Atwood was a very popular lecturer at Cambridge, giving many demonstrations in his lectures. He published details of his lecture course with descriptions of his demonstrations in 1776 :-
He demonstrated elementary mechanics and hydrostatics with pulleys, pendulums, and air-pumps, as well as electricity, magnetism, and optics, including Leonhard Euler's principles of achromatic lenses. He also taught astronomy, mentioning recent surveys of the earth's density by the mathematician Charles Hutton and the astronomer royal Nevil Maskelyne, plus Maskelyne's favoured lunar method for longitude.William Pitt, British prime minister (1783-1801, 1804-06), was one of the many students who attended Atwood's popular lectures and later, when Pitt had achieved high office, he employed Atwood in the Treasury. However this was still some way into the future when Atwood gave up his position as tutor at Cambridge in 1779 and tried unsuccessfully to obtain a position with the board of longitude. As part of his bid to obtain a position as secretary with the board he sent the details of his Cambridge courses to Sir Joseph Banks, president of the Royal Society. In the summer of 1781 Atwood sent the Royal Society details of his applications of geometry to the problems of correcting sightings through sextant mirrors. This work was, as he pointed out to Banks, in line with his belief in the application of mathematical techniques to problems in the physical science.
In 1779 Hutton had became foreign secretary of the Royal Society but was forced to resign in 1783 by Sir Joseph Banks, the president of the Society. It was an unfortunate affair which led to considerable controversy in the Society which is discussed in detail . Banks claimed that Hutton had failed to carry out his duties efficiently, but many in the Society supported Hutton and felt that it was in fact Banks who had failed to manage the affairs of the Society competently. Atwood supported Hutton, as did Maseres, Maskelyne, Landen, Glenie, Hornsby and others, accusing Banks of using excessive authority and of being "despotic". They threatened to secede from the Royal Society. In fact there was another element to the argument which reflected the rapid increase in the use of mathematics in physical sciences. Atwood, and the others in the mathematicians' mutiny, strongly supported this as we noted above.
In 1784 Pitt arranged that Atwood be given £500 a year and an office in the Treasury. His task was:-
... to devote a large portion of his time to financial calculation.Atwood is best known for a work A Treatise on the Rectilinear Motion and Rotation of Bodies (published by Cambridge University Press in 1784) which is a textbook on Newtonian mechanics describing impact and simple harmonic motion. It also describes in detail a machine, now known as Atwood's machine, to demonstrate the laws of uniformly accelerated motion due to gravity. The machine had been constructed by George Adams, a London instrument maker, to Atwood's specification and the first description of it appeared in French in 1780. Alessandro Volta had requested the machine, and copies had also been sent to Spain, but Atwood was pressed to publish a description. This is given in his 1784 publication. He also published a second work in the same year Analysis of a Course of Lectures on the Principles of Natural Philosophy which was an expanded version of his Cambridge course which he had first given detail of in 1776.
Atwood also published on equations for the use of Hadley's quadrant. He extended theories of Euler and Bouguer on the stability of ships. He was awarded the Copley Medal of the Royal Society in 1798 for this work. He also wrote on the construction of arches (1801) and on the design of a new iron London Bridge over the Thames at Blackfriars.
Atwood was a renowned amateur chess-player and among other opponents played games against the famous French player Philidor, who was regarded as the unofficial world champion. H E Bird records :-
Of the players who encountered Philidor, Sir Abraham Janssens, who died in 1775, seems to have been the best, Mr. George Atwood, a mathematician, one of Pitt's secretaries came next, he was of a class which we should call third or two grades of odds below Philidor, a high standard of excellence to which but few amateurs attain.One of most interesting features of Atwood as a chess player is that he recorded and preserved some of his games, an unusual practice at that time. These rcords have survived, among them the last games that Philidor played which were against Atwood at Parsloe's Club in London on 20 June 1795.
Atwood was highly involved with mathematical calculations which were needed by governments to run the country effectively. For example :-
... during violent wartime struggles over corn prices in 1800-01 he compiled a vast survey of the assize of bread, the system of price regulation in force since the thirteenth century, including trials of the grain quantity in standard loaves, and of data on bakers' profits, designed to support the Tory government's new policy on price regulation. It was said that this intense work and calculation had broken Atwood's health.Atwood's brother Thomas had succeeded his father as curate at St Margaret's, Westminster, and he still held that position at St Margaret's when Atwood was buried there.
Article by: J J O'Connor and E F Robertson