Hamilton never claimed to have invented the jet boat. He once said "I do not claim to have invented marine jet propulsion. The honour belongs to a gentleman named Archimedes, who lived some years ago". What he did was refine the design enough to produce the first useful modern jet boat.
In the 1950s Hamilton set out try to build a boat that could navigate the shallow fast flowing rivers where he lived. The rivers were too shallow for propeller driven boats to navigate as the propeller would hit the river bottom.
He investigated the American Hanley Hydro-Jet, a model which drew in water and fired it out through a steerable nozzle underneath the boat. Even when further adapted it did not work well. An employee suggested to have the nozzle just above the waterline.
When he took one of his early demonstration jet boats to the US, the media scoffed when he said he planned to take it up the Colorado River (U.S.), but in 1960 a Hamilton jet became the first boat to travel up through the Grand Canyon. The critics were silenced further when the boat also went down river through the canyon.
External links
Hamilton Jet boats biography on their founder (http://www.hamjet.co.nz/index.cfm/About_Us/Sir_William_Hamilton.html)
Hamilton worked through several examples, and eventually realised that the number that kept falling out of his calculations was Sewall Wright's coefficient of relationship.
Hamilton was a visiting professor at Harvard University and later spent nine months with the Royal Society's and the Royal Geographic Society's Xavantina-Cachimbo Expedition as a visiting professor at the University of São Paulo.
From 1978 Hamilton was Professor of Evolutionary Biology at the University of Michigan.