**J A Third**'s father was John D Third (born in Aberdeen in 1837) who was a stonemason. His mother was Ann Sinclair (born in Tyrie, Aberdeenshire about 1840). He was the oldest of his parents' children having younger siblings: James, Alexander, Henry Third, Helen and Andrew.

J A Third was educated at Robert Gordon's College and he graduated with Honours in Philosophy and Mathematics from the University of Aberdeen in 1885. In his student days he was one of the editors of *Alma Mater*, the Aberdeen University student magazine.

He was then appointed as an assistant in mathematics at Aberdeen University and later he became a lecturer at Aberdeen Training College. After studying at Jena, Germany, he took a D.Sc. at Aberdeen in 1889. Before that, in 1890, he had been appointed as Rector of Campbeltown Grammar School, Argyllshire, then five years later as Headmaster of Spier's School, Beith, Ayrshire where he taught English in addition to his administrative duties. S C 'Simmie' Jamieson of Beith was born on 18 September 1905. In an interview on 5 January 1994 he spoke about Spier's School at the time that Third was headmaster:-

Third joined the Edinburgh Mathematical Society in January 1897. He was an enthusiastic member publishing papers in theI was fortunate to win a bursary to go to Spier's School. The teachers all wore mortar boards and gowns. There was an air of authority and tradition about the place. In my day the school took in boarders as well as the majority of day pupils from the Garnock Valley. The school became very well known and respected because of the academic success of the pupils. It was a highly regarded school in Scotland. Morning prayers were held first thing every morning and you had to be there for them. The teachers were, I believe, far greater disciplinarians than you find in the schools now. Everything seemed to be much tighter and firmer and under very much more control than now. ... The headmaster at Spiers was Doctor Third. He was a well-known academic. He knew how to handle a school very well indeed. He was there throughout my time.

*Proceedings*such as the 30 page paper

*Systems of circles analogous to Tucker circles*(1898). He read papers to the Society such as

*Systems of Spheres connected with the Tetrahedron*to the meeting on 9 June 1899,

*Triangles Triply in Perspective*to the meeting on 14 December 1900, and

*Generalisation of the 'Orthopole' and Allied Theorems*on 14 March 1914. He served as president of the Society 1902-03. Third also published papers and posed questions in other publications. For example he posed a beautiful, and rather surprising, question in the

*Mathematical Gazette*in 1900:-

At the annual meeting of the British Mathematical Association, held on 20 January 1900, Third presented the paperThrough a given point in the plane of a triangle to draw three lines terminated by the sides of the triangle, two and two, such that their extremities shall lie on a circle.

*Triangles triply in perspective*. In the Mathematical Questions and Solutions section of the

*Educational Times*of 1902 he published

*The perpendicular from the isogonal conjugate of any point on the Euler line of a triangle to the trilinear polar of the point passes through the orthocentre*.

The Edinburgh Mathematical Society was not the only British mathematical society that Third joined for, on 9 May 1901, he paid the life-composition fee of the London Mathematical Society and became a member for life.

Third married Elizabeth Lamb Ramage. They had a son, John Third, who was awarded an Honours M.A. from Aberdeen in 1914, then later worked for ICI. They also had a daughter Edith Ramage Stewart Third who married Alexander Turnbull, a carpet manufacturer, in Glasgow Cathedral on 15 September 1926.

Third was Chairman of the Educational Institute branch in Kintyre and Ayrshire and in this capacity served on many committees. In 1919 he was President-elect of the Educational Institute but resigned the position on being appointed Director of Education. He was Director of Education for Ayrshire from 1919 until he retired in 1927. After retiring, Third moved to Edinburgh where he spent the final 20 years of his life. After his death the Dr J A Third prize was set up in the University of Aberdeen. It is awarded annually to the best student of mathematics.

**Article by:** *J J O'Connor* and *E F Robertson*