'Head School' of the town. A gentleman named Shafto employed Hutton in the evenings as tutor to his family, and lent him some advanced mathematical works. To Shafto Hutton dedicated his first book, 'The Schoolmaster's Guide,' 1764. At the same date Hutton made his first contribution to the 'Ladies' Diary,' of which he was editor from 1773 to 1818. Hutton's reputation as a mathematical teacher grew rapidly; among his pupils were John Scott, afterwards Lord-chancellor Eldon, and Elizabeth , subsequently the lord chancellor's . Hutton also worked as a surveyor, and was in 1770 employed by the mayor and corporation of Newcastle to draw up an accurate map of the city and its suburbs.
In 1773 the professorship of mathematics at the Royal Academy, Woolwich, became vacant, and the government decided that the new appointment should be made by open competition. Hutton offered himself as a candidate, and was elected after an examination of several days' duration. On 16 June 1774, Hutton was admitted fellow of the Royal Society, and afterwards contributed many important papers to the 'Philosophical Transactions.' His papers in 1776-8, on the 4 Force of Exploded Gunpowder and the Velocities of Balls, ' gained the Copley medal. After Maskelyne had completed his series of observations at Mount Schiehallion, Perthshire, to measure the attraction of the mass by the deflection of the plumb-line, Hutton was chosen to deduce the corresponding estimate of the mean density of the globe (viz. 4-481). He drew up his report to the Royal Society in 1778 (Phil. Trans, vol. xlviii. pt. xi. p. 33), and recommended a repetition of Maskelyne's experiment, advice which was adopted. Laplace (Connaissance des Temps, 1823) admitted the value of Hutton's work in computing the density of the earth. In 1779 Hutton was appointed foreign secretary of the society, and held the office till after Sir Joseph Banks became president, when Hutton resigned. The degree of LL.D. was conferred upon him in the same year by the university of Edinburgh. Hutton planned for himself a house on Shooter's Hill, and soon afterwards the Academy was removed from the arsenal to that part of Woolwich Common. Hutton designed and built a number of houses on the common, and thus took 'the first important step' towards making the suburb a favourite place of residence. Hutton resigned his professorship in 1807, after thirty-four years' service, and retired to Bedford Row, London. A pension was granted him, and the board of ordnance complimented him on the success of his work as a professor. Just before his death he drew up a paper, in reply to a series of scientific, questions addressed to him by the London Bridge committee, with regard to the proper curve which should be adopted for the arches of the new design.
Hutton died on 27 Jan. 1823, and was buried in the family vault at Charlton, Kent. Hutton was twice married.and a son (see . The second daughter married Henry Vignoles, captain of the 43rd regiment, and with her died of yellow fever in June 1794 at Guadeloupe, where were prisoners of war (Gent. Mag. 1794, In 1822 several of his friends, including Lord-chancellor Eldon, his former pupil, obtained his permission to have a marble bust of him executed by Sebastian Gahagan. Since his death the bust has stood in the library of the Philosophical Society of Newcastle, to whom he bequeathed it. Some medals by Wyon were struck, with a portrait copied from the bust.
Personally Hutton was distinguished by the simplicity of his habits and equability of temper. His skill and patience as an instructor were generally acknowledged. The assistance he gave to Dr. Olinthus Gregory [q.v.] illustrates his generous temperament. All the books written by Hutton were of a professional and practical character, and are invariably clear and accurate. They are: 1. 'The Schoolmaster's Guide, or a Complete System of Practical Arithmetic,' Newcastle, 1764; 2nd edit., 1766. 2. ' Mensuration,' Newcastle, 1767, by subscription, in fifty numbers, dedicated to the Duke of Newcastle, with diagrams by Thomas Bewick [q.v.], whose first essay it was at book illustration; an abridgment called 'The Compendious Measurer,' appeared in 1787. 3. 'Principles of Bridges, containing the Mathematical Demonstration of the laws of Arches,' Newcastle, 1772, on the occasion of Newcastle Bridge being injured by a flood. 4. 'The 'Diarian Miscellany … extracted from the "Ladies' Diary," 1704-1773,' London, 1775. 5. 'Tables of the Products and Powers of Numbers,' London, 1781. 6. 'Mathematical Tables, containing common Hyperbolic and Logistic Logarithms,' London, 1785, with an introduction, still valued as an interesting and learned history of logarithmic work. Hutton 'deprecates the theory of Napier's originality as the inventor of logarithms. His essay suggested the plan of the great work on logarithms which was afterwards compiled by Hutton's friend, Baron Maseres. 7. 'Elements of Conic Sections,' 1787. 8. 'Mathematical and Philosophical Dictionary,' 1795,