PRACTICAL SURVEYING AND
ELEMENTARY GEODESY
MACMILLAN AND CO., LIMITED
LONDON BOMBAY CALCUTTA
MELBOURNE
THE MACMILLAN COMPANY
NEW YORK BOSTON CHICAGO
DALLAS SAN FRANCISCO
THE MACMILLAN CO. OF CANADA, LTD,
TORONTO
PRACTICAL SURVEYING
AND ELEMENTARY GEODESY
INCLUDING
LAND SURVEYING, LEVELLING, CONTOURING, COMPASS
TRAVERSING, THEODOLITE WORK, TOWN SURVEYING,
ENGINEERING FIELD WORK AND SETTING OUT
RAILWAY CURVES
WITH NOTES ON PLANE TABLING, ASTRONOMICAL SURVEYING
AND HELIOGRAPHING
BY
HENRY ADAMS
LATE PROFESSOR OF ENGINEERING AT THE CITY OF LONDON COLLEGE
M.INST.C.E., M.I.MECH.E., F.S.I., F.S.E., F.R.SAN.I., M.S.A., ETC.
EXAMINER TO THE INSTITUTION OF MUNICIPAL ENGINEERS, THE SOCIETY OF
ENGINEERS, THE INSTITUTE OF SANITARY ENGINEERS, THE ROYAL
SANITARY INSTITUTE AND THE.SOCIETY OF ARCHITECTS
MACMILLAN AND CO., LIMITED
ST. MARTIN'S STREET, LONDON
19'S
"TA54S
COPYRIGHT
PREFACE.
AN endeavour has been made in this manual to present the
elements of practical land surveying in a form suitable for
students preparing for examinations in that subject held by
various educational and professional bodies, and also for private
workers. It is hoped and believed that the volume will be a
helpful guide to practical methods whether the intention of
the student is to undertake responsible work in the field, or
more particularly to qualify for an examination.
Many years' experience as a practical surveyor and teacher
of land surveying in all its branches has made the author
acquainted with the difficulties experienced by beginners ; and
although personal effort is necessary to master any subject,
progress is facilitated when principles and procedure are stated
precisely and concisely. This has been the aim in the pre-
paration of the present book. The course of work is so
graduated that the careful study of each chapter, together
with practical field work and the plotting of the accom-
panying surveys should enable the diligent student to become
qualified to undertake land surveying in a few months.
The questions at the ends of the chapters will serve as
exercises to test progress ; while those at the end of the
volume should be particularly useful to students preparing for
public examination in land surveying.
HENRY ADAMS.
60 QUEEN VICTORIA ST., E.G.
29092,3
CONTENTS.
CHAPTER I.
Scope of subject Definition of land surveying Geometry and men-
surationOrigin of the term geometry Distinction between
theoretical or pure geometry, and practical or applied geometry
Principles upon which land surveying is dependent Difference
between old system of surveying and modern systems Objects in
view in measuring land Distinction between office and field work
Six selected problems in practical geometry Table of linear
measures Table of square measures. 1
CHAPTER II.
Linear measurement British standard of length Units of measurement
Units adopted in measuring land Form of working in calculating
area Pointing off Rule for area of rectangular figure Example
Rule for area of triangular figure when base and perpendicular are
given Example Rule for area of triangular figure when sides only
are given Example Rule for area of four-sided figure, having two
sides parallel Example Irregular four-sided figure divided into
two triangles by a diagonal The same divided into two triangles
and a trapezoid Example Method of tabulating the working. 7
CHAPTER III.
Drawing to scale or plotting Description and use of chain scales-
Decimal system Base line of survey Direction Points of the
compass Direction of north obtained by a watch Magnetic
meridian Magnetic variation North point. 13
CHAPTER IV.
Measuring straight-lined figures Tie and check lines Rule for dis-
tance from angle Well-conditioned and ill-conditioned triangles
viii CONTENTS
Use of box tape Measurements put on sketch plan instead of in
field-book Testing tape for shrinkage Gunter's chain General
description of its use Tally points Entries in field-book Steel
tapes. 20
CHAPTER V.
Measurement of straight- sided fields Use of station poles How chain
lines and stations are indicated in field-book Conventional signs
Offsets, how measured and recorded Examples of offset pieces-
Plotting from field notes Drawing in the outlines. - - 26
CHAPTER VI.
Nature of boundaries Hedge and ditch Why hedge is on inside of
ditch Allowance for width of ditch Owner's side of boundary,
how marked Poling out chain line when view of ends obstructed
by rising ground Numbering and naming stations. - - 33
CHAPTER VII.
Hedges and trees on plans Area of field by equalising lines Area by
computing scale Area by planimeter Simpson's rule for area
Plotting a survey plan with junctions in boundaries. - - 41
CHAPTER VIII.
Cutting-up a plan, or arranging chain-lines, for a survey Complete
survey of small field to explain routine Office plans and finished
plans Estate in detached portions, how plotted Colouring plans.
48
CHAPTER IX.
Surveying woods, lakes, marshes, standing crops, etc. Example of
survey of a wood and a lake Measuring past obstructions Cross
staff, construction and use Optical square, construction and use
Setting up perpendiculars by chain only. 55
CHAPTER X.
Measuring gaps and detours, view unobstructed Special precautions
when view is obstructed Measuring across a lake, quarry or bend
in river Measuring across a stream, river or valley Example of
survey at Hilly Fields. 63
CONTENTS ix
CHAPTER XI.
Plans and maps Various systems of projection Curvature of earth not
taken into account in ordinary surveys Ordnance survey maps
Surveying over hilly ground Correction for inclination, how made
Instruments for obtaining angle of slope Indicating hilly ground
on maps Hachures Contour lines. 71
CHAPTER XII.
Field notes for survey of small farm Sketch of chain lines Secondary
lines not falling on previous station Plotting notes and preparation
of survey plan. - - - 82
CHAPTER XIII.
Instructions of "The Copyhold, Inclosure and Tithe Commission" for
the preparation of "First Class Plans" Regulations for testing
plans Charges for surveys Errors in chaining. - - 90
CHAPTER XIV.
Traversing with chain Traversing with prismatic compass Reducing
bearings Circumferentor Definition of terms used in traversing.
96
CHAPTER XV.
Examples of open and closed traverses Reducing to a single meridian
Tables of sines and cosines Traverse tables Plotting traverse
surveys. 105
CHAPTER XVI.
Copying plans by tracing and photography Use of triangular compass
Pricking through and transfer Enlarging and reducing by pro-
portional squares Use of proportional compasses Use and adjust-
ment of pantagraph and eidograph Ordnance maps. - - 111
CHAPTER XVII.
Definition of levelling Datum line Gravatt's dumpy level Construc-
tion of level Construction of level staff Curvature and refraction.
118
CHAPTER XVIII.
Simple and compound levelling Parallax and collimation, and adjust-
ments therefor Bubble error and its adjustment Setting up a
level Holding the staff. - .... 126
CONTENTS
CHAPTER XIX.
Levelling a section Running or flying levels Check levels Bench
marks Ordnance datum Reducing levels Plotting sections
Minus readings. 133
CHAPTER XX.
Notes for part of a main section Plotting of same Working section of
short piece of railway Description of features shown Rise and
fall method of keeping level book contrasted with collimation
method Telemetry, or optical measurement of distances. - 141
CHAPTER XXI.
Levels of building plots Equal vertical and horizontal scales Spot
levels Building plot with sections Building plot with sections
and contour lines Levelling with barometer Surveyor's compen-
sated aneroid barometer and method of using. - - - 148
CHAPTER XXII.
Principles of angular measurement Old definition of an angle Trigo-
nometrical definition Instruments for setting off or measuring
angles Semicircular and rectangular protractors Circular pro-
tractor with pricker arm and vernier Scale of chords. - 156
CHAPTER XXIII.
Construction and reading of diagonal scale Construction and reading
of vernier scale Construction and reading of verniers on the
theodolite Construction and adjustment of box sextant Method
of using same Construction and use of plane-table The three-
point problem. 162
CHAPTER XXIV.
Construction of theodolite Primary horizontal circle and verniers
Vertical circle and verniers Setting up and adjusting theodolite
Reading verniers Repeating an angle. - - - - 170
CHAPTER XXV.
Traversing with theodolite, surveying by the back angle Field notes
of traverse survey Traversing by angles from magnetic meridian
Triangulation or surveying from two stations Field notes of
CONTENTS xi
survey from two stations Observations required for obtaining
heights and distances. 176
CHAPTER XXVI.
Principles of town surveying Choice of base lines Chain or steel tape
Triangulated offsets Sketching details Field notes of lines and
angles with offsets omitted Plotting of same Field notes of one
street with measurements Plotting of same Connecting chain
lines. - .... 184
CHAPTER XXVII.
Difference in lay-out of old and modern towns Available accuracy
depending upon scale employed Double chain lines Example of
field-book Plotting of same Tape surveys Sketch of back pre-
mises with measurements Plotting of same. - - - 192
CHAPTER XXVIII.
Principal features of railway surveying Limits of deviation Reference
book Railway gauges Engineering field work Location field-
book Permanent stakes Level pegs Earthwork terms Batters
and slopes Earthwork formulae. - . - - - 201
CHAPTER XXIX.
Railway curves Nomenclature of curves Minimum radius Curve
" elements " and formulae Simple and compound curves Reverse
curves. - - 207
CHAPTER XXX.
Difference in length of inner and outer rails Centrifugal force and
super-elevation of outer rail Widening of gauge on curves Transi-
tion curves. 220
CHAPTER XXXI.
Ranging a curve By chain and offsets By one theodolite By two
theodolites Practical example Points and crossings Sidings.
227
CHAPTER XXXII.
Finding true merii
mean time Astrono
time Finding the latitude of a place. - - - - - 236
Astronomical surveying Finding true meridian Celestial sphere-
Longitude and local mean time Astronomical, civil and nautical
xii CONTENTS
CHAPTER XXXIII.
Signalling at a distance The Morse alphabet and Universal code Flag
signalling Flashing signals Heliographing. - - - 242
APPENDIX.
300 Examination questions. - 245
INDEX. - - - 272
CHAPTER I.
Scope of subject Definition of land surveying Geometry and men-
suration Origin of the term Geometry Distinction between
theoretical or pure geometry and practical or applied geometry
Principles upon which land surveying is dependent Difference
between old system of surveying and modern systems Objects in
view in 'measuring land Distinction between office and field work
Six selected problems in practical geometry Table of linear
measures Table of square measures.
Scope of the subject. Geodesy comprises several branches
of work that will perhaps be better recognised under their
ordinary titles of chain surveying, levelling, theodolite work,
compass traversing, town surveying, engineering field work,
etc. It is proposed to deal with these in the order named.
Land surveying, as it is usually called, consists of accu-
rately measuring and recording the lengths and positions of
carefully selected lines, indicated by temporary poles placed
in the ground adjacent to the boundaries of the various pro-
perties. Land is measured usually for one or both of two
purposes, either to find the area or to enable a plan or map
of the place to be prepared ; in either case equal care must be
taken in the measurements to produce correct results.
Many text-books commence with a chapter on Practical
Geometry, and rightly so, because this forms the ground-work
of the method of recording upon paper the plans of any
surveys of which the measurements may have been obtained,
while Mensuration is the art of determining the areas of the
various plots or surveys by calculation, the two branches
forming together that part of surveying which may be called
office work, as distinguished from outdoor or field work.
Geometry. The word Geometry is derived from two Greek
words, signifying earth-measure or land-measure, and from this
it may readily be assumed that Geometry had its origin in
p.s. A <
PRACTICAL SURVEYING
attempts to measure exactly certain portions of the earth's
surface. The science of Geometry is supposed to have had
its birthplace in Egypt some 3000 years ago, and to have
been necessitated by the annual overflow of the Nile obscur-
ing any minor landmarks which might have been set up by
the respective owners of property adjacent to its course. The
theoretical investigations of Geometry have, however, far
outstripped the direct practical use of the science.
Theoretical or Pure Geometry, of which Euclid, who lived
in the third century before the Christain era, is the well-known
exponent, teaches us, by reasoning, what are the properties of
lines, surfaces, and solids, irrespective of matter or substance.
Practical or Applied Geometry shows us in what way the
properties may be made subservient to our various handicrafts.
Before use can be made of any of these properties, it is
essential to know (1) the meaning of the different names or
terms employed, (2) their fundamental relationships, and (3)
what may be possible in the way of employing them. These are
the (1) definitions, (2) axioms, (3) postulates given by Euclid.
A definition is simply a strict description of what is meant
by a certain name.
An axiom is something intuitively known to be true or
self-evident, and is so simple that it cannot be proved by any-
thing simpler.
A postulate is something which it is admittedly possible
to do.
Six simple and useful constructions in Practical Geometry
are given below.
From a given point in a straight
line to erect a perpendicular.
Let AB be the given line in
any direction, and C the given
point. Then from C, with any
radius Cd, describe the arc defg,
and from points d and g, with
the same radius, cut the arc at e
and /. From points e and / de-
scribe arcs intersecting in h, and
FIQ. 1. To erect a perpendicular from . . 7 i i n t
a given point in a straight line. ]Oin AC, which Will be
dicular to AB.
GEOMETRICAL PROBLEMS
3
It will be observed that the given lines are shown thin, the
construction lines dotted, and the lines found by construction
thick. They are also lettered in the order of construction,
the given parts with capital letters and the construction lines
with small letters, so that what may be called the " life-
history " of the problem is presented at a glance, and does
not really require any description to enable anyone to work
it out.
To let fall a perpendicular from
a given point on to a given straight
line.
Let AB be the given line and
C the given point. From C,
with any radius greater than
the distance from the line, draw
arcs cutting the line at d and e.
From points d and e, with a
radius less than the distance
to C, describe arcs intersecting
at /, and draw line from C
through / to meet the base line in g.
required perpendicular to AB.
FIG. 2. To let fall a perpendicular
from a given point on to a given
straight line.
Then Cg will be the
To copy a given angle.
Let ABC be the given angle. With any radius ~Bd describe
arcs cutting BA and BC at d and e. Then draw line fg
indefinitely, or the same
length as BC, and from /
strike the arc ih with
radius equal to Ed, then
from point h with radius
de cut hi in, point i, and
through i draw fj equal in
length to BA. If BC is at
any given angle with the
horizontal, this angle may
be first copied to give an
identical position for the lines
forming the angle.
7
FIG. 3. To copy a given angle.
PRACTICAL SURVEYING
To construct a
e whose sides shall be equal to three given
4
Pro. 4. To construct a triangle haying
sides equal to three given straight
lines.
Let A, B and C be the three
given lines any two of which
must be greater than the third.
Draw de equal to A, from point
d with radius equal to B describe
an arc, and from point e with
radius equal to C describe
another arc to intersect the
previous one in point /;
join fd and fe, then dfe is
the required triangle.
To construct a triangle on a given line
length of its perpendicular given.
Let AB be the given line
(Fig. 5), C the position of the
perpendicular and CD the length
of perpendicular. Draw line AB
and mark position C, then from
C with any radius cut AB with
arcs e and /, and from points e
and / with any radius draw
arcs intersecting in g. Then
from point C through g draw CD
equal to the given length CD, and
join AD and BD.
the position and
FIG. 5. To construct a triangle on
a given line having the position
and length of its perpendicular
given.
To make a triangle equal to a given trapezium.
Let ABCD be the given trapezium (Fig. 6). Join CA. Pro-
duce DA to e, meeting Be, drawn parallel to CA. Join Ce.
Then the triangle CeD is equal to the trapezium ABCD, as the
piece cut off the trapezium at B is equal to the piece added
on to the triangle at Ac.
The solution really depends upon the proposition of Euclid,
" Triangles upon the same base and between the same parallels
are equal." The triangles are ABC and AeC, and the parallels
SYSTEMS OF SURVEYING
Fio. 6. To make a triangle equal to a
given trapezium.
AC and eE ; the triangle ACD is common to both the trapezium
and the equivalent triangle.
We need not trouble at
present with anything relat-
ing to angles or angular mea-
surement, as in chain surveying
we are only concerned with
the length of the sides of
the triangles, and from these
lengths the work can be plot-
ted and the areas calculated
without knowing what the
angles are.
Old and modern systems of surveying. In the old
system of land surveying, each field was measured separately,
often by the village schoolmaster, and added on to the bulk
already measured, large estates being sometimes checked by
the theodolite used round its boundary.
In the modern system, if there are several fields, a base line
or two main lines are laid out, running to each extreme of the
survey, and triangles are set out from these following the
irregularities of the various boundaries, so that the whole is
tied into a network of triangles with the fewest possible lines.
In large surveys the theodolite is used to measure the angles
of the main lines, in order that the distances may be checked
by calculation, as will be shown later.
Inches.
TABLE OF LINEAR MEASURE.
Links.
7'92
12
36
198
792
7,920
63,360
1
1-515
4-545
25
100
1,000
8,000
Feet.
Yards.
Poles.
Chains.
Furlongs.
1
3
16-5
66
660
5,280
1
5-5
22
220
1,760
1
4
40
320
1
10
80
I Miles.
8 1
PRACTICAL SURVEYING
Sq. Links.
TABLE OF SQUARE MEASURE.
Sq. Feet.
2-296
20-661
625
10,000
25,000
100,000
64,000,000
1
9
272-25
4,356
10,890
43,560
27,878,400
Sq. Yards.
Perches.
Sq. Chains
1
30-25
484
1,210
4,840
3,097,600
1
16
40
160
102,400
1
2-5
10
6,400
Roods.
Acres.
1
4
2,560
Sq
I Mil
640 1
QUESTIONS ON CHAPTER I.
1. Give a brief description of land surveying under the two
heads of field work and office work.
2. Draw two lines at right angles to each other by a rule and
set square, and test them by geometrical construction.
3. Draw the outline of one of your set squares, and by con-
struction drop a perpendicular from the largest angle to the
opposite side.
4. Measure the length of the sides of a set square, and draw a
similar triangle whose sides are half the length.
5. Repeat the last triangle on both sides of the longest line as a
common base, and draw a single triangle equal to the combined
area of the two.
6. Describe the general principles upon which a survey is made.
CHAPTEE II.
Linear measurement British standard of length Units of measurement
Units adopted in measuring land Form of working in calcu-
lating area Pointing off Rule for area of rectangular figure
Example Rule for area of triangular figure when base and
perpendicular are given Example Rule for area of triangular
figure when sides only are given Example Rule for area of four-
sided figure, having two sides parallel Example Irregular four-
sided figure divided into two triangles by a diagonal The same
divided into two triangles and a trapezoid Example Method of
tabulating the working.
Linear measurement. Linear measurement is the mea-
surement of straight lines referred to some known length called
a unit, or standard, of length. This length is purely arbitrary,
and differs in different countries. The yard is the British
standard of length. It is subdivided into feet and inches, and
multiplied into chains of 66 feet, and into furlongs and miles. The
fifi x 19
chain again is subdivided into 100 links, each = 7 92
inches long, so that the apparently odd length of 7 '92 inches is
strictly derived from the British yard.
In linear measurement, when the total length of any
measured distance is given, it may be stated in different ways.
As a general rule, long distances are given in miles and fur-
longs, or miles and chains, or miles and yards ; and short
distances in chains and links, or feet and inches.
Square measure is called also superficial measure, because
it is the measure of surfaces. A square foot is a space that
measures a foot each way ; or a surface measuring half a foot
one way and two feet the other way will likewise be a square
foot. The term " square feet " must not be confused with
the term "feet square." Thus, 9 square feet make 1 square
yard, but the expression 9 feet square means a square each
8 PRACTICAL SURVEYING
side of which is 9 feet long, arid therefore has an area of
81 square feet. There is as much difference between square
feet and feet square as between a horse chestnut and a chest-
nut horse*
In square measure the denominations most used by land
surveyors are acres, roods and perches, any small amount
over being put as the fraction of a perch, J, * or j, whichever
is nearest to the true result. Decimal fractions of a perch,
such as are recorded in the Ordnance Survey, give the appear-
ance of minute accuracy which, however, the facts of the case
do not warrant. It may be taken as a rule that no field
survey can be relied upon for accuracy within less than one
perch per acre (five-eighths of 1 per cent.), but straight-sided
building plots measured with a steel tape may be accurate
within a tenth of 1 per cent.
The tables at the end of the last chapter (pp. 5 and 6) give a
concise view of the common linear and square measures. In
some tables of square measure, areas are stated as acres, roods
and poles, instead of acres, roods and perches, as here given.
The reason is that the length of 1 6 J yards is known as a rod,
pole, or perch, and the corresponding square with that length
of side as a square rod, pole or perch.
In order to avoid confusion, surveyors have generally
adopted the term pole for linear measure and perch for square
measure, and it is well to bear in mind this distinction.
Areas Of regular figures. We are now in a position
to consider the methods of finding the areas of any regular
figures or those bounded by straight lines.
The area of any rectangular figure is found by multi-
plying together its length and breadth.
Ex. 1. In a field 7 chains long and 3 chains wide (Fig. 7)
how many acres, roods and perches ?
7
3
2,1
8
4
"^
4
7-00
40
160
Ans. :
2 a. Or. 16 p.
FIG. 7. Rectangular field.
AREAS OF PLANE FIGURES
9
Explanation. 1 square chains make 1 acre, therefore divide
21 square chains by 10, or, what is the same thing, point off
one figure. Then multiply the remainder by 4 to bring to
roods and point off. Then multiply the remainder by 40 to
bring it to perches and point off. The figures to the left of
the pointing show the acres, roods and perches.
The area of a triangle is found by multiplying together its
base and perpendicular height and dividing by 2.
There is a special reason for not saying multiply the base
by half the height, which will be seen later.
Ex. 2. In a triangular field (Fig. 8), one side of which is 13
clmins long, and the perpendicular to the opposite angle 9 chains long,
how many acres, roods and perches ?
FIG. 8. Triangular field
Ans. :
5 a. 3r. 16 p.
When the length of the three sides only of a triangle is
given, the calculation is a little more complicated. The
rule is :
From half the sum of the three sides subtract each side
severally, and multiply it and the three remainders together
and take the square root for the area.
This is usually expressed by the formula,
Area = >Js(s-a)(s-b) (s-c),
where a, b and c are the three sides respectively, and s = half
a + b + c
their sum, or - .
O
10 PRACTICAL SURVEYING
Ex. 3. In a triangular field (Fig. 9) the three sides are
3, 4 and 5 chains long. What is the area ?
6-4 = 2 6x3x2x1=36,
.736 = 680. ch.
6 5=1.
_4
24
40
160 Ans. : a. 2 r. 1 6 p.
With a four sided figure having two sides parallel and
perpendicular to the base, called by surveyors a trapezium,
the rule is :
Multiply the sum of the two parallel sides by the base, and
divide by 2.
Ex. 4. In a field (Fig. 10) with two parallel sides whose
8
*>.
FIG. 10. Four-aided field
having two sides parallel,
and perpendicular to the
FIG. 9. Triangular field. base, called a trapezium.
lengths are respectively 3 and 5 chains long, and their distance apart
7 chains, what is the area ?
28
<!5H= 28 . T2
4Q
8p Ans. : 2 a. 3 r. 8 p.
With irregular four-sided figures there are two ways of
finding the area depending upon the angles the sides make
AREAS OF PLANE FIGURES 11
with the base. For instance, in Fig. 11, the area can be
divided up into two triangles, with either diagonal as base,
from which perpendiculars are drawn to the opposite angles.
If both sides make angles of less than 90 degrees with the base,
12 -oo
FIGS. 11 and 12. Irregular four-sided fields.
the method just described is available, and also the method
shown in Fig. 12, where, by drawing perpendiculars to the
base, it is divided into two triangles and a trapezium.
For the first method the calculations are the same as for
a single triangle, the two perpendiculars being added together
and treated as one. In the second method the work must be
tabulated.
Ex. 5. A four-sided field whose longest side is 1 2 chains long
has perpendiculars to opposite angles on the same side of base 4 chains
long at 2 chains from one end, and 6 chains long at 3 chains from
the other end. What is the area ?
446 2|96
2 _6 _3 1^
8 10 18 4
_7 70 ^
70 40
22 8 Ans. : 4 a. 3r. 8 p.
The reason for putting the division by 2 last is that
one division suffices instead of one for each part, but care
must be taken not to omit it, or it would be as bad as the
quantity surveyor who omitted to " twice " his items for the
other wing of a hospital.
Generally the measurements are in chains and links, which
is the same as units and decimals, but the decimal point is
12 PRACTICAL SURVEYING
generally omitted, so that the measurement stands as links
only. Then, in multiplying out, the result is given in square
links, and as 100,000 square links make one acre, it is only
necessary to point off five figures to get acres and decimals.
Ex. 6. In 285,350 square links, how many acres, roods and
perches ?
285350
4
341400
40
Ans. : 2 a. 3 r. 16jp.
The remainder 0-56 is just over the \ perch, which would
be 0-5, but it is called \ in accordance with the rule laid down.
The area could also be written 2*8535 acres.
QUESTIONS ON CHAPTER II.
1. State what is the British standard of length, and explain how
the length of a link in a 4-pole chain is derived from it.
2. What will be the length of a side in feet of a square contain-
ing one acre ? (Ans. : 208'71.)
3. A circular pond is required to contain exactly one acre. What
will be its diameter in feet ? (Ans. : 235'457.)
4. If 25 ordinary walking paces equal one chain, how many paces
will there be in a mile 1 (Ans. : 2000.)
5. The three sides of a triangle are 4, 6 and 8 chains long
respectively. What is the area in acres, roods and perches ?
(Ans.: 1a. 6r. 19 p.)
6. How many acres will be covered by 60 plots of land each
30 feet frontage and 121 feet deep ? (Ans. : 5 exactly.)
CHAPTER III.
Drawing to scale or plotting Description and use of chain scales
Decimal system Base line of survey Direction Points of the
compass Direction of north obtained by a watch Magnetic
meridian Magnetic variation North point.
Drawing to scale. Suppose it were desired to mark
upon paper certain points representing the distance apart of
any objects, say telegraph posts, or to mark the length of
any structure, say a fence or building, the actual distance
cannot be marked on account of the smallness of the paper ;
all distances must therefore be reduced in some given pro-
portion, so that when they appear on the paper they give
a true idea of their relative values. This is called drawing
to scale, or, applied to land surveying, it is called plotting.
If, for instance, the distance between two points were found
to be 3 chains, and it was desired to appear upon the paper about
3 inches long, a scale of 1 chain to 1 inch would be adopted.
Chain scales are made of various patterns in boxwood,
/ Chain to / Inch
L I Q(Ll I C
imlmilimlnH
FIG. 13. Scale of chains and feet corresponding.
vulcanite or ivory, and containing either a single scale each,
with "feet equal" on the opposite edge (Fig. 13), or a dif-
14
PRACTICAL SURVEYING
ferent scale on each of the two edges (Fig. 14), or containing
all the eight usual scales upon one slip, using both edges on
/
|
1 1
1 1 1 1
1 1 1
1 1
1
X
!
1 1
1
2
c^
*
\
2
z
7,
gj
i
Z OJZ 6
i
'Mil
1 II 1
\ \ \
Illl
III!
1 III
II 1
1 1 1
Mil
Illl
Illl
FIG. 14. Duplex scale.
both sides (Fig. 15). This is called the Universal Chain Scale,
and is a very handy implement for class use, as all the scales
10 s, 20
(Front)
O8 Of
3O & GO
(Back)
OQI i OS
FIG. 15. Universal chain scale.
are decimally divided. For office work it is usual to have
a set of scales similar to Fig. 1 3 in a box.
There are also special scales to suit special cases; for
88
J_L
II I II II
FIG. 16. Special scale for use on ordnance maps.
example, the most commonly used Ordnance maps are drawn
to a scale of 88 feet to 1 inch, or 5 feet to 1 mile, and it may
CHAIN SCALES
15
The
be desired to scale off a distance either in chains or feet,
special scale made for this purpose is shown in Fig. 16.
Upon the universal chain scale it will be observed that
one edge is marked 10 and 20 ; there are two rows of figures,
the one with the widest spaces relating to the 10 scale and
the other to the 20. The 10 scale can be used for 1 chain
to the inch, or 10 or 100 to the inch ; if for 1 chain to the
inch, then the smallest divisions will represent 5 links, because
there are 20 divisions to the inch, and 20x5 = 100, the
FIG. 17. Pocket compass.
number of links in a chain. If used for 10 chains to the inch,
the smallest divisions will each represent 50 links, and if for
100 chains, each division will stand for 5 chains. All the
other scales may be used in the same way, and they may also
be used for feet and tenths, so that they become handy for
other purposes.
Base line Of survey. The longest side of a triangle, or
the longest chain line used in making a survey, is generally
considered to be the base line. A base line must not only be
carefully measured, but must be on fairly level ground, and
16
PRACTICAL SURVEYING
its direction with regard to the points of the compass must be
noted. This is found by means of a pocket compass (Fig. 17),
or the compass attached to any of the surveying instruments,
or by comparing it with the direction of the shadow cast from
an upright stick, by the sun at apparent noon, that is, when
the sun has reached its highest point for the day, or is due
south, or approximately by means of a watch, as follows :
Stand over the- chain line facing the further end, hold the
watch so that the hour hand points to the sun. Bisect with
the eye the angle between 12 and the sun, producing it back-
wards to give the direction of true north, note the minute
TIME 9.3OA.M. TIME 2.15 P.M.
Fio. 18. Use of watch to find N. point.
indicated by this direction and also the minutes indicated by
the direction of the chain line ; then six times the difference in
minutes can be plotted as the angle in degrees made by the
chain line with true north. Fig. 18 shows two examples of
this use of a watch. The shadow and the watch give approxi-
mations to the direction of the true or geographical north.
Magnetic meridian. The direction in which the north
end of the compass needle points is known as the magnetic
north, and any line coinciding with it is said to be in the
magnetic meridian. This direction differs from the true north
by an amount which differs more or less in different parts of
the world and at different times at the same place. It oscil-
lates slowly backwards and forwards during a course of years
between about 30 degrees east and west of true north, and is
VARIATION OF THE COMPASS
17
assumed to point towards the centre of magnetic attraction in
the earth, which travels in a circle round the north pole
during the same period. There is a daily variation of the
needle, as shown by Fig. 1 9 ; a monthly variation, as shown by
Fig. 20 ; and also a mean annual variation, as shown by
FIG. 19. Daily variation of compass.
^1
^
^r
m /r.
^^1
^ ,
A
/
X^O T
^^>
^
\
X.
*.
>
CO
N
\
V
*^
s
*O
^
^
V
1
1
V)
t
Jan Feb. March dpnL May June JuLy dug. Sept. Octr Norr Deer
Fio. 20. Monthly variation of compass.
P.S. B
18
PRACTICAL SURVEYING
Fig. 21. In London the mean annual position is now about
15J degrees west of true north, and is reducing at the rate
of about 7 minutes per annum. The exact variation will be
found in the Nautical Almanac for the current year.
The north point. In the field-book the bearing of the
'/V5'
FIG. 21. Mean annual variation of compass.
base line with regard to tha magnetic north is generally
entered as so many degrees east or west of north or south ;
thus, N. 20 W. would mean a direction of 20 degrees west of
north, but on all plans, whether manuscript or lithographed,
both the true north and the magnetic variation should be
shown, in order to make quite clear what the bearing of the
plot really is. This is generally done by means of a north
NORTH POINT
19
point, as Fig. 22, but which may be very much more elaborate.
In maps and Ordnance sheets it is customary to make the top
of the sheet north, but in detached surveys, if the shape of
FIG. 22. North point.
the plot should render it desirable, the plan may be placed in
any position, provided the north point is placed accordingly.
QUESTIONS ON CHAPTER III.
1. What will be the length in inches of a line representing
19 chains 12| links to a scale of 3 chains to 1 inch ? (Ans. : 6.)
2. Make a scale of 40 feet to 1 inch to represent chains and tens
of links.
3. Find the area in square yards of a rectangular plot of land,
two adjacent sides of which measure 4 chains 34 links and 2 chains
15 links. (Ans. : 4516-204.)
4. In 395,590 square links how many acres, roods and perches ?
(Ans.: 3 a. 2r. 33 p.)
5. A line measures 6 chains 13 links ; what is its length in feet
and inches? (Ans. : 404ft. Tin. nearly.)
6. With a magnetic variation of 16 degrees west, what will be
the true bearing of a line whose compass direction is N. 82 W. ?
(Ans. : 262 or S. 82 W.)
CHAPTER IV.
Measuring straight-lined figures Tie and check lines Rule for distance
from angle Well-conditioned and ill-conditioned triangles Use of
box tape Measurements put on sketch plan instead of in field-
book Testing tape for shrinkage Gunter's chain General
description of its use Tally points Entries in field-book Steel
tapes.
Measurement of straight-lined figures. In the rules
laid down for the mensuration of areas it was assumed that
the outlines were more or less regular, and that, for instance,
in a rectangular four-sided figure it was only necessary to
multiply the length by the breadth. In practice, it must not
be assumed that there are any regular figures.
If it were desired to obtain the plan of a single room it
would not be sufficient to measure the length and the breadth,
and assume the angles all to be right angles, although they
might appear to be so ; some method must be adopted by
which measured lines representing the four sides can be trans-
ferred to paper in their true relative positions. It might be
divided into two triangles by means of a diagonal across two
opposite corners, but in a large room there might be obstruc-
tions in the way, and there is another method of which
constant use is made in surveying. It is founded upon the
method of copying an angle shown among the selected pro-
blems in Practical Geometry.
Suppose distances are marked from one of the corners
on each of the walls meeting there, and then the distance
is measured between the two marks, these three measure-
ments will give the sides of a small triangle, two of which
produced to a sufficient length give two of the walls, and
the third one is a tie between them, deciding their relative
positions.
TIE AND CHECK LINES 21
Tie and check lines. In a four-sided figure (Fig. 23) the
measurement of the sides a, b, c and d, and one angle e,
enables it to be put down to scale ; but in that case the accu-
racy of the result depends solely upon the carefulness with
which the work has been done, as there is no check upon it.
If, however, a second angle be measured, /, there is a perfect
check upon the work, as it would be found impossible to close
the figure entirely if a mistake is made in either measuring or
plotting any one of the lines. The rule in surveying for
a
Fm. 23. Measuring sides and angles of a room.
these tie and check lines is that the points should be taken
not less than one-fourth of the length of each main line from
the angle, and not necessarily at equal distances, so long as
the triangles formed are welt-conditioned, i.e. having no angle
less than 30 degrees nor more than 120 degrees. An ill-
conditioned triangle is one that would not conform to these
conditions. The rule only applies to ordinary surveys ; for
important work the complete diagonals should be taken.
Use of box tape. The box tape (Fig. 24) is commonly
employed for all measurements about buildings and yards,
where the general distances are under one chain in length. It
is marked off to a total length of 66 feet, one side being
divided into feet and inches, and the other into poles and
22 PRACTICAL SURVEYING
links, so that either denomination can be used for the
measurements.
In using a tape line the starting point is always the furthest
extremity of the brass ring. There must be no twist in the
tape, and it must be pulled sufficiently tight to prevent the
sagging from affecting the measurements. As the surveyor
cannot be at both ends of the tape, he takes the box and gives
the ring end to an assistant, and, unless the assistant is
experienced,, care must be taken that he does not take a turn
of the tape round his wrist to keep his hold firm.
About buildings and yards the tape is much simpler than
the chain, and handier to carry about, and the measurements
being short and intricate are generally entered upon a sketch
plan instead of in the columns of a field-book.
Testing tape for shrinkage. Although the 66-feet
Chesterman metallic tape has wires woven in to prevent
on one sio/e
and inches
potes and
FIG. 24. Box tape.
stretching, it is worthy of notice that one of these tapes used
on wet grass and wound up again was found, when tested two
days later at the Guildhall, to have shrunk to 65 feet 4 inches,
and when tested three weeks later it had recovered so far as
to measure 65 feet 9 inches long. It is useful to practise
pacing as a rough check upon distances ; a long step is 3 feet
or 1 yard, and a natural step or pace about 2| feet ; therefore
multiply the number of paces by 4 and point oft' two figures ;
the result is chains and links.
Gunter'S chain. For land surveying the chain is always
used, but the tape sometimes comes in as an accessory for
measuring long offsets. The surveyors' chain is called a
Gunter's chain, after its inventor, Rev. Edward Gunter, who
was a professor of astronomy about the year 1640 at Gresham
College. It is sometimes called a 4-pole chain, to distinguish
GUNTER'S CHAIN 23
it from the 1 00-feet chain used by civil engineers. The 4-pole
chain is more useful for land measure, as it is an exact decimal
of a mile, one-eightieth, and the square formed by it is exactly
one-tenth of an acre. It consists of a series of links and rings
(Fig. 25), measuring altogether 66 feet, and is always used on
the ground, as its weight would cause it to sag if held up, as
the tape often is. It requires at least two operators, the sur-
veyor and his assistant, or surveyor and chainman, or driver
and leader.
Use of Gunter's chain. The chain is accompanied by
ten galvanised iron arrows or pins, to indicate the various
Brass tatty M 3O or 70
FIG. 25. Gunter's chain and arrows.
chain lengths as they are reached in a measurement. These
are inserted in the ground by the leader and withdrawn by
the driver, an exchange taking place at every ten chains which
is entered in the field-book. In using the chain the driver
passes his fingers through the end ring, holding it vertically
on the ground at the starting point ; the leader holds the
other end leg high, with his fingers through the ring and
an arrow held against it by his thumb through the loop ; he
sees that it is straight, and then watches the signals made by
the surveyor with his free hand, the palm of the hand facing
the side the leader must go to to put himself in line, and the
fingers moved to show it, reversing the palm and movement
of fingers when the leader goes too far, and putting the palm
24 PRACTICAL SURVEYING
downwards and moving the fingers in the same direction when
the leader is in the right spot. As he nears the right spot
he will, of course, be stooping down, with the point of the
arrow just clearing the ground.
To get the chain to lie straight on the ground, the leader
gives the end held by him a few sharp vertical jerks, which
causes a wave-like motion to pass along the length of the
chain. The jerks must not be too vigorous, or the pull on the
chain too tight, as that would cause it to stretch by opening
the links.
As soon as the arrow is fixed the two operators walk on for
another chain length, unless there are any interim measure-
ments to be made for offsets, or notes to be entered. In the
old days there was an eleventh arrow made of brass to insert
in the ground when the tenth was withdrawn by the surveyor,
but the writer has not seen one for many years, and the
custom now is for the surveyor to put his toe on the spot,
count the ten arrows at every change, and hand them over to
the leader again.
The divisions of the chain are indicated by brass tallies at
each tenth link -one point stands for 10 or 90 links, being the
same from each end, two points for 20 or 80, three points
for 30 or 70, four points for 40 or 60, and a round tally with
the maker's name for 50 links. No confusion arises from the
number of points being the same for two readings, as it is
easy to see which is the nearer end.
Entries in the field-book. In the field-book there is one
column only, down the centre. This is for entering any
measurement obtained by the chain in a direct line, all the
measurements being reckoned from the starting point. The
left-hand space is for recording anything occurring to the left
of the chain line, and the right for anything occurring on the
right. An important and curious point in connection with
the field-book is that the surveyor begins at the end and
finishes at the beginning, working backwards all the way. He
begins at the bottom of the last page and makes his entries
consecutively upwards, so that he stands with regard to the
book exactly in the same position as he stands with regard to
the chain line.
Steel Tape. In modern work a 66-feet or 100-feet steel
tape is often used instead of a chain, consisting of a ribbon of
USING THE CHAIN 25
steel | inch wide, with brass plugs riveted in to mark the links.
It is more accurate than a chain, but requires more care in
handling. A 100-feet standard steel tape is a very delicate
instrument, marked in feet, inches and eighths, needing as
much care as an infant, difficult to keep free from corrosion
and consequent indistinctness of divisions, and only used for
building surveys.
QUESTIONS ON CHAPTER IV.
1. A chain is one link short, next to the 50 tally, a line measured
by it is given as 13'47 ; what is the true length ? (Ans. : 13'34.)
2. A triangular plot of land has its sides 4'32, 3'51 and 2'17 ;
plot this to a scale of 1 chain to 1 inch, and find the distance along
the base line, from the shortest side, where a perpendicular from
the apex would fall. (Ans. : V28 nearly.)
3. What will be the area in acres, roods and perches of 10 square
inches on a map drawn to a scale of 3 chains to 1 inch ? (Ans. :
9 a. r. p.)
4. Describe the instruments used for measuring distances in the
field.
5. Describe the operation of poling out and chaining a line in the
field.
6. Explain, by a sketch, the reason for measuring check lines as
well as tie lines in a survey.
CHAPTER V.
Measurement of straight-sided fields Use of station poles How chain
lines and stations are indicated in field-book Conventional signs
Offsets, how measured and recorded Examples of offset pieces-
Plotting from field notes Drawing in the outlines.
Measurement of straight-sided fields. In surveying
a field with straight sides it is, in theory, only necessary to
divide it into triangles and measure the base and perpen-
dicular of each, but in practice very few straight- sided fields
occur, and the only spaces of the sort likely to be found are
building plots. Generally, the chain lines cannot be laid
along the boundaries, but must be some little distance inside
them, so that the position of the boundary must be measured
by perpendicular offsets from the chain line. These offset
measurements are put in the right or left-hand column of the
field-book according as they occur to the right or left-hand
side of the chain line when facing forwards from the starting
point.
Use of Station poles. The positions of the chain lines
are marked out on the ground by light poles, painted in red,
white and black bands (Fig. 26), with a small red and white
e'o'
Scac/on poie
FIG. 26. Station pole.
flag about 12 in. square nailed on the top, to distinguish
them at a distance, a pole being placed at each junction of the
CONVENTIONAL SIGNS
27
lines and at one or two intermediate points when the line is a
long one.
Conventional signs. In measuring the lines, whenever a
station pole is reached, the measurement is recorded and the
pole indicated in the field-book by a small circle with a dot in
the centre (Fig. 27). There are other conventional signs used
MARKS
(3) Number of (.tne
Q Ordinary scat/on
TnqoriomeCricaL station
Direction marks
1H-
*
IN FIELD BOOK
D = Broty of of/tch
H = Centre of hedge
F " Face of fence
rp. - Footpath
R - Road
& = Brick buiictinq
W = Wood.
FIG. 27. Marks in field-book.
by surveyors for indicating in the field-book and on plans the
various details of a survey, as roads, fences, footpaths, etc.,
which are here given. In chain surveying the lines are
numbered in the order in which they are measured. It is
useful to record the chain lines on the plan and show the
direction in which they were measured, as in Fig. 28.
of Line t'n circLe
than '/*' oJtam
Direction of measurement
tatton c/rcte not mo re th&n
Me" a/iometer
Fia. 28. Drawing chain lines on plan.
When the offsets are short they are measured by an offset-
staff, which is simply a ten or fifteen-link rod, divided into
28
PRACTICAL SURVEYING
links, painted alternately black and white, the fifth link
having a red ring painted round its end, as in Fig. 29. The end
K -
Offset staff
- - /O Links -
Reef nnq
FIG. 29. Offset-staff.
of the offset-staff is finished with a flush hook for pulling the
chain through a hedge. In a well-arranged survey no offset
should exceed one chain in length. Sometimes it may happen
that there is a strip of grass, a footpath, and a roadway
occurring between the chain line and the boundary ; with an
offset-staff the measurements would be recorded as in Fig. 30,
1
23
12
20
5
8
1
2
J 3
5- ^15
76
c
^
V
I
I
O
I
1
^
/
1
|
I
1
<j
I
<$
N/ \
Offset staff
FIG. 30. Measurements taken with
offset-staff.
Taken fr/th tape
FIG. 31. Measurements taken with
tape.
being placed between the lines to indicate the number of links
in width ; but time may often be saved by using a tape in
such a case, and the measurements would then be continuous
from the chain line. This is shown by putting the measure-
ments on the lines, as in Fig. 31, instead of in the spaces.
Measuring and recording offsets. In taking offsets
with the staff, the surveyor judges by his eye where the
perpendicular from the point required would fall upon the
chain line, and then keeping the point in view, he passes
the staff hand over hand from the chain to the point.
Generally, it is desirable to look round the field and sketch
the proposed chain lines in the field-book, numbering them in
the order in which they will be measured. Then the surveyor
MEASURING OFFSETS
29
walks round and puts in the station poles, and is ready to
commence chaining.
The first entry in the field-book is the name of the place
and the date. After that comes the position of the base line
with regard to the points of the compass, or its "bearing."
OB
3' 70
3'20
20
2'90
15
2-40
30
1-80
2O
l'20
J5
O'6O
/S
O-4O
20
O'OO
O
OA
N 20* W
FIG. 33.-
for
-Field notes
Fig. 32.
FIG. 32. Offset piece.
This is generally taken by a pocket compass, and is therefore
the bearing from the magnetic north ; but, in plotting the
plan, due allowance must be made for the "variation of the
compass " and both the true north and magnetic north shown
by the north point, as previously explained. The approximate
30
PRACTICAL SURVEYING
direction of all chain lines after the first may be very clearly
indicated by a "signal-post" or mark in the offset column
opposite the commencement. The upright or "post" repre-
sents the previous line, or line from which the departure is to
8-54
2'84
2'3
2-10
FIG. 34. Supplementary triangle
on chain line.
FIG. 35. Field notes for
Fig. 34.
be made, and the " arm " shows the direction taken by the
new line. Some illustrations of these marks are shown on
Fig. 27. In plotting, the approximate direction facilitates
finding the intersecting points in constructing the triangles.
An offset piece is the irregular strip of land between a
PLOTTING FROM FIELD NOTES
31
straight chain line and the boundary, as in Fig. 32, of which
the field notes are given in Fig. 33. Where several long
offsets would occur, a supplementary triangle should be laid
down, the base being on the chain line and the sides approxi-
mating to the outline of the field, as in Fig. 34, of which the
field notes are given in Fig. 35.
Plotting from field notes. In plotting from the field
notes, the base line should be drawn in first, with the correct
bearing, taking the total length between the first and last
stations, then the lines forming the great triangles, and lastly
the check or proof lines. When these agree, the plotting of
FIG. 36. Plotting with offset-scale.
the smaller triangles may be proceeded with, and after these
the offsets. The importance of having the base and tie lines
correctly measured is therefore evident, as if they are wrong
all the other measurements are useless, and the work must
be done over again.
In a survey occupying more than one day, it is especially
desirable to plot the day's work each evening, in order that
mistakes may be rectified ; and, in fact, however simple the
survey may be, the sooner it is plotted the better, the various
details being fresh in the memory. On large surveys, with
experienced surveyors, the routine is somewhat different, as
a survey party may be away from headquarters for many
weeks or months, and the practice is to have two field-books,
32 PRACTICAL SURVEYING
one being sent to headquarters each week, for plotting by
a different set of men, and returned at the end of the week.
Drawing in outlines. Having plotted the chain lines to
the most convenient scale, the readiest way to lay off the
offsets is to place the chain scale exactly against the line,
with its zero opposite the commencement of the line, then
to put a leaden weight on each end of the scale to keep it firm,
and to slide the offset scale against it like a set-square. A hard
pencil, or needle point, or pricker, should be used to mark the
various points, as in Fig. 36. No mark is wanted on the chain
line, nor any line perpendicular to it, but when the offset
scale reaches the right distance along the chain scale, a point
may at once be placed at the right distance on the offset
scale, reading the distance from the chain line. The points
thus found are joined either by straight or curved lines,
according to the sketches made in the offset columns of the
field-book at the time of taking the measurements, to show
the character of the boundaries. French curves should be
used whenever necessary to obtain a steady curved outline.
QUESTIONS ON CHAPTER V.
1. Name the appliances used in simple chain surveying and
describe their use.
2. Give an example of the entries in a field-book for a chain
line 7 '42 long, with offsets to a hedge on the right.
3. Show by a sketch how chain lines and stations are recorded
on a survey plan.
4. What is the usual limit for the length of an offset in
measuring fields, and what practical reason exists for so limiting
the length ?
5. What is meant by " magnetic variation " ? What are the
extreme limits of the variation and what is the annual change in
England ?
6. Give a sketch showing the use of a supplementary triangle
on a chain line and state what advantage results from it.
CHAPTER VI.
Nature of boundaries Hedge and ditch Why hedge is on inside of
ditch Allowance for width of ditch Owner's side of boundary,
how marked Poling out chain line when view of ends obstructed
by rising ground Numbering and naming stations.
Nature of boundaries. Various methods are adopted for
indicating the boundaries of property, and there are compara-
tively few cases in which a surveyor can tell, by simple
inspection, what the precise boundary line is. In the case of
a parish, stones or posts are often fixed at intervals, and these
are sometimes in such out-of-the-way places that local enquiries
have to be made to find them. Parish boundaries, if such
occur, should always be put upon any survey plan when they
can be ascertained. When a brook or running stream forms
the boundary between two parishes, the centre is usually the
division line, and lawsuits have occurred from the course of
the stream shifting by natural causes.
When land is laid out in building plots the boundary of each
plot is marked by pegs driven in the ground at the angles,
the face of the peg with the number of the plot painted on it,
forming the outer boundary, and imaginary straight lines
roughly cut in the grass form the division lines between
the plots.
With brick or stone walls, the centre sometimes forms the
division line, in which case it is called a party wall, but in
other cases the wall is built entirely on one property, and the
boundary line is then the outer face of it. If there are foot-
ings, they usually stand on the neighbour's land, and may be
built upon or cut off, or proceeded against for trespass as the
neighbour may determine.
Hedge and ditch. A hedge without a ditch on either
side may be taken as a party wall, the division line being the
p.s. C
34
PRACTICAL SURVEYING
centre ; but when it has a ditch, or the remains of one, on one
side of it, the ditch with the hedge usually belong to the land
on the opposite side of the hedge, the clear side, or brow of
the ditch, forming the boundary line as in Fig. 37. This is
Limit of boundary
for this fieLot
FIG. 37. Hedge and ditch boundary.
said to arise from the fact that in digging a ditch the earth
must not be thrown on to the neighbour's land, but is utilised
for planting the hedge. It would, however, be just as easy to
dig the ditch sufficiently within the boundary to plant the
hedge outside it, and the writer's opinion is that the relative
position of hedge and ditch is simply a survival of the old
custom, when a wall and ditch were built as protective boun-
North
South
To London
Exist mo. outiin<L
Stone
foundation
FIG. 38. Grsem's dyke.
daries, as in the case of the Eoman wall and ditch, or vallum
and fosse, known as Grsem's Dyke, and built by Antoninus
Pius between the Forth and the Clyde, A.D. 140, shown in
Fig. 38.
If a
surveyor is measuring in a field with a ditch belonging
to it on the further side of the hedge, he cannot, of course,
NATURE OF BOUNDARIES
35
get the exact measurement to it in taking his offsets, and he
therefore measures to the centre of the hedge, and makes an
allowance of 5 to 1 links for the width of the ditch, according
to local custom. Usually the allowance is :
5 links when between fields belonging to the same owner.
6 to 7 when between fields belonging to different owners.
7 to 1 links when abutting on public lands.
Owner's side of boundary. With a wooden fence or
paling, the face of it is usually the boundary, as in Fig. 39, or
Oivner's
side
rA/v
FIG. 39. Fence boundary.
Open pale fence
and rail fence
Close boarded fence
FIG. 40. Methods of showing fences
and boundaries.
as they say, the nails are driven " home," i.e. towards the pro-
perty to which the fence belongs, so that the owner looks on
the back of it ; but when the fence is next to a road there is
sometimes a ditch outside it to be included in the boundary.
With all boundaries of whatever nature, the owner's side
should be marked on the plans by a letter T placed against it,
showing that the fence, etc., as the case may be, belongs to T
" this " side, and when a smaller enclosure is taken in with the
area of a larger one, a brace or long I is put across the boun-
dary, as in Fig. 40.
The simplest fields to survey are three-sided, and in these
a single triangle, with offsets, can generally be adopted;
but sometimes, if one side is very irregular, a supplementary
triangle may be required having a part of the side of the
36 PRACTICAL SURVEYING
Oa. ir
FIG. 41. Small survey.
POLING OUT A FIELD
37
original triangle for its base, to avoid long offsets. Before
commencing the survey, it is necessary to walk round and
notice particularly whether there are any obstructions, at the
same time observing which positions for the station poles will
PIG. 42. Field notes for Fig. 41.
give the longest lines. If the field be small, the arrangement
of the lines can be decided upon at once ; the station poles can
be carried round at the same time and fixed where required,
to save unnecessary walking. Although the size and shape of
a triangle are determined when the three sides are known,
38 PRACTICAL SURVEYING
that is not enough in a careful survey. It is necessary to
obtain a check upon the measurements, either by finding the
length of a perpendicular, or by finding the length of a check
or proof line from intermediate stations on two of the chain
lines, not less than one-fourth of their length from the
junction. A small survey (Fig. 41) is here given with the
field notes (Fig. 42). It is a triangular strip of grass just
below the summit of Primrose Hill, in the north-west of
London.
Obstruction by rising ground. In this survey, owing
to the rise of the ground between, the station poles at
either end of the first line could not be seen from the other
end, and a method had to be adopted in poling out the line
that is often used when surveying over hilly ground. It may
be explained from Fig. 43, where A and B are the poles at the
extremities of the line. Two operators, C and D, with a pole
each, then take up intermediate positions, from which C can
see pole B, and D can see pole A. C then signals to D to put
him in line with pole B, and D signals to C to put him in line
with pole A. With very little labour the poles A, C, D and B
will be in true alignment, and the line can then be chained
through. It is only necessary to leave in one of the poles, C
or D, which can afterwards be used for a check line.
A station is known by its position on the chain line, thus
. r .. 0-00 2-00 , 5-47 ,.
in line 1 the stations are known as , and , reading
O'OO on 1, 2'00 on 1 and 5 '47 on 1 ; and whenever a station is
arrived at a second time it is not only marked in the field-
book as a station, but an entry is made against it of its
original position, as shown in lines 2, 3 and 4.
QUESTIONS ON CHAPTER VI.
1. Make a sketch showing the section across a hedge and ditch,
and mark, by a vertical arrow, the usual position of the boundary
line.
2. Describe and illustrate by a sketch the method of chaining
a line when the further end is hidden by rising ground.
3. Give a simple rule for marking stations in the field-book, so
that they may be identified when reached a second time.
POLING ON HILLY GROUND 39
Sccrte
FIG. 43. Method of poling out the line over hilly ground.
40 PRACTICAL SURVEYING
4. Make a sketch of a small field, add chain lines, and make up a
field-book to correspond with the plan. State the scale to which it
is drawn.
5. In measuring a field with a hedge and a ditch beyond it, how
is the width of ditch allowed for ?
6. Explain the use of the marks T and / on a survey plan.
CHAPTER Vir.
Hedges and trees on plans Area of field by equalising lines Area by
computing scale Area by plani meter Simpson's rule for area
Plotting a survey plan with junctions in boundaries.
Hedges and trees on plans. The chain lines of a survey
are not necessarily all within the field or estate, and wherever
Fio. 44. -Sketch of a hedge, magnified.
Fio. 45.- Sketches of trees and bushes, magnified.
a better lead can be obtained outside the boundary the lines
may be taken there, subject to any "Notice to Trespassers."
Hedges on small scale plans are shown by single
lines, but on a larger scale they may be sketched
with a pen as Fig. 44. Trees may also be
sketched as in Fig. 45. These figures are
magnified to show the kind of stroke used in
making them, but the proper scale must be borne
in mind on each plan. Another mode of in-
dicating trees on plan is shown in Fig. 46,
which is more in accordance with reality but not so picturesque;
Fio. 46.
Another
method of
showing trees.
42
PRACTICAL SURVEYING
the centre of the cross marks the centre of the tree, but
sometimes a section of the tree-trunk is shown.
Area of 'field by equalising lines. The ordinary mode
of obtaining the area of a field or estate is to run equalising
lines in pencil through the boundaries after they are inked in,
and before the plan is coloured ; then to divide the whole plot into
triangles, measure the base and perpendicular of each, calculate
the areas, and total up. An example of this is shown in Fig. 47.
PIG. 47. Obtaining area of irregular figure.
Area by computing scale. Another method of obtaining
the area is by means of a computing scale (Fig. 48). To use
this, horizontal lines are drawn one chain apart upon tracing
paper or upon the plan itself ; then it is evident that for every
length of 10 chains between two of these lines there will
be included one acre.
COMPUTING SCALES
43
A different computing scale is required for each different
scale ; they are usually 24 inches long, set off as shown, the
only difference between them being the size of the divisions.
The metal frame carrying the wire slides in the central groove
and indicates in its passage over the parallel strips of the plan,
the number of acres, roods and perches.
In using the scale it is set parallel to the lines across the
FIG. 48. Computing scale.
plan, with the wire cutting the boundary as at c. Fig. 48A, so
as to form an equalising line for the angular piece ab. The
scale being held, the slide is then moved to a similar position
at the other end of the strip, then the scale is lifted bodily and
the wire placed over the commencement of the next strip, the
scale held and the slide moved.
This goes on until the slide reaches c t>^~~ -
the end of the groove, when a mark
is made under the wire, the scale is
turned upside down, the wire placed
to the same mark and the slide then
shifted along the groove towards
the commencement again. When the end of the groove is
reached, a mark is put under the wire and 8 acres written
against it, which is the value of the double travel along the
scale. Then the scale is put the right way up again and the
slide moved as before. At the finish the slide may be in such
a position as shown in Fig. 48, when the reading should be
as many 8 acres as had been recorded, plus 1 acre 3 roods
20 perches if the slide was travelling forward, or plus 6 acres
FIG. 48A. Method of using
computing scale.
44 PRACTICAL SURVEYING
roods 20 perches if the slide had been to the end of the
groove and was on its way back.
Area by planimeter. The planimeter is another instru-
ment for measuring areas. It is a small and delicate instrument
requiring a steady hand, and is used chiefly for obtaining areas
from Ordnance maps and parish plans. It consists, as seen by
the diagram (Fig. 49), of two arms jointed together so as to
FIG. 49. Planimeter.
move with perfect freedom in one plane, and a wheel which
records by its revolutions the area of the figure traced out by a
point on the arm to which the wheel is attached, while the
point on the other arm is made a fixed centre about which the
instrument revolves.
The principle of its construction is based on Euclid II.,
12, 13, and it is fully described in Heather's Mathematical
Instruments (Crosby Lockwood, 3 vols. in 1, 4s. 6d.), vol. 1,
p. 81. In its usual form the wheel has a vernier attached to
it, and is connected by gearing to an index wheel which counts
the revolutions of the main wheel. The fixed point may be
either within or without the area to be measured. In small
plots it must be outside, and the reading given by the wheel
gear when the tracing point is moved round the whole of the
boundary is the area of the figure. When the fixed point
is within the boundary, the area of a circle, varying with the
size of the instrument, and given by a number stamped on the
top of the bar, must be added to the reading.
Simpson's rule for the area of any irregular figure is :
Divide the area up into any even number of parts by an odd
number of lines, or ordinates. Take the sum of the extreme
ordinates, four times the sum of the even ordinates, and twice
SIMPSON'S RULE
45
the sum of the odd ordinates (omitting the first and last
ordi nates), multiply the total by one-third of the distance
between the ordinates ; this equals the area.
In the survey (Fig. 50), of which the field notes are given
r l 1
Set.
Scate
FIG. 50. Survey of field.
46
PRACTICAL SURVEYING
in Fig. 51, it should be observed that the junction of the
boundaries with adjacent boundaries should be shown on the
7-92
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ac 2 'SO
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to
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N1TM
FIG. 51. Field notes for Fig. 50.
plan, but only to a very short distance, as, no offsets having
been taken to these other boundaries, some error might creep
in if they were extended more than a few links.
TEST QUESTIONS 47
QUESTIONS ON CHAPTER VII.
1. Show by neat sketches how hedges and trees are indicated on
a large scale survey plan. State the scale you have in mind.
2. Make a sketch of a field, and describe how the area is obtained
by scaling.
3. Make a sketch of a computing scale, and describe the method
of using it.
4. A planimeter is set to the 0'01 in. mark on the arm ; after
setting to zero and traversing the boundaries of a field on the plan
the reading is 2 + on the horizontal wheel, 4 by main divisions and
3 by small divisions on the rolling wheel, and 5 on the vernier.
What is the area indicated? (Ans.: 24'35 sq. in.)
5. If in the last question the plan is drawn to a scale of 2 chains
to 1 inch, what is the area in acres, roods and perches ? (Ans. :
9 a. 2 r. 38 p.)
6. A plan was assumed to be drawn to a scale of 3 chains to
1 inch, and the area found to be 10 a. 3 r. 24 p. It was afterwards
found that the true scale was 5 chains to 1 inch. What was the
true area ? (Ans. : 30 a. 1 r. 4| p.)
(NOTE. In the last answer the ratios of the areas will be as 5 2 to
3 2 , or 25 to 9.)
CHAPTER VIII
Cutting-up a plan, or arranging chain lines, for a survey Complete
survey of small field to explain routine Office plans and finished
plans Estate in detached portions, how plotted Colouring plans.
Arrangement of chain lines. It should be considered
a fundamental principle that all the main lines of a survey
should be so tied together as mutually to check each other, or
any one not so proved should have a special check line for the
purpose. These check lines may generally be made useful for
FIG. 52. Main lines for surveys.
taking offsets from, or getting the position of fences, etc.
With a little consideration one check line may often be
continued through two or three triangles, and by this much
labour is saved.
The base line, or principal line of a survey, should be laid
ROUTINE OP SURVEY 49
out on the most level and unobstructed portion of the estate,
and should be as long as possible in one straight line, although
it may be much too long for marking the side of a triangle ; in
fact, there may be two or three triangles upon it. It should
be looked upon as the backbone of the survey. Fig. 52 shows
some examples of how the main lines may be laid out;
generally they appear much more complex, because so many
subsidiary lines are required to get the intermediate fences
and boundaries. The dotted continuations are the check
lines. What are called false stations are frequently made in
poling out a base line, and the true stations are afterwards
placed as the survey proceeds.
Explanation of routine. The small survey shown in
Fig. 53 is very suitable for explaining the general routine.
The top of the field is bent inwards, forming virtually two
sides, as there must be a chain line approximating to each
important change in the direction of the boundaries, and this
will form a guide in placing the station poles. Having walked
from the gate right across the field to see the nature and
relative position of the boundaries, a commencement is made
at the top right hand corner where a station pole is placed.
Then, walking along by the brook, a pole is placed at the
further end, near the fence, in such a position that the chain
line will just clear the brook from the previous station. Then,
walking along by the fence, the buildings are taken into
consideration, and, seeing that they are small and unimportant,
it is decided to take them by offsets and sketches in the field-
book, so the next pole is placed in such a position that the
previous station can be seen and a direct chain line obtained
to the next angle of the field. Then a pole is put in at the
next angle, and the footpath, which is observed to be straight,
is crossed, and another pole put opposite the bend, where it
projects furthest into the field, in such a position that the pole
previously put in, and the one first placed, can both be
seen.
Having now obtained all the principal stations, the chaining
is commenced from the first pole and continued alongside the
brook. While proceeding, a look-out is kept and the distance
on the chain line noted and entered in the book where a line
through the fourth and fifth poles would fall. Another
station pole is put in here ; or, if short of poles, an arrow with
P.S. D
SURVEY
IN TMt PARISH OF
LONGMEAD
/JLEXANDER JONES ESQ.
BY
Surveyor
Scale -.J inch to I chain.
a
it
n
u
n
11 te&sec/ At/ Cblanet FuUarCon
. Co /K.exancter' Jones Esq.
1 1 AREA 2A. I ft. 3Oe.
FIG. 53. Survey of Brook Meadow.
COMPLETE SURVEY OF FIELDS
51
a small white flag tied to it, as in Fig. 54 ; or a " white," which
is a twig with a piece of white paper inserted in a single slit or
in a cross slit, as Fig. 55.
On completing the first chain line, the second is started,
taking care to note in the field-book everything occurring to
the right or to the left of it, or crossing it.
In commencing the third line it will be found necessary to
start some distance back from the station, against the fence,
FIG. 54. Arrow ''white" to
denote subsidiary station.
FIG. 55. Ordinary " whites.
in order to get the road, gate, and boundary properly shown
by offsets. Then, on this third line, when the point is reached
where a line through stations 1 and 5 would fall, it is marked
by a " white." Line 4 is continued through station 5 and up
to the " white " which had been left on the first line. And,
finally, line 5 would be measured from station 1 through 5 to
the " white " on line 3. The continuation of line 4 between
lines 5 and 1 forms a " tie," and the continuation of line 5
between lines 4 and 3 forms a "check," or both these
continuations may be looked upon as " ties," and then line 2
forms the check.
The field book for this survey is given in Fig. 56. In
plotting the work, which is reduced to half size for printing,
it should be remembered that a surveyor's duties do not end
in the field, and that unless he is able to submit a fairly
presentable plan to his employer, he loses credit for skill in
his work, and no one would trust a surveyor who cannot
52
PRACTICAL SURVEYING
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ier Jone
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FIG. 56. Field notes for Fig. 53.
PREPARATION OF PLANS 53
make a neat plan of his work. Neatness and accuracy
generally go together.
Office plans and finished plans. Survey plans of
estates are usually of two kinds : office plans and finished plans.
Office plans have little or no colour upon them, and the
chain lines are shown in crimson lake with the number,
direction, and station points, as shown in last chapter.
On finished plans neither chain lines nor stations should
appear, and, according to the purpose for which the plan is
required, so would be the expenditure of labour upon it in
printing and colouring.
When an estate consists of detached portions they may
appear on separate sheets in the office copy, but on the
finished plan they should, when possible, all be placed upon
the same sheet in their true relative positions and with one
north point only. Office plans are drawn to a large scale for
obtaining the area, but are often reduced upon the finished
plan for sake of appearance.
Colouring plans. When there are any large washes of
colour to be put on, or the plan is likely to be long in hand, it
may be strained down on the board by damping and glueing
the edges, but otherwise this is neither necessary nor desirable.
The -effect is increased when the green tint used for pasture
land is varied in adjacent fields. Hooker's green No. 2 may
be used in a pale tint, with more or less of Hooker's green
No. 1 added. Any blue and any yellow mixed will make a
green of some sort, but anything approaching emerald green
should be avoided. Arable land may be coloured a pale
brown by using a light tint of burnt umber or sepia. Roads
are coloured with Roman ochre. Trees and hedges are shown
in a darker green. Water is tinted with Prussian blue, dark at
the margin and softened towards the centre. Brick buildings
are shown in crimson lake. For wooden buildings Indian
yellow or Indian ink is used. Property surrounding the
estate is always left uncoloured, the only departure from the
rule being that buildings beyond the boundary are sometimes
hatched in black.
The area of the various fields is frequently marked upon
the centre of each, together with the name of the field, if it
has one. In other cases the fields are lettered or numbered,
and a reference table is put in the corner of the plan, the area
54 PRACTICAL SURVEYING
of each field is given separately, and the total added up at the
bottom. The title or heading to the plan may be put in
ornamental lettering on the finished plan, but on the office
plans plain block letters are quite sufficient. The north point
must always be put on the plan, and it is useful to show both
the true north and the magnetic variation.
QUESTIONS ON CHAPTER VIII.
1. Make a sketch of four adjacent fields, and show how you
would lay out the chain lines.
2. What are " whites " in a survey ?
3. What colours are used in finishing a survey plan ? How are
buildings indicated ?
4. Print neatly, in plain block letters g inch high, the words
"Survey Plan of," and underneath, in ornamental letters ^ inch
high, the word "Estate."
5. What are " false stations " in a chain survey, and what is the
advantage of using them ?
6. Describe the method of undoing a chain preparatory to
making a survey and doing it up again after completion.
CHAPTER IX.
Surveying woods, lakes, marshes, standing crops, etc. Example of
survey of a wood and a lake Measuring past obstructions Cross
staff, construction and use Optical square, construction and use
Setting up perpendiculars by chain only.
In surveying woods, lakes, and sometimes standing crops,
swampy ground, etc., by the chain, a system of triangulation
has to be laid down outside the boundary, and this always
involves more difficulty than measuring open land, and more
labour compared with the area, than when the lines can be
run inside the boundary. An example of the survey of a
wood is given in Fig. 57 (p. 56) with the field notes in Fig.
58, and the survey of a lake is given in Fig. 59 (p. 58) with
the field notes in Fig. 60.
Survey of a lake. In the latter case, it will be observed
that the brook feeding the lake is just under a chain wide,
and the end of the first chain would fall in the water if
measured direct. The figures at the side, crossed through,
show how the matter was dealt with. The line was first
measured to the edge of the brook in line with the station
poles, the end of the chain was then carried across the narrow
part further up and the width measured on the chain line ;
the chain then pulled forward to where the end of the second
chain would fall, and the line then proceeded in the ordinary
way.
Measuring past obstructions. In measuring past ob-
structions, one of the first necessities of the surveyor is to be
able to set up a true perpendicular ; this is easily and effec-
tively done with the cross staff or the optical square.
One form of the cross staff is .shown in Fig. 61 ; this has a
cylindrical body, with a compass on the top, and having at the
lower end a socket to go on a stick, or a screw to go on a
56
PRACTICAL SURVEYING
tripod. Smaller instruments are octagonal, with a plain
socket and without a compass. They all have slits on four
sides, i.e. at the extremities of two diameters at right angles
to each other. These slits are narrow for half their depth
and wide for the other half ; the wide part contains a wire
or horse-hair, and the narrow part is left plain for sighting
PIG. 57. Survey of a wood.
through. The narrow part on one side is opposite the wide
part on the other side, so that, in looking through, the wire
may be sighted with the station pole at each end of the chain
line. Then, looking through the slit at right angles, an
assistant may be directed to place a pole to be cut by the
wire, which will then give a line at right angles to the chain
line. A simple form of cross staff may be made by saw cuts
' /
45
75
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Survey
Hampton
FIG. 58. Field notes for Fig. 57,
58
PRACTICAL SURVEYING
in a disc of wood, say 6 inches diameter and 1 inch thick,
fixed on a pointed stick about 4 feet long.
Links
100 O i
I.... i.n.l I
FIQ. 59. Survey of a lake.
The optical square is a small circular bronze box about
2J inches diameter and J inch thick, as shown in plan in Fig. 62.
FIELD NOTES
59
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^vey of
'E&rtsmere Lake
FIG. 60. Field Notes for Fig. 59.
60
PRACTICAL SURVEYING
It contains two fixed mirrors, A and B, and sight hole C.
Mirror A is half plain glass and half silvered, as shown in
Fig. 63, and B is wholly silvered. In the position shown,
the instrument would be held in the left hand, or turned
FIG. 61. Cross staff.
FIG. 63. Enlarged view of mirror.
over for use in the right hand, according to which side the
reflection was to come from. Standing on the chain line and
sighting the pole X at the end through the plain part of mirror
A, a pole Y may be set at right angles from the position of the
SETTING UP PERPENDICULARS
61
Ehrfaf
'^chain
FIG. 64. Setting off right angle with chain.
surveyor, the exact spot being determined by the reflection
from the pole to mirror B and from there to mirror A, coin-
ciding with the pole X seen by direct vision. The position
of the mirrors is fixed by the geometrical construction shown
on the diagram, viz. perpendicular to the bisection of the
angle found by joining their centres with the two axes, the
angle of incidence being equal to the angle of reflection.
Setting up perpendiculars by chain. A perpendicular
may be set up approximately by the chain alone, use being
made of the well-known
property of three lines in
the proportion of 3, 4, and
5, forming a right-angled
triangle, as in Fig. 64.
Let a be a point in the
chain line, at which a
perpendicular is required ;
measure back 40 links to
b, and at this point put
an arrow through the 80th
link, fix the commencement of the chain at a, and taking
hold of the 30th link, pull it steadily and gently until the
sides cb and ca are tight and straight; then ac will be a
perpendicular, and may be
extended to any required
length. Although in theory
this method is perfect, in
practice it cannot be relied
upon to give the perpen-
dicular exactly, and an
error of 2 to 3 inches in a
chain length may easily
occur.
Another useful direction
is an angle of 60 degrees,
which, being repeated,
makes an equilateral triangle (Fig. 65). Measure 50 links
back and fix the ends of the chain at a and 1); take the
50th link, and pulling equally, abc will be an angle of 60
degrees.
The best perpendicular with the chain is obtained by
50* Link
FIG . 65
FIG. 65. Setting off 60 degrees.
62
PRACTICAL SURVEYING
pegging down the ends as in the last figure and marking
point c; then, reversing the chain to the other side of the line,
mark point d, as in Fig. 66, cd is then at right angles to ab.
Link
so? t,n*
FIG. 66. Setting off perpendicular to line.
QUESTIONS ON CHAPTER IX.
1. Show by a sketch how you would lay out the chain lines for
making a survey of a small compact wood of, say, 2 acres in extent.
2. Sketch and describe the use of a cross staff.
3. What is the use of an optical square in a survey ? Make a
sketch of one full size, and describe its construction.
4. In setting out a rectangular plot of land with the chain
only, how would you ensure the perpendicularity of the sides ?
5. Show by a sketch how you would make a survey of an
approximately circular gravel pit 20 yards across.
6. An optical square is found to be out of adjustment ; describe
how you would set off a true right angle with it in that condition.
CHAPTER X.
Measuring gaps and detours, view unobstructed Special precautions
when view is obstructed Measuring across a lake, quarry or bend
in river Measuring across a stream, river or valley Example of
survey at Hilly Fields.
Gaps and detours. The simplest case of obstruction to
the chain line is a pond, or bend in a brook or river, or a piece
of marshy ground, or a gravel pit or quarry, where the direction
is entirely visible but the ground cannot be walked over. In
such cases the true distance is required from the point where
the chain line breaks off to where it is again resumed ; and
frequently offsets are required at the same time to the outline
of the obstruction.
To take the case of a bend in a stream (Fig. 67), the chain
FIG. 67. Chaining round bend of river.
line proceeds up to a, and a perpendicular is there erected and
extended to b, making ab of sufficient length to clear the
obstruction. Fix a pole at c in the direction of the chain line,
setting it true by sighting through, and then set up a perpen-
dicular cd, equal to ab. The length bd will be equal to ac.
Remember to take offsets wherever necessary. If the perpen-
dicular required is very short, the offset staff may be used, being
64
PRACTICAL SURVEYING
Pio. 68. Chaining round bend in
lake.
placed by the eye, but this should only be done when it is
within, say, 15 links.
Another method of making a detour would be as shown in
Fig. 68. Measure back 50 links
from a, set up an angle of 60
degrees from b, continue be to
such a point d that an angle of
60 degrees from bed would clear
the obstruction, then at d set off
an angle of 60 degrees and place
a pole at e in such a position that
it sights truly with the chain line
and also with the angle from d.
The length be will be equal to bd,
and also de, which latter can be
measured as a check. Or the
distance de can be chained through, equal to bd, and if correctly
worked the point e will sight truly with the chain line.
Another mode of measuring the omitted portion of a chain
line when the direction is
visible is shown in the next
diagram (Fig. 69). A triangle
is laid out, all the lines mea-
sured, and the necessary off-
sets taken. In plotting the
work, the omitted portion is
calculated by the formula
given and checked by draw-
ing the complete triangle,
or, without calculating, the
triangle may be plotted to a
large scale as in Fig. 70, and
the distance ad measured off.
When the view is obstruc-
ted, extra precautions have to
be taken to ensure the chain
line being continued in the
exact direction required. In such a case, as Fig. 71, the follow-
ing method may be adopted : Set up equal perpendiculars from
a and b, of the requisite length to clear the obstruction, taking
care that the distance apart is twice the length of the perpen-
FIG. 69. Measuring omitted portion
of chain line.
GAPS AND DETOURS
65
diculars. Then before going further check the two diagonals
ad and cb, which should be equal to one another ; and cd which
should be equal to ab. Continue the line cd sufficiently beyond
the building, tree, or other obstruction, to be able to repeat the
FIG. 70. Drawing to check same.
operation with exactly the same measurements on the other
side. Make ef equal to ab, the perpendiculars eg, fh, equal to
ac and bd, and the diagonals eh, fg, equal to the diagonals ad, be;
then gh will give the true direction of the chain line, and the
distance de will be equal to the gap bg.
Measurement across a river, etc. When a river or
lake is too wide to be measured by the chain, or when the chain
FIG. 71. Chaining round building.
line has to be continued across them, the distance may be
obtained by a practical application of the properties of similar
triangles. The simplest case is that of equal triangles, as in
Fig. 72. Let ab be the chain line which it is required to con-
tinue across the river, and therefore to obtain the distance be.
From ab set up a perpendicular bd and produce it, making de
equal bd. At e set up another perpendicular ef, and then fix a
p.s. E
PRACTICAL SURVEYING
pole in such a position that it sights truly with cd and also with
ef, at point g. Then the distance eg is equal to be. Point c
is a station pole fixed to sight with the chain line before the
measurements begin.
This method answers equally well when the chain line
crosses the river at an angle as Fig. 73, the only difference
being in the order of laying out the lines. The letters show
the order of working, d is a pole put at any distance along the
bank in order that point e may be found by the cross staff or
FIG. 72. Measuring width of river at
right angles.
FIG. 73. Measuring width of
river diagonally.
optical square so that dec is a right angle. Then bf is made
equal to be and the cross staff or optical square held at / to
direct an assistant to point g, where he can place himself at the
same time in line with be, then gb is equal to be.
Another method, which has the advantage of requiring
linear measurement only, is shown in Fig. 74. The points ab
and c on the chain line are first marked by poles, then any point
d is taken, ad measured and repeated to give de, also bd to give
df, then holding a pole the surveyor proceeds to point g, where
he can sight through fe and dc. Then fg will be equal to the
required length be.
A modification of this method is shown in Fig. 75 applied
to the case of a quarry or gravel pit, occurring on the chain
GAPS AND DETOURS
67
line. The poles a, b and c on the chain line are first set up, and
then a pole is set up at d, so that both b and c can be sighted, and
FIG. 74. Another method of
measuring across river.
FIG. 75. Measuring across quarry or gravel pit.
also so that the chain lines clear the edge of the quarry. Con-
tinue bd and cd to e and /, making bd = de and cd = df, then ef
will be equal to the required distance be.
FIG. 76. Measuring river by cross
staff.
FIG. 77. Another method.
There is another method of measuring across a river by the
use of a cross staff or optical square and a little calculation, as
shown in Fig. 76. Take bd perpendicular to ab and any length.
68
PRACTICAL SURVEYING
At d set the cross staff to sight with c and direct an assistant
to e, where he places himself in line with be.
(Mg
be '
Then be :M::bd: be, or be =
Another method (Fig. 77), is to take the chain line ab
through to b, and from b set off a line be at 60 degrees with the
chain line. From c set off cd at 60 degrees with be, so that d
FIG. 78. Survey of part of Hilly Fields, Brockley.
may be sighted with ab. Then be will be equal to the required
distance bd.
Example Of a survey. Fig. 78 shows the survey of a
part of Hilly Fields, Brockley, London, S.E., the field notes
for which are given in Fig. 79. All the examples given in this
series should be drawn out for practice to at least four times
the published size, and properly finished and coloured. The
principles may be fully understood by merely reading and
examining the diagrams, but it is necessary to do the actual
plotting to a reasonable scale to obtain the full advantage.
EXAMPLE OF A SURVEY
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70 PRACTICAL SURVEYING
QUESTIONS ON CHAPTER X.
1. It is found in drawing a line between two stations that the
bend of a stream intervenes, show by sketch how this would be
dealt with practically.
2. Sketch and describe two methods of procedure when an ob-
struction occurs to the continuation of a chain line.
3. Describe how a chain line may be continued across a river and
the omitted portion measured.
4. Show by a sketch the special precautions that are necessary
in continuing a chain line when it is obstructed by an intervening
building.
5. At what distance apart would you place pickets or station
poles in poling out a long chain line, and how would you ensure
that they were in a straight line ?
6. Illustrate by sketches what is meant by gaps and detours in
chain lines and some of the methods of overcoming them.
CHAPTER XL
Plans and maps Various systems of projection Curvature of earth
not taken into account in ordinary surveys Ordnance survey
maps Surveying over hilly ground Correction for inclination,
how made Instruments for obtaining angle of slope Indicating
hilly ground on maps Hachures Contour lines.
Systems of projection. All plans and maps are drawn
upon flat surfaces, but they have to represent portions of the
earth's surface, which is, roughly speaking, spherical. An
attempt to lay a piece of orange peel flat would illustrate the
difficulty that arises in representing any large tract of country
upon a flat sheet of paper. If a terrestrial globe be examined
the lines of longitude will be seen meeting at the poles. If
all these lines were cut through and the paper removed, there
would result a number of strips with pointed ends, as Fig. 80,
which would for all practical purposes lie flat, and would
contain the representation of the whole surface with blank
spaces between the ends, and the same scale could be applied
to any part. Suppose the tapering points, with everything
marked upon them, to be widened until the strips were
parallel, then the whole of the length and breadth would be
covered and the lines of longitude would be parallel, but the
scale would be variable, increasing from the centre to the top
and bottom. This is known as Mercator's projection.
Examining the terrestrial globe again, lines of latitude will
be seen as circles, at equal distances apart from the equator
to the north and south poles, and therefore varying in
diameter, getting very small towards the poles. Looking
down upon one of the poles the circles upon that half of the
globe will be seen to be concentric, i.e. all struck from the
pole as a centre, but, owing to the curving of the surface, as
the circles get larger they will appear to be closer together,
72 PRACTICAL SURVEYING
and the countries near the equator will appear cramped along
the lines of longitude although having their proper dimensions
in the other direction. If the circles be drawn, not as they
appear, but at equal distances apart, then the scale will be
uniform along the lines of longitude and enlarged along the
circles in proportion to the distance from the pole. This is
known as Polar projection.
--- 1-
i i f\
/
t
H*
FIG. 80. Mercator's projection.
There are also Orthographic, Stereogmphic, Giwmonic, and
Flamsteed's projection applied to representations of the hemi-
sphere. These may be found described in various works on
map projection, but are of no immediate use to the land
surveyor.
Ordnance survey maps. In the Ordnance Survey,
where a considerable tract of country has to be delineated,
the difficulties are not quite so great, but are of the same
TANGENTIAL PROJECTION
73
kind, and in measuring long base lines and taking the angles
between them, spherical trigonometry has to be employed to
enable the necessary corrections to be made. In practice the
principle adopted is shown in Fig. 81, where the flat surface
FIG. 81. Tangential projection.
of the paper is tangential to the globe at its centre point, so
that the distortion is reduced to a minimum.
Surveying over hilly ground. \Vhen the area is
smaller, as in a parish or estate, difficulties due to curvature
of the earth are inappreciable, but local curvature due to
hilly ground, necessitates the reduction of inclined chain lines
to horizontal lengths. If ab, Fig. 82, represents the slope of
the ground or inclination of the chain line, ac a horizontal
line, and be a vertical one, then ab will always be longer than
ac, and as ac is the length to be put upon the plan, the
74
PRACTICAL SURVEYING
FIG. 82. Inclination of ground.
measured chain line must have some correction made. But it
may be said that if ab represents the actual surface of the
ground, and ac is the length it is bought and sold by, it would
be better to buy hilly ground, because there would be more
for the money. A mo-
/> merit's consideration
would show that there
would be no increase in
the number of houses of
a given frontage that could
be put upon it. With
corn and trees, of course,
the growth is vertical
towards the light so that
on any slope the actual
direction of the stalk or
tree is at right angles to the horizontal. There is a certain
natural distance apart for the stalks to grow whatever the slope
may be, so that although the surface may be larger on sloping
ground, the crop will be regulated by the horizontal area, and
the value will not be augmented ; in fact, hilly ground is often
less valuable, from the extra labour entailed in any operation
upon it.
Corrections for inclination. In measuring hilly ground,
whether the sur-
veyor is going up-
hill or downhill, the
same correction has
to be made, and the
practical method of
doing this is shown
in Fig. 83. Each
chain length upon
the ground is mark-
ed by an arrow,
and the chain then
pulled forward ac-
cording to the slope,
and the arrow shifted to the new position, so as to indicate
a horizontal chain length. This is better than measuring
straight through and then calculating the reduction on the
f /2 chain
to each
^ chain uphitt or down
FIG. 83. Method of allowing for sloping ground
in chaining.
STEPPING WITH THE CHAIN
75
length to give true horizontal distance. If any offsets occur
on the chain it may be pulled forward pa*rt of the way
according to the position of the offsets, so that all the offsets
will be recorded the same as in ordinary chaining.
When the angle of inclination is known the amount of
correction may be taken from the following table :
Angle.
4 degrees.
Allowance.
J link.
i
1
Angle.
14 degrees.
16
18
19|
20
Allowance.
3 links.
4
5
6
6J
Trigonometrically the additions = secant - radius.
Objections to Stepping. Some of the books and some
practical men recommend stepping with the chain on inclined
ground, as shown in Fig. 84, but it is a very objectionable
FIG. 84." Stepping " with chain.
method. The weight of the chain renders it physically
impossible to pull it out straight; very few men are able to
judge when it is horizontal, and the common plan of dropping
an arrow to plumb the end is a clumsy termination to an
altogether inadequate method. The writer has several times
tested the method with parties of students, and frequently
the corrected horizontal distances in a length of six or seven
chains has come out longer than the measurement on the slope
itself. When the method is used, a half length of the chain
should be taken, and the end on the low side held up until it
76
PRACTICAL SURVEYING
appears to be horizontal, then an arrow should be dropped,
ring downwards, to mark the plumb point under the end, the
chain then laid down and the difference between this point
and the end of chain noted, as in Fig. 83. Twice this
difference will be the amount to pull each chain forward in
measuring on the slope. This may be tried two or three
times to get the allowance as accurate as possible. If the
chaining is going to be uphill, Fig. 84 could not be adopted,
FIG. 85. Protractor with plummet.
but there is no difficulty in determining the allowance by
Fig. 83 before the chaining is commenced.
Angle of slope measured by instruments. The angle
of a slope may be taken by instruments, such as a common
brass protractor with a plummet on a long thread, as Fig. 85,
or a surveyors' card, as Fig. 86, or by an Abney's reflecting
level, as Fig. 87.
In using these instruments the surveyor sights the top rail
of a fence, or a man's head, or anything at a distance, about
the height of the surveyor's eye, as the line of sight will then
be practically parallel with the surface of the ground.
The Abney level consists of a square tube, sometimes with
OBTAINING ANGLE OF SLOPE
77
a draw-out eyepiece but no lens in it, and sometimes with a
small telescope, but neither of these accessories is of much
There is a mirror placed at an angle of 45 degrees in a
use.
draw tube at the other end, and occupying half its width ; a
FIG. 86. Surveyors' card.
horse-hair " wire " is fixed across this draw tube, cutting the
central axis and in the same line of sight as a mark cut across
the mirror. A small spirit level is attached to a vernier arm
which can be rotated by a milled wheel over a divided arc.
Bubble
FIG. 87. Abney's reflecting level.
In sighting to any point cut by the wire, the wheel is turned
until the reflection of the bubble is cut centrally by the mark
on the mirror, then the vernier is read off.
78
PRACTICAL SURVEYING
Fio. 88. Indicating hilly ground on plans.
How hilly ground is shown on maps. To indicate
hilly ground on plans there are two principal methods in
use ; one is by a special sort of shading formed by hachures
or strokes put in the direc-
tion in which water would
flow from any point on the
ground, as Fig 88. They
are darkest near the crest
of the hill, i.e. thicker and
closer together; they are
also shortest there, and it
will be noticed from the
diagram that they are all
tapering and slightly wavy.
Continuous lines would not
give the same effect ; they
require to be broken in
order to keep them fairly
close together down the
hills, and so at each joint,
as it may be called, the lines increase in number. Another
way of showing hills, principally used in military surveying,
is by putting the lines in the reverse direction, i.e. running
round the hills, as in Fig. 89,
but keeping them thicker and
closer upon the steeper ground.
In both these methods the right
and lower sides of the hills are
made rather darker than the
other parts, as will be seen on
looking at the mountain chains
in any good atlas.
Another system which has
been known and practised for
many years, is now coming into
more general use ; it is not so
pictorial, but admits of greater
accuracy and usefulness. The system is known as contouring
and the lines as contour lines. These may be called the out-
lines of horizontal sections taken at equal vertical distances.
They may be 10 to 100 feet apart vertically according to the
Fio. 89. Another method, used in
military surveying.
CONTOUR LINES
79
nature of the surface, the former, say, in London arid the
latter in a mountainous country, but the distances will also
vary with the scale, the smaller the scale the greater must
be the distance apart. In any drainage operations, especially
surface drainage, particular attention must be paid to the
Section on Line AA
FIG. 90. Plan of contour lines round a hill.
contour, and advantage taken of the natural surfaces in
obtaining the required fall at a nearly uniform depth.
Fig. 90 shows a plan of four contour lines round a hill,
which may be looked upon as coast lines formed by water
rising to different levels. When the contours are further-
apart, as across line AA, it is evident that the slope is flat, as
shown by the section A A ; and when they are closer, as at
PIG. 91. Hand reflecting level.
BB, the slope is steeper, as shown in section BB. The
highest point on a contoured surface is generally marked by
a small triangle.
Contour lines are set out in various ways according to the
circumstances of each case. A good method for a limited
80
PRACTICAL SURVEYING
area is shown in Fig. 92. Poles are set as shown by the
small circles. Levelling from a bench mark in the neigh-
bourhood by means of a dumpy level and staff, a point is
fixed between one of the outer poles and the centre one, as at
a, at the height of a given number of feet above Ordnance
datum. Another point, b, is fixed in the same way at the
required difference of level between the contours, and
afterwards point c, and so on according to the height. The
same series of operations takes place on each of the radial
lines, giving the points marked by small crosses. Then an
FIG. 92. Method of setting out contour lines.
assistant holds the levelling staff on point a, and the surveyor
stands near with a common hand reflecting level, Fig. 91.
He observes what height the wire cuts on the staff, and then
directs, the assistant to walk along the probable line of
contour, and signals him up or down until the level gives the
same reading. This is repeated to give a series of positions
shown by the short lines across the contours, working half
way from each of the radial lines. Then all the lines are
chained and the contour points taken by offsets. Contours
frequently form two or more closed rings within single larger
rings. This occurs when more than one hill rises out of the
earlier slopes, and there may be a series of contours within
these inner rings if the hills rise to any considerable extent.
QUESTIONS FOR PRACTICE 81
QUESTIONS ON CHAPTER XI.
1. How can a map which is flat represent part of the earth's
surface, which is a portion of a sphere ? Describe one method of
overcoming the difficulty.
2. Describe a method of chaining on hilly ground to ensure
true horizontal measurements.
3. With a slope of 1 in 10 state what will be the correction per
chain for length of line, and whether it will be added or deducted.
(Ans. : J link, added).
4. Show by sketch what is meant by " stepping with the chain,"
and describe the precautions necessary to be taken.
5. Sketch and describe the use of a hand instrument for ascer-
taining the slope of ground.
6. Define a contour line. Give a small specimen of hill shading.
p.s
CHAPTER XII.
Field notes for survey of small farm Sketch of chain lines Secondary
lines not falling on previous station Plotting notes and prepara-
tion of survey plan.
Survey Of a Small farm. The accompanying plan and
field notes are for the survey of a farm near Hampstead, made
some years ago when the land
was more open, by Mr. J. H.
Castle, a celebrated land sur-
veyor. Plotted to a scale of
1 chain to 1 inch on "double
elephant " paper (40 in. by 27
in.), it will occupy a net space
of 32 in. by 22 in., or on
"imperial" paper (30 in. by
22 in.) to a scale of 2 chains
to 1 inch it will occupy a net
space of 16 in. by 11 in.
True north should be at the
head of the paper, each field
should be numbered, and the
areas tabulated in one corner
of the plan. Fig. 93 shows a
rough sketch plan of the chain
lines which will be of consider-
able use in plotting the notes.
Bearing N23w. The magnetic variation was
Surrey of Fam near 20 W -> and allowance must
tvesc En\f. Han^tead. *>e made for this in plotting.
Each page of the field-book
is here shown separately. It
is sometimes difficult to get a line to fall exactly on a previous
84
PRACTICAL SURVEYING
%
f\ ^1
o o ^- o o
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FIELD NOTES OF SMALL FARM
85
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8
OD
86
PRACTICAL SURVEYING
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FIELD NOTES OF SMALL FARM
87
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88
PRACTICAL SURVEYING
station, the junction is then recorded as in the case of V70 on
line 9 in this survey, which is located by being described as
112 back from 7 '00 on 4. This difficulty often arises from the
6-ft. or 10-link pickets, or station poles, being too short to be
seen far over rough ground, and although long poles are more
inconvenient to carry about owing to their length and weight,
they are found very useful in a large survey. A flag on the
(Zl
7'
J3XI5.
19)
IO)
16)
Fio. 93. Chain lines for survey.
top of the pole, even although it is not more than 12 in. square,
by its fluttering in the wind enables the station to be seen
from a very long distance by the naked eye.
In a survey made by the writer at Epping Lower Forest,
one of the lines was 26 chains long, and yet the small flag on
a 6-ft. pole could be seen by the naked eye, which was rather
good, considering the proximity of London smoke.
QUESTIONS FOR PRACTICE 89
QUESTIONS ON CHAPTER XII.
1. What are the advantages of making a sketch plan of the
principal lines of a survey in the field-book before commencing the
chaining ?
2. What considerations would guide you in fixing the direction of
the base line of a survey ?
3. Describe how the bearing of a line may be taken in the absence
of a compass.
4. What degree of accuracy in measurement is necessary in order
that no error should exceed the thickness of a line on a scale of
1 chain to 1 inch ? (Ans. : To 1 link.)
5. A boxwood scale is marked on one edge " chains," and on the
other "88," and it is found by trial that 8 chains measure 6 inches.
Explain the proportion and use of the scale.
6. Show by a sketch how you would connect two detached
portions of an estate by chain lines so as to plot them in their true
relative position on the same map.
CHAPTER XIII.
Instructions of The Copyhold, Inclosure and Tithe Commission for the
preparation of "First Class Plans "Regulations for testing plans
Charges for surveys Errors in chaining.
First Class Plans. Very little remains to be said under
the head of Land Surveying. The Copyhold, Enclosure and
Tithe Commission published instructions some years ago (Dec.
1, 1861) for the preparation of First Class Plans which may be
usefully studied at the present time. They represent the best
procedure in official work, and are given below by permission
of the Board of Agriculture :
DESCRIPTION OF PLAN EEQUIRED.
The Plan is to be made on good drawing paper previously
mounted on linen, and is required to represent, in their true
relative positions, the several objects which occupy the surface
of the ground, such as railways, roads, rivers, lakes, ponds,
canals, streams, drains, parks, woods, fences, houses and other
buildings, bridges, etc. ; also the boundaries of counties and
their various subdivisions, such as ridings, lathes, wapentakes,
rapes, hundreds, parishes, townships, etc., and all the details
usually given in estate surveys. Plates showing the boundary
and other characteristics to be used, may be obtained by appli-
cation to the Commissioners.
The ordinary usage in other respects is to be observed, of
placing the north towards the top of the Plan, writing the
name of the parish and county and other necessary information,
as a title, the name and address of the surveyor, the date of
performance, the scale, and the total contents. And when a
parish is mapped in two or more distinct parts, a notice to
that effect must be added to the title.
TITHE COMMISSION INSTRUCTIONS 91
The Plan is to be drawn to the scale of three chains to one
inch in rural parishes or districts, and two chains or one chain
to an inch in towns. With a view to the easy determination
at any time of the contraction of the paper, a long single-line
scale, graduated to thousands, is to be drawn at the foot of the
plan when the plotting is commenced.
The lines of construction or main lines should, wherever
practicable, be laid out before they are chained, and be disposed
in the form of triangles, each triangle having a proper proof
line measured within it from one of the angles to the opposite
side.
All lines measured over hilly ground are to be reduced to
the horizontal plane.
The entries in the field-books are to be made with ink in
the field, and the chained lines are to be numbered consecu-
tively throughout the books.
The name of the person by whom the survey is actually made
is to be entered at the beginning of each book, and the date is
to be noted at the commencement of each day's work.
When alterations are made in the field-books, an explanation
of the cause of the alteration is to be entered at the same time,
and erasures in the field-books can on no account be allowed.
The chained lines are all to be drawn upon the Plan in red
ink, and marked with a reference to the number of the line in
the field-books, or to the page of the book in which the notes
of the measurement are entered ; thus, L 1, L 2, L 3, etc., if
referring to the lines, or P 1, P 2, P 3, etc., when referring to
the pages. And when several field-books are used, each book
should have a distinctive letter assigned to it, which may be
added to the reference upon the plan after the number referring
to the line or page ; thus, L 1, A ; P 1, B ; etc. The lengths of
the construction or main lines should also be added to their
respective reference numbers.
Each separate parcel of land is to be numbered upon the Plan,
the numbers following in succession from No. 1 to the highest
number required. These numbers are to correspond with those
given in the Reference Book.
The boundaries or limits of all land and parcels of land are
to be treated separately, are to be marked on the Plan, whether
they are defined by fences or not ; and where no boundary
fences exist, the exact limits are to be shown by a dotted line.
92
PRACTICAL SURVEYING
The Quantities are not to be written upon the Plan, but in
the Reference Book only.
The Quantities in the Reference Book are to be arranged in
the consecutive order of their reference numbers, and figures are
invariably to be used for the reference.
When the quantity of two or more contiguous parcels of
land is given in one sum, the reference number must be
repeated on each parcel, or the parcels must be connected by a
brace, as in the annexed sketch (Fig. 94), where it is shown by
the brace (J) that four parcels of land, the house, and the
pond are all included in the quantity assigned to No. 47.
Where the whole breadth,
or any portion of a road,
stream, etc., is included with
the adjoining field, the brace
must also be used ; and where
only part of the road, stream,
etc., is included, the exact
limit to which the quantity
applies must be marked with
a dotted line on the Plan.
See No. 48 in the annexed
sketch (Fig. 94), of which the
quantity is thus shown to in-
clude the whole breadth of the
lane, half the road, and half
the stream.
.STREAM j j s e ss en tial that the ac-
Pio. 94.-Method of indicating parcels of Curacy of the Plan, when COHl-
land taken in one area. pleted, should DC SUch that
the measurement on the Plan of the inclosures thereon re-
presented should correspond with the quantities assigned to
them in the Book of Reference, and such also as to bear the
test of comparison with any proof lines which the Commissioners
may desire to have measured upon the ground.
The working Plan, prepared as above, together with the
original field-books and Reference Books, must be sent to the
office of the Commission for examination, otherwise the accuracy
of the work can only be proved by the measurement of test-
lines upon the ground.
REGULATIONS FOR TESTING PLANS 93
The Commissioners will not pledge themselves to seal a
Plan to which any of the following objections apply,
without testing it upon the ground :
1. Where there is any reason to distrust the authenticity or
integrity of the survey.
2. Where the means afforded are insufficient to prove the
accuracy of the work in all its details.
3. Where the Plan does not agree with the field-books.
4. Where the field-books have been kept in common or
metallic, pencil.
5. Where erasures have been made in the field-books.
6. Where alterations have been made in the field-books
without a satisfactory explanation being afforded.
7. Where the offsets exceed a chain in length.
REGULATIONS FOR TESTING PLANS UPON THE GROUND.
The Commissioners will require to appoint the Surveyor to
be employed, and that a sum of money sufficient to cover the
expenses should be lodged in their hands before the testing is
commenced.
The lines which the Commissioners will require to have
measured on the ground, for testing the accuracy of the Plan,
are three lines in the form of a well-shaped triangle, with a
proof line from one of the angles to the opposite side.
In measuring the testing lines, all intersections of fences are
to be noted, and offsets taken within the ordinary limits of a
chain's length.
Distances, measured along the fences joined, are to be given
to all junctions of fences which fall within two chains of the
test lines.
The fields in which the angular points of the triangle occur
are to be wholly surveyed, or enough of their boundaries
ascertained to determine precisely the position of those points
on the Plan.
The entries in the field-books are to be made with ink in the
field, and any alterations which require to be made in them are
to be attested by the initials of the surveyor. An explanation
of the cause of the alteration is also to be entered.
A projection of the testing lines on the scale of the original
94 PRACTICAL SURVEYING
Plan is to be sent with the field-notes to the office of the
Commissioners.
The cost of testing on the ground will not, as a general
rule, exceed 1 5 for a parish or district under 3000 acres ; and
for a parish of larger size will be at the rate of 5 per
thousand acres, not including travelling expenses."
Generally speaking, in ordinary chain surveys an error of 1
perch per acre is allowable, or say 1 link in 10 chains, but in
tithe or parish surveying perfect accuracy is expected ; or, in
other words, no error must be so great that it is possible to
be detected. In railway surveying for Parliamentary Plans,
only a generally close approximation to accuracy is required.
A scale of 1 chain to 1 inch allows a difference of 3 inches upon
the ground to be detected upon the plan, and this will give
some idea of the accuracy in plotting which is attainable.
Usill says that " 40 acres per day is good average surveying,"
but this will obviously depend upon the nature of the land and
whether there are many buildings and small enclosures.
Charge for surveys. The charge for surveys may be
assumed to be approximately as follows :
For surveys of country estates : With map showing external
boundary and gross area 3 guineas, plus 1s. per acre for first
100 acres, and 9d. per acre for remainder. With map showing
boundary and area of each farm 4 guineas, plus 1s. 6d. per
acre for first 100 acres, and 1s. per acre for remainder. With
map showing fields, buildings, etc., with area of each inclosure
5 guineas, plus 2s. per acre for first 100 acres, and 1s. 6d. per
acre for remainder. Copies of the map :
Scale J in. to 1 chain, - - 1d. per acre.
J to 1 2d.
1 to 1 - - 3d.
Reductions or enlargements one-half more, but no charge less
than half-a-guinea. Elaborate plans according to time. Sur-
veys of building plots by special arrangement, from 3 guineas.
Travelling and hotel expenses in addition to above charges.
Town surveys by special arrangement.
Note on errors in chaining. Capt. J. E. E. Craster
(1911) had 208 lines chained by 40 surveyors across rough
ERRORS IN CHAINING 95
country in all weathers. The correct length of each line was
determined by triangulation unknown to the surveyors.
A few large errors in booking occurred, and other consider-
able errors were unaccounted for. Rejecting all lines with errors
of over 50 links, there only remained 196 lines giving 92
positive and 104 negative errors. The lines were grouped for
analysis as follows ;
No. of Lines. Length in Chains. Mean Error in Links.
27 70-80 10-21
32 80-90 9-5
23 90-100 10-8
34 100-110 1153
21 110-120 13-8
30 120-130 13-6
General average error, say V16 links in 10 chains.
QUESTIONS ON CHAPTEB XIII.
1. Name the usual scales for survey plans and the conditions
under which they are used.
2. Why are lines chained on sloping ground reduced to horizontal
measurement ?
3. Describe the method of testing the survey plan of a parish.
4. "What percentage will an error in area of 1 perch per acre be ?
(Ans. : i. per cent.)
5. What degree of accuracy is required in Parliamentary Plans ?
6. What would be the approximate cost of making a survey of
250 acres in a rural district, and supplying a map showing fields,
buildings, etc., with their areas? (Ans. : 26 10s.)
CHAPTER XIV.
Traversing with chain Traversing with prismatic compass Reducing
bearings Circumferentor Definition of terms used in traversing.
Traversing with chain. Traversing is the name given to
a method of surveying by which, without covering the whole
area with a network of triangles, a boundary or route, as of a
PIG. 98. FIG. 99.
FIGS. 95 to 99. Tie lines in traversing.
road or river, can be surveyed in the course of passing along
it. This may be done roughly with the chain only, the end
of each line being tied to the next by a small measured
triangle, or two triangles, variously formed according to the
PRISMATIC COMPASS
97
angle between the lines as in Figs. 95 to 99, and so enabling
any number of lines to be plotted without forming them into
the ordinary large triangles. The lines may be ten or twenty
chains long if necessary, while the sides of the triangles will
not be more than one or two chains long.
In plotting the survey it will make for accuracy if the
triangles are set off to twice the scale of the lines, but it is
quite evident that this method, although very simple, is not
PIG. 100. General view of prismatic compass.
Compass card
FIG. 101. Section of same.
very precise, as an error at any point of the survey affects the
whole of the remainder, and there is practically no check upon
the work. With proper care it may be useful in certain
circumstances, its chief advantage being that with no more
knowledge than that possessed by an ordinary chainman a
survey of considerable extent may be made with some approxi-
mation to accuracy, without any instruments beyond the chain
and station poles. Two independent surveys at considerable
distance apart may be connected upon the same principle ; all
p.s- G
98
PRACTICAL SURVEYING
that is requisite is to run a chain line between them and tie
the ends to a line in each survey by one or other of the little
triangles.
Traversing with prismatic compass. By the use of the
prismatic compass (Fig. 100 general view, Fig. 101 section
and Fig. 102 plan) greater accuracy may be obtained, as,
although the instrument is not very trustworthy, the error is
practically confined to the individual lines upon which it is
FIG. 102. Flap of prismatic compass.
used. Its construction combines a reflecting prism with a
magnetic compass. It is marked in the reverse way to what
it would be if the card were observed by direct vision ; for
example, when the needle is pointing north the eye is looking
at the south end of the card and the zero or north must be
indicated there. For the same reason the divisions appear to
be numbered backwards. The lines are chained in the ordinary
manner, but instead of tying their junctions with triangles, the
direction of each line is taken with regard to the magnetic
meridian, or, in common language, its " bearing " is taken.
REDUCING THE BEARINGS
99
There is still the liability to error in measuring the length of
the lines from omitting a chain length, but if a sufficient
distance is sighted there will ndt be any great error of direction.
A short staff is useful to rest the compass on if the hand is at
all unsteady, and if there are large water mains under the
ground, or the observation is taken in proximity to iron
railing, the compass may be affected. In compass surveys it
may be stated that the allowable error is one link in five
FIG. 103. Forward and
reverse bearing of line.
w-
FIG. 104. True direction of lines.
chains. All the stations may be known by the number of the
line which commences at that station. A circular protractor
will be found convenient to use for the plotting. The reverse
bearing should be taken on every line as a check upon the
forward bearing ; see Fig. 103.
Reducing the bearings. In reducing the bearing of any
given line to its true direction, it is well to make a sketch of a
north point with the magnetic variation upon it, as it will then
be seen by inspection whether the magnetic variation is to be
added or subtracted from the given bearing, and how many
100
PRACTICAL SURVEYING
right angles have to be subtracted to get the true bearing
(Fig. 104).
Compass surveys are usually confined to rough preliminary
work, or to filling in the details of a large survey after the
main points have been fixed by more accurate means. The
survey should be checked by taking frequent bearings to
surrounding objects that can be observed from two or more
stations.
A recent form of the surveyors' compass made by Messrs. F.
Barker & Son, Camberwell Road, London, to take the place of
a prismatic compass, is shown in Fig. 105. This compass is a
PIG. 105. Surveyors' compass.
FIG. 106. Circumferentor.
good instrument for approximate work, and, being made very
substantial in every way, will stand the rough usage often
happening when using this class of compass. The folding
sights are made with hair and slit vane on each ; this gives
the advantage of taking a reverse sight when in alignment.
The sight vanes attached to the outer limb of the compass are
made to revolve around its circumference, and a vernier also
is attached. The compass is fitted with two spirit levels, bar
needle, jewelled centre and stop, and is used with a ball-and-
socket head " Jacob-Staff."
A circumferentor (Fig. 106) is a more elaborate compass
with sights to it, which can be used for the same class of work.
It is also called a miner's dial, as it is frequently used under-
ground for surveying mines, but is not in any way to be
TERMS USED IN
compared with a theodolite for accuracy. There are certain
terms used in connection with compass surveys that it will
be well to explain.
w
Meridian of/stance -
FIG. 107. Illustration of terms used in compass traversing.
Terms used in traversing. Meridian lines are lines
lying due north and south, and all meridian lines are assumed
to be parallel.
The bearing of a line is the angle made by it with a meridian
line, and is measured either by degrees up to 360 East of
Kf2 } PRACTICAL SURVEYING
North, or by degrees up to 90 E. or W. of N. or S., according
to the mode in which the compass card is divided.
The reverse bearing is the bearing taken at the end of a
() THESE ST^RS IN UR.S* MAJOR
ARE. KNOWN AS THE POINTERS
FIG. 108. Constellations round the pole star.
line instead of the commencement, and will differ from the
latter by 180.
The difference of latitude or Northing and Southing is the
distance the end of the line is further north or south than the
beginning.
BASIS OF MAPPING 103
The difference of longitude or Departure is the distance
the end of the line is east or west from the beginning.
The meridian distance of any station is the distance east or
west from some previous fixed point, such as the first station,
and is equal to the difference between the sums of the eastings
and westings, being actually east or west from the fixed point
as the total of one or the other is greater.
These terms are illustrated in Fig. 107.
Maps are generally made on rectangular pieces of paper, and
so the positions of points on it came naturally to be spoken of
in reference to the length and breadth of the map. Also, that
part of the world best known to the Romans lay along the
coasts of the Mediterranean Sea, so that the length of the map
lay from west to east, its breadth from north to south.
Hence distances measured eastward or westward were longitudes
(lengths), distances measured northwards and southwards were
called latitudes (breadths). This method of indicating the
positions of places by means of longitude arid latitude, made
use of by geographers, has been extended to geometry and
land surveying. (Sang.)
The latitude of any place is found approximately by taking
the angle of elevation of the pole star, when the angle equals
the latitude. The constellations round the pole star are shown
in Fig. 108, and as the pole star rotates round the pole it is
clear that there are only two points in its course that will give
an exactly accurate result.
EXAMPLES.
The following examples are given for practice in reducing
bearings. A sketch should be made in each case to help the
work.
1. Given AB, S. 86 23' E., variation 23 W., what is the
true bearing 1 ? (Ans.: N. 70 37' E.)
2. Given reverse bearing N. 5 17' E., variation 21 30' W.,
what is the true forward bearing? (Ans.: S. 16 13' E.)
3. Given AB making an angle of N. 237 E., variation 18
W., what is the true bearing? (Ans. : S. 39 W.)
4. Given bearing of 1st line N. 16 W., and 2nd line
N. 57 E., variation 20 W., what is the angle between them 1
(Ans.: 107.)
104 PRACTICAL SURVEYING
5. Required the difference of latitude and departure of a
line which bears S. 16 30' E., and is 3'47 long. (Ans. : Diff.
lat. 3 33' S., diff. dep. 99' E.)
6. Given a line bearing N. 13 30' W. and 610 long., find
the latitude and departure. (Ans.: Lat. 5' 93' N., dep
1 42' W.)
7. What are the latitude and the departure of a line
bearing N. 41 9' E., and 4*47 long. 1 ? (Ans.: Lat. 3 37' N.,
dep. 2 94' E.)
8. A line bears N. 22 45' W., and is 27 '62 long. ; required
its latitude and departure. (Ans. : Lat. 25 47' N., dep.
19 68' VV.)
QUESTIONS ON CHAPTER XIV.
1. Explain by sketches what is meant by traversing with a chain,
and state why the method cannot be relied upon for accuracy.
2. Make a sectional sketch of a prismatic compass, and explain
why the north end is marked 1 80.
3. What precautions should be taken in the use of a prismatic
compass in a survey ?
4. Explain the terms " meridian line," " bearing," " reverse bear-
ing," and " meridian distance."
5. Explain how a point in a survey can be located in reference to
the starting point.
6. Make an approximate sketch showing the pole star and the
surrounding constellations.
CHAPTER XV.
Examples of open and closed traverse Reducing to a single meridian
Tables of sines and cosines Traverse tables Plotting traverse
surveys.
Open and closed traverses. An open traverse is one
where several lines are taken, which, when plotted, make
an open figure.
A closed traverse is one making a closed figure, or a survey
which is completed upon arrival at the point from which it
started.
Although the plotting may be done very carefully with a
vernier protractor, there is much risk of error, and to avoid
this risk, the whole of the traverse may be reduced to a single
meridian. That is, a north and south line may be drawn
through the first station, and all succeeding stations may be
calculated as offset points by rectangular co-ordinates, the
distances being found by a table of sines and cosines or by
traverse tables. In a closed traverse the sum of each set of
ordinates should equal zero.
Sines and cosines. A table of sines and cosines is
generally given in books of mathematical tables,* of which that
on page 106 is a sufficient extract to show the construction
and method of use.
In using a table of sines and cosines for rough work, only
the first three figures need be used, increasing the last figure
by unity when the fourth figure is 5 or higher, then multiply
by the length of the line. It should be noticed that the
figures given are all decimals. The columns headed "Diff."
show the difference between the value of one entry and the next,
so that a proportional amount may be added for the seconds in
T^TP seconds ... , 1 1 i
the bearing, viz. Diff. x = quantity to be added.
60
*See the author's Practical Trigonometry (Whittaker & Co., 2s. 6d.
net), or for a fuller set of tables, Chambers' Mathematical Tables.
106
PRACTICAL SURVEYING
TABLE OF NATURAL SINES AND COSINES.
NATURAL SINES.
'
30
Diff.
31
Diff.
5000000
2519
51 50381
2493
1
5002519
2518
5152874
2493
2
5005037
2519
5155367
2492
34
Diff.
'
5591929
2411
60
5594340
2411
59
5596751
2411
58
58
5145393
2494
5294258
2468
*
5730998
2383
2
59
5147887
2494
5296726
2467
*
5733381
2383
1
60
5150381
2493
5299193
2466
#
5735764
2383
'
59
Diff.
58
Diff.
*
55
Diff.
'
NATURAL COSINES.
Traverse tables. Traverse tables are given in some of
the larger works on surveying, of which the following extract
will be sufficient to show the construction and use :
TRAVERSE TABLES.
DISTANCE IN CHAINS, ETC.
Deg.
and
Min.
1
2
3
4
^
*
9
10
Deg.
and
Min.
66
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
4-07
24
914
407
1-83
813
2-74
1-22
3-65
1-63
8-22
3-66
9-14
3
913
408
1-83
815
2-74
1-22
3-65
1-63
*
8-22
3-67
9-13
4-08
57
6
913
408
1-83
817
2-74
1-22
3-65
1-63
*
8-22
3-67
9-13
4-08
54
9
912
409
1-82
818
2-74
1-23
3-65
1-64
*
8-21
3-68
9-12
4-09
51
PLOTTING TRAVERSE SURVEYS
107
In using traverse tables only addition is required instead of
multiplication,, but be careful to notice that between 45 and
90 the figures for latitude and departure are reversed as
marked at the bottom of each page and read upwards.
Open
IO 2
(?)
G'/S
8 73
9-24
56
T)
Compass
Mag var
O
N.I
O
O
N. 30* W.
by
Fia. 109. Field notes for
open traverse.
Fio. 110. Plotting for same.
Plotting 1 traverse surveys. The field notes above,
without offsets (Fig. 109), give the lines of an open traverse,
with their bearings taken from an ordinary pocket compass,
so that they are stated in degrees east or west of north or
108
PRACTICAL SURVEYING
south. The plotting may be done to a scale of 5 chains to
1 inch.
In order to carry out the plotting successfully it will be
necessary to reduce the bearings, and the proper way of
doing this is shown in the accompanying table. The reduced
bearing being obtained by sketching a north point, as shown
in Fig. 104 in the last chapter, the co-ordinates will be ob-
tained by calculation from the reduced bearings. With this
table the plotting may be done in various ways :
(1) Each line may be plotted from the length given in
REDUCTION OF QFEN TF&VERSE TO
Survey of _ Date
S/HCLE MER/D//7M
Mag, for. 18* til
Station
or
Observed
i//ie bear/ng
Distance
Reduced
bearings
Consecutive Co-ord/nates
LaC or cos. Dep. or sin.
Independent Co-ordinaces
Latitude
Departure
s/rw
456
Cf-24-
S-73
I0'62
3'05/Z JT
IO'6/SO^
8- 6866 W
8~ 7/80 Jf
5-5248 ^r
Surveyed by
Reduced
Checked by
the distance column and the bearing given in the column
headed reduced bearings.
(2) Each line may be plotted by measuring the consecutive
co-ordinates, the latitude or cosine vertically and the de-
parture or sine horizontally, the direction being up or down
for N. or S. and left or right for W. or E.
(3) Each line may be plotted by using the independent
co-ordinates, measuring all the latitudes from the commence-
ment of the survey and all the departures from the meridian
line through the first station.
For practice, all three methods may be carried out upon
the same survey plan as in Fig. 110.
The following field notes, without offsets (Fig. Ill), give
the lines of a closed traverse, with the bearings taken by a
PLOTTING TRAVERSE SURVEYS 109
prismatic compass or circumferentor, all the angles being
taken east of north, the compass ring or card being marked
continuously from to 360. The bearings may be reduced
as before and latitudes and departures taken from traverse
tables. In the previous example these were entered in single
columns, but it is a little more convenient to place them in
11 SO
G
275*30
O
5-IQ
3/7
827
250
10-20
@
/57 e
O
5-62
S-/4
4
57*
7-22
Closed
Jby Compass
Mag for. /8/y
FIQ. 111. Field notes for
closed traverse.
Scale
t O
Illlll I
of cha/'ns
8 IO t2
I I I I I I I
FIG. 112. Plotting for same.
double columns, as in the following form of reduction (p. 110).
It is seldom that the measurements and observations will
be so accurate that a closed traverse will exactly close. In
the above example it will be seen that there is a small error,
making the last position 0*1328 chains N. and 0'1527 chains
W. of the true place. The plotting of this survey is given
in Fig. 112.
Surveying on the meridian and perpendicular system is the
same as the method used in reducing a traverse survey' to
110
PRACTICAL SURVEYING
a single meridian. It consists of calculating and plotting the
latitude or cosine and the departure or sine of every observed
REDUCTION
Survey of
OF CLOSED TR/1VEXSE
Date
BY
TABLES
Mag. for
Station
or tine
Observed
bearing
Distance
Ffeductd
bear/ngs
Latitude
Departure
A/on/i/ngs
Southings
Eastings
Westings
1
37'
72Z
Jiq'S
G-8279
23506
2
V
S'/U-
JW&
5-6573
S'5507
3
S3'
5-62
J65'$
2-372^
s-oq2i
4-
/57'
IO'20
db/
7-GQ80
66QI8
5
230"
8-27
d32'W
7'OOq-
4--3Z3!
G
3/7
s-/s
J/G/W
2-^7/6
^5275
7
27530'
H'50
J77Vtt
2-^8qo
II 2273
J7-32Q2
/QQS52 20'/37Q
Surveyed by_
Error
-/328
'/527
Reduced bu
by.
angle and distance instead of plotting the angle with a pro-
tractor and marking oft' the distance'. In plotting a traverse
by chords a table of sines can be used. Strike an arc with a
radius of 5 units and cut it with a chord to the same scale of
5 times "twice the sine of half the angle," i.e. 10sin(jA)-
QUESTIONS ON CHAPTER XV.
1. Show by a sketch the difference between an open traverse
and a closed traverse, and explain how they are plotted.
2. What is meant by "rectangular co-ordinates," and what is
their application to a compass survey ?
3. How do traverse tables differ in their use from tables of sines
and cosines ?
4. Describe the method of using a " Scale of Chords " in plotting
an angle.
5. In calculating a closed traverse, why do the first and last
positions seldom agree ?
6. In a protractor 10 inches diameter, what will be the linear
measurement of 10 minutes of arc ? (Ans. : 0'0145 in^)
CHAPTER XVI.
Copying plans by tracing and photography Use of triangular compass
Pricking through and transfer Enlarging and reducing by pro-
portional squares Use of proportional compasses Use and adjust-
ment of pantagraph and eidograph Ordnance maps.
Copying plans. Reference was made in Chapter VIII. to
the two principal kinds of plans produced by the surveyor,
viz. office plans to a large scale uncoloured and with the chain
lines shown, and the finished plans reduced to a small scale,
coloured, and finished off artistically, for the use of the
surveyor's client. It happens from time to time that copies
of plans have to be made either upon the same scale as the
original, or to a reduced scale ; and sometimes, but rarely, to an
enlarged scale. The various methods by which these copies of
plans are made will now be described.
Tracing. The simplest way is to copy the plan by tracing,
tracing paper or linen being put over the original plan and the
lines inked in, exactly in the way the original drawing was
inked in. The tracing when on paper may afterwards be
mounted by nailing down a piece of cotton, linen, or holland
upon an old drawing board, then pasting and sticking upon
it a piece of lining paper, and lastly pasting and sticking the
tracing upon that. Linen tracings are made upon prepared
linen to save the expense of mounting, and now photography
is very largely used. A tracing in bold lines is made upon
blue shade tracing paper, and this being used as a negative, a
"blue print " with white lines on a blue ground is produced,
or, at slightly greater expense, lines in purple, brown, or black,
upon a white ground.
If the original plan is to be copied upon drawing paper, it
must be traced through upon a tracing frame, which consists of
a sheet of plate-glass in a hinged frame, which can be set up at
112
PRACTICAL SURVEYING
an angle of say 30. It is put in front of a window and the
blind pulled down to the level of the top of the frame so that
the light from the lower part of the window enters underneath
the glass and shows up the lines through the paper.
Pricking through. Another mode of copying plans to the
same scale, upon drawing paper, is to place the original over a
clean sheet of paper and to prick through with a needle at
every angle or junction of lines, and at a sufficient number of
points along an irregular boundary to enable all the lines to
be drawn when the original is removed. If the paper upon
which the original drawing is
made is sufficiently thin, the
drawing may be transferred by
inserting a piece of carbon trans-
fer paper, or what is better a
sheet of tracing paper black-
leaded on the underside, between
the original and the clean sheet
of paper. The whole of the out-
lines are then traced over with a
blunt tracer of agate or steel, the
pressure transferring the black-
lead where required to the plain
sheet of paper. These outlines
are afterwards inked in and
coloured in the ordinary man-
ner. A pair of compasses with
three legs, known as triangular
compasses and shown in Fig. 113,
is extremely useful for copying small plans, two of the legs
being set to the extremities of a base line ; the third one will
give any required point with regard to this line, so that all
points of a plan can be transferred in sequence.
Enlargement and reduction of plans. When the copy
has to be enlarged or reduced the method adopted will depend
upon circumstances. The simplest method without special
instruments is by the use of proportional squares, as shown in
Fig. 114. If squares be drawn upon the original plan measur-
ing say one chain each way, or tracing paper with similar
squares be used to lay over it, then lines may be drawn upon
the clean sheet of paper representing the squares shown to the
FIG. 113. Triangular compasses.
ENLARGING AND REDUCING PLANS 113
Scale _ 6O feet Co / inch
P.S.
Scale.. 4O feet. Co /
FIG. 114. Method of enlarging by proportional squares.
H
114
PRACTICAL SURVEYING
required scale, all the outlines upon the original being drawn
across the squares of the required plan by the eye.
Proportional compasses, as shown in Fig. 115, may be used
for fixing the proportionate distance along any square where a
line to be copied should cross, also for enlarging or reducing a
straight lined plan. The pivot is adjustable, so that the legs
may open in any required proportion. Various scales are
marked upon these compasses, but the scale of lines is the only
one commonly used. Suppose the pivot to be set to 5 on the
scale of lines, it means that the long points will open 5 times
as far as the short points in any position
of the legs, so that any distance upon an
original drawing may be enlarged or re-
duced in any given proportion for the
required drawing. With this instrument
the drawing has to be constructed, or the
survey plotted, almost as fully as if the
original drawing were being made.
The Pantagraph and Eidograph are two
very important instruments used for copy-
ing plans ; they are sometimes used for
copying to the same size, rarely for en-
larging, and very frequently for reducing.
The Pantagraph, shown in Fig. 116, is
supposed to be the most ancient of all
mathematical contrivances for copying on
an enlarged or reduced scale, and is said to
have been invented about the year 1 603 by
the Jesuit Scheiner, then a professor in the German Academy
at Dillingen. It consists of two long arms pivoted together at
one end, and two short arms pivoted together at one end,
and each pivoted to the centre of one of the long arms. These
are supported by small rollers, and one of the long arms is
pivoted upon a weight which holds the instrument in place.
The other long arm carries a tracing point for passing over the
lines of the original plan, and one of the short arms carries a
lead pencil for drawing reduced copies. The pencil is connected
by a cord to the tracing point, where a loop is placed for the
finger in order that the pencil may be raised when passing over
the space between two lines.
There are two ways of using the Pantagraph, the erect and
Pio. 115. Proportional
compasses.
ENLARGING AND REDUCING PLANS 115
reverse, the former showing the copy the same way up as the
original, and the latter producing it reverse or upside down. For
erect copies the fulcrum is placed on the long arm B and the
pencil point on the short arm A, and in reverse copies the posi-
tions of the fulcrum and pencil are simply reversed. There are
two rows of numbers on the beams the right-hand row refers
to reduction in the erect manner, the left-hand column to reduc-
tions in the reverse manner, so that remembering this no
calculation is required. The numbers relating to erect copying
may, however, be used for reverse copying, and vice versa ; but
they will give other proportions which are only occasionally
FIG. 116. Pantagraph.
required and a student need not trouble about them until they
are actually wanted.
The Eidograph (Fig. 117), invented by Professor Wallace in
1821, is used for similar purposes to the Pantagraph, but is
more elaborate and expensive, and also more correct. It
consists of a centre bar with a vernier, pivoted upon a heavy
block. At each end is a roller connected with the other by an
adjustable steel band ; these rollers each carry clamping boxes
through which the tracer and the pencil arms pass. To set
the instrument to reduce or enlarge to any required propor-
tion, take the sum and the difference of the two proportional
numbers, then say, as the sum is to the difference so is 100
to the numbers required upon the arms and centre bar. Thus,
to reduce in the proportion of 3 to 2, say 3+ 2 = 5, 3-2 = 1,
116
PRACTICAL SURVEYING
then 5:1 : : 100 : 20, 20 will be the division to set the centre
bar to, on the pencil side of 0, the tracer arm is to be lengthened
to 20 and the pencil arm shortened to 20. When the drawing
is to be enlarged in the same proportion the tracer arm will
be shortened and the pencil arm lengthened, the centre bar
being set to 20 upon the side away from the pencil.
Fio. 117. Eidograph.
Common scales of ordnance maps. The common scales
of Ordnance maps are as follows :
= 1 inch to a mile, is the small scale.
63360
1
10560
1
= 6 inches to a mile, is the medium scale.
= 25*344 inches to a mile, is the large scale.
2500
= 5 ft. to a mile = 88 ft. to an inch, is a special scale
for towns.
=10 ft. to a mile = 44 ft. to an inch, larger scale for
528
towns.
=10*56 ft. to a mile = 41 '66 ft. to an inch, is the new
500
Ordnance scale for towns.
SCALES OF ORDNANCE MAPS 117
Tithe and parish maps are usually - = 3 chains to an
2376
inch, which gives nearly one acre to the square inch.
Small estates and single fields are often plotted to ^rr =
792
1 chain to an inch.
Engineers' working plans are sometimes drawn = 100 ft.
1200
to an inch, but the Ordnance scale of is more convenient.
1056
As areas depend upon square measure, a mistake in scaling
requires the use of squaring to correct it. For example,
having used a 3-chain scale for computing the area of a field
upon a plan drawn to a scale of 2 chains to an inch, the
result was 5 acres 3 roods, whereas the true area would be
2 2
5a. 3r. x 2 = 2a. 2r. 9p. nearly.
3
Scales can be converted from one to another with a little
consideration. For example, to convert " 25 '344 ins. to
1 mile," to "chains to 1 inch," the ratio is 25'344 ins. to
80
80 chains, hence in 1 inch there will be =315 chains.
*
To make a scale to measure the chains note that 25 '344 : 80
is practically 5:16, therefore draw a line 5 inches long and
divide it into 1 6 parts each 1 chain.
QUESTIONS ON CHAPTER XVI.
1. What different methods are in use for copying survey plans
to the same scale ?
2. Describe and illustrate the method of enlarging a plan by
proportional squares.
3. Make a sketch of a pantagraph and describe its use in reduc-
ing a survey plan to half size.
4. State the general scales of Ordnance Maps for various purposes.
5. Explain the use of triangular compasses and proportional com-
passes.
6. What will be the value in feet to 1 inch of a scale of ^Q.
CHAPTER XVII
Definition of levelling Datum line Gravatt's dumpy level Construc-
tion of level Construction of level staff Curvature and refraction.
Levelling". Chain surveying forms the first portion of a
land surveyor's professional education ; it enables him to
map any plots or districts of tolerably level land, but with
that knowledge alone he cannot attempt to set out any new
roads, or lay out a system of sewerage, or project a line of
railway ; or, in fact, deal with any of the more important
work of the profession. Chain surveying may be described
as surface work, whereas levelling has to do with the height
of the different portions.
Levelling may be denned as the art of determining the
heights of any number of points above an imaginary line
everywhere equidistant from the centre of the earth.
This line, technically know^n as a datum line, is usually
spoken of as level, but it must neither be looked upon as
horizontal nor straight ; it is really curved with a radius of
rather less than 4000 miles, the mean radius of the earth, and
is the shape assumed by a vertical section through the surface
of still water.
Gravatt's dumpy level. The instrument generally used
for determining these heights is called a level, and is a
combination of a spirit level with a telescope. The one most
used by surveyors in ordinary work is Gravatt's dumpy level
(Fig. 118). It is preferred because it is less liable to get out
of adjustment than older forms, but it contains many
unnecessary details, particularly the compass. The compass
is an instrument of direction, whereas the level, in its
ordinary use, has nothing to do with direction, and the
compass in the Gravatt level is in such an awkward position
that it is very difficult to read it accurately. A 10-inch
GRAVATT'S DUMPY LEVEL
119
builders' dumpy is a light handy instrument, quite sufficient
for ordinary work, but the larger instrument is necessary for
railway work and road surveying of any magnitude.
The level is screwed on top of a tripod, as three legs will
stand firm, however irregular the ground may be.
The parallel plates, A A, hold between them a ball and
socket joint, so that the upper portion can be tilted in any
direction by the four parallel plate screws, BBBB. C is a
N
FIG. 118. Gravatt's dumpy level.
socket attached to the upper plate in which the vertical
spindle of the telescope rotates. D is a centre-bubble spirit
level for roughly adjusting the legs. E is a compass with
a tripping screw F. G is the eyepiece of the telescope
containing lenses, making it virtually into a microscope for
magnifying the image thrown upon the intersection of the
cross wires in the diaphragm at H. The object glass J is
focussed by means of the milled head screw K and internal
rack. The bubble of the main spirit level L is adjusted by
setting it over a diagonal pair of the parallel plate screws,
while the cross spirit level M is adjusted by the other pair.
120
PRACTICAL SURVEYING
N and are sight vanes for putting the telescope approxi-
mately in the right direction.
There are many details in connection with the instrument
which only an expert need trouble about, as the full
description would probably mislead most young surveyors.
For instance, in Mr. Gravatt's description we find the
following paragraph : " On the bubble tube slides the mirror
C, which is of great assistance in reading the bubble on
PIG. 119. Builders' or contractors' level.
spongy ground or in windy weather; a little practice
enabling the leveller to observe the staff through the
telescope with one eye, whilst with the other he observes that
the bubble is not disturbed by his shifting his position. If it
be disturbed, he can set it right without changing his
position ; and if he have the free use of both his eyes, he can
read the staff' and correct the bubble at once by simply
pressing the level legs."
The builders' or contractors' dumpy level is shown in
Fig. 119. This has no unnecessary fittings, but has every-
thing that is requisite for ordinary work. Its cost is under 5.
CONSTRUCTION OF LEVEL STAFF
121
The theoretical object of a level is to obtain a perfectly
horizontal line of sight from the observer's eye, the height
being taken upon a staff at the other extremity of the line.
Construction of level Staff. There are various forms of
1-60
PIG, 120. Level staff.
2-00-
FIG. 121. Enlarged view of portion of staff.
levelling staves, but that most used by surveyors is known as
the Sopwith pattern (Fig. 120), arranged in telescopic lengths.
This consists of a mahogany box, 5 feet long, 4 inches broad,
and 2 1 inches deep, within which is another hollow box,
4 feet 6 inches long, made so that it will slide easily within
the other, whilst a solid mahogany staff again works within
the latter, so that when pulled out to their full length,
122
PRACTICAL SURVEYING
having springs or clips to secure them, they represent a
staff 14 feet long.
Fig. 121 shows an enlarged view of a portion of the level
staff as it appears upon looking through the telescope. It is
divided in feet by red figures, the figure for 2 feet being
shown in the diagram ; each foot is divided into ten parts, the
alternate tenths being indicated by black figures as shown,
each figure extending over the whole space. The tenths are
divided again into ten parts by black strokes and white
INSTRUMENT
<5 CENTRE
OF CA.HTH
Pig. 122. Difference between level and horizontal lines.
spaces, each measuring one hundredth of a foot. Several
"readings" are marked upon the diagram to indicate the
method of using the staff. When a half division is cut by the
wire, the third decimal is omitted as at V925. The staff
appears upside down in the telescope, so that the readings are
taken from above downwards, and the surveyor experiences
no difficulty in this after a little practice ; in fact, he is so
used to it that he is not aware of it being upside down, unless
a stranger looks through the telescope and calls his attention
to it. It would be possible, by increasing the number of
lenses, to get an erect image, but this would be at the expense
CURVATURE AND REFRACTION
123
of some of the light passing through to the eye, and all the
light that is possible is needed in taking long sights, i.e.
reading the staff at a considerable distance.
Curvature and refraction. When the difference in
level between two distant points is required, correction must
be made for curvature and refraction.
Curvature is the difference between a truly horizontal line
and what is properly known as a level line, i.e. one following
the curve of the earth.
HORIZONTAL LINE OR TANCCNT
'CENTRE
'OF EM*TH
FIG. 123. Correction for curvature.
Refraction is the apparent raising of the object observed,
by reason of the bending of the rays of light from the object
in passing through the atmosphere.
Fig. 122 will make quite clear the distinction between the
terms straight, level and horizontal. Seeing that the instrument
gives horizontal lines only, while for determining the heights
of various points level lines are required, the reduction from
one to the other, or the correction for curvature becomes an
important matter. Fig. 123 shows how rapidly the correction
increases with increase of distance. In this case the horizontal
line appears in the position that would ordinarily be called
124 PRACTICAL SURVEYING
horizontal, but a tangent line perpendicular to any radius of
the earth would equally be entitled to be called horizontal.
The apparent height of any object reaching the horizontal line
when seen through the telescope would be that of the
observer's eye, say 5 feet, but the actual height will vary
according to the distance. The difference is about 8 inches or
two-thirds of a foot for the first mile, but increases as the
square of the distance, and thus a very simple formula may be
obtained :
(Distance in miles) 2 x | correction in feet.
The refraction is variable according to the state of the
atmosphere, but it is generally assumed to be one-seventh of
the curvature, and is always deducted from it, or in other
words the effect of curvature is always lessened by the effect
of refraction.
In some text-books it is stated that if the observation be
taken to some fixed point at a distance, as the crest of a hill,
the correction for curvature must be added, but if taken on a
staff it must be deducted. Now, the observation is never
taken practically without a staff, and therefore all cases will
come under one rule, which is as follows :
Height of reading - height of instrument - correction for
curvature + correction for refraction = comparative level of the
two stations.
It has been stated above that the correction for refraction
is always deducted from that for curvature, and it is really so
in this rule, for the whole curvature having been deducted the
refraction must be added, which is the same as first reducing
the curvature by the refraction. For example, if the reading
on the staff by the telescope at a distance of 25 chains is 7 '49,
the height of the telescope 5 -26, the difference of level
(25\ 2 2 1250
7^1 X o =
80/ 3
0065 = 0-009, 7-49 - 5-26 - (0'065 - 0'009) = 2174 ft. difference
of level, the instrument being higher.
It is necessary to be aware of all the facts above stated, but
for short distances, such as occur in ordinary work, no
correction is required. By the method adopted in adjusting
the level for collimation, which will be explained later, the
QUESTIONS FOR PRACTICE 125
allowance is adjusted automatically, although if it were not,
the error in a length of 10 chains would be only about To ^j of
a foot.
QUESTIONS ON CHAPTER XVII.
1. Explain what is meant by " levelling a section."
2. What is a datum line and how is it determined ?
3. Explain how a level line differs from a horizontal line.
4. Sketch the construction of a level and describe its adjustment.
5. Explain the corrections for curvature and refraction.
6. Sketch full size, six inches of a levelling staff, marking the
divisions upon it, including a foot figure, and indicate three
readings.
CHAPTER XVIII
Simple and compound levelling Parallax and collimation, and adjust-
ments therefor Bubble error and its adjustment Setting up a
level Holding the staff.
Compound levelling. All the remarks in the previous
chapter have been directed to what is called simple levelling ;
but there is another method, called compound levelling, by
which all the difficulties of curvature and refraction are legiti-
mately avoided, even in long lines. The expedient is very
simple and is shown in Fig. 124.
FIG. 124. Compound levelling.
By placing the level midway, or thereabouts, between the
successive stations which are selected, the effects of curvature
and refraction are neutralised, for it is evident that if the
instrument were exactly midway between two stations, upon
the same level as in Fig. 125, the back and fore sights would
show the same reading, being both subject to the same amount
oi correction, and if any difference of level existed it would be
shown simply by the difference of reading without needing
any correction. This is the method adopted in practical
PARALLAX AND COLLIMATION 127
levelling, and although the instrument cannot often be set
exactly midway between two positions of the staff, the error
cannot exceed that due to the difference of distance on the
two sides. Briefly, we may say that "simple levelling" is
reading forward to the staff from one station only, while
" compound levelling " is when the level is placed between
two staves, or two positions of the staif, and a reading taken
from each.
Parallax and collimation. There are two adjustments
requiring attention in connection with the level, one is for
parallax and the other for collimation.
Parallax is the apparent movement of the cross wires when
taking a reading, which is so perplexing to beginners. It is
partly due to the foci of the object glass and eye piece not
falling together upon the cross wires, and partly to the width
FIG. 125. Corrections equal when distances equal.
of the aperture of the eye piece allowing too great a range of
movement to the eye.
The adjustment for it consists in first focussing the eye
piece so that the wires are perfectly distinct, and then focuss-
ing the object glass so that the figures on the staff are also
perfectly distinct. Sometimes, owing to the position of the sun
in front of the telescope, it will be necessary partly to shade
the object glass with the hand, or to hold a piece of white
paper in front of it, to see the wires distinctly. To overcome
the difficulty of width of aperture the eye must be kept as
nearly as possible in the centre of the aperture. With a single
* observer there is no difficulty in adjusting for parallax, but
with a class of students using the same instrument it may need
alteration to suit individual eyesight. When the cross wire
seems to make a regular pulsation it will be due to the heart-
beats of the observer, as he will find by placing his fingers on
his wrist and noting the coincidence of the movements.
Astronomically, parallax is the apparent change of position
of an object when viewed from different places, and when it
128
PRACTICAL SURVEYING
is said that a fixed star has no parallax, the meaning is that,
when viewed from opposite extremes of the earth's orbit,
roughly a base line of 200 million miles, the angle appears to
be unaltered, showing the infinite distance of the star compared
with this comparatively long base line. Even in the case of
the nearest star Alpha Centauri the angle between two
lines drawn from the star to the ends of this great base line is
only V5 seconds of arc.
Under the head of collimation two or three different adjust-
ments are usually included. In the first place, a line joining
the centre of the object glass with the intersection of the cross
wires is called the "line of collimation." A line joining the
centre of the eye piece with the centre of the object glass is
called the "optical axis" of the telescope. A centre line
Levet, &rgre Let/et Theo&oLite
FIG. 126 Arrangement of wires in levels and theodolite.
through the spindle or axis upon which the level turns is
called the " vertical axis." Then the spirit level may be con-
sidered to have an axis or centre line such that this line is truly
horizontal when the bubble is in the centre of its run. Now
when the level is in adjustment the line of collimation must
pass through the optical axis and be parallel to the axis of the
spirit level and perpendicular to the vertical axis.
The adjustments for collimation vary in the different forms
of level, and should as a rule be left to the makers, except in
the case of the diaphragm requiring a new wire, which every
surveyor should learn to put in and adjust afterwards. Fig. 1 26
shows the general appearance of the aperture in the diaphragm
with the wires. Suppose one of these to be damaged, the
surveyor must take the diaphragm in his hand and put a drop
of stiff gum or glue on each side and then lightly strain a
thread from a spider's web across it, give it a minute or two
to set, and then cut the loose ends off with a pair of scissors.
ADJUSTMENT FOR COLLIMATION 129
Marks will generally be found upon the diaphragm to show
where the wire should cross it. The diaphragm should then
be replaced, and the adjustment will be carried out by proceed-
ing as in Fig. 127.
Set the level up midway between two stakes driven in the
ground about four chains apart. With the bubble central
for each reading, whether it reverses properly or not, sight
the staff at A and B and drive down the stake that gives
the lesser reading until they are both equal. Then shift the
instrument to about 20 links from one of the stakes and
take the reading from both. As they are both at the same
Set JbuobLe central for each
Dr/ve a/own n/gher stake
both awe same
V
A
Stake
2 chains - *& - 2 cfia/ns - +1
Ac//ts$C Gf/<yphrcK?sr> to recraf same on C crnaf D
C '1T"
Fio. 127. Adjustment of level for collimation.
level they should give the same reading, and if they do
not, by slackening one of the diaphragm screws on the vertical
line and tightening the other, it will soon be seen which
way the diaphragm should be moved to make both readings
alike.
Bubble error. If the bubble does not remain central when
the telescope is reversed there is a bubble error. This may
generally be neglected if the bubble is set in the centre of its
run for each direction of reading, but it may be easily corrected
by shifting it half the required distance by means of the parallel
plate screws and the other half by the clamping nut under the
end of bubble tube.
Setting up a level. In setting up a level preparatory to
taking a reading, first see that the parallel plates are parallel,
p.s.
130 PRACTICAL SURVEYING
or nearly so, and alter if necessary by the screws. Let the
screws be just up to their work, not jammed, nor off the lower
plate. Then open the legs equally to an angle at the top of
about 30 degrees, or 75 degrees elevation from the ground.
Stand between two of them and grasp the head of the tripod
with the left hand just below the parallel plates. Turn the
telescope across the direction of the leg on the right, and hold-
ing the leg about the middle, move it to or from you until the
bubble is central, when the point of the leg is on the ground.
Then turn the telescope in the direction of the leg on the right
and move it in or out to bring the bubble central in that
direction. See that the legs are firmly set in that position,
and then with both hands released, set the telescope over a
diagonal pair of the parallel plate screws and obtain the final
adjustment by the screws, the direction for movement being
" thumbs in for bubble to the right, thumbs out for bubble to
the left." Then turn the telescope over the other pair of screws
and adjust. The bubble should now remain central in any
position of the telescope, and if it does not it is better to let
the maker examine it and put it right.
The next step is to focus the eye piece until the wires are
distinct, always turning it to the right while moving in or out,
to avoid the chance of losing the cap or pulling out the eye
piece like a cork and damaging the wires by the rush of air
into the telescope. The object glass is adjusted for each reading,
and no attempt should be made to raise or depress the eye piece
in order to get a red figure within the field of vision. When
the telescope is so close to the staff as not to show a red figure,
the latter can be read from the outside by looking along the
barrel of the telescope level with its centre to see where it
points.
To adjust the screws of a tribrach or three-screw level, the
telescope is first placed parallel with the paired screws and
adjusted in the ordinary way, and then over the single screw
which is adjusted to bring the bubble central. A surveyor who
has been used to the four-screw level fails to find any advantage,
in time or convenience, in the newer form, unless perhaps on
rough ground or hill-sides, where it may afford rather more
range in the position of the legs without straining the
screws.
" An ounce of practice is worth a pound of theory," and an
HOLDING THE LEVEL STAFF
131
early opportunity should be taken to practise the operations
described above. A beginner after a little practice should be
able to set up and adjust a level in one minute and level twice
over the same mile, i.e. there and back, without a greater
difference in the result than one-tenth of a foot. If anyone is
nearer than that without much practice the accuracy is acci-
dental. Learn first to work accurately and afterwards rapidly,
speed soon comes with systematic work. In levelling long
lines the permissible error is proportionately less, varying as
the square root of the distance, e.g. 9 miles = ^ foot.
There are some curious points in connection with levelling
F
PIG. 128. Obtaining reading when staff is vertical.
which a careful study of a surveyor's notes will reveal. For
instance, Mr. Bunt, a surveyor, in 1837-8 found in 74 miles,
that each stage of 2 to 6 miles, although levelled very carefully
both ways, always came out less by levels returning than by
levels going, or the starting point appeared lower upon return-
ing than upon setting out. In levelling uphill there will be a
general tendency to make the backsights too great, and vice
versa. Also the settlement of the staff in turning round on
soft ground increases the reading of the backsights.
Holding the Staff. The greatest care should be observed
in holding the staff so that it is perfectly vertical when the
reading is taken. The staff holder should see that, when
wanted, each length is drawn out to its full extent and the
132
PRACTICAL SURVEYING
spring clips are secure. Some surveyors instruct their staff
holder to stand behind the staff and to wave it slowly back-
wards and forwards as in Fig.
128, they then take the lowest
reading that is seen, as that
must necessarily occur when the
staff is vertical. It is better,
however, that the staff holder
should stand at the side and
be responsible for keeping it
upright, a chance assistant is
liable to wave the staff without
reaching the vertical. There
should be an intelligible code
of signals between the leveller
and the staff holder, and when
once upon a back or fore sight
the holder must never move
until so directed by the sur-
veyor.
The illustration (Fig. 129) is
Fio. 129. How NOT to use a level. , - , v &
an example of how not to use
a level. No part of the hands, body or clothes should touch
the legs while taking a reading.
QUESTIONS ON CHAPTER XVIII.
1. Explain the difference between simple and compound levelling.
What corrections have to be made in the former case ?
2. What is parallax in the telescope of a level and what adjust-
ment is made for it ?
3. Define the " line of collimation " and explain how this may
differ from the optical axis of a level.
4. Illustrate by sketches and describe how a level is adjusted for
collimation.
5. In using a level with a bubble out of adjustment what pre-
caution must be adopted in taking a reading ?
6. Describe the setting up and adjusting of a three-screw level
ready for taking a reading.
CHAPTER XIX.
Levelling a section Running or flying levels Check levels Bench
marks Ordnance datum Reducing levels Plotting sections
Minus readings.
Levelling a section. In levelling over any ground for
the purpose of obtaining a section, it is requisite to measure
the distance between the various stations of the staff, but the
completeness of the Ordnance Survey maps renders this in
some cases unnecessary. In all cases it is of very great assist-
ance to have the Ordnance map of the district traversed, but
where this is not available the operations generally involve
chaining as well as levelling. For merely finding the difference
in level between two distant points, or checking the levels of a
previous survey, no measurements are needed.
Running or flying levels. The simplest work in levelling
consists of taking running or flying levels for the purpose of
ascertaining the relative height of two points, the starting
point and the terminal point. In this case, if the distance
require more than one sight to be taken, compound levelling
is adopted, as explained in the last chapter, the stations for the
staff being taken as far apart as the figures can be read, irre-
spective of the nature of the ground, i.e. without regard to the
level of intermediate points.
Check levels and bench marks. Almost as simple is
the work of taking " check " levels, which consists of checking
the heights of various points along a line previously levelled.
These points are, at certain levels, greater or smaller according
to the nature of the work, selected by the person who made
the original section, and are generally curbstones, milestones,
coping stones of bridges, plinths, hinges of gate posts, stakes,
marks cut on trees, walls, etc. in fact, anything easily found
again and not likely to shift. All these points are known as
134 PRACTICAL SURVEYING
bench marks. They are marked on the survey plan " B.M.
No. ," with a description of where they are to be found.
Bench marks should be recorded about every half mile, so
that in case of accident a return may be made to the last bench
mark without much extra labour. The first bench mark should
be referred to some well-known level in the neighbourhood.
Ordnance datum. The standard or Ordnance datum is the
assumed mean half-tide level of the sea at Liverpool, marked
on the entrance to the Mersey Docks, and all the figures indi-
cating the level on Ordnance Maps are the heights above this
datum. It is now found, however, that Ordnance datum as
fixed at Liverpool is 0*65 feet below the general mean level of
the sea as determined by observation at 32 places on the coast
of England and 1 8 on the coast of Scotland.
The H.W.M. of ordinary tides on Ordnance maps represent
mean tides, i.e. tides half-way between spring and neap, and
are generally surveyed at the fourth tide before new and full
moon. Trinity High- Water Mark, which is much used as a
datum in London, and is required to be marked on all draw-
ings of sections of property adjacent to the river when sub-
mitted to the Thames Conservancy, is 1 2 feet 6 ins. above the
Ordnance datum (or, more exactly, 12 - 48 feet). It is the level
of the lower edge of a stone fixed in the face of the river wall
upon the east side of the Hermitage entrance to the London
Docks. It may be remarked here that all retaining walls, em-
bankments, etc., adjacent to the river Thames must be carried
up to a height of 5 ft. 6 in. above T.H.W. This was formerly
5 feet, but in consequence of floods, said to be due to the
Thames Embankment, it has been increased to 5 ft. 6 in.
The ordinary ruling of a level book for each opening is shown
below in Fig. 130.
In taking running levels, the staff is first of all set up on
some point which is to be the starting place, and should be
such as may be easily recognised at a future time. The level
is then carried forward to a distance of 2 or 3 chains, less or
more, according to the nature of the ground, the clearness of
the weather, and the size of the instrument. It is then
adjusted and directed to the staff. The height is recorded
in the level book under the column "back sight," and
in the column of remarks is entered "B.M. so and so,"
describing its position exactly. Then the level remaining in
REDUCING LEVELS
135
the same position, the staff is carried forward an equal distance
beyond it, and the height read off and entered in the column
" fore sight," in the next line. The staff is then turned round,
but kept upon the same spot, while the level is carried forward
to any convenient distance, the height of the staff being now
read as a " back sight " and put on the same line in the book
as the last fore sight, because it is really the same point read
from a different position. The same course of operations is
repeated until the destination is reached. Then by adding up
the two columns and putting the smaller under the greater, and
subtracting, the difference in level will be obtained. If the fore
sights make the greater total, the starting point was the higher,
and vice versa, or the larger reading for fall, smaller for rise.
-Severe for name of place one* a/oce
BACH.
SiCMf
INTER-
MEDIATE
FORC
SCMT
RISC
^
REDUCED
LEVELS
DISTANCE
TOTA L
C5iS T AN < :E
I*. - - - ifffc hand page 4* /?/<?/* hand txxae -*\
PIG. 130. Ruling for level book.
Reducing levels. Now it is evident that between each
back and fore sight there must be a certain rise or fall; if then
the rise or fall at each point be entered in the proper column,
it can be carried further, and under the column of reduced
level or " height above base," by addition or subtraction, an
entry can be made of the level of each point above the datum
line. Every page should begin with a back sight and end
with a fore sight. Then at the foot of each page the rise
column and fall column should be added up, the lesser total
put under the greater and subtracted, and if the reductions
have been made correctly, the remainder will exactly equal the
remainder found under the back and fore sight columns. This
is a valuable check upon the accuracy of the entries, and each
page of the book should invariably be served in this way,
carrying forward to the next page, not the final balance, but
the total of each column.
136
PRACTICAL SURVEYING
When a true section of the ground is to be made, the
distance between each position of the staff must be measured
and entered in the column of distances, or all the positions
measured in one line from the starting point, and the entries
made in the columns of total distance similar to a chain line.
When the ground varies in level at short distances, intermediate
sights are taken and entered in the column of intermediates,
the back sight columns being reserved for the first reading
after shifting the level forward, and the fore sight column for
the last reading before shifting it forward again.
It is necessary to bear in mind that after every back sight,
Levels at H/grnbury , London, N. 3
| BACK
1 SIGHT
INTER-
MeDlATE
FORE
SICHT
R,*E
FAU.
DEDUCED
LEVELS
>STANCE
TOTAL
DISTANCE
REMARKS
7 O2
7-95
667
3-01
2-03
4-01
S-92
10-00
14" Ol
/9'93
1-20
/88
o-oo
1-20
3-O8
8M on /oovemenc
uoper siclt of lamp
pose . courier of
Highbury Oescenc n
660
O-38
4-rv
24-72
2-00
5-08
5-J6
f-31
529
30-01
2-52
7-6O
333
O-39
437
34-38
2-80
IO-4O
r02
231
36-69
O-80
n-20
O4i
O-G/
37-30
OB M <y> e>'tr comer
35-93
863
27-30
27-3O
II- 2O
863
2T30_
Fh
x to s
cafes o
f Hor
/ch -/
in, Vei
TV >O f
C / in.
FIG. 131. Levels at Highbury, London, N.
however many intermediate sights there may be, there must
come a fore sight. These back and fore sights forming two
ends of one stage in the levelling. The columns headed back
sight, intermediate, fore sight, distance, and remarks, are called
field columns ; while the rise, fall, reduced level, and total
distance columns are called office or plotting columns, because
they can be filled in afterwards.
The method of working out the levels will be understood
clearly by reference to the above example (Fig. 131), the
levels being plotted as in the section Fig. 132.
Plotting sections. In plotting a section a horizontal line
should first be drawn for a datum or base line. This should
always be low enough to allow of the surface of the ground
PLOTTING SECTIONS
137
appearing above it at all parts of the survey ; common depths
are 20ft., 50ft., 100 ft.
After the datum line on a plan is drawn, the distances noted
FIG. 132. Section plotted from Fig. 131.
in the level book, which have been corrected for inclination
when chained, should be set off along it, and a perpendicular
drawn at each point. Upon these perpendiculars the heights
FIG. 133. Ordnance bench mark.
FIG. 134. Reading to Ordnance bench mark.
or reduced levels should be marked, and the outlines of the
surface of the ground drawn through. The vertical scale of
the section is generally much larger than the horizontal, in
order to magnify the irregularities of the ground for instance,
138
PRACTICAL SURVEYING
a common proportion is 4 in. to the mile horizontal, and 1 00
ft. to the inch vertical.
The Ordnance bench mark, as cut on piers and walls, is
shown in Fig. 133. In reading to an Ordnance bench mark,
as shown on the pier in Fig. 134, if the wire cuts above the
PIG. 135. Reading downwards from string course.
centre of the horizontal groove, the blade of a pocket knife can
be put in the groove and the staff rested upon it while the
reading is taken ; but if the wire cuts below the mark, the
operation will be as shown in the diagram. The staff is rested
on the ground against the pier and the reading taken as 0*82,
then the centre of the groove is sighted across to read 1 '53,
then the difference between 0'82 and 1 -53 = 0'71, entered in the
book as - 0-71, because it is a reading from above downwards.
MINUS READINGS
139
H/'U t Main ancf Cross -Section
/9OO
BACK
SIGHT
INTLR-
MEDlATC
Font
SIGHT
RISE
FALL
DEDUCED
LtVtLS
)lSTA,NCC
TOTAL
DISTANCE
R.MA,.,
2 80
100 '00
o-oo
fl ''^
&70
390
96 -SO
1-44
1 44
on cop of toil
165
IT4O
4 70
9/-4O
/42
286
382
2-19
8921
1 45
431
*f func of cross-rooas
2-50
f32
90-53
fSOuo road on (eft
923
-73
8380
2-OO r/ght
075
739
t-84
85-64
1-20
SSI
O-5O
/2-95
-18
7346
2-00
751
O-40
//6S
//J5
62-11
1-44
895
2 87
ft- 54
II -14
5097
142
10-37
9-OS
6-/8
44-73
1-96
t2'53
8-M. o* fXt^n^nC cf
8-75
63-96
3/C
5937
55-21
/2-3J
. &ae of /Y yafe/vat/
8-75
3/6
53- 21
55-21
Pioc CO scates of fior 'ch //>., Verf 20 ft - tin.
PIG. 136. Levels at Primrose Hill.
Another case of reading downwards occurs when the underside
of a string-course is made a bench mark, as in Fig. 135, giving
a minus reading of 8 37. In reducing levels a minus reading
is treated in the opposite manner to an ordinary reading,
deduct instead of add, or vice versa.
ROSS - SCCTION ftr <J'3I
FIG. 137. Sections plotted from Pig. 136.
140 PRACTICAL SURVEYING
The preceding levels (Fig. 136) taken at Primrose Hill,
London, show examples of main and cross sections, and the
method of plotting them is shown in the accompanying
section (Fig. 137).
QUESTIONS ON CHAPTER XIX.
1. Explain what is meant by running or flying levels.
2. Define the terms "check levels," "bench mark," "Ordnance
datum."
3. What is the level of Trinit}*- High Water Mark in London
compared with Ordnance datum ?
4. Show by a sketch the columns used in a level book, and give
three lines of entries.
5. When are "intermediate sights" used in levelling, and how
is the reduction of the levels checked ?
6. Sketch an Ordnance bench mark full size, and indicate at
what part the level is taken.
CHAPTER XX.
Notes for part of a main section Plotting of same Working section
of short piece of railway Description of features shown Rise and
fall method of keeping level book contrasted with collimation
method Telemetry, or optical measurement of distances.
Part of a main section. The following notes (Fig. 138),
form part of a main section, and are typical of the work
required in levelling over the route proposed for a line of
road or railway, and in practice, at each point of a road
crossing the line of levels, cross sections would be taken in
order to judge of the approaches and what alterations they
would require. The fall of the ground across the line of
section must be noted in railway surveying to enable the side-
widths to be calculated, but this will be dealt with later under
engineering field-work.
The plotting of this section is shown in Fig. 139. A study
of the remarks column in the level book will show how it is
utilised as a field book to give particulars of features and
points on the line of section, which are required to be
indicated, but where levels are not required to be taken. It
should be noted that each page begins with a back sight and
finishes with a fore sight, and that the entries are checked by
totalling up at the bottom of the page as already described.
The working section of a short piece of railway is shown in
Fig. 1 40, where the gradients laid down upon the section are
the flattest available, being so placed as to cause the
excavation and embankment to balance each other, and
avoiding the provision of a "spoil bank" for excess excavation,
or the purchase of embankment material owing to deficient
excavation. The part from A to L is in cutting, and that
from L to D in embankment, with a bridge over the river at
C. The gradient is so arranged as to give headway under
142
PRACTICAL SURVEYING
71
11
II
!
I J ?
^
8 CiK&S 8
6 <i)<a(\4 ^
II
5 S
X. X
i*
II
$ S 5
fn (
MAIN SECTIONS
143
338?"
OO-OO/ (MO
144
PRACTICAL SURVEYING
the road bridge at B and over the river at C. At D a road is
crossed on the level. The gradient from D to M is placed so
as to give headway for the road bridge at M and will
necessitate raising the approaches to the road bridge at E, as
shown by the cross section. From M to the terminus the
gradient is kept up to give extra headway over an important
Fio. 140. Working section of short piece of railway.
river. This will be sufficient to show the general principles
that govern the work.
Keeping the level book. The mode of keeping the level
book in the examples shown above is known as the rise and
fall system, and is applicable to all cases, but there is another
method of keeping the book used by some surveyors, known
2$ 59 /24 >52 H6 08 SSO $4 JOOchs
Fio. 141. Section for comparison of methods of keeping level book.
as the collimation method. This is more particularly
applicable to level sections where there are many inter-
mediates, such as spot levels in land drainage, etc. ; an
example of the same section will be given, worked by both
methods. Surveyors who use the collimation method speak
of the line of collimation as an imaginary level line drawn
from the back sight reading on the staff through the telescope
to the fore sight reading, and this perhaps gives the clearest
idea. Fig. 141 is a single section, Fig. 142 is the level book
TELEMETRY
145
by rise and fall method, and Fig. 143 the level book by
collimation method for the same section.
BACK
SIGHT
INTCK-
MEDIATC
FORC
SIGHT
RISE
FALL
DEDUCED
LEVELS
^STANCE
TOTAL
DISTANCE
REMARKS
4-Z8
2O-OO
o
B.M.
-28
2-00
18- OO
25
8-59
2 -SI
IS'GS
59
3-96
7-88
071
16-40
124
2-75
121
17-61
/S2
4-9G
2-21
/S-4O
/86
5-20
7-58
2-62
12-78
208
T2S
2-05
JO-73
250
e-ca
O'G3
lt-36
254
'25
0-37
U'73
3OO
13-44
21 7 1
2-92
///9
2O-OO
1344
2-32
11-73
8-27
8-27
8-27
FIG. 142. Level book for Fig. 141 by " rise and fall' method.
DISTANCE,
READINGS
COLUMATION
REDUCED
LEVELS
O
25
53
124-
/as
208
230
254
300
4-28
6-28
7-88
2428
17-98
20-00
18-00
I5-G3
16-40
/7'6/
I5-4O
I2'78
12-78
tO-73
11-36
/I-73
81-44
71-52
3-9G
2'7S
7-58
6-20
T2S
6-62
7/-6O
/78~88
2SO-48
178-88
7/-60
REMARKS
PIG. 143. Level book for Fig. 141 by "collimation" method.
Telemetry. The optical measurement of distances, or
telemetry, is extremely useful in connection with levelling.
Every schoolboy is aware that when he views distant objects
p.s. K
146
PRACTICAL SURVEYING
through a telescope, while they are apparently brought
nearer, they still appear to vary in size according to their
distance. All that is required to convert an ordinary
telescope, whether independent or connected with a level or
theodolite, into a telemeter, is to fix two additional wires
upon the diaphragm in such a position that when the staff is
100 feet away they shall appear exactly a foot apart, then for
50 feet they will appear to be separated by five-tenths of a
foot, 30 feet by three- tenths, 120 feet by one foot and two-
tenths, and so on.
Upon the Continent, where the metric system is in use, this
mode of measuring distances is extensively practised, with a
very considerable saving of time and labour. The telescope
is arranged with three horizontal wires, one of them central,
and the others indicating a space equal to two metres upon the
(e)
FIG. 144. A, Ordinary webs in a level ; B, stadia points in a level ; c, extra webs for
telemetry ; D, lines engraved on glass diaphragm ; E, stadia points for telemetry.
staff when at 1 00 metres distance. The staff is marked with
metres and centimetres, but of double size, i.e. 2 metres is
marked 1 metre, 40 centimetres as 20, etc. ; then when the
telescope is set level the top reading minus the bottom
reading, multiplied by 100, gives the distance, and the top
reading plus the bottom reading gives the level. For
example, if the top reading be V69, and the bottom be 0'83,
the distance will be (1 *69 -0'83) x 100 = 86 metres, and the
level will be 1 -69 -f 0-83 = 2'52 metres; the middle wire reads
V26, and this, being doubled on account of the enlarged
divisions, will prove a check upon the latter figures.
The webs for ordinary use in a level are shown in Fig. 144A,
and stadia points of platmum-iridium, as in Fig. 144B, are
sometimes substituted for them. For purposes of telemetry,
extra horizontal spider webs may be put in the diaphragm, as
Fig. 144C, or a glass diaphragm with lines engraved on it, as
Fig. 144r>, or platinum-indium stadia points, as Fig. 144E.
QUESTIONS FOR PRACTICE 147
QUESTIONS ON CHAPTER XX.
1. In plotting a main section of levelling how are cross sections
indicated ?
2. Show by sketches how the difference between cutting and
embankment is indicated on a plan.
3. Explain the collimation method of keeping a level book.
4. What do you understand by telemetry ; how is it carried out
and what are its advantages ?
5. Explain how the cross wires of a level are adjusted in the
telescope. What substitutes can be used for spider web ?
6. What are "stadia points" in a level? Give an example of
their use.
CHAPTER XXL
Levels of building plots Equal vertical and horizontal scales Spot
levels Building plot with sections Building plot with sections
and contour lines Levelling with barometer Surveyors' compen-
sated aneroid barometer and method of using.
Levels Of building plots. Architects frequently require
the levels of building plots taken so that they may design the
building to suit the ground, or determine what alteration
must be made to the ground to suit the building. As their
FIG. 145. Plan of plot showing method of taking levels from two points.
drawings are generally to the scale of J in. to 1 ft. that will
be the scale, both vertical and horizontal, to which the levels
of building sites should be plotted.
Fig. 145 shows a very simple case, where the whole of the
readings can be taken from two points, marked respectively
1 and 2. The instrument being set up at 1 and adjusted, a
reading is taken to the staff held on the boundary at A and
entered as a back-sight. Then at any required intervals,
LEVELLING BUILDING PLOTS
149
measured and recorded, intermediate sights are taken, and
the last entry sighting to B before shifting the instrument to
Levels of but'lafing /XoC.
BACK,
SIGHT
INTER-
MEDIATE
FORC
SIGHT
R.SE
FALL
DEDUCED
LEVELS
5l5TANCt
"IOTA.L
DISTANCE
r66
20-00
/?
2-2S
O'SB
/3-4f
10
^79
O'S4
18-67
2O
3'47
O'68
I8'I9
30
4-O4
O'S7
/7-6?
40
4-93
O'SS
/6-7
BSO
5-54
0'55
/6-/2
20
36
O'8Z
rs-so
40
7-26
O'9O
I4'40
60
8-35
/'09
13-31
C80&
7-25
no
1441
25
6-48
077
/S/8
D. SO
4-45
2-05
t72l
40
/66
273
2000
A
6-6S
6-69
FIG. 146. Levels of building plot.
the new position is entered as a fore-sight, which becomes the
back-sight when the instrument is set up at 2.
18/9
14 4 O
I5-3O
FIG. 146A. Plan of same.
Fig. 146 gives the copy of the level book with sketch and
Fig. 146 A the plotting of the plan of a site where one position
150 PRACTICAL SURVEYING
of the level was sufficient, and there was therefore only a
single collimation line for the whole survey.
Spot levels. When the levels are marked upon the plan,
they are called spot levels, and this applies also to random
levels taken anywhere about a plan so long as they can be
located with sufficient accuracy to be suitable for the purpose
intended. They are used when a section is not required to be
drawn, as in many cases of land drainage, etc. From the spot
levels a section can of course be drawn in any direction, the dis-
tances being scaled from plan and the levels used as ordinates.
Fig. 147 shows the plan of a building plot with measure-
ments and levels marked on. A section is also given along
each boundary, and this must always be drawn as seen when
facing the side, to be of any use in connection with the design
of the building.
Fig. 148 shows the same plot contoured from the sections
just drawn with the addition of levels on the diagonals. The
verticals being marked on the sections at every 1 ft. difference
of level, the points are transferred to the plan, and a line
drawn through all those points indicating the same level.
Levelling with barometer. In hilly countries another
instrument is sometimes used for approximate levelling, viz.
the aneroid barometer, invented by M. Vidi in 1844.
The ordinary barometer contains a glass tube, closed at the
top, about 32 inches long with a column of mercury in it,
the lower end of the tube being turned up and enlarged to
form a reservoir. The top end of the tube being closed, and
having a vacuum in it, the mercury is supported by the pressure
of the atmosphere upon its surface in the reservoir, and as the
pressure varies by atmospheric disturbances so the top of the
mercurial column varies in height, which is registered against
a scale of inches and tenths. The mercury would fall in the
tube if this instrument were carried up a hill, because there
would be less weight of atmosphere above to balance the
mercury, but it would not be possible to carry it about
without extreme care, as the mercury would hammer the
top of the tube off.
In levelling with a mercurial barometer the approximate
difference in level in feet is given by the formula
H-fe ( +117 for each degree J(T + J) exceeds 60,
X 55?6 1 - 117 falls short of 60,
LEVELLING WITH BAROMETER 151
where H = height of barometer at lower station, h = height of
barometer at upper station, T = temperature in F at lower
station, t = temperature at upper station.
The aneroid barometer contains no mercury or other liquid,
and, being small, is specially adapted for portable use. The
principle of it is that two concentrically corrugated discs are
fixed together inside by their edges, so that the pressure of
the air outside them may compress them or allow them to
expand. When carried to a higher level the pressure is
reduced, the plates separate more and the movement is in-
dicated by a pointer attached by gearing to the moving
plate.
Fig. 149 shows a surveyor's aneroid compensated to allow
for changes of temperature. The face is marked with a fixed
scale of inches and tenths and half-tenths to which the pointer
is adjusted at sea level. Outside this it has a scale indicating
feet altitude from up to 8000, or when employed for mining
purposes indicating from 3000 ft. below to 5000 ft. above sea
level, or the whole 8000 below. This scale is movable by a
rack and pinion inside the ring-handle, so that it can be ad-
justed to zero at the bottom of any ascent.
In going up a hill, the difference of level from the starting
point is given, but not the height above Ordnance datum ; it
is not possible to adjust it to any such standard. In order to
read the indications clearly, the barometer is encircled by a
ring, to which is attached a fine pointer and a magnifying
glass, so that it can be placed exactly over the needle. To use
the barometer for practical purposes, it is necessary to have
two similar instruments, one to remain at the first station all
day so that its fluctuations can be recorded, say, every half-
hour ; the other to be taken by the surveyor to register his
altitudes. He enters the time of each observation so that
when he returns he is able to correct his reading according to
the variations in the atmospheric pressure which have occurred
throughout the day, which are presumed to have occurred also
at the various positions which the surveyor reached, but which
he would not be cognisant of unless he had the stationary
barometer to check by. At a temperature of 55 F. the
mercurial barometer falls about T o inch for each 10 ft. rise in
position, and by interpolation the aneroid barometer can be
read to a difference of level of 5 ft. Upon several trials of the
152
PRACTICAL SURVEYING
s
^ dui? u/njoq
$
I
W^^V^^V^,..
mAMam**********
-fllOS- - - - H
CONTOURING BUILDING PLOTS 153
"M'N No
8
&&
154
PRACTICAL SURVEYING
instrument against actual levels the author has found the
indications reliable within about 3 ft.
FIG. 149. Aneroid barometer.
QUESTIONS FOR PRACTICE 155
QUESTIONS ON CHAPTER XXI.
1. Describe how you would survey and level a simple building
site on falling ground.
2. What are " spot levels " and when are they used ?
3. Describe the construction and use of an aneroid barometer.
4. What causes the rise and fall of a barometer when kept at one
station ?
5. How much does the mercurial barometer fall for each 10 ft.
rise in position ?
6. Explain how contour lines can be plotted from sections taken
through a building plot ?
CHAPTER XXII.
Principles of angular measurement Old definition of an angle Trigo-
nometrical definition Instruments for setting off or measuring
angles Semicircular and rectangular protractors Circular pro-
tractor with pricker arm and vernier Scale of chords.
Angular measurement Before entering upon the use of
instruments for angular measurement, it will be desirable to
say a few words about angles.
The theodolite is an instrument by which vertical and
horizontal angles can be measured with great accuracy, theo-
dolite surveying being distinguished from chain surveying by
the measurement of angles instead of tie lines, although all
theodolite work involves some amount of chaining, or measur-
ing distances, even if it is only a base line to start the work.
Trigonometry, or three-angle measurement, is the science by
which the complete dimensions of triangles may be calculated
from certain given portions, viz. three sides, two sides and the
included angle, or one side and two angles. It is essential to
understand trigonometry for advanced work, but the author's
little book on Practical Trigonometry 1 will be found to deal
with the subject fully enough for actual use. At present it
will be sufficient to consider the general principles upon which
angular measurement depends.
An angle is the opening made by two straight lines which
meet together in a point (Fig. 150), or would do if produced
(Fig. 151), and in trigonometry an angle may be described as
the opening between two radii. The first thing to observe
is that the angle is quite independent of the length of the lines,
and any given length may, therefore, be assumed for them in
dealing with the properties of an angle. Take two lines, say
1 Practical Trigonometry for Engineers, Architects and Surveyors.
(Whittaker, 2s. 6d. net.)
MEASUREMENT OF ANGLES
157
1 inch long, meeting at a point, as Fig. 152, one of them fixed
horizontally and the other hinged at the meeting point, being
free to revolve round the point as a centre. These lines can
be closed together or opened to any extent, and if in opening
them the movement is continued right round until the starting
point is again reached, the outer end of the moving line will
have described a circle. The line can readily be imagined as
stopping at any intermediate position, and wherever that may
be a definite angle will be formed. If the movement is stopped
FIG. 151.
FIG. 152.
FIGS. 150 to 152. Angles.
ninety times at equal distances from the horizontal base line to
a vertical position at right angles to the base line, there will
have been marked 90 spaces, each of which will be called 1
degree, and continuing the movement of the line through the
remainder of the circle, with stops of equal duration, there will
be marked in all 360 degrees. This is the substance of angular
measurement.
Any other interval might have been taken, giving a greater
or less total number of divisions ; for instance, the French use
grades or 100 divisions in a right angle, but the accepted
English standard or unit of 1 degree is just large enough to
make 90 divisions in a quadrant, or 360 in a whole circle. If
longer lines were taken the circle would be larger, and the
158 PRACTICAL SURVEYING
divisions, if marked on its circumference, would be larger, but
the respective inclinations would be the same for equal angles,
that is, angles containing the same number of degrees.
In circular measurement an angle of 180 degrees may be
spoken of, which is simply the space above or below any straight
line with regard to a given point in the line. An angle of 400 or
more degrees may be talked about, which is more than a com-
plete revolution of the line, and the meaning is perfectly clear
when the angle is looked upon as being formed by a moving
radius, but would be unintelligible by Euclid's definition.
In order to allow of very exact measurement, a degree is
subdivided into 60 parts, called minutes, and these again may
each be subdivided into 60 parts, called seconds, so that a
second is the 3600th part of a degree, or the 1,296,000th part
of a complete circle. By a further subdivision into thirds, 60
of which equal one second, very minute divisions for astro-
nomical purposes are obtained, a " third " being approximately
equal to one 80-millionth part of a circle, but astronomers
usually express angles less than one second as decimals of a
second. It is interesting, and possibly useful, to note that
1 minute of arc equals 18 inches at a distance, or radius, of
one mile.
Protractors. In order to save the trouble of dividing a
circle every time it is desired to measure an angle, certain
scales are provided, the commonest of which is a semi-circular
protractor, with the edge marked off into degrees as shown in
Fig. 153. These degrees are numbered from the base line in
both directions, so that an angle opening either to the right
hand or left hand may be set off or measured.
Another form of the instrument is the ivory or boxwood
rectangle shown in the same diagram, and the relative position
of these two instruments with the divided circle shows exactly
the method upon which they are constructed.
An improved form of the protractor is a complete circle,
which in its most complete form carries an arm with a pricker
to mark off any required angles, having also a special scale
called a vernier, for estimating minute divisions, which will be
explained in connection with the theodolite.
Scale of chords. There is still another way to measure
an angle, and that is by a scale of chords. This, being a plain
straight scale, can be marked in any narrow space upon another
MEASUREMENT OF ANGLES
159
scale, but it is a little more trouble to use. If any circle be
drawn and the degrees marked upon it, it will be found that
J50V-
the distance from to 60, measured in a straight line, will be
exactly equal to the distance from the centre to the circum-
FIG. 154. Scale of chords.
ference, or in other words, the chord of 60 is equal to radius.
This holds good for any size of circle, because as the radius
160 PRACTICAL SURVEYING
increases or decreases, so does the chord, and it is a very im-
portant property, as will be seen when the mode of using the
scale of chords is explained.
The above diagram (Fig. 154) shows the construction of this
scale. If a quarter of a circle be drawn and the degrees
marked off, lines may be drawn from the zero point to each
degree ; these will represent chords of the various arcs. The
respective lengths of these chords may be transferred to one
line and numbered consecutively from zero, making an ordinary
scale of chords. Now it will be seen at once that if we have
part of a circle of the same radius as the one from which the
scale was set off, any number of degrees can be marked upon
it by taking the distance off the scale and applying it to the
circumference as a chord. Kemembering that the chord of 60
is equal to radius, the size of the circle employed in construct-
ing the scale can always be found by taking the distance from
to 60.
To set off an angle of 37 from point A (Fig. 155), take the
Fro. 155. Setting off angle by scale of chords.
scale of chords, open the compasses from to 60, and strike
the arc BC. Then open the compasses from to 37 and from
B strike an arc with this radius to intersect the previous arc,
and give point C, when the angle BAG will be 37 degrees. To
measure an angle already drawn, strike an arc with radius to
60, take the chord of the arc upon the angle and apply it to
the scale of chords to ascertain the angle.
In the best scales of chords a brass peg is let in at and at
60 to avoid the damage resulting from compass points being
continually applied.
QUESTIONS FOR PRACTICE 161
QUESTIONS ON CHAPTER XXII.
1. Draw an angle BAG = 180, and state how many right angles
there are in a circle.
2. Find how many degrees, minutes, and seconds there are in 1|
right angles, and how many seconds there are in 35 1 9' 53". (Ans. :
128 34' 17V'. 127193.)
3. State in what other way you could define an angle of 540,
and find how many degrees and decimals there are in 4139 seconds.
(Ans.: 6 right angles. 1 '14972.)
4. If the distance from to 60 on a scale of chords be 3 inches,
what will be the length of a chord of 45 degrees ? (Ans. : 2 '296 in.)
5. In a right-angled triangle one acute angle measures 47
15' 23"; what does the other measure? (Ans.: 42 44' 37".)
6. In two triangular fields of different size, but whose angles at
corresponding extremities of the base are equal, the base and
perpendicular of the smaller one are respectively 13'40 and 6'17,
and the base of the larger is 19'21 ; what is its perpendicular, and
what is the area of each triangle in a. r. p. ? (Ans. : 8'84.
4 a. r. 21 p. 8 a. 1 r. 39 p.)
P.s.
CHAPTER XXIII
Construction and reading of diagonal scale Construction and reading
of vernier scale Construction and reading of verniers on theo-
dolite Construction and adjustment of box sextant Method of
using same Construction and use of plane table.
Diagonal scales. Now that we are considering how very
accurate measurements may be made, it may be as well to
show how minute sub-divisions on a straight line may be
obtained by what is called a diagonal scale.
Suppose a scale is required upon which hundredths of a
unit may be measured. Divide the given line into units by
the application of an ordinary scale, draw ten other parallel
lines, say ^ inch apart, as in Fig. 156; divide the first unit
UtoCS
FIG. 156. Diagonal scale.
into tenths by the method shown, then, with the tee and set-
square, project all the unit divisions through to the bottom
line and the tenth divisions on the bottom line only. Then
with the tee-square shifted so that the set-square will join the
end of the first tenth on the top line with the beginning of
it on the bottom line draw parallel diagonal lines. As a
diagonal line progresses one-tenth of a unit in passing over
the ten spaces of the depth of scale, it will progress only
one tenth of a tenth, or one-hundredth of a unit from one line
VERNIER SCALES 163
to the next. The lengths marked by the dots on three of
the horizontal lines shown in Fig. 156 will be respectively
2-52, 1-255, and 3-67.
Verniers. The same minuteness of sub-division may be
obtained by the use of a vernier, which is a small movable
scale placed against a longer one called the primary scale. It
is shown in Fig. 157 for the reading of hundredths of an
J
FIG. 157. Vernier scale.
inch, and is similar to that attached to a standard mercurial
barometer.
The principle is as follows : If the vernier is desired to give
tenths of the smaller divisions on the primary scale, nine of
these divisions will be taken and the length divided into ten
equal parts. Then each of the vernier divisions will be one-
tenth less than each of the primary divisions, and if, say, the
third division on the vernier coincides with a division on the
primary scale, the commencement of the vernier will be three-
tenths of a division in advance of the nearest division on the
primary scale. With the vernier in the position shown, it
will be seen that the arrow on the vernier is in advance of
or 2 '3 on the primary scale, and, looking along the
Fio. 158. Theodolite vernier.
vernier, the seventh division is found to coincide with a
division on the primary scale, so that the reading becomes
2-37 in. If two intermediate lines on the vernier are equally
upon the point of coinciding with lines on the primary scale
it will add O'OOS to the reading from the lower division, and
so on, by estimation for any other position.
Theodolite vernier. The primary scale or horizontal
circle of a 6-in. theodolite is usually divided to degrees and
thirds of a degree, as in Fig. 158, so that the arrow of the
164
PRACTICAL SURVEYING
vernier reads to 20 minutes of arc, but the vernier, having
39 of these divisions sub-divided into 40 equal parts, enables
half minutes, or intervals of 30 seconds, to be read. The
reading shown on the figure is 4 30'.
It will be observed that the scale on a theodolite is marked
from right to left, because the eyepiece of the telescope is
always turned that way, the object-glass travelling from left
to right between the objects observed.
In using the theodolite for horizontal, or azimuthal angles,
as they are sometimes called, the angle through which the
telescope has been turned is marked by the position of the
vernier zero, the circle being a fixture. When the arrow
coincides with a division on the circle, the angle is read off as
Fro. 159. Box-sextant vernier.
if from an ordinary protractor, being exactly so many degrees,
or degrees and 20 minutes or 40 minutes, or degrees and
30 minutes, according to the mode in which the circle is
divided. The odd minutes and seconds are read off by a
microscope placed over the vernier, search being made for the
lines which most nearly coincide with the divisions of the
primary circle.
The vernier on a box-sextant is a flat arc of about 150
degrees, commencing at 5 degrees below zero, with a radius of
about 2 inches, and divided into degrees and half degrees.
The vernier has 29 of these divisions divided into 30 equal
parts, so that single minutes may be read from it by means of
a magnifying glass. Fig. 159 shows a highly-magnified view
of this vernier and part of the primary arc, the reading indi-
cated being 56 32'.
THE BOX-SEXTANT
165
As the box-sextant is the simplest instrument for observing
angles, its construction and use will be described next.
Construction and use of box-sextant. The general
appearance of a box-sextant is as shown in Fig. 160, and an
enlarged diagrammatic plan of it is shown in Fig. 161. It is
about 3 in. in diameter, and is made with or without a
telescope ; it is used for measuring approximately the angle
between any two lines by observing station poles at their
extremities from the point of intersection. In Fig. 161, A is
the sight-hole, B is the horizon glass, a fixed mirror having
one half silvered and the other half plain ; C is the index
glass, a mirror attached to the same pivot as the vernier arm
FIG. 160. General view of box-sextant.
D. The side of the case is open to admit rays of light from
the observed objects.
In making an observation of the angle formed by lines to
two poles, one pole would be seen through the clear part of
mirror B, and at the same time rays of light from the other
pole would fall on to mirror C, which would be moved until
the pole is reflected on the silvered part of mirror B, exactly
in line, vertically, with the pole seen by direct vision, then
the angle between the two poles would be indicated by the
vernier. Take the case of a single pole, then the angle
indicated should be zero, but whether it would actually be
so depends upon circumstances, which may be explained as
follows :
Suppose the pole to be fixed at E, which is extremely close,
166
PRACTICAL SURVEYING
it will be found that the arrow on the vernier arm falls short
of the zero of the scale owing to what may be called the
FIG. 161. Diagram showing principle of box-sextant.
width of the base line of the instrument. If the pole is
placed farther off, as at F, the rays of light from the pole will
take the course of the stroke-and-dot line, and the vernier
THE PLANE TABLE 167
arm will require to be shifted nearer the zero of the scale.
After a distance of two chains between the pole and sextant
is reached, the rays of light from the pole to JB and C are so
nearly parallel that the error is under one minute, and the
instrument can be used under such conditions without difficulty
occurring by reason of error. To adjust the box-sextant, the
smoked glass slide should be drawn over the eye piece, and
then, if the sun is sighted, it should appear as a perfect
sphere when the vernier is at zero, in whatever position the
sextant may be held. When reading the angle formed by the
lines from two stations, the nearer station should be sighted
through the plain glass, which may necessitate holding the
instrument upside down. When the angle to be read between
two stations exceeds 90, an intermediate station should be
fixed and the angle taken in two parts, as in viewing large
angles the mirror C is turned round to such an extent that
its own reflection and that of the image upon it is viewed
almost edgeways in the mirror B.
It should be noted that the box-sextant only indicates angles
in the plane of the instrument, so that if one object sighted is
at a lower level than the other, the angle read will be the
direct angle between them, and not the horizontal angle, as
given by a theodolite.
The plane table. The plane table is principally used
as an aid in rough military sketching, but it may be occa-
sionally useful for an approximate general survey. It consists
of a small drawing board fixed upon a tripod, so that it can be
levelled and clamped in any given position. A sheet of
drawing paper is pinned upon it, on which the directions
of any prominent objects may be obtained by means of a
loose sighting-arm or sight-rule, called an alidade, which may
be placed in any position on the paper. The base of the
alidade may conveniently contain a rectangular compass box,
i.e. with a needle having a scale of degrees and half or thirds
of degrees extending say 5 degrees each side of North ; then
turning the instrument so that the needle points exactly to
zero, a line may be drawn alongside, which represents the
direction of magnetic north. The sides of the base may be
divided into convenient scales, such as 88 feet to 1 inch,
10 chains to 1 inch, or 6 inches to 1 mile.
In using a plane table, it is set up at a convenient point
168
PRACTICAL SURVEYING
facing the part to be surveyed, the paper fixed upon the
board and the direction of magnetic north determined. Then
the distance to some other point facing the survey is measured
to serve as a base line, the direction sighted and ruled on the
paper by the right-hand edge of the sighting rule, and the
length cut off according to the scale that is adopted. Then
the prominent features of the part to be surveyed are sighted
B
FIG. 161 A. Three-point problem in plane-tabling.
and ruled in from the first station, and either the lines
numbered to correspond with a description of the object in
the field-book, or the description briefly noted on each line.
The plane table is then moved to the other end of the base
line and set by the compass mark, so as to be in the same
relative position with the meridian, and directions sighted to
the same prominent features from the second station and
ruled in to intersect with the other lines.
The distinctive points being thus obtained by automatic
triangulation upon the paper in their true relative positions,
THE THREE-POINT PROBLEM 169
the other features can be sketched in with a close approxima-
tion to accuracy. As in large triangulation surveys, new base
lines can be located when necessary, so in plane tabling a
new base line can be set up anywhere so long as the ends are
observed from both ends of the previous base line. In drawing
the lines of direction, it will be found very convenient to
insert a needle or a small pin on the point from which the lines
radiate as a guide to the rule. Fig. 169, although drawn for
another purpose, shows exactly how the intersecting lines
from the two ends of the base determine the positions of
the principal points of a plane table survey.
The three-point problem in plane tabling is similar to that
in hydrographical surveying, viz. locating the position of a
point from which the angles made by three given points have
been observed. Let A, B, C (Fig. 161 A) be the three given
points on a map whose angles ADB and BDC, subtended at D,
are found to be respectively 45 and 30. Join AB and set off
at each end angles = 90 - 45 = 45 to give the centre of a
circle which will pass through AB and D. Then join BC and
set off at each end angles = 90 - 30 = 60 to give the centre of
a circle which will pass through BDC. The common inter-
section of the circles gives the point D.
QUESTIONS ON CHAPTER XXIII.
1. Make a diagonal scale to measure inches and hundredths of
an inch.
2. Draw about 30 degrees of the arc of a circle 3 in. radius and
construct a scale and vernier to read to 10 min.
3. Show by a full-sized sketch the arrangement of a box-sextant
and describe how the vernier arm is moved.
4. Sketch a method by which an angle of 175 may be read with
a box- sextant.
5. Explain why a box-sextant cannot be used for taking hori-
zontal angles on undulating ground.
6. Give a brief description of the method of surveying known as
plane-tabling.
CHAPTER XXIV.
Construction of theodolite Primary horizontal circle and verniers
Vertical circle and verniers Setting up and adjusting theodolite
Reading verniers Repeating an angle.
Construction of theodolite. The theodolite consists
essentially of a telescope mounted upon bearings by which the
object glass can be elevated or depressed, with a vertical axis
upon which it can be rotated. Attached to the frame
supporting the telescope is a circular base plate containing two,
or sometimes three, verniers ; and this plate can be rotated on
a base attached to the upper parallel plate which is divided
round the whole circumference in degrees and half degrees,
and sometimes degrees and thirds of degrees. This is called
the primary circle and enables horizontal angles to be
measured accurately.
The vernier plate has a clamp and tangent screws so that it
can be accurately set in any desired position ; and the primary
circle has also a separate clamp and tangent screw, so that
when the verniers are at zero the telescope can be directed
and clamped in any required position.
Some theodolites have the primary circle fixed so that the
telescope cannot be set to zero upon the first station, but this
is of very little consequence, as the angle is easily obtained by
taking the difference of the first and second readings, and
some surveyors even consider it an advantage. At any rate,
it avoids the constant setting of the vernier to zero and the
consequent wear upon the clamp at one spot, which is apt to
prevent it from holding firmly.
There is also a vertical circle in the transit instruments, or
a half circle in the Everest theodolites, divided similarly to
the primary circle and attached to the telescope. The frame
carries two verniers by which the vertical circle can be read
to minutes or half-minutes, and the arm to which the verniers
ADJUSTMENT OF THEODOLITE 171
are fixed is adjustable by tangent screws, so that when the
verniers are set to zero the telescope will have the spirit
bubble in the centre of its run. The detail of the arrangement
varies in different instruments, but there is no difficulty in
finding the necessary adjustment. The lower portion of the
instrument has two parallel plates and screws similar to the
level, and the whole stands upon a substantial tripod. The
general arrangement is as shown in Fig. 162.
Some theodolites have a compass between the A frames, so
that it may be used as a circumferentor, but it is difficult to
read the compass needle in this position, and a better
arrangement is to have a long compass needle in a narrow box
on the top of the telescope, with about 5 degrees marked on
each side of the centre, so that it can be clearly seen, and the
telescope can be readily set in the magnetic meridian. If the
vernier be set to zero on the primary circle, and the telescope
turned and clamped so that the needle is at zero, the verniers
may be undamped and the telescope turned to read the
compass bearing on any line.
If facility has been attained in using a level, no serious
difficulty will be found in using a theodolite, and considerable
practice may be obtained with both instruments in a back
garden. As in the level, the parallel plates are first adjusted
by the screws, so that they are as nearly parallel as can be
seen by the eye ; then, all clamps being loosened, the bubbles
are placed across and in line with the right hand leg, and the
leg adjusted to bring both bubbles central. The plummet is
then observed to see how far it is away from the centre over
which the instrument is to be fixed, and in what direction.
Then the two legs that have not been adjusted are shifted the
required amount and direction, and the right-hand leg again
adjusted to bring the bubbles central. This is repeated until
the plummet is exactly over the required point or station,
when the legs are equally and firmly pressed into the ground.
Then the first vernier to the left of the eye piece is set
approximately with the arrow to zero or 360 by the eye, and
adjusted exactly by clamping the vernier plate, looking
through the microscope, and turning the tangent screw as
required. Then the lower clamp being loose, the bubbles are
set over the diagonal pairs of screws, and they are adjusted to
bring the bubbles exactly central.
172 PRACTICAL SURVEYING
The telescope is now turned to sight the end of the first
line, the lower plate clamped and adjusted by its tangent
PIG. 162. General view of theodolite.
screw. The vernier plate is then undamped and the telescope
turned by means of the A frames to read the first angle, the
RECORDING ANGLES ON CHAIN LINE 173
plate clamped, the telescope adjusted exactly by the vernier
tangent screw, and the angle read off by the microscope. In
setting the zero, both ends of the vernier should be examined
to see that they equally coincide with the divisions on the
primary circle, and in reading an angle the adjacent divisions
should be observed to see that they are equally displaced, so
that the coinciding line may be determined with certainty,
and it should then be in the middle of the field of view of the
microscope.
In making an open traverse with the theodolite, the
instrument is generally set up at the end of the first line and
the reverse bearing taken, but in a closed traverse it may be
set up at the beginning of the first line and the forward
bearing taken ; the angle at this station will then be taken
FIG. 163. Recording angles on chain lines.
between the first line and the last line. When the theodolite
is used as an accessory to the chaining, the angles are
recorded upon a plan, as shown in Fig. 163.
As all the angles taken with a theodolite are clockwise from
the base line, or from the old line to the new line, it often
happens that the required angle must be obtained by taking
the difference between the observed angles, as shown in
Fig. 163. If the telescope is set to zero on the magnetic
meridian, all observed angles will be east of north up to 360
degrees. In rough work it is sufficient to read a single
vernier, but in careful work the other vernier, or verniers,
should be read and the mean taken. In a good instrument
the readings will not differ by more than one minute.
When an angle is to be observed with great accuracy, it
may be obtained by repeating twice or more, each time
keeping the vernier clamped at the observed angle, and
174 PRACTICAL SURVEYING
setting back the primary circle, and adjusting it by the
tangent screw, so that the telescope is on the first station.
Left -hand vernier ft/grhc -hand rfrnie.
from O'. O'. from /79". S9'
/s. reading 264. 26'
2nd. 348 S4'
passing 3GO". O'
3rd, reading-.
6
84 27! SO' = (4times
__ 84' 26'. 40'
2 /G8'. 54'. 3D'
84. 27'. /S'
FIG. 164. Repeating angles.
The ordinary method of recording the observations is as
shown in Fig. 164, and an abbreviated method is shown in
Fig. 165. In the latter the minutes only of the second
vernier are entered and the mean of the readings. The entry
Left -hand Right -hand
vernier vern/er Mean
AST. reading 359. GO' - $' 353 S3'. JO'
LasC 2SJ'. 22' - . 21' 2S3'.2/'.3O'
Difference 253:22' -
O/ricted by J repetiCio,->s 84. 27'. 20
FIQ. 165. Another method of repeating angles.
under difference is the mean space passed over by the
verniers, viz. : second reading + 360 - first reading.
QUESTIONS ON CHAPTER XXIV.
1. Make an outline sketch of a theodolite sufficient to indicate
the general construction.
2. Describe how a horizontal angle is measured with a theodolite
when the stations observed are at different levels.
3. Explain the operation of repeating an angle on the theodolite.
QUESTIONS FOR PRACTICE; 175
4. What practical uses are made of the vertical circle on a
theodolite ?
5. How are compass needles attached to theodolites, and what is
their use in connection therewith ?
6. Describe in detail the operation of setting up a theodolite and
reading an angle.
CHAPTER XXV.
Traversing with theodolite, surveying by the back angle Field notes
of traverse survey Traversing by angles from magnetic meridian
Triangulation or surveying from two stations Field Notes of sur-
vey from two stations Observations required for obtaining heights
and distances.
Using the theodolite. There are three methods of using
the theodolite :
(a) Traversing or surveying by the back angle ;
(b) Traversing by taking all angles from the magnetic meri-
dian;
(c) Triangulation or surveying from two stations.
o-oo
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174'
A
112*30'
Sydney
24
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2-J4
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PIG. 166. Notes for traverse survey with theodolite.
SURVEYING BY THE BACK ANGLE 177
Surveying by the back angle is the method used in railway
surveying. It consists chiefly in setting up the instrument at
the end of the first line with zero on the primary circle, and
m'.so'
FIG. 167. Plotting from same.
bringing the telescope to bear upon the station at the com-
mencement of the line, then reading the angle to the station at
the end of the second line. The telescope is always supposed
to be turned clockwise, but whichever way it is turned the
result is the same, as the reading of the angle depends upon
p.s.
178
PRACTICAL SURVEYING
which way round the primary circle is marked. When the
angle is less than 180 the new line will run to the left of the
old line, and when more than 180 to the right.
Theodolite traverse survey. Fig. 166 gives the field notes
of a small theodolite traverse survey in a field at Sydney
Road, Homerton, and Fig. 167 the lines. The offsets and
boundaries were taken, but are omitted to simplify matters, so
1
1
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FIG. 168. Notes for survey of field with theodolite.
that only the first and last readings on the chain lines are
given, and the angle read at each junction is placed where it
was read. Any error in alignment or in reading the angle is
by this method carried through the remainder of the survey,
but in practice every care is taken by reading round to 360
on the original direction, and, if need be, reading the angle
again. In railway work three repetitions are made and the
mean taken.
To avoid this possibility of carrying on an error, some sur-
veyors recommend the second method of working named above,
SURVEY FROM TWO STATIONS
179
taking angles from the magnetic meridian at each station
instead of from the previous line ; but with ordinary instru-
ments and observers it is difficult to read a bearing closer than
half a degree instead of single minutes. For this method of
using the instrument a circumferentor or miner's dial is
better.
The other method of using the theodolite is surveying from
Fia. 169. Plotting from same.
the two ends of a base line by triangulation. This was the
method adopted in the Ordnance Survey of Great Britain.
The base line of the Ordnance Survey was a line measured by
glass rods in 1794 on Salisbury Plain, about 36,578 feet long,
or nearly 7 miles, and from its extremities observations were ex-
tended to 250 trigonometrical stations over the whole kingdom.
The line of verification, about 41,641 feet, or nearly 8 miles
long, measured on the border of Lough Foyle in Ireland,
180 PRACTICAL SURVEYING
360 miles from the base, differed from its calculated length by
a little over 5 inches.
Fig. 168 gives the field notes for a small theodolite survey
from two stations, where the angles were first taken to station
poles placed round the field and the chain lines and offsets
were afterwards measured. The offsets are omitted in the
notes now given. Fig. 169 shows the plotting from the notes,
FIG. 170. Sketch showing necessary observations to find the height of a church finial.
the dotted lines being the lines of sight for its various angles.
It will be observed in these field notes that the "trig. "stations
or places where the theodolite is set up are marked by a small
triangle, while the ordinary stations are marked by a circle
with a dot in it.
Owing to London smoke, there are great difficulties in the
way of theodolite work on a scale of any magnitude without
going some distance out. Some time previous to 1847,
Mr. Castle, the elder, a celebrated teacher of surveying, made
observations at Streatham Common to St. Paul's Cathedral
MEASUREMENT OF HEIGHTS 181
(5 miles), and to Highgate Church (8| miles), but the writer
has found in recent years that only occasional glimpses of
St. Paul's Cathedral can be obtained from Highgate Archway
(4 J miles), although he has on two occasions, between 1 890 and
1910, seen the Alexandra Palace from Forest Hill (12J miles)
right across London.
In trigonometrical surveying on a large scale, allowance has
to be made for the curvature of the earth, but in the ordinary
way this is negligible. A knowledge of plane trigonometry, so
far as the solution of triangles, is essential to work out the
simplest cases when plotting is insufficient, and this may be
learnt from the book before mentioned.* The examples in
books and the questions in examinations generally assume
ideal conditions, so that when a student attempts practical
observations of heights arid distances he is perplexed by circum-
stances for which he has no precedent.
Typical survey. One example only will be given to show
the additional measurements that have to be made in practice
beyond a simple base line and two angles. A base line was
measured carefully with a level staff, and observations taken to
the top of the finial of Park Church, Grosvenor Road, London,
N., in accordance with Fig. 170, the object being to find the
height of the finial above the entrance step.
It is often convenient to use a theodolite as a level when
only a few short sights are required as in this case. To do
this, the vertical circle is set to zero with the telescope bubble
in the centre and the horizontal verniers clamped ; the instru-
ment is then used exactly as a level would be used. Vertical
angles taken above the zero are known as angles of elevation,
and below zero as angles of depression. First reduce the base
line to true horizontal length
(5-25 -4-86) + (5-50 -512) =
2
True base = >/20 2 - 0'385 2 = 19-9963
Then find the reduction of base (x) due to the prolongation of
the angle 44 4' down to the level of the axis of the lower
theodolite, as in Fig. 171.
* Practical Trigonometry (Whittaker & Co.; 2s. 6d net).
182
PRACTICAL SURVEYING
Difference of level of the axes of instruments
(5-50 - 5'25) + (512 - 4'86)
= 0-255
then x = 0-255 cot 44 4' = 0*2634
.'. virtual base = 19'9963 - G'2634 = 19*7329.
Then we have the plane triangles as Fig. 172 to solve, where
FIG. 171. Sketch showing method of
finding virtual base line.
FIG. 172. Sketch of triangle to be
solved by trigonometry.
= 40 42', B = 44 4', a = 19-7329, and the labour of calcula-
tion is much reduced by the use of logarithms,
log d = log a + L sin C + L sin B - L sin (B - C) - 10
= log 19-7329 + L sin 40 42' + L sin 44 4' -
L sin (44 4' - 40 42') - 10
= 1 -2951910 + 9-8143131 + 9'8422939 - S'7688275 - 10 =
2-1829705
whence ^ = 152-395 and the required height = 152 -395 + 5 -87 -
0-255 = 158-01 feet.
In the above calculation the - 10 is put in because, in the
tables of logarithmic sines, 10 has been added to each group of
numbers to keep the value positive, and when there are two plus
items and only one minus item, the result would be too great if
the 10 were not deducted.
QUESTIONS FOR PRACTICE 183
QUESTIONS ON CHAPTER XXV.
1. Give a sketch showing what is meant by " Surveying by the
back angle " or traversing with a theodolite.
2. Why is compass traversing comparatively ineffective with a
theodolite ? What alternative would you adopt ?
3. Describe the general method of triangulation surveys with a
theodolite.
4. What is meant by trigonometrical surveying, and what is the
particular importance of the base line ?
5. Make a sketch showing how the height of a spire may be
obtained by observations in one plane.
6. AB is a base line 400 feet long and C a distant point whose
height is required above A. The angle CAB = 73 20' and CBA =
84 35'. The vertical angle to C from A is 1 2 1 6'. Find the height
of the point.
CHAPTER XXVI
Principles of town surveying Choice of base lines Chain or steel tape
Triangulated offsets Sketching details Field notes of lines and
angles with offsets omitted Plotting of same Field notes of one
street with measurements Plottingof same Connecting chain lines.
Town surveying. For town surveying, or the prepara-
tion of plans of land more or less covered by buildings and
laid out in streets, the ordinary methods of surveying require
some modification to suit the peculiar circumstances of the case.
The chief difficulty is that the chain lines are necessarily con-
fined to the streets, and can only in rare cases form part of the
general triangulation of the district.
Choice of base lines. Where there is a high street or
main thoroughfare through the town, the line through it
should be made the base line, and be connected, when possible,
with the triangulation outside ; but if not, it can still be made
the backbone of the survey with the smaller streets branching
out from it like ribs. When there is more than one good
thoroughfare, each should have a line through it equivalent
to a subsidiary base line, and then any streets running through
from one main thoroughfare to the other, straight enough for
a single chain line, form good checks upon the work by their
length without their angles being required. It is seldom that
the ordinary station poles can be used, except for a very short
period and for the part of the survej^ which is in immediate
progress, so that small iron spikes, or dogs, are driven between
the joints of the paving stones, or elsewhere, when it is required
to mark a station for future reference. The chain used may
be the 4-pole chain, the 50-feet chain, or the 100-feet chain;
for a large survey the 100-feet chain or a 100-feet steel tape is
best.
The offsets are taken with the tape, using preferably the
TOWN SURVEYING 185
side with feet and inches. In narrow and unimportant streets
they are simply taken at right angles to the chain as in
surveying common field boundaries; but, at all corners and
at intervals along important streets, particularly where the
frontage line alters, they are taken by triangulation from the
chain line. The measurements are taken to the outer boun-
daries of the various properties, the width of footpaths, fore-
courts, and other variations, being left until the details are
measured.
The field-book for this purpose is kept upon the same prin-
ciple as for any combined theodolite and chain survey, with
the exception that in addition to numbering the lines the
names of the streets through which they pass are given, and
the angles are marked as taken because the sketches in the
field-book make it a rough plan of the survey. As in the
field surveys, the main lines are first plotted and afterwards
the offsets, so in town surveying the chain lines are first
plotted and then the triangulated offsets.
The detailed measurements are generally left until after the
main work is done and plotted, but they may be carried on at
the same time with another set of assistants. So far the par-
ticulars obtained enable a skeleton, or block plan, to be made
sufficient for tramway purposes, or any object that involves
roadwork only, the plan being a map of the roads and what-
ever abuts upon them. Town plans, however, are generally
expected to show the buildings themselves and any land there
may be in the rear. This is all done by tape measurements
within the boundary of each property, and is generally a long
and tiring job.
This field-book differs from the former, and is generally a
small quarto into which each block from the skeleton survey is
plotted on a separate page to a scale of 20 to 50 feet to the
inch according to the amount of detail that is wanted. Then
a sketch of the individual premises is made, and the length
of every straight part marked down, together with a sufficient
number of diagonal distances to enable the whole to be drawn
accurately.
Some prefer the book made of paper ruled in small squares
so that the premises may be sketched roughly to scale at the
time, but a neat draughtsman will find very little assistance
from this, as the best and most expeditious work is done by
186
PRACTICAL SURVEYING
from
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SKELETON TOWN SURVEY
187
slightly exaggerating all the natural features, making a slight
bend more excessive to emphasise its direction and a straight
Cham sfafons
& Trig scacions
Scale of chains T ^
* 4 ff ffChs. >0 jt,
...! i I i I r I i I i I i I f I i I i^^^"^
Fig. 173. Skeleton town survey.
line shorter than its real length because it requires fewer
measurements upon it. This is the general procedure, when
188
PRACTICAL SURVEYING
Fig. 174. Extract from field notes of town survey with 100-feet chain.
SURVEYING STREETS
of feet
!
i
i
i
i
i
h
Fig. 175. Plotting of same.
189
190
PRACTICAL SURVEYING
the scale upon which the plan is ultimately required does not
exceed 5 feet to the mile = 88 feet to 1 inch. The common
parish map scale of 3 chains to 1 inch is 198 feet to 1 inch or
26| inches to 1 mile, nearly corresponding to the Ordnance
le of 2FOO or 25-344 inches to 1 mile.
Fig. 176. Tying junction of
streets in chaining.
\
\
I
^////////////////////^
Fig. 177. Tying bend in street in
chaining.
The field notes on p. 186 omit all details and give only the
chain lines and angles, which may be looked upon roughly as
giving the centre lines of the streets. The plotting of the
lines and angles is given in Fig 173.
Field notes of one street. Fig. 174 shows the field notes
of one street with the frontage of the various properties, the
TYING BENDS AND JUNCTIONS 191
plotting of which is given in Fig. 175. Sometimes the bends
and junctions of the street have to be tied by chaining only.
Figs. 176 and 177 show examples of the methods employed.
In Fig. 176 two chain lines, AB and CD, are shown inter-
secting at C. A point is taken at E and sighted through
to D, tangent to the corner of the building at F. Then from
D, tangent to G, a line is sighted to H, and the measurements
between the letters along each of the dotted lines are taken.
If the road is a cross road passing on both sides of the main
road, the same set of operations is repeated on the other
side of the base line. If a larger survey is being made and
a village is included within the area, and a main line does not
run through the village, there should be, if possible, a large
triangle surrounding the village, within the three corners of
which the smaller survey may be made, and to which it may
be connected. In Fig. 177 by keeping the chain lines on the
side of the street where the salient angles occur, longer ties
may be obtained, and the tie triangles may be drawn to twice
the scale of the plan to ensure greater accuracy.
QUESTIONS ON CHAPTER XXVI.
1. What are the general principles of town surveying ?
2. Give an illustration of a triangulated offset and state what is
its advantage over a common offset.
3. What are double chain lines, and why are they used ?
4. How are the stations marked in a town survey when not
actually in use for observations ?
5. Show by a sketch how the angles of intersecting roads are
recorded in a town survey ?
6. How may angles be plotted with the greatest accuracy ?
CHAPTER XXVII.
Difference in lay-out of old and modern towns Available accuracy
depending upon scale employed Double chain lines Example of
field-book Plotting of same Tape surveys Sketch of back
premises with measurements Plotting of same.
Old and modern towns. There is a considerable
difference in the labour of surveying an old and a modern
town, particularly if the old is English and the modern
town Colonial or American. In olden times, there was no
systematic arrangement of thoroughfares; in fact, it almost
seems as if, to avoid mending the holes in a bad road, the
inhabitants went round them, and so made winding roads.
Taking a view of the old towns as a whole, it looks as if
originally there were a few isolated houses, and from every
one to every other there was a direct footpath, afterwards
formed into a road, the streets being short cuts from road
to road.
In modern towns and cities, particularly in America, the
roads are straight and the junctions rectangular, making
the work of the surveyor, and also the architect, much
simpler, but giving considerable trouble to the inhabitants
who want to go from N.E. to S.W., or in any diagonal
direction. On the whole we prefer our own picturesque
and convenient arrangement, which does not necessitate
barrack-like buildings on every side.
In the last chapter the modus opemndi was described, when
a comparatively small scale for the finished plan was required.
The detail that can be shown on any map varies with the
scale. The amount of accuracy required so that the plan may
be without appreciable error, may easily be determined.
Suppose every part of the plotting to be true to Tol5 of an
inch, then the limit of necessary minuteness on the various
DOUBLE CHAIN LINES 193
scales (provided there is no accumulating error) will be as
follows :
1 mile to 1 inch = about 50 feet.
6 inches ,, 1 mile= ,, 10
3 chains ,, 1 inch = 3
100 feet 1 ,, = 1 foot.
5 ,,1 mile- 10 inches.
10 55 55 1 55 = 55 ^ ,,
J inch 1 foot = 1 inch.
Double chain lines. A 4i-inch set-off in a brick wall can
be shown clearly upon plans of 20 feet to the inch or any
larger scale, and this is a good general guide. When any
part of a town survey is required to be plotted to a scale
of 20 feet to 1 inch or larger, it is necessary to have
double chain lines down the streets, and then rectangular
offsets may be taken to the boundaries, but additional oblique
offsets will be requisite to all important points where the chain
line is more than 2 or 3 links away. Double chain lines
are occasionally used for the main thoroughfares of a town,
while only single lines are adopted for the side streets.
The ordinary field-book may be adapted for double chain
lines by ruling another line outside each red line about | inch
off, leaving the original central column for entering anything
which occurs between the two chain lines. As illustrating the
principle of double lines arid close detail, the writer now gives,
by special permission of Messrs. Crosby, Lockwood & Co., the
notes and sketches of a survey published in Jackson's Aid
to Survey Practice. These should be plotted carefully to a
scale of 20 feet to 1 inch, when they will appear as shown in
Fig. 178. In filling in the details of back premises, the tape
is the only instrument used. An approximate sketch is made
and the walls measured round, then diagonals are taken to
those angles required for tying and checking the work.
A steel tape is the only accurate kind, but these are
expensive and difficult both to use and to keep in order.
Generally, the work is done with one of Chesterman's metallic
tapes ; that is, a painted linen tape with wire threads woven
in. These tapes vary considerably in length, according to
their dryness. The writer has known a good 66-feet tape
P.S. N
194
PRACTICAL SURVEYING
FIELD - RECORD
OF
TOWN SURVEY
WITH THE CHAIN
FOR PLOTTING ON THE SCALE OF TZo OR
!O FEET TO THE INCH.
Chain* lines are, taken, in, links,
fitter dimensions and offset^ in, feet a/id inches
The coal Shoots when, not marked are
1 foot S or / foot in, diam/.
GENERAL SKETCH.
55
J sjy*
H
LANCASTER BUILDINCS
I I
O
EXAMPLE OF DOUBLE CHAIN LINE 195
of Surrey
196
PRACTICAL SURVEYING
End of Survey
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PLOTTING A STREET
197
OF TOWN SURVEY
DOU5LE. CHAIN LINES.
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Fio. 178. Detail plotting of street in town survey.
198 PRACTICAL SURVEYING
to vary 1 8 inches in length between wet and dry. The common
tapes are no better than a piece of string would be.
Before leaving the premises the sketch must be carefully
examined to see that all the necessary tie lines have been
taken ; it is very annoying to have to go over the same
ground a second time solely through carelessness.
Frequently the surveyor will have to rely for assistance
upon any boy or man picked up in the neighbourhood, and
although it appears a simple matter, it is very difficult to get
them to understand that the end of the brass ring is the part
SKETCH PLAN or TIMBER YARD
WITH DIMENSIONS
FIG. 179. Sketch plan of timber yard with dimensions.
to be held against the wall. If not watched, they will take
the ring between their thumb and finger, and hold it at right
angles to the line of the tape so that the length is measured
minus the length of ring. The only way to prevent it is
to make them put their finger or thumb through the ring, and
then it is necessary to see that when they get tired they do
not twist the tape round their hand. It seems as if, because
the figures are read from the other end, they think their end
does not matter.
When independent measurements are taken of piers and
panels on a wall, the whole length should always be taken
also and used in the tie lines, because a number of small
SURVEY OF A YARD
199
GATE:
ROAD
Sccrfe c*
O 10
J L_
so so
Fio. 180. Plotting of same.
200 PRACTICAL SURVEYING
measurements will never agree exactly with the total. Parts
that cannot be reached easily may be estimated with great
accuracy by observing the number of bricks, either in height
or length, dividing by 4 for height in feet, and deducting
J for length in feet, two headers counting as one brick.
Fig. 179 shows the sketch plan of back premises measured
with a tape, and Fig. 180 shows the plotting of the same.
QUESTIONS ON CHAPTER XXVII.
1. Give some idea of the degree of accuracy required in measure-
ments according to the scale of map required.
2. A plan is drawn to a scale of J inch to 1 foot ; what is the
nearest measurement that can be indicated on the paper by scaling?
3. How are the details of a town survey obtained and recorded ?
4. Describe the method of using a box tape for taking detail
measurements. How would you check the work ?
5. A house in the London suburbs has 100 courses of bricks
from the ground up to the underside of cornice ; what is the
height in feet ? Would the same number of courses give the same
height in a Midland town ?
6. Make a sketch of an irregular town building site and show
what measurements you would take to obtain a true plan. How
could you obtain the measurements before the site is cleared ?
CHAPTER XXVIII.
Principal features of railway surveying Limits of deviation Reference
book Railway gauges Engineering field work Location field
work Permanent stakes Level pegs Earthwork terms Batters
and slopes Earthwork formulae.
Railway surveying. Railway surveying begins with the
work of the engineer who rides, or walks, over the district
with an Ordnance map and sketches upon it the route he con-
siders best. Then trial levels are taken along the proposed
line, with additional levels where it is probable that a deviation
from the first suggestion will be approved. A set of Ordnance
maps with the finally proposed centre line of railway is then
given to the surveyor, who has to make a chain survey along
the course, taking in all features within the limits of deviation,
and the complete boundaries of those properties of which any
part commences within.
The limits of deviation are usually 5 chains on each side of
the centre line, but they may be 100 yards each side in the
country and 10 yards in town, and only within these limits
may the promoters vary the line of railway without fresh
statutory powers. The survey for a railway is made by
running base lines within the limits of deviation and connect-
ing them where a change of direction occurs by theodolite
angles, repeated to ensure accuracy.* The chain lines are tied
to these base lines by ordinary triangulation. Each parcel of
land shown on the plan is numbered and the plan is accom-
panied by a Reference Book giving the numbered list with
* The best practical description of railway surveying known to the
writer is given in Chapters VI. to X. of H. J. Castle's Engineering Field
Notes on Parish and Railway Surveying and Levelling. Second edition
(Simpkin, Marshall & Co., London, 1847). It has, however, long been
out of print.
202
PRACTICAL SURVEYING
description and the names of the owner and occupier of each
parcel. The referencing is usually done by a separate staff.
Main and cross sections are also prepared as explained under
levelling, and the adjustment of gradients is made as shown
previously in Fig. 140.
The various gauges are as follows :
RAILWAY GAUGES
(between inner edges of rails).
Broad gauge .
Indian
Irish
Standard narrow gauge
Australian ,,
Metric
Hill and tramway
7 ft. 0*
in. = 7 -06 ft
5 , 6
, =5-5 ,
5 ,
3
,
= 5-25 ,
4 ,
8*
,
= 4-71 ,
3 ,
6
>
-3-5
3 ,
3|
,
= 3-281,
3 ,
6
>
= 3-5 },
to
to V
1 6
., =15),,
Engineering field work. Engineering field work in its
full sense comprises all branches of land surveying and level-
ling, together with the setting out of intended works, but
as usually understood it is limited to the "setting out" or
" location " of proposed works by means of centre lines, side
widths, and levels whether for roads, railways, canals, or any
incidental structures. Land surveying, as so far described,
consists of ascertaining all particulars of existing features of
the ground, "setting out" assumes all features known and
places upon those features certain marks for future use.
The centre line of the route is the part which first receives
attention ; it is drawn out carefully upon an accurate (or sup-
posed accurate) plan and has to be transferred to the ground.
A diary should always be kept for recording the date of setting
out any work, particularly detached works, such as bridges,
culverts, etc., as in the event of delays the date is always
disputed. The book varies in different cases, but the following
shows a typical form.
Location field-book. Ranging straight lines may be done
by the eye with a few station poles when for short distances
only, but generally speaking a 6-inch transit theodolite reading
STAKES AND PEGS
203
to 20 or 30 seconds is required. The ranging of curves will
be taken later on, and in considerable detail, as it is the most
important and difficult part of the engineer's work. In English
practice, Gunter's chains have been generally used and the
distances marked in miles and chains, or miles, furlongs and
chains ; but in the most recent work 100 feet chains have been
used.
The permanent stakes to mark the centre line are 3 inches
square and 3 feet long, painted and numbered, the distance
apart being say 5 chains in open country, 1 or 2 chains through
towns, and J chain on curves. At every 10th chain two pegs
tre
ra/s
IS
S 1
Gracf'enCs,
Curves.
5/ocrns.
rfeaa/tvays.
&c
of bench
marks.
& L
FIQ. 181. Working section book.
are placed, and at every tangent point where a curve starts
or terminates three pegs. In American practice where the
100-feet chain is used, the permanent stakes "are generally
placed at distances of 100 feet apart through the whole line
from the commencement, in towns or crowded localities they
are interpolated by pegs at every 50 feet apart, and on sharp
curves at 25 feet apart." The difficulty of setting out is
largely dependent upon the nature of the country; when
tolerably flat it is simple enough, but in hilly countries where
cutting and embankment, tunnel and viaduct, rapidly succeed
each other, the labour is very heavy.
Level pegs are generally round when separate pegs are used,
but sometimes the level is cut on the permanent stakes. Level
204 PRACTICAL SURVEYING
pegs are required at every alteration of gradient, at all junc-
tions and crossings, and at all sites of bridges, culverts, stations,
etc. For embankments, poles are set up clear of the bank and
cross pieces nailed upon them to show the intended final level.
For tunnelling, iron staples and spikes are used driven into the
timbers of the headings. In setting out the foundations of
bridges and other structures, the marks have to be kept quite
clear of the work, so that they may be referred to at any time
during its progress. E.g. a square block would be marked as
T T
^_ i __ ___ __ __ _ _ ___ __ (
1
FIG. 182. Pegs for setting FIG. 183. Pegs for setting out a
out a square block. trench.
Fig. 182, and a trench as Fig. 183. In each case the measure-
ment of the two diagonals from the corners checks the accuracy
of the setting out.
Earthwork terms. Formation breadth = Actual width
of roadway.
Side- width = Half formation breadth + Extra portion due to
slope of ground and intended side slope.
Land-breadth = side-width + additional land for hedge, ditch,
etc.
Batters and slopes. Batter of 2 inches per foot = 2 inches
horizontal in 1 foot vertical.
Batter of 1 in 1 = 1 horizontal in 1 vertical.
Slope of 1 J to 1 = 1 J horizontal to 1 vertical.
Slope of 1 in 20 = 1 vertical to 20 horizontal.
-r>- t o T . . . COS A . . 1
Eise of A = slope of 1 in - -? = 1 in r T~ O -
sin A tan A
CALCULATION OF SIDE WIDTHS
205
After setting out and marking the centre line of the railway,
a cross section of the ground surface is taken at each per-
manent stake and plotted in the office to a natural scale, i.e.
horizontal and vertical scales equal. The central heights or
depths of the formation level are marked on them and the
CALCULATION OF SIDE WIDTHS
IN CUTTINGS OR E.MBANKME1NT
h cencrat he/qhc or c/epch of earchwork crC any
secdon or hoLf- secCion.
b ** che formation brepatth
f Co / Che inCena/fat sic/e-sLojoe
g Co / m Che itiCurat t&Cerarl /ncifnorC/on of Che
/fB - Che <siafe * wafch
FIG. 184. Formulae for earthwork calculations (side- widths).
formation level shown by a horizontal line cut off on each side
at formation breadth, which is 30 feet for two lines of way,
occupied with 27 feet by 10 inches of ballast and two 18-inch
ditches, or 28 feet of ballast with 1 2-inch drain pipes. A card-
board templet, having on it the half formation breadth and
proper side slope to suit the soil, enables the slope to be ruled
in, from which the side width may be scaled off and the con-
206
PRACTICAL SURVEYING
tents estimated. If it be desired to calculate the side width
the formulae shown on the diagrams in Fig. 184 must be
employed. The same diagrams inverted or turned from left
to right will give all the other cases that can arise. For
FIG. 185. Indication of cuttings anc embankments on completed plans and sections.
the land-breadths 8 feet or 10 feet "cess" is usually allowed
between edge of slope and fence ; this is marked on the plan
and set out on the ground when required. On the completed
plans and sections, cuttings and embankments are shown as in
Fig. 185.
QUESTIONS ON CHAPTER XXVIII.
1. What do you understand by the " limit of deviation " ?
2. The survey for a railway being very long and narrow but not
straight, how are the various portions connected ?
3. Name and give the dimensions of the most common railway
gauges.
4. What does " engineering field work " consist of ?
5. Show by sketches the difference in the use of the terms
"batter" and "slope."
6. How far apart are the " permanent stakes " usually placed in
setting out a railway, and under what conditions would they be set
closer ?
CHAPTER XXIX.
Railway curves Nomenclature of curves Minimum radius Curve
" elements " and formulae Simple and compound curves Reverse
curves.
Railway curves. It is not possible to construct a road or
railway of any considerable length in a straight line on account
of obstructions and the necessity of slight deviations to avoid
expensive work such as tunnels, bridges, and riaducts. The
change of direction, however slight, has to be made by the
intervention of a curve of as large a radius as possible, and it
PIG. 186. "30 degree curve."
is therefore desirable to consider the question of curves, first
theoretically and afterwards practically.
Formerly the curves were designated by their radius in
chains of 66 ft. up to 80 chains and beyond that in miles, but
on new railways they are now generally expressed in hundreds of
feet. In the American system they are named by the number
of degrees in the centre angle subtendiug 100 ft. on the curve,
so that the greater the radius the smaller the angle. Fig. 186
208
PRACTICAL SURVEYING
shows the method, where the curve would be called a "30
degree curve." The radius in feet is given by the constant
5730 divided by the number of degrees.
FIG. 187. Simple curve.
Nomenclature. A simple curve is one consisting of a
single arc of any given radius, as in Fig. 187.
Fio. 188. Compound curve.
CURVE ELEMENTS 209
A compound curve is one that is composed of two or more
arcs of different radii, as in Fig. 188.
Inverted, reverse or S curves are alternatively concave and
convex, as shown in Fig. 189.
Fio. 189. Inverted, reverse, or /S curves.
For main lines on first-class railways, 4 ft. 8^ in. gauge, the
minimum radius of curve is 1 mile. The minimum radius for
branch lines is 25 chains and for sidings 5 chains.
Curve elements. Fig. 190 shows the various curve ele-
ments, or lines and angles occurring in connection with circular
curves, together with their names, and the following equations
give the mathematical value of each.
Chord of i arc = V(J span) 2 + rise 2 - N/(Js) 2 + ?; 2 .
Radius (R) =
2v
or
span s
2 sin y 2 sin y
(Chord of whole arc) 2 s 2
cos p = 1 r . 5 = 1 - 9>
2 x radius 2 2R 2
whence ft is obtained from table and a = 180 - /?.
P (1 span) 2 is 2
sin v sin ^ 2, r > _ **
2 Curve tangent (radius - rise) T (R - v)
p.s. O
PRACTICAL SURVEYING
2 rise x (^ span) 2
Curve tangent {(J span) 2 - rise-}
2 rise x J- span vs
rise 2 + (-J span) 2
Chord of whole arc
Centre
angle
/3
FIG. 190. Diagram showing curve elements.
Angle between tangent and any chord = J centre angle of
chord.
CURVE FORMULA 211
Curve tangent (T) = R cot ~ = R tan ^ = R tan (00 - - J
22
1/2 rise x span
= A/I i --
\ \ s
i -- 9 - 9 + s P an
J span 2 - rise 2 /
Span (s) = 2R sin ^90 - |j.
H = v/(curve tan) 2 + rad. 2 - radius = \/T 2 + R 2 - R,
or R(sec y 1) = Rf cosec - - 1 j.
-P.. x , /7j9 chord 2 \ Curve tan - i span
Rise (r) = rad. - A / ( rad. 2 - - ) = R - ^
\ \ 4 / Curve tan
AF = H 4- v or ^f ^ or R A /cot 2 ** + 1 R + 2R sin 2 - ",
n-v \ 4
FG = R-v = R-2R sin 2 ,
4
y for x = Vrad. 2 - x 2 - (rad. - rise) = \/R 2 - a? 2 - (R - v),
?y for 5: = rad. - v/rad. 2 - ^ = R ~ N/R 2 - ^ 2 .
Length of the whole curve (L) = E( 90 )
360 \ 2/
= '0349066 R^90 - ^ in degrees and decimals Y
Curve to touch 3 given lines BD, DE, EC ; R = 3 r-
tan - + tan
2 2
212 PRACTICAL SURVEYING
Curve co touch 2 given lines BA, AC, and one of them in a
T x s
given point B. Make AC = AB = T, then R = . >
To find a when T and ,9 are given,
. a S . a . _/a
Sm 2 = 2T' whence 2' \2
The above will be found to give all the information needed
for calculating from certain particulars the remaining portions
so far as regards simple circular arcs. A few questions and
worked examples upon these formulae will render them clearer.
Ex. 1. With an angle of intersection of 75 degrees, a radius of
100 feet, what will be the length of the curve tangents, length of
whole curve, distance from point of intersection to middle point
of curve, and the chord, or span of whole curve ?
100 x 1-3034 = 130-34 feet. Ans.
0-039066
0-0349066 x 100 x ^90 -
183-26 feet. Ans.
R(cosec^- M
lOO^cosec ^ - 1) = 100(1 -6427 - 1)
64 -27 feet. Ans.
2Rsin
2 x 100 x sin 52 30'
2 x 100 x 0-7933 = 158-66 feet. Ans.
CALCULATIONS FROM FORMULAE
213
Ex. 2. With the angles a = 75, 6 = 45, < = 60, and cross tangent
to curve = 99 15 feet, what will be the required radius of curve ?
Cross tangent 9915
R
tan- + tan -
99-15
45 60
tan - + tan
2 2
Ex. 3. With an angle of intersection of 75 degrees, curve
tangents of 130*32 ft. and whole chord of 158-66 ft., what will
be the radius of curve ?
T 130-32 130-32 -,
cot-
cot
or R
2 sin
158-66
1 -5866
100 ft. Ans.
Ex. 4. Given R = 1 00 ft., what " degree " curve will it be called ?
Circumference of whole circle = 7rd = 3'1416 x 100 x 2
= 628-32 ft.
100
.*. angle subtended by 100 ft.
628'32
- x 360
= 57-29578 degrees. Ans.
Ex. 5. With a span of 50 ft. and versine of 1 2 ins., what will be
the radius of the curve ?
See Fig. 191. c
CD : DB : : DB : DE
DE + DC
25 2
+ 1
625 + 1
= 31 3 ft.
PIG. 191. Finding radius of
curve fi-om chord and versine.
Ans. : 313 ft.
214
PRACTICAL SURVEYING
Compound Curves. Attention may now be directed to
compound curves, or those made up of two separate curves of
different radii.
FIG. 192. Problem in compound curves.
Fig. 192. shows the general type of problem required to
be elucidated, and the various formulae involved are as
follows : Given a, t, ?', and R, to find T.
FORMULAE FOR COMPOUND CURVES 215
(Note. x = imaginary angle, used as a means to an end.)
_ R + sin a(r cot a - 1)
n X + 90 - a
Cn = rtan - - - ,
Cm = CnAC = t-Cn
AB =
,
sm (90 - x)
BC = v/AB 2 -f AC 2 - (2 x AB x AC x COS a),
ABC = 90 - x, ACB = x + 90 - a,
Bm = B0 = BC - Cm,
T =r cot a sec a + cos a(t - r cot a) + cos a(R - r)
= AB + Bo.
Given a, T, R, and om, to find r.
y = 180-a-ft
_ R{cos (180 - a) - cos y} + T sin(180 - a)
1 - cos y
Given T, t, a and m, to find R and r.
T 2 + om 2 - Am 2 .
cos Aom = whence angle Aom,
2 . L . OUl
then R = x cosec Aom,
-
cosAnm= - whence angle Anm,
2.t.mn
mn
then r = x cosec Anm.
For example :
Let a = 52 1' 50", = 142-5, r = 50, R = 150,
find the remaining elements.
150 + 0-7883(50 x 0'7804 - 142'5)
150-50 '
216 PRACTICAL SURVEYING
Cn = 50 x tan 40 34' 5" = 50 = 0'8561 = 42 8,
AC = 142-5 - 42-8 = 99'7,
99-7 x sin 81 8' 10" 99'7 x 0'988053
AB = - : r^r^r^- =134'9,
sin 46 50'
0-7294
BC l34-9 2 + 99'7 2 - 2 x 134'9 x 99-7 x 0'61522 = 107 '7,
ABC = 90 - 43 1 0' = 46 50',
ACB - 43 1 0' + 90 - 52 1 ' 50" = 81 8' 1 0",
T = 50 x 0-7804 x 1 "62542 + 0'61 522(142'5 - 50 x 0'7804)
+ 0-72937(150-50)
= 63-28 + 63-67 + 72'93 = 1 99'88,
Bo = 1 99-88 - 1 34-9 - 64'98.
It is sometimes necessary to make a detour on a single
o'
FIG. 193. Detour on a single track with four curves of the same radius.
track, as in Fig. 193, where all four curves have the same
radius. Then given BC and QH,
BG = GQ = QG' = G'C = \/BO x QH.
REVERSE CURVES 217
Given QH arid BO,
BH = HC = v/QH(4BO - QH).
Fig. 194 shows reverse curves of equal radius to join two
pieces of straight making any angle with each other. The
formulae will be as follows :
FIG. 194. Reverse curves to join two pieces of straight.
Given A, B, a and /3, to find R and the junction of the curves.
COS a + COS 8
AB sin y
sin + sin </>
AB
sin a + sin ft + 2 sin (90 - y)'
AD = Rv/2 - 2 cos 0,
CD = AD. sin CAD =
a On
-"xsm^-",
AC = R\/2 - 2 cos 6 x cos
0-2a
~2~'
CB = AB - AC = R\/2 - 2cos < x cos
218
PRACTICAL SURVEYING
Generally it is stipulated that reverse curves shall be
separated by a length of straight to prevent a sudden change
of cant in passing over them, and in colonial work the direc-
tions of the various straight portions are given by their
bearings east of north, clockwise. Fig. 195 gives an example,
which is worked out as follows :
Angle ABC = 55 + (180 -129 16') -105 44' = a.
Angle BCD = (180 - 129 16') + 77 28' = 128 12' = a r
Centre angle opposite ABC = 180 - 105 44' = 74 1 6' = /?.
Centre angle opposite BCD = 180 - 128 12' = 51 48' = /3 r
Let T and T! = length of curve tangents, then
T + T = 11 -70 - 3-00 = 8'70.
s\
PIG. 195. Reverse curves separated by a piece of straight.
Let x = required radius.
7 = 90-- = 37 8'.
T = a; tan 7 = 0; tan 37 8' = xx 0*75721
Tj = x tan y l = x tan 25 54' = x x '48557
V24278
'24278 x =
but T
j = 8-70 .*. x = 1 .
24278
= 7 chains radius.
QUESTIONS FOR PRACTICE 219
QUESTIONS ON CHAPTER XXIX.
1. How are railway curves designated to indicate their curva-
ture ?
2. Show by sketches the difference between simple, compound,
and reverse curves.
3. The angle of deflection of a railway curve is 14 28' 30" and
the chord 1000 feet, what is the radius ? (Ans.: 2000 ft.)
4. The angle of intersection of two centre lines is 57 34' and the
radius 1320 feet. What is the length of the curve tangents?
(Ans.: 2402-73 ft.)
5. Why are reverse curves made with a short piece of straight
between them ?
6. Explain what is meant by centrifugal force, and state what is
its effect upon a train going round a curve.
CHAPTER XXX.
Difference in length of inner and outer rails Centrifugal force and
superelevation of outer rails Widening of gauge on curves
Transition curves.
Inner and outer rails. In going round a curve the outer
rail will be longer than the inner rail, but the maximum
difference allowed in the radial line of the joints is 3 inches.
This is effected by having a certain number of rails 3 inches
shorter than the others, so that when the projection reaches
3 inches a short rail is laid next.
By calculation the difference in length between the inner
and outer rail is found thus :
R = radius of curve to centre line of rails.
G = width of gauge inside to inside of rails.
w = width of rail top.
L = length of outer rail.
I = length of inner rail.
(All in feet).
^ = L R-^G-W
Or, the difference in length in feet per chain of 66 ft. on the
centre line = , or approx.
R R
e.g. 20-chain radius, = 0-25 ft., or 3 miles radius,- = 0-021 ft.
In bending rails by a "Jim Crow," if L be length of rail in
feet, and R radius of curve in feet, the versine at centre will be
1 -56 L 2
EFFECT OF CENTRIFUGAL FORCE
221
Effect Of centrifugal force. When rails are laid on a
curve it is necessary to raise the level of the outer above
the inner rail, or cant the track to counteract the effect of
centrifugal force. Centrifugal force is the tendency of the
vehicle to mount the rails at any point and continue in a
straight line instead of following the curve. If the rails were
laid on the same level, the pressure of the flanges against the
outer rails, or in other words, the centrifugal force, would be
measured by the formula
gr
where F = centrifugal force in tons, W = weight of vehicle in
PIG. 196. Double-headed rail in a cast-iron chair.
tons, = velocity in ft. per sec., g = force of gravity = 32 '2,
r = radius of centre line of curve in ft.
Taking the velocity in miles per hour (V) and the radius of
curve in ft. (r) the super-elevation of outer rail in inches (or
difference of level of the two rails for standard 4 ft. 8J in.
V2
gauge) will be 3-8 , therefore the needful super-elevation
varies as the square of the velocity and inversely as the radius.
The "platelayers' rule" for super-elevation is to make it
equal to the versine of the curve of outer rail for a chord one
chain (66 ft.) in length, with a maximum of 5 inches. More
222
PRACTICAL SURVEYING
accurately, the length of chord upon which the versine is
, , ill v ft. per sec.
measured should be = - -~- ~xj gauge in feet. In
America, the common allowance for super- elevation is -| inch
FIG. 197. Plan of the chair.
per degree of curve. A check rail is sometimes fixed on the
inside of the inner rail at a curve.
The rails themselves are usually fixed in the chairs with a
cant of 1 in 18 towards the centre of the track. Fig. 196
shows a double-headed rail in a cast-iron chair; Fig. 197 a
SO kilos Le m$tre
\43kiLos te
i*'iG. 198. Goliath flange rail.
FIG. 199. Bull-headed
rail.
plan of the chair; Fig. 198 a Goliath flange rail weighing
100 Ib. per yard; and Fig. 199 an 86-lb. bull-headed rail.
WIDENING OF GAUGE 223
Widening of gauge. On curved tracks it is not only
necessary to give super-elevation to the outer rail to overcome
the effect of centrifugal force at the maximum velocity, but,
to allow for the rigid wheel base in the type of rolling stock
in general use, a widening of the gauge is required.
D = degree of curve, standard gauge.
p = flange play in inches.
I = rigid wheel base in ft.
_ 3825y
I 2
The widening of gauge should begin with a 6 degree curve and
increase ^ inch per degree up to 1 inch. Beyond 16 degrees
guard rails should also be used. The standing clearance to
flange is | inch.
For the least possible radius, let
W = wheel base of rolling stock in feet.
G = gauge of railway in feet.
R = minimum radius of curve in feet.
^ = 5 for keyed wheel, 2j for loose wheels.
For an approximate rule to estimate existing curves it may be
noted that if a 2-feet chord has rise of n inches, then radius of
= V + 24
On the London and North-Western Railway it was decided
in 1897 that all curves under 1 mile radius should be com-
pounded, leaving the straight with J chain at 1 mile radius,
\ chain at f mile radius, J chain at J mile radius, and branch
lines should have no curve less than 28 chains radius.
Fig. 200 shows a diagram for a simple case of compounding,
the formula for which are as follows :
Given T, R, r and a, to find the lengths of the curves.
224
PRACTICAL SURVEYING
DAG= ADF=-.
4-
AF = A/ AD 2 + R 2 - 2 . AD . R cos -.
sin DAF = , whence angle DAF.
A T^
AFD-180-DAF-ADF.
GAF = DAF - DAG.
FG = \/AF 2 + R 2 - 2 . AF . R cos GAF.
FIG. 200. Compounding curves.
n /r> n,\2 "FT 1 2
cos FHG = : ~- p , whence angle FHG = BHC.
TJTTC 1
Length of EC = 2?rR x -
360
sin GAF x AF
sinAGF =
FG
, whence angle AGF.
TRANSITION CURVES 225
cos HGF = j r, whence HGF.
2 (R - r)
EGA = HGF - AGF.
BGA
Length of AB or CD = 2-n-U x
360
Transition curves. A transition curve is based upon the
principle of compound curves, but when a pure circular curve
is entered directly from the straight, centrifugal force acts
very suddenly on each vehicle ; this sudden action of the
centrifugal force produces a swing, similar to the swing of a
pendulum bob when drawn aside and released. As a rule, the
outer rail on the straight leading to the curve is gradually
superelevated, so that the proper amount of cant is attained at
the entrance to the curve, but this cannot lessen the extent of
the swing, although it lessens the sense of discomfort to the
passengers. The over-swing or pendulum effect is augmented
by reversal of curvature, and consequently it is at such points
discomfort is most felt. The true purpose of a transition curve
is, therefore, to enable the centrifugal force to be applied
gradually.
An efficient transition curve should allow of a rate of gain
or loss of radial acceleration for the fastest trains just equal to
the maximum amount that will pass unnoticed. The radial
acceleration of a car moving v feet per second in a curve of
r feet radius equals v z /r ; so that, neglecting the easing effect
due to the length of a coach, the rate of gain of acceleration
when a car enters a curve of r feet radius with a transition
I feet long, at v feet per second, equals ifl/lr. In Mr. W. H.
Shortt's experience on the London and South- Western E ail way
the maximum rate of gain or loss of acceleration that will pass
unnoticed is 1 foot per second in a second, so that I, the length
of transition necessary, equals v s /r feet.
Let V = velocity in miles per hour, R = radius in chains,
L = length of transition in chains, then the maximum speed
attained over the curve will be V = 11v/R up to a speed of
about 82 miles per hour, and L = s/R, when R is not more than
54*3 chains. Where speeds as high as 11\/R are not probable,
0*000724 V^
the length of transition may be , where V is the
R
p.s. P
226 PRACTICAL SURVEYING
maximum speed. The form of transition should satisfy the
relation - = Xrl, where p = the radius at any point, A is the length
of transition traversed up to that point, r = radius of main
curve, and Z = the length of the transition. Mr. Glover,
in a paper appearing in Vol. cxl. of the Minutes of Proceed-
ings of the Institution of Civil Engineers, shows that the spiral
A = m -J(f> completely satisfies this condition and is the simplest
form of transition curve to use.
QUESTIONS ON CHAPTER XXX.
1. How is the difference in length of the inner and outer rail
on a railway curve dealt with in practice ?
2. What practical expedient is adopted to neutralise the effect
of centrifugal force on a railway curve ?
3. Give a simple rule for the super-elevation of the outer rail
on a curve.
4. Make a sketch showing the fixing of a rail in a cast-iron
chair.
5. Explain what is meant by transition curves and the reason
for their adoption.
6. What methods are available for enabling the rectangular
wheel base of a vehicle to travel round a railway curve ?
CHAPTER XXXI.
Ranging a curve By chain and offsets By one theodolite By two
theodolites Practical example Points and crossings Sidings.
Ranging a curve. Ranging a curve consists in placing
pegs at intervals along the centre line or railway from the
tangent point where the curve leaves the straight. The dis-
tance from peg to peg depends upon the sharpness of the
curve to some extent, and is independent of the position of
the permanent stakes which have to be placed round the curve
COMMON METHOD OP SETTING OUT
OR CHECKING CURVES
FIG. 201. "Platelayer's method" of setting out or checking curves.
at even distances from the commencement of the line, irre-
spective of the tangent points. The two things may be and
sometimes are combined : the first point in the curve is then
set out to range from the last permanent stake. Various
simple methods may be first described, and then the more
usual methods, as practised. Fig. 201 shows the " plate-
layer's method " of setting out or checking curves, where
ft. in. 1 ch. .. . . , 7 b fJ _ - rn *
_ : j = ft. in offset o, c. etc., - = it. in onset a.
rad. in. ch. 2
228
PRACTICAL SURVEYING
Ex. 1. Say curve 3 chains
radius (4 pole chain).
6 = ^ = 22 feet.
3
oo
a = = 11 feet.
Ex. 2. Say curve 3 chains
radius (100 ft. chain).
6 = = 33J feet.
= = 16f feet.
2 3
Theoretically, there are two closely allied methods which are
shown with their formulae in Figs. 202 and 203.
SETTING OUT CURVES
BY RECTANGULAR OFFSETS
r - radius. ? m o>
5 -o
FIG. 202.
\
SETTING OUT CURVES
BY OBLIQUE OFFSF.TS
, . d - S, - % . &
FIG. 203.
FIGS. 202 and 203. Curves bj chain and offsets.
CURVES ON BRIDGES
229
Fig. 204 shows how a curve is placed on a bridge, and
Fig. 205 the same principle extended to a curve on a viaduct.
Fig. 206 shows a practical method of finding the radius of
77>ese fro d/mesisiora
made equal.
FIG. 205.
FIG. 204. Curve on a bridge.
FIG. 205. Curve on a viaduct.
an existing curve where C = length of chord on outer rail
tangent to inner rail, g = width of gauge, then mean radius
The principle of setting out curves by angles of deflection
is that equal arcs on the circumference of a circle subtend
Radius of curve -
FIG. 206. Finding radius of existing curve.
equal angles at any one point on the circumference. Let
8 = angle of deflection for an arc of a feet or chains, when the
radius = r in same units, then 8 in minutes
J80*eO x a a
2?r r r
PRACTICAL SURVEYING
When arc a> ~ r, chord c = a (1
230
Where arc &~ ?*> chord c = a approx.
Use of one theodolite. In setting out the angles of
deflection by one theodolite as in Fig. 207, unless the curve
FIG. 207. Setting out curves with one theodolite.
commences exactly at a given number of chains from the start-
ing point of the railway, it will be necessary to make the first
angle to fall upon the first chain-end on the curve. For instance,
if the tangent point occurs at 8 m. 37 ch. 45 1., then 1 00 - 45
55 55
= 55, - _- 8 = first angle, S + 8 = second angle, and so on.
1 OO 1 00
The end of the curve may be treated in the same way. When
two theodolites are used, as in Fig. 208, one is placed at
FIG. 208. Setting out curves with two theodolites.
each tangent point, and the angles set off in an identical
manner, the lines of sight intersecting at the successive chain
ends, 8 being set off from one station and (7 -8) from the
other, 7 being the total angle of deflection.
A brief series of instructions for elementary field work, by
means of which a couple of students, without further assist-
SETTING OUT A CURVE
231
ance, could set out a curve with one theodolite, may prove
useful at this point.
Required : Theodolite and legs, 6 poles, chain and arrows.
(1) Locate directions of straight portions, Fig. 209.
FIG. 209. Practical example of setting out curve.
(2) Decide radius, say 3 chains.
(3) Find point of intersection (A).
(4) Take angle of intersection (a), say 120.
(5) Find length of curve tangent (T)
= R tan | = 3 x -577 = 1-73.
(6) Chain and mark points B, C.
(7) Say first tangent point B occurs at 3*17 on line, and
stakes required 1 chain apart.
(8) Owing to short radius, there will be appreciable differ-
ence between chord and arc.
(9) The arc is to be set off in 1 chain lengths,
'" 537 ' say " 4 Hnks '
232
PRACTICAL SURVEYING
(10) Tangent point does not fall on chain end,
.'. first angle = 8 = 0*838.
(11) AndS = 28 38-8734' ^ = 9 33' for each angle after the
first.
(12) First angle = 9 33' x 83 = 7 55' ; first chord = 0'83
x 0-99537 = 82 J links.
(13) Second angle = 9 33' + 7 55' = 17 28'; second chord,
= 99J links.
(14) Third angle = 17 28' + 9 33' = 27 1'; third chord
= 991 links.
(15) Find whole deflection to see when to stop,
7 = 90-1=30,
therefore now stop, as would be seen by peg at C in
the field.
(16) To find length of remainder of curve, find whole
length of curve and deduct distance traversed.
(17)
L = 0-0349066R( 90 --J = 3-141594,
3-14 -(0-83 + 1+1) -0-31 =31 links.
1 00 - 31 = 69 links from tangent point to end of chain on
straight.
The planning of the various junctions in the railway metals
does not come under the purview of this work, but a very
short description, with illustrations, of some of the arrange-
ments may increase the usefulness of the book to young
railway engineers. A simple turnout or pair of points or
switches is shown in Fig. 210, and the crossing where the new
FIG. 210. Pair of points or switches
CROSS-OVER ROADS
233
line leaves the old is shown in Fig. 211. A cross-over road is
shown in Fig. 212, with trailing points, and it should be
FIG. 211. Crossing.
noted that facing points are not allowed on main lines.
Fig. 213 shows the usual method of connecting sidings with
FIG. 212. Cross-over road with trailing points.
the main lines of a railway, but the scale is unequal in length
and breadth to keep within the limits of the page. Crossings
FIG 213. Connection of sidings with main line.
should not be flatter than 1 in 8, or sharper than 1 in 6.
Switches vary in length according to the radius of the turnout,
from 10 to 20 feet.
234 PRACTICAL SURVEYING
QUESTIONS ON CHAPTER XXXI.
1. What is meant by " ranging a curve " ?
2. Describe the simplest method you know of for ranging a
curve of short radius.
3. How are bridges and viaducts arranged to allow railway
curves to pass over them 1
4. Explain the method of setting out a railway curve with two
theodolites.
5. Make a sketch of a cross-over road in railway work, marking
the direction of the traffic by arrows.
6. Explain a method of setting out a railway curve when the
point of intersection of the tangents is inaccessible.
CHAPTER XXXII.
Astronomical surveying Finding true meridian Celestial sphere
Longitude and local mean time Astronomical, civil, and nautical
time Finding the latitude of a place.
Astronomical surveying. It is often necessary for a
surveyor to be able to locate his geographical position, in
other words to find his latitude and longitude. This is a
matter of some difficulty if exactitude is required, but it may
be done approximately without very much trouble.
Roughly, the latitude of a place in the northern hemisphere
is given by the mean altitude of the pole star, less 45 seconds
for refraction, but to obtain it more correctly much subsidiary
work is involved, which must first be explained.
To determine the meridian of a place, i.e. a true north and
south line, there are various methods :
(a) Bisect the angle formed by the bearing of the sun at
sunrise and sunset, when the lower limb is a semi-diameter
above the horizon.
(b) Bisect the angle formed by the sun, or a star, in east
and west positions of equal altitude.
(c) Take the mean between the eastern and western elonga-
tions of a circumpolar star.
(d) Find the direction when a vertical circle cuts both the
pole star and the star Alioth in Ursa Major, otherwise "the
shaft-horse of Charlie's wain," see Fig. 214.
The pole star is not precisely at the North Pole, but is
nearer than any other star, being only 1 deg. 1 6 min. 42 sec.
away from it and rotating round it, so that it crosses the
meridian twice in twenty-four hours.
Celestial sphere. Fig. 215 represents a celestial sphere
as if it were a hollow globe surrounding the earth, with the
visible heavens projected upon it. The point immediately
236
PRACTICAL SURVEYING
overhead is called the zenith, and the opposite point below is
the nadir. Culmination is the term used for the passage of a
celestial body across the meridian of a place, and in the
northern hemisphere most of the bodies observed culminate
southwards. Decimation is the celestial term corresponding
to the terrestrial one of latitude. Any celestial body would
serve for observations of latitude as well as a star, but the
IN URSA MAJOR
ARC KNOWN AS THE POINTERS BECAUSE
THEY POINT APPROXIMATELY TO THE POLE STAR
FIG. 214. Position of the circumpolar stars.
declination of the bodies of the solar system varies from
day to day and, in order to get the correct declination from
the almanac, it is necessary to know the Greenwich mean
time, whereas the declination of the fixed stars varies so little
that no knowledge of longitude or time is required.
Let S (Fig. 215) = the apparent position of a body culmi-
nating to the south of the observer, then its declination
will be north = SE, its altitude = HS, and the co-latitude = HE.
LONGITUDE AND LOCAL TIME 237
Let U be the position of a body culminating south and with
a south declination, then EU = declination, UH = altitude,
HE = co-latitude.
When a body culminates to the north of the observer above
the pole, VR = altitude, VP = co-declination, PR = latitude ; and
below the pole, V'R = latitude, V'P = co-declination, PR = lati-
tude. Therefore, HE = SH - SE, HE = EU + UH, PR = VR - VP,
PR = V'R + V'P.
R HORIZON
FIG. 215. Diagram of celestial sphere.
The " prime vertical " is due east and west of the observer,
i.e. at right angles to a meridian, and the apparent motion in
altitude is greatest there.
Longitude and local mean time. The centre of the
sun passing the meridian, or the maximum altitude of the
sun, gives approximate local noon. Longitude is determined
by the difference between mean local time and Greenwich
mean time. Noon is later on a west longitude and earlier on
an east longitude, the difference in time being 4 minutes per
degree.
238 PRACTICAL SURVEYING
Ex. Suppose the longitude is 3 45' W., then local mean time
(noon) is 4x3| = 15 min. after Greenwich mean time. Say
WTiifaker^s Almanac under given date shows "sun 2 m 22* after
clock," this is the " equation of time," and the apparent local
time (noon) = 12' l + 15 wl + 2 w 22* = 12* 17 m 22*. Or vice versa:
Local noon = 1 2 h 1 7 m 22 s , Greenwich time - 2 m 22 s = + 1 5 min.
Then 1 hour = 1 5 degrees of arc ; therefore time x 1 5 = longi-
tude, 15x15 = 225 min., % 2 <? = 3 45' W. longitude, or as is
stated, longitude in time x 15 = longitude in arc.
Divisions of time. Now, as to time, Fig. 216 shows the
relation, in order of succession, of the various divisions of time
ASTRONOMICAL , SID&RCAU
AND GREENWICH TIMF
/ co 24 i o'ciocft
"f
CIVIL TIME
/ Co/la*. | / co 12 *M
noon
NAUTICAL TIME TIME NOMENCLATURE
/to/2 P.M , /co 12 A.M.
noo/? noon
FIG. 216. Relation of various divisions of time.
in use, with the name to each. It will be seen from this why
the Nautical Almanac is said to be always a day behind. To
find astronomical time from the civil time for P.M., make
no change ; for A.M., diminish the day of the month by 1 and
add 12 to the hours. The mean solar day is the average
interval between two consecutive passages of the sun over the
same meridian, or true north and south line. The apparent local
day is the actual interval between two consecutive passages of
the sun over the meridian. A sidereal day is the interval
between two successive transits of a star over the meridian of
a place ; and it is 3 min. 55-908 seconds less than a mean
solar day. The equation of time in the Nautical Almanac is
the difference between apparent and mean time, and is used
for reducing apparent local to mean local time.
The time may be found by observation on a celestial body
whose apparent position is given in the Nautical Almanac ; or
the transit of a star across the meridian gives true sidereal
time of the locality from its Right Ascension (R.A.). Right
ascension is the angular distance measured along the equator
FINDING THE LATITUDE 239
from the intersection of the equator and ecliptic at the vernal
equinox (commonly called the first point of Aries, because it
was originally there, but has since retrograded). Eight
ascension and declination are the two co-ordinates which
define any point on a celestial sphere with regard to the
equator as a fundamental plane, just as longitude and latitude
define a terrestrial point. " Southing " is the time a heavenly
body passes the meridian, or is the time of greatest altitude ;
right ascension may be called " Sidereal time of Southing."
Finding the latitude of a place. A writer in Building
World describes a method of obtaining the latitude approxi-
mately with a 2-feet rule and spirit level as follows :
"The instruments required are a fourfold rule and a
small spirit level. Open the rule out its whole length, and
raise up one fold at right angles to the other three. When
the sun is on the meridian that is, at local apparent noon
turn the rule to the sun so that the length of the shadow
thrown by the upright fold may be measured on the three
extended folds when the latter are held horizontally, as shown
by the bubble of the small level, which must be placed on the
extended part of the rule, in such a position that the eye may
see at the same time the bubble at the centre of its run, and
the end of the shadow. After a small amount of practice, this
operation is easy to perform. The time of the sun's passage
of the meridian can be obtained, for places near London, from
Whitaker's Almanac. For any other place allowance should
be made for the longitude at the rate of 15 to the hour.
Where the longitude is unknown, the sun crosses the meridian
at the time that it shows the shortest shadow, and the length
of this shadow should be taken for calculating purposes."
The following is the calculation of latitude made from
observations taken on February 6 (cloudy, with bright
intervals). Rule, 2-feet fourfold ; spirit level, 3 inch brass.
Length of vertical fold, 6 inches ; length of shortest shadow,
14 1 inches.
Y = = - 4138, by reference table of natural tangents
l4g 29
0'4183 = tan of 22 30', which is the altitude of sun. Then
240 PRACTICAL SURVEYING
Angular zenith distance from horizon = 90 0' 0"
Altitude of sun's centre - - = 22 30' 0"
Angular distance of sun from zenith - = 67 30' 0"
Sun's distance from celestial equator ^
or declination south (from Whit- J 1 5 37' 45"
aker) -
Latitude of place of observation - =N.51 37' 15'
Should the declination be north, it must be added to the
sun's angular distance from the zenith instead of subtracted,
to give the latitude. The latitude of the garden, where these
observations were made, is, according to the Ordnance map-
(of 6 inches to the mile), 51 37' 0" N.
With a theodolite, or other angular instrument of precision,
latitude would be obtained practically by observing the meridian
altitude of the sun as follows. Set up and level the theodolite
ten minutes before apparent noon, put the dark glass on the
eyepiece, direct the telescope to the sun, cut the lower edge with
the horizontal wire, and follow the sun by the tangent screws
as the altitude increases, stopping directly the highest point is
reached. Note the reading of the vertical circle, and the
remainder of the work is effected by reference and calculation.
The inversion in the telescope of the object and its move-
ments must be duly remembered in making the observation.
Example. Plymouth, 9th Oct., 1901.
Observed altitude, - 33 6'
Add semi-diameter, - - 1 6'
Apparent altitude, - 33 22'
Deduct refraction, - - - 1 '
33 21'
Add parallax, - 9'
True altitude, 33 30'
Add declination south, - - - 6 6'
Co-latitude, 39 36'
Latitude = (90 - co-latitude), - --50 24' N.
QUESTIONS FOR PRACTICE 241
The semi-diameter, refraction, parallax and declination are
taken from the Nautical Almanac. Note that a north de-
clination must be deducted and a south declination added.
The resulting latitude above is approximate only ; for exact
work, the observations and corrections must be carried out to
seconds, personal and instrumental errors allowed for, etc.
If, instead of a theodolite, a nautical sextant and artificial
horizon be used, the angle taken will be a double altitude, to
be divided by 2 before making the corrections.
QUESTIONS ON CHAPTER XXXII.
1. What is meant by the meridian of a place ?
2. What is the position of " the pole star " with regard to the
North Pole?
3. What is meant by local noon and how is it ascertained ?
4. What is the relationship between "solar," "sidereal,"
" nautical," and " Greenwich mean " time ?
5. What is meant by " the equation of time," and where may it
be found ?
6. What are the items required in order to determine the
latitude of a place ?
P.s.
CHAPTER XXXIIL
Signalling at a distance The Morse alphabet and Universal code Flag
signalling Flashing signals Heliographing.
Signalling 1 at a distance. As surveyors may have to
transmit signals to long distances they should learn the Morse
code and telepost alphabet, or universal dot-and-dash code,
consisting of long and short intervals indicated as below, in
whatever way they may be produced.
LETTERS.
A ._ K U . ._
B L V . . ._
C M W
D _.. N _. X
E. O Y_.
F P. . Z ..
G . Q . _ . (full stop)
H . . . . R . _ . , (comma) . _ . _
1 .. S ... If (paragraph) _ __ _ _
J. T_ & . .
FIGURES.
1 5 8 .
2 . . 6_.... 9 .
3... 7 ...
4 ... . _
To attract attention or to denote completion of message
Repeat . . _ _
Flag signalling. A station pole or picket with a flag on
it forms a good medium for transmitting signals over moderate
distances, of say half a mile to a mile in daylight, without using
binoculars. Holding the pole diagonally the flag should be
moved sharply from the left to the light shoulder for dots and
from the left shoulder to the ground for dashes.
HELIOGRAPHING
243
Heliographing. Sun-flash signals on the Morse code may
be transmitted by heliograph over distances of several miles.
Fig. 217 shows the method of carrying out the work. A is a
mirror from which the sun's rays are reflected and B a screen
for obscuring it in the direction the signals are to be trans-
mitted. C is a horizontal bar carrying cross wires D. To
adjust for signalling, the operator looks through a hole E in
Fia. 217. Sketch of operations in heliographing.
the mirror A, while an assistant adjusts the cross wires D until
the point of intersection and the distant place to which the
rays are to be directed are as nearly as possible in a straight
line with observer's eye at E. The arm and wire frame are
now fastened by means of screws. A white disc is next placed
at the centre of the cross wires and a black one at the hole E.
If the light reflected from A be now thrown upon B, a black
dot will be seen upon it, this portion of the light having been
244 PRACTICAL SURVEYING
absorbed by the black disc. The screws of the signalling
mirror are now turned until this shadow of the black disc is
thrown on to the white one at the junction of the cross-wires.
The rays now proceed in the required direction ER. The
screen B is now adjusted so that the shadow of the white disc
falls on the hole. The arm C being removed, everything is
now ready and the screen B is operated by means of the thumb-
screw G to give the required flashes. If the sun is so placed
as to make it difficult to reflect its rays in the required direc-
tion a second mirror S is used to throw them on to A.
At night a signalling hand lamp, with flashing shutter, may
be used for sending messages over moderate distances.
In case of necessity the signals can be communicated by any
method of alternately shutting off and exposing a light of any
kind, or by a series of knocks, it is well known that experienced
operators can read off a transmitter by the sound only.
QUESTIONS ON CHAPTER XXXIII.
1. Describe the principle of the Morse code.
2. Translate the following message :
m ,: .',.:':,,.''/,/'..!: :' '" '<*"'
3. How are Morse signals transmitted by flag ?
4. Describe a heliograph and explain the method of using it ?
5. How can code signals be transmitted at night ?
6. What colours are seen most distinctly against the followin
back-grounds : (a) green trees, (b) dark earth mounds, (c) the sky
APPENDIX.
EXAMINATION QUESTIONS IN LAND SURVEYING.
THE following questions have been given in various examina-
tions, the source being named at the end of each. They are
roughly classified in the order in which the subjects are
dealt with in this book, arid comprise the following list :
Admiralty Assistant Civil Engineers (12) ; Admiralty Assistant
Surveyor (6) ; Architectural Association (8) ; Institution of
Municipal and County Engineers (7) ; City and Guilds of
London Institute (2) ; City of London College (56) ; Eastern
Cadets (13) ; Engineers' Examinations, New South Wales (9) ;
India Forest Service (9) ; Institute of Sanitary Engineers (4) ;
Institution of Civil Engineers (68) ; Institution of Municipal
Engineers (1) ; Public Works Department, India, Assistant
Civil Engineers (18) ; Public Works Office, Ireland, Assistant
Surveyor (6); Mason College, Birmingham (4) ; Owens College,
Manchester (6) ; Royal Agricultural College, Cirencester (5) ;
Royal Institute of British Architects (9); Society of Architects
(8); Survey Department, Brisbane (13); Surveyors' Institu-
tion (4) ; Valuation Office, Ireland, Surveyor and Valuer (10) ;
University College, London (4).
1. With 100-feet frontage what depth in feet will contain one
acre? (Arch. Assoc.)
2. What is the length of a link in a 4-pole chain ? Upon a scale
of 88 feet to one inch what will be the length of 1 chain ?
(Arch. Assoc.)
3. Convert 17 acres 1 rood 20 perches statute measure into
square yards. (Surv. Inst.)
4. Required in feet, the side of a square that shall contain an
acre. (R.I.B.A. Inter.)
5. With the use of a chain of one hundred foot-links, how many
square chains are there in one square mile 1 (City Lond. Coll.)
246 PRACTICAL SURVEYING
6. What is the scale of a map which shows 250 acres in 1 square
inch ? (City Lond. Coll.)
7. What is the object of measuring the area of a field without
the aid of plotting ? (Owens Coll.)
8. Distinguish between plotting scales and mechanical draughts-
men's scales, the latter designated as so many inches or parts of an
inch to one foot. Also fully explain the expression "feet equal"
upon a plotting scale. (City Lond. Coll.)
9. For what purpose are Ordnance Maps chiefly employed, and
what are the comparative advantages of published maps which are
drawn to the scale of (a) one inch to one mile, (b) six inches to one
mile, (c) vxao or 25'344 inches to one mile, (d) five feet to one
mile, and (e) 2 D or 1 0'56 feet to one mile ? To which of the above
Ordnance Maps is a scale of 88 divisions to one inch applicable and
how is it applied? (Oity Lond. Coll.)
10. What are the representative fractions of the following
scales : 5 chains to an inch, 6 inches to a mile 1 What scales are
represented by the following fractions : ^g, asW an ^ 2500 ?
(India Forest Service.)
11. If a plan is plotted to a scale of 3 chains to an inch, what
proportion does the area of the plan bear to the ground ?
(Surv. Inst.)
12. Find the area in acres, roods and perches of a trapezium
whose parallel sides are 45 links and 130 links, and base 3 chains
27 links. (City Lond. Coll.)
13. The outline of a certain piece of ground may be indicated by
a square of 3 chains side, with an equilateral triangle on one side
and a semi-circle on the opposite side. What is its area in acres,
roods and perches ? (Arch. Assoc.)
14. The distance from Hyde Park Corner to Cooper's Hill is 20
miles, and measures on map 2*75 inches. Draw the scale of the
map showing 40 miles on right of zero, and 10 miles (subdivided
into miles) on the left of it. (Civ. Eng. P. W.D. India.)
15. Make a scale of chains and links equivalent to 40 feet to 1
inch. (City Lond. Coll.)
16. A plan is to be plotted to a scale of 5 chains to an inch, but
after it is completed it is found that the opposite side of the scale
representing " feet equal " has been used by mistake. Draw the
true scale of feet for the plan as plotted. (India Forest Service.)
17. In an old survey of 30 acres the chain used is found to have
been 4'54 inches long. What is the correct area ?
(Surv. Dept. Brisbane.)
18. Having calculated the area of an estate from a plan drawn
to a scale of one chain to the inch, upon the supposition that a
EXAMINATION QUESTIONS 247
chain of foot-links (consisting of the usual 100 links) had been
employed, the result was found to be 69 acres, 1 rood, 20 perches ;
but it was subsequently ascertained upon enquiry that Gunter's
chain of 22 yards length had been employed for taking the mea-
surements in the field. What is the correct area ?
(City Lond. Coll.)
19. Upon what geometrical principles is land surveying based ?
(City Lond. Coll)
20. Describe the field-book used by land surveyors, and the
method of using it. (City Lond. Coll.)
21. How can an irregular four-sided figure be converted into a
triangle, and what use is made in surveying of this principle ?
(City Lond. Coll.)
22. Explain the use of the parallel ruler in reducing crooked
fences to straight ones, and lay down a right-lined offset piece from
the following notes ; reduce it to a triangle by the parallel ruler,
and find its contents both by calculation from the offsets and the
casting of the ruler :
To B
751
550 150
400 51
250 99
50 75
000
From A range W. (R.LB.A. Inter.)
23. State Simpson's rule ; and calculate the area contained
between the fence and the line in the following example of distances
and offsets: 0-0, 10-7, 20-13, 30-11, 40-9, 50-9, 60-10,70-12,
80-14. (Owens Coll.)
24. What are the chief scales of Ordnance maps ? What infor-
mation is given in Ordnance Survey Keference Books ? What are
the representative fractions corresponding to 24 inches to a mile,
and 3 chains to 1 inch ? (City Lond. Coll.)
25. Take out the area of the wood numbered 1001 on the plan
P, and reduce it to acres, roods and perches, etc. Show all your
calculations. (Eastern Cadets.)
26. A surveyor walks from A to B at 4 miles an hour, and he
then walks back again by another road at 3 miles an hour ; the
last-named road is longer than the former by 2 miles. If he takes
9 hours in all, how long is each road ? (Survey Dept. Brisbane.)
27. A four-sided figure has two diagonals respectively 325 links
and 450 links in length, with an angle of intersection of 75, what
is the area of the figure in square chains ? (City Lond. Coll.)
248 PRACTICAL SURVEYING
28. The area in acres, roods and poles [sic] is required of an
irregular field, which was surveyed by running one line through it
from end to end (A to B) with offsets taken as under.* No plan to
be drawn. (pity Guilds.)
29. Give the formula for calculating the area of a triangular
piece of land with sides respectively 300 chains, 236 chains and
126 chains long ; state the area in acres and decimals of an acre.
(Mun. & County -Eng.)
30. The sides of a triangle are in the proportion of 5, 6 and 7,
and the area is 100 square chains, what are the lengths of the
sides ? (City Lond. Coll.)
31. How many acres of horizontal ground would be covered by
a bank 35 chains long, 7 yards wide at the top, 6 feet above the
ground at one end and 27 feet above the ground at the other end,
the slopes being two to one throughout ? (Inst. Mun. Eng.)
32. Divide the triangle ABC into three equal portions by lines
parallel to the side AB. AB = 2500 links; AC = 2100 ; and
BC = 1 800. Give the area of ABC and the distances Aa, ab,
and 60. (Surv. Inst.)
33. The sides of a triangular field containing x acres, are in the
proportion a : b : c, find each side. (Surv. Dept. Brisbane.)
34. Write out a list of any instruments which are useful in
enlarging or reducing maps or drawings, and describe shortly the
two principal instruments. ( Valuation Office, Ireland.)
35. Construct a diagonal scale of 3 inches to 1 mile, to read
miles, furlongs and chains, and long enough to read 2 miles.
(Admiralty Civ. Eng.)
36. In chaining the base line of a survey, a pond is met with
crossing the line, which is too wide to be chained across ; explain,
with the help of a sketch, how the chaining can be accurately
extended beyond the pond. (Inst. C.E.)
37. The length of a survey line was measured with a Gunter's
chain and noted as 5000 links. It was re-measured with a 100-
foot chain and noted as 3300 feet. The error of the Hunter's chain
was +0'2 link. What was the true length of the 100-foot chain?
(Inst. C.E.)
38. Plot the survey, from the field-book accompanying this
Paper, to a scale of 1 inch = TOO links. (Inst. C.E.)
* The field-hook part of many of the questions being often voluminous
and of an ordinary character, or containing diagrams, has been omitted
here and in other similar questions. Such questions serve, however, to
show what is expected of candidates in the Examinations concerned.
EXAMINATION QUESTIONS 249
39. Describe the manner in which the light band chain suspended
free of the ground, is used. What degree of accuracy may be
expected from the use of this system of measurement ? (Inst. C.E.)
40. How are base lines measured by steel tapes ? What should
be the length of the tape ? What precautions should be taken
during the work and what accuracy would you expect ? (Inst. C.E.)
41. The accompanying extract from the pages of a field-book
represents the survey of two adjoining fields. A plan is to be
drawn out of these fields and the exact area comprised within the
base lines of the survey is to be ascertained. (Inst. C.E.)
42. State briefly the points to be attended to in selecting
positions for the stations of a chain survey ; also the precautions to
be taken to secure accuracy in chaining the lines. (Inst. C.E.)
43. The following perpendicular offsets were taken, at consecu-
tive intervals of 20 feet, from a straight line to a wavy boundary :
9, 15, 12-3, 17, 5-2, 9'4, 7. Find the area between the straight
line and the boundary line by Simpson's rule. (Inst. C.E.)
44. Distinguish between compensating and cumulative errors in
chaining. A field was measured with a chain 0'3 of a link too long,
the area thus found was 30 acres. What is the true area ?
(Inst. C.E.)
45. One of the lines of a chain survey crosses a pond. Give
three methods of finding the distance across the pond without
using any instruments for measuring angles. (Inst. C.E.)
46. Describe a Gunter's chain ; state what precautions are
necessary to ensure accurate work. (Mun. and County Eng.)
47. What is the proper presumption as to where the dividing
line between two estates is situated ; (a) where separated by a
hedge and ditch ; (b) where separated by a hedge and ditch on
either side of the hedge ; (c) where separated by a fence ?
( Valuation Off. Ireland).
48. What is the present " magnetic variation," and what use is
made of it in land surveying ? (Arch Assoc.)
49. Describe a complete set of instruments required by a land
surveyor in field work, giving the size of each instrument where
desirable. ( Valuation Off. Ireland.)
50. Describe the methods of lineal measurement (a) with short
tapes ; (b) with long ribands. (Surv. Dept. Brisbane.)
51. Compare the relative merits of a Gunter's chain, 66 feet
long, with a chain of 100 foot-links, and state under what circum-
stances the use of the one is to be preferred to the other.
(City Lond. Coll.)
52. Describe Gunter's chain, and state for what purpose it is of
the prescribed length ; to what branch of surveying is it particularly
250 PRACTICAL SURVEYING
applicable? Also, describe the 100-feet chain and its divisions;
how many arrows are attached to each chain, and what is their
use ? (Civ. Eng. P. W.D. India.)
53. Show by a sketch the usual method of taking offset measure-
ments to a fence boundary, and any variation you would adopt to
accurately delineate the intersection of one fence with another
fence. (City Lond. Coll.)
54. Explain the object of a base line. What is the purpose of a
tie line, and what is meant by an offset ? (City Lond. Coll.)
55. How are the lines of a chain survey fixed in position, and
how is the correctness of the work tested? What is meant by
" tying " the lines ? Give a sketch. (Mun. and County Eng.)
56. Can you make a survey without using any instrument for
measuring angles ? If so, prove the correctness of the method you
would employ. ( Val. Off. Ireland.)
57. What considerations would guide you as to the limit of
length of an ordinary offset in making a survey ? What considera-
tions would determine the number of offsets which you would deem
it necessary to take, and what value would you attach to a split
offset scale, when plotting ; that is, an offset scale with the zero in
the centre. (City Lond. Coll.)
58. In what manner would you record measurements from a
base line to some well defined point in a survey, such as the corner
of a building, which it is, of course, necessary to fix in position most
accurately. (City Lond. Coll.)
59. What is a "north-point"? What is meant by "magnetic
variation" ? (City Lond. Coll.)
60. Sketch the cross section through a hedge and ditch between
two fields, and mark the point of the usual boundary. What is the
usual allowance from the centre of > hedge to brow of ditch when
they separate the property of two different owners ? (Soc. Archs.)
61. Sketch an irregular five-sided field, the longest side, about 3
inches long, being taken as the base. Rule on the chain lines you
would use in making the survey, assuming the scale to be 2 chains
to 1 inch, and give the field-book entries, with offsets for the base
line. (Soc. Archs.)
62. Show by sketch, and describe how you would continue a
chain line across a circular pond 100 feet diameter. (Soc. Arc/is.)
63. Describe the method of setting the poles and chaining over
rising ground when the station pole at one end cannot be seen from
the other. (Soc. Archs.)
64. How would you proceed to set out a straight line, between
two points, the intervening land being too high to allow of your
sighting from one to the other. (Assist. Surv. P. W.O. Ireland.)
EXAMINATION QUESTIONS 251
65. Explain how you would range out a base line over a hill of
moderate slope, and give a sketch showing how you would proceed
in order to measure the length of this base line with a chain 100
feet long. (City Lond. Coll.)
66. Describe how perpendiculars to a chain line are set out in the
field. (R.I.B.A. Inter.)
67. Describe a means of erecting a perpendicular to a base line
with the use of a chain only; and the method you would take with
the chain, to check the direction of the perpendicular in the field, if
you had any fear of your chain being out of adjustment.
(City Lond. Coll.)
68. Show by a sketch how you would continue a station line past
an obstacle, such as a tree. (Owens Coll.)
69. How would you chain past an obstruction in the field when
(a) it can be seen over ; (b) it cannot be seen over ?
(Arch. Assoc.)
70. Explain and illustrate by diagram how you would obtain the
distance to an inaccessible point, using only chain and poles.
(Surv. Inst.)
71. Illustrate and describe in what way you would produce a
survey line obstructed by a large tree or building ? (Surv. Inst.)
72. In chaining a line up or down a slope, would you consider
the total length accurately arrived at by stepping with the chain in
short lengths, and using a dropping arrow or a plumb-bob ? Do
you prefer a plumb-bob being employed to a heavy dropping
arrow, and if so, state your reason. (City Lond. Coll.)
73. Give a sketch showing in what manner the length of a base
line may be accurately measured when required to be continued (1)
over a broad stone wall, 5 feet high ; (2) over a thick-set hedged
fence ; (3) over a hill of moderately steep slope ; and (4) across a
pond more than one chain wide. (City Lond. Coll.)
74. State three ways of carrying a chain line past an obstruction,
and describe how the width of a river can be determined without
actually measuring across it. (R.I.B.A. Inter.)
75. Give a sketch showing in what manner the length of a base
line may be accurately measured when needed to be continued (1)
over a broad stone wall, 5 feet high ; (2) over a thick hedge fence ;
(3) over a hill of moderately steep slope ; (4) across a pond ; or (5)
round a detached house. (City Lond. Coll.)
76. How may the ranging and chaining of a base line in open
country be conducted in each of the following cases, with the use of
the chain and ranging rods only: (a) when the first station and the
direction of the line is obstructed by a building which can only be
passed upon one side of the line ; (b) when both stations are given,
252 PRACTICAL SURVEYING
but the station at one end of the line cannot be seen from the
station at the other end of the line, owing to the hilly nature of
the district. (City Land. Coll.)
77. Two lines, AB and CB, meet at an inaccessible point, D,
in the centre of a large lake. Show how to find the position of
point D without the aid of any regular instrument.
(India Forest Service.)
78. How would you ascertain the distance of a point in the
middle of a broad river, 1st, with a chain ; 2nd, without anything
but a few pickets? (Civ. Eng. P. W.D. India.)
79. From the accompanying notes (a) lay down the survey lines
and plot the plan to a scale of 2 chains to an inch. Also find the
area of the field. (Assist. Surv. P. W.O. Ireland.)
80. The accompanying sketch represents two level fields to a
scale of 3 chains to 1 inch. Show upon it the lines you would use
to make a survey. (City Lond. Coll.)
81. Plot the following field notes of the survey of a lake to a
scale of 1 chain to 1 inch, and give the area of the lake in square
yards. (Arch. Assoc.)
82. Required from the following field notes, the plan and area of
a wood, two of the fences of which are straight. (Ll.I.B.A. Inter.)
83. From the field notes given, lay down the survey lines, and
plot a plan to a scale of 2 chains to an inch. (Surv. Inst.)
84. What are the instruments in general use for surveying ?
Mention the object of each. (Eastern Cadets.)
85. Measure the acreage of the lake on the plan A. Show your
field-book, with all the notes you would take in making the survey
of the lake. (Eastern Cadets.)
86. Draw on the plan A the main survey lines you would use in
the field to enable you to make this plan, rule a form of field-book,
and enter up the field notes you would take on any one of your
main lines. ( Val. Off. Ireland.)
87. Enlarge the lower half of Plan A to double its present scale.
You are recommended to ink in and completely finish part as a
specimen of your work before completing the whole enlargement.
(Val. Off. Ireland.)
88. Draw two adjoining irregular fields, show the survey lines
on same which you would run, and enter up your field notes in such
a way that you would reproduce your plan from the notes. The
measurements may be assumed. (Admiralty Assist. C.E.)
89. A survey with the chain only is to be made from the outside
of the wood shown on the accompanying plan A. Show in red on
the plan all the lines you would set out and chain for this purpose.
(India Forest Service.)
EXAMINATION QUESTIONS 253
90. Enter in pencil in the " Field Book " supplied to you all the
notes you would make in chaining the lines in the last question, so
as to enable you to plot your survey at any future time.
(Indian Forest Service.)
91. Make a sketch of the accompanying plan, sufficiently ac-
curate to indicate upon the sketch the position in which you would
probably lay out the base lines. Number these lines and letter the
main stations without filling in all the detail, which is drawn to a
scale of 3 chains to 1 inch, supposing the ground to be intersected
by railway which is partly in cutting and partly in embankment as
shown upon the plan. (City Lond. Coll.)
92. Given a plan in which the base lines CA, AD, I)B, BC,
and AB are run and chained, indicate what other base lines you
would run to complete the survey. (.City Lond. Coll.)
93. Make a sketch-copy of the accompanying plan, showing by
fine lines, how you would run and connect your base lines for
making a complete survey of the ground. Rule a form of field-
book, and enter in it a few of the notes you would make in con-
ducting the survey, indicating both upon the plan and the field-
book all "check lines" and "tie lines." (City Lond. Coll.)
94. Assume you had to make a survey similar to that shown on
plan A ; mark in red on this plan the survey lines you would take,
and calculate the area of field No. 3 on plan A. Enter up in the
form of a field-book the notes you would take in the field of the
main survey lines required to produce plan A.
(Admiralty Assist. C.E.)
95. Taking AB as a base line on plan P, show by fine red lines,
on the plan, all the lines you would set out and measure in order to
make a plan of the field numbered 1000 with the chain only and
without entering the wood. Rule a form of field-book and enter
in it all the notes you would make in chaining the base line AB,
recording also the stations on it. (Eastern Cadets.)
96. On the plan given draw in pencil the lines it would be
necessary to run to enable you to make a complete survey with the
chain only. (Surv. Inst.)
97. Compute the areas of the enclosures in the corner of the
plan above mentioned, giving the result in acres, roods and perches ;
one of these enclosures must be computed by means of the ordinary
plotting scale, and the other in any way the candidate may elect.
(Enclosure No. 1, if well done and a correct answer arrived at by
the ordinary plotting scale, will carry full marks.) (Surv. Inst.)
98. Having a pole fixed at the points marked A and B upon the
plan show how you could ascertain the width of the river between
A and B, without the use of an angular instrument, supposing the
254 PRACTICAL SURVEYING
distance greater than one chain across. Show by dotted lines upon
the plan, the direction and position of such longitudinal and trans-
verse sections as you might consider it advisable to take, in order
to give a general idea of the levels of the ground. Also indicate
by marks thus +, the positions of any extra spot levels which
might be added, and number the section lines in order.
(City Loud. Coll)
99. Describe the clinometer. When is it used by land sur-
veyors to great advantage ? (Survey Dept. Brisbane.)
100. For what uses is a clinometer valuable? (City Lond. Coll.)
101. Explain the construction and use of an optical square.
(City Lond. Coll.)
102. Explain by a sketch the construction and use of a simple
cross staff. (City Lond. Coll.)
103. Explain the use of a planimeter and the application of its
readings to a plan, drawn to a scale of 6 inches = 1 mile, when the
area of an enclosure is required. (City Lond. Coll.)
104. Explain the construction and adjustments of the box
sextant. Point out the errors to which the instrument is liable,
from its construction and in use. (Inst. C.E.)
105. Explain the principle and use of a box sextant and any
difficulty there is in adjusting it. (City Lond. Coll.)
106. How can you ascertain whether a pocket sextant is in ad-
justment, and why, in trying its adjustment, should the object
observed be at least half-a-mile away ? The areas of the theodolite
and sextant both read to minutes, why is the former the more
accurate instrument ? (Civ. Eng. P. W.D. India.)
107. Show with a diagram, that the angle measured by the
sextant is only half of that actually subtended by the objects
observed. (Civ. Eng. P. W.D. India)
108. State the reasons why the sextant is but seldom used for
ordinary surveying. (Owens Coll.)
109. How can you ascertain your position on a plan of any
ground by the aid of the sextant ? (Civ. Eng. P. W.D. India.)
110. Explain the principle of the Vernier scale, and illustrate
it with a sketch of a Vernier reading to half minutes, to any
primary scale you like. (City Lond. Coll.)
111. Define the meanings of the words "bearing" and "azimuth."
What is, approximately, the variation of the magnetic needle at
Greenwich ? Give its direction with regard to the true meridian.
(Inst. C.E.)
112. Three sides of a quadrilateral field were surveyed by com-
pass and chain and their bearings and lengths were determined as
EXAMINATION QUESTIONS 255
given in the following notes.* Assuming that the work has been
correctly done, calculate the bearing and length of the fourth side.
(Inst. C.E.)
113. A prismatic compass traverse closes on its starting point.
In plotting the field observations you find there is a closing error.
How would you eliminate it ? The bearings have been corrected
for local attraction before plotting. (Inst. C.E.)
114. The latitude of B from A is 106'42 feet N. and its departure
is 273-62 feet W. What is the bearing of the line AB ?
(Inst. C.E.)
115. Define magnetic declination. Write down its present value
in one of the following places : London, Edinburgh, Dublin,
Bombay, Cape Town, Toronto. What are the variations to which
this quantity is subject ? (Inst. C.E.)
116. A piece of waste land has been marked out by pegs at its
six corners, A, B, C, D, E, and F, and the following bearings,
angles, and measurements have been taken : A is west-north-west
of F, and north-east of B ; angles BAG 21 1 5', CAD 24 1 5',
DAE 33 30', BCA 30 15', ACD 107, DEA 86 15', AEF
30 15', and AB = 15'6 chains. Make a plan of the piece of land,
and ascertain the length of straight fencing between the corners
required to enclose it and the area. (Inst. C.E.)
117. From a point A on the surface of the ground a drained
tunnel is to be driven in a straight line rising along a grade of 1 in
1 00 to meet a shaft which is sunk centrally round a point B. A
and B have been connected by the traverse.
A 1 = 225 feet N. 43 W.
1 2 = 310 feet N. 15| W.
B2 = 415feetN. 53* E.
and the level of B is 85*37 feet above formation level of the tunnel
at A. Find the length of the tunnel from A to the centre of the
shaft and the depth of its formation level at B. (Inst. C.E.)
118. Define " magnetic declination " and write short notes on :
Secular variation and diurnal variation of the declination, isogonic
lines and agonic lines. (Inst. C.E.)
119. What is meant by " error in closure " in a traverse survey ?
Describe clearly the different methods used in adjusting this error.
(Inst. C.E.)
120. Describe a method of determining the declination of the
magnetic needle. What is approximately the declination about
London at present 1 (Inst. C.E.)
121. What is meant by the three-point problem ? How is it
solved mechanically in plane-table work ? (Inst. C.E.)
* See previous footnote.
256 PRACTICAL SURVEYING
122. Describe the method by which any definite point on a plane-
table can be centred over a particular station on the ground and
discuss the question as to the necessity for accurately centering the
table. (Inst. C.E.)
123. Sketch the form of level staff you are most familiar with,
showing the principle upon which its graduations are marked for
reading, and state the precautions to be observed by the staff
holder to ensure accuracy in your records, when at work over
undulatory ground. (City Lond. Coll.)
124. Describe the various instruments used in levelling, and the
way in which each is used. Illustrate by sketches. (R.I.B.A. Inter.)
125. Describe the principal points of difference between a Y
level and a dumpy level, and the advantages classified for each
type of instrument. (City Lond. Coll.)
126. What are the adjustments of a level and how would you
test it ? (Eastern Cadets.)
127. What is meant by the diaphragm of an ordinary dumpy
level ? Explain by an illustrative sketch its usual mode of attach-
ment within the telescope of a level, and its use in adjusting the
instrument for collimation. (Gity Lond. Coll.)
128. If on looking through a level the crosshairs were indistinct
what part of the instrument would require adjustment ? State
also what other test besides that of distinctness can be applied for
this adjustment. (Owens Coll.)
129. If you were able to choose, would you make any special
arrangement as to the relative distances of the back-staff and fore-
staff from your level 1 State your reasons.
(Assist. Surv. P. W.O. Ireland.)
130. In taking accurate levels over a series of stakes, how would
you work to neutralise errors of " curvature " and " collimation,' 1
and why ? (Mun. and County Eng.)
131. Describe briefly the setting up and reading of a dumpy
level. What influence has the height of the telescope on the read-
ing, (a) in simple levelling, (b) in compound levelling ?
(Arch. Assoc.)
132. Briefly describe how a dumpy level is tested to ascertain if
it is in adjustment. (R.I.B.A. Inter.)
133. What is the line of collimation in a level 1 How would you
adjust a dumpy level for collimation ? What is the nature of the
error likely to occur from using a level that is not in adjustment ?
Illustrate your answer by a sketch. (Eastern Cadets.)
134. Explain the meaning of the terms " parallax " and " colli-
mation " in the level, and describe how a dumpy level may have
EXAMINATION QUESTIONS 257
these adjustments tested either in a well paved road or upon an
open field. (City Lond. Coll.)
135. Describe the operation of levelling by means of a dumpy
level. ( Vol. Off. Ireland.)
136. Show in large detail, 1 foot in length of a levelling staff,
and sketch the spring joint in common use between the various
lengths of the staff. (Admiralty Assist. Civ. Eng.)
137. What are the various forms of levels ? Explain the kind
you prefer and your reasons for the preference.
(Admiralty Assist. Civ. Eng.)
138. Show a section through the telescope of a level and state
how you would test and adjust a dumpy level.
(Admiralty Assist. Civ. Eng.)
139. How is the spirit level made parallel with the line of colli-
mation in a Gravatt's level ? (Ry- Agr. Col. Cirencester.)
140. Before commencing to take a series of levels briefly describe
how you would ascertain if your level was in adjustment.
(Surv. Inst.)
141. Describe the " dumpy level," and how it is set up for use.
Give a specimen of a " level book," showing u back," " fore," and
"intermediate" sights and the mode of getting the "reduced levels."
(Mun. and County Eng.)
142. How would you test the object glass in a telescope ; and
give an explanation of the effect known as parallax.
(Surv. Dept. Brisbane.)
143. Describe carefully the setting up and adjusting of the level
before taking a reading. (Soc. Arch.)
144. Sketch the divisions of a level staff from 3'85 to 4'15 arid
mark a line through 4*01. (Soc. Arch.)
145. What is meant by a level line ? And what is the meaning
of each of the following terms : Ordnance datum, bench mark,
mean sea level, Trinity high water, gradient ? Also describe in
what manner the datum level should be recorded upon a parlia-
mentary plan and section. (City Lond. Coll.)
146. Illustrate by diagram the difference between "true" and
" apparent " level, and give a rule for determining same. (Surv. Inst.)
147. Explain the effect of the curvature of the earth on levelling
operations. When is a correction on its account necessary, and
what, in general terms, is the amount of such correction ? Is it
an additive or subtractive quantity ? What is the correction for
curvature due to a distance of 29,040 feet ?
(Civ. Eng. P. W.D. India.)
148. What do you understand by " refraction " ? Are the effects
constant or variable, and to what cause are they attributable?
p.s. R
258 PRACTICAL SURVEYING
What is the mean correction ordinarily applied on its account to an
observed angle ? And how, in practice, may the effects of curvature
and refraction ordinarily be obviated ? (Civ. Eng. P. W.D. India.)
149. Give the full entries in a level book for three settings of
the level, reading from a bench mark. (Soc. Arch.)
150. What is meant by an intermediate sight in taking levels ?
And, with the use of a level book in which a column headed " inter-
mediate" is introduced, in what way are the entries in that column
dealt with, when making up and checking a page of reduced levels ?
(City Lond. Coll.)
151. Rule a page of level book, and give the names of the several
columns that you would adopt, stating in which columns the entries
are made in the field and which columns are used for plotting the
levels. How may accuracy in the book work be secured ? What
kind of notes would you enter in the field upon the columns or page
of remarks ? (City Lond. Coll.)
152. In a series of levels, if the first back sight read 3'25 on an
Ordnance bench mark of 28'30, the sum of the back sights be 12'95
and the fore sights 17*20, what will be the Ordnance reading of the
last fore sight ? (City Lond. Coll.)
153. What form of level book do you prefer ? Sketch a page,
giving the headings and their use, and state why you prefer this
method to other systems with which you may be acquainted.
(City Lond. Coll.)
154. Reduce the following levels and plot them to a scale of
& inch to 100 feet for horizontals and inch to 10 feet for verticals.
(Roy. Agr. Coll. Cirencester.)
155. Rule a form of level book, enter 8 or 10 imaginary readings
and complete the column, reading on the staff 5'43 on a bench
mark, 103'65 above datum, and without moving the level, 4 - 07 on
the first point in the section. The level afterwards to be moved
two or three times to complete the section.
(Assist. Surv. P. W.O. Ireland.)
156. Rule a form of level book, classify the following staff read-
ings, and work out the reduced levels upon a datum of 60 feet
below the point A of commencement, where the level staff was first
held when taking the levels :
At point A, back sight reads 2'20 ft.
B, fore sight reads 12'09 ft., back sight reads 1-11 ft.
C, 11 -70 ft., 2-30 ft.
D, 7-51 ft.,
E, V90 ft,
F, 3-30 ft,
G, 8-81 ft.
8-28 ft.
11 -00 ft.
6 37 ft.
2-39 ft.
H, 8-92 ft. (City Lond, Coll.)
EXAMINATION QUESTIONS 259
157. In running a line of check levels the staff readings in feet
were as follows : back sights 4'23, 2'75, 5'31 , 9'42, 1 1 '24, 8*78, 7'29,
10-34; fore sights 3'90, 11 -07, 1O25, 6'38, 2'50, V33, 6 "44, 6-11.
The first reading was taken on a bench mark, 70'36 feet above
Ordnance datum. Eule a form of level book on the sheet of paper
provided for the purpose and enter in it the above readings in their
proper columns. Make up the level book and check it completely.
{India Forest Service.)
158. Describe the operation of levelling and a form of level book.
Enter up sample figures in each column of the level book and show
how the arithmetical work can be checked.
(Admiralty Assist. Civ. Eng.)
159. Show how you would arrange the columns in a level book
suitable for obtaining the cross sections along the line of a proposed
road. Give an example. (Inst. C.E.)
160. Explain how it is possible to eliminate the effects of
curvature and refraction in levelling across a wide river by the use
of two levels. (Inst. C.E.)
161. Show clearly the nature of the corrections for curvature
and refraction in taking long sights in levelling. What correction
should be applied for a sight of 1 mile, assuming that the correction
for refraction is one-sixth of that for curvature 1 (Inst. C.E.)
162. Give a specimen page of a levelling book, and describe the
method of checking to be observed in cases where extreme accuracy
is desirable. (Mun. and County Eng.)
163. In levelling across the river Severn, the horizontal wire cuts
the underside of a signboard, 14'35 feet above the level of the
ground, the distance being 2 miles 5 chains from the instrument ;
the back sight to a bench mark close by was 7*25 feet, the level of
the bench mark being 52'80. Determine the level of the ground
at the signboard. (Surv. Inst.)
164. Reduce the entries in the following level book, and show
how you would check the arithmetical operations. (Inst. C.E.)
165. Plot the following section to a horizontal scale of 2 chains
to an inch, and to a vertical scale of 20 feet to an inch.
(Surv. Inst.)
166. Cast up the following level book, and make a rough sketch
of the section. (Owens Coll.)
167. Reduce the following levels, and plot them to a scale of 1
chain to 1 inch horizontal, and 10 feet to 1 inch vertical.
(Arch. Assoc.)
168. Plot the following section to a scale of 2 chains to the inch,
horizontal, and 20 feet to an inch, vertical. Datum line, 100 feet
below the bench mark A. (R.I.B.A. Inter).
260 PRACTICAL SURVEYING
169. Make up the level book on the back of this sheet, and plot
the same to scales of 2 chains to 1 inch, and 1 feet to 1 inch.
(Surv. Inst.)
170. Show by a sketch what is meant by contour lines, and
describe how you would obtain them in the field. (Soc. Arch.}
171. An engineer's pupil runs a line of levels along some miles
of a road with steep gradients. On checking the work, an ex-
perienced surveyor finds that he makes the gradients flatter than
the pupil did. What is the most likely cause of the discrepancy,
and what precautions have probably been overlooked by the pupil?
(Inst. C.E.)
172. What is a contoured survey? Describe the field work
required for such a survey. (Eastern Cadets.)
173. State what you think about contouring and cross-sectioning
the land to be traversed. Compare railways, roads and canals in
this respect. (Mason Coll.)
174. What do you understand by contour lines ? How do you
trace them upon the ground with a spirit level or theodolite ? and
for what purpose and with what objects are contoured surveys
ordinarily executed ? (Civ. Eng. P. W.D. India.)
175. Describe a hand- level which may be used in surveying.
Show clearly by the aid of sketches and specimen field-notes, how
it may be used to determine the contours on a route along which
the surface levels have been found at every station. (Inst. C.E.)
176. You have to make a longitudinal section along a centre
line which has been pegged out in a field. What instruments,
equipment, and labour would you take into the field with you ?
(Inst. C.E.)
177. Explain the method of tracing contours with a dumpy
level. At what vertical distances apart may contour lines be most
usefully applied, according to the scale of the plan, the nature of
the country, and the purpose for which such contours are usually
required. (City Lond. Coll.)
178. The sketch herewith is a portion of a map with contour
lines, the figures indicating the height in feet above a certain
datum level. Sketch freehand on your paper a set of contour lines
approximately similar to them, then draw a section by the vertical
plane PP. The vertical scale may be taken 20 feet to an inch.
(City Guilds Cent. Inst.)
179. What is a contour survey? How would you make one
of a mountain, say, 1000 feet high? Illustrate your answer by
sketches. (Admiralty Assist. Civ. Eng.)
180. How would you make a contour survey ? (Eastern Cadets.)
EXAMINATION QUESTIONS 261
181. Describe what precautions you would take if you were to
use an aneroid barometer to determine the difference in elevation
between two places. Note the accuracy you would expect in any
particular case. Explain what is meant by saying that the instru-
ment is "compensated," and why a "correction" for temperature
has to be applied. (Inst. C.E.)
182. You are given a 6-inch Ordnance map, with contours of
1 00 feet vertical interval. How would you interpolate contours at
25 feet interval, using a clinometer? (Inst. C.E.)
183. On some of the Ordnance Survey maps, two kinds of
contours are shown, viz. : instrumental contours and interpolated
contours. How have these been located ? (Inst. C.E.)
184. It is required to find the difference of level of two pegs on
opposite banks of a river, and it is known that the colliuiation line
of the level you have to use is out of adjustment. How would you
find the difference of level required? (Inst. C.E.)
185. Give an account of the methods by which the heights of
mountains can be ascertained, in cases in which the ordinary
process of levelling is inapplicable. (Inst. C.E.)
186. What is meant by the variation of the needle 1
(K.I.B.A. Inter.)
187. What are the meanings of the terms, magnetic meridian
and variation of the compass ? Explain the method of finding the
latter in the field, and state how a meridian line can be marked out
on the ground without the aid of any instrument, with sufficient
accuracy for common purposes. (Civ. Eng. P.W.D. India.)
188. Sketch and describe a prismatic compass.
(Vol. Off. Ireland.)
189. Describe the method of using the prismatic compass.
State how you would survey a road with it. Also, explain the
method of finding your station by interpolation, by means of two or
more stations already fixed. (Civ. Eng. P. W.D. India.)
190. What is meant by surveying on "the meridian and perpen-
dicular system " ? (City Lond. Coll.)
191. Having taken the angle with a theodolite set up over a
station point at the intersection of two base lines, show how their
relative positions may be accurately plotted with the aid of trigono-
metrical tables, and without the use of a protractor.
(City Lond. Coll.)
192. In a traverse survey, state what steps you would adopt to
ensure accuracy in recording the value of the angles between your
base lines in the field with the use of a theodolite.
(City Lond. Coll.)
262 PRACTICAL SURVEYING
193. Plot to a scale of 3 chains to an inch, the following traverse
round a wood, and scale the length of AF.
A to B, length, 1075 bearing 34315
B C, 810 5110
C D, 660 104-56
D E, 745 139-14
E F, 1000 188-17
(Assist. Surv. P.W.O. Ireland.}
194. ABCD is a four-sided figure. For AB, BC, and CD, the
azimuthal angles are 40, 110, and 225, and the lengths are
350, 420, and 390 links respectively. Plot the figure to a scale of
inch to a chain. Find the azimuthal angle and length of AD.
Find the four included angles : reduce the figure to its equivalent
triangle, and find its area in acres and decimals.
(Roy. Agr. Coll. Cirencester.)
195. From the point A on plan, lay off" a portion of 1 60 acres,
exclusive of road, and having a frontage of 2828 links.
(Surv. Dept. Brisbane.)
196. The sketch is a plan of an old survey, the posts and corner
trees of which have disappeared, except those at A and F. It being
necessary to establish the intermediate corners for road purposes,
a traverse is run from A on the lengths and bearings of the plan ;
but in closing on to the corner F, the final bearing was found to be
80 56', and the length 1498 links instead of 80 and 1480 links.
Find the difference between the old and the new chain, and modify
the lengths and bearing in accordance, so that the positions of the
old corners shall be obtained as nearly as possible.
(Surv. Dept. Brisbane.)
197. In reconnoitering in unmapped countries, it sometimes
happens that the only available check upon your route survey is
to find the latitude and longitude of your halting stations. De-
scribe simple methods of ascertaining these points.
(Civ. Eng. P. W.D. India.)
198. A trial line bearing 270 is run 4192 links to pick up an
old fenced line. In starting an offset of 5 links due south is taken,
and on reaching the end of the line the offset is found to be 4|
links due north ; using circular measure. Explain the principle of
the method. (Surv. Dept. Brisbane.)
199. Explain how in the field the time may be approximately
ascertained by the prismatic compass. (Civ. Eng. P. W.D. India.)
200. Find all boundaries and make the necessary computations
for laying off from A towards B the portions A, B, C of 2 acres each,
by lines parallel to A C. (Surv. Dept. Brisbane.)
201. How would you plot long lines and angles without the aid
of a protractor ? (India Forest Service.)
EXAMINATION QUESTIONS 263
202. Explain the method of surveying with the plane table,
describing the instrument employed and stating the circumstances
which limit the accuracy of the method. (Inst. C.E.)
203. The vernier of a box sextant is set to 0. A vertical rod at
a distance of about 500 feet is sighted. The portion of the rod
seen through the clear glass and the portion reflected in the mirror
appear in the same vertical line. Without altering the adjustment
of the instrument a rod about 10 feet away is observed. The
portion now seen in the mirror is no longer in the same vertical
line with the portion seen through the clear glass. Explain this.
(Inst. C.E.)
204. It is suspected that the horizontal circle of a theodolite is
unequally divided. How would you test for this supposed error.
(Inst. C.E.)
205. Sketch and explain the principles of either an Abney level,
a Watkins clinometer, or any instrument of a similar type with
which you may be familiar. (Inst. C.E.)
206. Sketch in detail any arrangement of levelling screws, such
as are fitted to a level or a theodolite : one sketch should be a
section through the vertical axis. (Inst. C.E.)
207. A dumpy level has accidentally fallen and been put out of
adjustment. How would you proceed to put the instrument into
working order ? (Inst. C.E.)
208. In a transit theodolite, when the horizontal plates are
exactly level, it is found that the horizontal axis of the telescope is
not horizontal. Show how this error affects the horizontal angle
subtended at the instrument by two observed points, and how the
error due to the axis being out of the horizontal may be eliminated.
(Inst. C.E.)
209. Describe with aid of sketches the theory and use of (a) the
optical square, (b) the reflecting level, (c) the prismatic compass.
(Inst. C.E.)
210. Explain the principle upon which the construction of a
vernier is based. Why have some theodolites two sets of figures
on the vertical arc verniers, while others have only one set ?
(Inst. C.E.)
211. What is the rate per chain (in feet and decimals) of a
gradient rising 1 in 250 1 (Surv. Inst.)
212. A brick wall is laid in horizontal courses along a line ABC,
from A to B the ground rises at angle 10, from B to C it rises at
22. Distance A to B is 230 feet, and B to C 150 feet. Give the
number of steps required 1 foot in height between A and B and
the number 2 feet in height beeween B and C. Also give the
horizontal distance apart. (Surv. Inst.)
264 PRACTICAL SURVEYING
213. In a 5-inch theodolite reading to minutes a line on the
vernier coincides with a line on the primary circle, what interval
occurs between the next two lines which nearly coincide ?
(City Lond. Coll.)
214. What arc does an angle of 1 minute subtend at a distance
of 10 chains ? (City Lond. Coll)
215. Explain the principle of the vernier, and in what manner
would you construct a vernier to read 15 seconds when the arc is
divided into quarter degrees. (Civ. Eng. P. W.D. India.)
216. Give a sketch showing how you construct the divisions
upon a vernier scale to a theodolite, the primary divisions of which
read to degrees and thirds of a degree, in order to be able accurately
to record angles to 30 seconds or half minutes by the aid of the
vernier scale. (City Lond. Coll.)
217. Give a sketch showing how you would construct the
divisions upon a vernier scale to a theodolite, the primary divisions
of which read to degrees and thirds of a degree, in order to be able
accurately to record angles to 20 seconds or thirds of a minute by
the aid of the vernier scale. (City Lond. Coll.)
218. Give a sketch and description of a plain theodolite.
( Vol. Off. Ireland.)
219. Describe how you make the adjustments of the line of
collimations in the Y theodolite. (Roy. Agr. Coll. Cirencester.)
220. In a transit instrument, explain the usual adjustments to
test the accurate traverse of both the horizontal and vertical circles.
Also describe the process of taking and booking an angle with the
use of a theodolite set up over the intersection of two base lines.
(City Lond. Coll.)
221. Describe road traversing with the theodolite, what points
should be especially attended to, and in what manner can the work
be checked ? What is the peculiar character of theodolite travers-
ing, and why may this character not be equally maintained by
using the magnetic meridian] (Civ. Eng. P. W.D. India.)
222. What is a transit theodolite ? Show the principal parts to
a large scale, and describe these by reference letters.
(Admiralty Assist. Civ. Eng.)
223. Describe the operations of testing and setting up a theodo-
lite, and all the uses to which this instrument can be put.
(Admiralty Assist. Civ. Eng.)
224. What are the various forms of theodolite? Make a detailed
sketch of the simplest form. (Admiralty Assist. Civ. Eng.)
225. Describe the method of adjusting the line of collimation of
a level and theodolite, having two firm station points on level
ground 7 chains apart. (Assist. Surv. P. W.O. Ireland.)
EXAMINATION QUESTIONS 265
226. State accurately the methods for adjustment for collimation
in azimuth in a 5-inch transit theodolite ; state your reasons for
accepting one method before another. (Surv. Dept. Brisbane.)
227. On what scientific grounds would you condemn at once a
theodolite or level, and state your methods of arriving at the
conclusion. (Surv. Dept. Brisbane.}
228. How would you proceed to adjust a 5-inch transit theodo-
lite ? (Inst. C.E.)
229. How would you survey, with a theodolite and chain, the
boundary of a thick wood through which it is impossible to range
lines] In making a plan of the outline, how would you deal with
errors of observation in angles and lengths? (Inst. C.E.}
230. Describe the theodolite and the successive operations
necessary for the measurement of angles with it. (Inst. C.E.}
231. Give all the details of the methods you would adopt to run
a straight line with an engineer's transit so as to eliminate experi-
mental errors. (Inst. C.E.}
232. You have to make a plan of the boundary of a dense forest
in a country where the compass is unreliable. How would you
carry out the work 1 (Inst. C.E.}
233. What is a satellite station, and when is it used ? How are
observations from the satellite station reduced to the centre ?
(Inst. C.E.}
234. A base for a topographical survey is measured with a steel
band. Explain the corrections applied to the field measurements
in order to reduce the base for computation of the triangulation.
(Inst. C.E.}
235. Explain how distances measured by triangulation are
reduced to " mean sea-level." (Inst. C.E.}
236. How would you survey a town, and how would you com-
mence to run the main lines in surveying a whole county ?
(Vol. Off. Ireland.}
237. State under what circumstances you would employ the
method, (a) of trigonometrical and (b) of chain surveying.
(Eastern Cadets.)
238. Describe the method of measuring a base line by the aid of a
chain and theodolite, pointing out the correction necessary for each
angle of elevation or depression. (Civ. Eng. P. W.D. India.}
239. In a trigonometrical survey it is sometimes desirable to
prolong a base line by triangulation. Explain the method of doing
this, and illustrate it by a diagram. In a similar survey show by a
diagram how the sides of the principal triangles may be increased
as rapidly as possible from the measured base.
(India Forest Service.}
266 PRACTICAL SURVEYING
240. In the triangle ABC, given a = 1000, B = 104, and C =
24 30', find A and b. (Roy. Agr. Coll. Cirencester.)
241. Describe briefly the several steps taken in making a large
trigonometrical survey, from and including the setting out and
measuring up of the base lines to the filling in of the details.
(Eastern Cadets.)
242. Construct a triangle ABC having its sides AB = 3 inches,
BC = 2J inches and AC =1 inches. Suppose the points ABC to be
trigonometrical stations of a survey, and that from a point D of a
traverse A bears 120, B 150, and C 165, find the point D by
construction. (Surv. Inst.)
243. Where an object is selected as a trigonometrical point on
which the theodolite cannot be set up, the angles taken from its
vicinity require " reduction to the centre." Explain how this is
done and illustrate it by a diagram. (Civ. Eng. P. W.D. India.)
244. How would you determine the latitude of any position (on
land), and what instrument would you require ? (Surv. Inst.)
245. How would you determine the height of a point on the
opposite side of a river to yourself ? An easily accessible point on
the ground on your side is 150 feet above datum level ; on it a
level staff can conveniently be placed. The river is about 250 feet
wide ; the ground is fairly level, and there is no obstruction to the
view. A chain and theodolite are to be used. (Inst. C.E.)
246. B is 1 000 feet due east of point A. A theodolite is set up
at A and B, and is at the same height in both cases. Point C when
sighted from A has a whole circle bearing of 1 00 6', and an eleva-
tion of 1 2 30', and when sighted from B a whole circle bearing of
105 18'. What is the height of point C above the theodolite ?
(Inst. C.E.)
247. Indicate the fundamental principles upon which surveying
with the tacheometer is based, and explain briefly the method of
applying tacheometry to the survey of rugged country. (Inst. C.E.)
248. A river has a width of 200 feet and an average depth of
7 feet. If the current is about 5 miles per hour, describe how
you would proceed to determine the cross section as accurately as
possible. (Inst. C.E.)
249. Explain how soundings are measured and located in making
a hydrographical survey of a harbour. (Inst. C.E.)
250. Give three methods of finding the width of a river without
using any instrument for measuring angles. The river is too wide
to stretch a tape across. (Inst. C.E.)
251. A yachtsman measures the angle subtended by two light-
houses whose positions are shown on the chart. He then takes the
EXAMINATION QUESTIONS 267
bearings of the two lighthouses. Show that the second observation
is sufficient to fix his position, while the first observation is not.
(Inst. C.E.)
252. Describe the principal parts of the sextant, and explain by
diagrams how you would use it in locating soundings. (Inst. C.E.)
253. Describe the method of setting out curves with and without
a theodolite. (Eastern Cadets.)
254. Explain fully the method of setting out a curve of given
radius with a theodolite. (Eastern Cadets.)
255. Make a figured sketch and show your calculations for join-
ing two lines with a curve half a mile radius, the included angle
between the lines being 120 degrees. (Eastern Cadets.)
256. Marking out a canal in a given direction, AB, you find that
the alignment, if prolonged, would take you through a village ; to
avoid this you change the direction to a line, BC, and between the
points A and C you trace a curve with a radius of 4 miles. Describe
the method of doing this in the field and, without going through
the necessary calculations in detail, explain how they are made,
when required, the distances AB and BC being measured and the
angle ABC observed. (Civ. Eng. P. W.D. India.)
257. The following bearings and distances were taken along a
centre line of a road survey :
AB bearing 1 5 degrees, distance 1 200 feet.
BC 45 1000
CD 310 1400
Connect AB and CD by an S curve from B to C, the two portions
having equal radii. (Civ. Eng. P. W.D. India.)
258. Explain the construction and formulas for the calculation
of cuttings and embankments, and how and when to use them.
(Mason Coll. B'ham.)
259. What are the chief things to aim at as regards cuttings and
embankments ? What is the quantity it is best to try to reduce to
a minimum ? (Mason Coll. B'/iam.)
260. What would be the cost of a cutting 33 feet wide at the
formation level, with slopes 1 to 1 and depths 0, 9, 24, 15, feet
taken at 1 chain distances, the price of excavation being 3s. per
cubic yard ? (Mason Coll. B'ham.)
261. A cutting is to be made through the solid rock for a straight
road 350 feet long. The depths in feet at 50 feet apart are 0, 5, 7,
10, 13, 9, 6, ; the width of the road 15 feet and the slopes to 1.
Calculate the contents of the cutting. (India Forest Service.)
262. A straight level road runs east and west ; the summit of a
hill observed from a point in the road, due north, at an angular
elevation of 32 degrees, from another point a quarter of a mile
268 PRACTICAL SURVEYING
along the road the elevation is found to be 19 degrees. Find the
height of the summit above the road in feet.
(Admiralty Assist. Surv.}
263. The sides of a triangle are 2040, 5095, and 5960 links.
Find (1) the angles, (2) the area. (Surv. Dept. Brisbane.}
264. The telescope of a theodolite is set 4*25 feet above the
point A having a level value of 25 feet, is directed towards the
bottom of a statf at B and shows an angle of elevation of 10 4', it
is then directed to 1 feet on the staff, when it shows an angle of
elevation of 10 35'. Required the horizontal distance A to B in
feet and also the level of the point B. (Surv. Inst.)
265. The point A being inaccessible and at a considerable
altitude above the surrounding country, illustrate and describe in
what way you would ascertain its height above the point B (the
nearest convenient point of observation) using a theodolite for the
purpose. (Surv. Inst.)
266. What are the simplest methods of surveying in a town and
in the country ? Describe each method and any desirable method
of checking these surveys. (Admiralty Assist. Civ. Eng.)
267. Describe and prove any method of obtaining the distance
between two marked points on the oppoite sides of the river with-
out the use of angle measuring instruments. How would you
make this measurement if you had a theodolite or sextant at your
disposal. ( Univ. Coll. London.}
268. Describe the process of setting up a theodolite at the first
two stations of a survey. Show that by the method employed, the
telescope will always point to the north if, at any station whatever,
the instrument be put to zero. (Univ. Coll. London.)
269. What are the objects and advantages of the method of
plotting by "traversing"? What essential condition must be
fulfilled by any instrument in order that its results may be used in
this way ? ( Univ. Coll. London.}
270. Describe briefly the system used in carrying out the
Ordnance Survey of this country. (Univ. Coll. London.}
271. Describe the information that has to be obtained, and the
surveys with sketches, which have to be made for locating a rail-
way through a mountainous district. (Inst. C.E.}
272. The formation level of a railway embankment is 30 feet
wide, the side slopes are 1^ horizontal to 1 vertical, and the height
of the centre 8*8 feet above the original surface of the ground,
which has a slope of 5 horizontal to 1 vertical in a direction at
right angles to the line of the railway. Find the area of the cross
section of the embankment. (Inst. C.E.}
EXAMINATION QUESTIONS 269
273. Explain the principle upon which the setting out of railway
curves with a theodolite is based, and find a general formula for
the tangential angle suitable for any radius and any length of
chord. (Inst. C.E.)
274. Two straight lines meeting at a known angle are to be
joined by a 2 curve. Describe the computations required and the
method of lining out the curve in 100-feet lengths. (Inst. C.E.)
275. Two converging lines of railway which would if produced
meet at an angle of 140 are to be joined by a curve of 20 chains
radius. What would be the distance from the intersection to the
starting point of the curve, and the length of the curve in chains ?
How would you set out this curve in practice ? (Inst. C.E.)
276. Describe the setting out of a double junction, the main lines
being straight and the radius of the branch line 15 chains ; length
of stock-rail 1 8 feet. Give the distance of each crossing from the
point of the switch and the spread of each crossing. (Inst. C.E.)
277. The tangents to a curve meet at an angle of 1 50. On the
bisector of this angle is a point 53 feet from the vertex through
which the curve must pass. Find the radius of the required curve
and the tangent distance. (Inst. C.E.)
278. In lining out a curve for the centre line of a railway, what
are the practical advantages in using a curve of x 3 curvature rather
than a curve of y feet radius ? What is the fundamental formula
connecting the radius of a curve and its tangential angle ?
(Inst. C.E.)
279. A pipe line has been laid on a curve of unknown radius
joining two straight lengths. It is found that the tangents measure
83*2 feet, and that the contained angle is 156 30'. Find the
length and radius of the curve, also the chord and the distance of
the centre of the curve from the point of intersection.
(Eng. N.S. W.)
280. The pipe line as above has been marked at every 50 feet to
the commencement of the curve, which is found to start at 784'6
feet on the continuous chainage. It is desired to carry on this
chainage round the curve, fixing the points with a theodolite by
tangential angles. Calculate and tabulate the tangential bearings
to be set off on the instrument, and fully describe how you would
carry out the marking, and check the close of both bearings and
chainage (a) If all the points can be observed from the tangent
points, (b) if the two tangent points cannot be seen from one
another. (Eng. N.S. W.)
281. In case (a), how could the curve be marked without chain-
ing the chords ? Describe the process. (Eng. N.S. W.)
282. The following staff readings have been taken with a dumpy
level: Back sight 13-06 feet at 700 feet. Intermediate sight
270 PRACTICAL SURVEYING
10-43 feet at 800 feet. Intermediate sight 6 '86 feet at 900 feet.
Fore sight 1'22 feet at 1,000 feet Back sight 12'74 feet at 1,000
feet. Intermediate sight 8*31 feet at 1,100 feet. Fore sight 216
feet at 1,200 feet. The reduced level at the starting point is 100
feet above datum. Rule off the proper columns for booking these
readings, enter the readings, compute the reduced level at each
station, make the ordinary test checks of the calculations, and give
the gradient between the extreme points. (Eng. N.S. W.)
283. Give the method of testing and correcting a theodolite (a)
for error in collimation in azimuth, (b) for error in collimation in
altitude. (Eng. N.S. W.)
284. State the methods you would adopt, apart from adjusting
your theodolite, to eliminate slight errors in adjustment (a) in
running a straight line, (b) in observing horizontal angles. State
what errors are eliminated by the process you adopt.
(Eng. N.S. W.)
285. Describe fully the adjustment of the dumpy level for
parallax and collimation, and state what methods you would adopt
in observations to eliminate all probable errors in adjustment.
(Eng. N.S. W.}
286. In a triangle, ABC, the length of AB is 55 feet, of AC 70
feet, and angle A is 53 22'. Find side BC and angles B and C,
and compute the area of the triangle in square feet and in acres.
(Eng. N.S. W.)
287. In a circle of 40 feet diameter a segment has a chord of 28
feet : find (a) the versed sine of the segment, (b) the distance from
the centre of an ordinate 5 feet long, (c) the area of the segment in
square feet. (Eng. N.S. W.)
288. Sketch half-a-dozen adjacent fields, and illustrate by ruled
lines the method of surveying them with the chain only.
(Admiralty Assist. Surv.)
289. Make a sketch of an irregular plot of land and describe how
you would obtain the area. Chain lines are to be shown upon the
paper. (Inst. San. Eng.)
290. Show by sketch how you would lay out the survey lines on
a nearly regular five-sided field. Assuming your sketch to be to
scale of 3 chains to 1 inch, give the approximate area in acres,
roods, and perches. (Inst. San. Eng.)
291. In taking particulars for laying a sewer it was found that
it was impossible to see from end to end of the proposed route
owing to the centre of the land being higher. Illustrate by sketch
how you would obtain a straight line. (Inst. San. Eng.)
292. Give the levels of points B, C, and D on a continuous
EXAMINATION QUESTIONS 271
section, the level of point A being 25 feet, and the horizontal
distances and angles as follows :
A to B, 12 chains ; angle of elevation, 3 20'.
B to C, 9 depression, 4 25'.
CtoD, 15 elevation, 2 15'.
(Surv. hist.)
293. Construct a triangle ABC, having its sides AB = 3 inches,
BC = 2| inches, and AC = 1| inches. Suppose the points A, B,
and C to be trigonometrical stations of a survey, and that from a
point D of a traverse A bears 120, B 150, and C 165, find the
point D by construction. (Surv. Jnst.)
294. It is proposed to fence round a piece of open ground and to
convert it into a recreation ground. Pegs have been driven in at
the five corners A, B, C, D, and E. The relative positions of the
pegs were found to be as follows : B is south-east of A, C is south-
south-west of B, and D is due west of C ; angles BAG 28 30', CAD
35, DAE 36, AED 95 ; and the distance between pegs A and B
10*40 chains. Make a plan of the piece of ground, state the length
of fencing required to enclose it, and find the area.
(Admiralty Assist. Surv.)
295. With the aid of sketches, describe the construction and
method of use of one of the following instruments : (1) prismatic
compass, (2) optical square, (3) box sextant.
(Admiralty Assist. Surv.)
296. In the construction of a railway tunnel, what methods
should be adopted for determining the alignment above and below
ground? (Admiralty Assist. Surv.)
297. What errors in direction are likely to arise in surveys made
with the magnetic needle, and how can such errors be controlled
and corrected ? (Admiralty Assist. Surv.)
298. Describe the process of setting out a large rectangular
building, by means of the theodolite. Illustrate your answer by
sketches. (Inst. San. Eng.)
299. Show by the aid of a sketch diagram, accompanied by a
brief description, in what way you would proceed to take and fix a
series of soundings from the shore to a distance of half-a-mile from
land, describing the instruments you would use, and the appliances,
fixed marks and assistants you would deem essential.
(City Lond. Coll.)
300. How would you obtain a cross section of a river when there
is neither a boat nor a raft available ? (Mun. & County Eng.}
INDEX
Abney's reflecting level, 77.
Acres, roods and ^perches, 6, 12.
Adjustment for collimation, 128.
for parallax, 127.
Allowance for slope of ground, 75.
for width of ditch, 35.
Alphabet, Morse, 242.
Amsler's plani meter, 44.
Aneroid barometer, 150, 154.
Angle, Definition of an, 156.
Angle of slope, Measuring the, 76.
Angles on chain line, 173.
Angular measurement, 156.
Annual variation of the compass,
18.
Area by equalising lines, 42.
by computing scale, 43.
by planimeter, 44.
of rectangle, 8.
of triangle, 9.
Areas of regular figures, 8.
Arrangement of chain lines, 48.
Astronomical surveying, 235.
Backbone of survey, 49.
Back sights and fore sights, 134.
Barometer, Aneroid, 150.
Levelling with, 150.
Mercurial, 150.
Base line of survey, 15.
Ordnance Survey, 179.
Batters and slopes, 204.
Bearing of a line, 10.
Bench Marks, 133.
Boundaries, Nature of, 33.
Boundary, Owner's side of, 35.
Box sextant, 165.
vernier, 164.
tape, 21.
Brace, Use of, 35.
British standard of length. 7.
Brook Meadow, Survey of, 50.
Bubble error, 129.
Builders' dumpy, 120.
Building plots, Surveying, 150.
Bull-headed rail, 222.
Casting by equalising lines, 42.
Celestial sphere, 235."
Centrifugal force, 221, 225.
Cess, Allowance for, 206.
Chain and arrows, 23.
lines, how marked, 27.
mode of using, 24.
scales, 13.
traversing, 96.
Chaining across a gravel pit, 67.
river, 66, 67.
round a bend, 63.
building, 65.
Signals in, 23.
Charge for surveys, 94.
Charlie's wain, 235.
Check levels, 133.
lines, 21.
Chesterman's metallic tape, 22,
193.
Chords, Scale of, 158.
Circumferenter, 100.
Closed traverse, 105, 109.
Collimation, 127.
system of booking levels, 144.
Colouring plans, 53.
INDEX
273
Compass, Pocket, 15.
surveys, Use of, 100.
traversing, 98.
Compound curves, 209, 214, 223.
levelling, 126.
Computing scales, 43.
Constellations, 102.
Contouring building plots, 150,
153.
Methods of, 79.
Contour lines, 78.
Conventional signs, 27.
Copyhold, Enclosure and Tithe
Commission, 90.
Copying plans, 111.
Cost of surveys, 94.
Correction for curvature and re-
fraction, 124.
Cross sections, 139.
staff, 55, 60.
Curvature, 123.
Curve by one theodolite, 230.
by two theodolites, 231.
elements, 209.
formula, 209.
To find radius of, 229.
ranging, 227.
tangents, 210.
Curves by oblique offsets, 228.
on bridges, 229.
by rectangular offsets, 228.
Railway, 207.
Crossing, Railway, 233.
Cross -over roads, 233.
Culmination, 236.
Cutting up a plan, 48.
Daily variation of compass, 17.
Datum line, 136.
Declination, 236.
Definition, axiom and postulate, 2.
Degree curves, 207.
Degrees and grades, 157.
Departure or longitude, 101, 103.
Detours and gaps, 63.
Diagonal scales, 162.
Difference of latitude, 102.
longitude, 103.
Ditch and hedge, 33.
P.S.
Dot or spot levels, 150.
Double chain lines, 193.
Drawing field outlines, 32.
to scale, 13.
Dumpy levels, 118.
E
Earthwork terms, 204.
Eidograph, 114.
Engineering field work, 202.
Enlargement and reduction of
plans, 112.
Entries in field book, 24.
Equalising lines, 42.
Equation of time, 238.
Errors in chaining, 94.
levelling, 13L
scaling, 117.
Everest Theodolite, 170.
F
Facing points, 233.
False stations, 49.
Fences, 35.
Field book, Entries in, 24.
columns, 136.
Finished plans, 53.
First-class plans, 90.
Flag signalling, 242.
Flying levels, 133.
Focussing a level, 130.
Fore sights, 134.
Formation breadth, 204, 206.
Forward and reverse bearings, 99,
101.
Fractions of perch, how dealt with,
12.
G
Gaps and detours, 63.
Geographical north, 16.
Geometry, Definition of, 1.
Give-and-take lines, 42.
Goliath rail, 222.
Grades and degrees, 157.
Grsem's Dyke, 34.
Gravatt's dumpy level, 118.
Great triangulation, 179.
Gunter's chain, 22.
mode of using, 23.
274
INDEX
Hachures, 78.
Hand reflecting level, 79.
Hedge and ditch, 33.
Hedges and trees on plans, 41.
Heights, Measurement of, 181.
Heliographing, 243.
Hill shading, 78.
Hilly ground, Corrections for, 74.
how indicated, 78.
Poling over, 39.
Holding the staff, 131.
I
Inclination, Corrections for, 74.
" Instruction to surveyors," 90.
Intermediates, 136.
Inverted curve, 209.
Jacob staff, 99.
Lake, Survey of a, 57.
Land-breadth, 204.
surveying, Scope of, 1.
Latitude, Difference of, 101.
Finding the, 239.
Level and horizontal lines, 122.
book, Keeping the, 144.
pegs, 203.
staff, 121.
Levelling, Definition of, 118.
Errors in, 131.
with barometer, 150.
Levels of building plots, 148.
Limit of accuracy in plotting, 192.
Linear measure, Table of, 5.
measurement, 7.
Link, Length of a, 7.
Location field book, 202.
Long chain line, 88.
Longitude and local mean time,
237.
M
Magnetic meridian, 16.
Main sections. 141.
Map scales, 116.
Marks on plans, 35.
Mean solar day, 238.
Measurement of straight -lined
figures, 20, 26.
Measuring across a river, 66.
offsets, 28.
Mercator's projection, 71.
Meridian distance, 101, 103.
lines, 101.
Magnetic, 16.
To determine the, 235.
Miner's dial, 100.
Minimum radius of curves, 209.
Minus readings, 138.
Monthly variation of compass, 17.
Morse code, 242.
N
Nadir, 236.
Nomenclature of curves, 208.
Northing and southing, 101.
North point by watch, 16.
on plan, 19.
Obstruction by rising ground, 38.
Obstructions, Measuring past, 55.
Office columns, 136.
plans, 53.
work in surveying, 1.
Offset piece, 30.
scale, 31.
Offsets, 26.
Open and closed traverses, 105,
107, 109.
Optical square, 58, 60.
Ordnance bench mark, 137.
datum, 134.
map scales, 116.
survey, 179.
Owner's side of boundary, 35,
Pantagraph, 114.
Parallax, 127.
Parish boundaries, 33.
plans, 90.
INDEX
275
Parliamentary plans, 94.
Party waU, 33.
Perch, Fractions of, 12.
Permanent stakes, 203.
Perpendiculars, To set up, 61.
Plane table, 167.
Planimeter, Use of, 44.
Platelayers' curves, 227.
Plotting, 13.
columns, 136.
from field notes, 31.
sections, 136.
traverse surveys, 107.
Pointers, 102.
Points or switches, 232.
Pocket compass, 15.
Polar projection, 71.
Pole Star, 102, 235, 236.
Poling over hilly ground, 38, 39.
Practical curve ranging, 231.
geometry, Exercises in, 2.
Pricking through, 112.
Primary circle, 170.
Prime vertical, 237.
Prismatic compass, 97.
Projection, Various systems of, 71.
Proportional compasses, 114.
squares, 112.
Protractor and plummet, 76.
Protractors, 158.
Pure and applied geometry con-
trasted, 2.
Quarry, Chaining across a, 67.
R
R.A. (Right ascension), 238.
Radial measurement of angles, 157.
Railway chair, 221.
crossing, 233.
curves, 207.
gauges, 202.
surveying, 201.
Rails, Length of, 220.
Ranging a curve, 227.
Rectangle, Area of, 8.
Reduced level, 135.
Reducing the bearings, 99.
levels, 135.
Reduction of closed traverse, 110.
open traverse, 108.
to single meridian, 105.
Reference book, 201.
Refraction, 123.
Regulations for testing plans, 93.
Repeating an angle, 174.
Reverse bearing, 101.
curve, 209, 217, 218.
Right ascension, 238.
Rise and fall system of booking
levels, 144.
Roman wall and ditch, 34.
Routine of a survey, 49.
Running levels, 133.
S
S curve, 209.
Scale of chords, 158.
Scales for maps, 116.
Setting out foundations, 204.
Setting up a level, 129.
Sextant, Box, 165.
Nautical, 241.
Shrinkage of tape, 193.
Side width, 204.
Sidings from main line, 233.
Sight vanes, 100.
Signalling, 242.
Simple curve, 208.
Simpson's rule, 44.
Sines and cosines, 105.
Skeleton town survey, 187.
Slopes and batters, 204.
Sloping ground, Chaining on, 74.
Sopwifh level-staff, 121.
Split vernier in Abney level, 77.
Spoil bank, 141.
Spot levels, 150.
Square measure, Explanation of, 7.
Table of,' 6.
Stadia points, 196.
Staff, Holding the, 131.
Standard of length, 7.
Station poles or pickets, 26.
Steel tape, 24.
Stepping with a chain, 75.
Super-elevation of outer rail, 221.
276
INDEX
Survey, Base line of, 15.
of small farm, 82.
of woods and lakes, 55.
Surveying by the back angle, 177.
from two stations, 179.
Surveyor's card, 76.
compass, 100.
Switches, 232.
Systems of surveying, 5.
T, Meaning of, 35.
Tallies on chain, 24.
Tangential projection, 73.
Tape measurement. 21.
Shrinkage of, 22
survey, 198.
Telemetry, 145.
Telepost alphabet, 242.
Testing plans, 93.
Theodolite, Adjustment of, 171.
angles on chain line, 173.
Construction of. 170.
Methods of using the, 176.
traverse, 177.
vernier, 163.
Three-point problem, 168.
Tie and check lines, 21.
lines in traversing, 96.
Time, Astronomical, 238.
Divisions of, 238.
Greenwich mean, 238.
Local mean, 237.
Sidereal, 238.
Town planning, 184.
surveying, 184, 194.
Tracing, 111.
Transit theodolite, 170, 172.
Transition curves, 214, 223, 225.
Trapezium, Area of, 10.
Traverse tables, 106.
Traversing with chain, 96.
with prismatic compass, 98.
Terms used in, 101.
Trees on plans, 41.
Triangle, Area of, 9.
Triangular compasses, 112.
Triangulated offsets, 188.
Tribrach level, 130.
Trigonometry, Principle of, 156.
Trinity high- water mark, 134.
True north, 16.
Turnout, Railway, 232.
U
Unit of measurement, 7.
Universal chain scale, 14.
Variation of the compass, 17.
Vernier scales, 163.
Vertical circle, 170.
W
Watch, North point by, 16.
Whites, 61.
Widening of gauge on curves, 223.
Wires in levels and theodolites,
128, 146.
Wood, Survey of a, 56.
Working section, 141.
Zenith, 236.
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