After studying ophthalmic medicine in England at the Royal College of Physicians and Oxford University (1928–29), he returned to Tasmania to set up his own practice.

In 1937, Hamilton and Dr W. D. Counsell presented a paper on hereditary eye disease and proposed remedies to the National Health and Medical Research Council, which was awarded the Royal London Ophthalmic Hospital's Gifford Edmunds prize.

He served in the Middle East as ophthalmic surgeon for the 2nd/7th Australian General Hospital, before returning to Australia and leaving the AIF on 1 November 1943.

Also in 1943, he re-issued a 1933 paper by Henrik Sjögren, with his own foreword, and his own study of conjunctivitis, The Significance of Heredity in Ophthalmology — A Tasmanian Survey (1951) earned him a doctorate from the University of Sydney.

[1] Hamilton, known for being a perfectionist and for having "a very real belief in himself and his abilities", died of hypertensive heart disease on 11 April 1968, aged 67 at Sandy Bay, Tasmania.