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 1807, and was promoted first lieutenant on 14 July the same year. In March 1809 he sailed for Lisbon, and joined the army under Sir Arthur Wellesley at Abrantes in May. He was present at the battle of Talavera, and on the enemy abandoning their position in front of Talavera he reconnoitred the river Alberche. He succeeded in reaching Escalona by the left bank, but on attempting to return to the army by the right bank in order to complete the reconnaissance, he was surprised by the enemy, who captured his attendant with his horse and baggage. He accompanied the army in the retreat from Talavera to Badajos, and was subsequently employed in the construction of the lines of Lisbon. He returned to England on 20 June 1810 in consequence of ill-health.

He was employed under his father on the ordnance survey, and was for some years in charge of the drawing department at the Tower of London. He was promoted second captain on 21 July 1813. In 1817 he was directed to assist Jean Baptiste Biot, who was sent to England as the commissioner of the Bureau des Longitudes of Paris to take pendulum observations at certain places along the great arc, and he accompanied Biot to Leith Fort, near Edinburgh, to Aberdeen, and to Unst in the Shetland islands. At Unst Mudge fell ill, and had to return to London. In 1818 he was engaged in superintending the survey of Lincolnshire.

In 1819 he went to Dunkirk in connection with the survey, and in 1821 to various places on the north coast of France. He first appears upon the list of Fellows of the Royal Society in 1823. He was promoted first captain on 23 March 1825, and regimental lieutenant-colonel on 10 Jan. 1837, remaining permanently on the ordnance survey. On the death of his uncle, Richard Rosedew of Beechwood, Devonshire, in 1837, he succeeded to the property.

About 1830 the question of the boundary between Maine and New Brunswick came prominently to the front. The United States claimed certain highlands running from the heads of the Connecticut river to within twenty miles of the St. Lawrence, which, if allowed, would have cut off the direct routes from Quebec to New Brunswick, and would have given the United States positions commanding Quebec itself. Great Britain objected that the claims were incompatible with the terms of the treaty of 1783. The question was referred to the arbitration of the king of the Netherlands, but the United States declined to abide by the compromise he proposed, and the subject assumed a more serious attitude. The British government in 1838, desiring to bring the matter to a settlement, appointed Mudge and Mr. Featherstonehaugh, who was well acquainted with America, commissioners to examine the physical character of the territory in dispute and report on the claims of the United States. In the spring of 1839 the commissioners prepared their expedition, and reached New York in July. They then went to Frederickton in New Brunswick, from whence, on 24 Aug., they commenced the journey which was the object of the expedition. The survey was completed, and the party reached Quebec on 21 Oct. From Quebec Mudge went to Niagara, and thence to New York, where he met the remainder of the expedition, and returned with them to England at the end of the year. In 1840 the commissioners carefully examined the whole history of the boundary question, and reported that the line claimed by the United States was inconsistent with the physical geography of the country and the terms of the treaty, but that they had discovered a line of highlands south of that claimed, which was in accordance with the language of the treaty. The report was laid before parliament, and the result was a compromise based on the report and settled by the treaty of Washington in 1842. Mudge retired from the army on full pay on 7 Sept. 1850, and resided at Beechwood. He died at Teignmouth, Devonshire, on 24 Sept. 1854, and was buried at Denbury.

Mudge married, on 1 Sept. 1817, Alice Watson, daughter of J. W. Hull, esq., of co. Down, Ireland, and left two daughters, Jane Rosedew, who married the Rev. William Charles Raffles Flint, and died in 1883, and Sophia Elizabeth, who married the Rev. John Richard Bogue. His portrait, painted in 1807 by James Northcote, R.A., is in the possession of his daughter, Mrs. Bogue.

Mudge wrote ‘Observations on Railways, with reference to Utility, Profit, and the Obvious Necessity of a National System,’ 8vo, London, 1837.

 MUDGE, THOMAS (1717–1794), horologist, second son of Dr. Zachariah Mudge [q. v.], was born at Exeter in September 1717. Soon after his birth his father became master of the grammar school at Bideford, and there Thomas received his early education. The mechanism of watches, however, interested him much more than his school studies, and in 1731, when he was only fourteen, his father bound him apprentice to George Graham [q. v.], the successor of