Simple in manners, cheerful and mirthful in temper, with a dress approaching that of the higher class of the venerable old quakers of the dales, without any stiffness or affectation of superiority, yet did he bear at first sight a very commanding presence, and it was impossible to glance at him for a moment without feeling that we were before one to whom God had given gifts above those of a common man. His powerful projecting forehead and well chiselled features told of much thought, and might have implied severity, had not a soft radiant benevolence played over his fine old face, which inspired his friends, of whatever age or rank, with confidence and love.’
Dawson published little, though he wrote several valuable papers on abstruse mathematical subjects, especially Newton's ‘Principia.’ He engaged in controversy with William Emerson on his Newtonian analysis, and with Dr. Matthew Stewart on the ‘Sun's Distance.’ On this subject he published anonymously in 1768 a pamphlet called ‘Four Propositions,’ pointing out a serious error in Stewart's calculations. He also attacked, in Hutton's ‘Miscellanea Mathematica,’ under the signature ‘Wadson,’ a principle advanced by the Rev. Charles Wildbore, ‘On the Velocity of Water issuing from a Vessel in Motion.’ But his reputation must not be measured by his writings. He was well known to the leading mathematicians of his time, and was visited at Sedbergh by Playfair, Lord Webb Seymour, and Lord Brougham.
Besides mathematics Dawson paid much attention to metaphysics and theology, as is shown by his correspondence with the Rev. Thomas Wilson, who had been his pupil in early life. The quotations in these letters prove that he had also at least a respectable knowledge of Latin and Greek, though he laments his inability to read the fathers in
