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SCIENTIA
VERITAS
LIBRARY
OF THE
UNIVERSITY OF MICHIGAN
Ž PLURIOUS UNVE
•
TUEBOR
QUÆRIS PENINSULAM·AMŒNAMI
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A
PRACTICAL TREATISE
ON
TOPOGRAPHICAL
SURVEYING AND DRAWING;
CONTAINING
A SIMPLE AND EASY MODE OF SURVEYING THE DETAIL
OF ANY PORTION OF COUNTRY,
BY WHICH THE ACTUAL MEASUREMENT OF LINES AND ANGLES,
HITHERTO REQUIRED, MAY BE DISPENSED WITH;
TOGETHER WITH
A VERY IMPORTANT IMPROVEMENT IN THE DELINEATION
OF GROUND,
BY WHICH HEIGHTS AND DECLIVITIES ARE CLEARLY AND SATIS-
FACTORILY EXPRESSED.
TO WHICH ARE ADDED,
INSTRUCTIONS
IN
TOPOGRAPHICAL MODELLING ;
OR THE
ART OF REPRESENTING THE SURFACE OF A COUNTRY IN RELIEF.
WITH SEVEN ILLUSTRATIVE PLATES.
BY
WILLIAM SIBORN,
LIEUTENANT IN THE 47TH REGIMENT, AND ASSISTANT MILITARY SECRETARY
TO THE COMMANDER OF THE FORCES IN IRELAND.
LONDON:
PUBLISHED BY C. AND J. RIVINGTON,
WATERLOO PLACE, PALL MALL.
1827.

SION COLLEGE
LIBRARY.
SOLD PY ORDER OF THE
PRESIDENT AND GOVERNORS 1938.
LONDON:
PRINTED BY C. H. REYNELL, BROAD STREET, GOLDEN SQUARE.
39 140
Sib comm.
Hodgson
7-5239
386x7
ΤΟ
LIEUTENANT GENERAL
THE RIGHT HON. SIR GEORGE MURRAY,
G. C. B. & G. C. H.-M. P.
COMMANDING THE FORCES IN IRELAND,
&c. &c. &c.
THIS TREATISE
IS
(WITH PERMISSION)
MOST RESPECTFULLY DEDICATED,
BY HIS OBLIGED
AND GRATEFUL SERVANT,
THE AUTHOR.
PREFACE.
THE time and labor which have been hi-
therto required in topographical surveying
and drawing, have been such as to confine
this art almost entirely to land-surveyors,
engineers, and others, of whose professional
occupations it forms an essential part.
Very few persons have pursued it from
inclination, and none, probably, have con-
sidered it in the light of an attractive and
agreeable study; on the contrary, it has
generally been looked upon as complete
vi
PREFACE.
drudgery. To remove this impression by
simplifying and facilitating the operation
of detail-surveying, combining at the same
time extreme accuracy with great dispatch,
and by introducing such an improvement
into the representation of ground, as shall
enable draughtsmen to exhibit at once in
their drawings, all the local information
which these are capable of affording, is
the object of the present work; and that
nothing may be wanting which can render
this complete, and add to the interest of
the subject, the author has annexed some
instructions in the art of modelling the
surface of a country, which afford a prac-
tical proof of the importance of the
improvements he has suggested in the
topographical delineation of ground. That
this will be the means of rendering the art
of surveying, drawing, and modelling the
surface of any portion of country, at once
pleasing and attractive, even among per-
PREFACE.
vii
sons who are not obliged to pursue it
professionally, there can be little doubt.
Those who are fond of the study of geo-
logy and mineralogy, will be anxious to
avail themselves of the means of retaining
correct miniature copies of such striking
and peculiar features of ground as they
may happen to meet with. But even
those who have not studied these subjects.
or who are, at most, but superficially
acquainted with them, will derive an inex-
haustible fund of pleasure and instruction
from tracing, delineating, and modelling
different portions of the surface of the
earth, whether adorned by rich alterna-
tions of river and valley, of hills undulating
in countless variety of form, or by the
rugged and more magnificent features of
rock and mountain.
The improvement which the author
proposes in the delineation of ground,
vili
PREFACE.
and which consists in introducing a few ho-
rizontal lines or sections at certain vertical
distances from one another, with a ready and
easy method of tracing them on the survey-
sheet, and in laying down an extremely sim-
ple rule by which the inequalities of surface
may be most satisfactorily expressed, has
induced him to supersede by the present
work, the one which he published a few
years ago, containing "Instructions in
Topographical Plan-Drawing," founded
upon a foreign system, the general adop-
tion of which would require a complete
alteration, both in the execution and
reading of topographical plans, from the
usual methods practised in this country;
whereas, the improved British system now
submitted to the Public, and which exacts
no change in the principles upon which
the shading of ground is at present regu-
lated, will, he trusts, be found far superior
PREFACE.
ix
in practice, and much more generally
useful.
With regard to the foreign system here
alluded to, the author feels it incumbent
on him to state in this place, that a close
attention to the subject has convinced him
that, undeniably correct as that system is,
when strictly adhered to, it is attended
with many inconveniences. Thus, it requires
that the reader should, in order to ascer-
tain either the relative or actual heights
of particular points, set to work with ruler
and compasses, and minutely estimate the
proportion of the thickness of the shading
lines to their intervening white spaces;
it has the disadvantage that slight errors.
committed by the draughtsman or the
engraver, in delineating the ground, may
lead to very considerable ones when the
plan comes to be proved; and, above all,
it requires a complete deviation from the
usual methods of expressing ground prac-
X
PREFACE.
tised in this country. These inconve-
niences do not attend the system which
the author now proposes for adoption, for
it enables the draughtsman, without at all
altering the mode of expressing ground to
which he has been accustomed, to show,
upon the face of the plan itself, without
further reference, the differences in height
between the various points of a country;
to indicate the general and relative steep-
ness of the ground; to construct vertical
sections in any direction; and to give the
reader of the plan the ready means of
ascertaining the quantity of ground visible
from any particular point.
One very great advantage of the im-
proved system consists in the facility which
it offers to persons engaged in an extensive
topographical survey, in detecting the errors
committed by the different surveyors in the
representation of ground, by enabling them
to institute a comparison between the ter-
PREFACE.
xi
minations of the before-mentioned horizon-
tal sections at the marginal lines of one sur-
vey-sheet, with the corresponding ones of
the adjoining sheet sent in by another sur-
veyor, and which, should they not coincide,
prove that errors have occurred, and these
can be rectified before the completion of the
survey. In the Ordnance Survey of Eng-
land, the scientific skill and practical address
with which the great operations of trian-
gulation have been conducted, are univer-
sally admired, and exhibit indeed a speci-
men which is not surpassed, if equalled, by
any similar undertaking in Europe. The
topographical detail, however, or filling in
of the triangles, has been very generally
criticised, being imperfect and by no means
commensurate with the rest of the work;
and it was expressly stated by an eminent
engineer, Mr Nimmo, before the Committee
appointed by Parliament in 1823, to consi-
der of the Survey of Ireland, that this im-
xii
PREFACE.
perfection arose chiefly from the want of a
check upon that part of the operations.
But decidedly the most important fea-
ture of this system is, that it enables a per-
son to construct, with the greatest ease,
from a topographical drawing, a correct
model of the country which it represents;
that it impresses at once upon the mind of
a person viewing such a drawing, a correct
image of nature, and this too, without re-
quiring him to have recourse to ruler and
compasses, or to the estimation of minute
proportions, (at all times subject to consi-
derable error), in order to ascertain relative
degrees of altitude or inclination of ground,
as is the case with most of the foreign sys-
tems. Surely the most fastidious will not
require a greater approximation to perfec-
tion.
In the Report, published by Parliament,
on the Irish Survey, already alluded to, we
find that the practicability and advantages
PREFACE.
Xili
of modelling are subjects repeatedly sug-
gested by the engineers who were examined
before the committee; and that it is invari-
ably recommended as the most effectual
mode of representation, and for military
purposes especially, as being decidedly su-
perior to every other. Mr Bald, who ex-
hibited for the inspection of the committee
several specimens which he had constructed
in the course of his extensive surveys, ap-
pears in particular to have directed great
attention to this subject. He states his
opinion that "it is the nearest approxima-
tion of art in representing the features of
a country, and, for military purposes, su-
perior to any map representation," and ex-
presses his regret that a model of Eng-
land had not been carried on cotempora-
neously with the Ordnance Survey.
model," says Mr Bald, "on the scale of
four inches to the mile, of Great Britain and
Ireland, with their numerous isles, their long
66
" A
xiv
PREFACE.
broken, indented outline of coast, the lofty
extensive ranges of mountains in Wales,
Scotland, Ireland, and the Islands, would
give a character and expression to this work
of art which could not be surpassed." Mr
Nimmo, when asked whether he thought the
topographical representation by a system of
modelling would be applicable to the sur-
vey of Ireland, replied, "No doubt it would
be the most perfect system of representa-
tion you could obtain, but it would be pro-
digiously expensive." In short, the evidence
produced before the committee was unani-
mous in favour of modelling. Two very
great difficulties, however, appear to have
stood in the way of its adoption; namely,
the want of a fixed system of topographical
drawing, by means of which the modelling
could be carried on, either upon the
the ground
by the surveyors themselves, or subsequent-
ly at the depôt of the survey, from the
survey-sheets, by persons specially em-
PREFACE.
XV
ployed for that purpose; and the very great
expense, which, in consequence of this want,
would be incurred by the employing of ar-
tists to model from nature. The author of
the present work conceives, therefore, that
as he has succeeded in removing these diffi-
culties, he will not be considered presump-
tuous in submitting it more particularly to
the notice of those who are superintending
the Survey of Ireland, which the committee,
in the concluding paragraph of their Report,
"trust will be carried on with energy as
well as with skill, and that it will, when
completed, be creditable to the nation, and
to the scientific acquirements of the age."
It is needless to point out to military
imen the facilities which Topographical
Drawings, executed according to this sys-
tem, must offer to the study of particular
tactical movements in regard to their con-
nexion with the peculiar features of the
ground upon which they have taken place.
xvi
PREFACE.
They must not, however, confound them
with another branch of drawing-Military
Sketching; a branch of very great import-
ance, and presenting great and peculiar
difficulties. A military sketch differs from
a military survey, both in its purpose and
its execution. The former is a hurried and
imperfect delineation of the general charac-
ter and most important features of a coun-
try destined to be the theatre of military
operations; the latter is a minute and ac-
curate representation of every natural and
artificial object which can exercise any in-
fluence on the movements of an army.
The sketch of a field of battle precedes the
time of action; the survey of it is made
afterwards, when sufficient time and oppor-
tunity can be granted for the purpose. The
one is dashed off with all the rapidity which
the most practised skill can command;
the other is the deliberate and finished pro-
duction of ample leisure. The object of a
PREFACE.
xvii
military sketch is to enable the commander
to make the most effective dispositions for
attack or defence; that of a military sur-
vey to show the connexion of these dispo-
sitions with the conformation of the ground,
and consequently the local circumstances
which contributed to their failure or success.
It is obvious, therefore, that as the value of
an officer's sketches will often depend much
more on his tact and sagacity than on the
observations and measurements which he
can actually take, and as much will depend
on his habits of estimating the forms of
ground, from a rapid and hasty glance, he
who has been in the habit of drawing on the
principles of the present improved system,
and who is rendered familiar, by his practice
in modelling, with the various conformations
exhibited by the earth's surface, will be the
most likely to possess that tact and sa-
gacity.
With regard to Land-Surveying, as applied
b
xviii
PREFACE.
to estates, the author feels confident that
the present work will be the means of sub-
stituting neat and correct models for those
gaudy productions of the brush, in which
the landscape and the plan are so strangely
combined. In the sale of estates, models
are of very great utility, since they enable
purchasers to form just notions of their local
properties, instead of trusting to the gene-
rally exaggerated descriptions given by
auctioneers.
To land-surveyors, who are in the habit
of computing the area of land from the
scale of a plan, by dividing the latter into
triangles, trapezia, &c., the proposed sys-
tem of surveying offers every facility, by
the extreme accuracy with which the situa-
tion of all lines and points is laid down,
and by which a much greater reliance can
be placed upon this mode of computation,
when applied to a large scale, (as should
always be the case in land-surveying,) than
PREFACE.
xix
that which is founded on actual mea-
upon
surement alone.
It might probably be expected, in a work
of this kind, that the author would have
passed in review the different modes of
Topographical Drawing and Surveying pur-
sued both on the continent and in this
country, and have compared them with his
own system; but this, he conceives, would
have been only making a book, since the
generality of his readers, that is, of those in-
terested in the subject, are supposed to be
already acquainted with the present state
of the art, or, if not, they can ascertain it
from other works, and then judge for them-
selves of the value of his improvements.
He has preferred laying down, in the most
concise manner, a system which he is confi-
dent will be found at once the most simple,
the most expeditious, and the most gene-
rally useful:-the most simple, because a
person almost entirely unacquainted with
XX
PREFACE.
mathematics, can execute it with the great-
est ease; the most expeditious, because it
dispenses with linear and angular measure-
ments; and the most generally useful,
because it offers to the reader of a topo-
graphical drawing, that just and ready con-
ception of the country represented, which
enables him, if he wishes, to construct its
correct model.
Dublin,
4th of June, 1827.
ERRATA.
Page 51, 7th line from the bottom; for to, read at.
52, 1st line; for 42, read 30.
66, 5th line; for 12, read 8.
66, 9th and 10th lines; for marked the one; read marked, the one,
77, 6th line; insert In, as the last word of the line.
CONTENTS.
TOPOGRAPHICAL SURVEYING AND DRAWING.
РАОБ
Description of the improved Plane Table, and of the
mode of determining by it the height of any
point, and the degree of inclination of ground 1
Relative distinction between trigonometrical, topogra-
phical, and land surveying.....
12
Commencement of a topographical survey unconnected
15
with a trigonometrical survey...
Commencement of a topographical survey connected
with a trigonometrical survey...
29
38
Instances in which linear measurement may be required 45
To find a station taken at pleasure
To carry on the work from one survey-sheet to another
49
General rules in topographical surveying
51
Topographical scales
54
The topographical delineation of detail
56
The topographical delineation of ground
Classification of ground.
•
60
82
xxii
CONTENTS.
PAGE
To construct vertical sections of the ground represented 84
To ascertain the boundary of view from any point upon
a plan
TOPOGRAPHICAL MODELLING.
85
Introduction
91
Difference between the horizontal and vertical scales
96
To make the preparatory model....
98
To make the mould
100
To make the cast.
To represent and fix the detail upon the cast or model.. 103
102
TOPOGRAPHICAL
SURVEYING AND DRAWING.
TOPOGRAPHICAL
SURVEYING AND DRAWING.
DESCRIPTION OF THE IMPROVED PLANE TABLE,
AND OF THE MODE OF DETERMINING BY IT
THE HEIGHT OF ANY POINT, AND THE De-
GREE OF INCLINATION OF GROUND.
THAT the Plane Table is a most useful and ex-
peditious instrument in surveying, is an obser-
vation which has been made by nearly all those
who have written upon this subject; but when
we consider the defects in the construction of
the description of Plane Table hitherto used,
and the still greater defects in the mode of
working with it, which require numerous angu-
lar and linear measurements, and compare these
with the simple construction of the instrument
B
2
TOPOGRAPHICAL SURVEYING
we propose to substitute, the very plain and easy
manner of using it, and the extreme accuracy
and great dispatch with which its operations are
attended, it may be confidently asserted that it
is of all instruments the one best suited to the
purposes of Topographical Surveying.
Independently of the great correctness and
expedition which follow the use of the Plane
Table, it possesses considerable advantages over
other instruments. Its plane gradually as-
sumes the representation of the country, so
that the surveyor can constantly compare one
with the other, estimate the distances of
various objects from his station, and from
one another, and immediately ascertain whether
his estimate be true, and, if not, the probable
causes of his error; a practice which will very
soon enable him to determine with great accu-
racy, by the eye alone, numerous short distances
comprised in the minutiae of detail, which those ac-
customed to survey with other instruments would
be compelled to measure. The value of such an
advantage to the military surveyor is obvious: he
cannot possibly lay a better foundation for that
AND DRAWING.
3
correct coup-d'œil by which he may, at some
future period, be required to give the represen-
tation of a country, under circumstances which
do not admit of the use of such an instrument
as the Plane Table, nor perhaps of any instru-
ment whatever. Such a representation would
certainly be nothing more than a sketch; but
there can be no doubt that those sketches will
be the most faithfully as well as the most
rapidly executed, that are undertaken by officers
whose qualifications for this description of ser-
vice are the result of practice in military surveys.
Various alterations have been made, in diffe-
rent countries, in the construction of the Plane
Table, since it was first brought into use; the
greater part of which have only tended to render
it more complicated. The one which is the
most simple in construction, however, is the
most useful in practice. The instrument here
recommended consists of a plain square board,
fixed upon a stand, by which it may be made to
turn round upon its centre, preserving a perfectly
horizontal position; the index, by means of
a simple contrivance, enables the surveyor to
4
TOPOGRAPHICAL SURVEYING
determine the heights of all points above, or
their depths below, his station, without requiring
any further calculation than that of multiplying
two numbers together.
Fig. 1, Pl. 1, represents the improved Plane
Table, with its index. It is composed of a
brass staff-head, having three leaves, two of
which, a and b, are seen in the figure, equi-
distant from one another. To these leaves
the legs are fastened by means of an axis
passing through each, having a square at one
end to prevent its turning in the wood, and a
screw-worker and winged nut at the other, by
which the surveyor is enabled to give them
any degree of tightness they may require.
Down through the centre of the head runs a
long conical hole or socket, into which is accu-
rately ground a bell-metal centre. The upper
part of this central piece is made of a bell-
like shape, and to it the drawing-board is fixed
by means of three screws, two of which are seen
in the figure. A clamp is attached to the instru-
ment in such a manner as to take in both the
bell-metal centre and socket, so that by loosen-
AND DRAWING.
5
ing or tightening the clamp-screw c, the table
may be turned freely round, or fixed firmly
in any position. The outside of the clamp
is racked to receive a tangent-screw, the milled
head of which is seen at d: this admits of the
finest possible circular horizontal motion being
given to the drawing-board.
To procure the horizontal position of the
drawing-board, a very portable circular spirit-
level e, about three inches in diameter, is laid
upon it, and the legs of the instrument are moved
or thrust into the ground, more or less, until the
bubble is brought within the small circle in the
centre of the glass: f represents a compass
which can be attached to a side of the drawing-
board, by means of a screw and two holes under
the board made to receive the two nobs or pins
shown in the figure. It will be seen, however,
in the following pages, that a compass is not
absolutely necessary in surveying with the
Plane Table.
The size of the drawing-board varies accord-
ing to the extent of the survey and the scale upon
which it is to be executed. When the scale of
6
TOPOGRAPHICAL SURVEYING
6 inches to a mile is used, a drawing-board
20 inches square will contain 9 square miles
within an inch margin: when the scale is 5
inches to a mile, a drawing-board 17 inches
square will contain the same extent and margin;
and when the scale is 4 inches to a mile, a board
14 inches square will answer the same purpose.
The drawing-board itself is prepared in the
following simple manner, which entirely removes
a very great objection hitherto urged against the
use of the Plane Table, namely, the expansion
and contraction of the paper according to the
state of the atmosphere:-Lay upon that side of
the sheet of paper which is to be fixed to the
board, the white of an egg well beat up; press
the paper gently and gradually down upon the
board from one side to the opposite one, and
paste the edges which hang over to the under
part of the board. With drawing-boards thus
prepared, I have stood with an umbrella over
the instrument during heavy showers of rain,
without the slightest alteration taking place in
the smoothness or firmness of the paper.
Fig. 2 represents the index upon a large scale.
AND DRAWING.
7
The distance between the outer surfaces of the
two sights may be made equal to either 200
Paris lines, or 200 tenths of an English inch:
smaller lengths may be given to this distance,
but the former are preferable, as obviating the
necessity of dividing in order to ascertain the
exact length of the two hundredth parts. On
the outer surface of the object-sight a b, com-
mencing from a height above the base or rule,
equal to that of the lowermost sight-hole c, of
the near sight de, as many of these Paris lines,
or tenths of an inch, (or two hundredth parts of
the distance between the sights,) are marked,
as the length of the sight (somewhat more than
half that of the rule) will admit. The distance
between the sights being equal to 200, every
two of these divisions forms one-hundredth part
of that distance, and these hundredth parts are
numbered 5, 10, 15, &c., upwards on one side
of the sight, and in a similar manner downwards
on the other, as shown in the figure. The thou-
sandth parts are read off by means of the no-
nius-slide ƒ g. On the inner side of the object-
sight are marked the angles of inclination of
8
TOPOGRAPHICAL SURVEYING
ground between 0° and 45°, both upwards and
downwards; and, on the inner edge, (as seen in
the figure,) those between 0° and 20°: their use
will be shown presently.
The near-sight has an aperture cut down
through the middle, similar to that in the object-
sight, which is covered by a plate fixed to the
sight by means of an axis or screw at the lower
part, and a tangent-screw at the top. Very fine
sight-holes are drilled into this plate, at a dis-
tance from each other, equal to five of the divi-
sions on the object-sight.
To find the Height of an Object above your Station.
The table being set in its horizontal position,
direct the index towards the object; look through
the lowermost sight-hole c, and move the nonius-
slide so as to make the cross-hair coincide with
the object. Then observe the number cut off
by the cross-hair on the outer surface of the
object-sight, and multiply it by the distance of
the object from the station, taken from the scale
of the plan, for the height required.
AND DRAWING.
9
To find the Depth of an Object below your Station.
Look through the uppermost sight-hole o, and
multiply the distance by the number cut off by
the cross-hair upon the line of divisions num-
bered downwards.
Suppose, in the former case, the division cut
off by the cross-hair to be exactly 30, and the
distance to be 1200 feet; then, 30, or 300, or
•3,×1200=360 feet, the height required.
Suppose the cross-hair to pass between the
division 30, and the half division beyond it, and
the nonius to mark 4; then 304 × 1200-364.8
feet, the height required.
Suppose it to pass between the half division
beyond 30, and the 31st division, and the nonius
to mark 3; then, 308x1200=369.6 feet, the
height required.
The proof of this simple rule is obvious
when we consider that cf. Fig. 2, must be in the
same proportion to fg as that of the distance of
the object to its height-that is, 1 number cut
off distance of object its height-whence,
::
the number cut off multiplied by the distance
10
TOPOGRAPHICAL SURVEYING
of the object gives the height required. To the
height thus found, must of course be added that
of the instrument.
To find the Angle of Inclination of Ground.
•
If the angle does not exceed 20°, (and those
of most frequent occurrence do not,) look
through the lowermost sight-hole, if the ground
is above you, and through the uppermost, if it
is below you, and move the nonius-slide so as to
make the cross-hair pass a little above the top
or bottom of the slope (in order to take the
height of the instrument into account) and it
will then mark the degree of inclination upon
the inner edge of the object-sight. Should the
angle exceed 20°, the object-sight must be re-
moved to s, where the distance between the
two sights and their length form a square, and
the angle is then to be looked for on the inner
side of the object-sight.
To adjust the Index.
The adjustment of the index, to which the
surveyor should attend previously to his going
AND DRAWING.
11
out to work, is effected in the following manner:
-fix the table in its horizontal position, in a
room, about nine or ten feet from a window, and
attach to the latter a silk thread with a weight
suspended to it. Place the index on the table,
and look through the adjusting sight-hole i, whe-
ther the hair in the object-sight coincides with
the silk thread at the window; if it does not,
move it to the right or left, by means of the
small tangent-screw t at the upper part of that
sight, until both hair and
thread appear to be
Now look through
in the same vertical plane.
the uppermost sight-hole o, whether the hair
and thread coincide, and, if they do not, you
must effect the coincidence by means of the
screw n* in the near-sight. Return to the ad-
justing sight-hole, and see if any further alter-
ation is necessary, and continue this operation
until the sight-holes, hair, and thread, are in the
same vertical planet.
Both screws t and n are made to fit one key.
This kind of Plane Table may be had of Jones, Charing
Cross, London; or of Scott, Stafford street, Dublin; but the
*
12
TOPOGRAPHICAL SURVEYING
The index is rendered portable by the sights
being made to fold down upon the rule, the one
partly over the other, and the whole packed
into a case.
RELATIVE DISTINCTION BETWEEN TRIGONO-
METRICAL, TOPOGRAPHICAL, AND LAND
SURVEYING.
SURVEYING may be divided into three parts;
Trigonometrical, Topographical, and Land Sur-
veying.
Trigonometrical Surveying comprises the art
of carrying on a series of connected triangles
over an extensive tract of country, from a long
and accurately measured base or fundamental
line, and of transferring upon a plane or paper,
on a reduced scale, the true position of the
points of these triangles, which generally con-
sist of the most conspicuous objects, such as
above description and the engraving form a sufficient guide
to any expert mathematical instrument-maker for its con-
struction.
AND DRAWING.
13
the summits of high hills, steeples, towers,
&c. The great triangulation which has been
carried on in this country for several years
past, under the direction of some of our most
eminent engineers, appointed by the Board of
Ordnance to lay down a survey of England
and Wales, who, to ensure the perfect accuracy
of this undertaking, have been enabled by a
liberal government to bring into aid all the
advantages and improvements that have been
effected in this branch of science,-may be con-
sidered as a model by which all future trigono-
metrical operations should be regulated. Those
who are desirous of obtaining information on this
branch of surveying should therefore have re-
course to the account of the Trigonometrical
Survey of England and Wales*, published by
Colonel Mudge and Mr Dalby, two of its late
principal directors. And also to a "Treatise
on Topography," by General Malorti de Marte-
mont, of Woolwich.
* This great national work, called the Ordnance Survey,
which has lately been extended to Ireland, is at present un-
der the able superintendence of Colonel Colby.
14
TOPOGRAPHICAL SURVEYING
Topographical surveying comprehends the
filling up of the space contained within these
triangles with the correct position and repre-
sentation of the remaining objects situated
upon and composing the surface of the country.
It also includes the surveying of a portion of
country not exceeding 250, or at most 300
square miles, without the aid of trigonometry,
the mode of proceeding in which will be ex-
plained in the following pages.
Land surveying does not require the represen-
tation of the inequalities of ground, but consists
simply in planning the boundaries of fields and
other enclosures of estates, and determining
their respective areas.
Topographical surveying and drawing may
also be divided into two parts, namely, detail
and ground; the former comprising the deter-
mining and delineating of all natural and arti-
ficial objects situated upon the earth's surface,
such as woods, roads, rivers, canals, boundaries,
towns, villages, &c.; and the latter, that of the
formation of the surface itself.
AND DRAWING.
15
COMMENCEMENT OF A TOPOGRAPHICAL SUR-
VEY UNCONNECTED WITH A TRIGONOMETRI-
CAL SURVEY.
We will first suppose the topographical survey
of a small portion of country is to be taken un-
connected with a trigonometrical survey. In
this instance, should the scale be rigidly pre-
scribed, one line, called the base of the survey,
must be measured; and, since it is the only one
which requires to be so, (except in some parti-
cular cases, as will be explained hereafter,) the
surveyor will not object to bestow great care
and attention, in order to obtain its exact length.
Should however any error be committed in the
measurement, it will not, as in surveys con-
structed entirely from measured lines and angles,
communicate itself to the whole work, but merely
to the scale of the plan, which can be corrected
before the plan itself is completed; for, since the
remaining horizontal lines, and the angles which
they contain, are not measured, but all objects
16
TOPOGRAPHICAL SURVEYING
are determined, on the ground, by means of lines
of sight drawn in their true vertical planes, no
distortion of parts can take place; the whole
will be in exact geometrical proportion with the
country represented.
If the scale on which the plan is to be drawn
✩ be rigidly prescribed, it will generally be neces-
sary to commence by measuring the base; but,
should this not be the case, and the features of
the ground be such, that from two or three high
summits, a considerable portion of what is to
be surveyed can be seen, it will be more conve-
nient to commence the survey at once from these
points, and to measure a base subsequently, upon
a piece of ground convenient for that purpose.
In choosing the best situation for a base, the
surveyor should attend to the following direc-
tions:
1. Let the base be situated in a level plane,
or at least in one not inclined to the horizon in
an angle of more than 2º. Should the ground, of
which the survey is to be taken, not admit of a
plane sufficiently level for this purpose, the hy-
pothenusal lines along the base must be reduced
AND DRAWING.
17
to horizontal ones, and the true horizontal ex-
tent of the whole line accurately obtained.
2. Let it be so situated that several conspi-
cuous objects may be seen from its extremities,
and also, if possible, that it may lie in a direct
line with two very distinct objects, in order
that its measurement may be carried on in a
true direction, and that its situation may be
easily and accurately ascertained at any time.
3. Let it be of such a length that the lines of
sight drawn from its extremities towards the
distant objects on either side of it, may inter-
sect each other in angles containing not less
than 30°.
Having fixed upon the situation of the base,
and marked out its true direction by means of
staves placed at convenient distances between
its extremities, proceed to take its exact length
with a measuring instrument. In an ordinary
survey, the chain is generally used, though rods
are considered by some surveyors to be prefer-
able. Two persons hold the chain, one at each
end; the foremost, or leader, must be provided
with a certain number of arrows, one of which
C
18
TOPOGRAPHICAL SURVEYING
he fixes perpendicularly into the ground at the
end of the chain when stretched out, and which
is afterwards taken up by the follower, by way
of keeping an account of the number of chains.
The follower keeps one end of the chain close
to the first extremity of the base, and sends for-
ward the leader with the other, directing him,
by a motion of the hand, after he has drawn the
chain tight, to place it more either to the right
or to the left, until he gets it in a straight line
with the other extremity, or with the other in-
tervening staves. The leader then thrusts an
arrow into the ground at the point where the
chain terminates; carries it again forward;
fixes another arrow as before, and proceeds in
this way with the measurement of the whole
base, which should be repeated until no doubt is
entertained as to its correct length.
The measurement of long bases of extensive
trigonometrical surveys, in which the utmost
degree of accuracy is required, is carried on by
means of rods of platina, iron, or of wood; glass
rods were used in the measure of the base on
Hounslow Heath. The reader who may wish
AND DRAWING.
19
for information on this subject must consult
the account of the Trigonometrical Survey of
England and Wales, by Colonel Mudge and Mr
Dalby; the account of the measurement of a
base on Hounslow Heath, by General Roy;
the Méridienne de l'Observatoire de Paris, par
Cassini; the Mesure d'un Arc du Méridien, par
Delambre, &c.
Suppose you have chosen and measured the
line A B*, Fig. 1, Pl. 2, as the base of the sur-
vey, and accurately laid down a b upon the
drawing-board, in its exact proportion, accord-
ing to the scale, to the length of A B upon the
ground. Then fix the instrument over the ex-
tremity A; set it horizontal; loosen the table
by the clamp-screw, turn it so as to bring a b
pretty nearly into the direction of a B, and screw
*In this plate the capital letters indicate the points or ob-
jects upon the ground; and the small letters, their corre-
sponding positions on the plan. A and B in this figure are
therefore concealed by the plane of the instrument, which, it
is scarcely necessary to remark, is made, for the sake of ex-
emplification, of a very disproportionate size to the space
occupied by the objects.
20
TOPOGRAPHICAL SURVEYING
it tight again: fix a needle* in the point a;
place the index along the line a b, and, by
means of the tangent-screw, make this line
coincide exactly with A B upon the ground.
Try with the plummet whether a is now per-
pendicularly over the extremity A of the base;
if it is not, alter the position of the table accord-
ingly, and go through this operation until you
have a over A, and a b in the true vertical plane
of A B.
Having thus obtained the true position of the
instrument, proceed to draw lines of sight from
a towards the most conspicuous objects, which,
The heads of the fine needles used in this mode of sur-
veying should be covered with sealing-wax, to enable the
surveyor to press them gently into the drawing-board.
This may be a line suspending a bullet from one point.
of a pair of callipers (compasses with bowed shanks) under-
neath the drawing-board, while the other is fixed upon the
station-point on the plan. It is only required in laying down
the position of the base; and, in general, any small heavy
substance let fall from that part of the board which is immedi-
ately underneath the station-point, is sufficient to determine
whether the latter is perpendicularly over its corresponding
station on the ground.
↑ The surveyor should be provided with two pencils, one
AND DRAWING.
21
in this instance, we will suppose to be C, D, E,
F, G, H, taking care to distinguish each line by
a letter, number, or particular mark, or by the
name of the object to which it is drawn. Ob-
serve that there is no necessity for drawing a
line of sight all along the index, which would
give to the work a confused appearance; you
need only draw a small portion of it upon that
part of the board where you expect the point
corresponding to the object will fall.
Now leave a mark at A, and proceed to B.
Fix the instrument over this extremity of the
base, and procure its true position, namely, so
as to have b over B, and b a coinciding with the
line of sight b A, in the same manner as was
observed at the station A with regard to the
mark B. Fix a needle in the point b; direct
for drawing the lines of sight, and the other for affixing to
these lines their distinguishing signs; the former must be of
the hardest kind that can be procured, and cut square and
flat, so that it may be held perfectly close to the fiducial edge
of the index, and be made to produce the finest line possible;
the other must of course be cut to a point.
22
TOPOGRAPHICAL SURVEYING
the index to the objects C, D, E, F, G, H, suc-
cessively, and intersect the lines of sight drawn
from a, as shown in the figure. These intersec-
tions will indicate the true positions of the above
objects, provided no mistake have been made in
drawing the lines of sight. In order to ascer-
tain this, draw an alignment in a convenient
direction, such as b I; that is, apply the index
close to the point b, directing it to some distant
object I, draw small portions of the line of this
direction upon the margin of the plan, and upon
that part where the station-point is expected to
fall, as seen in the figure. Leave a mark at B,
having previously drawn lines of sight, (as was
done at A,) towards other objects advantageously
situated as directing-points, and proceed with the
instrument to a convenient spot, from which A
is visible, somewhere about O, in a line with B
and I. Having placed it exactly in this direc-
tion and set it horizontal, apply the index close
to the point b and to the above-mentioned parts
of the alignment drawn upon the margin; turn
the table by means of the tangent-screw into the
direction of B and I, and observe whether these
AND DRAWING.
23
objects are seen through the sights; if they are
not, shift the instrument accordingly until its
true position is obtained. This last operation
can always be easily and readily performed by
altering the position of the legs of the instru-
ment, such as taking one of them out of the
ground, and fixing it further in the required
direction, and thrusting the other two deeper
into the ground. Fix a needle in the point a,
apply the index to it, directing it to A, and
intersect the alignment of I B, which intersec-
tion will give your true station-point. Apply
the index to this point, directing it successively
to such of the objects C, D, E, &c. as are visi-
ble, and observe whether each is situated in a
vertical plane with its corresponding point upon
the plan, and with the present station-point o.
Should each be exactly in this direction, its
correct position in the plan is proved; but, if
the index, when directed to one of those objects,
does not pass over its corresponding point upon
the plan, the line of sight must be drawn, and
the true position of this point determined by a
line of sight drawn from some subsequent sta-
24
TOPOGRAPHICAL SURVEYING
tion, by which the false line will be detected.
Thus, suppose that when at O, Fig. 2, Pl. 2,
(which represents the work upon the board,) you
apply the index to the points o and e, and that
in directing it to the object E, you find it does
not pass over the intersection of the lines of
sight a e and be; then draw the line of sight o e,
from which it will appear that one of the lines
a e, be, and o e, has been incorrectly drawn.
The true position of this object upon the plan is
therefore, at present, unknown; but is found at
some subsequent period of the survey, for in-
stance, from a station taken at Q. The line of
sight qe, drawn from this point to E, passes
over the intersection of the lines be and o e,
whence it is evident that this must be the true
situation of E upon the plan, and that an error
must have been committed at A in drawing the
line a e.
Suppose that, in the course of the work, it
should be found desirable to fix a station some-
where about M, Fig. 1, and in a line between the
objects G and L. Then, in order to bring the
instrument into this alignment, send forward
AND DRAWING.
25
your assistant about fifty or a hundred yards
towards G; motion him to the right or left, so
as to get him in a line with G; after which let
him motion you in the same manner, so as to
get you in a line with L; and proceed in this
way until you see each other in the true align-
ment. Fix the instrument in the latter, set it
horizontal, apply the index to g and l, and draw
a line in that part where your station-point will
fall. Turn the table pretty nearly round to its true
position, and fasten it by means of the clamp-
screw; then give to it a gentle horizontal mo-
tion with the tangent screw, until you see the
object G through the sights; after which place
the index in the direction of L, applying it to
the points / and g as before; and if the object G
coincides with the hair in the object-sight, the
table is in its true position; if it does not, you
must remove the table to the right or left accord-
ingly, by shifting the legs as before described.
Having rectified the position of the instrument,
determine the station-point by a back intersec-
tion from some object already laid down, such
26
TOPOGRAPHICAL SURVEYING
as E, and by a verification from another, such
as P or Q.
In order to facilitate the subsequent opera-
tions of the survey, (such as the finding one's
station upon a spot of ground over which no
alignment has been drawn), it is desirable to
have points upon the plan corresponding to
several conspicuous objects upon the ground,
the accuracy of which cannot possibly be ques-
tioned. These are called directing-points, and
are distinguished in the plan, as well as the
station-points, by being encircled with a pencil-
line, as seen at Fig. 2, Pl. 2. The surveyor
should not consider one of them as determined
upon the plan by the intersection of two lines of
sight, until verified by a third one; and he
should observe that, when the lines of sight
drawn from two stations to any object, for the
purpose of determining its situation on the plan,
intersect each other in an angle less than 30°,
the point of intersection must be more distinctly
shown by a third line drawn from another sta-
tion. Indeed, he will find it very little, if
any,
AND DRAWING.
27
trouble, to verify every object by means of a
third line of sight, (excepting the minutiae of the
detail), whenever he possibly can; and he will
then have the satisfaction of knowing that all
points are laid down with the greatest accuracy
on his drawing-board, and this too, without any
measurement beyond that of the base, without
any calculation, and even without the assistance
of the compass.
The above will suffice to shew, that by pro-
ceeding in this simple, correct, and expeditious
manner of determining the most conspicuous
and well-defined objects of the country, a num-
ber of directing-points is attained, which serve
to facilitate the planning of the minutiae of the
detail, and the configuration of the ground.
Should no particular scale be prescribed, and
supposing two commanding points to offer,
whence a great portion of the ground can be
seen, fix the situation of these points upon your
survey-sheet, as you may find most convenient.
Commence the survey from them in the same
manner as from A and B, Fig. 1, Pl. 2, and upon
arriving, at a subsequent period, upon a flat
28
TOPOGRAPHICAL SURVEYING
piece of ground of sufficient extent, measure a
base, the extremities of which you can deter-
mine from directing-points already laid down on
the plan. This is by far the best and most ex-
peditious mode of commencing a survey, and
answers particularly well when you wish to
determine only a small portion of country, and
when you have fixed in your mind whereabouts
upon your drawing-board you wish the situation
of the two points to fall. It can also be adopted
when the scale is not rigidly prescribed, that is,
when one or more in the number of inches to
be fixed upon for a mile is of no consequence,
since the situation of the two points may then
be laid down with sufficient accuracy, as far as
regards a scale, by the eye. Much assistance
may be derived in this respect from maps, (and
there are few portions of country of which maps
have not been constructed), whence the horizon-
tal distance between these points can be taken,
or at least calculated sufficiently near the truth
to agree with the prescribed scale. In survey-
ing ground in England or Wales, recourse might
be had to the published account of the trigono-
AND DRAWING.
29
metrical survey of those countries, in which are
given numerous distances between conspicuous
points, all calculated with the greatest nicety;
a most important advantage, which enables us,
in such cases, to dispense with the measurement
of a base, and to commence a survey at once
from the most commanding situations, even
though the scale should be rigidly prescribed.
COMMENCEMENT OF A TOPOGRAPHICAL SUR-
VEY CONNECTED WITH A TRIGONOMETRICAL
SURVEY.
We will now suppose that a triangulation has
been carried on in the country of which a topo-
graphical survey is to be made, and in such a
manner, that upon every survey-sheet of the
latter fixed upon the Plane-Table, the situation
of at least two points, trigonometrically deter-
mined, is given to the surveyor, by which his
work is to be regulated. In this instance no
measurement of a base is required, the distance
between the two given points having been mea-
1
30
TOPOGRAPHICAL SURVEYING
sured or computed in the trigonometrical survey.
The objects, however, which correspond with
these points, frequently consist of spires, towers,
&c., on which the instrument cannot conveni-
ently be placed; whence it will be necessary to
explain the modes of proceeding in the different
cases that may occur: which are,
1st. When the instrument can be placed upon
both points.
2nd. When it can be placed only on one
point.
3rd. When it can be placed on neither point;
and then, either in an alignment with the two
points, beyond or between them.
The proceeding in the 1st case being exactly
similar to the commencement of a survey from
the extremities of a measured base already de-
scribed, requires no further explanation.
In the 2nd case, after having rectified the
position of the instrument by means of the point
over which it can be placed, and the line between
that point and the other given one, and having
drawn lines of sight towards the most conspi-
cuous objects, determine an alignment with one
AND DRAWING.
31
convenient for the purpose, and proceed in it
until you arrive at a spot of ground favorable
for viewing objects, and where a back intersec-
tion from the other given point with this align-
ment would not be too acute: then set up
the Plane-Table, and determine your station-
point by means of this back intersection accord-
ingly.
In the 3rd case, suppose that a and b, Fig. 3,
No. 1, Pl. 2, are the two given points on the survey-
sheet, corresponding to A and B on the ground,
over which it is impossible to fix the instrument,
and that a convenient station can be taken in
the prolongation of A B, as for instance, at C.
Then, having adopted, by the eye, the point c in
this alignment to represent your station C, and
brought the prolonged line ab on the Plane-Table
to coincide with that of A B on the ground, de-
termine a convenient alignment over a part from
which both A and B are visible, such as gcg;
proceed in this to a good spot for viewing ob-
jects, and set the instrument in its true position
accordingly; fix a needle in a, apply the index
to it, directing it towards A, and draw the line
32
TOPOGRAPHICAL SURVEYING
of sight ah backwards, and, in the same way,
draw the line of sight bh backwards. The point
of intersection h of these lines will indicate the
present station. For, since a b is parallel to A B,
and ah and bh respectively coincide with A h
and B h, the triangles A h B and a hb are simi-
lar, whence h must be the true station-point.
Then, to determine the correct station-point of
the former station, which was adopted by the
eye, fix a needle in h, apply the index to it,
directing it to the object of alignment G, and
draw a line to intersect the prolongation of a b,
which intersection i is the true position of C*
*Though this part of the problem is not perfectly cor-
rect in theory, it is sufficiently so in practice; for the assumed
station-point c will seldom be situated farther from the true
station-point i than one, or at most two inches; but even sup-
posing the distance ic to be considerably greater, still when
we compare it with the actual distance, upon the ground, from
the object G, or between the stations H and I, it is quite evi-
dent that the point i will fall in the alignment G C G. Be-
sides, the distance ic, on the ground, is too small to be
assignable even upon the largest topographical scale; and,
upon a moderate scale, the whole instrument itself, when
AND DRAWING.
33
If, in this case, it is not possible to adopt a
station in the prolonged alignment of the two
points, but only in one between them, the mode
of proceeding is precisely similar to that shown
in the last problem, as is evident from a view of
Fig. 3, Pl. 2, No. 2.
We will now suppose that no station can be
taken either in the prolonged alignment of the
two points, or in the alignment between them.
1st Method. Let a and b, Fig. 4, Pl. 2, be the
two points in question. Choose some conveni-
ent station about C; set the table in as nearly
its proper position with respect to A B as your
eye can guess, or refer to the compass, should
one be attached to the instrument; draw lines.
of sight, directed to A and B, backwards through
a and b respectively, and adopt their intersec-
tion c, as a temporary station-point. Deter-
mine an alignment with some convenient object
over a part of the country from which A and B
are visible, which we will suppose to be gc G.
fixed at I, and viewed from H, might be considered a point
in the alignment G C G.
D
34
TOPOGRAPHICAL SURVEYING
Having fixed the instrument about H, bring the
line cg into the alignment C G; fix a needle in
a, apply the index along it towards A, and draw
a line of sight backwards, intersecting cg in h.
Draw a line of sight from h towards B, which,
if the instrument were in its true position, would
pass through the point b, a circumstance of
course not to be expected, and, from the point
of intersection i of this line with the line of sight
drawn from c towards B, draw a line to a.
Now, since the figure a chi is similar to the
figure A Ch B, ai is parallel to A B. But it is
necessary to bring ab into a parallel position
with AB. To effect this, apply the index to
the line ai, and observe what well defined dis-
tant object is seen through the sights; should
there be none, send forward your assistant a
good distance with a mark, which he is to fix
exactly in this direction: now apply the index
to the line ab, and turn the table round by
means of the tangent-screw, until the same ob-
ject or mark is seen through the sights, whence
the position of the table will be altered by the
angle i a b, and the line ab become parallel to
AND DRAWING.
35
A B. In order to obtain the true point corres-
ponding to the present station, draw lines of
sight backwards from A and B through a and b
respectively, and their point of intersection / will
give the required station-point; and to obtain
the one corresponding to the former station at
C, draw the line kl towards the distant object
of alignment G :* bring the table into the posi-
tion it had there, (by turning it round with the
tangent-screw until the sights of the index,
when this is applied to a i, coincide with the be-
fore-mentioned object or mark in the alignment
of ai in the first, and of a b in the second posi-
tion,) apply the index to ac, and observe what
distant object is intersected by the hair in the
object-sight; bring the instrument into its se-
cond or true position again; fix a needle in a ;
direct the index along it to the same distant
object, and draw the line of sight a p backwards,
the intersection of which with kl, namely o,
gives the station-point required.
2nd Method. Let a and b, Fig. 5, Pl. 2, be the
* See the note at page 32.
36
TOPOGRAPHICAL SURVEYING
Draw
two given points. Choose two convenient spots.
of ground C and D, from which A and B are
visible, and fix their positions c' and d' arbitrarily.
on tracing paper fastened to the drawing-board,
or upon a blank part of the board itself.
from each of these stations lines of sight towards
A and B, by which the angles a' c'b', b' c'd',
a d'c, a' d'b', will be made respectively equal
to the angles ACB, BCD, ADC, AD B,
whence the figure a' b' d'c' will be similar to the
figure A B D C. Construct therefore upon ab,
the figure abdc similar to the figure a' b'd' c′;
place the index along ca, and turn the tangent-
screw until the object A is seen through the
sights, by which means a b will become parallel
to A B, and c d will be the station-points cor-
responding to C and D.
The required station-point might, it is true,
be determined very readily by means of the
compass, but with no certain degree of accu-
racy; for the state of the atmosphere, the hour
of the day, the proximity of ferruginous matters,
AND DRAWING.
37
and other causes, frequently produce a consider-
able variation in the declination of the needle.
The truth of this will be very apparent to a per-
son surveying with a Plane-Table to which a
compass is attached, upon his observing the
position of the needle at every station, which,
if correct, should constantly be directed to the
same point; and he would likewise find, in all
probability, if he had solved this problem with
the compass, (that is, by rectifying the position
of the Plane-Table by making the needle always
point to the same degree of the compass, and
by drawing lines of sight backwards from the
two objects, through their respective given
points on the survey-sheet, and adopting their
intersection as the station-point,) that in verify-
ing from his third station, the points correspond-
ing to the objects determined by lines of sight
drawn from the two first stations, his intersec-
tions would not coincide with these points; on
which account he would be under the necessity
either of recommencing the survey according to
the accurate method here explained and recom-
mended, or of continuing it in error constantly
38
TOPOGRAPHICAL SURVEYING
increasing, deriving no satisfaction from his work,
and entailing on himself a vast deal of trouble
and uncertainty.
TO FIND A STATION TAKEN AT PLEASURE.
Ir has now been shown how to determine the
relative positions of objects upon the plan, by
the intersection of lines of sight; and also to
determine stations by means of alignments and
back intersections; but, as it frequently happens
during the course of a survey, that the surveyor
arrives upon a spot of ground favorably situated
for viewing several objects, over which he has
drawn no alignment from a former station, and
which is not situated in a line with any two
visible objects already determined upon his
plan, it becomes very necessary for him to know
how to determine any station taken at pleasure.
There are different methods of solving this pro-
blem by means of three visible objects, the
positions of which on the plan are already de-
termined; the two following, however,
recommended as the best:
AND DRAWING.
39
1st Method. Having set the table horizon-
tally, and brought it into its probably true posi-
tion, fix a piece of tracing-paper over that part
of the plan which includes the three given
directing-points and the part where the present
station-point is likely to fall, and fasten it firmly
to the sides of the table with drawing-pins: fix
a needle in this last part, as, for instance, in d,
Fig. 6, Pl. 2, and draw lines of sight to the ob-
jects A, B, and C. Now remove the tracing-
paper, and fix it again on the drawing-board, in
such a manner that the three lines of sight
drawn towards A, B, and C, coincide respec-
tively with the three points a, b, and c; when
the point d pricked through the tracing-paper
upon the plan, will give the present station-
point; for it is evident that the visual rays A d,
Bd, and Cd, will form the same angles as the
lines a d, bd, and cd, by which they are repre-
sented. Apply the index to this point d and to
a, and turn the table round by the tangent-
screw, until A is seen through the sights; then,
if B and C are also seen through the sights on
40
TOPOGRAPHICAL SURVEYING
the index being similarly applied to b and c,
the table is in its true position. This is the
most simple method; but in the event of an ex-
pansion of the tracing-paper not admitting of
the station-point being determined with very
great accuracy, (of which however there is little
fear,) or of the surveyor not having any paper of
this description with him at the time, the follow-
ing, which is infallibly correct, and, after a little
practice, very expeditious, may be adopted.
2nd Method. If three lines of sight drawn
backwards through the points a, b, and c, cor-
responding to three objects A, B, and C, meet in
one point, as at d, Fig. 6, Pl. 2, this is the true
station-point; but if they do not, they will form
a small triangle efg, Fig. 7, Pl. 2, which we will
denominate the false triangle. It is therefore
necessary to know how the latter can be re-
moved, so that the lines of sight may meet in
one point.-Let A, B, and C, Fig. 8, Pl. 2, be
three objects on the ground, by means of which
the true position of the Plane-Table is to be ob-
tained. From this figure it appears that the
AND DRAWING.
41
latter may have the following situations with
respect to the triangle formed by these points
and a circle described through them :-
Within the triangle, as at d;
Without the triangle and within the circle, as
at e;
Without the triangle and opposite to an angu-
lar point, as at ƒ;*
Without the triangle, opposite to one of its
sides, and without the circle, as at g.
Two other cases might be added; namely, in
one of the sides of the triangle, and in the circum-
ference of the circle. The former situation, how-
ever, being in an alignment with two objects,
may be easily determined by a back intersection
from a third object, as already explained; but
the latter is indeterminable, for at every station
in the circumference, the angles formed by the
lines of sight directed to A, B, and C, forming
angles standing upon equal arcs, will intersect
* It is to be considered opposite the angular point, when
situated within the prolongations of the two sides of the tri-
angle by which such angle is formed.
42
TOPOGRAPHICAL SURVEYING
in one point, however false the position of the
table may be; for which reason, it is very
necessary, in choosing the three objects, to ob-
serve that your station does not lie in the cir-
cumference of a circle described through them.
Suppose de ƒ g, Fig. 9, Pl. 2, to be the false
triangles produced in the above four cases; then,
to find the true station-point in each, observe
that—in the first, as at d, the station-point lies
within the false triangle;
In the second and third, as at e and f, it lies
on that side of the intermediate line of sight,
which is reversed to the false triangle ;
In the fourth, as at g, it lies on the same side
of the intermediate line of sight, as that on
which the false triangle is situated.
Now, since the sines of equal angles of cor-
rection are in the same proportion as their radii,
after having found, by the above observations,
whereabouts your station-point will fall, deter-
mine its exact position by the following Rule:--
Let the distance of the station-point from each
of the lines of sight be in the proportion of the
distance of the station from each of the three
AND DRAWING.
43
objects, respectively. Thus, at d, the respec-
tive distances from the station to the objects
A, B, and C, or from the probable station-point
to the three points a, b, and c, are nearly in
the proportion of 1, 1, 3; which proportion
must consequently be given to the distances
from the station-point s to the lines of sight re-
spectively. Now fix a needle in the present
adopted station-point s, apply the index to it and
to one of the points a, b, and c, and turn the
table round by the tangent-screw, until the cor-
responding object upon the ground is intersected
by the hair in the object-sight. Apply the in-
dex to the other two points successively, and if
the corresponding objects upon the ground are
also seen through the sights, the present station-
point is the true one; if they are not so, efface
the former lines, direct the index again to the
three objects, and draw fresh lines of sight;
these will form a new, though very small false,
triangle, which must be made to disappear by
the same rule. The surveyor will very soon be
enabled to determine the true point by means of
the first false triangle; it very seldom happens
44
TOPOGRAPHICAL SURVEYING
that more than two such triangles are formed.
To prevent mistakes, and to facilitate the solu-
tion of the problem, the proportions of the dis-
tances from the station to the objects should be
respectively marked upon the lines of sight, as
in Fig. 9.
It is scarcely necessary to remark that, in
practice, neither the circle nor the triangle re-
quires to be drawn; but merely small portions
of the three lines of sight upon that part of the
board where the station-point is expected to
fall.
In choosing the objects by which the required
station-point is to be determined, according to
either of these methods, you should endeavor
to have the farthest situated at a greater dis-
tance from the station than any of the objects
which are to be determined from it, since the
position of a line can be determined with much
greater accuracy according to that of a longer
than of a shorter one; and you would do right
to choose two distant objects and a near one, or
two near objects and a distant one, whose situ-
AND DRAWING.
45
ation shall cause the lines of sight drawn back-
wards from the two most distant objects, as in
the first instance, or from the two nearest, as in
the second, to intersect each other in an angle
not less than 40°.
INSTANCES IN WHICH LINEAR MEASUREMENT
MAY BE REQUIRED.
In general, this method of surveying with the
Plane-Table requires no linear measurement be-
yond that of the base, but it will sometimes
happen, in flat countries much covered with
wood, that the surveyor cannot determine his
station in the manner explained, on account of
the objects already drawn upon his plan being
entirely concealed from his view. He must then
have recourse to measuring station-lines, much
of which, however, may be avoided by his pre-
viously determining a number of the most con-
spicuous objects in the interior of the wood,
(such as particularly high or remarkably shaped
trees), from more elevated or commanding situ-
46
TOPOGRAPHICAL SURVEYING
ations on the outside, and principally by his at-
tending to this general rule in surveying, namely,
to work from the highest and most open towards the
lowest and most covered parts, so that when he
arrives at the latter, he finds a sufficient number
of points already determined on his plan to
enable him to fill in the detail, or at all events
requires but very few new stations.
If an
extensive flat wood possess no conspicuous
objects, or not a sufficient number of them,
but the tops of the trees in the interior can
be seen from a few stations on the outside, it
will be a good plan to let an assistant ascend
such trees in the wood as are situated close
to the principal bends and intersections of the
roads and streams; and when at the top of each
wave a white flag. The lines of sight drawn
towards these trees from one station should
be numbered, and the assistant be previously
desired to number the latter, and ascend them
in the same order when their situation on the
plan is to be determined by intersecting the
former lines respectively from another station.
In this way, an active and intelligent assistant
AND DRAWING.
47
might prevent a surveyor having occasion to
measure a single line in this description of coun-
try.
A compass attached to the Plane-Table might
be used with advantage in delineating the course
of a road or a river in a plain covered with
thick wood, in cases where the degree of accu-
racy afforded by it is considered sufficient.
Thus the surveyor could rectify the Plane-Table
at the different bends and intersections of the
roads, &c., (by placing it so as to have the
needle always directed exactly to the same
point), draw lines of sight from one station to
the other, and measure the distances between
them. The following, however, is the most
correct method of obtaining the above delinea-
tion by means of the Plane-Table alone.
Suppose a, Fig. 10, Pl. 2, to be the entrance of
a road into a wood, which has been determined
upon the plan, and that it is required to deli-
neate the course of the road through the wood.
After having fixed the table in its true position,
by means of some objects situated without the
wood, draw a line of sight from a towards the
48
TOPOGRAPHICAL SURVEYING
first principal turning of the road which you
can see from a, for instance, b, where a paper-
mark should be placed by an assistant. Before
you remove the instrument from a, fix a mark
in the direction of a b, either before or behind a,
as at c. Measure the distance ab, and fix the
table again in the direction of a b, either behind
or before b, as at d, bringing the line ab upon the
plan, into a vertical plane with its correspond-
ing one on the ground: set off the measured
distance from a along the line of sight a k, and
add to it that of d from b; by which means the
present station-point is determined. The wind-
ing of the road between a and b is then very
easily determined by the eye. Now direct the
index to the next mark set up at e; leave another
one at ƒ in this direction; measure the distance
de, and fix the instrument either before or be-
hind e, as at g; set off the measured distance
de+eg from d along the line of sight drawn
in this direction, whence you will determine
the station-point g. Proceed in the same man-
ner with that part of the ground between e and
Suppose that some conspicuous objects
h.
*
}
AND DRAWING. :
49
within the wood have been determined from
previous stations taken on the outside, and that
i is one of them. Then, when the surveyor is
at g, he should place the index along g and the
determined object on the plan, and proceed in
this direction of the index, through that part of
the wood between these two points, to search
for the object i, which, if found in this direction,
proves the work to be correct; if not, some
error in the latter has been committed, which
must be rectified as soon as possible.
TO CARRY ON THE WORK FROM ONE SURVEY-
SHEET TO ANOTHER.
WHEN the extent of ground requires more than
one survey-sheet, it will be advisable to have
three or four drawing-boards made to fit the
same stand. Always allow of an inch margin
upon your board, upon which you can determine
any conspicuous objects which properly belong
to the adjoining sheets. Let the distances of
such points, should there be any, as well as of
E
50
TOPOGRAPHICAL SURVEYING
others within the marginal line of the survey-
sheet, from the latter and from one another, be
accurately transferred to the adjoining sheet
upon another board. The margin is also of
very great advantage to the surveyor when
working near the sides of the sheet, since it
frequently happens that a part of the ground
can be more easily seen from that which comes
into the adjoining sheet; upon the margin of
which, the situation of the objects upon such
ground can be determined, and afterwards
transferred to their corresponding one in the
plan.
When the survey is connected with trigono-
metrical operations, and two or more points are
given upon each survey-sheet, then, instead of
the work being carried over from the marginal
line of one sheet to the corresponding one of
another, it must be commenced in each sheet
from these points.
AND DRAWING.
51
GENERAL RULES IN TOPOGRAPHICAL
SURVEYING.
PREVIOUSLY to the actual commencement of the
topographical survey of a country, proceed to
such points as afford the most commanding
views, and note down those best calculated for
the main stations, in the order which you con-
sider the most advantageous for the survey.
If the scale is rigidly prescribed, and no
points previously determined are given, and
you are consequently obliged to commence a
survey by measuring a base upon a piece of
level ground, let your order of stations be such
that you arrive as soon as possible to the higher
and more commanding ground.
If two points determined by a previous trigo-
nometrical survey are given on your survey-
sheet, repair to them, and note down the order
of stations to which the features of the country
seem most favorable, according to which of the
52
TOPOGRAPHICAL SURVEYING
three cases mentioned at page 42, applies to the
two given points.
In determining the position of objects, let the
lines of sight intersect each other in angles of
not less than about 30°; if the intersection be
more acute, the object should be determined by
another line of sight.
Complete as much of the survey as you can,
from the higher and more open ground, so as to
leave as little as possible to do in that which is
lower and more intersected. The facility and
expedition which this mode of proceeding en-
sures to the work, are very considerable. Thus,
from a few stations on the highest parts of the
sides of a valley, all, or the greater part of the
objects situated within it, can be determined on
the plan, sometimes indeed without requiring
the surveyor to descend into it, and in general a
station or two, here and there, on the lower
ground, will serve to complete what has been.
surveyed from the heights.
When towns or villages come into the survey,
determine from the outside, and, if possible from
commanding ground, their boundaries, and the
AND DRAWING.
53
most conspicuous objects within them, such as
spires, vanes, chimnies, or gable ends of the
most remarkable buildings, and draw the re-
mainder on your board by the eye* when you
enter them.
To keep your drawing-board free from all un-
necessary pencilling, let the remarks by which
you distinguish the different lines of sight be as
short as possible, such as for chimney; A for
gable end; b of rd, rt, or c', for bend of road,
river, or canal; hn, or 1 o, for high or low tree;
ab. for above; be. for below, &c.
In determining your station by means of either
an alignment or three points already laid down
on your plan, choose such objects as are situated
at a greater distance from you than any others
which you intend to determine from such station.
* In this and in other places where it is recommended to
draw anything by the eye, I refer of course to the usual topo-
graphical surveying scale of five or six inches to the mile;
but, when a much larger scale is adopted, the surveyor can
either take a few more stations, or have recourse to the com-
pass attached to his drawing-board.
54
TOPOGRAPHICAL SURVEYING
TOPOGRAPHICAL SCALES.
TOPOGRAPHICAL maps are usually drawn upon
1
1
1
1
scales of from 100,000 to 50.000 of the extent of
the country represented. In that of 100,000 we
can express every considerable hill, stream,
wood, town, and village, as also the main roads,
and principal cross roads.
The scale of 50,000
(about 1 inch to of a mile) admits of the repre-
sentation of every hill having an altitude of 100
feet, and an horizontal extent of from 700 to
800 feet; of every stream having a length of
course equal to 800 feet; of every pond having
a diameter of 100 feet; of every wood extending
from 200 to 300 feet; of all roads, towns, vil-
lages, and isolated large buildings. These scales
are well adapted to the topographical represen-
tation of an extensive tract of country, and are
particularly convenient for the study of military
operations, though more in a strategical than
tactical point of view.
The scales of topographical plans vary, ac-
AND DRAWING.
55
cording to the purposes for which they are
1
1
1
drawn, from 50,000 to 6,000. In that of 25,000
(about 2 inches to a mile), the various confor-
mations of ground can be clearly and faithfully
expressed; as also every stream having a length
of course not less than 300 feet; every pond
not less than 50 feet broad, and all woods,
roads, towns, villages, seats, farms, &c. This
scale is of great utility to military men, and
is made use of in the representation of any
portion of country forming the immediate seat
of war, or for reconnoissances, positions, plans
of battles, &c.
1
1
The scale of 10,000 (about 6 inches to a
mile) is the most suitable for the complete topo-
graphical representation of a country, and is
used in surveys for maps which are to be en-
graved upon that of 5000; as also for positions,
encampments, marches, &c., in which it admits
of every battalion, squadron, and battery, being
indicated in the exact proportion of the extent
of ground which it occupies, together with the
outposts, vedettes, &c.; in short, the complete
detail of a position.
56
TOPOGRAPHICAL SURVEYING
1
Scales larger than 10,000 are generally used
for plans of estates, towns, villages, fortifica-
tions, roads, canals, rivers, &c.
THE TOPOGRAPHICAL DELINEATION OF
DETAIL.
THE delineation of detail, in which I offer no
material alteration in the conventional signs and
figures hitherto in general use, is fully given in
Pl. 3.
Standing Water. This is represented by fine
lines drawn from left to right; nearer to, or fur-
ther from one another, according as the water
is deeper or shallower, and more or less curvi-
linear, as its surface is of greater extent, as in
the Lake, Pl. 3, No. 1, or of smaller, as in the
Pond, No. 1. If the boundary line of the water
is distinct and invariable, it should be marked
out in the drawing; if, on the contrary, it is
variable, it need not be expressed.
Flowing Water. In rivers, the stream is re-
presented by fine lines, which are drawn closer
AND DRAWING.
57
to each other where the water is deep, and the
contrary where it is shallow; they are also
made straighter, or more curvilinear, according
to the rapidity of the current, as shown in No. 1.
Where it is possible, the depth of the water
should be given in numbers. See No. 1. The
banks of rivers, if distinct and invariable, are
represented as such in the drawing; but if the
contrary, they are only expressed by the outer-
most of the lines which denote the stream, as in
No. 1.
The sea is represented by fine lines drawn
from left to right, and made a little curvilinear.
See No. 1.
Sand is represented by small dots, as shown
in No. 1. Stones and sand mixed together, are
shown by dots of unequal size. A specimen of
a sandy coast is given in No. 1.
Pasture is represented by very small strokes,
arranged so as to give the appearance of tufts of
grass. See Pl. 3, No. 2.
Meadow-land is represented by small dots
arranged two and two. See No. 2.
58
TOPOGRAPHICAL SURVEYING
Heath is represented by tufts of grass, with
a few shrubs or bushes. See No. 2.
Corn-fields are distinguished only in plans
drawn upon a large scale, and are then repre-
sented by a number of parallel lines arranged
as in No. 2.
Morass, Marsh, and Swamp, are represented in
No. 1.
Vineyards, Hop-grounds, and Gardens, are drawn
as in No. 2.
Trees may be represented either in ichnogra-
phical projection, or in elevation. The latter
mode of representation however is preferable;
for, by it, they are more easily distinguished,
and are not liable to be confounded with other
objects, as is sometimes the case in the former.
The common kinds of trees are shown in eleva-
tion in No. 2, both upon a large and a small
scale.
Woods may be represented by the trees being
arranged either in small groups, or singly, and
at irregular distances from each other, according
to their real appearance. See No. 2. Care
AND DRAWING.
59
should be taken that the strokes expressing the
inclination of the ground upon which the woods
are situated, be not too much concealed; which
happens if the trees are drawn too close to one
another.
Roads are represented upon different scales in
No. 2.
Stone-buildings are drawn so as to occupy
their proportionate horizontal extent on the plan,
and when upon a large scale are filled with
diagonal lines, and those sides drawn thick, or
shaded, which are opposed to the lower right-
hand corner of the plan; upon a small scale
they are altogether black. See Pl. 3, No. 3, in
which are represented Houses, Churches, Mills,
a Town, a Village, &c.
Walls and Hedges are shown in No. 3, as are
also the different kinds of Bridges and Ferries.
For the Geographical and Military Signs, see
also Pl. 3.
60
TOPOGRAPHICAL SURVEYING
THE TOPOGRAPHICAL DELINEATION OF
GROUND.
THERE are four methods by which ground is
generally represented in topographical plans
and maps; first, by means of single shading
lines (or strokes ;) second, by means of shading
lines crossing one another, (crossed pen-work;)
third, by means of shading with diluted Indian
ink, with the addition of shading lines; fourth,
by means of shading with diluted Indian ink,
without the shading lines (generally adopted in
the light and shade system.)
These shading lines express, by their direc-
tion, that of the descent of the declivities which
they represent, and also by the gradations of
shade which they are made to produce, the cor-
responding gradations of inclination which these
declivities assume.
With respect to the first-mentioned property
of these shading lines or strokes, there can be
but one rule laid down, since the only true
AND DRAWING.
61
direction of the descent of a declivity is that in
which water would take its way, upon issuing
from the higher parts, or in which a heavy body
would roll in its course from the top to the bot-
tom. But, with respect to their last-mentioned
property, different rules have been proposed and
adopted.
On the continent, and more particularly in
Germany, systems of representing ground have
been adopted, in which every degree of inclina-
tion of a declivity is expressed upon a plan with
great mathematical precision, by means of cer-
tain proportions observed between the distances
of the shading lines from one another, or be-
tween the thickness of each shading line and its
adjoining white space, or by means of a certain
length given to the shading lines. These sys-
tems, however perfect and beautiful in theory,
are by no means readily reduced to practice; on
the contrary, they require from the draughtsman
the utmost nicety in the estimation of minute
proportions, and entail upon the surveyor a vast
deal of labor and inconvenience. In this coun-
try the delineation of ground is founded either
62
TOPOGRAPHICAL SURVEYING
upon the simple principle of relative steepness
being expressed by a corresponding relative
intensity of shade, or upon that of rays of light
proceeding from a point at an indefinite distance
and meeting the horizon in an angle of 45°, com-
monly called the light and shade system. The
former is the mode generally practised, though
no where so successfully, and with so much
beauty of execution as at the Royal Military
College; the latter is only resorted to by
draughtsmen who aim more at
more at effect than
utility in a topographical drawing.
I shall now explain the improvement which I
have made in the topographical delineation of
ground, which consists,
1st. In the introduction of horizontal sections
at certain vertical distances from each other,
with a ready and easy method of tracing them
on a survey-sheet, and
2ndly. In the adoption of a very simple rule
for regulating the shading of declivities, founded
on the principle of the British system, namely,
that of expressing relative steepness by a cor-
responding relative intensity of shade.
AND DRAWING.
63
In drawings made according to the light and
shade system, it is evident that the introduction
of horizontal sections is alone applicable; but
as these not only do not interfere with the effect
which that system of shading is intended to
produce, but serve to correct the errors so gene-
rally consequent upon the endeavors to attain
such effect, this improvement itself is of great
importance.
The ground is divided, according to the scale
of the survey, and the nature of the country, into
a certain number of horizontal sections at equal
vertical distances, and these are marked in the
drawing, together with their respective altitudes
above either the lowest point of the country, or
the level of the sea, so that the relative heights
of all points are at once shown upon a plan
without further reference. The vertical dis-
tances between the horizontal sections may be
determined by the surveyor according to the
professed object of his survey: the following
rules, however, appear to me well adapted to all
purposes:-
Suppose the scale of the survey to be about
64
TOPOGRAPHICAL SURVEYING
1
10,000 of the extent of the ground, or about six
inches to a mile; then, if the nature of the
country be mountainous and rocky, let the ver-
tical distance between every pair of horizontal
lines be 100 feet; but, if it be merely hilly, or
flat, let 50 feet be the difference of altitude.
25,000,
Suppose the scale to be, or about 24
inches to a mile; then, if the nature of the
country be mountainous and rocky, let the ver-
tical distance between every pair of horizontal
lines be equal to 300 feet; if it be hilly, 200
feet; and, if flat, 100 feet.
1
Suppose the scale to be 60,000 or about 1 inch to
of a mile; then, if the nature of the country be
mountainous and rocky, let the vertical distance
between every pair of horizontal lines be equal
to 500 feet; if it be hilly, 300 or 200 feet; and,
if flat, 200 or 100 feet, according to circum-
stances.
In the larger plan in Pl. 6, the horizontal
sections are placed at 50 feet vertical distance
from each other; in the smaller plan, 200 feet.
In the plan, Pl. 5, they have a difference of alti-
tude of 300 feet.
AND DRAWING.
65
In determining the vertical distances between
the horizontal lines in topographical maps, we
must also be guided by the size of the scale and
the nature of the country; but since maps fre-
quently embrace an extent of country, of which
some portions may be mountainous, some hilly,
and others flat, the vertical distances should
vary accordingly, and the altitudes of the hori-
zontal lines should be marked upon the latter
in several places, to prevent any misconception.
In such cases, an explanatory note might also
be given on the margin or any other conve-
nient part of the map. The horizontal lines on
the small map of a mountainous country in Pl. 5,
are placed at 600 feet vertical distance from one
another.
It now remains to be shown in what manner
these horizontal sections can be readily deter-
mined in the survey.
When drawing lines of sight from your sta-
tions for the purpose of obtaining the positions
of the different objects composing the detail of
the country, it will give you very little trouble
to mark the greater part of them with the num-
F
66
TOPOGRAPHICAL SURVEYING
ber cut off by the cross-hair in the object-sight
of the index, in order to ascertain, subsequently,
the heights of the objects above, or their depths
below the stations, respectively, according to
the simple rule given at page 12, namely, by
multiplying the number cut off, by the distance
from the station to the object, ascertained by
means of the scale of the plan. In Fig. 7, Pl. 7,
two lines of sight are drawn from * 1, marked
the one; 259 above o 1, and the other, 204
above 1; and also one, marked 05 below
o1; or, for the sake of brevity, 259 a 1,-
204 a 1,-and 05 b 1. The affixing of these
numbers to the lines of sight is of course a part
of the out-door work; the multiplying of them
by the distances from the objects to the stations
belongs to the in-door work.
When the heights above, or depths below, the
respective stations have been noted in the in-
door work, as shown in Fig. 8. (corresponding
to Fig. 7,) apply to the drawing-board a piece
of tracing paper large enough to cover the
O signifies station, and station-point.
AND DRAWING.
67
whole survey-sheet; trace upon it such station-
points and objects as have been determined
during the day, together with their heights or
depths as shown in Fig. 8, and then efface
these numbers from the board, which will con-
sequently become similar to Fig. 1. When the
whole detail has been entered into the survey-
sheet, and the heights or depths traced as above,
alter all the numbers marked on the tracing-
paper according to the highest or lowest point
of the country. Thus, suppose Fig. 8, to be
part of the tracing-paper, then since o is
marked 50 feet above the lowest point, 02 will
be 50-20=30 feet; the object e, 259+50=309
feet; the object ƒ, 320+50=370 feet; and the
object g, 50-40-10 feet, above the lowest point.
These altered numbers are then affixed to their
respective objects on the board, which conse-
quently assumes the appearance of Fig. 2.
The drawing-board being thus prepared, I
propose three different methods of laying down
the horizontal lines, any one of which the
draughtsman can adopt according to his incli-
68
TOPOGRAPHICAL SURVEYING
nation and the degree of accuracy required in
this respect.
It
1st Method. The most simple and expedi-
tious way is to lay down the horizontal lines, by
the eye, so as to agree with the marked heights
of the various objects of the detail near which
they pass, regard being at the same time had to
the direction and formation of the declivities.
must be evident to every one, upon a view of the
plan of the vicinity of Ledbury, Pl. 6, that more
than sufficient data are offered for this purpose
by the numerous intersections formed by hedges,
roads, and lanes, together with the conspicuous
objects, as houses, isolated trees, summits, &c.
2nd Method.
tion, Fig. 5, Pl. 7, and draw c d parallel to the
base a b, and at a distance from it equal to the
height of the horizontal sections above each
other, namely, 50 feet.
between the point c and the intersections of the
line c d with the lines forming the angles 45º,
40°, 35°, &c. are respectively equal to the dis-
tances between every pair of horizontal lines
Construct a scale of inclina-
Then, the distances
AND DRAWING.
69
under corresponding angles of inclination. Sup-
pose yourself upon the ground, at the upper
corner of the little pool P, near the lower left-
hand corner of the outline-plan, Fig. 3, Pl. 7.
The height of this being marked 130 feet, you
know that it lies between the 2nd and 3rd
horizontal sections; namely, 30 feet above the
2nd, and 20 feet below the 3rd. The angle
of inclination of the ground at this place (which
you may estimate by the eye, or measure by
means of the index of the Plane-Table, accord-
ing to the degree of accuracy necessary, or the
expertness you have acquired in this respect,)
is about 10°. Take therefore the corresponding
horizontal distance from the line c d, Fig. 5, in
the compasses, and since the vertical distances
from P to the two nearest horizontal sections are
as 3 to 2, place the feet of the compasses in
such a manner, by the eye, that the horizontal
distances Pe, and Pf, be also in this proportion:
e will then be situated in the section marked
150 feet, and ƒ in that marked 100 feet. Now,
to carry on the horizontal sections through e and
f, observe what objects on the right and left
70
TOPOGRAPHICAL SURVEYING
have their heights marked on the drawing-board.
On the left, at a little distance, the height of
the corner of a field, h, is marked 120 feet.
This point is therefore also between the 2nd
and 3rd horizontal sections; namely, 20 feet
above the former, and 30 feet below the latter,
Take in the compasses, from the scale of incli-
nation as before, the breadth between the two
horizontal sections, corresponding to the angle
of inclination at this part of the ground, which
is about 7º, and since the difference in height
between h and the 2nd horizontal section, is to
that between it and the 3rd one, as 2 to 3,
place the compasses so that, by the eye, hi
may be to h g as 2 to 3, or nearly so. You
have now only to draw the two horizontal lines
through e and g, ƒ and i, and to continue them
to the left side of the plan, according to the form
of the ground. On the right of P, the house
marked 148 feet, and another on the road near
the New Pool marked 150 feet, the spring S and
east corner of the New Pool, both marked 97
feet, form a sufficient guide for drawing the
2nd and 3rd horizontal sections in this part of
AND DRAWING.
71
the ground. The first section (50 feet) is also
easily laid down in this part, by means of the
two corners of fields q and r, marked 44 and 57
feet; namely, by making the line pass a little
above the former, and below the latter, and
also at right angles with the direction of the
ground.
This method of laying down the horizontal
lines is sufficiently correct for the general pur-
poses of plans, the scale of which does not
exceed that of six inches to a mile. They are
certainly not drawn with great mathematical
precision, and their position may frequently be
1
20
TO
1
or even of an inch distant from the true
one; but is it not sufficient that they indicate
the general direction of the horizontal sections,
and that they show at once the relative heights
of all objects? That they can be laid down with
extreme accuracy, will be shown presently by
the third method, suitable for plans drawn upon
a larger scale; but I have purposely refrained
from applying it myself, or recommending its
application by others, to plans upon a scale not
larger than six inches to a mile; conceiving
72
TOPOGRAPHICAL SURVEYING
such minuteness to be not only a waste of time,
but wholly unnecessary.
3rd Method. Suppose the plan of the vici-
nity of Ledbury to be drawn upon a scale as
large again; namely, twelve inches to a mile.
Then, in the same example, take, in the com-
passes, the difference in height between P and
the 3rd section; namely, 20 feet, and apply it
in such a manner to the scale of inclination,
Fig. 6, that one point may touch the base a b,
and the other the angular line marked 10°,
(keeping the direction of the points perpendi-
cular to the base,) the angle of inclination at
this part of the ground; by which means, the
distance a e Fig. 6, is obtained, equal to the
required horizontal distance (doubled) P e. In
a similar manner, the distance a f, Fig. 6, is
obtained equal to the required horizonal distance
(doubled) Pf. Should it be required to place
the instrument at e and f, on the ground, for the
purpose of carrying on the horizontal lines with
very great accuracy, the distances Pe and Pƒ
may be measured along the slope e ƒ, respec-
tively equal to those between a and the tops of
AND DRAWING.
73
the perpendiculars at e and f, Fig. 6, taken
from the scale. In plans upon so large a scale,
of course the heights of a greater number of
objects will be marked upon the drawing-board.
In tracing the horizontal lines according to
any one of the preceding methods, the sur-
veyor should, at the same time, sketch upon
his drawing-board, lightly with a pencil, the
features of the ground, in doing which he will
experience no difficulty whatever, since the di-
rections of the ridges, water-courses, ravines,
&c. depend entirely upon those of the horizon-
tal lines, as shown in Pl. 4, 5, and 6.
Although few portions of ground exhibit so
great a variety of objects, such as houses, iso-
lated trees, intersections of roads, lanes, hedges,
&c. as exist in the vicinity of Ledbury, still the
surveyor need never be at a loss for a sufficient
number of points by which to determine the
horizontal sections. In a mountainous and
rocky country, where neither houses, trees, nor
roads are met with, such as that represented in
74
TOPOGRAPHICAL SURVEYING
Pl. 5, conspicuous or peculiarly shaped rocks,
intersections of water-courses, ravines, rivu-
lets, &c. offer together with the stations, nume-
rous points by which the horizontal sections
can be determined. In a flat country, fewer
points are required, on account of the greater
distance between the horizontal sections; but
even supposing a difficulty in this respect to
present itself at any time, the surveyor, or his
assistant, can very easily set up a few marks,
such as flags, long sticks with white paper
attached to them, &c.
The system of horizontal sections in topo-
graphy is not new; it has been partially adopted
in France, especially in cases of ground sur-
veyed with a view to the construction of fortifi-
cations, and it is at present taught in the prin-
cipal military schools of that country; it is more
particularly the improvement in the practical
part of this system, namely, in the tracing of the
horizontal sections in the readiest and simplest
manner, which I offer as original, as infinitely
preferable to the laborious mode of tracing these
AND DRAWING.
75
sections by means of levelling, and as suffi-
ciently correct for all the purposes of topogra-
phical drawings.
*
When, in an extensive survey, certain points,
trigonometrically determined, are given to the
topographical surveyors, by which their work is
* The horizontal sections in the plan of the vicinity of
Ledbury have been laid down according to the heights of dif-
ferent objects obtained in that survey by means of an index
very inferior to, and indeed imperfect in its construction when
compared with, the greatly improved one already described.
I regret exceedingly that circumstances have prevented me
from adding to the present work a plan in which the above
simple mode of delineating the horizontal lines has been em-
ployed in the survey itself. I did, however, commence a survey
for that purpose last summer, during a short leave of absence
which had been granted me for the benefit of my health; and
had the satisfaction to find that the method I have adopted
and recommended, fully answered my most sanguine expec-
tations; but a second and very severe illness prevented me
from completing the survey, and, upon regaining my health
in some degree, I was under the necessity of returning to the
duties of my situation. Should the present work, however,
be so far favorably received as to require a second edition, I
shall not fail to add to it a survey of some portion of inter-
esting ground, with a detailed explanation of its execution.
76
TOPOGRAPHICAL SURVEYING
to be guided, the altitudes of these points above
the level of the sea should also be given to guide
them in constructing the horizontal sections
according to this level, and at the required
vertical distance between each pair, by which
means the sections in all the survey-sheets will
be made to correspond, and thus to coincide
respectively at the marginal lines.
The improvement which has been proposed
in the delineation of ground, renders it op-
tional on the part of the draughtsman whe-
ther to make use of single or crossed shading
lines, either of which may be made to produce
a pleasing effect; but, if from a topographical
drawing an engraving is to be made, the single
shading lines are most suitable. It may be further
observed that a good draughtsman will generally
prefer drawing with single shading lines, since
with these he can express more freely the va-
rious directions which the features of the ground
assume, and can finish his drawings in one half
the time required by the crossed shading lines.
This simple mode of laying down horizontal
lines according to the determined heights of the
AND DRAWING.
77
objects marked in the outline of a topographical
drawing, possesses also the very great advantage
of superseding the necessity of recourse being
had to any of those rigorous and minute systems
of shading in the representation of ground, which
have obtained so much on the continent.
shading ground according to the British system,
that is, in expressing relative steepness by rela-
tive intensity of shade, it is obvious that the
horizontal lines offer one plain and general rule,
namely, that the shade encreases or diminishes
in proportion as these lines approach towards,
or recede from, one another. But as it is
very
desirable that uniformity in the representation
of ground should be preserved in all topographi-
cal drawings, it is necessary that some fixed
standard should be adopted for the guidance of
draughtsmen. This, I conceive, may be easily
deduced from the principles of the British sys-
tem, in the following manner :-The two ex-
tremes of the inclinations of ground, are the
horizontal plane and the angle of 45°; and, if
the former is to be expressed by the fullest
light, or perfect white, and the latter by the
78
TOPOGRAPHICAL SURVEYING
deepest shade, or perfect black, it is evident
that the due proportion of light to shade cor-
responding to any particular angle of inclination
would be that of its supplement to the extreme
angle 45°, to the angle itself; thus, the propor-
tion of light to shade corresponding to the
angle of inclination of 5° would be as 40 to 5;
that of 10°, as 35 to 10; that of 15º, as 30 to 15,
and so on. I therefore distinguish three of
the angles of inclination, namely, 15°, 221º (the
mean angle,) and 30°, (see Fig. 7, Pl. 4,) which,
with the two extremes, serve to regulate the
shading of declivities in the easiest and simplest
manner, for, according to the above, the pro-
portion of light to shade required to express the
angle of inclination of 15°, is as 2 to 1; in the
mean angle 2210, the light and shade are in
equal quantities; and, in the angle of 30°, the
proportion of light to shade is as 1 to 2. Hence
follows this general Rule. That, in viewing the
ground represented in a topographical drawing,
1st. Wherever the quantity of light predomi-
nates over that of shade, the inclination of the
ground does not amount to 220, but wher-
AND DRAWING.
79
ever the contrary takes place, it exceeds this
angle:-
2nd. Wherever we observe the quantity of
light to be more than double that of shade, the
inclination of the ground does not amount to
15°:-
3rd. Wherever the quantity of light is not so
much as double, nor less than half that of shade,
the inclination of the ground is between 15 and
30°:—
4th. Wherever the quantity of shade is more
than double that of light, the inclination of the
ground exceeds 30°.
This rule is sufficient for all practical pur-
poses, particularly as we are enabled by means
of the horizontal lines and the scale of inclina-
tion, to ascertain, if required, the general slope
between the former at any place; and to exact
from the draughtsman a more rigid observance
of the proportions of light and shade required
in expressing the inequalities of ground, would
be to impose a restraint which would have the
effect of producing a stiffness in that part of his
80
TOPOGRAPHICAL SURVEYING
drawing, in which a freedom of hand is so very
desirable.
The utility of this rule in a military point of
view is obvious; for,
1st. Wherever the quantity of light is more
than double that of shade, the ground admits of
manœuvres:
2nd. Wherever the quantities of light and
shade are equal, or nearly so, the ground can
be ascended and descended obliquely by light
cavalry :-
3rd. Wherever the quantity of shade predo-
minates over that of light, riflemen and light
infantry are the most suitable description of
troops to be employed.
Since rocky declivities generally exceed in
their inclination the angle of 45°, and there-
fore require to be represented by perfect black,
it is necessary, in order to assist the reader of a
topographical plan, to affix to their summits, or
ridges, their altitudes in numbers, and to annex
vertical sections of them, as in Pl. 5. Recourse
is sometimes had to perspective drawing for this
AND DRAWING.
81
purpose; it is, however, a departure from the
principle of relative steepness being expressed
by relative intensity of shade, and generally
requires, in order to produce effect in the draw-
ing, an encrease of the horizontal extent occu-
pied by the rocks, which must evidently occasion
a distorted and consequently an incorrect repre-
sentation of the adjacent ground.
To beginners in topographical drawing, I
would recommend the copying, upon separate
pieces of paper, of the figures in Pl. 4, in order
to acquire a free use of the pen in expressing
the declivities of hills, and their connexion
with one another. The horizontal lines should
be drawn first; then the shading lines or strokes,
commencing with the uppermost rows, and
taking care to draw the latter always at right
angles with the former. The fine strokes should
be drawn with the side of the pen, the full ones
with the broad part of the nib.
82
TOPOGRAPHICAL SURVEYING
CLASSIFICATION OF GROUND.
THE component parts of the various conforma-
tions exhibited by the earth's surface may be
classed in the following order:—
1st. Summits, or the uppermost parts of hills.
See a,* Fig. 1, 2, 3, 4, 5, and 6, Pl. 4.
They may be
2nd. Declivities, or slopes.
straight, as a b, Fig. 2, Pl. 4; concave, as a b,
or a c, Fig. 1; convex, as a b, or a c, Fig. 4 ; or
rocky, as bc, Fig. 6.
3rd. Ridges. They are formed by the upper
intersections of declivities, and, according to the
degree of obtuseness or acuteness of these inter-
sections or joinings, are called broad or narrow.
See the narrow ridge in Pl. 6, which enters the
plan at A, extends to the gap or opening O,
by which it is interrupted, and is thence conti-
* The letters in Pl. 4, are affixed to the corresponding
outline figures, in order that they may be more distinctly
seen.
AND DRAWING.
83
nued, in nearly the same direction, under the
name of the Dog Hill.
4th. Water-courses. They are formed by the
side intersections of the declivities. See ƒ g,
de, hi, and k l, Fig. 6.
5th. Ravines. They are formed by the lower
intersections of the declivities. See o p, Fig. 6.
6th. Defiles, or narrow passes between steep
or rocky declivities. See pc, Fig. 6.
Although the conformations themselves do
not, on account of their infinite variety, admit
of a regular classification, still there are some
hills whose forms are of more frequent recur-
rence, to which corresponding names are accord-
ingly given. These are-
The conical hill or peak, the sides of which
have a concave inclination, and terminate in a
very small summit, Fig. 1, Pl. 4.
The slanting hill, which is of an oval shape,
having a steep slope at one extremity, and a
gentle one on the opposite side, the inclination
of which is less than, or does not much exceed
10°. Fig. 2.
84
TOPOGRAPHICAL SURVEYING
The table hill, which has a broad and level
summit. Fig. 3.
The vaulted hill, the sides of which have a
convex inclination. Fig. 4.
The saddle hill, so named from its saddle-like
shape. Fig. 5.
TO CONSTRUCT VERTICAL SECTIONS OF THE
GROUND REPRESENTED.
THE Construction of vertical sections, which are
sometimes required for the purpose of showing
the contour or profile of the ground in any par-
ticular direction, is rendered extremely simple
and easy by means of the horizontal sections
already drawn upon the plan. It is evident
from a view of Plates 4, 5, and 6, that a line
being drawn in the direction of which a section
is required, it is only necessary to transfer from
it, to another of equal extent, the distances
between the horizontal lines by which it is inter-
sected; to erect perpendiculars at these points,
AND DRAWING.
85
and to draw as many parallel lines to the base
as there are horizontal sections, at the pre-
scribed vertical distances between them; and
then to join the intersections made by these
perpendiculars and parallel lines, paying at the
same time due attention to the contour of the
ground in the intermediate spaces.
TO ASCERTAIN THE BOUNDARY OF VIEW FROM
ANY POINT UPON A PLAN.
It is frequently important to know, more espe-
cially in military surveys, what parts of the
ground are visible from any particular point.
This is easily ascertained by means of vertical
sections, the construction of which has been
explained. Thus, suppose it is required to find
what parts of the ground are visible to an ob-
server, standing upon the summit of Kilbury
Camp Hill, Pl. 6, (at a in the section A B,) and
looking towards the summit eastward of the
Hill Farm.
86
TOPOGRAPHICAL SURVEYING
Draw a tangent from a to b in the section
A B, and produce it, until it meets the profile-
line by the Eastnor road. This tangent plainly
shows that that part of the ground which is
situated between a and b, is visible to the ob-
server at a; but that the remainder between b
and the above-mentioned road, is concealed
from his view. Draw also a line from a to
the height marked c, corresponding to the
summit eastward of the Hill Farm; from which
it appears that the ground between the road
and the summit is visible to the observer
at a.
Suppose, again, it is required to find what
parts of the ground are visible to an observer,
standing by the hedge on the summit of Kil-
bury Camp Hill, which corresponds to h in
the section A B; and looking in the direction
of A.
Draw a tangent from h to the tops of the
trees at t, and produce it to meet those which
are upon the height A; draw also d h, a tan-
gent to the ground at h; whence it appears
that, with the exception of the foot of Kilbury
AND DRAWING.
87
Camp Hill, the whole of the ground bstween h
and the Mitchell Wood, and a part of the latter,
are visible to the observer at h; but that the
remaining part of the wood, excepting a very
little at A, is concealed from his view.
INSTRUCTIONS
IN
TOPOGRAPHICAL MODELLING.
INSTRUCTIONS
IN
TOPOGRAPHICAL MODELLING.
INTRODUCTION.
NOTHING can tend more to facilitate the ac-
quirement of a proper knowledge of physical
geography than the study of models of different
portions of the earth's surface. Maps and
plans, owing to the multiplicity of lines required
both in the delineation of topographical detail
and in that of the features of ground, soon
fatigue the eye, even of a person long habituated
to the use of them, and rarely succeed in
impressing upon the mind that correct and
distinct image of nature which we derive from
the view of models. In the latter, we have all
92
TOPOGRAPHICAL MODELLING.
the various conformations of ground standing
before us in relief; we perceive at once the
directions and relative heights of the main ridges
and of their different ramifications, the courses
of the principal rivers and the confluence of
their tributary streams, the various land and
water communications, the woods, habitations;
in short, we see all the objects situated upon
and composing the surface of a country, repre-
sented in so clear and distinct a manner, by
the aid of form and color, that a child cannot
mistake them. On the other hand, a map
requires previous study, obliges us to estimate
the inequalities of surface from the strength
of the shading lines and other conventional
signs, (though, in this respect, the greatest
possible facility is derived from the improve-
ments which have just been explained,) and
admits only of very small portions being exa-
mined at a time; whence a just conception of
the whole face of the country and of the rela-
tive properties of its different features cannot
be so readily formed, nor so strongly and faith-
fully impressed, as by the view of a model.
TOPOGRAPHICAL MODELLING.
93
This view is, in fact, preferable to any which
can be had even upon the ground itself; and it
is this, or rather the knowledge we acquire by
such a view, which the leader of an army would
be most anxious to possess of a country, on the
capabilities of which his dispositions must
entirely depend.
The importance of Topographical Modelling
in a military point of view is sufficiently obvious:
-the government, in possessing a model of the
country which has become the seat of its mili-
tary operations, can more fully enter into, and
more justly appreciate the dispositions taken
by the general, to whom it has entrusted the
command of its army;-the comparison of models
of celebrated fields of battle with authentic
descriptions of the military movements by which
they have been distinguished, forms an impor-
tant branch of military study; for by means of
them, the whole scene of action is brought at
once to our view, we see the extent and nature
of the ground, we are enabled to discern clearly
the advantages and disadvantages, as also the
relative strength of the adverse positions, the
94
TOPOGRAPHICAL MODELLING.
circumstances which determined the necessity
of acting upon the offensive or defensive, the
manner in which the movements of different
bodies of troops depended upon one another,
and the probable local causes which led to the
failure, or promoted the success, of any parti-
cular manœuvre:-the practice of constructing
models from topographical drawings cannot fail
to prove of very great utility to students at
military seminaries and to officers in general,
since it teaches them fully to comprehend the
meaning of a topographical map or plan, and to
reject, as faulty and imperfect, such drawings as
do not offer sufficient data for the construction
of their corresponding models, and also enables
them, in a short time, to acquire, from the view
of a topographical drawing, a correct know-
ledge of the character of the country it is
intended to express. In the field, however, the
great advantage of maps and plans, in point of
portability, gives them a decided preference to
models, at least to such as are executed upon
a large scale; but I may venture to assert that
a model of the immediate seat of war, upon a
TOPOGRAPHICAL MODELLING.
95
small scale, (such as that of one inch to three or
four miles,) would be considered by a general a
great acquisition in a strategical point of view ;*
in respect to movements purely tactical, the
more detailed local information must of course
be gained through the medium of plans, sketches,
and reconnaissances.
Geologists, in constructing topographical
models, will add very considerably to their value
by dividing them into several parts, and exhi-
biting, as far as lies in their power, on the sides.
of the latter, (which are vertical sections of the
model,) the internal geological structure of the
country represented. In the same manner, the
direction and extent of mines may be very
distinctly shown.
Land-surveyors will not be under the neces-
*
Upon a scale of one inch to four miles, the model of an
extent of country equal to a square, the side of which is 200
miles, might be contained in a box of about four feet square.
When the military operations are conducted upon a more
extensive scale, a model of the whole country to which they
relate might be divided into parts of a convenient size, to be
used separately, according to circumstances.
96
TOPOGRAPHICAL MODELLING.
sity of making complete topographical drawings
of estates, in order to construct their corres-
ponding models; they will only require plans
showing the detail and the horizontal lines.
DIFFERENCE BETWEEN THE HORIZONTAL AND
VERTICAL SCALES.
IN topographical modelling, it is necessary to
augment the scale of altitudes by a certain
quantity beyond that of the horizontal distances;
for, if the two scales were made equal, the
model of a country, having only a gently undu-
lating surface, would present the appearance of
an almost undeviating plain, and that of a moun-
tainous country would only strike us as the
representation of hilly ground. The reason of
this is obvious; it results from the great dispa-
rity between the view which we obtain of a
country, when actually going over it, and that
which is presented to us by its model. In the
former, the eye being only five or six feet above
the ground, sees all objects in profile, or nearly
TOPOGRAPHICAL MODELLING.
97
so, and consequently in their greatest apparent
magnitude; but, in the latter, the eye is per-
haps, according to the scale, several miles above
the ground represented, and, if this view could
possibly be obtained of the country itself, the
natural effect would be similar to that of a mo-
del, as above-mentioned, in which the vertical
and horizontal scales are made equal.
In choosing the size of the vertical scale for
a model, regard must be had to that of the
horizontal scale, and to the character of the
country represented. The following proportion
between the scales, for models having horizontal
scales of six inches or more to a mile, appears
to me best suited to produce the effect desired.
Add to the horizontal scale, for the vertical one,
if the country be mountainous, one third; if hilly,
one half; and if composed of gentle undulations,
two thirds. In proportion as the horizontal scale
is less than six inches to a mile, let these ad-
ditions for the vertical one be encreased. Should
a model, however, be so small as to admit of
being taken up in the hand, the above differ-
ences between the horizontal and vertical scales
H
98
TOPOGRAPHICAL MODELLING.
may be somewhat diminished; and when, in
this case, the country represented possesses a
decidedly mountainous and rocky character, the
two scales may even be made equal.*
TO MAKE THE PREPARATORY MODEL.
HAVING made an outline plan of the ground
of which you intend to construct a model, fix
a tracing of it upon either a well seasoned board,
or, what is much better, a slab of plaster of
Paris. Procure pins of a sufficient length,-
and, if your model is upon a very large scale,
pointed pieces of wire for the highest parts,-
fix them, with a small hammer, into the princi-
pal bends of the horizontal lines, and their in-
tersections with roads, rivers, or other boun-
daries; beginning with the highest horizontal
section, and cutting them off, with a small wire-
The model of the country represented in the plan in
Pl. 5, and which may be seen at the Publishers', is con-
structed in this manner.
TOPOGRAPHICAL MODELLING.
99
cutter, according to the respective altitudes of
the sections. The simplest way is, after having
hammered in a pin or wire, to take the horizon-
tal section in the compasses, to place one point
at the part where the pin is driven into the
board or plaster, and to make, with the other, a
scratch upon the pin, which will of course show
where you are to apply the wire-cutter, in order
to give the required height to the pin. (In
Fig. 4, Pl. 7, I have marked by large round
dots, the points upon the horizontal lines, at
which I considered it necessary to fix pins for
the construction of the model from the plan in
Pl. 5.) Then take fine clay, and fill up the
space below the pins until the tops of them are
barely seen. In this manner, the general form
of the ground will be obtained, when it becomes
an easy matter to model the more minute fea-
tures between the horizontal sections corre-
sponding to the horizontal lines upon the plan
respectively. For this part of the work, you
should be provided with pieces of box-wood or
ivory, in size similar to pencils, and variously
shaped at their extremities, some being slightly
100
TOPOGRAPHICAL MODELLING.
turned and flattened, others squared or pointed,
&c., with which the clay can be moulded into
the most intricate forms. The advantage of
having a slab of plaster of Paris under your
clay, is that if you have occasion to leave your
work for any length of time, the clay may be
kept quite moist by a wet cloth being folded
underneath the slab, and that the latter does
not warp; which a board would probably do
under so much moisture.
TO MAKE THE MOULD.
PROCURE a wooden frame of about an inch
thick, and an inch higher than the highest point
of the model, and of an extent exactly equal
to that of the space occupied by the latter, and
fix it to the clay in such a manner that its inner
sides press closely to the outer sides of the
model. With a camel's-hair brush, pass some
sweet oil over the whole surface of the model,
leaving the sides of the frame perfectly dry.
Then pour plaster of Paris, mixed with water
TOPOGRAPHICAL MODELLING.
101
to a proper consistency, over the clay, until it
becomes level with the top of the frame. The
easiest and best way of mixing the plaster is to
put a sufficient quantity of water into a basin,
or other utensil, according to the size of the
model, and then to add to it the dry plaster
or powder gradually and gently until it reaches
the surface of the water, when, after stirring it
very gently once or twice with a stick, the whole
may be poured into the frame. As soon as the
heat of the plaster has subsided, that is, in about
fifteen or twenty minutes, remove the mould,
which is now formed, from the clay, and set it
to dry, either by the heat of the sun, or very
gradually before a fire. When perfectly dry,
give the mould two or three coats of drying oil,
and let it stand for a couple of days.
When it is required to make very large mo-
dels, they should be divided into parts, not ex-
ceeding three or four feet square, and the frames
of the moulds should be made much thicker,
and strengthened by cross pieces of wood.
102
TOPOGRAPHICAL MODELLING.
TO MAKE THE CAST.
PASS some sweet oil over the surface of the
mould and the inner sides of its frame, and pour
the plaster into it, in the same manner as over
the preparatory model. When it is time to re-
move the plaster or cast, begin by knocking
with a hammer upon the upper sides of the
frame, all round the mould, by which means
the cast will soon be sufficiently detached from
the latter to enable you to take it up entirely,
or you may turn the whole over carefully, and
remove the mould from the cast.
Should any
pieces have been broken off the cast, in the re-
moval, they can again be fixed into their proper
places with glue; or should they be so much
broken as to render this a troublesome matter,
they can be replaced by papier-maché, shaped
accordingly, and fastened to the cast with glue.
When the cast is perfectly dry, give it a coat
or two of a solution of isinglass while quite hot,
by which it will be prepared to receive colors.
TOPOGRAPHICAL MODELLING.
103
The solution should be of such a strength, that
when the model dries, its surface may shine a
little, but not much.
TO REPRESENT AND FIX THE DETAIL UPON
THE CAST OR MODEL.
PROCURE a wooden frame, the inner extent of
which is equal to that occupied by the model,
and having placed the latter upon a smooth sur-
face, put the frame over it, so as to contain it
exactly in the space within. Divide the plan
by which the construction of the model is regu-
lated into a certain number of squares, and set
off their respective lengths upon the upper sur-
face of the frame; when, by laying a ruler
across the latter, and applying it to the dis-
tances set off, respectively, the corresponding
number of squares can be drawn upon the sur-
face of the model. In doing this, the pencil
must be kept upright, and moved gently over
the surface of the model, and its point must be
in the same plane with the side which is kept
close to the ruler, as in the sliding-pencils.
104
TOPOGRAPHICAL MODELLING.
Now, by the aid of the squares, and the forma-
tion of the ground, (already shown in the cast,)
draw upon the model the situation and direction
of such of the various objects of the detail as
your scale will admit of being represented.
This being done, the objects themselves are
imitat and fixed upon the model in the follow-
ing manner:
Hedges are represented, when the scale is
large enough, by green chenille, laid along their
corresponding pencilled lines, which you pre-
viously pass over with a brush containing strong
gum-water or isinglass, mixed with green color.
If upon a scale of six inches to a mile, green
cotton must be used instead of chenille: upon
a smaller scale, their representation is inad-
missible.
Walls are represented by narrow slips of
white card, and fixed in the same manner as the
hedges.
Trees are represented by chenille cut into
small pieces, which are stuck upon the model,
in their respective situations, previously gum-
med to receive them. The following is the
readiest mode of fixing the trees :-cut a num-
TOPOGRAPHICAL MODELLING.
105
ber of bits of chenille, of a size corresponding to
the vertical scale of the model; dip a very fine
brush into strong gum-water, and fix this upon
the model in small but well filled patches,
(about six or seven at a time,) where the trees
are to stand; then take a small convenient piece
of wood, somewhat flattened at the one end, and
damp the latter with your tongue, so that upon
applying it to one of the ready cut pieces of
chenille, this may adhere to it, when you have
only to press it gently down upon one of the
above spots of gum: fix the chenille upon the
other spots in the same manner, taking care
that the latter do not previously dry up, which,
however, will not be the case if you put on the
gum properly. The spots should appear like
so many very small drops of gum let fall upon
the model, and be as little spread as possible,
otherwise, after the chenille is fixed, the surface
of the model immediately round it will possess
a shining appearance, producing a disagreeable
effect. When modelling upon a very large scale,
the trees may be formed by small bunches of
chenille, fastened with fine wire, which is
I
106
TOPOGRAPHICAL MODELLING.
twisted (most conveniently with a small wire-
cutter) so as to form a stem, and cut off at a
proper length; the ends of the loops of the
bunch are cut, and the chenille is then trimmed
to the proportionate size. They are fixed into
narrow holes formed in the model with some
finely pointed instrument, and firmly attached
to it with gum.
Houses are cut out of cork in their proportion-
ate dimensions, and stuck on the model with
gum or glue; their sides colored white, and
their tops red; except in models upon a very
large scale, in which they must of course be
more minutely imitated.
Streams are coloured pale blue.
Lakes, large rivers, and sea, are best repre-
sented by means of glass, fitted in the hollow
parts (previously colored) of the cast, and
which are made in the preparatory model for
that purpose.
Roads, lanes, and paths, are covered with a
drab or dust color.
In coloring the fields, care must be taken to
avoid a sameness; light and dark greens should
TOPOGRAPHICAL MODELLING.
107
be contrasted together, and a few browns intro-
duced to represent fallow land.
In coloring rocks, a dark ground should be
laid on first, and then the other colors, such as
grey, red, light-brown, &c., slightly and deli-
cately with a brush almost dry.
Body colors ground with very weak gum-
water are employed in coloring the models.
The selection and disposition of them of course
depend greatly upon the taste of the artist,
who must adhere as closely to nature as the
materials at his command will admit.
The models should be provided with cases to
protect them from dust, and should never be
exposed to the sun.
Models after the plans given in Pl. 5 and 6,
exhibiting all the varieties of topographical de-
tail, are left at the Publishers' for inspection.
THE END.
LONDON:
PRINTED BY C. II. REYNELL, BROAD STREET, GOLDEN SQUARE.
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Plate 2.

UNIV
M
OF

N°1.
Swamp
Morass
Spring No 2.
Sand
Lake
Pond
Pool
River
Pasture
Meadow"
Heath
Corn Fields.
PPP
Vineyards.
Hop-grounds.
Gardens
Trees.
Nº3.
Houses upon a
large Scale
Houses upon a
small Scale
Stone or Brick
Wall.
RIVER
at a moderate height of water
8
Island
6
Shoal
Fruit Oak. Lime: Beach. Elm. Willow. Poplar Pine. Fir: Scotch Fir: Larch,
upon a
large Scale
upon a
smaller Scale
upon a
large Scale
upon a
small Scale
Town
Rocky Coast
Rocks above water
River
Rocks below water
Shoal always
covered
8
7
11
Shoal seen at low water
Low water mark
High water mar
Military Signs.
Cannon. Intrenchment.
+++++ ^^
Infantry.
Artillery.
P
engaged
encamped
Cavalry.
Park
engaged.
encamped,
Mines.
DO
Vedettes. 55 55 5,5
Non Commissioned
Officers Party.
Guard of Cavalry.
Lien Siborn del
Tête de Pont.
Trous
de Loup.
FORTIFICATION.
Roads.
Lane
Hollow-way
Field-way
High
Cross Road
Road
Foot path
moderale Scale-
upona
upon a
small Scale.
or
Batteries.
Cannon
Abatis.
Mortars
Grow's-feet.
AAAAAA
Trenches.
Village
Stone or Brick House
L
Wooden House.
L
Redoubt.
Chevaux de Frise
**********
Palisades.
Field of Battle.
X X
gaind. lost.
River
Navigable River......
Canal...
Geographical Signs.
Wood of Oaks, Elms, &c...
Wood of Pines, Firs, &c..
High Road.....
Cross Roads.
Fortress..
Walled Town...
--
Wind-mill.
Water-mill..
Saw-mill..
Iron-foundery.
Copper-mill.
Paper-mill.
Oil-mill....
Powder-mill.
Salt-work.
Paling
ப்பு
.
Church with Spire.
+
® Wind-mill.
Water-mall
Plate 3
Field Hedge
Hurdle Hedge
Bridge
Wooden Bridge with Stone Piers.
Wooden Bridge with Drawbri
Ponton Bridge
Flying Ferry.
Rope Ferry
Horse Ferry
Boat Ferry
Ford
Landing
Place
Gold.
Silver.
Mineral Water or Bath.
Post-house.......
Copper.
Mines.
Lead.
보
​28
Quicksilver.
Vitriol..
Coal...
* Quarry.
Boundary of a Country
Boundary of a County.
or Province.
Hewitso Carburton StrNI
OF
MICH
Open Town..
亞
​burnt.
Villages.
inundated
Village.
$
Village with a Church..
Inn.
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London. Published by C&J. Rivington Sept 1827

Drawn by Lieut.iborn.
Fig. 1.
Fig. 2.
,
Fig. 3.
Fig. 4.
75
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
London. Published by C&JRivington Sept. 1827
450
350
25
20
35
20
59
b
Engraved by E.Kennion.
UNIW
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OF
Plate 4.

Drawn by Lieu, Siborn.
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1800
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E
1300
1200
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300
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1900
1800
3500
1200
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1200
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1500
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900
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B
2060
600
600
1800
1500
600
300
600
600
008
2100
1800
1500
1200
900
600
300
B
TOPOGRAPHICAL PLAN AND MAP
of a
Mountainous and Rocky Country:
of 1 to 25860;
the former upon the Scale of
the latter upon that of 1 to 103440.
1800
200
2700
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POLL
foo
1500
Scale of the Plan.
1000
2000
2000
4000
5000 Feet.
900
2200
D1300
Scale of the Map.
1000
10000 Feet.
Scale of the Profiles.
1800
4000
1000
2000
2000 Feet
1500
1200
900
600
Scale of Inclination.
300
F
London Published by C&J.Rivington, Sept 1827.
Engraved by W. Lowry.
Plate 5.
UNIC
OF
MICH

400
450
A
450
400
350
300
250
525
North
500
400
300
200
300
Surveyed & Drawn by Lieut Siborn.
200
750
100
350
300
250
200
F
ront
Wellington's Heath
Ledbury
350
729 220
Mitchell Farm
E
22
100
White House Farm
To Kastnor
P
Q
The Hill Farm
200
422
250
Upper
B 250
500
400
300
200
100
250
250
200
B
Topographical Stan
of a
Part of the Tlicinity.
OF
Ledbury, Herefordshire.
upon different Scales.
200
250
200
250
200
200
200
250
Ledbury Church
50
50
100
D
100
50
Height of the Lowest Point above the Level of the Sea
about 1030 feet.
London, Published by C&Rivington Sept 1827
500 4 3
500
1000
1500
2000 feet.
6 $101234873 2000 feet,
500
450
400
350
20
300
250
25
D
200
450
100
150
Plate 6.
Engraved by E. Kennion
300
250
200
150
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276
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Fig. 2.
153
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186
$197
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145
183
1800 1600
1200
900
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Fig. 4.
600
1800
231
1500
1200
$198
1200
17:11
1500
150
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183
$215
718
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129
235
30
200
500
1000
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2000 Feet
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135
201
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Londen, Published by C&T. Rivington, Sipt'18-
231
1500
200
200
150
100
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Fig. 6.
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1600
900
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© 2017
Plate 7.


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