Appendix II
HINTS ON MAKING, AND METHOD OF REDUCING,
THE FIELD OBSERVATIONS.
IT will probably be found useful if I
give here a few hints as to the
precautions which must be taken in
making the field observations and an
example of their reduction to an
astronomical. basis.
For the azimuths of the sightlines the
investigator of thesemonuments cannot
do better than use the 25inch, or
6inch, maps published by the Ordnance
Survey. Their accuracy is of a very high
order and is not likely to be exceeded,
even if approached, by any casual
observer having to make his own special
arrangements for correct time before he
can begin his surveying work.
In some eases, however, it may be found
that the Survey has not included every
outstanding stone which may be found by
an investigator on making a careful
search many of the stones are covered by
gorse, &c., and are not, therefore,
easily found.
In such cases the azimuth of some object
that is marked on the map should be
taken as a reference line and the
difference of azimuth between that and
the unmarked objects determined. By this
means the azimuths of all the
sightlines may be obtained. When using
the 25inch maps for determining
azimuths it must be borne in mind that
the side=lines are not, necessarily, due
north and south. The DirectorGeneral of
the Ordnance Survey, Southampton, will
probably on application state the
Correction to be applied to the azimuths
on this account, and this should
beapplied, of course, to each of the
values obtained.
If for any reason it is found necessary
or desirable to make observations of the
azimuths independently of the Ordnance
Survey, full instructions as to the
method of procedure may be found in an
inexpensive instruction book 1 issued by
the Board of Education: The instructions
given on p. 49, § 3, are most generally
applicable, and the form on
p. 76 will
be found very handy for recording and
reducing the observations.
In making observations of the angular
elevation of the horizon a good
theodolite is essential. Both verniers
should be read, the mean taken, and then
the telescope should be reversed in its
Ys, reset, and both readings taken
again. One setting and reading are of
little use.
The Ordnance Survey maps may also be
employed in a preliminary reconnaissance
to obtain approximate values of the
horizon elevations. This may be done by
measuring the distances and
contourlines shown on the oneinch
maps. This method, however, is only very
roughly approximate owing to the fact
that sharp but very local elevations
close to the monuments may not appear on
these maps and yet be of sufficient
magnitude to cause large errors in the
results.
Where trees, houses, &c., top the
horizon, they should, of course; be
neglected and the elevation of the
ground level, at that spot, taken.
Should the top of the azimuth mark
(stone, &c.) show above the actual
horizon, its elevation should be
recorded and not that of the horizon.
Having measured the angular elevation of
the horizon along the sightline, it is
necessary to convert this into actual
zenith distance and to apply the
refraction correction before the
computations of declination can be made.
The process of doing this and of
calculating the declination will be
gathered from the examples given below:—
Data.
Monument:—E. circle Tregeseal, lat. 50°
8" N. i.e. colat = 39° 52´.
Alignment. Centre of circle to Longstone.
Az. (from 25" Ordnance Map). N. 66° 38´
E.
Elevation of horizon (measured) 2° 10.´
Reference to the MaySuncurve, given on
p. 263,
indicates that this is probably an
alignment to the sunrise on May morning.
Therefore, in determining the zenith
distance, the correction for the sun's
semidiameter (16´) must be taken into
account, allowing that 2´ of the sun's
disc was above the horizon when the
observation was made.
Zenith Distance:—
Bessel's tables show that refraction, at
altitude 2° 10´, raises sun 17´. If 2´
of sun's limb is above horizon, sun's
centre is 14´ below.
∴ True zenith
distance of sun's centre=87° 50´ + 17´ +
14´ =88° 21´.
Declination:—
Having obtained the zenith distance, and
the azimuth, the latitude being known,
the N.P.D. (North Polar Distance) of the
sun may be found by the following
equations:—
(1)
tan θ = tan z. cos
A,
where θ is the
subsidiary angle which must be
determined for the purpose of
computation, z is the true zenith
distance, and A is the distance from the
North point.
(2)
1,
where Δ is the
N.P.D. of the celestial object, and c is
the colatitude (90°  lat.) of the place
of observation.
In the example taken this gives us—
Reference to the Nautical Almanac shows
that this is the sun's declination on
May 5 and August 9. We may therefore
conclude that the Longstone was erected
to mark the May sunrise, as seen from
the Tregeseal Circle.
Had we been dealing with a star, instead
of the sun, the only modification
necessary in the process of calculating
the declination would have been . to
omit the semidiameter correction of
14´.
Having obtained a declination, we must
refer to the curves given on
pp. 1156 in
order to see if, there is any star
which, fits it, and to find the date.
Take, for example, the
case of the apex of Cam Kenidjack, as
seen from the Tregeseal circle—
Az. = N. 12° 8´ E.; hill=4° 0.´ lat.=50°
8´.
This gives us a declination of 42° 33´
N., and a reference to the
stellardeclination curves (p.
1156) shows that Arcturus had that
declination in 2330 B.C. From the table
given on p. 117, we see that at that
epoch Arcturus acted as warningstar for
the August sun.
In cases where the elevation of the
horizon is 30´, or in preliminary
examinations, where it may be assumed as
30´, the refraction exactly
counterbalances the hill, and therefore
the true zenith distance at the moment
of starrise is 90°. Hence the N.P.D. of
the star may be found from the following
simple equation
(3)
cos Δ = cos A cos
λ
where Δ and A have
the same significance as before and
λ is the latitude
of the place of observation.

Footnotes
329:1 Demonstrations and Practical Work
in Astronomical Physics at the Royal:
College of Science, South Kensington.
Wyman and Sons, 1s.
331:1 cos (c  θ)
= cos  (c  θ).
