•YmE'WJMKYEI&SirirY'
Illllillh.Hil W^»"^^^M^MM«
Bought with the income of the
William C. Egleston Fund
191-9

MAPS AND SURVEY

CAMBRIDGE UNIVERSITY PRESS
ftmtBDtt: FETTER LANE, E.C.
C. F. CLAY, Manager

«n>it<6urgfj : 100, PRINCES STREET
Berlin: A. ASHER AND CO.'
ILtipjia: F. A. BROCKHAUS
£eto iorfs: G. P. PUTNAM'S SONS
aSomfaij anil Calcutta: MACMILLAN AND CO., Ltd..

All rights reserved.

MAPS AND SURVEY

BY

ARTHUR R. HINKS, M.A., F.R.S.
CHIEF ASSISTANT AT THE CAMBRIDGE OBSERVATORY
AND UNIVERSITY LECTURER IN SURVEYING AND CARTOGRAPHY

Cambridge :
at the University Press
i9x3

Camfirilrge :
PRINTED BY JOHN CLAY, M.A.
AT THE UNIVERSITY PRESS

PREFACE
r*HIS book is designed as an introduction to the study of
-*- Maps and the processes of Survey by which they are
made. In planning the work it was necessary to decide in the first
place whether to call it Maps and Survey, or Survey and Maps :
that is to say, whether to take the logical order, of Survey
before Maps, or the order of general interest and use, which is
Maps before Survey.
Since many more people use maps than are engaged in
making them, or than need to know the details of how they are
made, it seemed better to begin with the consideration of the
map as it is published and used. A clear understanding of the
best results that have been produced up to the present time,
leading to an appreciation of the ways along which progress is
desirable, will make a convenient basis for the study of the
methods of Survey, and the manner in which our representation
of the world's surface may be extended and improved.
Some years of experience in teaching the elements of
Geodesy and of Topographical Survey to the students of the
Department of Geography in the University of Cambridge
have shown me that there is need of a book which shall give
a general account of the many-sided art of Survey. The two
official military textbooks, the Textbook of Topographical Sur
veying, by Colonel C. F. Close, and the Manual of Map Reading
and Field Sketching, are invaluable for instruction in all the

vi PREFACE
details of the various processes, and there is no need to make
any attempt to replace them. But it seems to me that the
student needs some explanatory introduction, unobscured by
much detail, which shall exhibit the general nature of the
operations, and the relations to one another of the various parts
of the subject.
It is certain, also, that the student of geography requires an
elementary account of the operations of Geodesy proper, that
is to say, of the higher survey whose aim is to contribute to the
knowledge of the size and shape of the Earth ; and which has
in recent years extended its enquiries into the constitution of
the Earth's interior. These subjects are entirely excluded from
the official books mentioned above, and I do not think that
there is any book which gives a general account of this most
interesting part of the subject.
The ultimate refinements of Geodesy cannot affect the maps
in the slightest degree, cannot be said to be of any practical use
whatever, can offer no return in cash for the money which may
be, and which ought to be, spent upon them. Their justification
is on a higher plane. A nation is judged, and rightly judged,
by the public spirit and the public taste which it shows in its
buildings, its pictures, and its gardens, which any educated man
is, or thinks he is, competent to appreciate. And equally a
nation is judged, though by a smaller circle of judges, for the
contributions which it can make to pure knowledge. An ex
quisite piece of Geodesy may give as real a pleasure, and be as
genuine a source of pride, as the masterpieces of art and
literature. I have made no attempt to describe the minutiae of instru
mental adjustments or processes, believing that a general view
of the subject should not be obstructed by a mass of detail
which is tedious to read, but had better be avoided until the
student comes to deal with the instruments themselves, and

PREFACE vii
carry out an actual piece of survey with them. Nor have I
been able to give anything more than the slightest sketch of the
large subject of cadastral survey. This is an intricate subject
whose methods are to a great extent governed by the system
of land registration and taxation in force in the country to be
surveyed. There is a recent treatise on the subject — The
Cadastral Survey of Egypt, by Captain H. G. Lyons, F.R.S.,
Surveyor-General — to which students may be referred if they
wish to find a lucid account of the most interesting problems
involved in this class of survey.
In the treatment of the topographical and geodetic survey
I have tried to follow as closely as possible the principles under
lying the methods employed by the Ordnance Survey, the
Survey of India, and the School of Military Engineering at
Chatham, to whose hospitality I owe my first introduction to
the subject. I have profited also by the publications of the
Geodetic Survey of South Africa, the United States Coast and
Geodetic Survey, and the Survey of Egypt. Part of the charm
of Geodesy is due to the general compatibility of the ideas
which govern the operations of all countries, which may be
traced without doubt to the influence of the International
Geodetic Association, and to the benevolent authority exer
cised by the illustrious Director of its central bureau at
Potsdam. While the literature of Geodesy and Topographical Survey
is extensive, comparatively little has been written on the subject
of topographical representation on the map. The subject is
new, because until the introduction of the present processes of
colour printing there was not a great deal of scope for enter
prise. It is still in the experimental state, as is evident from
the continual change in the style of the publications issued by
the principal map reproduction offices. Under these circum
stances discussion and criticism are doubly interesting, and

viii PREFACE
I have devoted more space than might seem necessary at first
sight, to the detailed analysis of typical sheets produced by the
leading surveys of the World. But since it is impracticable to
give adequate specimens of these maps, this analysis can be
effective only if the student is able to study a selection of the
actual sheets. For this reason I have given the sheet numbers
of good specimens, in the hope that the schools of geography
who may be interested in the subject may find little difficulty
in procuring a characteristic series of maps.
By permission of the Controller of H.M. Stationery Office,
and with the very kind assent and help of Colonel C. F. Close,
C.M.G., R.E., Director-General of the Ordnance Survey, I am
able to give in Plates I to V small specimens of the maps of
the Ordnance Survey of Great Britain and Ireland. It is not
possible to do justice to these maps in the small page of this
book ; but I trust that these specimens are sufficient to show
the high quality of the work of the Survey, and to serve as an
incentive to the study of the complete sheets. I am especially
indebted to Colonel Close for undertaking the complete pro
duction of these plates in the printing department of the
Ordnance Survey at Southampton.
Plates VI to IX I am able to give by the kindness of
Colonel Hedley, R.E., Chief of the Geographical Section of
the General Staff. He has been so good as to take great
interest in the choice of specimens from the wide range of
maps produced by his department; and in particular he has
kindly placed at my disposal a specimen of the new edition
of the beautiful map of Persia and Afghanistan which is in
course of preparation. These four plates have been printed
in the map reproduction department of the War Office. I owe
to Colonel Hedley my sincere thanks for thus making it possible
to include in my book four attractive examples of small scale
maps.

PREFA CE ix
The material for the plates showing instruments and methods
I owe to many sources. Commandant Lucien Durand, of the
nth Regiment of Artillery of the French Army, was so kind
as to give me the three pictures reproduced in Plate XVII,
showing the reconnaissance ladder and beacon scaffold which
he introduced into the equipment of the Service Geographique
de l'Armee. To Captain E. M. Jack, R.E., British Commissioner
in the survey and delimitation of the Uganda-Congo boundary,
I owe the two pictures of beacons which make Plate XVIII,
and the two pictures of base measurement on Plate XIX. The
two latter were given me by Captain Jack to illustrate a paper
read before the Research Department of the Royal Geographical
Society, and the Society has kindly lent the blocks from which
this plate is printed.
The three figures of Plate XXI are taken from the Account
of the Principal Triangulation of Great Britain, published by
the Ordnance Survey, and those of Plate XXII from recent
volumes of the Survey of India. The view of Banog mountain
in Plate XXIII is from the same source.
The diagrammatic figure of the plane table used by the
United States Coast Survey is borrowed from one of their
official publications, and the picture of the geodetic level on
Plate XXIII was given me by Messrs E. R. Watts and Sons,
who make this pattern. The remaining figures are from photo
graphs of instruments belonging to the Department of Geography
of Cambridge University.
A. R. H.
Cambridge,
May, 191 3.

CONTENTS

CHAPTER I
MAPS
The necessity for Maps
Conventional signs ....
Roads 
Railways ......
Scale 
Construction of scales for Maps .
Problems in the construction of Scales
Rivers 
Woods and forests ....
Sheet margins 
Representation of hill features .
Hachures 
Hill-shading 
Spot heights 
Contours and form lines
Layer colouring 
Combined systems
Map reading 
Sections and profiles ....
Problems of intervisibility .
Identification of distant objects .
Measurement of areas ....
Measurement of distances .
Map reproduction ....

PAGE 25
6
9
io1314 1517
1719
20 21
23 23
27
29 3°
3°
32 3333
34
35

CHAPTER II
MAP ANALYSIS

Ordnance Survey Maps
Maps of the General Staff
Foreign Maps
International Map
Aero maps

37
4i43 5°56

Xll

CONTENTS

CHAPTER III
ROUTE TRAVERSING PAGE
The object of the Route Map  59
The astronomical observations  60
The compass traverse ........ 62
Distances by cyclometer  62
Distances by time  63
The field book ...  64
The compass  65
Check by astronomical observations .... 67
Greenwich time  68
Azimuth ... .... .69
Dead reckoning  71
Heights by Aneroid Barometer  74
Instrumental precautions . . . . 76
Theory of the process .  77
Tables for barometer heights  80
Boiling point thermometer .... . . 80

CHAPTER IV

SIMPLE LAND SURVEY

The settler's land survey
Elements of property survey
Simple theodolite triangulation
Base 
Advantages of triangulation
Dangers of patchwork survey
Simple levelling .
Detailed sections .

8384
88 90
92 9395

CHAPTER V
COMPASS AND PLANE TABLE SKETCHING
Compass sketching  101
The compass  102
Local deflections  104
The compass sketch  .105
The base  106

CONTENTS

xin

Ruling points
The clinometer
Contouring with the clinometer
The plane table .
Plotting the base .
Choice of stations
Graphical triangulation
Intersected points
Trough compass .
Resection ....
Triangle of error .
Plane table traverse
Heights and contours .
Accuracy of graphical plane tabling
Tacheometer and subtense traverses
Summary of methods .

PAGE 107109111"3H5 "7
118119
120 121
122 125
127128129130

CHAPTER VI

TOPOGRAPHICAL SURVEY
Preliminary considerations  132
Mean sea level  133
Plane table reconnaissance ....... 135
Plan of triangulation  136
Beacons  137
Heliograph .  138
Permanent marks underground ... .140
Initial latitude, longitude, and azimuth . . . . 141
Base measurement ........ 144
Suspended tape or wire .... 145
Correction for slope  147
Reduction to sea level . ... 148
Theodolite triangulation  . 149
Triangular error ... .151
Spherical excess  . . 152
Trigonometrical heights . . 153
Barometer heights  156
Calculation of the triangulation ... .156
Calculation of geographical positions  158
Calculation of rectangular co-ordinates . 159
Plane table graticule  160
Detail by plane table  160

CONTENTS
PAGE
Precise traversing  162
The Ordnance Survey  163
India : Canada : Australia  167
British Africa .... .... 168
Boundary Surveys  .169

CHAPTER VII

GEODETIC SURVEY

Figure of the Earth ....

171

Deviations of the vertical .

172
Attraction of the Himalayas
173
Gravity survey with the pendulum
175
Gravity in India 
176
The theory of isostasy
177
The form of the ocean surface .
178
Geodetic measure of arc of meridian.
179
Principal geodetic arcs .
181
Geodetic triangulation .
183
Principal chains ...
184
Geodetic bases ...
185
Geodetic levelling.
187
Future progress of geodesy .
189
Figure of the Earth
191
CHAPTER VIII
SURVEY INSTRUMENTS
The Sextant .
The Theodolite
LevelsInvar wire apparatus .
Longitudes by telegraph
Longitudes by wireless
Geodetic pendulums
192194
196 197197198
200
Index .
203
PLATES
To face page
I. Conventional signs : One inch Ordnance Survey Map . 6
i. Double and single railways.
2. Mineral lines and canals.
3. Roads of different classes.
4. Footpaths and parish boundaries.
5. Characteristic sheet attached to One inch map, O.S.
II. Conventional signs, continued  10
1. Hachures and cliff drawing.
2. Confusion of contours with other detail.
3. Correct method of figuring contours.
4. Misleading effect of unequal vertical interval in
contours.
III. Conventional signs, continued  16
1. Marsh.
2. Sands.
3. National boundary.
4. Rock and water lines.
IV. Ordnance Survey of England. One inch scale. 1/63360 24
1. In outline, without hills.
2. In colour.
V. Ordnance Survey of Ireland. Half inch scale. 1/126720 28
I. With hill shading.
2. Layer system.
VI. Geographical Section, General Staff. Basutoland. 1/250000 42
VII. Geographical Section. General Staff. Persia and Afghani
stan. 1/4055040  43
VIII. International Map. Sheet North K. 35 Istambul . . 54
IX. International Map. Sheet South H. 34 Kenhardt . 55
X. Measurement of areas  58
1. Amsler planimeter.
2. Central parts of planimeter.
XI. Determination of Heights  74
1. Aneroid barometer.
2. Boiling point apparatus or hypsometer.
XII. Levelling  96
1. Levelling staff.
2. Twelve inch Y level.
XIII. Compass sketching. The Service protractor . . 102
XIV. Instruments for compass sketching ... 104
1. Prismatic compass, Mark VI.
2. Compass in use.
3. Compass in position for use.
4. Clinometer in use.
5. Watkin clinometer.
6. Interior of clinometer.

xvi PLA TES
To face page
XV. Instruments for plane-tabling ... . . 112
1. Plane table and sight rule.
2. Indian clinometer on plane table.
XVI. Instruments for plane-tabling  120
1. Trough compass.
2. Plane table and telescopic alidade.
XVII. Reconnaissance ladder and beacon : Commandant Durand 136
1. Ladder on the march.
2. Ladder in course of erection.
3. Double tripod scaffold.
XVIII. Uganda-Congo Boundary  140
1. Beacon for intersected point.
2. Quadripod beacon for triangulation.
XIX. Measurement of Semliki Base, Uganda-Congo Boundary 146
1. Taking readings on the wire.
2. Adjusting the straining trestles and wire.
XX. Five inch Micrometer Theodolite  150
1. In position for triangulation.
2. From the eyepiece end.
3. With reflector over objective for lamp illumination.
4. With electric illumination.
XXI. Ordnance Survey: Principal triangulation. . . . 164
1. Measurement of Lough Foyle Base.
2. Great Theodolite.
3. Scaffold on Gravelines Church.
XXII. Survey of India  176
1. Half-second pendulums.
2. Clock and flash box.
3. Latitude with zenith telescope.
XXIII. Precise levelling  188
1. Banog mountain.
2. Precise level: U.S.C.G. S. pattern.
XXIV. Invar tape base apparatus  197
1. Straining trestle.
2. Tape on drum.
3. Mark on tripod.
4. Alignment sight on tripod.

CHAPTER I
MAPS
TOPOGRAPHY means, in the original Greek, the description
of a place. A map is a drawing to illustrate such a description.
By gradual steps it has been found possible to make these
drawings in such a way that they convey the necessary informa
tion without the description in words, and what is now called
a topographical map can give, to those who know how to read
it, all the information which is wanted to enable a man to judge
of the natural obstacles which may hinder his getting about
the country, or the means of communication which have been
established by man to facilitate his journey. In this book we
shall be concerned chiefly with these topographical maps.
The amount of information which can be compressed into
a map depends in the first place upon the perfection of the
system of conventional signs in which the map is drawn, and
secondly upon the size of the map in comparison with the ground
which it represents, or, in other words, upon the scale of the
map. It is clear that the larger the scale, the more detailed is
the information which can be given. But, on the other hand,.
the larger the scale, the greater is the number of sheets required
to cover a given area, and the more cumbrous is the map to use:
For purposes of local administration and government it is
necessary to have maps on which every separate property, how
ever small, is distinctly shown ; but such detail would be only
confusing to those who wished to learn the way about the
country. And again, the details of roads, the shapes of the
hills, and all the other information essential to the traveller on
foot or on wheels, are equally unessential to those who use the
map for the study of broad questions of history, of commerce, or
any such matters.
H. M. S. I

2 MAPS
Hence we shall find that maps may be classed in three
principal divisions :
Cadastral maps, on large scales, show boundaries of property,
and individual buildings. They are required for local administra
tion and taxation ; the management of estates ; the identification
of property in legal documents ; and for detailed affairs of every
kind. But it should be remarked that the English map on the scale of I in
2500, commonly called the 25 inch map, shows the visible hedges and fences,
whereas the real boundary of the property is very frequently « some feet
beyond the hedge. Hence the 25 inch map is not strictly a cadastral map,
though it is commonly called so.
Topographical maps show the natural features of the country,
hills and rivers, forests and swamps ; and in addition such
artificial features as man has added to the country in the shape
of towns and villages ; roads, railways and canals ; bridges and
telegraphs. They serve as guides for travel on business or
pleasure, or for the operations of war. They are on smaller
scales than the cadastral maps, and cannot show the boundaries
of individual properties. The inch to the mile map is the
standard topographical map of the British Isles.
Atlas maps are on scales still smaller. Most of the topo
graphical details have been suppressed ; only the principal
ranges of hills and the main streams of the rivers, the chief
towns, and perhaps the main lines of the railways can be repre
sented, for they aim at representing on a single sheet a whole
country, a continent, or even the World.
The necessity for maps.
It is a little hard for one who lives in a country long settled
and completely mapped to realise the difficulties which confront
at every turn those who find themselves citizens of a new and
unmapped country. The need of maps appears most urgently
in case of war, and in the past it has usually happened that
military necessities first compelled the production of a map.

MAPS 3
The beginning of the Ordnance Survey of Great Britain may be
traced, for example, to the Highland Rebellion of 1745. In
peace the necessity of maps for all purposes of administration is
less conspicuous, but none the less real. Until a country is
mapped it is impossible to devise any well considered schemes
of communication ; until it is surveyed on a fairly large scale
it is impossible to make grants of land to settlers, or at least it
is impossible to give them a clear and undisputed title to their
holdings. In larger affairs the need of maps is equally great.
Until a country is mapped it is impossible to agree upon a
boundary which shall be satisfactory to both sides, and in the
absence of maps the most costly mistakes have been made
through sheer ignorance.
Let us take two or three examples.
During the war in South Africa the British army in Natal,
advancing to the relief of Ladysmith, found the Boers entrenched
in a strong position at Colenso, on the north bank of the River
Tugela. On the right of the British was Langwane Hill, which
appeared to lie to the north of the river, though in reality the
river turned away sharply to the north, leaving the hill easily
accessible to the British troops. Although the country had been
settled for many years there were no maps in existence.
Langwane Hill was the key to the position. The failure of the
British commander to realise that it was accessible cost the
country many hundreds of lives and weeks of prolonged fighting.
The mistake could not have been made had the country been
mapped. Again, until a country is mapped there is continual waste in
making surveys for special purposes. If a railway is projected
it is necessary to make a special survey of the proposed course
of the line. This survey costs a large sum of money, but since
it is made for a special purpose it is not complete ; it is never
published, and cannot be made use of as a contribution to
the proper mapping of the country. In the earlier part of the
nineteenth century, while the Ordnance Survey was in the initial
stages, several million pounds were spent in England on railway
surveys, surveys for the commutation of tithe, enclosure of

4 MAPS
common lands, and so forth, nearly all of which money might
liave been saved had the regular survey of the country been
finished earlier. It is the truest economy to push forward the
survey of a country at the earliest possible moment.
To take, a somewhat different case : it is most important that
the responsible officers of Government should be trained to
discriminate between maps which are reliable and those which
are not. It frequently happens that the first rough maps of

Scale of Miles
o io 20 30
Fig. 1. True position of the 30th meridian, which was supposed
to pass through the middle of the lake.

a newly explored country are compiled from inaccurate observa
tions made under great difficulties by the early explorers. For
example, the early maps of central Africa showed the thirtieth
meridian passing through Lake Albert Edward, and on the
partition of Africa in 1894 it was agreed that the boundary
between Uganda and the Congo Free State should follow this
meridian, so that both countries should have access to the lake.
Some years afterwards it was found that the thirtieth meridian
was actually some miles to the east of the lake. Prolonged
negotiations were necessary for a rectification of the frontier,

MAPS 5
and some considerable sacrifice of territory was required to gain
that advantage which the treaty was in the first instance
supposed to secure. This costly mistake would have been
avoided had the diplomatists realised the necessary limitations
of the maps which they were using.
We need not spend more time in insisting on the importance
of making maps, and of understanding how to use them.
Conventional signs.
In order that it may be possible to compress as much
information as is required into the minimum of space, to ensure
clearness and legibility, it is necessary to adopt a carefully
considered scheme of conventions, so that the character of every
line and the style of every letter may convey a definite meaning.
The map thus becomes a kind of shorthand script, whose full
meaning cannot be understood without a thorough knowledge
of the system employed. It is therefore clearly advantageous
that mapmakers should come as soon as possible to some general
understanding on the subject of conventional signs, in order that
it may not be necessary to learn, as it were, a new language
whenever one tries to read a new map.
The resolutions of the International Map Committee, which
met in London in 1909 to frame a scheme for the one-in-a-
million map of the World, are in this respect of great importance,
and we shall often refer to them in what follows.
The characteristic sheet.
The characteristic sheet is the key to the system of con
ventional signs employed on the map. It is usually, though not
invariably the case, that each sheet of a map bears a small
characteristic sheet of the principal conventions (see Plate I) ;
but for a complete understanding of the system it is always
necessary to refer to the complete characteristic sheet that is
published separately.
Conventional signs for use in the field.
These are necessarily simpler and less minute than the signs
which are employed on the engraved or carefully drawn sheets

6 MAPS
that are issued from the reproduction office. The surveyor in
the field has neither the skill nor the time to imitate the finely
devised style which is suitable for the engraved map. We must
therefore be careful to distinguish between the systems to be
employed in the two cases. (For a conventional sign sheet for
field use, see the Manual of Map Reading and Field Sketching?)
Roads. In reading the representation of roads on a map, it is
necessary to remember first of all that the road is not represented
true to scale in width, but that the width is conventional,
signifying the class of the road. Such a convention is clearly
necessary. On the scale of one inch to the mile a road sixteen
yards broad would, if shown true to scale, be only one hundredth
of an inch broad ; and this is far too little for legibility, or to
allow distinctions between the representation of different classes
of roads. Hence roads must be shown of a conventional width ;
and when the scale of the map is doubled it is by no means
necessary that the road shall be drawn twice as broad as before.
There are considerable differences in the conventional signs
for roads in use in different countries. We will examine three
typical cases: the British Ordnance Survey; the French 1/50,000
map published by the Service Ge'ographique de TA rme'e ; and the
1/1,000,000 International Map.
Ordnance Survey. 1/63,360, or one inch to the mile. (See
Plates I and IV)
A distinction is made between fenced and unfenced roads,
the former being shown by double continuous lines, the latter
by dotted lines. The distinction is of military importance,
since fenced roads afford cover and obstruct the free passage of
troops across country. Three grades of metalled roads are
distinguished by differences in breadth, and the first two grades
are coloured orange. Unmetalled roads or cart tracks are shown
by still narrower double lines, and footpaths are long-dotted,
but are with difficulty distinguished from parish boundaries,
which are not needed on a topographical map. (See Plate I.)
It is often found that the distinction made on the map

CONVENTIONAL SIGNS PLATE I
One Inch Ordnance Survey Map

^|* •^y^3^2nl /¦'•"

'raw 1^'^x/"'
rag f ^r%jX*^!

^^Kl V^

\— -/#- '^ /Pff^H"''',',\ 

^^p^\ \vj"^ \ 

&Sr * ^^V \. mLM"&li*h ¦¦¦

^Uyir-N . ^^aS&vW1™'*''?' 

JJlf^^^=:;5— ^tiJ^^5lt^-^l0^B' C 3

^^^S^*11*—  '7^f3Q[k^ll$-r? £'<**M04frftl {

=^ HWs. S ¦?

\t*JA»s ^5*. r 216^-

mu£! y// J \ i X^ f " -

i ^ *

#__/ -^ \ ,¦'

Am* Cff?tllt~j

IS \ / <_^

> y/ I jff ^ .^/^

L  £1  La  ^ — -V -|

Double and Single Railways

P35"

Mineral Lines and Canals

Roads of Different Classes

Footpaths and Parish Boundaries

Metalled. JHoaeLt, First Class . . .
Second Class . !?
' s
&'
77m>v/ Gto*r  a.
VhmetaMed, Roads  ...
Footpaths   - --
Rail-ways ¦, Single Line 

( 5 (Jtfil* duttiintf

tAltitudj'JZU

Churdi or Chapel with lower'   2
„ „ ,, , Spire  1
„ without Tower or Spire.  ¦»
WindrruJl . . £ WindpunTp  1
Letter Box-  L B
Contours  ._   3S*-— ^__  ~~~-

Jioutidaries, County ..
Palish

Cumiw\\  MrnbtuJvrrnsnt . _„ j Post Office  f.
Two or more lines  _  ***=B\ I|^**^*S™^ AW%« „ , _ . , --,
^^\\B^7oy^r Ilgdff* Phd*r \Fost& Telegraph Offiw  T
Mineral Lines and Ty^arnwovs  — .  ,  1  1  1^. |— |
Rivers and Streams when exceeding 15 feet in width are. shewn with two lines
For other irtlb/Tnation see Characteristic sheet .

Characteristic Sheet attached to One Inch Map. O.S.
Ordnance ri'u/^e\ Southtu,tptoit.J9t5

MAPS 7
between first and second class roads has little relation to the
actual condition of the road. Roads which should be in first
class condition are pulled to pieces by heavy motor traffic, while
second class roads are constantly being brought up to first class
condition. Generally speaking all the roads coloured orange
are fit for motor traffic, and the uncoloured roads are not.
Ordnance Survey. 1/126,720, or two miles to one inch. (See
Plate V.)
First and second class roads are shown narrower, but still
coloured orange. The distinction between metalled roads of the
third class and unmetalled roads disappears.
" So far as the half-inch maps are concerned the old
classification of roads is somewhat inadequate to present day
needs. A committee was formed during 1911-12 to discuss
the matter.... It is not possible to obtain absolute unanimity of
opinion on such a subject as the classification of roads on a map,
but there is no doubt that the classification proposed by the
committee is a good one, and is an improvement on the former
classification. It will be applied to the new engraved issue of
the half-inch maps of Great Britain." (Report of the Progress of
the Ordnance Survey, 191 2.)
Ordnance Survey. 1/253,440, or four miles to one inch.
First class roads only are coloured orange. Second class
roads are shown by double line uncoloured, and other roads by
single line. On this smaller scale minor roads are sometimes
omitted, and this often leads to mistakes, since what ends in
a farm track often begins as a well made road. In using the
smaller scale maps it is most important to bear in mind a time
scale, as explained under that heading.
France. 1/5 0,000.
The principal differences from the system of representation
employed on the Ordnance Survey are :
None of the roads are coloured.
Variety in the signs is obtained by making the two lines
bordering the road of different intensities.

8 MAPS
. Where a road passes through a town (shown in red) the
black lines cease, and the absence of colour belonging to the
road is then an especial disadvantage.
International Map. 1/1,000,000. (See Plates VIII and IX.)
On this small scale the representation is naturally less
elaborate. Roads of all classes are shown in red :
First class by double red line.
Second class by one continuous and one dotted line.
Third class by single red line.
Footpaths, or tracks not suitable for wheeled traffic, by single
dotted red line.
None of the roads have any body colour, such as the orange
of the Ordnance Survey ; and they are all shown very lightly.
They are scarcely conspicuous enough under the best of circum
stances, and when they fall on the redder tints of the layer
colouring they become almost invisible. (See Plate IX.)
In general it may be said that all existing topographical
maps fail in the representation of hill paths. These have an
importance quite different from paths of equal quality on the
level. They are very generally well marked and permanent
features of the ground, and should be shown much more con
spicuously than they are. On most maps they are very hard to
follow when they run through hill-shaded and wooded ground.
It seems reasonable to demand that all well made and easily
followed paths in mountainous parts of Great Britain should be
shown by a single line of orange and black.
The want of some such convention is particularly marked in
holiday country. For example, in the Lake District there are
many paths well made, and as permanent in location, and very
nearly as obvious to follow, as the high roads. Such are the
principal ways up Helvellyn, or the path over Grisedale Pass
from Patterdale to Grasmere. On the half inch map with layers
these are not shown. Again, in Switzerland the principal paths
are well made and most elaborately marked with signs and
patches of colour on the rocks. But it is almost impossible to
follow these paths on the 1/50,000 map. It would seem that

MAPS 9
from the military point of view also it must be of importance to
show these paths.
On the other hand, there is a tendency in the modern
coloured maps to over accentuate the main roads. This arises,
no doubt, from the fact that as they were originally engraved, in
black, it was necessary to mark the importance of the main
roads by showing them in heavy double black lines. Now that
they have in addition a filling of colour they are often unduly
prominent, and much diminish the legibility of the contours.
There is also a tendency to confuse the representation of
towns by multiplying the yellow coloured roads. A residential
road in a good neighbourhood is always a first class road in the
sense that it is broad and well made ; but it is not a main road,
and probably it should not be coloured yellow. It would be,
for example, far more easy to discover the main roads out of
London if all the well made suburban roads were not coloured.
In a modern coloured map, especially on those of smaller
scale, it would probably be enough to represent the main roads
by a single broad line of dark grey, and the lesser roads by a
narrower line.
Railways. These are almost universally shown in black. There is
generally a distinction between double or multiple and single
tracks, narrow gauge railways, and tramways. No provision
has been made as yet to distinguish between railways worked by
steam and by electricity ; but it is clear that the distinction is
important, especially from the point of view of public safety on
the one hand, and of military adaptability on the other.
Ordnance Survey. 1/63,360. (See Plate I.)
Railways are elaborately engraved, with distinction between
double and single lines as in the figure. Embankments and
cuttings, very important as obstacles or cover, are clearly shown.
Ordnance Survey. Smaller scales.
Railways are shown as heavy single black lines, and there is
no representation of embankments or cuttings.

io MAPS
France. 1/50,000.
Four and two way tracks are in heavy black ; single tracks
somewhat like the British double track ; narrow gauge lines like
the British single track ; and tramways distinct from narrow
gauge lines. There is no general way of showing embankments
and cuttings.
International Map. 1/1,000,000. (See Plate VIII.)
A simpler system, as shown in the plate. A feature not
generally found is that lines under construction, and also
projected lines, are to be distinguished. The latter seems to be
open to objection, since it must be difficult to decide at what
stage a projected line establishes its right to be shown.
It is often useful to have special railway maps, in which
the other topographical features are subordinated. The Swiss
railway maps are excellent examples of the best system for this
purpose. The general map is printed in light brown, and the
railways, with names of the stations, are overprinted in heavy
black. This is far better than suppressing the topographical
detail, as is too often done in railway maps.
The representation of railways running underground through
towns involves difficulties which have not been successfully
overcome. In a country such as India, where there are several different
gauges in use, it is most important to distinguish between them.
And it is even more important in mountainous countries, as
Switzerland, to distinguish between railways of the ordinary
kind, rack railways, and funiculars.
Scale. The question of scale is of prime importance ; the aim of the
map-maker is to show as much as the scale on which he works
will permit, and he must learn in the first place what are the
possibilities of the different scales, and secondly how to make
the most of them.
The scale of the map is defined by a statement of the relation
between a distance measured on the map and the corresponding

PLATE II
REPRESENTATION OF HILL FEATURES
One Inch Ordnanee Survey Map

iJEB

~%&&*'

¦ - ¦•
wiT-dM19
SE8»rjH(BMffl8

&

^ilitailgfe

Hachures and Cliff Drawing

Confusion of Contours with
other Detail

Correct Method of Figuring
Contours

Misleading Effect of Unequal
Vertical Interval in Contours

Ordnance Survey. Soutiiuiuj 'tun ,.7-913

MAPS u
distance on the ground. The distance on the map will be
measured in one of the smaller units of length, that on the
ground by one of the larger ; thus, we say that the map is on
the scale of one inch to the mile, or one centimetre to the kilo
metre, or again, we may invert the statement and say, that the
scale is one mile to the inch, or one kilometre to the centimetre.
There is no very definite rule in English practice, whether to
say, one inch to the mile, or one mile to the inch. In general
one avoids the use of fractions in the statement : thus, one says
one inch to the mile, but four miles to the inch, not one quarter
of an inch to the mile. On the other hand it is common to
speak of the equivalent in inches of one mile as the characteristic
of the scale, and to speak of the inch map, the half or quarter
inch map, and so on.
This is the common way of speaking, but it is being super
seded by the more accurate method of giving the " representative
fraction," that is to say, the ratio of the distance on the map to
the distance on the ground. There are 63,360 inches in a mile.
Therefore the representative fraction of the one inch to the mile
map is 1/63,360 ; and the representative fraction of a map on the
scale of one centimetre to the kilometre is 1/100,000.
We shall note at once that the British system of measures of
length produces awkward fractions : for the half inch map the
R.F. (usual abbreviation for representative fraction) is 1/126,720;
and for the quarter inch map it is 1/253,440. This arises of
course from the fact that the number of inches in the mile is not
a round number. In countries where the metric system is used
this difficulty does not arise, since all the units of length, large
and small, are related decimally. It follows that the R.F. for
a map of such a country is naturally a round number, and it has
become the practice to speak of " natural scales," meaning
thereby, scales for which the R.F. is a round number, 1/250,000,
1/100,000, 1/80,000, and so on. The term does not seem to be
a good one, since there is not anything natural in the use of a
decimal system of units, but rather the contrary, if it is proper
to argue from the fact that the metric system, a late creation,
has not yet displaced altogether the complicated non-decimal

12 MAPS
systems which natural man had evolved. Natural scales, in fact,
are natural only in countries which have become habituated to
the decimal system of measures ; in other countries they are not
natural, but their scientific convenience has led to their gradual
introduction. We may notice that there is some diversity of opinion as to
the choice of a convenient range of so-called natural scales :
Shall the series run
1/200,000, 1/100,000, 1/50,000,
or shall it run 1/250,000, 1/125,000, 1/62,500 ?
There is an undoubted convenience in subdivision by two, so
that a sheet on one scale is subdivided into four sheets on the
scale next larger, and so on. This appears in either series.
But the second series is derived by such steps from the one in
a million scale, while the first is not. On the other hand the
numbers in the first series are simpler, more round, than the
numbers in the second. The divergence illustrates very well the
difficulty that continually occurs in the application of any purely
decimal system, that for many purposes continual division by
two is more convenient than division into so many tenths.
Again, there is the advantage in the second series of scales
that it differs very little from the series in inches to the mile.
Half an inch to the mile is 1/126,720. This differs from
1/125,000 by little more than one per cent, or about the un
certainty in the scale of the printed map which is due to the
expansion of the paper with damp. Hence in all ordinary use
of the map there is no practical difference between the two, and
this fact certainly tends to the choice of the series derived from
the one in a million by continual division into halves. More
over, the recent standardisation of the one in a million map, and
the convenience of making all other sheets subdivisions of this,
must tend to the adoption of the second series rather than the
first. It seems probable, therefore, that the series
1/250,000, 1/125,000, 1/62,500
will gradually be adopted more and more widely.

MAPS

>3

Method of writing tlte Representative Fraction.
It is not unimportant to remark that the R.F. is better
printed 1/126,720 or 1 : 126,720, than in the fractional form T¥^j,
which requires figures so small that they are read with difficulty.
There can be no hard and fast rule as to the scales suitable
for maps intended for definite purposes. But in general one
may say that cadastral maps are larger than 1/15,000; topo
graphical maps between 1/20,000 and 1/1,000,000, the larger
scales being for military purposes tactical maps and the smaller
strategical ; while anything on a smaller scale than one in a
million can hardly be considered topographical, but may be
called for convenience an Atlas map.
Construction of scales for maps.
The word scale is used in two senses. In an official manual
we find on consecutive pages these two statements :
" The scale of a map is the relation between a measured
distance on the map and the corresponding distance on the
ground." " The scale of a map should be, for convenience, about six
inches long."
In the second sense the scale of a map is the diagram which
allows one to translate distances on the map into distances on
the ground expressed in any unit desired — not necessarily that
employed in the first instance when the map was made. Thus
it may be convenient to put on an inch to the mile map a scale
of hundreds of yards ; or to construct a scale of miles for a
French map on 1/80,000.
A scale should be constructed so that any length taken from
the map with a pair of dividers can be read off at once from the
scale. Suppose that the scale is to give thousands and hundreds of
yards. The main scale is divided simply into thousands of yards,
set off to the right of the zero. To the left of the zero one
additional space of a thousand yards is subdivided into hundreds,
and if it is numbered at all, which is usually not really necessary,

14 MAPS
it is numbered to the left, that is to say, in the opposite direction
to the numbering of the main scale.
A few moments' trial will show the advantages of this plan.
Suppose that the distance is between 3000 and 4000 yards.
One leg of the dividers is set on the division 3000 ; the other
leg reaches beyond the zero, and the odd hundreds are read off
from the subsidiary scale. On this system the actual figures
required are read directly from the scale. On any other system
the figures shown by the scale must be modified in some way or
other. Example : For the one inch to the mile map, construct a scale of
thousands and hundreds of yards.
iooo yards = 1000/1 760 inches =0*568 inches.
j 1 ri 1 1 1 1 1 1 1  1  1  1 I : I
0 12 3 4 5
Fig. 2. Scale of thousands of yards, for the one inch to the mile map.
Note that :
(1) If the zero were placed at the extreme left of the scale,
or (2) If the subdivided portion were numbered from left to right,
or (3) If the scale had been constructed for the unit 500 yards instead of
iooo yards,
it would not have been so convenient as in the above form.
The scales given on the Field Service Protractor will generally serve for
the construction of any desired scale without calculation.
Problems in the construction of scales.
Exercises in the construction of scales are often set in
military examinations, and many rules for the solution of these
problems are given in the military textbooks. It seems to the
author that these rules, like the old fashioned multiplicity of
rules in arithmetic, defeat their purpose by suggesting that there
is a rule to be remembered, instead of a common sense sum to
he worked.
Thus, for example : Given a map on the scale 1/100,000 : To construct
a scale of miles.
On the scale one mile to the inch the R.F. is 1/63,360. For the smaller
scale 1/100,000 one mile is obviously 63,360/100,000 or 0*63 inches, and the
scale is easily constructed with a rule graduated to inches and tenths, or
¦with the diagonal scale of the protractor.

MAPS 15
Rivers. Rivers and streams should be always shown in blue. Their
importance is great, not only the obvious importance which they
possess as sources of water supply, means of communication, or
obstacle to getting across the country, but the subsidiary yet
very real importance which they derive from their use in helping
realisation of the relief of the land. When the streams are shown
conspicuously in blue they make it easy to follow the run of the
valley bottoms, and to distinguish valleys from ridges. (See
Plates IV and V.)
The characteristic sheets attached to the maps of the
Ordnance Survey (see Plate I), give no information as to the
methods of representing rivers and streams. In general a stream
more than fifteen feet broad is represented by a double blue
line on the one inch map, and perhaps also on the maps of
smaller scale. There are no special signs for locks, wiers, or
falls ; and there is no indication of the navigibility or otherwise
of the stream. Nor is there any distinction between natural
streams, canalised streams, and wholly artificial canals. Con
fusion is avoided, however, by the consideration that the shape
of natural and artificial waterways is very different, and that the
latter tend always to run along the contours.
But the need for some distinguishing sign is sometimes very
conspicuous, as in the map of Dartmoor. Here there are many
"leats" or small canals for water supply of towns or of
mines. These naturally run along the contours, or nearly so.
Occasionally they cross the course of a natural stream by an
aqueduct. But there is not on the Ordnance Survey maps any
sign for or representation of this aqueduct; and consequently
the maps show the impossible feature of a stream dividing into
three. At first sight it appears that a contour has been shown
blue instead of red, in error. The absence of any sign of the
aqueduct by which the leat crosses the stream is a serious
blemish on the map.
A further difficulty is sometimes caused by the failure to
show streams that run in deep ditches by the roadside, which
is not uncommon in fiat country such as the fen districts of

1 6 MAPS
England. It should be easily possible to show the necessary
blue line alongside the black line which borders the road ; its
absence makes it impossible to discover what becomes of a'
stream which runs by the roadside.
In general a stream will cut a contour at right angles to its
general direction, the contour being thrown back upstream
where it crosses. When the fall of the stream is rapid, and
particularly when the ground is rocky, the contours are V-shaped
at the crossing ; when the ground is flat and alluvial the crossings
of the contours are more rounded. It is clear that in general
a stream cannot cross a contour more than once. There are,
however, exceptions to this rule which are at first sight puzzling.
They occur in very flat country, where the streams are some
times confined by banks much above the level of the ground on
each side. In such cases it is possible for a stream to cross
a contour several times. It would be well that streams of this
character should be distinguished by some special sign, for they
are important from the fact that it is easy to breach their banks
and flood the surrounding country.
The characteristic sheet of the French 1/50,000 map distin
guishes between important rivers, shown double ; streams, shown
by single lines ; and canalised rivers, margined by thick blue
lines, with signs for locks. Bridges of stone, steel, and wood ;
suspension and swing bridges ; ferries, and wiers, are all given
conventional signs.
The International Map has a quite different set of signs,
suitable to its smaller scale. Perennial rivers are shown by
a solid blue line of varying width; non-perennial are heavily
long-dotted. Unsurveyed rivers are lightly dotted ; and navi
gable rivers are shown by a double line. Navigable canals have
cross strokes similar to those often used for railways, and non-
navigable are distinguished from natural streams by their
uniformity. There are signs for rapids and falls, and for the
limit of navigation.

PLATE III

CONVENTIONAL SIGNS

S a'y/'t?. d,

lctin£. •!¦¦--<

% .. ,NN JFA-AK E^S|g

National Boundary

Rock and Water Lines

Oi+lnrmce Survey, Xnuth.mnptov.2913.

MAPS 17
Woods and forests.
In black engraved maps these are shown by small tree signs,
sometimes, as in the Ordnance Survey one inch map, of two
varieties to distinguish between deciduous trees and conifers
which are mostly evergreen. (See Plate II.) The effect is
heavy, obscuring details, and rendering names almost illegible.
On the British coloured maps the woods are overprinted with a
tint of bright pale green. (See Plate IV) This brings them
out, perhaps somewhat too conspicuously, but leaves the under
lying detail of roads and names more illegible than ever. The
smaller scale half inch and quarter inch maps have the same
system. It seems to be decidedly better to leave out the tree signs,
and to show woods by a uniform tint of green, except on layer-
tinted maps, where the woods shown thus become confused with
the tints representing height. In the latter case the woods may
be shown by tree signs printed in green, as in the International
Map, though this is hardly clear enough on the green layers.
The French 1/50,000 map shows woods in green tint, without
tree signs ; and has special signs for nurseries, gardens, and
vineyards. Where tree signs are used trees in rows denote
orchards, while trees irregularly disposed denote woods. The
International Map, on the small scale of 1/1,000,000, has no sign
for orchards and vineyards, which are seldom so extensive that
they need be shown on this scale. It remains to be seen how
they will be shown on those sheets of France, Germany, and
California where the vineyards and orchards are of great extent,
and might be shown.
Sheet margins.
It is important that all margins of sheets should be divided
in latitude and longitude, and that the origin of the system of
longitudes should be stated clearly.
It is also desirable that the margins should be divided into
sections of some convenient unit of length, and that each section
should bear a letter or a number, to provide a ready means of
referring to a particular region of the map.
H. M. S. 2

1 8 MAPS
It is further desirable that the margins of contiguous sheets
should overlap to some extent, so that it should never be
necessary to refer to two sheets for the detail of a small district.
The inconvenience of having a town or village on the extreme
edge of the sheet is sufficiently obvious ; yet no general attempt
has been made to provide overlaps in the sheets of any topo
graphical series. Some of the sheets of the large sheet series of
the half inch map of England overlap north and south, but not
east and west ; and on the one inch map there are sheets which
overlap irregularly rather than show a large extent of empty sea.
On the French 1/50,000 map there is a partial attempt to
mitigate the inconvenience of having important detail cut in two
by the sheet margin. East and west, and to a very slight extent
north and south, there is room to show important detail beyond
the strict limits of the sheet ; but the principle upon which the
irregular boundary is drawn is not clear; and there does not
seem to be any advantage over the plan of making all the sheets
overlap by a definite amount.
It is highly convenient to have the sheet divided up by lines
drawn right across it ; and in general it would seem that these
lines should be the meridians and the parallels of latitude. The
map is thus divided into trapeziums, and there is no reason why
they should not be distinguished by letters and numbers to
facilitate reference, as is very commonly done in atlases. There
is, however, a certain advantage in dividing the map into squares
rather than into trapeziums ; it much facilitates the enlargement
of small pieces of the map by the method of squares. For this
reason all the recent half inch maps of Great Britain are divided
into squares of two inches to the side, while the meridians
and parallels are not carried across the sheet. This system
is especially appropriate to the British sheets, which are
rectangular, and not bounded by meridians and parallels, as
more modern sheets are. There seems to be no reason why
both systems should not be used, provided that the two sets of
lines were printed in different colours. (See Plate V.)
In the use of the British squared maps it is most important
to avoid the very common mistake of supposing that the vertical

MAPS 19
sides of the squares are meridians; they may be as much as four
degrees out of the meridian. Yet it is common to find such
statements as that for " practical purposes " the edges of an
Ordnance Survey sheet may be considered north and south.
The sheets of the Ordnance Survey, unlike most, have on
their margins a diagram showing the true meridian and the
magnetic meridian of a given date, with a statement of the
amount of the variation of the magnetic meridian annually. It
is, however, not safe to use this diagram for the purpose of
laying off either true or magnetic meridians. The lines shown
are too short, and they are too close to the edge of the sheet for
¦convenient use. Moreover on some at least of the sheets they
are not accurate, having become a kind of conventional sign, in
which the angle as engraved does not correspond with its
numerical value as stated, while there is no means of knowing
which if either of the meridian lines is engraved at its proper
inclination to the margin of the sheet. This is particularly
embarrassing in the use of the large sheet series of the one inch
map, from which the division of the meridians and parallels has
most unfortunately been omitted.
The representation of hill features.
The real difficulty in mapmaking is to represent the relief of
the ground. This is naturally so, for we are trying to find
a method of representing a solid figure by drawing on a flat
sheet, or to represent three dimensions in two. Moreover, we
have not a free hand to do the best we can with this particular
problem, but are limited by the condition that we must not
obscure the other details on the map.
Until the last few years little progress was made in the
solution of this problem. So long as the map was printed in a
single colour, almost necessarily black, very little could be done.
Recent improvements in the processes of colour printing have
made it possible to produce maps in colour, sometimes with
twelve or fifteen separate printings. This has altered completely
the conditions of the problem, and, while great progress has been
made already, it seems probable that much more may be done. We
.shall therefore discuss this part of our subject as fully as possible.

20 MAPS
The relief of the ground may be shown in a number of
different ways : by hachures or hill-shading ; by contours ; by
spot heights ; by hypsometric tints, generally called in England
" the layer system." And these methods may be, and usually
are, combined so that three or four are in use on the same map.
We shall begin by considering them separately, and then discuss
how they may be used in combination.
Hachures. Hachures are lines drawn down the directions of steepest
slope. On slight inclines they may be delicate and not too
close together. As the slope gets steeper they may be drawn
heavier, and be closer together. If they are drawn faithfully
they are very expressive, and give a good idea of the shape of
the ground. But the system of hachuring has the following
defects :
Its range is small ; that is to say, it is impossible to show
many different degrees of slope. Slight folds in the ground, if
they are shown at all, are exaggerated ; really steep slopes
cannot be shown proportionately heavy without obscuring all
other detail. Moreover, it is impossible to preserve uniformity
of treatment on the different sheets of one and the same map.
The steepest slope on a sheet of nearly flat country may be
actually less steep than a relatively moderate slope on a
mountainous sheet ; and slopes which are important in the
former may be insignificant in the latter. Hence hachures can
be used to indicate that there is a slope, but they cannot give
much information as to the absolute degree of the slope.
It is difficult to draw hachures properly in the field; and
when the field sheets come into the hands of the engraver it is
certain that they will be improved in appearance, and generalised,
so that they become untrustworthy in detail.
Hachures, then, belong to the days of delicate and expensive
engraving upon copper, and with the changing conditions of
map reproduction they are rapidly becoming obsolete. Excellent
examples of the system are to be seen in the old engraved sheets
of the one inch Ordnance Survey maps of the United Kingdom
(see Plate II), and in the older maps of Switzerland ; and it

MAPS 21
survives on the modern colour printed maps that have as their
basis transfers from the engraved plates. (See Plate IV.) But
it is not probable that hachures would be used nowadays on any
entirely new series of maps.
The term hachure has the definite meaning assigned to it
here, and should not be confused with hill-shading, described in
the following paragraph. It is regrettable that in the 191 2
edition of the Manual of Map Reading the distinction between
hachures and hill-shading is not maintained.
Hill-shading. Hill-shading aims at producing very much the same effect as
hachures in an easier and cheaper way. The draughtsman
colours the slopes in rough proportion to their intensity, with
brush or stump. The drawing is then photographed and a hill-
shading plate produced in "half-tone," by a process similar to
that by which photographic illustrations are produced in books
and newspapers. Thus hill-shading consists of series of dots,
whereas hachuring consists of series of lines ; and the two are
very easily distinguished. (Compare Plates IV and V.)
It is difficult to do hill-shading effectively in the field, and it
is generally added by the draughtsman in the office ; but since
it is in its nature more generalised than hachuring, and is quite
unsuitable for showing detail, this is of small consequence.
Both hill-shading and hachuring suffer from the defect that
they do not readily show which direction is uphill and which is
downhill. By themselves, in fact, they cannot give any indication
at all on this important point. A ridge and a valley, each with
shaded sides, cannot be distinguished one from the other simply
by the shading, and one must rely on other details, such as
rivers in the valley bottoms, or heights marked at various places,
to indicate the interpretation of the shading. A sheet with hill-
shading and nothing else might be interpreted equally well in
opposite ways.
We are speaking now of shade which depends only on the
degree of slope, without any convention as to the way in which
the shade is cast ; without, indeed, any possibility of imagining

22 MAPS
it as a shade produced by contrast with light from a definite
source. It is sometimes spoken of as vertical shade — an ex
pression which can have none but a conventional meaning ; in
other places it is called the shade cast by a vertical light, which
is meaningless. These expressions serve, however, to distinguish
it from the other form of hill-shading, which represents the
shadow which would be cast on the ground by oblique light
from a low source, such as the sun near setting. For some
reason which is not clear the source of light is generally
imagined in the north-west. Oblique hill-shading is very much
used in European maps, and it produces a strong effect of relief.
But it has the disadvantage that it makes the slope in the
shadow look steeper than the slope in the light, left unshaded.
In fact it is only by induction that one gets any suggestion at
all of the slopes towards the light.
We may compare thus the effects of the vertical and the
oblique systems of shading. Imagine a ridge and a valley, each
running north-east, with the slopes on each side the same. Under
the vertical shade they would be indistinguishable. Under the
oblique shade they would be readily distinguished one from the
other ; but the ridge would appear steeper on its south-east side,
the valley on its north-west side.
To avoid this difficulty an ingenious system has been devised
for the new map of France on the scale of 1/50,000. The map
is hill-shaded on both systems, printed in different colours.
There is a vertical shade in bistre, and overprinted is an oblique
shade in purple grey. On moderately undulating ground the
effect is excellent ; in mountainous country the colour becomes
too heavy. And the system is of course expensive.
It is clear that no system of hill-shading can give any
information as to the actual height of the ground above sea
level. Hill-shading should therefore be considered as a means
of bringing up the relief of the country graphically, to supple
ment the more precise information which can be given in other
ways. This being so, it is important to notice that the hill-
shading should be kept very light. The least tint that will serve

MAPS 23
to show the difference between one side of a hill and the other
is enough, since the degree of slope should always be denoted
by the closeness of the contours. Hill-shading often suffers
from being too heavy, as in the half inch O.S. map. (See
Plate V.) A pale transparent grey, as in the 1/250,000 Bavarian
Staff map, is probably the best colour.
Spot heights.
Spot heights are the heights above sea level marked at
various points on the map. They are sometimes called spot
levels ; but the misuse of the word level in this connection is to
be condemned. On cadastral maps the height of each bench mark is usually
given ; these are not strictly speaking spot heights, since they
refer to the height of the bench mark, not of the ground. The
heights which, on the British cadastral maps, are given along
the crown of the road are spot heights, and a selection of them
is given on the smaller scale topographical maps. There is
a strong tendency to give spot heights for summits, and not for
the bottoms of depressions.
Spot heights are very useful as exact points of reference, but
they cannot by themselves give any idea of the form of the
country. Contours and form lines.
A contour is a line joining a series of points which are all at
the same height above mean sea level. If the sea suddenly rose
a hundred feet the new coast line would follow the hundred foot
contour. A form line is an approximate contour, not accurately
surveyed, but sketched upon the ground.
There is some difference of practice in the use of the two
expressions, but for our present purpose it is not material to
define the precise difference, in degree of accuracy which divides
contours from form lines. It will be sufficient to keep the term
contour for the product of instrumental methods, even if rough,
and to call the much less accurate contours which are merely
sketched, form lines.

24 MAPS
Thus, the Ordnance Survey maps (Plates IV and V) have
contours ; the Basutoland map (Plate VI) has form lines.
Contours give a maximum of precise information with a
minimum of obstruction to the map. They may be considered
the standard method of showing relief, to which all others are
subsidiary. But to be effective they must be drawn on carefully
considered principles.
Contours should be drawn at uniform intervals of height ;
any departure from this rule is certain to lead to inconvenience.
(See Plate II.) The interval chosen will naturally be a simple
multiple of the unit of length employed : 50 or 100 feet ; 10 or
20 metres. The contours must be numbered ; and when possible they
should be numbered according to the rule adopted in the British
one inch map :
The figures stand on the contours on the 7tpper side. (See
Plates II and IV.)
It is somewhat strange that this excellent rule is not followed
in the later maps of the Ordnance Survey, for it affords a ready
means of distinguishing between uphill and downhill. To do so
it is not necessary that the map should be examined so closely
that the figures of the height may be read. So long as one can
see the places in which the figures are, one can see at once which
way is uphill, for the figures stand on the contours on their
upper sides.
The annexed figure shows the one way which is right and
the three ways which are wrong, according to this principle of
figuring the contours. A comparison of the British one inch
map with any other map will show the undoubted advantage of
this method. It fails only when the contours come so close
together that there is not space to draw the figures between
them. In such cases, and in no other, the number must be
inserted in the line of the contour. A close scrutiny is then
needed to discover in which direction the numbers increase, and
the map is much more difficult to read.
When the country is steep the contours come close together,
and it is difficult for the eye to follow them, even on close

ORDNANCE SURVEY OF ENGLAND

PLATE IV,

One Inch Scale 63,360

In Outline, without Hills

In Colour

OlituilHCt' Sun,;,. Soilthum-pfaii . MIS

MAPS

25

examination ; while if one tries to obtain a general view of the
map, the contours merge into one another, and become a mere
shade. Many of the Swiss maps suffer from this defect.
In such cases it is necessary to guide the eye by accentuating
every tenth or every fifth contour. If, for example, the map is
contoured at ten metres interval, every tenth contour, that is to
say, the hundred metre contours, should be drawn heavily. This

(a)

(<0
Fig. 3. Methods of figuring contours.
[a) right; (b), {c) and (d) wrong.

enables the eye to follow the run of the contours, and is a great
help in reading the form of the ground. It tends to give the
map a stepped appearance, and isolated hills seem to be ridged
like oyster shells, as may be seen especially in the 1/62,500
maps of the United States. But this is a small matter in com
parison with the real advantage of being able to follow the
contours readily.

26 MAPS
The worst way of accentuating each tenth contour is to
chain-dot it, as in the Swiss maps on the scale of 1/50,000.
These dotted contours, which are the only ones figured, dis
appear except under close attention, and the whole system
becomes nearly unreadable. It is instructive to take one of
these maps and to ink in the dotted contours, thus rendering
them heavier than the rest. Immediately the map becomes
readable. We have said that the contour interval must be equal
throughout, and that any departure from this rule is very
inconvenient. There are certain cases in which it may be
legitimate, indeed necessary, to interpolate intermediate con
tours. For example, in flat country nearly at sea level, such as
the fen country in the East of England, there may be a large
area which is all comprised within a single contour interval, and
in such cases an elevation of a few feet may be more important
than a rise of several hundred feet in more elevated regions.
Intermediate contours at close intervals are then very useful ;
but it is evident that they should be readily distinguishable from
the contours of the normal series. They may be chain-dotted,
or distinguished in some other way. But they should not be
drawn exactly like the others, as is done in the British one inch
maps, which show the 50 foot contour, and above that only the
100 foot contours up to iooo feet.
A more serious defect of the British map is that above
iooo feet the contour interval becomes 250 feet, and higher up
the interval becomes wider still. This is destructive of all
facility in reading the map, as may be seen at once in the
example appended. (Plate II.) At iooo feet all the slopes
suddenly seem to become less steep, and it is very hard to train
oneself to ignore this misleading appearance. If the objection
is made that in every steep country contours at uniform intervals
come so close together that they can leave no room for any
other detail, one may reply that in country so steep as this there
is little detail to show, except the contours ; and that the close
ness of the contours gives the effect of hachuring or hill-shading,
with far greater precision than the latter is capable of.

MAPS 27
It is desirable to have some guide to the choice of the
contour interval. An examination of the best examples of
British and foreign maps shows that the rule
Contour interval = 50 feet divided by the number of incites
to the mile
represents pretty well the result of experience. It should be
understood, of course, that this rule is entirely empirical, derived
simply from a number of maps treated as experiments.
Layer colouring, or hypsometric tints.
The layer system, as it is generally called in English, is a
comparatively new system which improvements in colour print
ing have rendered possible. Its aim is to give to the map
the general effect of relief which the contours alone cannot give,
because they can be read over only a small piece of the map at
one time. A scale of gently graded colour tints is chosen, and
all the ground which lies between two certain contours is
coloured a certain tint, while that included between the next
pair of contours is coloured to the next tint on the scale.
An early example of the use of the layer system is found in
the well-known half inch maps of the United Kingdom produced
by Mr Bartholomew. More recent examples are the Ordnance
Survey half inch map (Plate V) ; several Continental maps,
notably the Bavarian General Staff map ; and lastly, the new
International one in a million map of the World. (Plates VIII
and IX.)
The layer system is exceedingly effective in country which
is suited to its use ; and it is very often exceedingly unsuccessful
in general use. We will examine it in some detail.
It is successful in country which does not require more than
seven or eight contour intervals. The colour scale can then be
formed of eight tints of one colour, and progress from light to
dark or from dark to light will denote progressive increase in
height, while even the heaviest tint will not seriously obscure
the underlying detail of the map. Where more than eight
tints are necessary it is difficult to ensure that the heavier tints
shall be transparent enough to leave the detail legible ; and it

28 MAPS
becomes necessary to pass from one colour to another. At this
point difficulties begin.
It is not possible to work up in tints of one colour to the
point of change, from light to dark, and begin the new colour
with the lightest tint, for the contrast is then too violent ; the
scale must be inverted at the change of colour, and if the first
series ran from light to dark, the next must run from dark to
light. This inversion of the colour scale introduces difficulties
in reading the map, which it seems to be impossible to avoid.
They can, however, be diminished by care in choosing the colours
of which the scale is composed. It is asserted, and apparently
rightly, that the change from one colour to another is least
disagreeable when the colours run in their spectrum order. A
colour scale which runs from green through yellow to orange
and red is more agreeable than one which passes from green to
orange without the intervening yellow. How far this principle
rests on physiological foundations is not at all clear; but it
seems to be true in effect. Undoubtedly the most successful
layer system maps are those which follow this rule in the
selection of the colours for the scale of tints.
A more serious difficulty is that even when this system of
choosing colours is pushed as far as possible, it is still impossible
to provide enough tints to serve for a great range of layers at a
uniform contour interval. And were it possible to select the
tints, the number of printings required would be prohibitive. It
is necessary, therefore, in the higher ground, to widen the interval
which is represented by one tint (Plate VII, Afghanistan); and
this produces the same inconveniences as the wider spacing of
the contour interval produces in contoured maps without the
layers. This difficulty is felt especially when the country to be
represented is a high plateau, such, for example, as the Trans
vaal. In such a case differences of a hundred feet are as
important as they are at sea level ; yet if a uniform scheme
were applied throughout they would be shown by differences of
colour in the latter case and not in the former. It is not easy
to see how to overcome this difficulty.
A good deal may be done, however, by drawing in the
contours at uniform vertical intervals (as in the Kenhardt sheet,

ORDNANCE SURVEY OF IRELAND
_1_
Half-inch Scale 126,720

PLATE V

Matin Bay I
¦\

With HiU Shading

Layer System

Oithioruv Snfi'tn: Southampton J.913

MAPS 29
Plate IX), even if it is not possible to assign a separate tint to
each interval. The advantage of this may be seen on comparing
the Bavarian Staff map with, let us say, the layer map of
Scotland. In the former several contours are included in the
limits of a single tint, on the higher ground ; in the latter this is
not done. There can be no doubt that the former is the more
effective. Combined systems of showing relief.
We have discussed separately the merits of spot heights,
hachures and hill-shading, contours, and colour layers. In
practice several of these systems are generally used on one
map. Contours and hill-shading make an effective combination,
and if the contours are drawn strongly they make it possible
to use oblique shading without much danger of the slope in
the shade looking steeper than the slope in the light. (See
Plate V.)
Hill-shading combined with layers demands great skill in
its application, or the shade changes the tint of the layers, and
gives a misleading effect. On the other hand, a layer map with
out hill-shading is very liable to look flat in the higher regions,
where the layer interval is large. (See Plate IX.)
The merits of any combination cannot be discussed with
profit, except by reference to particular maps. We will there
fore defer criticism until we discuss in some detail the best
existing examples of topographical maps of all countries.
Other conventional signs.
It is hardly possible within the limits of this book to give
a complete account of the many other conventional signs
adopted in different series of maps. A study of the conven
tional sign sheets of the different survey departments will show
how varied are the ideas of what is desirable. Some of the
signs for the Ordnance Survey are shown in Plate III.
The tendency of modern map-makers is to elaborate the
conventional signs. The new French map on the scale 1/50,000
is an example, and the special maps for the use of aviators go

30 MAPS
much further. We shall discuss the difficult question of aero
maps in a separate section.
Until recently it was the rule in British maps that no
military or naval works were to be shown, and that no contours
were to be shown within 5000 yards of any fortification. The
result of this rule was that the public maps of garrison and
dockyard towns were meaningless, which probably caused as
much trouble to the Services as to the public, though of course
there were complete confidential editions. As a precaution
against knowing the position of a fortification the rule by its
strictness defeated its own object, since it was easy to mark the
points where the contours were suddenly discontinued, to draw
the circle through those points, and to conclude that a fort was
at the centre. The newly published smaller scale maps now
show the positions of the forts, and the contours have been
completed. Map reading.
Facility in reading from a map all the information that is
implied in its conventional representation of the ground is an
accomplishment only to be attained by constant practice in the
field, and it is useless to attempt to lay down many rules for it.
Much excellent advice on the methods of learning the art is
given in the Manual of Map Reading and Field Sketching;
and we will not attempt to cover again the ground which is
thoroughly gone over in that book. But we will try to supple
ment what is said there by a few'additional notes.
Sections and profiles.
In the solution of many practical problems it is required to
draw a section across the country, from the information which
is given on the topographical map. Suppose a line drawn
across the map along the line of the proposed section : it will
cut the contours at a number of points, and these points will
furnish the principal material for the construction of the section.
Lay a strip of paper along the line, and mark on it the points
where the line cuts each contour. Draw perpendiculars from

MAPS 31
the edge proportional in length to the heights of the contours
above sea level : this will be facilitated if the paper is furnished
with equally spaced lines parallel to the edge, and distant from
one another by the contour interval on the adopted vertical scale
of the section.
A broken line joining the summits of these perpendiculars
is a rough approximation to the section, which can be much
improved by studying the other indications of height upon the
map. Thus, it is improbable that a spot height will fall exactly
on the line of the section, but a good deal may be learned from
those that fall near. Hill-shading is useful in suggesting the
probable shape of the country between the contours, and care
should be taken to utilise the information which is given by
streams. By taking advantage of these subsidiary sources of
information it is possible to construct a fairly good section from
a topographical map ; and of course the closer the contour
interval the more accurate the result.
It is however inevitable that a section drawn in this way
should be conjectural in its details, and if accuracy is required
it is necessary to run a line of levels across the country along
the line of the section. For this process we refer to the chapter
on Levelling (page 95).
A profile of a road is a section run along the course of the
road, instead of straight across country. It is constructed in
the same way as a section, by laying a strip of paper along
successive lengths of the road and marking off the points where
the contours are crossed. In addition there are generally a
number of spot heights marked along the road, and these are
especially useful because they give summits. When a road
rises above a contour and falls below it again there will usually
be found an intervening spot height, which will mark the
summit. It is often useful to have the profile of a road along which
it is necessary to send traffic, and profiles of the main roads
of the country are being published for the use of motorists.
Unfortunately the makers of these books have adopted the
wrong name " contour road book," instead of " profile road
book." This bad mistake should be avoided.

32 MAPS
Problems of intervisibility.
Questions on the use of maps very often demand the solution
of the problem, whether one point is visible from another. It is
evident that this can be solved, in some degree, by drawing a
section from one point to the other, and seeing if any intervening
point on the section rises above the ray joining the given points.
Since the section can be only approximate it is_.clear that caution
must be used when the ray clears the intervening ground by only
a little. In most cases it is not necessary to draw Js?re than a part,
if any, of the section, for it is easy to see where are the critical
points. J
It should never be forgotten that in undulating wooded
country the trees are the principal obstacles. to mutual visibility
of points, and it is not possible to estimate from the map the
effect of the trees. Hedgerow trees, which are not marked on
the map as woods, since they offer little obstacle to the passage
of men, are often a complete obstruction to the sight. Conse
quently problems of mutual visibility of points are more useful
in testing the understanding of the map than in deciding whether
it is actually possible to see from one point to the other.
Reconstruction of the view from a given point.
It is an excellent exercise in map reading to try to recon
struct from the map the view of the country from a point of
vantage, and to draw it as a panorama. From the chosen point
of view radiating sections are run across the country, and it is
usually not hard to discover what heights form the sky line in
different directions, and what features are prominent in the
middle distance. When these are determined, a study of the
contours gives a general idea of the shape which these features
will present, and then by the exercise of some ingenuity it is
possible to construct a panoramic sketch which reproduces the
broad features of the view. A few exercises of this kind are
very useful in teaching facility in reading relief, especially in
town schools where it is difficult to reach actual ground on
which to practise.

MAPS 33
Identification of distant objects.
It will often happen that a wide view, say in the Lake
District, or on Dartmoor, presents a confused panorama of
peaks which cannot be identified by their relations to one
another as shown on the map. To identify such a distant
object it is necessary to take its bearing by compass, subtract
the westerly deviation, as given on the margin of the Ordnance
Survey map, and with the protractor to lay off" a line on the
resulting true bearing from the point of observation. For the
instrumental process reference may be made to page 105.
The distant object will then lie on this line drawn upon the
map ; and of the several objects at varying distances which may
chance to lie on it, it will not in general be difficult to select the
right one.
The reverse problem sometimes arises. It is desired to
identify on the ground, or at least to discover in what direction
it lies, an object which is marked on the map, but which is not
apparent to the sight. In such a case draw on the map a line
from the point of view to the object in question, measure with
the protractor the true bearing of this line, and add the compass
deviation west. Then with the compass to the eye turn slowly
round until some object is found which has the given compass
bearing. The object sought will lie in the same straight line
from the observer, and with this indication it is often possible to
discover it, or at any rate to find exactly where it lies.
Measurement of areas.
The first consideration which arises in this problem is : are
the areas correctly represented on the map ; or is the projection
on which the map is constructed an equal area projection.
Topographical maps are not usually constructed on a pro
jection which is theoretically an equal area projection ; but the
misrepresentation of areas will always be much less than the
uncertainty which is introduced by the expansion and contrac
tion of the paper with damp.
Atlas maps will very often be on projections which mis
represent areas grossly ; but for a consideration of this question
h. m. s. 3

34 MAPS
reference must be made to a treatise on the somewhat intricate
subject of Map Projections.
An easy way of measuring areas on a map is by superposing
a sheet of tracing paper regularly ruled in small squares. First
count the number of whole squares embraced by the area, and
then estimate how many whole squares more are equivalent to
the array of partially included squares along the boundary of
the area. From the scale of the map calculate the area repre
sented by one square of the tracing paper, and thence derive the
whole area of the figure in question.
More elaborate methods involve the use of special instruments
such as the planimeter.
The "Amsler" planimeter is a beautiful instrument whose
use is simple, but whose theory defies explanation in an
elementary book. ,It consists essentially of an arm carrying
a pointer which is moved round the boundary of the area to
be measured, and a wheel which rolls on the surface of the
paper. A second arm is pivoted to the first between the
pointer and the wheel, and its other end is free to turn about
a fixed point. As the pointer moves round the boundary the
wheel revolves, sometimes forwards, and sometimes backwards.
The nett amount of rotation forwards is measured by a revolu
tion counter and by divisions on the drum attached to the
wheel. The nett rotation, multiplied by a suitable constant,
gives the area. (See Plate X.)
The precise computation of areas is an important part of the
work of a cadastral survey, but its methods are beyond the scope
of this book.
Measurement of distances on a map.
As in the measurement of areas, it is first necessary to know
if the distances are correctly represented on the projection which
is employed. And a treatment of this matter is beyond the
scope of the present book. On all topographical maps the
distances are shown so nearly true that they may be measured
to within the error caused by paper shrinkage. For the methods
of construction of scales see page 13.

MAPS

35

Map Reproduction.
It would be impossible within the scope of this book to
describe in detail the many processes which are employed in
the engraving and printing of maps. But a very slight sketch
of the principal methods may be of interest.
The best of the old maps, in black only, were engraved on
copper, and from the copper a steel-faced electrotype was made.
The whole plate was covered witlTink, and the surface wiped,
leaving the engraved lines charged as in the ordinary process
of printing from steel engraving. The print was made in a
heavy press, which forced the paper into the engraved lines,
from which they took up the ink. Maps printed from engraved
plates can be distinguished by the relief of the lines. This
process gives the best results, but it is slow and expensive,
and does not lend itself to printing in many colours, which
is now a necessity. In the production of modern maps, there
fore, the various processes of photolithography on stone or zinc
have displaced printing from engraved plates.
Where, however, the expense of engraving on copper can be
afforded, an engraved plate still forms the basis of the process.
From the engraved plate a print in light blue is taken, and the
draughtsman inks in on this the portions which it is desired to
print in any one colour. When this drawing is photographed
the light blue disappears, and only the inked-in portion is
transferred to the stone or zinc from which the coloured im
pression is made. Thus it is possible to prepare from the
basis of an engraved original as many colour plates as may
be required. Recent improvements in colour printing presses have greatly
increased both the speed and the accuracy of register of the
impressions, so that it is possible to produce at a reasonable
cost maps with a dozen or more impressions. The success of
modern topographical maps is due largely to the greatly ex
tended possibilities afforded by these processes.
Engraving on copper is costly, and many attempts have
been made to find a substitute for it ; the engraving of the
names, in particular, seems at first sight to be very wasteful.
3—2

36 MAPS
But no method of stamping the names from steel dies has
proved satisfactory. Some excellent results have been obtained,
however, by drawing with a graver on glass coated with a white
pigment which can be blackened chemically, and from which
the printing plates can be made by photography. Another
process which has given good results involves drawing on an
enlarged scale on tracing paper, and photo-etching on copper
from the drawing. But in each case the names have to be
drawn — a tedious process.
All these are for maps of the highest class. For cheaper
work there is a variety of processes of photozincography, and
of preparing zinc plates by contact printing from a tracing.
For rapid work in the field on active service, field lithographic
presses have been designed, and a Printing Company, R. E.,
accompanies the Intelligence Division on service, ready to re
produce in short time any plans, enlargements, or sketches that
may be required. For an interesting account of the equipment
and organisation of such a company, reference may be made to
the Textbook of Topographical Surveying.
For a complete technical treatise on the methods of engraving
and printing, reference may be made to Methods and Processes
adopted for Production of the Maps of the Ordnance Survey,
Second Edition, 1902.

CHAPTER II
MAP ANALYSIS
Ordnance Survey Maps.
Until within comparatively recent years the Ordnance
Survey produced excellent maps but appeared to have little
interest in the question whether they sold or not. The maps
were published in the form of flat sheets only, and before they
could be used out of doors it was necessary to spend at least as
much as the price of the map in having it mounted on linen
and put into covers. The means of distribution and sale of the
maps were also very inadequate.
About fifteen years ago maps mounted on linen and folded
in covers were put on sale, and more recently the method of
mounting in book form was introduced. This last simple ex
pedient has done more than anything else to increase the
convenience of using the map, yet strangely enough it has
not been imitated, and it is still difficult to get an unofficial
map-mounter to understand how to do it. A map so mounted
can be opened at any desired section with one hand, while the
other hand remains free for driving or bicycling. The map does
not catch the wind, nor does it offer much surface to the rain,
and it can be consulted without attracting attention.
It is a mistake, to buy for field use any maps but those so
mounted on linen, and folded without dissection. The dissected
map is more flexible and lasts longer ; but it is impossible to
make measurements upon a dissected map, and this should be
sufficient to condemn it.
Ordnance Survey maps can be bought at the local agents,
and at the principal booksellers and railway bookstalls. It is

38 MAP ANALYSIS
not so well known that they can be obtained also by return
of post from the Ordnance Survey Office at Southampton ; and
this is very useful when a map is suddenly required while on a
holiday. The large scale cadastral maps on the scales of 1/2500 and
1/10,560 and the town plans of five and ten feet to the mile
hardly concern us here.
The topographical maps are
the 1/63,360, or one inch to the mile, which is the standard topo
graphical map of the country, and in its recent form on large sheets is
the most valuable for local use1.
the 1/126,720, or half inch map, which is the standard military map
for war and manoeuvres, and is also the most generally useful for motoring
and bicycling. the 1/253,440, or quarter inch map, which is the most useful for
planning long distance journeys, and for intelligent railway travelling.
The smaller scale maps, ten miles to the inch, and the one
in a million map, are for strategical and general purposes.
The student should make a point of analysing examples of
the different series, since in no other way is it possible to obtain
an idea of the possibilities of the different scales, or of the
difficulty of finding a uniform system of mapping that shall
be satisfactory in all varieties of country. The following notes
on selected sheets are given merely as illustrations of some of
the more obvious points of interest.
Ordnance Survey of England and Wales. 1/63,360.
Sheet 42. (Large sheet series.) Third Edition. Llandudno.
Printed in colour at the Ordnance Survey Office, Southampton. Dated
1909. Relief by contours and hachures. Contours at 50, 100, and each 100 to
iooo, then at 250 feet interval to 3000. Printed in red, figured in black.
The break in the contour interval at iooo feet has particularly noticeable
results on this sheet.
Vertical hachures in brown; cliff drawing in black, very conspicuous.
Spot heights frequent.
1 This map can be obtained in the coloured edition, which is far the best (see
Plate IV), and in the outline edition in black. The editions with hills in black and
in brown have now been withdrawn.

MAP ANALYSIS 39
Contours in the sea bed 25 and ^ofeet below mean sea level, not fathoms
as on the half inch map.
Metalled roads: first and second grades, black filled yellow; third grade,
thin double black. Unmetalled roads same, but narrower. Footpaths long-
dotted, and very likely to be confused with parish boundaries.
Woods, tree signs in black, over printed heavy green with boundaries.
Margin divided into two-inch divisions, not carried across sheet, but
lettered and numbered. No indication whatever of latitudes and longi
tudes, a grave omission.
Small characteristic sheet attached.
This sheet is a very good example of the present one inch map of Great
Britain.
Ordnance Survey of England and Wales. 1/126,720.
Sheet 39. (Large sheet series.) Brighton.
Printed in colour at the Ordnance Survey Office, Southampton. Dated
1908. Relief by contours, hill shading, and layers. Contours at 50, 100, 200,...
and by 100 feet interval to iooo; printed in brown, very lightly, and figured.
Spot heights. Layer colours change at each contour, green passing through
light brown to very heavy brownish green. Vertical hill-shading. The
relief of the country is well shown, but underlying detail is obscured by
the heavier colours, and the contours are confused by the hill-shade and the
tree signs.
Roads: black filled yellow, two grades, and inferior roads double black
only. No tracks or hill paths. Water blue. No contours in sea. Woods
green tree signs, no boundaries1.
Scale of miles. Latitude and longitude in margin, not carried across.
Magnetic meridian and annual variation.
Names black, stamped and ugly.
Small characteristic sheet.
The same: new edition, ign.
New scale of layer colours, changing at ioo, 200,... 700, 800, iooo, green,
through yellow, to pale brown. No hill-shading. The map is much more
legible, but the strong effect of relief is lost.
Contours in sea bottom: low tide, 5 and 10 fathoms. Layer tints of blue.
Ordnance Survey of England and Wales. 1/126,720.
Sheet 5. (Large sheet series.) The Lake District.
Printed in colour at the Ordnance Survey Office, Southampton. Dated
1908. Relief by contours, layers, and some hill-shading.
1 Note : On some sheets of this edition the woods are shown by plain green tint
without tree signs, e.g. Sheet 24, Huntingdon.

40 MAP ANALYSIS
Contours 50, 100, 200,. ..iooo, 1250, 1500, 1750, 2000, 2500, 3000, lightly
printed in brown and figured. Layer colours change at each contour, green
into pale brown, ascending to brownish grey, descending to bluish grey,
ascending to dark slate colour. An exceedingly ugly map, showing the
layer system at its worst.
Other details as in Sheet 39 above.
Ordnance Survey of Scotland. 1/126,720.
Sheet 32. The Border Country.
Printed in colour at the Ordnance Survey Office, Southampton. Dated
1910. Relief by contours and layers. Contours 50, 100, 200, and at 100 feet
interval right up, printed in brown, and figured. Spot heights frequent.
Layer colours change at 100, 200, 300,. ..800, iooo, 1500, 2000, 3000, green,
yellow, leading to brown, and finally to an ugly shade of magenta (on the
map), not conforming with colour scale in margin. No hill-shading. This
colour scale adopted after the breakdown of the English scale on high
ground. Result on this sheet unsatisfactory : colour uniformly heavy,
obscuring contours.
Roads : double black filled with yellow (two grades), and inferior roads
double black only. Tracks and hill paths not shown. Water blue. Woods :
green tree signs, no boundaries.
Scale of miles. Latitude and longitude on margin, not carried across.
Magnetic meridian and annual variation.
Trans-border country shown fully (a welcome improvement in British
practice). Names black : stamped and ugly.
Small characteristic sheet.
Ordnance Survey of Ireland. 1/126,720.
Sheet 3. Donegal.
Printed at the Ordnance Survey Office, Southampton. Dated 191 1.
Relief by contours and hill-shading. Contours uniformly at 100 feet
interval throughout, printed lightly in red, and figured in brown. Hill-
shading vertical. Spot heights. 5 and 10 fathom contours in sea, and
blue layers. Woods green, with black tree signs and boundaries.
Sheet divided into two inch squares, with reference letters and numbers
in margin. Other characteristics as on the British sheets of this scale.
The same, with layer colouring instead of hill-shading : see Plate V for
small example.
The new scale of tints is very successful. The series begins with two
descending shades of pale green ; from 200 to 400 is left almost white, which
is a new idea in layer colouring ; above 400 the successively increasing clear
brown tints change at every 200 feet. This is by far the best layer map
yet produced by the Ordnance Survey.

MAP ANALYSIS 41
Ordnance Survey of England and Wales. 1/253,440.
Sheets 19 and 23 combined. Second Edition. Berks, Wilts, Hants, etc.
Printed in colour at the Ordnance Survey Office, Southampton. Dated
1911. Relief by hill-shading in brown. Spot heights. No contours.
Roads: first class, black filled yellow; second class, double black; third
class, single black line.
Woods : tree signs in black, over printed pale green with boundaries.
Margin divided in latitude and longitude, and meridians at 20' interval,
parallels at 30' interval carried across the sheet. Notice the obliquity to the
meridian of the sheet edges.
The second edition differs from the original edition in the following
points : The names are re-engraved and much improved ; the woods have
tree signs added, and the colour is much paler; the sign for railway station
is much improved.

Maps of the Geographical Section, General Staff.
The Geographical Section of the General Staff, War Office,
publishes a very large and varied selection of maps of British
territories, and of other parts of the world in which Great Britain
has special interests, or for which it is not likely that maps will
be made by the local governments.
Some of these maps represent the work of the Colonial
Survey Section; others are compilations from route traverses
and miscellaneous work, and are of a provisional character ;
others, again, as the map of Canada now in progress, are
published by arrangement with the Dominion authorities. The
series of maps of Turkey in Europe, and of China, cover regions
which have not been mapped by the local authorities, while the
maps of Arabia, Mesopotamia, and Persia provide material for
the consideration of strategic and political interests.
The style of production of these sheets is varied, and many
of them, being provisional, are comparatively rough. Of recent
years, and especially since the building of the new War Office
gave the Geographical Section adequate accommodation, great
improvements have been made in the execution of the maps,
and the latest productions, particularly the Canadian map, and
the first sheets of the International Map, are of the highest
class.

42 MAP ANALYSIS
The following notes are intended only to call attention to
the importance of a study of these maps for all students of
geography. Orange River Colony. 1/125,000.
Sheet 125. V. iv. Odendaal's Rust.
Lithographed at the War Office, 1906.
Relief by contours, in brown, at 100 feet vertical interval, and occasional
hill-shading. Spot heights plentiful.
Roads shown in three grades, principal roads filled yellow. Water blue.
Bush shown by green tree signs.
Margins show latitude and longitude, and index numbers and letters.
Magnetic meridian and variation.
Full characteristic sheet, and index to character of the river drifts, and
of the water, grazing, and fuel at various halting places.
There is little detail to be shown on the sheet, leaving room for notes on
roads and character of country.
Basutoland. 1/250,000.
N.E. Sheet. (See Plate VI.)
Printed and published by Geographical Section, General Staff. June,
1911. Relief by approximate contours, at 100 feet vertical interval, printed in
brown. Cliff drawing brown. The contours are figured occasionally, but
generally they are too close for figuring.
Roads practically none. Bridle paths dotted black. Water blue.
A very interesting example of the ability of contours to show the relief of
a mountainous and difficult country where there are few names and no roads
or other detail to break up the run of the contour lines.
Uganda. 1/250,000.
_. North A. 36
Sheet  ^  (reference number on the new International Map system).
Printed in colour and published by the Geographical Section, General
Staff. 191 1.
Relief shown by approximate contours at 200 feet vertical interval, with
interpolated contours at 100 feet interval long-dotted. Contours drawn
exceedingly fine and printed in pale brown. Spot heights very numerous,
brown. Main roads coloured brown. Water blue. Forest by green tree signs.
Cultivation yellow. Names very numerous, in black.
Full characteristic sheet. Magnetic meridian.
An unsatisfactory map, the relief of the ground quite illegible, owing
to the confusion of the very faint contours with other detail. It should be
compared with the map of Basutoland produced in the same year in the
same office.

Plate VL

Geoi/rapTiuXbLSectu/n., General.StatT

Wii-0fhce,ISI3

PART OF N.E. SHEET
BASUTOLAND
Scale — 250,000
FORM LINES AT APPROXIMATE 100 FT. V. I.

Hate VEL

G&jt/rtipluMztiLS&iiAn,, GencraliSUifT
PART OF SHEET
PERSIA AND AFGHANISTAN
Scale - «,o5s,o4o
NEW EDITION 1913.

Wu-omoe,?yi3.

MAP ANALYSIS 43
Persia and Afghanistan. 1/4,055,040.
Published by the Geographical Section, General Staff, War Office. 1906.
Relief by contours and layer system. Contours at 500, iooo, 2000,
4000, 6000, 8000, 1 0000, 15000, and 20000 feet, printed in brown, not figured.
Layer colours in increasing shades of brown, changing at the above contours.
No spot heights.
Railways in red, with distinction of gauge.
Roads in red. Water in blue.
Meridians and parallels at 5° interval carried across the sheet.
International boundaries green.
An interesting example of the difficulty of representing the tremendous
mountain region of the Indian N.W. Frontier. Even with the great vertical
interval of 5000 feet the contours in many places are too close for a clear
appreciation of the layer tints.
A new edition of this map is in preparation, which is a great improvement
on the old, and has many features of interest. The system of layer tints,
green through orange (of a brownish shade) to clear red, is light and clean.
There is some hill-shading in greenish ray, and contours are in grey.
We are much indebted to the Chief of the Geographical Section, General
Staff, for placing at our disposal the specimen of the new edition given on
Plate VII.
Foreign Maps.
Nearly all the countries of Europe are now more or less
completely mapped, and the publications of the respective
Survey Departments exhibit every variety of style, and of
success or comparative failure. In other continents the work
of survey is naturally less advanced; but there are now few
civilised states which have not realised the importance of an
accurate survey of their territories.
Within the limits of this small book it is impossible to do
more than make notes on some of the interesting characteristics
of a selection of foreign topographical maps. It is hoped that
the selection is fairly representative, but it is far from complete,
and the specimens chosen for annotation are doubtless not
always the best. The author is, however, so convinced of the
importance of a study of these foreign maps that he has thought
it best to give in all cases the number of the sheet to which
these brief notes refer, in order that students may have some
guide in purchasing examples of the work of the principal
foreign surveys.

44 MAP ANALYSIS
Since the object of this study of various examples is to
compare the respective merits of different systems, it is inevitable
that the question will arise, How do the British maps compare
with those of other European countries ? The answer appears
to be that there are isolated examples of topographical maps,
new series of which only a few sheets have appeared, which are
in some respects better than British maps : notably the 1/50,000
map of France, and the 1/250,000 map of Bavaria. But on the
other hand there is no country which has maps of greater variety
and completeness, and of more uniform excellence.
France. 1/50,000.
Sheet XXII. 14. Versailles.
Not dated. Printed in colours by the Service Geographique de PArmSe.
Relief : contours and double system of hill-shading. Contours in brown
at 10 m. vertical interval, but not figured. Spot heights frequent. Vertical
hill-shade in bistre ; oblique shade from north-west in purplish grey.
Roads in black, four grades ; tracks in black, two grades.
Buildings in red, so that where a road approaches a town and becomes
bordered with houses it loses its black outline and becomes less conspicuous.
Water blue.
Scale of kilometres. Latitudes and longitudes shown on margin in the
ordinary and the centesimal division. Origin of longitudes Paris. Meridians
and parallels not carried across the sheet.
Woods, meadows, and gardens in different shades of green ; orchards
and vineyards in purple, which becomes confused with the grey hill-shading
and sometimes destroys its effect.
Population of each village shown in red, but the date of census not
shown. An excellent feature is that the margins are left open, and the principal
roads, railways, etc. are continued off" the sheet, together with anything
which would surfer from being cut across by the sheet margin.
Railways, three grades, narrow gauge, and tramways, all in black.
Writing very plain. Names of water in blue.
Elaborate characteristic sheet, including separate signs for factories
operated by steam, water power, and electricity respectively.
The most elaborate topographical map yet produced.
France. 1/200,000.
Sheet 8. Abbeville.
Printed in colour and published by the Service Giographique de VArmee.
No date.
Relief shown by contours and vertical hill-shading. Contours at 20 metres

MAP ANALYSIS 45
vertical interval, very finely drawn, printed in pale brown, and not figured.
Hill-shading brown.
Roads and tracks, six grades, in red. Railways in black. Water in
blue. Woods in green ; tree signs.
Meridians and parallels carried across map, inclined to margins, figured
in centesimal division of the quadrant. Margin divided also in kilometres.
Full characteristic sheet.
The contours drawn so lightly and so much overlaid with names and
detail that the relief is illegible.
Bavaria. i/ioo,ooo.
Sheet 637. Landsberg.
Published by the Bavarian General Staff. 1904.
Relief by contours and hachures. Contours at 50 metres vertical interval,
printed and figured in brown. Vertical hachures in brown.
Roads in three grades, double and single black.
Water blue. Woods by tree signs in black.
Names of water sloped to left.
Margin shows latitude and longitude (East of Ferro).
Scale of kilometres and "geographical miles": one mile = 7420-44 metres.
The contours drawn so lightly and so much overlaid with detail that
relief illegible.
Bavaria. 1/250,000.
Sheet 8. Munich to southern frontier.
Dated 1906. Printed in colours. K. Topograph. Bureau.
Relief by contours, hill-shading, and layers. Contours at 100 m.
interval throughout ; contours at boundaries of layer tints strengthened ;
all printed in brown ; some intermediate contours in brown long-dotted.
Contours not figured, and spot heights infrequent. Hill-shading light grey,
oblique, north-west light. Layer colours in spectrum order, leading to very
clear red for high mountains. Colours change at 300, 400, 500, 600, 800,
iooo, 1200, 1500, 2000, and 2500 m.
Roads in black. Water in blue. Woods not shown.
Scale of kilometres. Latitudes and longitudes on margin. Origin of
longitudes not stated ; evidently Ferro. Meridians not carried across sheet.
Trans-frontier country left nearly blank.
Writing : place names italic ; mountain names block ; water names in
blue, sloped to left.
No characteristic sheet attached.
The general effect of this map is exceedingly good ; it is perhaps the
best example of its kind.
Saxony. 1/25,000.
Sheet 15. Wellerswalde,
Engraved, lithographed, and printed at Leipzig for the Saxon General
Staff. 1906.

46 MAP ANALYSIS
Relief by contours, in brown, at 5 metre intervals, the intermediate 5's
broken, and the 20's strengthened. Also subsidiary dotted contours when
required, at variable intervals down to I m. Contours not figured, except in
the margin, but spot heights numerous, and the contours easy to read on
this sheet.
Railways and roads black. Water blue. Woods by tree signs, black.
Elaborate characteristic signs, but no explanation attached.
Margin shows latitudes and longitudes (East of Ferro).
A very well-engraved and clear sheet.
Switzerland. 1/25,000.
Sheet 376. Pilatus.
Dated 1894. Revised to 1906. Printed in colour by the Eidg. Topograph.
Bureau. Relief by contours in brown, at 10 m. vertical interval ; every tenth
contour long-dotted and figured. The contours are so close that they are
very hard to follow. Cliff drawing in black.
Roads in black, of two grades. Tracks in black, long-dotted.
Scale of kilometres, and map divided into squares of approximately 6 cm.
Latitudes and longitudes shown on margin. Origin of longitudes not
stated, apparently Paris.
Meridians and parallels not carried across the sheet.
Woods shown by very minute tree signs in black, making the pale brown
contours still more difficult to read. Water blue.
Writing in italic ; no distinction between physical features and village
names. No characteristic sheet attached.
Switzerland. 1/100,000.
Sheet XVIII. Rhone Valley and Simplon.
Dated 1854, revised to 1907. Engraved, and printed in black.
Relief shown by hachures, darkened on the side away from a north
west oblique light. Good cliff drawing. Glaciers only contoured. Spot
heights in metres, small and rather illegible.
Trans-frontier country shown in full.
Roads double black lines, white between, showing up well on the dark
hachures. Tracks long-dotted, not very distinct.
Scale of kilometres and hours. (One hour equals 4-8 km.)
Latitudes and longitudes shown on margin in the ordinary and also in
the centesimal system. Origin of longitudes not stated. Meridians not
carried across the sheet.
No characteristic sheet attached.
Switzerland. 1/250,000.
Special railway map.
Published by the Swiss Topographical Bureau, Bern. 1908.

MAP ANALYSIS 47
The ordinary engraved and hachured map is printed in brown. Rail
ways with names of stations are heavily overprinted in black.
An excellent example of the map for special purposes.
Italy. 1/100,000.
Sheet 32. Como.
Dated 1907. Printed in colour at the Istituto Geografica Militare.
Relief: contours and hill-shading. Contours in light brown, at 50 m.
vertical interval. Hill-shade oblique, north-west light, brown. Frequent
spot heights. Roads in black. Three grades metalled, two grades un-
metalled, and various kinds of tracks distinguished. Railways, double and
single, tramways narrow gauge and tramways distinguished. Water blue.
Houses black. Woods not shown.
Scale of kilometres.
Latitudes and longitudes on margin. Origin of longitudes : Rome,
Monte Mario.
Meridians and parallels not carried across the sheet.
Mountain names in engrossing. Water names in black.
Good characteristic sheet attached.
Italy. 1/200,000.
Sheet n. Brescia.
Dated 1908. Printed in colour, by the Istituto Geografica Militare.
Relief by contours and hill-shading. Contours at 100 m. vertical interval.
Hill-shade in grey brown, oblique.
First and second grade roads in red ; third grade, black in the plains
and red on the mountains. Minor roads made and unmade, muletracks,
footpaths easy and difficult, and mountain passes all distinguished by
characteristic signs. Railways black. Water blue. Towns by signs to
indicate degree of importance. Double, single, narrow gauge, and tram
ways of various kinds, all distinguished by signs. Woods pale green.
Scale of kilometres.
Latitudes and longitudes shown on margin. Origin of longitude : Rome,
Monte Mario. Meridians and parallels not carried across sheet.
International frontier with broad band of colour. Trans-frontier country
in full detail.
Mountain names in engrossing, difficult to read.
Good characteristic sheet attached.
Central Europe. Austrian General Staff Map. 1/200,000.
Sheet 41° 41°. Saloniki.
Dated 1903, revised to 1909. Printed in colour.
Relief by hill-shading and contours. Hill-shade vertical, pale brown.
Contours darker brown, at 100 m. interval.
Roads in black, two grades ; and tracks long-dotted. Railways black.
Water blue, but not the names of water. Woods shown by pale wash of
green.

48 MAP ANALYSIS
Latitudes and longitudes on margin. Origin of longitudes : Ferro.
Meridians and parallels not carried across sheet. Sheet not bounded by
meridians and parallels.
Scale of kilometres and schritte. (iooo schritte=075 km.)
Mountain names in engrossing.
No adequate characteristic sheet attached.
A very ugly map.
Central Europe. Austrian General Staff Map. 1/750,000.
Sheet 8. Skoplje.
Dated 1900. Printed in colours.
Relief by contours and layers. No hachures or hill-shading. Contours
at 150, 300, 500, 700 and thence at 300 m. intervals; layer tints in ascending
shades of brown, rather heavy. Contours in darker brown are the boundaries
of the layers ; no intermediate contours. " Thalsohlen und Thalebenen,"
apparently plains in the bottoms of valleys, in two shades of greenish blue.
Roads of two principal grades in red ; third grade in black ; tracks in
black, long-dotted. Railways in black. Water, including names of water,
in blue. Scale of kilometres.
Latitudes and longitudes on margin. Origin of longitudes : Ferro.
Meridians and parallels drawn across sheet.
Woods not shown. Mountain names in engrossing.
No characteristic sheet.
Austria-Hungary. School district maps. 1/100,000.
Sheet Deutsch-Lansberg.
Dated 1910. Printed in colours by Freytag and Berndt, Vienna.
Relief by contours, oblique hill-shading, and layers. Contours in brown
at 50 m. vertical interval. Hill-shading in grey, by north-west light. Layer
tints in pale green, yellow, orange, and red. Contours at iooo and 2000 m.
long-dotted. Colour changes at 400, 500, 700, and 1500 metres. Difference
of tints so slight, and so much obscured by hill-shading, that practically only
the change at 500 from green to yellow is of much account.
Roads in black, two grades ; no tracks shown. Railways in black.
Water blue.
Scale of kilometres. Section across the country.
Woods not shown.
Latitudes and longitudes on margin. Origin of longitudes : Greenwich.
Meridians and parallels not carried across the sheet.
Writing: no distinction between place-names and physical features.
Characteristic sheet attached.
Price 50 heller (about $d.). Very good maps for the price.
Greece. 1/75,000.
Sheet 400 i° E. PA*ANH-TEMIIH.
Dated 1909. Printed in colours by the K. K. Geog. Inst., Vienna.

MAP ANALYSIS 49
Relief by vertical grey shading. Contours at 20 m. darker grey ; 100 m.
contours strengthened ; occasional intermediate 10 m. contours long-dotted.
Sea bottom contoured, at 2, 5, 10, and by tens to 60 m. Cliff drawing
brown. Principal features across frontier shown, with 100 m. contours and hill-
shade. Roads red, in three or more grades. Tracks in red. Water blue.
Woods black, with tree signs.
Scale of kilometres and Bemata (paces). Scales of slopes corresponding
to contour intervals (this an unusual feature).
Latitudes and longitudes on margin. Origin of longitudes : Athens, with
reduction to Greenwich. Meridians not carried across sheet.
Writing in modern Greek character. Mountain names engrossing.
Complete and elaborate characteristic sheet attached-
Sweden. 1/200,000.
Sheet 58. Kolasen.
Date 1905. Printed in black and slight colour.
Relief by hachures below about 550 metres and contours above; both
black. Hachures vertical; contours shaded to bring up relief, apparently
arbitrarily. Contours not figured, and spot heights insufficient to show
contour interval. Combination of hachures and contours in this way unusual.
Principal roads double black line, yellow between. Lakes blue. Rivers
black. Scale of kilometres.
Latitudes and longitudes on margin. Origin of longitudes : Stockholm,
with reduction to Greenwich. Meridians but not parallels carried across
sheet. Woods not shown very clearly ; small black tree signs on the hachures
hardly distinguishable.
Trans-frontier country left entirely blank.
Writing : no distinction between hill names and villages ; names of lakes
sloped to the left.
No characteristic sheet attached.
Sweden. 1/500,000.
Sheet 11.
Date 1896. Printed in colour by the Swedish General Staff.
Relief by contours and layers. Contours at 100 metres vertical interval,
in brown, with intermediate contours at 33 and 66 metres up to 500 metres.
Layers changing tint at each 100 metres, in shades of yellow, brown, bluish
grey, to white. Colour scale ascending, then descending. No hachures or
hill-shading. Latitudes and longitudes shown on the margin. Origin of longitudes :
Stockholm. Meridians and parallels carried across the sheet. Edges of
sheet not meridians but much inclined.
H. M. S. 4

50 MAP ANALYSIS
Lakes blue ; rivers black. No roads on this sheet. Woods not shown.
Trans-frontier country left entirely blank.
Writing all in black. River and lake names in character sloping to left.
Mountains in separate character, but not engrossing.
Scale of kilometres. No characteristic sheet attached.
United States. 1/62,500.
Glens Falls Sheet.
Published by the United States Geological Survey. 1906.
Relief by contours, printed in brown at vertical interval 20 feet; every
fifth strengthened, and every fifth or tenth figured. Occasional spot heights
in brown. Roads and railways black. Water blue.
Meridians and parallels carried across sheet. Longitudes from Greenwich.
The representation of the relief by contours very successful, depending
largely on absence of names and other detail.
Full explanation and conventional signs on back of sheet.
The International Map on the scale of 1/1,000,000.
At the international Geographical Congress which assembled
at Berne in 1891 it was proposed by Professor Penck, then of
Vienna, and now of Berlin, that steps should be taken to urge
the publication of a map of the whole World on the scale of one
in a million, with sheets uniform in size and shape, systematic
ally arranged, and drawn in uniform style. Such a series of
maps would clearly help the comparative study of different
regions of the World.
At the next meeting of the Congress, held in London in
1895, the proposal was discussed in detail, a number of reso
lutions were voted, and schemes for the division of the sheets
and the methods of construction were adopted. Two preliminary
difficulties had to be overcome. The choice of the initial meridian
had to be made; and some means had to be found of reconciling
the differences between metric and non-metric countries.
As to the former, there could be little real difference of
opinion, for the maps and charts whose longitudes are referred
to the Greenwich meridian were greater in number than those
referred to all other meridians together. The question of a unit
of length was nearly unessential, because it would be easy to
draw on the margin of the map scales expressed in as many

MAP ANALYSIS 51
units of length as might be desired. But the question whether
heights should be expressed uniformly in metres was difficult,
because the British delegates at that time refused to have any
thing to do with the metric system on British sheets. Eventually
it was agreed to adopt the meridian of Greenwich as the prime
meridian, and the other question was left undecided.
For thirteen years little was heard of the scheme. The
resolutions of the Congress bound no one ; and though several
countries undertook the publication of maps on that scale, they
did so independently and in different styles. This delay was
useful in that it allowed the accumulation of experience in the
use of this scale, which is intermediate between the scales
ordinarily used for topographical maps and for atlas maps.
And systems which give excellent results on one scale very
often fail altogether on another.
At last the question of the International Map was revived
at the Congress held in 1908 at Geneva. More resolutions were
voted, and there seemed every likelihood that they would remain
as inoperative as those that had gone before, for the Congress
that voted them was not in the position to undertake itself the
construction of the map, and in default of an official agreement
between the Governments interested, very little could be ex
pected. At this point the British Government resolved to take
the steps necessary to put the project on an official basis, and
issued invitations to the principal Governments of the World,
to send delegates to a committee, which should discuss the
question and make definite recommendations. This committee
met in London on November 19, 1909, and speedily arrived
unanimously at an agreement which was ratified by all the
Governments concerned. The official report of the proceedings
was published in February, 19 10; the following is a short sum
mary of the decisions.
1. A uniform set of symbols and conventional signs was adopted, and
a characteristic sheet prepared.
2. Each sheet covers an area 4 degrees in latitude by 6 degrees in
longitude ; but nearer the poles than latitude 60°, two or more sheets of
the same zone may be joined. The limiting meridians are reckoned from
Greenwich, and the limiting parallels from the equator.

52 MAP ANALYSIS
3. The sheets are numbered according to a diagram attached to the
Report on a plan which is somewhat complicated. Each sheet has a
number, such as North K. 35.
The letter K signifies the zone of latitude 40° to 440, the eleventh zone from
the equator, as K is the eleventh letter of the alphabet. The number 35
signifies the 35th lune of longitude, each of six degrees, reckoned eastward
from the meridian opposite that of Greenwich. Thus a short calculation
leads to the result that sheet North K. 35 is the sheet covering Latitude
N. 40° to 44° and Longitude E. 240 to 30°. The merits of this system of
numbering are not obvious.
Each sheet must also bear the geographical coordinates, that is to say,
the latitude and longitude of its central point ; and there seems to be no
reason why these numbers should not have been used as the sheet numbers.
4. The projection is a slightly modified form of the polyconic projection
proposed by one of the French delegates, M. Lallemand. It has all the
properties necessary for such a map ; that neighbouring sheets shall fit
along their edges ; that the representation of distances and bearings within
the sheet shall be sensibly perfect; and that it shall be constructed with
ease. The upper and lower parallels are constructed as in the ordinary poly
conic projection, but they are brought slightly closer together, so that the
meridians 2° from the centre are their true lengths, instead of the central
meridian ; and the meridians are drawn as straight lines instead of being
slightly curved. These refinements on the ordinary polyconic projection
are practically not detectable on the printed sheet, but are theoretically
elegant. The tables necessary for the construction of the sheets are given
in the Report ; they occupy only two pages.
5. Contours are drawn at vertical intervals of 100 metres, "but in very
hilly districts the contours may be at larger vertical intervals, provided that
they are spaced at 200, 500, or iooo metre intervals." The map is coloured
on the layer system, according to a scheme attached to the Report, following
the spectrum order of colours, except that an ugly shade of magenta is used
instead of red.
The tints are changed at the contours given in the following scheme :
From sea level at every 100 metres to 600;
thence at intervals of 200 metres to 1200;
thence by two steps of 400 metres to 2000 ;
thence by two steps of 500 metres to 3000;
thence by steps of iooo metres to 7000.
It is not made clear whether the contours should be shown uniformly at
intervals of 100 metres, irrespective of the changes of tint ; but it may be

MAP ANALYSIS 53
noticed that steps of 400 metres are specified in the colour scheme, whereas
they are excluded in the specification for the contours which immediately
precedes. 6. Minor features of importance, which would not be shown by the
contouring, may be represented by shading, but not by hachuring ; and
the method of lighting which is most effective for the district may be
selected. Thus there is liberty in hill-shading, but not in contouring.
7. Precise rules are laid down for the spelling and transliteration of
place-names. The basis of these rules is that the spelling of every place-
name in an independent country or self-governing dominion shall be that
adopted by the country or dominion. This is of great importance, since it
abolishes the customary corruptions of place-names as used by foreigners in
such countries as Turkey.
8. Water features and glaciers are in blue ; contours in brown, for the
land, and in blue for the sea bottom; roads are in red, and railways in
black. 9. Heights above mean sea level are in metres, mean sea level being
deduced in each country from tidal observations on its own coasts.
These are the principal resolutions in the Report of the
International Map Committee. How far they can be put into
practice uniformly cannot be predicted. The few sheets which
have appeared at the time of writing have already shown some
not unimportant deviations from the strict letter of the scheme,
which are noted in the brief analyses which follow. Doubtless
there are excellent reasons for each departure from the strict
rule. Nevertheless it seems to the writer that it would have
been better to make the first few sheets in strict conformity
with the resolutions of the Committee, because it would then
have been easier to see how far it is necessary to give greater
latitude in the application of these rules.
The International Map was necessarily an experiment, be
cause the Committee which drew up the Convention for its
execution had not before it any example of a map on that
scale elaborately printed in colour ; none had been produced at
that time. This being so, we are not bound to consider the
existing scheme as fixed for better or worse, and it is legitimate
to discuss what improvements are possible.

54 MAP ANALYSIS
But let us first note any special points in the sheets already
published.International Map. 1/1,000,000.
Sheet North O. 30. Scotland. The Highlands.
Published by the Ordnance Survey. 1912.
The following variations from the Conventional signs sheet may be
noticed. Above 200 metres the contour interval is 200, instead of 100. This
deranges the layer tints, whereby one tint of green and both of yellow are
lost. No hill paths are shown.
The coast line is drawn as a sea-contour (blue) instead of as a land-
contour (brown). This gives a weak effect to the islands.
In spite of the increased vertical interval the contours in the mountains
come so close together that the layer system loses effect.
International Map. 1/1,000,000.
Sheet North M. 31. Paris.
Published by the Service Gdographique de FArmfe. 191 1.
Although the country is generally of slight elevation, only the 100 metre
contours are shown, and the representation of relief is therefore very
inadequate. The colours do not follow the adopted scale very closely, and in
particular the blue is bad.
The compilation of the part of Holland shown has mistakes in spelling,
an'd the main stream of the Rhine through Dordrecht and Rotterdam is not
shown as navigable. Hook of Holland, Flushing, Queenborough, and New
haven are not shown as ports with regular mail service.
International Map. 1/1,000,000.
Sheet North K. 35. Istambul. (See Plate VI.)
Printed and published by the Geographical Section, General Staff. 1912.
The following variations from the Conventional signs sheet may be
noted :
The lower contours are at intervals of 200 metres.
This disarranges the layer tints. Green goes to 400 instead of 300, and
there is only one tint of yellow.
The blue of the sea below the 200 metre contour is very intense, and this
gives a weak appearance to the coast line, which might perhaps have been
avoided if the coast line had been drawn in brown as a land contour.
The names — which are the real names of the places, and not the con
ventional Anglicized forms — make a very interesting study, and there is
a valuable glossary of pronunciation of Bulgarian, Rumanian, and Turkish.
This sheet is a beautiful example of the merits of the style of lettering
adopted for the International Map.

Plate VHI.

CeoyrajotacalS&Htm,, GfneraLSt&fT.

WhrOmce.1913

INTERNATIONAL MAP OF THE WORLD
Scale - 1,000,000
PART OF SHEET "NORTH K 35 ISTAMBUL"

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INTERNATIONAL MAP OF THE WORLD
Scale — j,ooo,ooo
PART OF SHEET "SOUTH H 34- KENHARDT"
MAP ANALYSIS 55
International Map. 1/1,000,000.
Sheet South H. 34. Kenhardt, Cape Colony. (See Plate VI.)
Printed and published by the Geographical Section, General Staff. 191 1.
This sheet follows very closely the Conventional signs sheet of the
International Committee.
Contours are shown at uniform intervals of 100 metres, but are not
carried across the frontier into German South- West Africa.
The ground rises steeply from the sea to iooo metres, and the greater
part of the sheet is heavily coloured brown. A good example of the failure
of the layer system on high plateaux.
The impression to be derived from a study of these first
sheets is, that in most respects they are very successful, but
that in the most important of all, the representation of relief,
they are not entirely satisfactory.
The style of the lettering serves admirably to distinguish
between features of different kinds by differences in the character
of the letters. Physical features are perfectly distinguished from
names of towns, and both are equally legible. The systematic
transliteration of the place-names, and the glossaries of pronun
ciation of the Slavonic names, are features of great value. The
indication of the population of a town by its characteristic sign
is good, and so is the retention of the real name of the town in
place of the name by which it is habitually known in other
countries. The hard and fast rules for the boundaries of the sheets work
badly in Scotland, where the six degrees of longitude assigned
as the width of the sheet are diminished by the convergence of
the meridians so that the sheet is nearly half as tall again as it
is broad. It would have been more convenient to extend the
sheet westward to include the Hebrides, which by the rule must
be shown on the eastern edge of a separate sheet. North of
latitude 6o° the sheets are doubled in width, so that the
Shetlands will have to themselves a sheet nearly double the
width of the Scotch and English sheets.
The result of the first application of the layer system to the
scale of one in a million is not encouraging. The wide vertical
interval of the contours on the lower ground — 100 metres — is
too coarse for the effective representation of the lower land ;
while the small horizontal distance between the contours in the

56 MAP ANALYSIS
more mountainous country, due to the small scale of the map,
makes the interlacing of the layer tints too complex for a clean
result. The mingling of very narrow strips of various tints
produces only a quiet ineffectual colour, in the same way that
brilliant coloured threads are blended into a tweed of the most
unobtrusive kind. A strip of layer tint must be at least five
millimetres broad if it is to have size enough to develop its
effect ; but this principle was not recognised when it was resolved
to construct the International Map upon the layer system.
It is understood that the Ordnance Survey will publish an
edition of the British 1/1,000,000 sheets without the layer colours.
That will give an occasion to try whether there is not a simpler
plan of achieving the desired effect. It appears to the author
that on maps of the small scale of one in a million it would be
possible to obtain all the effect of relief required in mountainous
regions by printing the simple contours in colours chosen after
the plan of the layer system of tints. But it must be confessed
that no one in command of a map office, and in the position to
make a trial of this notion, has ever shown much inclination to
adopt it.
Aero maps.
The rapid advance of flying two years ago produced a sudden
demand for maps of a new kind, in which some attempt should
be made to depict the country as it appears from above, and
especially to emphasize the objects which serve as leading marks
to the pilot in charge of the aircraft. Experimental maps were
produced by the General Staffs of Great Britain and of France,
by the Aero-Club de France, and by the promoters of the great
flying " circuits " which had a brief success.
At the meeting of the British Association held at Portsmouth
in 191 1 there was an interesting discussion on aero maps, and
strong divergences of opinion were manifested. The military
flying men were not pleased with the special maps, and declared
that the ordinary half, inch or quarter inch maps, though not
perfect, were better than any others. The civilians complained
that they needed something more simple and easy to read
than the Survey maps. But it was pointed out that the only

MAP ANALYSIS 57
competitor in the Circuit of Britain who never lost his way was
the French naval officer who flew over ground with which he
was quite unacquainted by the aid of the quarter inch map ;
and that all who relied upon the route maps specially prepared
for them had come to grief.
The special maps prepared by the General Staffs showed the
roads white, as it was imagined that they would look from above.
But just at that time the main roads were extensively tarred,
and thus they lost their whiteness, and became less conspicuous
from above than the secondary roads. Moreover, it was found
that the appearance of the ground below changed so greatly
with the change of light that the attempt- to imitate it to some
extent is doomed to failure.
If special maps are to be made in the future, it seems likely
that the most useful modification will be to accentuate the
characteristic shapes of road junctions and crossings. On the
ordinary maps these are generally masked by the exaggerated
conventional width of the road. But it should not be difficult
to exaggerate also the special shape of the crossing which is
often perfectly characteristic, and thus to make use of the
natural signs which much exceed in size and distinctness any
that could be erected for the special purpose of acting as
guides to flying.
The whole subject is hardly as yet in the experimental stage,
however, and the information gathered in the manoeuvres of 191 2
is not at present available.
The following notes on the special maps issued in 191 1 may
be of interest.
England. Aero map of the ign Manoeuvre Area. 1/253,440.
East Anglia.
Printed at the War Office. 191 1. In colour.
General groundwork of the sheet greenish grey.
Coarse vertical hill-shading. Spot heights in feet.
Roads in white; two grades. Water blue. Towns red.
Woods in green. Parks in very pale green. Churches with spires (but
not those with towers), windmills, and isolated trees in black.
Railways in very heavy double or single black.
It is believed that this map was not considered a success by the military
aviators.

58 MAP ANALYSIS
France. Carte Aeronautique. 1/200,000.
Sheet: Chalons.
Printed in colour and published by the Service Gdographique de t'Arme'e.
Paris. [191 1.]
The ground of the map is grey. Relief is shown by vertical hill-shading
in brown. Spot heights.
Woods in uniform tint of bright green. Water blue.
Roads are white between black lines. Villages in red.
Railways in black, three grades.
Ground dangerous for landing hatched in red.
Special characteristic signs for hangars, landing grounds, and hydrogen
depots ; cathedrals, chateaux, factory chimneys ; high tension electric cables,
etc. An interesting example of special map, rather heavy and dull in colour.
Carte de l'Aero-Club de France. 1/200,000.
Sheet 93. Laon.
Printed in colour and published by Ed. Blondel la Rougery. Paris.
No date.
Relief by rough grey vertical hill-shading. Spot heights, summits
distinguished. Railways black, grades distinguished. Roads double black line, principal
roads filled red.
Water blue. Woods plain green tint.
A large variety of special characteristic signs, of importance to aviators :
aerodromes, landing grounds, hangars, hydrogen factories, gas works, etc.
Sketches of the principal buildings in the margin.
A crudely executed but interesting attempt to provide the special
information required by aircraft.

Plate X

I. The Amsler Planimeter.

. *

O It A V 7 c h i: s / /; /,'

iirrrji !5;,h.79$

Central parts of planimeter (from above).

Measurement of A reas.

CHAPTER III
route traversing
The Explorer's Route Map
The object of the Route Map.
The first care of a traveller who passes through an unknown,
or but partially explored, country is to make a record of where
he has been, and of the main features of the country along the
route by which he has travelled. Often singlehanded, encum
bered by transport, compelled to keep to the track, and unable
to leave his party, he cannot hope to make anything in the
nature of a map, in the ordinary sense of the term. But for his
own guidance, to avoid getting lost, he is compelled to determine
his position day by day in much the same way that the position
of a ship is determined at sea, by observation of the Sun and
the stars, so that he is able to say roughly in what latitude, and
perhaps in what longitude his halting places were. Moreover,
as he goes along he is able to make such observations of the
shape and course of his path as to enable another man coming
after him not only to arrive more or less at the same place, but
to follow the same route. And finally, he can keep a sort of
running record of the things that lie immediately to the side of
his path. All this he does by the construction of a " route
traverse " or " route map."
It is essentially the work of the pioneer, whose main business
is to get through the country, and who can afford to give to
mapping and survey only a small part of his attention, and
no voice in the determination of his plans. Such is the first
exploratory survey of a country. Route traverses were run

60 ROUTE TRAVERSING
across Africa by the explorers of last century, and the published
accounts of their travels contain maps of vacancy traversed by
thin red lines, the results of these route surveys. These travellers
opened up the country, and they made determinations of the
latitudes and longitudes of a great number of places, which got
on to the maps, but which necessarily were often wrong. A great
deal of trouble has been caused by these errors, owing to the
ignorance on the part of diplomatists and officials generally of
the unavoidable roughness of preliminary maps not based upon
regular survey. It is essential that the sources of information
should be stated on the margin of all maps pretending to show
detail. The astronomical observations.
These differ very little in kind from those used in much
more elaborate work, and we may defer a detailed consideration
of them, confining ourselves for the moment to an examination
of the general principles, which are common to voyages on sea
and on land.
Latitude, the distance north or south of the equator, is found by the
observation of the altitude of a heavenly body as it crosses the meridian : the
Sun about noon, or stars at their meridian passages during the night.
Longitude, the angle between the meridian of the observer and the
standard meridian, generally that of Greenwich, is measured by the difference
of times of the two meridians. The local time is determined by observation
of a heavenly body as nearly due east or west as possible : the Sun in the
early morning or late afternoon, or stars at the appropriate time of night.
The Greenwich time is carried by chronometer or watch. (For simplicity
we exclude for the moment the alternatives of finding the Greenwich time by
observation, or of receiving it by telegraph cable or wireless.)
Azimuth, or true bearing, required for the correction of the compass, is
determined with the local time.
At sea the ordinary mariner works almost entirely by the
Sun, and the observation which is familiar to all passengers is
the noon altitude of the Sun, which gives the latitude. It is a
very common mistake to suppose that this observation gives the
instant of noon. This is not so ; the observation which gives
local time is made somewhat early in the morning or late in
the afternoon. Thus latitude and longitude are determined at

ROUTE TRAVERSING 61
different times. But meanwhile the ship is under way, and it is
necessary to have some method of carrying forward the morning
longitude to the latitude at noon, or of carrying forward the
noon latitude to the afternoon longitude. This is done by
keeping the "dead reckoning" of the ship's course. A continuous
record of the course and of the speed of the vessel on that course
is kept in the log (the journal of the voyage, not the instrument
of the same name by which the speed is measured). The dead
reckoning enables the navigator to make the required allowance
for the run of the ship between the successive observations, and
to carry on during cloudy weather.
The traveller on land works in very much the same way.
There are obvious reasons why it may be necessary to avoid as
far as possible observation of the stars by night : mosquitoes
and the risk of fever are sufficient. In the ordinary course of
things he will rely largely on observations of the Sun, though
star work is more accurate. But the requisite observations of
the Sun must be made, as we have seen, at widely different
times of day, and the traveller cannot as a rule afford to wait for
a great part of a day at every place whose position he wishes to
fix. He is therefore compelled by the nature of the case to use
some means of keeping account of what the sailor calls his "dead
reckoning," that is to say, of keeping a current account of his
position, carried on from one place to another by observation of
the course he is steering and the rate at which he is travelling.
He makes, in fact, what is called on land a " compass traverse."
In modern practice the navigator does not confine himself to
the old routine of the noon altitude for latitude and the morning
or evening sight for time and longitude, but in doubtful weather
he gets an observation whenever he can. An altitude of sun or
star, at a known standard time by chronometer, fixes a small
circle of the sphere on which the observer must be at the moment
of the observation ; and a portion of the circle sufficient to cover
the range of possible positions can be laid down as sensibly a
straight line on the chart. A subsequent observation made on
a different bearing defines another small circle, which intersects
the first at the position of the observer. Intelligently used this

62 ROUTE TRAVERSING
method is of wide generality, and has the great merit of .giving
its full weight to any observation made at any time, while
avoiding the often troublesome necessity of stopping to make
the observations at closely defined instants. It does not appear
that the method has been employed on land, but it is equally
applicable there for at any rate the rougher determinations of
position with a small theodolite or sextant. Within a few
degrees of the pole the application of the method becomes of
remarkable simplicity. See, for example, a paper by the author
in the Geographical fournal, March 1910.
The compass traverse.
A traverse is defined as a connected series of straight lines
on the Earth's surface, of which the lengths and the bearings are
determined. In a compass traverse the bearings are determined
with the prismatic compass, which differs from an ordinary
pocket compass in two principal respects : it is fitted with sights
which can be directed upon a distant object ; and with a prism
which brings into view at the same time the scale of degrees
marked round the edge of the compass card. The bearings are
invariably reckoned in degrees from o" right round to 360°,
from magnetic north through east. The complicated system of
" points," now becoming obsolete at sea, is never to be used
on land.
Selecting the most distant conspicuously recognisable point
upon the line of march, the traveller observes and records its
bearing, and proceeds to determine, as accurately as circum
stances will allow, the distance he has travelled by the time he
arrives at it, or the length of the " leg." Accurate measurement
is of course inconsistent with rapid travel. A short distance
can be paced, but it is not possible to count paces all day for
days at a time. The legs of a traverse are therefore generally
measured by cyclometer or " perambulator," or merely estimated
by time.
Distances by cyclometer or perambulator.
The perambulator consists of a wheel of known circumference,
frequently ten feet, mounted in a fork with a handle, very

ROUTE TRAVERSING 63
much like the common child's toy, and fitted with a counting
mechanism to record the number of turns which the wheel has
made. If a man can be spared from the caravan to trundle this
instrument — an easy duty which fills the native carrier with
pride — it is simple to record the length of each leg of the
traverse in terms of the number of revolutions ; but it is hard to
tell how much to deduct for the windings of the path and the
inequalities of the ground.
The sledge-meter used by Sir Ernest Shackleton and Captain
Amundsen on their South Polar journeys was a "perambulator"
wheel carried out on a light spar behind the sledge. Its
indications were in general remarkably accurate.
The ordinary cyclometer registers only eighths or tenths of a
mile, and is too coarse ; a more refined instrument of the kind
would sometimes be useful. But it is easy to calibrate any
bicycle so as to know the value of a revolution of the front;
wheel.

Distances by time.
The apparent advantages of the perambulator method of
measuring distances are in practice much discounted by the
difficulty of knowing what allowances to make for the windings
of the path. An experienced traveller will obtain results which
are pretty well as good, without being obliged to spare a man
for the work, by the simple process of timing each leg of the
traverse, and estimating the rate of march. The average rate of
a party on fairly level and unobstructed ground is found to vary
very little. Practice will enable the traveller to make allowance
for change of rate over rough or hilly country. The most
common error is a persistent over estimation or under estimation
of the rate ; and we shall see later how it is possible to keep
a check on systematic errors of this kind. The most serious
difficulty is common to all methods of route traverse — that of
keeping the average direction and estimating how fast one is
really covering the ground, when marching along a winding
track through thick bush.

64 ROUTE TRAVERSING
Details on the flanks.
If the country through which the traveller is marching is
fairly clear he can fix roughly the positions of its principal
features as he goes along by the method of cross bearings.
The compass bearings of prominent peaks and other easily
recognisable objects are taken from different points, and the
intersections of these lines of bearing, when plotted at the end
of the march, give positions of the objects in question with a
degree of accuracy comparable with the general accuracy of the
traverse. At the same time the bearings of all cross tracks and streams
are taken at the points where they meet the line of march ; the
character of the ground is recorded at intervals, with any other-
information which can be obtained readily.
Check by cross bearings.
A similar process can be used for the opposite purpose, of
checking the accuracy of the traverse by bearings of a distant
object whose position is known. For example, in traversing
round about Ruwenzori occasional bearings of the peak will
serve as a check on the traverse, and lay down its position on
the ground. A like method is much used at sea for fixing the
position of the ship when a known object is in sight, such as the
Peak of Teneriffe, visible sometimes at a distance of ioo miles.
The field book.
The method of recording a traverse is best shown by a page
of the field book, which is kept by well recognised rules.
The essential is that it begins at the bottom of what would
ordinarily be the last page of the book, and goes upwards and
backwards to the beginning. The columns up the centre contain
the time of each observation, the bearing of each leg, and the
estimated rate of progress on that leg, or the number of turns
made by the perambulator wheel. Detail to the right or left
flank is recorded in the right or left margin, and it is important
to note that the page becomes a kind of diagrammatic repre
sentation of the country traversed, of which the central columns
represent a line, the line of march. Hence if a straight stream

ROUTE TRAVERSING

65

or track crosses the route obliquely, the portions represented on
each flank must not be drawn as parts of one straight line, but
in the manner shown in the example below. A similar con
vention will be found later in the methods of keeping field
books for other kinds of survey.

Peak A

Halt at Z.
Shade trees and
good water

Snow peak A 146°

Village W

1 1. 14

10.52 10.41

198

3 2|

10.34

220

10.7

234

3

8.52

8.40
202
3
2*
8.22
8.57-57
219
223
246
2!2|
7.46
214
3
Leave Camp at Village X
Time Compass Rate
Bearing M.P.H.
Specimen field book.
Shallow stream
10 ft. wide
Track to Y 308°
Cultivation
The compass.
For instrumental details as to the care and use of the
compass, see page 102. We shall deal here with the particular
points which are special to compass traversing.
It is usually essential that the march of the party shall
not be interrupted while the observations are made, and it is
generally undesirable that the observer should have to run in
order to catch up with the party after the observation.- If he is
on foot he will try to walk on ahead to the point of'observation ;
if he is mounted he can afford to spend more time, perhaps
to dismount and set up, the compass on a tripod, which much
h. m. s. 5
66

ROUTE TRAVERSING

improves the accuracy of the observation. It is clearly impos
sible to prescribe any exact rule or programme. Two points
are to be remembered : the rate of march which is recorded is
that of the main party, which keeps on steadily, and it is there
fore unnecessary for the observer to take account in his time
records of the short intervals during which he himself is halted
to make the observations. And secondly, the whole operation
is a rough and ready affair ; he must therefore be careful not to

Z Trees and
good water

^

vv

Mag. North
A

Fig. 4. Plot of compass traverse.
waste time in trying to record minute details which have no real
importance; small deviations of the track will be ignored so
long as the general direction is preserved, and it is not necessary
to take a careful bearing of a cross track which disappears round
a corner in a few yards.
In thick bush, where the direction of the path changes every
few yards, or on the march in a hostile country, when it is

ROUTE TRA VERSING 67
impossible to leave the column of march even for a moment, it
is possible to do a good deal simply by watching the average
position of the compass card as it is held in the hand while
marching, and recording the bearing every five minutes.
The check by astronomical observations.
Even under the most favourable circumstances the error in
the recorded length of a route traverse will often be ten per cent. ;
and in a country where the rocks are- magnetic, and the compass
consequently unreliable, the bearings may be affected by large
errors. It is therefore very important to lose no opportunity of
checking the traverse by astronomical methods. Particularly
on long journeys, extending over months, it would be folly to
rely on the compass traverse only, just as it is dangerous to rely
for many days on the dead reckoning at sea.
We may sum up the possibilities of astronomical determina
tion as follows :
Latitude. Observation of latitude, either by the Sun or the
stars, is easy, and there is no difficulty at all in getting latitude
within a mile by sextant, or within a small fraction of a mile by
micrometer theodolite.
Longitude. Observations to find local time are easy, though
the calculations are a little long. But the longitude is the
difference between local time and Greenwich time, and the
practical impossibility of getting longitudes right within a
number of miles while upon the march is due to the difficulty
of carrying or obtaining Greenwich time. To carry Greenwich
time means to carry such a number of chronometers, or better,
-of half chronometer watches, that the mean of their indications,
corrected for their rates so far as known, is right within a small
number of seconds. A difference of four seconds of time is
¦equivalent at the Equator to a difference of one geographical
mile. The cost of the chronometers, the anxiety of their care and
transport, and the little reliance that can be placed upon their
rates when they are exposed to jolting and great changes of
temperature, make their employment practically impossible.
5—2

68 ROUTE TRAVERSING
Watches carried carefully in the pocket are a little more satis
factory, but cannot be trusted absolutely for long.
Greenwich time. Occultations.
To find Greenwich time by observation on some other
meridian, as distinct from carrying it with one, requires the
observation of the occultations of stars by the Moon. This
involves, firstly, half an hour's drawing and computation, to
predict approximately the circumstances of the occultation at
the place; for without such a prediction it is impossible to make
the observations successfully, or even to know whether there
will be anything to observe. Secondly, there is the observation
of the phenomenon with a fairly large telescope, of say three
inches aperture and three feet long — a telescope which is rather
large and cumbrous to carry. Third, if the observation is
successful, there is a long computation afterwards, to deduce
rigorously the Greenwich mean time of the occurrence. And
finally, a comparison between the calculated time and the time
recorded by the chronometer at the moment of the occultation,
gives the quantity we seek, the error of the chronometer on>
Greenwich mean time. It will be believed readily that the
comparative infrequence of occultations observable, the labour
involved in the prediction and observation, and the length of
the subsequent calculations, make this method of limited use to
the traveller.
Under special circumstances, however, the method of occul
tations may still prove of value. Whenever a skilled and
enthusiastic observer finds himself compelled to spend a con
siderable time in a place of which the longitude is badly known
he will find it worth his while to predict and observe some
occultations. Such cases might be, for example, the stay of
a scientific expedition on an island ; or a polar expedition in
winter quarters ; or a missionary or consul at some out of the
way station in China. But wherever the telegraph or wireless is
within reach the method of occultations is superseded.
Lunar distances.
An alternative method of finding Greenwich mean time is by
.the observation of lunar distances, in the way which used to be

ROUTE TRAVERSING 69
practised at sea before the vibration of fast steamships made
accurate observation impossible. This method requires a sextant,
whereas for every other observation the traveller will do better
with a small theodolite ; it can be practised whenever the Moon
is visible with a bright star or planet, and to that extent is
superior to the method of occultations ; but the results are less
accurate, and the calculations are long and troublesome.
We may conclude that the determination of longitude by
astronomical observation is possible only to those travellers who
are so fortunate as to have plenty of technical skill, plenty of
time on the march, and unusual freedom from the ordinary
anxieties of an expedition. Those who are not so happily
situated can scarcely hope to keep their longitudes within a
number of miles.
Azimuth. The azimuth or true bearing of a ray, the angle between the
ray and the meridian through the line of sight, is different from
the compass bearing of the ray by the amount of the deviation
of the compass. Were this deviation constant it would have
the effect of slewing all compass work round in azimuth, but not
of altering its shape. But the deviation of the compass varies
not only from place to place, but also to some extent from
month to month at the same place. Hence all compass work is
incomplete unless it is accompanied by determinations of the
compass deviation. Such observations consist in finding from
the Sun or the stars the true azimuth of a given ray,-and com
paring it with the compass azimuth.
The determination of true azimuth is made in much the
same way, and under the same circumstances, as the observation
for local time, and if necessary can be combined with it. It is
not a very laborious process, and should therefore be practised
frequently. At sea the observation for the deviation of the compass is
more frequent than any other observation ; on a well run ship
an observation ' is taken every watch, if the weather allows, for
an unknown error of even a quarter of a degree is by no means
negligible in the day's course of a fast steamship.

7o

ROUTE TRAVERSING

On land, where the rate of progress is much slower, and the
compass used is smaller and less accurate, such very frequent
control is not necessary. But it is essential to control the
general accuracy of a compass traverse by taking a true azimuth
from time to time, and an example will illustrate the whole
process. Before starting in the morning the traveller may be informed
by his guides that the day's march will take him near a distant
well-marked point. He sets up his theodolite, sets it on the
distant point, and reads the horizontal circle. Then he turns
to the Sun and obtains simultaneous readings of the horizontal

To Sun
^or Star

Fig. 5. Observation of Azimuth.

circle and the Sun's altitude. From the altitude, and an approxi
mate knowledge of the latitude, the true azimuth of the Sun can
be calculated. Apply to this the angle between the Sun and
the distant point, as measured on the horizontal circle, and the
azimuth of the distant point is found. Compare this with the
compass bearing of the point, and the deviation of the compass
is known. Now when at the end of the day's march the route is plotted,
and the position of the object observed to in the morning has
been laid down with reference to the route by cross bearings
aken from near at hand, the azimuth of this object from the

ROUTE TRAVERSING 71
starting point, as shown on the drawing, may be compared with
its true azimuth as found from the morning observation. This
will provide an excellent check on the general accuracy in
azimuth of the whole day's traverse. It must not be forgotten
that, except near the equator, the " convergence of the meridians "
must be taken into account in plotting a long traverse, but the
discussion of this refinement may be postponed.
Check on the length of the traverse.
We have seen that latitudes may be found very easily to
within a fraction of a minute of arc, that is, of a geographical
mile. A comparison between the latitudes taken at each end,
and the distance made north or south, as shown by the traverse,
will give an admirable check on the scale of the traverse in this
direction. But it should be noted carefully that before proceeding to
resolve the traverse into its north-south or east-west components,
all the bearings must be reduced from magnetic to true bearing.
The resolved parts of each leg of the traverse may then be
calculated directly, or they may be taken out from Traverse
Tables, or from the tables which are called, in the curious
terminology of the navigator, " Latitude and Departure Tables."
A similar check on the scale east and west cannot be
obtained by observations for longitude, for the reasons given
above ; or at least, it is beyond the reach of the ordinary
traveller. But if care is taken to check by differences of latitude
whenever the route leads considerably north or south, there will
be an excellent indirect control upon the lengths of the traverses
running east and west.
Dead reckoning.
The observation for time or azimuth, morning or evening,
requires a knowledge of the latitude, which is found from the
Sun only near noon ; while the observation for latitude requires
a knowledge of the local time, except in rough sextant work,
and of the approximate Greenwich time, which cannot be found
near noon by any practicable field methods. Suppose the
traveller has obtained an observation for time before setting out

72 ROUTE TRAVERSING
in the morning. By noon he will probably have moved into
a different longitude, and his local time will have changed.
But his route traverse will give him very nearly the change of
longitude, and so he can apply the necessary correction to the
error of his watch which he found in the morning, and thus he
can obtain his true local time near noon. In the same way, he
can bring forward the noon latitude to give him the approximate
latitude required for the time or azimuth observation morning
or evening. It will be seen that this process of carrying forward the
change of latitude or longitude between one observation and
the next is very like the process practised continually at sea, of
carrying on by dead reckoning.
The details of these astronomical processes need not be
studied at the present stage. But it seems to be essential that
the student should have a general idea of the nature of the
control which field astronomy can exercise over traverses plotted
by the compass, such as the pioneer traveller makes in his first
journey through an unmapped country.
Thus, for example, in the Geographical Journal for January
19 1 3, among the notes on new maps we find an account of
a map of a part of the Sahara, published by the French
Ministere des Colonies, 19 12, "constructed from the itineraries
and sketches of Captain Cortier, officers attached to his expedi
tion, and others.... It has been adjusted to 33 astronomical
positions determined by Captain Cortier, a useful table of which
is given in the lower right hand corner of the map."
Route traverses cannot make a map.
A route traverse carefully made is admirably adapted to
illustrate the account of a journey, and to enable future travellers
to follow the same route. But it is altogether wrong to suppose
that anything in the nature of a satisfactory map can be made
by combining a number of these traverses. Each individual
traverse will serve very well by itself, until it comes to be fitted
to other traverses. Then it is invariably found that the separate

ROUTE TRAVERSING 73
traverses will not fit accurately together. The reason for this is
easily seen. Each traverse is a zigzag line, which may have
been stretched by error in estimating distances, and distorted
by errors in the mean bearings of tortuous tracks. A certain
number of points will have been tied down, so far as displace
ments north and south are concerned, by the astronomical
latitudes, and the general bearings of considerable lengths will
have been controlled by the astronomical azimuths. But within
these constraints there will always have been plenty of room for
errors to accumulate.
Moreover, a number of traverses run across a country leave
large areas unvisited, and a map cannot be considered worthy
of the name which shows detail in one part, and leaves out more
important detail of the same kind in another. Thus the com
pilation of traverses cannot make a map.
The impossibility of making a map by compiling traverses
is one example of a general principle which underlies the whole
of Survey : a map must be constructed on a rigid framework.
And how can such a framework be obtained ? The answer is
the same in all branches of surveying. By building it up of
triangles in which the angles are measured, not the lengths of
the sides.
It must be understood, however, that when we speak of the
impossibility of making a map by the compilation of route
traverses, we mean that a final and accurate map cannot be
made by such means. A study of the maps of Africa issued by
the Geographical Section of the General Staff will show that
many of these are compiled from such material ; but such
sheets always bear the legend " None of this country has been
surveyed"; the compilation is provisional, a little better than
nothing at all, and as soon as possible it is superseded by
a regular survey.
We must make the reservation also that there are cases in
which the final work of survey must be done by traversing: in
dense forest regions, and in cities. But this is precise traverse,
of an altogether different order of accuracy, which will be dealt
with briefly in Chapter VI, page 162.

74 ROUTE TRAVERSING
Heights by Aneroid Barometer.
The clinometer is good for determining relative differences
of height over a small range of ground, but is useless for
carrying forward such determinations over a long distance : the
accumulation of error would be soon intolerable. The traveller
therefore requires some instrument to give him rough determi
nations of absolute height at a point, and to measure considerable
differences of elevation under such circumstances as the ascent
of a mountain peak, where the clinometer is quite inapplicable.
The pressure of the atmosphere varies with the height above
sea, and the reading of the barometer varies accordingly.
Roughly, the barometer falls one inch for each thousand feet of
ascent. But the pressure of the air and the height of the barometer
are affected also by the disturbances moving in the atmosphere
which affect the character of the weather; and they are also
dependent upon the temperature of the air. Hence the reading
of the barometer at any moment is dependent upon a compli
cation of circumstances, and can give no precise determination
of height above sea. One may say, however, that the barometer
at sea level is rarely above 3 1 inches, and rarely below 29 ; so
that if it is observed to stand at 24 inches, the presumption is
that the observer is somewhere between 5000 and 7000 feet
above sea.
To obtain a clear understanding of the way in which the
barometer can be used to obtain more precision than this,
consider the case of a recording barometer carried by train from
Lancaster to Carlisle. At Lancaster it will draw a trace showing
the variations in the pressure of the air associated with the
passage of disturbances or the establishment of anti-cyclones.
Between Lancaster and Carlisle the train climbs nearly iooo feet
over Shap Fell ; the barometer will fall about an inch on the
ascent, and will rise again as the train runs down the steep
descent through Penrith. At rest at Carlisle the barometer will
draw still a variable trace, depending again upon the passage of
disturbances in the atmosphere. The question is therefore, how
to disentangle the variations due to height from those due to
weather, including changes of temperature.

Plate XI

i. Aneroid Barometer.

Boiling Point Apparatus or Hypsometer.

Determination of Heights.

ROUTE TRAVERSING 75
It is not safe to assume that the sea level pressure is the
same at two places fifty miles apart. Therefore if one wishes
to disentangle the weather changes from the altitude changes,
it is almost necessary to have a barometer stationary in altitude,
as nearly as possible below the barometer which is being carried
uphill. The weather changes of pressure are given by the
former and applied to the latter ; what is left of change may
be ascribed to the variation in height of the travelling baro
meter. In many cases it is not possible to leave a barometer at the
base camp, to be read while the travelling barometer is away.
One must then do the best possible by returning to the base
camp as soon as possible after the ascent, and determining the
change in the reading there which has taken place during the
day. Thus, suppose that a climber reads his barometer at 4 a.m.
before setting out, and records frequent readings during the
ascent and descent. He reaches the top at noon, and is back
in camp at 5 p.m. Comparison of the morning and evening
records at the camp shows that the barometer has fallen half an
inch during the time the expedition was away, and to compare
with the noon reading at the summit one must interpolate
between the morning and the evening readings below. If the
barometer has been falling regularly throughout the day, this
will give the correct noon reading at the lower station ; but
otherwise not ; and the advantages of having a second observer
remaining below are sufficiently clear.
Barometer heights in exploratory survey.
We have seen that accurate results can be obtained only
when the barometer is used to obtain differences of height
between two stations which are occupied as nearly as possible
simultaneously. In general this is not practicable for an ex
plorer, who has to push on through a country, and cannot retrace
his steps, or leave another observer behind at a base camp.
Such a man must do the best he can to obtain information as to
the average pressure at sea level in the region where he is
travelling, and must be careful to make allowances for the
seasonal and daily variations of the pressure, which in tropical

76 ROUTE TRAVERSING
countries are often surprisingly regular, and quite worth taking
into account.
In the survey of Southern Nigeria, for example, it is found
that the diurnal changes of the barometer are so regular that it
is possible to run fairly accurate contours in the thick forest, if
care is taken to study and apply the corrections for the diurnal
variation. But with all care it is not possible for a traveller single-
handed to obtain much accuracy with the aneroid barometer,
and this explains why the heights of mountains and lakes in
Africa are often found to be several hundred feet wrong, when
the early barometer heights are at last compared with the results
of precise surveys.
Instrumental precautions.
The aneroid is a delicate instrument, and must be treated
with all care. It must be allowed some minutes to come to rest
before a reading is taken after a rapid change of altitude ; the
process is hastened by gently drumming with the fingers on
the case of the instrument ; but hard tapping is bad for the
instrument, and all shocks must be avoided.
An ordinary aneroid carried for a long time at a great
height, say over nine thousand feet, is liable to become strained,
and its readings inaccurate. Special types of instrument, called
Mountain Aneroids, are made for use at great heights. But if
it is necessary to use an instrument of the ordinary pattern,
a simple device will preserve it in good order. A well-fitting
tin has a bicycle valve soldered into it. The aneroid is placed
inside, the joint sealed with surgeon's rubber paster, and the tin
is pumped up with a bicycle pump until the pressure inside is
near the normal sea level pressure. The aneroid will travel thus
without strain, and can be taken out when required. This
arrangement was found to work very well by a traveller in the
Andes.
Temperature corrections.
The aneroid barometer is corrected for the effects of
temperature upon the instrument itself; but it is necessary to

ROUTE TRAVERSING 77
take into account the temperature of the intervening air between
the upper and the lower stations. This cannot be done accu
rately, and the method suffers in consequence. It is seldom
possible to do more than to take the mean of the temperatures
at the upper and the lower stations, and to treat this as the
mean temperature of the intervening column of air. When
there is no lower station for comparison, and some assumption
has to be made as to the temperature below, the results become
still more uncertain.
Heights by Barometer.
There are two sets of tables in common use, those calculated respectively
by Loomis and by Baily. Both are given in Atixiliary Tables of the
Survey of India ; the former are given in Hints to Travellers, published
by the Royal Geographical Society ; and the latter in Textbook of Topo
graphical Surveying (Close).
In none of these places is there an adequate account of the basis of
construction of the tables, and it does not appear that any such account
is readily available. A brief summary is therefore given here.
An investigation of the theory of the subject is to be found in Laplace,
Micanique Celeste, Vol. IV, p. 289 of the edition of 1805. With some
modifications, this leads to the following formula :
If //=height of barometer at lower station,
H'= „ „ „ „ upper „
T = temperature of barometer at lower station,
T'= „ „ „ „ upper „
/ = „ „ air at lower station,
t' = „ „ „ „ upper „
X = the latitude,
s = height of lower station above sea level,
x = difference of height of two stations,
ft, = modulus of common system of logarithms,
6 = difference of expansion between mercury and the metal of which
the barometer scale is made,
a — radius of the Earth.
Then x=Px{\ogH-logH'-p8(T-T')} , t+f- 64) r ,
1 -I  (• [when temperatures are on the

»{

Fahrenheit scale]
x (1 +0-00265 cos 2X}
2flP+X + 2s)
1 -I 

t + t' — 6a\
i + —

78 ROUTE TRAVERSING
Taking heights in feet, the constant P is 60159, according to Loomis ;
^ = 2089 x io° feet, and the constant multiplied by pd is 2-341.
Hence ^-={60159 (log H- logH')- 2341 (T- T')}
- ) to allow for the mean temperature of the air
900 /
and an average amount of aqueous vapour
1+0-00265 cos2\) to allow for the variation of gravity with
the latitude
jr+52',5i*-r 2s\
1 -)  ^f2  — to allow for the diminution of gravity
20-89 x IO /
with height.
Loomis' Table I gives the values of 601 59 log /f- 27541 for values of H
from 11 to 31 inches. He gives no explanation of the reason for the choice
of this constant 27541, and its significance is not obvious. He remarks
merely that it does not change the difference of the two quantities taken
from the table.
We enter Table I with the two quantities H and H', and take their
difference. This gives a first approximation to x, the difference of height
between the two stations.
Table II gives the values of 2-341 (T- T'). It should be noted that this
correction is required only when mercurial barometers are used, which is
seldom. Aneroid barometers are mechanically compensated for their tem
perature, and no correction is then required on this account.
The resulting difference of height is then multiplied by the factor
I + '_±£^6_4\ 900 /'
no table being provided for this process. The result is a close approxima
tion to the final result.
Table III gives the value of jrxo-oo265 cos 2X, by a table of double entry
with arguments x and X.
The correction for the variation of gravity with the height is split into
two parts.
Table IV gives the correction equivalent to multiplication by the factor
X 4- C 2 2 5 I
1 -|  x-2 — 2_ : the part involving the difference of heights. This is a table
20-89 Xio6
of single entry with argument x.
Table V gives the correction equivalent to the remainder of the factor
— . But since s is not necessarily known, though to the approximation
a
required it may be deduced from the barometer reading at the lower station,
* 52251=60159x2,11.

ROUTE TRAVERSING 79
the correction is arranged in a table of double entry with arguments H
and x. It may be noted that this table is unnecessarily extended. If x,
the difference of heights, is 25000 feet, the barometer at the lower station
can hardly be so low as 16 inches, corresponding to an elevation of about
16000 feet.
The above is the form of the tables as given by Loomis, and reproduced
without comment in English books up to the present day. But it should be
remarked that they are slightly erroneous in Table IV. The factor
jr+52251
20-89 x IO°
is required in the reduction of observations made with mercurial barometers.
But the aneroid is equivalent to a spring balance, which in itself is inde
pendent of variations in the intensity of gravity. A reference to the theory
shows that when aneroid barometers are used, the term 52251 should be
omitted ; and this is the greater part of the correction tabulated in Table IV.
We shall avoid this error if we omit altogether the correction from Table IV;
and enter Table V with the mean of the barometer heights at the two stations,
instead of with the barometer height at the lower station.
We may note also that as Loomis' tables are commonly printed, the
argument at the side of Tables IV and V in the column headed "height"
is misleading. The column should be headed " difference of height of the
two stations." The examples given in Hints to Travellers are wrong in
this respect. The height of the upper station has been entered, instead of
the difference of heights.
The tables in the form given by Baily are a modification of the above.
Baily takes as an average case that s, the height of the lower station, is
4000 feet, and that x, the difference in height of the two stations, is about
3000 feet (though he does not say so in the latter case). With these as
sumptions, the tables are shortened ; but they are arranged so that the
computation must be done by logarithms, which is less convenient for
the traveller. It does not appear, then, that the form given by Baily
has any advantage over the form given by Loomis ; and the results are
not quite so accurate in theory, because of the assumptions indicated
above. Both Loomis and Baily neglect the variation in the amount of moisture
in the air, and are content to arrange their constants to correspond to an
average amount of moisture. The recent tables by M. Angot, as now
published in the Annuaire du Bureaic des Longitudes, give means of
allowing directly for the moisture of the air, and are in this respect a
great improvement on the older tables.
But it may very well be doubted if it is of much avail to take account
of refinements such as the variations of gravity with height and latitude,
and variations of the aqueous vapour present in the air, while the crude,
though inevitable, assumption is made that the average temperature of the

8o

ROUTE TRAVERSING

column of air between the two stations is the mean of the temperatures at
those stations. This cannot be exact; and it will be seen that the error
introduced by this assumption may very well be much greater than the small
corrections due to the other causes.
The tables for the calculation of Barometer heights.
The following brief table is not sufficiently extended to be
convenient in the actual calculation of observations. It is given
here only that we may have an example of the style of the
principal table, and of the magnitude of the quantities involved.
For the reasons given above, we have not thought it necessary
to give any table of the small corrections whose effect is trifling
compared with the uncertainty of the principal temperature
correction.

Bar.

Diff.

Bar.

Diff.

in

Feet

for

in

Feet

for

inches

o-i inch

inches

o'i inch
I2'0
3670
217
22'0
19506
119
130
5761
201
230
20668
114
14-0
7698
187
24-0
21780
109
15-0
9500
174
25-0
22846
104
i6"o
1 1 186
164
26-0
23871
IOO
170
12770
154
27-0
24857
97
18-0
14264
H5
28-0
25807
93
19-0
15676
m
29-0
26724
90
20'0
17016
130
30-0
27610
87
2IO
18291
124
310
28466
84
Take the difference of the heights corresponding in the above table to
the barometer at the upper and lower stations.
To correct for temperature, multiply this difference by
TOa (sum of air temperatures at the two stations — 64°).
The boiling point thermometer.
The pressure of the air affects the temperature at which
water boils, and a determination of the boiling point of water
thus affords an independent determination of the pressure of
the atmosphere, and gives the same kind of limited information
as to height above sea as is given by the aneroid barometer.
Since it is not possible in the field to carry thermometers which
can be read to less than one-tenth of a degree Fahrenheit, and
ROUTE TRAVERSING 81
one-tenth of a degree in the boiling point corresponds to a
difference of pressure which is in its turn equivalent to a dif
ference in height of about fifty feet, it follows that the boiling
point thermometer is less sensitive than the aneroid for deter
mining differences of height. But on the other hand, it is less
likely to become deranged, and it is therefore well to carry both
instruments on a journey, and to use the boiling point apparatus
to control the general accuracy of the barometer.
The following is an abbreviation of the usual table for the relation
between the boiling point, the barometer, and the difference of height
between stations.

Height in feet above the

Boiling Point

Equivalent Barometer

point at which water
boils at 2120

212° Fahr.

29-921

0

2IO

28-746

1046

208

27-613

2097

206

26-521

3151

204

25-466

4210

202

24-447

5278

200

23-461

6354

; 198

22-507

7439

196

21-584

8533

194

20-690

9638

192

19-828

10750

190

18-998

1 1 867

188

18-199

12988

186

17-426

14124

184

1 6-68 1

15266

182

15-964

16412

180

15-275

17567

178

14-611

18725

176

13-970

19897

A second table is usually added, giving the factor by which the above
differences should be multiplied to allow for the mean temperature of the
intervening air. This is based on the assumption that the temperature at
the upper station only is observed, and that the mean temperature may be
derived from the approximate law that it decreases 1° F. for every 330 feet
of ascent. It appears that when the temperature at the lower station is observed,
or can be estimated approximately, it is better to correct for temperature
as in the calculation of barometer heights.
H. M. S. 6

82 ROUTE TRAVERSING
In a collection of survey tables it is usual to find the tables
for the reduction of boiling point observations given in the
above form; and no allowance is made for the small corrections
due to change of gravity in different latitudes, or for different
altitudes of the lower station. These are small compared with
the uncertainties of the thermometer reading. But it is well to
note that the most correct way of reducing the observations is
to translate the boiling points to the corresponding barometer
heights, by tables such as that given above, only more extended ;
and to complete the calculation as for aneroid readings.
Instrumental precautions.
The principal point to attend to is that the bulb of the
thermometer must not be allowed to dip into the water which
is being boiled, because any impurity present in the water
alters the temperature at which it boils. The bulb should be
suspended so that it is fully exposed to the steam which is
coming off, but is just clear of the liquid itself. With this
precaution it is possible to make the determination of boiling
point a part of the ordinary cooking operations, as was done
on the recent British Antarctic expeditions. The thermometers
were inserted through the lid of the cooking pot and were read
at each halt. This check upon the barometers was particularly
valuable under the circumstances, because there was good reason
to doubt the unconfirmed results of aneroid barometers working
at elevations of over 10,000 feet, in intense cold.
It is of course essential that the errors of the thermometers
employed should be verified at the National Physical Laboratory
before the start of the expedition, and again on its return. The
thermometer tends to lower its zero point for a long time after
manufacture, at a gradually decreasing rate. Old thermometers,
well standardised, are therefore more trustworthy than new ones.

CHAPTER IV
SIMPLE LAND SURVEY
The settler's land survey.
As soon as a country becomes settled townships are projected,
mining areas are pegged out in claims, and the land is parcelled
out into farms. These operations are usually simultaneous with,
if they do not actually precede, the establishment of a settled
government. Thus, for example, we read in the Colonial Survey
Report, No. i, page 23: East Africa Protectorate, 1903, "Since
no survey existed, and it was imperatively necessary to settle
the people on the land advertised as open for selection, every
kind of makeshift had to be adopted to meet the situation.
Much wasteful expenditure was incurred, and the settlers had
legitimate grievances against the Government." On the average
a settler was kept waiting i2-6 months for allotment.
The need of a map of the country is felt acutely from the
first day of its opening up. But the production of a map is
a long and costly business, and almost always has to wait. In
the meanwhile some kind of plan of each township, mine, and
farm is absolute necessity, both to the occupier and to the local
administration. Land surveyors set to work to survey the
properties as they are ready for allotment, or perhaps as they
have been already occupied, and the result of their labours is
a series of plans, which accumulate in the office of the Com
missioner of Lands.
We must remember that these are not maps. A topographical
map shows the natural features of the country, and in addition
the principal features in the way of communications that have
6—2

84 SIMPLE LAND SURVEY
been added to it by man. But a map does not show the
boundaries of property, and a map is not on a scale large
enough to show details and areas sufficient for the purposes
of property record or of local taxation. The cadastral, or
property survey, on the other hand, is made on a scale suffi
ciently large to show all the details of boundaries, walls, fences,
and ditches ; and areas of each plot may be measured from it.
But in general it shows nothing of the relief of the ground.
A topographical map is in the nature of a picture, a cadastral
map is a mere diagram of the ground. For reasons which will
appear in due course it is not possible to construct a map by
piecing together a set of contiguous property surveys ; and to
a great extent the work put into the original surveys of property
is wasted because it has to be done over again when the time
comes for a regular survey of the country. The sooner that
comes, the greater the eventual economy. But since it is not in
practice possible to insist that a regular survey of the country
should precede any of this detailed property survey, it will be
convenient to consider here very briefly the principles upon which
these preliminary land surveys are conducted. It will be under
stood that since this book is to deal with maps, and not with
the minutiae of property and town survey, the treatment of this
latter can be nothing more than a sketch.
The elements of property survey.
Suppose, in the first place, that the plot to be surveyed is
small in extent, but that there is a great deal of detail in the
nature of crooked boundaries, buildings, etc., that must be shown.
The plan will be made by the simple process of land survey with
chain or tape.
The principle of land survey is that every detail must be
fixed by measuring its perpendicular distance from a straight
line, and the position on that line of the foot of the perpen
dicular. Suppose, for simplicity, that a boundary is made up
of a series of short straight lengths AB, BC, CD, DE, EF, ....
Suppose a straight line KL is laid out as near as may be to the
boundary, and that perpendiculars Aa, Bb, Cc, ... are drawn from
A, B, C, ... to KL. Measure the lengths of the perpendiculars,

SIMPLE. LAND SURVEY

85

and the distances Ka, Kb, ... KL. A plan of the boundary
AB ... F ... may now be drawn as follows: Draw the line KL
on any desired scale, and lay off the distances Ka, Kb, ... on it.
Erect perpendiculars from a, b, ... and lay off on them to scale
the measured distances aA, bB, ... ; we have then transferred to
the plan the relative positions of A, B, C, ... F. Join them up,
and we have a plan of the boundary.
The measurements along the line KL are made with the
surveyor's chain or with a steel tape ; the perpendicular distances,
called offsets, are measured with a graduated offset rod, if they
are short, as they should be.

B

C

D

E

-___F

A 

G
d
Fig. 6.
f
When offsets are not short they must be measured with the
chain or tape ; and it is then necessary to have some such
instrument as the cross staff or the optical square, to set out the
offsets perpendicular to the chain line. But long offsets are
used only in rough work, and it is a cardinal principle of
accurate land survey that offsets must not be long. A chain
line must pass near every point that has to be fixed. The first
thing to attend to, therefore, in making a land survey, is to lay
out a suitable system of chain lines.
Suppose, for example, that the plot ABCD is to be surveyed. The
elementary, often practised, but es
sentially bad method, would be to
chain from A to C, and take offsets
on each side of A C to the salient
points of the boundary. This would
be a bad, or at least untrustworthy
method, (1) because the offsets are
long, and the perpendiculars must
be laid out with some elaboration ;
and (2) because there is no check
upon the result except doing it all
over again.
The proper method is to break
up the ground into triangles. Chain from a to b, b to c, and c to a, taking
86 SIMPLE LAND SURVEY
offsets to the boundary along each chain line. The offsets are now short,
and are easy to measure with sufficient accuracy. Do the same from
a to d, and from d to c. But
now note that the construction on ^--*U^
our plan of the triangles abc, adc, ^s^- ^^>^^
depends on the accuracy of the /^ ^^s^
measures of the lengths of our /¦ ' ' ~^s.
chain lines. An error in one would A^j  \  ~eyC
completely wreck the whole plan. X • ,y
Therefore they are to be checked \« '. „ /
by measuring the lines across the \- _, '/
corners kl, mn. When the plan \\ '^S
is drawn out these distances, as \\ ,yr
measured on the plan, must agree ^^^^is
with the actual distances measured D
in the field. If they fulfil this con- jr;„ g
dition, then we have a complete
check on the main structure of the work. If they do not, the fact that
there is an error somewhere is detected at once.
It has been mentioned already that a plan does not generally
show the inequalities of the ground. It is one of the principal
objects of a map to do so. But whether the inequalities are
indicated or not, the plan or map must indicate the relative
positions and distances of all objects as if they are projected by
vertical lines on to a level surface. Distances must be measured
and represented as horizontal distances, and the distinction is
by no means insignificant in the case, for instance, of property
on the side of a hill. In all land surveying by chain and offset
rod, therefore, the chain and rod must always be held horizontal ;
and the horizontal equivalent of a distance down a slope will
be measured in a series of steps. When a slope is steep this
becomes difficult, and it is evident that the chain lines must
be chosen so that they are as level as may be.
In theory land surveying is exceedingly simple, consisting
only in measuring along the sides of the triangles, and taking
offsets to all detail. The whole art of it in practice lies in
selecting the system of chain lines so that they shall form as
rigid a framework of triangles as can be made. If the three
sides of the triangle are known with absolute precision the
triangle can be constructed rigidly, within the limits of accuracy

SIMPLE LAND SURVEY 87
of the draughtsman. But errors will creep into the measure
ment of sides, and the draughtsman cannot draw with absolute
accuracy, It is therefore necessary that the triangle shall be
" well conditioned," as nearly equilateral as may be.
For consider the construction of a triangle with an acute
angle C opposite the base A B. The
point C is to be found by describing
circles with centres A and B, and of
radii equal to the measured lengths
AB, AC. These circles will inter
sect at an angle equal to C, and
it is evident that the more acute
the angle, the greater will be the
error in the position of C caused F'g- 9-
by an error in one of the measured lengths.
The same kind of argument applies in all branches of
surveying that depend upon triangulation of any kind : that
is to say, in all kinds of survey except the simple route traverse.
There must be no unduly acute angles in the triangle.
The method of chain survey is well adapted to making plans
of small detail. The plan of each triangle, and of the points
fixed to it by offsets, has considerable accuracy in itself. But
it will be understood easily that a large estate cannot be
surveyed in this way, in a number of small triangles, because
every triangle is inaccurate to a small degree, and the effects of
these small errors rapidly accumulate when an attempt is made
to fit a large number of the triangles together. In this, as in
all branches of survey, it is impossible to make an accurate
extensive map or plan by piecing together small portions
surveyed independently, to build up a large map from small
blocks. To take the exactly opposite way is the right course.
Construct a simple framework covering the whole extent of
land to be surveyed ; . get this framework so accurately made
that it cannot be in error by an amount visible to the. eye on
the scale which is proposed for the map ; and hang the detailed
survey upon this framework. An accumulation of error is then
impossible.

88 SIMPLE LAND SURVEY
It follows from this principle that a property survey of
whatever size must begin with a few big triangles covering the
whole property, and work downwards from these to the smaller
triangles in which the detail is surveyed. But lines a mile
long cannot be measured conveniently with a chain, except in
very flat and open country : some obstruction or other will be
continually intervening to break the line and make a detour
necessary. Hence in making the survey for a township, a large
estate, or a mining concession, we must lay out the principal
triangles with some more handy and convenient instrument
than the chain. Such an instrument is the theodolite.
Our next section will therefore deal with the elements of
triangulation with a theodolite.
Simple triangulation with the theodolite.
Considered in the simplest possible way, the theodolite, as
used in triangulation, consists of a graduated circle fixed in a hori
zontal plane ; a telescope which can be rotated about a vertical
axis passing through the centre of this circle ; and a pointer
attached to the telescope, which can be read against the circle. !
We shall postpone to Chapter VIII the consideration of all
the instrumental details of the theodolite, and for the moment
confine our attention to the outlines of the method.
Suppose that we have three points A, B, C marked on the
ground in some visible way, and that the theodolite is set up
over A. It is pointed on B, and the
reading of the pointer on the circle
is recorded ; it is then pointed on C,
and the circle is read again. The
difference between the two circle
readings will be the angle BAC.
The theodolite is then moved to B,
and the angle ABC is measured ; " Fi I0
then to C, and the angle ACB is
observed. These three angles should of course add up to 1800,
unless the triangle is so large that the curvature of the Earth
must be taken into account ; and this will be a check upon the
accuracy of the observations.

SIMPLE LAND SURVEY

89

When the three angles are known the shape of the triangle
is known, but not its size. To get its size we must measure the
length of one of its sides ; and then by a very simple piece of
trigonometry we calculate the lengths of the other sides, from
the known values of the angles.
In a triangulation, therefore, we must measure the length of
one of the sides of one of the triangles. The lengths of all the
other sides of the whole triangulation will be worked up by cal
culation from the observed angles and the length of the initial
side, which we call the base.
Suppose, then, that we have selected six points on our ground, A, B, C,
D, E, and F, disposed so as to form the triangles of our figure, of which, it
will be observed, no one has a very acute angle. Each point must be visible
from the other points of the triangles to which it belongs ; but it is not at all
necessary that all the points should be intervisible. For example, C must
be visible from all five others ; B from A, C, and D ; but E need not be
visible from A or B. These points are marked by pegs driven into the
ground, and signals are erected over them.

The theodolite is set up over each peg in turn, the signal being removed
if necessary, and the angles in the triangles are measured. Each triangle
is checked by the necessity that the sum of its angles should differ from
180° only by the small quantities which may be allowed as errors of
observation. It is important to notice that, though the points of the triangulation may
be at different elevations, the angles that are measured are the angles of the
projection of the figure upon a level surface. For suppose that in the triangle
ABC the point B is higher than A, and C higher than B. If we wished to
measure the true angles of the triangle ABC we should have at each station

90 SIMPLE LAND SURVEY
to tilt the theodolite so that the graduated circle lay in the plane of the
triangle. If, on the other hand, we keep the circle horizontal, what we
actually measure is not the angle BA C, but the angle between the vertical
planes through AB and AC respectively; which is of course equivalent to
the angle at A in the triangle ABC projected on the level. But this is
what we want ; we have already remarked that the plan or map must
represent the projection upon a level surface, not the actual configuration
upon the undulating surface of the ground.
When all the angles are observed we have the shape of the figure. One
side must be measured, and any one of these will do. We shall naturally
select the one that lies on the most level and unobstructed ground. We
suppose it is AB which is measured with chain or tape. Then in the
triangle ABC, knowing all the angles and one side, we can easily calculate
the lengths of AC and BC.
One of the sides of A CD thus becomes known, and the others follow
immediately, since all the angles are known, as before.
In this way, from one measured side of one triangle only, we arrive
at the lengths of all the sides of all the triangles.
For an example of the calculation, see Chapter VI, page 156.
Choice of base, and connection with triangulation.
Having arrived at the principles of triangulation, we must
now see how they can be put into practice conveniently.
The stations of the triangulation will naturally be for the
most part on the summits of hills, from which an extensive
view can be obtained. But it will generally not be convenient
to measure from one of these stations to the next, because the
intervening ground will not be open and level, and otherwise
suitable for the purpose. In practice, therefore, one chooses a
site for the base, and arranges a special piece of triangulation to
connect it with the nearest side of the main system of triangles.
Suppose AB is the base, and EF the nearest side of the triangulation.
Select two points C and D, lying on opposite sides of the base, so that the
triangles ABC, ABD are well shaped or conditioned ; and at the same time
the triangles CDE, CDF are also well conditioned. Erect beacons at
A, B, C, D, and, of course, also at the principal triangulation points. For
the present we shall not examine the method of constructing beacons. For
this see Chapter VI, page 139. Set up the theodolite successively at the six
stations, and observe along the rays drawn in the figure. For example, at C
observe to E, A, D, B, and F.
Now in the triangle CAB we have all the angles known, and one side
AB ; hence we can find the length of BC. Similarly in the triangle DAB

SIMPLE LAND SURVEY

9i

we find DB from A B. Then in the triangle BCD we know both sides BC,
BD, and through either of them we find the length of CD. Then working
through the triangles CED, CFD, we find CE or CF, and thence from the
triangle CEF we find EF.
Our base AB has now been extended through a series of carefully planned
triangles to EF, which is several times the length of AB, and is one of the
sides of the principal triangulation.

It will be noticed that we might have arrived at the length of EF from
AB by a. number of different ways. For simplicity we have spoken as if
there were only one way round, but at a later stage we shall see that the other
ways must not be neglected in accurate work. If, however, we consider
more than one way round, this difficulty will arise, that since all the
measured angles are subject to errors of observation, the whole figure is
slightly inconsistent in its various parts, and we should get slightly different
results for the length of EF according as we derived it from AB by one
route or the other. This would be intolerable in practice, and we must
devise a way of getting over the difficulty before we come to deal with really
accurate work. In small pieces of isolated survey the question hardly arises.

The main triangulation.
Having derived the length of the side EF, a side of one of
our main triangles, from the measured base AB,we can complete
the triangulation through G, H, K ... until the whole ground
that we propose to survey has been cut up into a small number
of relatively large triangles, of which all the angles have been
observed with the theodolite, and the lengths of all the sides
deduced from the measured base through EF.

92 SIMPLE LAND SURVEY
The next step depends upon the size of our ground. If it is
not more than say ten miles square we shall make no serious
error if we neglect the curvature of the Earth, and treat it as
plane. In that case the triangulation may be laid down upon
the sheet of the plan simply by constructing the triangles in
succession from the calculated lengths of their sides ; or more
accurately by calculating the rectangular co-ordinates of the
triangulation points with reference to one taken as origin. But
in order to get the plan orientated we shall want to know the
true bearing of one side, say EF. This may be obtained very
roughly with the compass, or very quickly and accurately from
an azimuth of the Sun.
If the ground is much larger than ten miles square we may
not be able to afford to neglect the curvature of the Earth. But
this case may be reserved for the chapter on Topographical
Survey. See Chapter VI, page 152.
The advantages of triangulation.
Let us look again for a moment at the reasons for making
this framework of a few big triangles covering the ground which
we propose to survey in detail afterwards. Suppose that our
base is only a few hundred feet long, and that the country is so
rough that we cannot hope to find a place where we can measure
a longer length on the ground with any accuracy. It is very
easy, and does not require any special precautions, to measure
this base with an accuracy of one in ten thousand. If our
triangles were quite exact we should arrive at the lengths of our
longest sides with the same proportional accuracy. This will
not be achieved in practice, but the diminution in accuracy can
be controlled by the amount of carer that we are willing to give
to the triangulation. Suppose that it is so done that the error
in the side most remote from the base is increased to an
uncertainty of one in three thousand. The principal points
being related to one another with this degree of accuracy it is
not possible for error to accumulate over any considerable part
of the plan to a greater extent than this. In cutting up the
bigger triangles into smaller, either with the theodolite or with
the chain, local errors may be made, but their effects are not

SIMPLE LAND SURVEY 93
cumulative. They cannot extend outside the particular triangle
in which they are made.
Again, if only we can find points for the principal triangles
which are visible from one another, the accuracy with which they
are fixed is independent of the character of the intervening
ground, which may be of a kind to render any sort of linear
measurement impossible.
Or, to put it another way : It is very hard to measure
distances accurately with chain or tape except upon open and
level ground ; it is very easy, by means of the theodolite, to
measure angles from one well-defined point to another. We
shall expect, therefore, to do well with a method that gives us
the triangles by measuring their angles, and requires that one
side only shall be measured, for which a site can be chosen in the
most favourable place.
Town and forest survey.
There are two cases in which the ordinary method of
triangulation with the theodolite breaks down: in towns, where
the walls and buildings make the triangulation impossible ; and
in dense forest such as the Gold Coast, where the hills are round
topped and cannot be cleared, and where it is impossible to
obtain a view of any importance.
In such cases it is necessary to traverse with the theodolite.
For this method see Chapter VI, page 162.
The dangers of patchwork survey.
We began this chapter with the needs of a survey more
extensive than could be undertaken by chaining alone, yet only
an isolated piece of work, such as the plan of a township,
a mining concession, or an area open to allotment or sale to
settlers. The principles of triangulation are the same, whether
the survey is an isolated patch or part of a complete scheme for
the whole country. But it is important to have a precise idea of
the dangers and the bad economy of doing survey work in small
patches instead of making each operation part of a large scheme
for the complete map.
In a new territory, where land belongs originally to the

94 SIMPLE LAND SURVEY
Government, and is sold piecemeal, the only secure method of
delimiting the boundaries of property is by reference to a
complete triangulation of the country. This is forcibly stated
in a letter addressed by Sir David Gill, then Her Majesty's
Astronomer at the Cape, to Earl Grey, who in 1897 was
administering the Government of Rhodesia. The following
extracts from this letter are taken from the introduction to the
Report on the Geodetic Survey of South Africa, Volume III.
"The point which it is always difficult to bring home to the lay
administrative mind is that it is impossible to survey a country properly or to
grant indisputable titles to land by surveys made in a patchwork way.
" When Government has a particular bit of land to be disposed of, it seems
to be supposed that one has only to send a surveyor to set up beacons,
survey the ground, and bring back a diagram of those beacons— and sell the
land according to this description.
"Assume the surveyor to be competent and honest, the result will be
certain points marked on a piece of paper, representing pretty accurately the
shape of the piece of land so surveyed ; but in many places there will be no
sufficiently well-marked topographical features, such as well-defined river
boundaries, etc., to locate precisely where in the country the particular farm
is ; there will be nothing to indicate the latitude and longitude of any
particular feature of the map (i.e. its position on a general map of the
country) ; and there will be no accurate topography on the diagram, because
the price which the surveyor receives for such survey makes it impossible for
him to include accurate topography in his work. With the approximate
methods of base measurement necessarily used by such a surveyor there will
also be some appreciable error in the scale of the map ; and beyond a rough
orientation by compass (and the direction of the magnetic meridian is subject
to large secular variation), there is nothing to indicate the true north of
the diagram.
"Afterwards, when you come to patch such surveys together, you can see
that no small trouble must arise, and that shortcomings and overlaps occur....
Then comes the further possibility, the dishonest proprietor. A particular
piece of land is bought from Government. The proprietor finds a
convenient spring or piece of rich land outside his boundary ; there is no
neighbour to be hurt, or perhaps only a distant proprietor. It is not a
difficult matter to shift a beacon — there is no one particularly interested, and
the beacon is shifted.... In this way large tracts of land have been stolen from
Government in Cape Colony.
"There is one, and only one remedy for all this, and that is to connect all
detached surveys with a general system of triangulation ; and it will save
the Government and the inhabitants generally a vast amount of money to
establish this triangulation as quickly as possible."

SIMPLE LAND SURVEY 95
We are here in the difficulty that embarrasses all Governments
of new territories : they cannot grant proper titles to the land,
nor carry on any of the operations of settlement, until the
country is properly surveyed ; and they cannot afford to have
the survey made until the country has begun to pay its way,
and the more urgent demands for roads, bridges, and railways
have been met. All that can be insisted on is that there must
not be a month of unavoidable delay in setting to work on the
complete survey of the country. Every pound that is spent in
patchwork survey for special purposes is very largely wasted.
Simple levelling.
The plan which results from triangulation, either by chain or
theodolite, represents the ground as if it were all projected upon
a level plane ; and no attempt has been made, so far as we have
gone, to show the undulations and inequalities of the surface.
To do so fully would require the construction of contours, to
represent the courses of lines running at definite intervals of
height above sea level. But this belongs rather to topographical
mapping than to the survey of a small area, and it will be
treated later.
Without aiming at a complete system of contours, it will
usually be necessary to have some knowledge of the variations
of height above sea, for local purposes of drainage or irrigation ;
and this at its simplest involves running certain lines of levels
across the plan, by the use of the surveyor's level and staff.
Putting aside for the time all the details of construction and
adjustment of the instrument, the level may be described as a
telescope which is set at right angles to a vertical axis, and can
be swept round in a horizontal plane. Any object seen on the
cross wires of the telescope is on the same level with them, or
with the centre of the object glass of the telescope.
The levelling staff is a pole, usually rectangular in section,
with a face divided into feet, tenths, and hundredths of a foot,
numbered from the bottom upwards. (Plate XII.)
Suppose that this staff is stood upon the ground at a distance from the
level, and that the observer, looking through the telescope, sees that the
horizontal wire cuts the image of the staff at the height 7-61 feet, whereas

96

SIMPLE LAND SURVEY

the centre of the object glass is 4-27 feet above ground. It is clear that the
ground at the base of the staff is 7-61 —4-27 = 3-34 feet below the ground on
which the level stands, provided that the telescope is really pointing
horizontal. Similarly, if the reading of the horizontal wire is 9-03 feet upon a second
staff, the ground at the foot of the second staff is 9-03 — 7-61 = 1-42 feet lower
than at the foot of the first. And it should be noticed that this result is
obtained without requiring any knowledge of the height of the object glass
above ground, which varies each time the instrument is set up, by variation
in the spread of the legs of the tripod, and is not quite conveniently
measurable in ordinary instruments. The essence of the method is the use
of the two staves, so that the height of the level itself is eliminated.
In the above explanation of the use of the level we have
made the important reservation " provided that the telescope is
really pointing horizontal." The surveyor in the field cannot
be continually revising the adjustment of his instrument, and it
is characteristic of a good method of survey that the way in
which the instrument is used should eliminate automatically
errors due to imperfect adjustment.
In the use of the level this end can be attained with great
simplicity. All that is necessary is that the two staves should
be placed at equal distances from the telescope. The reason
for this will be seen at once, when we consider in what way the
instrument is likely to get out of ad
justment. Reduced to its simplest
parts, the level consists of a telescope
fixed on an axis V, with a bubble B
firmly fastened to the tube of the
telescope. The axis V must be set
up vertical, and the test of verticality
is that the ends of the bubble B should
not move along the scale when the
instrument is rotated about V. The
bubble may not be central on the scale, but so long as it does
not move along the scale when the instrument is rotated, the
axis is vertical. Hence the process of getting the axis vertical,
which is required every time the instrument is set up, does
not in theory depend upon the adjustment of the bubble or
of the telescope.

_£

3_

Fig. 12.

Plate XII

,*JJw  ,

12 inch Y Level.

Levelling.

SIMPLE LAND SURVEY

97

Now if the bubble is not in the centre of its run when the
axis is thus found to be vertical, the bubble is out of adjustment.
And even if the bubble is in adjustment, it does not follow that
the telescope below is parallel to it.
These errors are adjusted from time to time by the methods given in any
textbook on the use of the instrument. But they are apt to vary from day
to day or from hour to hour while the instrument is in the field. The former
does not affect the results if care is taken to make the test of verticality of
the axis as above, not that the bubble is central, but that it remains at rest
when the instrument is turned about the vertical axis. But the effect of the
second error is that the telescope is pointing up or down at some small
angle to the horizontal when the axis of rotation is made truly vertical. The
resulting error of reading on the staff will be strictly proportional to the
distance of the staff. Hence if two staves are at the same distance, the
errors in reading will be the same, and the difference of the two readings,
which is the quantity required, will be unaffected by the error.

F'g- 13-
Suppose, then, that we wish to run a line of levels from A to B. We
mark out suitable stations K, L, M,... in the line AB, for the staves. We
set up the level midway between A and K, and find the difference of height
of the ground at A and K. Then we set up midway between K and L, and
so on. Each difference of height is then independent of the errors of
adjustment of the instrument, and it is not possible for the effects of these
errors to accumulate, since they are automatically eliminated at each step.
We should notice also that this process eliminates the effect
of the curvature of the Earth. The line of sight of the telescope,
being perpendicular to the vertical of the observer, is a tangent
to the sphere and consequently passes higher and higher above
the surface as it proceeds. Owing, then, to the curvature of the
H. M, S. 7

98 SIMPLE LAND SURVEY
Earth, all staff readings are too high by a very small amount,
which would become serious in time if sights were taken always
forward from one station to the next, but is eliminated without
conscious trouble by the method of setting up the instrument
always half-way between the two staves. Thus no correction
for the curvature of the Earth appears in ordinary levelling
operations at all, even though they extend over hundreds of
miles. Paradoxers who imagine that the Earth is flat are fond
of quoting this as a confirmation of their idea.
In a precisely similar way, there is no need to take any
account of refraction if the level is always set up midway
between the two staves. The effect of refraction will be to
raise each staff in the field of view of the level, so that the
readings are slightly too small. If observations were taken
always to a forward staff this effect, extremely small for any
one ray, would accumulate steadily, and would be very difficult
to calculate. It is important, therefore, to notice that by the
proper use of the two staves the effect of refraction is completely
and automatically eliminated.
Detailed sections.
If we wish to make a section in great detail we may modify
the above process without any damage to the essentials.
The staff may be set up at any number of intermediate
points between A and K, and the difference of height from
A or K found. These observations will be affected by the
instrumental error, but since the distances are short the effect
will be small. And these observations will be used only to
refer points between A and K to either A or K ; nothing will
be carried on from them into the next section, which will start
from K unaffected, as we have seen, by the instrumental error.
The limitations of this process.
We have been considering the process of running a line of
levels as it may be used for particular purposes in a piece
of isolated survey. The heights will be reckoned from a quite

SIMPLE LAND SURVEY 99
arbitrary datum, and will have no connection with mean sea
level. The process of determining a general system of heights
above mean sea level, as part of the organised survey of a whole
country, will be considered in a later chapter ; see Chapter VI,
page 133.
And we should notice that the process here described is
quite unsuited for a preliminary determination of heights and
contours for an exploratory map. We shall deal with the
processes proper to this purpose in Chapter V.

CHAPTER V
COMPASS AND PLANE TABLE SKETCHING
In previous chapters we have dealt with the route traverse of
the explorer ; and with the methods of mapping an isolated
township or mining concession. We have to deal now with a
problem of quite another kind : the production of the first
attempt at the topographical map of a district, or of what is
called in the language of military topography " a sketch." It is
a map, in the sense that it covers all the area with a uniform
degree of thoroughness, and does not merely draw a line across
the country ; and it is a map also, in the sense that it aims at
representing the whole topography of the ground, the relief as
well as the plan. It is a sketch, in the sense that it is made
with simple and portable instruments, rapidly, and with strictly
limited means ; and it has no claim to great precision.
Exploratory mapping of this kind has many uses. In war
fare it serves to produce temporary maps which shall serve all
the purposes of a regular topographical map far in advance of
the possibilities of a regular survey : such, for example, was the
map of Burmah made in 1885 by two officers of Royal Engineers
at the time of the expedition to Mandalay. In peace it may
serve as a necessary preliminary to more detailed operations of
survey, or to illustrate the work of a scientific expedition making
a thorough study of an unmapped region, in geology, archaeology,
or what not. And finally, in the teaching of geography it is
admirably adapted to serve as a means of instruction in mapping
which is within the powers of students, and can be executed
in a limited time, with relatively simple instruments.
Such a topographical sketch may be made with the prismatic
compass and a simple instrument for measuring slopes, such as

COMPASS AND PLANE TABLE SKETCHING 101
the Watkin clinometer. Or it can be made with much greater
accuracy, but at the expense of heavier and more costly tools,
with the plane table and a clinometer of the pattern used on the
Survey of India, and known familiarly as the Indian clino. In
all the operations of survey the accuracy obtainable is limited
by the time which can be given to the work, and the amount of
baggage which it is possible to carry with the party. It is of
great importance to have a clear appreciation of this principle.
Much time may be saved by careful consideration before
starting, of the degree of accuracy aimed at, and of the precise
equipment necessary to obtain this in the most economical way.
And much time is wasted by aiming at minute accuracy with
rough and rapid methods, on the one hand ; or by using for
what should be rapid work an instrumental equipment more
suited to a higher degree of deliberation and precision.
Whatever the instrumental outfit adopted, the same principle
runs through all sketching, that a framework must be constructed
by triangulation from a measured base, and that all detail must
be hung upon this framework. If the position of one point of
the triangulation can be determined in latitude and longitude
by astronomical methods, such as we have already sketched in
Chapter III, so much the better ; and again, if the sketch can be
orientated correctly by an azimuth determined astronomically,
again so much the better. But such determinations should be
regarded as outside the limits of the methods of field sketching
themselves. They add an excellent finish to the result, but they
are not an essential part of the process, and we shall not deal
further with them in these chapters.
Compass sketching.
The instruments are
(i) the prismatic compass, of which the military pattern
is by far the best, and also the most expensive, because it is
fitted with arrangements for marching by night, which are not
essential in work by day. (See Plate XIII);
(2) the protractor, a graduated scale by means of which
the observed angles are laid down on the drawing board, and

102 COMPASS AND PLANE TABLE SKETCHING
distances are scaled off. Again, the military pattern, as described
in the Manual of Map Reading and Field Sketching, is the best,
and more expensive than simpler patterns, which can be used,
though not so conveniently ;
(3) a board on which drawing paper can be mounted, and
which should have some kind of waterproof cover to protect the
work from damage by rain ;
(4) a good pencil, of the degree of hardness HH or
HHH, which will take and preserve a fine point like a needle,
and which should be protected in the pocket by a point
protector. It may not be superfluous to observe, for the benefit of the
beginner, that good quality in paper and pencil is essential to
success. The paper has to stand a great deal of wear and much
rubbing out ; and it will often get damp. At the end of work
in the field it must be in condition to be cleaned up, inked in,
and perhaps coloured. Only good drawing paper will be in this
good condition when the sketch is finished ; inferior paper will
have gone to pieces. Nor can any good work be done unless
the pencil will take and keep a fine point ; and inferior pencils
are the cause of endless waste of time and inaccuracy in work.
Therefore do not grudge the few pence that will buy the best^
paper and pencils instead of the very inferior stuff in ordinary
use. The compass.
It would be tedious to describe in detail the features of an
instrument which cannot be understood until the instrument
itself is taken in the hand, but which then become almost self
obvious. We will confine ourselves to some general remarks on
compasses and their use.
The compass card must be graduated right round from o" to
360°. Any other method of division is almost useless. The
readings increase as one turns from magnetic north, reading
zero, through east to south, and round again by west to north.
It is essential that the compass, when not in use, should have
the card raised off the point by the catch fitted for this purpose,

X

-aH

^

¦¦o

¦^

COMPASS AND PLANE TABLE SKETCHING 103
or the card will rattle about, and the point of the needle on
which it rests will be blunted.
To try if the point is in good condition, open the cover out
flat and lay the compass on a level table (as in Plate XIV).
When the card has come to rest, turn the compass steadily in a
horizontal plane, and see that the card remains at rest though
the case is turned. If the point is good the card will not drag
after the case but will remain almost unmoved.
The prism, with one face ground into a lens, allows the eye
to see at the same time the graduated compass card, and the
distant object. To provide for differences in the focal length of
different eyes, the prism is mounted on a slide, so that the card
can be brought into clear focus for any eye. Place the compass
at the edge of a level table, and draw out the prism to the end
of its slide. Look in at the compass card, and gradually depress
the prism until the divisions of the card are seen perfectly
distinctly. Note the position of the prism in its slide, and if
the compass is your own property make a mark to show where
the prism should be placed without having to redetermine it on
another occasion.
In the use of the compass it is necessary to acquire the trick
of seeing comfortably at the same time the distant object, the
line in the cover of the compass superposed on it, and the com
pass card mingling with it, so that one may read the degrees of
the card to which the line points.
It is possible to see at the same time the distant object
and the line close by, because they are viewed through the slit
above the prism ; this slit restricts the pencils of light entering
the eye to pencils of narrow angle, so that the eye can focus on
them readily enough, though they come from objects at such
different distances.
It is possible to see the wire coming down over the compass
card, because the view slit crosses the pupil of the eye from top
to bottom. The light from the distant object enters the upper
part of the pupil, and forms an image on the retina. The light
from the compass card, reflected by the prism, enters the lower
part of the pupil, and also makes an image on the retina. Across

104 COMPASS AND PLANE TABLE SKETCHING
the centre of the field of view, where the illumination from the
two sources is fairly equal, the two images are visibly superposed,
and one may see the wire as if it were actually coming down and
cutting the compass card. To get the right effect, it is necessary
that the two images should be nearly of the same brightness.
Their relative brightness can be altered by moving the eye up
and down along the slit, so that more or less of the pupil is
exposed to the light from the object, and less or more to that
from the card. The compass card, or dial, is engraved on
mother-of-pearl in the best compasses, because that reflects a
great deal of light, and gives an image of the card as bright
as the image of the distant landscape, which is often very bright
indeed. It is very common to see a beginner with the compass tilting
it forward and downward, in the effort to see the two images
plainly at the same time. This has the effect of dropping the
card away from the prism, and putting the scale divisions out
. of focus. When one has determined the proper position for the
prism, as explained above, the loss of focus is a plain indication
that the compass is not being held level, which is dangerous,
because the card may foul and give a quite wrong reading.
Therefore it is well to be very sure about the proper position
of the prism, and use this control over the tilt of the compass.
Avoidance of local deflections.
It is a commonplace that the compass becomes deranged
and gives false readings if there is a mass of iron anywhere
in the immediate neighbourhood. Yet it is very common to
see beginners with the compass leaning against a bicycle or
an iron gate, or taking bearings from the point of vantage that
a bridge over a railway gives. Such mistakes are, of course,
soon realised and avoided ; but it is not so easy to guard against
less obvious sources of error, such as a water main under the
road. Should there be any suspicion that abnormal attraction
exists at the spot from which bearings are taken, it is easy
to walk directly towards the objective, and repeat the bearing
observation twenty or thirty yards further on. If there was

Plate XIV

i. Prismatic Compass. Mark VI. Opened out flat.

Compass in use.

3. Compass in position
for use.

4. Clinometer in use.

5. Watkin Clinometer.
Instruments for Compass Sketching.

6. Interior of Clinometer.

COMPASS AND PLANE TABLE SKETCHING 105
local attraction at the first point, it will probably be different
at the second, and the error will be detected.
These remarks apply to strictly local attractions, such as
are caused by fairly small masses of iron at close quarters. In
some countries, such as South Africa, the whole ground is full of
magnetic rocks, and the compass is practically useless.
The compass sketch.
The principle is exactly the same as in triangulating with
the theodolite. A base is measured, and a framework of
triangles is observed. The principal difference is, that the
angles of the triangles are not determined as such, but as
the differences between the observed magnetic bearings of the
respective sides. Each side of a triangle is drawn as a line
making a certain observed angle with the magnetic meridian,
and is subject to the errors which are inseparable from these
determinations of magnetic bearing. Hence we may expect
errors of at least half a degree to occur with frequency. And
a deviation of half a degree is equivalent to a shift of one-
twentieth of an inch at a distance of six inches, which is very
much larger than the uncertainty of drawing. Hence we must
realise that compass sketching is far from being an exact process,
and must avoid putting too much time into a method which is
incapable of giving anything like accuracy. Its merit is that
it is quick, and that the instruments required are easy to carry
about.Plotting the bearings.
The observed magnetic bearings are plotted with the pro
tractor. The paper is ruled with parallel lines to serve as
magnetic meridians, and one end of these lines is marked North.
To protract a given bearing from any point the protractor is
placed with its centre on the point, and its long side parallel
to the meridians as drawn on the paper. If the angle is
between o° and 180° the ray will lie to the east, and the
protractor will be placed so that it lies east of its centre.
(Note : the centre of the protractor is the centre from which the
angular divisions are struck, and is marked by a small arrow

106 COMPASS AND PLANE TABLE SKETCHING
pointing to one edge.) If the angle is between i8oc and 360°
the protractor is put down to the west of the centre, and an inner
line of figures is used. All this is complicated to describe, but
it may be learned by inspection of the instrument without any
difficulty. To save mistakes, one should always ask oneself,
Where roughly is the ray? If this is done, the protractor cannot
be placed in the wrong position.
The base.
The necessary qualifications for a base are that it should be
possible to see plenty of surrounding points from each end ; and
that it should be practicable to measure roughly from one end
to the other. Generally speaking, one has little opportunity for
picking and choosing in selecting the base for a compass sketch.
The sketch must be made without delay, and it is necessary
to start without an elaborate search for a good base, which is
always hard to find. The length of the base may be determined
by pacing, or by measurement with a calibrated bicycle wheel.
And it should be remembered that even if the base is ten per
cent, wrong in length, the effect on the sketch is only that it is
increased or diminished in scale ; it is not distorted, and if an
opportunity occurs it is easy to make a new determination of
some length and draw a new scale for it.
In the Manual of Map Reading and Field Sketching the
base is defined as a line carefully chosen and accurately mea
sured, upon which the accuracy of the sketch depends. This
definition evidently needs qualification. In sketching and ex
ploratory work generally the first possible site must be chosen
for the base, without delay for consideration of other and perhaps
better sites which might be found on further reconnaissance.
And the base will be measured, not accurately, but as well as
the circumstances of the case permit. The accuracy of the scale
of the sketch depends upon it, but not the shape. The unneces
sary stringency of the official definition might lead to a great
waste of time in an operation where rapidity is often the first
consideration. In pacing a base, it is often necessary to make some allowance
for curvature of the way which the observer is compelled to go

COMPASS AND PLANE TABLE SKETCHING 107
from one end to the other. Care should be taken that the
correction is not overestimated. On looking along a road, the
divergences to right or left look very much more important
than they really are. Divergences of fifty yards will make a
road look very crooked, but they have very little effect upon the
length of a mile of road between two points. Two or three per
cent, reduction will be enough to allow for apparently quite
considerable deviations.
The measured length of the base is laid off by means of the
scale on the protractor, giving hundreds of yards on the scale of
two inches to the mile.
The ruling points.
The points that are chosen to make the triangles are termed
ruling points. They will be natural objects such as church
towers, isolated trees, haystacks, and so on. Trees are to be
avoided as much as possible, because a tree that seems to
be very easily distinguished from one point of view may be
quite inconspicuous from another, or another tree may be mis
taken for it.
Objects which can be seen but not occupied are also to be
avoided, because to carry on the triangulation it is necessary to
occupy points in succession. Such objects as steeples among
trees, which cannot be occupied, and from the base of which
nothing is visible, are not much good as ruling points. But
they serve subsidiary purposes as " intersected points," as we
shall see.
The process of sketching.
Select the base. Occupy one end of it. Take the bearing of
the other end, and plot it. Then take and plot the bearings
of any points round about that seem to be suitable for ruling
points.. Be sure that plenty of these points are taken at the
start, for as the work proceeds one will find that some of
the chosen points prove to be unsuitable, and must drop out
of use. Unless plenty have been taken to start with, there is
danger that too few may be left.

108 COMPASS AND PLANE TABLE SKETCHING
Pace from one end of the base to the other, and scale off
the distance from the protractor, making if necessary a suitable
deduction for crooked pacing and slope. The further end of
the base is now fixed. Take bearings to as many of the ruling
points as possible. At least two points should now be deter
mined, one on each side of the base. Proceed to these, and
continue the process of observing and plotting the rays to the
ruling points.
When the framework is thus built up, the second stage of
the process begins. There will be important points, say at cross
roads, which have not been fixed by intersections ; they will
now be fixed by resection, that is to say, by taking bearings
from each to two ruling points already fixed, and drawing rays
back on those bearings until they intersect. The point of
intersection will evidently fix the point under occupation.
Round about the intersected and resected points, the detail
is sketched in by eye estimation. This will not be very accurate,
but it will be rapid, which is the most important consideration.
And error cannot accumulate to a serious extent, because the
whole is controlled by the triangulation. The accomplished
sketcher learns to economise in the use of instruments, and
after the triangulation is done, he relies principally upon esti
mation for his intermediate detail. Also, he does not wait till
the triangulation is done to begin the detail, but puts in as much
as possible around each point that he occupies.
Facility in sketching cannot be taught except in the field,
and success depends upon cultivating an eye for country, so
that the greatest possible economy of means may be practised.
But it is possible to show certain ways of economising.
For example, if it is important that a given road should
be fixed as accurately as possible : it is sufficient to fix every
alternate angle by resection, and to put in the intermediate
angles by rays drawn down the road. Or again, if a village
is to be sketched, it is usually wasteful of time to work right
through it from one side to the other. Instead of doing so, work
round the outside of the village, fixing points on the roads that
approach it, and the directions of those roads. Having laid

COMPASS AND PLANE TABLE SKETCHING 109
down the roads leading to the village, it will generally be easy
to sketch the whole of the necessary detail of the village itself
without being obliged to make any instrumental fixings inside.
Many time-saving methods such as this will be learned by
experience. The clinometer.
This instrument measures the angle of slope. As with the
compass, it is tedious and unnecessary to describe the instru
ment minutely, since its use is almost self-evident when the
instrument is taken in the hand. (See Plate XIV.) But a few
principles that are not quite evident may be examined here.
In the first place, remember that an error in the zero of the
clinometer is fatal to success in its use. If the compass has an
error of zero, the whole sketch is slewed round by that amount,
but no further harm is done. But if the clinometer has such an
error, that is to say, if the clinometer reads angles of elevation
too small, and angles of depression too large by the same
amount, the effect on the differences of height measured with
the instrument are very serious. The difference of height be
tween the top and the bottom of a hill would seem to depend
upon whether the observations were made from the top or the
bottom. Hence the state of adjustment of the clinometer should be
examined every day that it is used, for the process takes only
a minute or two. Observe the same ray from opposite ends.
Suppose that it reads Elevation 2° at one end, and Depression 3°
at the other. Then evidently the clinometer reads half a degree
low, and a correction to allow for this must be applied to all the
readings made with it. It is better to determine this correction
and apply it mentally, than to try and adjust the instrument
by opening it up and turning the adjusting screw. This is a
tedious process ; and it is apt after a little to leave the screw
loose, so that the error varies with every jar that the instrument
receives. The clinometer measures the elevation or depression of one
point as seen from another, in angle. To convert this into

no COMPASS AND PLANE TABLE SKETCHING
difference of height in feet we must know the distance between
the two points in yards. This is taken from the sketch by
means of the scale of yards on the protractor. We then apply
the rule I horizontal distance in yards,
„.„. r, . , r divided by twenty, and
Difference of height in feet = < li. ,. , , ., ,
fa multiplied by the slope
\ in degrees.
The proof of this rule is very simple. A slope of one degree is equi
valent to a rise of one foot vertically in a distance of 57-3 feet horizontally.
Since 57-3 is an awkward number to deal with mentally, we substitute 60,
which is near enough to correspond to the accuracy of the whole process.
The 60 becomes 20 because the vertical intervals are measured in feet, while
the horizontal distances are measured in yards, by old standing tradition.
The rule now becomes evident.
It is easy to see that the process is the more accurate the shorter the
distances involved. Suppose the slope is one and a half degrees, and
the distance 2460 yards. The vertical interval is 2460 divided by 20,
and multiplied by 1-5, or 185 feet. But suppose that the slope had been
one and three quarter degrees ; the vertical interval would then have
been 215 feet. A quarter of a degree, which is less than the instrument
can give with certainty, makes a difference of 30 feet in the result, and
this difference is evidently proportional to the horizontal distance between
the two points. At a thousand yards a quarter of a degree makes a dif
ference of twelve feet, so that it is useless to expect to obtain heights with
the clinometer which are correct within a few feet. In gently undulating
country, where the distance from point to point will tend to be large, while
the uncertainty in the measure of the slope is an important part of the
whole quantity, the results given by the clinometer are very likely to be
inconsistent and confusing.
Assumed datum height.
In making a compass sketch it is not commonly the case
that the height of any point above sea level is known. It is
then necessary to make an intelligent assumption of some height
to start with. This is called the assumed datum, or given
height; and all others are reckoned from it as zero. All figures
of heights entered on the sketch should be referred to this
datum ; they should never be entered as differences from some
other point, but always as heights above sea level or datum,
with the assumed datum.

COMPASS AND PLANE TABLE SKETCHING in
Sometimes it is convenient to determine the height of the
top of a tower which may be visible though the base is not.
Such heights should be entered in a list on the edge of the
sheet ; no figure, except the height above sea of the ground
itself, should ever be written alongside the object on the
sheet.
Contouring with the clinometer.
The most ready method of showing the relief of the ground
is by sketching the contours or form lines : the latter being the
rougher and more sketchy attempts at the former. Since time
is always of the greatest importance in this class of work we
must be careful that we limit the use of the instrument to the
smallest possible number of observations, and that these observa
tions are so disposed that they produce the greatest effect.
The first step is to obtain the heights above sea, or above
datum, of the ruling points ; this gives a framework of spot
heights upon which to construct the contours. We have already
seen how the height of one point is found when the height of
some other visible point is known.
The second part of the process is to find how the contours lie
round about one of these spot heights. Suppose that the ground
slopes away uniformly in a given direction, at a slope of 2°.
What is the interval in yards on this slope between contours
having a given vertical interval ? The question is easily solved
by inverting the relation given above, and writing it
'vertical interval in feet,

Horizontal interval in yards =

multiplied by twenty and
divided by the number
of degrees in the slope.

Thus if the vertical interval adopted for the contours is 25 feet, on a slope
of 2° the contours are spaced at a distance of 250 yards apart.
Suppose then that the spot height is 284 feet. Down the slope the first
contour is that for 275 feet. Here the vertical interval from the spot height
to the first contour is 9 feet, and its horizontal distance is therefore nine
twenty-fifths of 250 yards, or 90 yards. Take the protractor and scale off
90 yards along the line which marks the direction in which the slope has
been measured. This brings us down to the 275 contour ; thence scaling off

112 COMPASS AND PLANE TABLE SKETCHING
successive distances of 250 yards we obtain points on the 250, 225, 200, and
succeeding contours, so long as the slope remains uniform.
Repeating this process in a different direction we obtain other points on
the same contours ; and these are eventually joined up by sketching.
It is clear that this process may be very wasteful of time
unless care is taken that the lines of points so determined are
dominant in the construction of the contours. It is almost
impossible to lay down in a book the principles of economy in
contouring which can be learned only by practice in the field.
But one general rule is clearly useful. Run these lines of points,
or contour ranges, as we may call them, along the ridges and the
valley bottoms. With a range along each crest and one up the
floor of the valley it is possible to sketch the whole of the valley
contours without the possibility of going far wrong.
Beginners are apt to find this process of contouring with a
clinometer somewhat confusing, and are to be seen working out
the necessary small calculations on paper. This should never
be required. The student should train himself to do all the
calculation mentally, always remembering that the process is at
best only a rough one, and that quantities of a foot or two have
no real significance. Otherwise it would not be legitimate to
use the convenient whole number 20 in place of the more
accurate 19*1.
The older pattern Service protractor has scales which show
the horizontal distances between contours for each degree of
slope on two different scales. These are not of much use, since
it is difficult to interpolate for the fractions of degrees. It is far
better to accustom oneself from the start to work out mentally
the distances in yards, and to take these off the scales of yards
found on the protractor.
Height above ground of the observer's eye.
In strictness it should be necessary to take account of the
fact that the observations are made from a point about five feet
above ground. On short rays one may take sufficient account
of this by observing to some object such as a bush or the top of

Plate XV

I. Plane Table and Sight Rule: School of Military
Engineering pattern.

2. Indian Clinometer on Plane Table.

Instruments for Plane Tabling.

COMPASS AND PLANE TABLE SKETCHING 113
the hedge, which is judged to be of about the same height as the
observer. On long rays the effect of neglecting this precaution
becomes inappreciable.
The plane table.
The plane table is unique among survey instruments in that
it enables the surveyor to draw a map without measuring any
angles or doing any numerical work, except in the contouring.
The plane table is, in fact, a drawing instrument, by means of
which the map is drawn in the field without the intervention
of any angle measuring instruments. It is exceedingly well
adapted for rapid survey, and is very much used for making
maps in a hurry, as may be necessary in military operations
in an unmapped country, or during any rapid exploration.
The instrument consists of a drawing board covered smoothly
with drawing paper, and mounted on a light but rigid tripod,
upon which the board can turn, and can be clamped in any
position desired. The accessories are :
(1) a sight rule, preferably of boxwood, having folding sights
which can be turned up at each end. One sight has a narrow
vertical slit in it ; the other consists of a vertical wire stretched
across an open frame ;
(2) a trough compass, which is a long compass needle
mounted in a narrow box, with a short scale at each end. When
the needle is pointing to the centre of the scale at each end it is
parallel to the sides of the box ;
(3) a hard, well pointed pencil of good quality.
The sight rule should be graduated along one edge in inches,
and along the other with a scale of yards corresponding to the
scale on which it is proposed to work : very frequently the scale
of two inches to one mile.
The plane table has two principal uses, which must be
distinguished one from another. It can be used to produce a
complete map, entirely by its own resources, without the use
of any other instrument than the accessories which normally
accompany it ; the triangulation can be made with it, and the
whole detail filled in with it. Or it can be used to fill in the
H. M. S. 8

114 COMPASS AND PLANE TABLE SKETCHING
detail after the triangulation has been made with the theodolite.
The first is the use to which it is put in rapid and exploratory
mapping ; the second is its r61e in the more leisurely operations
of the precise survey of a large country, such as India or
South Africa.
We will begin by considering its use in rapid survey or
reconnaissance. Graphical plane tabling.
By graphical we mean that the plane table is to be used as a
drawing instrument, to make the complete map without other
instrumental aid. Both triangulation and detail are to be done
with it.
The principles of the triangulation are naturally the same as
those which we have already considered in compass sketching,
and it will not be necessary to repeat that the process consists of
measuring a base, and building up on it a framework of well
proportioned triangles.
Measurement of the base.
The base must be chosen in as open and level a piece of
country as can be found, and its ends must be marked in some
conspicuous way, so that they are visible one from the other, and
from the surrounding points which will be occupied in succession
to extend the base and start the triangulation. Plane tabling is
a much more accurate process than compass sketching, and a
correspondingly greater degree of care is required in choosing
the ground for the base.
If time allows, beacons may be erected to mark the ends of
the base and the ruling points. But beacons are by no means
necessary in a rapid graphical triangulation, and we shall suppose
that they are dispensed with. But we shall remember always
that the more accurately defined the ruling points are, the more
accurate will be the result.
Let us take two solitary trees or posts on a straight open road,
being careful to see that they can be identified with certainty from
the surrounding country, and not confused with neighbouring

COMPASS AND PLANE TABLE SKETCHING 115
trees or posts. We shall get the base as long as possible :
perhaps from half a mile to a mile long.
We have now to measure the base, and the more accurately
the better. If chain or steel tape is available, it should be
used. Failing these, a good deal can be done with a carefully
calibrated bicycle wheel ; and failing any kind of measuring
instrument the base must be paced. The error of the result may
in this case be three or four per cent. But this affects only the
scale of the map, not the relative configuration of points marked
upon it. And for many purposes the exact scale of the map is
not very important, so long as the topography is correct.
Plotting the base on the plane table sheet.
The base is measured in yards, and the length corresponding,
on the scale of the intended map, is taken from the scale of yards
on the edge of the sight rule. Consider the position of the base
in the area which is to be mapped, whether it is to the centre or
to the side ; draw a fine line with the sight rule in the convenient
position, and lay off on it the length representing the base
measure, making fine perforations in the paper with the sharp
hard point of the pencil, so that other rays may be passed
accurately through these points when required. It is well to
draw continuations of the line on which the base is to be laid off,
at each end of the sight rule, so that the rule may be laid down
accurately along its original direction in a subsequent step of the
process ; usually the base line is so short that the rule cannot be
laid down on it again with any great precision.
Call the ends of the base A and B.
Set up the plane table at A, as close as possible to the mark.
In plane tabling on the scale of two inches to one mile, one
hundredth of an inch represents about eight yards on the ground,
so that divergences of a yard or two from the exact position of
the station are hardly visible upon the map, being within the
limits of error in drawing. Lay the sight rule along the line of
the base on the table, and turn the table till the line of sight falls
on B ; then clamp the table. Beginners find some difficulty in
sighting along the rule, and are seen looking sideways in very
awkward positions. It may be helpful to say that the correct

116 COMPASS AND PLANE TABLE SKETCHING
position for plane tabling is as nearly as possible the correct
position for wicket-keeping in cricket.
Beginning the triangulation.
The last process has set the plane table. That is to say, the
base line drawn on the table is parallel to the base line on the
ground. And the point A on the table is over the corresponding
point on the ground. We can therefore draw the ray from A to
any other point by placing the sight rule so that its edge passes
through A on the table and is directed to the point C on the
ground. A convenient way of manipulating the sight rule is to
stand the pencil (hexagonal) with one corner on A, holding it
with the left hand, and with the right hand swing the sight rule
about this corner as a pivot until it is sighted on the point C.
Then carefully rule a line passing
through A towards C. It is essential \/ \/
that the pencil have a fine needle-like c j\ ^*
point, and that it be held carefully to
make a line really parallel to the edge
of the rule. It is not necessary to
draw the whole line AC. Make an
estimate of the distance of C; suppose
it is one mile and a half. This will
be three inches on the paper if we are b a
working at two inches to one mile.
Draw then a piece of the line only,
about three inches from A. If the
piece is not long enough it may be
lengthened later. But it should be
remembered that all the rays drawn Ig' I4'
must be rubbed out in the end, so that it is economy to draw
as little of the ray as will serve its purpose.
In the same way draw rays to other points D, E, F ... which may be
useful as ruling points. We leave A with the knowledge that all the points
C, D, E, F, ... which are to be mapped lie somewhere on the lines AC,
AD, ... which have been drawn ; their precise positions will be determined
by other rays drawn from B ... intersecting these first lines.
Now move the table to B, and set it by laying the sight rule along the
line BA and turning the table until the rule is set on A. The table is now

COMPASS AND PLANE TABLE SKETCHING 117
set ; that is to say, it has been moved from A to B parallel to itself, so that
any line already drawn on the table is parallel to its position on the ground.
Having set the table we draw rays BC, BD, ... to the points already observed
from A, or to as many of them as are visible from B ; and thus C, D, ...
are fixed.
Two points, one on each side of the base, must be fixed by the intersections
of two rays only, from A and B ; and it is important to see that these
intersections are as nearly at right angles as possible. A good intersection
is a blunc intersection. When the rays cut one another acutely a small error
in either will make a good deal of difference in the place of the intersection.
From C and D we proceed to fix other points ; and we must not accept
any point as well fixed unless it depends on three rays which intersect in
a point without visible deviation. Working on in this way we build up a
framework of triangles upon the base in the same way as we did in compass
sketching. But the accuracy of the result is considerably greater.
Choice of stations.
Only experience in the field can teach how to select the
stations of a triangulation with advantage ; and the selection will
naturally be governed by the nature of the country. The stations
must fulfil many conditions :
(1) they must be in commanding positions, so that stations
all round are visible from them ;
(2) they must be well marked natural or artificial objects,
such as a sharp summit of a hill, or the trunk of an isolated tree,
or the top of a tower. The top of a tree surrounded by low
growth, and the point of a steeple, are not suitable objects to
select for the continuation of the triangulation, since they
cannot be occupied in their turn ;
(3) they must make well conditioned triangles, with no very
acute angles.
It will often happen that without a preliminary reconnaissance
and occupation of the proposed stations, the surveyor will be
deceived. A point ahead may appear to be an admirable station,
but when it is occupied it may be found that further progress is
obstructed by natural or artificial obstacles which could not be
seen from the last station. It is therefore advisable to draw rays
to more points than are really required for the triangulation.
This will allow for the dropping out of stations which prove in
the end to be unsuitable.

118 COMPASS AND PLANE TABLE SKETCHING
It is one of the great advantages of plane tabling that a great
number of rays may be drawn with very little trouble, so that
superfluous rays need cause no regret, and the survey can go
ahead without preliminary reconnaissance. In a theodolite
triangulation the case is very different. Here a reconnaissance
is absolutely necessary, for selecting and beaconing the stations,
and by far the best kind of reconnaissance is a plane table
triangulation. The use of the triangulation.
When the triangulation is complete our plane table sheet is
covered with a series of rays intersecting in points, which are
conspicuous points about the country, tops of hills, isolated trees,
church towers, and so on. The triangulation is the skeleton of
the map, but the visible map is not yet begun. It may be that
we do not propose to go any further immediately. We have laid
out the framework of triangles ; from this we can select the
particular scheme best fitted for observation with the theodolite,
and we are then ready to beacon the country for the deliberate
observation. But if time presses, and we wish to have an
approximately complete map as quickly as possible, we must
dispense with the precise triangulation, and proceed at once to
fill in the detail of our plane table sheet.
The map is to show the natural features of the country, hills,
valleys, and rivers, and the artificial features, railways, roads, and
towns. These, the most important topographical features, are
not as a rule marked by upstanding conspicuous points suitable
for triangulation stations, while, on the other hand, very excellent
triangulation stations, such as isolated rocks or trees, are not
features that will eventually appear at all upon the topographical
map. Our skeleton, then, is no part of the map proper, and is
destined to disappear in the end, leaving no sign of the rays
which constructed it, and only the small triangular signs to mark
the stations which were used.
Accuracy of the graphical triangulation.
The sight rule can be set upon an object with an accuracy of
two or three minutes of arc ; this is readily seen if we consider

COMPASS AND PLANE TABLE SKETCHING 119
that the diameter of the sun or moon is about thirty minutes of
arc, and that they are very large objects to set upon if we view
them along the sight rule when they are near the horizon. It
is not hard to set with an accuracy less than one tenth of the
diameter of the moon. On the other hand, the error of a
compass bearing, observed without a tripod or other rest for the
compass, is likely to be at least half a degree. Hence the rays
drawn on the plane table are very much more accurate than
those plotted from compass bearings. By increasing the bulk
and weight of our apparatus we have much increased its
accuracy. This is a simple example of the general principle
that the accuracy of any survey process is limited by the weight
one is prepared to carry and the money to be spent.
Difference in principle between plane tabling and compass
sketching.
It is important to note the difference in principle between
plane tabling and compass sketching, as regards the construction
of the triangulation. In compass sketching each ray is plotted
independently as an absolute magnetic bearing. In plane tabling
the board is set up at each new triangulation point by sighting
back with the sight rule on one of the other points already well
fixed. The process depends only on the care with which the
settings are made, and the stability of the table. Up to this
point the compass does not enter at all into the work ; and we
are free of the various errors, such as local attraction and daily
variation of the compass, which limit so much the accuracy of
compass work.
Intersected points.
The stations of the triangulation are perhaps two or three
miles apart. As each one is occupied we take advantage of its
commanding position to draw rays to all the conspicuous objects
round about — not with the idea of occupying them in turn as
triangulation stations, but in order that they shall be well fixed
by intersecting lines. In this way a great number of steeples,
chimneys, well marked trees, and such objects, will have been
put in on the plane table sheet. These are called Intersected

120 COMPASS AND PLANE TABLE SKETCHING
points. In what follows they serve as auxiliary to the principal
points of the triangulation ; and like them, are destined in great
part to disappear from the finished map, since they are often of
no topographical importance.
The use of the trough compass.
At some point of the triangulation, when the table is
orientated by setting on another triangulation point, the trough
compass is taken from its case and laid on the table, with the
end of the needle which is marked with a cut toward the north.
The compass is turned until the needle points to the zero of the
scale at each end. The needle now lies in the magnetic meridian,
and the sides of the box, being parallel to the line of zeros of the
scales, are also in this meridian. Draw pencil lines along the
sides of the box, and mark the north end. (See Plate XVI.)
Now at any point whatever of the ground we are able to set
up the plane table in approximate orientation. Set up the
table ; take out the trough compass and place it on the compass
lines drawn as above, taking care that the north end of the
needle lies to the end marked north. Then turn the table until
the needle points to zero. The table is now orientated as
accurately as the compass permits, that is to say, within about
a quarter of a degree, unless there are magnetic disturbances
about. The purpose of this orientation by compass is to facilitate
the process of resection which follows.
Filling in the detail.
Up to the present we have been fixing well marked points
by drawing intersecting rays from other points previously deter
mined. When a sufficiency of these have been fixed, we begin
the new operation of putting in the important topographical
detail, the roads, fords, railway bridges, and so on, which are
inconspicuous objects in general, as viewed from the ruling
points, and cannot be determined by intersections. But, on
the other hand, the ruling points should be quite conspicuously
visible from them ; and if three are visible we can (with certain
limitations to be discussed at a later stage) set up the plane table

Plate XVI

i. Trough Compass and Case.

W-'

Plane Table and Telescopic Alidade: United States
Coast and Geodetic Survey.

Instruments for Plane Tabling.

COMPASS AND PLANE TABLE SKETCHING 121
and determine the place on the map, by the process known as
resection. Perhaps retrosection would have been the better
term, since the process consists of drawing rays backwards from
the ruling points. A point determined by resection is often
called a plane table fixing.
Plane table fixing by resection.
Whenever three ruling points, suitably disposed, are visible,
a plane table fixing may be made. The conditions for suit
ability are
(1) that the points are not too close together, neither is one
nearly opposite another ;
(2) that they do not lie nearly on a circle passing through
the point which is to be fixed.
The reason for these restrictions will appear in due course.
By means of the trough compass set up the table in approxi
mate orientation. Set the sight rule so that it is directed to one
of the points, while its edge passes through the place of this point
on the table ; and draw a ray back. Do the same for the other
points. If the three ruling points were correctly fixed, and the
table in correct orientation, the three rays would meet in a point,
which would be the point on the table corresponding to the place
where the table stands on the ground.
More often than not the three rays do not meet accurately
in a point, but make a small triangle, which is called the triangle
of error. This is not due primarily to any error in the positions
of the ruling points, nor to inaccuracy in drawing the rays, but
to error in the orientation of the table as set up by the trough
compass. The compass cannot be relied on to within half a
degree at the best ; and there may be iron pipes under the road,
affecting it. Moreover, owing to the convergence of the magnetic
meridians, lines drawn along the magnetic meridians at different
parts of the sheet will not be accurately parallel to one another.
In dealing with the triangle of error we assume that the whole
of the error is due to this faulty setting up of the table.

122 COMPASS AND PLANE TABLE SKETCHING
Solution of the triangle of error.
It might be supposed that when there is a triangle of error,
the true place which we are trying to fix would be at the centre
of gravity of the triangle. But this is entirely wrong. It is not
necessarily inside the triangle at all, as will be seen from the
following considerations.
Let A, B, C be our three ruling points on the map, and O the
point in process of fixing. If the table is not rightly orientated
it is rotated about the point where it stands on the ground, and
we may represent this by turning it in our figure about the point 0
on the map, so that A, B, C are moved to A', B', C on the table.

Fi.g- IS-
Now draw the rays again. Since the real points are distant, the
new rays will pass through A', B ', C, and will be parallel to the
old rays. They will intersect to form a triangle ; but 0 is more
likely to be outside than inside the triangle.
The student is advised to draw a few cases for himself. He
will then easily understand, and be able to prove, the following
rules for constructing the point O from the triangle of error.
Rule i. If the table is set up within the triangle formed by
the three points on the ground, the place of the table on the map
will be inside the triangle of error ; if not, it will be outside.

COMPASS AND PLANE TABLE SKETCHING 123

Rule 2. The point 0 will lie always to the right or always to
the left of the three rays, as one looks along them to the points-
from which they are drawn. (It will be seen that Rule 1 is
really included in Rule 2, but it is convenient in practice to
state the two separately.)
Rule 3. The perpendicular distances of O from the three
rays are proportional to the distances from the table of the
corresponding points on the ground.
To take an example as in the figure. Let the three rays be
drawn as shown, and let 0 be outside the
triangle ABC on the ground.
By Rule 1 O on the map is outside the
triangle of error.
By Rule 2 it cannot be in either of the
sectors marked by shading.
By Rule 3, for the proportions of the per
pendiculars, it cannot be in the remaining
right-hand sector, but must be in the left,
at the point indicated.
1 Fig. 10.
The method of making a plane table fixing is complicated to
explain. After a little instruction and practice in the field it
is perfectly easy and rapid in execution. And it is the most
ordinary operation in plane table survey. Point by point plane
table fixings are made all along the roads, rivers, and railways ;
and thus the detail of the map is quickly filled in. It will be
understood that only practice in the field can show how to
economise effort by making the fixings at the points where they
are most effective. No written explanation can give an eye for
country.Check on the solution of the triangle of error.
If the triangle of error is large, or the surveyor inexperienced,
it is well to have a check on the accuracy of the solution that
has been made. This is very simple. By hypothesis the triangle
has arisen from bad orientation of the table. When the first
solution has been made, lay the sight rule along the point which

124 COMPASS AND PLANE TABLE SKETCHING
the solution gives, and one of the ruling points which has been
used. Look along the sight rule, and the distant point will be
off the cross wire. Unclamp the table, and turn it till the point
comes on. Then clamp, and repeat the resection. This time
the triangle of error should be exceedingly small, if not an exact
point, and the solution should give a result very near the first
solution. If it does not, something is wrong. Inspection of the
solutions will probably show that an error has been made. If,
however, the solutions are made according to the rules, and yet
give discordant results, then it is probable that there is some
error in one or more of the ruling points, and this must be put
right by revisiting the triangulation points until all is verified.
It is no use trying to get good results from resections until the
ruling points are really laid down in their true places.
Case in which the solution fails.
The solution fails when the point which is to be fixed lies on
or near the circle passing through the three chosen ruling points.
If it lies exactly on the circle the solution becomes quite inde
terminate. However wrong the orientation of the table may be,
the three rays meet in a point, and it will appear that a perfect
result has been achieved. But turn the table round into another
orientation, and repeat the process. Again the three rays meet
in a point, though quite a different point. This curious result
depends on the well-known proposition that all angles in the
same segment of a circle are equal to one another.
If the point to be fixed lies very nearly on the circle, the
result is very nearly as indeterminate, and no good solution can
be obtained. Great care must be taken, therefore, that the three
ruling points are chosen so that there is no chance that the
problem may become indeterminate in this way. If the three
points in order are A, B, C, try to ensure that B is nearer than
either A or C. The circle passing through them will then lie
far away from the point which is occupied, and the solution will
not fail.
Remarks on the part played by the compass.
It is essential that the beginner should plainly understand
the part played by the compass in this operation. The compass

COMPASS AND PLANE TABLE SKETCHING 125
is an uncertain instrument, and cannot be relied upon to give
the orientation right within half a degree. For this reason the
orientation of the plane table, when it is set up by compass for
the resection, is always to be considered suspect. The size of
the triangle of error is an indication of how much it is wrong ;
and the solution of the triangle of error eliminates completely
the effect of the wrong orientation. In fact the compass is used
only for convenience, in order that the triangle of error may be
small. The compass is not indispensable, and if it is lost or
broken the process may be worked without it. Set up the table
by estimate in about the right orientation, and make a solution.
The triangle of error will be very large, but it can be solved
approximately. Re-orientate the table on the result of the first
solution, and make a second. This will come out with a very
much smaller triangle. If necessary repeat the process again,
and this time the result will be satisfactory.
It is clear from this that the role of the compass is quite
subordinate, and that any error in it will not affect the ultimate
accuracy that is achieved.
The plane table a modern instrument.
The discovery of the right use of the plane table is of
comparatively modern date, and its credit belongs to the Survey
of India. The instrument itself is ancient ; but so long as it
was employed only for fixing points by intersection, or so long
as it was set up by compass, and resections were made by two
rays only, it was not a very valuable instrument. The intro
duction of the method of resection by the solution of the
triangle of error made it at once an instrument of precision,
unexcelled for convenience and rapidity of work.
Plane table traverse.
In closely wooded or otherwise obstructed country the
method of resection may fail because three points cannot be
seen. In such cases it is necessary to make a plane table
traverse through the awkward area.
Suppose it is required to map a road passing through a
village. Make a plane table fixing on the road as near the

126 COMPASS AND PLANE TABLE SKETCHING
village as possible. Draw a ray to represent the direction of
the road to the furthest visible point. Take up the table, leaving
a mark to show where it stood, and pace to the forward point ;
then measure off the paced distance along the ray which has
been drawn. This will give the place of the forward point with
fair precision. Set up the table there ; orientate it on the back
point ; draw a new ray forward as far as possible ; and proceed
as before. In this way the road can be drawn in, leg by leg,
until it comes out again into open country, and the whole can
then be checked by a plane table fixing. Probably the result of
this will not agree with the position as carried through by the
traverse, and it will be necessary to adjust the traverse to make
it fit on to the plane table fixings.
Adjustment of a traverse.
Suppose that the traverse ABC...M ends at M, and that a
plane table fixing at this end makes the position M'. It is

Fig. 17. Adjustment of traverse. The full line is the original; the dotted
line is the traverse adjusted to close on Til' ¦
required to adjust the traverse so that it closes on M'. Join
MM' and draw lines parallel to MM' through each angular
point of the traverse. Each of these points must be moved
along its corresponding parallel by a fraction of the length MM'

COMPASS AND PLANE TABLE SKETCHING 127
proportional to the distance from A. This rule is of course
arbitrary. It is not pretended that the result is precisely right ;
but some systematic method of adjustment is required, and this
appears to be the best.
In practice the rule is simplified thus : Suppose there are ten
legs to the traverse, ending at B, C, D, ... M. The B is moved
one tenth of MM', C is moved two tenths, and so on, which
brings M to M' ; and the traverse is adjusted.
Heights and contours.
For rapid and approximate work the heights and contours
can be done with the Watkin clinometer, precisely as in compass
sketching, and it is not necessary to repeat here what we have
already said on pages 109- 112.
For more accurate work the relative heights of the triangula
tion points are determined with the theodolite, and other heights
are determined from them with the Indian pattern Clinometer,
commonly called the Indian clino. We will defer a description
of this instrument to the chapter on Trigonometrical Survey.
See Chapter VI, page 161.
Characteristic signs, and style of drawing.
The appearance of the finished sheet will depend very much
upon skill and care in draughtsmanship, and particular attention
must be paid to the conventions which are adopted for the
representation of both natural and artificial features. These
conventions vary to some extent with the style of the survey —
for rapid reconnaissance work the style is less elaborate than in
the more leisurely operations of an organised survey. For the
former, see the characteristic sheet in the official Manual of Map
Reading and Field Sketching. For the latter, reference may be
made to the margins of published maps, or to the characteristic
sheets published by the Survey departments.
Elaborate plane tables.
The instrument that we have described is the pattern adopted
in the British military service, and carried by field companies of
the Royal Engineers. It is set up level by estimation only, and
its sight rule has only plain sights, without any optical aid.

128 COMPASS AND PLANE TABLE SKETCHING
Much more elaborate instruments have been introduced,
with levels and levelling screws to set the table truly horizontal ;
with telescopes on the sight rules (then called telescopic
alidades), and other refinements which add very much to the
cost and the weight of the instrument, while detracting very
much from the convenience and rapidity of handling it. (See
Plate XVI.) Opinion is divided as to the utility of these
elaborations, and it is not possible to decide dogmatically for or
against them. But there is one consideration which is weighty
against the elaboration of the plane table. The work is done on
a sheet of paper ; and however carefully this may be seasoned
and mounted on linen, it is subject to distortion by moisture,
especially in the tropical climates where it is so much employed.
This is an argument in favour of keeping the instrument as
simple as possible, and not trying to obtain with it too minute
an accuracy. It should be said, however, that within the last few years
there has been a change in the opinion formerly held at the
School of Military Engineering, Chatham. The Close-Brooker
telescopic alidade, with a parallel rule attachment, has come into
ordinary use, and it is found that the increased accuracy which
may be obtained with it compensates for the greater weight and
cost.Limitations to the accuracy of graphical plane tabling.
The method of graphical plane tabling discards numerical
measurement and computation, and relies upon pointing,
generally without optical aid, and upon drawing. Every line
drawn upon the table is liable to be in error by an amount on
the border line of visibility ; these errors accumulate until they
become quite considerable, and cannot be tolerated on a map
with any pretensions to accuracy.
Further, there is a difficulty to be discussed more in detail
later — the question of the projection, and the effects of the
Earth's curvature — which make it impossible to carry on a
survey continuously through a number of sheets, and trouble
some to derive latitudes and longitudes of the places mapped.
Hence plane table triangulation has strictly limited uses. It

COMPASS AND PLANE TABLE SKETCHING 129
is admirable for exploratory and reconnaissance work, but it
cannot be used as the basis of a deliberate survey. This must
depend upon theodolite triangulation and calculation.
But as an instrument for filling in the detail of a precise
triangulation the plane table is unsurpassed, and we shall have
further occasion to consider it.
Tacheometer and Subtense Traverses.
The principle of subtense measurement is simple. It is
required to measure the length of a ray over rough country
unsuitable for ordinary traversing. At one end of the ray two
marks are erected in a line at right angles to the ray. Their
linear distance apart is measured by the party who erect them ;
and their angular distance apart is measured with a theodolite
from the other station.
Then if 20 is the angle subtended by a length 2s, the distance
is s tan 6.
This is the method generally employed on long rays. The
marks are poles set up perhaps fifty feet apart, and the angles
are measured by the method of repetition. The method has
often been used on boundary surveys.
Over shorter rays it is possible to invert the process, and
instead of measuring the angle which is subtended by a definite
distance, one measures the distance included in a fixed angle.
Wires or marks at fixed distances are inserted in the field of the
theodolite or level, and a graduated staff like a levelling staff is
observed. The further away the staff, the greater is the length
of it included in a fixed angle of sight. The fixed marks in the
telescope, called stadia marks, are standardised so that one has
the factor, frequently 100, by which one multiplies the length
read on the staff to obtain the distance of the staff from the
observer. The factor evidently varies with the distance of the stadia
marks from the optical centre of the objective of the telescope,
which is changed in bringing to focus objects at various
distances. It is not hard to prove that the necessary correction
for this can be obtained by the simple process of adding, to the
distance computed as above, the distance from the centre of
h. m. s. 9

130 COMPASS AND PLANE TABLE SKETCHING
motion of the instrument to a point on the axis, outside the
objective, at a distance from the optical centre equal to the focal
length. Thus there is a small and slightly variable correction
to be added to the observed distance to obtain the correct
result. This is not difficult to do ; but the necessity for doing it can
be avoided by introducing into the telescope a third lens, called
the anallatic lens, which eliminates the small correction just
described, and gives at once the true distance from the centre of
motion of the instrument. A theodolite or level fitted with this
device is called a tacheometer. The instrument is more useful
in making detailed plans of a small area than in geographical
work. Correction for slope.
There is often some confusion as to the correction required
when the ray is observed on a slope. Without going into the
proofs, which are quite simple, we may state the rules shortly as
follows :
When the subtended angle is measured on the horizontal
circle of the theodolite, no correction for slope is required.
When stadia lines or tacheometer are used with a graduated
bar placed horizontal, the apparent distance must be multiplied
by the cosine of the slope to give the horizontal distance.
When the graduated bar is placed vertical, the apparent
distance must be multiplied by the square of the cosine of the
slope. Summary of exploratory methods of survey.
It will be useful to sum up briefly the methods which we
have been considering, suitable for preliminary mapping, ex
ploration, or reconnaissance.
A single-handed traveller, whose main business it is to get
through the country, on exploration or on official duty, cannot
make a map. But he can
(i) make a compass traverse of his route, and fill in a
small amount of detail on each side ;

COMPASS AND PLANE TABLE SKETCHING 131
(2) make astronomical determinations of latitude and
azimuth, and with much more difficulty of longitude, which fix
the main points of his traverse, and serve as a general check
upon it.
(3) Small areas of country can be sketched with the
compass and clinometer.
(4) Larger areas can be mapped by graphical plane
tabling. A traveller like Dr Sven Hedin, who makes long journeys
alone in Central Asia, relies on methods 1 and 2.
Soldiers on active service, who want to illustrate a report on
the dispositions they have made in a certain position, may use
method 3.
A small party of surveyors, sent into unmapped country to
make a rapid exploration and map, will use method 4, supported
if possible by 2.
The most successful explorer will be the man who knows
precisely the advantages and possibilities of all the methods, and
makes skilful use of any or all of them as circumstances may
dictate.

CHAPTER VI
TOPOGRAPHICAL SURVEY
Regular topographical survey.
In the preceding chapters we have considered the various
operations of survey which may, and should, form part of the
work of any explorer, or of any pioneer in the development of a
new country.
Such work is of the utmost value in the early stages of the
development of the country. But the time soon comes when a
systematic survey of the whole must be undertaken.
No compilation of patchwork .survey can produce a map
worthy of the name, and the sooner the survey of the country is
put upon a systematic footing, the greater will be the ultimate
saving of expense, because the less scattered and incomplete
survey will there be to scrap.
Preliminary considerations.
Before laying out the plan of our operations we must con
sider whether our aim is restricted to producing a map which
shall have no sensible error anywhere ; or whether we desire
that our operations shall be of the refinement required when
they are to make a contribution to geodesy, properly so called :
that is to say, to the determination of the size and shape of the
Earth. For the present we will deal with the former case, and
suppose that we are to undertake the topographical survey of a
large isolated island, of area about 10,000 square miles. The
work is to be good, but not of geodetic accuracy. The methods

TOPOGRAPHICAL SURVEY 133
employed are to be as economical as is consistent with the
production of a first-rate topographical map. The island is
mountainous and the country fairly open, so that it does not
present any difficulties of an exceptional nature. It is suitable
for a good theodolite triangulation, with plane table detail.
The operations divide themselves into the following sections :
1. Determination of mean sea level.
2. Preliminary plane table reconnaissance.
3. Beaconing for the triangulation.
4. Determination of a latitude, longitude, and azimuth.
5. Measurement of the bases.
6. The theodolite triangulation.
7. Determination of heights by theodolite.
8. Calculation of the triangulation and heights.
9. Transference of the triangulation points to the plane
table sheets. 10. Mapping by plane table.
Determination of mean sea level.
The zero point for heights must be the mean level of the sea
on the coasts of the island. This must be determined at one or
more points by the maintenance of tide gauges.
The tide gauge consists essentially of a well, connected with
the open sea by a pipe of small diameter, allowing the water in
the well to assume the average level of the open sea, but damping
down the quick oscillations of the waves. A float in the well is
connected with an indicator and scale, so that the height of the
water in the well can be read at intervals ; or better, it is con
nected with a pen drawing a trace upon a clock-driven drum,
giving a continuous record which can be measured up and the
results tabulated.
The selection of a site for the tide gauge is often a matter of
some difficulty. We require the height of the open sea, and not
the height of the water in some inlet or harbour, which is often
modified by prevailing winds and currents. We require that
the record shall be continuous over a long time, not interrupted
by choking of the pipe with sand or weed.

134 TOPOGRAPHICAL SURVEY
The observed oscillation of the tide is the sum of a great
number of oscillations of very different periods and amplitudes,
the shortest periods being the halves of the solar and the lunar
days, the longest the period of revolution of the Moon's nodes,
nineteen years.
Further, variations of the barometer affect the height of the
sea, a fall of the barometer by one inch being accompanied by a
rise in the sea of about one foot.
Hence it is not possible to lay down any definite period
during which tidal observations should be continued. Fifteen
days' observation will cover the principal lunar tides, and this
may be taken as the absolute minimum. The best procedure
is to set up the tide gauge as early as possible, and to prolong
the observations as long as possible.
For the ordinary purposes of topographical mapping one
station is enough. But if it is proposed to carry out precise
levelling, and especially if there is any chance that questions of
rising or tilt of the land will arise, then several tide stations will
be required. In the present chapter we shall be content with
one station.
It is essential that the tide gauge shall be set up on solid
ground, so that there shall be no question of the permanence ol
the zero of the scale. It has usually happened that the longest
series of tidal observations have been made at ports ; but the
value of these series has been much depreciated by the fact that
ports are very often on made ground, with no guarantee against
gradual settlement. Sometimes indeed it is found that the
whole ground itself rises and falls with the tide.
The zero of the tide gauge must be connected with one point
of the triangulation by a carefully observed line of levels. (See
pages 95, 187.)
A discussion of the instrumental details of tide gauges, or of
the manner of reducing tidal observations, is entirely outside the
scope of this book. Reference may be made to the Publications
of the Survey of India, the Handbooks of this Survey, and
to Sir George Darwin's work, The Tides.

TOPOGRAPHICAL SURVEY 135
The plane table reconnaissance.
The success of the whole operation depends upon obtaining
a good triangulation ; and the difference between a good and
a bad triangulation depends largely upon the efficiency of the
reconnaissance which must precede the choice of the stations.
It is surprising how many small impediments combine to
interrupt the mutual visibility of stations that might be expected
to be in full view of one another. Hence it is not safe to take
for granted the most seemingly obvious suitability of any
particular station. A plane table reconnaissance starts without
taking much trouble over the measurement of a base, for the
precise scale of the sketch is immaterial. Rays are drawn to
three or four times as many points as are likely to be wanted,
for it is certain that as the work proceeds it will be necessary to
drop many of the points for obstruction on one ray or another.
At the conclusion of the reconnaissance the surviving points
will be carefully studied, from the point of view of planning a
well-conditioned system of triangles, and of obtaining a good
connection with the measured bases.
During the preliminary reconnaissance the ground should be
beaconed, and care should be taken that not only the general
localities are intervisible but the beacons themselves. Want of
care in this respect may cause endless trouble afterwards, for the
actual triangulation with the theodolite is a slow and laborious
business, and the failure of a single station means that a number
of other stations must be re-occupied. Hence no pains may be
spared in making sure that every ray in the selected arrange
ment is really observable.
It is hardly necessary to say that the most anxious attention
must be given to the selection of sites for the bases.
The reconnaissance ladder.
In suitable country the plane table triangulation is easy.
But it may be required to cross a low and forest-clad district
where it will be necessary to build towers for the instrument,
and the selection of the sites for these towers is difficult, because
until they or their equivalents are erected it is impossible to
judge of the suitability of their positions. To get over this

136 TOPOGRAPHICAL SURVEY
difficulty a French officer of Artillery, Commandant Lucien
Durand, has introduced into survey the tall observation ladder
that is used for the control of artillery in modern practice. This
ladder can be carried on a waggon and run up in an hour.
From the opening in the platform at the top the surveyor can
work his plane table, and can decide very well whether or not
the position is suitable for the erection of a tower station. The
same officer has designed a very steady construction of poles
which makes an excellent and inexpensive tower. (See
Plate XVII.)
Plan of the triangulation.
It is not necessary that the principal triangulation should
cover the whole country with a net of triangles. If the country
is long and narrow a backbone of quadrilaterals is sufficient, as
in the figure. If the breadth is too great to make this sufficient,
a chain of quadrilaterals at right angles to the first will strengthen
the skeleton.
The purpose of forming the triangles into chains of quadri
laterals is to provide the necessary control without unnecessary
repetition or duplication. Were the chain a chain of triangles
only, there would be no check upon the survival of a gross error.
A regular system of quadrilaterals gives the most simple
arrangement consistent with strength.
It will often happen that more rays can be observed from a
certain station than are required by the plan. To observe these
rays would confuse the work without adding anything of im
portance to its accuracy. Hence the desirability of making a
strict programme of the rays to be observed at each station,
neglecting all others.
The triangles must be well conditioned : that is to say, they
must be strong in shape, having no angles less than 30° about,
and if possible none less than 400. The size of the triangles will
depend so much on the nature of the country that no general
rule can be laid down, beyond saying that the larger they are
the better.
The connection of the bases with the chains of quadrilaterals
also depends very much on the ground. The main idea is that

Plate XVII

I. Reconnaissance ladder on the march.

-i£*

2. Reconnaissance ladder in
course of erection.

3. Double tripod scaffold for
theodolite and observer.

Reconnaissance ladder and beacon.
Service Geographique de PArmie.

Designed by Commandant L. Durand,
ii1' Regiment d' Artillerie.

TOPOGRAPHICAL SURVEY 137
a chain should start from one base and close on another. Then
the comparison between the length of the second calculated
through from the first and the length of the second as actually
measured gives the best possible control over the accuracy of
the whole chain.

Fig. 18. Diagram of Geodetic Triangulation up the Nile Valley from Cairo
to Beba. The two heavy lines are bases.
Beacons. Beacons are of two principal kinds : the luminous and the
opaque. In most countries, when the ray is more than eight or
nine miles long it is necessary to use luminous beacons or

138 TOPOGRAPHICAL SURVEY
signals, for the haze in the air very quickly obliterates the
contrast between the opaque signal and its surroundings, so that
it becomes invisible.
Luminous signals are either heliographs, for use with the Sun
by day ; or powerful lamps, nowadays usually acetylene, for
work at night. In a fine climate like South Africa, the ' helio '
can be observed at a range of ioo miles and sunlight is sufficient
to let the work proceed without undue delay. In less favourable
climates lamps provide a more certain mark for observation ;
but there may be difficulties in observing at night, for reasons of
health or safety, that make it necessary to restrict operations
to the day. On cloudy days it is sometimes possible to use
powerful lamps instead of helios. Night observation has the
great advantage that irregular refraction and disturbance of the
air are much less than by day, so that the results are more
accurate. In either case, the effective use of luminous signals requires
that the organisation and control of the signal parties shall be of
a high order. Each party must use every endeavour to send its
signal in the right direction so long as it is required, and must
then move without delay to the next station. In general the
discipline must be military to ensure the punctual carrying out
of the lonely, dull, but all-important duties of the helio or lamp
parties.The heliograph.
It is impossible to enter into details of the mechanical con
struction of this instrument. Essentially it is a plane mirror
from three to eight inches in diameter, mounted on a tripod in
such a way that it may be turned by means of a slow motion
screw to follow the Sun, and cast the reflected beam in a constant
direction. There is a sight vane carried on an arm, which is set
in the first instance upon the station to which the beam is to be
directed ; and a small round patch is left unsilvered in the
centre of the mirror. So long as the black spot thus formed in
the beam is kept centred on the white patch of the sight vane,
the beam is being sent in the right direction.
It is sometimes a matter for surprise that the beam can be

TOPOGRAPHICAL SURVEY 139
directed with the necessary accuracy, until one remembers that
the Sun, and therefore the beam, has a diameter of half a degree.
The light from the mirror therefore diverges in a cone of angle
half a degree, equivalent to about 1 in 115. At a distance of
ten miles the beam covers a front of about 150 yards, and a
careful operator has no difficulty in directing the beam within
this distance right or left of the object.
When lamps are used, at night, the distant station is invisible,
and some means must be devised for sending the beam in the
right direction. But it is hardly possible to go into such detail
in this place.
It is interesting to remember that the limelight was invented
by an officer of the Royal Engineers to make the connection
between Wales and Ireland, after many weeks had been wasted
in waiting for the Sun.
Opaque signals.
The opaque signals must be large, so that they may be
visible at a distance ; and they are best constructed so that
the theodolite may be placed in position without taking down
the signal ; otherwise there is some danger that the signal will
not be re-erected in its original position, and there will be a dis
continuity between the observations made to that station before
and after its occupation.
The construction of the beacons will vary with the materials
locally available and with the ease or otherwise of transport.
They should be symmetrical about their vertical axis when seen
from any position ; therefore the quadripod is preferable to the
tripod. A good form of signal is that shown in the frontispiece
to Colonial Survey Reports, Vol. 2. Its appearance on service is
shown by the accompanying photograph of a beacon on the
Uganda-Congo boundary, for which I am indebted to Captain
Jack, R.E., British Commissioner. (See Plate XVIII.)
In unsettled countries the surveyor has the advantage that
he can cut down trees to make his signals ; an official manual
recommends a form of beacon built of 120 saplings. He can

140 TOPOGRAPHICAL SURVEY
also clear the tops of hills of inconvenient timber, leaving the
best tree standing in which to build a station. In civilised and
closely settled countries this is not possible ; but church towers
and other buildings go far to supply the need. The Ordnance
Survey of England constructed a station above the cross on the
dome of Saint Paul's, and took off temporarily some feet of the
top of the spire of Norwich Cathedral. Such operations being
impracticable under ordinary circumstances, it is very difficult to
carry out a piece of triangulation in England for instructional
purposes on any considerable scale.
Permanent marks underground.
In all cases the visible signal should be considered as a
temporary representation of an underground mark, which is
buried for safety, and so protected and identified that it may be
recovered at any time. To ensure this is not easy. Some of
the principal stations of the Ordnance Survey of England are
now lost, owing to insufficient attention to this question of
permanent marking.
The form of the underground mark depends on local circum
stances. It will take some such form as a copper bolt let into
the rock at a depth of say two feet, and protected by a pyramid
of masonry, or a large cairn of stones. In settled countries a
few square yards of ground should be bought and enclosed ; it
may then be committed to the charge of the local authorities.
In unsettled countries it is much more difficult to protect the
stations, because the natural tendency of the native is to take
the first opportunity of digging to see what it is that the white
man has buried so carefully. In these countries also great
trouble is often experienced in maintaining the opaque signals,
and much time is wasted through their destruction during the
course of the work.
Self-centering beacons.
With the usual construction of beacons a great part of the
time taken in setting up the instrument is consumed in centering
it over the station mark. And a considerable part of the gradual
loss of accuracy in the progress of the chain of triangles is

Plate XVIII

mmim

v . _ mmm
I. Beacon for intersected point.

2. Quadripod beacon for triangulation.
Uganda-Congo Boundary. Phot, by Capt. E. M. fack R.E.

TOPOGRAPHICAL SURVEY 141
caused by errors in this setting up and centering. To avoid
these difficulties an excellent form of self-centering beacon has
been introduced by the Survey of Egypt. The beacon consists
of a concrete pillar carrying on top a brass casting with three
radial V-shaped grooves planed at 1200 apart. The three
levelling screws of the theodolite base, or the three feet of the
helio, stand in these grooves. The instrument can be put up
only in one position, which is automatically the correct one, and
no error of centering is possible. When the station is not in use
the pillar is covered over and protected in the usual way. This
self-centering device seems to be worthy of general adoption.
Beaconing. The selection of sites for the beacons is done by a
reconnaissance party making a plane table sketch well ahead
of triangulation party, and erecting the beacons on the points
which make the best conditioned system of triangles. The
beaconing party is responsible for leaving everything in order
for the triangulators ; and they must take great care that all the
rays are cleared and fully visible.
Initial latitude, longitude, and azimuth.
The triangulation and plane tabling will eventually produce
a map in which all parts of the ground are shown in their
correct relation one to another; but they will give no information
as to the place of that country on the Earth. To fix the map
down on the Earth, and to obtain its orientation, we must make
astronomical observations.
By determining the latitude and longitude of one of the
triangulation points we, so to speak, pin the map down at one
point, leaving it free to turn about that point. By determining
the azimuth of one of the rays from this point to any other, we
fix the map in its right orientation.
Hence the necessary astronomical observations are
An initial latitude and longitude.
An initial azimuth.
It might be supposed that there would be some advantage in
determining the latitudes and longitudes of a number of different

142 TOPOGRAPHICAL SURVEY
points. But for our present purpose this is not so. The reason
will be discussed more fully in the chapter on the astronomical
observations for geodetic purposes. For the time being it will
be sufficient to say that every observed latitude and longitude, is
affected by local irregularities in the direction of gravity, due
to the unequal distribution of mass in the crust of the Earth.
Hence if one observes the latitudes of two stations in the
triangulation one will probably find that the difference of the
observed latitudes does not correspond with the difference of
latitude resulting from the triangulation. Such discordances are
of the highest importance in geodesy. But in a simple topo
graphical survey they are embarrassing ; and it is usually best
to confine oneself to a single latitude and longitude ; and a
single azimuth.
Observation of latitude.
The determination of latitude will be made by the observa
tion of stars near the meridian : the method of circum-meridian
altitudes. Observations of the stars are always to be preferred
to observations of the Sun, both because they are more accurate
in themselves, and because a number of stars can be observed
on one night, so that a determination of the accuracy desired
can be obtained very much more quickly than if the Sun were
used. Two or three nights' observation with a five-inch micrometer
theodolite taking four pairs of north and south stars each night,
should give the latitude correct to one or two seconds of arc,
which is less than the probable value of the local deviation of
gravity, and is sufficient for all topographical purposes.
Should a more elaborate determination of the latitude be
desired, it will be obtained with the zenith telescope, or with a
large theodolite constructed to serve as a zenith telescope.
Observation of longitude.
The longitude of the initial station is the difference between
its local time and the time of the meridian of Greenwich.
The local time at the initial station will be determined by the
observation with the theodolite of pairs of stars east and west, as

TOPOGRAPHICAL SURVEY 143
near the prime vertical as possible. Or, more elaborately, it will
be determined by a portable transit instrument set up at the
initial station.
The difficulty, as always, lies in obtaining the time of the
Greenwich meridian. With the extension of wireless telegraphy
this difficulty becomes less year by year, and will shortly dis
appear. It is therefore not necessary to discuss the difficult and
now out of date methods of obtaining Greenwich time indepen
dently of the telegraph or wireless. By the use of wireless it
becomes relatively easy to determine longitude well within a
second of time. When it becomes a question of one or two
tenths of a second all kinds of complications arise, which need
not be discussed here. (But see Chapter VIII, page 198.)
Observation of azimuth.
The azimuth is obtained by observation of stars east and
west, near the prime vertical, or of circumpolar stars at their
greatest elongations. These observations give the difference of
azimuth between the stars and the terrestrial station, and also
the true azimuths of the stars at the moments of comparison ;
whence the true azimuths of the station are immediately derived.
If the triangulation is being made with opaque signals, so
that no provision is made for illuminating the signals at night, it
will generally be convenient to establish a supplementary mark
at a moderate distance, say one mile, from the initial station.
This mark can be more easily illuminated than one at a greater
distance; and the difference of azimuth between the mark and
the triangulation station chosen for the initial azimuth can be
determined during the ordinary course of the triangulation by
day. There will be no difficulty in determining the initial azimuth
in this way with an accuracy of two or three seconds of arc,
which is sufficient for the purposes of the survey with which we
are dealing at present. Local deviations of gravity have their
effect on azimuths as well as on latitudes and longitudes; and it
is useless to aim at a degree of accuracy which cannot be achieved
except by the elaborate discussions of geodesy.

144 TOPOGRAPHICAL SURVEY
The bases.
Recent improvements in the means of measuring bases have
altered our conception of the relation of the base to the triangu
lation. When base measurement was difficult one thought of the
triangulation as built upon a single base, whose measurement
was by far the most delicate, the most anxious, and the most
uncertain part of the whole operation. If it were possible to
measure a second base in another part of the country, well and
good. But it would never have been thought remarkable if a
whole survey rested upon one base.
Nowadays base measurement has become so relatively easy
that it is possible to plan a chain of triangulation and to stipulate
that bases shall be measured at intervals of 200 or even 100
miles apart all along the chain. The measurement of a base
becomes a kind of control carried out at intervals as part of the
foutine; it is no longer the solemn and fundamental operation
that it was.
Essentials of base measurement.
The essential steps in the process of base measurement are
the following :
1. Determination of the field standard in terms of the
national standard of length.
2. Measurement of the distance between the base terminals
on the ground in terms of the field standard.
3. Correction of the measure for temperature and any other
causes of variation, and reduction to national standard.
4. Reduction to the horizontal, and then to mean sea level.
For topographical purposes bases may be measured by means
of tapes laid along a straight and level road or railway track,
and stretched to a constant tension with a spring balance; or by
a wire or tape hung under constant tension in the natural curve
— the catenary — supported at each end by frictionless pulleys
suspended from trestles, and carrying near each end a divided
scale which is read against marks carried on tripods set up along
the line of the base.

TOPOGRAPHICAL SURVEY 145
The tape laid on the ground serves very well when there is a
convenient railway track with little traffic, such as is often avail
able in large and new countries. In the absence of such ready-
made sites for the base, it is easier to use the wires hung on
tripods some feet above the ground. Much rougher country can
be crossed, and it is easier to go up and down hill. We shall
consider the latter method as the standard modern method, and
shall deal with it first.
The tape or wire.
The modern tape or wire is either 100 feet or else 24 metres
long between the divided scales. It is made of an alloy of nickel
and steel (36% nickel) which has the remarkable property that
its coefficient of expansion is only one tenth that of ordinary
steel, -000,000,5 of its length per degree Fahrenheit, instead of
•000,006. The trade name of this alloy is Invar.
These tapes or wires have the great advantage that they are
extremely portable. When wound upon their reels they may be
sent by post to the National Physical Laboratory or to the
Bureau International des Poids et Mesures at Breteuil, and there
compared with the laboratory copies of the national standards
of length. For a comparatively small fee the laboratory will
determine the correction to the assumed length, and make a
determination of the coefficient of expansion with temperature.
Thus without any difficulty a survey department in, we will say,
Fiji, may send home the standard tapes from time to time to be
re-compared with the laboratory standards, and may thus ensure
a very strict control over the lengths of the wires or tapes that
are in actual use in the field.
This provides in a very simple and inexpensive way for the
reference to the national standards of length.
Use of the suspended tape in the field.
The base will be from four to twelve miles long : the longer
the better. It must be chosen so that one end is visible from
the other; and it is generally convenient that the ends shall
be on slight elevations, which much facilitates the choice of
the stations for the base extension, that is to say, of the small
h. m. s. I0

146 TOPOGRAPHICAL SURVEY
triangulation connecting the base with one of the principal sides
of the main triangulation.
The ends of the base will be marked by terminals sunk in
the ground, or perhaps carried on concrete pillars.
Simple but firm tripods, carrying small upright pillars
engraved with fine lines, will be set out in the line of the base,
at distances apart equal to the tape length between its zeros of
the engraved scales.
The tape is suspended over frictionless pulleys, carried on
straining trestles which can be adjusted easily so that the tape
Can be brought up close to the marks on the tripods. The tape
is kept in tension by weights hung on each end.
At given signals observers at each end make series of
simultaneous readings of the scale on the tape, against the
marks on the tripod.
The tape is then carried on to the next tripod section, and
the operation is repeated.
As soon as the tape party is clear a levelling party determine
the difference of height between one tripod and the next. When
this is done, the tripods in rear can be carried forward and set
up ahead in the line of the base. With good organisation and
drill it is possible to measure five kilometres per day in this
manner. At the beginning and end of each day's work the field tapes
are compared with the tapes which have been standardised in
the laboratory, and which are not subjected to the risks of injury
in the field.
The accuracy obtainable in this way is limited only by the
number of wires which are employed, the number of times that
the measures are repeated, the precautions that are taken to
avoid damage to the wires, and finally, by the residual error in
the comparison of the standard tapes with the laboratory
standards of length.
With very little precaution it is possible to measure topo
graphical bases in this way with an accuracy of I in 200,000,
which is amply sufficient for any work which does not aim at
geodetic accuracy. We shall consider the refinements desirable
in the measure of geodetic bases in a separate chapter.

Plate XIX

I. Taking readings on the wire, Semliki Base.

Adjusting the straining trestle and wire before reading.

Measurement of Semliki Base,
Uganda-Congo Boundary.

Phot, by Capt. E. M. fack, R.E.

TOPOGRAPHICAL SURVEY 147
Use of the flat tape in the field.
The tape laid on the ground will probably soon become
obsolete, except for operations on a small scale.
A convenient way of operating with such a tape is as
follows :
Provide the tape with two handles filed flat at their ex
tremities. The distance between these extreme surfaces is the
length of the tape which is compared with the standard. The
handles are furnished with lugs, over which are hooked wire
stirrups with a loop at the end, to take the hook of a spring
balance. Pickets are driven into the ground in the line of the base, at
tape lengths apart, and strips of zinc are nailed to the tops of
the pickets. The tape is held at one end by a spike through
the loop of the stirrup, and is strained to the right tension by a
spring balance hooked into the other stirrup. The flat ends of
the handles should then come over the zinc strips. At a given
signal observers at either end steady the tape, and draw a sharp
point along the flat ends of the handles, so as to make marks on
the zinc strips. The tape is then carried on to the next section,
and the operation repeated. No attempt is made to join up the
tape lengths accurately, but the distances between the pairs of
cuts on the zinc are measured with scales or dividers, and the
small excesses or defects added to the tape lengths. The
thermometer is laid alongside the tape on the ground, and is
read at frequent intervals to give the temperature correction.
Working in this way it is easily possible to measure a base
with an accuracy of 1 in 75000, provided that a good site can
be secured. But unless a straight railway track is available the
suspended tape is easier to manage though it requires a larger
party. For details of the use of tapes laid flat on the ground refer
ence may be made to Wilson's Topographical Surveying.
Correction for slope.
With modern ideas of ground suitable for base measurement,
the correction for slope sometimes becomes considerable ; but it
is always very simple.

148 TOPOGRAPHICAL SURVEY
The correction may be expressed in terms of either the
vertical difference in height of the ends of the tape, or the slope
of the straight line joining the ends.
Considered in its simplest possible form the problem is as
follows :
Let L be the length of the tape, or the distance between the
zeros at the two ends ; and let H be the difference in height of
the two ends. If 6 be the slope of the tape, then sin 6 = H\L ;
and the correction for slope is — L ( i — cos 6) = — H2/2L.
Hence, whether the slope or the difference of vertical height
is measured, the correction to the measured length of each span
is very simple. Modern practice favours the use of the differ
ences of vertical height, measured with an ordinary Y-level,
rather than slopes measured with an instrument such as the
Abney level.
It may seem to be likely that the above simple assumption
as to the form of the correction is not applicable to the case of a
tape hanging in its natural curve. An exact investigation shows,
however, that except in the most minutely refined work, the
above formula is amply accurate. (See page 187.)
Reduction to sea level.
It is an invariable principle that maps should be drawn as if
the ground were projected on the sea level surface. A moment's
consideration shows that this is necessary. Think of two parallels
of latitude crossing the Drakensberg from Natal to the Orange
Free State. The ground on the latter side is nearly a mile
further from the centre of the Earth than the low land in Natal.
Hence the linear distance between the parallels will be greater
by about one part in four thousand on the west side of the
range. But it would be quite impossible to represent the
difference on the map, since such a representation would require
that the sheet should be stretched locally wherever the ground
was high. Hence the necessity of reducing always to sea level.
The reduction is of great simplicity, being almost automatic
in its operation. Let h be the mean height of the base above

TOPOGRAPHICAL SURVEY 149
sea level, and R the radius of the Earth, supposed spherical-
Then the simple reduction of the measured length L of the base
is evidently - Lh/R very nearly. This is quite sufficient except
in extremely accurate geodetic work ; the latter we will consider
in a later chapter.
With our base thus reduced to sea level the calculation of
the whole triangulation, depending on the base, is automatically
reduced to sea level also, as we shall see almost immediately.
The theodolite triangulation.
The theodolite is set up directly over the station mark, and
is levelled, so that the horizontal circle of the instrument is truly
horizontal. The telescope is sighted on each of the other stations
in turn, according to the programme ; and the horizontal circle
is read by the microscopes at each setting. It is important to
notice that the angles thus measured are not the actual angles
between the successive pairs of beacons, such as would be
measured by a sextant, but are those angles projected on to the
horizontal plane of the station occupied. If the Earth is con
sidered spherical these angles are the same whatever the height
of the stations above sea level, even when the various stations
are at very different heights. Hence the justification for the
statement of the preceding section, that when the measured
base is reduced to sea level the whole of the triangulation is
automatically reduced to sea level also.
The details of the manipulation of the theodolite are dealt
with in the Textbook of Topographical Surveying. We will
confine ourselves here to the points which are especially con
cerned with the horizontal triangulation.
Suppose that there are four stations A, B, C, and D to be
observed. A round of angles consists of settings on A , B, C, D,
and A in turn. It is important to notice that the station A is
observed to twice. The reason for this is that small errors are
introduced into the measured angles if the instrument is not
perfectly stable during the course of the round ; and this cannot
be ensured absolutely. If we repeat the observation of A at the
end of the round we ensure that the measure of the angle DO A
is independent of any settlement of the instrument that may

.?So

TOPOGRAPHICAL SURVEY

have occurred during the course of the round from A to D. In
fact any such movement affects Only the particular angle under
measurement at the time when . it occurred. At the same time

Fig. 19.
the near concordance that there should be between the first and
the last settings on A is a measure of the stability of the instru
ment during the round. This is an important principle, to which
attention should be paid.
There are, however, cases in which the simple process .
described above must be modified. In a bad climate it will
happen that sometimes one and sometimes another station is
visible ; but never all at once. In such a case one establishes a
reference mark at such a distance that it is always visible ; and
one measures the angle between this mark and any other station
that may become visible. The differences between the bearings
of all the stations from this reference mark give eventually the
angles that should have been observed directly. For simplicity
we shall assume in what follows that the whole round of angles
can be observed in the manner first described.
To obtain the necessary control and to detect blunders, as
well as to eliminate by repetition the accidental errors of the
observations, the round of angles must be repeated one or more
times. We take care to arrange the work so that each repetition

Plate XX

^Sv

I. In position for Triangulation.

From the eyepiece end.

3. With reflector over objective for
lamp illumination.

4. With attachment for
electric illumination.

Five inch Micrometer Theodolite.

Cambridge Observatory.

TOPOGRAPHICAL SURVEY 151
is made on a different part of the circle, whereby accidental errors
of the circle graduation are to some extent eliminated. In the
very best instruments these errors rarely exceed two or three
seconds of arc ; but there are many instruments in use, made by
well-known makers, in which the errors of graduation are by no
means so small. It would be a very long and tedious business
to determine them and introduce corrections for them ; and it is
usually sufficient to so arrange the observations that repetition
tends to eliminate them.
Check on the accuracy of the triangulation. Triangular
error.
In a small triangle, of one or two miles per side, the curvature
of the Earth may be considered negligible, and the three angles
of the observed triangle should add up to 180°. In larger
triangles this is not strictly the case. We remember that the
angles are measured in the horizontal planes through each
station ; and when the triangle is large the curvature of the
Earth throws these planes out of parallelism with one another.
The result of this is that the three angles of the triangle should
add up to more than 180°, the excess being called the 'spherical
excess.' This is easily calculated, and depends on the area of
the triangle. Deduct it from the observed sum of the three
angles, and the result should be 180° exactly. In practice it
will differ from this quantity by a small number of seconds,
and this difference is called the 'triangular error.'
The average triangular error is a measure of the precision
of the triangulation. In the most precise work, of geodetic
accuracy, the average error will be less than one second of arc.
In good topographical triangulation it will be two or three
seconds. Experience will show what limit should be set to the
average triangular error on any particular piece of work ; and
when the standard is laid down the observations must be repeated
as many times as may be necessary to arrive at the desired
degree of accuracy.
This test of the triangulation by considering the triangular
error gives a simple and invaluable means of control, and of
securing that the work is up to the standard required.

152 TOPOGRAPHICAL SURVEY
Spherical excess.
The spherical excess of a triangle may be calculated from the formula
cosec i"

E=ab sin C

2 (radius)2 '

When the ellipticity of the Earth is taken into account it is usual to work
with the radius of an oblique section making an angle 450 with the meridian.
See Auxiliary Tables of the Survey of India, Table III.
If the triangles are less than 100 miles a side it is sufficiently accurate to
apply to each angle a correction of one third of the excess.
Except in very accurate work it is sufficient to measure the area of
the triangle from a chart, and to use the formula
„ area of triangle in sq. miles ,,
E=  x 13 -15.
iooo
Refraction of horizontal angles.
Refraction is usually supposed to act in a vertical plane ;
and so long as it does so it can have no sensible effect upon the
horizontal angles. But in the neighbourhood of steep slopes the
layers of air of different temperatures are not horizontal, and
a ray of light passing through such a region may suffer deviation
in the horizontal plane. Such effects will in general take place
only near the ground ; and for this reason it is important to
avoid rays which in their course approach near intervening
ground. Such rays are called ' grazing rays.'
It is difficult to say how high a ray must pass over inter
vening ground to avoid the disadvantage inherent in a grazing
ray ; but so long as obviously grazing rays are avoided it is
usually safe to hope that such small remaining effects of
horizontal refraction as may be left will be of a non-systematic
character, and will be eliminated in the average. There are,
however, certain cases where this is not necessarily true, such as
in the triangulation up the valley of the Nile, where the stations
are alternately on opposite cliffs, and the cooling of the air over
the water might very well produce systematic effects. Much
attention is being given to this problem by the officers of the
Survey of Egypt.

TOPOGRAPHICAL SURVEY 153
A recent publication of the United States Coast and Geodetic
Survey, on the Texas-California arc of primary triangulation,
gives a striking instance of well determined lateral refraction.
The line between two stations Clayton and Kennard passes very
close to a steep slope of a flat topped hill. During most of the
observations the wind was blowing from the hill across the line
between the stations, and the results gave excessive closing
errors to the triangles involving this line. The observations
made when the wind was blowing across the line towards the
hill gave values which closed the line in a satisfactory manner.
It became evident that the former were in error by about seven
seconds of arc.
Determination of heights by theodolite, or Trigono
metrical Heights.
The method of trigonometrical heights provides a rapid way
of determining differences of height of the triangulation points.
During the occupation of each station, after the horizontal
angles have been measured, the apparent angular elevation of
the beacons at the other stations are measured with the vertical
circle and microscopes of the theodolite. These measures differ
from the horizontal angles in that they are absolute elevations
or depressions, and not merely differential measures.
By careful attention to the rules for the measurement of
vertical angles the errors of the instrument may be very nearly
eliminated, except that there is no possibility of eliminating the
errors of division of the circle by repetition on different parts of
the arc. The serious errors inherent in this method are those
due to refraction.
The vertical refraction of a horizontal ray is large; it depends
upon the density of the air intervening in the path of the ray,
which varies very rapidly during the day, and is almost im
possible to calculate. But there are two principles of working
by which this effect may be in great part avoided : the observa
tions should be made at the time of day when the refraction is a
minimum, that is to say, in the early afternoon ; and the rays
should be observed from opposite ends under circumstances as
nearly the same as possible. It is then assumed that the effect

J 54

TOPOGRAPHICAL SURVEY

of refraction on the observation at each end is the same ; and it
is easy to see that the effect is thereby eliminated.
When it is not possible to take the reciprocal observations
from each end, some assumption must be made as to the law of
refraction, based upon an analysis of the observations that have
been made reciprocally. But to pursue this part of the subject
is beyond the scope of the present chapter. The results are
especially unsatisfactory in mountainous regions with glaciers
and perpetual snow. Hence the heights of the inaccessible
snow-clad peaks of the Himalayas, which are determined by this
method, are subject to some uncertainty.
It will be noticed that when two points at a considerable
distance apart, and of no great difference of height above sea,
are reciprocally observed, each is measured as a depression at

Fig. 20.

Fig. 21.

the other, in spite of the fact that refraction raises each of the
rays to some extent. This is a necessary consequence of the
curvature of the Earth ; but the size of the effect is a little
surprising to the student, until he remembers how small the
Earth really is, and that two points four geographical miles
apart subtend an angle of four minutes of arc at the centre of
the Earth, so that each is depressed from the other by 2'.
The formulae are very simple.
Let A, B be the two stations, and M a point vertically below B at the
same distance from the centre of the Earth as A.
Since AB is very small compared with AC, we may take
BM=AM tan BAM. (Fig. 21.)

TOPOGRAPHICAL SURVEY 155
And it is easily seen that BAM is equal to half the difference in the
depressions of the two stations, seen from one another : provided that the
refraction is the same at the two ends.
Hence if s be the distance in feet between the two stations, their difference
of height in feet is Jtan| (difference of depressions).
If only one angle is observed it is necessary to introduce a numerical
allowance for refraction. Whenever reciprocal observations are obtained, as
above, the refraction at either station is R = \ (8 - sum of observed depressions)
where 6 is the angle ACB, which can be calculated from j and the radius of
the Earth. It is found that the ratio R : 8 is generally about 0-07.
Now it is easily seen that for an observed depression D at B the angle
BAM=\8 - refraction -Z).
And if refraction = 0-07 8 this becomes
BAM =0-42,6 -D.
Or since the distance along the surface corresponding to an angle of
1" at the centre is about 101 feet
BAM= 4"'2 5 X distance in feet ry
IOOO
= k — D say.
And then as before difference of height = s tan {k-D).
This is the simple theory on which the table for k given in the Textbook
of Topographical Surveying is based.
The whole of the above theory is a rough approximation ; but it is
probably sufficient, in view of the uncertain effects of refraction.
We must also take into account in the calculation the height of the
theodolite above ground at each station, and also the heights of the signals
to which the observations are made. It is tedious to puzzle out the rules
of signs for these small corrections ; but it is quite easy to apply them when
the rules are given. See Textbook of Topographical Surveying, pp. 28
et seq. When all precautions are taken the errors of this process
amount to one or two feet on a ray of thirty miles, when the
angles are observed at each end. For rays observed only from
one end, and especially when there is a probability of anomalous
refraction, such as occurs in mountainous regions with glaciers,
the uncertainty is considerably greater ; but it may of course be
reduced by combining the results of a number of observations
taken from different stations.

156 TOPOGRAPHICAL SURVEY
The heights of most of the principal peaks in the Himalayas
depend upon rays observed from one end only. Lines of
levelling have been carried up to stations in the hills, and from
these trigonometrical heights of all or of many of the 10,000
permanently snow-clad summits have been observed. During
the course of such work Mount Everest had been observed to
on many occasions without any suspicion that its height was
extreme, for it is very inaccessible, and does not appear
strikingly prominent compared with other peaks. Only when
the observations were computed in due course in the Survey
Department at Calcutta was it found that this peak is higher
than any other known ; and not until after the Tibet Expedition
was it certain that there is not a higher peak behind it.
Barometer heights in topographical survey.
Although the barometer cannot be relied upon for the
principal determinations of height in regular survey, it is often
useful in special circumstances, when the other methods fail.
For example, suppose that it is necessary to determine
the depth of a canyon with almost perpendicular walls. Very
probably the bottom of the canyon cannot be seen from the top,
and methods depending upon observed rays are useless, or at
any rate can be employed only at the cost of great trouble
in occupying many intermediate stations. In such a case a
barometer trip to the bottom and up again will give results
which are sufficiently accurate, in a few hours. Similarly the
barometer may be employed in contouring densely wooded hill
country, in which no view can be obtained, and which is being
surveyed by traverse. This method is much used in Nigeria.
Calculation of the triangulation.
The observations made at each station are entered in ' angle books,' from
which the observed angles are abstracted, the means taken, and the results
brought together in the form of ' abstracts of angles.'
Let the figure represent a part of a chain of quadrilaterals under observa
tion. A portion of the abstract of angles may read thus :
Observed angles at Y : EYD 31° 57' 28"
DYF 45 6 15
FYE 282 56 9
359 59 52

TOPOGRAPHICAL SURVEY

'57

It will be noticed that the angles at the station do not add up to precisely
360° as they should. This is due partly to the errors of observation, partly
to the errors of the divided circle, and partly to movement of the instrument
in the course of the round.
Now suppose that in the course of the computation we have arrived at
the length of the side DE and that we wish to proceed. Let us do so by
solving the triangle DE Y. From the abstract of angles at Y we take out
EYD 310 57' 28"
and from the abstracts of angles at D and E we take out
YDE 55° 28' 16"
DEY 92 34 42.
The sum of these is 180 o 26,
and by calculation we find that the spherical excess is inappreciable, which
leaves the triangular error + 26".
Now we cannot solve the triangle until it has been made into a perfect
triangle, whose angles add up to
exactly 180°. If we are concerned
with this triangle alone, the best
thing that we can do is to divide up
the error into three equal parts and
apply one to each of the angles, so
that the sum of the thus corrected
angles is exactly 180°.
This being done we can find the
length of either of the sides EY or
DY, being given the other side DE
and the angles of the triangle.
For by elementary trigonometry
sin DEY

DY DE~~
whence
and similarly

sin DYE'

D Y=DE cosec D YE sin DE Y,
E Y= DE cosec D YE sin YDE.

Thus either D Y or E Y is easily found.
Distributing the excess of 26" over the three angles we have for the
corrected values : Angle at D 55° 28' 7"
Y 31 57 20
E 0.2 34 33
180 00

158 TOPOGRAPHICAL SURVEY
Thus if log DE = 3'8337549>
log D Y= log DE 3'8337549
+ log cosec DYE 0-2763299
+ logsinZ>£'F 1-9995610
4-1096458
and similarly log £¦^"=4-0259149.
This example is taken from the work of a vacation survey class in the
Isle of Wight.
Proceeding to the next triangles we can find FY from the triangle
EYE, since YE has been found ; or we can find it from the triangle FYD
since YD has been found. We thus arrive at two values of FY which will
probably not agree precisely with one another, because of the arbitrary
character of the corrections which have been applied to reconcile the slightly
erroneous angles in the triangles. And if we had gone a different way round,
deriving FY through FD or FE we should have obtained other slightly
differing values of FY.
In ordinary topographical work not of high precision we shall take the
mean of the various values we obtain for any side ; and proceed. But in
precise work this is not possible, and some way must be found of determining
such a set of corrections to the angles that we arrive in the end at the
same result precisely, whichever way we go round. This is called the
adjustment of the quadrilaterals, and is a process much too elaborate to be
described here.
Closing one base on another.
By the above process we may start from the measured length
of one base and calculate right through the chain of quadrilaterals
until we arrive at another measured base. We shall then have
two values for this base : the directly measured value ; and the
value carried through by calculation from the first base. These
two values will generally differ from one another by a slight
amount; and it is usually assumed that the former is correct.
We have then to investigate the corrections that are to be
applied to the triangulation, in order to make the measured and
the calculated lengths of the base agree with one another. It
will be evident that this is a more elaborate piece of adjustment
than the first, and far more unsuitable for description here.
Calculation of the geographical positions of the triangu
lation points.
For general purposes the most convenient way of defining
the position of each point is to give its latitude and longitude.

TOPOGRAPHICAL SURVEY 159
We have determined an initial latitude and longitude of a
station A, the azimuth of the line AB, and the length in feet of
AB. The problem is to determine the latitude and longitude
of AB, and the azimuth of A at B. For the purposes of precise
survey it is not sufficient to resolve AB along and at right
angles to the meridian through A, and convert these resolved
distances into differences of latitude and longitude. We have
to take account of the curvature of the Earth, and of the fact
that owing to its spheroidal shape the curvatures along and at
right angles to the meridian are not the same. The necessary
formulae are somewhat complicated, and the analysis by which
they are established still more so. It must be sufficient to say
here that the Survey Tables of India, reproduced in extended
form in the Textbook of Topographical Surveying, pp. 209 et seq.,
have reduced the computation to a simple form, by a process of
great ingenuity.
We should note that this process demands a knowledge of
the size and shape of the Earth, as a basis for the tables.
The calculation gives the differences of latitude and longitude
between A and B ; which being added to the co-ordinates of A
give those of B. It gives also the azimuth of A from B, tech
nically called the 'reverse azimuth,' which is not quite 1800
different from the initial azimuth, on account of the convergence
of the meridians towards the pole.
Now to proceed from 5 to C: We have the measured angle
ABC and the azimuth of BA, from which we deduce the azimuth
of BC, and the process of carrying on from B to C proceeds as
before. Thus we obtain the geographical positions of all the triangu
lation stations. Any selection of them can now be plotted on
any plane table sheet in the manner to be described presently.
Calculation of rectangular co-ordinates.
If however the area surveyed is small, and it is a question
only of plotting a single sheet or small number, it may not be
worth while to perform the above calculation of the latitudes
and longitudes. For the purpose of plotting the plane table
sheets it is sufficient to calculate the rectangular co-ordinates of

160 TOPOGRAPHICAL SURVEY
the other stations with respect to axes through the initial station,
treating the triangulation as if it were on a plane instead of
being on the spheroid. This is simpler to calculate, but we
shall see that it is not so simple to plot ; and there is great
difficulty eventually if geographical positions should be wanted
after all.
Construction of the plane table graticule.
The plane table graticule is a construction of meridians and
parallels drawn on the table, so as to permit the plotting of any
station whose latitude and longitude have been derived from the
preceding calculation. The projection upon which the graticule
is drawn is an approximation to the polyconic projection. The
quantities required are derived from tables such as those given
in the Textbook of Topographical Surveying, pp. 227 et seq., and
the method of construction is given on p. 93. See also the
author's Map Projections, pp. 58, 118. This work can be done in
the field, with only the sight rule of the plane table and a pair
of dividers. When the graticule is plotted it is easy to inter
polate and plot any station whose geographical position has been
determined. At first sight this method may seem to be elaborate, and the
beginner may imagine that something much simpler might be
devised to serve its purpose. It will be found, however, that for
the orderly conduct of a regular survey nothing less systematic
will serve. Generally speaking, when the triangulation is com
plete and calculated, the work of plane tabling the detail is
divided up between a number of surveyors, who undertake each
a definite block bounded by certain meridians and parallels.
Each plane table will be plotted so that it includes an area
somewhat larger than that assigned to the particular table ; and
the triangulation points will be plotted all over the sheet. To
have these well determined points all round outside the area
actually being mapped is a great convenience.
Mapping the detail by plane table. *
When the surveyor goes out into the field with his plotted.
sheet he first visits some of the principal points, sets up the

TOPOGRAPHICAL SURVEY 161
table there, and sights round to the other points within view, to
see that the rays come right, and that no mistake has been made
in the plotting. At one of the stations, while the table is set,
he puts on the compass lines for the trough compass. He also
takes the opportunity of drawing rays to prominent objects
which will serve as intersected points.
This being done, the work of mapping proceeds as in
graphical plane tabling, and we need not repeat what has been
said on the methods of fixing by resection. Since the positions
of the calculated points are correct far within the limits of visible
error, the general accuracy of the whole will be much better than
in the graphical process, and a second resection should always
give an exact cut of the three rays, without any triangle of
error. The determination of heights and contours will be very
much more exact than in the graphical process, because they
will be all based on the theodolite heights of the triangulation
stations. The spot heights at the resected points will be determined
with the Indian pattern clinometer (see Plate XV), which consists
of a brass bedplate with a bubble and levelling screw, set up
along the ray on the board, and levelled. Two leaves standing
up at either end of the base plate carry respectively a small
sight hole, and divided scales of degrees, on one side, and of
tangents of degrees, on the other side of a vertical slit. The
observer, looking through the sight hole at the distant point,
reads off the tangent of the elevation or depression of the
distant point. He then scales off its horizontal distance, multi
plies it by the tangent, and obtains at once the vertical interval
between the plane table and the distant station. He must not
forget to take account of the height of the table above the
ground, in calculating the spot height.
This process is about ten times as accurate as determining
spot height with the Watkin clinometer ; and being based upon
accurate fundamental heights, it gives points for contouring with
all the refinement which can be desired, except for detailed
engineering. H. M. S. II

162 TOPOGRAPHICAL SURVEY
When the spot height is fixed, the slopes are observed with
the scale of degrees on the other side of the opening in the vane,
and the process of calculating mentally the places and spacing
of the contours are almost exactly similar to those which we
have already described fully in Chapter V, pages 109- 112.
When the section allotted to the surveyor is complete he inks
in all the lines and figures which are to stand, clears up with
rubber all those which are not required, and sends in the field
sheet to headquarters. The great advantage of this system is
easily seen. The field work comes in block by block all ready
for the draughtsman, who has only to redraw it on the finished
sheet, when it is ready for reproduction. There is very little
possibility of confusion or misunderstanding, or of some portion
of the work being missing. All this tends strongly to good
order, efficiency, and economy in the operations of the survey.
Precise traversing.
It must always be remembered that in certain types of
country triangulation and plane tabling are impossible, as on
the Gold Coast, a nearly flat and densely forested region, where
it is impossible to obtain a view of any importance. In such
country it is necessary to construct a framework of traverses,
run with the theodolite and steel or invar tape along lines of
clearance cut through the forest. This is expensive, and
exceedingly unsatisfactory, because in a few months the lanes
are grown up again, and the labour seems to be lost.
The methods of work vary much in different countries, and
for an account of them we may refer to such books as the
Handbook of the Southern Nigeria Stirvey.
The process of topographical survey which we have described
here is that which, with small differences, is in use in all the
principal surveys of the world. It is admirably suited to the
rapid production of maps on topographical scales, especially
where the detail is not too crowded.
It is not, on the other hand, so suited to the production of
large scale cadastral maps showing intricate boundaries of
property. In such cases it is usually necessary to break down

TOPOGRAPHICAL SURVEY 163
the triangulation into small triangles of about a mile a side, by
the theodolite, and to cut these up in turn and fill in the detail
with the chain. This was the method by which the whole
of the detailed survey of the United Kingdom was carried
out. It is very accurate, and very expensive. But it has no
geographical interest, and we shall not consider it further in
this book.
The Ordnance Survey of Great Britain and Ireland.
The beginnings of the Ordnance Survey may be traced to
the Highland rebellion of 1745, when the Quartermaster General
to the forces of the Duke of Cumberland made a map of the
Highlands, which proved so useful that it was extended to the
Lowlands, and the intention was formed of making a map of
the whole kingdom. The project was continually interrupted
by war, and not very much progress was made with it.
In the year 1783 Count d'Adhemar, the French Ambassador,
transmitted to Mr Fox a memoir of Monsieur Cassini de Thury,
proposing to connect Greenwich and Paris by a triangulation, in
order to determine the difference of longitude between the two
Observatories. The British Government accepted the proposal,
and entrusted to General Roy the task of planning and directing
the enterprise. The first step was to measure a base on Houns-
low Heath. Thence a chain of triangles was carried across the
Surrey Hills and through Kent to Dover, from which the con
nection was made to Boulogne, Calais, and Dunquerque. It is
interesting to notice that in this early work the observations
were made to lamps, at night.
These operations made it possible to bring out a really
accurate map of Kent. Immediately the demand arose for
equally good maps of Sussex and of Essex; the Admiralty
required that the chain of triangles should be continued west
ward to the Land's End and Scilly, for the improvement of the
Channel Charts ; and then began that movement in favour of a
complete survey of the Kingdom, for which General Roy had
been looking ever since his early experience in the Highlands.
The principal triangulation of the United Kingdom occupied
roughly the first half of the nineteenth century. Unlike modern
11 — 2

164 TOPOGRAPHICAL SURVEY
triangulations of the first class, it was extended over the whole
country, and not merely confined to chains along the meridian
and parallel. It was made with the celebrated three foot theodo
lites constructed by Ramsden.
The survey of a thickly settled country cannot be conducted
without the right of access to property of every kind ; and in
the English survey this right was interpreted very liberally. A
great platform was erected over the Cross of Saint Paul's Cathe
dral in London, and a section of the spire of Norwich Cathedral
was temporarily removed to make a station for the instrument.
These stations are marked beyond any probability of loss. But
the stations in the open country are not so well identified, and
some of them could not be recovered if they were required for a
revision of the triangulation. More unfortunate still, one end of
the principal base on Salisbury Plain is lost, by the mischievous
enterprise of some persons unknown, who dug up the bronze
gun which was sunk in the ground to serve as a terminal. It is
now generally recognised that the right way to preserve triangula
tion stations and principal bench marks of the levelling is to buy
the small plots of ground on which they stand, fence them in,
and entrust them to the care of the local authorities.
The connection between Wales and Ireland involved great
difficulty owing to the rarity with which very long rays can be
observed in the moist climate of the west. The difficulty was
overcome in the end by the invention of the limelight, and
observation at night. The extension northwards to the Shet-
lands was possible only because of the fortunate situation of the
small islands Faira and Foula. Further extension to the Faeroes
is impossible. The triangulation of the United Kingdom rests on the two
bases of Salisbury Plain and Lough Foyle ; it was not found
possible to measure a good base in Scotland. Indeed it was the
opinion of the surveyors that there was not in the whole of Scot
land a site on which a base could be measured with possibility
of connection to the triangulation. Modern improvements in
base apparatus have at last removed from Scotland this reproach.
The ' breaking down ' of the principal triangulation into the
smaller secondary and tertiary triangles eventually covered the

Plate XXI

j : ¦ rrrSp-

LMsM,

^£&^z:~.

¦sggim&b ~~~-

I. Measurement of the Lough Foyle Base.

2. The Great Theodolite.

3. Scaffold on Gravelines Church for
the connection with France.

Ordnance Survey. Principal Triangulation.

TOPOGRAPHICAL SURVEY 165
country with a net of triangles averaging little more than a mile
a side. So minute a subdivision was required because the detail
was all to be fixed by chaining. It is a peculiarity of the survey
of the United Kingdom that not only the horizontal detail, but
also the contours, are all chain surveyed. The great expense of
accurately surveyed contours made it impossible to place them
as close as was desirable ; and it is now recognised that less
accurate contours at a smaller vertical interval would have been
more valuable than the less frequent levelled, pegged, and
chained contours which-must in course of time become obsolete
by changes due to weathering and to cultivation.
The latest report of the Ordnance Survey, dated 1912 May 28,
gives much interesting information on the present state and
future intentions of the Department. The Survey is now 118
years old. In that time it has completed the trigonometrical
framework of the United Kingdom, which occupied altogether
some sixty years ; it has produced the one-inch map of the
whole Kingdom, and revised it twice ; the six-inch and twenty-
five inch maps of Great Britain, with one revision ; and the six-
inch map of Ireland with one revision. The twenty-five inch
map of Ireland will be finished in 1914.
A great part of the work of the Survey now consists in the
systematic revision. It is now the rule that no large scale map
shall be more than twenty years unrevised, and that the small
scale maps shall never be fifteen years out of date when they are
issued. And the more important alterations, such as new rail
ways, are shown very nearly to date. With the rapid extension
of industrial development the amount of detail to be shown, and
the complication of the map, become continually greater.
" A hundred and seventeen years ago the surface of the three
Kingdoms presented an appearance on the maps very different
from what we are accustomed to, and this is of course especially
the case in and near what are now the great centres of popula
tion. We must picture a map which shows no railways, no
system of metalled roads, no post or telegraph offices, few factories,
a map dotted with small towns, showing by their plans their
medieval structure. Yet in the country we should find the
boundaries of counties and parishes but little changed, and

1 66 TOPOGRAPHICAL SURVEY
we should find the same immemorial hedges." (O. S. Report,
1912.) After a rather long repose the scientific side of the survey
has been awakened within the last few years, and important
works are in progress. Owing to its early date, and to its
pioneer character, the principal triangulation of the country,
though absolutely sufficient for the practical needs of mapping,
is possibly below the standard required in modern discussions
of the figure of the Earth ; but owing partly to the difficulty
of measuring a base in Scotland, it was not easy to define
precisely how far it falls short of the desired standard. To test
this matter a base has been measured at Lossiemouth, and a
portion of the triangulation is being re-observed in connection
with it. At the same time all the principal stations of the
triangulation are being examined, and re-marked in more
permanent fashion than was thought necessary at the time
when they were occupied for observation.
" So far as the mean sea level is concerned, the datum in use
on Ordnance Survey maps at present has no scientific value.
Steps are being taken to determine with all available precision
satisfactory values of the mean sea level in Cornwall, and on the
North Sea. The revised network of levels and the precise
values of mean sea level will not only serve practical purposes
better than these have been served in the past, but will provide
data for the determination of the vertical movements of that
portion of the earth's crust which is Great Britain." (O. S. Report,
1912.) An important feature of the new programme of levelling
is the provision of fundamental points based on the solid
rock. The cost of the Ordnance Survey is nearly a quarter of a
million per year, and about one tenth only of this is received
from the sale of maps to the public. But on the other hand,
it is probable that the amount saved to the public by the exis
tence of the Ordnance Survey maps is several millions per year.
And the work of Government could not proceed without the
Survey. The value of maps and plans furnished to Government

TOPOGRAPHICAL SURVEY 167
Departments during the year 191 1 — 191 2 was more than three
times the value of those bought by the public.
India. The Survey of India has a long and honourable history, and
no country of the world has contributed more to the advance
ment of geodesy, the thorough organisation of topographical
survey, or the methods of work in difficult frontier country.
Only in the methods of map reproduction has the Survey of
India failed to maintain the highest level ; and great improve
ments have been made in this respect in recent years. The
frequent references to Indian methods in the British official
textbooks show how great an influence this celebrated depart
ment has exercised on the survey work throughout the Empire.
Canada. Until within the last few years the great amount of survey
that was done was for special purposes, and since it was not
done under the control of any one authority, nor in any systematic
manner, the greater part of it was inevitably wasted, from the
point of view of the production of a topographical map of the
country. This is now happily changed. A geodetic survey is
in progress under the direction of the Chief Astronomer and
the topographical survey is being pushed forward by the Militia
Department, while the reproduction of the maps has been under
taken by the Geographical Section of the General Staff in
London. The diagram of sheets published is to be found in
the Catalogue of Maps published by the latter department.
Australia. The conditions in the Commonwealth very much resemble
those in Canada. A great deal of miscellaneous survey has
been carried out without much result in the production of topo
graphical maps. A good deal of primary triangulation is now
being done, but there is not yet much information available, and
it does not appear that the publication of maps has yet been
begun.

168 TOPOGRAPHICAL SURVEY
South Africa.
The geodetic triangulation is complete, and a great part of
it is included in the arc of the 30th meridian, to which reference
has already been made. The Orange Free State has been
surveyed topographically on the basis of the geodetic survey, at
the joint expense of the British and the Colonial Government.
A reconnaissance survey of Cape Colony has been made in part,
but this is now suspended. No topographical survey exists in
Natal, the Transvaal, or in Rhodesia, and the want of such a
survey is not only a danger from the point of view of defence,
but is a standing obstacle to the development of the country.
British Tropical Africa.
The tropical possessions in Africa are in a much more for
ward condition, in regard to survey, than the much older states
to the south. At first much money was spent rather ineffectively
in desultory survey, but great progress has been made since the
establishment of the Colonial Survey Committee in 1905. It is
the duty of this committee to make such recommendations as
will ensure the rapid and economical prosecution of accurate
surveys where these are required, and the rendering the results
available as speedily as possible for use by the Home Govern
ment, the Colonial Governments, and the public.
This committee publishes an annual report, which is full of
the most interesting information, and should be read by all
students who are interested in the survey of the Empire. In the
first report, dated August 1906, special attention was drawn to
"the importance of enforcing the rule that work should be taken
up systematically by blocks according to a definite programme.
This is a principle which cannot be too strongly insisted on, but
which has been largely neglected in the past ; the observance of
this principle is a fundamental condition of efficient and econo
mical work.'' The excellent results of the criticism exercised by
the committee may be seen in the very satisfactory records of
progress in the later reports.
The work of the Colonial Survey Committee was at first
principally in tropical Africa, but it has gradually extended its
interest to other colonies and dependencies.

TOPOGRAPHICAL SURVEY 169
Boundary Surveys.
The survey and delimitation of international boundaries in
Africa have been the means of surveying many of the outlying
portions of the tropical protectorates, and the great variety of
the conditions to be faced has led to great improvements in the
technical methods employed. It is unfortunate that there is not
available any general account of these operations, which are of
the highest interest.
A detailed summary of the length of each boundary, the
date of its survey, ratification, and demarcation, is given in the
Colonial Survey Report. The general course of the operations
is as follows :
"First there is an international agreement drawn up on broad
lines ; each government then appoints Commissioners, who meet
at one end of the boundary and march along it, exploring
and mapping the boundary zone. The Commissioners, having
arrived at the other end, agree upon the geographical position
of the principal features and decide upon the details of the
frontier, paying special attention to the incidence of tribal
boundaries, and to the future nationality of the villages. They
then march back along the line, erect pillars, and inform the
chiefs. The protocol in duplicate is drawn up and signed, and
each Chief Commissioner forwards the protocol and maps with
a report to his Government. The protocol is then approved by
the two Governments, and in some instances a fresh agreement
on the terms of the protocol (with perhaps some minor modifi
cations) is drawn up and signed by the representatives of the
Governments." Great Britain is interested in about 17,000 miles of boundary
in Africa, of which about 10,000 have now been surveyed,
principally within the last fifteen years. The result of this
activity is that the perimeters of our African possessions are
more accurately surveyed than the interiors, and the land
boundaries better than the sea coasts.
In other parts of the world also the demarcation of boundaries
has involved interesting surveys, notably on the Alaska Boundary,
the boundary between Chile and Argentina, surveyed by the

170 TOPOGRAPHICAL SURVEY
officers of the British Arbitration Commission, and the Akaba
boundary between Egypt and Sinai.
These have provided instances of the delicacy with which
the fixing of an international boundary must be conducted, or
the dangers which arise from any looseness or ambiguity in the
definitions, so long as there is not a chain of conspicuous beacons
erected at intervals along the boundary with the consent of both
parties. There are now no "hinterlands" in Africa, the partition
of the continent is complete, and the boundaries are well defined
by treaty or convention. It is highly satisfactory to know that
the actual delimitation of these boundaries is making such rapid
progress that there will soon be very little left unmarked.

CHAPTER VII
GEODETIC SURVEY
The present meaning of the word Geodesy is the same as
the old meaning of the word Geometry : the measurement of
the Earth. And it is a great pity that the word is sometimes
used, in examination schedules, to mean elementary survey.
Figure of the Earth.
The principle which underlies the measurement of the
Figure of the Earth is exceedingly simple.
Suppose first that the Earth is, to the best of our knowledge,
spherical ; and consider how we should measure the radius of
the sphere. Take two stations on the same meridian, and
determine the latitude of each. This gives the distance between
the two stations in angular measure on the sphere. Now, by
triangulation, measure the distance between the two stations in
terms of the unit of length that we prefer, say metres. We then
have the result that so many metres are equivalent to so many
degrees, minutes, and seconds of the arc on the sphere. If the
difference of latitude is n", and the distance between the stations
along the meridian is M metres, then the radius of the meridian
in metres is given by the equation
Radius = j^f cosec \"\n.
This is the principle of the method used by Eratosthenes in
his celebrated attempt to measure the Earth, in the third
century B.C.
If similar operations carried out in many different latitudes
on various meridians gave always the same value for the radius,

172 GEODETIC SURVEY
we should have the clearest evidence that the Earth was a true
sphere. But in fact we get different values for the radius when
we determine it in different places. This was suspected in the
latter part of the seventeenth century ; but the errors incidental
to early operations of the kind led to some confusion ; and it
was not until the celebrated measures made under the auspices
of the French Academy in Peru and in Lapland had been
brought to a successful conclusion that the law of the variation
was definitely established for the northern hemisphere. The
further one goes north, the larger is the distance corresponding
to a degree of latitude : the flatter, therefore, is the Earth.
The measures made in Peru and in Lapland, combined with
those made in France, were consistent with the hypothesis that
the Earth is a spheroid of revolution, or, in other words, that all
the meridians are similar ellipses. They were consistent with
this idea, but they were by no means sufficient to prove it ; and
in the middle of the eighteenth century grave doubt was cast on
the matter by the result of the Abbe de Lacaille's measure of
an arc of meridian at the Cape of Good Hope, which seemed
to show that the southern hemisphere was prolate, the degree
decreasing in length as the pole was approached.
It was some time before the explanation of this difficulty
was discovered ; and in the meanwhile a somewhat similar
discrepancy had been found in England, the curvature of the
southern half of England appearing to be less than that of the
northern half.
Deviations of the vertical.
The origin of these abnormal results is in the existence of
local deviations of the vertical, which have been mentioned
already in Chapter VI, page 142. The latitude of any station is
the inclination of the Earth's polar axis to the horizontal plane of
the station. The horizontal plane is the plane at right angles to
the direction of gravity. The direction of gravity is determined
by the distribution of matter within the crust of the Earth. If
this distribution is abnormal in the neighbourhood of a station
the horizontal plane is no longer a tangent plane to the spheroid
which represents the general form of the Earth ; and if such a

GEODETIC SURVEY 173
place is chosen by bad luck as one of the terminals of an arc
of meridian the curvature of the meridian deduced from these
measures is not representative of the general average curvature
of a meridian in that latitude.
We have said that the direction of the vertical is influenced
by the distribution of matter within the Earth's crust. It is also
of course affected by the attraction of the visible mountain
masses above the level surface. But these latter can be allowed
for ; and when this is done it nearly always happens that the
visible masses prove to be quite insufficient to account for the
results obtained. Indeed it not infrequently happens that the
deflection of the vertical is in the direction opposite to that
which would result from the attraction of the visible mountain
masses alone. Such is the case at Dunnose, the station in the
Isle of Wight which is the southern terminal of the arc of
meridian of Great Britain. Here there is high down to the
north, and the English Channel to the south. The density of
the water is only about two-fifths that of the surface rocks, and
it might be expected that in such a situation the direction of
gravity would deviate away from the sea, and towards the land
masses to the north. At this station an opposite effect is found.
The direction of gravity is deflected to the south ; the horizontal
plane is tilted to the north ; the angle which the Earth's axis
makes with this plane is diminished ; the latitude of the place
comes out too small ; the amplitude of the arc of latitude is
increased and finally the southern half of the British arc of
meridian appears to be flatter than the northern half.
What happens at Dunnose happens to a greater or less
extent at most stations. These deviations in the direction of
gravity are the most disturbing factor in geodetic work ; and
we will discuss them a little more fully before we deal with
modern determinations of the size and shape of the Earth.
The attraction of the Himalayas.
The problem of the effect of the Himalayas on the direction
of gravity in India has been present continually to the Indian
surveyors. North of the Indian arc is the immense mass of the
greatest mountain range in the world ; to the south the Indian

174 GEODETIC SURVEY
ocean is very deep, and the consequent deficiency of density
considerable. It might be expected that in India the direction
of gravity would be deflected towards the north ; and calculation
shows that the effect of the visible excess of density to the
north, the visible deficiency to the south, should extend all over
India. A great number of careful determinations of latitude were
made at stations along the great arc of meridian, but the
expected effect was not obtained. The discordances between
the astronomical and the geodetic latitudes were considerable ;
but they did not fit in at all well with the deviations which the
visible masses should have produced. It appeared that some
cause was at work which in great part annulled the effect of the
mountain attraction. This was the first indication of the law
which now plays so large a part in these enquiries, that in some
way the expected effect of mountain masses is compensated, as
if there were underlying deficiencies of density which nearly
balanced the visible masses.
About the year i860 Archdeacon Pratt, of Calcutta, a dis
tinguished mathematician from Cambridge, applied himself to
the mathematical investigation of this problem, and arrived at
the above result, that the attraction of the mountains is not so
great as their visible masses would lead one to expect. The
then Astronomer Royal, Sir George Airy, proposed to explain
this in the following way : Conceive that the Earth is composed
of a solid crust about forty miles thick, with a liquid below.
The strength of the crust would not be nearly sufficient to
support the weight of the superincumbent mountain masses ;
therefore there must be some support for them, and this may be
in the form of protuberances beneath the mountains, of the
lighter crust into the denser liquid below. In such a way the
mountains would be in equilibrium because they are practically
floating like icebergs in the ocean, buoyed up by the intrusion
of their " roots " into the liquid.
This "roots of the mountains" theory has been the subject of
much interesting discussion, especially by the Reverend Osmond
Fisher, in his Physics of the Earth's Crust. Mathematicians
have in general felt themselves compelled to reject the internal

GEODETIC SURVEY 175
fluidity of the Earth, on account of certain tidal phenomena,
into which we can hardly enter. But the important idea that
the principal mountain masses are nearly in equilibrium, their
visible excess of weight balanced by invisible defect of density
below, as if they were floating, has by gradual steps become an
established principle of geodesy.
If the visible excesses of dense material in the mountains are
counterbalanced by deficiencies underneath, it is clear that we
may expect also that the visible deficiencies of matter in the
oceans should be balanced by excesses of matter in the ocean
beds. Evidence for this supposition cannot be found however
in the observations for latitude, so well as in the conclusions to
be drawn from the determinations of gravity by the pendulum,
to which we must now refer.
Gravity survey with the pendulum.
The mathematical theory of the attraction of a spheroid at
any point of its surface, or at an external point, provides a
formula which expresses the force of gravity, and thence the
time of oscillation of a pendulum of known length, at any place.
Knowing the shape of the Earth, we can predict the rate of
swing of the pendulum ; and alternatively, it is evident that if
we carry an invariable pendulum about the world, and determine
the time of its swing at different places, we have a means of
determining the figure of the Earth independent of the triangu
lation and latitude method explained above. When sufficient
observations were accumulated it was found that the two inde
pendent methods of arriving at the ellipticity of the Earth gave
results which were in tolerable agreement, though they were
not identical. For the moment the discrepancy need not con
cern us.
But it was also found that the- pendulum observations on
high mountains, as in the Himalayas, gave peculiar results. It
is easy to calculate the intensity of gravity at a given height
above the surface of the Earth, and to allow for the increase
which should be due to the mass of the mountain on which the
pendulum is established. But observation discloses the remark
able fact that the mountain mass itself has not the expected

176 GEODETIC SURVEY
effect ; the pendulum swings pretty much as if it were somehow
supported at the height of the mountain, but unaffected by the
mountain mass. In other words, the attraction of the mountain
is more or less compensated.
Further, it was pointed out by the French geodesist Faye
that a similar effect is found on oceanic islands : similar in
cause, though opposite in its immediate effect on the time of
swing of the pendulum. On those volcanic islands which rise
steeply from deep ocean the force of gravity, as deterirfined by
the pendulum, is in excess, the excess being about that amount
which can be attributed to the mass of the island standing above
the ocean floor. In other words, if the pendulum could be
swung on the surface of the sea, without the material support of
the island, then the time of swing would be normal.
This important result has been confirmed, within recent
years, by the work of Hecker, who has made several long
voyages, including a circumnavigation of the world, comparing
all the while the readings of a large number of mercurial
barometers and of boiling point thermometers. Both these
instruments determine the pressure of the atmosphere ; but
whereas the height of the barometer is affected by the intensity
of gravity, the boiling point of the thermometer is not. It may
well seem remarkable that this method can be made of delicacy
sufficient for the purpose in view, and there are indeed many
instrumental difficulties to be overcome. But these observations
seem to place beyond much doubt the result suggested by the
island pendulums, that over the surface of the ocean gravity is
normal ; it is not diminished as might be expected by the small
density of the water as compared with rock ; and the simplest
explanation seems to be that the rocks below the ocean floors
are extra dense, to balance the deficiency above.
Gravity in India.
Recent very interesting work of the Survey of India shows
that the problem in India is more complicated than had been
supposed. In the foothills of the Himalayas the "compensation"
is partial ; immediately to the south of the mountain range the

Plate XXII

I. Half-second Pendulums. 2. Clock and Flash Box.
Gravity Survey.

3. Latitude with Zenith Telescope.

Survey of India.

GEODETIC SURVEY 177
compensation is more than complete, so that there is a defect of
density underlying these regions.
A few figures will serve to show the nature of these results.
All observations are referred to Kew as the base station. The value of
g, the acceleration due to gravity, is taken to be 981-200 centimetres at Kew.
The Indian pendulums were swung at Kew, and the mean time of vibration
was 0-5067001 seconds. The same pendulums swung at Dehra Dun gave for
the mean time of vibration 0-5072528 seconds. That is to say, as compared
with Kew they lost one swing in something less than ten thousand. Now
by the theory of the pendulum the square of the time of oscillation multiplied
by the value of gravity is constant for all stations. Hence we deduce for
Dehra Dun the value £-=979-063 cm.
This has now to be corrected for the diminution of gravity due to the
height of Dehra Dun above sea level. Without allowing for the attraction
of the ground above sea level the reduction is +0-210. The correction for
the attraction of the "visible masses" is —0-075 ; so that the value at sea
level is 979-198 cm. But the sea level value computed for Dehra Dun from
Helmert's general theory for the whole Earth is 979-324, which is greater
than the observed value even without the allowance for the visible masses.
Instead of having to allow for the attraction of the equivalent of a plateau
some 2200 feet high, it appears that the effective attraction is as if a depth
of 3600 feet were annihilated. There is a large deficiency of gravity, there
fore, at Dehra Dun.
Similar observations made at many stations show that while
in the foothills of the Himalayas the attraction of the mountain
masses is partially, but not fully compensated, immediately to
the south is a " ditch " of deficient density, before the attrac
tion becomes normal. It is clear that results of this kind must
eventually throw much light on all questions of the theory of
the Earth's interior, and especially on the methods of mountain
formation. They have a general interest outside their technical
geodetic importance, and for this reason we have dealt with
them in some detail.
The theory of " isostasy."
The convergence of these various lines of investigation to
the same point seems to have fairly established the general law
of balance : where there is excess of mass above it is balanced
by deficiency below, and vice versa. To this condition the
American geodesist Major Dutton gave the name "isostasy,"
h. m. s. I2

178 GEODETIC SURVEY
signifying that the crust of the Earth is in a general condition
of hydrostatic equilibrium, as if it were floating, though it is not
necessarily doing so.
The question then arises, to what depth must one go before
this state of balance is fully established? Very elaborate investi
gations on this subject have been made of late years by the
United States Coast and Geodetic Survey. Starting with the
assumption that there must be some definite depth at which
the compensation becomes complete, they have tried to deter
mine the depth, and have arrived at the result 120 km. It is
quite impossible to deal here with the methods of this exceed
ingly elaborate and arduous piece of work ; and it does not
seem to the author to be sufficiently established that there is
any one depth at which the compensation becomes complete.
Much light will be thrown upon this question by the discussion
of the Indian results which has been undertaken to test the
applicability of the hypothesis to India.
It should be understood that the theory of isostasy does not
require that the compensation is locally complete everywhere,
but only that there is general compensation of the principal
masses which are raised above the Earth's surface. In India
great complications are introduced by the existence of a
subterranean range of excessive density running parallel to
and south of the Himalayas, with a "ditch" of deficient density
between this and the mountains.
The form of the ocean surface.
In connection with this subject of mountain attraction it is
natural to speculate what effect is produced upon the form of
the ocean surface by the attraction of great mountain masses.
Several calculations have been made which show that if the
mountains can exert the full effect that their visible masses
entitle them to, the elevation of the free surface of the ocean
must be considerable. Colonel Clarke (Geodesy, p. 94 and
following) gives a method of calculating the order of the effect
upon the height of the sea surface produced by the attraction of
the Himalayas, and shows that it might amount to as much as
600 feet. " This calculation," he proceeds, " shows us that large

GEODETIC SURVEY 179
tracts of country may produce great disturbances of the sea
level, but it is at least questionable whether in point of fact they
do." The compensation of the mountain masses nullifies the
effect in great part, we may be sure, and leaves little scope for
the existence of great differences in the sea level radii of the
Earth. Nevertheless it is common to meet in books the statement
that the sea level at Calcutta is about 330 feet higher than it is
at Cape Comorin ; and that the sea on the Pacific coast of
South America, close under the Andes, is 2000 feet higher than
it is at the Sandwich Islands. These statements are based on
calculations such as Colonel Clarke gives ; but they are some
times said to be supported by the results of direct levelling.
Such a statement is on the face of it absurd. The surface of the
sea must be a level surface in the sense that spirit levelling from
one point to another could give no evidence of rise or fall. Any
attraction of mountain masses which changed the form of the
sea surface would have an equivalent effect on the results of the
instrumental levelling.
Geodetic measure of an arc of meridian.
From what we have seen of the effect of local irregularities
of gravity it is clear that no close accordance may be expected
between the geodetic amplitude of an arc, measured by triangula
tion, and its astronomical amplitude, measured by determinations
of latitude or longitude at each end. In order that the effects of
these local abnormalities may be eliminated as far as possible it
is usual to proceed in a way which may be described briefly
as follows :
Select as the initial point a station which seems to be free,
as far as may be judged, from the influence of attraction by
visible masses. Starting from this point we may from the
triangulation calculate the latitudes of any number of points in
the chain, using in the calculation tables founded upon one or
other of the well-known results for the figure of the Earth : let
us say Clarke's first figure. Compare these geodetic latitudes
with the observed latitudes of the same points. The differences
Geodetic minus Astronomical latitude

180 GEODETIC SURVEY
are the material on which we shall found a revision of the figure
which was adopted in the tables.
If these differences are scattered at random, and show no
tendency to grow steadily bigger or smaller, or first bigger and
then smaller, they must be due in great part to local irregularities
of gravity. But if they run in a systematic way the probability
is that some modification in the adopted figure would make
them smaller, and we proceed to find that figure which gives the
best fit between the astronomical and the geodetic places. It
is not hard to calculate the effect upon each comparison of a
definite change in the assumed axes of the Earth, a change in
its assumed ellipticity, and a correction to the adopted initial
latitude. The various corrections will appear as the unknown
quantities, with calculated numerical coefficients, in a series of
equations, one for each latitude station. The solution of these
equations of condition by the method of least squares gives the
values of the corrections which reduce to a minimum the sum
of the squares of the residual differences. And the theory of
probability shows that this is the most probable result that can
be found from the mass of somewhat contradictory material given
by the observations. In other words one finds what corrections
must be made in the original assumptions to produce the best
fit between astronomy and geodesy over the arc in question.
Similar considerations determine the method by which the
observations of longitude and azimuth may be made to contribute
to a revision of the size and the shape of the Earth.
The outstanding discordances between the observed astronomical lati
tudes and the figure of the Earth which fits them best are by no means
inconsiderable. For example, Clarke's 1866 figure is deduced from 40 latitude
stations. The discordances of the British stations are as follows :
Greenwich Geod. minus Astron. +o"'94
Arbury + i"-4o
Clifton (Yorks) -2"- 19
Kellie Law -o"-65
Stirling -o"-24
Saxavord + 1 "'95
The extreme discordances of all are at two Indian stations :
Dod'agoontah + 3"'87
Kalianpur .— 3"'69

GEODETIC SURVEY 181
If we remember that one second of arc in latitude is
equivalent to one hundred feet it at once becomes clear that
it is hopeless to try to make an accurate and consistent map on a
basis of astronomical positions. Discordances of several hundred
feet will arise, which are intolerable.
The principal geodetic arcs.
The first man to apply the principle of triangulation to the
measurement of an arc was Snellius, whose work was published
at Leyden in 1617.
The first long arc of meridian was begun by Picard, and
extended by the Cassinis. It had an amplitude of eight and a
half degrees, and was at first supposed to show that the Earth
was a prolate spheroid, contrary to the theory developed by
Newton. This was early in the eighteenth century.
In 1735 the French Academy undertook the measurement of
the arc of Peru, and of another in Lapland. These, with the
French arc mentioned above, provided the first accurate deter
mination of the figure of the Earth.
In 1783 the triangulation of England was begun by General
Roy, and connected with the French triangulation.
In the nineteenth century the great meridian arc of Europe,
on the 30th meridian of East longitude, was measured from
Hammerfest to the mouth of the Danube, under the principal
direction of the eldest Struve. Later the whole of Europe was
covered with triangulation, which was then extended into Africa.
Several arcs both of latitude and of longitude were measured in
India; very considerable geodetic operations were undertaken in
the United States; and at the end of the century the African
arc of meridian, also on the 30th meridian East, was carried from
the south of Cape Colony through the Transvaal towards Lake
Tanganyika. At the present day there is great activity in geodetic work.
A joint commission of Russians and Swedes have measured an
arc of meridian in Spitsbergen, which is probably the most
northerly arc possible, while the Service geographique de UA rme'e
has re-measured the "Arc of Peru," in territory which now is Ecua
dor. An attempt is being made to join up the triangulations

1 82 GEODETIC SURVEY
of India and Russian Asia. Egypt is actively pushing its portion
of the 30th meridian arc southwards to the Great Lakes; while
another part of this arc has been measured in connection
with a boundary survey on the Uganda-Congo frontier. The
United States is steadily carrying forward its chains of triangles
over the west and north, and Canada has begun its share of the
triangulation of North America. Further south good work is in
progress in Mexico and in Chili. The arc of the 30th meridian
is of special importance because it is the longest latitude arc
that can be measured on the Earth. There seems to be good
hope that the African portion will be finished within fifteen or
twenty years ; the greatest difficulty will be the junction be
tween Egypt and the Danube, through Turkish territory up the
Eastern shore of the Mediterranean.
A word should be said on the state of the British triangula
tion. It is the earliest in date of any of the great triangulations,
and on that account is necessarily somewhat old fashioned. In
a report on the triangulations of Europe, made to the Inter
national Geodetic Association by General Ferrero, the triangular
error of the British work is given as about 3", with the inference
that the work is not of sufficient refinement to be attached to
the general European net. It seems likely that this criticism is
not quite just. The triangulation of England covered the whole
country, and much of it was difficult because the country was so
flat. Many of the more unfavourable triangles entered scarcely
at all into the arcs of meridian and of longitude, and it is hardly
fair to burden these with the error of triangulation in other
parts of the country. Within the last few years a base has been
measured in Scotland by the Ordnance Survey, and some tri
angulation done to connect it with the existing net. This will
provide a check upon the whole which will show how far the
criticisms which have been passed upon it are justified. Should
it be found that there is room for improvement it is much to be
hoped that for the scientific honour of the country there will be
no delay in the provision of funds for revision, so that Great
Britain may take its rightful place in the arcs of latitude and
longitude of Europe.

GEODETIC SURVEY 183
Geodetic triangulation.
Geodetic triangulation differs from ordinary triangulation
principally in the degree of refinement with which the angles
are measured.
Accuracy is increased by increasing the size of the theodo
lite, up to about a twelve inch circle. The modern theodolite of
this size is more precise than the older instruments of much
greater size, and it is doubtful whether anything is gained by
employing larger instruments than the twelve inch. Accuracy is
increased by increasing the number of observations of each angle,
care being taken to begin each round of angles at a different
part of the circle, so that errors of division are eliminated as far
as possible. Greater care in the construction of beacons, and
especially the use of self-centering beacons, as on the Egyptian
Survey, add much to the accuracy of the result; so also in many
places does the use of lamps at night, when refraction is more
regular. Recent improvements in base measurement, and the result
ing possibility of measuring many more bases than formerly, are
important aids to the control of the chains of triangulation. At
the same time these instrumental refinements have much simpli
fied the work of adjustment of the triangulation ; while an even
greater influence in the same direction has been the modern
view that it is absurd to give different weights to the observed
angles according as the separate determinations of them are
more or less accordant among themselves. It is now realised
that the errors to be feared are not so much the accidental
errors that show themselves in roughness of individual measures,
as the systematic errors that repeat themselves and thus escape
notice at first. The tendency is therefore to simplify the re
ductions and to avoid the immense calculations which are so
remarkable a feature of such work as the earlier Indian triangu
lations. Excellent examples of work thus simplified may be
found in the published accounts of the geodetic triangulation of
South Africa, executed by Colonel Sir William Morris under
the superintendence of Sir David Gill, His Majesty's Astronomer
at the Cape.

1 84 GEODETIC SURVEY
The question arises often, under what circumstances is it
worth while to undertake the expense of the greater refinement
which shall make a triangulation suitable merely for the frame
work of the topography into a first class triangulation fit to take
its part in the general problem of determining the size and
shape of the World ? The answer must depend to a great extent
upon the relation of the country in question to the principal
land masses of the world. If it is isolated, and of moderate size
only, then it can contribute little to the solution of the problem.
But wherever there is a possibility of junction with other exten
sive work of the same kind it should be a point of honour with
the country to contribute its share in the solution of the great
problem. Principal chains.
In the Ordnance Survey of England the primary, or geodetic
triangulation covered the whole country. In modern practice
the primary triangulation is run in chains along arcs of meridian
and parallels of longitude, so that a large country is divided up
into a series of quadrilaterals. On the framework thus built the
secondary triangulation is hung.
The chain is usually a chain of quadrilaterals, and complex
figures are avoided as much as possible. Bases will be measured
at least every two hundred miles along the chain.
The test of the accuracy of the triangulation is, as we have
seen, the size of the average triangular error; in the best modern
work this is about o"75. To obtain this remarkable degree of
accuracy it may be necessary to observe each round of angles
nine times.
It is highly desirable that a preliminary calculation of the
triangles shall be made as the work proceeds ; this tends to give
confidence in the success of the operations, and serves to detect
at once any considerable error or unusual difficulty that may
arise. But to carry out this programme requires a large and
strong party.
The astronomical observations.
For precise work the observations for latitude will be made
by Talcott's method, with the theodolite fitted to serve as a

GEODETIC SURVEY 185
zenith telescope. It is outside the scope of this book to enter
into the details of this work.
The azimuths will be determined in general from circumpolar
stars at maximum elongation.
The longitudes will be determined by the interchange of
time by telegraph, or by wireless. The time observations will be
made with portable transit instruments, and great precautions
are necessary to eliminate the personal errors of observation.
The introduction of the Repsold Transit micrometer has done
much to eliminate this source of error.
The effect of all the visible mountain masses on the direction
of the vertical will be calculated rigorously for the nearer masses,
and by an approximate graphical process for the more distant.
In the future it will be considered necessary to examine how far
these effects are compensated by isostasy.
Geodetic bases.
In the chapter on topographical survey we have dealt with
the use of invar wires in the field, for the measurement of bases.
We will mention now some of the refinements that are necessary
when the work is to be of the highest precision.
At the headquarters of an important geodetic survey provision
will be made for the standardisation of the wires, to ensure a
more complete control than is possible when they are merely
returned to some far distant laboratory at intervals.
First it is necessary to provide a standard bar, which should
be the unit of length, yard or metre, multiplied by some power
of two, so that it can be compared by successive duplication.
Four metres or four yards will be the most convenient length.
But in fact, ten feet has been the usual length of English bars,
though this involves an awkward comparison with the British
standard yard. It is not quite clear why, when the yard is the
standard unit of length, geodetic measurements have been made
in feet. The modern bar will be made of invar. It will be
compared with the standard metre at the International Bureau
of Weights and Measures at Breteuil, or with the standard yard
at the Board of Trade Standards Office, or with the copies of
this standard at the National Physical Laboratory or at the

1 86 GEODETIC SURVEY
Ordnance Survey Office, Southampton. At the same time the
laws of its expansion will be minutely studied.
To avoid duplication of statement we shall speak of the
operations in future as conducted in metres. India has recently
decided to make the change, and it is probable that the yard and
the foot will gradually disappear from geodesy.
The next step is to establish a 24-metre comparator at head
quarters, standardised from time to time with the 4-metre bar.
This comparator will be in the form of a wall, preferably under
ground to escape temperature changes as much as possible. It
will be provided with tanks in which water can be circulated, to
allow for the study of the temperature coefficients of the wires.
On this comparator the wires will be standardised before they
go into the field, and when they return.
The constancy of the wires depends very much upon the care
with which they are treated in the field. They must always be
wound upon the special aluminium drums which are made for
them, and they must be treated as instruments of precision
should be treated, not after the fashion of coils of wire. One of
the principal difficulties in the field has been to ensure continuous
careful treatment for the wires, and it has sometimes been
suggested that if they cost 3000 francs each instead of 30 they
would be treated with more respect.
When they are first manufactured they are subject to
molecular changes and their lengths are not constant. As they
become aged they settle down into stability, and the process
may be quickened to some extent by successive very careful
annealing. But it does not seem that anything can complete
the natural process of ageing except use in the field.
It is essential that the coefficient of expansion should be
found for each separate wire. At first it was the practice to test
a sample of the rolling from one ingot, and to assume that all
the batch had the same constants. It is now recognised that
this is not safe and that each wire must be examined after it
has been made up into its working form.
There is still some difference of opinion as to the relative
merits of wires and tapes. The advantage of wire is that it is
ess subject to the disturbing influence of wind. Tapes have

GEODETIC SURVEY 187
several advantages ; twist can be detected very easily ; they are
not so liable to kink ; and the small divided scale can be engraved
on the tape itself, instead of on a soldered attachment, the
" reglette." The last is of considerable importance.
Experience of their use in rough country has shown that the
wires or tapes can be used on much greater slopes than was
considered desirable when they were first introduced. But this
requires that the provision for determining the slope of the tape
shall be more thorough than was made in the first patterns.
Recent experience on the Semliki base in Uganda, and on the
Lossiemouth base in Elgin, favours the use of an ordinary Y
level, and a special light levelling staff which can be stood on
the tripods carrying the fiducial marks against which the tape is
read. With this equipment it is possible to measure up slopes
of 1 in 3, and to choose for the ends of the base situations which
provide a good view of surrounding stations favourable for the
base extension.
This involves a thorough discussion of the effect of slope on
the horizontal distance between the end marks of the tape,
arising from the change in the form of the catenary, and from
the difference of tension at the upper and lower ends — a differ
ence which may become so considerable that the pulleys must
no longer be frictionless, or the tape will run away down hill.
A very complete investigation of the problem has been made by
Professor Henrici and his son Captain Henrici, R.E. ; the results
are too complex for summarisation here. See Ordnance Survey :
Professional Papers. New Series. No. 1.
For rapid work it is essential that the base party shall be
well drilled. With a well-trained party a base of 10 km. can be
measured completely in 12 days; and it is good economy to
arrange that all the bases required for the whole triangulation
shall be measured consecutively in a single season if possible.
Geodetic levelling.
The immediate practical importance of the main lines of
precise or geodetic levelling is to provide a foundation for all
the subsidiary lines upon which the local determinations of
height, and the contours, are based. Its ultimate scientific, and

1 88 GEODETIC SURVEY
perhaps also practical importance, is to discover whether the
whole country is gradually rising from the sea, or sinking, or
tilting ; and at what rate the mountains are growing or becoming
denuded. Within the limits of this book we cannot deal with the
instrumental precautions which are essential in the conduct of
precise levelling. The general procedure is quite similar to that
which we have sketched in Chapter IV, page 95 ; but there are
many precautions to be taken to avoid the small but cumulative
effects of temperature, of refraction, and of local deviations of
the vertical.
It is now realised that the original net of levelling in Great
Britain was not observed with sufficient precautions to give an
ultimate verdict on the above points. In particular the deter
mination of mean sea level was not satisfactory. A revision of
the principal levelling is now in progress ; and great attention is
being paid to the important question of placing the fundamental
bench marks on solid rock.
In India the great earthquake of 1905 provoked a very
interesting enquiry into the changes in relative heights produced
by the shock. It was found that the difference of height between
Dehra Dun and Mussooree had been diminished 5-5 inches, and
it was at first supposed that Mussooree had subsided by this
amount. But a revision of the line of levels into the plains
showed that this was not the case. Mussooree in the Himalaya
and Saharanpur in the plains were found to be at the same
relative height after the earthquake as before ; but the inter
mediate station of Dehra Dun was higher by five inches both
with regard to Mussooree and Saharanpur.
There is great reason to think that this movement was only
an exaggeration of a movement that is always going on, and
that the Himalayas are gradually pressing forward and up the
lower lying ranges to the immediate south of them. For this
reason several lines of precise levelling have recently been
carried up into the Himalayas, and these are being connected
with the older formations to the south. It is hoped that in time
this work may give information on the rate of growth of the
mountains.

Plate XXIII

i. Banog Mountain: Terminal station of an Indian line of precise levels.

2. Precise Level : United States Coast and Geodetic Survey pattern.
Precise Levelling.

GEODETIC SURVEY 189
Future progress of geodesy.
Since four-fifths of the Earth's surface is covered with ocean,
over which geodetic operations are in general impossible, it is
clear that we shall never be able to obtain a complete deter
mination of the size and shape of the Earth. We shall be
compelled to make certain assumptions, as for example that its
figure is an ellipsoid of revolution or spheroid, or that it is an
ellipsoid with three unequal axes. Then, taking the measured
arcs of meridian or of longitude as samples of these figures, we
can determine the size and the form which fit them best. Any
determination of the figure of the Earth must rest upon a
discussion of such a kind ; and the result will be the more
satisfactory the wider the extent of the Earth's surface repre
sented in these " samples."
At the present time we have the following material available :
The triangulation of Europe, and its connection with Northern Africa.
A certain amount of work in Russian Asia.
India.South Africa up to Lake Tanganyika, and short arcs in Uganda and in
Egypt. The United States and a little in Canada.
Spitsbergen.
The arc of Peru.
A certain amount in Mexico, Chili, and in Japan.
The most important work of the future is evidently
The connection of India with Russian Asia, and the extension of the
meridian arc to the Arctic Ocean.
The extension of the European longitude arc across Russian Asia to the
Sea of Japan.
The completion of the African arc. and its junction with the European
triangulation. The extension of the Canadian arcs of meridian to the Arctic Ocean.
An arc of meridian down the chain of the Andes.
Meridian and longitude arcs in Australia.
It will be long before this programme is finished. Mean
while we may say a few words on the present state of the
problem.

190 GEODETIC SURVEY
No recent attempt has been made to bring into discussion
all the available material. The greater part of modern work
is discussed with reference to the figures of Bessel and of
Clarke. Bessel's determination was based on the European and
Indian results available in 1841, and the old measure of the
arc of Peru.
Clarke's several determinations of 1858, 1866, and 1878
depend on considerable extensions of the same material; they
take into account the extensions of triangulation in Europe
and in India, but have nothing to add from other parts of the
world. The recent determination by Hayford is based on the United
States only.
At the end of this chapter we give a table of these results.
It will be seen that the differences between them are not very
great, and that the contribution of the United States does not
suggest that the shape of the western hemisphere is very different
from that of the eastern.
Bessel, Hayford, and Clarke in one of his solutions, assume
that the Earth is an ellipsoid of revolution. In a second solution
(1878) Clarke assumes that the Earth is an ellipsoid not of
revolution, or that the equator is elliptical. In a third he
assumes that the Earth is a figure of revolution, but not the
revolution of an ellipse. He finds that the evidence for the
second or third of these hypotheses is so slight that they cannot
be said to lead to any positive result. At present there is no
real reason for supposing that the equator is not a circle, or the
meridian an ellipse.
It would seem that the time has come for a new solution of
the problem, to take into account all the material which has
accumulated since Clarke's last solution was made. But the
necessity of including a discussion of isostasy and compensation
very much increases the labour.

GEODETIC SURVEY

191

Figure of the Earth.
The following table gives the results of the principal dis
cussions of the dimensions of the spheroid :

Equatorial
Semi-diameter

Flattening

Polar
Semi-diameter

Bessel 1 841
Clarke 1866
Clarke 1880
Hayford 1910

6377397 m.
6378206 63782496378388

1/299-21/295-0i/293"5 1/297-0

6356079 m.
6356584 63565156356909

From a general discussion of pendulum observations Helmert finds (1901)
for the flattening 1/298-3.
Bessel's results were based on the various triangulations of Europe
executed at that date.
Clarke's 1866 figure included the French, British, Indian, Russian, South
African, and Peruvian arcs so far as they were then complete.
Hayford's figure depends entirely on the geodetic arcs of the United
States, and includes an elaborate discussion of isostasy.
With Clarke's figure of 1880 the quadrant of the meridian is 10,001,868
metres, so that the metre is shorter by about one part in five thousand than
the ten millionth of the quadrant.

CHAPTER VIII
SURVEY INSTRUMENTS
This book is not intended to supply the place of a technical
handbook in which all the details of the instruments, the methods
of adjustment, and of observation, are given minutely. Such
information may be found in full in the Textbook of Topographical
Surveying, to which reference is made so often, or in other
technical works. But it will be well to give here a few notes to
supplement the slight accounts of the various instruments given
throughout the book.
The Sextant.
The sextant is pre-eminently a sea instrument, and it is not
well adapted for use upon land, except under special circum
stances. The sextant will measure angles up to about 130° but not
more. Held in the hand, it can be adjusted to allow for the
motion of the ship in a way that becomes for the skilled observer
almost automatic. It fulfils all the needs of the sailor, who
measures elevations above the visible sea horizon, and occasion
ally angles between the moon and the sun or a star, for the
almost obsolete method of lunar distances. It gives results
which are nominally correct to 10" and actually correct to
within half a minute of arc, which is just the degree of accuracy
required in navigation. The principal systematic error to which
the instrument is liable is the error of eccentricity of the graduated
arc — the error which in the theodolite and other more precise
instruments is eliminated by reading the circle at two opposite
points, which is impossible in the sextant.
It is the possibility of this error developing undetected that

SURVEY INSTRUMENTS 193
makes it waste labour to equip a sextant with a stand, as has
been done, and to try to make use of it upon land.
On land the sextant cannot give altitudes directly, because
there is no visible sea horizon from which to measure. It is
necessary to employ what is somewhat confusingly termed the
"artificial horizon": a dish of mercury which forms a naturally
level reflecting surface, or a reflector of blackened glass which
can be set level by levelling screws and a bubble. The sextant
then measures the angle between the direct and the reflected
images of the sun or star, that is to say, double the altitude of
the body. But angles greater than 1300 cannot be measured.
Hence when the sun at noon is higher than about 65°, which
is very frequent in tropical and subtropical regions, the noon
altitude of the sun cannot be taken on land with a sextant.
This serious limitation is enough to condemn the use of the
instrument on shore. Moreover, the sextant cannot measure
azimuths except in a roundabout way, which involves a great
deal of observation and unnecessary calculation.
If, then, it is necessary to retain the sextant as a subsidiary
instrument for work on land, its use should be restricted to those
cases in which it must be employed for reasons of secrecy.
There are native tribes which would interfere with a surveyor
working at an instrument mounted on a tripod who would not
be so likely to notice a man lying down on his face taking sights
with a sextant. It is said that native Indian surveyors have
done good work in trans-frontier regions with a sextant disguised
as a praying wheel.
The sextant has often been employed on polar expeditions,
on account of its small size and lightness. The observation of
such small altitudes as the Sun has in spring in polar regions
offers, however, peculiar difficulties when an artificial horizon
must be employed ; and it is now generally admitted that a
small mountain theodolite should always be employed on such
work. It has the great advantages that its errors are self-
eliminating, and that it can be used with facility to measure
azimuths. A modern mountain theodolite of the smallest size
weighs no more than a sextant with artificial horizon, and the
results that it gives are far more satisfactory.
h. m. s. 13

194 SURVEY INSTRUMENTS
The theodolite.
For many years the ordinary surveyor's theodolite suffered
from a want of intelligence in its design, of which traces still
survive in the patterns manufactured especially for engineers.
The most conspicuous of these is the foiir screw levelling device,
which inevitably strains the instrument, makes the screws work
loose, is thoroughly bad in design, but is still very often made.
The old-fashioned theodolite was effective only for horizontal
angles, in which reversal is not much required. When it was
found to be advantageous to make the instrument reversible,
which requires that the telescope shall be able to pass through
the frame, the new pattern was called on this account a " transit
theodolite," which name still survives in the makers' catalogues :
a stupid name which suggests that the theodolite can be used as
a transit instrument.
The circles of the old-fashioned theodolite were read by
verniers only, and verniers are awkward to read by day, almost
impossible to illuminate properly for reading at night. The
greatest modern improvement in theodolites has been the
application of the micrometer microscope, which increases the
accuracy of reading the circle at least fivefold, and at the same
time makes it much more simple and easy : a very unusual
accompaniment of gain in precision. The five inch micrometer
theodolite has now established itself as the standard instrument
for survey of the second order, that is to say, in which geodetic
accuracy is not required. The instrument is sufficiently portable
for the employment upon boundary survey under the roughest
conditions ; and the facility with which it can be used for field
astronomy makes it invaluable both in teaching and in actual
use in the field. (See Plate XX.)
The modern theodolite is especially adapted for the accurate
measurement of vertical angles, in which the old instruments were
very deficient. The improvements in construction which have
led to this result are two : making the instrument reversible,
already mentioned ; and the mounting of a sensitive bubble upon
the frame which carries the verniers or microscopes for reading
the vertical circle. Since there is often some misconception as

SURVEY INSTRUMENTS 195
to the part played by these two devices, we may examine them
shortly. It must be remembered that there is a great difference
between the measurement of horizontal and of vertical angles :
the former are relative, the latter are absolute determinations.
Or in other words, on the horizontal circle one measures the
difference in bearing between one point and another ; on the
vertical circle one measures the elevation of a point above
the horizon, which is not a visible object on which settings can
be made, but must be defined by means of sensitive levels or
bubbles mounted on the instrument. To measure an absolute
elevation naturally demands that all the effects of errors of
adjustment, collimation, zeros of microscopes, and so on, shall
be eliminated ; and this can be secured by reversing the
instrument about a stable axis very nearly vertical. If the
approximately vertical axis of the theodolite could be trusted to
remain fixed during the series of settings and reversals of the
instrument which take place in the course of a series of obser
vations on an object, or even to remain fixed for the pair of
observations, " face left and face right," which constitute a
complete observation, then the reversal would eliminate all these
errors of collimation and zero automatically, and nothing more
would be required. But in practice the foundation of the
instrument is not perfectly stable. Under the influence of the
movements of the observer and the weight of the instrument
itself, slight settling takes place between one setting and the
next ; and perhaps also the position of the microscopes on the
frame changes a little by reason of change in the temperature.
It is the function of the bubble mounted on the microscope arms
to eliminate these changes, and the introduction of this device
has very much increased the accuracy of the results.
When the errors of the instrument are eliminated there
remain the personal errors of the observer ; and these also can
be eliminated in great part by a proper use of the principle of
reversal. An observer will have a tendency, quite unknown to
him, and almost ineradicable, to make settings systematically
high or low. This is called the personal error of bisection. It
13—2

196 SURVEY INSTRUMENTS
may be eliminated by combining observations in which the error
comes in with opposite effects upon the quantity which is to be
determined. Observations made north and south of the zenith
will be affected with the same error in altitude, but this will
produce opposite errors in the resulting latitude. Similarly the
personal errors in observations made east and west will have
opposite effects upon determinations of time. Thus by preserving
a balance between north and south or east and west stars the
consequences of these errors will be eliminated in the mean.
Formerly the astronomical observations for latitude were made
with a special instrument, the zenith telescope (see Plate XXII).
Modern geodetic theodolites are now fitted with the necessary
micrometer eyepieces, so that observations for latitude by Tal-
cott's method may be made with them, and the zenith telescope
is becoming obsolete.
Levels. Very great improvements have been made in the construction
of precise levelling instruments during recent years. In the
older instruments it was necessary first to adjust the foot screws
so that the bubble was in the centre of its run, and then to walk
round to the eyepiece and make the reading on the staff. In the
meanwhile the bubble had probably shifted. In the modern
level it is possible to see both ends of the bubble by a second
telescope fitted alongside the principal, and read with the other
eye. The final adjustment of the bubble is thus made imme
diately before reading the staff, and without changing position.
Further, all the essential parts of the instrument are constructed
of invar, so that the effects of temperature are almost eliminated.
Three parallel horizontal wires are fitted, and the staff is read
against all three. This helps to eliminate accidental errors of
reading, and also provides, on the principle of the tacheometer,
for the control of the equality of the distances between the
forward and the back staves.
The staves are graduated on both faces, the second graduation
being from an arbitrary zero, so that the second set of readings
is not a close repetition of the figures of the first. And special

Plate XXIV

i. Straining trestle.

2. Tape on drum.

*'¦ 9

:

3. Mark on tripod.

4. Alignment sight on tripod.

Invar Tape Base Apparatus.

Department of Geography,
Cambridge University.

SURVEY INSTRUMENTS 197
precautions are taken to control at frequent intervals the lengths
and the graduation of the staves.
Invar tape or wire base apparatus.
As a result of experience in the field certain modifications
have been made in the apparatus as it was designed by M.
Guillaume at the International Bureau at Breteuil. We have
already mentioned the improvement in the levelling arrange
ments, which make it possible to measure up slopes as great as
one in three. The straining trestles and the mark tripod have
also been improved. The apparatus which we illustrate was
designed at Cambridge, after learning the experience of measure
ment on the Lossiemouth and Semliki bases. It was made in
the Observatory workshop, largely by the skill of Mr Gordon
Dobson, B.A., of Gonville and Caius College. (Plate XXIV.)
The straining trestle has, as is now usual, one leg prolonged
to rest on the shoulder of the operator, so that he can take the
weight of the wire while he adjusts the other two legs. The
novel feature of the design is the swivelling hinge of these legs,
so that the tripod is capable of some lateral motion without
taking the points of the legs from the ground. This is very
convenient in adjusting the wire to the line of the tripod marks.
For convenience and rapidity of work it is essential that the
tripod mark should be adjustable over a range of a foot without
moving the tripod itself; for on rough ground it is not possible
to set the tripod up level at any exact point desired, nor to
move it readily by small amounts. The head of the Cambridge
form of tripod is a skeleton triangle ; and the post for the mark
is carried through two battens, one above and the other below
the triangle. A wing nut at the base of the post tightens the
two battens and holds them, or allows a range of motion and
possibility of clamping at any point over a circle of about a foot
in diameter.
Longitudes by telegraph.
When two stations are connected by a land line it is easy to
arrange for an exchange of time signals, for the determination
of the difference of longitude of the stations.

198 SURVEY INSTRUMENTS
The arrangements usually described for this purpose, with a
clock and one or more chronographs in circuit with the signal
keys of the observers at the transit instruments, are excellent
when the distance is not too great, and the line is in the best
condition. When, as often happens in tropical countries, the
insulation of the line is poor, and it is not possible to send
enough current to operate sounders or chronograph pens, it is
possible to get quite good results with the telephone " buzzer."
The technical difficulties are naturally much increased when a
submarine cable is interposed in the connection between the two
stations. It would be out of place here to describe the details
of the operations. But whatever the instrumental arrangements,
the principle of the method must remain the same. In its
simplest form it is as follows.
The observers at each station determine their local time with
transit instrument or theodolite ; that is to say, they determine
the errors of their chronometers on those times. At agreed
instants each sends to the other a series of signals in beat with
his chronometer. Thus there is a double comparison between
the chronometers 'at the two stations ; and the error of each
being determined, there is a double determination of the differ
ence of longitude.
The accuracy of the comparison is increased if one of the
chronometers keeps sidereal, and one mean solar time. To
eliminate the personal equation of the observers it is usual to
exchange stations ; but this is not always efficacious, and it is
better, if possible, to adopt the transit instrument with the
moving wire, by which the personality of the observer is very
much reduced.
So long as telegraphic longitudes depended upon the main
tenance of long land connections, or on the courtesy of the
Cable Companies, the opportunities for longitude work were
necessarily limited. But the recent rapid development of Wire
less has entirely altered the conditions of the problem.
Longitudes by wireless.
In the year 1910 the Bureau des Longitudes of Paris organised
a service of time signals from the military wireless post of the

SURVEY INSTRUMENTS 199
Eiffel Tower, in co-operation with the Paris Observatory. Twice
in the 24 hours they send out a series of signals which can be
received all over the Eastern Atlantic and Mediterranean, and as
far south as Dakar and Lake Chad. A well equipped survey
party can carry the necessary receiving apparatus without much
difficulty, and transmitting apparatus is not needed. It has
thus become possible to determine longitudes with facility, which
will have a great effect upon the methods of survey in northern
Africa. Triangulation in the Sahara is difficult and costly,
owing to the great distances over which supplies must be
carried. It seems probable that in country such as this triangu
lation will be superseded by determinations of latitude, and of
longitude by wireless. Owing to local deviations of the vertical
the results will not be so consistent as those of triangulation, but
they will have the great advantage that they can be obtained in
country which is almost impracticable for any other method ;
and especially they will facilitate the rapid mapping of country
which is too poor to afford triangulation.
At the time of writing arrangements are in progress for
a great improvement in the accuracy of these wireless time
signals, and for a world wide extension of their range. At a
conference held in Paris in October 191 2, at the instigation of the
Bureau des Longitudes, it was resolved to create an international
organisation, which will receive from a great number of Observa
tories their deduced corrections to the wireless time signals,
which will be utilised in correcting the subsequent signals. By
this means it will be possible to ensure that, however bad the
weather may be in Paris, and however long it may be since the
Paris Observatory obtained star observations, the combined
resources of European observatories will supply the time correct
to within a few hundredths of a second.
The time of transmission of the wireless signal is infinitesimal,
so that any observer within range of the Eiffel Tower, whether
on land or sea, will be able to determine his longitude with
a precision hitherto quite impossible. It will be interesting to
see how far it will be practicable to eliminate errors in retrans
mitting the signals from station to station round the world.

200 SURVEY INSTRUMENTS
Geodetic pendulums.
The form of apparatus now in general use is due to Major-
General von Sterneck. It consists of a set of several small
pendulums adjusted to swing in very slightly more than half
a second. The pendulums are made of brass, heavily gilded to
avoid change by corrosion. They rest by delicate agate knife
edges on an agate plane carried by the stand. Each pendulum
carries a small vertical mirror on its head, just above the line
of the knife edges. There is an arrangement for giving the
pendulums a small displacement and then allowing them to
swing freely ; the arc of vibration is less than half a degree.
They are set swinging and gradually come to rest.
A dummy pendulum similar to the others contains a
thermometer, to determine the temperature of the pendulums.
The stand is massive ; but it is not possible to consider it as
perfectly free from flexure and vibration. There is therefore
a special arrangement attached to the stand to enable the
correction for flexure to be determined. The principle of this
determination is elegant. If two pendulums hang side by side
and one is set swinging, while the other is initially at rest,
the latter will gradually take up the oscillations of the former,
unless the stand is perfectly rigid. The flexure of the stand
is thus determined from the rate at which the first pendulum
influences the second.
The periods of vibration of the pendulums are found by
comparing them with the beats of a half-seconds clock, which
is rated by star transits. Each half-second the clock momen
tarily opens the shutter before the slit of the " flash-box," and
the illuminated slit is reflected in the vertical mirror on the
pendulum, and viewed in a small telescope on top of the
flash-box. (Plate XXII.)
Thus a line of light is seen in the field of the telescope
every half-second ; and, as the clock gradually gains on the
pendulum, the position of the line moves down in the field,
and the time when it coincides with a central horizontal wire
can be determined. The interval between one coincidence and
the next is the interval in which the pendulum loses one swing

SURVEY INSTRUMENTS 201
on the clock. The observations being continued over a period
of several hours, the comparison between the clock and the
pendulum becomes of great precision, with a probable error of
only three or four parts in ten million.
This apparatus is fairly portable, and the necessary observa
tions for the determination of the value of gravity at a single
station may be made in a couple of periods of three or four
hours, generally chosen so that one is at night and one by day.
But it takes several days to get the clock properly rated by star
transits ; and thus in the past the greater part of the time at
each station has been spent in determining time and rating the
clock. It seems likely that in the future much time will be
saved by using the wireless time signals to rate the clock.

INDEX

Adjustment of traverse 126
 of triangulation 158
Aero-maps 56
Africa, British : Survey of 168
 : arc of meridian 181
Airy: attraction of mountains 174
Amsler planimeter 34
Aneroid barometer : use of 76
Angot : barometer heights 79
Arc of meridian 171
 : geodetic measure 179
 : principal determinations 1 8 1
Areas : measurement of 33
Artificial horizon 193
Astronomical observations : route traverse
60, 67
 : navigation 60
 : with compass sketch 101
 : topographical survey 141
 : geodetic survey 171, 184
Attraction of mountains 173
Australia : Survey of 167
Austria- HuDgary : school maps 48
Austrian General Staff: map of Central
Europe 47
Azimuth : determination of 60, 69, 143
 : initial 141
 : reverse 159
Baily : barometer heights 77
Barometer heights 74
 : theory 7 7
 : tables 80
Barometer : relation with level of sea 1 34
Base in simple theodolite survey 90
 : for compass sketch 106
 : for plane table sketch 114
 : for topographical survey 144
¦  : correction for slope 147
 : reduction to sea level 148
¦  : closing one on another 159
 : for geodetic survey 185
 : Cambridge apparatus 197
Bavaria : analysis of select maps 45
Beacons 137
 : self-centering 140

Bench marks 23, 188
Bessel : figure of the Earth 190
Boiling point thermometer 80
Boundary surveys 169
Breteuil : Bureau des poids et mesures,
standardisation of wires 145
 :  of bars 185
Bureau des Longitudes : wireless time
signals 198
Canada : Survey of 167
 : map published by British General
Staff 41
Cassini : arc of meridian 181
Chain survey 84
Chains of triangulation 184
Characteristic sheet 5, 127
Chatham, School of Military Engineering
vii, 128
Chronometers 67
Clarke: form of ocean surface 178
 : figure of the Earth 179, 180
Clinometer, Indian 101
 :  description 161
Clinometer, Watkin 101
 : adjustment 109
Close viii
 : Textbook of topographical survey
ing v
 field printing company 36,77
 ¦ theodolite triangulation 149
 trigonometrical heights 155
 Survey tables 159
 instrumental adjustments 192
Close- Brooker alidade 128
Colonial Survey Committee : Report 83,
168, 169
 : work of 168
Comparator for wires 186
Compass, prismatic 65, 101
 : deviation of 69, 70
 : local deflections 104
-.  : plotting bearings 105
 : use of 102
Compass, trough 113, 120, 124
Compass sketching 101, 105, 107

204

INDEX

Compass-traverse 61, 62
 check by latitude and azimuth
71
  cannot make map 72
Compensation of mountain attraction
174, 176
Contours 23
 with clinometer in
 with level and chain 165
Conventional signs 5, 29, 127
Cross-bearings 64
Curvature of Earth : in levelling 98
 : in plane-tabling 128
 : in triangulation 92, 152
Cyclometer 62
Dead-reckoning 61, 71
Dehra Dun: gravity at 177
 : change of height 188
Diplomacy : importance of maps in 4
Distances : measurement on map 34
 :  by time 63
Dobson: base apparatus 197
Durand : reconnaissance ladder ix, 135
Dutton : isostasy 177
Egypt, Survey department vii
 : self-centering beacons 141, 183
 : horizontal refraction in Nile valley
 : triangulation up the Nile 137
 : arc of meridian 182
Eiffel Tower: time signals 199
Exploratory survey: methods 130
Faye : gravity on islands 176
Ferrero : report on triangulations 182
Field book of compass traverse 64
Figure of the Earth : method of finding
171, 180
 : basis of Survey tables 159
 : present knowledge of 190
Fisher : Physics of the Earth's Crust 174
Forest : Survey of 73
Form-lines 23
France : analysis of select maps 44
General Staff : Geographical Section 41
 : analysis of select maps 42
 : map of Africa 73
 : map of Canada 167
Geodesy vi
 : definition 171
 : figure of Earth 179
 : principal arcs 181
 : future progress of 189
Geographical positions from triangulation
158
Gill : use of geodetic survey 94
 : geodetic survey of S. Africa 183

Graticule : construction 160
Gravity: local deviations 142, 143
 :  in geodesy 172
 : pendulum survey 176
Great Britain : see Ordnance Survey
Greece : analysis of select map 48
Greenwich time 68
Guillaume : invar base apparatus 197
Hachures 20
Hayford : figure of the Earth 190
Hecker : gravity at sea 176
Hedley viii
Heights : by barometer 74, 77, 80, 156
by clinometer 127
by theodolite 153
datum no
Heliograph 138
Helmert : flattening of the Earth 191
Henrici : theory of base measures 187
Hill features : representation of 19
Hill paths, failure to show 8
Hill-shading 2 1
Himalayas, attraction of 173
 : partial compensation of 177
 : effect on form of ocean surface 178
 : levelling in the 188
Hypsometer, or boilingpoint thermometer
80
Hypsometric tints 27
Identification of objects 33
India, Survey of vii, 167
 : Survey tables 77, 159
 : gravity in 173, 176
International Geodetic Association vii
International Map 5
history of 50
analysis of select sheets 54
conventional signs : roads 8
¦  railways 10
 rivers 16
 woods 17
Intersected points 107,
Intel-visibility of points
Invar wires 145, 186,
 bars 185
Isostasy 177
Italy : analysis of select maps 47
Jack : beacons on the Uganda-Congo
boundary ix, 139
Kew, base station for gravity survey 177
Lallemand : projection for international
map 52
Lamps for beacons 138
Land Survey 83
Laplace: barometer heights 77

"9
197

INDEX

205

Lapland : arc of meridian 181
Latitude : determination of 60, 67, 142,
196
 : initial 141
 : local deviations 1 74
Latitude and departure tables 71
Layer colouring 27
 on international map 55
Level 95, 96, 196
Levelling 93
 of precision in Great Britain 166,
188
 connection between tide gauge and
triangulation 134
 geodetic 187
Levelling staves 95
Longitude : determination of 60, 67,
142
 :  by telegraph 68, 197
 :  by wireless 198
 : initial 141
Loomis : barometer heights 77
Lossiemouth base 187
Lunar distances 68
Lyons : Cadastral Survey of Egypt vii
Magnetic meridian : shown on O. S. maps
19
 : on plane table 120
 : on compass sketch 105
Manual of Map Reading (Official) v
 conventional signs 6
Map reading 30
Maps, Cadastral : definition 2
 : Ordnance Survey 38
 : triangulation for 162
 : necessity for 2
 : topographical : definition 2
Margins of sheets 17
 : international map 55
Meridians on O. S. maps 19
Metric system 51
Military works 30
Morris : geodetic triangulation of South
Africa 183
Mount Everest : discovery of height 156
Mountains, attraction of 174
Names : transliteration on maps 55
Natal : want of maps 3
National Physical Laboratory: standard
isation of wires 145
 :  bars 185
 :  thermometers 82
Natural scales n
Navigation : astronomical observations 60
Occultations 68
Ocean surface, form of 178
Ordnance Maps 37

Ordnance Maps: analysis of select sheets
38
 : methods of reproduction 36
Ordnance Survey vii
 : conventional signs 5
 ': roads 6
 : railways 9
 : rivers 15
 : woods 17
 : contours 24
 : other signs 29
 : rule for figuring contours 24
 : accuracy of principal triangulation
182
 : history 163
 : present state and plans for future
.l65
 : principal stations 140, 164
 : cost 166
Paris Observatory : time signal 199
Patchwork survey 95, 132
Pencils 102
Penck: proposal for International Map 50
Pendulum-survey 175
Perambulator 62
Personality in observation 195
Peru : arc of meridian 181
Picard : arc of meridian 181
Plane table and accessories 113,125, 127
 : graphical use of 114, 128
 : accuracy of 118
 : resection 121
 : traverse 125
 : triangle of error 122
 : failure of solution 124
Planimeter 34
Poles, determination of position near 62
Pratt: attraction of Himalayas 174
Profiles 31
Projections, Map 34, 160
Protractor 101, 105
 : scales on 14, 112
Quadrilateral chains 136, 184
Railways, representation of 9
Reconnaissance: plane table 118, 135
Reconnaissance-ladder 135
Rectangular coordinates of triangulation
159
Refraction : in levelling 98
 : in trigonometrical heights 153
 : of horizontal angles 152
Representative fraction n, 13
Reproduction of maps 35
 : in the field 36
Repsold transit micrometer 185
Resection by compass 108
 by plane table 121

206

INDEX

Rivers : representation of 15
Roads : representation of 6 ; and see
Map Analysis, Chap. II
Route map 59
Roy : first director of Ordnance Survey
163
 : triangulation of England 181
Ruling points 107
Salisbury Plain base 164
Saxony : analysis of select map 45
Scale of maps 10
Scales, construction of 13
 natural it
Sea-level: determination 133
 : reduction of triangulation to 148
 : revision of British datum 166
Sections 30, 98
Semliki base 187
Sextant 192
Sight-rule 113
Signals : luminous 1 38
 : opaque 139
Sketch : definition roo
Sketching detail 108
Snellius : measurement of arc 181
South Africa : Survey of vii, 168
Southern Nigeria : barometer heights 76,
156.
 : precise traverse 162
Spherical excess 152
Spitsbergen : arc of meridian 181
Spot-heights 23
 : by Indian clinometer 161
Standardisation : of base bars 185
 : thermometers 82
 : wires 1 45
Station-marks 140
Struve: European arc of meridian 181
Subtense methods 129
Survey : cadastral 2
 : topographical 1, 132
 : geodetic 171
Sweden : analysis of select maps 49
Switzerland : analysis of select maps

Tacheometer 129, 196
Talcott's method for latitudes 184, 196
Tapes for base-measurement 145
Theodolite: geodetic 183
 : mountain 193
 : triangulation 88, 91
 : method of observation 149
 : horizontal angles 149, 195
 : vertical angles 153
 : instrumental adjustments 194
 ¦: micrometer 194
Tide gauge 133
Time signals 199
Topographical survey 1, 132
Traverse: precise 73, 162
 : compass 6i, 62, 71, 72
 : compass checked by astronomical
observation 67
 -: plane table 125
 : adjustment of 126
Traverse tables 71
Triangle of error, in plane tabling 122
Triangular error 151, 184
Triangulation 88, 92
-.  : with compass 107
 : with plane table 116
 : use and accuracy of graphical 118
 : with theodolite 136, 149
 : computation 156
 : geodetic 183
Trigonometrical heights 153
 : accuracy 155
Trough compass 113, 120, 124
Uganda-Congo boundary 4
United States : analysis of select map 50
 : geodetic survey 178, 190
War Office, Geographical Section 41
Wilson : Topographical Surveying 147
Wireless telegraphy 68, 185, 198
Wires for base measurement 145
Woods and forests : representation of 17

46 Zenith telescope 15

CAMBRIDGE: PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS.

BY THE SAME AUTHOR
Map Projections
By Arthur R. Hinks, M.A., F.R.S., Chief Assistant, Cambridge
Observatory, and University Lecturer in Surveying and Cartography
Demy 8vo. pp. xii -t- 126. With a frontispiece and 19 figures
Price 5^. net
Press Notices
"Notwithstanding the large amount of surveying which has been done in this
country and throughout the Empire, there are few works in English which treat of the
various ways in which portions of the earth's surface may be most conveniently and
correctly represented on the plane surface of a map. The subject has been treated
partially by several eminent mathematicians, and valuable summaries occur in some
encyclopaedias, but we do not in this country possess any works such as those by
Germain, Tissot, Hammer, and others. There are also many works of a less
advanced type which are available to Continental geographers, but this class, too, is
very insufficiently represented here. We therefore welcome the appearance of the
present volume, in which the subject is treated clearly and in a manner which makes
but small demand upon the mathematical training of the geographer, while at the
same time the important points in any projection, suitability for special purposes, and
facility of construction are given especial prominence. After indicating the inevitable
limitations of all projections, in representing length, area, and shape of any portion of
the earth's surface, the author reviews the principal systems. ...Conical, cylindrical
and zenithal, as well as certain conventional projections, are well described and
clearly explained, their special advantages and points of weakness being indicated.
A chapter on the projections in actual use is an instructive addition. The chapter on
the simple mathematics of projections treats of the theory of each particular case, and
discusses the errors which may arise in its use under different conditions  The present
volume will be of great use to all geographers, and should pave the way for a more
serious study of cartography on scientific lines than yet generally obtains. Great care
and labour are expended on the measurements of various regions in order to produce
trustworthy surveys, and the utilisation of the results should be based on sound carto
graphical principles, and in such a work this book will be a valuable assistance." Nature
" Writers who have dealt with the matter in the past have, as a rule, been
mathematicians who, after elaborate investigations, have arrived at conclusions,
frequently expressed in lengthy formulae, which the ordinary man who has to
construct maps fails to follow ; or they have been those who have gone to the other
extreme, and seeking to free the subject from supposed complications, have left out
most of the mathematics, and produced books which, though giving diagrams and
more or less approximate rules, fail entirely to satisfy students desirous of following
the subject intelligently. The sort of book that was for a long time almost entirely
wanting for the ordinary geographer and map draughtsman was a mean between these
two. Mr Hinks, who is well known as an astronomer, has now taken up the subject,
and while he fully admits his indebtedness to Colonel Close and others, has produced
a work of considerable interest, which should go a long way towards meeting this
need, and one which possesses decided originality as regards some of its subject-
matter and method of treatment.... The Introduction is specially good, and the.
explanations, both in this and other sections of the book, are illustrated by small
diagrams that must be of great assistance in making matters clear. ...A specially
interesting chapter is that on the Errors of Projections. Some six to nine different
projections are dealt with and the results are not only interesting, but will be of
considerable value to those engaged in map drawing." — Geographical Journal
Cambridge University Press
Fetter Lane, London. C. F. Clay, Manager

03487 9909

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