Damn, this Concise 300 circular slide rule is satisfying to use. But it's going to take me a while to wrap my brain around all the different scales so I can form calculation plans in my head. Multiplication using the C and D scales is straightforward: you align the 1 with one of the multiplicands and move the cursor to the other, and the product is on the opposite scale. To multiply using the CI and D scales, you align the two multiplicands and then the product will be at the index. But then you can do chained multiplication by moving the cursor to the third multiplicand on the C scale! You can repeat that forever by then moving the next multiplicand on the CI scale under the cursor.
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Ooh, I learned how to raise a number to an arbitrary power, which also taught me something else: the importance of logarithms! It's the same as multiplying using the C and D scales, only you use the LL1 or LL2 scale instead of the D scale: line up the 1 on the C scale with the base on the LL1 or LL2 scale, then move the cursor to the exponent on the C scale. and read the result off the LL1 or LL2 scale (LL means log-log).
The function you're computing is exp(ln(x)*y), because moving from an LL scale to the D scale is taking the natural log, moving back is exponentiation, and ratio between the C and D scales is set by where the 1 on the C scale points on the D scale.
Arbitrary roots is easy, too: just line up the root you want on the C scale with the number you want the root of on the LL1 or LL2 scale, then move the cursor to the 1 on the C scale and read the result off the LL1 or LL2 scale.
Ooh, apparently the log-log slide rule was invented by Peter Mark Roget, M.D. The Roget's Thesaurus guy!
I had thought the L scale meant "logarithm" since it's the base 10 logarithm of the C scale, but it actually stands for "linear". It's the A, B, C, D, and K scales that are logarithmic!
https://en.wikipedia.org/wiki/Slide_rule has a good description of all the scales. The letters are apparently standard across all slide rules. Which is good, because this one is Japanese!
Oh geez I just learned what the ST scale is for, and it blew my mind. ST means sine and tangent. It starts at 40 minutes (a lot of slide rules use hexagesimal for angles) and goes up to six degrees. This is the arctangent *and* the arcsine *and* the conversion from radians to degrees of the C scale, because they're all basically the same within the precision with which you can read the slide rule! You have to divide the C scale by 10 to use it with this scale, so 5.7 degrees on the ST scale lines up with the 1 on the C scale. 5.7 degrees is approximately 0.1, and the sine and tangent are both approximately 0.1.
I noticed that both the LL2 and LL3 scales are marked with "e" over the 1, but that didn't seem to make sense, because on the LL2 scale that should be exp(0.1). But then I realized that there are no marks just to the right; the first mark is 1.11, over the 1.04 mark on the C scale. So the 1 on the C scale is actually 10 when using the LL2 scale!
To add and subtract you use… pencil and paper.
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@freakazoid oh damn, i had no idea about that!