George H.H. Fincham matriculated through the University of the Cape of Good Hope in 1901. He then studied at the South African College, Cape Town, from 1902 to 1905. In 1904 he was awarded the degree Bachelor of Arts (BA) with Honours in physics by the University of the Cape of Good Hope, as well as the College's gold medal in science.
In 1905, at the suggestion of Professor J.C. Beattie*, he undertook an analysis of the magnetic observations made at the Royal Observatory, Cape of Good Hope, during 1842-1846 by a detachment of the Royal Artillery led by Lieutenant F.M. Eardley-Wilmot*. The purpose was to determine the effect of the sun-spot cycle on the variability of magnetic declination and magnetic field strength at the Cape, using the method of least squares.The results were written up in his masters thesis, The effect of the sun-spot frequency on the daily variation of the magnetic elements at the Cape of Good Hope, and he was awarded the degree Master of Arts (MA) in physics by the University that same year. The University also awarded him the Cornwall and York Prize for 1905 on the basis of his thesis.The next year he was selected by the College as the holder of the 1851 Exhibition Science Research Scholarship, but he was unable to fulfill the conditions of the award, as he left for England that year.
The results of his MA study were reported also in a paper that Fincham read in Cape Town on 18 August 1905 at the joint meeting of the British and South African Associations for the Advancement of Science. A summary was published as part of the Addresses and papers read at the joint meeting... (Vol. 1, pp. 49-51) under the title "On the nature of the effect of the sun-spot frequency on the variability of the magnetic elements at the Cape of Good Hope". The paper was read also before the South African Philosophical Society on 28 March 1906 (although he was not a member) and published in its Transactions (Vol. 16, pp. 301-312) as well as in the journal Terrestrial Magnetism and Atmospheric Electricity (1906). Fincham became a member of the British Association in 1905.
After returning to South Africa he settled at Imvani, a railway station some 25 km south-east of Queenstown, and became a member of the Royal Society of South Africa. He was still listed as a member, living at Imvani, in 1917, the year before his death.