NavList:
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Re: Measuring Dip in the 18th Century
From: Bruce J. Pennino
Date: 2013 Dec 22, 10:09 -0500
From: Bruce J. Pennino
Date: 2013 Dec 22, 10:09 -0500
Bruce
Alexandre:
I'm going to try to simply answer your comment
without causing any more "brain ache" on this topic. Surveyors,
navigators, astronomers especially, and even mathematicians.....ouch....(just
kidding and trying to add a little levity to a weary topic) realized there
are two major issues to dip. First, the relatively simple geometric
issue due to a person viewing the horizon created by a so-called round
ball , earth. A true tangent was needed at the person's
location to do the CN triangle math. There are second-order issues such as the
earth is an oblate spheroid, etc, but forget about those. Once a radius
has been selected, with a relatively simple trigonometric right triangle
geometry setup, one (even I could do it) will calculate that the dip coefficient
due to geometry only is about 1.06-1.07. REPEAT geometric dip
only: dip (minutes of arc) = 1.07 sqrt HoE ft.
It has been known "almost forever" that
this value 1.07 is too large due to the second issue, the bending (refraction)of
light from the horizon . Early surveyors who did a lot of celestial measurements
to determine true north etc estimated that the 1.07 value for the dip
coefficient was about 5-10 % too large because of light refraction.
I've found this in my oldest surveying book which goes back to the 1880s, and
can also be found in books dated the 1950s-60s.Corrections are given in the
textbooks, but usually without any "backup".
I've done some research and in the very earliest
almanacs there is a dip table which includes the total dip. I've not been
able to find the exact British astronomer who did it, but it was
about or just before Maskelyne. He (they) developed the modern dip table
that has not been changed significantly since the mid to late 1700s.
In the present nautical almanac, dip (which includes geometry and light bending)
is given as 0.97 sqrt Height of Eye(ft). The refraction of light to the
celestial body is in the other NA tables.
The coefficient 0.97 has worked marvelously well
for over 200 years and is certainly good enough for all practical purposes, even
if there is some "funny business" going on at the horizon. From shore, I've made
dip measurements with my theodolite and concluded that using 0.97 as
an average value may be slightly too high, but I have only about 40
data points. I'm in the process of tabulating all of my data and writing notes.
I'll eventually let NavList have my data and notes. I tend to agree
with the work done by Peters (he took over 3000 measurements
offshore) that a better average total dip coefficient might be
about 0.89. But the practical difference of a couple of minutes is so small
that it is only of interest to those aiming for the highest
average accuracy over a number of observations. And unfortunately, of
interest to those of us who have chosen to investigate (gotten hooked)
onto this oddity?!
A good day to all, Merry Christmas and Happy
,Healthy New Year.
Bruce
----- Original Message -----From: Alexandre EremenkoSent: Saturday, December 21, 2013 9:48 PMSubject: [NavList] Re: Measuring Dip in the 18th Century
For the dip, you don't have to take any measurements, Dip (under normal conditions) it is a simple geometric problem. Such dip tables could (in principle) be made by any mathematician in 2-nd century BC. Refraction is another matter... Alex. > I'm not so sure how tricky it was to make those measurements because they > sure got accurate results. I am absolutely blown away by the accuracy of > the refraction and the dip tables in the 1799 edition of the New Practical > Navigator, edited by Bowditch. I compared a sample of the values in the > 1799 tables with the modern tables and only rarely did the discrepancy > exceed six seconds of arc, 0.1'. See attachments. > > gl > > > > > ________________________________ > From: Marcel Tschudin> To: garylapook---.net > Sent: Friday, December 20, 2013 1:24 AM > Subject: [NavList] Measuring Dip in the 18th Century > > > > > ________________________________ > Andy Young draw my attention to the following publication: > > Huddart Joseph (1797): Observations on Horizontal Refractions Which Affect > the Appearance of Terrestrial Objects, and the Dip, or Depression of the > Horizon of the Sea. Philosophical Transactions of the Royal Society of > London, Vol. 87, (1797), pp. 29-42 > > a pdf copy of it can be obtained from JSTOR > http://www.jstor.org/betasearch?Query=Huddart+joseph&fq=py:[1796+TO+1798] > > Andy wrote: "Huddart managed to measure the altitudes of the Sun's limbs > above both the northern and southern horizons around noon, interpolating > to find the apparent altitudes exactly at culmination. This was evidently > a difficult and tricky measurement to carry out, especially with the > rather primitive instrumentation available to him; he comments that the > instrumental limitations prevent it from being done except in a restricted > zone of latitude, and that it can't be done near the equator because of > the rapid change in azimuth as the Sun passes near the zenith. > Nevertheless, he apparently was able to get useful information from this > work." > > He thought that this publication may eventually also be of interest to > some members of NavList. > > Marcel > > : http://fer3.com/arc/m2.aspx?i=125858 > Attached File: http://fer3.com/arc/img/125869.1799 refraction and dip > tables.jpg > > Attached File: http://fer3.com/arc/img/125869.img_0002.jpg > > Attached File: http://fer3.com/arc/img/125869.img_0001.jpg > > > : http://fer3.com/arc/m2.aspx?i=125869 > > > > : http://fer3.com/arc/m2.aspx?i=125883
