Willem Hendrik Logeman was the son of Willem Sybrand Logeman, professor of modern languages at the South African College, Cape Town, and his wife Henriette Maria Weijenberg. The family emigrated to the Cape Colony from England in 1890 or 1892 and after two years in Stellenbosch settled in Cape Town. Willem junior attended the school of the South African College from 1896 and during that year, at the age of 14, worked as a volunteer assistant to the government electrician, Alexander P. Trotter*, at the newly established Government Electrical Laboratory. After matriculating in 1898 he continued his studies at the college and was awarded the Bachelor of Arts (BA) degree in mathematics and natural science with honours by the University of the Cape of Good Hope in 1901.
At the beginning of 1902 Logeman was appointed assistant in the Physics Department of the South African College under Professor J.C. Beattie*. The latter was conducting a study of atmospheric electricity, in cooperation with James Lyle* of Bloemfontein, and Logeman became responsible for the observations in Cape Town. In 1903, at the first annual meeting of the South African Association for the Advancement of Science in Cape Town, the three presented a "Preliminary note on some observations on atmospheric electricity in Cape Town and Bloemfontein" (Report, 1903, pp. 102-105), dealing with their study of the variable conductivity of the air by observing the tempo at which an electric charge leaked from an aluminium leaf electroscope. Logeman alone also contributed a paper on "Observations of atmospheric electricity at Cape Town" to the Transactions of the South African Philosophical Society (1903-1904, Vol. 14(2), pp. 129-131) on the same work. Also during 1903 he qualified as Master of Arts (MA) in Physics. Soon thereafter he read a paper on "Some modern applications of the gyrostat [or gyroscope] and the mono-railway" before the Philosophical Society of the Orange River Colony; an abstract was published in its Transactions (1903-1907, Vol. 1, p. 73).
Having been awarded the 1851 Exhibition Research Scholarship Logeman resigned from the Physics Department in 1904 in order to take up research studies in England, working under Sir J.J. Thomson at the Cavendish Laboratory for three years. The results of this work were published in "Note on the production of secondary rays by alpha rays from Polonium" in the Proceedings of the Royal Society of London in 1906. Back in Cape Town he returned to the Physics Department of the South African College in the latter half of 1908 as a lecturer, following the resignation of William J. Horne*. The next year he acted for Professor Beattie, who was on long leave for the whole year. In 1911, at the Bulawayo meeting of the South African Association for the Advancement of Science (of which he had been a member since 1903) he gave an evening lecture on the gyroscope. He resigned his post at the South African College in 1913 to succeed W.A.D. Rudge* as Professor of Physics at Grey University College (later the University of the Free State) in Bloemfontein, where he remained until his retirement in 1941. From 1905 to 1916 he was an examiner in physics for the University of the Cape of Good Hope. On 10 January 1917 he married Mary Isabella Gardyne Gordon, with whom he had two children.
Logeman was a clear and interesting lecturer and presented many lectures to general audiences outside the college. Though he inspired his students with his own interest in research, he was hampered by inadequate assistance, equipment, and laboratory space. He was particularly adept at designing scientific apparatus of various kinds and spent much time in a workshop making the necessary equipment for his department. For example, he reported "On a minor improvement in the multi-range potentiometer" in the Transactions of the Royal Society of South Africa (1924, Vol. 11, pp. 1-5), having been a member of this society from 1917 or earlier. He was a life member of the South African Association for the Advancement of Science and was president of Section A (which included physics) at the Boemfontein meeting in 1923. His presidential address dealt with "The structure of the atom" (South African Journal of Science, 1923, Vol. 20, pp. 28-38). For some years he represented the senate of Grey University College on its council. His hobbies were golf, motor-cycling and photography.