P.F. Burnett Adams was educated at King's College, London. He served in the Anglo-Boer War (1899-1902) with Colonel (later Lord) Baden-Powell, and was present at the siege of Mafikeng from October 1899 to May 1900. After the war he settled in Bloemfontein in the Orange River Colony (now the Free State), but in April 1902 applied to the new British administration of the Transvaal Colony for admission as a government surveyor. He was appointed surveyor-general of the Orange River Colony in August that year. In addition he became acting head of the Mines Department (and hence acting chief inspector of mines) in April 1903. In March 1904 he attended the Geodetic Congress in Cape Town in his official capacity to participate in planning the further geodetic survey of southern Africa. He became a member of the Legislative Council of the Orange River Colony, served on its Executive Council from 1903 to 1907, and on a committee that investigated the so-called poor white problem in the territory.
In his annual report for 1907 as acting chief inspector of mines, Adams commented on the widespread prospecting for oil in the colony and the lack of scientific information about the origin of oil and the strata in which it was most likely to be found. Reviewing the available evidence he concluded that indications of oil in South Africa were confined to the rocks of the Karoo Supergroup, and more specifically to the Stormberg Series, the Beaufort Group east of Heilbron, and the Ecca Group near Bloemfontein on the Modder River.
Adams was a member of the (British) Institution of Civil Engineers and of the (British) Institute of Mining and Mechanical Engineers. In 1904 he became a member of the management committee of the National Museum of the Orange River Colony in Bloemfontein. He was elected a member of the Philosophical Society of the Orange River Colony (1903-1914) in 1905 and contributed a note to its Transactions (Vol. 1, pp. 65-66) dealing with rock specimens presented to the museum by the Lieutenant-Governor of the colony, Sir J. Goold-Adams. By 1910 he was a member of the South African Association for the Advancement of Science. After the formation of the Union of South Africa in 1910 he was appointed Surveyor-General in the Orange Free State province. He remained in Bloemfontein until his death in 1915 and was survived by his wife, Julia Mary Adams (born Wyatt).