Mathematical Treasure: Babbage’s Tables of Logarithms

Frank J. Swetz (The Pennsylvania State University)

Title page of Charles Babbage's table of logarithms, 1872 edition.

Charles Babbage (1791-1871) was a British mathematician, philosopher, mechanical engineer, and inventor. As Professor of Mathematics at Cambridge University, he was approached by the British Admiralty to produce an accurate table of logarithms. The early nineteenth century was the period when “Britannia ruled the waves” and the British navy maintained the nation’s far-reaching empire. Maritime navigation required accurate logarithmic tables. Babbage undertook this task and published his tables in 1827. The images shown are from the 1872 edition of the tables which passed through several editions including German and Hungarian translations. Babbage’s experiences in constructing his table convinced him that such numerical tables could be better produced by mechanical means and he began work on a “Difference Engine,” a mechanical computer, to accomplish this chore.

Preface, Charles Babbage's table of logarithms.

In his Preface, Charles Babbage described his work in constructing his table of logarithms.

Preface continued, Charles Babbage's table of logarithms.

In the continuation of the Preface, we learn of the available resources Babbage employed. He also listed twelve properties necessary for the construction of a “good” Table of Logarithms.

Instructions for the technique of interpolation, Charles Babbage's table of logarithms.

Instructions for the use of the Tables are provided in the opening pages. Here instructions are given on the techniques of interpolation.

For more information about Charles Babbage, visit the Charles Babbage Institute, Center for the History of Information Technology, University of Minnesota Libraries.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.