Log tables (or formally Mathematical Tables) were used for hundreds years in many areas of science and engineering to perform complex mathematical calculations. In early high school around 1970, students were expected to own a 4-figure book of tables and we were taught how to perform basic calculations. I recall that the tricky part was using the differences columns and keeping track of the decimal point.

Around 1968 I obtained a copy of the Castle-Macmillan book of 5-figure tables. I couldn't use the book in school lessons, but it was quite thilling to own the book and look at the dense pages and ponder over the extra pages of advanced functions that I wasn't familar with at the time.

In 1986 I purchased a modern copy of the legendary Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables by Abramowitz and Stegun (which looks like a log table book sent back in time from some advanced civilisation). It's a bit sad that the tables in the book are now redundant due to the rise of computer algebra systems like Matlab and Mathematica, but everything else is timeless and a great reference. The whole book is available as a PDF (47MB).

Around 2014 I accidentally discovered that seven figure tables had been published since the 1940s, but I was never previously aware of their existence. I quickly found a copy available from a bookshop in Adelaide and ordered it for about $15 plus postage. It's a dense and impressive small hard-cover book, with about 200 pages devoted to tables of logarithms. If you look at the table of contents (click thumbnails below) you will see some tables that seem quaint and strange by modern standards. It's clear now that I never knew about these sorts of tables because they were only in the hands of specialists in science, engineering and navigation.

I might have been one of the last generations of students to use log tables. By 1970, electronic calculators had made books of tables completely obsolete for professional use, and a few years later the price of calculators had dropped so much that students and the general public could easily afford them. I obtained my first calculator (a Sharp PC-1802) in 1974. See the Calculators page for a more detailed history. The slide rule became obsolete around the same time.

In Early 2023 I wondered how difficult it would be to reproduce some of the pages from the log tables books. I started with the 1969 edition of Frank Castle's' Five Figure Logarithmic and Other Tables, mainly because it's my sentimental favourite in the group. I felt compelled to tackle the most difficult pages first: pages 2 and 3 that contain the classic logarithms with mean differences. Page 2 is particularly tricky because the leading 10 rows have two difference rows, breaking the simple pattern seen in all other tables.

Below are some attempts to reproduce selected pages using values generated by a C# program with tables rendered using basic HTML and CSS. The tables with RED TITLES are unfinished. The finished reproductions are quite close, but not perfect of course due to differences in fonts and small peculiarities from the ink printing process.

I was quite relieved to discover that the numeric characters 0 to 9 in the modern Georgia font are rendered by Windows and the Edge and Chrome web browsers with an appearance that is nearly identical to the digits in the printed pages. You can see that the descenders of the 3 4 5 7 9 characters are the key to the matching appearance. The books do not state which typeface they used, but the lucky match with Georgia avoided the need for deeper research and the use of unusual fonts. Hopefully, the following line will display in your web browser as a correct example:

0 1 2 3 4 5 6 7 8 9

It's surprising and worrying that the calculated values do not match exactly. The discrepencies only appear randomly scattered through the last digits of the Logarithm Mean Differences before row 20. The mismatching calculated table values are always one higher than the book value. The very first difference value is an example: the book value is 42, but the calculated value is 43. I have checked that the calculated values are correctly rounded, so I'm unsure if (1) The 1909 calculations failed to round-up (2) I'm calculating the differences incorrectly.