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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 
    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 ;-)
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