The transference of the measurements determined by the survey from the
field-book to the paper is termed _plotting_. The operations of plotting
are very simple, and the ability to perform them properly may be
acquired with a little practice. But their due performance demands the
same extreme care and attention as that of the operations in the field,
for it is obvious that the precautions taken to ensure accuracy in the
latter may be rendered nugatory by inaccurate plotting. The angular
instrument used in plotting is the protractor, and to ensure correct
results this instrument must be accurately divided. When, however, the
survey has been made without the aid of an angular instrument, the
protractor is not required in laying down the results. In such a case,
which frequently occurs in surveys of small extent, the lines, having
all been chained and registered in the field-book, are laid down
directly from the scale by means of an ordinary straight-edge and a pair
of compasses. The several methods of plotting and the various operations
involved have now to be considered.
_Reference Lines and Points._--The lines chained over in a survey and
recorded in the field-book are not usually the actual lines existing on
the ground, but imaginary straight lines chosen for the purpose of
referring other lines and points to them. They are, therefore,
appropriately termed _reference lines_, and all points situate in them
to which other lines are referred, in other words, all points in a
reference line in which other reference lines intersect it, are termed
_reference points_. Reference lines are generally made to form triangles
for facility of computation, and these triangles enclose the area to be
surveyed. But to determine the details included within them, it is
necessary to form other and smaller triangles within the larger ones
first laid down. The latter are, therefore, distinguished as Primary and
the former as Secondary triangles, and the lines of which they are
composed are called primary and secondary reference lines.
_Plotted Points._--In laying down a line of definite length upon paper,
the positions of its extremities are determined and marked by pencil
dots; such dots, or rather the points indicated by such dots, are termed
_plotted points_. The line is drawn by joining the plotted points.
_To Plot Reference Lines and Points._--To plot a reference line of a
given length when the position of neither of its extremities is given, a
light dot must be made upon the paper in a convenient part to indicate
the position of one extremity. The pencil-point mark should be as light
and well defined as possible, and hence it is essential that the pencil
used should be hard, and always kept pared to a fine conical point. The
scale must then be applied, in the direction of the line to be drawn,
with its zero point coincident with the plotted point. The scale should
be lightly but firmly held in this position with the left hand. The
distance of the other extremity of the line must then be found upon the
scale, and the eye placed directly over the line of the graduation; this
is necessary to the correct placing of the point, and it is well to
train the eye to trace accurately the prolongation of the line of
graduation upon the paper. A dot must be placed in the prolongation of
this line and close to the edge of the scale, to mark the position of
the other extremity. The reference line is then to be drawn between
these two plotted points with a sharp chisel-pointed pencil. Reference
lines, like reference points, should be well defined, but drawn as fine
and light as possible. The degree of fineness and lightness should be
such that when the detail is finely but firmly outlined, the reference
lines and points may not be visible, except on a close inspection of the
surface.
To plot secondary reference lines, as, for example, a number of offset
lines, apply the scale so that its edge may be parallel to and almost
over the pencil trace of the primary line and its zero point coincident
with the point at which the line begins. Care must always be taken to
place the zero of the scale at the beginning of the line, and not at the
end of it. At the distances recorded in the field-book as those at which
the offsets were taken, plot upon the line, in the manner described
above, the points indicating the extremities of the offset lines. All
other points, such as stations and intersection of fences, roads, and
streams, should be plotted at the same time. Around all stations, a
light, hand-drawn circle should be placed, and intersections marked by
small cross lines. This being done, place the offset scale so that the
zero may coincide with the plotted point in the reference line and the
edge be perpendicular to the line. To bring the edge into this position,
the end of the scale should be placed parallel to the reference line;
this is, of course, assuming the scale to be perfectly rectangular, as
it ought to be. The other extremities of the lines may then be plotted
in the same manner as those of the primary lines.
To illustrate the foregoing remarks, let it be required to plot the
following portion of a field-book.
+------+
{| 00 | 1346 | or 000 Line 1.
{| 75 | 1170 |
{| 96 | 1000 |
{| 105 | 650 |
{| 66 | 400 |
{| 00 | 000 |
+------+
Line 3. From | 1946 | last.
+------+
| ↰ |
+------+
| 1946 | 00 |}
| 1420 | 88 |}
| 1200 | 144 |}
| 1000 | 110 |}
| 600 | 75 |}
| 520 | 50 |}
| 000 | 00 |}
+------+
Line 2. From | 2504 | last.
+------+
| ↙↑ |
+------+
| 2504 | 00 |}
| 2000 | 65 |}
| 1790 | 95 |}
| 1610 | 115 |}
| 1440 | 87 |}
| 1220 | 110 |}
| 1000 | |}
| 850 | 28 |}
| 420 | 100 |}
Line 1. | 000 | 00 or 1346
| | Line 3.
+------+
Begin at south corner and range N.
Having laid down in a convenient part of the paper the beginning of Line
1, place the edge of the scale so that the zero may coincide with the
plotted point and the edge be parallel to one of the meridians. Holding
the scale firmly in this position, plot the distance 2504 links, and
join the plotted points. Then, without removing the scale, plot upon
this reference line the distances at which the secondary or offset lines
were taken, that is at 420, 850, 1220, 1440, 1610, 1790, and 2000 links.
In this case we have nothing but offsets; had there been stations or
intersections of fences, roads, or streams, these would have had to be
plotted at the same time, and distinguished by an appropriate mark. Line
2 begins at the end of Line 1, and returns on the left at an acute
angle, as indicated by the arrow in the field-book. But as the magnitude
of this angle is not known, the survey having been taken with the chain
alone, the exact direction of Line 2 must be ascertained in the
following manner. Take the length of the line in the compasses, and with
this distance as a radius, strike an arc from the end of Line 1. Also
with the length of Line 3 as a radius, strike an arc from the beginning
of Line 1, at which point Line 3 closes, intersecting the former. The
point of intersection will be the end of Line 2. Join this point to the
end of Line 1, and plot the offset reference points upon this line in
the manner already described for Line 1. Line 3 begins at the end of
Line 2, and terminates at the beginning of Line 1; hence both
extremities being determined, we have only to join these points, and to
plot the offset reference points as before. Had a split line been taken
for the sake of accuracy from the angle A C B to the base Line 1, the
intersection of this line should have been plotted upon Line 1, and the
position of the end of Line 2 found by striking an arc from this point
also with a radius equal to the length of the split line. If the
distances have been correctly measured in the field and correctly taken
from the scale, the three arcs will intersect at the same point. If they
do not so intersect, the error must be noted in an error-sheet, and
corrected in the field before proceeding further. It may be remarked
here that on account of the irregularities of the surface chained over,
all measured lines are liable to be recorded a little too long. One link
in ten chains may be allowed for this source of error. Assuming,
however, that the primary reference lines “close” properly, the offset
lines may be plotted in the manner already described, and the detail or
boundary lines drawn in, which in the present instance are hedges. Fig.
82 shows the survey as laid down in the foregoing notes.
When the survey has been made with the aid of an angular instrument, the
method of plotting the primary reference lines differs somewhat from the
foregoing. In this case, the paper should be first covered with a number
of parallel straight lines ruled about an inch and a half apart to
represent magnetic meridians. The first station may then be marked upon
one of these meridians in a convenient part of the paper. To lay down
the first reference line, apply the protractor to this meridian with its
centre point coincident with the plotted point, and from the bearing
recorded in the field-book, lay off the given angle. Join the two
plotted points and produce the line indefinitely; and upon this line lay
off a distance equal to the length of the measured line. The second
reference line must be drawn in the same manner, from the end of the
first, by laying off from that point the recorded angle. But as the end
of the first line will probably not fall upon a meridian, the protractor
will have to be moved up to the point by means of a parallel ruler
adjusted to the nearest meridian. A more convenient and a more accurate
method, however, is to make the left of the drawing represent the north
while plotting, and to use the [T]-square instead of the parallel ruler.
All subsequent lines are plotted in the same way. Instead of covering
the paper with meridians before commencing to plot, it may, in some
cases, be found more convenient to draw with the set and [T] squares a
short meridian through the point as required.
[Illustration: FIG. 82.]
To lay down Fig. 82 in this manner, having fixed the first station A,
the length of the first primary reference line A B may be laid off upon
the meridian, because in this case the bearing being due north, the
reference line will be coincident with the meridian. This done, the
protractor is to be placed over the plotted point B and the second
bearing laid down. Having plotted the length of this line in the point
C, the third reference line C A will be determined both in length and
direction by the plotted points C A, which should be joined and the line
measured to ascertain whether its length corresponds with the measured
distance. If these do not correspond, the angle must be replotted and
the lengths laid off anew to discover the source of the error. Assuming,
however, that the lines close properly, the offsets and other secondary
points may be next plotted in the manner previously described.
Angles may be more accurately laid down by means of a table of _natural
sines_ and _cosines_ and a linear scale than by means of a protractor.
This is especially true when the angles are subtended by long lines, as,
for example, lines of 3, 4, and even 6 feet. In such cases, a protractor
is of little use. This mode of laying down angles is also convenient in
some cases where angles have been taken, but some of the sides not
measured. In using the table, it must be remembered that the radius of
the sines and cosines is taken as unity; therefore, to find the sine and
cosine for any other radius, the sine and cosine in the tables must be
multiplied by that radius. To lay down the angle A B C in Fig. 82, the
reduced cosine of the angle should be plotted from B in the point _a_,
according to some scale. The scale length of the reduced sine should
then be scribed from _a_, and the scale length of the radius scribed
from B. A line drawn from B through the point of intersection of the
scribes will lay down the angle corresponding to the sine and cosine in
the table. Suppose the radius chosen to be 5 chains, the angle being 32°
30′. The cosine of 32° 30′ is ·8434, which multiplied by 5, the assumed
radius, = 4·2170. Lay off this distance from B on the base A B. The sine
of 32° 30′ is ·5373, which multiplied by 5, = 2·6865. From the point
_a_, which is distant 4·2170 chains from B, with a radius equal to
2·6865 chains, describe an arc; and from the point B, with a radius
equal to 5 chains, describe another arc. From B draw a line through the
intersection of these arcs, and lay off upon it the measured length of
1946 links as recorded in the field-book.
If only the length of the base A B and the magnitudes of the angles
A B C and B A C were given, the lengths of the sides B C and A C would
have to be calculated by trigonometrical formulæ. This method of
calculating the lengths of the sides of triangles and plotting them with
the beam compasses, like chained triangles, is the most accurate for
laying down the great or primary triangles of a survey.
When it is required to plot according to this principle a solitary
angle, as, for example, that between a station line and the meridian, a
circle should be drawn with as large a radius as practicable round the
station at which the angle is to be laid down. The distance between the
points at which the two lines enclosing the angle cut that circle is
then found by multiplying the radius by the _chord_ of the angle, that
is, by twice the sine of half the angle.
It sometimes happens, particularly in extensive surveys, that all the
angular points of some triangles cannot be plotted upon the same sheet
of paper. In such cases, the plot of the outlying points and the sides
of the triangles may be laid down in the following manner. Plot the
intersected triangles independently and trace them on tracing paper.
Then, having drawn a fine line upon both sheets to represent the sheet
edge, lay the points on the trace corresponding to those already plotted
on the first sheet down upon, and make them to coincide with, the
latter. Secure the trace in this position and trace the sheet edge line
upon it. The intersected lines may now be plotted on the fair sheet with
a pricker at points outside the sheet edge line. Next apply the trace to
the second sheet and make the sheet edge lines coincide. Having secured
the trace in this position, the points and the intersected lines on this
second sheet may be plotted upon the fair paper by means of the pricker.
_To Plot Traverse Reference Lines._--In plotting a traverse survey in
which the angles have been measured from a fixed line of direction, the
magnetic meridian, the direction of the lines may be all laid down at
the first angular point. An example will best show the method employed
in this case. It is required to lay down the traverse shown in Fig. 83.
[Illustration: FIG. 83.]
In a convenient part of the paper draw the straight line N S to
represent the magnetic meridian, and plot upon it the first station A.
Set the protractor with its centre accurately placed over this point and
its 360th and 180th divisions coinciding with the meridian. Holding the
instrument securely in this position, lay off around it all the bearings
as entered in the field-book, numbering them in the order in which they
were taken. Against each of these numbers it is well to place the page
of the field-book on which the measurement of the angle and the survey
of the line are entered. The plotting must now be commenced by laying
down the first line through the first bearing and determining its
length from the recorded measurements. The direction of the second line
has next to be transferred from the first station A to the extremity of
the first line, or the second station B. This is accomplished by means
of the parallel ruler, by placing the edge of the ruler through the
plotted point and the point marked as bearing 2, and extending it till
the same edge intersects the point B. A line is then to be drawn from
this point and its length laid off from the field-book as before. The
direction of the third line will then be transferred from the first
angular point to the end of the second line, or station C, in the same
manner. This will be continued for all the lines in the traverse, and if
all the measurements have been correctly laid down, not only will the
last line pass through the point A, but it will be of the same length as
the chained line. Also the bearings taken from A to E and H will pass
through these latter stations. These proof line bearings should be laid
down at the same time as the reference line bearings, from which they
should be distinguished by some sign. The directions of the reference
lines should be consecutively transferred, and the length of each line
should be plotted in its proper place before the direction of the next
is transferred. To ensure the work closing properly, great care must be
taken to plot the points accurately and to draw the pencil lines fine.
[Illustration: FIG. 84.]
The degree of accuracy to be attained will depend in a great measure
upon the extent of the traverse. With long lines the difficulties
increase, and with a great number of angles the chances of error are
multiplied. If the angles are carefully taken, it is probable that
seconds have been read off in several instances, and these if neglected,
especially upon long chain lines, may lead to an error of some
importance. Also when the lines are long, the parallel ruler becomes
practically useless, and some other system has to be adopted. One way of
overcoming these difficulties is to draw a parallel to the first
meridian through every third or fourth angle; in such a case, great care
must be observed in drawing the parallels. A more easily practicable
method, however, is to use the [T]-square in the manner already
described. If the left-hand edge of the drawing board be made the north,
the blade will determine meridional lines, and by laying the straight
side of a semicircular protractor against the edge of the blade, its
zero will be adjusted to the fixed line of direction. The first bearing
having been laid down, the line is drawn and made the scale length of
the chain line; the blade of the square is then pushed to the station
thus found, and the next bearing set off. This operation is repeated
until all the lines have been laid down. If the work closes properly,
the plotting of the secondary lines may be proceeded with.
The most accurate method of plotting a traverse is by rectangular
co-ordinates, or, as it is usually termed, Northings, Southings,
Eastings, and Westings, because the position of each station is plotted
independently, and is not affected by the errors committed in plotting
previous stations. This method consists in assuming two fixed lines or
axes crossing each other at right angles at a fixed point, computing the
perpendicular distances or co-ordinates of each station from those two
axes, and plotting the position of each station by means of the [T] and
set squares and a linear scale. The meridian is usually made to
represent one of the axes, and in this case the co-ordinates parallel to
one axis will be the distances of the stations to the north or south of
the fixed point, and those parallel to the other axis will be their
distances to the east or west of the same point. Let N S, Fig. 84,
represent the meridian, and A B the first bearing taken, and the first
line measured. The angle in this case is N A B = θ. If θ is an acute
angle, the second station B is to the north of the first station A; if
it is an obtuse angle, B is to the south of A. If the angle θ lies to
the right of the meridian, B is to the east of A; if to the left, to the
west. Thus it will be seen that if the northernly and easternly
directions are considered positive, the southernly and westernly
directions will be negative. From the foregoing it is manifest that the
co-ordinates of B are as follows:--
Northing A _a_ = _b_ B (or if negative, southing) = A B × cos. θ.
Easting A _b_ = _a_ B (or if negative, westing) = A B × sin. θ.
To plot the point B, draw through the point A, with the aid of the
[T]-square, a horizontal line. Multiply the chained length of the line
A B by the sine of the angle N A B as entered in the field-book, and set
off this distance along the horizontal line. From the point thus
determined, erect, with the aid of the set square, a perpendicular,
which will be parallel to the meridian. Multiply the chained length of
A B by the cosine of the angle N A B, and set off this distance along
the perpendicular line. The point thus determined will be the position
of the second station B, which may then be joined to A by a straight
line.
[Illustration: FIG. 85.]
The mode of laying down the survey in Fig. 85 will now be obvious.
Having determined the position of the second station B in the manner
just described, draw a horizontal line through B and determine the third
station C in the same way. The fourth station D being to the left of the
meridian passing through C, _c d_ is a westing and is to be considered
as negative. Therefore the horizontal line through C must be drawn to
the left of that station, and the station D determined in the same
manner as the preceding stations.
The results of all these calculations should be entered in a book, in
four columns, for northings, southings, eastings and westings
respectively. Also in four other columns should be entered the total
northing or southing, and easting or westing, of each station from the
first station, computed by adding all the successive northings and
subtracting the southings made in traversing to the station, the result
being a northing if positive, and a southing if negative. The same
treatment is applied to the eastings and westings. This affords a means
of testing the accuracy of the work. It is also obvious that the
position of the last or any station may be determined by this means
without plotting the intermediate stations.
Let it be observed that both θ and sin. θ are positive or negative
according as that angle lies to the east or to the west of the meridian;
and that the cosines of obtuse angles are negative.
_To Plot Detail._--By “detail” is meant outlines or objects whether
natural or artificial, such as fences, walls, rivers, canals, roads,
lakes, water margins, beach marks, seas, or imaginary boundary lines. In
plotting from the entries of measurements for detail, these measurements
should be laid down upon the paper in the order and manner indicated in
the field-book. The mode of plotting the perpendicular reference lines
by means of which the position of the detail is fixed has already been
fully described and illustrated. The proper connections for detail, as
shown by the field-book, should be made by drawing a firm pencil line
through the detail points with the aid of an offset scale adjusted
successively to the adjacent points. All such connections should be
clearly and elegantly made. When all boundaries, roads, and streams have
been drawn and inked in, tracings should be taken in small portions of
all that has been laid down for the use of the “examiner.” The duties of
the examiner are to make on the ground the necessary corrections for
omissions and detail in error; to give, in position and character,
woods, water, marsh, commons, vegetable and geological features, and
permanent artificial structures; and to furnish the descriptive names of
places and things, or any other desirable information. The topographical
character of mountains, marshes, bogs, rough pasture, woods and water,
should be drawn in character on trace and tinted. If required, hill
sketching should also be supplied on the examiner’s trace. On being
returned to the office, the plotter should replot from the field notes
the detail corrected, and transfer the details from the trace to the
map.
_To Plot Contours._--The student who has made himself familiar with the
methods of laying down angles, and plotting reference lines and points,
will find no difficulty in laying down contour traces. When the contour
points have been surveyed with the chain, the contour is obtained by
drawing a free line of feature through the plotted points. But when the
contour points have been surveyed by measuring magnetic angles to known
points, such angles must be laid down at these points, and produced to
meet in the contour point. The drawing of contours differs from the
drawing of ordinary detail insomuch as each contour point is shown by a
small dot, and each carrying point by a similar dot surrounded by a
small hand-drawn circle to distinguish it. The former should be so
plotted as to be distinguishable in the trace or contour line, which
should be readily traceable, but not conspicuous. The line joining
adjacent points should be true lines of feature. Colour is usually
employed for these lines, and it is well to give them a broken or
somewhat undefined character. When the French system is adopted, contour
lines are drawn continuous, a broad but faint line of colour.
_To Plot Sounded Points in Submerged Districts._--When the angles have
been measured on dry land with the theodolite, these angles should be
laid down at the dry-land points, and the lines produced to meet in the
sounded point. But when the angles have been measured on the water with
a sextant, a station pointer is required. The arcs of the pointer should
be adjusted to read the measured angles, and the instrument applied to
the plotted points of the observed objects so as to bring the hair lines
accurately to their respective object points. The sounded point may then
be correctly plotted through the centre of the pointer. If the angles
have been measured by the magnetic compass, that is, if the angles are
those made with the magnetic meridian, the angles should be laid down at
the plotted points of the observed land objects, and the lines produced
to meet in the sounded point. Instead of the station pointer, a piece of
tracing paper may be used in the following manner. Draw three straight
lines radiating from one point so as to make with each other angles
equal to the measured angles. Lay the paper on the plan and move it
about till the three lines traverse the observed objects. The point from
which they diverge will then mark the position of the sounded point,
which may be plotted by being pricked off.
The sounded point determined by angles measured with the sextant may
also be plotted by describing circles on the land-object lines as
chords, to contain segmental angles equal to the measured angles. Such
circles will intersect in the common land-object point and the sounded
point. To plot the sounded point in this manner, requires the solution
by construction of the problem, “to describe on a given line a segment
of a circle that shall contain a given angle.” But this method is
generally found too tedious in practice.
_Errors and Error-sheets._--There is a tendency, as we have previously
remarked, for the measured lengths of lines to be a little too long, by
reason of the irregularities of the surface. It is usual to allow for
this source of error 1 in 1000 in fair open country, and 1¹⁄₂ in 1000 in
close country. When the measurements differ by an amount exceeding these
limits, the pencil trace should not be drawn between the reference
points, but the line should be entered on an “office error-sheet.” The
error-sheet should show the number of the plot-sheet, the triangle, the
book and page in which the measurements are entered, and the scale and
measured lengths of the line. To ascertain the source of the error,
other lines referenced to the reference point or points of the line in
error should be plotted, and the apparent source should be entered on
the error-sheet. If the lines referred to the same point be found to
plot to another point in the reference line, the scale measurement of
this point should also be entered. And if the reference point in error
be not directly surveyed in the survey of their respective lines, the
measurements for reference and the arithmetical reductions will have to
be examined. Besides the office error-sheet, there should be a field
error-sheet for each book and triangle, upon which should be entered the
book, the page, and the line in error, and some indication of the source
of the error. This sheet will be forwarded with the field-book to the
surveyor for correction. The following are examples of a common and very
good form of error-sheet, but it may be varied in many ways if thought
desirable:--
OFFICE ERROR-SHEET.
_Plotter’s Name_____________ _Date_ ____________
-----+------+--------+---------+--------+----------+------------------
Book.|Lines.| Scale |Reference|Apparent|Triangles.| Observations.
-----+ |Measure-| Points | Correc-| |
Page.| | ment. |of Lines.| tions. | |
-----+------+--------+----+----+--------+----------+------------------
200 | | |1118|1551| 1651 | |Examine reference
-----+ 1953 | 1907 +----+----+--------+ |point and line.
23 | | |2094|4020| 4020 | |
| | | | | | |
200 | | |2814|1308| | [Illus- |
-----+ 3000 | 3056 +----+----| 3056 | tra- |Examine line.
28 | | |4020|3082| | tion] |
| | | | | | |
200 | | |1551| 85 | 1651 | |Examine reference
-----+ 1314 | 1323 +----+----+--------+ |point and line.
42 | | |4020|3028| 4020 | |
-----+------+--------+----+----+--------+----------+------------------
FIELD ERROR-SHEET.
_To A. B., Surveyor._ _Date_ ____________
-----+------+----------+----------------------------------------------
Book.|Lines.|Triangles.| Observations.
-----+ | |
Page.| | |
-----+------+----------+----------------------------------------------
| | |_Examine reference points and line._
200 | | |1651
-----+ 1953 | |---- Reference point (August 10th, 1874).
23 | | |4020
| | |
200 | | [Illus- |
-----+ 3000 | tra- |_Examine line._ Line 3056 (August 10th, 1874).
28 | | tion] |
| | |_Examine reference points and line._
200 | | |1651
-----+ 1314 | |---- (August 12th, 1874).
42 | | |4020
| | | Corrected in the field, A. B.
-----+------+----------+----------------------------------------------
_To Plot Vertical Sections._--In plotting a vertical section, a fine and
firm horizontal line is first drawn to represent the _datum line_. The
reference points are then plotted upon this line from the level-book by
means of a linear scale, in the manner already described for plotting
such points. The reference points to be plotted upon the datum line are
the chain lengths entered in the field-book in the column headed
Distances. These distances are the points at which the levels were
taken, and between them, unless otherwise stated in the field-book, the
ground is supposed to slope uniformly. Moreover, these distances are
assumed to be measured horizontally, and therefore care must be taken to
ascertain whether or not they were so measured in the field; if not,
they must be reduced before plotting, or the section will be too long.
Having plotted the reference points on the datum line, a perpendicular
must be erected from each of them, and a length laid off upon this
perpendicular equal to the vertical height above the datum line
indicated by the entry in the column of the level-book headed Reduced
Levels against the distance to which the perpendicular corresponds. To
render the differences of altitude more apparent, these vertical
distances are plotted to a much larger scale than the horizontal, as
explained in a preceding Section. To erect the perpendiculars, the [T]
and set square furnish the most convenient means. The detail points thus
determined upon the perpendiculars represent the points in the surface
of the ground at which the levels were taken, and by joining these
points we obtain the surface line. An example will clearly show the
method pursued. Let it be required to lay down the section from the
following level-book:--
-------+-------+-----+-----+-------+-------+-------------------------
Back | Fore |Rise.|Fall.|Reduced| Dis- | Remarks.
Sights.|Sights.| | |Levels.|tances.|
-------+-------+-----+-----+-------+-------+-------------------------
feet. | feet. |feet.|feet.| feet. |chains.|
| | | | 100·00| .. |{B.M. north-west corner
| | | | | |{of church tower.
16·41| 9·37| 7·04| .. | 107·04| 230 |
19·36| 10·43| 8·93| .. | 115·97| 465 |
16·42| 19·36| .. | 2·94| 113·03| 640 |
8·36| 14·36| .. | 6·00| 107·03| 794 |
9·37| 12·49| .. | 3·12| 103·91| 1030 |
11·64| 19·76| .. | 8·12| 95·79| 1200 |
19·46| 9·32|10·14| .. | 105·93| 1564 |
17·64| 13·62| 4·02| .. | 109·95| .. |{Centre of road at 123
| | | | | |{links.
18·76| 12·64| 6·12| .. | 116·07| 1823 |
19·84| 16·92| 2·92| .. | 118·99| 1964 |
19·76| 11·64| 8·12| .. | 127·11| 2100 |{Forward station ☉ at
| | | | | |{corner of wood.
17·64| 19·72| .. | 2·08| 125·03| 2250 |
9·73| 18·64| .. | 8·91| 116·12| 2376 |
8·64| 17·64| .. | 9·00| 107·12| 2590 |
18·76| 16·24| 2·52| .. | 109·64| 2700 |
-------+-------+-----+-----+ | |
231·79| 222·15|49·81|40·17| | |
222·15| |40·17| | 100·00| |
-------+ +-----+ +-------+ |
| | | | |{Difference between datum and
9·64| | 9·64| | 9·64|{last reduced level, or height of
| | | | |{B above A.
-------+-------+-----+-----+-------+---------------------------------
[Illustration: FIG. 86.]
Draw the datum line D L, Fig. 86, and set off along it the distances
230, 465, 640, 794, &c., links; these points will be the reference
points for the perpendiculars. Erect a perpendicular from each of these
points, and lay off, to a suitable scale, upon these lines successively
the vertical heights 100, 107·04, 115·97, 113·03, 107·03, &c. The points
thus determined will be the surface detail points, and by joining these
we shall obtain the surface line. Then will A D L B represent a section
of the ground between A and B. A description of objects on the surface
worthy of notice should be written over such objects.
In working sections, where great accuracy is required, larger scales are
employed, and the levels are taken at more frequent intervals. Thus, in
a railway working section, for example, the levels are taken at every
chain’s length, and also over every little undulation in the surface of
the ground. In preparing such sections, vertical lines are drawn in blue
at every chain’s length up to the surface of the ground from the datum
line, and on each vertical is written the reduced height above datum
from the column of reduced levels in the level-book.
Sections, especially working sections, are usually drawn upon ruled, or,
as it is called, “section” paper, the nature of which we have already
described. This method, which was introduced by Mr. Brunel, possesses
many practical advantages, inasmuch as it obviates the necessity of
plotting the “distances” and erecting perpendiculars, the latter already
existing. It also greatly facilitates the computation of the contents of
a given section. Its chief defect lies in the difficulty of making the
horizontal lines coincide when joining the sheets end to end. Of course
scales are not required upon section paper.
_To lay down Gradients._--The method of laying down the gradients of
railways and roads usually adopted in practice consists in applying one
end of an extended silken thread to the section at the point in which
the road commences, and the other end in such a position that the thread
may cut the profile of the earth’s surface so as to leave equal portions
of space above and below the thread, as nearly as can be judged by the
eye. The cuttings from the parts above the thread will then furnish
sufficient materials to form the embankments in the spaces below. This
is called “balancing” the cuttings and embankments. When the first
gradient has been determined in this way, it may be found unfavourable
to the second in respect to the extent of cuttings and embankments; in
such a case it must be modified to suit the requirements of the latter.
In this way the gradients must be modified successively until the
compound result evidently gives a _minimum_ of cuttings and embankments,
due regard, of course, being had to the limits imposed by the nature of
the case, both with respect to the ruling gradient and the proper
heights for bridges.
_To Plot a Section from a Contour Map._--The mode of plotting a section
from a contoured plan was explained when treating of contour lines. The
contour map used for this purpose should give the features of the
surface configuration in sufficient detail without serious error. Having
drawn a line of section on the map and a datum line upon the fair paper
for the vertical section, the points in which the section line
intersects the contours should be measured on the scale of the map from
a zero point in that line, and the measurements plotted upon the datum
line. Perpendiculars should then be drawn through these plotted points,
and on these perpendiculars the reduced altitudes of their respective
contour points should be plotted. A line drawn through these surface
plotted points will be the surface line. When the horizontal scales of
the map and the section are the same, the contour plane lines may be
drawn on the paper for the section parallel to the section line on the
map, and perpendiculars raised to intersect them from the points on the
map in which the section line intersects the contours, in the manner
previously described. The points of intersection with the parallel lines
will be the surface contour points in the vertical section. For
practical purposes, the parallel lines and the perpendiculars are only
temporarily drawn in pencil until the surface trace shall have been
obtained and drawn in ink, with the datum line.