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One way to compare the scales is by looking at the length between the 
same points on the Bygrave versus a normal ten inch slide rule. My 
measurement of the cotangent scale on an original Bygrave shows a 
circumfrence of 174 mm making the diameter of the scale of 55.4 mm, 
slightly greater than the 54 mm measured by van Riet. Using my 
measurement, the length of the 44 spirals from 20' to 89° 40' is 7.656 
meters, 25.1 feet.

See: http://www.fer3.com/arc/m2.aspx?i=109446


The space between 5° 42' 32" and 45° on the tangent (or cotangent) scale 
of a ten inch slide rule is ten inches. The log cotangent of 45° is zero 
and the log cotangent of 5° 42' 38" is one. This equates to ten spirals 
on the Bygrave since each spiral represents a change of log cotangent of 
.1. This makes the space between those values on the Bygrave cotangent 
scale is 1.740 meters, 68.5 inches almost 7 times greater than on a 
standard slide rule.

gl

douglas.denny@btopenworld.com wrote:
>
> Another thought: in continuation of the scale length issue of the 
> Bygrave Slide Rule I have raised.
>
> The Log CoTangent scale is of course asymptotic at both ends where the 
> degrees are approaching less than one towards zero; and at 89 degrees 
> approaching 90; so the "full" scale length cannot be easily defined as 
> they would become infinitely long.
> The LogCos scale is similarly afflicted at the top end approaching 90 
> degrees; and is crowded at zero.
>
> Hence 'scale lengths' become meaningless as one approaches the limits 
> of the scales. In practical terms I suspect the slightly different 
> diameters between the tubes and their scales does not affect accuracy 
> significantly if made to the same or very similar scale factor because 
> of the very log scale length - as I mentioned before in the previous 
> posting.
>
> Douglas denny.
> Chichester. England.
>
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