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In 1827 Charles Babbage published his Table of Logarithms of the Natural Numbers, from 1 to 108,000. His logarithms were generally considered to be the most accurate in his day and were reprinted on numerous occasions, well into the 20th century. This paper describes Babbage's motivation for producing the tables, and the measures taken to ensure their accuracy. An assessment is given of Babbage's contribution to the art of table making.