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>
>
> Brad and Lu,
>
> I also think that these simple methods are not as simple if you try to
> implement them in real life.
>
> a) Taking the altitude of Polaris.
> For this you need to divide a circle, say to 1 degree accuracy.
> Can you do this without instruments? I cannot. I need at least a divider,
> and even then this is a highly non-trivial task.
> Alternatively, you can make an instrument of straight sticks (kind of
> cross staff). Then the same problem arises: to measure the length
> of these sticks. Dividing a ruler is no simpler task than dividing
> a circle.
> All this is BEFORE you "use trigonometry". But how exactly you use
> trigonometry without a calculator/tables? You compute a table of sines
> and or tangents? With Ptolemy method, or using a Taylor series?
>
> It is true, you will need the tangent of only one angle when measuring
> Polaris altitude with a cross staff, but the problem of making a ruler
> remains.
>
> I already mentioned on this list a Russian captain Golovnin who spent 10
> years in captivity in Japan in the early XIX century. He taught the
> Japanese
> some modern navigation, and
> his mate computed tables of trig functions for the Japanese.
> I wonder how many modern captains or mates are capable of doing this:-)
>
> b) Using Sun. Certainly the method is not practical on a ship.
> To find the noon altitude of the Sun with a gnomon (vertical tick),
> you need a flat horizontal ground, a plumb line to install your stick,
> then you probably have to observe for several days to find the noon
> altitude on a certain day.
> Declination does not seem to be such a big problem in principle:
> you can compute it approximately from the dates of the solstices
> and the angle between the equator end ecliptic.
> (Assuming that Sun rotates on a circle not an ellipse, as the ancients
> did). If you can make trigonometric tables, then you probably can
> do this as well.
>
> With any of these methods, determination of latitude, say to 1-2 degrees
> will take many days and only possible from land.
>
> By the way, all this is described with some details in Jules Verne novel
> Mysterious Island. According to Jules Verne, Cyrus Smith used his height
> (which he knew precisely) as a unit of length. But the details how he
> divided this unit into smaller units are omitted:-)
> Jules Verne apparently did not understand that to measure an angle
> you can use arbitrary unit of length, and its relation to feet or
> inches is irrelevant. The main difficulty is in dividing this unit
> with sufficient accuracy.
>
> Alex.
>
>
>> Brad:
>>
>> I must respectfully disagree.   If I plant a stick in the ground
>> and are
>> willing to measure its shadow for a full year (or at least from one
>> solstice to the other), I can indeed deduce my latitude.   If I
>> want to
>> do it in less time (say in just a day or in a week) I must have a
>> declination table  and an idea of what date it is.   While the
>> latter
>> was not necessarily forbidden by the statement of the problem, the
>> former
>> certainly is.
>>
>> I had originally wondered if I could have applied the Rule of Twelfths
>> to
>> approximating the sun's declination for any particular date, but it
>> turns
>> out that the curve of the sun's declination is NOT a sine wave (nice
>> explanation in Wikipedi
>
>
>
>
>
> : http://fer3.com/arc/m2.aspx?i=119938
>
>
>

   

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