Re: Light into Darkness : Wingate

Andreas Poschinger
 

Hi,

I uploaded the scales of Wingate into a folder:

https://groups.io/g/sliderule/files/AntiqueRules/Wingate

I think I understand now the folded scale to a certain extent.

The scale arrangement of the first scales is: D K DF A aTan(A) aSin(A) lg(D)

The DF scale is folded by sqrt(10).

D can be used by K to read the cubicroot (without compasses!) with K
interpreted the common way from 1...1000 and D from 1...10.

DF can be used to read (without compasses) the sqareroot from A with DF
being interpreted from 1/sqrt(10) to sqrt(10) and A interpreted from 0.1
to 10. That is now what somehow looks strange, to interpret A from 0.1
to 10 instead of 1 to 100. But why not. For sin and tan however A again
is interpreted from 0.01 to 1 as on Mannheim compatible rules.

I wonder whether Wingate published this scale layout also in France, and
whether this may be the reason how they came to the Beghin rules by
using "sliding wingates" first.

Best regards

Andreas


Am 04.05.2020 um 21:56 schrieb Andreas Poschinger:

Hi Tom,

yes I found it. It seems that the scale layout is the same in the 1645
edition.

Mostly I still wonder about the folded scale and while scanning through
the book I  did not find an explanation. I must admit however that my
main aspect while scanning was the use of the compasses.

It seems to be that he is the inventor of the D A K scales for getting
square and cubic roots without taking into account the L scale or any
other equal length stuff.

Maybe the folded scale is to find numbers quicker and to be faster in
compass setting. Then he might be also seen as inventor of speed
calculation...

Best regards

Andreas

Am 04.05.2020 um 20:13 schrieb Tom and Lu Wetmore via groups.io:
Did I sent you the short article I wrote comparing the scales found
in his first, French edition, to the scales in a later English edition?

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