His father was John Frazer, minister of the Associate Church at Auchtermuchty, in Fife, Scotland; his mother was Margaret Erskine. He became minister of the Associate Church at Saltcoats in Ayrshire, in 1796, but within months inherited an estate through his mother, at Lassodie, Beath, in the Fife coalfield. The inheritance required that he changed his name to Dewar: it originated with his great-grandfather Ralph Erskine and his first wife Margaret Dewar. At this point Dewar left the ministry.
Dewar began a new life as an army surgeon, with the 30th Regiment of Foot. In Egypt under Ralph Abercromby, he underwent some formative experiences, writing later on dysentery and ophthalmia. He also came under the influence of French physicians (Savaresi, Larrey, and Desgenettes).
Dewar graduated M.D. at Edinburgh in 1804, with a dissertation De ophthalmia Aegypti. He was a Manchester Infirmary staff physician, from 1804 to 1808, a common step for Edinburgh medical graduates because of the breadth of professional experience there. He became a member of the Manchester Literary and Philosophical Society in 1806. He then returned to Edinburgh, becoming a member of the Royal College of Physicians there and lecturer at the Medical Institution. He may have dropped medical practice, and become a writer. He was elected a Fellow of the Royal Society of Edinburgh in 1816.
Dewar engaged in an embittered controversy with Thomas Trotter on the chemistry of choke damp and fire damp. Trotter had proposed "oxygenated muriatic gas" (i.e. hydrochloric acid) as a fumigant. As far as chemistry went, both their theories were inaccurate. Dewar was a friend of the Newcastle physician John Clark, and Trotter's criticism of Clark has been given as one possible reason for the personal attacks included with the scientific and practical arguments Dewar gave. A scale or chemical slide rule mentioned by Thomas Charles Hope as "Dr. Dewar's" has been considered to be unpublished work of Henry Dewar.
An inquiry into the principles by which the importance of foreign commerce ought to be estimated (1808) was an economic pamphlet. It was taken to be a comment on the Continental System, and a reply to William Spence. Spence's Britain Independent of Commerce (1807) had come under heavy criticism. Dewar was somewhat sympathetic to Spence's positive views of autarky.
Dewar wrote an early paper on what was then called "double consciousness", now diagnostically identified with dissociative identity disorder. It is considered that Dewar was alluding to the celebrated case of Mary Reynolds of Pennsylvania, which was published in 1816 by Mitchill. He wrote in 1817 on a smallpox outbreak at Cupar, giving statistics showing the effectiveness of vaccination.
Dewar wrote a Treatise on Universal Grammar (1816), and on other topics, for the Edinburgh Encyclopædia. He began a translation, Universal Geography, of work by Conrad Malte-Brun. He wrote also for the Encyclopædia Britannica, and the Transactions of the Royal Society of Edinburgh.
- Erskine Beveridge, A Bibliography of Works relating to Dunfermline and the West of Fife (1901), p. 60 note 3; archive.org.
- Sir Walter Scott (1824). The Edinburgh annual register. J. Ballantyne and Co. p. 320. Retrieved 1 May 2012.
- George Robertson (1820). Topographical description of Ayrshire; more particularly of Cunninghame. p. 157. Retrieved 2 May 2012.
- Scottish Mining, Lassodie History.
- Edward Mansfield Brockbank, Sketches of the Lives and Work of the Honorary Medical Staff of the Manchester Infirmary, from its foundation in 1752 to 1830 when it became the Royal Infirmary (1904), pp. 214–5; archive.org.
- Observations on diarrhoea and dysentery, particularly as these diseases appeared in the British campaign of Egypt in 1801 (London, 1805)
- Catherine Kelly, Medicine and the Egyptian Campaign: The Development of the Military Medical Officer during the Napoleonic Wars c. 1798–1801; PDF, p. 334.
- Henry Dewar; George Husband Baird (1804). Dissertatio medica inauguralis de ophthalmia Aegypti: quam annuente summo numine ... D. Georgii Baird S.S.T.P. academiae Edinburgenae praefecti ... pro gradu doctoris ... Excudebat Gulielmus Creech Academiae Typographus. Retrieved 2 May 2012.
- Donald Stephen Lowell Cardwell (1974). Artisan to Graduate: Essays to Commemorate the Foundation in 1824 of the Manchester Mechanics' Institution, Now in 1974 the University of Manchester Institute of Science and Technology. Manchester University Press ND. pp. 51–. ISBN 978-0-7190-1272-3. Retrieved 2 May 2012.
- Complete list of the members & officers of the Manchester Literary and Philosophical Society, from its institution on 28 February 1781, to 28 April 1896 (1896), p. 22; archive.org.
- "Membership Directory / Aslib Computer Group". Archive.org. Retrieved 7 April 2013.
- A letter to Thomas Trotter, M.D : occasioned by his proposal for destroying the fire and choak damps of coal mines
- A Proposal for Destroying the Fire and Choak-Damps of Coal Mines…Addressed to the Agents and Owners of Coal Works (Newcastle: J. Mitchell, 1805); and his "second address".
- Durham Mining Museum, Robert L. Galloway, A History of Coal Mining in Great Britain, Ch. XIV.
- Brian Vale; Griffith Edwards (20 January 2011). Physician to the Fleet: The Life and Times of Thomas Trotter, 1760–1832. Boydell & Brewer. pp. 180–3. ISBN 978-1-84383-604-9. Retrieved 2 May 2012.
- Letters, Chemical Slide Rules, Bull. Hist. Chem. 13–14 (1992–93);PDF, p. 75.
- Thomas Thomson; Richard Phillips; Edward William Brayley (1813). The Annals of philosophy. Baldwin, Cradock, and Joy. p. 462. Retrieved 2 May 2012.
- "Spence, William". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900.
- James Hogg; Peter Garside (1824). The Private Memoirs and Confessions of a Justified Sinner: Written by Himself, With a Detail of Curious Traditionary Facts and Other Evidence by the Editor. Edinburgh University Press. pp. 54–. ISBN 978-0-7486-6315-6. Retrieved 2 May 2012.
- Patricia B. Sutker; Henry E. Adams (2001). Comprehensive Handbook of Psychopathology. Gulf Professional Publishing. p. 264 note. ISBN 978-0-306-46490-4. Retrieved 2 May 2012.
- Ch. Ch Steinbrenner (1846). Traité sur la vaccine ou Recherches historiques et critiques sur les résultats obtenus par les vaccinations et revaccinations ... (in French). Labé. p. 56. Retrieved 2 May 2012.
- Literary and Philosophical Society of Manchester (1819). Memoirs of the Literary and Philosophical Society of Manchester. The Society. p. vi. Retrieved 2 May 2012.
- Transactions of the Royal Society of Edinburgh – Google Books. Books.google.co.uk. Retrieved 7 April 2013.
- Sir Walter Scott (1811). The Edinburgh annual register. John Ballantyne and Co. p. 323. Retrieved 2 May 2012.
- "Scottish Record Society. [Publications]". Archive.org. Retrieved 7 April 2013.
- Ebenezer Erskine Scott, The Erskine-Halcro genealogy: the ancestors and descendants of Henry Erskine ... his wife, Margaret Halcro of Orkney, and their sons (1895), pp. 41–2; archive.org.
- "History of Texas, together with a biographical history of Milam, Williamson, Bastrop, Travis, Lee and Burleson counties : containing a concise history of the state, with portraits and biographies of prominent citizens of the above named counties, and personal histories of many of the early settlers and leading families, Page: 814 | The Portal to Texas History". Texashistory.unt.edu. 3 April 2013. Retrieved 7 April 2013.