Dear Frank & all,
On the meaning of "PI Long":
Waugh uses the symbol P in his computational treatment of the declining
dial on p. 80. The P values for each hour line in table 10.2 are "what
Holwell (in Clavis Horologiae, London 1712) calls the polar angles". The
polar angle for noon equals the so-called difference in longitude DL.
Converted to time, this is the time of the sub-style line. So here is at
least a link between P and Long.
On the slight difference between the value PI Long = 35°43'40" and Fer's
value of 35.75° for the hour angle of the sub-style:
The equation for DL is: tan(DL)=tan(Dec)/sin(Lat).
The values given on the dial for DL and Lat are very accurate, down to
seconds of arc. The declination is merely given as 30°20' and thus seems
to be rounded, to perhaps 10 or 20 minutes of arc. The value actually
used for Dec can be calculated ('reverse engineered') from the equation,
yielding 30.3127° or 30°18'46". This value might have been the
calculated result of an actual measurement, perhaps involving the shadow
length of a rod perpendicular to the wall at noon. As the designer
realized too well that the accuracy of such a measurement is limited, he
put a rounded value on the dial.
Hope this helps,
Frans Maes
Frank Evans wrote:
> Greetings fellow dialists,
>
> John Foad has written to say that Keith Scobie-Youngs of the Cumbria
> Clock Co, Dacre, Penrith, last restored the Hawkshead dial in 1997. He
> asked the restorer if there was any clue from its original state, for
> example whether any of the lettering had been uncertain. But Keith
> Scobie-Youngs assured him that, though in poor condition, there was no
> doubt about the previous inscription. He unfortunately had no
> information or theory on what the "PL Long" meant, nor indeed as to why
> the dial is canted to no apparently significant declination!
>
> It has now been made clear to me by Fer de Vries, who has a good clear
> photograph, that the letters "PL" that I cited are in fact "PI".
> Moreover his picture reveals the missing declining values printed beside
> the locations values as "Decl. 30 deg 20 min."
>
> Here I take the liberty of passing on his message to me:
>
> In the mean time I found a larger picture of this dial and there is
> more text as you describe.
> The part of the text I mean is in the attached picture.
> A new value I read is: Decl 30 (degrees) 20 (minutes)
> Now we are able to calculate all the constants of the sundial.
> I get with ZW2000:
> Style height 30.19
> Angle of substyle 160.1 or 29.9
> Hourangle of substyle -35.75
> All decimal degrees.
>
> I thought: bingo, hour angle of the substyle. But the value you
> mentioned gives 35.7277.. decimal.
> Still not all questions answered but perhaps this gives you another
> idea how to solve it."
>
> Well, this looks pretty close indeed and we may be nearing the answer.
> Can anyone consequently suggest a relationship between the letters "PI"
> and hour angle? Polar something? Moreover, actual longitude values
> having proved pretty unlikely (problematic observatories in Brazil,
> rural Russia, South Georgia, etc.) it is worth observing that actual
> longitude values are not common on nineteenth century dials anyway.
> Frank 55N 1W
>
>
>
>
>
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