TA
1911
BOUGHT WITH THE INCOME
FROM THE
SAGE ENDOWMENT FUND
THE GIFT OF
Hettrg M, Sage
1S91
A^-XC=.S>rVS>\ ^NVV
x-x
The date shows when this volume was taken.
To renew this book copv th» call No. and give to
■ t he Ubraria n.
HOME USE RULES.
All Books subject to Recall.
Books' not used for
instrucUon or research
are returnable within
4 weeks.
Volumes of periodi-
cals and of pamphlets
are held in the library
as much as possible.
For special ptrrposes
they are given out for
a limited time.
Borrowers should
not use their library
privileges for the bene-
fit of other persons.
Books not needed
during recess periods
shoidd. be returned to
the library, or arrange^
ments made for their
return during borrow-
er'sabsence.if wanted.
Books needed by
more than one person
are held on the reserve
list.
Books of special
value and gift books,
when the g^ver wishes
it, are-, not allowed to
circulate.^
Readers are asked
to repovt all cases of
b ooks marked or muti-
lated.
REiitfei***'
ice books by marks and writini;.
TA 590.S5Tl9'l"r""'' """''
Militan
3 1924 022 865 897
The original of tiiis book is in
tine Cornell University Library.
There are no known copyright restrictions in
the United States on the use of the text.
http://www.archive.org/details/cu31924022865897
MILITARY TOPOGRAPHY
FOR THE MOBILE FORCES
MILITARY
TOPOGRAPHY FOR THE
MOBILE FORCES
INCLUDING
MAP READING, SURVEYING
AND SKETCHING
With More Than 175 Illustrations and One Map of
Vicinity of Fort Leavenworth
BY
CAPTAIN C. O. SHERRILL
corps op enoineerSj u. s. army
instructor in the department op engineering
u. s. service schools
fort leavenworth, kansas
Second Edition
Adopted by direction of the Commandant for use as text book
in the Army Service Schools, Fort Leavenworth, Kansas,
Adopted by the War Department as a text booh in Garrison
Schools for Officers, and as the basis for all promotion
examinations in Topography, also for the use
of the Organized Militia.
Adopted by the Coast Artillery School, Fort Monroe, Va.
Copyright 1910 and 1911
h
Captain C. O. Sherrill
Press of
George Banta Publishing Co.
Menasha, Wis.
TABLE OF CONTENTS.
PARS.
Introduction ........ 1-9
PART I.
MILITARY MAP READING
Chapter I. — Classes of maps; Map Reading; Scales
of Maps; Methods of Representing Scales; Con-
struction of Scales ; Scale Problems ; Scaling Dis-
tances from a Map; Problems in Scaling Distances 10-21
Chapter II. — Methods of Representing Elevations;
Contours; Relation of Map Distances, Contour
Intervals, Scales and Slopes; Problems; Hachures 22-32
Chapter III. — Directions on Maps; Methods of
Orienting a Map; To Locate One's Position on a
Map; The True Meridian; Conventional Signs 33-40
Chapter IV. — Visibility; Visibility of Areas; Visi-
bility Problems; On Using a Map in the Field;
Maps Used for War Games and Tactical Problems 41-54
PART II.
MILITARY TOPOGRAPHICAL SURVEYING.
Chapter I. — Scales and Verniers on Instruments;
Problems; Angular Measurements; To Locate the
True and Magnetic Meridians ; Retracing Old Sur-
vey Lines; Problems ...... 55-70
Chapter II. — The Transit: Care and Handling of
Instruments; Rules for the Use and Care of the
Transit; The Plane Table; To Set Up; To Level . 71-80
Chapter III. — Adjustments of Transit and Plane
Table: Plate Levels; Line of CoUimation; Hori-
zontal Axis of the Telescope; Vernier of the Ver-
tical Circle; Needle and Pivot of Compass . . 81-108
V
VI Table of Contents
PARS.
Chapter IV. — Horizontal and Vertical Measure-
ments: Steel Tape and Chain; Measuring a Line
With Tape; Ranging Out a Line; Passing Obsta-
cles ; Stadia Rods and Stadia Measurements ; Meth-
ods of Graduating Stadia Rods; Horizontal Dis-
tances and Differences of Elevation from Inclined
Stadia Readings; Stadia Computer . . . 104-123
Chapter V. — The Wye Level: The Level Rod; To
Set Up the Level; To Focus the Eye Piece and
Object Glass; Adjustments of the Level; Methods
of Using; Profile Leveling; To Plot the Profile;
Cross Section Leveling . . . . . . 124-141
Chapter VI. — The Selection of the Scale of a Map ;
The Execution of a Military Survey; Methods of
Making a Plane Table Survey; Triangulation ;
Filling in Details ; Resection Locations ; Intersec-
tion Locations; Traverse Locations; Errors and
Their Adjustment; To Locate Side Shots; Plane
Table Survey, Using Transit for Reading Stadia;
Determination and Plotting of Contours and Mili-
tary Details ; Interpolation of Contours ; Aids to
Accuracy ........ 142-171
Chapter VII.- — Transit and Stadia Survey; Tra-
versing Side Shots for Detail; Table of Notes;
To Locate Station ( 1 ) ; To Move to a New Sta-
tion; To Orient by Back Sight; Checks On the
Accuracy of Transit Readings; Plotting the Sur-
vey, (a) With Protractor, (b) from Rectangular
Co-ordinates; Adjustment of Errors; Table Show-
ing Computation of Latitudes and Departures . 172-188
Chapter VIII. — Contour Surveying . . . 189-192
Chapter IX. — Instruments Used in Finishing Maps
and Methods of Using Them; Finishing the Map . 193-209
Chapter X. — Reproduction of Maps; Mechanical
Reproduction; Photographic Reproduction . . 210-213
Table of Contents vii
PARS.
Chapter XI. — Instruments Occasionally Used in
Military Topography and Methods of Using
them; Weldon Bange Finder; Penta-Prism Range
Finder; Sextant; Slide Rule .... 214-222
PART III.
MILITARY SKETCHING.
Chapter I. — Sketches; Scales of Sketches; Meas-
urements made in Sketching; Estimation of Dis-
tances 223-236
Chapter II. — Methods of Measuring Horizontal Di-
rections; Instruments Used in Position and Out-
post Sketching; Estimation of Slopes; Estimation
of DiflFerences of Elevation; What Military
Sketches Should Show; Classification of Sketches 237-265
Chapter III. — Methods of Sketching; Horizontal
Location of Points; Methods of Contouring; Exe-
cution of a Position Sketch; Methods of Work;
Contouring the Sketch; Points to be Observed in
Sketching; Execution of Outpost Sketches . . 266-288
Chapter IV. — Execution of Road Sketch; Methods
of Work Dismounted; To Locate Horizontal De-
tails; Contouring the Road Sketch; Road Sketch-
ing Mounted ; Execution of Place Sketches . . 289-309
Chapter V. — Topographical Reconnaissance Re-
ports: Road Reconnaissance; River Reconnais-
sance; Reconnaissance of: Railroad, Wood or For-
est, Mountains, Camp, Position .... 310-346
Chapter VI. — Exercises in Sketching . . . 347-349
MILITARY TOPOGRAPHY FOR THE
MOBILE LAND FORCES.
PREFACE.
1. The ability to read a map and to comprehend
the military possibilities of the terrain is now rec-
ognized by aU military authorities as an absolute
essential for aU officers who hope to be efficient in
time of war. General Kuropatkin, who command-
ed the Russian forces in the recent Russo-Japanese
War, says: "A regimental commander could not, as
a rule, read a map himself, much less teach those un-
der him how to do so. This was especially the case
at the beginning of the war, and had considerable
influence on the conduct of operations, as regiments
often arrived late at their rendezvous or went to
points where they were not wanted."
2. It is further recognized that one of the best
methods of learning, in time of peace, how to handle
troops in time of war is by solving map problems*
and by playing war games (map maneuvers).
These methods are much used in all leading foreign
armies and have been adopted by our own Regu-
lar Army, Marine Corps, and by some of the Na-
tional Guard organizations, always with the great-
*The student is reeommended to read "Tactical Solutions and
Problems" by Capt. M. E. Hanna, 3d. Cavalry.
IX
X Preface
est success. But to solve these problems the first
requirement is the ability to read, quickly and accur-
ately, a contoured mihtary map.
3. Lt. General Litzman, Commandant of the
German Staff College in his work on the solution of
Tactical Problems forcibly emphasizes the same
idea and lays especial stress on the advantage de-
rived, in solving tactical problems, by practical
work in topography. He says : "A practical solu-
tion can nearly always be f oimd by him who has
sufficient talent and experience to see the map plas-
tically before him and not only to comprehend
mechanically the information in the problem con-
cerning both forces but actually to see the opposing
parties with his mind's eye and, as it were, actually
experience the events portrayed.
The necessary basis for the solution of problems,
therefore, is a correct comprehension of the map
and of the opposing forces. The map lies before
the solver; he only needs to be able to read it; this
does not mean merely that he must be able to un-
derstand the meaning of all conventional signs and
to reckon distances, but also that he must be able to
comprehend all details so that thej'^ form themselves
into a complete and harmonious whole, and this to
such an extent that he actually feels the nature of
the terrain in the map before him. Every soldier
who is at all fitted for the duties of leadership can,
by practice, gain this ability, though the time re-
quired may be long or short, according to the natur-
al ability of the worker. The frequent compari-
Peeface XI
son of the map with actual terrain conditions is
particularly helpful. *****
For him who has been for a few years engaged in
topographical work (in representing nature on the
map), the reverse operation of understanding act-
ual terrain from the map will be especially easy."
4. This book has been written with the inten-
tion of giving to line officers of the Mobile Land
Forces the principles and methods of making and
using military maps and sketches necessary for a
complete mastery of the military possibilities of
ground and maps. With this special object in view,
all difficult mathematical discussions and obsolete
or unnecessary surveying instruments are omitted,
and only those subjects are treated which should
be thoroughly understood both theoretically and
practically by every officer. The end in view is not
only to give instruction in rapidly making good
topographical maps and sketches under service
conditions; but especially to assist officers in ac-
quiring that trained topographical eye which grasps
instantly the possibilities and limitations of the ter-
rain in its influence on the military situation.
5. The object of Part I, Military Map Read-
ing* is to give a statement of the principles and a
solution of the problems essential to the accurate
and rapid use of maps for military purposes, such
as tactical map problems, war games, and maneuv-
ers. The treatment has been made as simple as
*A revised and enlarged edition of the book "Military Map
Beading" of which 10,000 copies were sold.
XII Preface
possible, but the ground is covered fully in order to
provide a complete reference book on Military Map
Reading. There are a large number of problems
and their solutions given, but these have been lim-
ited to such as have practical military utility to
prevent an erroneous idea of the possibilities and
limitations of maps.
6. Part II, Military Surveying, lays especial
stress on the use of the plane table and stadia meth-
od, as the best means of acquiring skill in accurate-
ly estimating distances, slopes, and elevations.
7. Part III, Military Sketching, gives in de-
tail the methods used at the Army Service Schools
in rapid military sketching, illustrated by a de-
tailed study of the steps followed in particular
sketches. Especial emphasis is laid on practical
methods of estimating distances, horizontal angles,
slopes and elevations; and each detailed step in the
work has been explained carefully, for the benefit
of those learning to sketch without the guidance of
an instructor.
8. Messrs. Keufi'el and Esser kindly furnished
a large number of plates of their instruments, for
which the author is duly appreciative.
Acknowledgement is made to the Chief of Engi-
neers for permission to make use of matter from the
"Engineer Field Manual"; to the Superintendent
Smithsonian Institute for tables; to Messrs. Pence
and Ketchum for permission to refer to their excel-
lent "Surveying Manual."
The Author acknowledges his obligations to M.
Preface xiii
S. E. John Howry and Sergeant D. S. Shea for
excellent drawings and Sergeant Frank Argen-
bright for photographs.
To Major E. R. Stuart, Captain J. A. Wood-
ruff, Lieut. Geo. C. Marshall, Jr., and Lieut. R. E.
Beebe, U. S. Army, especial acknowledgement is
made for suggestions and criticisms.
XIV List of Books Consulted
LIST OF BOOKS CONSULTED.
Engineer Field Manual.
Military Topography, Larned.
Topographical Surveying and Sketching, Rees.
Military Topography and Sketching, Root.
Catalogue, Keuffel and Esser.
Text Book of Military Topography, Richards.
Pamphlet on Conventional Signs, War Depart-
ment.
Field Service Regulations.
Infantry Firing Regulations.
Military Topography, Verner.
Elements of Military Topography, Demangel.
Manual of Field Sketching and Reconnaissance.
Engineers' Surveying Instruments, Baker.
Surveying Manual, Pence and Ketchum.
INTRODUCTION.
GENERAL PRINCIPLES.
1. By the term "Military Topography" is
meant the various features of ground important in
military operations, and the principles governing
the study and methods of representing these feat-
ures. The subject of Military Topography natur-
ally divides itself into three parts, Military Map
Readings Military Topographical Surveying, Mili-
tary Topographical Sketching.
2. Military Map Reading treats of the nature
of maps, of the objects represented on maps, their
military uses and the methods of interpreting them.
3. Military Topographical Surveying treats of
the means and methods used in making military
topographical maps with instruments of precision.
4. Military Topographical Sketching treats of
the means and methods used in making Military
Road and Area sketches, and the reports on the
topographical features thereof.
5. Military Map Reading is considered first
because a general knowledge of the meaning of
maps and sketches, of the information conveyed by
them, and of the military uses to which they may be
applied, is essential before an intelligent idea can
be obtained of the necessary features to be repre-
sented thereon.
XV
XVI Introduction
Military Surveying is treated next, because of
the necessity of studying, in detail, ground forms in
comparison with their map representations as a pre-
Uminary foundation for the perfect knowledge of
maps and ground reqxiired by military men. This
study should be prosecuted with the assistance of
surveying instruments of precision, in order that
the student's ideas of horizontal distances, differen-
ces of elevation, slopes, and shapes of all kinds of
ground forms may be immediately checked and cor-
rected on the spot by the readings on the instru-
ment. There is no other method of learning to es-
timate distance (so important in battle firing, scout-
ing, ranging etc. ) which can compare with the study
of surveying and sketching. The same is true of
learning to estimate every other relation foimd on
the ground such as the cover possible for an attack-
ing line, the strong points of a position, etc. The
artilleryman may know his gun fire will just graze
a slope of so many degrees, but he will have no idea
what that particular slope looks like on the ground
if he has not had some correct means of measuring
such slopes until he can accurately estimate them.
6. Military Topographical Sketching is consid-
ered last because the basic principles of topography
must first be learned by the study of surveying with
the exact instruments as a constant guide and cheek
on every estimate made of ground forms, before a
sufficient grasp and comprehension of ground is se-
cured by the student to enable him to make military
sketches truly representing features before him with
the rapidity required by the military service. No
Introduction xvii
man can become an excellent sketcher until he in-
voluntarily sees the map forms which would cor-
respond to the ground observed; nor can he be a per-
fect map reader or scout until to see a map is at once
to picture to himself intuitively the ground form
from which the map is made. A conscientious study
and application of the subjects treated herein will
give the average military man the topographical
knowledge and the training of the eye essential to
every soldier. It is to be remembered that the final
end of the study of Surveying and Sketching is not
alone to become proficient in these two subjects but
also to learn everything about the military features
of ground and their representation on maps, as a
basis for the accurate and prompt solution of all
mihtary problems.
7. Not every officer has facility for making
maps and sketches^ and consequently there are some
who cannot hope to become experts in this work;
yet this fact should not deter any one from the
study of this subject, because of the military knowl-
edge thereby obtained. However, f acUity in hand-
ling a pencil is of small importance, as is witnessed
by scores of poor draftsmen who have become ex-
cellent sketchers, able to show clearly and accurately
the essential military features of the area sketched ;
but the facility that is required for learning to rep-
resent groimd forms correctly, is the facility for
mastering the details of these forms. This knowl-
edge of ground is an absolute essential in every mili-
tary operation, and ofileers deficient in it, who
would become great tacticians or strategists, must
XVIII Introduction
learn by patient effort that which very few know
intuitively — the relation between ground and its
corresponding map.
8. The subjects discussed in this book are strict-
ly limited to those required by officers of the Mo-
bile Land Forces in securing the topographical
knowledge demanded by the modem Art of War;
and the treatment is made as simple and as free
from mathematics as possible while fully covering
the subject.
9. Geodetic methods are not conisdered, for the
reason that not one Line officer in a hundred will
ever be called on to make a geodetic survey ; but all
officers must have a good grasp of topography to
excell in the miUtary profession. Those officers
who may be caUed on to make a geodetic survey
should provide themselves with a good work on gen-
eral surveying such as Johnson's or Wilson's.
PART I.
MILITARY MAP READING.
CHAPTER I.
CLASSES OF MAPS.
10. Maps are representations to scale (usually
on a plane) of portions of the earth's surface. They
are of various kinds, depending on the use for
which they are intended, and may or may not rep-
resent relative heights as well as horizontal distan-
ces and directions. For instance, the ordinary
County Map shows only roads, boundaries, streams
and dwellings. A Topographical Map shows the
horizontal relation of points and objects on the
ground represented and in addition gives the data
from which the character of the surface becomes
known with respect to relative heights and depres-
sions.
11. Suppose an officer is sent out by his com-
mander in unknown country to pick out a good posi-
tion for camp and outpost, and to report upon his
return the military features of the site selected. On
visiting the ground selected his eye can only take in
avvery limited portion from any one position, and
even with the most careful examination from vari-
ous points he would get only a very general idea of
the larger features. But if on returning he tries to
1
2 Military Topogbaphy foe Mobile Forces
describe in words to his commander the position se-
lected, he would find his task almost impossible.
The simplest sketch, however, made by him on the
ground, even if not correct as to scale or elevations,
would enable him to give his commander as good an
idea as he had himself obtained ; but a report based
on an acciirate map or sketch would be full and
complete. It is almost impossible to organize and
carry out marches, reconnaissances, concentrations,
etc., without maps upon which to base the orders.
12. Almost all classes of maps have some mih-
tary uses. For example, an ordinary map showing
the location of important towns, large rivers, and
roads, is useful for arranging the concentration of
large bodies of troops or for following the opera-
tions of a campaign, but it is far from being in
sufficient detail for the purposes of those who plan
or study the smaller operations of war. A complete
military map, on the contrary, must give both the
horizontal and vertical relations of the ground and
also a representation of all military features of the
area.
A Military Map, therefore, is one which gives
the relative distances, elevations, and directions of
aU objects of mihtary importance in the area rep-
resented.
MAP READING.
13. By Map Reading is meant the abihty to
grasp by careful study not only the general features
of the map, but to form a clear conception or mental
picture of the appearance of the ground represent-
ed. This involves the ability to convert map distan-
Military Map Reading 3
ces quickly to the corresponding ground distances;
to get a correct idea of the network of streams,
roads, heights, slopes, and all forms of military cov-
er and obstacles. The first essential therefore, for
map reading is a thorough knowledge of the scales
of maps.
SCALES OF MAPS.
14. A map is drawn to scale — ^that is, each unit
of distance on the map must bear a fixed proportion
to the corresponding distance on the ground. If
one inch on the map equals one mile (63360 inches)
on the ground, then ^ inch equals ^ mile, or
63360-=-3=21120 inches on tiie ground, etc. The
term "Distance" in this book is taken to mean hori-
zontal distance; vertical distance to any point is
called elevation or depression, depending on wheth-
er this point is higher or lower than the one from
which the measurements are made. For example,
the distance from Frenchman in a straight hne to
McGuire (Leavenworth Map) is 2075 yards, but
to walk this distance direct would require the ascent
and descent of Sentinel Hill, so that the actual
length of travel would be considerably greater than
the horizontal distance between the two points.
In speaking of distance between towns, cities,
etc., horizontal distance is always meant. In re-
ferring to such distances, that by the shortest main
road is usually intended. For example, from Fort
Leavenworth to Kickapoo (Leavenworth Map) is
5 miles, measured over the 5-17-47 road. The fixed
ratio (called the scale of the map) between distan-
4 Mn.TTABY TOPOGBAPHY FOR MOBILE FoKCES
ces on the map and the corresponding distances on
the ground should be constantly kept in mind.
METHODS OF REPRESENTING SCALES.
15. There are three ways in which the scale of
the map may be represented :
1st. By an expression in words and figures; as
3 inches=l mile; 1 inch=200 feet.
2d. By what is called the natural scale or the
Representative Fraction (abbreviated R. F.) , which
is the fraction whose numerator represents units of
distance on the map and whose denominator repre-
sents units of horizontal distance on the ground,
being written thus: R. F. li!^ _?_, 1:63360,
^ 1 mile , 63360
or 1 is to 68360, — all of which are equivalent ex-
pressions, and are to be understood thus: — 2/
Ground
that is the numerator is distance on the map, the
denominator is horizontal distance on the ground.
This fraction is usually written with a numerator
of unity, no definite length of unit being specified
in numerator or denominator. In this case, the ex-
pression means that one unit of distance on the map
equals as many of the same horizontal units of dis-
tance on the ground as there are \mits in the de-
nominator.
The R. F. is synonymous with the term scale of
the map. Therefore, if the scale be changed the
R. F. will be changed in exactly the same manner
and amount. To increase the R. F., (being a frac-
tion), its denominator is decreased. For the same
MiLiTAUY Map Reading 5
reason the greater the distance on the ground rep-
resented by an inch on the map, the smaller is the
scale of the map. The greater the dimensions of a
map to represent a given area the larger is the scale
(that is R. F.) and the smaller the denominator
of the latter.
3rd. By what is called a Graphical Scale. A
Graphical Scale is a hne drawn on the map, divided
into equal parts, each division being marked, not
with its actual length, but with the distance which
it represents on the ground, (see figure 1. and
Leavenworth Map).
Every map should have a graphical scale because
this gives true readings no matter how the size of the
map is changed in reproduction or due to weather
conditions; whereas the R. F. and the mmiber of
inches per mile placed on the original map are no
longer true if the size is altered. The R. F. is im-
portant, however, because it is intelligible to per-
sons xmf amiliar with the imits of distance used in
making the map. An expression of the scale in
words and figures is also valuable because rapid
mental estimates can be made of the distance be-
tween points on the ground by estimating the num-
ber of inches between these points on the map.
16. Graphical Scales are of two kinds depend-
ing on the purpose for which they are constructed :
(1) Working Scales anA. (2) Beading Scales.
A Working Scale is used in making a sketch or
map and shows graphically the value of tens, him-
dreds, etc. of the units of distance used in making
6 Military Topography foe Mobile Forces
the map or sketch. For example, if distances were
measured by counting strides or taking the time of
a horse trotting, in making a sketch, then it would
be necessary to construct a scale of strides or min-
utes of horse's trot on the desired scale of the sketch.
This enables you to lay off on the sketch distances,
measvu-ed thus, directly from the working scale
without the necessity of calculating at each halt how
many inches on the sketch are equal to the ntun-
ber of strides or minutes, passed over.
A Reading Scale shows the distance on the map
corresponding to even tens, hundreds etc. of some
convenient and well known imit of measure, such
as the foot, yard, mile. For example, figure 2
shows a reading scale of yards, reading to hundreds
on the Main Scale^ and to 25 yards on the Exten-
sion (see fig. 1). A scale may be both a working
and a reading scale when the imit of measure used
in making the map is a well known length such as
the foot, or yard. A reading scale in the units of
one country often will not be satisfactory for use
by persons of a different nationahty, because of
their unf amiharity with the length of tmits of dis-
tance used. An officer coming into possession of
such a map would be unable to get a correct idea
of the distances between points represented. He
would find it necessary to convert the scale into fa-
miliar tmits as yards or miles, see problem 4, par.
19.
It will readily be seen that a map's scale must
be knoAvn in order to have a correct idea of distan-
Plate I
o
a..
8 Military Topography for Mobile Forces
ces between objects represented on the map. This
is essential in determining lengths of march, rang-
es of small arms and artillery, relative length of
marches by different roads, etc. Therefore, if un-
der service conditions you should have a map with-
out a scale or one expressed in unf amihar units, you
would first of all be compelled to construct a graph-
ical scale to read yards, miles etc., or one showing
how many miles one inch represents. Or, if you
were required to make a sketch by pacing, it would
be necessary to construct your scale of paces on the
proper R. F.
CONSTRUCTION OF SCALES.*
In the construction of scales the following are
the steps taken:
(1). Find from the given data the R. F. of
the map; (2) the length in inches of the unit of
measure used, as pace, chain, rate of horse's trot,
yard, mile etc.; (3) the number of the units of
measure corresponding to one inch on the map ; and
(4) the length in inches on the map corresponding
to an even number of tens etc. of these units of dis-
tance.
•The following relations are constantly used and should be
familiar to every one:
1 mile=63360 inohes=5280 feet=1760 yards.
_, ™ 1 o 1 1 • I. i. 1 -1 In the scale prob-
K. F =Scale 1 inch to 1 nule. , .. - ,.
63360 lems, units of dis-
■, tance on the ground
R. F. — -^--=8cale 3 inches to 1 mile. wiU be indicated by
small CAPITALS,
E. ji =Scale 6 inches to 1 mile, where any confusion
lOSeO may exist.
MiLiTABY Map Reading 9
SCALE PROBLEMS.
Having Given the R. F.
19. Problem 1. Assume R. F. -^ — (a)
21120 ^
To find the value of one inch on the map in miles
on the ground. Solution : If one inch on the map
represents 21120 inches on the ground, then one
inch (on the map) , will represent as many MILES
(on the ground) as one mile (=63360 inches) is
contained in 21120 inches. 21120-=-63360=J, or
one inch^J MILE is the scale of the map, usually
expressed thus: 3 inches=:l MILE.
(b) To construct a graphical scale of yards.
Solution: If one inch=21120 INCHES, then
one inch=21120^36=586.66 YARDS. Now
suppose a scale about 6 inches long is desired. 6
inches=6X 586.66=3519.96 YARDS, so that in
order to get as nearly a six inch scale as possible to
represent even hundreds of YARDS, assume 3500
YARDS to be the total number to be represented
by the scale. The question is then, how many inch-
es are necessary to show 3500 YARDS. Since 1
inch^586.66 YARDS, as many inches are neces-
sary to show 3500 as 586.66 is contained in 3500
YARDS, or 3500-^586.66=5.96 inches. Now lay
off with scale of equal parts A I, figure 1,=5.96
inches (5 inches+48 50ths) and divide it into 7
equal parts by construction shown in figure 1, as fol-
lows: Draw a line A H making any convenient an-
gle with A I and lay off on it 7 equal convenient
lengths, so as to bring H approximately opposite
10 Military Topography foe Mobile Forces
I. Join H and I, and with ruler and triangle draw
the intermediate lines through B, C, D, etc., paral-
lel to H I. These lines divide A I into 7 parts
each=500 yards. The left division, called the ex-
tension, is similarly divided into 5 parts each equal
to 100 yards.
Problem 2. R. F. — ^, length of stride 60
10000
inches. Construct a working scale of strides.
Solution: 1 STRIDE=60 INCHES. 1 inch=
10000 INCHES=i^^ STRIDES.
60
Suppose a 3 inch scale is desired. 3 inches^3X
lOOOO^gQQ STRIDES. Construct the scale by
60
dividing up three inches into 5 parts of 100
STRIDES each by the method of figure 1.
Problem 3. A sketcher's horse trots one mile in
8 minutes. Construct a scale of minutes and quar-
ters, R. F. Solution:
21120
8 MINUTES=63360 INCHES.
1 INCH= i ^ j MINUTES.
(63360)
From which 21120 INCHES=(,^^^^^ ^ -J-A
( 63360)
MINUTES=i=2f MINUTES.
Since 1 inch=21120 INCHES,
1 inch=2§ MINUTES.
6 inches=(6X2f) MINUTES=16 MIN-
UTES.
MiLiTABY Map Reading 11
Construct the scale by dividing the 6 inch Une in-
to 16 equal parts for MINUTES, and the left one
of these spaces into 4 equal parts to read quarters
of a minute.
R. F. NOT GIVEN.
Problem 4. An American officer in Germany
secm^es a map showing a scale of 1 centimeter^l
KILOMETER.
Required (a) the R. F. of this map, (100 centi-
meters==l meter; 1000 meters^l kilometer.)
o 1 . • 1 cm .01 m 1 -r» 171
Solution: — ^5^,^=^= ^rir= =R- F.
1 KM 1000 M 100000
(b) How many inches to the MILE in this
scale?
(c) Construct a reading scale of MILES, for
this map.
Problem 5. (Where a map has a graphical
scale on which the divisions are not in even parts of
inches and are marked in ground distances of some
unf amihar unit as kilometers, meters, chains, etc. It
is required to construct a graphical scale in familiar
units) . By measurement on the scale of a German
map, 1.08 inches reads 1 KM. (a) What is the
R. F. of the map? (b) Construct a graphical scale
to read YARDS. Solution 1.08 inches=l K=
1000 METERS (1 m=39.37 in.). 1.08 inches=
39370 INCHES or 1 inch=36453 INCHES, or
R. F.= ; whence construct graphical scale
36458
as in Problem 1 (b).
12 Military Topogeaphy fok Mobile Forces
Problem 6. (Where a map has no scale at aU.
In this case measure the distance between two defin-
ite points on the ground represented, by pacing or
otherwise, and scale off the corresponding map dis-
tance. From this find the R. F. and construct the
graphical scale as above). For example, suppose
the distance between two road crossings, identified
on map and ground, is found to be 500 PACES
(31 inches each), and on the map to be f inch. In
this case I inch=( 500X31) INCHES.
1 inch= ^^^ '^ ^^ =20666.66 INCHES; R. F.=
20666.66
From this R. F. a scale of yards is constructed
as in Problem 1 (b) .
CHANGING THE SCALE OE THE AREA OF MAPS.
Note the difference between increasing or de-
creasing the scale {linear dimensions) of a map,
and its size (area). To double the size of a map
whose sides are six inches and 4 inches (6X4^24
square inches), the reproduction would be 48 sq.
inches that is 6 V 2 by 4 \/ 2 on the sides. To re-
duce a 9 inch by 6 inch map to J its size (area) , the
sides would be — -- and ——. X
V3 V3 V3 \/3
54
-^ =18^^ of 54. The general rule is that to
change the area of a map any multiple, as 2 times,
3 times, J times, J times, its original area, each of
MiLiTABY Map Reading 13
the linear dimensions is mviltiplied by the square
root of the multiple as yj~2, V^ — — . — etc
Problem 7. A map, R. F. , is enlarged so
^ 6000 ®
that the distance on the map between two towns A
and B is 3 times as great as on the original. What
is the new R. F.? Answer. R. F. ^ , (R. F.
2000 ^
multiphedby 3).
Problem 8. A map has R. F. . (a)
8000 ^ '
What is the scale of this map in inches per MILE
if its linear dimensions are decreased one-fifth in
reproduction? (b) The original area of the map
was 8 by 16 inches. What is the new R. F., if its
area is four times as large as that of the original?
Solution to (b) : ^ X \f~i= ^ X 2=
^ ' 8000 ^ 8000
^ =R. F.
4000
CORRECTION OF ERRONEOUS SCALES.
It sometimes happens that in making a map an
error exists in the length of the unit of measure
that is not discovered xintil later. The question is
then (1) how to find the true scale of the map as
made, and (2) how to correct the working scale so
it will be true for the future work.
Problem 9. An ofiicer is ordered to make a posi-
tion sketch, scale 6 inches=l MILE. He uses a
working scale of 62 inch strides. Afterwards he
finds that his stride is actually 58 inches.
14 Military Topography for Mobile Forces
Required: (a) What is the R. F. of the sketch
actually made, and (b) is the scale larger or small-
er than ordered?
Solution: (a) R. F. assumed Since
^ ' 10560
his stride was shorter than assumed, in plotting any
given distance on the sketch (as 1 inch), he had
actually passed over a shorter distance on the
ground than he thought. Consequently his true
R. F. would have a smaller denominator in the pro-
portion of the true and assumed rates, 58 to 62.
105601 X :^ =9878.70 INCHES.
62
The true R. F. of sketch was I
9878.70
(b) The R. F. ^g g is larger than R. F.
having a smaller denominator, and therefore
10560
the scale of the sketch as made is too large.
Problem 10. A mounted sketch is made on the
scale of 3 inches=l MILE, with a horse rated at
5.5 MINUTE S=l MILE. The true rate of the
horse is 1 MILE in 6 MINUTES.
Required : The true R. F. of the sketch.
Solution: Since the horse took longer to pass
over a mile, than was thought, he traveled slower
than he was rated. There was accordingly too short
a distance covered at the end of any given number
of minutes. Hence the distance on the groimd
corresponding to any plotted map space, say one
MiLiTABY Map Reading 15
inch, was less than supposed, or the denominator of
the R. F. is really less than 21120, in the propor-
tion of the two rates: 21120 X —=19360. The
6
true R. F. is ^— . See Rule p. 232.
19360 ^
Problem 11. A sketcher is ordered to make a
sketch on the scale R. F. He supposes he
21120 ^^
takes a 29 inch pace and uses this for his working
scale. Afterwards he finds that a distance of 4000
yards scaled from his sketch measures on the ground
4125 yards.
Required (a) His true length of pace.
(b) The true R. F. of the sketch as made.
iS ^4965=n\imber of paces taken in
29 ^
traveling the distance, whether he assumed the cor-
rect length of pace or not. But in-as-much as the
corresponding distance on the ground measured
4125 yards, therefore dividing this distance by the
number of paces taken in passing over it, gives the
true length of each pace : — =29.9 inch-
4965
es=actual length of pace.
(b) If the distance of 4000 yards scaled from
the sketch actually measured 4125 yards on the
ground, the sketch is smaller than intended and
■1
the R. F. is too large and must be decreased
21120
in the proportion of these two distances, i. e. its
16 MiiiiTAEY Topography for Mobile Forces
denominator must be increased. See par. 15. There-
„ 1 w 4000 1 X -D -c^
fore, X = ^true R. F.
21120 4125 21780
THE LARGEST SCALE POSSIBLE ON A GIVEN
SHEET.
Problem 12. A sheet of drawing paper 28 inch-
es by 21 inches is to contain a map of an area of
ground ten miles by seven miles and leave a border
of at least Ij inches.
Required: The largest scale that can be used.
Solution: Taking out the border of Ij inches
on every side leaves 25X18 inches available. The
largest possible scale will be determined by finding
the R. F. of a map that would require 25 inches
to show 10 MILES, and one that would require 18
inches to show 7 miles and using the smaller of the
two. 25 inches=10 MI.=63360 X 10=633600
INCHES.
1 inch = ^^?^ = 25344 INCHES. R. F.
25
is the scale of a map that wiU exactly fit the
25344 ^ ^
length.
18 inches=7 MI.=63360X 7=443520 INCH-
ES.
1 inch=24640 INCHES. R. F. ^ is the
24640
largest scale that can be used on the width.
The map that just will go on the 25 inch length
will cover less than the 18 inch width and therefore
Melitaey Map Reading 17
•^' ^- K^WTJ ^^ *h^ greatest scale that can be used.
The map on any larger scale, as for instance
— — — - , would not go on the length of 25 inches.
24640
GENERAL SCALE PROBLEMS.
Problem 18. Construct a working scale of paces
for a map on the scale of 12 inches=l MILE, one
hundred and twenty paces being equal 100 yards.
14. A reduction of the General Staif map of
France is pubhshed on a scale of R. F.
^ 200000-
(a) Construct a graphical scale to show 15 miles
on this map. 4.752 inches = 15 Mi.
(b) Construct a graphical scale to show 15 kilo-
meters (1 meter=39.37 inches, 1 kilometer=1000
meters) . 2.75 miles ^ 7.5 c. m. = 15 K. M.
15. The R. F. of a map size 10 x 12 inches is
1
62500 '
(a) What is the scale of this map when reduced
1
to one-fourth its present size?
^ 125000
(b) Suppose that the length of the map be-
comes 9.5 inches in a photographic reproduction.
Is the map enlarged or reduced? What is its R. F. ?
16. What is the R. F. of the Leavenworth Map
herewith? How many inches on it equal one mile?
17. A map was drawn on the scale R. F.
^ 10000'
but in reproduction its dimensions were changed so
18 MlLITAEY TOPOGBAPHY FOB, MOBILE FOBCES
that 800 yards on the ground scales 875 yards on
the map.
Required: (a) Construct a reading scale to
give correct distances from this map. (b) What
is the correct R. F.? 1 -=- 9143.
18. Draw a suitable scale of yards for a map
10 by 12 inches to show an area of 5 by 6 nules.
19. The R. F. of a map is lH-10000.
Required: (a) the distance in miles shown by
one inch on the map. (b) Construct a graphical
scale of yards; also one to read miles (problem lb).
20. The map from which figure 16 was reduced
has a graphical scale on which 1.56 inch=one kilo-
meter. Reqmred (a) the R. F. of the original
map. (b) Number miles represented by one inch.
(c) Graphical scale to read hundreds of yards;
one to read miles.
21. A map has marked on it R. F. 1-4-62500.
Required: (a) graphical scale to read miles, halves
and quarters, (b) What is the value in yards of
one inch on the map? 1 inch = 1736.1 Yds.
22. You are in hostile country and secure a map
of the locahty without a scale. 20 inches on the
map is the distance apart of the 20th and 21st de-
grees of latitude. Required: (a) a graphical scale
of yards, (b) The R. F. of the map. (1° lati-
tude=68.8 miles) .
23. What is the R. F. of map, figure 20 A?
SCALING DISTANCES FROM A MAP.
20. Having considered the scale relation and
the construction of scales, it is well to mention the
use of scales in taking distances from a map.
MiLiTAKY Map Reading 19
1st. Apply a piece of straight edged paper to
the distance between two points to be measured
and mark the distance on the paper. Now apply
the paper to the graphical scale as shown in figure
2, and read the number of yards on the main scale
adding the nimiber on the extension, with a total of
600+75=675 yards.
2d. Take the distance A B, figure 2, off with
a pair of dividers figure 104 and applying the di-
viders, thus set, on the graphical scale read off 675
yards.
3d. Use an instrument called a map measurer,*
figure 3. Setting the hand on its face to read zero,
roll the small wheel from A to B. Now roll the
wheel back to zero in an opposite direction along
the graphical scale, noting the nimiber of yards
passed over on the scale. Or, having rolled from
A to B, note the number of inches on the dial and
multiply this by the ntunber of miles per inch given
on the map. A map measurer is especially valua-
ble for use in map problems and war games.
4th. Apply scale of inches to the hne and mul-
tiply the nimiber of inches between the points by
the nimaber of miles per inch given on the map.
5th. Copy off the graphical scale on the edge
of a piece of paper, and then apply this directly to
the map.
If the line to be measured changes direction, the
same methods are used.
By the 1st Method. Each portion in succession
is taken off on the straight-edge paper.
•For sale by Keuffel * Esser Co., New York. Price $2.00.
20 Military Topography for Mobile Forces
By the 2d Method: The dividers are first ap-
plied to B a (figure 4), then the leg at B is placed
at B' in the extension of h a; now the leg at a is
placed at h, making h B'=& a + « B. Now rotate
the leg from B' to B" in prolongation of h c. Move
leg at b to c. The total distance is now included in
the spread of the legs and the dividers are applied
to the scale. By the Sd Method: The map measvir-
er is rolled from B to a^ a to b^ b to c (figure 4),
causing the small wheel always to rotate in the same
direction. By the 4 | irae J\/'or-iA
Fig. 12
'a^.J\r.
true, South
Fiql3
Fig. 10
M.D.
Directions on Maps 39
Having constructed the magnetic meridian on the
map, orient it as imder the 1st method.
If the magnetic decUnation at the locality is not
more than 4 or 5 degrees, the orientation will be
given closely enough for map reading pvirposes by
taking the true and magnetic meridians to be iden-
tical.
2nd Method. When neither the magnetic nor
the true meridian is on the map: (a) If you can
locate on the map your position on the ground, and
can identify another place on the map which you
can see on the ground, join these two points on the
map by a line and hold the map so that this line
points toward the distant point seen on the ground,
whereupon the map is oriented, (b) If you can
place yourself on the line of any two points visible
on the ground and plotted on the map, rotate the
map until the line joining the two points on the
map points toward the two points on the ground,
whereupon the map is oriented. (To place yourself
in Hne with two points, when you are between them
see par. 113.)
TO LOCATE ONE'S POSITION ON A MAP.
36. (1) When the map is oriented by com-
pass, (a) Sight along a ruler at an object on the
ground while keeping the ruler on the plotted posi-
tion of this object on the map, and draw a line to-
ward your body. Do the same with respect to a
second point visible on the ground and plotted on
the map. The intersection of these two points is
your map position.
40 Military Topogeaphy for Mobile Forces
(2) When the map is oriented by the 2nd meth-
od (b). Sight at some object not in the line used
for orientation, keeping the ruler on the plotted
position of this object and draw a line until it cuts
the direction hne used for orienting the map. This
is your position on the map. Any straight line on
the map such as fence, road, etc., is useful for ori-
enting and thus finding your position. Usually
your position may be found by characteristic land-
marks, as cross roads, a crossing of railroad and
highway, a juncture of streams, etc.
37. Having learned to orient a map and to find
your position on it, you should secure a map of
your vicinity and practice moving along roads at
the same time keeping the map constantly oriented
and noting exact features on the map as they are
passed on the groimd. This practice is of the great-
est value in learning to read a map accurately; to
estimate distances, directions and slopes correctly.
The scale must be constantly kept in mind during
this work, to assist in identifying your position at
all times. Check oflf on the map the prominent
points passed, such as bridges, cross roads, hill tops,
villages etc., and be sure that you identify correctly
all objects of the terrain in your vicinity. You will
find it difiicult at first to constantly judge your
position correctly, and from time to time will "lose
yourself." When this occurs try to pick up your
position again by careful observation of landmarks,
assisted by an estimate of the map distance you
should have traveled, at your present rate, from
some point passed at a known hour.
DiEECTIONS ON MaPS 41
TRUE MERIDIAN.
38. The approximate position of the true merid-
ian may be found as follows : Point the hoxir hand
of a watch toward the smi; the line drawn from
the pivot to the point midway between the outer
end of the hour hand and XII on the dial will point
toward the south, figure 13. To point the hour hand
exactly at the sun, stick a pin, or hold up a finger,
as shown, figure 13, and bring the hour hand into
the shadow. At night a line drawn toward the
north star from the observer's position is approxi-
mately a true meridian; to pick out the north star,
see figure 37, p. 74.
CONVENTIONAL SIGNS.
39. Having learned the means used to repre-
sent horizontal distances, elevations, and directions
on a map, it is next in order to study the method of
representing the military features of cover, obsta-
cles, communications and supply. They include
various kinds of growths, water areas, and the works
of man. These features are represented by Con-
ventional Signs, in which an effort is usually made
to imitate the general appearance of the objects
as seen from a high point directly overhead. On
account of this similarity of the object to its repre-
sentation, the student will usually have no trouble
in deciding at once the meaning of a new symbol.
There is a constant tendency toward simplicity in
the character of conventional signs, and very often
simply the outline of an object, such as forests, cul-
tivated ground, etc., is indicated with the name of
Fiq.18
Trees
oooooooooo
ooo oooopoo
O O O Orchard q q
OOOOOOOOOO
Palms ^
f
i.l. -1' ^/
Bamboo * ^
Cultivated
■^ f
TTTTT
Vineyard }
) < r ' 1 t
O O O O'O Q.a-0 .3 .
■0.O -^ L^orror/^ g ^
ooooooaooa
Railroads
Single Tr-och
Double Tfoch
Eiectnc
■\ \ \ \ \ \ >• — *■
I I I I I I 4=t:
Roads
Improved
Unimproved
Trail
t+ + f +
CemetBty.
t n ^ t ^
Church
Postoffice
WaferworMs
Hedge
Stone
Worrn
Wire barbed
Wire smooi-h
Fences
i«^(3n4<»f|»«lt«'MBUM>3'
-M M X X—
Streams
Und^ IS' wide
rordable
Unfordable
Infantry
Cavalry
Artillery
Sentry
Vidette
Hospital
Trencti
Camp
<|m|>
6
Obstacles
Abattis 'if M4' V
W/re Erttanglem't
Depression f C«»' J
c///r5
••^iiUIUlilillUililpllJ^
Directions on Maps 43
the growth printed within the outline. Such means
are especially frequent in rapid sketches, on account
of the saving of time thereby secured, see figures
144 and 145, pps. 259 and 260.
By referring to the map of Fort Leavenworth
submitted herewith the meaning of most of its
symbols are at once evident from the names printed
thereon; for example, that of a city, woods, roads,
streams, etc. Where no conventional sign is used
on any area, it is to be understood that growths
thereon are not high enough to furnish any cover.
As an exercise, pick out from the map the follow-
ing details: Unimproved road, cemetery, railroad
track, hedge, wire fence, orchard, streams, lake.
The numbers at the various road crossings have no
equivalent on the ground, but are placed on the map
to facilitate descriptions of routes or positions (as
in the issue of orders) . Often the numbers at road
crossings on maps denote the elevations of those
points.
40. Figure 18 shows the conventional signs pre-
scribed by the War Department for surveys; and
figures 144 and 145, pps. 259 and 260, those for
rapid sketches.
The conventional signs in figure 19 are those
used in German maps and are generally very sim-
ilar to those used in the United States. Every of-
ficer should be familiar with them to properly use
the German War Game and Tactical Problem
maps.
In the following table are the English equiva-
44 Military Topography for Mobile Forces
lents for words and abbreviations found on German
maps.
WEGE— ROADS.
Saumpfad — Bridlepath (in Gebesserter — ^Weg — Improved
mountains).
Fusstveg — Path, Footpath.
Feld & Waldweg — Field and
forest road.
Gen. VerhindungsTveg — Gener-
al connecting road.
road.
Gebauter Weg — Constructed
road.
Chaussee — Highroad (macad-
am).
Daemme — Dams.
EISENBAHNEN— RAILROADS.
Eisenbahn — Railroad. Strassenbahn — Street railroad.
GEWAESSER— STREAMS, Water.
Schilf — Reeds.
Bake — Beacon, buoy.
Tonne oder Boje — cask or bar-
rel used for buoy.
Strauchbesen — ^broom corn.
Duene — sand dune.
Nasse Graeben — wet (damp)
ditch.
Strom — Stream.
Bootshafen — Boat-landing
Eisenbahnbruecke — Railroad
Bridge.
Kanal — Canal.
Schleusse — Canal lock.
Trockener Graben — Dry ditch.
Muehle — Mill.
Wehr — ^Weir, Dam.
Steinerne Bruecke — Stone
bridge.
Hoelzerne Bruecke — ^Wooden
bridge.
Furt — Ford.
Fluss — Stream, creek, river.
Bach — creek.
Steg — Narrow foot bridge.
Bruecke mit Steinpfeilern —
Bridge with stone piers.
Bruecke mit Holzpfeilem —
Bridge with wooden piers.
Shiffsbruecke — Pontoon bridge
Wagenfaehre — Wagon ford,
(or ferry for vehicles).
Kahnfaehre — Ferry (for foot
passengers).
Fliegende Faehre — Flying fer-
ry.
Leuchtturm — Lighthouse.
Buhne — Pier (landing stage).
GELAENDE BEDECKUNGEN— FEATURES OF THE
TERRAIN.
Laubholz — trees with leaves.
Nadelhols — trees with needles.
Gemischtes Hole — trees of
both kinds (mixed woods).
Trockene TViese — Dry Mead-
ow.
Nasse Wiese — ^Wet Meadow.
Einselne Baeume — Single
trees.
Bruch, Sumpf — Swamp.
Waldboden — Woods.
Heide — Prairie.
DiBECTIONS ON MaPS
45
Stadt — City.
Flecken — Town.
Dorf — Village.
Gut — Manor, farm.
Vortverh — detached farm.
Gehoeft — Farm.
Schloss und Parkanlaege —
Chateau and park.
Weinberg — Vineyard.
Baumschule — Nursery.
Hopfengarten — Hop Orchard.
Kirche, Kapelle, Kp. — Church,
Chapel, Ch.
Forsthaus — Forester's lodge.
Windmuehle — Windmill.
Wassermuehle — Watermill.
Mauer — Wall (stone).
Knich — part wall, part fence.
Zaun — Fence.
Kirchhof — Churchyard, Ceme-
tery.
Kirchhof fuer Juden — Jewish
Cemetery.
Ausgezeirhn Baum — Lone
Tree.
Warte, Thurm — Town.
Bergwerhsbetr — Mine.
Rune — Ruin.
Denkmal — Memorial (statue or
anything else).
Steinbruch, Stbr. — Quarry.
Grube — Pit, hole.
Felsen — Rock.
Alte Schanse — Old (abandon-
ed) trench (rifle pit).
Trignometrischer Hoehenpunkt
— Triangulation Station.
Reichs — und Landes Grense —
Kingdom and state frontier.
Regier — Bezirk Grenze —
Frontier of governmental
districts.
Kreis — Grenze — District fron-
tier.
FlQ-lS C«la3idjeledeciim|e
"We^e r 1U-1>^ t«la3i(lebeaecJam|en.,
Lamm.
JJbTdroeg
FusSTveg
. Gm. PerHndicngsiBeg ^akenT^a^
. Geb'essertiT Weff /yr^^yy^:^^^^yx^
trchaicterWe//
i^ OuLULSsee
DoTnme
ITaite D%se
GebiiscJ),
Eisenbalinen.
fsc-^^
Miseniain,
STADT necken
. StrtuseniaJut'
(jewasser
tSbvwAJbesetv
SchUfj,
darf
Gekoft
''-iKahn/ahrB
SSdossmid J^Wir^r. -.
t ♦ JGrc/te . KapeUe. Xp.
V Jbrsthaus
* WindmiikU
« WasseTTntiXZe
^ mrajiof
^ Frief^TioffurJudoh
*X IBergioerksbetr
i- Jiicuta. xDaikmal
€3 Stbr. Stein2}T%Ldv
ReichswidMmdesCrenze <^ ^hnOte
.•Bez.Grenxe '=*^ Fdseri.
O JIuSAanae.
CHAPTER IV.
VISIBILITY.
41. The problem of visibility is based on the
relations of contours and map distances previously
discussed, and includes such matters as the deter-
mination of whether a point can or cannot be seen
from another; whether a certain line of march is
concealed from the enemy; whether a particular
area can be seen from a given point ; whether slopes
are convex, concave or uniform.
On account of the inherent inaccuracy of aU
maps it is impossible to determine exactly how much
ground is visible from any gtven point over a given
obstructing area; that is, if a correct interpretation
of the map shows a given point to be just barely
visible, then it would be unsafe to say positively
that on the ground this point could be seen or could
not be seen. It is, however, of great importance for
the student to be able to determine whether such
and such a point isn^isible or not, within about one
contour interval; or whether a given road is gen-
erally visible to a certain scout, etc. In the solu-
tion of visibility problems, it is essential to thor-
oughly understand the meaning of profiles and their
construction, consequently these matters will be ex-
plained here.
4^. A Profile is the line cut from the surface
of the earth by an imaginary vertical plane. The
47
48 MiLiTAEY Topography for Mobile Forces
projection of this line to scale on a vertical plane
is also called a profile. Figure 20 B shows a pro-
file on the line Ti a f, figure 20 A, in which the
horizontal scale is the same as that of the map,
and the vertical scale is 1 inch = 40 feet. It is
customary to draw a profile with a greater vertical
than horizontal scale, in order that the slope of hills
on the profile may appear more clearly to the eye
for purposes of comparison. Always note especial-
ly the vertical scale in examining any profile; the
horizontal scale is usually that of the map from
which the profile is taken.
A profile is constructed as follows, Plate 8:
Draw a line D' y' equal in length to D ^ on the
map.* Lay oif on this line from D' distances equal
to the horizontal distances of the successive contoiu-s
from D toward y on the map. At each of these
contour points drop a perpendicular down to the
elevation of this particular contour, as shown by
the vertical scale on the left. For example, a is on
the contour 870 and the perpendicular is dropped
down to a" (870). Join successively the ends of
these verticals by a smooth curve, which is the re-
quired profile of the ground on the line D y. Pro-
file or cross section paper, figure 103, simplifies
the work of construction, but ordinary paper may
be used.
43. Examining the profile, and drawing from
•The line D'y' may be assumed to have an elevation as great
as the highest point, or as low as the lowest point in the profile,
so that the profile will be entirely helow or entirely above this line
of reference.
sso
9*0
920
900.
860.
860
&iO-
8Z0
ao 1
Cav. arte/ FA. —Trof- —Z20yc/s psftniM.
r
Ca V. anci FA. Wa/k anc/ Trot /^ 7ye/s.^erm/n
1— I ^
M»/' Afe^se^yer 6a//op 440yc/s.t>er mirt.
r =
Road Spaces
Conipany 4-0 yds
Bci,itaJion wifh Combaf irait7 -ZIO yds .
Troop- SOyiJs.
SauaJroM ivii/? Comha/ /ra/fr- 4 ZOyals.
Lijhf Bfry(//'r/'rJj) /QOyds.
E
LiqhfBi^fy. at^cL Cofnbaf- train- 320 yds.
B/ry.cofffp/e^e./fe/, . 012 3456189 10
Cb) ., > I I . I I T I I II IVE RNIIER
T
I I I I I I II IVE RNIIER
111 .xl .II.0L1J.1 muMB
(1) The least reading of the vernier {L. R.
F'.)^the value of a smallest space on the Limb
{L. R. L.), divided by the number of the smallest
spaces actually shown on the vernier (n) ; that is, L.
n
(2) The two spaces of a direct vernier on each
side of coincidence, figure 32 (c), lie entirely inside
the corresponding spaces of the limb, and of a retro-
grade vernier, figure 33 (c), extend beyond the two
corresponding spaces of the limb. (By a corres-
ponding t space of the limb is meant one, two, or
*For a double vernier n ^iz one-half the total number of spaces
shown on vernier.
fSee fig. 33d, which is part of a direct vernier with every alter-
nate division line omitted.
68 Military Topography foe Mobile Forces
more of the smallest spaces of the limb which most
nearly equal one smallest space of the vernier) .
(3) The total number of smallest spaces (n)
of a direct vernier cover n — 1 corresponding spaces
of the limb; the (n) spaces of a retrograde vernier
cover n-{-l corresponding spaces of ike limb.
(4) To read a scale with direct vernier: Read
from the zero of the limb up to the division line im-
FiR. 84
Fig. 35
mediately preceding the index of the vernier, then
read in the same direction on the vernier from its
zero up to the coincidence. The same rule apphes
where the vernier is retrograde, except that the ver-
nier is read in an opposite direction from that in
which the limb is read.
59. Figure 34 shows the direct vernier of the
horizontal plate of a transit, of which the least read-
MiLiTAEY Topographical Surveying 69
ing of the limb is one-half degree and of the vernier
is one minute. 30 spaces of the vernier cover 29
spaces of the limb, and the vernier is direct. This
is called a Double Vernier, because it has two coin-
cidences and gives two sets of readings, one corres-
ponding to the outer graduation on the left half
and the other to the inner graduation on the right
half of the vernier. The scale reads 27° — 00'+
25'=27° 25' from left to right, and 1.52° 80'+05=
152° 35' from right to left.
60. Figure 35, is the scale on the vertical arc of
a transit, reading to single minutes. On account of
the small space available for the vernier beside the
transit standard, a Folded Vernier is used. This re-
quires only half as much space as a double vernier
giving the same reading. It is read in either direc-
tion depending on its position, from the index (ar-
row head) to 15, and then from 15 on the opposite
end, forward in the same direction to 30. The read-
ing in the figure is 7° 50' from right to left, (see
arrow) A folded vernier has but one coincidence;
a double vernier has two.
All the scales upon engineering instruments with
few exceptions have direct verniers. Barometers
have indirect verniers, because the mercury column
rises as the air pressure falls.
PROBLEMS.
61. 1. The least reading of the limb of an an-
gle measuring instrument is 1 minute. Its vernier
has 6 spaces covering 5 spaces of the limb.
(a) Is this a direct or retrograde vernier?
70 Military Topography for Mobile Forces
(b) What is the least reading of the vernier?
(a) Direct. (See rule 3, par. 58.)
(b) L- R- L- =jg^=io//. The least reading
n 6
of the vernier is 10 seconds.
2. Construct a vernier to read one hundredths
on a limb whose least reading is one twentieth of a
foot.
1_
Solution: — '- — '- — '-= — =— -— =L. R. V.
n n 20n
Hence = and ?i=5. For a di-
100 2Qn 100
rect vernier 4 spaces on the limb are to be equalled
bj' 5 spaces on the vernier; for a retrograde, 6
spaces of the limb are covered by 5 of the vernier.
To divide the line of given length into 5 or 6 equal
parts, foUow method of par. 19, problem (b).
In case each alternate or each third etc. division
line of the vernier is omitted, so that one space on
the vernier corresponds to two, three or more small-
est spaces on the hmb the effect is to increase the L.
R. V. twice, three times etc., and 1, 2, and 4 rules
above still remain true. For instance, figure 31, if
each alternate vernier division line were removed
the least reading would be twice its present least
reading (that is .002), as seen from figm-e 33d
and from the formula — '- — '- — ' =L. R. V. In
n
other words instead of the small space "a", there
would be a small space "2a" at the new 1st division
line of the vernier to the left of the index, and n
spaces of the vernier equal 2n — 1 spaces of the limb.
Military Topographical Surveying 71
3. Ten smallest spaces on a vernier cover 19
spaces of the limb. The least reading of the limb
is 1 foot. What is the L. R. V., and is the vernier
J T> T
direct or retrograde? Solution: ^ — =L R V
n
== ^.1 foot. It is a direct vernier because
one space on the vernier is smaller than the corres-
ponding spaces (two) of the limb.
4. Construct a double retrograde vernier to read
5 seconds on a limb whose least reading is 1 minute.
5. Construct a folded vernier to read 30 seconds
on a limb reading to single degrees. See figure 35.
ANGULAR MEASUREMENTS.
1. HORIZONTAL ANGLES.
62. In all measurements a known point is neces-
sary, with the position of which the locations of
other objects are compared. This necessity has led
to the use from the earliest times, of the position of
the magnetic needle as the reference (or starting)
line of all horizontal angular measm-ements, be-
cause it is the only object known to man which
maintains its position with respect to horizontal an-
gular motion. The Magnetic Needle points to the
magnetic pole of the earth. The vertical plane in
which lies the magnetic needle is called the Magnet-
ic Meridian. The vertical plane containing the true
north and south line at any point on the earth is
called the True Meridian. The angle, measured
at the north point, which the magnetic meridian
makes with the true meridian at any place on the
72 Military Topogbaphy for Mobile Forces
earth is the Magnetic Declination. Although the
magnetic needle is more nearly fixed in position
with respect to angles in the horizontal plane than
any other object; yet at any point on the earth it
varies from year to year in what is known as secu-
lar variation, so called because the change contin-
ues through a series or cycle of years. The declina-
tion also varies through an arc of about 8 minutes
from day to day in what is known as diurnal
(daily) variation. At 10:30 a. m. the needle has its
true variation for the day. The declination of the
needle is often increased or diminished by the pres-
ence of iron, steel, electric currents etc. The vari-
ation of the direction of the needle from these caus-
es is said to be due to "Local Attraction."
There is an imaginary line on the earth's sur-
face, joining all points at which the magnetic decli-
nation is zero. This line is called the Agonic Line,
that is the needle at any point in this line is with-
out magnetic declination. At points on the earth
to the east of the Agonic Line the magnetic decli-
nation is west and at points west of the agonic
line the magnetic declination is east. The agonic
line in the United States at the present time extends
from South Carolina through Michigan.
Since the true meridian at any point on the earth
is definitely fixed and is forever unchanged in posi-
tion, it is desirable to have measurements made from
it instead of from the constantly varying magnetic
meridian. In order to accomplish this result the
magnetic declination should be known at the place
Melitaby Topographical Surveying 73
and time of the survey. This is found by locating
on the ground the position of the true meridian and
the angle made with this line by the magnetic need-
le is the magnetic declination.
TO LOCATE THE TRUE AND MAGNETIC
MERIDIANS.
63. 1st Method; from the sun. — Prick a small
hole in a piece of tin or opaque paper and fix over
the south edge of a table or other perfectly level sur-
face, so that the simlight coming through the hole
will f aU on a convenient place on the surface, fig-
ure 36. The hole may be two feet above the table
for long days and 18 in. for short ones. Half an
hour before, to half an hour after noon, mark the
position of the spot of sunlight on the horizontal
surface at equal time intervals of about 10 min.
Draw a curve as hd^ figure 36, through the points
marked, and from a point c in the horizontal sur-
face and in a vertical line with the hole a sweep an
arc ef intersecting hd in two points. The line eg
drawn from c through a point on the arc midway
between the intersections, is the true meridian. The
74 MiLiTABY Topography for Mobile Forces
line bd illustrates the method merely. Its form
varies with the sun's declination. (Engineer Field
Manual. )
64. Snd Method; Observe the magnetic azimuth,
see par. 69 of the sun (or a bright star) at rising
and setting on the same day, or one night and the
following morning. Subtract the eastern azimuth
from the western (both measured from the north
around through the east). Adding ^ of this dif-
ference to the eastern azimuth gives the magnetic
azimuth of the true south point, figxu-e 38. The
two observations should be taken at the same gra-
dient and both at zero gradient if possible. See fig-
ure 38, angle 5^ '- wangle ^ =yos. Angle
^^— +a^ =magnetic azimuth of the true south.
( 2 )
Having found the magnetic azimuth of the true
south, the diiFerence between this and 180° is the
magnetic declination. This method will give the
true meridian within 15'.
MiLiTABY Topographical Sueveying 75
3rd Method; from Polaris. — The true north pole
is about 1° 12' distant from Polaris on a line join-
ing that star with one (Zeta) in the handle of the
dipper, and another (Delta) in Cassiopeia's Chair,
figure 37. One of these stars can be seen whenever
Polaris is visible. The polar distance of Polaris is
decreasing at the rate of 19" a year. It also varies
during the year by as much as 1'. The latter varia-
tion may be neglected and the former for a series
'0/3
-TO
..^
SO*
s
Fig. 38
of years. Imagine Polaris to be the center of the
clock dial, of which the line joining 12 and 6 o'clock
is vertical. Let the position of the line from Polaris
to either of the two stars mentioned be considered as
the hour hand of the clock. The distance in azimuth
of Polaris (see par. 69) from the true north may
be taken from the following table:
65. Table showing the azimuths of Polaris in
diiferent positions with respect to the pole. Epoch
1911 ; polar distance 70'. Latitude 0° to 18° north.
This table may be used vmtil 1930.
76 Military Topography foe Mobile Forces
Clock reading of —
Azi-
muth
of
Polar-
is
Clock reading of —
Azimuth
Clock reading of —
Azimuth
A
Cass.
Z
Ursae
Maj.
A
Cass.
Z
Ursae
Maj.
of
Polaris
A
Cass.
Z
Ursae
Maj.
of
Polaris
XII :30
I
1:30
II
III
nil
VI: 30
VII
VII :30
VIII
IX
X
18
35
49
61
70
61
1111:30
V
V:30
VI:30
VII
VII :30
X:30
XI
XI:30
XII:30
I
1:30
o /
49
35
18
359 42
359 25
359 11
VIII
IX
X
X:30
XI
XI:30
II
III
nil
1111:30
V
V:30
e /
358 59
358 50
358 59
359 11
359 25
359 42
Lat.
31°-
-37
Lat.
38°-
-42
Lat.
43°-
-46
Lat.
47°-
-50
For higher latitudes add to the small azimuths or
subtract from the large ones, as follows :
Lat. 19°— 30°, 1/10 Lat. 51°— 53°, 6/10
2/10 Lat. 56°— 57°, 7/10
3/10 Lat. 58°— 59°, 8/10
4/10 Lat. 60°— 61°, 9/10
5/10 of the true bearing of Pol-
aris.
It is well to keep track of the position of Polaris
by noting it frequently and taking the correspond-
ing clock time. Then if on a cloudy night a glimpse
of Polaris is had, the observation may be taken even
though the other stars cannot be seen.
66. For practical details of the observations, the
following may serve as a guide : Select a clear space
of level ground not too near buildings or any object
which might cause local disturbance of the needle.
Drive a picket, leaving its top smooth and level,
about 18 ins. above the ground. Six feet north of
the picket suspend a plumb hne from a point high
enough so that Polaris, seen from the top of the
picket, wall be near the top of the line, figure 39.
The line should be hard and smooth, and about
1/10 inch diameter. The weight at the bottom of
the line should hang in a vessel of water or in a hole
Military Topogeaphical Surveying 77
dug in the ground to lessen its vibration. Drive a
second picket in range with the first one and the
plumb line, a short distance north of the latter.
Make a peep sight by punching a hole about 1/10
inch diameter in a piece of paper and hold it on the
top of the first picket; adjust it so that the star is
behind the pltimb line when looking through the
peep. Note the position of one of the stars on the
imaginary clock face at the moment the observation
D
^s
''«*>- .
Ficr.39
'g
is taken. Mark the position of the peep on the top
of the first picket, and lay a straight edge or stretch
a line from that point touching the plumb line to
the second picket. Place the north — south edge
of the compass box against the hne or straight edge,
and read the magnetic azimuth. Find the true
azimuth of the star at the time of the observation
from Table par. 65.
Rules:* (1) If the true Azimuth of Polaris
(Table par. 65) and the reading of the needle are
both less or greater than 180° ^ their difference is the
dechnation ; east is the needle reading is less, west if
it is greater. (2) If one of these quantities is less
and the other greater than 180°, add 360° to the
*A figure similar to figure 40 will show the relative positions
of the magnetic meridian, Polaris and the true meridian without the
use of Rules.
78 Military Topography for Mobile Forcks
lesser and take the difference which is the declina-
tion; east if after the addition is made the needle
reading is less, west if it is greater than the tabu-
lated azimuth. This method will give results true
to within J°. (Engineer Field Manual). Having
found the Declination by one of the methods shown
above, it may be set off on the transit or plane ta-
ble compass, so that all the readings of the needle
would be from the true meridian, (see par. 74).
PROBLEMS IN FINDING THE DECLINATION BY
THE THIRD METHOD.
67. Example 1. Clock reading of A Cassiop-
eia, V-30, azimuth of Polaris, (from table par. 65)
18', magnetic azimuth 355 deg.
18'+360°=360°18'. 360° 18'— 355°= 5° 18'.
Compass reading is less than 360 degrees, hence the
declination is 5° 18' east. (Rxile 2).
2. Clock reading of Zeta Ursa Major is II,
Azimuth of Polaris, 358° 59', magnetic azimuth is 3
degrees.
360°+3°— (358°59')=4° 1' Declination west,
because the needle reading plus 360° is greater than
the azimuth of Polaris.
S. Suppose you have located the true meridian
on the ground, and reading its magnetic azimuth
with yotu" compass, find it to be 347° 20'.
What is the magnetic declination?
Answer: 12°40' east. (Show by figure)
Suppose the magnetic bearing of the true merid-
ian is N 4°5'E.
What is the declination? 4° 5' W.
MlLITABY TOPOGRAPHICAIi SURVEYING 79
RETRACING OLD SURVEY LINES.
68. For topographical survey work the compass
which was formerly the miiversal survey instrument
for angle measuring, has been supplanted by the
plane table (see par. 78), and the transit (see par.
71), in both of which the compass is used only to
orient these instruments at the first station of the
survey, that is to refer all measiu-ements to the mag-
netic meridian (or the true meridian if the declina-
tion is set off) at the initial station, and to give
check bearings on all azimuth readings (see par.
74). But an officer may be called upon to re-
survey an area formerly surveyed with the com-
pass; it then becomes necessary to retrace the
boundary lines of the old survey of a reservation
or other area in order to locate the old monu-
ments as the basis of the new survey. For instance,
if it were required to survey the reservation of Fort
Leavenworth, it would be necessary to find the old
monuments marking the boundary corners. To do
this it is necessary to find the present true bearings
of hnes which were surveyed on magnetic bearings
at some former date. All problems arising under
these conditions may be most rapidly solved by
drawing a figure similar to 40 assuming the posi-
tion of the line on the ground and the true meridian,
and determining from these the position of the old
and the new magnetic meridians. Since the line
itself and the true meridian are always in the same
position on the ground, the measurements are to be
made from them to locate the two positions of the
80 Military Topogeaphy foe Mobile Fokces
magnetic meridian and thus show how it has
changed since the old survey.
69. The true azimuth of a line is the horizontal
angle which the line makes with the true meridian,
measuring from the north point clockwise (to the
east) around the circle. For example, the angle
TOL (figure 40)=72°=the true azimuth of the
hne OL,
The magnetic azimuth of a line is the angle which
the hne makes with the magnetic meridian, meas-
F.|.40
Neod I* moving East
F.g.4l^
ured from the magnetic north point clockwise
around the circle. For example, the angle POL'
is the old magnetic azimuth of the line OL'.
The true bearing of a line is the angle less than
90° which the line makes with the true meridian.
For example, the angle TOL=true bearing of line
OL and is read N 72° E. Angle T' OL'=the true
bearing of OL' and is read S 30°E.
The magnetic bearing of a line is the angle less
than 90° which a line makes with the magnetic
Mdlitaiiy Topographical Surveying 81
meridian. For example (figure 40) the angle R'
OL'=the new magnetic bearing of OL', and is read
S 35° E. By an azimuth is usually meant a true
azimuth imless otherwise specified, and by a bear-
ing is meant a magnetic bearing unless otherwise
stated. In the -first quadrant the true hearings and
azimuths are equal.
70. Problem 1. The old magnetic bearing of
a course is N 38° E. The old declination N 12° E.
The new declination is N 5° E. What is the true
azimuth of the course? (See figure 40)
Let the angle LOP=38° ; the angle T0P=12°.
Therefore the angle LOT=50°=the true azimuth
of the line.
Problem 2. What is the new magnetic bearing
of the hne?
The new magnetic bearing of the line:^the an-
gle LOR=50°— 5°=45°.
Problem 3. If the old magnetic bearing was
S 30°E, the old declination N 12°E, the new de-
clination N 5°E. What is the present magnetic
bearing of the line? (see figure 40.)
Measuring from the position of the line OL',
assume the angle L' OP'=30°=the old bearing; T'
OP'=the old declination=12°. Therefore L' OT'
^30 ° — 1 2 ° =1 8 ° =the true bearing of the line. L'
OT'+T' OR'=18°+5°=S 23° E= the new mag-
netic bearing of the line.
Problem A. If a line has an old magnetic bearing
of N 50°E, the new declination is 12°E, the old de-
clination is 8°E, what is the new magnetic bearing
of the line? (Figure 41)
82 Military Topography for Mobile Forces
Measuring from the line OL, assume the angle
LOP=50° ; the angle P0T=8° . Therefore LOT
=LOP+POT=50°+8°= 58°=the true azimuth
of the line OL. LOT— TOR=58°— 12°=N 46°
E^the present magnetic bearing.
If the old declination is not known, it is comput-
ed from tables showing the yearly change of de-
clination.
In case the old declination is not known and
the date of the old survey is not given, but one end
of the course is known, the other end of the course
is found by rimning a trial line with the old mag-
netic bearings and using the present magnetic de-
clination. The monument marking the unknown
end of the course wiU be as far from the known
end as is the point which has been located, and may
be found by searching in the vicinity of this point
just located. When this monument, of the un-
known end of the course, is found the present mag-
netic bearing of the com-se is measured with the
compass and the difference between the old record-
ed magnetic bearing and the new magnetic bearing
of the line is the change in the decHnation from the
date of the old survey to that of the new.
Problem 5. In an old compass survey the bear-
ing of a course was N 40°23'E. The present bear-
ing of the same line is N 41°16'E. What are the
present bearings of courses in the old survey read-
ing (a) N 89°42'E; (b) S 23°12' W?
Solution: The magnetic declination has moved
53' west ( 41 ° 1 6'— 40 ° 23' ) ( a ) This change in de-
chnation must be added to the old bearing: 89° 42'
Military Topogeaphical Surveying 83
+53'^90°35'^the azimuth from the present mag-
netic north. 180°— 90°35'=S 89°25'E=new mag-
netic bearing.
(b) S 23°12'W+53'=S 24°05'W. Since the
magnetic meridian has moved west at the north end,
its south end has moved east, hence the 53' is added.
(Draw a figure similar to 41 to show old and new
positions of magnetic meridian and the positions of
the lines.)
Problem 6. The azimuths of the following
courses are measured from the true meridian.
E A 35°4'; A B 111°19'; B C 201°40'; C D.
258°3'; D E 351 °43'. (a) Give the magnetic
bearing of each course when the dechnation is 8° 17'
east.
Solution: E A, 35°4'— 8°17'=N 26°47' E. A
B, 180°— 111°19' (to reduce to true bearings)=S
68°41'E+(8°17')=S 76°58'E. B C, 201° 40'—
180° (to reduce to true bearings) =S 21°40'W—
(8°17')=S 13°.23'W. C D, 258°3'— 180 "=S 78°
3'W— (8°17')=S 69°46'W. D E, 360— (351°
43') =N 8°17'+(8°17')=N 16°34'W. (A fig-
ure similar to 41 showing the true and magnetic
meridians and the lines AB, CD etc., will indicate
the method of solution.)
Problem 7. You are required to resurvey a res-
ervation, but do not know the present declination.
A line of the survey made in 1902 is recorded S 10°
W. The present magnetic bearing of the same line
is S 4°E.
In which direction has the dechnation been
changing and how much has it changed?
84 MiLiTAKY Topography foe Mobile Foeces
Answer: Thtf deelination has moved east 14°.
Problem 8. The old magnetic bearing of a line
is S 89°W . The true azimuth of this line is 269°
15'. The present magnetic bearing of a second line
is S 63°35'E. The present declination is 5°W.
(a) What is the difference in azimuth between
the two lines?
Answer: 157° 50'.
(b) The old declination?
Answer: 15'E.
CHAPTER II.
THE TRANSIT AND PLANE TABLE.
TRANSIT.
71. The Transit, figure 42, is an angle measur-
ing instrument with which two sets of angles are
measured, one in the horizontal plane, the other in
the vertical plane. The line of the instrument
which determines the direction of any point to be
located, is called the line of collimation. It is the
straight line determined by the optical center of the
object glass (at 0, figure 42) of the telescope, and
the intersection of the cross wires, a figure 44.
Fig. 44
When the intersection of the cross wires falls on
the image of any point, this point is said to be sight-
ed. When the telescope has two additional horizon-
tal cross wires called stadia wires, 6 figure 44, the
instrument measures' distances and differences of
elevation, thus completely determining the position
in space of the point sighted, with respect to the lo-
cation of the transit. The transit is shown and the
85
A Verinier
BBase Plate
CPIate Clamp
D " Tang. Screw
E LImbClamp
F " Tang.Screwj
G Leveling t>
H Adj. Nut, Tel. Level
I Plate Levels
J Standard Adj Screw
K Vert. Limb
L Adj Nut, Vernier
M Gradienter
NVert. Limb-
Clamp
OTelescope
P ■>■> Level
Q Eye Piece
RR Reticle Adj.
Nuts
SNeedleStop
TLevelAd) Nuts
U MovableCeater
V EyePieceFocusing
Screw
W Object Glass
Focusing Scr'e«/
X Needle
YYStandards
Q Z Hor. Axis
Fig. 42
The Tkansit and Plane Table
87
names of its parts indicated in figure 42. These
parts should be learned by using a transit in con-
nection with the figiu-e.
The gradienter screw M allows the measurement
of angles in gradients, see par. 29. The silvered
edge of the head (M) is divided into 100 parts, and
the screw and scale are so made as to give an eleva-
tion of 1 foot to the line of sight at a distance of
100 feet for one complete revolution of the screw.
In addition to the base plate (B, figure 42), the
transit has an upper plate containing the compass
circle X and verniers A. This plate rests and re-
volves freely in a third saucer-shaped plate called
the lower plate which contains a horizontal circle
(limb, figure 47) and is fixed in position by clamp
C when the transit is oriented, for measuring angles
from the meridian (called azimuths) or the angle
between any two lines (difference of azimuths).
Figure 45 shows a horizontal circle with two sets
of graduations. The inner set of the two shown
would be used.
The vertical circle K, figure 42, is for measuring
88 Military Topogeaphy for Mobile Forces
angles of elevation or depression and is usually
graduated in quadrants (up to 90° ) as in figure 46.
The transit has a compass attached to the upper
plate, fig. 47. The compass circle a, is graduated in
quadrants like the vertical circle figure 46, or, pref-
erably, from north around the circle counter clock-
wise (reading at north, 90° at east, 180° at south,
360° at north). This latter style is better because
the needle reading checks that of vernier A with-
out its being first converted to azimuth from bear-
ings. The face of the compass is also marked N,
E, S, W at the positions of the north needle point
when the telescope sights in those directions.
The point at which the azimuth reading on the
horizontal circle is taken is indicated by the index
of vernier A, figure 42; similarly for the vertical
circle at vernier L's index.
72. 1. To set up the transit: Lift the instru-
ment from the box by placing the hands under both
plates, screw it on the tripod with the legs spread
about 3 feet apart, so that when they rest on the
ground the base plate B, see figure 42, will be ap-
proximately level. Attach the plumb bob to the
plummet (hook underneath U). See that the
clamp screws of the tripod legs, are taut enough
to prevent too free a motion of the legs. Lift the
transit and set it over the desired point, (just as
you set down a chair) so that the plumb bob is over
the stake. Force each leg into the earth firmly be-
ing careful to keep the pliimb-bob over the sta-
tion. Release two adjacent leveling screws G figure
42, and slip the entire upper part of the transit
The Transit and Plane Table 89
about the leveling base (base plate) until the plumb
bob is over the exact station, by means of the shift-
ing center, U. The transit is now said to be ''set up."
73. To level the transit: Bring the telescope
over one diagonally opposite pair of leveling screws,
bring the bubbles of both level tubes to the center
by turning in succession the two pairs of leveling
screws, G G, so that both thumbs move towards or
both away from each other. The bubble will move
in the direction in which the left thumb moves. Ro-
tate the ahdade (telescope and upper plate) hori-
zontally until the telescope is directly over the oth-
er pair of leveling screws and relevel if the bub-
bles are not exactly in the center.
"Fig. 41
74. To set off the declination on a transit or
surveyor's compass: Move, with rack and pinion
{c, figure 47) the north zero of the compass circle
toward the declination (actual east if the declina-
tion is east and vice versa) , reading the exact angle
on the decUnation vernier, b. When the declina-
tion has been set off, the readings of azimuth will
be from the true meridian and the bearings will be
true bearings.
90 MiLiTAEY Topography for Mobile Forces
CARE AND HANDLING OF INSTRUMENTS
75. All surveying instruments are of delicate
construction and are very liable to injury if not
handled with the greatest care. They should be
protected from rain with waterproof sheets, and all
dampness should be removed with chamois at the
end of the day's work. No blows or force should be
used to move any of the parts, all of which move
freely if the proper clamp is released. When the
instrument is set up, only the finger tips should he
used to move its parts and no weight should be
placed on it. The observer should avoid stepping
close to the legs of a tripod as this throws the in-
strument out of level.
TRANSIT.
76. Rules for its use and care: The telescope
and the lower clamp, C, should be released tvhen the
instrument is being carried. The needle should be
raised from the pivot up against the glass, except
when in use, by stop d, fig. 47. In putting the in-
strument away indoors the needle should first be
allowed to settle naturally so that its magnetism
will not be reversed, and then be raised off its pivot
to avoid wear.
Never test a needle's activity with knife or other
metal, as this tends to decrease its magnetism.
The object glass and eye piece (Q, figure 42)
lenses should be kept constantly free from dust and
grease with chamois skin or silk cloth.
To wash any part of the instrimient use alcohol
and chamois.
The Transit and Plane Table 91
Before adjusting the instrument make a contin-
uous mark on the object glass ring and its shde so
that the object glass can always be kept screwed
up to this position in future, and that errors due to
lack of luiif orm grinding of the lens may be avoid-
ed.
77. Before commencing to use or adjust the
transit, focus the eye piece (Q, figure 42) by sight-
ing on the sky and turning the focussing screw V*
until the cross wires appear full and black. This
adjustment should be made for each person but
having been made for anyone, need not be changed
again for him. Then for each sight, carefully fo-
cus the object glass with the focussing screw W un-
til the image appears sharp and distinct; now move
the eye slowly up and down in front of the eye
piece always observing the image on the crosswires.
If the image of the object sighted seems to shift on
the crosswires, either the object glass is not focussed
or the eye piece has not been properly adjusted. If
several tests of the object glass do not remove this
shifting of the image, readjust the eye piece and
continue until no matter where the eye is placed in
sighting, the image remains fixed. This shifting is
called ParalkLX and when it exists accurate work is
impossible. For some eyes it wiU be necessary to
focus the eye piece so that the cross wires are not at
their most distinct position, in order to remove the
parallax.
*In some instruments there is no eye-pieee focussing screw and
the eye-piece is focussed by revolving it about the axis of the teles-
cope.
92 MiLiTABY Topography foe Mobile Forces
THE PLANE TABLE
78. The Plane Table is a universal distance and
angle measuring instrument, especially reliable in
military surveying and in its simplest form consists
of a drawing board, figure 48, and ruler, figure 137,
p. 243, along with lines are drawn to points sight-
ed, and then plotted to scale.
A complete Plane Table consists of a drawing
board, mounted on a tripod, with attachments as
shown in figure 49. The alidade is that part of the
instrument which contains the line of sight and in
Fig. 48
the figure consists of a ruler, K, and telescope. A,
connected by a vertical pedestal J. Instead of a
telescope the ahdade may have sighting slits, fig-
ure 48, in which case the distances to points ob-
served must be determined by intersection, par. 156,
resection, par. 155, or chaining. When there is a
telescope it is usually provided with three horizontal
and one vertical cross wires, figure 44, for accurate-
ly sighting any point and for reading distances on
The Transit and Plane Table 93
a stadia rod, figure 67, p. 117. The telescope is sup-
ported by the pedestal, in such a manner as to al-
low a free vertical motion to the telescope about its
horizontal axis, for measuring angles of elevation
or depression but no horizontal motion with respect
to the ruler. The Declinator or Compass Box (P,
figure 49) is used for placing meridians on the sheet
and for orienting the table. The table is arranged
so that it can be leveled and then rotated horizontal-
ly about a vertical axis for bringing it exactly into
a desired position each time it is set up. (N) is the
plumbing arm to which a plumb line is attached at
the plummet (R), for centering any plotted point
over a rod station stake. (LL) are level tubes for
levehng the plane table. (G) is the vertical cir-
cle for measuring angles of elevation. E is the tele-
scope level tube for assistance in using the telescope
as a Wye level. S is one of the levehng screws, for
making the table horizontal.
TO SET UP THE PLANE TABLE:
79. The board is screwed to the levehng head at
the holes made to receive the screws. The tripod
legs are opened out about thirty degrees from the
vertical, so as to give a firm bearing for the table.
The plane table is then set up over the station point,
the legs being adjusted so that the base plate ap-
pears level to the eye. The plane table is then ori-
ented as nearly as possible by eye and the location
of the station point on the paper with respect to the
station on the ground is noted. This being done the
entire plane table is hf ted and moved bodily until
(0
by
W. ft L. E. Uurlcy, Troy, N. V.
r
Fig. 72
too
iboo
Designed by Wm. Cojl
Assume a stadia reading of 397 feet ; vertical an-
gle,+14°10'; c+/=1.00. Set the zero (index) of
the inner circle opposite 397 of the outer circle.
Opposite+14°10' find on the Elev. scale of the out-
er circle 94.00. Add correction for (c+/)=0.25
(found in the small table on the computer, not
shown in the figure) 94.0+. 25=94.25 feet, to be
added to the height of the instnmaent station.
On the Hor. Dist. scale, opposite 14° 10' find
372.0. Add c+f correction .97. 372+.97=372.97
feet total distance horizontally of the rod from the
instrument station.
CHAPTER V. -
THE WYE LEVEL.
124. The Wye Level shown in figure 73 is an
instrument designed for accurately determining
differences of elevation between points on or near
the Earth's surface. The sighting line of the in-
stnmient is determined by the line of collimation
of the telescope^ which is the straight line joining
the optical center (practically the actual center)
of the object glass and the intersection of the cross
wires, a figure 44, p. 85. When the intersection
of the cross wires is exactly on the image of the
point, it is said to be sighted. The essential parts
of the Wye Level are shown in the figure. V is
the tangent screw for giving the instrument small
horizontal motion after it is clamped in position by
clamp W.
THE LEVEL ROD.
125. There are several kinds of level rods made,
but the one most generally used is the New York
Rod, figure 75. It is a target Rod, reading 6.5 feet
on the vernier of the target when folded and from
6.5 to 12 feet on the side vernier when extended.
There is a set screw to clamp the two parts of the
rod together at any height. To read above 6.5 feet
the target is set at 6.5 and the rod extended until it
is bisected by the horizontal cross wire. The rod is
128
«
e
Q.
1
<
o
tJ
^^
Sii,
J
'n
Z2
sx
«
I.
<0
«»
«»
_o
u
1
<- 1-
I. £ »<^
c o +■
« -^ <0
o J;
iS-- .'
/ /
cr>
H-
O
C- 9
•■ft
i.D
V
>
C
>
-i
a:
O t.
O c
i <£>
(0 o
to H
o
CO
a.
S
JS
CO
4-
«
c
CO
^ P s
«t- tn RS
^
M"(®i1
T^EH
r
^B
. . <
5
^^'--"H
o
t-
O -1 <
Ui-~»f
1 'fie.j;
L
■'' ' '[
■■ _ ff^
/
3
>
§ X N
vE., ■
.'•'-??
i =
i| ':
1
^
ik
\
II ']
K
f^
1^
>-
«}
^ «
ll
1
|B|
evelT
gArm
m
E^'f
1 ^ fl
IM-:
'\M
_1 c
Wtik '■' ''
|-;t J
1^1
Ti./^;|i] ■
ffl.f
T''iV'
'C «
■-'i;: i
J
.- t. >
HIH
^^^H
'-.i
;,?»' ;i
a t« 01
Ifr' ,
- ^^^B^^
V
to CQ -1
''Mm
II 5
ir^B/^
^-
\
to
o Q- cy
^V.IU
It 1
'^H *~
^ (t
jiF
f ■ i
(i
B
in
4t
•"^
4
\
n
o
o
o s
4-
(0
<0
c
>
4-
'Z.
-« a
>• to
i^ST
!
W'^' ' ''■
\ _)
L
B b
S: to
3
o
<0
-4- f
3 ■"
2
^
:
w c OJ
5:e
Q.
a.
"0 "^
1
8 -s
- %
4> - -"' -^ 1
«i
•
1- to X
u. (C
Id
-1
UJ
to
_l s z
< CD O
D Hi
L.
O X
-3
ic
J 2 Z
Fig. 78
130 Military Topography for Mobile Forcks
graduated in feet,, tenths and hundredths,
the least reading being .001 foot on the ver-
niers.
For rapid work in which the greatest ac-
curacy is not required a speaking rod gradu-
ated into feet and tenths with designs like
the stadia rod, figure 67, p. 117, may be
used. With a speaking rod, the observer
reads through the telescope the rod at the
point indicated by the horizontal wire.
126. To set up the Wye Level: Remove
the instrument from its box and screw the
base plate below T, figure 73, to the tripod
head; place the telescope carefully in the
wyes. Seciu-e the clips CC; release clamp
W, and the instrument is ready for use.
The level need not be set up over any exact
point in leveling consequently no plumb line
is fiu-nished. Separate the tripod legs about
30 degrees from the vertical and force them
firmly into the ground, until the base plate
appears level to the eye.
127. To Level the Instrument: Revolve
the instrument head (containing the teles-
cope) horizontally until the telescope is ex-
actly over a diagonally opposite pair of
leveling screws R. Rotate these screws with
thumbs and forefingers, moving both
Fig. 75 thimibs either toward or away from each
other, until the bubble stands at the center
of the tube. Repeat with the telescope over the other
The Wye Level 131
pair of leveling screws. The bubble should now re-
main in the center of its tube when the instrument
head is revolved completely around its vertical axis.
If it does not do so relevel as just described. If the
bubble can not by careful leveling be made to re-
main at the center, the instrument is out of adjust-
ment.
128. To Focus the Eye Piece and Object Glass:
Before commencing to use the instnmient, the eye-
piece should be focussed on the cross wires for the
eyes of the observer. To do this, point the tele-
scope at the sky and looking through the eye end
of the telescope at the cross wires, turn the eye piece
focussing screw, G, until the cross wires are most
distinct and black. When this is done for one pair
of eyes the screw G should not be touched agaia
while this person alone continues to use the level.
129. To sight any object as the level rod: Point
the telescope at the rod and looking through the
eye end, turn the object glass focussing screw D,
until the rod appears sharp and distinct. Now
slowly move the eye up and down before the eye
piece, and the image of a particular point of the
rod should remain fixed in position on the intersec-
tion of the cross wires. If it does not, the focus is
not correct; refocus the object glass and retest. If
there is still displacement of the image, refocus the
eye piece and so on until the rod is seen without
the least displacement on the cross wires. This dis-
placement is called parallax and is fatal to accur-
132 Military Topography for Mobile Forces
ate work xinless removed. For some eyes it will be
necessary to adjust the eye piece so that the cross
wires are not exactly at the most distinct position,
in order to remove the parallax.
TEST AND ADJUSTMENT OF THE WYE LEVEL.
130. 1st. Ldne of Collima-
tion (see par. 124) Parallel to
the axis of the Bearing Rings.
Test: Sight some distinct
point as a tack head, A, figure
'® 77, release the clips (holding
the telescope in its rings) and revolve the telescope
180° about its own axis. Direct the telescope to-
ward A, if the tack is still accvu-ately sighted this
adjustment is correct.
Adjustment: If another point, B, is sighted,
mark at the point midway from B to A, as D, and
place the intersection of the crosswires on this point
by moAdng the reticle with screws c or d, figure 44,
p. 85. If B is obliquely above or below A, the
reticle must be moved both horizontally and verti-
cally to sight the point D.
131. 2nd. Aads of Bubble Tube in a Horizon-
tal Plane Parallel to that containing the Line of
Collimation.
Test: Place the telescope over two diagonally
opposite leveling screws and clamp it there. With
these screws E,, figure 73, bring the bubble to the
center of its tube, release the clips C, gently lift
out the telescope and turn it end for end. If the
The Wye Level 133
bubble retains its position at the center, the adjust-
ment is correct (see under transit, par. 84).
Adjustment: If the bubble moves from the cen-
ter, bring it back one half the distance by means of
the leveling screws R and the remainder by means
of the upper and lower adjusting nuts N, figure
73. Repeat until it remains at the center.
132. 3rd. Axis of the Bubble Tube in a Ver-
tical Plane Parallel to that containing the Line of
Collimation.
Test: Having made the preceding adjustment
and with the bubble at the center of its tube, ro-
tate the telescope around its axis about 15°. If the
bubble remains at the center the adjustment is cor-
rect.
Adjustment: If the bubble moves from the cen-
ter, bring it all the way back by means of the hori'-
zontal adjusting nuts at one end of the tube. Re-
peat this and the preceding adjustment until both
are correct. Since the 2nd and 3rd adjustments
bring the axis of the bubble tube into two planes
both parallel to the plane containing the line of
collimation, therefore the axis of the bubble tube is
parallel to the line of collimation.
The preceding adjustments are the only abso-
lutely essential ones, because now, if the bubble is
at the center of its tube (which can be verified by
observation), the line of collimation must be hori-
zontal.
133. 4th. Axis of the Wyes Perpendicular to
the Vertical Axis of the Level.
134 Military Topography for Mobile Forces
Test: Place the bubble in the center of the tube
with the telescope over a pair of diagonally oppo-
site screws; revolve the telescope horizontally 180°.
If the bubble remains in the center of its tube the
adjustment is correct.
Adjustment: If the bubble moves from the cen-
ter, bring it back half way by means of the leveling
screws, and the remainder by means of the adjust-
ing nuts M.
The 4th adjustment is not essential, but conven-
ient to avoid the necessity of relevehng when the
telescope is revolved horizontally. Since the leveler
determines the horizontality of his line of sight by
placing the bubble in the center of the tube, it is
of the greatest importance that the 1st and 2nd ad-
justments are correctly made. They should be
tested every day. The Wye adjustment (4th) is
convenient but does not affect the accuracy of the
work if the bubble is accurately brought to the cen-
ter of its run for each sight on a turning point. If
the line of coUimation is not parallel to the axis of
the bubble tube errors occur except for back sights
and fore sights of exactly equal length (see par.
94 and figure 55, p. 103) .
METHOD OF USING THE WYE LEVEL.
134. A Bench Mark (B. M.) is a specially se-
lected or prepared point on the ground whose ele-
vation is known or assumed with reference to some
datum plane (see par. 22), and to which are re-
ferred the elevations of other points whose eleva-
tions are unknown. Any permanently fixed ob-
The Wye Level
135
jects such as stone coping, concrete pillar etc., may
be used as B. M.'s. A Turning Point (T. P.) is
a temporary B. M., so called because it is used as a
reference point of elevations while the instrument
is moved or turned from one station to another. It
may be marked by a turning pin, figure 78, or a
stake.
An Instrument Station, as station I, figvu-e 79,
is the point on the ground where the level is set up.
It need not be in the straight line joining the
known and unknown points A and B. A Rod sta-
tion as C, 1, 2, etc., is a point where the rod is held
for securing the elevation.
A Back Sight (B. S.) is a plus ( + ) reading
on the rod held on a point of known elevation (as
A) to obtain the height of the line of sight of the
telescope, (called the height of the instrument or
H. I. ) above that point. A Fore Sight is a minus
Vertical Section
136 Military Topography foe Mobile Forces
( — ) reading on the rod held on a point of un-
known elevation as 1, 2, etc., figure 79, to determine
its elevation, measiuing down from the known
height of the instrument.
The wye level is used in connection with a plane
table survey for determining the elevation of the
ends of the base, and frequently that of the trian-
gulation stations.
DIFFERENTIAL LEVELING.
135. To find the elevation of one point (B)
with respect to another point (A) whose elevation
is known or assumed, figure 79.
The observer sets up and levels the instrument
at station I, at which the axis of the telescope is
higher than point A (located from a B. M), and
directs the rodman to move the target of the level
rod held exactly vertical on A, up or down until it
is bisected acciu'ately by the horizontal cross wires.*
*The Rodman standing directly behind the rod shonid hold
it lightly with one hand, while moving the target np or down
with the other as required. To enable the observer to determine
when the rod is vertical (not inclined to front or rear) the rod-
man waves the rod slowly back and forth, figure 80. If at any
point of the instrument, the zero of the target appears to rise
above the horizontal cross wire, as at c, the rod was not being
SO
The Wye Level
187
The rodman then reads and records the reading of
the rod at zero of the target vernier, figure 81, and
moves to station I (counting paces), where his rod
reading is checked by the observer.
The rodman then moves to C (turning point)
counting as many paces as he took from A to I,
gl8
Fig. 81
At C the rodman drives a turning piQ, figure 78,
or a stake, and a rod reading is taken at this point
as explained for A. The observer now moves to
some convenient place as station II, so located that
the level here will give a reading on the 1st turn-
ing point (C) and on a second turning point (D)
held vertical when the target was set as at B. This test should
be made at every T. P., and the zero of the target at its high-
est point made to appear tangent to the center horizontal wire, as
at D. An angle target, figure 81 shows when the rod is vertical.
A motion of the arm above the hip palm up, means to elevate
the target; below the hip palm down, to depress it. A rapid move-
ment of the arm means to move the target a foot or more; a slow
movement of the arm means to move the target slowly but con-
tinuously until the signal to stop is given by a horizontal motion
of the arm. Both arms waved means "clamp." The arm held
outstretched obliquely means to incline the rod in the direction
of the palm. All yelling from the observer to the recorder indi-
cates lack of systematic control of the work.
138 Military Topography for Mobile Forces
in the general direction of the required station B,
but not necessarily in the straight line A B (T. P.'s
need not be in the profile line). These steps are re-
peated until a F. S. is taken on the point B whose
elevation is required. The record is kept as fol-
lows:
FORM OF RECORD FOR DIFFERENTIAL LEVELING.
136. (See figure 79)
Instrument men-
Rodmen-
Place-
Date-
Station
Observed
Elevation
B. S.
+feet
H. I. ft.
F. S.
— feet
Remarks
B. M. A
800
1.249
801.249
Elev.+BS=H. I.
800+1.249=801.249
T. P. I (C)
793.015
8.234
H. I.— FS=Elev.
801.249—8.234. =793.015.
T. P. I (C)
9.340
802.355
—17.679
T. P. II (D)
801.560
0.795
+17.079
—00.600
T. P. II (D)
6.490
808.050
B
799.400
8.650
+17.079
—17.679
137. The above operation of finding the differ-
ence in elevation of two points is called Differential
Leveling. A check on the work is to add aU the
B. S.'s together and all the F. S.'s together; take
the smaller sum from the larger, and the result is
the difference in elevation required between A and
B, if plus ( + ) B is higher, if minus ( — ) B is
lower than A. It will be observed that a back sight
(see figure) on B. M. or turning point is always
added to the elevation of that point to obtain the
H. I.; the fore sight on any point is subtracted
The Wye Level 139
from the preceding H. I. to get the elevation at
that point. The distance from the B. S. station to
the level, should be about equal to the distance to
the next turning point, in order to eliminate er-
rors due to lack of adjustment of the instnmient
and to curvature of the earth. For even if the line
of sight is inclined up or down, still two positions
of the target at equal distance from the level will
be at the same elevation. See 4th adjustment of
the transit, par. 94, and figure 55, p. 103. In the
same manner, errors of refraction which cause ob-
jects observed to appear too high are eliminated if
observations are taken at equal distances from the
instrument.
PEOFILE LEVELING.
138. Profile leveling consists in finding the ele-
vation of a number of points along the profile line
A B, figure 79. The only difference of method
from that described above for differential leveling
is that there may be a number of foresights taken
from any instrument station to points desired. The
elevation of these points does not affect the record
otherwise as will be seen by comparing the form
below with that for differential leveling on the line
A B. It will be seen that the levels are carried for-
ward from one T. P. to another, exactly as in dif-
ferential work. The distance from A to the criti-
cal points J par. 166, are measured with steel tape
or chain and recorded as 1, 2, 8, 3+40 etc., mean-
ing 100 feet, 200 feet, 300 feet, 340 feet from A.
140 Military Topography for Mobile Forces
FORM OF RECORD FOR PROFILE (OR CROSS
SECTION) LEVELING.
139
Figure 79.
station
Observed
Eleva-
tion
BS.
+
H. I.
FJ.
Remarks
B. M. A.
800
1.249
801.249
1 (100 ft.
from A)
793.749
7.500
801.249—7.50=793.749
H. I. — F. S.=Elevation
T. P. 1. (C)
793.015
8.234
801.249—8.234=793.015
T. P. 1. (C)
9.340
802.355
B. S.+Elev. T. P. (or B. M.)=H.
9.340+793.015=802.355
I
2
793.055
9.3
2+40
792.2
10.1
T. P. 2 (D)
801.560
0.795
T. P. 2 (D)
6.490
808.050
B (4+20)
799.400
8.650
TO PLOT THE PROFILE.
140. Select a sheet of profile paper or cross
section paper, par. 196, with equally spaced hori-
zontal and vertical lines, figure 82, and assume a
eoo'
195
ISO
^
?M
'~
~
1
r
~
""
■" ■
■ ^
s
K'.
fe
iw
C.L
s
^
p
^
«H
fe
»
/
\
m
p?t
iriirn
'^
^^
ii
F%
V
/
■~
III 1
■ ■■
\
9,
%
>?
/
\,
%
%
■-
\
%
fRl
■
v"^
i'
r
% \
^SSl
^?
N
/
I
%
'""
\
1
/
1
*J
^
/
1
\
>^
/
1
"^s
i
1
^
i
1
■"
1
1
1
1
1
1
1
I
[
1
1
'
.; A
so ^
3oo| _ 4
to
a
ti
n
i
<
s
2
+
*e
n
fe
X
The Wye Level 141
convenient scale which should be larger than the
horizontal scale in order to exaggerate the eleva-
tions as compared with the horizontal distances and
thus show clearly the various changes of slope. The
vertical scale in the figure is assumed as 1 inches
feet; horizontal scale 1 inch=150 feet. The hori-
zontal scale of a profile is usually the same as that
of the map made of the area from which the pro-
file is taken. Opposite a (zero of the horizontal
scale) locate a' on the 800 foot line of the profile
paper. Similarly, opposite 100 locate sta. 1 at
793.7; opposite 200, locate 2 at 793.0 and so on to
the end as shown in the figure. The points at which
5 foot contours would cross a h, which is the hori-
zontal projection of the profile on the map, are
found by projecting down to the hne a b the points
at which the 795, etc., lines of the profile paper in-
tersect the profile a', 1, 2, 2+40, &'. For example,
the 795 contoiu" crosses the profile at m'. (see con-
tour interpolation, par. 167)* If no profile or cross
section paper is available the profile can be plotted
on ordinary paper by drawing the vertical and hori-
zontal coordinates of each station on the assumed
horizontal and vertical scale.
If the profile has been determined for the pur-
pose of locating a road, railroad, etc., a Grade Line
of the required slope is plotted on the sheet as
shown in the figure and the lineal cut or fill at any
point as m is f oimd by scaling off at that point the
•This is the basis of the method given, par. 167, for the inter-
polation of contours, except that in that work no profile is drawn
in.
142 Military Topogeaphy fob, Mobile Forces
elevation of the profile and the elevation of the
grade line then subtracting the smaller from the
greater. The difference is the mmiber of feet cut
or fill. Elevation of grade=799.2 — 795 (elev. of
m) =4.2 feet of fill.
CROSS SECTION LEVELING.
141. The record and method of levehng are the
same as above whether the points whose elevations
are sought are in one straight line or are in a num-
ber of lines. For instance suppose the ground area,
figure 83, is to be Cross Sectioned; stakes are set
at the corner of each square.
E
>
o'i^
C
^
1
8
^'
'■2.^
J
1
?'
\
/
\
/
^ /■
.83\
The leveling is carried on as shown in profile rec-
ord, fore sights being taken from each instrument
station to any points of the area on which the rod
is visible from this station and are recorded as A
R 1, B L 2 etc., meaning 100 feet to the right of
A, 200 feet to the left of B, etc., looking from A
to E. A rough sketch of the area should be made
as a part of the notes. For example, the instru-
ment is set up at sta. I, a B. S. is taken to A of
The Wye Level 143
which the elevation is known and a F. S. read on
the critical points visible in the vicinity, as A R 2,
B R 3, C R 3, etc.
To Range Out Ldnes Perpendicular to A E: lay
off on the ground, lines at right angles to A E as
described, par. 114, and range out and measure the
lines to the edge of the area, driving stakes at criti-
cal points (see par. 166).
CHAPTER VI.
PLANE TABLE SURVEYING
THE SELECTION OF THE SCALE OF A MAP OR
SKETCH
142. Two conflicting conditions must be consid-
ered in choosing the scale on which a nulitaiy top-
ographical map is to be made.
1st, the map must be large enough to show clear-
ly the smallest details required. Assuming that
1/20 in. is the smallest map distance that can be
readily scaled in solving problems on such maps in
the field, this distance must be made to represent
the smallest ground distance necessarily shown.
Suppose, for instance, that artillery ranges are to
be shown to within 15 yards. Then 1/20"=15
yards; 1"=300 yards; 6"=1800 yards; or practi-
cally 6"^1 mile. This then would be a suitable
scale for position and outpost sketches, and maps of
reservations and small areas.
2nd. The next question to be considered is
whether the map on the desirable scale is too large
for convenient handling. A combined position
sketch covering a division front of about 3 miles,
and a depth of 2 miles would give a map 12"xl8"
— ^not inconveniently large for the purpose.
3rd. A third condition is whether the scale is of
smtahle size for ready execution in the field. In
general, plane table work can be most satisfactorily
144
Plane Table Surveying 145
executed on a scale of 6"=1 mile. Position and
outpost sketches giving all details of military im-
portance have also been found to be most readily
executed at 6"=1 mile. If smaller scale maps of
large areas are required they can be readily secured
by reducing those mentioned above, see par. 210.
The relative accuracy of the instruments and meth-
ods used should also be considered in map work.
For example, it would be absurd to use a transit
reading to minutes if distances were obtained by
pacing, in which errors 1 in 100 are probable; be-
cause an error of one minute in angle causes an
error of one foot in a course of about 700 feet;
whereas the error of pacing might be 35 to 40 feet.
In the same manner it would not be necessary to
make a road sketch on a scale where 5 yards could
be accurately plotted if, in the average length of
courses, an error of rate of the horse might be as
much as 20 yards.
The amount of detail desired on the map is an
important consideration in miUtary maps, and the
larger the scale the greater the amount of detail
that can be shown in such a form as to be readily
comprehended by an inspection of the map. In
tactical maps every small feature aifording cover
is of importance, hence a large scale is necessary
for the representation of details; but strategical
maps need only show general features such as main
roads, mountains, etc., hence the scale may be very
small.
143. Considerations similar to the above have
146 Military Topogkaphy for Mobile Forces
led to the adoption of the following scales for mili-
tary maps and sketches in the U. S. Army:
1st. Road sketches 3 inches=l mile, with con-
totirs at 20 feet vertical interval (V. I.)
2nd. Position and outpost sketches, 6 inches^
1 mile; 10 foot (V. I.)
3rd. Fortress and war game maps or those used
in sieges, 12 inches^l mile, 5 foot (V. I.)
This is called the "Normal System" of map
scales, because any given M. D. (see par. 25), be-
tween contours represents the same slope on all the
maps, see par. 27 (3).
THE EXECUTION OF A MILITARY SURVEY.
144. The Plane Table and Stadia Survey. The
object of Part II of this book is to teach a begin-
ner how to make a complete military topographical
map covering an area of 1 to 20 square miles with
the assistance of officers or enlisted men. Such a
map may be made by a number of different meth-
ods among which are the transit and chain; the
transit and stadia; and the plane table and stadia
methods. The plane table and stadia method is
most suitable for mihtary surveying both because it
gives the most faithful representation of the
ground and also because the topographical train-
ing of the eye is by it best secured. This method
consists of plotting in the field on the map sheet,
the topographical details of the area. The various
essential points on the ground are sighted through
the telescope, lines are drawn along a ruler and the
distances of the points from the instrument are
Plane Table Surveying 147
read (see par. 117) on the stadia rod, and plotted
at once on the lines.
145. The Instruments Used in the Plane Table
Survey :
1. Plane Table ^ figure 49, p. 94.
2. Stadia Bods, figure 67, p. 117.
3. Wye Level, figure 73, p. 129, and Level
Rodj figure 75.
4. 100 foot steel Tape figure 57; or 100 foot
chain, figure 60.
5. Eraser, note book, plotting points (wax
headed needles), hatchet, stakes, marking chalk.
6. Stadia Computer, figure 72, p. 127.
SURVEY PARTY.
146. The Survey Party shotdd consist of a
chief; an assistant; two rodmen; one or more axe-
men depending on the amoimt of underbrush in the
area. In addition to the above, there will be re-
quired for survey parties, when in the field away
from a garrison, a cook and a man to care for the
animals of the party.
The Chief of the party is responsible for all parts
of the work, has full charge of the party and as-
signs the members as he sees fit. The assistant
should be prepared to relieve the chief of any part
of the work. He should especially be able to read
and reduce stadia readings rapidly and accurately.
The two rodmen should have a good knowledge of
ground forms so that they can select the necessary
critical points with but shght direction from the
instrument-men.
148 Military Topogeaphy for Mobile Foeces
METHOD OF MAKING PLANE TABLE SURVEY.
147. The steps in the work are:
1. Triangulation.
2. Location of Details, including Contours.
3. Finishing map.
TRIANGULATION.
148. In all classes of surveys, from the most
extensive geodetic survey of thousands of square
miles, down to a limited position sketch, the frame-
work or skeleton of the survey is the triangulation
system, figure 85. It consists of a series of tri-
angles generally covering the area to be mapped,
and giving points accurately located horizontally
and vertically as starting and controlling points
from which details of the area are plotted. The
vertices of triangles can be located by intersection
with great accuracy and thus the accumulation of
large errors is avoided.
The triangulation system is determined by first
Fi§r.85
Plane Table Surveying 149
accurately locating and measuring a Base Lane A
B, figure 85, from whose ends a series of triangles
as in the figure are extended.
THE BASE LINE.
149. A Base lAne is selected as near the center
of the area as practicable from which a good view
is obtainable over the ground to be mapped. It
should be on ground as level as possible and should
be of sufficient length to give a series of triangles
with angles greater than 80° and as nearly isoceles
as possible. The Base Line should be measured
with an accuracy proportioned to the size of the
area to be surveyed and the requirements of the
map ; and the elevations of its two ends, accurately
determined with wye level as described par. 135.
In topographical surveys of mihtary positions, res-
ervations, camp sites and maneuver groxmds with
precise instruments, an accuracy of base line meas-
urement of is sufficient. An accuracy of
5000 ^
1
means that for every 5000 feet horizontal dis-
5000 ^
tance, the measured distance is most liable to be be-
tween 4999 and 5001 feet.
TO MEASURE A BASE LINE WITH AN ACCURACY
1
OF
^ 5000
150. Two measurements are made with the 100
foot tape, one in each direction. For the required
accuracy, the tape can be held sufficiently horizontal
150 MiLiTAEY Topography for Mobile Forces
by hand. The pull should be as uniform for each
tape length as can be estimated. The ends of the
tape are marked with pins, and the direction is
maintained by lining in (see par. 112). If the
slope is too great for the full tape length to be held
horizontal, on account of the height above the
grovmd of the tape at the high end, half or quarter
tape lengths must be used, figure 62, p. 113. A
plumb line should be used on sloping ground to
exactly mark the tape end, figure 62. On a imi-
form slope, the measurements may be made along
the surface and converted into horizontal distances,
figure 62, by the formula CB^D B cos a^corect
horizontal distance. Or CB=VE>B'— DC in
which DC is the difi^erence in elevation between
B and D.
The elevation of A is determined with Wye level,
see par. 135, with reference to the nearest known
B. M. of a government or reputable private siu*-
vey. B is similarly determined with reference to A.
DETERMINING THE TRIANGLES.
151. Having measured the base line with the
required accuracy, the triangulation system may be
determined, either with a transit or plane table.
For large areas necessitating geodetic methods the
transit is generally used because of the errors ha-
ble to occur due to imunif orm shrinkage and expan-
sion of the plane table paper, and the desirability
of calculating the exact direction of the lines with
vespect to the true meridian. But having given a
drawing surface (paper, celluloid etc.) in which
Plane Table Surveying 151
there is only a slight and uniform expansion or con-
traction, the plane table triangulation is sufficiently-
accurate, because the exact directions observed are
obtained free from inaccuracies of angle reading
and plotting. As long as the expansion or contrac-
tion is uniform in all directions no errors result.
152. For military topographical surveys, such
as considered in this book, the triangulation sys-
tem is pest ewtended with the plane table, as fol-
lows:
Plot the base hne A B* to the desired scale of the
triangulation on a sheet of Unchangeable Drawing
Boards which has been seasoned by several weeks
of exposure to the air. This board is specially
made so that it wiU not contract or expand due to
atmospheric changes. Draw on the board two ac-
curate graphical scales of yards along two per-
pendicular edges of the board, and test the accuracy
of these scales at the time of plotting each side of
the triangles to see if there has been any change
of the dimensions of the sheet. The base line shordd
be so located on the sheet that the entire area to be
mapped will be included by'i^.ii- ^ ■>
Intersection: Set up and level the plane table
over station A (figure 86, 1st position) orient (see
•Throughout this book when a ground area and the correspond-
ing map are discussed the small letters a, h, c, etc., and Boman
numerals 1, 2, 3, etc., are used to represent map locations; Capi-
tals, A, B, C, etc. and Arabic numerals I, II, III, etc. are used to
represent the corresponding positions on the ground.
tSold by Keuffel & Esser, New Tork.
152 Military Topogeaphy foe Mobile Forces
C
"^7<'
,f^X„
Ground
i
•"-w
^^
.'->
/
31:^
--
-a^ax-b
iwPosilion
aw
•^'
B
\
■♦tS)
^
>=>Ov
v^S.
->'" 1
^y
:^'
D
Fig. 86
par. 34) the table by placing the alidade ruler
along a b and rotating the plane table horizontally
until a rod on B is accurately bisected by the cross-
wires of the telescope. The point a on the plane
table sheet is placed exactly over A by the use of
the plumbing arm N, figure 49, p. 94.
The sheet having been thus oriented, direct the
telescope toward triangulation stations, such as C
and D, figvu-e 86, which, with A and B, wiU make
triangles, no angle of which will be less than 30°
nor greater than 90°, in order to insure accurate in-
tersections. Draw indefinite lines toward C and D.
Next move the instrument to B (figure 86, 2nd po-
sition) . Set up level and orient as at A. Sight C
and D and draw hnes intersecting those drawn from
A at c and d, which are the plotted positions of C
and D. The points thus located from A and B
may be similarly used as new base ends for locating
new triangulation stations such as E, F, etc. In
this manner the entire area to be mapped is covered
with points whose horizontal positions are plotted
Plane Table Surveying 153
on the map sheet and whose elevations are recorded
as the basis for the work of fiUing in details.
Vertical angles are read from A by sighting on
an elastic band fixed at the height of the telescope
axis above A, on the stadia rod held on C and D
(see c fig. 67, p. 117), to determine the elevation
of C and D. This method of finding the diifer-
ences of elevation is described in par. 120. These
elevations should not be in error more than .5 foot
per mile from A to the point under consideration
in the triangulation. The elevation found should
be corrected for curvature of the earth and refrac-
tion by the air, as follows : add to each at the rate
of 8 inches times the square of the length of sight in
miles decreased by 1/7 to allow for refraction. For
example, suppose a sight is 2 miles long. 8 X (2)^
= 32". 32— j(32 X 1/7) = 32—4.5 = 27.5 inches
^the correction to be added.
TO PLACE THE TRUE AND MAGNETIC MERIDIANS
ON THE PLANE TABLE SHEET.
153. Draw on an edge of the oriented sheet the
magnetic meridian parallel to the west or east side
of the compass box in position with the north end
of the needle reading zero.
(1) Lay off with a protractor a line making
with the magnetic meridian an angle equal to the
declination but in an opposite angular direction
(that is west if the declination is east and vice ver-
sa) . The Une thus located is the true meridian.
(2) Or, rotate the compass box in a direction
opposite to the declination until the needle reads the
154 Military Topogeaphy for Mobile Forces
exact angle of the declination. Draw a line along
the east or west side of the box, and this is the true
meridian. (To determine the position of the true
meridian see par. 64)
FILLING IN DETAILS.
154. This consists in determining the horizontal
distances, the elevations, and the relative directions
of sufficient critical points (see par. 166) to enable
the topographer to accurately represent the area by
contours (see par. 22) and conventional signs (see
fig. 18, p. 42).
Locations for filling in details are made (1) by
Resection, (2) by Intersection, (3) by Traverse.
RESECTION LOCATIONS.
155. To locate a point by resection, the plane
table is set up at the desired point on the ground
whose map position is unknown, and sights are tak-
en to two or more points on the ground "whose map
positions are plotted.
1st method of Resection: Having given a di-
rection line and a plotted point outside of that line,
to determine the map position of any point lying in
the direction line.
Set up and level (pars. 79 and 80) the plane table
at the desired point, as C, figure 87, then orient by
placing the alidade along a c and rotating the table
horizontally until a rod at A is accurately sighted.
Clamp the table in this position. Pivot the alidade
about a plotting point (needle) at b, sighting B.
Draw a hne from b back toward the observer until
Plane Table Surveying
155
it crosses the line a c. This point of intersection is
the map position of the plane table's ground posi-
tion C. This method of resection is of great value
in extending a secondary system of triangulation
(one with sides from J to 2 miles) or for filling in
detail in a plane table survey and in all forms of
rapid area sketching. For example, the topogra-
pher at one of the plotted stations as a, h, c^ etc., ob-
serves that it will be desirable to set up near a cer-
tain ridge, he draws an indefinite line toward a tree,
telegraph pole, or other well marked spot, in the de-
sired direction. At any later time he can set up
at any point in this line and determine his position
as above, in order to plot with stadia readings the
details in the vicinity.
2nd method of Resection: Having given two
plotted points a and h to determine a third point c,
orienting with the compass.
Set up, level and orient the table at C, by plac-
ing the N S line of the compass box along the mag-
netic meridian on the sheet as at oc, figure 87, and
then rotate the table until the north end of the
needle reads zero. Clamp the table in this position.
156 Military Topogeaphy for Mobile Forces
Pivot the alidade on a, at the same time sighting A,
and draw a line along the ruler toward the ob-
server. Similarly pivot the alidade on bj sighting
B and drawing a line back along the ruler until it
cuts the line from a. The point of intersection is
the required point c. This method is especially val-
uable in determining plane-table stations for locat-
ing details aroimd any point from which a good
view is obtainable. Any shght error in the location
of the point due to local attraction (see par. 62) of
the needle is of no consequence because it apphes
only to this one location and does not affect other
determinations with an accumulative error.
Having located the horizontal position of the un-
known point by either of the above methods, the
vertical angle is read from C to a known station, as
A, figure 87, to determine the elevation of C. ( See
par. 120, determining elevations by vertical angles) .
3rd. Method of Resection : Having given three
plotted points a^ b and c whose grovmd positions are
all visible from the unknown point D.
Set up and level the plane table at the unknown
point D, figure 87, and attach a sheet of tracing
paper on the table. Assume the location of the vm-
known point d on the tracing paper, from D sight
toward the three known points A, B and C, draw-
ing lines toward each from d. Now loosen the
tracing paper and so shift it as to bring the line da
over a of the map, the line d b over b of the map, the
line d c over c of the map. When this is done, prick
through with a needle the position of d into the map
Plane Table Sukveying
157
and the xinknown point is thus correctly located.
The board is now oriented by placing the alidade
along one of the lines as d a and rotating the board
until A is accurately sighted through the tele-
scope.*
4th method of Resection: Having given two
plotted points on the map a and & (figure 88, 3rd
position of plane table) both of which are visible
on the ground, to locate the map position d of an
unknown point D, using an auxiliary point, as C,
whose map position and distance from D are im-
known. Set up and roughly orient at C (figm'e
88, 1st position) from which A, B and D are visi-
ble. Attach a sheet of tracing paper on the table
and assume a point on it to represent C at c'. Draw
Fig. Sl.a
*Care should be taken in choosing the known points, A, B, and
C on which to sight, that the circumference of the circle contain-
ing them does not also contain d. For if this condition exists
then the location of d is indeterminate since at any point of the
circumference, figure 87 (a), the angles d' and d" are constant, be-
ing measured by arcs be and ab respectively. To be on the
safe side, the unknown point should lie where practicable outside
the angle included by the three points as at d.
158 Military Topogbaphy for Mobile Forces
at* Position
Fiff.Sa
,5 asllPosition
rays toward A, B and D. Move to D, assiime the
point d' on the tracing paper in the hne c' d' (2nd
position) and set up the plane table {n' o' p' q'),
orienting by a back sight on the hne c' d'. Draw
rays from d' toward A and B. The intersection at
a' and h', of these rays, with those previously drawn
from c\ determines a quadrilateral a' h' c' d' , of
which the scale was assumed by assuming the length
d d' , exactly similar to the quadrilateral A B C D
on the ground. Now shift the tracing paper and
fasten it with h' lying over h on the map sheet, and
the line a! h' on the hne a b (3rd position of table) .
Revolve the table until the line b'd' points toward B.
This orients the table in the position n o p q. Re-
move the tracing paper and pivot the ahdade on b,
sighting B, and then on a, sighting A; draw the
latter ray back imtil it cuts the line b din d (that is,
resecting on B and A. This locates the required
point d on the map. C may be found by drawing
Plane Table Surveying 159
a c on the map parallel to a' c' on the tracing paper
(&' on h and a' on the line ah), and extending
the last position of c' h' until they intersect at c.
This method of resection is valuable for extending
a triangulation in which the topographer would not
wish to depend on the needle for orientation. The
auxiliary point C may be selected as close to D as
the securing of good intersection angles will allow.
LOCATIONS BY INTERSECTION.
156. It will be necessary to locate points by in-
tersection, when the point, at which information is
desired on the map, can be seen from located sta-
tions but cannot be used as an instrument station.
As for instance, the jimctiu'e of two streams whose
horizontal positions and elevations are important,
but from which the very limited view possible pre-
vents setting up there. These points will be locat-
ed by intersection as described par. 152, except
that the same degree of care will not be necessary
and the intersection angles may vary from 30 to
120 degrees. The elevation of such a point would
be obtained by reading the vertical angle and re-
ducing the stadia reading as described par. 120.
One of the greatest advantages of the plane-table
over the transit is that the instrument, due to its
capacity for resection and intersection, need not
be set up at points barren of detail, as is required
in the transit traverse simply to move from one de-
sired station to another. As soon as two or three
points are located on the sheet the plane table can
be set up at any desired point by resection, and the
work of plotting be begun.
160 MiLiTAEY Topography fob. Mobile Forces
LOCATIONS BY TRAVERSE.
157. In the area to be mapped there will usual-
ly be critical points, par. 166 which are invisible
from any known station such as those low down in
valleys or in woods, etc. In such cases a traverse is
run with the plane table and stadia, as follows : Set
up and level the plane table at the known station A,
figure 89 (a) and orient by a back sight to the last
known station, par. 152. The front rodman meas-
F.g 89 b
lu-es the H. I. above A, places the elastic cord at
this point on the stadia rod (par. 120, foot note)
and holds the rod vertically on a well driven stake
at C, from 400 to 800 feet in the general direction
desired for the traverse. The observer sights the
comer of the rod directly over a tack on stake C.
He then sets the lower stadia mre on an even hun-
dred division of the rod [or at the top of a {c-\-f)
division if these are on the rod] reads and calls out
to the recorder the number of divisions between this
and the upper stadia wire. The observer then ele-
vates or lowers the telscope about its horizontal axis.
Plane Table Surveying
161
until the middle horizontal wire bisects the elastic
cord, then reads on the vertical circle the angle of
slope and calls it out to the recorder. The observ-
er then draws a hne along the ahdade ruler toward
C and marks the distance a c, figure 89 (a) , to scale,
as given by the recorder. He then writes at c its
proper elevation as given him by the recorder, and
interpolates contour points on a c (see par. 167).
As soon as the observer calls out the stadia reading
and vertical angles the recorder writes them down
in the note book (see par. 158, form of notes), and
immediately reads from the stadia computer (see
par. 123) the correct horizontal distance a c. He
similarly reads and records the difference of eleva-
tion between a and c, and adds (or subtracts) this
difference to the known elevation of a, according as
the vertical angle to c was positive ( + ) or nega-
tive ( — ). The observations are plotted at once
but in order to keep a record of them in case a later
verification is necessary, the recorder enters them in
the note book.
FORM FOR PLANE TABLE AND STADIA NOTES.
NOTES
v. A.
Stadia
Hor. Dist.
Diff. Elev.
Elev.
Remarks
Point
Observed
At Stat
ion A.
Elevation A=830
C
4» 45'
5 47
542 ft.
+45'
875
158. Having located all details in the vicinity
of C, the traverse is similarly carried forward to
other stations as D, etc., until another known point
is reached. Suppose E is such a known point plot-
162 MlLITAKY TOPOGEAPHY FOR MoBILE FoRCES
ted in ei (870). From D the observer sights E
and locates e as prescribed for locating C above.
ERRORS AND THEIR ADJUSTMENT.
159. The difference in this position of e, and its
position as formerly located by triangulation (ci) is
the accumulated error of the traverse. This error
for traverses of 1 to 2 miles would usually be less
than 20 feet. An error of 20 feet on the scale of 6"=
1 mile is — inch and negligible in such filling in
work. If the error is large enough to represent as
much as \ inch it is distributed among the last few
courses as follows, figiu-e 89 (b) : A line a! e' is
laid off equal in length to a c-\-c A-\-d e. At e', a
line e' e" is drawn perpendicular to a' e' and equal in
length to the error e Ci. e" and a' are joined by a
straight line, and d' d" , c' c" are drawn parallel to e'
e". d' d" and c' c" are the amounts to scale of the
corrections respectively at d and c. At c and d
draw lines parallel to e Ci, and equal respectively to
& c" and d' d" , thus locating the adjusted positions
of the stations c, d, etc., at Cx, d i, etc. As will be ob-
served, the adjustment at any station is proportion-
al to the distance of that station from the first sta-
tion a, and assumes that the error was accumulat-
ed gradually throughout the traverse.
If the elevation of e as determined by the trav-
erse is not equal to that of Ci, the elevation of the
traverse station may be adjusted in exactly the
same way. In this case e' e'" would be taken equal
to the error of elevation on any convenient scale.
Plane Table Surveying 163
Suppose the elevation of e is (920), of e-i is (870).
Then lay off e' e'"=50 feet. Assume a scale of \
mch=50ft. Then e' e"'= J inch. (Z' ^x?
ji> YlTri
ago _ __^''^ ^<'
i-^ 'f'n "m
- - ^^^^
^^ ^
-p^.^^
680- - _ __^ i^^ ' - _ *"
^t<^ "l"' ---,--
-^ VYI '"tH
-A ^ff ■ M
-jp^^ - -- L
eio _ ■^ _^ _ L
j^ ^ 1--
^'^^- ' ~ r-
"
sebJZ.Jl- .V^ " ~ ^
'^ ^-\ "^^ '"-^^^V^
h and c. The number of cross-section vertical di-
visions representing 10 feet is assumed at pleasvu-e
for each location depending on the difference in
elevation between the two points such as a and h,
between which interpolations are being made. The
elevation of the lower of the two points is assumed
on the cross-section sheet so that the heavy lines
172 Military Topography for Mobile Forces
will represent contoiir elevations. The contour
points onb d are likewise determined and then the
contours along this hillside are drawn in so as to
conform to the slope of the ground as it lies before
the observer.
168. TJie use of cross-section paper for inter-
polating contours fvuTiishes a rapid graphical so-
lution which gives the same results as if the profile
(see par. 140) oi ah,h c etc., were each constructed
as in figure 82, p. 140, the contours located on it
and then projected down on a & etc. The contours
could be located by arithmetical proportion but this
method is much slower especially where decimal
parts of feet are considered.
To locate hy proportion the point m where the
880 contour crosses a h : Suppose the base a' h" of
triangle a' &"^2.89 inches, and is at elevation 862.
Then we have the proportion h" h' :m" m' : '.a' h"
33
'.a' m". That is 33:18 : : 2.89 : a' m". Whence -,g =
2.89 18X2.89 _^ . .
— — -, or am^ =1.58 m. from a.
a'm" 33
Care must be used never to interpolate contours
between two points lying on opposite sides of a
hill top as M and N in the profile, figiu-e 93 (a),
p. 169, or on opposite sides of a stream line as N
and E. In these cases the interpolations should be
made between H and B, between B and C, etc.
When drawing in contours in the field on the plane
table sheet, after locating the contour points on any
line, the observer would, when necessary, vary the
Plane Table Surveying
173
spacing as required by the slope of the ground on
the area between the lines abj bd and bc^ figure 94 ;
if it is concave they w^ould be closer together near the
top than near the bottom and vice versa for convex
slopes (see plate 3, p. 23). This aUovps the use of
fewer critical points than if every shght variation
of slope is used as a point to be observed, and much
time is saved while the result is a true representa-
tion of the groimd.
g.95
169. Figure 95 shows the critical points observed
in an area to be mapped ; the broken lines show the
rays along which interpolations are made at the
points marked; the fxill lines show the contours as
actually drawn in by the observer who constantly
has the ground in view while doing the work. It
will be observed that the lines on which interpola-
tions. are made divide the area into a series of trian-
gles and this should in general be the case, each one
of the triangles being so chosen that it may be as-
174 Military Topography foe Mobile Forces
sumed as a plane surface for the work of interpola-
tion. In selecting critical points the scale of the
map should always be kept in view, and only as
many points be chosen as are necessary. For in-
stance, if the scale is 6"==1 mile, 100 feet is repre-
sented by approximately .1 of an inch. It would be
obviously unnecessary to take observations to show
irregularities in the contour of 15 or 20 feet hori-
zontally. One carefuUy selected critical point is
better than half a dozen selected at random.
170. The topographer's eye must he constantly
trained to appreciate slopes and ground forms and
to comprehend the map distance of a given ground
distance so that he can gradually dispense with
more and more critical points and yet put in ac-
curately the intervening contours and ground feat-
ures. This method of surveying with plane table
and transit is rapid and accurate, and its use is
urged for all small area military surveys. It gives
an excellent training to the eye in appreciating the
possibilities of ground in all mihtary operations.
AIDS TO ACCURACY.
171. Well sharpened 6H pencils should be used
and fine lines should be drawn for location work.
The pencil should be held exactly vertical and
the point close to the ruler.
Excellent plotting points may be made of medi-
um sized needles with sealing wax heads. The
points pricked for stations or critical points should
be very minute.
One or more check sights should be taken, from
Plane Table Surveying 175
every station occupied, on triangulation stations
where visible, as a verification of the orientation of
the table.
CHAPTER VII.
TRANSIT AND STADIA SURVEY.
172. The transit may be used in making a mili-
tary topographical survey instead of the plane-
table, the essential difference being that the obser-
vations taken with the transit are recorded in a
note book (see par. 177) and these notes, with
rough sketches as a guide in plotting, are subse-
quently plotted indoors. It is therefore not possi-
ble to secure by this method the topographical train-
ing or the accuracy of representation of the ground
forms and features possible with the plane table.
173. The field work of the transit and stadia
survey is executed with the following instruments:
1. Transit J figure 42, p. 86, and par. 71.
2. Stadia Rods, figure 67 and par. 117.
3. Wye Level, figure 73, p. 129 ; Level Rods,
figure 75 and par. 134.
4. 100 foot steel tape, figure 57, or chain, fig-
ure 60, and par. 107-
5. Note Book, see par. 177.
6. Hatchet, stakes, marking chalk.
Survey Party, see par. 146.
TRAVERSE WITH TRANSIT AND STADIA.
174. Having established triangulation stations,
as xmder the plane table, par. 148, the detail is filled
in by running traverses with transit and stadia over
176
Transit and Stadia Suevey 177
the area in a series of loops, each of which should
begin and end at a triangulation station. The fol-
lowing steps are taken in traversing:
1. Set up J level (par. 72) and orient the transit
at a point of the triangulation the starting pcnnt of
the traverse (as A, figure 96); and take a sight on
the nearest B. M. whose elevation is known.
2. Take side shots for detail around A.
3. Locate a forward station in the desired direc-
tion, as I, and read the azimuth, vertical angle and
stadia.
4. Move the transit to station I, set up, level
and orient by a back sight on a rod held on A.
5. Bead vertical angle and stadia on A, as a
check on the forward readings.
6. Take side shots for detail in the vicinity of I.
7. Traverse to II, III, IV, etc., until B is
reached, as prescribed for traverse to I.
To Orient the Transit: At the first station. A,
to orient the transit in the meridian, set the zero
of the vernier (A, fig. 42, p. 86) opposite the zero
of the horizontal limb (main scale) and clamping
the two plates together, by E figure 42, loosen the
lower clamp C, and revolve the clamped limb and
ahdade* horizontally until the north point of the
magnetic needle points at the north zero of the
compass circle. Clamp the lower limb C and se-
cure accurate zero reading of the needle with the
tangent screw D. Release the upper clamp E.
*The alidade is all that part of the instrument which carries
the line of sight. The upper plate forms a part of the alidade.
178 Military Topography for Mobile Forces
The horizontal scale is now in a fixed position (ori-
ented) with the index of vernier A reading zero
when the line of collimation lies in the meridian.
The vernier moving with the telescope marks on the
limb the angle which any line sighted makes with
the meridian. At aU subsequent stations where
the transit is oriented, the horizontal scale (limb) is
parallel to its present position.
175. To read on B. M. : The rodman now places
an elastic cord (see par. 120) on the rod at the H.
I. above A. The observer sights the edge of the
rod on B. M., figure 96, clamps the upper plate
(by clamp E, fig. 42), reads the intercept between
the stadia-wires, and, elevating the telescope about
its horizontal axis Z until the cord is bisected by
the middle horizontal wire, clamps (with N) the
telescope. He then reads the azimuth on vernier
A, and the vertical angle on vernier L, to the re-
corder, who records them in the proper column in
the note book (see par. 177).
176. Side Shots for Detail (see par. 160) : A
rodman places a stadia rod on C. P. I, C. P. II, etc.,
which are located as prescribed for locating the
B. M. and the record is made as shown in the notes.
In these sights it will usually be sufficiently accurate
to read the vertical and horizontal angles to the
nearest 10' and the stadia to the nearest 5 feet. A
rough sketch of the ground to be mapped should
accompany each sheet of the note book on the right
hand page, left blank for this purpose. In order to
sketch forward as the traverse progresses, the notes
may be conveniently kept from the bottom of each
sheet to its top.
Tbansit and Stadia Suevey
179
-•om
0--
I
-<^
CPJt
Fig. 96
TABLE OF TRANSIT AND STADIA NOTES.
177. (Figure 96)
Topographical Survey at with Transit and
Stadia. Azimuths from Magnetic Merid-
ian, Magnetic Declination 8° 23' E.
Chief of Party — John Jones.
Assistant — Henry Smith.
Bodmen — George Price, Wm. Sievert.
September SO, 1909.
Point
Observed
Azimuth
Check
Bearing
Vertical
Angle
Stadia
Horiz.
Dist.
Diff.
Elev.
Elev.
Remarks
At Station A 800 H. I.=4.5 (Measured on Stadia Rod)
B. M.
10° 10'
N10°E
— 3°20'
125'*
125'
—7.2
792.80
C. P. I.
70° 00'
175° 10'
130° 23'
N70°E
S5°E
S49°30'E
+S°00'
— 7°35'
+10°
200'
170'
600'
581'
C. P. II.
I
+102.6
902.6
At Station I Elevation 865.2 feet H. I.rrS.eO.
A
310° 23'
N49°30'W
— 6°19'
602'
II
89° 14'
N89°15'E
0°00'
300'
300'
00
At Station II. Elevation H. I.=4.90
I
269° 14'
S89°15'W
0°00'
300'
300'
00
III
69° 00
N69°E
+9°00'
690'
At Station III. Elevation H. T.— 5.00
*For angles smaller than 5°, no correction of the horizontal
distance is made except on main traverse stations. Let the stud-
ent reduce the uncompleted parts of the above set of notes.
180 Military Topogkaphy for Mobile Forces
178. To Locate Station I: The front rodman
places the front comer of the stadia rod on the tack
in the top of the stake driven to mark station I.*
The Observer accurately bisects the comer of the
rod directly over the tack and as near it as possible
and clamps the ahdade with clamp E, figure 42;
reads the stadia to the recorder, then elevating the
telescope bisects the elastic cord at H. I. on the rod,
before removing his eye from the telescope. He
then reads the azimuth (see par. 69) on Vernier
A, the check beariog on the compass; and then the
vertical angle on the vernier L to the recorder who
enters them in the notes.
179. To Move to a New Station: The lower
clamp (C) is loosened and the telescope loosened
(at N) to prevent strains on screw threads from
accidental blows. The needle stop, dj figure 47,
p. 89, is screwed doAvn to take the needle off the
pivot. The transit is then carried to station I, set
up, leveled and the needle stop released.
180. To Orient by a Back Sight: The transit is
oriented by setting vernier A (fig. 42, p. 86) to
read an angle differing from the forward azimuth,
A to I by 180°. That is, 180° is added to the for-
ward azimuth unless this simi is greater than 360°,
in which case 180° is subtracted from the forward
*The error arising, due to failure to place the plumb bob of
the transit or plane-table exactly over the tack marking the sta-
tion, Increases as the distance to the next station observed is de-
creased. At one mile an error of 1 inch in position of the plumb
bob causes an error of about 3 seconds of arc; but at 100 feet, the
error would be about 3 minutes. Keep in view that 1° at 57.3
feet=l foot (see par. 25).
Tbansit and Stadia Survey 181
azimuth. The two plates are clamped together by
means of E fig. 42, and the rod on station A is then
sighted; the lower clamp, C, is tightened and accu-
rate bisection secured with the tangent screw, D.
The stadia and vertical angle from I to A are then
read as a check on the forward readings. If the
two vertical angles are different in numerical value
(indicating an index error of the vertical hmb, see
par. 98) one-half their arithmetical sima is the cor-
rect slope between the stations. The traverse is now
continued in the same manner imtil B is reached.
CHECKS ON ACCURACY OF READINGS ON A
TRANSIT:
181. Be sure the proper set of graduations is
read, i. e., inner or outer, figure 45, p. 87; that the
vernier is read in the same direction as the limb;
that the correct vernier is read (vernier A) ; that
angles such as 28° for S2°, 49^° for 50^ ° are not
read; that the half degrees on the limb be added
when necessary to the vernier reading, as 60° 60',
instead of the erroneous reading 50° 20'. The north
point of the needle should always be read at each
sight as a check on the azimuth read on the vernier,
to prevent large errors of a degree or more. Re-
member that you read on the limb from zero of the
limb up to index (zero) of the vernier, and then on
the vernier from its zero up to coincidence, see par.
58. Estimate the fractional part of the division of
the limb to be read with the vernier, as this shows
at about which vernier line to look for coincidence.
If no division line of the vernier exactly coincides
182 MiLiTAKY Topography for Mobile Forces
with one of the limh, read that vernier division line
which has both of the two adjacent ones entirely
within two divisions of the limb, as in figure 32 (C) .
After orienting by a back sight, par. 180, always
release the upper clamp E and turn the vernier A
to zero to see if the north point of the needle also
reads zero. This test is to check large errors of a de-
gree or more, due to turning the wrong screw etc.
PLOTTING THE TRANSIT SURVEY.
182. There are two methods of plotting the
transit traverse:
1st. With a protractor.
2nd. By means of rectangular coordinates.
The equipment required for plotting is,- — a sheet
of drawing paper or cross-section paper, figure 102,
p. 196, of sufficient size to contain the area; a T
square and triangle, figure 108, scale of equal parts,
figiu-e 106, a protractor, figure 107; wax headed
needles for plotting points; pencils No. 6 H and
H; rubber eraser; pair of dividers, figure 104.
PLOTTING WITH PROTRACTOR.
183. A celluloid protractor, figure 107 (a), or
one machine made on card board, should be used.
The small brass protractors in instrmnent sets are
too inaccurate.
Assume a point a, figure 97, on the sheet to rep-
resent the starting point A on the groimd and write
in parenthesis its elevation, (800). Draw through
a the line n s io represent the meridian (magnetic
or true according as the declination was not or was
Transit and Stadia Survey
183
Fig. 91
set off, par. 74). Lay the center of the protractor
on a, the zero and 180° points on the n s line. With
plotting point vertical^ prick a minute hole at the
edge of the protractor exactly opposite the azimuth
reading to station I (see notes, par. 177). Draw
the light indefinite line a 1, through a and the point
pricked. With scale of equal parts, figure 106, or
a working scale, see par. 16, lay off the distance
A I to scale and prick the point 1. With T square
or ruler and triangle draw n' s' parallel to n s^ see
par. 200, and continue the main traverse to 2, 3, 4,
etc., to b as prescribed for I. Having plotted the
main traverse, plot in b. m. and all side shots in like
manner. If the main traverse does not "close"
that is if &' does not fall on the b on the sheet as
plotted from the triangulation, adjust the locations
and elevations of the traverse stations, as prescribed
for plane table traverse, see par. 159, and then plot
all side shots from the adjusted stations.
184 MiLiTAHY Topography foe Mobile Forces
PLOTTING FROM RECTANGULAR COORDINATES
184). Instead of laying off the azimuth of each
course with a protractor and plotting its length to
scale along the line joining the two stations, as
above described, the traverse courses may be plot-
ted with reference to two lines perpendicular to
each other called "Rectangular Axes." These lines
are the meridian {n s), figure 98 (a), and the east
Fig. 98 b
and west line {e w). The position of any station,
as 1, figure 98 (a), may be located with reference
to another station as a, by plotting the distance a ac
along e w from a to the point where a perpendicular
from 1 meets the line ew; and by plotting a y along
TO s from a to the point where a perpendicular from
1 meets n s. To plot 1, a ac and a y are scaled off
and at x and y perpendiculars are erected \o e w
and n s respectively, and the point where these per-
pendiculars intersect each other is the location of 1.
a X and a y are called the projections of a 1 on the
axes e w and n s respectively. In the same manner,
any other station as 2 can be determined with re-
spect to any other station as a or 1.
Transit and Stadia Sukvey
185
Distances measured along e w are called "De-
partures" and along n 8, "Latitudes" For in-
stance, X an" is the departure of course 1 2. In order
to plot by the above method, it is necessary to find
the latitude and departure of a course of any length
and azimuth.
184. (a) From trigonometry, figure 98 (a),
ax . ay ^
—: =sm m; -^ =ca% m.*
al a\
aao=a 1 (sin m), or the departure of a course
equals the length of the course multiplied by the
sine of the azimuth.
ay^al (cosm), or the latitude of a course
equals the length of the course multiplied by the
cosine of the azimuth. These equations are true
for all azimuths, but it wiU simplify the trigo-
nometrical work, if it be remembered that where
the azimuth is in the 1st, 2nd, 3rd or 4th quadrants,
figure 99, that the angles m, n, p, q, respectively are
4tfc Quatirant
ivauadrant
30^ Quadrant
C-)
^Itf Quadrant
F.g.99
the ones whose sine or cosine is used. For example,
suppose the azimuth is 195°, length of course, 500
feet. Then p=195 — 180=15°, and the departure,
= — 500 X sin 15°, and the latitude== — 500 X cos
*See explanation of table 111, p. 342.
186 Military Topography for Mobile Forces
15°. The signs to be given to the latitude or de-
partures are plus ( + ) when measured toward north
or east, minus ( — ) when measured toward the
west or south. In figure 98 (a), the latitudes of a
1, 4s h are plus (measured north) ; the latitudes of
1 2, 2 3, 3 4, are minus (measured south) . The de-
partures of a 1, 1 2, 2 3 are plus (measured east.
The departures of 3 4, 4& are minus (measured
west) .
185. To find the latitude {or departure) of any
course, pick out from the table of natural cosines
(or sines for departures) Table III, Appendix,
p. 341, the cosine of the angle less than 90° corres-
ponding to the azimuth, (see par. 184 a) and mul-
tiply it by the length of the course, prefixing ( + )
or ( — ) according to the above rule. For example;
course 2 3, figure 98 (a), is 800 feet long with an
azimuth of 145°30'. What is the latitude and the
departure of the course? 180°— (145°30')=34°
30'^angle n, figure 99. From table III, the nat-
ural sine 34°30'=.5664. 800X.5664=+453.12
feet, (measured east, hence+)^the departure.
Natiu-al cosine 34°30'=.8241. 800X.8241=
— 659.28 feet (measured south hence minus) =lat-
itude of the course.
186. Each of the successive courses ending at
2, 3, etc., figure 98 (a), may be plotted from the
preceding station, as 2 from 1, 3 from 2, or from
the original starting point, or origin, as a. Thus 4
may be plotted by laying off the departure ( — of"
a?'^) and latitude ( — y'" y") of the course 3 4, from
Transit and Stadia Suevey 187
x'" and y"'\ or by laying off the sum (a x-\-ccx"
-\-x" x'" — x'" x") from a along e w; and the sum
(a y — yy" — y"y'" — y'" y") from a along n s. The
advantage of the latter method is that all the plot-
ting starts from one point and there is no accumu-
lation of errors of drafting as in the 1st method.
It is evident that the algebraic simi of the latitudes
or departures of the courses from a through 1, 2,
etc., to any other station, as 4, is equal to the lati-
tude or departure of the line direct from a to 4.
This gives a most valuable check on the accuracy of
the traverse, for if the latitude and departure of b
have been previously determined from the trian-
gulation, they should be equaled by the latitude
and departure of &' as found from the traverse.
If the final station of the traverse falls at b', then
the error of latitude:= — b z^ and the error of de-
parture= — z b'. The error of closure^&&':=
y ( — z by-\-{ — b' z)^ The error of closure bb'
divided by the total length of traverse (a l-\-l 2-\-
2 3-\-3 4-^4 b) is called the ratio of error of the
traverse and is usually expressed as a fraction with
the numerator of unity. The ratio of error of a
traverse with the transit and stadia of ^ to 2 miles
should not be greater than The limit of error
^ 300
in that case would be , because that amount
300
must not be exceeded in the work.
188 MiLiTABY Topography for Mobile Forces
ADJUSTMENT OF ERRORS.
187. The error is distributed at each station by
the following proportion: Error of latitude (de-
parture or elevation) of any course: total error of
latitude (departure or elevation) at the end of the
traverse: : the length of this course: the length of
the entire traverse. The corrections should be made
as shown in the table par. 188, hy either adding or
subtracting so as to reduce the whole error, before
plotting. The adjusted latitudes etc., are then
plotted; that is, if &' falls to the south of h, all the
latitudes are moved north; if the elevation of h' is
too small, the corrections are all added. Since the
principal advantage of plotting by latitudes and de-
partures is that errors may be adjusted before plot-
ting begins, it is not necessary to graphically solve
the above proportion by similar triangles as was
done in the correction of the plane-table traverse,
(par. 159) ; this may be done, however, as shown in
figure 98 (b). AB is the total length of the tra-
verse; BC is the error at the end of the traverse; F
D, G H, etc., the the errors of courses whose lengths
are A D, A H, etc.
Transit and Stadia Survey
189
TABLE— COMPUTATION OF LATITUDES AND DE-
PARTURES OF TRANSIT TRAVERSE
IN FIGURE 96.
188. (Not including the side shots)
Bearings
Dis-
tance
feet
Latitude
Departure
Balanced
From Sta. I.*
o
North
+
Soutli
East
+
West
Lat.
Dep.
Total
Lat.
Total
Dep.
I
S49°37'E
581
376.4
442.50
—383.22
+436.96
—383.22
+ 436.96
II
N89°14'E
300
4.01
299.90
+ .49
+297.03
—382.73
+ 733.99
III
N69'E
690
247.27
644.20
+239.17
+637.66
—143.56
+1371.65
IV
N88°W
400
13.96
399.7
+ 9.27
—403.51
—134.29
+ 968.14
B'
NeS'W
600
253.50
543.78
+246.46
—549.49
+112.17
+ 418.65
Totals 2571
518.74
376.4
376.4
1386.60
943.48
943.48
+112.17
+418.65
Difference A to B'
+142.34
+443.12
C
Dep
in p
latio
orrect La
A to B.
revious tr
n.)
t. and
found
iangu-
+112.14
+418.62
Corrections. . .. — 30.20
—24.5
Correction of Latitude at end of any course =
( — ) — ^ X length of course.
Correction of Departure at end of any course =
24 5
( — ) ' X length of course.
^o i X
All stations in the table are moved west and south.
*Tlie total latitudes and departures are used in plotting from the original
origin, see par. 186.
CHAPTER VIII.
CONTOUR SURVEYING.
189. The plane-table and transit are used for
locating contours on the ground and plotting their
position on the map as foUows, two distinct opera-
tions being performed:
1st. Points on the contour are located, using
the transit as a level to carry the elevation from the
nearest B. M. The position of the T. P.'s and lev-
el stations are not plotted on the sheet.
2nd. Each critical point located on the contour
by the leveling operation is plotted on the plane
table sheet.
With the transit used as a level (see leveling,
par. 134) a line of differential levels is run from
the nearest B. M., figure 100 (a), until a T. P. is
set about one foot above the first contour to be lo-
cated (T. P. II). Having located this T. P. on
the ground, a plane table traverse is run from the
nearest triangulation or other known station, as
A, using the transit for reading the stadia distance
only, and plotting the courses a 1, 1 2, 2 3, figin-e
100 (b), on the plane table sheet, until a plane
table station, as III, figure 100 (a), is reached
where the H. I. of the transit will be about 8 or 10
feet above the contour. The plane table and tran-
sit being set up side by side (par. 163) at this sta-
tion, a B S. is taken with the transit (telescope
190
Contour Sur\'eying
191
c..-.*^.
J
lOOa
Oa
Fig. lOOb
bubble in the center of the tube) on T. P. II, and
added to the elevation of T. P. II, giving the H. I.
at station III. The elevation of the contour sub-
tracted from this H. I. gives the difference of ele-
vation from the H. I. down to the contour, or the
point at which the target must he set so that the
foot of the rod will be on the contour when the tar-
get is bisected by the cross-wires of the leveled tele-
scope. With the target set at this reading, the ob-
server directs the rodman to critical points on the
contour as C. P. I, C. P. II, etc., motioning him
up or down hill until the center horizontal cross
wire is on the target. Each contour point thus
found is located on the plane table-sheet, as 1, 2, 3,
etc., figure 100 (b), by a sight taken through the
alidade for direction, and a stadia distance-reading
192 Military Topography for Mobile Forces
with the transit, plotted in the direction just found.
After each stadia-reading the telescope is careful-
ly leveled again by placing the telescope bubble in
the center of the tube. Having located aU critical
points within range of stadia-readings, the work
is moved forward by the two steps following:
190. 1st. To locate a new T. P. [as T. P. IV.
figure 100 (a)] with the transit used as a level.
2nd. To locate a new plane table stationj sta-
tion IV figure 100 (a), on the ground and plot it
on the sheet, station 4 figure 100 (b).
The level rodman is directed to pick out, about
one foot above the contour a T. P. (as T. P. IV)
which can be seen from the station III and from
the station point in advance, as sta. IV. A F. S.
is taken on the T. P. from sta. III. The stadia
rodman is now directed to place a plane table sta-
tion forward along the contoiu- (as at station IV),
so that the H. I. at that point, wiU be about 8
or 10 feet above the contour. This station is plot-
ted as above described. The plane-table and tran-
sit are set up side by side at station IV. The
plane table is oriented by a back sight on sta-
tion III, and the work proceeds similarly to the
end. The level notes and a record of the stadia
readings should be kept as shown below, so that in
case the traverse does not close in elevation, or hori-
1
zontally within about , on a triangulation sta-
^ 300 ^
lion near the end of the contour, an adjustment of
the traverse can be made (see par. 159) and the
Contour Surveying
193
contour points can be plotted from the adjusted
positions of the stations.
191.
CONTOUE SURVEY NOTES.
Plane Table Notes |
Level Notes
At
Station
Point
Observed
Stadia
Vertical
angle
Hor.
Dist.
Eleva-
tion
B. S.
+
H.I.
F. S
Remarks
01
B. M.
835.000
10.000
845.000
(Level Sta-
tions marked
0)
OI
T.P.I
843.625
1.375
(Plane-table
stations
marked D)
Gil
T.P.I
12.000
855.625
OH
T. P. II
851.500
4.125
DI
A
220
— 6°30'
213
( No reduc-
DI
nil
300
+ 30'
300
zontal made
BII
DI
300
— 30'
300
5°)
QII
Dili
500
+1-30'
500
0III
HIII
T. P. II
9.000
860.500
860.500--850.
000=10.5 =
set rod tar-
get.
QUI
QUI
nil
500
— 1°30'
500
C.P.I
800
—
800
C. P. II
300
—
300
C. P. Ill
ISO
—
150
T. P. IV
851.500
9.000
a IV
800
—
800
DIV
niii
800
800
T. P. IV
8.00
S59.500
192. Two contours can be run at once by hav-
ing two targets on the level rod one contour inter-
val apart, or two level rods with their targets set
a contour interval apart. The transit alone could
be used, instead of the plane table, to determine
horizontal directions but a large part of the topo-
graphical training of the eye would thus be lost.
194 Military Topography for Mobile Forces
This method of contour location is not as rapid
as that of par. 165, but is of the greatest value in
learning to estimate the position of contours on
the ground and their map representation, also to
estimate distances and elevations, all of which are
important in learning to make rapid sketches. Each
distance should he estimated and then checked with
the stadia; each elevation estimated and then
checked with leveled transit; each contour point,
estimated and then checked hy the sight on level
rod. Constant practice of this kind will increase a
student's knowledge of ground rapidly.
CHAPTER IX.
INSTRUMENTS USED IN FINISHING
THE MAP AND METHODS OF
USING THEM.
193. Kohinoor Pencils: Numbers 6H and
HB (or H), figure 101. The 6H are very hard
Fig. 101
and suitable for drawing fine construction lines;
the HB are soft and suitable for drawing heavy
black lines as on a tracing to be blue-printed. All
of the field sheet should be executed with a well-
sharpened 6H pencil, because of the fine lines pos-
sible, the ease with which erasures are made, and
because of the cleanliness of its lines as compared
with those of HB.
194. To draw a pencil line: Hold the pencil
vertical with its point close to the straight or curved
ruler determining the hne. To draw an accurate
free hand line, such as a contour: rest the right side
of the hand on the paper, knuckles to the front.
Sketch in with very light strokes toward the body
the desired line, correcting it until the exact posi-
tion desired is secured.
195
196 Military Topogeaphy for Mobile Forces
195. Drawing Paper: For plane table work
Unchangeable Drawing Board, a heavy paper
which does not appreciably change its size under
varying atmospheric conditions, is the best. For
indoor plotting Whatman Hot Pressed Paper has
a fine surface for pencil or ink lines.
196. Standard Cross Section Paper: see figure
102, with squares 5 x 5 to the half inch, or Profile
Fig. 102
Fig. lOS
Paper, figure 103, is the most suitable for the in-
terpolation of contours see par. 167; for plotting
profiles, see par. 140 ; or for plotting a transit sur-
vey from rectangular co-ordinates, see par. 184.
197. Universal Pocket Compass and Dividers:
figure 104. With this instrument, pencil and ink
circles or right lines can be drawn. With the needle
point ends in position for use, distances may be tak-
Instruments Used in Finishing Map 197
Fig. 105
en from a map or from working scales or
scale of equal parts. This is one of the
most conveniently carried and generally
Fig. 104 useful of drawing instruments. It is
about the size of a knife and may be car-
ried in the pocket. (Figure 105 shows a conven-
ient set of drawing instruments).
198. Scale of Equal Parts: figure 106, has on
its different faces scales of lOths, 20ths, 30ths,
Fig. 106
40ths, 50ths and 60ths of an inch. To lay off a
distance with the scale, place the zero on the known
point and prick a very minute hole exactly oppo-
site the unknown point, being careful to hold the
plotting point (wax headed needle) exactly ver-
tical.
198 Military Topogbaphy for Mobile Forces
199. Circular Protractor^ figure 107 (a) , of cel-
luoid. Angles are laid off with it by laying the zero
— 180° line exactly on the given line on the map,
with the protractor center at the given point. The
Fig. 107o
Fig. I07fc
given angle is marked with a minute hole in the
paper opposite the proper angle marked on the
circumference of the protractor, and a fine hne is
drawn from the given point through this pricked
hole. Figure 107 (b) is a more accurate protrac-
tor.
Instruments Used in Finishing Map 199
200. T Square and Right Angle Triangle'.
Figure 108, for drawing parallel and perpendicu-
lar lines. The T head should be used along only
Fig. 108
one edge of the plotting board, because of the dif-
ficulty of securing a board with two sides perfectly
perpendicular to each other. To draw perpendicu-
lars to the parallel lines, the triangle is placed and
moved against a leg of the T square.
201. To draw more exact perpendiculars to a
given line, through a given point outside of the
Une, as a figure 109: with the compasses figure
104, describe an arc of a circle with the radius a b
Yd
-fe^
Fig. 109
Fig. 110
200 MlIiITAE,Y TOPOGKAPHY FOE MOBILE FORCES
cutting the line in b and c. Bisect a c at d, (see
par. 202) join a d which is perpendicular to b c.
To draw a perpendicular at the end of a line as a^,
figure 110, assiune a point c outside the line and
draw an arc through a. From b draw the line b c
to the arc at d. da is perpendicular to a b.
202. To bisect a line as b c; with b as a center
and a radius somewhat greater than J {be) cut the
two arcs at a and e; cut arcs similarly from c at a
and e. Join the points of intersection of the arcs
a and e with a straight line which bisects the line
b c. This line a e is perpendicular to & c at dj and
its construction gives a method of drawing a per-
pendicular to a line b c from a point on that hne as
dj first locating b and c at equal distances from d.
203. To divide a line into any number of equal
parts, see par. 19.
Right Line Pen, figtire 105 ; this pen is used for
drawing hues along the edge of a straight or curved
ruler. It is inked by dipping the nib of an ordinary
pen in the ink and then inserting it in the opening
between the points. The width of hne is fixed by
the screw on the pen. The two edges should never
be forced entirely together. The pen should be held
vertical, points close to the ruler's edge, and the line
be drawn toward the right. To clean the pen, pass a
clean piece of heavy paper between the points. If
a very heavy line is desired, first draw two parallel
Instruments Used in Finishing Map 201
medium lines and when dry fill in between them
with an ordinary fine pointed pen.
204. Contour P^n, figure 112: This is intended
for drawing a regular free hand curve such as a-
contour. Considerable practice is required before
it can be used well. The pen hand should rest only
Fig. 112
on the tip of the little finger, and the pen point
should rest lightly on the paper, inclined shghtly
away from the draftsman's body and always fol-
lowing the movement of the hand. The line is
most easily drawn away from the body toward the
right. With practice the draftsman can draw the
lines in any direction.
205. Tracing Paper: The pencil field sheet is
traced on this paper previous to blue printing the
map.
Tracing Cloth is used for trac-
ing where greater durability is de-
manded. The smooth side of the
cloth is intended for ink lines;
pencil or ink lines may be drawn
on the rough side.
206. Drawing Ink, comes in
bottles fig. 113, or sticks fig. 114.
The best for general use is India
Ink in stick form. This is pre-
pared for use by rubbing the stick
Fig. lis
202 Military Topography for Mobile Forces
in a small mortar, figure. 115, with a small quantity
of water until the lines drawn appear perfectly
hlack.
Fig. 114
Fig. 115
Thumb Tacks, figure 116, have flat heads so as
to be easily forced with the thumb into the draw-
ing paper and are used to secure it to the plotting
board.
Fig. 116
A sharp knife figure 118, is a good eraser; a
soft rubber eraser, figure 117, is necessary for eras-
I ll O* \ WON > t * 1 1 ( i -t t ( t !■ 1 1 1 ( M <
Ffeiilroads Double track iMi ii iii i iimiM ii i ii i i ii ii ri i
Trollev 1 1 1 1 1 ■ i m ■ 1 1 rWT' i i m 1 1 1 ■ i m 1 1 1 1 1
Improved =
Roads Unimproved ============== = ==== = = -
Trail
barbed wire - »■■ *'' — — « — » •' "
smooth wire — • — »— • — • — ■ ■ « — ■ — — ~-
Fences wood aaaaaaaaaaaaaaaaaaa
hedge — . -Tjjgp —
Fig. 144
•The sign for hedge given above is not as satisfactory as
that shown in figure 147, p. 284, along the west edge of the
sketch. The symbols for wire fences along roads should be
placed on the lines used to mark the roads.
260 MiLiTAHY Topography foe Mobile Forces
the name of the growth in a given enclosure, as
CORN, WHEAT, CULT, (for Cultivated). In the same
manner, with marginal notes and simple drawings,
the character and condition of roads, ferries, bridg-
Bridgs
Indicate character and span by abbreviations.
Example:
!LikB,
MeanmlwocxJen kingpost brid§e.40feetlon|, 20 feet wide,
and 10 feet eJxive the water
Streams
Indicate character by abbreviations.
Example: ^^'~^^!!^*jv„f
Meanin|a stream 15 feet wide, 8 feet deep, and not fbrdable.
House • Church* School house -S.K
Woods f'wbods y Orchante lTTTl Cultivated Land lCult |
If boundary lines are fences th^ are indicated as such.
Brush, crops or gpass. important as cover or fora^
Cemetery | *♦ ** **\ Trees. isolated
, Cut
Brush, corn,:
&ios.etc.
Cut and fill —
10'
Fill
cut 10 feet deep
fill 10 feet high
For more elaborate map work the authorized conventional sigis are used.
Fig. 145
All lettering on Position, Bead and Place Sketches, except
names of streams and Toads, should be made so as to be read
facing north. The lettering on Outpost sketches is to be read
facing toward the enemy.
Sketching Methods 261
es, fords, buildings, etc., should be described; the
sketch should be amplified by a Reconnaissance Re-
port of the terrain, where conditions make it nec-
essary, see par. 312. Points from which excep-
tionally extended views are obtainable should be
marked in the margin, see reference to d, figure
143.
Prominent ridges, commanding positions, church
spires, towns, etc., when visible, should have their
direction marked by an arrow, with their approxi-
mate distance marked on it (see figiu-e 143, to Sol-
diers' Home from C) even when several miles dis-
tant.
263. Sketches should be made on tracing paper,
in firm pencil lines using a soft black pencil (HB) ,
so that blue prints may be made directly from the
sketch without the waste of time and labor of trac-
ing. Since a mmaber of copies of almost every mil-
itary sketch must be made in the shortest possible
time, they should never be finished on heavy draw-
ing paper (except in the early practice work) nor
in colors, unless copies of the original are not de-
sired. In combined sketching, the work of all the
sketchers should be uniform as to heaviness of hnes
and size of conventional signs. In case colors are
used, the following system should be followed:
Yellow for roads; green for trees; blue for water;
red for stone structures; brown for contours and
wooden structures. On the finished sketch, as in-
tended for issue (whether blue print or original
drawing), colors may be used with added clearness.
262 MiLITABY TOPOGEAPHY FOR MOBILE FORCES
264. In making a military sketch the import-
ant considerations are clearness, accuracy sufficient
for all military requirements, simplicity and the
completed sketch in the time available.
Only details of military importance should be
shown. Objects which are valuable from a tactical
standpoint should be constantly kept in mind. It is
of far greater importance to show location, shape
and character of a wooded area by drawing its out-
line of conventional signs, within which is written
its character, than to carefully fill up an area of
incorrect size and shape with symbols for woods.
Information of a wide dead space formed by a con-
vex slope in front of a proposed defensive line is
more important to the commander than the exact
height of the position; therefore care should be used
in spacing contours to show the ground as it really
exists.
Under service conditions, the importance of fin-
ishing the entire assigned area in the allotted time
can hardly be overestimated; but in learning to
sketch, accuracy and clearness should be the only
considerations. The sketcher should, therefore, in
his early sketches, measure every distance, slope and
elevation, after making in each case careful esti-
mates; and he should only begin to depend on his
estimates when positive that they are sufficiently
accurate.
Distances to individual points off the main con-
trol lines (traverse or triangulation) should not be
in error more than fifteen per cent; plainly visible
Sketching Methods 263
slopes should be correct to within one degree; dif-
ferences of elevation, within one contour at distan-
ces up to five hundred yards from the traverse.
In case the sketcher has had a course of surveying
with precise instruments as described in Part II, he
should be able, on its completion, to estimate dis-
tances, slopes, and elevations so accurately that he
may dispense with many of the measurements to
points off the main control lines after his fourth or
fifth sketch. It is well for the sketcher to bear in
mind that on the principal control lines accuracy is
of first importance, but in locating any single point
from which no other points are determined, its gen-
eral position relative to the remainder of the sketch
is sufficient. Rapidity is gained at the expense of
accuracy in some parts of the work, and the differ-
ence between a fair and an excellent sketch depends
much on the correct choice of the part of the sketch
where accuracy is paramount and where it is unim-
portant. The balancing of accuracy and rapidity is
taken up in detail vmder Position and Road Sketch-
ing ; but in the first sketches accuracy is everything.
CLASSIFICATION OF MILITARY SKETCHES.
265. Military sketches are classified as individ-
ual or combined sketches. An individual sketch is of
limited extent, executed by one person. A combined
sketch is the result of the simultaneous work of a
number of sketchers, so combined as to make a map
covering a number of parallel roads (Combined
Road Sketch), or an area extending across the
264 Military Topography for Mobile Forces
front of the command (Combined Position
Sketch) .
Mihtary sketches are also classified according
to their object or the method of their execution as:
1. Area Sketches, which are of three kinds (a)
Position, (b) Outpost, (c) Place Sketches.
2. Road Sketches.
A Position Sketch is one of a military position,
camp site, etc., made by a sketcher who has access
to all parts of the area to be sketched.
An Outpost Sketch, as its name indicates, shows
the military features of groim^d along the friendly
outpost line and as far toward the hostile position
as may be sketched from the rear of and along the
line of observation.
A Place Sketch is one of an area, made by a
sketcher from one point of observation. Such a
sketch may cover ground in front of an outpost
line, or it may serve to extend toward the enemy a
position or road sketch from the farthest point
which can be reached by the sketcher.
CHAPTER III.
METHODS OF SKETCHING.
266. The Location of Critical Points. Having
learned the uses of military sketches and the details
to be represented, it is next in order to take up the
methods used for determining the location of the
necessary critical points, see par. 166, figure 93,
around which the features themselves are sketched.*
Every critical point desired must be determined :
(1) Horizontally, that is its horizontal distance
and its horizontal angle of direction (azimuth)
from the north-south line must be found, with ref-
erence to a starting point, assumed or known; (2)
Vertically, either by finding its difference of eleva-
tion directly or by determining this difference of
elevation from the slope and distance to the desired
point with reference to the known point. A begin-
ner finds it much simpler to become thoroughly fa-
miliar with the making of horizontal locations, be-
fore attempting the vertical locations, from which
contours showing the slope of the ground are deter-
mined. For this reason contouring is taken up aft-
er the description of plotting in the horizontal de-
tails ; and the beginner should practice making hori-
zontal traverses, and triangulations, and dra^ving
*A critical point is one at which there is an abrupt change of
general slope, or an abrupt change of horizontal direction.
265
266 MiLiTAHY Topography fob, Mobile Forces
details such as roads, woods, buildings, streams, be-
fore he attempts a contoured sketch.
267. The Horizontal Location of a Point may
he determined either by:
(1) Traverse, or
(2) Intersection^, or
(3) Resection, or
(4) Of set, or
(5) By estimation of distance and measure-
ment, or estimation, of direction.
268. 1. The location of an unknown point, as
B, with respect to a known point, as A, by travers-
ing.
The drawing board, figure 135, p. 245, is set up
at A, figure 147, p. 284, and levelled as accurately
as possible by eye. The board is then oriented by
rotating it horizontally until the magnetic needle of
the attached compass points north. At every sta-
tion the board must have this same angular position,
so that every line on the sketch will always be par-
allel to the corresponding line on the ground. As-
suming a point a on the paper in such a position
that the ground to be sketched will fall on the
sheet, lay the ruler on the board and point it toward
B all the while keeping the edge of the ruler on the
point a. Draw an indefinite line along the ruler's
edge from a toward b. Now walk to B, counting
strides and keeping a record of them with a tally
register, par. 229. With the scale of the sketch-
er's strides on the ruler, lay off the number of strides
found from A to B and mark the point b. Other
Methods of Sketching 267
points, as C, F, etc., would be located in the same
m.inner.
269. 2. The Location of an Unknown Point,
as K, with respect to two known and plotted points,
as T and C, figure 147, hy intersection.
Set up, level, and orient drawing board at T, by
laying the ruler along the line t c and rotating the
board horizontally until the ruler points exactly to-
ward C. (This is called orientation hy hack sight,
as opposed to that described at station A, which is
orientation with the needle.
Lay the ruler on the board, sight and draw a ray
toward K. This ray need not be drawn entirely
up to t, but only for a short length at the estimated
distance to scale of K from T. Now move to C, as-
sumed to be already plotted on the sheet in c, and
having set up, levelled and oriented by a back sight
to T, sight toward K, as done from T. The inter-
section of these two rays locates K on the sheet at k.
Having c and k thus located, they may be used in
the same manner for determining other points by
intersection. It is seen from the above that a point
is located by intersection without the sketcher's go-
ing to that point. To locate a point by resection
the board must be set up on the ground at the point
whose position on the sketch is desired.
270. 3. The Location of a Point by Resection.
1st Method. Having given a direction line, as c g
figure 147, p. 284, on which lies the desired point,
and a plotted point, as k, outside of that line; to
determine the position on the sketch of any point
268 MiiiiTAHY Topography for Mobile Forces
on the line C Q, as Z: Set up, and level the board
at Z, then orient by laying the ruler on c g and ro-
tating the board until the ruler points at C. Clamp
the board in this position. Pivot the ruler about a
w^ax headed needle stuck at k and sight K. Draw
a ray along the ruler and its intersection with the
line c q locates Z on the sketch at z. This method
is as accurate as the method of intersection because
of the exact orientation secured by back sight on C.
2d Method. Having given two plotted points,
as t and c, fig. 147, to determine the position on the
sketch, kj of a point K on the ground. Set up, and
level the table at K, orienting with the needle.
Clamp the board. Pivot the alidade on t, at the
same time sighting T, and draw a ray along the
ruler toward your body at the estimated position of
k. Similarly, pivot the alidade on c sighting C,
drawing a ray until it cuts the one from t and this
point of intersection is the required point k. This
method is available as soon as two visible points are
plotted, and finds very frequent use in sketching in
details around a point such as K^ which is not to be
used to extend the triangulation. Both of these
two methods are of great value in position sketch-
ing. The 3d and 4th Methods of resection, par.
155, Part II, may also be used, but they will only
be advisable in rare instances.
271. 4. The Location of Points by Offset.
This consists in measuring distances perpendicular
to the traverse for locating details. For example,
a winding road Z L might be located by sighting
Methods of Sketching 269
from Z towards L and drawing the ray z I, figure
147. The distance from Z to L is then measured
along the ray (or along the road itself) and the crit-
ical points 3, 4 and 5 located by offsets perpendicu-
lar to the ray. The most general use of this meth-
od is in locating details along a traverse where the
offsets are made by estimation.
272. Methods in detail of -finding the elevation
of an unknown point D from a known point A,
figure 148, p. 284, and the location of contours on
this line.
1. Measure the slope from A to D with clino-
meter, or slope board, and the horizontal distance by
traversing, intersection or resection. Plot to scale
the distance found and apply the M. D. for this
slope successively along the plotted length. The
nimiber of times the M. D. is applied, multiphed
by the contour interval (V. I.) equals the differ-
ence of elevation between A and D. For example,
suppose A, figure 148, is at elevation 800; distance
a to d as plotted 2.5 inches; V. I.^IO feet; slope
from A to D=+li°. The M. D. for 1^° is found
to be contained 5f times between a and d; 5f X10=
57.5 feet. D is therefore at elevation 800+57.5=
857.5. Now looking at the ground along A D, you
find it to be a slightly concave (hollowed out) slope
north of the bridge and steeper near the top. There
are to be placed in the space a d contours 800 (at
a) , 810, 820, etc. to 850; they would be spaced close
together at the top and farther apart towards the
bottom in order to give a true representation of the
270 Military Topography foe Mobile Forces
slope. South of the bridge (1) the ground is level
and consequently no contours appear here.
In rare cases only do the slopes of hills change
so suddenly at any one point that the actual condi-
tion of slope can be shown by a mechanically ex-
act interpolation of contours by the application of
the scale of M. D.'s. above or below this point of
change. Suppose, however, such a case does exist as
shown between ao and e at y, figure 143, p. 255. This
condition could be shown only by reading the slope
and measuring the distance from X to Y and from
Y to E. 00 y and y e could then be plotted to scale
and the 6 degree contom-s spaced uniformly along
X y, using the scale of M. D.'s. This assumes that
the point of change of slope Y on the ground can
be exactly located, but in reahty there is always
more or less vmcertainty as to the exact point at
which the change takes place. Moreover, it is ex-
ceptional to find ground sloping exactly uniformly
as X Y. The usual case is either a convex or con-
cave slope, changing so gradually from point to
point that the observer can not pick out the exact
points of change, much less be able to mechanically
show these points by contours. He can however
represent by contours the general character of the
slope accurately by contours properly spaced.
In the older text books a laborious method of
contouring was prescribed in which the sketcher
would pace along a slope to each point of change
and plot the contours on these portions. This meth-
od is impossible for rapid sketching on accoiuit of
Methods of Sketching 271
its slowness and is moreover inaccurate on account
of the accumulation of errors due to frequent short
readings to unimportant points.
In military sketching the essential feature sought
in contouring is to convey to the reader of the
sketch a correct representation of the ground as it
appeared to the eye of the sketcher. The sketcher
can only give this information by determining the
difference of elevation between two definite points,
at the top and bottom of the hne, and then, know-
ing the number of contours required, spacing them
to show the variations of slope as they appear to
him. For this reason great stress has been laid on
the necessity of acquiring by dihgent practice the
ability to estimate the map distance corresponding
to each degree of slope usually met with.
Sd Method — Measure the difference of elevation
directly with the barometer, and space the contours
required by this determined difference of elevation
to show the actual slope of the ground.
Method of Contouring After Acquiring Skill in
Estimating Distances, Elevations and Slopes.
273. 1. Estimate the difference of elevation
between A and D, Fig. 148, and, space the con-
tours by eye. Or the nvmiber of contour intervals
between A and D may be estimated. In this case
the number of contours, including the top and bot-
tom ones, is one greater than the nimiber of contour
intervals.
272 Military Topography for Mobile Forces
When a Generally Uniform Slope Extends to the
Ldmits of the Sketch.
274. 1. Read the slope with a clinometer or
slope board, and with the scale of M. D.'s for the
slope locate contours to the limits of the sketch
without determining the elevation of any point on
the Une other than the one known.
2. After skill in estimating is acquired^ estimate
the slope and plot the contours with the scale of
M. D.'s.
3. After skill in plotting by estimation of the
Map Distances corresponding to different slopes is
acquired, estimate the slope and space the contours
by estimation.
THE EXECUTION OF A POSITION SKETCH IN
DETAIL.
275. The instruments required by a beginner
are preferably the following, but others may be
used as noted below:
1. Drawing Board with Declinator on Tripod,
figure 135, p. 241, see par. 240.
2. Loose Ruler, figure 137, with scales de-
scribed par. 243, figure 136, p. 242.
3. Service Clinometer, figure 138, see par. 244,
carried in upper right blouse pocket, and seciu-ed to
it by a strong cord.
4. Tally Register, par. 229, attached by a string
and carried in the left trousers pocket.
5. Equipped Pencil, Knife and Ruler Holder,
figure 146. This may be made of heavy canvas
sewed over a board frame. It should be secured to
Methods of Sketching
273
Fig. 146
the sketcher's blouse on his left breast. The knife
and ruler may well be fastened to the holder as
shown, to prevent their being lost.
It will be of great value to the sketcher to have
one definite place for each article of equipment,
and one well fixed method of performing each op-
eration in sketching so that there may be no hesita-
tion in the work. Sketching utensils have a remark-
able habit of losing themselves, unless they are tied
to something or placed in some particular recepta-
cle after each use. Pencils of different degrees of
hardness should be marked clearly so as to avoid
delay in taking out the proper one. The points
should be protected by rubbed-tipped brass covers.
6. A Soft Rubber Eraser may be carried at-
tached to a cord around the sketcher's neck.
274 Military Topography foe Mobile Fokces
7. Field Glasses are of considerable value in
picking out distant points for intersection or re-
section, and for studying the details of ground
forms at a distance. If used they should be car-
ried on a waist belt. It is well to have a reserve of
at least one each, of the ruler, rubber eraser, pencils
and a sheet of celluloid for use in rain, all carried
in a haversack, or dispatch case.
METHODS OF WORK.
276. The detailed methods of using the instru-
ments have been given heretofore. A description
will first be given of the methods of locating the
horizontal details only, followed by the methods of
contouring the area. It will be best for the begin-
ner to pursue this system in his first two or three
sketches, of locating and drawing in roads, streams,
woods and all other horizontal details, and on this
frame-work later locating his contours. To do both
simultaneously will at first prove confusing because
of the large nimiber of matters to be kept in view.
However, both horizontal details and contours can
be carried on together from the start if so desired,
but no effort should be made to do rapid work un-
til the methods are familiar.
1. Select and Traverse a Base Ldne.*
2. Locate a Series of Critical Points over the
area by Intersection.
3. Fill in the detail, par. 260, in the vicinity of
these triangulation points, see figures 144 and 145,
*It is assumed that you have previously determined your
length of stride and have constructed a scale of strides, par. 229.
Methods of Sketching 275
p. 260, for conventional signs prescribed by Field
Service Regulations for sketches.
A. Fill in detail around other important points
located by Resection.
6. Fill in all other required details by Traverse
to all necessary points not visible from the Inter-
section or Resection Stations.
277. The Base is a line in the area to be
sketched, as centrally located as possible, and from
one-fourth to two miles long depending on the size
of the area. It should be long enough so that lines
drawn from its ends to locate necessary critical
points by intersection, wiU intersect at angles be-
tween 30° and 120° to give accurate locations. Its
length should generally be not less than one-third
as long as the greatest dimension of the area to
avoid having to extend small triangles too great a
distance from the original base. Often a shorter
base can be used if located in the middle of the area
than if near one end, because the extension of in-
tersection points would be made on both sides of the
base.
The ends of the base should be marked by some
well defined objects, such as telegraph poles, trees,
comers of buildings, or even temporary poles,
branches of trees, weeds, etc., set up by the sketch-
er so that they may be seen by him from a distance
in sighting back on these points. If an object such
as a telegraph pole is chosen as an end of the base,
so that the board cannot be set up exactly imder
the point which will later be used to sight back on,
276 MiLiTAEY Topography for Mobilk Forces
the sketcher orients his board near the pole and
draws a short ray toward it, pacing and plotting its
distance, to scale, measured from the board's loca-
tion. The pole is thus located accurately on the
sheet for back sighting purposes though the board
is never set up exactly at that point. This method
would also be useful where local attraction is known
to exist at the desired station point, as in the vicini-
ty of poles carrying heavy electric currents.
An extensive view of the area should be possi-
ble from the ends and from several intermediate
points of the base. If the area is intersected by
ridges and valleys, the best base is usually to be
found along a central ridge ( because from this po-
sition the two adjacent valleys are visible as far as
the tops of the two ridges beyond. If the ridges
are very flat topped and convex in shape, so as to
prevent a good view into the two adjoining valleys,
it may be advisable to locate the base perpendicu-
lar to the axes of the ridges, though the pacing up
and down hiU is less accurate. A road or railway
crossing the area more or less perpendicular to the
ridges and valleys, gives a very good base. The ac-
curacy of pacing the base is of great importance,
becaus,e errors made in this part of the work ex-
tend and accxmiulate over the entire area. To se-
cure this accuracy, the base should, where possible,
be generally level and lie over firm soil such as
roads, trails, railroads or pasture land.
In figure 147, p. 284, the broken base ABC,
along an edge and extending across the middle, is
Methods of Sketching 277
chosen because of the good view obtainable, the
good pacing possible along the road and railroad,
and the central location afforded. It is started
from A because this happens to be the first point
of the area reached in going to work; and also be-
cause sights to B and to D determine two boundar-
ies of the area. The length of this base is such that
triangles with suitable angles of intersection are
possible as shown in figure 147. The telegraph
poles along B C give good points to resect on. In
figure 143, p. 255, the base used was A, B, C, E,
because from this line a better view over the area
was possible than from any base in the center of the
area.
278. To Traverse the Base. Set up, level and
orient the board at one end of the base. A, figure
147. Draw a meridian on the edge of the sheet par-
allel to the declinator trough's edge. It is well to
form the habit of placing the sheet on the board
with an edge parallel to the N-S line of the declin-
ator, so that you can always use this edge and the
other parallel edge as meridians. Assume a point
a on the sheet corresponding to A on the ground.
In this sketch a telegraph pole is selected, and the
corresponding point on the sketch is taken near the
southeast corner of the sheet because the area hes
to the north and west.
From the first station, prominent easily distin-
guishable points are sighted, such as hiU tops,
stream junctions, stream heads, etc., to begin the
278 Military Topography for Mobile Forces
location of these critical points, by intersection.* In
figure 147 sight along road A B and A D and to-
ward the stream junction Y, drawing light indefin-
ite lines (rays) with 4 H pencil towards these
points. Traverse from A, noting the number of
strides recorded on the tally register opposite the
house and the wire fence north of road A B but
without halting until B is reached.
279. Procedure at B. Halt, set up, and orient
the board by a back sight on A. With the scale of
strides on ruler, scale off the distance from A to
B also from A to house and to wire fence. Now,
before the orientation has been disturbed by the
work done on the board, pick out with your field
glasses the next station, C, an ehn tree on top of
a railway cut, sight and draw a ray in its direction.
Next draw in with H (or HB) pencil the road A
B, the house at its estimated distance from the road
and sketch the wire fence in the direction it was ob-
served to lie. Take a careful sight at the chimney
of Flint House, which is a prominent point visible
*lt is well to have a systematic order of taking the inter-
section sights from any station, as for instance, from right to
left across the front, so that no desired object will be overlooked
by a haphazard method. These objects sighted should also be re-
corded systematically so that the different rays will not be con-
fused when the time comes to finish the intersections. This is
best accomplished by placing a serial number exactly on each
ray from a station; and on the edge of the sheet, placing a tabu-
lated list of these sights for each station as follows:
From Station A —
Sights:
1. Road A D.
2. Wire fence corner.
3. Stream junction.
Methods of Sketching 279
from all parts of the area and will be useful as a
point to resect on. Traverse toward C, halting at
X. On the top of the bank here, set up, orient by
a back sight and take the following observations:
Flint chimney; bridge north of A; hill top at road
A D north of this bridge (north limit of sketch) ;
directly up the ravine line north of X; to the stream
jimction just east of the railroad track; to Y. Now
sketch the Flint House and bam; the wire fence
east of X running toward the north and its branch
to the road A D ; the stream from Y to road A D
and trees along it; the three small ravine lines join-
ing this part of the main stream from the south;
telegraph hne along the railroad right of way to-
ward B; the orchards at Fhnt and at A.
280. Traverse toward C, noting the recorded
strides at G and the ridge north of it. Halt and set
up at T (south end of bridge). Scale off T, G,
etc., from B. Sight on K and along the main
stream to the east and west, also up the draw east of
C ; to intersection of roads A B and L Z also ridge
top at M ; sketch in the main stream east to Y and
the branch ravine lines on this section ; the trees and
stream banks (shown by hachures or brief statement
of condition), and the railroad track back to X.
M is at the intersection of the north edge of road A
B with the ridge top, and its map representation m
is at the intersection of t m and a h prolonged. In
the same way, later on, from station K the other
critical points (ridges and valleys in this case) on
the road are located by drawing rays to intersection
280 Military Topography for Mobile Forces
with a b prolonged. It is well here to call attention
to the importance of locating all straight hnes in
the area such as the boundary fence of this road,
wire fences, hedges, straight line of telephone poles,
etc., because they furnish a valuable means of lo-
cating any points on them by intersection as was
done in the location of M from T.
Continue the traverse to C, noting number of
strides at wire fence corner without halting. At C
halt, set up and draw in detail between C and T,
also the wire fence east to D. The east end of this
fence was found from X by intersection on the line
a d from the 1st station, A.
It wiU be observed that you have now located aU
the horizontal details east of your Base without
traversing any of this area, with a great resultant
saving of time. All of this work has been done
by traversing along the Base and locating the neces-
sary critical points east of it by intersection. Sight
to K to complete its location, also to the point where
road Z L crosses stream, and the ravine line junc-
tion with the main stream south of C.
281. Resection at Z. It is now necessary to
carry the work forward from C, but on hill Z there
is no definite point which could be located with cer-
tainty from T and C by intersection. You there-
fore look for something to sight on, so as to estab-
lish a direction hne on which you can place your-
self after reaching hill Z. You observe that you
can look exactly up a small ravine toward a tree
at Q, so draw a ray in this direction. (A well de-
Methods of Sketching 281
fined fence corner, bush, etc., woxild be equally as
satisfactory as the ravine to sight on.) Move at
once to the top of hiU Z and place yourself on the
direction line from C, at the most convenient point
of the hill for observing the ground (on road Z L) .
Set up and locate your position by resection on K,
and sight the stream junction toward K, also
the draw S by estimating its number of yards
from Z. Sight along the general direction of
road L Z. You observe that a hedge fence ex-
tends along the western boundary through Q. You
have not located this hedge, but observe that you
will be able to do so by intersection from Z and K
on two of its points, Q and R. Therefore, sight
from Z at these two points on the hedge, then move
to K and complete their location. Draw in the
hedge R Q, thus locating all the critical points
sighted on this line from E. From K locate the
critical points on road A B as described above.
Draw in aU the water course and water shed lines
west of the railroad, for which sufficient critical
points are now known; also the other details such
as roads, trees, houses, wire fences, etc.
282. It will be observed that the horizontal de-
tails of this sketch have been put in by use of the
methods of traversing, offsets (along the base), in-
tersection {dj m, h, q, etc.), and resection (z). S
was located by estimation, since it was only about
200 yards from Z. A small amount of estimating
has been done in getting the directions of ravines
and of water sheds of ridges, between the two or
282 Military Topography for Mobile Forces
more points located on them. Gradually you can
increase the amount of freehand sketching hased on
estimation as you acquire skill from practice. The
portions of the area located by resection, intersec-
tion or traverse wiU vary in amount for each par-
ticular sketch, depending on the nature of the
ground, the amount of woods, etc., preventing good
views.
It is evident that the work from a carefully
paced base over fairly level groxind is more accurate
than if traverses were run all over the rough and
steep parts of the area. Therefore, as much of the
work is done by intersection and resection as possi-
ble, traversing (except along the base) being done
only where desired critical points are hidden by
woods, etc.
You will also observe that all sketching of de-
tails has been done toward the rear — ^that is, from
the last located point back to others previously de-
termined. This is a vital principle in all this work,
that no sketching should be done in front of the last
located point. (Except that local details may well
be put in by estimation for 50 to 100 yards forward
from each station. ) There is with beginners a strong
tendency to do this, especially in drawing contours,
but such work will usually be incorrect and have to
be erased, causing a waste of time and great confus-
ion to the sketcher.
CONTOURING THE POSITION SKETCH.
283. Having thus completed the location of the
horizontal details of the area, start in again at A
HORIZONTAL FRAME WORK OF POSITION) SHETCM AREA I
Scale - 6 in " I mile
_ RAYS TO CRITICAL POINTS
TO PROGRESS
18MILC5
Fig. 147
COMPLETE POSITION SKETCH. AREA!
Scale 6in.-1M;la
too IQO 3po 4f)0V08
TO PR00RC3S
18 MILES
SL 'SIO 600
^ V''\\TO LEAVEN-vVORTH
\\ J MILES
Fig 148
Methods of Sketching 283
to determine the vertical locations — ^that is, eleva-
tions, slopes, and the contours to represent the shape
of the ground. Suppose A to be at elevation 800
feet above sea level. On the sketch you now have
located the horizontal position of all stream lines^
draws (water flow hnes), and hill tops, figure 147,
From station A read carefully the vertical angle
(+1^°) to the top of hill D. Apply the M. D.
scale on the ruler to a A, and you find that there are
5 contours required, see par. 272, between A and D,
the 810, 820, 830, 840 and 850; but reading the
angle to the bridge north of A, you find its value is
zero degrees, or horizontal. Therefore all five of
the contours fall beyond the bridge and you can see
that the slope is gently concave. You therefore
sj^ace the contours accordingly to show this fact as
in the figure, 148.
284. Procedure at B. Next move to B and
read the angle to A ( — 1°), and applying the M.
D. scale, you find two contour intervals between
A and B the groimd is quite steep near B and flat
near A. You therefore space the contours as
shown in the figure. To verify your idea of how
close together to space the 810 and 820 contoiu-s,
read the slope from B to the foot of the hiU. You
find it to be ( — 3°) by applying the M. D. scale;
this agrees with the spacing already estimated.
While at B note the general slope of the road to
the west for use in spacing contoiu-s along it later.
Next move to X, set up and read the slope to
B (—3°), to Y (—3°), to G (—3°). Apphca-
284 MiLiTAUY Topography for Mobile Forces
tion of the scale of M. D., shows that B (820)
is 3f intervals below X. Hence X is at eleva-
tion 857. The slope from X to B is practically
uniform and the contours are spaced as shown.
Applying the M. D. scale, you find 5j intervals
from 00 to y. This is a gently convex hill and the
contours are drawn as shown. Since X is 7 feet
above the 850 contour, this is placed nearly one
M. D. distant from oo; and for a similar reason
the 810 contour falls a short distance south of
the stream. Join up the contours between the line
00 y and x h a, with due regard to intermediate
slopes of the ground. Also, having determined
the elevation of Y (805), you are able to draw in
the contours on the ridge y d hj examining its
slope through your field glasses. Extend these
contours to join those already located south of d,
keeping in mind the variation of the ground and
remembering the small map distance correspond-
ing to small inequalities noted.
285. Estimation. Instead of reading the slope
to the top of Flint hiU you observe that it is only
5 or 6 feet higher than X, and hence only one con-
tour (860) goes in; this falls about 50 yards from
X, and is drawn in by eye as shown. You also draw
in those required between the 850 contour and B
along the road.
Now move to T and stop a moment to read the
slope up ravine G, without setting up the Board;
likewise at the ridge just north of it. Continue
to T, set up the Board here and put in contours
between X and ravine G, and on ridge to M.
Methods of Sketching 285
Read the slope from T to X and find the ele-
vation of T as heretofore described for B and X.
From T read the slopes to ridge and valley points
on the fence running east to D, and draw in the
contours down to the main stream.
Proceed to C ; read the vertical angle to X, to K
and to stream junctions south of C, locating con-
tours as already explained. Continue over the en-
tire area, always remembering to locate contours in
rear of the last known point, and not to leave a
station until all the details up to that point are
drawn in.
286. Locating Horizontal Details and Con-
tours Simultaneously: Having finished locating
the contours over your first area, go back again to
A and carry on both horizontal and vertical deter-
minations together. This can now be readily done
simultaneously on the area you have studied by
the two separate operations. For example, at A,
set up, orient with the needle, draw a meridian,
sight D, B, Y, and fence comer; read vertical an-
gle to D draw in road A D. Move to B, set up,
orient by back sight on A, plot h, house and wire
fence; sight C; draw in road A B (note slight
curve), cattle chute and switch; sight Flint House
chimney. Now read the vertical angle to A and
contour a h, and so on continue the work, being
careful to follow a regular order in the different
steps. It is well to keep in mind, however, that
there are really two independent sets of determin-
ations being made at each station, one horizontal
286 Military Topography for Mobile Forces
the other vertical, as this helps to systematize the
work.
287. As you acquire skill in sketchings in esti-
mating and tracing contours^ you will constantly
require fewer and fewer controlling located points,
such as Bj XjY etc., with a corresponding gain of
speed and accuracy of representation.
EXECUTION OF OUTPOST SKETCHES.
288. The Making of an Outpost Sketch dif-
fers from that of a position sketch in nothing ex-
cept that in the former the sketcher cannot ad-
vance beyond the hne of observation, but must
show the ground from one-half to two miles in
front of this line toward the enemy. Consequent-
ly, he will be limited to locations by traverse along
the base and intersections from stations on the base
to determine critical points over the area out in
front. The method of resection is not usually ap-
plicable because this requires that the sketcher go
to the point located. The Base might, however, be
located some distance in rear of the outpost line,
(if the sketch were being made under fire of the
enemy, to avoid exposure in traversing along the
hne of observation) ; and from this retired base
critical points could be located on the line of ob-
servation by intersection or resection. The sketch-
er would then approach these located points by
creeping up from the rear, orient his board flat on
the groimd and sight necessary critical points over
the foreground. The information to be represent-
Methods or Sketching 287
ed on the outpost sketch is the same as is shown on
a position sketch and on the same scale.
There will often he portions of the hase from
which good views to the front are not possible. It
is therefore necessary to study the ground most
carefully from each base station, in order that crit-
ical points may be selected which can be seen from
at least one other point located along the base, so
as to give good intersection angles. For the criti-
cal points only a short distance in front, observa-
tions must be taken from points correspondingly
near each other along the base. To locate critical
points far to the front, the extreme ends of the base
would probably be used as stations from which to
intersect.
It will often be impossible to see more than a
small part of one hiU lying beyond another, or the
lower part of a small ravine may be seen, of which
the upper part lies beyond a hill. If, as is often
the case, a good estimate can be made of the nature
of the hidden area, judging from the visible parts,
then the concealed portions should be drawn in
broken lines to indicate the method of location used.
Field Glasses are of great assistance in this work
in picking out definite objects to intersect on, and
in discovering folds of the groimd not visible to
the naked eye. If two ridges lie generally parallel
to the front and at some distance from the base, it
will often be possible to discover the farther one
only by the line of different light made by the
nearer one against its side slope.
CHAPTER IV.
THE EXECUTION OF A ROAD SKETCH
IN DETAIL.
289. The instruments required by a beginner in
road sketching are preferably as follows, but oth-
ers may be used as noted below:
1. Drawing Board,
with dechnator, on folded
tripod, figure 151, p. 290,
or Cavalry Sketching Case
figure 149.
2. Loose Ruler, figure
137, with scales shown,
figure 136, p. 242.
3. Service Clinometer,
figure 138 (see par. 246)
Fig. 149 carried in upper right
breast pocket, secured to it by a strong cord.
4. An Equipped Pencil, Knife and Ruler
Holder, figure 146, p. 273.
5. Soft Rubber Eraser.
6. Stop Watch and Note Pad, figure 150 (for
mounted work).
METHOD OF WORK, DISMOUNTED.
290. A Road Sketch is normally made mounted
on account of the rapidity of work thereby se-
sured. It is well, however, for the beginner to make
288
Road Sketch in Detail
289
his first one or two sketches
dismounted to become accus-
tomed to the three inch scale
and twenty foot contours, be-
fore attempting to manage a
horse in addition to the work
of sketching. There may be
occasions too when a horse is
not available, so that a sketch-
er should be able to work with
equal facility either mounted
or dismoimted.
52
±
Fig. 150
The method previously
given for traversing the base,
ABC figure 147, in making
a position sketch is, in general,
identical with that used in a
dismounted road sketch, except that intersection lo-
cations are not usually required at more than four
himdred or five hundred yards from the road, and
no resection work is usually possible. A large part
of the work is done by traversing the road and es-
timating offsets. After the first one or two
sketches, the sketcher will not usually leave the
road, except to go to the top of some crest a few
yards distant to get an extended view. Details
will be limited to four hundred yards from the
road, except for prominent positions, etc.
There will often be areas within the 400 yard
limit, which are not visible from points directly
opposite them on the road. These areas, however.
290 Military Topography for Mobile Forces
may usually be seen from some point along the
road before or after passing opposite them.
The drawing board may be used in road sketch-
ing, with or without the tripod. If the tripod is
used in mounted work it should be folded to a sin-
gle length, figure 151, as it thus furnishes a firm
support and also a convenient hand-hold for car-
rying the board on horse back. More accurate
work can be done by using the tripod in this way,
without loss of time, than can be done by hold-
ing the board in the hands. Some good sketch-
ers use a board with wrist strap, and for important
Fig. 151
Road Sketch in Detail 291
sights place it on the ground and lie down prone
on the opposite side of the board from the point
sighted.
In unimportant sights and in locating details
around any station, even when the tripod is at-
tached, the board need not be set up on the ground
but is held pressed against the breast, figure 151.
The sight is taken by fixing the eye on the dis-
tant object and then glancing quickly down at the
ruler and making the necessary adjustment of the
ruler's direction. In practicing this method, you
should use a board on tripod and check each sight
by carefully looking along the ruler. Never sketch
with the cord holding the board around your neck.
The method of using the Cavalry Sketching Case
is identical in principkl with that of the drawing
board without a tripod. A sketcher having learned
one of these instruments will have no difficulty in
using the other.*
TO LOCATE HORIZONTAL DETAILS.
291. 1. Orient the hoard j par. 268, at station
A, figure 152,t p. 302, holding it in front of your
body, that is between you and the object sighted.
*The advantages of the Drawing Board over other forms of
Bketehing cases:
1. Its larger size gives sufficient area for two miles of posi-
tion sketch in both directions; and about twelve miles of road
sketch by running three traverses across the sheet. It is equally
as portable as the Boiler Sketching Cases.
2. Being practically square, the full length of the board is
available, no matter what the direction of the traverse may be,
•f-From sketch made by Captain A. W. Bjornstad, 28th Infantry,
in the Army School of the Line.
292 MiLiTAEY Topography foe Mobile Forces
By glancing every moment or two at the declina-
tor (or compass) see that the needle remains in
the meridian. With the declinator, the orienta-
tion is effected most rapidly and is free from pos-
sible errors of needle reading. The sides of the
declinator trough check the vibrations of the need-
le, and the orientation is correct when the needle
without the necessity of orienting this board in some special po-
sition. The Cavalry Case and all similar ones have such a small
drawing surface that it is necessary to orient the sketching case
so that the traverse extends in the direction of the rollers. This
direction of the road to be sketched will often not be known, thus
causing the sketch to run off the paper frequently, with resulting
delay and annoyance.
3. It has been found of great value in rapid sketching to
have flat sheets, so that when the parts of the sketch are to be
pasted together, the sheets will lie out flat without twisting and
curling up, due to being on rollers.
4. The attached ruler of the cavalry case is a time consuming
device, and should be removed and a loose ruler substituted.
Simplicity of each article of equipment is absolutely essential to
rapidity of work.
5. The note book and compass method has no advantage
over the drawing board method and is much slower, because the
taking of intelligible notes from compass readings requires as
much time as the making of a complete sketch with the board.
The notes then require as much time to plot as was used in tak-
ing them. The errors mentioned in paragraph 240 are more lia-
ble to occur in this method and, in addition, other mistakes and
omissions occur because the ground is not visible at the time of
plotting. The reason often given for this method is that it can
be used in the rain. The taking of notes in the rain is almost as
difficult as sketching, and by use of celluloid with a ground sur-
face, a pencil sketch can be made in the rain. This celluloid
takes pencil lines readily even when it is perfectly wet. These
lines may be readily erased with a soft rubber, but are not erased
or smudged due to rubbing of hand and ruler in sketching. This
celluloid is more transparent than tracing paper and allows blue
prints to be made from the pencil sketches without retracing.
6. The Drawing Board equipment is easily improvised using a
box top for the board and any straight stick for the ruler. The
compass and tripod are not absolutely essential.
Road Sketch in Detail 293
strikes both sides of the trough with equal force.
This can be easily determined by observation, and
by listening to the click of the needle against the
sides. To orient rapidly, note which side of the
trough the north end of the needle (marked N)
rests against, rotate the board continuously in this
direction until the needle leaves this side and
swings equally on both sides of the meridian. If
the needle is very sensitive it wiU not come to
rest quickly but you need not wait for this if you
observe the above rule as to equality of swing. Re-
member to see that the orientation is correct dur-
ing all important sights, especially along the main
traverse. The needle of the Cavalry Case being
very short and often sluggish, may appear to be
more easily kept on the meridian than a longer
needle. This does not mean that the orientation
thus secured is better, but quite the contrary.
292. 2. Take a forward sight along the tra-
verse toward B. Next sight the prominent criti-
cal points within three hundred or four hundred
yards of A, figure 152, for example the directions
of road to the north, and southwest up the stream
south of A B.
In making this sketch, you observe that the road
A B is generally straight until the high hill at E is
reached; you can therefore afford to spend a little
extra time on this forward sight along the tra-
verse, because of the amount of sketching depend-
ing on it and the consequent necessity for accura-
cy. Traverse to station B, noting the strides re-
294 MlLITAHY TOPOGBAPHY FOE MoBILE FORCES
corded on the tally register opposite the wire fence
and railroad track. You should be able by this
time to record your strides so automatically, see
par. 229, that your entire attention can he given to
the study of the details to he put in. You observe
that the stream north of the road A B runs paral-
lel to it at about two hundred and fifty yards dis-
tance. At first you would verify this estimate by
halting at the railroad crossing and taking an in-
tersection sight on the bridge north of A. You
also observe in passing that the wire fence, noted
before, runs parallel to the road north from A.
At the railroad you observe that the track is per-
pendicular to the road on the south, and curves
off to the northwest into a cut ten feet deep and one
himdred and fifty yards long.
293. Methods at B. Having reached B, ori-
ent the board, plot in the roads branching from A
and all details between A and B, first scaling off
the distance to the wire fence, railroad track and
B. The best method of doing this sketching in of
details is to sit on the ground facing toward A,
and draw in all details free hand, except roads and
fences. The board need not be exactly oriented
for sketching in details. With a little practice
parallel lines for road boundaries can be easily
drawn with the ruler. First draw the further line,
then slip the ruler toward you and draw the near-
er one. This allows you to keep the one first
drawn in view and enables you to get the two paral-
lel.
Road Sketch in Detail 295
294. The conventional signs for roads, trees,
houses, etc., should be drawn about the size of those
in the figure. Telephone and telegraph lines are
sufficiently indicated by conventional signs at wide
intervals as shown. Information concerning bridg-
es, may be shown as indicated in the sketch for the
railroad bridge,* figure 152, p. 302, (W. T.
), meaning wood truss, 100 feet long, 10
100X10^ ^ ^
feet wide, 15 feet high ; or it may be tabulated on an
edge of a sheet as for bridge (1) and (2), figure
147, p. 284.
295. Having located the details from B to A,
sight the stream junction southeast of B, to com-
plete its location. Continue the traverse in the
same manner to E, halting from time to time to
plot the details in rear of the point reached. At E
orient the board carefully, sight along the new di-
rection of the road to the crossing F, and toward
the prominent hiU top X. (If you are using the
short tripod your orientations should be by back
sight; if you are holding the board in your hands,
the orientation will be by compass). Take a sight
to G to serve as a check on the traverse to that
point by way of F. Where a stretch of road has
a number of small bends, but is generally straight,
these accurate check sights far to the front are
valuable in keeping the correct direction, the small
bends being drawn in by estimated offsets at the
number of strides noted in passing them. To take
* According to F. S. E. Signs, p. 260, this should be thus: (w. tr.
300 X 10,
15 ^'
296 MiLiTABY Topography for Mobile Forces
a large number of short sights of one hundred and
two hundred yards tends to accumulate errors. In
a long traverse in one generally straight line as
from A to E, strides should he recorded continu-
ously for the entire distance, to avoid confusing
the point from which the plotting is done and the
accumulation of plotting errors.
Now traverse to the crossing F, without halting
at Kennedy, but noting the nimaber of strides to
the road bend, to the house, and to both ends of
orchard. Houses at cross roads (or other promi-
nent points) should be located in their correct po-
sition, and the names of owners should be shown,
for use as landmarks in the designation of routes
of march, etc.
Having arrived at F, you would continue the
sketch in the same manner as already explained.
CONTOURING THE ROAD SKETCH.
296. Having located the horizontal details of
the sketch, you shoiold go back over the road put-
ting in contours. (It is assumed here, for purpos-
es of description, that you start in again at A to
put in contours.) Looking north from A you ob-
serve that the ground rises only two or three feet
above your present position and falls below your
level (800) at the stream. You verify this by
noting that the zero reading of the chnometer
strikes the ground just beyond the bridge. Ori-
ent the board and draw the 800 contotu* up both
sides of the stream to the point estimated as at your
present elevation. Also draw in the 800 contour
Road Sketch in Detail 297
on both sides of the stream in the immediate vicin-
ity of A.
Move to B, and read the vertical angle to A
( — 14°), being careful to sight a point as high
above the ground at A as your eye is above B.
Apply your 1^° M. D. and find it contained two
and a half times between B and A, or B is at eleva-
tion 850. The 820 and 840 contours must be put
in between the two stations. You observe that the
ground near A is flat with a rise of about three de-
grees near the railroad track, so space the contour
to show this. In all your road sketching be sure
that the contours (especially on every steep slope)
show accurately the slope of the steepest part of
the road to convey to the commander correct in-
formation of the heaviest slopes over which the
trains must pass. The spacing of contours on the
flatter portions is less important, but must show
the character of the slope — concave, uniform or
convex.
Now read the slope to the stream junction to
the southeast ( — 3^°). Remembering that you
are at 850 elevation, and noting that the slope is
uniform, you place the 840 contour about J a full
M. D. from B.
You now observe that the Fhnt House is only
about 10 feet above you, and consequently that
there can only be the 860 contour around this hill-
top as shown. To verify this you read the angle to
the highest point of the hiU and find a +2° slope
just west of the house. Application of M. D.
scale shows the hilltop is 15 feet above B or 865.
298 Military Topography for Mobile Forces
You now draw in the contours on both sides of the
road between B and A as shown, spacing them to
show correctly the ground forms and slopes. The
contours should be numbered as soon as finished.
297. The difficulties which you encounter at this
station B are exactly those encountered at all sub-
sequent stations throughout the work, but what
seem to be insurmountable obstacles to you at first,
will gradually become perfectly simple. And this
skill will be acquired quickly or slowly, depending
on how carefully you analyze the essential elements
of ground forms around each station in the early
stages of the work. The beginner arriving at B
looks aroimd him hopelessly trying to pick out the
important points to be considered; but as he grows
accustomed to the work he will grasp at a glance
the critical points to be located and the details to
be shown. Constant study in converting ground
distance to map equivalent^ and in plotting the lo-
cation of the contours around the station is most
valuable practice. You now look ahead and ob-
serve the slope of the ground on both sides of the
road, and note that the road falls gently about 12
feet at the first draw, then rises nearly to the height
of B opposite Mottin. You also observe that there
is a ridge line (shown dotted in the figure) ex-
tending along the north side of the road from Flint
to Mottin, where it crosses through the grove, and
that consequently the 840 contour must be about
equal distance on each side of this ridge line, since
the slopes of the hill near its top seem uniform.
Road Sketch in Detail 299
298. Carrying Elevations Forward. — From B
you can see the road some distance forward; there-
fore lie down with your eye near the level of the
road and take a zero clinometer reading forward.
This line of sight strikes the ground ahout 15 feet
below the top and some distance east of the ridge
at Himd, and the trees at Mottin about 4 feet above
the road. Note this point near Htmd for later ref-
erence as at 850 elevation. Note carefully the
shape of the ground forward, especially the rela-
tive heights of the points where ravines cross the
road. The horizontal locations of these points have
already been determined in your previous work
over this course to locate horizontal details. The
question often comes up as to the necessity of tak-
ing the vertical angles to each small depression such
as H and K, where you can readily see that no con-
tour, or at most but one, is to be put in. Such ob-
servations are impracticable and unnecessary and
would give less accurate results than a direct esti-
mate of the height of these points on account of the
short distance involved.
299. Now move to the high point north of Mot-
tin, and looking back observe that B seems a httle
higher than your position, so you read the angle
and find it about (+J°). Being curious to see
how this agrees with your estimate from B, (see
above) you apply the scale of M. D.'s. and find the
difference about 6 feet. In order that direct esti-
mates of differences of elevation may agree with
those foimd by clinometer reading and scale of M.
300 Military Topogkaphy fob, Mobile Forces
D.'s., you must have determined your stride scale
correctly; and your clinometer must be in adjust-
ment, or its error known.
Now draw in the contours on both sides of the
road back to B, making a careful estimate of their
position, and noting that the ridge is flat topped
and convex shaped.
You already have a reference point of elevation
located; so proceed to the top of Hund ridge,
studying the ground and noting the number of
strides opposite the selected reference point. Es-
timate the difference of elevation between your
position and the reference point (15 feet) and ver-
ify it by a slope reading and apphcation of M. D.
Continue the work of contouring in this manner
throughout the sketch, slowly and with many meas-
urements at first; but gradually depending more
on estimates of slopes, elevations and contovu* po-
sitions, as you acquire skill in analyzing ground
forms. For instance, from B you should have
made an estimate of its height above A to see how
it checked with yovu* other determination; similarly
the height of Hund ridge should have been esti-
mated from B.
ROAD SKETCH MOUNTED.
300. After you have made about two dismount-
ed sketches, it is well to begin mounted work. The
general methods involved are identical with those
used in the dismounted work. The greatest dif-
ference arises due to the necessity for controlling
the horse, in the greater training of the eye re-
Road Sketch in Detail 301
quired to fix in mind the ground forms while mov-
ing rapidly from one station to another, and the
necessity for a more systematic method of work to
secure rapidity. When moimted you have a con-
siderably better position for observation of the
ground on account of your height above the sur-
rounding country. You should do all plotting dis-
mounted because of the greater rapidity and ac-
curacy of working in this position. The time re-
quired to ride between stations at a trot and to dis-
mount and mount at each is small compared with
that required for the actual work of sketching.
Every step of the work should be done according
to a fixed system. For instance you should work
out one definite method of carrying your board;
one certain position to take for sketching immedi-
ately on dismounting at each station; a method of
keeping time notes, and of keeping the horse at a
uniform gait, a definite order of plotting distances,
details, and contours.
301. Use of an Assistant. If you have an as-
sistant, decide whether he is to keep the uniform
rate; to learn the names of owner's of houses; to
read slopes ; to call your attention to details such as
orchards, windmills, telegraph lines, cross roads,
etc. Each man must work out the system best
suited to his own needs, but the following sugges-
tions are offered (assuming that you have no as-
sistant) for carrying pencils, clinometer, etc.:
302. To Move Between Stations. On start-
ing from a station stop the needle ^ swing the board
302 MiLiTAKY Topography for Mobile Forces
over your back, figure 153, and grasp the reins in
the right hand. Best control of the horse can be
secured by tying a knot in the reins in front of the
pommel, and grasping this knot. The folded trip-
od does not interfere with your freedom of action
in taking notes. The left elbow is supported by
the board and in turn presses the Board firmly
Fig. 153
against your side. If you have an assistant he
should carry the Board, grasping the tripod at its
top.
Immediately on mounting take the stop-watch-
and-note pad (from the lower left blouse pocket)
in the left hand, figure 150.*
*The stop-watch-note pad may be purchased through Secre-
tary, The Army Service Schools at 35 ets. each. It consists of a
piece of heavy cigar box board 2|x9 inches, to which is glued
Fig. 152
Road Sketch in Detail 303
At the moment the horse starts, press the stop
with first finger to start the watch, being careful
to see it is set at the proper reading.
303. Taking Notes on Horseback. — As import-
ant details are passed along the road, note the time
and opposite the proper line of the pad jot down
a rough symbol on the center line or at the esti-
mated distance from it, according as the location
of the detail is on or off the road. These notes
will be a great aid to the memory; but as httle time
as possible must be spent in putting them down,
the greater part of the time being used to impress
features of the ground on yom* mind. Some men
find it very difficult to make even the simplest notes
on a trotting horse; but you can learn to keep suf-
ficiently clear notes on even the roughest horse,
by standing up in your stirrups, leaning the body
well forward and holding the arms close against the
sides while writing. You can also record notes
while posting. During the entire time spent in
passing from one station to another, except for
the note pad shown. Each fitth horizontal line is marked to show
minutes of travel. The three light lines between each two heavy
ones represent 15 seconds (quarter minutes) each. The spaces
between the vertical lines represent 100 yards each. The stop
watch is secured to the back by two wooden pieces screwed on.
The best type of stop watch is one which can be stopped and then
will continue forward from this point when the stop is pressed
again, so that continuous record may be kept over long straight
courses. The watch should have a device for quickly setting the
hand back to zero. A foot ball timer (price $1.50 Secretary
Service Schools) is fairly satisfactory but not as reliable as a
good stop watch. It is well to make a pencil holder on the side
of the pad, as shown in figure, for a soft blunt pencil, so that the
drawing pencil need not be used in taking notes.
304 Military Topography foe Mobile Forces
the brief intervals required to record notes, you
should devote every faculty to a careful study of
the ground, the trace of contours, and other es-
sential details.
304. Distance Between Halts. In the first
two or three sketches you should not travel more
than about one minute between stations. Later
this distance may be increased as your skill pro-
gresses until you can travel for 3 or 4 minutes
without halting. Suppose you pass a little draw on
the road (at 1 minute and 15 seconds) falling to
the left; a house distant 190 yards to the right at
1 :80 ; an orchard on the left extending from 1 :30
to 1:45; a ridge Une at 1:30 found to be 850 ele-
vation from your last station, extending 45 degrees
to right front, with a — 2 degree slope. These facts
can be recorded in a moment as shown on the pad.
Or some simple system of letters may be used, such
as R for ridge, V for valley, on lines in the proper
direction; an arrowhead for down slopes, etc.
305. Procedure at a Station. On arriving at a
station, immediately upon halting press the stop to
get the correct time. Dismount, throw the Board
cord from over your head, release the needle, spread
out the tripod legs, at the same time rotating the
board horizontally to orient it. Back sight orien-
tation is more accurate and will often be possible
even when no tripod is used, by laying the board
on the ground, and turning it imtil the last station
is sighted. Waste no time in orienting.
The horse should be trained to stand without be-
Road Sketch in Detail 305
ing held; but if necessary throw the rein over a
post or place your foot on it (if you have no as-
sistant). With tripod, you will find it easier to
take your observations for direction kneeling on
the opposite side of the Board from the point sight-
ed. For sketching in details, however, a sitting
position on the road side is best and most comforta-
ble. After your traverse and other important di-
rections are located do not worry about keeping an
exact orientation during the work of sketching de-
tails. As soon as your Board is oriented plot your
present station; pick out and sight your next for-
ward point, also take any intersection or forward
check sights, so that exact orientation wiU then not
be so necessary for the remaining work. Deter-
mine the elevation of your present station with ref-
erence to the last laiown point by the methods here-
tofore given, that is with chnometer and M. D.
scale, or barometer, or estimation, etc., according
to the practice you have had. Locate any other
necessary elevations and plot all details and con-
tours up to your position. After several sketches
have been made, you can begin to plot details for-
ward from each station for about 15 seconds of
travel, by estimation. This will relieve you of the
necessity of taking notes until about 30 seconds
have been passed. Move to next station using the
same methods.
306. In rapid sketching, time may be saved on
roads with frequent bends by halting only at each
alternate bend. For example from E draw a ray
306 MiLiTAEY Topography foe Mobile Fokces
to F, noting the time of passing F but not halting
there. At G plot f on the ray drawn from E ; ori-
ent by needle, and pivoting the ruler on f draw a
ray toward G, plotting on this ray the position of g
from the time scale.
O i-i gi nal Sheet.
1^7 section in positioM
Fig. 154
307. In case the sketch runs off the sheet beyond
&, figure 154, draw in the details a few yards in
front of station B. Then assume a new point (&')
near the edge of the sheet, also to represent B, so
chosen that the sketch forward from here wiU fall
across the longest dimension of the unused part of
the sheet. On the sheet near h' sketch in the details a
few yards in rear of B, before moving forward.
If no space is available on this sheet replace it by
one of the extra sheets carried under it on the
Board. When the sketch is completed, cut apart
its different sections (on the broken and dotted
lines) and place them together with all meridian
edges parallel and the two corresponding points on
the sheets for any ground pointj ^ing one directly
Road Sketch in Detail 307
over the other. Lay the ruler perpendicular to
the traverse through the station point (as &) and
cut both sheets through on this line. Remove the
two ends cut off and join the parts together with-
out overlap by means of adhesive tape or on
another piece of heavy paper. Join up the detaUs
across the cut edges. Where the sketch is made on
tracing paper and reproduction is required, the ad-
hesive tape should be used. B, C, etc., should be on
a straight portion of the road and not at a bend, to
aid in orienting the sections.
308. The rate of sketching possible by these
methods should be about 2 to 2 J miles per hour for
men of average abihty, after a month's practice.
Men with greater aptitude can make from 3 to
4 miles per hour; and the best sketchers can make
as much as 5 miles per hour. These rates refer to
the completely finished sketch, ready for use. In
ordinary service 2 J to 3 miles an hour would be suffi-
cient, but the more rapid methods are very valua-
ble for making a reconnaissance in a limited time,
and of especial value to staff officers in reconnoit-
ering routes and positions.
EXECUTION OF PLACE SKETCHES.
309. A Place sketch is made imder the suppo-
sition that the sketcher is limited to a single point
of observation overlooking the area to be sketched.
The details to be shown are the same as on a posi-
tion or outpost sketch. If made to extend a road
or position sketch farther toward the enemy than
can be reached by the sketcher the place sketch wiU
308 MiLiTAHY Topography for Mobile Forces
be on the scale of the sketch thus extended, other-
wise at 6 inches^l mile, 10 foot contours.
The sketcher must have acquired considerable
skill in sketching and in making estimates of dis-
tances, slopes and elevations before he can success-
fully make a place sketch. The methods of work
heretofore described for position sketching are fol-
lowed except that all control points are located by
determining distance with range finder (or by esti-
mation), elevations with clinometer (or by estima-
tion), horizontal angles of direction, with plane
table or compass. For use of range finder see par.
214. First locate stream lines, next roads, then hill
tops, and finally contours and minor details.
The place sketch is made under the same condi-
tions as a perspective sketch, but has the advan-
tage that it represents truly to scale the features of
the ground in their relation to each other as esti-
mated by the sketcher, and to be interpreted need
not be examined from the point occupied by the
sketcher. The sketcher's estimates may be in er-
ror, but his sketch will show the ground according
to these estimates. A perspective drawing, on the
contrary, furnishes no means of determining re-
lations of distance, slope and elevation. They are
valuable, however, for persons ignorant of map
reading, or to illustrate descriptions of military po-
sitions for non-military readers. All staff officers
and especially artillery reconnaissance officers,
should be skillful place sketchers, since this abihty
will save the time ordinarily used in explanation of
important features of the terrain to battery on
Road Sketch in Detail 309
battalion commanders and enable the batteries to
open fire more quickly and accurately than other-
wise.
POINTS TO BE OBSERVED IN SKETCHING.
1. Be sure your intersection and resection points
are well marked to avoid sighting hack on the
wrong point.
2. Study your area carefully and do not sight
any point that is not going to help your work.
There is a tendency with all beginners to try to
show too minute details and to take too many con-
trolling points. A few minutes used in studying
the area before commencing work will usually be
well spent.
3. Keep constantly in view the scale of your
sketch, the contour interval, and remember the
smallest distance that can be shown.
4-. Be sure your orientations are correct and
that the Board is clamped after orientation. The
forward sight to the next station should be made as
soon after orientation as your position is plotted.
5. After the first set up always orient by a back
sight if possible, especially if in the vicinity of iron,
or strong electric currents. However, if you can't
locate a point in rear to orient on, use the needle
wihout hesitation.
6. Do not leave a station until all the details
up to that point are put in. You may not have
time to return that way. Finish your sketch as you
go, the lines may be retraced and the sketch cleaned
up indoors if the emergency demands it, but aU
310 Military Topography for Mobile Forces
data should be put on in the field. You should
make it a fixed rule to have a fi/nished sketch up to
the point occupied, before moving on to another.
7. Try to put equal care and time on all parts
of the sketch. Avoid excessive care at first fol-
lowed by excessive haste near the end. A good
sketcher should be able to do from one to two square
miles of accurate sketch per day depending on the
difficulty of the ground.
Note: For Exercises in sketching see par. 347.
CHAPTER V.
TOPOGRAPHICAL RECONNAISSANCE
REPORTS.
310. Reconnaissance is the military term used
to designate the work of troops or individuals when
gathering information in the field. The general
subject of Reconnaissance is divided into two parts:
(1) that which relates especially to the strength,
position and intentions of the enemy, and (2) that
which relates especially to the terrain in its rela-
tion to the military situation.
Reconnaissance of the enemy is within the pro-
vince of tactics and is treated under the head of the
Service of Information in the Field Service Regu-
lations.
311. By Topographical Reconnaissance is
meant the obtaining and recording of all the need-
ful information of a portion of the terrain in the
shortest possible time and within the limits of ac-
curacy required for the operations of troops in the
field.
A Topographical Reconnaissance in general con-
sists of:
1. A Sketch.
2. A Report.
The method used to secure and record the de-
sired information of the terrain are therefore treat-
311
312 Military Topogeaphy for Mobile Forces
ed under the two headings, Military Topographi-
cal Sketching and Topographical Reports.
As much as possible of the desired information
should be shown on the sketch, on account of the
greater clearness and brevity thus secured. The re-
port should amphfy the sketch in matters which
cannot be shown thereon, such as conditions of
roads, quantities of supphes, etc. It should in gen-
eral be written on the face of the sketch sheet in
tabulated form; or on a letter size sheet of paper
attached thereto.
For the means and methods used in making Mih-
tary Sketches, see Part III, pars. 223-309.
312. Military Topographical Reports: The
Report should relate only to those subjects which
are required by the orders for the reconnaissance so
that no time may be wasted in gaining irrelevant
information. It should be written clearly^ and be
as brief a* possible consistent with clearness. The
paragraphs should be numbered serially for ready
reference. References to the sketch should be
made by means of numbers enclosed in parenthesis,
thus: "Road (1) — (2) 18 feet wide, macadam,
good repair." It is well to place all numbered ref-
erences on the sketch before writing out the com-
plete report so that these references on the sketch
will extend from beginning to end in order and thus
be easily referred to. It is a good plan to make
these references on the sketch in red pencil so that
they will catch the eye at once. The report should
be dated and signed by the officer making the recon-
naissance.
Reconnaissance Reports 313
Names of Places should be in block capitals^
and should be spelled phonetically when the spell-
ing and pronunciation are different. Relative
Terms (such as before, behind, etc.) should be
avoided, points of the compass being used except
that the terms "right," "left" are to be apphed to
the banks of a stream assimiing the writer to be
looking down stream. The term "open country"
means that it is free from hedges, undergrowth
and other obstacles obstructing view and passage;
"close country" is the reverse of this.
318. A Road Reconnaissance should procure
data on the following subjects:*
314. The Road: Gradients, especially the
steepest; width of roadway; if paved, width, kind
and condition of paving; width and depth of side
ditches, and whether wet or dry; if not paved,
character of soil, sand, clay or gravel; kind of fen-
ces and width between them. The sketch should
also show whether the road is an embankment or
cutting; where wagons cannot double or pass, and
where foot troops cannot march along the side be-
tween the wagon track and fences; commanding
heights tcithin infantry or artillery range.
315. Bridges: Material of piers and abutments
type and material of superstructure, as girder,
truss, arch, suspension, wood, steel, stone etc.;
width or roadway, and clear headroom; safe load.
*From the Engineer Field Manual. Items of a reconnaissance,
shown in italics should usually be shown by the sketch; those in
ordinary tjrpe by the report. Features not fully shown in the
sketch are amplified by the report.
314 Military Topography for Mobile Forces
Of bridges over the road, clear width and height;
over streams, the nearest bridge above and below
and whatever information can be obtained about
them.
316. THE COUNTRY.— Character of culti-
vation or natural vegetation; areas and density of
timber^ underbrush, vines, especially poisonous
ones; marshes and fords, kinds of fences, nature of
soil, general configuration of surface, especially
high hills, long ridges or valleys, bluffs or slopes
too steep to scale, and practicable routes to their
crests.
317. STREAMS CROSSED.— Name, loca-
tion, isoidth, depth and surface velocity in swiftest
cvurent; velocity noted as sluggish, moderate, quick
or swift; elevation of high water marks in relation
to the road; which bank is the higher at crossing
and above and below, and how much; accessibili-
ty of water for stock; fords at or near crossing;
length, depth and steepness of approaches; levees
or embankments, height and thickness on top; if
navigable, to what distance above and below and
for what class of vessels — steamers, flatboats, row-
boats.
318. TOWNS AND VILLAGES passed
through — Name, location on map, and population.
Names of streets to be traversed. Material, as
stone, brick, frame, log; size, 1, 2, 3 stories; and dis-
tribution, close or scattered, of the houses in those
streets; gradients of intersecting streets; location
of depots, post telegraph and telephone offices; of
Reconnaissance Reports 315
drinking foimtains and watering troughs; of ele-
vators, storehouses, or other accumulations of food
and forage; of blacksmith, wagon and machine
shops.
When ordered to make a complete examination
of a town or village, note besides the foregoing,
location and size of prindpjjf buildings, halls, court
and school houses, churches, banks, jails, and their
ownership; sources, maximum quantity and distri-
bution of water supply; sanitary conditions and
disposal of wastes; location of railroads, depots,
freight houses, sidings, etc., for all roads entering
from the surrounding country the same informa-
tion as scheduled above for streets; location and
extent of open spaces, and of large substantial
buildings standing apart; location and extent of
high ground within range, especially that from
which streets can be enfiladed.
319. RAILROADS CROSSED.— Name, lo-
cation, gauge, single or double track, sidings, and
loading platforms at point of crossing; crossing at
grade, over or under; distance, and name of near-
est station each way; direction of nearest round-
house, shops, etc. General condition of stations
as to defensibihty — command of surrounding
ground, and material of construction in the build-
ings.
RIVER RECONNAISSANCE.
320. If, when standing on the bank facing
across the stream, the current flows from left to
right, the observer is on the right bank; if from
right to left, he is on the left bank.
316 Military Topography for Mobile Forces
321. THE VALLEY—General configura-
tion, heights of limiting ranges, and positions of
passes and roads crossing them; commanding
ground from which a stretch of the channel of con-
siderable length can be enfiladed by artillery; for-
est growth on or near banks; soil and cultivation of
the valley ; roads parallel to river and means of ac-
cess to them from the river.
322. THE STREAM— Its width, depth and
velocity, navigability, as for steam boats, row boats,
and head of navigation for each ; nature of obstruc-
tions to navigation and possibihty of removing
or avoiding them; season of high and low water,
average rise and fall; rapidity of rise and fall and
causes; amount of drift; character of banks and
relative command. Quality of water, amoiuit and
kind of sediment borne; usual period and thickness
of ice. ( Ice 2 inches thick will support single men ;
3 J inches will bear infantry in column; 10 inches
will bear any military load.)
323. Tributaries and Canals. — Width, depth
and navigability, means of crossing. Nature and
purpose of canals; dimensions and lifts of locks;
time for lockage; means of destroying locks and
effect of destruction ; floating plant found.
324. Bridges and Fords. — As in road report.
Also for bridges note position of the channel and
navigable width between piers; height of arches
and lower chords above the water at different stag-
es ; dimensions and operation of draw spans. Note
the exact position of fords and marks on both banks
Reconnaissance Reports 317
by which they may be found; length, width and
nature of bottom; velocity of current; position of
deep holes; aids to crossing. Fords should not be
more than 4 ft. 4 ins. for cavalry, 3J ft. for infan-
try and 2 ft. 4 ins. for guns and ammtmition. Note
nature of approaches to bridges and fords; width
of roadway, slopes, soil, effect of water and traf-
fic. Note especially the defensibility of bridges
and fords.
325. Ferries, Boats and other means of cross-
ing. — Position of ferries and approaches, practi-
cability for horses and loaded wagons; size, number
and kind of boats; method of propulsion; sites for
military bridges or ferries; character of site for
construction, use and defense ; proooimity of islands
and other tributary streams; approaches and slope
of banks ; width of river and maximum surface ve-
locity of current; materials for the construction or
repair of boats, bridges or ferries.
326. Inundations. — Places suitable for inunda-
tions by damming or obstructing a narrow bridge
span, or by cutting a levee or dyke. Note raised
roads on ground liable to natural or artificial in-
undations and the safest routes to foUow by known
land marks when the road is overflowed. (An ex-
tensive inundation 2 ft. deep on level ground is a
serious obstacle tmless the roads are very soimd
and marked by trees, posts, etc. Even when so
marked a dip in the roadbed of 3 or more feet may
render the road impassable. A railroad bed is soon
washed out even by a slight overflow.)
318 Military Topography for Mobile Forces
RECONNAISSANCE OF A EAILROAD.
327. The line. Local name, terminal points and
distances bettveen stations and other points; gauge ;
single or double track; condition of roadbed, ties
and rails; drainage and liability to overflows or
washouts; facilities for repair; condition of right
of way for marching troops along the line,
328. Tunnels and Bridges. — Number and lo-
cation; dimensions; strength of bridges; means of
destroying and repairing; of blocking trafiic.
329. Rolling Stock. — Number and nature of
engines and cars available; capacity for transport-
ing troops between given points; facilities for con-
structing armoured trains, as spare rails, old boil-
ers, etc.; location and capacity of the shops and
store yards.
330. Stations: — Name and location; facilities
for entraining and detraining troops with wagons
and horses; platforms on through line and sidings,
ramps; side tracks, number and capacity; turn ta-
bles; tvater tanks; fuel supply; storage facilities;
derricks or cranes; cross-over for teams and pedes-
trians. Facilities at hand for hospitals, camps,
depots; for feeding men, heating coffee, watering
horses during temporary halts.
RECONNAISSANCE OF A WOOD OR FOREST.
331. Note all roads and paths, and all hills, ra-
vines, and streams within the wood or skirting the
edges; kinds of trees, density of growth; tmder-
brush, prevalence of poisonous shrubs and vines;
marshy or large open spaces; practicability of
Reconnaissance Reports 319
forming new roads by cutting: creation of obsta-
cles by felling trees; if there are no roads, traverse
the shortest practicable path between the point of
entrance and the point of exit, and mark boulders
or blaze trees, set stakes or otherwise indicate this
path, and also give compass bearings of the route
to be followed. Note the exterior from the woods,
whether parts of the edge flank other parts; connec-
tion with neighboring pieces of wood by scattered
trees or clearings; imdulations of the grotmd that
would give cover to attacking force or to defend-
ers.
RECONNAISSANCE OF MOUNTAINS.
332. Note the number and positions of passes
through the mountains, of roads and trails leading
to these passes, their condition, practicabihty, and
means of repair ; steepness of slopes on the sides of
roads; means of constructing additional roads;
water courses, their direction, nature, and time of
floods, means of crossing. Note ravines and open
glades on mountain sides, lookout points, and good
signal stations; note time and duration of snow
drifts on roads or passes; depth of drifts and pos-
sibility of removing them or traveling on the sur-
face of the snow. Note extent and nature of for-
est growth.
RECONNAISSANCE FOR A CAMP OR WINTER
QUARTERS.
333. Site, location, elevation, and area; sani-
tary features, such as drainage, dryness, and gen-
eral character of top soil; proximity of swampy
320 Military Topogkaphy for Mobile Forces
ground or stagnant ponds. For camp of a regi-
ment of infantry (65 men per company) allow ap-
proximately 280x350 yards; for a squadron (3
troops of 65 men each) 110x280 yards; for a bat-
talion of artillery 280x400 yards. (For reqiiire-
ments of camp sites see F. S. R., Art. VI.)
334. Communications. — Sufficiency of existing
roads and paths, maooimum grades, probable condi-
tion under heavy traffic and in bad weather, location
and kind of materials available for improvement or
repair; railroad or 'water communications and ter-
minal facilities of same.
335. Water and Fuel. — Location, kind and
quantity of fuel at hand; quality and quantity of
water, facilities for filHng water carts, for water-
ing animals and for washing and bathing; nature
of supply, as wells, springs, running streams, and
its reliability.
336. Shelter and Conveniences'. — Proximity
of trees, brush, wood, hay, and straw for huts and
bedding; of markets; of towns and villages.
RECONNAISSANCE OF A POSITION.
337. This problem usually includes the selec-
tion of the position and is therefore tactical as well
as topographical. Certain relations and conditions
must be observed in the selection and the extent and
degree in which they are found must be shown on
the map or in the report. The position and ground
in front to artillery range, to be shown by a con-
toured sketch at 6 inches to 1 mile.
Reconnaissance Repoets 321
338. The length of the position should be pro-
portional to the force available for its occupation.
Exact rules cannot be given.
339. The flanks must he secure. Impassable
natural featm-es, a river, a mountain or stream
form the best flank. Lacking these, a wood, a
cliff or a high hill will serve. Even with these feat-
ures absent the flank may be strengthened by the
construction of a strong earthwork, but the general
rule obtains that natural weakness of the flanks
must be made up by a greater number of men or
by the substitution of cavalry for infantry in case
the ground favors the movements of mounted
troops. If the flanks are naturally strong the line
should be withdrawn to make the entire position
reentrant ; if the flanks are naturally weak, the con-
necting line should be held so as to make the posi-
tion straight or sahent.
340. The depth of the position, or its extent in
rear of the firing line, should afford natural cover
for supports, reserves and trains, which may re-
quire a total depth of 800 to 2,400 yards; but a
short position may be relatively shallower than a
long one. Three or four parallel ridges, 300 to 600
yards apart, with the intervening ground practica-
ble, forms an excellent position. If the first ridge
is somewhat higher than the rest, so much the bet-
ter. What cover there may he for the component
parts of the force, whether natural or artificial, fen-
ces, ditches, trees, etc., should he shown or described.
If digging is necessary, its amoimt and the char-
acter of the soil should be stated. Strong points in
322 MiLiTAHY Topography fob, Mobile Forces
front of the line, which may be occupied as outposts
should be shown.
342. Communication should be free in every
direction, concealed so far as possible from the ene-
my's view. All communications perpendicular
and parallel to the front to be shown on the sketch.
343. Artillery positions are required when that
arm is represented in the occupying force, as will
usually be the case. They should permit the guns
to sweep all ground in front of the position over
which the enemy can advance, to the limit of ef-
fective range. Every point in front of the position
and within range which commands any part of it
is an element of weakness.
344. Ranges at which the enemy can be seen
and reached by artillery fire, the points beyond ri-
fle range covered by such fire and its relative com-
mand of adverse artillery positions should he shown
or described. If possible similar information should
be obtained of the ground likely to be occupied by
the enemy in forming for attack or in taking up a
counter position.
345. A position occupied by the enemy must be
reconnoitered from a distance and few details can
actually be seen. Valuable inferences may be
drawn by remembering that the enemy has probably
chosen his position according to the principles above
given.
346. Flanks. — ^Especial attention should be giv-
en to the flanks and to the feasibility of turning one
of them.
CHAPTER VI.
EXERCISES IN SKETCHING.
347. Sketching consists of measurements and
estimates of relations on ground and maps, and
more or less mechanical operations with pencils
and scales. There wiU be a large number of dis-
tinct operations in any single sketch. And though
each individual operation is in itself simple, yet the
beginner who attempts at first to draw a complete
sketch is invariably lost in a mass of details, imper-
fectly understood after a more or less careful read-
ing of the text. Consequently, it is important that
each detail be mastered singly; not by a study of
the text alone, but by study supplemented by prac-
tice on the ground. To assist beginners in sketch-
ing who have no instructor, and as a guide for a
systematic method to be followed in the instruction
of classes, the following exercises on the ground
are suggested. These exercises should be conduct-
ed in the vicinity of the Post on ground which has
been previously sketched by a good sketcher or of
which an accurate map exists:
348. Area 1. For position, outpost and place
sketches, an area about ^ to 1 square mile is suffi-
cient. Scale 6"=1 mile, V. I.=10 feet.
Area II. For road sketching exercises a road
sketch or map about two miles long is necessary.
323
324 MrLiTAKY Topography for Mobile Forces
Scale 3"=1 mile, V. I.=20 feet. Each beginner
should be furnished blue prints of these areas.
EXERCISES.
349. The work should be taken up in the fol-
lowing order: frequent indoor practice in tracing*
the contours on a well drawn map, in order to ac-
quire facility in representing the forms later to be
observed on the ground; then position sketch, out-
post sketch, road sketch, place sketch. The para-
graphs of the text referred to should be diligently
studied before the particular exercise is undertaken,
and should be read as necessary during the exercises.
POSITION SKETCHING.
Exercise 1.
(a) Determine your stride (pars. 228, 229).
(b) Make a working scale of strides (par.
229).
Note: Those who have difficulty in making scales may se-
cure them of any desired length of stride or rate of speed
from the Secretary Service Schools.
(c) Test the correctness of the scale (par. 230)
and make any necessary changes in it.
Exercise 2.
Choose in Area I some road or path having fre-
quent changes of direction and varying slopes.
Traverse this road (par. 268, 278) plotting only
the double lines (for width apart of bounding lines
of roads see figm-es 148, p. 284 and 152, p. 302) or
a single dotted line for the path. Halt (a) at
every change of direction, (b) at every change of
slope, (c) often to estimate the distance to points
Exercises in Sketching 325
in advance on the route. The halt (a) is first for
the purpose of noting and plotting the new direc-
tion on the sketch (par. 237) ; the halt (b) is made
to estimate the slope, par. 251, and difference of
elevation (par. 258) from top and bottom of the
slope. Having made all of these estimates as
carefully as possible, check each of them by com-
parison with the blue print, using the scale of M.
D's. to verify the slope, the marked elevations or
contours to check elevations; the coimted strides to
check the distances.
Now having fixed to your satisfaction the slope
between the two points, space in the contours along
that slope on your sketch by eye, checking the es-
timate with scale of M. D's. (par. 272). Next
note the number of contours along this slope from
the difference of elevation between its top and bot-
tom (par. 273). Space these by eye to show the
particular kind of slope (par. 272). Check the
results from the blue print.
Repeat the above exercises until (1) your length
of stride is accurately found (2) you thoroughly
understand the methods of orientation and plot-
ting of the traverse and the making and verifying
of estimates.
Note: Exercise 2 is to develop a fixed habit of verifying
all estimates. Rapidity comes later.
Exercise 3.
Traverse the same road as in exercise 2, perform-
ing the same operations and in addition, locate by
intersection (par. 269), (a) the top of each hill,
(b) the jimcture of each two streams and water
326 Military Topogeaphy for Mobile Forces
flow lines, and their heads on both sides of the
traverse for J mile. Use field glasses to pick out
definite points to sight on and see if you are at any
time imable to get a second observation on any
point sighted. If so find out why, and try it again.
Much time is wasted by taking one observation on
points and then not finishing their location.
Next move back over the traverse and (a) esti-
mate the slope to each point located, (b) check the
estimate by reading the slope with clinometer (par.
251 ) . Then estimate the difi^erence of elevation
from your stations to these intersection points.
Space the contours by eye, checking etc., as in ex-
ercise 2 for work on the traverse.
Exercise 4.
Having traversed the road in exercise 2, set up
your board (par. 268) at a station on it, and plot
the direction of three or four hill tops off the road.
Move to one of these hills and set up in the direc-
tion line observed and locate yourself by resection
(par. 270) . See how this location agrees with that
by intersection on this point. Repeat on each of the
other hill tops sighted, until you are entirely famil-
iar with this method of resection.
Next locate points by resection using the needle
for orientation (par. 270, 2nd method) and com-
pare the results obtained with those by the first
method of resection.
Exercise 5.
(a) Pick out a base line in Area I and see how
well it fulfills the conditions of par. 277.
Exercises in Sketching 327
(b) Traverse this base (par. 278), locate crit-
ical points (par. 266) over the area by intersection
and resection.
(c) Go back over the area and sketch in by eye
the horizontal details (figure 147, p. 284, par. 276)
such as streams, water flow lines, roads, railroads,
telegraph lines, trails, crest lines of ridgesi, hill
tops, orchards, houses, etc.
Exercise 6.
(a) Begin at your initial station and locate the
elevations of all critical points by estimation (par.
257), checked by slope readings and apphcation of
scale of M. D's., par. 272.
(b) Having found the elevations of the crit-
ical points space in the contours by eye, par. 284,
checking with the blue print.
Exercise 7.
(a) Make a complete sketch of the flat details
as in exercise 5 on an entirely new area.
(b) Contour the above as in exercise 6, par.
283.
Exercise 8.
Make the complete sketch of the area in exer-
cise 7, showing at the same time all horizontal de-
tails and the contours par. 286. In this exercise
finish up all work in rear of each station (par. 282)
before leaving it.
Exercise 9.
(a) Select an outpost hne and traverse this
as a base (par. 278) at the same time locating crit-
328 Military Topography foe Mobile Foeces
ical points as far to the front as the ground is visi-
ble (par. 288).
(b) Return along the base drawing in all hor-
izontal details and contours as indicated in preced-
ing exercises.
ROAD SKETCHING.
Exercise 10.
(a) Make your scale of strides at 3" to 1 mile,
par. 229.
(b) Rate your sketching horse (par. 231) at
a walk and trot.
(c) Construct a scale of walk and of trot (par.
232 and par. 19, prob. 3).
Exercise 11.
(a) Traverse (par. 291 et. seq.) the road area
II, dismounted, locating all flat details on the road,
and, by intersection, to within 400 yards on each
side. Each point should first be estimated as an
oiFset (par. 271) and then checked by careful lo-
cation.
(b) Go back over the road and contour it by
estimating the elevations Of critical points, par.
257, and the contour spacing, par. 272.
Note: Remember that contours are spaced the
same distance apart for the same slopes on both
road and position sketches (par. 226).
Exercise 12.
Make a complete contoured sketch carrying on
the horizontal locations and the contours together,
along the road in exercise 11, par. 296.
Exercises in Sketching 329
Exercise 13.
Repeat exercise 11 mounted (a), at a walk (b)
at a trot, par. 300.
Exercise 14.
Repeat exercise 12 at a trot, being careful to
have a complete sketch up to each occupied station
and about 15 seconds in advance before moving
forward, par. 305.
Exercises similar to the above may be drawn up
for place sketching following the principles in the
text.
330 Mllitaby Topogbaphy for Mobile Forces
TABLE I.
(H = (c + /) cos a + s cos" a.)
(C = (c + /) sin a + 4 s sin 2 a.)
Horizontal Distances and Differences of Elevation from
Stadia Readings.
1
2
3°
!
x"
N
X.S .
x" .
X.S .
X„ . .
X.S _.
xr .
><3 •^
100
Cos.i
Hor.
Dist.
o"!s6
25RQW
100
Cos.'
Hor.
Dist
SiRhS
100
Cos.
Hor,
Dist
100
Vz S
Diff.
Elev
100
Cos.
Diff,
Elev
ISII
100.00
0.00
99.97
1.74
99.88
3.49
99.73
5.23
2
100.00
0.06
99.97
1.80
99.87
3.55
99.72
5.28
4
100.00
0.12
99.97
1.86
99.87
3.60
99.71
5.34
6
100.00
0.17
99.96
1.92
99.87
3.66
99.71
5.40
8
100.00
0.23
99.96
1.98
99.86
3.72
99.70
5.46
10
100.00
0.29
99.96
2.04
99.86
3.78
99.69
5.52
12
100.00
0.35
99.96
2.09
99.85
3.84
99.69
5.57
14
100.00
0.41
99.95
2.15
99.85
3.90
99.68
5.63
16
100.00
0.47
99.95
2.21
99.84
3.95
99.68
5.69
18
100.00
0.52
99.95
2.27
99.84
4.01
99.67
5.75
20
100.00
0.58
99.95
2.33
99.83
4.07
99.66
5.80
22
100.00
0.64
99.94
2.38
99.83
4.13
99.66
5.86
24
100.00
0.70
99.94
2.44
99.82
4.18
99.65
5.92
26
99.99
0.76
99.94
2.50
99.82
4.24
99.64
5.98
28
99.99
0.81
99.93
2.56
99.81
4.30
99.63
6.04
30
99.99
0.87
99.93
2.62
99.81
4.36
99.63
6.09
32
99.99
0.93
99.93
2.67
99.80
4.42
99.62
6.15
34
99.99
0.99
99.93
2.73
99.80
4.48
99.62
6.21
36
99.99
1.05
99.92
2.79
99.79
4.53
99.61
6.27
38
99.99
1.11
99.92
2.85
99.79
4.59
99.60
6.33
40
99.99
1.16
99.92
2.91
99.78
4.65
99.59
6.38
42
99.99
1.22
99.91
2.97
99.78
4.71
99.59
6.44
44
99.98
1.28
99.91
' 3.02
99.77
4.76
99.58
6.50
46
99.98
1.34
99.90
3.08
99.77
4.82
99.57
6.56
48
99.98
1.40
99.90
3.14
99.76
4.88
99.56
6.61
SO
99.98
1.45
99.90
3.20
99.76
4.94
99.56
6.67
52
99.98
1.51
99.89
3.26
99.75
4.99
99.55
6.73
54
99.98
1.57
99.89
3.31
99.74
5.05
99.54
6.78
56
99.97
1.63
99.89
3.37
99.74
S.ll
99.53
6.84
58
99.97
1.69
99.88
3.43
99.73
5.17
99.52
6.90
60
99.97
1.74
99.88
3.49
99.73
5.23
99.51
6.96
Table of Corrections {to be
added'
fS
ctt
a
fl
ti
tt
A
CO
to
o
a
at
o
e
01
o
S
»
O
.s
u
u
u
+
*M
IJ
+
+
+
+
+
+
+
+
U
u
^^
**^
= 0.75
0.75
0.01
0.75
0.02
0.75
0.03
0.75
0.05
= 1.00
1.00
0.01
1.00
0.03
1.00
0.04
1.00
0.06
= 1.25
1.25
0.02
1.25
0.03
1.25
0.05
1.25
0.08
Table I
331
4
5
'
6
o
7°
1
M
M
I'l
99.51
6.96
99.24
8.68
98.91
10.40
98.51
12.10
2
99.51
7.02
99.23
8.74
98.90
10.45
98.50
12.15
4
99.50
7.07
99.22
8.80
98.88
10.51
98.48
12.21
6
99.49
7.13
99.21
8.85
98.87
10.57
98.47
12.26
8
99.48
7.19
99.20
8.91
98.86
10.62
98.46
12.32
10
99.47
7.25
99.19
8.97
98.85
10.68
98.44
12.38
12
99.46
7.30
99.18
9.03
98.83
10.74
98.43
12.43
14
99.46
7.36
99.17
9.08
98.82
10.79
98.41
12.49
16
99.45
7.42
99.16
9.14
99.81
10.85
98.40
12.55
18
99.44
7.48
99.15
9.20
98.80
10.91
98.39
12.60
20
99.43
7.53
99.14
9.25
98.78
10.96
98.37
12.66
22
99.42
7.59
99.13
9.31
98.77
11.02
98.35
12.72
24
99.41
7.65
99.11
9.37
98.76
11.08
98.34
12.77
26
99.40
7.71
99.10
9.43
98.74
11.13
98.33
12.83
28
99.39
7.76
99.09
9.48
98.73
11.19
98.31
12.88
30
99.38
7.82
99.08
9.54
98.72
11.25
98.29
12.94
32
99.38
7.88
99.07
9.60
98.71
11.30
98.28
13.00
34
99.37
7.94
99.06
9.65
98.69
11.36
98.27
13.05
36
99.36
7.99
99.05
9.71
98.68
11.42
98.25
13.11
38
99.35
8.05
99.04
9.77
98.67
11.47
98.24
13.17
40
99.34
8.11
99.03
9.83
98.65
11.53
98.22
13.22
42
99.33
8.17
99.01
9.88
98.64
11.59
98.20
13.28
44
99.32
8.22
99.00
9.94
98.63
11.64
98.19
13.33
46
99.31
8.28
98.99
10.00
98.61
11.70
98.17
13.39
48
99.30
8.34
98.98
10.05
98.60
11.76
98.16
13.45
50
99.29
8.40
98.97
10.11
98.58
11.81
98.14
13.50
52
99.28
8.45
98.96
10.17
98.57
11.87
98.13
13.56
54
99.27
8.51
98.94
10.22
98.56
11.93
98.11
13.61
56
99.26
8.57
98.93
10.28
98.54
11.98
98.10
13.67
58
99.25
8.63
98.92
10.34
98.53
12.04
98.08
13.73
60
99.24
8.68
98.91
10.40
98.51
12.10
98.06
13.78
»:
n
+
s
= 0.75
0.75
0.06
0.75
0.07
0.75
0.08
0.74
0.10
= 1.00
1.00
0.08
0.99
0.09
0.99
0.11
0.99
0.13
= 1.25
1.25
0.10
1.24
0.11
1.24
0.14
1.24
0.16
332 Military Topography for Mobile Forces
8
9
10°
11°
s
1
g
ii
taa
qU
w si
an
QW
i
98.06
13.78
97.55
15.45
96.98
17.10
96.36
18.73
2
98.05
13.84
97.53
15.51
96.96
17.16
96.34
18.78
4
98.03
13.89
97.52
15.56
96.94
17.21
96.32
18.84
6
98.01
13.95
97.50
15.62
96.92
17.26
96.29
18.89
8
98.00
14.01
97.48
15.67
96.90
17.32
96.27
18.95
10
97.98
14.06
97.46
15.73
96.88
17.37
96.25
19.00
12
97.97
14.12
97.44
15.78
96.86
17.43
96.23
19.05
14
97.95
14.17
97.43
15.84
96.84
17.48
96.21
19.11
16
97.93
14.23
97.41
15.89
96.83
17.54
96.18
19.16
18
97.92
14.28
97.39
15.95
96.80
17.59
96.16
19.21
20
97.90
14.34
97.37
16.00
96.78
17.65
96.14
19.27
22
97.88
14.40
97.35
16.06
96.76
17.70
96.12
19.32
24
97.87
14.45
97.33
16.11
96.74
17.76
96.09
19.38
26
97.85
14.51
97.31
16.17
96.72
17.81
96.07
19.43
28
97.83
14.56
97.29
16.23
96.70
17.86
96.05
19.48
3D
97.82
14.62
97.28
16.28
96.68
17.92
96.03
19.54
32
97.80
14.67
97.26
16.33
96.66
17.97
96.00
19.59
34
97.78
14.73
97.24
16.39
96.64
18.03
95.98
19.64
36
97.76
14.79
97.22
16.44
96.62
18.08
95.96
19.70
38
97.75
14.84
97.20
16.50
96.60
18.14
95.93
19.75
40
97.73
14.90
97.18
16.55
96.57
18.19
95.91
19.80
42
97.71
14.95
97.16
16.61
96.55
18.24
95.89
19.86
44
97.69
15.01
97.14
16.66
96.53
18.30
95.86
19.91
46
97.68
15.06
97.12
16.72
96.51
18.35
95.84
19.96
48
97.66
15.12
97.10
16.77
96.49
18.41
95.82
20.02
50
97.64
15.17
97.08
16.83
96.47
18.46
95.79
20.07
52
97.62
15.23
97.06
16.88
96.45
18.51
95.77
20.12
54
97.61
15.28
97.04
16.94
96.42
18.57
95.75
20.18
56
97.59
15.34
97.02
16.99
96.40
18.62
95.72
20.23
58
97.57
15.40
97.00
17.05
96.38
18.68
95.70
20.28
60
97.55
15.45
96.98
17.10
96.36
18.73
95.68
20.34
_^
tM
+
u
U,
= 0.75
0.74
0.11
0.74
0.12
0.74
0.14
0.73
0.15
= 1.00
0.99
0.15
0.99
0.16
0.98
0.18
0.98
0.20
= 1.25
1.23
0.18
1.23
0.21
1.23
0.23
1.22
0.25
Table I
333
12°
13°
14°
15°
1
M
II
a
qS
M
95.68
20.34
94.94
21.92
94.15
23.47
93.30
25.00
2
95.65
20.39
94.91
21.97
94.12
23.52
93.27
25.05
4
95.63
20.44
94.89
22.02
94.09
23.58
93.24
25.10
6
95.61
20.50
94.86
22.08
94.07
23.63
93.21
25.15
8
95.58
20.55
94.84
22.13
94.04
23.68
93.18
25.20
10
95.56
20.60
94.81
22.18
94.01
23.73
93.16
25.25
12
95.53
20.66
94.79
22.23
93.98
23.78
93.13
25.30
14
95.51
20.71
94.76
22.28
93.95
23.83
93.10
25.35
16
95.49
20.76
94.73
22.34
93.93
23.88
93.07
25.40
18
95.46
20.81
94.71
22.39
93.90
23.93
93.04
25.45
20
95.44
20.87
94.68
22.44
93.87
23.99
93.01
25.50
22
95.41
20.92
94.66
22.49
93.84
24.04
92.98
25.55
24
95.39
20.97
94.63
22.54
93.81
24.09
92.95
25.60
26
95.36
21.03
94.60
22.60
93.79
24.14
92.92
25.65
28
95.34
21.08
94.58
22.65
93.76
24.19
92.89
25.70
30
95.32
21.13
94.55
22.70
93.73
24.24
92.86
25.75
32
95.29
21.18
94.52
22.75
93.70
24.29
92.83
25.80
34
95.27
21.24
94.50
22.80
93.67
24.34
92.80
25.85
36
95.24
21.29
94.47
22.85
93.65
24.39
92.77
25.90
38
95.22
21.34
94.44
22.91
93.62
24.44
92.74
25.95
40
95.19
21.39
94.42
22.96
93.59
24.49
92.71
26.00
42
95.17
21.45
94.39
23.01
93.56
24.55
92.68
26.05
44
95.14
21.50
94.36
23.06
93.53
24.60
92.65
26.10
46
95.12
21.55
94.34
23.11
93.50
24.65
92.62
26.15
48
95.09
21.60
94.31
23.16
93.47
24.70
92.59
26.20
50
95.07
21.66
94.28
23.22
93.45
24.75
92.56
26.25
52
95.04
21.71
94.26
23.27
93.42
24.80
92.53
26.30
54
95.02
21.76
94.23
23.32
93.39
24.85
92.49
26.35
56
94.99
21.81
94.20
23.37
93.36
24.90
92.46
26.40
58
94.97
21.87
94.17
23.42
93.33
24.95
92.43
26.45
60
94.94
21.92
94.15
23.47
93.30
25.00,
92.40
26.50
^^
+
u
fb
= 0.75
0.73
0.16
0.73
0.17
0.73
0.19
0.72
0.20
= 1.00
0.98
0.22
0.97
0.23
0.97
0.25
0.96
0.27
= 1.25
1.22
0.27
1.21
0.29
1.21
0.31
1.20
0.34
334 MiLiTAKY Topography for Mobile Forces
16°
17°
18°
19°
BD
1
ii
IS «
ii
s'l
S.S
!SS
ii
id"
s
aa
QH
«a
QU
KQ
am
xa
qS
92.40
26.50
91.45
27.96
90.45
29.39
89.40
30.78
2
92.37
26.55
91.42
28.01
90.42
29.44
89.36
30.83
4
92.34
26.59
91.39
28.06
90.38
29.48
89.33
30.87
6
92.31
26.64
91.35
28.10
90.35
29.53
89.29
30.92
8
92.28
26.69
91.32
28.15
90.31
29.58
89.26
30.97
10
92.25
26.74
91.29
28.20
90.28
29.62
89.22
30.01
12
92.22
26.79
91.26
28.25
90.24
29.67
89.18
31.06
14
92.19
26.84
91.22
28.30
90.21
29.72
89.15
31.10
16
92.15
26.89
91.19
28.34
90.18
29.76
89.11
31.15
18
92.12
26.94
91.16
28.39
90.14
29.81
89.08
31.19
20
92.09
26.99
91.12
28.44
90.11
29.86
89.04
31.24
22
92.06
27.04
91.09
28.49
90.07
29.90
89.00
31.28
24
92.03
27.09
91.06
28.54
90.04
29.95
88.96
31.33
26
92.00
27.13
91.02
28.58
90.00
30.00
88.93
31.38
28
91.97
27.18
90.99
28.63
89.97
30.04
88.89
31.42
30
91.93
27.23
90.96
28.68
89.93
30.09
88.86
31.47
32
91.90
27.28
90.92
28.73
89.90
30.14
88.82
31.51
34
91.87
27.33
90.89
28.77
89.86
30.19
88.78
31.56
36
91.84
27.38
90.86
28.82
89.83
30.23
88.75
31.60
38
91.81
27.43
90.82
28.87
89.79
30.28
88.71
31.65
40
91.77
27.48
90.79
28.92
89.76
30.32
88.67
31.69
42
91.74
27.52
90.76
28.96
89.72
30.37
88.64
31.74
44
91.71
27.57
90.72
29.01
89.69
30.41
88.60
31.78
46
91.68
27.62
90.69
29.06
89.65
30.46
88.56
31.83
48
91.65
27.67
90.66
29.11
89.61
30.51
88.53
31.87
50
91.61
27.72
90.62
29.15
89.58
30.55
88.49
31.92
52
91.58
27.77
90.59
29.20
89.54
30.60
88.45
31.96
54
91.55
27.81
90.55
29.25
89.51
30.65
88.41
32.01
56
91.52
27.86
90.52
29.30
89.47
30.69
88.38
32.05
58
91.48
27.91
90.48
29.34
89.44
30.74
88.34
32.09
60
91.45
27.96
90.45
29.39
89.40
30.78
88.30
32.14
C*
+
u
= 0.75
0.72
0.21
0.72
0.23
0.71
0.24
0.71
0.25
= 1.00
0.86
0.28
0.95
0.30
0.95
0.32
0.94
0.33
= 1.25
1.20
0.35
1.19
0.38
1.19
0.40
1.19
0.42
Table I
335
20°
21°
22°
23°
■a
1
S.a
ui >
U
ui >
IB V
a
idS
ii
rui
i
BQ
qpS
BQ
QH
Bq
53
«S
S3
88.30
32.14
87.16
33.46
85.97
34.73
84.73
35.97
2
88.26
32.18
87.12
33.50
85.93
34.77
84.69
36.01
4
88.23
32.23
87.08
33.54
85.89
34.82
84.65
36.05
6
88.19
32.27
87.04
33.59
85.85
34.86
84.61
36.09
8
88.15
32.32
87.00
33.63
85.80
34.90
84.57
36.13
10
88.11
32.36
86.96
33.67
85.76
34.94
84.52
36.17
12
88.08
32.41
86.92
33.72
85.72
34.98
84.48
36.21
14
88.04
32.45
86.88
33.76
85.68
35.02
84.44
36.25
16
88.00
32.49
86.84
33.80
85.64
35.07
84.40
36.29
18
87.96
32.54
86.80
33.84
85.60
35.11
84.35
36.33
20
87.93
32.58
86.77
33.89
85.56
35.15
84.31
36.37
22
87.89
32.63
86.73
33.93
85.52
35.19
84.27
36.41
24
87.85
32.67
86.69
33.97
85.48
35.23
84.23
36.45
26
87.81
32.72
86.65
34.01
85.44
35.27
84.18
36.49
28
87.77
32.76
86.61
34.06
85.40
35.31
84.14
36.53
30
87.74
32.80
86.57
34.10
85.36
35.36
84.10
36.57
32
87.70
32.85
86.53
34.14
85.31
35.40
84.06
36.61
34
87.66
32.89
86.49
34.18
85.27
35.44
84.01
36.65
36
87.62
32.93
86.45
34.23
85.23
35.48
83.97
36.69
38
87.58
32.98
86.41
34.27
85.19
35.52
83.93
36.73
40
87.54
33.02
86.37
34.31
85.15
35.56
83.89
36.77
42
87.51
33.07
86.33
34.35
85.11
35.60
83.84
36.80
44
87.47
33.11
86.29
34.40
85.07
35.64
83.80
36.84
46
87.43
33.15
86.25
34.44
85.02
35.68
83.76
36.88
48
87.39
33.20
86.21
34.48
84.98
35.72
83.72
36.92
50
87.35
33.24
86.17
34.52
84.94
35.76
83.67
36.96
52
87.31
33.28
86.13
34.57
84.90
35.80
83.63
37.00
54
87.27
33.33
86.09
34.61
84.86
35.85
83.59
37.04
56
87.24
33.37
86.05
34.65
84.82
35.89
83.54
37.08
58
87.20
33.41
86.01
34.69
84.77
35.93
83.50
37.12
60
87.16
33.46
85.97
34.73
84.73
35.97
83.46
37.16
+
u
U
= 0.75
= 1.00
= 1.25
0.70
0.94
1.17
0.26
0.35
0.44
0.70
0.93
1.16
0.27
0.37
0.46
0.69
0.92
1.15
0.29
0.38
0.48
0.69
0.92
I.IS
0.30
0.40
0.50
336 MiLITAEY TOPOGBAPHY FOE MOBILE FORCES
24°
25°
26°
27°
8
3
i
a
%»
a
as
a
isl
ii
teS'
KO
QH
an
(33
KQ
q3
aa
■qS
83.46
37.16
82.14
38.30
80.78
39.40
79.39
40.45
2
83.41
37.20
82.09
38.34
80.74
39.44
79.34
40.49
4
83.37
37.23
82.05
38.38
80.69
39.47
79.30
40.52
6
83.33
37.27
82.01
38.41
80.65
39.51
79.25
40.55
8
83.28
37.31
81.96
38.45
80.60
39.54
79.20
40.59
10
83.24
37.35
81.92
38.49
80.55
39.58
79.15
40.62
12
83.20
37.39
81.87
38.53
80.51
39.61
79.11
40.66
14
83.15
37.43
81.83
38.56
80.46
39.65
79.06
40.69
16
83.11
37.47
81.78
38.60
80.41
39.69
79.01
40.72
18
83.07
37.51
81.74
38.64
80.37
39.72
78.96
40.76
20
83.02
37.54
31.69
38.67
80.32
39.76
78.92
40.79
22
82.98
37.58
81.65
38.71
80.28
39.79
78.87
40.82
24
82.93
37.62
81.60
38.75
80.23
39.83
78.82
40.86
26
82.89
37.66
81.56
38.78
80.18
39.86
78.77
40.89
28
82.85
37.70
81.51
38.82
80.14
39.90
78.73
40.92
30
82.80
37.74
81.47
38.86
80.09
39.93
78.68
40.96
32
82.76
37.77
81.42
38.89
80.04
39.97
78.63
40.99
34
82.72
37.81
81.38
38.93
80.00
40.00
78.58
41.02
36
82.67
37.85
81.33
38.97
79.95
40.04
78.54
41.06
38
82.63
37.89
81.28
39.00
79.90
40.07
78.49
41.09
40
82.58
37.93
81.24
39.04
79.86
40.11
78.44
41.12
42
82.54
37.96
81.19
39.08
79.81
40.14
78.39
41.16
44
82.49
38.00
81.15
39.11
79.76
40.18
78.34
41.19
46
82.45
38.04
81.10
39.15
79.72
40.21
78.30
41.22
48
82.41
38.08
81.06
39.1S
79.67
40.24
78.25
41.26
50
82.36
38.11
81.01
39.22
79.62
40.28
78.20
41.29
52
82.32
38.15
80.97
39.26
79.58
40.31
78.15
41.32
54
82.27
38.19
80.92
39.29
79.53
40.35
78.10
41.35
56
82.23
38.23
80.87
39.33
79.48
40.38
78.06
41.39
58
82.18
38.26
80.83
39.36
79.44
40.42
78.01
41.42
60
82.14
38.30
80.78
39.40
79.39
40.45
77.96
41.45
^^
+
u
h
= 0.75
0.68
0.31
0.68
0.32
0.67
0.33
0.66
0.35
= 1.00
0.91
0.41
0.90
0.43
0.89
0.45
0.89
0.46
= 1.25
1.14
0.52
1.13
0.54
1.12
0.56
1.11
0.58
Table I
337
28°
29°
30°
n
1
II
am
so
11
II
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
77.96
77.91
77.86
77.81
77.77
77.72
77.67
77.62
77.57
77.52
77.48
77.42
77.38
77.33
77.28
77.23
77.18
77.13
77.09
77.04
76.99
76.94
76.89
76.84
76.79
76.74
76.69
76.64
76.59
76.55
76.50
41.45
41.48
41.52
41.55
41.58
41.61
41.65
41.68
41.71
41.74
41.77
41.81
41.84
41.87
41.90
41.93
41.97
42.00
42.03
42.06
42.09
42.12
42.15
42.19
42.22
42.25
42.28
42.31
42.34
42.37
42.40
76.50
76.45
76.40
76.35
76.30
76.25
76.20
76.15
76.10
76.05
76.00
75.95
75.90
75.85
75.80
75.75
75.70
75.65
75.60
75.55
75.50
75.45
75.40
75.35
75.30
75.25
75.20
75.15
75.10
75.05
75.00
42.40
42.43
42.46
42.49
42.53
42.56
42.59
42.62
42.65
42.68
42.71
42.74
42.77
42.80
42.83
42.86
42.89
42.92
42.95
42.98
43.01
43.04
43.07
43.10
43.13
43.16
43.18
43.21
43.24
43.27
43.30
75.00
74.95
74.90
74.85
74.80
74.75
74.70
74.65
74.60
74.55
74.49
74.44
74.39
74.34
74.29
74.24
74.19
74.14
74.09
74.04
73.99
73.93
73.88
73.83
73.78
73.73
73.68
73.63
73.58
73.52
73.47
43.30
43.33
43.36
43.39
43.42
43.45
43.47
43.50
43.53
43.56
43.59
43.62
43.65
43.67
43.80
43.73
43.76
43.79
43.82
43.84
43.87
43.90
43.93
43.95
43.98
44.01
44.04
44.07
44.09
44.12
44.15
NH
+
u
= 0.75
= 1.00
= 1.25
0.66
0.88
1.10
0.36
0.48
0.60
0.65
0.87
1.09
0.37
0.49
0.62
0.65
0.86
1.08
0.38
0.51
0.64
338 Military Topogbaphy foe Mobile Foeces
TABLE II.
Logarithms of Numbers.
N.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
S3
54
0000 0043 0086 0128 0170
0414 0453 0492 0531 0569
0792 0828 0864 0899 0934
1139 1173 1206 1239 1271
1461 1492 1523 1553 1584
1761 1790 1818 1847 1875
2041 2068 2095 2122 2148
2304 2330 2355 2380 2405
2553 2577 2601 2625 2648
2788 2810 2833 2856 2878
3010 3032 3054 3075 3096
3222 3243 3263 3284 3304
3424 3444 3464 3483 3502
3617 3636 3655 3674 3692
3802 3820 3838 3856 3874
3979 3997 4014 4031 4048
4150 4166 4183 4200 4216
4314 4330 4346 4362 4378
4472 4487 4502 4518 4533
4624 4639 4654 4669 4683
4771 4786 4800 4814 4829
4914 4928 4942 4955 4969
5051 5065 5079 5092 5105
5185 5198 5211 5224 5237
5315 5328 5340 5353 5366
5441 5453 5465 5478 5490
5563 5575 5587 5589 5611
5682 5694 5705 5717 5729
5798 5809 5821 5832 5843
5911 5922 5933 5944 5955
6021 6031 6042 6053 6064
6128 6138 6149 6160 6170
6232 6243 6253 6263 6274
6335 6345 6355 6365 6375
6435 6444 6454 6464 6474
6532 6542 6551 6561 6571
6628 6637 6646 6656 6665
6721 6730 6739 6749 6758
6812 6821 6830 6839 6848
6902 6911 6920 6928 6937
6990 6998 7007 7016 7024
7076 7084 7093 7101 7110
7160 7168 7177 7185 7193
7243 7251 7259 7267 7275
7324 7332 7340 7348 7356
N.
8
0212 0253 0294 0334 0374
0607 0645 0682 0719 0755
0969 1004 1038 1072 1106
1303 1335 1367 1399 1430
1614 1644 1673 1703 1732
1903 1931 1959 1987 2014
2175 2201 2227 2253 2279
2430 2455 2480 2504 2529
2672 2695 2718 2742 2765
2900 2923 2945 2967 2989
3118 3139 3160 3181 3201
3324 3345 3365 3385 3404
3522 3541 3560 3579 3598
3711 3729 3747 3766 3784
3892 3909 3927 3945 3962
4065 4082 4099 4116 4133
4232 4249 4265 4281 4298
4393 4409 4425 4440 4456
4548 4564 4579 4594 4609
4698 4713 4728 4742 4757
4843 4857 4871 4886 4900
4983 4997 5011 5024 5038
5119 5132 5145 5159 5172
5250 5263 5276 5289 5302
5378 5391 5403 5416 5428
5502 5514 5527 5539 5551
5623 5635 5647 5658 5670
5740 5752 5763 5775 5786
5855 5866 5877 5888 5899
5966 5977 5988 5999 6010
6075 6085 6096 6107 6117
6180 6191 6201 6212 6222
6284 6294 6304 6314 6325
6385 6395 6405 6415 6425
6484 6493 6503 6513 6522
6580 6590 6599 6609 6618
6675 6684 6693 6702 6712
6767 6776 6785 6794 6803
6857 6866 6875 6884 6893
6946 6955 6964 6972 6981
7033 7042 7050 7059 7067
7118 7126 7135 7143 7152
7202 7210 7218 7226 7235
7284 7292 7300 7308 7316
7364 7372 7380 7388 7396
8
Prop
. Parts
1 2
3
4
5
6
7 8 9
4 8
12
17
21
25
29 33 37
4 8
11
IS
19
23
26 30 34
3 7
10
14
17
21
24 28 31
3 6
10
13
16
19
23 26 29
3 6
9
12
15
IS
21 24 27
3 6
8
11
14
17
20 22 25
3 5
8
11
13
16
18 21 24
2 5
7
10
12
15
17 20 22
2 5
7
9
12
14
16 19 21
2 4
7
9
11
13
16 18 20
2 4
6
8
11
13
15 17 19
2 4
6
8
10
12
14 16 18
2 4
6
8
10
12
14 15 17
2 4
6
9
11
13 15 17
2 4
5
9
11
12 14 16
2 3
5
9
10
12 14 15
2 3
5
8
10
11 13 15
2 3
5
8
9
11 13 14
2 3
5
8
9
11 12 14
1 3
4
7
9
10 12 13
1 3
4
7
9
10 11 13
1 3
4
7
8
10 11 12
1 3
4
7
8
9 11 12
1 3
4
6
8
9 10 12
1 3
4
6
8
9 10 11
1 2
4
6
9 10 11
1 2
4
6
8 10 11
1 2
3
6
8 9 10
1 2
3
6
8 9 10
1 2
3
5
8 9 10
1 2
3
5
6
8 9 10
1 2
3
5
6
7 8 9
1 2
3
5
6
7 8 9
1 2
3
5
6
7 8 9
1 2
3
5
6
7 8 9
1 2
3
5
6
7 8 9
1 2
3
5
6
7 7 8
1 2
3
5
5
6 7 8
1 2
3
5
5
6 7 8
1 2
3
5
5
6 7 8
1 2
3
3
4
5
6 7 8
1 2
3
3
4
5
6 7 8
1 2
2
3
4
5
6 7 7
1 2
2
3
4
5
6 6 7
1 2
2
3
4
5
6 6 7
123456789
By permission of Superintendent Smithsonian Institute.
Table I
339
Logarithms of Numbers.
N.
II
S7
SS
59
60
61
62
63
64
65
66
67
68
69
??
72
73
74
?l
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
II
97
98
99
N.
7404 7412 7419 7427 7435
7482 7490 7497 7505 7513
7559 7566 7574 7582 7589
7634 7642 7649 7657 7664
7709 7716 7723 7731 7738
7782 7789 7796 7803 7810
7S53 7860 7868 7875 7882
7924 7931 7938 7945 7952
7993 8000 8007 8014 8021
8062 8069 8075 8082 8089
8129 8136 8142 8149 8156
8195 8202 8209 8215 8222
8261 8267 8274 8280 8287
8325 8331 8338 8344 8351
8388 8395 8401 8407 8414
8451 8457 8463 8470 8476
8513 8519 8525 8531 8537
8573 8579 8585 8591 8597
8633 8639 8645 8651 8657
8692 8698 8704 8710 8716
8751 8756 8762 8768 8774
8808 8814 8820 8825 8831
8865 8S71 8876 8882 8887
8921 8927 8932 8938 8943
8976 8982 8987 8993 8998
9031 9036 9042 9047 9053
9085 9090 909S 9101 9106
9138 9143 9149 9154 9159
9191 9196 9201 9206 9212
9243 9248 9253 9258 9263
9294 9299 9304 9309 9315
9345 9350 9355 9360 9365
9395 9400 9405 9410 9415
9445 9450 9455 9460 9465
9494 9499 9504 9509 9513
9542 9547 9552 9557 9562
9590 9595 9600 9605 9609
9638 9643 9647 9652 9657
9685 9689 9694 9699 9703
9731 9736 9741 9745 9750
9777 9782 9786 9791 9795
9823 9827 9832 9836 9841
9868 9872 9877 9831 9886
9912 9917 9921 9926 9930
9956 9961 9965 9969 9974
8
7443 7451 7459 7466 7474
7520 7528 7536 7543 7551
7597 7604 7612 7619 7627
7672 7679 7686 7694 7701
7745 7752 7760 7767 7774
7818 7825 7832 7839 7846
7889 7896 7903 7910 7917
7959 7966 7973 7980 7987
8028 8035 8041 8048 8055
8096 8102 8109 8116 8122
8162 8169 8176 8182 8189
8228 8235 8241 8248 8254
8293 8299 8306 8312 8319
8357 8363 8370 8376 8382
8420 8426 8432 8439 8445
8482 8488 8494 8500 8506
8543 8549 8555 8561 8567
8603 8609 8615 8621 8627
8663 8669 8675 8681 8686
8722 8727 8733 8739 8745
8779 8785 8791 8797 8802
8837 8842 8848 8854 8859
8893 8899 8904 8910 8915
8949 8954 8960 8965 8971
9004 9009 9015 9020 9025
9058 9063 9069 9074 9079
9112 9117 9122 9128 9133
9165 9170 9175 9180 9186
9217 9222 9227 9232 9238
9269 9274 9279 9284 9289
9320 9325 9330 9335 9340
9370 9375 9380 9385 9390
9420 9425 9430 9435 9440
9469 9474 9479 9484 9489
9558 9523 9528 9533 9538
9566 9571 9576 9581 9586
9614 9619 9624 9628 9633
9661 9666 9671 9675 9680
9708 9713 9717 9722 9727
9754 9759 9763 9768 9773
9800 9805 9809 9814 9818
9845 9850 9854 9859 9863
9890 9894 9899 9903 9908
9934 9939 9943 9948 9952
9978 9983 9987 9991 9996
5 6 7 8 9
Prop. Parts.
1 2 3
1 2 2
1 2 2
1 2 2
1 1 2
1 1 2
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
2 3
2 3
2 3
2 3
2 3
2 2
2 2
7 8
5 6
5 6
5 6
5 6
5 6
5 6 6
5 6 6
5 6 6
5 6 6
5 6 6
123456789
340 MiLiTAEY Topography foe Mobile Forces
TABLE III.
Natural Sines and Cosines.
Natural Sines.
Prop.
Angle.
0'
10'
20'
30'
40'
50'
60'
Angle.
Parts
for 1'.
0°
.0000 00
.0029 09
.0058 18
.0087 27
.0116 35
.0145 44
.0174 52
89°
2.9
I
.0174 52
.0203 6
.0232 7
.0261 8
.0290 8
.0319 9
.0349
88
2.9
2
.0349
.0378 1
.0407 1
.0436 2
.0465 3
.0494 3
.0523 4
87
2.9
3
.0523 4
.0552 4
.0581 4
.0610 5
.0639 5
.0668 5
.0697 6
86
2.9
4
.0697 6
.0726 6
.0755 6
.0784 6
.0813 6
.0842 6
.0871 6
85
2.9
5
.0871 6
.0900 5
.0929 S
.0958 S
.0987 4
.1016 4
.1045 3
84
2.9 '
6
.1045 3
.1074 2
.1103 1
.1132
.1160 9
.1189 8
.1218 7
83
2.9
7
.1218 7
.1247 6
.1276 4
.1305 3
.1334
.1363
.1392
82
2.9
8
.1392
.1421
.1449
.1478
.1507
.1536
.1564
81
2.9
9
.1564
.1593
.1622
.1650
.1679
.1708
.1736
80
2.9
10
.1736
.1765
.1794
.1822
.1851
.1880
.1908
79
2.9
11
.1908
.1937
.1965
.1994
.2022
.2051
.2079
78
2.9
12
.2079
.2108
.2136
.2164
.2193
.2221
.2250
77
2.8
13
.2250
.2278
.2306
.2334
.2363
.2391
.2419
76
2.8
14
.2419
.2447
.2476
.2504
.2532
.2560
.2588
75
2.8
15
.2588
.2616
.2644
.2672
.2700
.2728
.2756
74
2.8
16
.2756
.2784
.2812
.2840
.2868
.2896
.2924
73
2.8
17
.2924
.2952
.2979
.3007
.3035
.3062
.3090
72
2.8
18
.3090
.3118
.3145
.3173
.3201
.3228
.3256
71
2.8
19
^0
.3256
.3283
.3311
.3338
.3365
.3393
.3420
70
2.7
.3420
.3448
.3475
.3502
.3529
.3557
.3584
69
2.7
21
. 3584
.3611
.3638
.3665
.3692
.3719
.3746
68
2.7
22
.3746
.3773
.3800
.3827
.3854
.3881
.3907
67
2.7
23
.3907
.3934
.3961
.3987
.4014
.4041
.4067
66
2.7
24
.4067
.4094
.4120
.4147
.4173
.4200
.4226
65
2.7
P
.4226
.4253
.4279
.4305
.4331
.4358
.4384
64
2.6
26
.4384
.4410
.4436
.4462
.4488
.4514
.4540
63
2.6
27
.4540
.4566
.4592
.4617
.4643
.4669
.4695
62
2.6
28
.4695
.4720
.4746
.4772
.4797
.4823
.4848
61
2.6
29
.4848
.4874
.4899
.4924
.4950
.4975
.5000
60
2.5
?P
.5000
.5025
.5050
.5075
.5100
.5125
.5150
59
2.5
31
.5150
.5175
.5200
.5225
.5250
.5275
.5299
58
2.5
32
.5299
.5324
.5348
.5373
.5398
.5422
.5446
57
2.5
33
.5446
.5471
.5495
.5519
.5544
.5568
.5592
56
2.4
34
.5592
.5616
.5640
.5664
.5688
.5712
.5736
55
2.4
35
.5736
.5760
.5783
.5807
.5831
.5854
.5878
f?
2.4
36
.5878
.5901
.5925
.5948
.5972
.5995
.6018
2.3
37
.6018
.6041
.6065
.6088
.6111
.6134
.6157
52
2.3
38
.6157
.6180
.6202
.6225
.6248
.6271
.6293
51
2.3
39
.6293
.6316
.6338
.6361
.6383
.6406
.6428
50
2.3
40
.6428
.6450
.6472
.6494
.6517
.6539
.6561
49
48
2.2
41
.6561
.6583
.6604
.6626
.6648
.6670
.6691 .
2.2
42
.6691
.6713
.6734
.6756
.6777
.6799
.6820
47
2.2
43
.6820
.6841
.6862
.6884
.6905
.6926
.6947
46
2.1
44
.6947
.6967
.6988
.7009
.7030
.7050
.7071
45
2.1
60'
50'
40'
30'
20'
10'
0'
Angle
Natural Cosines.
Table II
341
TABLE III
of
Natural Sines and Cosines.
Natural Sines.
Prop.
Angle.
0'
10'
20'
30'
40'
50'
60'
Angle.
Parts
for 1'.
tf°
.7071
.7092
.7112
.7133
.7153
.7173
.7193
44°
2.0
.7193
.7214
.7234
.7254
.7274
.7294
.7314
43
2.0
47
.7314
.7333
.7353
.7373
.7392
.7412
.7431
42
2.0
48
.7431
.7451
.7470
.7490
.7509
.7528
.7547
41
1.9
49
.7547
.7566
.7585
.7604
.7623
.7642
.7660
40
1.9
1?
.7660
.7679
.7698
.7716
.7735
.7753
.7771
39
1.9
.7771
.7790
.7808
.7826
.7844
.7862
.7880
38
1.8
52
.7880
.7898
.7916
.7934
.7951
.7969
.7986
37
1.8
53
.7986
.8004
.8021
.8039
.8056
.8073
.8090
36
1.7
54
.8090
.8107
.8124
.8141
.8158
.8175
.8192
35
1.7
II
.8192
.8208
.8225
.8241
.8258
.8274
.8290
34
1.6
.8290
.8307
.8323
.8339
.8355
.8371
.8387
33
1.6
57
.8387
.8403
.8418
.8434
.8450
.8465
.8480
32
1.6
58
.8480
.8496
.8511
.8526
.8542
.8557
.8572
31
1.5
59
.8572
.8587
.8601
.8616
.8631
.8646
.8660
30
1.5
60
.8660
.8675
.8689
.8704
.8718
.8732
.8746
29
1.4
61
.8746
.8760
.8774
.8788
.8802
.8816
.8829
28
1.4
62
.8829
.8843
.8857
.8870
.8864
.8897
.8910
27
1.4
63
.8910
.8923
.8936
.8949
.8962
.8975
.8988
26
1.3
64
.8988
.9001
.9013
.9026
.9038
.9051
.9063
25
1.3
fl
.9063
.9075
.9088
.9100
.9112
.9124
.9135
24
1.2
.9135
.9147
.9159
.9171
.9182
.9194
.9205
23
1.2
67
.9205
.9216
.9228
.9239
.9250
.9261
.9272
22
1.1
68
.9272
.9283
.9293
.9304
.9315
.9325
.9336
21
1.1
69
.9336
.9346
.9356
.9367
.9377
.9387
.9397
20
1.0
70
.9397
.9407
.9417
.9426
.9436
.9446
.9455
19
1.0
71
.9455
.9465
.9474
.9483
.9492
.9502
.9511
18
0.9
72
.9511
.9520
.9528
.9537
.9546
.9555
.9563
17
0.9
73
.9563
.9572
.9580
.9588
.9596
.9605
.9613
16
0.8
74
.9613
.9621
.9628
.9636
.9644
.9652
.9659
15
0.8
?f
.9659
.9667
.9674
.9681
.9689
.9696
.9703
14
0.7
.9703
.9710
.9717
.9724
.9730
.9737
.9744
13
0.7
77
.9744
.9750
.9757
.9763
.9769
.9775
.9781
12
0.6
78
9781
.9787
.9793
.9799
.9805
.9811
.9816
11
0.6
79
.9816
.9822
.9827
.9833
.9838
.9843
.9848
10
0.5
80
.9848
.9853
.9858
.9863
.9868
.9872
.9877
9
0.5
81
.9877
.9881
.9886
.9890
.9894
.9899
.9903
8
0.4
82
.9903
.9907
.9911
.9914
.9918
.9922
.9925
7
0.4
83
.9925
.9929
.9932
.9936
.9939
.9942
.9945
6
0.3
84
.9945
.9948
.9951
.9954
.9957
.9959
.9962
5
0.3
85
.9962
.9964
.9967
.9969
.9971
.9974
.9976
4
0.2
86
.9976
.9978
.9980
.9981
.9983
.9985
.9986
3
0.2
87
.9986
.9988
.9989
.9990
.9992
.9993
.9994
2
0.1
88
.9994
.9995
.9996
.9997
.9997
.9998
.9998
1
0.1
89
.9998
.9999
.9999
1.0000
1.0000
1.0000
1.0000
0.0
60'
50'
40'
30'
20'
10'
0'
Angle.
Natural Cosines.
By permission of Superintendent Smithsonian Institute.
342 Military Topography for Mobile Forces
EXPLANATION OF TABLE III.
The left hand column and top horizontal line
show angles in degrees and multiples of 10 minutes,
whose natural sines appear in the second to eighth
columns. For example: The sine of 40° 10' is
.6450. The second column from the right and the
bottom line, in the same way, show the angles whose
cosines are correspondingly in the table. For ex-
ample: the cosine of 59° 40' is .5050.
The right hand column headed "prop, parts for
1' " shows the change in the natural functions (sine
or cosine) for each change of 1' of the angle, and is
used to find the value of the function when the num-
ber of minutes in the given angle is not a multiple of
ten. For example, required the sine and the cosine
of 30° 16'.
The sine of 30° 10' is. 5025; the proportional
part for 1' (found at the right end of the same line)
is 2.5. Hence for 6' the proportional part = 2.5
X 6 = 15; 5025 -f 15 = .5040 natural sine of
30° 16'.
The cosine of 30° 10' = .8646. The proportional
part for 1' is 1.5. Hence for 6' it is 6 X 1.5 = 9;
8646 — 9 = .8637 natural cosine 30° 16'. (The 9
is subtracted because the cosine decreases as the an-
gle increases as shown in the table. )
To find from the table the tangent of an angle
divide its sine by its cosine ; to find the cotangent di-
vide unity by the tangent.
Explanation of Table III 343
The sine of an angle is the opposite side divided
by the hypotenuse of the right angled triangle; the
cosine is the adjacent side divided by the hypoten-
use ; the tangent is the opposite side divided by the
adjacent side. (See figure 98(a).
344
INDEX
A PARS.
Accuracy, aids to 171, 181
Adjustments of transit and plane table 81
Alidade, defined 78
Angles, horizontal 6S, 237
vertical 104, 152, 254.
Axis, horizontal of transit, adjustment 90
of bubble tubes, adjustment 82, 94
Attraction, local of needle 62
Azimuth, determination of in plane table survey 78
transit survey 174
sketching 237
Azimuth, measured from north 69
meaning of true and magnetic 69
plotting an 183
of polaris, table showing 65
calculation of latitudes and departures from 185
B
Barometer, in sketching 249
Base, measurement of 150
selection of 149
in sketching 277
Bearings, true and magnetic defined 69
Bench Marie, meaning of 134
Blue Prints, in reproduction of maps 213
Board, drawing 242
method of oriented 268
method with compass and protractor 237, 240
Board, slope, construction of 248
Bubble Tubes, to adjust of plate 82
of telescope 94
of Wye level 131
of Abney clinometer 247
Index 345
C PARS.
Care of instruments 75
Clinometer 244-247
Collimation, to adjust line of 85
Compass and dividers 197
attached to drawing board 242
basis of surveys 62
box and prismatic 237
intersection with 240
on transit 71
Computer, stadia 123
Construction of scales 18
profile from map 42
from level notes 140
Contours, information shown by 23
distance between 25
slopes shown by 22
plotting 164
survey of 1 89
Critical points, meaning of 166
Cross wires of telescope 71
Curvature of earth, allowance for 152
D
Datum plane of elevations 22
Declination, determination of 64
diurnal and secular 62
Declination, to set off on transit 74
to lay off on map 34, 1 53
Declinator, description and advantages 78, 291
Details, filling in of 154, 164, 176
shown on a sketch 260
Departure, table showing calculation of 188
Distance, estimation of 234
measuring instruments 106, 234
measured with tape 107
stadia 117
346 Military Topogkaphy fob. Mobile Forces
PARS.
by pacing 228
by time of horse 231
with range finders 214
Drawing Board (see Board drawing)
Drawing Instruments (see Instruments drawing)
E
Elevation, estimation of 257
measured with Wye level 134
stadia 122
clinometer and M. D 272
Elevations, table of from stadia readings 122
computed with Cox computer 123
Enlargement of maps 210
effect of on scales 19
Equipment for transit survey 173
plane table survey / 145
position sketch 275
road sketch 289
Equivalent, horizontal (H. E.) 25
Errors, adjustment of 159, 187
in base line 150
limit of 186
where permissible 264
Estimation of elevations 257
contour locations on the ground 255
directions 252
distances 234
map distances (M. D.) 236, 273
slopes 251
F
Forest, reconnaissance of 331
Foresights 134
Fraction, representative (R. F.) 15
Index 347
Cx PARS.
Grade line 14,0
Gradients represented 29
Gradienter, angles measured with 71
Graduations of compass 71
horizontal and vertical limbs 71
sextant 219
verniers 59
H
Hachures 32
Height of instrument 120, 134
Horizon glass of sextant 219
Horizontal angles 237
distance 14
plane, estimation of 254
reduction to of inclined readings 120
I
Image, distance proportional to size of 117
Index of scale 56, 71
Index glass of sextant 219
Ink, kinds of used in map work 205
Instruments used in finishing maps 193
Instruments used in plane table survey 145
position and outpost sketches 241
used occasionally in topography 214
Intersection, to locate a point by 1 52, 1 56
Interpolation of contours 167
Interval contour, relation to M. D. etc 25
L
Landmarks to be shown on sketch 260
Latitudes, table showing calculation of 188
Lettering title of map 209
Level, adjustments of wye ISO
hand 250
348 Military Topogkaphy fob, Mobile Fokces
PARS.
use of wye 134
rod, N. Y 125
method of holding 135
Level, to set up and level 126, 127
Leveling, cross section 141
differential 135
profile 130
Line, determination of direction of 237
ranging out Ill
retracing old survey 68
to run a straight 89
Location of one's position on map 36
points by intersection 239, 269
resection 240, 270
traverse 268
M
Map distance (M. D.) 25
reading 13
Maps, classes of 10
details to be shown on 39, 164, 260
Geological Survey 54
information given by contoured 12
normal system of scales of 143
reproduction of 210
title and border of 210
Methods of representing scales 15
Meridian, determination of true and magnetic 64, 65, QQ
N
Needle compass, basis of directions 62
straightness of 99
sluggishness of 102
Notes, transit 177
plane -table 158
level 186, 189
Index 349
PARS.
contour 19I
Notebook, method of sketching objections to 291
o
Observations for locating meridian 66
method of by range finders 215
with sextant, methods of 219 (a)
Obstacles, passing with chain 114
Odometer, use of 233
Offsets, location of points by 271
Oriented drawing board (see board drawing)
Orientation of drawing board with needle 268
transit 174, 180
by back sight 152
maps, methods of 34
Oscillations of needle, taking mean of 174
Outpost sketches 288
P
Pantograph, reproduction of maps with 212
Pace tally, use of 229
Paper, cross section 196
Paper, profile 196
tracing 205, 263
contraction and expansion of 152
Parallax, method of removing 77, 128
Pens contour 204
right line 203
Perpendicular, to locate on the ground 114
to draw 200, 201
Plane table 78
survey 1**
adjustments of 81
method of sketching 240
resection with -....155
to set up 79
350 Military Topography for Mobile Forces
PARS.
triangulation with 148
traverse with 157
survey, using transit to read stadia 163
Place sketching 309
Plotting with protractor 183, 238
from rectangular co-ordinates 184
Pins marking 108
Polaris, table showing azimuths of 65
Point, turning 134
Points to be observed in position sketching 307
Point critical 166
Position sketch 265, 275
reconnaissance of 337
Problems in scales 19
scaling distances 21
finding declination 67
M. D's 31
graduating stadia rods 118
retracing old survey lines 70
vernier construction 61
visibility 52
Prints, blue, bromide 213
Profile, construction from map 42
leveling 138
to plot from notes 140
Protractor, Abbott's use of 238
circular 183, 199
R
Radiation method of surveying l6l
Range finders 214
Ranging out a line Ill
Reconnaissance 310
for camp 333
of position 337
railroad 327
Index 351
wood or forest 831
mountain 382
river 320
Recorder, duty of l62
Reduction of maps 210
inclined stadia readings 120
Reference points, carrying forward in sketching 259
Reproduction of maps 210
Refraction, allowance for 152
Resection, to locate point by 155
Reticle, cross wire 71
River reconnaissance 320
Road sketch 289
reconnaissance 313
Rod, level 125
stadia readings on 118
stadia, to graduate 118
Rule, slide use of in topography 220
s
Selection of scales of maps 142
Scales of maps and sketches 225
of M. D's 26, 243
of instruments 56, 59
vernier 57, 61
reading and working l6
of equal parts 198
problems in 19
Sextant, description and use 219
Signs, conventional 39, 262
Sight, back and fore 134
check 171
Sketching case, cavalry 289
contours 273, 288, 296
Slope, — concave, convex and uniform 23
formula expressing relations of 26
352 MrLiTAHY Topography for Mobile Forces
PARS.
Stadia, principle of 117
method of rapidly reducing readings 123
reduction table 121
rods to graduate 118
reading reduction of inclined 120
Square T in drafting 200
Sun,_ magnetic declination by observing the 64
meridian approximate from observing 38
Survey, execution of military 144
transit and stadia 172
contour 1 89
plane table and stadia 147
System, normal of scales 143
T
Tape, measuring a line with 108
Timing a horse in sketching 232
Titles of mapSj to show what 208
Topography, military 1
Topographical signs 39, 262
Towns and villages, reconnaissance of 318
Tracing paper and linen 263
of maps 207
Traverse with compass and protractor 237
Transit, description of 71
to set up 72
to level 73
to set off the declination on 74
rules for use of 76
checks on accuracy of readings 181
to orient 174
Traverse with transit 174
plane table 157
oriented drawing board 268
Triangles right to construct 200, 201
Triangulation 148, 151, 152, 269
Index 353
PARS.
Tripod, metal telescopic 242
T square use of 200
V
Vernier, problems in constructing and reading 61
rules for 58
Vertical circle to adj ust 98
Visibility of areas 51
points 41
problems 52
w
Walk, of horse 231
Wires, cross 71
stadia 117
Wood reconnaissance of 331
MAP
FORT LEAVENWORTH, KAS
and
VICINITY
Corripxled from Survej/'S rria.de by the. Staff Class of 1904-05^190^-06.
Under tVie direction, of the
COMMANDANT
, of the
INfANTfiY AND CAVALRY SC HOOL . S' G N A L SCHOOL AND
STAFF COLLEGE.
January 1907
4 INCH MAP
AP
lNWORTH.KAS
nd
NJTY
' the Starr Class oF t904-05,1906-06
lirection of the
P '/iu.eri foi- the Di/:>artrnmnt off' 'if '<'-/ ■^'~t. ( flf-inOr- TuiiticsJ
DR^w 6 r.tAHAM CO PKOIO UTMOOaASnEfiS .vfcSMihv'O" C