56

limination of errors caused by false graduation on the limb of the Theodolite.

18. In order to diminish the effect caused
    by errors of graduation on the limb of the
    theodolite it is important that the bearings
    be read on the whole limb by successively
    shifting vernier A a certain number of degrees after every round of observations according to the number of repetitions required. Let a be the number of repetitions proposed, b the number of verniers,
    and x the shift of vernier A in degrees,

then x = 360/ab. Four repetitions will
generally be found sufficient, and as there
are two verniers to the 8 inch theodolite by

formula x = 360/4 x 2 = 45° or the
number of degrees vernier A has to be
shifted after every complete round of observations. If an Everest Theodolite having
three verniers be used, and the same number of repetitions be required, then the
shift on the limb would be 30°.

.Errors arising from dislevelment and want
of collimation.

19. The theodolite is further liable to
    errors arising from dislevelment, and from
    want of correct collimation. However
    carefully the mechanical adjustments for
    these errors may be performed they can
    never be made perfect, and are constantly
    liable to disarrangement. But by simply
    reversing the instrument in altitude and
    azimuth the whole of the above errors become destroyed. Therefore observations
    cannot be considered satisfactory unless
    this system of reversion is attended to,
    taking care that the number of observations
    are equal upon each reversion of the instrument.

Errors arising from false centring.

20. There is still another source of error
    arising from the centre of rotation of the
    instrument not being a fixed point. The
    reading off of all the verniers at every observation cancels this effect.

Method of observing Bearings.

21. The instrument being firmly fixed
    over the centre of the station and carefully
    levelled is to be set with vernier A nearly
    ou the back reading of a station from which
    observations have already been made, and
    the cross wire of the telescope brought to
    bisect exactly the signal of that station.
    Then unclamp and slowly move the instrument in azimuth from left to right until it
    points nearly to the next station in order
    for observation, clamp, bisect, and read off
    as before. In this manner observe and
    read successively each station round the
    circle, until the station first set upon is
    read again, and record its return readings.
    Should these not differ materially from the
    former readings it is a proof that the instru-

ment has not shifted in position during
the round of observations which may now
be considered as one set.

Second set of bearings.

22. Next set the instrument with vernier
    A 45° in excess of the given bearing of
    the back station referred to before, unclamp the lower plate, and turn the whole
    body of the instrument round from right
    to left until the cross wire bisects the said
    station. Then proceed to re-observe every
    station as before directed. This will give
    a second set of observations on the same
    face of the instrument.

Third set of bearings. Face reversed.

23. Now turn the instrument completely
    round in altitude, shift vernier A 45° further on the horizontal limb, then unclamp
    the lower plate, and turn the body of the
    instrument round in azimuth until the
    cross wire again bisects the reference station; the instrument by so doing will become completely reversed; the face of the
    vertical circle if before on the right hand
    side will now be found on the left of the
    observer. Re-observe all the stations for a
    third set of bearings to be termed “face
    reversed.”

Fourth set of bearings. Face reversed.

24. Lastly shift vernier A still further
    45° on the horizontal limb, and observe a
    fourth set of bearings also “face reversed.”

Arithmetical means of the bearings to be
taken.

25. By attending to the above directions
    four separate observations, taken equally
    upon both faces of the instrument, and
    comprising eight readings (since there are
    two verniers) are obtained for each station,
    and the arithmetical mean of the readings
    is to be taken as the mean bearing, with
    every chance of its being within a very few
    seconds of the truth, providing that the
    levelling of the instrument has been attended to, and the observations carefully
    taken. (See appendix for form of field
    book.)

Vertical Angles.

26. Vertical angles are to be observed to
    all principal stations upon both faces of the
    instrument; the mean readings will furnish the true angles of elevation or depression. The height of the instrument above
    the ground at the time of observing, and
    also of that part of the object observed to,
    should be recorded in the field book.

Base of Verification.

27. Similar observations are to be taken
    at every station until the base of verification is arrived at. This second base line