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I recently bought a copy of Godfrey & Siddons four figure tables. Looking through, I find tables for base 10 logarithms, antilogs, trigonometric functions, reciprocals, etc, all printed to 4 figures accuracy and all of fairly obvious utility, should our calculators turn on their masters.

But near the back is a short table consisting of only a handful of logarithms, running from $\log{1.01}$ to $\log{1.05}$ all printed to 7 figures precision.

I've been scratching my head trying to figure out why these were included. I'm sure if I had gone to school 50 years ago it would be perfectly clear, but as it is, I can't see how having a limited set of high precision logs would be useful, and I can't seem to find any reference to them online.

Are they to be used by interpolation to improve the accuracy of higher order roots who's logarithms are small enough that significant digits start to drop off the end of the main tables? That's the only use case I can think of, or am I missing something?

Can anyone with more experience or insight shed some light on this for me? I would much appreciate it!

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  • $\begingroup$ I take it there's no preface or introduction explaining the layout of the book? $\endgroup$ – Gerry Myerson Mar 22 at 0:57
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    $\begingroup$ Unfortunately not! $\endgroup$ – Tom Backhouse Mar 22 at 1:56
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I suspect that they are for calculating compound interest.

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  • $\begingroup$ That would make sense! I'd been scratching my head trying to think why one would need logs of small numbers to a higher precision than the anti log tables, compounding interest is obvious in retrospect. $\endgroup$ – Tom Backhouse Mar 22 at 2:01
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My guess is that it is for interpolation.

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