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+===========================
+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 <http://www.sliderule.ca/>`_ o `Eric Marcotte's one
+<http://www.sliderules.info/>`_.
+
+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 <http://en.wikipedia.org/wiki/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.