Infinite scales
Solutions for slide rules running out of scale...
When you calculate with an ordinary straight slide rule, you can "run out of scale".
For instance, if you want to multiply 5.7 by 1.77 by putting the left-most 1 of the C-scale over 5.7 on the D-scale, 1.77 on the C-scale will be over an empty space on the D-scale.
To find the answer, you'll have to shift the slide back and put the right-most 1 (the "10") of the C-scale over 5.7 on the D-scale. Just try it with the Virtual Pickett N909-ES.
If you were using the Texas Magnum TM1 this would require a 352 feet walk.
One solution for this problem is to use circular slide rules, like the ALRO.
In 1951 Joachim Neun got a German patent (DE898522) for several other solutions. They are shown at the right. I really like the one in Fig.1, because it can easily be made from an ordinary slide rule.
In 1910 British patent GB13852/1910 was issued to Sydney Herbert Stelfox in which the second claim describes a slide rule with a hinged or jointed slide. However, the aim was not an infinite slide rule but a short slide rule. This invention materialized as the 5" Stellfox Slide Rule with a 10" jointed slide in the John Davis and Sons Catalog 122A of circa 1910.
The 1930 Gebr. Wichmann catalogue displays a slide rule with a hinged slide. This one follows German Patent DE450305. Again, the aim was portability. Note that only the slide has a 1…10 scale. The body has 1…√10 scales.
Joachim Neun's solutions
An earlier Dutch version of this paper has appeared in MIR 56, May 2011.