The square root of ten revisited

[Palmer O. Hanson, Jr.]

In response to Gene Wright's "Happy Square Root of 10 day!" (16 March) I wrote:

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I am fairly sure that some slide rules were made with the CF scales folded at the square root of ten rather than at pi.

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Stan Keeley and Martin Pinckney reported that the Hemmi 250 has the CF and DF scales folded at the square root of ten. I have a Hemmi 250 in my collection.

Page 38 of SLIDE RULES - A Journey Through Three Centuries by Dieter von Jezierski as translated by Rodger Shepherd states in part

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Folded scales ... ... were seldom incorporated in slide rules until 70 years later [about 1887] ... ... when Tscherepaschinski [a Russian] arranged a pair of scales folded at 3.16 along the lower slide-stator interface. Eventually, folded scales became common, especially in American duplex slide rules, which had four slide-stator interfaces. Some early German models had scales that were folded at the square root of 10, but most folded scales were folded at the value of pi. ... ... In the case of merchants' slide rules, the folded scales were folded at 3.6, thereby permitting direct multiplication or division by 360 days when carrying out calculations involving interest.

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The CF and DF scales on my K&E 4094 Merchant's Mannheim, K&E 4095 Merchant's Duplex, and K&E GP12 Business-Science slide rules all have the CF and DF scales folded at pi. In my collection only my A.W.Faber-Castell 67/22R Business slide rule does have the CF and DF scales folded at 3.6 .

I can't recall needing the square root of ten in any of my calculations. Is there a technology where the square root of ten apprears frequently in calculations?

[BobVA]

I've got a guess. The wikipedia article below says there are two uses for the CF and DF scales. Besides convenience for calculations involving pi, it also recommends use in lieu of the C/D scales when it isn't obvious which index on the latter to use in order to keep the results on scale. I hadn't heard of this trick, but it makes sense.

So, if the folded scale was originally devised to solve the "index ambiguity" problem, it would have been logical to fold the scale in the middle (10^0.5). Then perhaps some other clever person came along and noted that you could do the same thing by folding the scale at the nearly equivalent value of pi, with the bonus of adding the pi computation features.

Just speculation, of course.

Wikipedia Slide Rule Article - "other operations"

Edited: 28 Mar 2010, 3:09 p.m.

[Martin Pinckney]

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... it would have been logical to fold the scale in the middle (10^0.5). Then perhaps some other clever person came along and noted that you could do the same thing by folding the scale at the nearly equivalent value of pi, with the bonus of adding the pi computation features.

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I think you hit on it!