stations in order to ensure identity of the
point observed. One observation on each
face of the instrument will be sufficient for
such points. Angles ranging from 15° to
150° give satisfactory results.

Computation of the Triangles.

46. The sides being small the triangles
    are treated exclusively as plane, and errors
    of observation are dispersed by equal distribution on the three angles. The system
    for computation of the triangles in extension, the elimination of errors in their
    sides and the subsequent process of protraction of the stations on the map are
    analogous to the methods detailed for major
    triangulation. The limit for errors in the
    sides as exhibited on closing with previously ascertained lengths is 4 links in
    100 chains. The scale of the map should
    be 40 chains to an inch, unless otherwise
    specially desired.

Topographical features to be truthfully depicted.

47. The delineation of topographical
    features furnishes a wide scope for the
    exercise of artistic talent. The master
    lines are—1st: The water courses, and 2nd:
    The leading mountain ranges. The junctions of principal streams and the most
    remarkable peaks ought to be accurately
    fixed by intersection from the stations, and
    the characteristic configurations of the
    ground whether in rounded and undulating
    or peaked and rugged hills, the general
    direction of the water courses, ridges, and
    spurs, the watersheds, bush and other
    natural features, after a careful study with
    the aid of a pocket compass, may become
    faithfully depicted on the map. It should
    be borne in mind that rude sketches from
    memory consisting of caterpillar like daubs
    for mountain ranges and spurs and vermicular lines for streams unlike nature
    and untruthful in existence only disfigure
    the map and render it incorrect, whereas
    drawings from nature with the relative
    distances of the features accurately delineated enhance to a high degree both the
    beauty and usefulness of the plan.

SURVEYING BY TRAVERSE.

The system of surveying by traverse explained.

48. After a sufficient number of Trigonometrical points have been fixed over a
    block of land undergoing survey, the delineation of its boundaries, streams, proposed road lines, and sectional subdivisions
    is to be operated upon by traversing, which
    is a system of measuring by a series of
    successive straight lines of various lengths
    and on dissimilar bearings, a circuitous
    route from any one point to another, however distant or placed with reference to each
    other. The sums of the meridian and perpendicular distances between the stations
    composing the traverse furnish data for the
    computation of the bearing and distance
    between the two points, and if these points
    are also trigonometrical stations of the
    survey it is obvious, if the work has been
    accurately performed, that the deduced
    bearing and distance from traverse should
    coincide with the trigonometrical values
    thereof. Again if when the traverse starts
    from a certain point, and after proceeding
    in a circuit it returns to this same point,
    then the sum of the distances gone north
    should be equal to that gone south, and
    the sums of the distances gone east and
    west should also be equal. Hence the traverse system furnishes an easy check for
    ascertaining the accuracy of the work, and
    thus practical limits to the errors committed may become assigned.

Degree of accuracy attainable by the traverse system of surveying.

49. Upon open and tolerably level
    country, where it is possible to obtain fair
    length of lines between the traverse stations, and where no great impediment to
    the horizontal lay of the chain is met with
    this system is susceptible of remarkable
    accuracy. The small unavoidable errors
    exhibited on computing the meridian and
    perpendicular distances ought not to exceed
    the limit of one link for every ten chains
    so traversed, and in the actual prosecution
    of such surveys they have proved not to
    exceed the one half of this amount. But
    over hilly and rough localities where the
    lines are necessarily short, and the horizontal measurement of a chain’s length
    over the ground may be said at best to be
    equivocal, this process entirely fails, and
    should therefore only be employed for obtaining the points of intersection of section
    corners, and the lengths of these important
    lines when there is evidence of the practicability of applying the system, or in the
    absence of all other available methods.

Rules for detecting errors in the bearings of the traverse lines, and for their elimination.

50. Euclid, Book I, Prop. xxxii, demonstrates that any rectilineal figure can be divided into as many triangles as the figure
    contains sides, and consequently that the
    sum of the interior angles, plus 360° is
    equal to twice as many right angles as the
    figure has sides. The application of this
    theorem furnishes a complete check upon
    the angular measurements of the traverse.
    Thus if the theodolite is set up at a Trigonometrical station, with the axis of the
    telescope pointing to another one, whilst
    the vernier reads the known bearing between these two points, the bearing of the
    first or any station visible of the traverse is
    obtained in terms of the Trigonometrical
    Meridian. Then when the instrument is
    removed to the station so observed and set
    back on the Trigonometrical Station with
    the vernier still on the same reading the