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I know that a vernier scale can be used to accurately read a linear scale, such as in vernier calipers. I'm wondering if there is a way the methods behind a vernier scale could be adapted for usage with a non-linear scale, such as a logarithmic scale. The reason I ask this is because I am designing a slide rule (actually a slide rule bracelet, it's pretty cool really) and I'm wondering if it's possible to read the results of multiplication and division to more significant figures without, of course, increasing the size of the slide rule. This doesn't seem possible to me, but I'm hoping somebody else might have some insights about logarithmic scales that I don't. The problem seems to be that since the scale is linear, there would need to be a unique vernier scale for every graduation on the main scale, perhaps even a vernier scale for every possible combination of matched graduations on the two logarithmic scales...

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It appears you already understand the difficulty. You can certainly etch in a pair of scales, matched to give additional accuracy in an uneven subdivision, as in logarithm. What I would like to see someday is one of these: en.wikipedia.org/wiki/Curta which I read about in a science fiction book, Pattern Recognition by William Gibson, pages 29-30, so originally i assumed they were also fiction. –  Will Jagy Dec 6 '12 at 1:52
    
The Curta looks interesting. I had never heard about it before, despite growing up with slide rules, log books, etc. –  copper.hat Dec 6 '12 at 2:52
    
Oh yes, the Curta is one of my all time favorites. But what do you mean by "You can certainly etch in a pair of scales, matched to give additional accuracy in an uneven subdivision, as in logarithm." –  Big Endian Dec 6 '12 at 3:28

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I am also trying to do something similar, however, it seems to me that you need an interestingly shaped scale, when I did it the hard way, I found that for 1-2, the scale ended at the original 5 line, and I've been trying to go even deeper into it, not sure where this will take me, I'll be experimenting with a slanted slide rule next, see where it goes. Good luck!

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You might like this: cs.smu.ca/~dawson/ComplexSlideRule.html I just found out about complex slide rules. Their pattern on this page isn't very good - the lines are quite wavy, so I am writing a program right now to generate a much more high quality, pixel perfect template. –  Big Endian Apr 17 at 0:26

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