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straight line drawn between any two opposite
corners of a road bisects the angle included
between the stages at those points,
and consequently the bearing of this line
is known. Again the distance between the
opposite corners is readily obtained by inspection from a Table of Natural Tangents
and Secants, being equal to the cosecant of
half the included angle above alluded to;
also the difference in length between the
opposite sides of the road to these points is
equal to the cotangent of the same angle.
For example: suppose the stages of a road
100 links wide run in directions bearing
26° and 155° then the included angle is
130° and the bearing from corner to corner
opposite is 90°. Now, by reference to a
Table, the Natural Cosecant and Cotangent of 65° or one half the included angle
to Radius 100 is 110.3 lks. and 46.6 lks.
respectively, the first indicating the distance
between the opposite corners and the second
what one side of the road is longer than the
other to these points. By successive computations for every angle that the road
makes the total lengths of the opposite sides
for every stage becomes known, which is
very important where sections front upon
tortuous road lines. The opposite corners
of cross roads are determined in the same
manner. Notwithstanding the very simple
manner by which these dimensions for
opposite sides of roads are obtained, they
have frequently been stated in impossible
quantities on the Maps, thus betokening on
the part of the Surveyor either a wilful
neglect or a gross ignorance of the first
principles of Geometry.

Computing Book.

70. The computations of a survey are to
    be kept in a book for the purpose and to
    accompany the plan when forwarded to the
    office of the Chief Surveyor. The writing
    of the figures must be clear and the statements methodically arranged so as to exclude all doubt in the mind of a second
    person who may have to recompute the
    work; besides neatness and order materially conduce to the accurate and expeditious
    working of any elaborate calculations.

Difficulties met with in a Survey and not
provided for in these instructions to be
dealt with by the Surveyor or by reference to Chief Surveyor.

71. As it is utterly impossible by written
    instructions alone to impart to the
    Surveyor a thorough knowledge of the
    various and often complex duties required
    to be performed or to provide for all contingencies that arise in the progress of
    actual operations, much must necessarily
    be left to his intelligence and discretion,
    and when difficulties are encountered which
    he is unable to overcome an immediate
    report detailing the circumstances should
    be made to the Chief Surveyor.

Concluding Remarks.

72. Lastly the Surveyor should endeavor
    by a careful study of the Standard works
    on Surveying to make himself thoroughly
    acquainted with not only the minor but
    also the higher branches of the profession
    and this combined with industry and zeal
    in the performance of his public duties
    will acquire for him a high professional
    reputation and the respect of his employers.

GENERAL MEMORANDA.

Returns and Vouchers.

The following Returns and Vouchers are
to be forwarded to the Survey Office by
each officer of the Staff.

Monthly: Abstract of laborers’ wages;
voucher for contingent expenses; journal
of work; report on the general progress of
the Survey.

Quarterly: Vouchers for field and instrument allowances.

Annual: Return specifying the nature
and quantity of work performed by the
Surveyor in each District or Block, and the
cost of the separate surveys.

Hours for Work.

The hours for work, whilst in the field
are from 8 a.m. to 5 p.m. during summer
months, and from 8.30 a.m. to 4 p.m.
during winter.

Trigonometrical stations to be repaired when
requisite.

The trigonometrical stations and other
important survey marks when visited by a
Surveyor should be repaired if found to be
out of order.

Surveyors to supply themselves with books
and instruments.

The Trigonometrical Surveyor is to provide himself with a five or six inch transit
or Everest theodolite, Galbraith’s Treatise
on Trigonometrical Surveying and Levelling; Shortrede’s Tables of Sines and
Tangents, Hutton’s Logarithms, and a
complete set of plotting instruments; and
the Sectional Surveyor with a four or five
inch Theodolite, a modern treatise on surveying, Hutton’s or Chambers’ Logarithms
and a complete set of plotting instruments.

HENRY JACKSON,
Chief Surveyor.