NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2013 Dec 28, 17:07 -0500
Alex & Frank
It appears that the resolution of the backstaff and expected accuracy of the back staff are being treated as if they are the same unit. This should be clarified, as they are not the same.
There is no doubt that the resolution of the instrument is to 1 arc minute. That is, with the scale and the vernier combined, we can obtain measurements to 1 arc minute. George Huxtable himself has agreed with this point http://fer3.com/arc/m2.aspx/backstaff-Huxtable-nov-2007-g3747
The expected performance is not 1 arc minute, just as Frank says and again something George agreed with. In practice, the observer simply could not reliably repeat measurements of the same angle to 1 minute. Frank has offered 10 minutes, a figure which I will not dispute.
I do agree with Alex's assertion, that because the resolution was to an arc minute, and that the early dip tables were to an arc minute, we can expect that they desired to observe to that resolution. Achieving that was another matter. It does not follow logically that because they were not achieving 1 arc minute accuracy in practice that the early dip tables were irrelevant, to those navigators. Those navigators had dip tables, back staffs and declination tables to an arc minute and USED THEM THUSLY. They could not compare their results with double reflecting instruments. They could not know that they were only good to 10 arc minutes because they had nothing to compare it to. (The same can be said of celestial navigation just before GPS. Nothing to compare it to. Our modern fascination with accuracy of celestial navigation is highly reliant on a better method, to wit GPS.) These early navigators no doubt followed practice as later ones did, by rote application of the rules, with little further speculation as to the statistical accuracy. After all, they were tooling along at 6-8 knots and being good to 10 miles (10 arc minutes) was certainly plenty good enough.
As greater understanding of the physics came about and instruments improved, the results of celestial navigation improved. At best, one could say by two orders of magnitude. At nominal, by one. The modern double reflecting sextant is resolved to 0.1 arc minutes (one order of magnitude better in resolution) and dip tables are resolved to 0.1 arc minutes (one order of magnitude in resolution).
I'll leave it to the cognoscente to rate the expected accuracy of the sextant. Is that two orders of magnitude better than the back staff?
Brad
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? >>> ---------------------------------------------------------------- >>> NavList message boards and member settings: www.fer3.com/NavList >>> Members may optionally receive posts by email. >>> To cancel email delivery, send a message to NoMail[at]fer3.com >>> ---------------------------------------------------------------- >>> >>> : http://fer3.com/arc/m2.aspx?i=125973 >>> >> >> >> >> : http://fer3.com/arc/m2.aspx?i=125980 >> >> >> >> > > > : http://fer3.com/arc/m2.aspx?i=125985 > > > >
