Re: Davis-Pletts Rule


Eamonn
 

Hi Bob,

Thanks for the pointer to your LN Scale presentation. I read it and found it to be very comprehensive and well written.

I especially appreciated the details regarding the gauge marks on the rule proposed by Cohen for evaluating exponentials with powers greater than 2.3. I do think that the proposed gauge marks would have made such calculations easier than finding the exponent modulo 2.3026, but the procedure still seems a bit cumbersome. On the Davis-Pletts rule, the larger range of the LN scale allows exponentials with powers up to 9.2 to be evaluated directly, at the expense of occupying more scale real estate.

There is one additional interesting detail on the Davis-Pletts Ln scale that is discussed in Pletts' patent. The top part of the Ln scale has a range of 0 to 4.6 and the bottom part has a range of 4.6 to 9.2. However, ln(100) is actually 4.605..., so the tick marks on the bottom part of the scale are offset by 0.005 from the correct values. This is half the distance between the tick marks, so it is definitely noticeable.

In the patent Pletts references a line/gauge mark labeled 'l' equal to the distance between 4.6 and 4.605 at each end of the scale to correct for this offset. I see a line in the appropriate position at the left end of the Ln scale in the photos uploaded by Alan. Looks like there may be also a line on the right end of the scale, but the picture is not so clear. There does seem to be a small '1' which I interpret as an 'l' indicator on the right end, but not on the left end.

Eamonn.

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