William Waterston is recorded in the 1861 England census, age 24, born in Blantyre, Lanark, Scotland; single; occupation carpenter crew on board the vessel Impregnable. The census place is Anglesey, Cornwall.
The UK List of Military Deserters (1812 - 1927) shows :
William Waterston Age: 25 Birth Year: Abt 1843 Birth Place: Blantyre, Lanarkshire
Desertion Date: 31 March 1868 Desertion Place: Chatham Publication Date: 14 April 1868
Regimental Number: 8822 Military Corps: Royal Engineers
William Watterson (sic) subsequently appears in the 1871 Scotland Census age 29, born Blantyre, Lanarkshire, occupation joiner, boarder in the Bryden household at at 26 Annfield St, High Church, Glasgow.
There is also an immigration record for a William Waterston, age 40, departing Glasgow on the vessel Bolivia for New York, arriving there on 21 September 1880.
If you think, this is your William Waterston, send me a PM and I'll forward those documents to you.
Cheers,
Rodeo