generate questions: The tide-predicting machine invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location.
When was the tide-predicting machine invented by Sir William Thomson invented? {sep_token} Who invented the first tide-predicting machine in 1872? {sep_token} What did Sir William Thomson's tide-predicting machine use to function?