It is a little more accurate to find the altitude by taking the
complement of the observed zenith distance, if the vertical arc has
sufficient range. This is done by pointing first to Polaris when at
its highest (or lowest) point, reading the vertical arc, turning the
horizontal limb half way around, and the telescope over to get another
reading on the star, when the difference of the two readings will be the
_double_ zenith distance, and _half_ of this subtracted from 90° will be
the required altitude. The less the time intervening between these two
pointings, the more accurate the result will be.
Having now found the altitude, correct it for refraction by subtracting
from it the amount opposite the observed altitude, as given in the
refraction table, and the result will be the latitude. The observer must
now wait about six hours until the star is at its western elongation,
or may postpone further operations for some subsequent night. In the
meantime he will take from the azimuth table the amount given for his
date and latitude, now determined, and if his observation is to be made
on the western elongation, he may turn it off on his instrument, so
that when moved to zero, _after_ the observation, the telescope will be
brought into the meridian or turned to the right, and a stake set by
means of a lantern or plummet lamp.
[Illustration]
It is, of course, unnecessary to make this correction at the time of
observation, for the angle between any terrestrial object and the star
may be read and the correction for the azimuth of the star applied at
the surveyor's convenience. It is always well to check the accuracy of
the work by an observation upon the other elongation before putting in
permanent meridian marks, and care should be taken that they are not
placed near any local attractions. The meridian having been established,
the magnetic variation or declination may readily be found by setting
an instrument on the meridian and noting its bearing as given by the
needle. If, for example, it should be north 5° _east_, the variation is
west, because the north end of the needle is _west_ of the meridian, and
_vice versa_.
_Local time_ may also be readily found by observing the instant when the
sun's center[1] crosses the line, and correcting it for the equation of
time as given above--the result is the true or mean solar time. This,
compared with the clock, will show the error of the latter, and by
taking the difference between the local lime of this and any other
place, the difference of longitude is determined in hours, which can
readily be reduced to degrees by multiplying by fifteen, as 1 h. = 15°.
[Footnote 1: To obtain this time by observation, note the instant of
first contact of the sun's limb, and also of last contact of same, and
take the mean.]