From a0cfe8c3ae74681335d9f004c65946fa4141b1a6 Mon Sep 17 00:00:00 2001 From: dakkar Date: Mon, 23 May 2011 20:53:57 +0100 Subject: new page: slide rules --- src/HW/logscale-calc-tools/document.en.rest.txt | 136 ++++++++++++++++++++++++ 1 file changed, 136 insertions(+) create mode 100644 src/HW/logscale-calc-tools/document.en.rest.txt (limited to 'src/HW/logscale-calc-tools/document.en.rest.txt') diff --git a/src/HW/logscale-calc-tools/document.en.rest.txt b/src/HW/logscale-calc-tools/document.en.rest.txt new file mode 100644 index 0000000..0c54161 --- /dev/null +++ b/src/HW/logscale-calc-tools/document.en.rest.txt @@ -0,0 +1,136 @@ +=========================== +Log-scale calculation tools +=========================== +:CreationDate: 2011-05-23 18:46:11 +:Id: HW/logscale-calc-tools +:tags: - hardware + - vintage + +Uh? What? +========= + +Maybe you know better the name "slide rules". Or maybe not even that +one… Short version: ``log(x*y) = log(x)+log(y)``, so if you have a +pair of rulers with a logarithmic scale, you can use them to perform +multiplications and divisions. More details on dedicated sites, like +`Ron Manley's one `_ o `Eric Marcotte's one +`_. + +All right, let's pretend we've understood that… +=============================================== + +I have here a classic slide rule, and a cylindrical slide "rule" (of +the `Otis King `_ variety). I +want to show how to perform a couple of simple operations. + +Multiplication +============== + +We want to multiply 7 by 3. Easy, right? + +Let's start with the slide rule: + +1) make 1 on the C scale match with 7 on the D scale + + .. image:: s7x3-1.jpg + :alt: 1 on C scale matching with 7 on D scale + +2) look with what, on the D scale, matches 3 on the C scale + + .. image:: s7x3-2.jpg + :alt: 3 on C scale matching with 21 on D scale + + 21, which is our result [1]_ + +With the cylindrical rule things are a bit more awkward. + +1) point to 1 on the lower scale, with the cursor + + .. image:: r7x3-2.jpg + :alt: cursor pointing to 1 on lower scale + +2) point 7 on the upper scale, *moving only this scale* + + .. image:: r7x3-1.jpg + :alt: cursor pointing to 7 on upper scale + +3) now move *only the cursor*, making it point to 3 on the lower scale + + .. image:: r7x3-3.jpg + :alt: cursor pointing to 3 on lower scale + +4) on the upper scale we read our result + + .. image:: r7x3-4.jpg + :alt: cursor pointing to 21 on upper scale + +It's totally equivalent to the linear rule: the two logarithmic scales +are equal, so a translation on one, "sums" to the other. + +Division +======== + +Let's divide 24 by 4. + +Linear rule: + +1) make 4 on the C scale match with 24 on the D scale + + .. image:: s24d4-1.jpg + :alt: 4 on C scale matching with 24 on D scale + +2) look with what, on the D scale, matches 1 on the C scale + + .. image:: s24d4-2.jpg + :alt: 1 on C scale matching 6 on D scale + + 6, again our result. + +Cylindrical rule: + +1) point to 4 on the lower scale, with the cursor + + .. image:: r24d4-2.jpg + :alt: cursor pointing to 4 on lower scale + +2) point 24 on the upper scale, *moving only this scale* + + .. image:: r24d4-1.jpg + :alt: cursor pointing to 24 on upper scale + +3) now move *only the cursor*, making it point to 1 on the lower scale + + .. image:: r24d4-3.jpg + :alt: cursor pointing to 1 on lower scale + +4) on the upper scale we read our result [2]_ + + .. image:: r24d4-4.jpg + :alt: cursor pointing to 6 on upper scale + +Some notes +========== + +The advantage of the cylindrical rule is that it allows longer scales +in a small space; the longer the scale, the more precise you can be in +reading it. + +The advantages of the linear rule are in the ease of use, and in the +simplicity of concatenating operations one after the one, especially +when using more than 2 scales (the slide rule you see above has 6 +scales: two regular ones, two quadratic, one reciprocal, one cubic). + +.. [1] OK, I cheated a bit, since at first glance you'd think of using + the other 1 on the C scale (the one on the left hand side), but + if you try that, the 3 on C ends up out of the rule; the trick + works because it's equivalent to: + + * divide 7 by 10 (10C:7D → 1C:7D (this 7 is outside the rule, + on the left hand side)) + * multiply that by 3 + + or, if you prefer, 7CI:1D 3C:21D (using the reciprocal scale). + +.. [2] just as in the multiplication with the linear rule, here too we + are reading on the "wrong side" of the scale; it works for the + same reason. -- cgit v1.2.3