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Kieran Kelly asked-

>As part of the research for an upcoming expedition, I am trying to ascertain
>how accurate were nineteenth century calculations of compass error when
>derived on land-based exploring expeditions. These calculations combined
>declination and compass error and in this case were expressed as variation.
>They were vital for turning explorers field books (based on magnetic
>bearings) into maps (orientated to true north)
>
>My main worry is the errors in the Nautical Almanac for the period, which
>have come to light on this site. An example calculation is shown below. I
>wonder if one of the list members could run the calculation though modern
>software and check for accuracy. The explorer is taking a bearing to the sun
>at sunrise using a magnetic compass. Longitude is approx 132? 20' East
>although this was not recorded in the field book calculation:
>
>Example 1
>Date:                July 3rd 1856
>
>Latitude:            15? 18'  South
>
>Azimuth:           N64?  0' E Magnetic
>(Sun Centre at sunrise)
>
>Altitude:            0? 0'
>
>Sun Declination: 23? 0' north
>
>Amplitude Sun: 23? 50'
>-------------------------------------------------------
>Calculation:
>Amplitude Sun:  E 23? 50' North
>                           90? 00'
>                        N 66? 10' East True
>Az                    N 64? 00' East Magnetic
>Var                        2? 10' East Variation
>
>This is an exact copy of the explorer?s field book entry. Declination and
>amplitude came, presumably, from the Nautical Almanac.
>
>Example 2
>This example was not worked in the field book but would appreciate an
>answer.
>
>Date:                March 1st, 1856
>
>Latitude:            19? 28' 05" South
>
>Azimuth:           N98?  0' E Magnetic
>(Sun Centre at sunrise)
>
>Altitude:            0? 0'
>
>Long was approx 127? 40'  east although not recorded in the field book.
>
>Any solutions would be greatly appreciated.
>
>The dates are for local time in northern Australia, not the date at
>Greenwich

====================

Response from George.

Tell us about the terrain, Kieran. That seems to be the most likely source
of error, if the explorer is taking the direction of Sunrise as the azimuth
at which he sees the Sun when it's bisected by his local land-horizon. How
horizontal is that land-horizon? If he wanted real accuracy, he would have
done better to take a magnetic bearing of the risen Sun, when a few degrees
up, using a sextant and artificial horizon to determine true Sun altitude.
But it's rather too late, now, to ask him to go back and do it again...

As for the calculation of amplitude (see Raper table 59), a factor that's
been neglected in the calculation is the correction for refraction (in
Raper, table 59A) which amounts, in the circumstances stated, to about 0.3
degrees. If that was allowed for, then in example 1 the expected azimuth of
Sunrise  would be greater by that amount, to be about 66deg 30' true,
rather than 66 deg 10' true. That would increase the calculated variation
from 2deg 10' E to 2deg 30' East, if I have all my factors the right way
round.

How accurately could the compass be read, though? From the two examples
given, it seems likely that compass readings were being taken to no better
than the nearest degree. Put that together with the errors due to a
non-flat horizon, and there we have the main sources of error.

What makes Kieran suspect errors in the Nautical almanac? What are the "the
errors in the Nautical Almanac for the period, which have come to light on
this site" that worry him? The Sun declination is about right, and changing
little from day to day. That's the only almanac prediction that's relevant.

George.

================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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