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I did not investigate the table myself.
The authors of the paper from which it is taken say that it incorporates
refraction, not only geometric dip.

Harriot actually had some theory of refraction.
I also understand from the article that Harriot's Instructions
were never published, and the originals are available in the British museum.

Harriot is mostly famous (among mathematicians) for his first rigorous
investigation of stereographic and Mercator projections.

He also discovered sun spots independently of Galileo, with a telescope which
was made also independently of Galileo.

Alex.


> Alexandre:
>
> What do you think? The 1595  dip table is probably a general "correction"
> table to include refraction, geometry, and whatever else might be a
> concern?
>
> The table you showed is just astounding given the instruments and
> knowledge available.  Very good mathematicians!
>
> Bruce
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>   ----- Original Message -----
>   From: Alexandre Eremenko
>   To: bpennino.ce---.net
>   Sent: Friday, December 27, 2013 10:41 PM
>   Subject: [NavList] Re: Measuring Dip in the 18th Century
>
>
>
> ------------------------------------------------------------------------------
>
>
> As I said, good backstaffs were divided to 1'.
> In principle, this instrument can achieve the same accuracy
> as a wooden octant without a telescope. These wooden octants
> were also divided to 1'.
>
> However there is one serious problem: the "parallax of the backstaff",
> the angle measured strongly depends on the position of your eye
> with respect to the staff, and there is no simple remedy for this.
>
> Thomas Harriot, whom I mentioned in a previous message
> has a table of corrections for the "parallax of a backstaff".
> It is clear from his recommendations and tables that they were aiming at
> 1'
> accuracy for determining latitude by Sun sights.
>
> Therefore a dip table and refraction table WERE relevant.
>
> Alex.
>
>
>> Here is a well-preserved backstaf:
>> http://www.ebay.com/itm/231110131338?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1438.l2648
>>
>> (Very rare item on e-bay, and the price is corresponding to this:-)
>>
>> If you magnify photo 3, you see that one of the arcs is subdivided to 1'
>> First every degree is divided into 6 parts, and then they are subdivided
>> by
>> the nonius into 10 parts each. Nonius is the grid on the arc.
>>
>> I've seen many backstaffs like this in museums but this is the first one
>> on
>> e-bay. The only missing parts are two movable sighting vans.
>>
>>>From the examples I saw in museums I conclude that dividing into
>> single minutes was the usual practice.
>>
>> Alex.
>>
>>> Hi guys,
>>>          Please help me understand the 'instrument time line'. What is
>>> the angular resolution of a cross-staff or back-staff?
>>> I always thought it was about +/- a degree, and if thats true why would
>>> you care about 1 arc minuet?
>>> I always thought the first sub degree instrument was the octant.
>>> ~Greg
>>>
>>> On 12/27/2013 06:04 PM, Alexandre Eremenko wrote:
>>>> ------------------------------------------------------------------------
>>>>
>>>> I am reading a book about Thomas Harriot (an outstanding British
>>>> mathematician) In 1595, he wrote "Instructions for assisting the
>>>> navigators of Sir Walter Raleigh's voyage to Guiana.
>>>> The instructions contain the following dip table
>>>> 1 3'
>>>> 2 4'
>>>> 3 5'
>>>> 4 5'
>>>> 5 6'
>>>> 6 6'
>>>> 7 7'
>>>> 8 7'
>>>> 9 8'
>>>> 10 8',
>>>> where the left column is the height in PASE's; according to the authr
>>>> of the paper,
>>>> 1 pase=5 feet.
>>>>
>>>> The paper also has a reference to an early Portuguese source: Pedro
>>>> Nunes, De arte ratione navigandi libri due (Coimbra, 1546).
>>>>
>>>> The article I am reading is Jon V. Pepper, Harriot's earlier works on
>>>> mathematical navigation: theory and practice.
>>>>
>>>> Gary: have you received my request sent off-the-list?
>>>> ----------------------------------------------------------------
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>>>>
>>>> : http://fer3.com/arc/m2.aspx?i=125973
>>>>
>>>
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>>> : http://fer3.com/arc/m2.aspx?i=125980
>>>
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>> : http://fer3.com/arc/m2.aspx?i=125985
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> : http://fer3.com/arc/m2.aspx?i=125986
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> : http://fer3.com/arc/m2.aspx?i=125988
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