In 1914, the US Bureau of Mines estimated that oil would last for another ten years.
In 1939, the US Department of the Interior was a bit more optimistic: 13 years.
Quite consistently, the same Deparment stuck to its 13 years figure in 1951.
Prof. Frank Notestein (Princeton): "We've been running out of oil ever since I've been a boy"

Stanley Jevons (Britain): "It will appear that there is no reasonable prospect of any release from future want of the main agent of industry", and he gave a bleak outlook that the industrial revolution would soon come to a halt. We was writing about coal and the year was 1865.

A source of similar errors predicting a quick running out of resources in the past is:
Simon, Julian L.; Guenter Weinrauch & Stephen Moore, 1994. 'The Reserves of Extracted Resources: Historical Data' , Non-Renewable Resources 3: 325–34

Wolfgang