He was born in London and arrived in Australia in 1894 during the Western Australian gold rush, returning to England following the end of his Senate term.

He spent two years travelling after leaving school, and in 1884 married Eleanor Money, the daughter of an English clergyman, in New Gisborne, Victoria.

[1] Matheson was elected to the Western Australian Legislative Council at an 1897 by-election, standing as an "advanced democrat" in North-East Province.

His election was contested by another candidate, Henry Saunders, who sought to have the result overturned on the grounds that Matheson had offered bribes to electors and to John Croft, the secretary of the Political Labor Party in Perth.

[1] Matheson's election platform included support for free trade, compulsory arbitration, old-age pensions, and universal white suffrage.

In the debate over the Commonwealth Franchise Bill in 1902, he moved an amendment that would have denied all Aboriginal people the right to vote in federal elections.

To me it is as repugnant and atrocious a legislative proposal as anyone could suggest.In 1903, Matheson came into renewed conflict with John Forrest, who had become the federal defence minister.

He asked 17 questions in parliament about Forrest's "Minute on Naval Defence", which had attracted attention in Britain,[4] and accused him of writing "in absurdly hyperbolic terms" in order to obtain an invitation to the 1902 Colonial Conference.