Robert Alfred Lehfeldt, physicist and economist, was the youngest son of Dr Francis William Albert Lehfeldt, at one time professor of physics at East London College, London, and his wife Maria Jane. He was educated at St John's College, Cambridge, where he was awarded the degree Bachelor of Arts (BA) in 1890. Proceeding to Sheffield he became demonstrator of physics at Firth College (later the University of Sheffield), and joined the British Association for the Advancement of Science in 1892. In 1896 he was appointed professor of physics at East London College, remaining there for ten years. During this time he was awarded the degree Doctor of Science (DSc) by the University of London and served on the council of the Physical Society. Among his publications were A textbook of physical chemistry (London, 1899, 308p); A textbook of physics (London, 1902, 304p; 2nd ed. 1910); Electro-chemistry. Part 1. General theory (London, 1904, 268p, with later editions to 1920); ten papers on various topics in physics; and several works on economics.
In 1906 Lehfeldt was appointed professor of natural philosophy and physics at the Transvaal University College, Johannesburg. This institution was renamed the South African School of Mines and Technology in 1910 and became the University of the Witwatersrand in 1922. Lehfeldt became a member of the South African Association for the Advancement of Science, serving as a member of its council from 1907 to at least 1913, and as honorary general treasurer for 1909/10. In 1908 he was the convener of the association's Committee for the Standardising of Weights and Measures. He read several papers at annual meetings of the association, though the first two were not published in full: "Acceleration of gravity at Johannesburg" (1907); "Note on a gas-voltameter for exact use" (1907); "The treatment of electrodynamics" (1908), in which he explained how the subject should be taught; "On the measurement of the period of a pendulum" (1912); "The South African national debt" (1912); and "Thermal conductivity of quartzite" (1916). In 1920 he served as president of Section F of the association, delivering his presidential address on "Labour conditions in South Africa", and a paper on "Agricultural economics - cost of production of maize". He was elected a Fellow of the Royal Society of South Africa in 1908 and published a paper on "Gravity in South Africa" in its Transactions (1910-1912, Vol. 2, pp. 83-126). From 1906 to 1916 he was an examiner in physics for the University of the Cape of Good Hope.
Lehfeldt was a brilliant mathematician and statistician and what interested him particularly was the application of mathematical models to economic and sociological problems. For example, in 1913 he read a paper on "The disturbance of economic equilibrium" at the fifth international congress of mathematicians, held in Cambridge. In 1917 he switched from professor of physics to professor of economics - the first in South Africa - and head of both the Department of Economics and Economic History and the Department of Statistics at the South African School of Mines and Technology. At this time World War I (1914-1918) was in progress, leading him to write a booklet on Economics in the light of war (Johannesburg, 1916, 56p). The next year he became a member of the newly founded Statistical Council of South Africa. In 1918 he wrote up his investigation into agricultural productivity in "The economics of agricultural production in South Africa", published as the first in the Industrial Bulletin Series. This was followed by a statistical study, The national resources of South Africa (Johannesburg, 1922, 79p), which contained the first estimation of the country's national income and represented the first attempt at a comprehensive analysis of the country's economic activities. Other publications by him included Gold, prices, and the Witwatersrand (London, 1919, 130p); Restoration of the world's currencies (London 1923, 146p); a textbook on Money (Oxford, 1926); Controlling the output of gold (London, 1926, 31p); and a textbook entitled Descriptive economics (London, 1927).
Lehfeldt was an early member of the South African Geographical Society, established in 1917, and for some time served as vice-president of the Economic Society of South Africa. When the South African School of Mines and Technology became the University of the Witwatersrand in 1922 he was elected as a senate representative on its first council. His wide interests included the arts and for years he was a music and drama critic for several South African newspapers. In 1915 he married Violet Douglas Renwick, but they had no children. He died under unexplained circumstances from an electric shock in his bathroom.