# How popular and used were logarithm tables?

I've heard that, for a time, logarithm tables "sold more than the Bible". Can someone produce some reliable documentation about how prevalent they were ? Would a common shopkeep have one ? Would a common merchant ship have one ?

(they would be used to make multiplications and divisions faster)

I am interested in information regarding any time period (though, as my wording suggests, the question was brought to my attention in the context of the 15th century)

• They were very useful for navigation. And not only plain logs, but logs of trig functions. Of course they were not available in the 15th century. Napier's work was in the early 17th century. Shopkeepers would not need such a thing. Jul 10, 2012 at 3:12
• My bad on the 15th century. How would ship captains use such tables ? What operations were they doing ? What kinds of scientist used them ? Apart from ship captains and scientists, who else would use them ? Jul 10, 2012 at 3:21
• All scientists who did calculations used them, for multiplication, division, exponentiation, work with trig functions. The earliest adopters were the astronomers. When I was a student, an elaborate book of tables was a necessity for situations where a slide rule was insufficiently accurate. A Bible was not needed. Describing nautical calculations is complicated. There were special "multiplicative" formulas, now largely forgotten, for solving plane and spherical triangles. It was only after accurate chronometers were devised that precision made sense. Jul 10, 2012 at 3:32
• I forgot surveying, an important application. Books on practical navigation, such as Pryde's 1867 Treatise on Navigation, included specially adapted log tables. Jul 10, 2012 at 3:43
• This seems to be a question about history, not mathematics. Are you aware that we have a history site? It's at history.stackexchange.com . Jul 10, 2012 at 3:48

I was in high-school in the US sixty years ago, and every trigonometry text had a log table in the back. These were not the seven-place tables that a navigator would use, but rather the much more basic four-place tables. But you simply needed a log table to solve triangles, and this was an important part of the one-semester trig course that typically would be taken in the third year of high-school.

Ship captains used logarithm tables for the same reason that astronomers and surveyors did: navigation required accurate calculation of the positions of the stars and other heavenly bodies, a calculation that without the use of tables would be quite expensive (timewise) in order to compute. Indeed, only once Kepler had seen the logarithmic tables of Napier was he inspired to compute his own logarithm tables and use them to formulate his famous Kepler's Equation. His subsequent use of the equation to tabulate the positions of various heavenly bodies (in the Rudophine Tables) would not have been possible without access to the logarithm tables for easy calculation. Calculations of the sort performed by Kepler were essential to any profession requiring accurate knowledge of the stars.

The use of logarithms in calculating ephemerides (tables charting the positions of heavenly bodies) was an invaluable tool even as late as the middle of the twentieth century (cf. the work of L.J. Comrie in encouraging their use), and indeed the slide rules upon which twentieth-century computers (the people, not the machines) relied so heavily were of course based on the same principle.

I used them in secondary school (high school) in Ireland in the 70's. Not everyone could afford calculators, but log books were provided at public exams. Slide rules were allowed. These books also had tables for trigonometric functions as well.

In engineering school, we used steam tables.

I still have log tables I 'borrowed' from my last exam.

Now I use tax tables (what's wrong with a formula?).

• What's a steam table? Jul 10, 2012 at 4:41
• @Daniel, something like this. Very useful when you're dealing with the manipulation of steam. Jul 10, 2012 at 4:51
• Tabulations of properties of water (steam, superheated) used in energy/power calculations. Jul 10, 2012 at 5:48
• Steam is still very relevant in power generation... Jul 10, 2012 at 5:51