# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Newton and Halley: was Re: the Shovell Disaster
From: Nicolàs de Hilster
Date: 2007 Nov 16, 20:22 +0100

```Just a while ago in NavList 3870 George Huxtable wrote:
> His words
> described it as being divided "by a diagonal scale, and the half-degrees,
> half minutes, and one-twelfth minutes, counted for degrees, minutes, and
> one-sixth minutes." At that point he had obviously not appreciated the sheer
> impossibility of dividing to 10 arc-seconds by a diagonal scale. No doubt,
> he would find that out the hard way.
>
Of course Newton's words sounded challenging to me. If he really meant
that he had diagonal scales down to those values what would he have
made. When we study his drawing it becomes clear that he left space for
the diagonal scale. Assuming his drawing was more or less to scale
(don't be surprised if it was as that is something I have proven before
for the spiegelboog) the dimensions can be scaled off. Based on a 4 foot
telescope his instrument has the following dimensions:

telescope: 4 foot
outer diameter brass plate: 3 3/4 foot
outer diameter diagonal scale: 3 1/2 foot (slightly more, about 3.6)
inner diameter diagonal scale: 3 foot (slightly more again, about 3.1)

So the diagonal scale was no less than half a foot wide, which is a
whopping 152.4 millimetres!

Now what is he saying to us?
> 1/2 Degrees, 1/2 Minutes, and 1/12 Minutes, by a Diagonal Scale; and
> the 1/2 Degrees, and 1/2 Minutes, and 1/12 Minutes, counted for
> Degrees, Minutes, and 1/6Minutes.

What he means that you have to divide the instrument in half degrees,
half minutes and twelfth minutes in order to get a read-out of degrees,
minutes and sixths of minutes (remember this is a double reflecting
instrument!).

So the final result would allow the observer to read his instrument down
to 1/6th minute. Well... even if it was to 1/12th it was not impossible.

Attached you will find the diagonal scale as it could have been. The 10
arc minute diagonals are 1.5 millimetre apart and the 120 concentric
circles 1.27mm. This diagonal scale reads down to 10/120 = 1/12th arc
minute! Newton only needed 1/6th of an arc minute so either we can skip
half of the diagonals (so they tilt a bit more) or half the concentrics,
I would choose for the latter.

If we compare this to contemporary Davis Quadrants, the intervals are
quite similar in size, so no problem in that (apart from the labour it
does not scare me off). Now we also know why he did not show the
diagonal scale in the drawing, it would simply be too much information.
All we have to wait for now is someone to put this in practise ;-)

Nicolàs

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