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On 2015-07-14 11:36, Hanno Ix wrote:
>
> On the cot() scale at around 45 deg the marks are the closest, and the
> distance
> between, say, 44 deg and 45 deg may be about 30mm. I am proposing 30
> additional
> small marks for 2 arc min steps which makes the distance between them 1mm
> which should be discernible from nearly 3 m away.

Graduations can be clearly resolved by the eye, but too close for
comfortable reading. An example is the Hemmi 259D, a beautifully made
Japanese slide rule. It features a K scale with unusually fine divisions:

http://www.sliderulemuseum.com/Hemmi/S358_Hemmi_259-D_dc-MB.jpg

In theory, this allows more precise reading. But to my middle aged eyes
it makes the scale hard to use. Although its graduations are readily
resolved by eye (better than in the scan), they're too close for
comfort. Compare the Hemmi to the K&E 4181, which divides K in the more
common pattern:

http://www.sliderulemuseum.com/KE/KE_4181-3_LogLogDuplexDeciTrig_sn004408.jpg

The reduced chance of making a mistake more than compensates for the
coarser graduations. I suspect the difference would be even greater on a
moving platform.

That's not to say Gary's Bygrave is optimum in this respect. It's hard
to tell without experience using the device. Graduations can be too
coarse. The Hemmi with the overly divided K scale has an ST scale with
strangely coarse graduations at the left end!

Again, the K&E rule has a different design for that scale (which they
label SRT). Better? In my view it is, but I won't deny mistakes are more
likely too. On the other hand, it's hard to blunder with the widely
spaced divisions on the Hemmi. And that's really the compromise:
interpolation accuracy vs. the probability of making a mistake.

   

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