Page 76 PLANE AND GEODETIC SURVEYING - Clark Volume II

The method of observing at least three stars at equal altitudes can,
of cOtlrBe, be used with a good theodolite provided proper readings are
taken on the striding level and the appropriate correction made. When
transport is difficult, the question may arise whether it is worth while
carrying both a theodolite and an astrolabe or whether to carry one f
instrument or the other. The theodolite is an " all-purpose " instrument c
and a good one is capable of doing all that an astrolabe can do, and much 1
else besides. The astrolabe, however, has been specially designed for the 1
special work that it is intended to do, and it is light in weight. Its i
principal use would therefore appear to be on geographical and other
similar surveys where determinations of latitude and longitude only are
required and observations for azimuth and of horizontal and vertical
angles are not needed. The 45° astrolabe has now been adopted as a
standard instrument for use by the Royal Navy in ordinary hydro.
graphical work.

Roelofs Solar Prism. In ordinary solar observations with a theodolite it
is impossible to observe the sun's centre directly and, in order to com-
pensate for this, the observations are made to its upper or left hand limb
or both and then to its lower or right hand limb or both, as shown in Fig.
46, and the results meaned to give the values which an observation to the
centre would give. This means two observations to the one only that would
be required if it were possible to observe the sun's centre. In addition, in
each observation the image of the sun is not central on the diaphragm. As
the dark shades necessary to protect the eye are at the eyepiece end of the
telescope, the unshaded image received by the diaphragm will tend to
heat the latter and, owing to the image being off centre, this heating will
not be symmetrical and this may produce some distortion of the diaphragm
and cross hairs which, in turn, will produce small errors in the observations.
Roelof's solar prism attachment, which is made to fit in front of the
objective of the telescope, is designed to overcome these difficulties.
The makers claim that with this attachment pointings to the sun can be
made as accurately as can pointings to a star.

The attachment, Fig. 37, consists of a pair of small prisms mounted at
right angles to one another in a small tube hinged to the front of a collar
which fits over the objective end of the telescope to which it can be securely
clamped. A green filter is fitted in front of the tube and a grey filter at the
other end. These filters take the place of the dark shade for the eyepiece
of the ordinary theodolite and not only reduce the brightness of the image
received by the eye but also help to cut out the heating effect on the dia-
phragm, thus reducing the possibility of errors arising from uneven heating
of the latter.

FIELD ASTRONOMY-OBSERVATIONS 77

In one position of the tube one of the prisms is in front of the upper half
of the objective and the other in front of the right hand portion. The
positions of the prisms are then as shown in Fig. 38. The top left hand
quadrant of the lens will be covered by the first prism, the bottom right
hand quadrant by the second prism, the top right hand quadrant by both
prisms, and the bottom left hand quadrant will be covered by neither

FIG. 37. ROELOFS SOLAR PRISM FITTED TO A WILD GEODETIC THEODOLITE.
(By permiBsion of Messrs. Wild Heerbrugg LId.)

prism. The refracting angle of the prisms is 23', which is less than the
angle, roughly 32', subtended by the sun's diameter. When the sun is
viewed in the telescope, four circular images will be seen as shown in Fig.
39, and these images will overlap in pairs, the overlaps forming a bright
cross with curved arms formed by shallow segments of circles standing on
opposite sides of a common chord. At the centre of the cross is a dark
square, the size of which varies with the apparent size of the sun's disc
from 19" X 10" (in December) to 75" X 75" (in June). Mter the attach.
ment has been fitted to the telescope, the latter is brought by means of
the horizontal and vertical tangent screws so that the cross hairs appear
to intersect at the centre of the dark square and to bisect the arms of the
bright cross as shown in the diagram. The vertical and/or horizontal
circles and the altitude bubble are then read, and this gives one complete

78 PLANE AND GEODETIC SURVEYING 

observation, If azimuths are being observed, the tube containing the
filters and prisms can be swung on its hinge to one side to give a clear field
of view for pointing to the R.O, Also, if one observation is tal{en face
right, the attachment can be reversed through 180° about its longitudinal
axis for the face left observation.
In Fig, 38 if the lower left hand quadrant contains the unrefracted
image, the upper left hand quadrant will contain the image formed through

FIG. 38. FIG. 39.

the horizontal prism. Hence, as the angle of refraction is 23' the angular
distance between the centres of the two images will be 23' and the angular
distance from the centre of the unrefracted image to the cross hair will
be 11'30". But the elevation read on the vertical circle will be that which
corresponds to the image of the dark square, Consequently, the true
elevation of the sun in the case shown will be the reading on the vertical
circle less 11' 30", If the attachment is reversed through 180° about its
longitudinal axis the elevation required will be the reading on the vertical
circle plus 11' 30" .From this it follows that the correction is cancelled
out in the mean of a face right and face left observation when the attach-
ment is reversed for the second observation.

Similarly the vertical prism will deflect the image through 23' in the
direction of the horizontal hair and the angle between the centre of the
direct image and the vertical cross hair measured in the plane containing
the horizontal hair and the optical axis of the telescope will be 11' 30".
As the optical axis of the telescope is inclined to the horizontal by the
angle of elevation h, this plane is also inclined to the horizontal by the
angle h. Consequently, in order to reduce the angle to the horizontal
plane, the plane in which it is measured by the horizontal circle, it must be
multiplied by sec h,* Hence, the corrections to be applied to a single
observation for reduction to the sun's centre are:-

*This correction is exactly similar to the correction AZ = a sec h given on page
116 to reduce an observation to the right- or left-hand limb of the sun to an equivalent
observat.ion to the sun's centre, and it is derived in exactly the same way.

80 PLANE AND GEODETIC SURVEYING

latitude is set off on the vertical circle, tl;1e line of sight of the main sh<
telescope will lie in the plane of the celestial equator, and the polar axis for
in the earth's axis (Fig. 41), parallax being considered negligible. If the COI
solar telescope were parallel to the main telescope, rotation of the former ,
about the polar axis would cause its line of IniJ
Z sight to sweep out the plane of the celestial mlJ
equator. But if the solar telescope is turned cru
about its horizontal axis through an angle by
equal to the sun's declination for the time of ohl
observation, with an allowance for refraction, Bpi
H R the solar line of sight may be brought on to J
the Bun by turning the solar telescope about Me
the polar axiB. This can be done only when
the polar axis is pointing to the pole, BO that,
when the declination and co-Iatitude are set ~;~
N off, an observation for meridian consists in ,~, ,"
FIG. 41. turning the solar telescope about the polar
axis and the main telescope about the vertical
axis until the sun appears in the field of the former .When, on manipu-
lating the respective tangent screws, the sun is placed in the square of the
reticule of the solar telescope, the line of sight of the main telescope has
been placed in the meridian, and the hour-circle reads the time. In the
absence of a declination arc, the declination iB set off by first bringing
both telescopes into the same vertical plane by sighting any convenient
point with each, setting the corrected declination on the vertical circle
by depressing the main telescope for a north declination and elevating it
for a south declination in the northern hemisphere, and then bringing
the solar telescope horizontal by reference to its attached level.
Watches and Chronometers. The most precise portable timekeeper is the "
box chronometer as employed in observatories and on board ship and is ~j
so called because it is generally kept in a padded box. In field astronomy
it is used for primary longitude determinations and in other circum-
stances where it can be kept either stationary or on board a vessel. The
instrument is too delicate to maintain a uniform rate during transport by
land. The pocket chronometer is better adapted for land journeys, but
is liable to stoppage if subjected to shocks in travelling over rough country.
The most serviceable timekeeper for field use is that known as the half- I.,
chronometer watch. which with due care gives results of a suitable 8\\
accuracy for ordinary topographical and mapping work. A stop watch is ne.
frequently a convenient accessory for this class of work, especially when cal
no recorder is available. This is used to measure the very short time
interval between the time of an observation and the time read on the by
chronometer or watch, and can be obtained to read direct to 1/5th, l/lOth thl
and l/l00th of a second. The method of using a stop watch is described thl
on page 87.

Watches and chronometers can be regulated to keep mean or sidereal LJ
time. For observations in which G.M.T. is obtained from the radio time ap.
signals a mean time chronometer is the more convenient but when much thl
star work is involved it is useful to have also a watch or chronometer which goc
keeps sidereal time. In all cases, it is important that the seconds hand