Rapson was born at Leicester, the son of the Rev. Edward Rapson, later vicar of West Bradley, Somerset, where Rapson spent much of his childhood. He attended the Hereford Cathedral School and then St John's College, Cambridge, where he was elected a classical foundation scholar in 1883. He won the Brotherton Sanskrit Prize in 1884 and the La Bas Prize in 1886.
Academic career
In 1887 Rapson was appointed assistant in the Department of Coins and Medals at the British Museum, and also elected a fellow of St. John's College. From 1903 he was Professor of Sanskrit at University College, London. In 1906 he left the British Museum and was appointed Professor of Sanskrit at St. John's. His application included eighteen testimonials. Following his successful appointment he remained there until his retirement in 1936 when he was succeeded by H.W. Bailey. His connection with the British Museum continued throughout his career and he assisted in the preparation of the Aurel Stein Collection.
''The Cambridge History of India''
Rapson edited the first volume of The Cambridge History of India, "Ancient India", where his expertise in coins was put to good use. The Times noted in their review of the volume that coin evidence provided some of the only sources for the earliest rulers mentioned, there being in many cases no surviving written sources. Rapson spent time on secondment from the College at the Department of Coins and Medals of the British Museum, where he was Assistant Keeper of Coins and Medals and was reckoned to have an uncanny ability to be able to identify ancient coins merely by feel. He was known for his scrupulous attention to detail and for checking not only his own references carefully, but the references of every other contributor. He also invariably agreed to help fellow scholars with their work. These factors, possibly combined with increasing age, meant that Volume II of the History, for which he was the editor, was incomplete at the time of his death in 1937. He had confided to colleagues that the slow pace of the work meant that large parts of it needed to be updated to include the latest scholarship. For all these reasons, and possibly the upcoming war too, it remained unpublished.
Other scholarly work
Rapson also deciphered and then edited various documents that his friend the archaeologist Aurel Stein had discovered in his 1900 expedition to Chinese Turkestan.
Rapson married Ellen Daisy Allen, the daughter of William Allen, of "The House", West Bradley, Somerset, in 1902. Rapson had spent much of his childhood in the village. Ellen died in 1921.
in Buhler's Encyclopedia of Indo-Aryan Research, Vol. II, Part 3, B. 1897.
"The Græco-Indian Kings Strato I Soter and Strato II Philopator" in Journal of the Royal Asiatic Society, Vol. 37, 1905, No.1, pp. 164–7.
"Coins of the Graeco-India Sovereigns. Agathocleia, Strato I Soter, and Strato II Philopater" in ' Henry Frowde, Oxford University Press, 1906, pp. 245–258.