I can't find more information, I just get a short piece from BBC as following:
In 1839, a Charles White was transported for stealing this tape measure. Charles was 22 years old when he was tried on 26 June, 1837, at the Oxford Court of Sessions. He sailed on the 'Portsea' on 24 July 1838 from Plymouth, bound for New South Wales. He arrived in NSW on 18 December 1838 after a voyage of 140 days. The surgeon on that ship was Thomas Bell. The first fleet of penal convicts left Britain for Australia in 1788, and the arrival at Port Jackson on 26 January 1788 is celebrated as Australia Day and the founding of Sydney. Transportation officially ended in 1868.
The official record says that he was transported for housebreaking and stealing a pair of shoes.