Gunter was a friend of Briggs, and would spend much time with him at Gresham College discussing mathematical topics. When the professor of astronomy at Gresham College resigned in 1620 Gunter was appointed to fill the vacancy, largely on the recommendation of Briggs. Gunter published seven figure tables of logarithms of sines and tangents in 1620 in Canon Triangulorum, or Table of Artificial Sines and Tangents (see  for details). The words cosine and cotangent are due to him.
He made a mechanical device, Gunter's scale, to multiply numbers based on the logs using a single scale and a pair of dividers. It was called the gunter by seamen and was an important step in the development of the slide rule. Gunter published his description in 1624 in Description and Use of the Sector, the Crosse-staffe and other Instruments. It is worth noting that in this work Gunter uses the contractions sin for sine and tan for tangent in his drawing of his scale although not in the text of the book.
He also invented Gunter's chain which was 22 yards long with 100 links. It was used for surveying and the unit of area called an acre is ten square chains. Gunter also did important work on navigation, publishing New Projection of the Sphere in 1623. He also studied magnetic declination and was the first to observe the secular variation. Higton writes in :-
In 1622 Gunter's investigations at Limehouse, Deptford, of the magnetic variation of the compass needle produced results differing from William Borough's, obtained more than forty years earlier. He assumed an error in Borough's measurements, but this was in fact the first observation of temporal change in magnetic variation, a contribution acknowledged by his successor, Henry Gellibrand, who discovered the phenomenon.His fascination with mathematical instruments went right back to his days at school and his main mathematical contributions are rightly seen to be in this area. His contributions are summed up in  as follows:-
Gunter was a firm advocate of the use of instruments in mathematics for easing the work of various mathematical practitioners, notably surveyors and navigators. His instruments were designed with these aims in mind. In particular his work on logarithms, their applications to trigonometry, and their inclusion on instruments greatly simplified the processes of mathematical calculation. His books were popular for many years after his death: an edition of all his works was produced by Samuel Foster in 1636 and this had three more editions, the last in 1680 ...
Article by: J J O'Connor and E F Robertson
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