Log tables

Before the invention of calculators, the only alternative to slide rules was to use tables of logarithms. These were published to varying degrees of accuracy.

The first example shows a page of logarithms to 4 figure accuracy and the second to 7 figure accuracy.

Four figure logarithms

These were the most common form of logarithms and until the 1970s would have been familiar to most school children. The following is one page from a book of tables. With 4 figure logs the whole range of values could be covered in 2 pages. Other pages would have included anti-logarithms and trigonometrical functions. One thing which should be noticed, and which is particularly relevant in a slide rule site, is that fixing the decimal point had to be done in a similar way to that of slide rules. The example given below shows that log 3.674, log 367.4 and log .003674 are respectively 0.5652, 2.5652 and -3 + 0.5652.

Slide rules were almost as accurate as 4 figure logs and were a lot quicker in their use.

log-4f.gif (73466 bytes)
Seven figure logs

These were used where higher accuracy was needed and were much more cumbersome. For example in my book of 7 figures logarithms, the logarithms alone occupy 200 pages (compared to 2 pages above).

For other calculations, say involving trigonometrical functions, the logarithms of the functions were tabulated. This facilitated such calculations as 3.764 x sin 40 since one could go straight to log (3.764) + log (sin40). The example below shows one page (of the 90) dealing with logarithms of sines, tangents, etc.

Note also the column of differences. If one wanted to calculate log (sin 13 15' 35" ) then from the table this would be calculated as:
     9.3602154 + (35/60) * 5361
Presumably for convenience of presentation, the values are given for a base distance of 10,000,000,000 units.

log-7f.gif (80728 bytes)