COMPILED BY
MAJOR WALTON C. CLARK, C. A.
ARTILLERY SCHOOL
FORT MONROE, VIRGINIA
HEAVY (COAST)
ARTILLERY
COAST
ORIENTATION
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HEAVY (COAST)
ARTILLERY
(REVISED)
COMPILED BY
MAJOR, WALTON C. CLARK, C, A.
U.S. COAST ARTILLERY SCHOOL
Sº . FORT MONROE, VIRGINIA
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[...] [T] [] [T]||

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N*.*
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COAST ARTILLERY SCHOOL
FoRT MoMROE, WA.
OCTOBER, 1918.
This book, prepared under the immediate supervision of
the Commandant, is published for use as a text in the Coast
Artillery School and in the Universities giving preliminary
military training. Care also has been taken to arrange in
convenient form for field use the information necessary for
making the topographical preparation for heavy artillery.
Valuable assistance in the preparation of this text has been
rendered by the staff of instructors on duty at the Coast
Artillery School. The personal interest shown by these in:
structors in contributing articles, in criticizing and correcting
the work of the compiler has made it possible to publish this
text in its present form.
By order of Lt. Col. R. R. WELSHIMER, C. A.;
C. L. KILBURN,
Major-C. A.
Secretary.
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HIS BOOK may be purchased
from the Jo URNAL OF THE
UNITED STATES ARTILLERY,
Fort Monroe, Virginia, at 75 cents
per copy, postage prepaid.
TABLE OF CONTENTS
Page
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . YI
& *
CHAPTER I
ELEMENTS OF Topography
1. Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Contours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.
4. Slope Scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5. Profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6. Conventional Signs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
CHAPTER II
CARToGRAPHY of FRENCH MAPs
1. Map Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2. Coordinates and Quadrillage.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3. Geodetic Triangulation. . . . . . . . . . . . . . . . . . . . . . . . . . . tº dº tº e g º ºs e º ſº g g g º º º 46
4. Battle Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
CHAPTER III
ANGULAR MEASUREMENTS
1. Units of Angular Measure...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2. Direction of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3. Instruments for Measuring Angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
* Verniers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5. Measuring Angles by Repitition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
CHAPTER IV
ADJUSTMENTS OF TRANSIT
1. Plate Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2. Crosswires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3. Line of Sight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4. Horizontal Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5. Telescope Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6. Vertical Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
CHAPTER V
LINEAR MEASUREMENTS
1. Units of Linear Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
; Methods of Approximate Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . ;
Stadia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Steel Tape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5. Triangulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
VIII TABLE OF CONTENTS
ii
i
i
;
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CHAPTER VI
PLANE TABLE Page
Materiel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Orientation....... . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Traverse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Intersection... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Resection. . . . . . . . . . . . . . . . . . . . * c e s e e s a s a s e s e s e s s e s e a e s • e º e s e s s e s e 113
e W
CHAPTER VII
LEVELING
Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Map Leveling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Barometric Leveling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Trigonometric Leveling.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Spirit Leveling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
TTOTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
CHAPTER VIII
MERIDIAN DETERMINATION
Mechanical Solutions.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Elements of Astronomy and Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Observation on the Sun.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Observation on Polaris...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Observation on a Star at Equal Altitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Observation on Known Terrestrial Points. . . . . . . . . . . . . . . . . . . . . . . . . . . 156
CHAPTER IX
TRANSIT TRAVERSE t
Methods of Running Traverses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Forms of Field Notes..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Adjustments of Coordinates and Altitudes. . . . . . . . . . ‘. . . . . . . . . . . . . . . . . 178
Plotting the Traverse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
CHAPTER X
INTERSECTION
Reduction to Center and Swing..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
U. S. Method of Intersection... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
French Method of Intersection... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
CHAPTER, XI
RESECTION
Trigonometric Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . g tº tº º te º 'º º e º ſº º ſº gº tº º 194
U. S. Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Relevement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
N.
TABLE OF CONTENTS
IX
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;
ii
i
CHAPTER XII
Topographic RECONNAISSANCE
Visible and Invisible Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Determination of Defilade. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum Range. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dead Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charts Showing Possibilities of Fire. . . . . . . . . . . . . . . . . . . . . . . . .
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER XIII
THE FIRING BOARD
Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER XIV
PANORAMIC SKETCHES
Essential Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Annotations and Conventional Signs. . . . . . . . . . . . . . . . . . . . . . . . .
Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER, XV
ORIENTATION FoR RAILWAY ARTILLERY
Principles of Railroad Curves. . . . . . . . . . . . . . ". . . . . . . . . . . . . . . . .
Types of Epis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surveys of Epis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graduation of a Curved Epi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . g º º
Resurvey of Old Tracks.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER, XVI
ERRORS IN MAPS AND FIELD WORK
Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER XVII
DUTIES OF THE ORIENTATION OFFICER
Survey Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observation Service. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
INTRODUCTION
During the early part of the war it was attempted to fire
the heavy artillery by the more or less approximate methods
that are used by the light field artillery in open warfare. The
range and direction of the target were determined to a fair
degree of accuracy, the effects of a few elements such as wind,
drift and difference in altitude of gun and target were estimated,
and the firing adjusted according to the fall of the shots. The
system broke down. Ammunition was being wasted, much
time lost, and targets were not destroyed. Extremely accurate
methods of firing the heavy artillery had to be adopted, and
now practically every condition that may appreciably affect the
gun or powder charge or the projectile in its flight is accounted
for in calculating the data for aiming and laying the gun.
The heavy artillery batteries are always located several
kilometers behind the first lines and frequently in defiladed
positions. Rarely, if ever, is a target visible from the gun, and
distances, directions and altitudes are determined by precise
topographic methods before the ballistic data for laying the gun
can be computed. The procedure of making the topographic
determinations is now referred to as orientation. The methods
of making these determinations are similar to those employed
in making the initial surveys before mounting a heavy Seacoast
battery of guns or mortars. The surveying instruments used
are essentially the same and the only difference in methods is
due to the unusual conditions brought about by the present
type of warfare.
In the use of heavy artillery in land warfare ranges and
directions must be determined with precision. Maps play
an important part in this work. When a battery is execut-
ing map firing, its position and that of its target must be
accurately known in order to calculate ranges and directions.
The location of targets on the map is, in general, the duty of
other branches of the service, but the location of the batteries,
and their observation stations, is the duty of the artillery
itself, as is also the computation of ranges and directions.
Because of the high cost of ammunition and the rapid ero-
XII INTRODUCTION
&
sion of the guns, an accurate execution of the preliminary
topographic work is essential for the heavy artillery. It is
not considered accurate until its errors are negligible com-
pared to those which are unavoidable, i.e., the dispersion and
the errors in the ballistic corrections, especially those due to
indeterminate atmospheric conditions. Erroneous topo-
graphic preparation may cause the shots to fall so far from
the target that aerial and terrestrial observers fail to see them,
thus making correct ranging and adjustment impossible.
In any event, there has been a waste of time and ammunition.
The question of time is very important, for unless the bat-
tery’s object is attained quickly the enemy's fire is likely to
drive back the aeroplane that is spotting the shots or to begin to
take effect on the battery itself, causing casualties in the gun
crews, driving them to their dugouts, and possibly destroying
the guns. When the opposing trenches are close together
erratic shots during adjustment may cause shells to fall among
friendly troops, and though the casualties may be slight,
nothing is more harmful to the infantry's morale than to be
fired upon by their own artillery.
If an attempt is made to improve an inaccurate topographic
preparation by keeping in mind during future firings the cor-
rections which had to be made during the first firing, it is
possible that all the unavoidable errors made in the estimation
of atmospheric conditions for the first firing and the position
of the first target will creep in. To correct the topographic
preparation by means of observation during the first firing will
result, therefore, in errors for each succeeding firing.
For a battery of several pieces the preparation for effective
fire includes the formation of a sheaf of fire, which sheaf may
be parallel, convergent or divergent. The different pieces of
the same battery have peculiarities which are unfortunately
difficult to determine with precision, such as the wear of the
piece, causing irregularities, especially in the range, which are
very important and which vary. The ballistic agreement of
guns in the same battery is a very delicate thing which has
never been perfectly solved. During the regulation of fire
with several pieces, in addition to the adjustment of the group,
there will always be small corrections which must be given to
the different pieces for the purpose of bringing into coinci-
dence their zones of dispersion. The positions of the dif-
ferent guns in the battery with reference to their directing
piece must therefore be determined with great accuracy, in
INTRODUCTION XIII
order to make it certain that any lack of agreement observed
during fire does not result from a topographic error. Know-
ing the topographic work to be accurate, any variations in
the zones of dispersion will be correctly attributed to pecu-
liarities of the piece, and corrections made accordingly.
Besides having to guard against errors, the battery officer
must always possess dependable checks which will eliminate
the possibility of costly blunders. In general every result must
be verified. All determinations must be made by two distinct
and independent procedures which may have unequal precision,
the less exact serving as an approximate control of the other.
Each battalion of the heavy artillery has an “Orientation
Officer,” sometimes called a “Survey Officer,” who is in
charge of this topographic work. Under their usual civil
meanings, the latter is the better title, but on the Western
Front the meaning of “Orientation” has broadened, so that
it now includes not only the determination of directions but,
also all surveying work, and the study and use of the terrain.
Therefore, “Orientation Officer” is the better title for the
position, and will be used herein. -
Normally the Orientation Officer performs certain fairly
definite duties: He determines the locations and altitude
of gun positions and observation stations, the directions
(Y-azimuths) of aiming lines, and secures all orientation or
topographic data related or incidental thereto. However,
like the normal atmospheric conditions assumed in range
tables, this normal condition rarely exists, and all battery
officers—lieutenants as well as captains—must be prepared
to perform any or all of this work. In a way, an orientation
officer can be compared to a resident engineer in charge of
construction work. He is an executive, who must plan,
Supervise and check the work of locating the required points,
lines, levels and directions, having various survey parties,
computers and draftsmen to perform the detailed work. To
train enlisted men to do this work properly, an Orientation
officer must understand it even more clearly than would be
necessary merely to perform the work himself. He must
also understand maps, their projections, construction, tri-
angulation systems, use, meaning and accuracy; Surveying
instruments and methods; plotting, drafting and sketching;
elementary astronomy and its uses and finally, their appli-
cation to the problems of the heavy artillery.
Suppose you are directed to emplace one gun on the lawn
XIV INTRODUCTION
in front of the Hotel Chamberlin and open fire on the Post
Office in Newport News. Before you can make the ballistic
calculations which are explained in “Gunnery for Heavy
Artillery,” it is necessary for you to make certain topographic
preparations for fire. What do you do? Briefly, you pro-
ceed as follows: (1) Examine the map (Battle Map) and
determine the coordinates of the Post Office and the approxi-
mate distance to it. (2) Examine the range table and deter-
mine the approximate angle of elevation necessary for a pro-
jectile to hit the Post Office. (3) Select a position for the
battery far enough from the Hotel so there will be no ques-
tion, under any condition, but that a projectile will clear it.
(4) Determine the coordinates of the gun position by topo-
graphic methods. (5) Similarly determine the coordinates
of the Fort Flag Pole, which you select as an aiming point.
(6) From the coordinates of the gun and of the target, compute
the distance and direction to the target. (7) From the coor-
dinates of the gun and aiming point, compute the direction
to the aiming point. (8) Determine the coordinates of one
or more observing stations and the distances and directions
from them to the Post Office. (9) If time permits, verify one
of the directions so obtained by an astronomic observation.
You now have not only the distance and accurate direction
to the Post Office, but also the data for pointing the gun at it.
These operations may at first be confusing and seem intan-
gible. Therefore, it is the purpose of this book not only
to explain them in detail, but also to give in a clear and con-
cise form all the information necessary either for an orientation
or a battery officer to solve the various problems of orienta-
tion that may arise in connection with a battery of heavy
artillery executing map firing.
The use, care and adjustments of surveying instruments
are explained in detail, together with the latest approved
methods of making computations from field data. The con-
struction and use of maps are discussed at length, with an
explanation of the application of coordinates and quadrillage
to heavy artillery problems. Typical examples are worked
out in full, illustrating the different methods of computation,
and every effort has been made to present the subject matter
in a manner that will be intelligible to an officer who has had
no training in civil engineering and whose knowledge of
mathematics includes only algebra, geometry and plane
trigonometry.
INTRODUCTION XV
IIST OF BOOKS CONSULTED
“Topography, Map Reading and Reconnaissance.”—Spalding.
“Plane Surveying.”—Tracy.
“Engineers' Pocket Book.”—Trautwine.
“Theory and Practice of Surveying.”—Johnson.
“Topographical Surveying and Sketching.”—Rees.
“Elements of Astronomy.”—Hosmer.
“Military Topography.”—Sherrill.
“Engineer Field Manual.”—Leach.
“Lambert Conformal Conic Projection.”—Deetz.
“Encyclopedia Britannica.”
“Manual Artillery Orientation Officer.”
Bulletins published by the Army Heavy Artillery School in
France.
Pamphlets published by the Army War College.
CHAPTER I
ELEMENTS OF TOPOGRAPHY
MAPs
SCALES
CONTOURS
SLOPE SCALES
PROFILES
CoNVENTIONAL SIGN's
i
1. MAPs
A map is a graphic representation of a portion of the earth’s
surface. All maps are plans, showing on a reduced scale, but
in their true locations, the principal plane features of the area
covered, such as roads, railroads, towns, buildings, rivers and
lakes. Many maps, especially military maps, are more than
plans; they show also the topographic features, hills, valleys,
ridges and plains, and their elevations; all objects being shown
in their true relations in regard to elevation as well as location.
Further, the word map, as normally used, conveys an impres-
sion of accuracy and completeness. A sketch, on the other
hand, is usually a rough map of an area, inaccurate, incom-
plete, and rapidly made.
Because a map is a plan, it must have a scale, that scale
being the ratio between distances on the map and the corre-
Sponding horizontal distances on the ground. As that ratio is
constant for all parts of the map, it necessarily follows that any
figure on the map, a triangle for example, is similar to the
corresponding figure on the ground; therefore an angle between
any two lines on the map is equal to the corresponding angle on
the ground. In order to show topographic features as well,
elevations must be indicated in some manner, usually by
Čontours. In order to indicate the nature of the terrain
(buildings, woods, roads, swamps and other local conditions)
conventional signs are used, the appearance of the sign usually
Suggesting the object it represents.
This chapter deals with map scales, the methods of indi-
cating topography, and conventional signs. Although it refers
particularly to French Battle Maps on the Metric System, the
Same principles apply to all maps, and once the student grasps
2 ORIENTATION FOR HEAVY (COAST) ARTILLERY
them he will understand American as well as French maps.
NOTE: For a description of the Metric System see the
beginning of Chapter V.
2. SCALES
Horizontal Distances.—In surveying, all distances are
measured in two planes only, horizontal and vertical. Any
distances not so measured are reduced to the corresponding
horizontal and vertical distances. Therefore, in plotting
points on a map or in Scaling distances therefrom, only hori-
zontal distances, and in plotting contours or determining
differences in elevations therefrom, only vertical distances
need be considered.
Map Scales.—If a map was made full size, i.e., if one meter
on the map represented one meter on the ground, every detail
on the ground could be shown on the map—every pebble on a
beach and every brick in a pavement—but such a map would
be worthless. Minute detail is of no value. Only important
features need be shown, and to be of value a map must show a
large area on a small sheet. Therefore maps are on a reduced
scale. One meter on the map represents many meters on the
ground. The scale of a map depends on the amount of detail
that must be shown, and that in turn depends on the purpose
of the map. A map of the United States cannot give the detail
that a map of Virginia can. A map can show only the general
features, and a map draftsman must clearly understand the
purpose for which the map is to be used before he can properly
select the data that should be shown. If too much detail is
shown the map becomes “cluttered up,” hard to read, and
loses much of its usefulness. On the French Battle Maps it
was necessary to show considerable detail. Therefore, the
scales are large. For infantry, interested in only a small area,
a large amount of detail (trench traverses, machine gun em-
placements, etc.) is necessary, while heavy artillery is only
interested in the principal features of larger areas. Therefore,
the battle maps are on several different scales.
Representative Fraction.—The ratio of a distance on the
map to the corresponding distance on the ground, which is
the scale of the map, is usually expressed as a fraction,
Map Distance
. no Distance’ called the Representative Fraction (R.F.),
It is a purely abstract quantity, no particular unit of meas-
ELEMENTS OF TOPOGRAPHY 3
urement being implied, and the numerator is usually ex-
pressed as unity. For example, if the R.F. is 1/10,000, it
means that one unit on the map represents 10,000 similar
units on the ground, regardless of what that unit may be.
This same relation between Map Distance and Ground Dis-
tance may also be expressed as a ratio, 1: 10,000. One inch
on the map would represent 10,000 inches on the ground, or
one meter on the map would represent 10,000 meters on the
ground.
For example, the Battle Maps used by French combatant
troops have Representative Fractions of 1/5,000, 1/10,000,
and 1/20,000, the first being used mostly by infantry and the
last two mostly by artillery. The maps used by the Army
staffs are, of course, smaller in scale and larger in area, their
R.Fs. being 1/50,000, 1/80,000, 1/100,000, 1/200,000, and even
smaller. The Representative Fraction of the Goast Artillery
Plotting Board is 1/10,800, and those of most U. S. Geologica
Survey maps are 1/62,500 and 1/125,000, which gives an idea
of the scales of French Maps as compared with maps fre-
quently used in this country.
Use of the R.F.—By means of the Representative Fraction,
which is given on the border of all French Battle Maps, the
distance on the ground representated by any distance on the
map, or vice versa, can be computed. For example:
Given R.F. = 1/10,000. Required, the distance on the map that represents
1 km. on the ground. -
1/10,000 =Xm/1,000 m, X=0.1 meter = 10 cm.
That is, 10 cm. on the map represents 1 km. on the ground.
Given R.F. = 1/20,000 and a map distance of 5 cm. Required, the distance
on the ground that this represents.
1/20,000 =5 cm./X cm., X=5x20,000 cm. = 1 km.
That is, 5 cm. on the map represents 1 km. on the ground.
Scaling distances off a map, with a ruler graduated in
centimeters, is very simple if the ground distance represented
by one centimeter on the map is known. This can be quickly
found from the R.F., viz.:
1/ 5,000 = 1 cm./X cm. X = 5,000 cm., or 1 cm. = 50 m.
1/10,000 = 1 cm./X cm. X = 10,000 cm., or 1 cm. = 100 m.
1/20,000 = 1 cm./X cm. X=20,000 cm., or 1 cm. =200 m.
Graphic Scales.—These relations are very simple, and by
their use distances can be scaled from any battle map very
quickly. If a ruler graduated in centimeters is used, the
distance must be mentally multiplied by 50, 100, 200, etc.,
according to the scale of the map. It is simpler, however, to
use a centimeter scale with the units marked according to the
4 ORIENTATION FOR HEAVY (COAST) ARTILLERY
ground distances in meters that they represent. Fig. I shows
Several centimeter scales marked in that manner.
Such a scale is called a graphic scale. Technically it is a
map reading graphic scale because it is used in reading maps.
Map making graphic scales, graduated in meters, paces, strides,
wheel revolutions of other units used in measuring ground
distances are discussed on the chapter on “Plane Table.”
—
/ 2 3 4 5 6 7 8 9
A4/V/AAZS OF AZZAAS Sco/e //0000.


F- F |--|-- — |--|--|--|--|-
2 42 6 8 /O /2 /4 v /6 /9
////VCAAZZS OF AZ7A/PS Scaſe /: 20000

ſ | | | | | | | | | | | | | i l | |
4 CŞ' /2 /6 20 24 28 J2 Jó
A/VOAA/X5 OF AZA 74/75 Sco/e /:20000
Fig. I.-SCALES FOR FRENCH BATTLE MAPS
Most American maps have graphic scales printed on their
borders, but French maps often do not, probably because the
relation between map distances and ground distances is so
simple in the metric system. If a graphic scale is printed on
the map, it should be used in preference to any other scale,
because of possible shrinking or expansion of the map, which is
apt to occur in printing or with climatic changes, and may
amount to two per cent. For instance, a map distance which
measured 10 cm. when the map was made may measure 10.1 cm.
a year later in a dry, well-ventilated office, or 9.9 cm. in a damp,
stuffy dugout. A scale printed on the map expands and
contracts with the map, and its use avoids possible error.
Furthermore, the use of a graphic scale avoids the trouble and
possible error involved in computing ground distances by
dividing map distances by the R.F.
3. CONTOURs.
Elevations.—Thus far maps have been considered as plans
only. But in addition to showing the relative locations of
different points, many civil maps and all Military maps show
also the relative elevations.
ELEMENTS OF TOPOGRAPHY 5
Elevations are usually referred to mean sea level and if the
elevation of a point is given as 75 m. it means 75 meters above
sea level. In some places, however, for local convenience
elevations are referred to a local datum plane. For instance,
elevations in cities on the Great Lakes are usually referred to
mean lake level. Common sense will usually show whether
any given elevation refers to sea level or to a local datum plane.
The elevations of certain important points, such as bench
marks and hilltops, are usually printed on the map, but to
print the elevations of a large number of points would result in
a confused jumble of figures. Therefore, some other device
is necessary.
Methods of Indicating Topography. The topography or
relief of an area must be shown. This can be done to scale in a
relief map, such as the War Game Board, but ordinary maps
are plane surfaces—sheets of paper— and the relief must be
projected on to that plane surface. There are three common
methods of indicating topography, viz.:
1. Color Shading. A wash in black or brown indicates
elevations by the density of the coloring, higher points being
lighter than lower. This method is often used on maps of
countries or continents, but is seldom used on large scale land
maps. It is also used on marine charts to indicate the depths
of water in harbors and lakes, shallow water being colored a
lighter blue than deep water.
2. Hachures.—In reality, hachures constitute a form of
shading done with fine pen lines instead of washes. The lines
or hachures run in the direction of the steepest slope (at right
angles to contours). They are equally spaced but the
hachures are heaviest where the slope is the steepest, being
very fine lines where the slope is nearly level. They are
seldom used because of the labor and expense involved, the
difficulty in securing uniformity, the difficulty in determin-
ing elevations from them, and the resulting subordination
of all other details on the map. They are used on Battle
- Maps in connection with contours to show cuts, fills or cliffs.
They are used on some maps of Germany on a scale of
1/100,000.
3. Contours.-This is the accepted method for all modern
maps and is undoubtedly the best system.
A contour is an imaginary line on the Earth's surface all
points of which are at the same elevation. They are the inter-
Sections of a series of equally spaced imaginary horizontal
6 ORIENTATION FOR HEAVY (COAST) ARTILLERY
planes with the surface of the Earth. More exactly, contours
are the intersections of the surfaces of equally spaced concen-
tric spheres with the surface of the Earth; but for small areas
they can be considered as planes. These lines, projected
downward onto the lowest plane (sea level) form a series of
smooth closed curves, each contour being inside the one formed
by the plane beneath it. This is illustrated in Fig. II, which
Lºs
L^
fe
23
:
2T
i
|
ſ
|
!
|
|
|
|
|
|
!
|
|
|
|
|
Fig. II.-CONTOUR PROJECTIONS
shows a cone 25 meters high, with six planes spaced 5 meters
apart cutting it, and a plane on which the intersections of the
various planes with the cone have been projected. Ground
forms are seldom as regular as this cone; therefore, contours are
seldom regular curves. Except in a map of an island, the eleva-
tions along the edges of a map are rarely constant; therefore
only part of the contours close on the map, the others ending at
the border line. The cone in Fig. II can be considered as
an island, with all the contours closing on the map, but if the
map covered only that part to the right of a line through the
center, only part of the contours would close on the map.
Ground contours are imaginary lines of constant elevation




ELEMENTS OF TOPOGRAPHY 7
on the ground. Map contours are actual lines of constant
elevation on the map, representing the corresponding lines on
the ground. If a man walks along a contour line he neither
goes up nor down hill, but always on a level. The surface of a
quiet pond that has no outlet is practically level; therefore its
shore line is a contour. If a man follows it in a clockwise
direction he must turn to the left at every entering valley, walk
up the valley until he heads the water line, cross the valley,
turn to the right, and return on the other side of the valley,
turning to the left again to pass around the spur that lies
between that valley and the next. Thus his course will bend
to the left at every inflowing drainage line, cross it and turn
to the right to avoid leaving the level. If the water in that
pond is at an elevation of 50 meters, the water line is the 50
meter contour. If the water level is raised 5 meters, the new
water line will be the 55 meter contour.
2Ts
/ N
/ º \
/ \
ſ o \
–
>
| N)
L/
Fig. III.-RELATIONS BETWEEN SPACING OF CONTOURS AND GROUND FORMS
Contour Interval.—The vertical distance between two
adjacent contours (their difference in elevation) is called the
contour interval. It is a whole number of meters—1, 5, 10 or
20—depending on the topography and the scale of the map,
but it is constant on any one map. As Belgium is very flat,
1 meter contour can be shown on most 1/20,000 Belgian maps,

8 ORIENTATION FOR HEAVY (COAST) ARTILLERY
but if 1 meter contours were shown on a 1/100,000 map, the
map would be a confusing mass of contours; therefore on that
map the contour interval is 10 meters. Most of the battle
front in France is rolling country, and even on large scale maps
the contour interval is rarely less than 5 meters. On a uniform
slope the contours are equally spaced, and the contour spacing
varies with the steepness of the slope; the steeper the slope, the
closer the contours. Thus, the spacing of the contours is a
measure of the steepness of the slope. This is illustrated in
Fig. II. The slope of the cone is much steeper to the right of
the vertex than it is to the left, and the contours are closer
together on that side.
Žºrž zºº * -
ºzº º == -
22% ~ _^ º ſº §§ § § - …” ~2. …” z 2/7
2% .* 22 2. Tº º |l\\ º |\NS I -, * > 2 T-2 -2&
- 22 °22 º aſſº - - /
222*2.22 mm& 2% W
22% º º
z & § ޺. * t . § W WN \\
// % Minº |%\;\. \\
.44–4–4%º- º º
Fig. IV.-CONTOUR SKETCH
Following this idea a little further, on a dome shaped hill
(one whose slopes are convex) the contours are closer together
at the bottom than at the top, while on a peak (a hill whose














ELEMENTS OF TOPOGRAPHY 9
slopes are concave) the contours are closer together at the top.
(See Fig. III.) On a hill whose sides have a constant slope
the spaces between the contours is uniform as shown in Fig. II.
Thus the contours indicate not only elevations but also the
shape or form of the ground.
Critical Points.—The data for contours is usually obtained
by plane table sketches and stadia, a rodman sometimes
following a contour under the direction of the sketcher. Fre-
quently, however, it is sufficient to locate the “breaks in
grade,” i.e., find the elevation and locations of points where
the slope of the ground changes. The contours can then be
drawn in by interpolation. The breaks in grade determine the
contours and are called “Critical Points.” For very accurate
work, such as is required for calculation of quantities in a
gravel pit, the area is gridironed by a system of lines 20 or 50
meters apart and elevations are taken at the intersections of
these lines as well as at breaks in grade, the contours then being
plotted by interpolation.
Master Lines in Topography.—Practically all the ground
forms existing on the earth today are the result of erosion, i.e.,
hills and valleys have been carved out by the action of running
water. Because water courses have created the ground forms
and the resulting contours, the drainage and ridge lines of an
area form a system of masterlines, which once traced out and
studied give a grasp of the main feature of topography that
can be had in no other way. Moreover, if these master lines,
and the critical points, are indicated on a sketch, the contours
can be intelligently traced in with little error. \
Characteristics of Contours.—From the foregoing, several
characteristics of contours that should be understood and
remembered, can be summarized as follows:
1. All points on the same contour have the same elevations.
2. Contours follow the slopes of streams and valleys,
forming a series of alternate Vs and Us, the Vs pointing up the
valleys with their points at the stream crossings, and the Us
outward around the hills between valleys. -
3. Between critical points slopes are nearly uniform and
contours are equally spaced.
4. Every contour closes on itself, either within or beyond
the limits of the map.
5. Every contour that closes on the map indicates either
a summit or a depression. If there is no water in the depres-
sion the contour is dotted.
10 ORIENTATION FOR HEAVY (COAST) ARTILLERY
6. Contours never cross each other except in the case of
an overhanging cliff or cave, when there must be two distinct
intersections.
7. On a uniform slope contours are equal distances apart.
8. On a plane surface contours are straight and parallel.
9. A contour is always at right angles to the steepest slope
and crosses ridge lines at right angles.
A
X400
X 399 X 409 X423 447X
44.5
X,
3.03. 377 x4/3 423 × 423x
Fig. V-STREAM LINES AND ELEVATIONS OF CRITICAL POINTS
©
NOTE.-On French Battle Maps occasional intermediate
contours are shown in level areas at less than the ordinary
contour or interval. Such intermediate contours are repre-
sented by broken or dotted lines, and are often allowed to end
without closing.
Plotting Contours.-Contours can best be understood by
actually plotting them on a sketch giving the drainage lines
and critical points. Fig. V is such a sketch taken from a

ELEMENTS OF TOPOGRAPHY 11.
French 1/20,000 Battle Map. The area is about 2 km. square
and the drainage lines and critical points are indicated. The
contour interval is to be 5 meters.
The first step is to interpolate between the critical points
along the drainage and ridge lines, to locate the contours,
remembering that along those lines the spacing should be equal,
although near the sources of streams the spacing should be
decreased because streams are usually steeper at their sources
than elsewhere.
423 x ~ 423 ×
*e. N 4/3'
* X
Fig. VI.-PROBABLE SPACING OF CONTOURS INDICATED
The next step is to draw in the contours between the points
thus located, remembering that the contours should be smooth
curves, forming a series of alternating Us and Ws, the Vs
pointing up stream and outlining the valleys, the US pointing
down stream and outlining the hills. Fig. VII shows the
completed map, which was traced directly from a French Map.

12 ORIENTATION FOR HEAVY (COAST) ARTILLERY
* A *...* * A
390 74 4.04 (e.
- 430
X4/7
408X.
xs .e.
X *s 2.4%
Fig. VII.-CoMPLETED MAP SHOWING 5M. CONTOURS
4. SLOPE SCALES
Slopes.—As stated before, contours on a map express
differences in elevation in the ground surfaces represented, and
their horizontal spacing indicates the relative steepness of
slopes. To artillery, slopes are very important because the
slope of the ground in front of a battery may limit the angle
of departure and the field of fire and protect the battery from
hostile observation and hostile fire; and the slope of the ground
in front of a target determines the value of its defilade or mask
and may limit the angle of fall necessary to secure hits. There
are three principal methods of expressing the slope of ground
surfaces, viz.:
1. Degrees.—The degree of slope means the angle meas-
ured in degrees between the plane of the slope and a horizontal
plane. This method is seldom used in civil life, but is the
standard method in armies.

ELEMENTS OF TOPOGRAPHY 13
2. Gradient.—The gradient is the ratio between the
vertical and horizontal distances, the former usually being
given as unity. Thus a gradient of 1 on 8 means that the
ground rises 1 meter vertically in each 8 meters of horizontal
distance. This method is mostly used for the slopes of fills,
cuts and steep banks.
3. Per Cent.—This is the number of units that the ground
rises in a horizontal distance of 100 units, expressed as a per-
centage. Thus in a 1.25 per cent. grade, the ground rises
1.25 meters in every 100 meters. This system is commonly
used on roads and railroads. The following table compares
these three methods for a few slopes; it is condensed from a
table on page 16 of the “Engineer Field Manual.”

Degree. . . . . . . . . . . . . . . 19 2° 3° 4° 5° 6° 70
Gradient. . . . . . . . . . . . . . . 1–57 || 1–29 || 1–19 || 1–14 || 1–11.4 || 1–9.5 || 1–8.1
Per Cent. . . . . . . . . . . . . . 1.74 || 3.49 || 5.24 || 6.99 || 8.75 | 10. 51 | 12.28
Slope Scales.—The distance between contours on a map is
called the “Map Distance” (M.D.); the corresponding hori-
zontal distance on the ground is called the “Horizontal Equiv-
alent” (H.E.). The former is equal to the latter times the
Representative Fraction, or M.D. = H.E.XR.F. The map
distance varies inversely with the slope; the steeper the slope,
the closer the contours and the less the map distance. A slope
scale is a scale on which the map distance corresponding to
various slopes have been laid off. With it the slope of the
ground can readily be determined at any point. American
military maps are provided with such scales, French maps
are not.
Construction of Slope Scales.—The gradient corresponding
to a 1° slope is 1 on 57.3; because the natural cotangent of
1° is 57.3. In other words, a 1° slope rises 1 meter in 57.3
meters. For any vertical interval (V.I.) between contours,
the horizontal equivalent on a 1° slope will be V.I. X57.3 and
the corresponding map distance will be V.I. X57.3XR.F.; then
M.D. (m.) =V.I. X57.3XR.F.
M.D. (cm.) =V.I. X57.3×100XR.F. 1° slope
= V.I. X5730 XR.F.
For slopes up to 10 degrees it can be safely assumed that
the gradient varies directly with the degree; i.e., if the degree
*
14 ORIENTATION FOR HEAVY (COAST) ARTILLERY
is doubled the gradient is doubled. Then the above formula,
divided by the degree of slope, can be applied to any slope, viz.:
M.D. (c V.I. X5730)× R.F.
m.) = Degree of Slope
As an illustration, compute the map distances for slopes up to 5° on a 1/20,000
Battle Map with 5 meter contours; then -
5730 X 5 × 1
M.D. (1°) == 1X20,000 = 1.43 CIOl.
2, 5730 × 5 × 1
M.D. (2 )=-jº--0.72 CII] .
1.43
M.D. (3° =-3--47 CII).
1.43
M.D. (4°) = -T = .36 cm.
1.43
M.D. (5°) = –E– = .28 cm.
A map distance scale can now be made by laying out these
distances successively on a straight line. (See Fig. VIII.)

/o 2 ° 3 * 2° 5° ejº 7°.9
|Z / = -5/77 //op 5ca/e /i/3000

yo 3 o 5° zo /o 3 ° 3° zo
V/-, 5/7 /v7.5 / 20,000 !//=/0/77 / 7.5/.40,000
Fig. VIII.—SLOPE SCALES
Use of Slope Scales.—Such slope scales are of great use in
determining quickly and roughly the slope of any road or
hillside. The slope of a road may govern the battery’s ability
to move over it, and the slope of a hill determines a target's
defilade. It is important that artillery officers be able to
construct and use these scales rapidly. The slope can be
determined by shifting the slope scale over the contours until
a space is found on the scale that equals the contour spacing
on the map. The slope can then be read directly from th
slope scale. .
5. PROFILEs.
Another important use of contours and contoured maps is
in the construction of profiles. For an exhaustive study of
any sector with the view of picking battery positions, supply
routes and observation stations it is necessary to construct
profiles along the controlling lines of vision and fire, both from
our positions and from known or suspected enemy positions
and observation stations, for in this manner alone it is possible to
ELEMENTS OF TOPOGRAPHY 15
determine the value of a battery defilade from all possible enemy
positions, the effect of enemy defilades on our fire, the areas
which it will be possible or impossible to reach from a tentative
battery position and the value of possible observation stations.
A profile may be explained thus: A vertical plane is passed
into the Earth along the line of the desired profile. The
irregular outline traced on this vertical plane by the surface of
the Earth is the profile of this line. Knowing the scale of the
map and the contour interval, such an outline can quickly be
constructed on a sheet of cross section paper.
The most convenient method is to use the same horizontal
scale in plotting the profile that is used on the map. If the
same scale were used in plotting vertical distances, however,
the profile would probably be useless, because elevations are
usually, so small compared to horizontal distances that most
points would fall within the width of a pencil line. Further-
more, there is no need of using the same scale for vertical as
for horizontal distances, provided a single vertical scale is used
for the entire length of any one profile. Hence, profiles are
usually exaggerated vertically. This brings out the details of the
ground much more clearly and facilitates the study of the terrain.
Method of Construction.—Take a sheet of cross section paper
or paper ruled with parallel horizontal lines. Choose a con-
venient vertical scale. Suppose, for example, that each
horizontal line on the paper is taken to represent a contour on
the map. The vertical scale is then the ratio of the distance
between the lines and the V.I. of the map. Mark each line
with the elevation of the corresponding contour, from the
lowest to the highest points which the profile is to include.
ſºc w
Lºs º: , ºr ..º §§§
#jºšSW/
Fig. IX.-CoNSTRUCTION OF A PROFILE FROM A CONTOURED MAP












16 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Place the edge of the paper along the line to be profiled on
the map and make a mark on each line on the paper opposite
each point where the corresponding contour crosses the line
of the profile.(See Fig. IX.) Connect the points so marked in
succession by a smooth curve. Note any features that might
affect the shape of the curve, such as streams, roads, etc., or
that might bear upon the purpose for which the profile is
made. For example, if the problem is one of visibility, note
trees and buildings that are situated along the lines of the
profile.
Limitations.—It is not necessary to draw a profile in order
to determine visibility and similar questions. Simple mathe-
matical principles are all that are required (see chapter on
“Topographic Reconnaissance”), but a profile is often simpler
and more convenient for any but very accurate work. How-
ever, in working with profiles which are exaggerated vertically
there is one limitation which must be remembered. Vertical
angles, angles of slope, etc., cannot be measured on such a
profile with a protractor, even if the angle so measured be
divided by the number of times the vertical scale is exaggerated.
In this case angles may be determined from their tangents.
6. ConVENTIONAL SIGNS
In very large scale map (1 to 500 or 1 to 100), such as
property maps in cities, it is possible to draw all objects to scale
and indicate their character by printed notations, viz., “2-
story frame house” or “brick pavement,” but on the scales
used for Battle Maps such descriptions are not feasible and
certain symbols called “Conventional Signs” are used. In
general, these are nearly the same as the ones in common use
on American maps, and their appearance usually indicates the
objects they represent. The sheets of Conventional Signs
attached hereto (Figs. X to XV) should be carefully studied
and used as a reference when working with Battle Maps.
In a general way the entire character of the terrain and the
objects thereon are indicated by conventional signs, so that
by merely studying the map it is possible to visualize the land-
scape. Water is usually indicated in light black or blue;
contours and elevations in light brown (burnt sienna); German
military works in blue and French in red; details of troop
dispositions in pencil marks, put on by the man using the map;
woods, trees, fields, marshes, cultivated lands, etc., by char-
ELEMENTS OF TOPOGRAPHY
17
acteristic symbols in black. It is not expected that the student
memorize these symbols in detail, but after a few days’ use of
the maps, should be able to read them rapidly.
§
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|S/77/e 77.7-4. Cºs *:::::
ZJoJ&/e 77.27CA. # =#
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18
ORIENTATION FOR HEAVY (COAST) ARTILLERY
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Fig. XI.-CONVENTIONAL SIGNS PRINTED ON FRENCH BATTLE MAPS


ELEMENTS OF TOPOGRAPHY 19
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Fig. XII.-ConventionAL SIGN's PRINTED ON FRENCH BATTLE MAPs
20 ORIENTATION FOR HEAVY (COAST) ARTILLERY
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Fig. XIII.-CONVENTIONAL SIGNS USED IN ALL INSCRIPTIONS PLACED BY
HAND ON FRENCH BATTLE MAPS
ELEMENTS OF TOPOGRAPHY 21

w Corſºye, § Grenadé's $ Jø/55/5/27ce
776/7c.h4/777&s § Wºſer 5%/es [5]
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Fig. XIV.-CONVENTIONAL SIGNS USED IN ALL INSCRIPTIONS PLACED BY
HAND ON FRENCH BATTLE MAPS
22 ORIENTATION FOR HEAVY (COAST) ARTILLERY

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Fig. XV.-CoNVENTIONAL SIGNS USED IN ALL INSCRIPTIONS PLACED BY
HAND ON FRENCH BATTLE MAPſ;
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CHAPTER II
CARTOGRAPHY OF FRENCH MAPS
MAP PROJECTIONS
COORDINATES AND QUADRILLAGE
GEODETIC TRIANGULATION
BATTLE MAPs
:
1. MAP PROJECTIONS
The use of heavy, long range artillery in trench warfare on
the western front has required more detailed, accurate and
larger scale maps than have heretofore been used by armies in
the field. Artillery officers who may have to use them must
have a clear understanding of maps, including the principles
of map making and the accuracy to be expected from the
various types. As the earth is a sphere (nearly) while a map is
necessarily a plane surface, it is impossible to represent a
portion (or all) of the Earth's surface correctly on a map. The
various systems of attempting to do this are called “Map Pro-
jections.” Those used in France are discussed herein.
Form of the Earth.-The Earth is a slightly irregular oblate
spheroid; i.e., itſis a figure formed by rotating an ellipse around
its shorter axis. Because of its topography. (mountains,
valleys, etc.) the surface of the Earth is slightly irregular, but
for most practical purposes it can be considered a true oblate
spheroid. The distance from the center of the Earth to the
Equator is 6380 km.; to the Poles, 6359 km. The mean
radius of the Earth is about 6371 km.
Geographic Coordinates. English System.—For defining
locations, the Earth's surface is gridironed by a system of
Meridians of Longitude and Parallels of Latitude, the Longi-
tude and Latitude of a point being called its Geographic
Coordinates. Meridians of Longitude are imaginary lines on
the Earth's surface cut by planes passing through its axis.
In the English or sexagesimal system the initial Meridian or
0° Longitude passes through Greenwich Observatory, near
London, and Longitude is measured from 0° to 180° both East
and West according to the angle in the plane of the Equator
between any meridian and the Greenwich Meridian. (See
Fig. I.)
24 ORIENTATION FOR HEAVY (COAST) ARTIALERY
The true or Geocentric Latitude of any point is the angle
which a line from that point to the center of the Earth makes
with the plane of the Equator. If that line is revolved around
the axis of the Earth, maintaining a constant angle with the
plane of the Equator, its path on the surface of the Earth forms
(ºr©2/Vych) s
Q Q
6
C29 - eff WN
90% H ------->|<------- 90%.
<22e
(20 O
§ ~záža ‘à, f
Nº. 9
Pane of the Eguafor Aøne of any/ſer/a/a/7
“how/7/07/rude .5%an/g Zoffode.
Fig. I.-GEOGRAPHIC COORDINATES, ENGLISH SYSTEM
a Parallel of Latitude, which is parallel to the plane of the
Equator. In the English system, true Latitude is considered
and is measured from 0° at the Equator both North and South
to 90° at each Pole.
Each degree of Latitude and Longitude is divided into 60
minutes and each minute into 60 seconds. When finer measure-
ments are desired each second is divided into tenths and
hundredths. A nautical mile (Knot), 6080.7', is nearly equal
to one minute of Latitude, or to one minute of Longitude at the
Equator. As an illustration, the Geographic Coordinates of
Fort Monroe are 37°–0' N. Lat. and 76°-18' W. Long.
Because the Earth is not a true sphere, a line normal to its
Surface passes through its center only at the Equator and the
Poles. The angle which such a line makes with the plane of the
Equator is called the “Geodetic Latitude.” It is always
greater than true Latitude, the difference varying from 0 at the
Equator and Poles to 11’–30" at 45°. (See Fig. II.)
French System.—In France a slightly different system is
used. The initial Meridian of Longitude (08) is the one
through the Paris Observatory (2°–20–14" E), and Longitude
is measured according to the centesimal system (the Quadrant

CARTOC, RAPHY OF FIRENCH MAPS 25
(90°) being divided into 100 grades, each grade into 100 minutes
and each minute into 100 seconds), from 08 to 2008, positively
to the West, negatively to the East. Geodetic Latitude is
used, being measured from 0° at the Equator to 100* at each
Pole, positively to the North, negatively to the South. One
kilometer is nearly equal to one centesimal minute of Latitude
and to one minute of Longitude at the Equator. The exact
value of a grade of Latitude is found from the formula, 27th/400.
/VA’o/2
Geoce/77/7c
Alaſ/77 Caſe
A 2//a/or
2 Tſ
Gcoºrd
Alaſ/foae
/
- S.A’2/2
Fig. II.-GEODETIC AND GEOCENTRIC LATITUDES
R is the radius of the Earth in kilometers. The value of one
grade of Longitude at any Latitude is equal to its value at the
Equator times the cosine of the Latitude. (See Fig. III.)
w 27R
Expressed as a formula it is, † X cos Lat.
/*775 ///ºo/e
2: +/00%
VSS .
<2<> .9
'4%/2/or 07
—/007
MO
Aze of 470.7%r 5/ow/y/on?” A272 of a/k/a/27 Show/27/0/0.7%
Fig. III.-GEOGRAPHIC COORDINATES—FRENCH SYSTEM


• 6 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Classes of Map Projections.—When a map is to be made of a
portion of the Earth's surface, that curved surface (the Earth)
must be represented on a plane surface (the map). There are
many different methods of doing this, called “Map Projec-
tions,” each of which has its own particular value for certain
kinds of work. These can be divided into three general classes,
VIZ. .
I. Perspective Projections.
II. Geometric Projections.
III. Mathematical Projections.
Perspective Projections.—In a perspective projection, points
on the Earth's surface are projected on a plane by straight
lines radiating from one point, the point of vision. That
point may be infinity, at some stated distance outside the
Earth, on the Earth's surface, or at its center. One type, the
orthographic, with the point of vision at infinity, is simple to
construct and gives a good general idea of a large area, but is
very inaccurate. Maps of hemispheres are often made in this
way. The sketches of the Earth in Figs. VI and VII are ortho-
graphic projections. Another type, the stereographic, with
the point of vision on the Earth's surface diametrically opposite
the center of the area to be mapped, is accurate and conformal,
but difficult to construct. A third type, the gnomic, with the
point of vision at the Earth's center, represents all great
circles as straight lines, but distorts distances and areas; it is
much used for ocean charts.
Geometric Projections.—In a geometric projection, points
on the Earth's surface are projected on a plane, cone or
cylinder, either tangent to or cutting the Earth (secant)
according to some geometric law. These are simple to con-
struct and for small areas are nearly correct. They are often
used for maps of counties, states, and even countries. The
polyconic projection, used for most parts of the U. S., and the
polyhedral projection (described herein), used for many
French maps, are of this class.
Mathematical Projections.—In a mathematical projection
points on the Earth's surface are plotted according to some
mathematical equation, the projection being primarily based
on a tangent plane, cone or cylinder. The Bonne and Lambert
projections (described herein), used in France, and Mercator's
projection, used for many navigation charts, are of this class.
Choice of a System of Projection.—An area less than 10
miles square on the surface of the Earth is indistinguishable
CARTOGRAPHY OF FRENCH MAPS 27
from a plane tangent at the center of the area; therefore, such
an area can be considered as a plane surface; but for larger
areas this assumption cannot be made. At the Equator the
Meridians are parallel and a small area bounded by two
Meridians and two Parallels is a rectangle; while at the Poles
such an area is a triangle. Every system of Projection has an
origin. That origin may be a point, a Parallel or a Meridian.
At the origin the Projection will be true; leaving it, errors
creep in. In any system of projection, angles, distances or
areas, or all three, will be distorted away from the origin; only
one can be preserved. Some systems are more accurate than
others, but involve more labor and, consequently, more ex-
pense. Therefore, the choice of a system of projection depends
on the requirements of the map, and five factors must be con-
sidered: -
1. The size of the area to be mapped.
2. Its location on the Earth.
3. Its shape, i.e., whether its greatest dimension is an
E. and W. or N. and S. direction.
4. Whether angles, distances or areas should be preserved.
5. The accuracy desired.
Theory of Projections.—In any system of projection it is
sufficient to plot the Parallels and Meridians over the area
involved until a fine network is constructed outlining sub-areas
small enough to be considered as planes. With such a frame-
work established, intervening topographic detail may be drawn
as flat surfaces. Therefore, in describing any system of pro-
jection only Meridians and Parallels need be considered. Lines
tangent to Meridians and Parallels at the intersections are at
right angles to each other. If angles are to be preserved this
must also be true on the map, and further, any area on the map
must be similar to the corresponding area on the ground.
This is illustrated by Fig. IV: “A” represents a small
area on the Earth between two Meridians and two Parallels;
“B” represents the same area on a map, where angles between
Meridians and Parallels have been preserved but where Par-
allel distances have been distorted much more than Meridian
distances. It is evident that angles between the dotted line
and a Meridian in “B” are greater than those in “A”; thus
all angles except those between Parallels and Meridians them-
selves have been distorted. “C” represents the same area on
a map such that Meridians and Parallels intersect at right
angles and distances are distorted equally in all directions
28 ORIENTATION FOR HEAVY (COAST) ARTILLERY
*
N ſ
A// SJ;
A”
(£ºva/Area)
/D
N ſ
/// SS OC
An’ -
A Æ (527eº)
(Conſa/B (Lamberſ;JTC
A" réoreyer/5 a sma/ area Aeſheen 2 //e7775 & 2 Aara/e6 on
he ground.
A C/DA & / represe/ ſhe same area as Show, on various maps.
A= /)3/ance abng Abra/e/3 on ground A. Some Zöf on Mø.
//=/23//ze a 67.7//eſa/ans on 9/ot/d/M* same/Xsſ on M32
21-#-ZX%rſon / Aya/e6: Zſ-É? =/23/070, ſo Meridans.
Comparkson of /Mao's (A, C/24 & / ) w/ſh Grovna (4)
//e77 A. C A) Aſ
O/7 Correcſ
(2/2
_L/a/a/e/5 Correcſ Correcſ
24//5 f X/ 1 || 1% X/
of Z1 ſo A^ * A=A - > -
Aeſh, Aya &/Mer: Correcſ | Correcy
Ze. OC
Corzecif
Aa3/3 of Aºo/ec/fo/75 5/7//e 3 |Poſco/
Conſc Aro/
*/7"º"A" refers fo aſsiance L Aaraſſeſs -
> means "Greaſer//ia7+ K means "Zess fºam."— L means "Aerzena/colar fo"
Fig. IV.--THEORY OF MAP PROJECTIONS
(i.e., “C” is similar to “A”). Angles between the dotted
lines and Meridians in “A” and “C” are equal; thus all
angles have been preserved. If M and P are the Meridian and
Parallel distances, respectively, on the Earth, M’ and P' the
corresponding distances on the map, and A and A’ are the
distortions in Parallel and Meridian distances, respectively,
/ /
then: p = A and TVI ºf A' and comparing “A” and “C”:—
P/ M7
P = M or A = A'
Thus, if A = A' (i.e., if at any point the distortion is the same


CARTOGRAPHY OF FRENCH MAPs 29
in all directions) small areas on the map are similar to the
corresponding areas on the ground, and the map is “con-
formal.” This condition can be exactly realized only for
infinitely small areas, but because of the size of the Earth it
can be practically realized for areas up to 10 miles Square, and
the error is negligible for areas up to 100 miles square. That is
the theory on which Lambert Projection, used for the new
French Battle Maps, is based. -
Referring again to Fig. IV, “D’’ represents the same area
on a map such that Meridians and Parallels intersect at right
angles, but distances along them are distorted inversely;
i.e., one distance is increased in the same ratio that the other is
* P’ M 1
decreased. Then comparing “A” and “D,” F= M, or A= W
‘. AXA' = 1 and PXM = P'XM'. Thus, if AXA' = 1, areas
are preserved. This will be true even if Meridians and
Parallels on the map do not intersect at right angles, providing
that either the Parallels or the Meridians are parallel, and
A and A’ are the distortions along, and at right angles to, the
parallel sides of the trapezoid. (See “E” Fig. IV).
This is the theory of Bonne Projection, used for the pre-
war maps of France and Belgium and for many maps of
countries in general use, and of the “Cylindrical Equal Area”
projection, used for many maps of the World.
The above is a brief summary of the theory of Map Pro-
jection. We will now describe the three principal projections
used on French maps, viz., the Polyhedral, Bonne and Lam-
bert, discussing them in that order.
Polyhedral Projection.—As stated before, a small area on
the Earth's surface is nearly identical with the plane tangent
at its center. This fact is the basis of the Polyhedral Pro-
jection used by the French before the war for mapping areas
around fortified towns. Meridians of Longitude and Parallels
of Latitude divide the Earth into a series of curved isosceles
trapezoids, because the Parallels are parallel to each other, the
Meridian distance between two Parallels is the same at all
Longitudes and at a given Latitude the convergence of all
Meridians is the same. In the Polyhedral Projection each
such small curved isosceles trapezoid on the Earth's surface is
projected on to a plane tangent at its center. In effect this
consists of assuming that the Earth is a polyhedron, instead of
a spheroid (see Fig. V), and that its surface consists of a large
number of facets, like a diamond. If these facets are small,
30 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Tº -
Partial *Ea ulator \ W
Development |
The Earth Considered as a
Polyhedron.
*—S. Pole
Fig. V.-POLYHEDRAL PROJECTION
there is little distortion and a few adjacent maps can be used
together without great error. However, for large areas,
mapped as a whole or in Sections, the errors rapidly increase,
and a different system must be used. For accurate Battle
Maps of the large Zone of military operations in France a single
unified system of projection, involving only minor errors, is
necessary. In the U. S. most maps of cities and townships are
really Polyhedral Projections.
Bonne Projection.—A point at the center of the area to be
mapped is taken as an origin.
The slant height CD (see Fig. VI) of a cone tangent to the
Earth at that Parallel is computed. It is CD = DW cot Lat.,
where DW is the length of a line normal to the surface of the


32 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Earth at that Parallel, from the surface to the Earth's axis
(if the Earth were a sphere the line would pass through its
center; as it is spheroid, the line intersects the axis below the
center), and the Latitude is the Geodetic Latitude of the
initial point. (In France the initial point is at 08 Long, and
+50& Lat.)
A straight line C'D' is drawn on the map to represent the
initial Meridian. With C’ as a center and C/D' as a radius
an arc is struck through D'. This represents the initial
Parallel. On the initial Meridian distances are laid off equal
to the true Meridian lengths between Parallels on the Earth’s
surface (F'D', D'B', B'A', etc.) and through the points thus
located arcs of concentric circles with centers at C’ are drawn.
Those represent the successive Parallels of Latitude. On
each of these concentric arcs true distances between Meridians
on the Earth's surface at that Latitude are laid off, starting
from the initial Meridian. Through the points thus located
curves are drawn representing the Meridians. These converge
at a point P’ which represents the North Pole.
Thus distances are preserved intact along the initial
Meridian and along all Parallels; also angles along the initial
Meridian and initial Parallel, because along those two lines
Meridians intersect Parallels at right angles and the distortion
is the same in all directions (A = A' = 1). Further, areas are
preserved, because at all points the radial distance between
Parallels is correct. Therefore, AXA' = 1, and any area on
the map is equal to the corresponding area on the Earth.
For these reasons Bonne Projection is excellent for ordinary
civil maps, where areas are of first importance, and for any map
of a country having only a slight range in Longitude, such as
Great Britain, Belgium, Japan or the northern parts of the
present Western Front. The results obtained from the Poly-
conic Projection, used for most maps of the U. S., are similar
to those obtained from the Bonne Projection, but the methods
of construction are radically different.
One extreme of Bonne Projection is when a point on the
Equator is taken as the origin, the tangent cone then becoming
a cylinder tangent at the Equator, and the radius of the Par-
allels becoming infinity. All Parallels then appear as parallel
straight lines, their correct distances apart, the initial Meridian
as a straight line at right angles thereto, and other Meridians
as curves concave towards the initial Meridian, distances along
all Parallels being correct. This is called the “Sinusoidal
CARTOGRAPHY OF FRENCH MAPS 33
Projection” and is the basis of many maps of the Tropics in
general use. The opposite extreme is when the Pole is taken
as the origin, the tangent cone then becoming a plane tangent
at the Pole, the Projection resembling the general case (Bonne)
in appearance. This is one type of “Zenithal Equal Area
Projection” and is the basis of many maps of the Arctics in
general use.
However, away from the initial Meridian or Parallel in
the Bonne Projection, angles, and all distances except those
along Parallels, are distorted, the distortion increasing with
the distance from the initial Meridian. At the edges of the
map of France, made on this Projection, the angular errors are
18' and the linear errors 1/379. These distortions are not
negligible in artillery fire. Moreover, if these maps were
extended into Western Germany, these errors would increase.
Therefore, a large part of the Western Front has been re-
mapped since the war began, using the Lambert Projection,
which minimizes errors and permits accurate extension into
Germany.
Theory of Lambert Projection.—In this projection, as in the
Bonne, a point at the center of the area to be mapped is taken
as an origin, its Parallel and Meridian becoming the initial
Parallel and initial Meridian of the Projection, and a cone with
its vertex in the Earth's axis and tangent at the initial Parallel
is the basis of the Projection. In a way points on the Earth
are projected on a cone, but, according to a mathematical
law rather than a geometric law. Meridians appear on the
map as straight lines radiating from a common point (the vertex
of the cone) and Parallels appear as arcs of circles concentric
about the same point (imagine the cone to be “developed,”
i.e., unrolled).
Lambert Projection is conformal. As stated before, to
attain this result, the distortion at any point must be the same
in all directions. From this condition (that A = A') a formula
is mathematically derived for the spacing of the Parallels.
This formula is P= K (tan Z/2)h, where P is the radius of any
Parallel on the map, Kan arbitrary constant, Z the co-Latitude
90°–Lat.) and h is the sine of the initial Latitude.
Distances will be correct (1) along the initial Parallel,
(2) along two Parallels or (3) they will not be correct along any
Parallel, depending on the value given K. This can be vis-
ualized as follows: In the first case the cone is tangent at the
initial Parallel; in the second case the same cone has been
34 ORIENTATION FOR HEAVY (COAST) ARTILLERY
pushed down, parallel to its original position until it cuts the
Earth at two Parallels; and in the third case, it has been lifted
up, parallel to its first position, until it does not touch the
Earth at all. In the second case, if the value of K is so selected
that one of the two Parallels is 9% of the map's range in Latitude
below the Northern limit of the map, and the other 36 above the
Southern limit, the linear distortion at the center of the map will
equal that at the edges, distances at the center being less than
the corresponding distances on the Earth and distances at the
edges greater, the total linear distortion being minimized.
The angle between Meridians on the map depends on the
slope of the cone, or in other words, on the initial Parallel.
It can readily be shown that the ratio of the angle between
two Meridians on the map and their difference in Longitude is
the sine of the initial Latitude (see Fig. VIII). This is the
exponent “h” in the above formula. It can vary from zero
to unity. At one limit (h+0) the cone becomes a cylinder
tangent at the Equator and the Meridians and Parallels are
straight lines at right angles to each other. This is Mercator
Projection, one of the earliest devised and still invaluable for
navigation. At the other limit (h = 1) the cone becomes a
plane tangent at the Pole; the Meridians intersecting at angles
equal to their differences in Longitude and the Parallels being
complete concentric circles. This is one type of the Stereo-
graphic Projection mentioned above.
This formula, P= K (tan Z/2)*, can be converted into one
that will give the distance of any Parallel from the initial
Parallel, the new formula appearing as a series of terms, each
term smaller than the previous one, the accuracy of the result
depending on the number of terms considered. For the range
of Latitude to be covered by the French maps only two terms
3
need be considered and the formula used is, B-B+;
2
where B is the Meridian distance from the initial Parallel to
any other Parallel, B' the corresponding distance on the map,
and R the mean radius of the Earth at the initial Parallel.
French Maps on Lambert Projection.—For the new Battle
Maps the origin was taken at a point whose Latitude is +55°
and whose Longitude is —68. This is about midway North and
South of the present battle front and about midway East and
West between the present front and Central Germany. It is
near Treves, Germany, which is on the Moselle just across the
Luxemburg border. The value of h (h+sine of initial Latitude)
CARTOGRAPHY OF FFENCEI MAPS - 35
is the sine 55* = 76. It was desired to have the maps extend in
Latitude from +52 to +58 grades (+528 is in Central Switzer-
land, +588 is in Northern Holland), therefore, the value
036
chosen for the factor K was 2037, which preserves distances
along Parallels +538 and +57° one grade (1/6x64) above
and below the Southern and Northern limits of the map, re-
spectively. All distances used in constructing the framework
of the map are multiplied by this factor, which amounts to
1
diminishing them by 2037.
The slant height (CoDo) of a cone tangent at the initial
Parallel is computed in the same manner as in the Bonne
1
Projection. (See Fig. VII.) This diminished by 2037 gives
the slant height (CoDo) from the vertex to the initial Latitude
of a second cone, parallel to the first, but cutting the Earth at
the two selected Parallels. This is used as the radius of the
initial Parallel on the map. A straight line, CoL)'o, equal to
C'ol)'ois laid off on the map and with C'oas a center and Cºol)'o
as a radius, an arc is drawn, representing the initial Parallel.
Along this arc, distances between Meridians on the Earth's
1
surface at that Parallel, dimished by 2037, as explained above,
are laid off, and through the points thus established radii are
drawn representing the Meridians. Along the initial Meridian,
distances between Parallels are laid off. These are computed
3
B
by the formula B' = B+ dramentioned above, and are diminished
1 º
by the factor 2037. Through the points thus established arcs of
circles concentric at C/o are drawn, representing the Parallels.
Angles.—All straight lines on the surface of the Earth are
actually great circles (a great circle is the line made by the
intersection of the Earth's surface with any plane through
its center): all horizontal angles are measured between straight
lines or great circles. To preserve angles, therefore, all great
circles must appear in a projection as straight lines intersect-
ing at their true angles. This result cannot be obtained, but
in a conformal projection great circles appear as slight curves
that for distances up to 100 km. can be regarded as straight
lines with an angular error of less than a minute.
36
ORIENTATION FOR HEAVY (COAST) ARTILLERY
Fig. VII.-LAMBERT PROJECTION

CARTOGRAPHY OF FERENCH MAPS 37
Convergence of Meridians.—In the Lambert Projection the
angle between any Meridian and the initial Meridian (Con-
vergence of Meridians) is equal to the difference in Longitude
times the sine of the initial Latitude and can be found by the
formula (M–Mo) XsinLo, where M is the Meridian in ques-
tion, Mo the initial Meridian (–68) and Lo the initial Lati-
tude (+558). (See Fig. VIII.) Substituting constant values
the formula becomes (M-H-68)X.76.
Proof of Formula.
ZACD = ZACB = Lo Z BAD = M — Mo
Z BCD = cy AD = CDXSin Lo
BD = ADX (M–Mo) (Circular Measure)
= CDXSin Lox (M–Mo) (Circular Measure)
BD = CDX.o. (Circular Measure)
BD = CDX aſ a CDX (M–Mo) × Sin Lo
o, = (M-Mo) XSin Lo– Convergence of Meridians
iCº
Fig. VIII.-CONVERGENCE OF MERIDIANS

38 ORIENTATION FOR HEAVY (COAST) ARTILLERY
In the Bonne Projection the convergence of Meridians
means the angle between the initial Meridian and a line
tangent to the Meridian at the point in question. It is equal
to the difference in Longitude times the sine of the Latitude of
the point in question and can be expressed as (M–Mo) Xsin L.
On Bonne Maps of France the initial Meridian is that of
Paris (0%) and the formula becomes M sin L, where M is the
Longitude and L the Latitude of the point in question. (See
Fig. VI.)
Results.-On Parallels +538 and +578 distances are correct;
between them distances on the map are less than the corre-
sponding distances on the Earth; and beyond them, greater,
1 .
the maximum linear distortion being 2037. Thus for a belt 65
of Latitude in width (600 km.) the linear distortions are
negligible (less than 0.05 per cent.); as the map is conformal,
angular errors are inappreciable; areas are nearly correct; all
the requirements for accuracy in artillery fire are met; and an
excellent map is produced. -
This projection can be extended indefinitely East and
West without increasing the distortion, but if extended North
or South, the errors in both distances and angles will be in-
creased.
The initial mathematics of a Lambert Projection (most of
which has been omitted herein) is very complicated, which is
probably the reason why it has been little used. The U. S.
Coast and Geodetic Survey is now preparing a map on the
Lambert Projection, extending from Duluth to Bagdad, and
from Greenland to the West Indies. The whole Western
Front is being mapped on the Lambert Projection as rapidly
as possible. - -
2. COORDINATES AND QUADRILLAGE
Rectangular Coordinates.—As stated before, Geographic
Coordinates determine the location of points on the Earth's
surface. From the Latitude and Longitude of two points
(such as a battery and its target) the length and direction of a
line joining them can be computed, but the computation is long
and difficult. In a system of rectangular coordinates, however,
CARTOGRAPHY OF FRENCH MAPS 39
if the abscissae (x) and ordinates (y) of two points are known,
the determination of the length and direction of the line joining
them requires only the solution of a right triangle. Therefore
a system of rectangular coordinates has been placed on the
Battle Maps.
Coordinates.—The position of a point on a plane can be
determined if the distances of the point from two intersecting
reference lines are known. For simplicity the reference lines
are drawn intersecting at right angles, the point of intersection
being called the origin. The vertical reference line is known
as the Y axis and the horizontal line as the X axis. The
distances of a point from the two reference lines are known as
the coordinates of the point. The X coordinate is always
measured parallel to the X axis and the Y coordinate parallel
to the Y axis.
X coordinates are positive if measured to the right of the
origin and negative if to the left. Y coordinates are positive
if measured upwards above the X axis and negative if below
the X axis. &
The coordinates of A in Fig. IX are x and y, and the coor-
dinates of B are x' and y'. If the coordinates of A had been
given, the point could be plotted by measuring off a distance
on the X axis from the origin equal to x, and at the point m
erecting a perpendicular equal to y. The extremity of the
perpendicular will be the point A.
Example: Plot the point C, x coordinate = —8, y coordinate
= —5. Since the x is minus it will be measured to the left and
k will be located 8 units from the origin. Measure down
on a perpendicular from k 5 units, since the y coordinate
is —5, and C will be located at the extremity of this perpen-
dicular.
D is plotted with coordinates, x = —4 and y = +6; the coor-
dinates of E are x = +2 and y = —8. If a coordinate is written
without a sign it is understood to be plus. Points may also be
plotted by measuring off the x coordinate on the X-axis and
erecting a perpendicular at that point, and measuring off the
y coordinate in the same manner and erecting a perpendicular;
the intersection of the two perpendiculars will locate the point.
Example: Plot the point D (x=A-4, y=6). Erect the
perpendicular vL) 4 units to the left of the origin and the
perpendicular wſ) 6 units above the origin. The perpen-
diculars intersect at D, the point desired.
Plotting a point when its distance and direction from given
40 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Y
| •ºm sº ºme sºme sºme
42----|-l.
ſ j"
| |Sºf
| & ºt
| ||
| *- Hà* * *- * * *-* = <= <= *- a-mº sºm, sºme sm as sºme a-
& | ſ ſ f | . X
| { V/ W t 'O *—º
| ––
| l
|
| º
|
! º
C* * *E= * * * * * * *= ºms —H/,
I_
Fig. IX.-RECTANGULAR COORDINATES
point are known. Let A (x, y) be a given point and the length
of the line AB and the angle 6 be given. Find the coordinates
(x', y') of B. (See Fig. IX.) Bs and gn are perpendicular to
the Y-axis and Br and fm are perpendicular to the X-axis.
The angle 6 equals angle 6'.
dx=Ag= AB sin 6
x = x +dx=x-HAB sin 9
dy = Af- AB cos 6
y' =y+ns =y+AB cos 6
If the coordinates of two points are known the length and
direction of line connecting them can be determined. Let
points A (x, y) and B (x', y') be given, find the length and
direction of AB.
Bf
tan 0=Af
Bf = rm =x' —x
Af-ns =y'—y

CARTOGRAPHY OF FRENCH MAPS - 41
x' —x
therefore tan 6 = y’—
From this formula 9 can be determined by looking up the
/
angle whose tangent is y’ —y in a trigonometric table of
natural functions.
The length of AB can be determined by the formulas:
(1) AB = −. (Since ABcos 0-Af-y—y)
COS 6
(2) AB = } — X (Since ABsin 6 = Bf = x'—x)
Sln 6
(3) AB = V(x' –x)2+(y’—y)?
Since AB is the hypothenuse of the right triangle ABf, AB =
V(Bf)2+(Af)2, Bf-x'-x and Af-y’—y; therefore
AB = V(x’—x)2+(y’—y)2.
Kilometric Grid. Lambert Maps.-In order to locate points
readily a system of rectangular coordinates has been placed on
Battle Maps now in use on the Western Front. On the
Lambert Maps the y-axis is the initial Meridian (–68), and
the x-axis is a straight line perpendicular thereto at its inter-
section with the initial Parallel (+55)*. (See Fig. X.) Thus
the origin of the Projection is also the origin of the Quadrillage
or Grid System, which simplifies the transformation of rec-
tangular into Geographic Coordinates and vice versa. To
avoid the use of negative coordinates the origin has been given
certain arbitrary coordinates, viz.: x = 500,000 meters and
y = 300,000 meters. If a and b are the distances of any point
from the x and y axis respectively, its coordinates are x = 500,-
000 = a and y = 300,000 = b. Lines 1000 meters (1 km.)
apart are ruled on the maps parallel to both axes. These form
a “Rilometric Grid,” from which the coordinates of any point
can readily be scaled on the maps, and vice versa, any point
whose coordinates are known can be located on the maps.
The coordinates of datum points (bench marks, towers,
church spires, etc.) are found by triangulation to the nearest
meter. Usually many of these datum points are indicated on
each map, from which any other point can be accurately
located. In some cases it is sufficiently accurate to locate
places (towns) to the nearest kilometer; and in other cases it
is sufficient to locate them to the nearest hectometer (100
meters). The large scale maps in common use do not extend
over greater distances than 10 km. and the first two digits of
42 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Aong/foae
-2 3 -4 , -5 -6? -7 , a -3, 70
!---L--- ; , | | | | | |_2:
TT-4---H----|--|. ---J.------------f-269
i ; | ; - .# TT l º
ſ º | I - ſ ; : ſº }
| | | ! $ ;
; } | ; | ! }| ;
TT1*------|-i- !-----L------4-57
500–1–Hºtte-H==#===4======4={------|--~~~~1
; | ; | ! ! }}-T
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§ --- | ! ; ! : } .
§ 400++=#===#=======H---|--|-}===#====#29
Š J .# ! ; $ P : ſº
S } r 0. | ſ B º
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§ | ‘A | | ! . . ! | : Q)
§ 300+++----|--|3——|-|--|--|--|33 &
- { - | - *
§ | | | | | | | | | | | | | S
S * º | i yº ; : N.
Nº. ſ | ſ | |} § { 3.
YS ! } f ! ſº ! * II. º j
§ 200++---4----4-------------------|--|-54
& ; | | | | | t
> | | [ f ; ; º
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| & - ; | : | l, i
| ſº ! § | {} 0. $
/06-#: - - t =; * * * I * --> h | --53
; ; ; {T} } }
$ | 1. , ſº r | :
ſ $ ! ſ: | | ! | :
; ; ; ; ; ; ; ; ; ; )
* malf ºf . *- . #- ======== ===== == p-# —— ==5&
A/lſ) 500 400 500 600 YQ0

A Codra/zoſºs in AZamefres
Fig. X.-KILOMETRIC GRID FOR THE LAMBERT PROJECTION MAPS
the hectometric coordinates can often be dropped when refer-
ring to only one map. These various ways of expressing
coordinates can best be illustrated by an example. Take point
& 4 A” in Fig. X; - -
Metric Kilometric Hectometric Hect. abbreviated
x=234,117 234 2341 41
y =301,047 301 3010 10
The abbreviated Hectometric coordinates are usually
written together, the first two digits being the x value and the
last two the y value; i.e., in the above example, 4110.
Lambert North (Grid North).-By Lambert North is meant
the direction of a line parallel to the y-axis at any point. Thus,
Lambert North is always parallel to the initial Meridian. The
divergence of Lambert North from True North at any point is
equal to the convergence of Meridians at that point and can
be computed from the formula (M+68)X.76, mentioned
above. At the initial Meridian (–64) Lambert North coin-
CARTOGRAPHY OF FEENCH MAPS 43
cides with True North. West of the initial Meridian, Lam-
bert North is West of True North. And East of the initial
Meridian Lambert North is East of True North. On the
Western Front the declination of the compass varies from
about 8& West to about 15& West, which is greater than the
divergence of Lambert North from True North. Therefore,
Magnetic North is always West of both True North and
Lambert North.
The angle between Lambert North and any line is called the
“Y-azimuth” of that line, and can readily be calculated from
the coordinates of any two points on that line. The French
measure it from Lambert North either clockwise or counter-
clockwise, according to the instruments at hand. Americans
will measure it from Lambert North clockwise only. Simi-
larly, the azimuth of any line, as used in France, means the -
angle between True North and that line (measured clockwise
by the American forces). -
Knowing the convergence of Meridians and the declination
of the compass at any point, Y-azimuth can easily be calcu-
lated from azimuth or magnetic bearings, and vice versa.
Kilometric Grid on Bonne Maps of France.—This is similar
to the grid on the Lambert maps, the origin of the grid being
the origin of the projection (Long. 0s., Lat. --508) and the
y-axis being the initial Meridian (08). In districts where both
Bonne and Lambert maps are in use (i.e., at the edges of the
area covered by the Lambert maps), the same point will have
two different sets of coordinates, one set in each system, and
confusion is apt to result unless great care is taken. Occa-
sionally both grids are put on the same map.
Use of Coordinates.—The locations of all points used by the
artillery, gun emplacements, targets, aiming points, etc., are
determined by their rectangular coordinates, from which the
range and Y-azimuth of a target and the corresponding deflec-
tion angles can be computed. As soon as a battery position
or observing station has been selected its coordinates should
be determined. The various methods used for this work are
taken up in later chapters.
In general only two problems arise for an artillery officer to
Solve in using these coordinates, both of which require only the
solution of a simple right triangle, viz.: First, from the
coordinates of two points to find the length and direction of
the line joining them; and second, vice versa, from the coor-
dinates of one point and the length and direction of a line
44 ORIENTATION FOR HEAVY (COAST) ARTILLERY

72/k/e7° AX
--ºf---|--|-- - * *m, sºme sº- - | -----|--- 220
N - |
\ |
\\ /Vo/-//7 |
\
N TK. N- I
\ § SA § |
\ TS S. § |
\ S. Q § |
N. QN S. |
\\ \ \ i 2/8
\ N. |
\ |
\\ |
N
N |
N |
\ AY
\ | 2/6
\ I
\ |
\ |
\
N |
\ |
\ | -
N |
\ |
N
N 2/4
N N i
N |
N V -
Coo/a/ia7/es |X y ºf N
&/reſy d/6650 2/2,600 N};
7&ryer 6//500 220,750 S
A 5550 7.550 N z 2/2
- NGVL’
Š § § §
Fig. XI.-COMPUTATION OF RANGE AND Y-AZIMUTH
joining it to an unknown point, to determine the coordinates
of the unknown point.
As stated before, the direction may be expressed in magnetic
bearing, azimuth or Y-azimuth, which are interdependent at
any one point, and it is essential that the relations between the
three be clearly understood in order to change one into the
other rapidly. (See chapter on “Angular Measurement.”)
The two cases will be illustrated by examples.
CARTOGRAPHY OF FERENCH MAPS
280
r— — — — — — — — — — — — — — — — — — —H - - -7arget
|
!
|
|
|
279 |
|
|
|
|
!
|
|
|
276 :
|
|
|
|
|
|
274
|
|--|<
. *
/ Aoffery
| - 85/650
7//€2/. 2
272 ºrrey :
{\! N. WO
§ & §
Fig. XII.-COMPUTATION OF COORDINATES OF TARGET

46 ORIENTATION FOR HEAVY (COAST) ARTILLERY
First Ezample. (See Fig. XI.)
Given:- x – Coordinate — y
Battery 616,650 212,600
Target 611,300 220,150
- Difference 5,350 7,550
Required—Range and Y-azimuth of Target.
5350 Solution
35 - 7550
Tan v = 7550 Range = cos v.
Log 5350=3.728354 Log 7550 =3.877947
Log 7550=3.877947 Log cos w =9.911644
Log tan v =9.850407 Log Range =3.966303
V = 35° 19' 20" Range =9254 m.
Y-azimuth (v)=360°-v-360°–(35°19' 20")=324° 40'40".
#5-? = —” + → = -FEB-1 + -===*
Check:-Range AX Ay 5350 7550
Range = V28,622,500+57,002,500 =9254 m.
Second Example. (See Fig. XII.)
Given: Battery, x=851,650 y =272,350
Range =8682 m.
Compass Bearing N 55.560 E
Compass Declination = 222 Mils West
Longitude = –138.
Required: Coordinates and Y-azimuth of Target.
- 222 Solution
Declination=222 mils *T6 grades = 13.g.87 West,
Convergence of Meridians = (M + § X.76
= (–135-H68)X.76 = 5.532
Angle between magnetic and Lambert North = 19.4:19
The point is east of Origin. Therefore, Lambert North is east of True North.
The compass declination is west. Therefore, Magnetic North is west of True
North. Magnetic North is also west of Lambert North: Therefore;
Y-azimuth (V) =558.60–198.19 =368,41 = 32°46'8"
Ax = Range Xsin W Ay = Range Xcos V
Log Range =3.938620 Log Range =3.938620
Log sin W =9.733399–10 Log cos W =9.924724–10
Log Ax =3.672019 Log Ay =3.863344
Ax = 4699.15 Ay =7300.35
X y
Battery 851,650 272,350
4,699 7,300
Target 856,349 279,650
v/Fº -
Check: Range= Y4695+7306
= V/22,080,601 + 53,290,000
=8682 meters.
3. GEODETIC TRIANGULATION
Geodetic Framework.-The system of projection having been
determined upon and the Parallels and Meridians and Quad-
rillage having been laid out, the next step in the construction
of a map is to plot on this grid what is known as a Geodetic
Framework.
CARTOGRAPHY OF FRENCH MAPS 47
All maps of large areas are based on Some system of triangu-
lation. Starting from one or more accurately measured base
lines according to the size of the area, a network of triangles
is laid out, whose sides vary from 10 to 200 kilometers in
length. There are three different types of triangulation nets
that are in standard use. (See Fig. XIII), viz.:
(A) A series of approximately equilateral triangles. This
is used when the survey is to extend over a long, narrow strip.
(B) A series of central polygons, each with an interior
station near its center. This is used for areas that are nearly
Square. -
(C) A series of quadrilaterals with both diagonals drawn
in. This is used for wide areas and is the best system because
it offers the greatest number of checks. -
Triangulation Points.--Whatever system is adopted, a
system of primary triangles is laid out so as to cover the entire
area to be mapped. These are generally large, with sides from
15 to 200 kilometers in length. The angles at each vertex are
measured with extreme accuracy—to decimals of a second—
with accurate, large size transits, and the length of each side
is calculated. Due to the curvature of the Earth such triangles
usually have to be reduced to the equivalent plane triangles.
Standard . Prºnoru
Triangulation tiets.
A €roup of Gºodrilaterals
"Central Stations. with Diogonals.
Fig. XIII,_TRIANGULATION NETs


48 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Each such vertex is called a “Primary Triangulation Point”
and in France is located to within 0.3 meter. Its Geographic
coordinates are found by astronomical observations.
Based on these primary triangles a secondary system of
smaller triangles is laid out (sides from 10 to 50 km. long)
whose vertices are located by computations based on measure-
ments of the angles and the computed lengths of sides in the
primary triangles, with consequently less accuracy, but with
a probable error of less than 0.5 meter. These are called
“Secondary Triangulation Points.”
On this secondary network of triangles is based a third
system, the tertiary, whose sides vary from 5 to 30 kilometers
in length and which are small enough to form a control for the
Scolle in Kilometres
C ) O 2C 5 o 4. O SO
i:ſ
Primary Net.
—- — Secondloru Net.
... • * * * * * * Tertioru Net.
Fig. XIV.-TYPICAL TRIANGULATION SYSTEM
whole area. The vertices of the tertiary net are called “Ter-
tiary Triangulation Points” and are located with a probable
error of less than 1 meter. Fig. XIV shows a typical complete
triangulation system. -
Primary and Secondary Triangulation Points are usually
marked with stone monuments on which the instruments can
be set up and over which a flag signal can be placed. Some-

CARTOGRAPHY OF FFENCH MAPS 49
times it is necessary to construct small towers over these points
to secure the required range of vision, and for the longer sights
heliographs replace flag signals. Sometimes tertiary points are
also marked by monuments but more often they are distinct
features of the landscape, such as church spires, chimneys,
towers, and isolated trees. Frequently an instrument cannot
be set up at such points and an “eccentric” point must be used
for the transit. This does not affect the use of these points in
resection, however. .
Local Detail.—The metric coordinates in the Lambert
System of all of these points are computed and used in plotting
them on the maps. These coordinates are given in full in the
lists of triangulation points that accompany each map. Trav-
erses are usually run between tertiary points to locate roads,
railroads, streams and benchmarks, while contours, buildings,
cultivation and other detailed information is usually secured by
plane table. As a result, the errors in the location of local
detail may run as high as 10 meters, although, because of the
scale of the map, such errors are negligible. For purposes of
orientation in the field preference should be given first, to
primary triangulation points; second, to secondary points;
third, to tertiary points, and fourth, to local detail. Tertiary
triangulation points are usually close together and there are
several accessible or visible from nearly all points on the front.
Local detail is often a valuable aid in rapidly finding a location
on the map.
4. BATTLE MAPs
Pre-war Maps.—At the beginning of the war the extensive
use of large scale maps was not contemplated. There were
several small scale maps of France, Belgium, and Western
Germany, which were expected to be used by the French,
British and Belgian armies as Staff maps in the direction of
mobile operations.
French General Staff Map.–Most important of these was
the 1:80,000 French General Staff Map, which covered the
whole of France and Alsace-Lorraine, though it had not been
kept up to date in the latter provinces. It is based on the
Bonne Projection with origin at +50s and the Paris Meridian.
It was started early in the last century and required some 60
years for completion. Each sheet is 50 cm. X80 cm. in size,
covering 40 km. X64 km. Geodetic points are fairly accurately
50 ORIENTATION FOR HEAVY (COAST) ARTILLERY
located, but the error in other points may reach 100 meters.
Elevations are shown by contours and hachures. This map
is the basis of most of the pre-war maps of France, e.g., the
1:50,000 black and white and the 1:200,000 colored maps.
Maps of Fortified Towns.—Another important series of
French maps was the Battle Maps of the regions immediately
about the French fortified towns. These are on scales of
1:10,000 and 1:20,000 and are fairly accurate. The Poly-
hedral Projection is used. Contours show elevations.
Maps of Belgium.—The basis of the pre-war military maps
of Belgium was a set of 1:20,000 maps compiled from land-title
(cadastral) plans, and verified and completed on the ground.
Bonne Projection was used, the origin being +56° and the
Brussels Meridian. Elevations are indicated by contours.
From these were made up maps on the scales of 1:40,000 and
1:100,000. All these maps are only fairly accurate.
Maps of Germany.—Most of Germany, including Alsace-
Lorraine and the Rhine Provinces, was covered by a map on
the scale of 1:100,000, made up from plane-table sheets of
1:25,000. The Polyhedral Projection is used. Relief is
shown by contours and hachures. These maps are fairly
accurate.
Development of Battle Maps.--When the war assumed a
more or less stationary character, it was found that accurate,
large-scale maps were absolutely indispensable for the use of
both infantry and artillery. Accordingly, as rapidly as possible
there were prepared Battle Maps (French, “Plans Directeurs”)
of the whole Western Front. The scales chosen by the French
were 1:20,000, 1:10,000, and 1:5,000; by the English,
1:40,000, 1:20,000, and 1:10,000. These maps were based
primarily on the small scale pre-war maps, but in order to get
sufficient local detail and to increase the accuracy, every
available source of material was used—maps and plans of
roads, railroads, canals, private estates, tax assessors’ land-
title maps (cadastral plans) of communes, etc. In addition,
surveying parties were immediately put into the field, and
countless aerial photographs were taken of the region near the
front lines. -
Revision of Battle Maps.-No sooner were the Battle Maps
prepared than some change in the battle lines or in the detail
of the terrain, due to artillery fire or mining operations, ren-
dered them out of date. The accuracy of points and the
number of trigonometrically located points must also be
CAERTOGRAPHY OF FERENCH MAPS 51
constantly increased. This necessitates continual topographic
work in the region of the front lines. So important and exten-
sive has this work become that special units, called “Topo-
graphical Sections,” have been organized in connection with
each army and corps, whose chief duty is the preparation,
revision, distribution and destruction of Battle Maps.
Description of French Battle Maps.-The French Battle
Maps are based upon the Lambert Projection, with origin near
Treves, and have a kilometric Grid System, or Quadrillage,
with the same origin, as described above. Relief is shown by
contours with a Vertical Interval of (usually) 5 meters. Each
map is dated to show the time to which it has been revised.
For a description of the conventional signs, see Chapter I.
In general, points of planimetric detail are accurate within
10 meters, though in regions taken directly from the General
Staff Map, or in case of blunder, errors may be as large a
100 meters. Often there is a marginal plan on a map showing
the sources of its various parts, as an aid in determining the
accuracy of points within them.
Areas, Detail and Typical Uses.—Most of the French
Battle Maps on all three scales are issued on sheets of the same
size—50 cm. by 80 cm. Therefore, the dimensions of the area
covered vary inversely with the scale. -
The detail shown also varies with the scale. The 1:20,000
maps usually cover an area 10 km. by 16 km., and show the
German works, but none of the French, except sometimes the
outline of the advanced line of trenches. The 1:10,000 cover
5 km. by 8 km. and show German works and the outline of the
advanced line of French trenches. The 1:5,000 cover 2.5 km.
by 4 km. and show German works and the first line French
trenches. Oceasionally special maps are made up of different
size and showing different detail.
While there are many uses for each scale of Battle Map, it
may be stated in general that the typical use of the 1:5,000 is
for infantry attack, of the 1:10,000 for the light artillery, and
of the 1:20,000 for heavy artillery.
Lists of Points of the General Control.—Of equal importance
with Battle Maps to heavy artillery officers are lists, also issued
by the Topographical Sections, of the trigonometrically located
points within each area. These lists, which are being con-
tinually enlarged, give the metric rectangular coordinates and
the altitude of all points whose locations have been determined
with an accuracy comparable to that of geodetic triangulation
52 ORIENTATION FOR HEAVY (COAST) ARTILLERY
points. Such points will usually appear on the latest Battle
Maps, but their exact coordinates and elevations can be
obtained only from these lists.
As will appear later, accurate data concerning trigonometric
points is absolutely essential to the correct determination of
positions and altitudes and to the determination of direction
by the method known as “Terrestrial Y-azimuth,” or “Wo.”
(See Chapter VIII.) As these are the two most important
topographical problems confronting a battery officer, the value
of these lists can be readily seen. Other uses of them are the
following: -
1. To increase the density of points of reference in the
regions occupied by our batteries; as the original points of
reference shown on the maps (steeples, windmills, isolated
houses) are generally destroyed. Even the planimetric details
of the map are not always sufficiently close together to serve
as a basis for surveys which must be both simple and rapid.
Furthermore, in the region of the first positions these plani-
metric details may have disappeared more or less completely.
2. To serve as a basis in preparing an accurate system of
reference points in the region of the enemy’s first line for use
in firing on auxiliary targets, etc., and also to facilitate the
organization of the fire of our artillery after its first rush
forward following an attack—an extremely important matter.
3. To permit the checking of the map in certain parts
where it might be in error because of changes that have occurred
since the latest revision (outlines of woods, roads, etc.).
Lists of Y-azimuths.—The Topographical Sections can also
furnish lists of observed Y-azimuths and oriented “tours d’hor-
izon,” which are used to orient the plane table of a traverse.
British Maps.-In the maps of Northern France and Bel-
gium used by the British those on a scale of 1:40,000 are the
basis of a Grid System in yards. These maps are issued on
sheets of the same size (50 cm. by 80 cm.) as the French Battle
Maps and therefore cover an area 32 km. (east and west) by
20 km. (north and south). Each sheet is designated by a
number. The metric coordination of each of the four corners
are given on the map. Thus, “57,240 m.n.” means “57,240
meters north of origin.” The divergence of Lambert North
from True North and the compass declination at the center
of the map are also give on each sheet. (See Fig. XV.)
These 1:40,000 maps are divided into quarters called N.E.,
N.W., S.W. and S.E., which are mapped separately on the
CARTOGRAPHY OF FRENCH MAPS 53
57240/M/V,
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57240/M/V
Fig. XV.-BRITISH BATTLE MAPS WITH ORIGIN AT BRUSSELS
scale of 1:20,000. Each of these in turn is divided into quar-
ters, numbered 1, 2, 3 and 4, each of which is mapped sepa-
rately on a scale of 1:10,000. Thus, all these sets of maps are
the same size. In a way this system resembles the method
of subdividing sections of land in the United States.
British Grid in Yards.--To facilitate the determination of
range in yards, the British superimposed a “Yard Grid” on
their maps. It consists primarily of a system of rectangles
6000 yards square, centered on the center lines of the 1:40,000
maps (see Fig. XVI), on which there are 24 such rectangles,
lettered from A to X. As the dimensions of the map in meters
do not coincide with any even distances in yards, there is a
slight overlap. On the East and West edges the overlap is
negligible (6/.5), but the East and West tiers of rectangles are
not full width, being only 5500 yards wide. On the North and
South edges the overlap is greater (192'.4) and the upper and
lower rows of rectangles are only 5000 yards long. Thus, only
the 8 center rectangles (H, I, J, K, N, O, P and Q) are full size.
Each of these large lettered rectangles is divided into 1000
yard squares, numbered from 1 to 36, as indicated in Fig. XVI.
The upper and lower rows of lettered rectangles have only
30 such squares, and the East and West tiers of small squares
are only 500 yards wide.
Each 1000 yard square is divided into quarters, each 500

54 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Órla System —-—/% O//ne -------00/mes of 34*//yos
Zoºgeſ/effered/Tecſon%25 øre 6000% $70,72
S/772//(W//776e/ed') Af * /OOO / A
Fig. XVI.-BRITISH GRID on A 1:40,000 MAP
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Fig. XVII.-BRITISH GRID on A 1: 20,000 MAP–No. 28 N.E.



CARTOGRAPHY OF FRENCH MAPS 55
yards square, and numbered a, b, c and d (see Fig. XVII). If
closer locations are desired the S.W. corner of a 500 yard
Square is taken as an origin and coordinates are expressed in
tenths or hundredths of the sides of the square, the x value
being given first. Points are thus located to within 5 yards.
If a point was designated as being at “28 K 17 b .4.2” it
would be found on map No. 28, rectangle K, square 17, small
(500 yard) square b, 200 yards East of the West edge and 100
yards North of the South edge of that small square.
Maps on 1:20,000 and 1:10,000 scales have the same grid
as the main maps. Thus, map No. 28 N.E. contains rec-
tangles D, E, F, J, K and L, and Map No. 28 N.E. 3 contains
most of the rectangle J and the West half of rectangle K.
CHAPTER III
ANGULAR MEASUREMENTS
UNITS OF ANGULAR MEASURE
DIRECTION OF LINES
INSTRUMENTS FOR MEASURING ANGLES
VERNIERs
MEASURING ANGLES BY REPETITION
:
1. UNITS OF ANGULAR MEASURE
There are three distinct systems of angular measurement
now in common use and a thorough knowledge of each system
and the methods of readily converting measurements made in
One system of units to their equivalents in other systems is
necessary.
Degrees (English System).-If a circumference is divided
into 360 parts each part will subtend an angle of one degree at
the center.
Table of English Units
60 Seconds (60") = 1 minute.
60 Minutes (60’) = 1 degree.
360 Degrees (360°) = 1 circumference.
Grades (French or Centesimal System).-The grade is an
angle subtended at the center by an arc of one four hundredth
part of the circumference.
Table of French Units.
100 Centesimal Seconds (100") = 1 cent. minute.
10 Centesimal Minutes (10’) = 1 decigrade.
10 decigrades = 1 grade.
10 grades (108) = 1 dekagrade.
400 grades (4008) = 1 circumference.
Mils. (1600 or Artillery System).-If a circumference is
divided into 6400 parts each part will subtend an angle of 1 mil
at the center. At a distance of 1000 meters 1 mil will subtend
one meter approximately. This fact makes the mil system
excellently adapted for the measurement of angles in con-
nection with artillery fire.
ANGULAR MEASUREMENTS 57
Table of Mils
1600 Mils= Quadrant.
6400 Mils = Circumference.
To convert readily units of one sytem to those of another
the relations given in the following table should be committed
to memory:
Table of Equivalents
1 degree = 1.11111 or 10/9 grades (log. 1.11111 =.04575)
= 17.77778 mils (log 17.77778 = 1.24988)
1. grade = .9 degree (log .9 =9.95424 – 10)
= 16. mils (log 16. = 1.20412)
1 mil = .05625 degree (log .05625 = 8.75012 — 10)
= .0625 grade (log .0625 = 8.79588 – 10)
2. DIRECTION OF LINES
The direction of a line is the horizontal angle made by the
given line with a reference line whose direction is known.
The reference line is determined by considerations of con-
venience. It is usually either, the Magnetic Meridian, the
True Meridian, or Lambert North. The direction of a line
is referred to by a name depending on the reference line selected,
as given in the following definitions:
Azimuth of a line is the angle which that line makes with a
true North and South Meridian as a reference line. In the
Coast Artillery, azimuth is measured clockwise from the
South. In the heavy artillery, azimuth is seldom used, but
when used it will always be measured from the North, generally
in a clockwise direction. Azimuth may be measured in either
direction from the North as, for example, in astronomical
observations.
Bearing.—If a North and South line passes through one
end of a given line two supplementary angles are formed; the
smaller of these two angles is the bearing of the given line.
Bearings are always measured from the North point or South
point so many degrees East or West, and written in the fol-
lowing form: N 27° E, or S 72° W. By definition a bearing
can never exceed 90°. True bearings are measured from a
Meridian or true North and South line. Magnetic bearings
are measured from the magnetic North and South line as
determined by the compass needle.
Y-azimuth of a line is the angle which that line makes with
Lambert North as a reference line. Y-azimuth is usually mea-
58 ORIENTATION FOR HEAVY (COAST) ARTILLERY
sured clockwise from the Lambert North, although sometimes
counter-clockwise, depending on the material being used.
That is, if the angle measuring instrument is graduated clock-
wise the Y-azimuths will be measured clockwise, and if the
graduations are counter-clockwise the Y-azimuths will be
measured counter-clockwise. In our service Y-azimuth is
almost invariably measured clockwise.
3. INSTRUMENTS FOR MEASURING ANGLES
In the heavy artillery there are several instruments in gen-
eral use for the measurement of angles. Some of the principal
ones are: the compass; the transit or, as the French call it, the
theodolite; the plane table; the Battery Commander's tele-
scope; the panoramic sight; and the goniometer (French coun-
terpart of our panoramic sight). All of these instruments will
measure horizontal angles with various degrees of precision.
For measuring vertical angles the transit, B. C. telescope, the
telescopic alidade on a plane table, and the Sextant are used.
The compass and the transit are the instruments most
frequently used. The others are generally used as substitutes,
when a compass or especially a transit is not available. Only
the compass and the transit will be discussed in this chapter.
The Magnetic Compass.—The compass is the standard
instrument for the determination of the direction of lines in
topographical reconnaissances. It consists of case, needle,
dial, pivot and stop. The dial may be fixed to the case or it
may be movable, that is, moving with the needle to which it
is attached. The stop raises the needle from the pivot and
clamps it against the glass cover. A good compass must have
a needle sufficiently magnetized to settle accurately and a
pivot which is true.
A needle loses part of its magnetism if kept for a long time
out of the plane of the magnetic meridian. In storing a
compass, therefore, care should be taken to see that the needle
is in the magnetic meridian with the N. end of the needle
pointing North.
. A symmetrical needle tends to point downward toward the
nearer magnetic pole of the earth. This displacement from
the horizontal is called dip. For reading azimuths the needle
must be kept in a horizontal plane, which is done by a small
movable counterweight made sufficiently heavy to overcome
the dip. For considerable changes in Latitude as in passing
ANGULAR MEASUREMENTS 59
from England to Northern Italy the counterweight will require
adjustment to keep the needle horizontal, and in passing from
the Northern to the Southern Hemisphere the counterweight
must be changed to the other end of the needle.
There are two adopted forms of compass for topographical
reconnaissance, one in which the dial is fixed to the case and
one in which the dial moves with the needle to which it is fixed.
The Boa: Compass.-The dial or face on which the gradua-
tions are marked is rigidly attached to the case. The type of
box compass best adapted to running courses by azimuth is
constructed as follows: The graduations read counter-clock-
wise continuously from 0° to 360°; the instrument reads 0° when
pointing North and 180° when pointing South; the E. and W.
points, if marked, are reversed.
To determine the azimuth of a line, point the North and
South line of the case along the line (the North point away
from the observer) and read the N. end of the needle. The
dial is graduated to single degrees, but when the needle is
stationary the reading can be estimated to half degrees. The
compass shown in Fig. I reads an azimuth of 45°.
Fig. I.-BOX COMPASS
Many box compasses are not graduated in the manner above
described. To use such compasses for azimuth reading they
should be altered to conform to the conditions cited. This is

60 ORIENTATION FOR HEAVY (COAST) ARTILLERY
ordinarily done by pasting paper over the stamped numbers on
the dial and renumbering in ink or pencil.
The Prismatic Compass.-The dial containing the gradua-
tions is attached to the needle and moves with it. It is read
by means of a small prism, adjustable for focus. This prism
is mounted on a hinge joint and can be turned down for carry-
ing. The line of sight of the instrument is determined by
front and rear sights, which fold down when not in use, at the
same time stopping the needle. The needle may be compen-
sated for dip by a bit of sealing wax on the under side of the
dial card. The graduations on the dial should be numbered so
as to read azimuths, as above described, beginning at the North
point. If the graduations are not so numbered, they should be
altered as follows: The zero should be at the South end of
the needle (which is on the under side of the dial) and the
graduations should run clockwise continuously to 360°. It is
to be noted that with such numbering the instruments will not
read azimuths if used as a box compass. The index is a point
on the case, and as the dial is movable the graduations are
numbered clockwise, instead of counter-clockwise, as in the
box compass. Readings should be made through the prism.
To determine the azimuth of a line with this instrument,
adjust the prism until the graduations on the dial are distinct,
raise the front sight, look through the slit in the prism plate and
bring the front sight in line with the forward station; when the
needle comes to rest, read the azimuth through the prism.
The prismatic compass shown in Fig. II is set to read an
azimuth of 315°.
Declination.—At most places the compass needle does not
point toward true North, its divergence from true North at any
point being called “the Magnetic Declination” at that point.
If the needle points West of North it is called a “West Declina-
tion”; if East, an “East Declination.” The declination is not
constant, however, but is subject to certain periodic variations,
called the daily, secular, annual and lunar variations. The
daily variation consists of a swing from the extreme Easterly
position at about 8 A.M. to the extreme Westerly position at
1:30 P.M., the mean position occurring about 10 A.M. and 5 P.M.
The daily variation is from 5 to 15°. The secular variation is
a long slow swing, covering many years. In the United States
all East declinations are now gradually decreasing and all
West declinations are gradually increasing at the rate of about
5 per year. The annual variation is small—less than 2° a
ANGULAR MEASUREMENTS 61
Fig. II.-PRISMATIC COMPASS
year— and the lunar variation is still smaller; neither need be
considered in ordinary surveying work. The mean value of
the declination at a certain date is shown on “Isogonic Charts,”
by means of curved lines, called “Isogonic Lines,” connecting
points of equal declination.
The charts giving the declination of the compass for the
Northeast of France and for Western Germany are based on
old data corrected to January 1,1917, by comparison with the
corresponding observations recorded at the magnetic obser-
vatories of Parc Saint-Maur and Val-Joyeux. Accordingly the
lines of equal declination shown on the maps can only be
considered as within 20 of the correct declination.
To use one of these maps, the station must first be located
On the map. A simple interpolation between the two lines of
equal declination enclosing the station will give the declina-
tion for January 1, 1917. This first result is then corrected
for the annual and the daily variations. -
The annual variation for the region covered by the two maps
is nearly constant and is decreasing about 16 per year. The
correction arising from this variation is proportional to the
length of time which has elapsed since January 1, 1917. The
correction for the daily variation is taken, according to the
month and the time of day, from the following table. The
correction is almost zero shortly after 10 A.M. and again
about 6 P.M.

62
ORIENTATION FOR HEAVY (COAST) ARTILLERY
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ISOGONIC LINES ARE MARKED IN GRADES AND
INDICATE WESTERLY DECLINATIONS


















ANGULAR MEASUREMENTS 63
TABLE OF DAILY MAGNETIC VARIATIONS

Months 6 h 8 h 10 h 12 b | 14 h | 16 h 18 h
January. . . . . . . . . . . . . . . . . 0\ } – 2\ 0\ | +6\ | + 6\ | +2\ O)
February. . . . . . . . . . . . . . . . –2" | —4\ | —2\ | +6\ | + 7" | +4^ O'
March. . . . . . . . . . . . . . . . . . . –2" | —6 —4\ | +7" | +11" | +6) OY
April. . . . . . . . . . . . . . . . . . . . –4" | –9" | —4\ || --9" | +13" | +6) O'
May. . . . . . . . . . . . . . . . . . . . –7 —9" | —2" | +9° +13" | +6% O'
June. . . . . . . . . . . . . .- * * g g g g –9" | –9" | —2" | +9" | +13" | +7 || +2\
July. . . . . . . . . . . . . . . . . . . . . . —7 | –7 | —2" | +9° | +11" | +6\ } +2"
August. . . . . . . . . . . . . . . . . . —6\ | – 7" 0" | +9" | +11" | +4^ 0\
September. . . . . . . . . . . . . . . —4\ } – 6\ 0\ | +9° + 9" | +4^ O'
October. . . . . . . . . . . . . . . . . . —2\ –6\ —4\ +7° + 9" | +4^ O'
November. . . . . . . . . . . . . . . 0\ | —2" | —2" | +6" | + 7" | +4\ 0\
December. . . . . . . . . . . . . . . . 0\ } – 2\ 0\ | +4\ } + 7" | +2\ O'
Eacample: To find the magnetic declination at 2 P.M. February 20, 1917,
#. a point situated approximately at Latitude 54.398, Longitude 2.97° East of
2.TIS.
The magnetic map for the Northeast of France shows for this point... 138 20°
Annual vairation, 0.14 of a year, – 16° x .14. . . . . . . . . . . . . . . . . . . . . . 2*
Daily variation, see table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S\
Westerly declination 138 26"
Setting off the Declimation.—The ordinary pocket compass
is not usually provided with a means of setting off the declina-
tion, but the larger compasses used in land surveying and the
box compasses built into the American transits are generally
constructed so that the declination can be set off. The circle
bearing the graduations is movable, within limits, about its
center. A declination scale is graduated on it, which moves
against a fixed mark when the circle is rotated. In this way
the circle bearing the main scale is rotated the amount of the
declination, so that when the needle points to the zero of the
scale, the line of sight of the instrument will point true North.
The needle will then indicate true bearings or true azimuths. If
the angle between the Magnetic Meridian and Lambert North
be set off, the needle will then indicate true Y-azimuths.
If a vernier be graduated each side of the fixed mark then
the declination can be set off very accurately, and by using a
magnifying glass (such as is provided on Some French com-
passes) to obtain coincidence of the North point of the needle
and the 0 graduation of the scale, a fairly accurate orientation
may be obtained. To carry the work to this refinement it is
necessary to know the Magnetic Declination at the station
very accurately. -
Compass Errors.—Irregular variations due to so-called mag-
netic storms are uncertain in character and cannot be predicted.
64 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Such variations are sometimes large. Local attractions may
greatly disturb the needle, and often come from unknown
sources. The observer should have them constantly in mind
and endeavor to keep all magnetic influences, such as magnetic
bodies, electric wires, railroad track, guns, wire entanglements,
etc., at a distance of 10 to 50 m. from the instrument when
the needle is being read.
A simple way to detect—not measure— such disturbances
is to take frequent back azimuths. If the position of the needle
is normal at both stations, the azimuth and back azimuth will
differ by 180°. If there is local attraction on the course, it
will usually be stronger or cause a greater deflection at one
station than at the other, and the azimuth and back azimuth
will not differ by 180°.
The geometric axis of a needle may not coincide with its
magnetic axis, hence the readings of two compasses at the same
station may differ slightly.
Use of Compasses.—A good needle requires time to settle,
even when the case is firmly supported, and the user should
cultivate the knack of catching it at the middle of its swing,
which is the desired reading. If the compass can be supported,
it is always better to do so. Then the sight can be carefully
taken and the position of the eye changed to read the needle.
The needle circle is graduated in degrees and half degrees
and, even with precautions, it will be found difficult to estimate
the reading of the needle closer than 15'. This difficulty,
together with the variations of the needle at different points
due to megnetic declination and local attraction, prevents
using the compass for anything except rough work. For
orienting a map or plane table and making a survey or traverse
where speed and not accuracy is essential the compass is a very
useful instrument, but where more accurate work is required a
transit or theodolite must be used to determine directions.
The Transit or Theodolite.—The Transit is a precise instru-
ment designed to measure horizontal and vertical angles very
accurately. (Large and especially well constructed instruments
of a special design are known as Theodolites. They are seldom
seen in this country.) If equipped with stadia wires it will
also measure distances, determine bearings with a magnetic
needle and do leveling by means of a bubble tube attached to
the telescope. A cut of the instrument is shown below with
the most important parts lettered and labeled. Named in
ANGULAR MEASUREMENTS 65
order from the tripod upwards these parts are as follows:
Tripod, tripod head, shifting head, leveling head, horizontal
limb, plate, telescope supports and telescope. The method of
assembling these parts can be readily understood by referring
to the Cross Section given later.
º
A-Tripod.
B- a head.
C } Plate glamp.
Vernier , ,
Plate tang.screw.sºjº
D; .g ºššiº.
Vernier . . . .
E- Limb clamp. §niº
F– “ tang, screw. “º
G-Main leveling
SC revºVS.
H-H-Werniers
4-1-Plate levels.
K-Vert limb.
L - . . . . . vernier. G *.
M- “ “tang, screw Kºś
N - 'i clamp. B\ºft
O- Attached level. g
P– Telescope
Q= Eye piece { §ºWºº
|R-R-Reticle screws. º *º
Y— Support % º
Fig. IV.-TRANSIT
Care of Transit.—The transit is a very delicate instrument
made of soft metal, and must be handled with extreme care.
The following precautions must always be observed:
1. In lifting never hold by the telescope or telescope
Supports. Grasp it beneath the horizontal limb or by the
leveling head.
2. Never force a screw—all screws should work easily.
If they do not, forcing them will probably strip the threads.
3. Do not set clamp screws as tight as possible—a small










66 ORIENTATION FOR HEAVY (COAST) ARTILLERY
pressure is sufficient to hold the part steady and the threads
will last much longer.
4. Never attempt to rotate telescope, plate or limb without
Seeing that the clamp screw is loosened.
5. Rubbing dust from the object glass with a cloth will
Scratch the lens. Blow it off or brush it gently.
6. Before lifting the transit to carry it from one position
to another, do three things:
(a) Loosen the lower clamp so that both plates will
turn freely if accidentally hit.
(b) Point the telescope straight up and clamp it very
lightly.
(c) Lift the needle from the pivot so that the delicate
point of the pivot will not be injured by a shock.
7. Do not carry the transit on the shoulder through an
open door.
8. Never leave the instrument exposed to the direct rays
of the Sun. Always shade it if possible. Unequal expansion
of the metal will throw the parts out of adjustment.
9. Keep the transit well protected from rain or dampness
at all times.
Setting up the Transit ready for use is accomplished in three
Separate, progressive steps.
1. Adjusting Plumb Bob over Stake.—With one leg firmly
grasped in each hand, place the tripod with the legs extended
far enough to give a stable base and so as to make the top
surface of the tripod head horizontal or nearly so. On level
ground the legs will be equally extended. On inclined ground,
two legs on the lower side should be on the same level and
relatively close together. The third leg is moved straight up
hill at right angles to the line of the lower two; the amount
this leg is thrown up hill is that sufficient to bring the tripod
head roughly level. If the instrument has not already been
Screwed to the tripod, remove the tripod cap and screw on the
instrument in its place. Attach the plumb line to the hook
underneath the shifting head. By moving the legs separately
bring the tripod head approximately level and very nearly
Over the point at a convenient height from the ground. Loosen
a pair of adjacent leveling screws and with the shifting head
bring the plumb bob exactly over the point.
2. Leveling.—Unclamp the vernier plate and turn the
transit so that one of the plate levels is parallel to one pair of
opposite leveling screws. The other plate level will be parallel
ANGULAR MEASUREMENTS 67
to the other pair. Bring the bubbles of the levels to the center
in succession by means of the leveling screws. Always turn
one of a pair down as the opposite one is turned up and avoid
more pressure of the screws against the plate than is necessary
for a firm bearing. If a screw turns hard at any time it is
either sprung or has been set too tight. In turning a pair of
leveling screws always move the thumbs toward each other or away
from each other. The bubble will follow the motion of the left
thumb. If the screws are too tight unscrew either but not both.
With the level bubbles in the centers of their tubes, the
plate will be level if the bubbles are in adjustment. Turn the
transit slowly through 180° in azimuth and watch the bubbles.
If they remain in the centers, the plate is level and the levels
are also correct. If either bubble leaves the center, the
amount of its motion indicates the amount by which it is out
of adjustment. If the amount is small, it may be neglected;
if large, the adjustment should be made as hereafter described.
For short lines the level error may be neglected if the entire
bubble remains in sight during the entire revolution. Adjust
the leveling screws in this case so that the travel of the bubble
will be equal on both sides of the center.
3. Focusing.—(1) Having leveled the instrument point the
telescope to the sky and focus the eye-piece until all roughness
on the cross wires stands out sharply. (2) Focus the objective
by directing the telescope on a distant object and moving the
objective lens until the outlines are distinctly visible. (3)
Test the two adjustments by moving the head laterally, watch-
ing the cross wires. If the cross wires and the image move
together the two lenses are focused correctly. However, if the
cross wires appear to move over the image the condition is
caused by parallax. Eliminate this by changing the focus of
the objective until the image lies in the plane of the cross wires.
To Measure a Horizontal Angle.—(1) Set up over the
vertex of the angle to be measured and clamp the limb with the
lower motion screw (see Fig. V). Loosen the plate clamp and
turn the plate which carries the telescope until the index on
the vernier is opposite the zero graduation on the limb. Clamp
the plate in this position with the upper motion screw. (2)
Loosen the limb clamp (this allows the plate and limb to move
together) and bring the intersection of the cross hairs in the
telescope to a point of the line. Tighten the limb clamp.
(3) Loosen the plate clamp (this allows the plate to move
independently of the limb which is clamped) and direct the
68 ORIENTATION FOR HEAVY (COAST) ARTILLERY
|
|
i
A2ZAZ"
Z
NS -
Elºs * - Ouſsiae Army of Aloſe
- -e ºs º-m-- A/M&
(Joaer Mohan 5crew)
4./M8 C/A/V/P
A ſy/f//WG //f40 (. ower Moffen 5crwºw/
-]
tº
[-
:-
º
|III
77/2OO //CAO
ºvrrºb Zirne YS (D 3//7/WG /#A0
N.
Fig. V.-DIAGRAMMATIC CROSS-SECTION OF TRANSIT
telescope to a point on the other line. Clamp and read the
index and vernier (to be explained later). As the telescope
was turned from the first to the second line, the index moved
over a certain number of graduations on the limb and by
reading this number of graduations (which are in degrees) the
angle between the two lines is determined.
Both upper and lower motions are equipped with tangent
screws for making fine adjustments in directing the telescope
on a given point and also in setting the vernier index. The
plate and limb must be clamped when using the tangent
screws, otherwise they have no effect on the adjustment.
The transit is equipped with two verniers and windows
where horizontal angles can be read on the limb. The one
called the “A” vernier is near the eye-pice of the telescope;
the other called the “B” vernier is diametrically opposite
under the object glass of the telescope. (See Fig. VI.) The
reading on the “B” vernier should be 180° greater than the


ANGULAR MEASUREMENTS 69
“A” vernier. It may happen, however, that on account of
irregularities in the graduation of the limb, angles read on the
“B” vernier may differ from those read at “A”; in that case
the average is taken. Example:
“A” Vernier “B” Vernier Average
1st line 0° 0' 180° 0'
2nd line 27° 36' 2070 37/
Angle 27° 36' 27° 37' 27° 36.5’
Horizontal limbs are usually marked with two circles of
graduations; the inner circle starting at 0° and increasing to
180°, then decreasing to 0°; the outer circle starting at 0° and
increasing clockwise to 360°. Caution: Always read angles
from the same circle of graduation in using both verniers.
For greater accuracy, the method of repetition is used. After
the first measurement is made, unclamp the limb–not the
Fig. VI.-HORIZONTAL VIEW OF TRANSIT

70 ORIENTATION FOR HEAVY (COAST) ARTILLERY
plate—and resight on the first point by means of the limb
tangent screw and proceed as before. The reading of the
vernier is now twice the angle. Continue the repetitions until
the desired number are made. The last reading divided by the
number of measurements is the value of the angle. To guard
against errors, it is well to read and record after each measure-
ment. It is important to distinguish between the inner and
outer circles of graduations, else serious mistakes will be made.
To Measure a Vertical Angle.—In setting up the transit to
measure vertical angles it is of advantage to have a pair of
opposite leveling screws on line toward the object to be sighted.
Point the telescope toward the object to be sighted, clamping
both limb and plate. See that the plate level bubbles are cen-
tered. Bring the horizontal wire on the object by clamping the
vertical limb clamps and using the vertical limb tangent screw.
The vertical angle is then read on the vertical limb. If the
instrument has a full vertical circle, greater accuracy may be
obtained by unclamping lower motion, revolving instrument
approximately 180°, plunging the telescope and taking a new
sight and reading. If the results differ use the mean.
To Run out a Straight Line.—Set up accurately over the
initial point. Point the telescope in the required direction
and establish a second point. These two determine the line
which is to be run out. Set up over the forward or second
point; lay the telescope on the initial point; clamp limb and
plate, plunge telescope, and set a point forward. If the adjust-
ments are good, this third point will be in line with the first
and second and the line may be prolonged by repeating the
steps taken at the second point.
If the adjustments are not good then proceed as follows:
After establishing the third point as described above, unclamp
limb, and with telescope inverted turn instrument and sight
again on the first point, clamping the limb. Plunge the
telescope and set a fourth point on line. This point will fall
to one side of the third point if the line of sight is out of adjust-
ment. Set a point halfway between the two points thus
obtained and this point will be on line with the first and second
points. This method is known as “Double Centering.”
4. VERNIERS
A vernier is a device for measuring the fractional part of a
division of the main scale between the index and the preceding
mark on the main scale.
ANGULAR MEASUREMENTS 71
Consider AB (Fig. VII-a) as part of a scale of equal parts.
Construct the auxiliary scale or vernier CD, the total length of
which is equal to nine of the smallest divisions of the principal
scale, but divided into ten equal parts instead of nine, which
makes each division of the vernier 9/10 the length of the
division of the scale.
When the zero division of the vernier, indicated by an arrow,
is coincident with a division, as 31 of the scale, the reading is 31
and it is obvious that the first division of the vernier is to the
left of 32 in the scale by 1/10 of the distance between 31 and 32.
Similarly, the second, third, etc., division of the vernier is 2, 3,
etc., tenths to the left of the 33, 34, etc., division of the scale.
To make any division of the vernier, as 2d, 3d, 5th, or 8th,
coincide with the division of the scale next ahead of it, the ver-
nier must be moved to the right 2, 3, 5, or 8 tenths of the
length of one division of the scale, and the arrow will then be
opposite a point on the scale 2, 3, 5, or 8 tenths of the distance
from 31 to 32, or at 31.2, 31.3, 31.5, or 31.8. The quantity
obtained by dividing the value of one division of the scale by
the number of divisions of the vernier is called the least count of
the vernier. Only one intermediate vernier division can
coincide with a scale division at the same time and the number
of the coincident vernier division, counting from the arrowhead,
is the number of times the least count must be added to the
last scale division passed by the arrow to get the true reading.
A vernier constructed as described is always read ahead of
the zero, or in the direction in which the scale graduations
increase, and is called a direct vernier. Werniers may also be
constructed by dividing the length of a certain, number of
divisions of the scale, as 11, into equal parts one less in number,
as 10. The principles of operation and method of reading are
the same, except that the coincident line is to be found behind
the zero of the vernier, or in the direction in which scale grad-
uations decrease. This form is called retrograde. It is but
little used.
If the scale is graduated in both directions, as is often the
case, the vernier is doubled, the zero in the middle and each
side forming a direct vernier for the graduations increasing in
the same direction. This form is called double direct (Fig.
VII-b). The most compact form is that shown in Fig. VII-c,
galled the folded wernier, in which the graduations are numbered
from the middle to one end and continue from the other end to
the middle. This is read as a direct vernier in either direction.
72 ORIENTATION FOR HEAVY (COAST) ARTILLERY
A *—i I D. A
T | | | | | | |- | | |
S SO | 2 3 4. 5 6 7 8 9 40 |
ZX/2c/
(C7)
Jo
30
210 /10 } /10 20
sºleso 3\40
O J|5O 20
/O
ZooZºº //ec/
(AE)
/O , 355
J5|O 5 O 5
355 J60
/5 4. 15
3O
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sºlo O
J43 /0 3%
350 360
awee?”
(C/)




Fig. VII.-VERNIERS
Rules for Reading Verniers.—1. The zero of the vernier
scale is the index and marks the point on the limb whose read-
ing is desired.
2. Determine the value of the smallest division on the
main scale. -
3. The least count of the vernier is obtained by dividing
ANGULAR MEASUREMENTS 73
the value of one division of the main scale by the number of
divisions of the vernier. Example: A vernier of thirty divi-
sions is used on a scale graduated in half degrees. Least
count is one-half a degree divided by thirty, equals one-
sixtieth of a degree or one minute. (See Fig. VII-b.)
4. Mistakes will be avoided and the reading facilitated by
estimating in advance the fractional part of the division of the
main scale. -
5. Read forward along the main scale in the direction of
increasing graduations to the last graduation preceding the
Zero of the vernier. Then read forward along the vernier until
coincident lines are found. The number of this line on the
vernier from the index is the number of least count units to be
added to the reading made on the limb. Example: Read
double direct vernier (Fig. VIII-b) using inside circle of grad-
uations. The least count has been found to be one minute.
The last graduation preceding the index is 350%. Reading on
the vernier ahead of the index in direction of increasing grad-
uations, the fourteenth line is found to be coincident. As the
least count is one minute, fourteen minutes is to be added to
the scale reading 350° 30', giving a final reading of 350° 44'.
If the outside circle of graduations on the scale is read the last
graduation preceding the index is 9° and the coincident line
on the vernier ahead of the index in the direction of increasing
graduations is 16, therefore the final reading is 9° 16'.
6. Read a folded vernier as a direct vernier in either
direction. If the coincident line is ahead of the index in the
direction of increasing graduations take its number from the
middle as zero, if it is behind the middle take its number from
the nearest end counting the end line as numbered on the
vernier. Example: Read folded vernier (Fig. VII-C) using
upper graduations. The least count is one minute, determined
by the method given above. The last graduation preceding
the index is 2°. There is no coincident line in front of the index
so begin at the right and read in the same direction, and the
twenty-third line is found coincident. The reading is then
2° 23'. Using the inner graduations the reading will be
357° 30' plus the vernier reading which is 7', the coincident line
being the seventh, of the vernier in the direction of increasing
graduations. Final reading is 357° 37'. A folded vernier
never has but one coincident line. A double vernier always
has two.
A special form of double direct vernier (used in transits de-
74 ORIENTATION FOR HEAVY (COAST) ARTILLERY
signed for very precise work) is shown in Fig. VII-d. The
method of reading and finding the least count of this vernier
is, however, the same as has already been given for the usual
type double direct vernier. Each degree of the limb is divided
into four parts and each of the fifteen full divisions of the ver-
nier into three parts. The least count then will be:
}{X1/45= 1/180 of a degree =20".
The reading of the vernier as it is drawn is 355° 0' 0" or
5° 0' 0".
Suggestions for Reading Verniers.-1. Look at the mark on
each side of the coincident line; they should be at the same.
distance from the marks on the limb. This will aid in setting
the vernier or in finding the coincident line.
2. If no line seems to be coincident take the average
reading of the two nearest coincidence.
3. Use a reading glass.
4. The order of reading an angle is:
(a) Determine the limb reading carefully.
(b) Estimate the vernier reading.
(c) Read the vernier.
(d) Add the vernier reading to the limb reading.
Common Mistakes in Reading Verniers.-1. Reading wrong
half of a double vernier. -
2. Failing to add in the half degree from the limb reading
as 68° 16' when it should be 68°46'.
3. Reading the “B” vernier instead of the “A,” or vice
Vel’Sã. -
4. Reading the inside circle of numbers on limb instead
of the outside, or vice versa.
5. MEASURING ANGLES BY REPETITION
In extending a triangulation system as described in Chapter
II, all of the angles of each triangle should be accurately
measured by repetition. The procedure at each station is as
follows: Level carefully with the telescope level and see that
the plate levels and other adjustments are satisfactory. For
each principal angle: Set the A vernier to read zero and, with
the telescope direct, set with the lower motion carefully on
the left-hand station. Read and record both verniers. Un-
clamp upper motion and sight on the right-hand station.
Read and record the A vernier for the approximate or trial
angle. Find the number of whole times 60 will go into this
approximate angle and call this M. Then
ANGULAR MEASUREMENTS 75
Unclamp lower motion and sight on the
left-hand station.
Unclamp upper motion and sight on the
right-hand station.
Unclamp lower motion and sight on the
left-hand station.
Unclamp upper motion and sight on the
right-hand station. ~
Plunge the telescope, and without disturbing the vernier setting,
Unclamp lower motion and sight on the
left-hand station.
Unclamp upper motion and sight on the
right-hand station.
Unclamp lower motion and sight on the
left-hand station.
Unclamp upper motion and sight on the
right-hand station.
Unclamp lower motion and sight on the
left-hand station.
Unclamp upper motion and sight on the
right-hand station.
Read and record both verniers. The mean of the “seconds”
of the two verniers will be taken with the degrees and minutes
of the A vernier as the vernier reading. To this must be added
360° multiplied by M as above determined. This large angle
is then divided by 6, the number of repetitions. This gives the
average value of the angle measured. Example: Angle to be
measured, about 135°.
135° gº \ e
M = 605- 2 (Fractions not considered)
* Second repetition.
# Third repetition.
Fourth repetition.
l Fifth repetition.
Sixth repetition.
Reading on “A” vernier after 6 repetitions is 92° 45'.
360°) (2 = 720°.
92° 45'--720° 0' = 812° 45'.
812° 45' divided by 6 = 135° 27.5".
M is dependent on the number of repetitions. Thus, if the
angle were repeated four times, the approximate angle would
be divided by }4 of 360=90 to obtain M.
Detailed Procedure.—The triangle ABC is given. To meas-
ure its angles proceed as follows, assuming the transit set
up at C (see Field Form for method of recording data):
(1) Set “A” vernier at zero. Clamp upper motion. Set
exactly, using the tangent screw. m
76 ORIENTATION FOR HEAVY (COAST) ARTILLERY
&
(2) Backsight on A. Clamp lower motion.
(3) Read and record zero setting on both verniers.
(4) Loosen upper clamp, turn telescope on foresight B.
Clamp.
(5) Read and record the single angle as a check on the
mean reading to be determined later.
(6) With this setting clamped loosen lower clamp and
again backsight on A. In this way add the angle on the limb
six times, three times with telescope normal and three times
inverted.
(7) Read and record both verniers.
FIELD FORM .
STATION READINGS CoRRECTED
Inst. Sighted | A Vernier B Vernier Mean VALUE
42
G A °–00'—00" | 180°–00'—00" 0-00-00 || M-à-0
B 42°–05'
B(6) 252°–311–00" | 72°–31’–00" 252°–31’–00"
ë) 259-31-007 *-º-º:
5"
42°–05'—10" —
42°–05'—15"
72
A B °–00'—30" | 180°–007–00” 0°-00-15" |M =#0–1
C 72°–43'
C(6) 76°–19–30" 256°-19'−00" 76°–19'—15"
360°–00'—00"
6) 436°–19–00" | 72°–43–10"
05"
72°–43’–10” —
72°–43’–15"
65
B C 0°–00'-00" | 180°–00'—00" *-00-00 || M-35–1
A 65°–11’ *
A(6) 31°–08–30" | 211°–08–30" 31°–08'—30"
360°–00'—00"
6) 391°–08–30" | 65°–11–25.
05"
B = 65°–11’–25" |—
A = 72°–43’–10" | 65°–11’–30"
C = 42°–05'—10" ---
179°–59'—45"
error = 15"
ANGULAR MEASUREMENTS 77
Adjustment of Angles of Triangle.—The sum of the three
angles of a triangle equals 180°. If after taking all possible
care in measuring the angles of a triangle their sum is greater
or less than 180°, distribute the error in the following manner:
Take one-third of the difference between the sum of the angles
of the triangle and 180°. Apply this correction to each of the
three angles, making their sum equal to 180°, as shown above
in the Field Form. º
Errors in Angle Measurement.—Contrary to the general
impression, the error due to the plumb bob being off the
station is not so important as the error due to the plates being
out of level. Particularly is this true on rolling ground where
sights are taken up and down hill. Time should not be taken
to bring the bob closer to the point than 3mm, but care must
be taken to level the plates very accurately. In sighting on a
point if the line of sight passes a short distance from it either to
the right or left an error in the angle read will be introduced
which will vary with the length of the sight, being relatively
large with short sights and decreasing as the distance to the
point increases. Some idea of the relation between linear and
angular errors may be gained from the approximate values
given in the following table:
Length of Sight Angular Error for Deviation for Error
in Meters 2.5 cm. of 1 Minute
30 3 minutes .9 cm.
90 1 minute 2.7 cm.
150 1/2 minute 4.6 cm.
300 1/4 minute 9. 1 cm.
450 1/6 minute 13.7 cm.
1500 1/20 minute 45.7 cm.
An error of one in 5000 is classed as fair work for measure-
ments with a steel tape. To come within this limit angles
should be read to 30", and this can easily be done with a transit
reading to minutes. For a precision of 1 to 10,000 the angles
should be read to 20", therefore a transit graduated to 20" is
necessary. For greater precision angles should be repeated.
CHAPTER IV
ADJUSTMENTS OF TRANSIT
PLATE LEVELS
CROSSWIRES
LINE OF SIGHT
HORIZONTAL AXIS
TELESCOPE LEVEL
VERTICAL CIRCLE
i
In order to measure angles correctly and to measure angles
in horizontal and vertical planes only, the different parts of a
transit, especially the movable ones, must bear certain fixed
relations to each other, or in other words, “the transit must be
in adjustment.” The plate and the horizontal axis (telescope
trunnions) must be level and parallel; one crosswire must be
vertical, the other horizontal; the line of sight must revolve
around the trunnions in a vertical plane; when the telescope
bubble is centered the line of sight must be horizontal and the
vernier on the vertical circle should read zero. Unless these
conditions exist, the transit is out of adjustment, precise work
is impossible, and after making a set of computations it may be
found that a long and tedious piece of field work is worthless.
Therefore, a battery officer should be able to tell whether an
instrument is in adjustment, and if it is not, he should be able
to make the proper corrections. No opportunity should be
lost to test a transit and make the necessary adjustments;
nevertheless, in order to minimize the probability of errors, a
transit should habitually be used so that any instrumental
errors will balance each other. ... "
Transit Errors.-A transit is a delicate instrument with a
large number of parts that are apt to get slightly out of adjust-
ment through ordinary use. Although a large number of parts
may be injured by rough usage—clamps bent, bubble tubes
broken, threads stripped, etc.—yet there are only six sources
of instrumental error when a transit is carefully used, viz.:
1. If the plate level tubes are not parallel to the plate, the
bubble may be centered, but the plate will not be horizontal;
consequently angles will be measured in inclined planes instead
of horizontal and vertical planes and will be distorted.
ADJUSTMENTS OF TRANSIT 79
2. If the vertical crosswire is inclined, angles will not be cor-
rect unless the same point on the crosswireis used on both sights.
3. Unless the line of sight through the vertical crosswire
is perpendicular to the horizontal axis of the telescope (the
trunnions) a foresight is not a continuation of a backsight.
4. If the horizontal axis is not parallel to the plate (i.e.,
not horizontal) vertical angles will be measured in an inclined
plane instead of a vertical plane, and horizontal angles between
objects at different elevations will be in error.
5. Unless the axis of the telescope level tube is parallel to
the line of sight, the latter will be inclined when the bubble is
centered, and vertical angles will be in error.
6. Unless the vernier on the vertical arc reads zero when
the line of sight is horizontal, there will be a constant error in
vertical angles.
These errors are given above in the order of their impor-
tance; the necessary tests and adjustments should be made in
the same order. However, as these errors are not independent
of each other, each successive adjustment may throw out a
previous one. Therefore, after the adjustments have been
made for all six of the above errors, the entire set should be
checked and, if necessary, repeated.
1. PLATE LEVELS
After leveling the instrument with each bubble tube parallel
to diagonally opposite leveling screws, revolve the plate through
180°. If the bubbles still remain centered, their axes are par-
allel to the plate and both are horizontal; if either bubble is
displaced, its axis is inclined to the plate, and neither is hori-
zontal. In the first position the bubble tube was horizontal,
but the plate was not; in the second position (plate reversed)
the plate is in the same inclined plane as before, but the bubble
tube is in another inclined plane (see Fig. 1), which makes an
angle with the horizontal (20) equal to twice the angle between .
the bubble tube and the plate (o). Thus half the displacement
of the bubble is caused by the inclination of its tube to the plate
and half by the inclination of the plate itself. Therefore, bring
the bubble halfway back to center by adjusting the capstan
screws in its supports, and then level the plate. If the instru-
ment is now reversed again, and the bubble is again displaced,
repeat the adjustment until the bubbles remain centered for
all positions of the plate,
80 ORIENTATION FOR HEAVY (COAST) ARTILLERY
~ks <^c
*-* -m- O, \ Aſºs? A os/f/on
//o//zo/7/a/~" CZ =
Y- ~}s =A // Or
& T-s
- S& *r
Sº
.
Fig. I.-PLATE LEVEL ADJUSTMENT
This adjustment illustrates the principle of “reversion” on
which four of the transit adjustments depend. It consists in
reversing the instrument so that an error becomes apparent.
. The apparent error is double the true error, because reversing
the instrument merely reverses the error, which exists in both
positions, but is not apparent in the first.
2. CROSSWIRES
The line of sight of a telescope is the line from the eye of
the observer through the intersection of the horizontal and
vertical crosswires to the object observed. For mechanical

ADJUSTMENTS OF TRANSIT 81
and optical reasons this line should coincide with the optical
axis of the telescope, which is supposedly also the center of the
field of vision and should be normal to the horizontal axis. In
other words, the vertical and the middle horizontal crosswire
should both bisect the field of vision, and they should also be
made vertical and horizontal, respectively, before the other
adjustments are made.
In most modern telescopes all the crosswires, stadia wires
included, are permanently placed upon a movable metal ring
called a reticle, which is held in place by four capstan-head
adjusting screws passing through slotted holes in the body of
the telescope. See Fig. 1, Chapter V. By loosening any two
adjacent screws, the whole reticle is loosened so that it may
either be rotated about the line of sight, or moved sidewise
across the field of vision, until the vertical wire is perpendicular
to the horizontal axis and the crosswires intersect on the center
of the field of vision. A simple method of placing the hori-
Zontal wire in the center of the field of vision is to focus the
telescope on a graduated rod at a short distance from the
instrument. With the telescope clamped in an approximately
horizontal position shift the reticle by turning the upper and
lower adjusting screws until the horizontal wire bisects the
intercept on the rod determined by the circle limiting the field
of vision.
If the vertical wire is set upon a sharply defined point or
object, and the telescope then elevated or depressed, using the
slow motion screw, the vertical wire should continue to follow
along the object within the limits of the field of vision, and
failure to do so indicates that the vertical wire is not normal
to the horizontal axis. To adjust, rotate the reticle until the
required condition is fulfilled, being sure that all four adjusting
screws are tight after the final adjustment.
The Line of Sight adjustment, which follows, may alter the
position of the vertical wire slightly, in a sidewise direction,
but the telescope level and vertical circle adjustments should
be made to conform to the horizontal wire as now placed in
the middle of the field.
3. LINE OF SIGHT
If the line of sight is truly perpendicular to the horizontal
axis of the telescope (the trunnions) it will generate a plane
when the telescope is plunged; if it is not perpendicular to
82 ORIENTATION FOR HEAVY (COAST) ARTILLERY
§
S
&es, % § Dire? f
C -a, - Telež = E//"Of
A. - ** _-- *T - -
fºeg fºº &
-º-'
Fig. II.-ERROR IN LINE OF SIGHT
the trunnions, it will generate a conical surface, the cone
lying entirely on one side of a plane through its vertex and
perpendicular to the trunnions. In the latter case (see Fig. II)
the deflection angle 20, between a backsight and a foresight
will be twice the deviation, o, of the line of sight from the nor-
mal. If the telescope is reversed and then plunged again a
similar cone will be formed by the line of sight but on the
opposite side of the aforesaid plane through the trunnions.
(See Fig. III.) -
If the two foresights with the telescope plunged—one
normal and one reverse—do not coincide, the line of sight is
not perpendicular to the trunnions, and the true foresight is
midway between the two observed foresights. Therefore, as
the deflection between each observed foresight and the true
foresight is twice the error, and the observed foresights are on
opposite sides of the true foresight, the total angle between the
two observed foresights is four times the instrumental error.
The adjustment is made as follows: Sight on a well defined
point, P (see Fig. III), about 100 meters from the transit.
Plunge the telescope and set a stake, Q, in the line of sight
about the same distance on the other side of the transit.
Reverse the instrument (i.e., rotate it about the vertical axis)
7A/ows
i...ºu. Fig. III.-ADJUSTMENT OF THE LINE OF SIGHT

ADJUSTMENTS OF TRANSIT 83
and with the telescope still inverted, sight on point P again.
Plunge and set a second stake, R, in the new line of sight and
opposite the first stake, Q. As explained above, the distance
between Q and R is four times the transit error. Therefore,
set a stake, S, one-fourth of the distance from R to Q, and
without disturbing the telescope or plates, bring the vertical
crosswire onto S by moving the reticle. Repeat the test and
make a further adjustment if required.
4. HORIZONTAL AXIS
As stated before, if the line of sight is perpendicular to the
axis of the trunnions, it revolves in a plane when the telescope
is plunged. However, unless the trunnions are level, that
plane (the plane of sight) will not be vertical. But in order to
measure angles correctly, it must be vertical. Therefore, the
axis of the trunnions must be horizontal or in other words, both
the plate and the trunnions must be level, and therefore parallel.
The usual method of making this test and adjustment is as
follows (see Fig. IV): Sight on some clearly defined, high
point, P, such as the corner of a roof, depress the telescope and
make a mark, A, on the building at the same elevation as the
telescope. The transit, point P, and mark A, determine a
plane; if the trunnions are level, that plane will be vertical;
otherwise it will be inclined. Reverse and plunge the instru-
ment, sight on the point P again, and depress the telescope. If
the trunnions are level, the mark A will still be in the plane of
sight, if it is not, put a second mark, B, in the new plane of
sight and opposite the first mark, A. . As in the first adjust-
ment, this operation is a “single reverse,” and the distance
AB between the two marks is twice the error of the instrument.
Bisect the distance AB; sight on this middle mark, C, and raise
the telescope until the high point, P, is in the field of vision.
Then raise or lower the adjustable end of the trunnions until
the vertical crosswire falls on the point P. The horizontal axis
should now be level. Repeat the test and make a further
adjustment if necessary.
5. THE TELESCOPE LEVEL
In order to read vertical angles or take level readings cor-
rectly, the axis of the telescope must be parallel to the axis of ist
bubble tube; otherwise, when the bubble is centered the tele-
scope will be inclined. This can be tested by the “peg method.”
84 ORIENTATION FOR HEAVY (COAST) ARTILLERY
i
ſº
O/7
- Aoazzo/77 a/
first--T
G-
A25///o/75 of
/7%//zo/77%/ Ax/5
[ ſº
gºź%:W/?ºgs% ãºã3%3%
Fig. IV.-ADJUSTMENT OF HORIZONTAL AXIS
On fairly level ground set two pegs, A and B (see Fig. V),
about 100 meters apart, so that their tops are at nearly the
same elevation. Set up the transit, as close to A as it can be
clearly focused (about 2 meters), level the telescope and take
rod readings (a and b) on each stake. If the telescope is level
the difference in elevation (c) between the two pegs is the
difference in the rod readings or a – b = c. Move the transit
and set it up near B, level the telescope and take rod readings
on the two pegs again, calling these readings aſ and b'. Simi-




ADJUSTMENTS OF TRANSIT 85

-º- | T * T - - -— — — — — — e.
Aſ l - 1
€ | –— — — — — — T gº d
Å
N \ \ (ſ f
//o//zo/7/27////7e % * &N Z
-*-* =s 4./72 of 5%f
Fig. V.-ADJUSTMENT OF TELESCOPE BUBBLE TUBE
larly, if the telescope is level the difference in elevation of the
two pegs is a'—b' = c', and c should equal c'; if it does not
the line of sight is not parallel to the axis of the bubble tubes.
This is merely an example of the single reverse, the whole
transit being moved and reversed instead of only the plate and
telescope. The true difference of elevation (d) of the pegs
/
C–H–C
A and B is d-ºº: the error (e) in the transit is d – c =
c’ – d = e, and the apparent error (c.—c') is twice the true error.
c—c' º ©
Compute the actual error, e = 2 ” If e is negative, the
line of sight is inclined upward; and if positive, downward.
In the former case the amount of the error should be subtracted
(as indicated by its sign) from the last rod reading a' on the
distant point, A, and in the latter case, added. Set the hori-
Zontal crosswire on this new rod reading and clamp the vertical
arc. Then center the bubble by adjusting the capstan screws
at either end of its tube. The line of sight and telescope level
are now horizontal and parallel. The test should be repeated
and a second adjustment made if necessary. The following
example illustrates this method:

ROD READINGS
TRANSIT
POINT
A B Difference
A 2. 176 0.013 2, 163
B 4.685 2. 122 2.563
86 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Difference = (c.—c') = — .400
(c—c')
2
4.685–0.200 = 4.485 = rod reading at A on which telescope
should be level when transit is at B.
6. VERTICAL CIRCLE
When the line of sight is horizontal and the telescope bubble
is centered, the vernier of the vertical circle should read zero;
if it does not there is a constant error in all vertical angles.
If the vernier is adjustable, it should be set to read zero when
the telescope bubble is centered. If it is not adjustable the
amount and direction of this “index error” should be recorded
and added algebraically to all vertical angle readings.
Summary.—Theoretically the instrument is now in perfect
adjustment; when the plate bubbles are centered, the plate is
level; the vertical crosswire is truly vertical; the line of sight
revolves around the trunnions in a vertical plane; and when the
telescope bubble has been centered the line of sight is hori-
zontal and the vertical circle vernier reads zero. However, as
stated before, the adjustments are not independent and some
of those made first may have been thrown out by the later ones.
Therefore, the test for all six adjustments should be repeated
in the same order until all adjustments are correct.
Elimination of Effect of Instrumental Errors.-Although a
transit should always be put into good adjustment before being
used yet in many cases that may not be practicable. If the
transit is used properly, slight instrumental errors may be made
to “balance out,” thus eliminating their effect.
If the plate level tubes are not parallel to the plate the latter
can be made horizontal by adjusting the leveling screws until
the bubbles remain in the same place (not necessarily centered)
for all positions of the plate. If one level tube is parallel to the
plate and the other is not, use only the one tube in leveling the
instrument.
If one point on the vertical crosswire is used for all sights it
makes no difference whether the crosswire is vertical or not.
The intersection of the two crosswires is the most convenient
point to use.
In prolonging a line one foresight should be taken with the
telescope direct and another inverted. The true foresight is
midway between the two, and by using the mean any error in
ADJUSTMENTS OF TRANSIT 87
the line of sight is eliminated. Similarly, if deflection angles
are measured twice, once normal and once reverse, the mean
value is correct and eliminates the same error as above.
If an angle is measured between two points at the same
elevation an inclination of the trunnions has no effect; if they
are at different elevations it causes an error. With the tele-
Scope normal the angle is too large; inverted, too small, or
vice versa. By measuring the angle twice, once with the tele-
cope normal and once inverted, one reading is the correct
angle plus the error, the other the correct angle minus the
error, and the mean is the true angle. -
If the vertical angle between two points is measured twice
—from the first point as a foresight and from the second as a
backsight, one being plus and the other minus—one will be the
true angle plus the error, the other the true angle minus the
error, and the mean will be the true angle. The index error
of the vertical circle should be checked before each traverse
and the proper correction made to all vertical angles.
Thus, by using the transit as suggested above the effect of
all small instrumental errors can be eliminated; the transit
should always be used in that manner. However, such use
does not excuse negligence in making required adjustments,
and is apt to leave errors if the instrument is much out of
adjustment.
CHAPTER V
LINEAR MEASUREMENTS
1. UNITS OF LINEAR MEASURE
2. METHODS OF APPROXIMATE MEASUREMENTS
3. STADIA
4. STEEL TAPE
5. TRIANGULATION
1. UNITS OF LINEAR MEASURE
English System.—The English system of units of measure
has been in such general use in this country that it is hardly
necessary to describe it. The system of “feet, inches and
fractions” is used principally in the industrial and commercial
world; while the “feet and decimals” system is used in Engi-
neering and Surveying.
The American Field Artillery and the Coast Artillery use
the yard as the unit of linear measure. Before the war all
instruments and tables were graduated or computed on that
unit as a basis.
Table of Units
12 inches = 1 foot
3 feet = 1 yard
1760 yards = 1 mile
5280 feet = 1 mile
There are many other units of measure in the English
system, for use in special work, but since they have no use in
the heavy artillery they are not included in the discussion.
Metric System.—The Metric System of units is in almost
universal use in the scientific world and is the most convenient
system of measurement that we have. It has been adopted in
our service for use in the heavy artillery. It is therefore
necessary that the officer of heavy artillery have a thorough
knowledge of the metric units of measure and the factors for
converting English units into metric units.
The fundamental unit of linear measure in the metric
system is the meter. The meter was intended to be 1/10,000-
000 of the length of the arc of a meridian at mean sea level,
extendingſ from the equator to the pole. Very accurate
LINEAR MEASUREMENTS 89
Surveys were made to determine this length. It has since been
shown that the intended relation is not strictly true, due to
errors in the original determination. However, the length of
the meter remains the same as originally determined.
In the Chapter on Angular Measurement it was shown that
100 grades = 1 quadrant. Therefore we have the relation
100 grades of Latitude = 10,000,000 meters (approximately) at
sea level. This relation is simple and has an application in
geodetic Surveying where all measurements are referred to sea
level. Ö
- Table of Units
1000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 meter
10 decimeters (dm) = 1 meter
10 meters = 1 dekameter (dkm)
100 meters = 1 hectometer (hm)
1000 meters = 1 kilometer (km)
Observe that the prefixes indicate decimal parts of a meter
or multiples of tens of meters. These relations should be
firmly fixed in mind.
Conversion Factors.-
1 m = 39.37 inches (log 39.37 = 1.59517)
1 in. = .0254 meters (log .0254=8.40483–10)
1 ft. = .3048 meters (log .3048 = 9.48401–10)
1 yd. = .9144 meters (log .9144 = 9.96114–10)
1 m. = 1.0936 yds. (log 1,0936 = .03886)
1 mile = 1.6093 km. (log 1.6093 = .20665)
1 km. = .6214 mile (log .6214 = 9.79335–10)
2. METHODS OF APPROxIMATE MEASUREMENTS
These methods of determining distances are used for sketch-
ing, reconnaissance or similar rapid work where the allowable
error is from one to three per cent.
Pacing.—In pacing, the steps of the sketcher, or of his mount,
are counted, usually aided by some form of tally dial. It is
first necessary to pace several times over a measured course,
taking from these trials the average length of step from which
to construct a pace scale. Ordinarily, as fatigue increases the
length of the pace decreases, hence it will probably be advisable
to get an average for both morning and afternoon, and use
them at appropriate times. The method of averaging, and
the construction of a pace scale, is covered in Chapter VI.
90 ORIENTATION FOR HEAVY (COAST) ARTILLERY
For mounted work, it will probably be more accurate and
somewhat easier to time the speed of a horse. If two mounted
men travel in company this will be even better, as horses travel
at a more uniform rate in pairs. If possible, the horses should
be rated over a measured course, both time and count of steps
being taken, at walk, trot and gallop.
The average walk of a horse is 110 yards per minute or 3%
miles per hour (one mile in 16 minutes), the horse taking 120
steps, each 33 inches long per minute. His average trot is
220 yards per minute, or 7% miles per hour (one mile in 8
minutes), the horse taking 180 steps, each 44 inches long, per
minute.
Odometer.—The odometer is an instrument attached to the
wheel of a vehicle for recording the number of revolutions.
It is not accurate, but it is very valuable for rapid, rough work,
where its use is possible. On heavy roads, mud or sand, there
is a slip, sometimes positive, sometimes negative.
Estimating.—Ability to estimate by eye can be developed
so that considerable dependence may be placed upon it, par-
ticularly for short distance. The distance to the visible hori-
zon on water in miles is 1.225 VH, where H = height of ob-
server's eye above water level in feet.
Sound.—The method of obtaining distance or range by
sound, known as “Sound Ranging,” has been developed to a
high state of accuracy on the Western Front. To obtain
accuracy with this method, extremely delicate instruments are
required. An accuracy of 10 to 30 meters in 10,000 meters is
usually obtainable by this means. A rough estimate of dis-
tance may be made by timing sound with a watch. Distance
in meters =340 multiplied by the time in seconds.
Mils.-The mil scale in type EE field glass is quite valuable
in the estimation of distance, if it is remembered that a mil is
the angle subtended by 1 meter at 1000 meters. By measur-
ing the angle in mils subtended by an object whose dimensions
are known, the following formulae will give close estimates of
distance.
- wº R = Range in meters
W = RXM W = Width or height
T 1000 in meters
M = WX1000 M = Number of mils
R.
LINEAR MEASUREMENTS - 91
For example, the telegraph poles on a distant railroad are
known (from previous measurement of such poles) to be 44
meters apart; the distance between two adjacent poles is 40
mils. The range of the railroad is therefore 1100 meters, for:
WX 1000 44 m. X 1000 44000
R=TNT=-10 mils -- ſo
Telemeter. (Coincidence Range Finder.)—A telemeter is
an optical instrument of precision which measures with
extreme accuracy the angle at a distant point subtended by the
length of the instrument placed at right angles to the line of
sight. The instrument, however, is graduated in yards or
meters instead of units of angular measure and is calibrated
to read the range direct and not the value of the subtended
angle. Telemeters are made in different sizes varying in
length from one to six meters, the two meter length being in
most common use with the artillery. With an instrument of
this size distances of 15 km can be measured with an error of
not more than .5 per cent, and at shorter ranges the error is
very small. Telemeters furnish the most rapid means of ,
determining distance and are of utmost value to the navy and
anti-aircraft artillery.
= 1100 meters.
3. STADIA
Telescopes used in plane table work and those mounted on
a transit are almost invariably equipped with stadia wires.
Previous mention has been made of the vertical and horizontal
wires in a transit telescope. The stadia wires are to be found
parallel to the horizontal wire, one above and one below it.
(See Fig. I.)
If the telescope is focused on a graduated rod held ver-
tically and the part of rod visible between the two stadia wires
is measured the distance to the rod from the telescope can be
determined. *
Theory of Stadia Measurements.-Let a and b (see Fig. II)
represent the position of the upper and lower stadia wires.
Let AB be the portion of a rod which appears to be exactly
included between the wires. Any ray of light from A which
passes through O will become parallel to the axis of the tele-
scope after passing the lens. The distance a'b' will therefore
be equal to the distance between the wires ab.
The focal length of the objective is marked “f” and “c” is
92 ORIENTATION FOR HEAVY (COAST) ARTILLERY

2.
àO
.
7
6:
W
#
\\\\\\\ o
O || |\\\\\\\\
&
#
O
ab Cross Wres
caſ Sfaza/7 W&S
Fig. I.-RETICLE IN TELESCOPE
the distance from the objective to the center of the telescope,
a slightly variable quantity, depending on the focusing.
From the similar triangles a'b'O and ABO, a'b':f::AB:D
f -
Or D = nºx AB. The ratio of f to aſb’ (= ab) in any tele-
scope is constant and is usually made 100 to 1. The expres-
f
sion D=ºxAB then becomes D = 100AB, AB being the
intercept on the stadia rod. But the distance required is from
the rod to the center of the instrument. This distance is

|A
-*. *—& 2–
-- c ->+4–f—- /0 –=A
/TV
Fig. II.--THEORY OF STADIA MEASUREMENTS (HORIZONTAL)
D+f-Hc. f--c is practically a constant and is usually taken
as .3m with an ordinary transit telescope. To measure a
LINEAR MEASUREMENTS 93
distance using a stadia rod and transit determine the intercept on
the rod between the wires, multiply this by 100, and to the result
add 1 foot, or 3 m. This rule applies only when the rod
and the transit are on the same level. If the line of sight is
inclined and the rod is held vertically a correction will have
to be made to reduce the reading to the horizontal.
amºm, ºsm, sº sºme sm- *-* *-* -
S.23
zºrs"
Fig. III.--THEORY OF STADIA MEASUREMENTS (INCLINED)
In Fig. III let the line of sight be inclined at an angle, X.
If the rod were held perpendicular to the line of sight the stadia
reading mn would give the distance OE and this added to the
constant c-H f would give the total distance from the center of
the instrument to the rod. This could be reduced to the
horizontal distance RS by multiplying RE, the total distance,
by cos X, but it is not practical to incline the rod until it is
perpendicular to the line of sight, the general practice being to
hold it vertical. This introduces another error since it makes
the reading AB longer than the true reading mn. The angle
AEm= X and AmE is approximately a right angle, hence
AB cos X=mn (very nearly). In other words, the distance
actually read must be multiplied by cos X to obtain mn.
RE=f-H c-H 100 mn=f-H c-H 100 (ABcos X)
RS = RE COS X
..". RS=[f-H c-H 100 (ABcosX)] cos X.
RS = (f-H c) (cos X)+100 AB cos^X,
let f-H c = 1
Horizontal Distance = R.S.
= COSX-H 100ABCOS*X.

94
ORIENTATION FOR HEAVY (COAST) ARTILLERY)
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LINEAR MEASUREMENTS
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96 ORIENTATION FOR HEAVY (COAST) ARTILLERY
\
The vertical distance h (see Fig. III) can be obtained by
multiplying the line RE by sin X.
RE=f-i-c-H 100ABcos X. (See above.)
h = (f-H c-H 100ABcos X) sin X
= (f-H c) sin X-H 100ABsin Xcos X; but sin Xcos X= %sin2X
and h = H therefore H = (f-|-c) sin X-H 100AB}/3sin2X.
By referring to the figure it will be seen that the height of
the instrument above the ground does not change the com-
putations of the height H, between the two points on the
ground. -
Obviously, it would be laborious to perform the computa-
tions indicated by the above formulae for each observation.
Tables known as “Stadia Reduction Tables” are given below
which greatly facilitate stadia computations. Their use is
illustrated by an example.
To Measure the Vertical Angle, X, proceed as follows:
(a) Set up the transit and level it. Bring bubble in level
tube underneath telescope to the center.
(b) Mark the height of the center of the telescope, HI,
above the station on the stadia rod by means of a rubber band.
(c) With the rod on the point whose elevation is desired
sight the telescope with the middle horizontal wire on the
height of instrument, HI, marked by the rubber band.
(d) Read the angle on the vertical limb.
Use of the Reduction Table.—To the rod intercept add the
equivalent of c (in metric units 0.3 m. is equivalent to 0.003 m.
on the rod). Select the tabular quantities for the observed
vertical angle, interpolating for odd minutes. Then the
horizontal distance will be the horizontal tabular number mul-
tiplied by the adjusted rod intercept; and the vertical distance
will be the vertical tabular number multiplied by the adjusted
rod intercept. By putting c into the rod intercept a slight
error is introduced but since this error is exceedingly small it
may be entirely neglected.
The following example will illustrate the use of the Table:
Rod Intercept 1.275 m. Adjusted rod intercept
Vertical Angle 8° 25' 1.275–H0.003 = 1.278
For 8° 25' the Tabular Numbers are
Hor. 97.86 Vert. 14.48
therefore
Horizontal Distance = 97.86 × 1.278 = 125.1
Vertical Distance = 14.48X1.278 = 18.51
Horizontal distances are usually computed to the nearest
decimeter and vertical distances to centimeters.
LINEAR MEASUREMENTS 97
Practical Suggestions for Reading Stadia.—1. Examine the
graduations on the stadia rod carefully before attempting to
read intercepts with the telescope. Rods are usually graduated
in feet or meters and these units subdivided into tenths and
hundredths. -
2. With horizontal wire near the HI on the rod bring the
lower stadia wire on a main division and read the upper wire.
Multiply the difference in the readings by 100 and add the
constant. The result gives the distance to the rod in the units
used, when the transit and rod are approximately on the same
level.
3. Do not take sights longer than 100 to 140 meters if
they can be avoided. With the average telescope errors at
this distance should be less than .50 m. With high grade
instruments and favorable atmospheric conditions sights up to
250 m. may be taken with an average error of about 0.18 m. or
1/1400, but as a rule it is better to divide the distance and make
two readings.
4. To avoid errors due to refraction do not make readings
near the bottom of the rod and avoid working during the
midday hours except on dull, overcast days. -
5. Read and record the vertical angle before reading the
stadia intercept. When proficiency is attained time may be
saved by reversing the process, reading the vertical angle
after the rodman has moved to the next station.
The stadia is primarily intended to secure rapidity rather
than accuracy; nevertheless, with proper care to eliminate the
chief sources of error a high degree of accuracy may be obtained.
4. STEEL TAPE
The steel tape furnishes a convenient, rapid, and economical
means of measuring any distance for any desired degree of
accuracy up to about 1 in 300,000. For topographical sur-
veying a length of 30m is usually most convenient. For base-
line measurement the length should be from 100 to 200m and
its cross section about twenty one-thousandths of a square
centimeter. -
The length of a topographical base will depend first on the
size of the triangulation net to be based on it, and second on
the stretch of level or evenly sloping ground available. Such
bases have varied in length from 3/3 km to 6 or 8 km. It is
nore important to be able to eactend the base by well proportioned
98 ORIENTATION FOR HEAVY (COAST) ARTILLERY
triangles than to measure a long base. The ideal site is on level,
even ground, from which good views of the surrounding coun-
try can be obtained. -
Measurement of Base.—A topographical base should always
be measured with a steel tape. This should be carefully com-
pared with a standardized steel tape before and after using.
A standardized steel tape is one whose exact length when sup-
ported throughout its length for a given temperature and pull,
as well as its coefficient of expansion, has been determined by
the National Bureau of Standards at Washington, D. C.
For an accuracy of 1 in 5,000 the tape may be used in all
kinds of weather, held and stretched by hand, the horizontal
position and amount of pull being estimated by the tapeman.
The temperature may be estimated or read from a ther-
mometer carried for the purpose. On uneven ground the end
marks are given by a plumb bob, which is held at some grad-
uation on the tape. These various distances are then added
together in order to find the total distance between the two
points A and B. (See Fig. IV.)
Fig. IV.-TAPING OVER ROUGH TERRAIN
For an Accuracy of 1 in 10,000 to 1 in 50,000.-The line of
the base should first be cleared of trees, bushes, or high grass;
Small mounds, etc., should be removed.
Each terminal point of the base should, if time allows, be
marked by burying a bottle 1 meter under ground; accurately
centered over this should be built a small masonry pillar, sur-
face flush with the ground. A fine mark should be made in
a metal plug sunk into the surface of the pillar.
Having marked the terminal points, set a transit over one
of them and direct it on the other, over which a pole should have
been fixed; with the transit align stakes at intervals of about
300 meters. By means of this alignment hammer into the
ground square-headed stakes, accurately in the line of the base

LINEAR MEASUREMENTS 99
and at tape lengths from each other, starting from one end of
the base. The tops of the stakes should be just flush with the
ground; on these stakes nail strips of zinc. The trace of the
line of sight of the transit should be marked on the zinc cap and
the edge of the tape should lie along this line when marking
measurements.
In measuring the base, stretch the tape from terminal point
to first stake and from stake to stake; the tension should be
taken on a spring balance and should be that given for the
standardized tape. The end of the tape should be marked by a
fine pencil line or knife cut on the zinc strip nailed on top of
each stake. The temperature of the tape should be taken at
frequent intervals by letting the bulb of the thermometer come
in contact with the underside of the tape.
At the other terminal the small space between the last
graduation and the end of the base should be measured with a
pair of dividers.
Now measure the inclination to horizontal from peg to peg
with a level or transit. Minor undulations crossed by the
tape are to be disregarded.
The base should be measured at least once in each direction,
On a still, dull day, if possible, or in early morning or late after-
IlOOIl.
Precautions to Insure Accuracy.—
1. Find exact points which mark the ends of the gradua-
tions on the tape.
2. Find by what method the tape is graduated and note
how it must be read.
3. See that the tape is straight and exert a steady standard
pull while measuring.
4. Keep tape horizontal and use short lengths on steep
slopes.
5. Keep the right count of tape lengths.
6. The rear tapeman should line in the head tapeman with
the forward point.
Causes of Errors.-The following table shows the conditions
that will cause an error of 3mm in a distance of 30m (1 in
10,000), using a 30m tape.
1. Length of tape differing from a standard by 3mm.
2. Tape not horizontal, one end .043m higher than the
other end. . . . . .
3. Tape not stretched tight. Center of tape 0.21m out
of line.
100 ORIENTATION FOR HEAVY (COAST) ARTILLERY
4. For every 15° F. or 8.3° C. change in temperature.
5. Alignment—one end of tape in line, the other 0.43m
out of line.
6. Sag—the middle of the tape .19m below the ends.
7. For every 15 pounds pull.
8. Marking tape-lengths. Error of 3mm in marking or
plumbing.
Base Line Calculations.—The measured length of a base line
is subject to five corrections:
For standard.
For temperature.
For inclination or slope.
For sag.
For height above sea level.
:
The following example will illustrate the method of applying these various
corrections:
A base line, measured length 1615.818 meters, has been measured as above
described. Two 30 meter tapes were supplied with the equipment, one being
reserved for a “reference tape” and not used in the field; the other was used
exclusively as the “field tape.” The reference tape, when standardized, was
found to be 0.015 meters short at 18° C.
The field tape (supposed to be 30 meters long) when compared with the
reference tape was found to be 0.006 meters longer than reference tape at 22°C.
The temperature of the tape during measurement of the base line was 28°C.
Height of base line above sea level, 1380 meters.
The base line was measured on a slope of 1° 15' for a distance of 700 meters,
the remainder was measured on the level.
1. Standard:
Reference tape was 0.015 m. short at 18° C.
Steel expands 0.00001125 of its length for 1° C.
Therefore, at 22° reference tape was
*****-000iml
10,000,000 = 0.001m Onger.
Therefore the reference tape was
0.015–0.001 = 0.014 m. shorter than standard at 22° C.
Tape used was 0.006 m. long on reference tape at 22°C.
2 ºld tape was therefore 0.014–0.006 = 0.008m shorter than standard at
2° C.
2. Temperature:
Temperature of field tape during measurement. . . . . . . . . . . . . . . . . . . . . 28° C.
Temperature of tape when compared with reference tape. . . . . . . . . . . . 22° C.
-
Difference 6° C.
Increase in length:
6 × 30 × 112.5
iOOOOOOO− =0.002 m.
The actual total variation in length of field tape is therefore:
For Standard 0.008m short
. For Temperature 0.002m long
. . * * Total, 0.006m short º
The total caráction for standard and temperature to be applied to the meas-
ured length of the base line is therefore:
1616
0.006 × T30T = 0.323m
LINEAR MEASUREMENTS 101
3. Inclination or Slope:
For 700 meters the base line has a slope of 1° 15'.
The correction is, therefore
700 (1 —cos 1° 15') = 0.168 meters.
4. Sag:
In the measurement of a base it is desirable that the whole length of the tape
should as far as possible be supported by the ground, so that no correction is
necessary for the sag of the tape. Where the ground is uneven, it is customary
to support the tape at intervals by stakes, but it may happen in the measure-
ment of a base that a ravine has to be crossed. In such a case the sag, i.e., the
difference between the length when suspended and when laid on a plane surface,
must be determined and corrected for.
If s = the correction for sag in meters.
l=the length of the tape suspended between two supports in meters.
w = the weight of the tape in pounds.
t=the tension applied in pounds.
s =lw?/24t2.
5. Height above Sea Level:
If the base line is measured at a mean height (h) above the sea level, it will
require a correction of h
-R × length of base.
Where R = the radius of the earth, which may be taken as 6,370,000 meters.
In this case h = 1380 m. The correction is therefore
1380
6,370,000 X 1616 = 0.350m.
Corrections 1 and 2 may be either positive or negative; 3 and 4 must always
be negative and 5 will usually be negative.
Combining all corrections Meters
1. Standard and Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . — 0.323
3. Inclination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . —0.168
4. Sag.:...:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . — 0.000
5. Height above Sea Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . –0.350
Total correction... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . — 0.841
Measured length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.818
Corrected length of base line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1614,977
5. THIANGULATION
A triangulation system is determined by first locating and
accurately measuring a base line as has just been described.
From this base line, triangles are extended by measuring
angles and computing the lengths of the sides trigonometri-
cally. The general method of extending a triangulation
system is discussed in Chapter II.
It is obvious that an error in the length of the base line will
be carried throughout the entire framework, and will be
multiplied in magnitude in the location of distant points of the
framework. In like manner errors in the measurement of
angles will cause errors in the coordinates of the points based on
the calculations. It is therefore necessary to keep both errors
within the allowable errors for the work being done.
102 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Computation of Sides.—In extending a series of triangles on
a given base line, the base line is the only side of the series of
triangles that is measured, the others being determined by
computation.
7.
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Fig. V.--TRIANGULATION
In Fig. V let c be the base line and T a tower whose dis-
tances from the ends of the base line are desired. The angles
are measured with the transit and their values adjusted. In
case the point C is inaccessible the angle y may be obtained by
the formula y = 180°– (o-H 6); this, however, leaves no check
on the accuracy in measuring the angles o and 8.
The length of the sides a and b are to be found from the
law of sines.
sin o. a c sin o.
e — — 8, 5 g
SIn y C ; SIn Y
sin 3 b - c sin 8
sin YT c; - sin Y
Applying logs,
log a = log c-Hlog sin o-H colog sin Y
log b = log c-Hlog sin 3+colog sin Y
Altitude.—Fig. V illustrates the method of obtaining alti-
tude or vertical distance in a triangulation system. The
angles q and 6 are measured when the transit is set up at the
stations A and B. The difference in altitude of stations
A and B must e determined by some available means. The


LINEAR MEASUREMENTS 103
horizontal distances a and b are determined by computation
in the triangle ABC. The height TC' is then computed by
using the formulas:–
TC' = a tanó TC' = b tan q
log TC' = log a-H log tanó log TC' = log b-Hlog tan (b
The two values of TC’ obtained are the altitudes of T above
horizontal planes through the transit at A and at B and should
differ by the difference in altitude of A and B if these points
are not of the same level. To obtain the altitude of T above
the ground plane it will be necessary to add to the height TC'
the height of the transit.
CHAPTER VI
PLANE TABLE
MATERIAL
ORIENTATION
TRAVERSE
INTERSECTION
RESECTION
i
The plane table is a surveying instrument consisting of
a drawing board supported on a tripod, and a ruler to which
a pair of sights or a telescope is attached. It is used in the
field for projecting the lines and points of a survey directly
upon the drawing, thus eliminating the measuring of hori-
Zontal angles and the use of the protractor.
On the western front the plane table is being extensively
used for such work as: - -
1. Running a traverse from a triangulation point to deter-
mine the coordinates of a gun position and the Y-azimuth of
an aiming line.
2. Facilitating the reconnaissance of aiming points and
the prevention of errors in their identification.
3. Verifying the fact that the operation which is to be
undertaken with a transit is geometrically correct (for ex-
ample, in locating an unknown point care must be taken that
it is not on the circle with the visible known points and that
all intersections are made at large angles).
4. Checking topographical work and computations by
furnishing approximate data.
5. Sketching a battery position to show details and main
plan.
6. Locating points by intersection and resection. Filling
in details on large maps.
In a warfare of movement where time becomes a very im-
portant factor the plane table is frequently used to determine
topographical data for tractor artillery. However, for railway
artillery the determinations are not sufficiently accurate and
more precise surveying instruments must be used.
PLANE TABLE 105
1. MATERIAL
Plane Table.—The table itself consists simply of a draw-
ing board mounted on a tripod equipped with leveling screws
similar to those on a transit. It is connected to the tripod
by means of a spindle allowing the board to be revolved in
a horizontal plane. A winged nut under the tripod head
makes it possible to clamp the board in any position desired.
A sheet of drawing paper is attached to the plane table by
means of thumb tacks or clamps at the corners. Some boards
are constructed with a magnetic needle pivoted in a trough in
the edge of the board, others are supplied with a simple box
compass. Both are used to give the board a certain position
with respect to the North line.
A-Table.
BaAlidade.
C-Telescope.
D-Wert, circle,
E-Vernier.
F- Level.
Fig. I.-PLANE TABLE
Alidade.—The alidade consists of a ruler with sight vanes
or a telescope. There are four types in common use and a
brief description of each will be given.
(a) The telescopic alidade is used for accurate work and
has a ruler 6 cm. to 7 cm. wide to provide a firm base for the
telescope. Level tubes are frequently mounted on the ruler
or on the box compass to assist in leveling the table. A brass
column firmly fixed to the ruler carries a telescope which is
similar to the one on the transit having stadia wires, vertical
limb, and level tube.

106 ORIENTATION FOR HEAVY (COAST) ARTILLERY
(b) A triangular wooden ruler can be used as an alidade
with fairly good results. The top edge is used for sighting
and the other two edges for ruling.
(c) The metal ruler with folding sight vanes is a common
form of alidade. One vane is simply a vertical slit and the
other has a fine wire stretched vertically across a narrow
opening. -
(d) Leveling alidade.—This instrument consists of a
ruler graduated in millimeters with a level mounted at its
middle. Two small cams, one at each end of the ruler, are
used for leveling it. Folding sight vanes are used and by
means of a scale on the forward vane that is graduated in
units equal to one one hundredth of the distance between the
vanes the slope between two stations can be read direct.
Clinometer.—In rough work vertical angles are some-
times measured by a small instrument known as a clinometer.
It consists of a circular scale of degrees pivoted at the center
with a weight attached to a point on the circle. When the
case in which the scale is mounted is held vertically the weight
swings to the bottom causing the circle to revolve. The
distant point is sighted through peepholes in the case and the
graduations on the circle are read at the same time. When
the line of sight is horizontal the scale reads zero; when it is
inclined upwards, the black figures on the scale come oppo-
site the index and when it is inclined downwards the red
figures appear. This method of reading vertical angles is
likely to be at least 1° in error and if accurate measurements
are desired a telescope with a vertical limb should be used.
Scales.—In making a plane table survey distances are
usually measured by stadia or pacing. Before beginning the
work in the field the scale of the drawing or survey must be
decided upon, and a working scale constructed accordingly.
It is usually best to use a scale that will make the map large
enough to fill the sheet of drawing paper on the board conven-
iently. When using stadia rods reading in meters the follow-
ing formula can be used to find the map distance. (Map
distance is distance measured on the map that represents a
given horizontal distance on the ground.)
Scale of Map X 100×100 = Map Distance in centimeters
per 100 meters. The scale of the map will be expressed as
a fraction, *10,000 meaning 10,000 units on the ground are
represented by one unit on the map.
PLANE TABLE * 107
- 1 º -
Example: Scale of map to be T0.005. Find the map distance in centi-
meters of 100 meters.
1
10,000 X 100 × 100 = 1 cm.
If distances are to be measured by pacing, first determine
the average length of your pace by walking over a measured
course several times keeping an accurate count of your paces.
Divide the total distance in centimeters by the total number
of paces. This gives the length of your pace in centimeters.
The map distance in centimeters for 100 paces is found
by using the formula:
Scale of Map XLength of PaceX 100 = Map Distance in
centimeters of 100 paces. -
Scale of map to be expressed fractionally and length of
pace in centimeters.
1 -
Example: Scale of map is TOOOT. Length of pace is 80 cm. Find map
distance in centimeters of 100 paces.
1. :
1000 X 80 × 100 = 8 cm.
If one prefers to count strides instead of paces the above
formula may be used by putting the length of a stride in
place of the length of a pace and the result will be the map
distance of 100 strides. -
Having determined the map distances for 100 meters or
paces a working scale should be constructed using a stiff strip
of paper about 3 cm. wide and 30 cm. long cut with straight
edges. Take a number of map distances that will give a
length of 24 to 26 cm. of the scale and divide this length graph-
ically into the number of distances used. Mark these points
in hundreds on the scale, beginning at the second mark from
the left with the zero. The space to the left of the zero sub-
divide into tenths or twentieths. If the map distance should
be a whole number of centimeters the scale can be laid off
with a scale of centimeters without having to make the divi-
sions graphically.
Example: Map distance in centimeters for 100 paces was
found to be 2.12 cm. Multiply 2.12 by some number that
will give a length of about 24 to 26 cm. as 12. The result
is 25.44 cm. Lay off on a line AB (see Fig. II) a length
equal to this distance. Draw AC making any convenient
angle with AB. On AC mark off with the compass from A
12 equal spaces of about one centimeter. Connect D with
B and draw lines from the divisions of AC parallel to DB cut-
108 ORIENTATION FOR HEAVY (COAST) ARTILLERY
ting AB. AB will then be divided into 12 equal parts. Mark
the scale by these divisions as shown in the figure.
C.
Scaſe ſºn
Fig. II.-CONSTRUCTION OF A WORKING SCALE
2. ORIENTATION
In making a survey with a plane table it is necessary after
occupying the first station to set up the board at each succeed-
ing station so that all lines on the drawing will be parallel to
the lines corresponding on the ground. This adjustment of
the table is known as orientation and is usually done by means
of a compass, or by backsighting.
To Orient the Board by Compass.-Set up the tripod with
board loosely screwed to it and level the board carefully by
means of the bubble tubes on the alidade. Free the needle
by turning the cam and turn the board slowly around until
the needle Swings from side to side in the trough. Let the
needle settle, turning the board as necessary so that the
needle when settled lies directly along the north and south
line (the median line of the trough). Without changing the
position of the board reach under and tighten up the screw
of the tripod. Care must always be taken not to turn the
tripod Screw too tight, as the threads are likely to be stripped
by rough treatment. The board is now oriented. Draw a
line parallel to the needle on the paper and mark the north
end with a half arrow. Above this write M. M. or N. (mag-
netic meridian or north).

PLANE TABLE 109
If a box compass is used on the board instead of the needle
pivoted in the trough the plane table is turned into such a
position at the first station that the survey will lie entirely
on the drawing. The box compass is then placed on the
board near the edge and turned until the needle points to
the North mark on the needle circle. Draw a light line at
the edge of the compass box parallel to the needle and mark
this as before described with an arrow and the letter “N.”
The compass can now be removed while drawing rays with
the alidade. (Any line drawn with the alidade on the map
is called a ray.) At the next station after leveling the table
the compass is placed against the North line and the board
turned until the needle lies along the north and south line of
needle circle. The board is now oriented.
To Orient the Board by Backsighting.—Having plotted
(located and drawn in) a station and arrived at a point far-
ther on to which you have sighted and drawn a ray, set up
the tripod and board, measure off with the scale the distance
between the two points on your ray and stick a pin in the
point found. This is your present position. Place the ali-
dade against the pin and along the ray between the two points
and turn the board until the station you have just come from is
sighted. Tighten up the clamp screw without moving the board
and it will be oriented. Verify this by reading the needle.
3. TRAVERSE
The term traverse is applied to the route followed by a
surveyor in making a map of a number of points on the ground.
Being at a point A it is desired to make a map of the points
ABCD on the ground (see Fig. III).
First set up the plane table over the station A. In setting
up a plane table over a station it is necessary to:
1. Place the table so that the point on the map is verti-
cally over the station on the ground it represents.
2. Level accurately by the same method as used with a
transit.
3. Orient carefully by compass or backsight.
The point “a” on the map is located so that the complete
survey will be well spaced on the paper.
With the table properly set over “A,” stick a pin in the
110 ORIENTATION FOR HEAVY (COAST) ARTILLERY

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Fig. III.--—TRAVERSE
point “a” on the map. (Capitals are used to represent
points on the ground and small letters points on the map.)
Lay the alidade against the pin and pivot it until the point B
is sighted. Draw a ray toward B. Read the stadia inter-
cept, if measuring distances by stadia, and also the vertical
angle. Move to B and upon arrival set up the board approx-
imately over the station. With the working scale measure
off the distance (corrected to the horizontal) from “a.” Now
set up the table carefully over B as described above, using
particular care to orient accurately. As the needle may be
affected by local attraction the orientation should be checked
by back sighting. With the alidade pivoted at “b” draw a
ray toward C, read the stadia intercept and vertical angle.
Move to C and repeat the steps taken at B. Each station on
the traverse is occupied in the same manner and if the work is
done accurately the last ray drawn from “d” toward A will
pass through “a.” Very likely there will be a small closing
error which may be adjusted by changing the direction and
length of the last ray or by distributing the error proportion-
ately over the entire traverse.
Adjustment of Traverse.—Figure IV shows method of
graphical adjustment for a traverse run between two points,
the positions of which are already plotted on the record sheet.
Proceed as follows:
PLANE TABLE 111
Figs. IV and V.-ADJUSTMENT OF TRAVERSES
Plot the traverse, as actually measured in the field. In
plane table work this is already done. Draw a line AB from
the starting point to the ending point of the plot. Now from
the record sheet measure the straight line distance between
the record positions of A and B. Measure off this distance
from A on line AB. Call the end of the distance b.
Take any convenient point O and draw OA and OB. Now
from b draw a line parallel to OA. Where this line crosses
OB is the new position (B') for B. From B' draw a line
parallel to AB. Where this line intersects AO is the new
position of A.

112 ORIENTATION FOR HEAVY (COAST) ARTILLERY
To find the new position of station 1, draw a line from A'
parallel to A1 and where it intersects O1 is the new position
1' of 1. From 1 draw a line parallel to 1–2, etc.
The traverse A', 1’, 2’-B' is now adjusted and can be
traced off on to record sheet.
Fig. V shows a method when a traverse is run from a known
point back to the same point. Plot the traverse as measured
in the field. The point A’ should be at A, but due to errors,
does not so plot. On a long straight line OA lay off from O,
in succession, the lengths of courses (A–1, 1–2, 2–3, etc.).
From the end of this line lay off in any convenient direction
the line AB equal to the error in closure A'A. Connect the
outer end of this offset line to O. Now from each succeeding
station point on the long line, draw a line parallel to the offset
line AB. *.
Returning to the plot of the traverse, draw through each
plotted station a line parallel to the final closing line A/A and
in the direction of the closing station. On each line lay off
its respective offset length, giving new positions for each sta-
tion. Connect these new stations and the traverse is adjusted.
In locating a position by a traverse the closing error should
be less than 1 per cent. of the total distance traversed; however,
in making a rough sketch of a battery position a three per
cent. error may be allowed. The importance of the work will
determine the permissible error. In case a traverse is to be
made between a known and unknown point it should be made
to close by returning to the known point by a different route,
or continued beyond the unknown point until another known
point is reached.
An angular traverse has for its object the determination
of the direction of an unknown line by referring it to a line
of known direction. In this case only angles are measured,
the lengths of the sights not being determined. Careful
orientation is particularly essential and short sights are to
be avoided.
4. INTERSECTION
In making a traverse, points visible from the stations may
be located on the map without measuring the distances to
them. This is done by drawing rays to the points from two
or more stations of the traverse when the table is oriented.
This method of locating points is called intersection.
When the station A was occupied suppose rays were
\ PLANE TABLE 113
drawn toward the points E and F (see Fig. VI). After mov-
ing to B and orienting the table draw the ray E from “b.”
The intersection of the two rays drawn toward E locates the
point “e” on the map. The second ray to F was drawn from
the station C and its intersection with the first ray determined
the point “f.” Rays to locate points off the traverse should
always be drawn from stations selected so that the inter-
sections will be at large angles. In very accurate work three
or more rays are drawn to locate a point by intersection.
They should meet in a point but frequently a small triangle
of error is formed and the true point is taken to be about the
center of this triangle.
5. RESECTION
This method of locating points on the map is a modifica-
tion of the method of intersection. Its chief characteristic
is that the point determined by the intersecting rays is the
station occupied by the plane table. This means that a
plane table can be set up anywhere and the corresponding
point on the map can be found by resection provided three
points already plotted are visible from the unknown station.

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114 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Solution. With Oriented Board.—Having previously plotted
the position of points “a,” “b,” “c,” and “d” it is desired to
locate the station G on the map from which the stations B and
C can be seen (see Fig. VI). Set up the table over the station
G and orient it carefully with the compass. With a pin at
“b” pivot the alidade and with it sighted on B draw a ray
past the approximate position of “g.” Repeat the operation
using “c” as a pivot. The intersection of the two rays
locates the point “g.” If other stations are visible from G
other rays may be drawn as a check on the accuracy of the
work. If the rays form a small triangle instead of intersect-
ing at one point the center of the triangle may be taken as
the true point.
Solution when the board is not oriented. This is known
as The Three-Point Problem and is the most important prob-
lem that can be solved by using the plane table. It permits
the location on the plane table of any unknown point at which
the plane table may be set up having plotted the positions of
three or more visible known points. There are three distinct
methods of solving the problem and several different solu-
tions under each method. However, only the most impor-
tant solutions will be given.
With tracing paper.
1. Field Method 3 Triangle of error.
Italian Method.
2. Graphical—Construction of “segments capable.”
3. Mathematical { U. S. Method.
Relevement.
The first method is customarily used in plane table work.
The second can be used either on a plane table or in connection
with transit measurements of the angles between lines from
the unknown point to the known points. The third method
requires the use of a transit and trigonometry. The first two
methods will be discussed in this Chapter and the third in
Chapter XI.
Field Method with Tracing Paper.—This method can be
used with any number of visible points that are plotted on
the map. The table is set up over the unknown station and
leveled but not oriented. Fasten a piece of tracing paper
over the map with thumb tacks and stick a pin into the board
at Some convenient point to represent the unknown station.
With the alidade pivoted at this point draw rays to the visible
stations and mark them. Next loosen the tracing paper on
PLANE TABLE 115
the board and shift it over the map until each ray passes
through the point on the sketch representing the station to
which the ray was drawn. With the sheet in this position
prick the map at the intersection of the rays. This gives the
location on the map of the station occupied.
Triangle of Error.—Orient the table as accurately as pos-
sible by estimation. Clamp and draw rays toward your
position from “a,” “b,” and “c” by pivoting the alidade on
these points and sighting on A, B, and C respectively.
If the table has been oriented correctly these three rays
will intersect in a point which will be the point sought. Most
likely, however, a small triangle of error will be formed. (See
Fig. VII.) By certain rules that will be given later the true
Fig. VII.-LOCATION OF POINTS BY RESECTION
position of the point can be closely approximated. Place
the alidade with one edge against this approximate position
of the point and also pivoted against “a,” “b,” or “c.” Now
turn the board until the alidade is sighted on the station
represented by the point where it is pivoted. With this new
orientation draw the three rays as before. The rays will
possibly form a very much smaller triangle than was made
on the first trial. (See Fig. VIII.) The small triangle to
the right of the triangle KLM was formed by the rays drawn

116 ORIENTATION FOR HEAVY (COAST) ARTILLERY
A-A2/27. Sooyºr T ~ – ——
A-A/32/277/2/2/2//
Fig. VIII.-TRIANGLES OF ERROR
when the board had been given the new orientation. Con-
tinue the process until the triangle disappears and the rays
intersect in a point.
Rules for Reducing the Triangle of Error.—The term “point
sought” will be understood to mean the true position on the
map of the station where the plane table is set up. The sur-
veyor is assumed to be facing the signals or stations and the
directions right and left are given accordingly.
Rule I.-The point sought is always distant from each
of the three rays in proportion to the length of the rays.
Rule II.—It will always be on the right or left of all three
rays, never to the left of one and to the right of others or
vice versa. -
Rule III.-The “great triangle” is the one formed by
the three points a, b, and c on the map and the “great circle”
refers to the circle through these same points. When the
point sought is within the great triangle it is within the tri-
angle of error. (See Fig. VII, Station E.) -
Rule IV.-When the point sought is without the grea
triangle but within the great circle the ray drawn from the
middle station lies between the point sought and the inter-
section of the other two rays. (See Fig. VII, Station D.)
Rule W.--When the point is without the great circle it is

PLANE TABLE 117
always on the same side of the ray from the most distant point
as the intersection of the other two rays. (See Fig. VII,
Station F.)
Rule VI.—After forming the first triangle of error deter-
mine on which side of the triangle the point sought lies. (This
rules does not apply if the point sought is within the triangle
of error.) -
Rule VII.-Turn the table slightly and draw new rays from
the visible stations. These rays will form another triangle of
error similar to the first. (See Fig. VIII.) It is advantageous
to turn the table in such a direction that it will pass through the
position of true orientation. The triangle obtained in this case
will be similar to the first but inverted. The intersection of
the lines joining the corresponding vertices of these two
similar triangles will be near the point sought, being always
between it and the great triangle.
Rule VIII.—If the point sought lies on the great circle it
Fig. IX.-ITALIAN METHOD

118 ORIENTATION FOR HEAVY (COAST) ARTILLERY
cannot be located graphically or by any other known method.
To locate its position it will be necessary to use another com-
bination of three points that are not on a circle through the
point sought. Usually one new point together with two of
those first selected will give the desired combination.
Italian Method.—Let a, b and c be the three known points
and P the unknown point. (See Fig. IX.) Draw the base
ab. Place the edge of the alidade along it with the objective
toward B. Without disturbing the alidade turn the plane
table so as to sight on the point B. With the plane table in
this position turn the alidade about a and sight on C. Draw
a line along the edge of the alidade. This will be the line am.
Next place the edge of the alidade along ba with the objective
toward A and turn the plane table so as to sight on the point
A. Turning the alidade about b, sight on C and draw the
line, which will be bn. The intersection of am and bm, deter-
mines the point y. The plane table is now oriented by plac-
ing the edge of the alidade on the line ye and sight on C.
The plane table being oriented, it is only necessary to sight
on A and B and draw the two lines which should intersect at P.
The proof of this method involves only simple geometrical
theorems and can readily be understood by drawing a circle
through the points a, b and y.

f b S
Fig. X-CONSTRUCTION OF “SEGMENTS CAPABLE”
PLANE TABLE 119
Graphic Solution.—With the table set up at the unknown
station P (See Fig. X) place a sheet of paper over the map
and pin it down with thumb tacks. Stick a pin in the board at
any convenient point and with this as a pivot draw rays to
A, B, and C, exactly as described when using a sheet of trac-
ing paper. Remove the sheet, which will have on it the
angles subtended by the lines ab and be. At “a” on the
map construct an angle equal to the angle subtended by ab
and at “c” construct an angle equal to the angle subtended
by be. (See Fig. X.) (This will require a pair of compasses
in addition to the regular plane table equipment.) At “a”
draw a perpendicular, x, to the line AR; draw y perpendic-
ular to cs. Draw m, the perpendicular bisector of ab; and n,
the perpendicular bisector of bc. With the intersection of m
and x as a center draw the circle through a and b; similarly
draw the circle through b and c using the intersection of n
and y as a center. The intersection of these two circles locates
the position of the unknown station on the map.
This is a rapid solution of the three point problem and can
be made very accurate if care is used in handling the dividers,
laying off the angles and keeping a fine point on the pencil.
The most accurate determinations are made by this method
when the rays from “a,” “b,” and “c” intersect at large
angles and the unknown point is some distance from the great
circle. The errors in the determination of a point by this
method can be made extremely small by observing the above
precautions and using a large scale map.
If three known points, visible from an unknown point, are
plotted on a map the angles between the lines to the known
points can be measured by a transit and the location of the
known point on the map determined graphically as described
above without the use of the plane table.
The common practice is to use coordinate paper on the plane
table and plot the known stations from their coordinates as
given in the “Lists of Triangulation Points.” In locating a
point by resection or intersection the coordinates can then be
read directly from the plot. In running a traverse the start-
ing point (usually a triangulation point) is plotted and the
board carefully oriented from a line of Y-azimuth. The
coordinates of every station on the traverse can now be read
direct and in this way the position of a gun can be determined
within 10 to 20 m. very quickly.
CHAPTER VII
LEVELING
DEFINITIONS
MAP LEVELING
BAROMETRIC LEVELING
TRIGONOMETRIC LEVELING
SPIRIT LEVELING
ERRORS
i
The principles governing linear measurements have been
discussed with particular reference to horizontal distances.
It is now proposed to discuss the measurement of vertical
distances, or what is the same thing, the measurement of
differences in altitude or elevation. The heavy artillery
officer is concerned with the difference in altitude between his
battery and the target and between the different guns in the
battery. It is therefore necessary that he understand the
means of obtaining this difference in altitude.
1. DEFINITIONS
Leveling.—In this discussion “leveling” will be taken to
mean the determination of difference in altitude between
given points or stations. -
Datum.—An imaginary level surface all points of which are
assumed to have an elevation of zero, and to which all eleva-
tions in a given survey are referred. Mean Sea Level affords
the most convenient datum, although an arbitrary datum may
be assumed. The distinction between a horizontal surface and
a level surface should be kept in mind. It is readily seen that
due to the curvature of the earth, the level surface of mean sea
level is in reality a curved surface. Datum, datum line, and
datum plane are synonymous terms.
Elevation or Altitude.—The distance of a given point or
station above or below the datum. The term “altitude” will
be used exclusively in this discussion.
Plane of Sight.—The line of sight of a telescope instrument
used as a level will always lie in a horizontal plane of sight no
matter in what direction the telescope may be pointed, pro-
vided the instrument is in adjustment and properly leveled.
LEVELING 121
Bench Mark (B.M.).-A fixed point of reference whose
altitude with respect to some assumed datum is known. It is
used either as a starting or closing point for leveling.
Stations (Sta.).-Points whose altitudes are to be ascer-
tained or points that are to be established at a given altitude.
It is where the level rod is held and not where the instrument
is set up as is the case in a transit traverse. n
Height of Instrument (H.I.).-The altitude of the plane of
sight with respect to the assumed datum.
Backsight (B.S. or +Sight). —A sight taken on a rod held at
a point of known altitude to determine the H.I.
Foresight (F.S. or -Sight).-A sight taken on a rod held at
a point whose altitude it is desired to ascertain.
Turning Point (T.P.).-A more or less temporary point of
known altitude used to hold the altitude while the instrument
is being moved from one set-up to another. *
2. MAP LEVELING
Use.—One of the first things a Battery Commander must
do when he occupies a battery position is to determine the
altitude of the directing gun. As a general rule, this is taken
directly from the Battle Map (or Plan Directeur). The Battle
Map, as has been shown, is constructed with great care and
shows by means of contours the elevations of all points on the
terrain.
The position of the station whose altitude is desired is
plotted on the map. It is then possible by reading the altitude
of the nearest contour line, to determine the altitude of the sta-
tion within one contour interval. By interpolating between
bracketing contour lines the altitude may be more accurately
obtained. In determining altitudes in this manner the limits
of accuracy of the map must be borne in mind. If the contour
lines are close together, indicating steep slopes, it is obvious that
a slight error in plotting the position of the station on the map
may result in an error in reading its altitude from the map.
Moreover, the errors inherent in printing contours on a map
may cause an appreciable error in their use in this connection.
Accuracy.—The usual contour interval employed on the
1:20,000 Battle Map is 5 meters. In rough country this may be
increased to 10 or even 20 meters. The altitude of the directing
gun must be known to within 5 meters. It is therefore obvious
that the artillery officer must exercise due judgment in reading
122 ORIENTATION FOR HEAVY (COAST) ARTILLERY
an altitude from the map. If there is likelihood that map
leveling may give errors in altitude which are inadmissible in
the firing data, it is necessary to use a more accurate method.
3. BAROMETRIC LEVELING
Atmospheric Pressure.—At 0° C. the weight, at sea level,
of a column of dry air one inch square is equal to a column of
mercury 29.92 inches (760 mm.) high. As we ascend, the
weight of the air column decreases so that the height of the
equivalent mercury column decreases at the approximate rate
of 0.1 inch for every 90 feet ascent above sea level. In the
metric system this rate is 9 mm. for an increase in altitude of
100 meters.
Aneroid Barometer.—If, then, we have an instrument which
will measure the difference in atmospheric pressure between
two points we have a means of leveling. Such an instrument
is the aneroid barometer. However, the problem is not as
simple as it may at first appear. Atmospheric pressure varies
not only with altitude above sea level, but also with temper-
ature, hygrometric state (humidity) and latitude. In Baro-
metric Leveling the effects of these other causes of variation
must be eliminated as far as possible.
The Aneroid Barometer usually employed in America is a
watch-shaped instrument with a dial face about 2% inches
in diameter, provided with a pointer which is connected to an
airtight metallic coil or vessel in the case of the instrument
which is sensitive to changes in atmospheric pressure. The
dial is graduated with a scale of altitudes from zero to 3000
feet with a least reading of 10 feet, and also a scale of heights
of a mercury column. Means are usually provided for setting
the zero of the scale of elevations at any barometric height,
and also for adjusting the scale of height of the mercury col-
umn. Change in pressure causes a change in the shape of the
coil, which movement is communicated to the pointer, causing
it to move over the dial, thus enabling the observer to read the
amount of change in pressure in terms of difference in altitude.
The best method of barometric leveling requires the use of
two aneroids. Simultaneous readings are then taken at each
station. If the stations are not far apart all causes of variation
will be substantially the same at each and therefore eliminated,
except temperature, which with considerable difference of
altitude will always be less at the upper than at the lower
LEVELING 123
station. When simultaneous observations cannot be made,
the stations should be occupied with as little interval of time
as possible. Better results will be obtained if the time of
observation can be so chosen as to take advantage of calm,
bright, dry weather. The difference in temperature at the
two stations is of no consequence if aneroid barometers are
used. These instruments are usually compensated for tem-
perature and are, moreover usually kept at the temperature
of the body. If mercurial barometers are used it is necessary
to apply a temperature correction.
Accuracy.—Barometric leveling should be employed only
in case exact methods are impracticable or great accuracy is not
required. It will be seen from a consideration of the causes of
variation in the weight of the atmosphere and the fact that a
slight variation in weight corresponds to a relatively large
change in altitude, that it is impossible to obtain results of even
moderate accuracy except under ideal conditions, which will
rarely exist. If possible a mean of several observations made
under apparently similar conditions should be taken.
General Rules.—(1) Keep the barometer at a temperature
as nearly constant as is practicable. This is best done by
keeping it in an inner pocket, where it will have nearly the
temperature of the body. Remove it from the pocket only for
the purpose of reading and return it as soon as possible.
(2) Always hold the barometer with its dial horizontal
when reading it and tap it gently two or three times with the
finger or pencil before reading.
(3) In clear, settled weather it will be found that the
pressure variation due to change of temperature follows a
regular law. Beginning at about 9 A.M. the elevation scale will
show a rise of about 10 feet per hour for about 4 hours. It will
then remain stationary until about 4 P.M., and will then fall
regularly until about 7 P.M. when the same reading as at 9 A.M.
will be reached. A knowledge of this change will enable
proper corrections to be made.
(4) In unsettled weather, before or after a storm, note, if
possible, the movement of the needle for an hour before starting
work to ascertain its direction and rate of change, and thus be
enabled to make proper corrections.
4. TRIGONOMETRIC LEVELING
Method.—Trigonometric Leveling consists in the deter-
mination of the difference in altitude between two points by
124 ORIENTATION FOR HEAVY (COAST) ARTILLERY
means of the angle measured at one of them between the
horizontal or level line, and the other; or by measuring the
zenith distance of the other. This method will be of frequent
application in the topographical operations pertaining to the
artillery. The shorter the sights, the more accurate will be the
results obtained. This form of leveling has been discussed
briefly under the Chapter on Linear Measurement.
By Stadia.—In the discussion of Stadia measurements it
was shown that the vertical distance from the instrument
to the point sighted on can be obtained if the rod intercept and
the vertical angle to the point are known. The vertical
distance is computed by means of tables. If the rod be in-
clined so as to be perpendicular to the inclined line of sight,
then it is possible to obtain the inclined or slope distance
directly without referring to tables. Let the slope distance
be m, the vertical angle be q, and the vertical distance be h.
Then,
h = m sin q
It is necessary to take into consideration the height of the
instrument above the ground when the altitude of an object on
the ground is to be determined. If the object is situated at
about the same distance above the ground as the instrument,
this correction need not be made. For long distances it is
also necessary to make certain corrections for atmospheric
refraction and for curvature of the earth.
Correction for Apparent Level.—This correction, which is
negligible for sights shorter than two or three kilometers, takes
into consideration the refraction of the atmosphere and the
curvature of the earth. The curvature of the earth makes a
point appear lower than it really is, and refraction makes it
appear higher. The effect of curvature is the greater.
If NA = the combined correction for the refraction and
curvature and D = the distance in kilometers, the following
table may be used:

D (in kilometers). . . . . . . . . . . . . . . ... || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 | 12
N A (in meters). . . . . . . . . . . . . . . . . . 0.3|0.61.1|1.72.43.34.35.56.88.29.7
2
C = Refraction Correction.
K= Curvature Correction.
When the altitude H of the ground at the station A is
known and the altitude H’ of the sighted point B is unknown,
LEVELING 125
let o = the slope measured, positive for an ascending slope
and negative for a descending slope,
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D = the horizontal distance AB,
h = the height of instrument at A above the ground,
and h' = the height of the sighted point B above the ground.
Then the formula becomes, with due regard for the sign of
“a,”
H’=H+D tan a-i-NA--(h—h')
in which NA is the correction for apparent level applied only
for long sights. The quantity h-h' becomes zero if the sighted
point is exactly the same height above the ground as the
sighting instrument. &
When the altitude H' of the sighted point is known, and the
altitude H of the ground at the station is unknown, we can find
the altitude of the instrument station by using the same
formula with the signs changed. Thus,
H = H'—D tan a –NA— (h—h')
Example: Assume that it is desired to obtain the altitude of a distant station,
B, from station A. Elevation of A is given as 693.7 meters and from the coor-
dinates of the stations the distance, AB, has been computed to be 67.95 meters.
We set up at A and find that we cannot see station B, because of trees, but we
can see the lower limb of a tree alongside it, which we afterward measure and
find to be 3.3 meters above B. Sighting on the lower limb of this tree we find the
vertical angle to be 4° 36'. The telescope is 1.4 m. above A. Our computations
are then as follows:
D tan o' NA from Table
log 6795 = 3.832.189 NA for 7 km. =3.3 m.
+log tan 4° 36' =8.905570 NA for 6 km. =2.4 m.
log D tan o' = 2.737759 - Diff. for 1 km. = 0.9 m.









126 ORIENTATION FOR HEAVY (COAST) ARTILLERY
, 795
D tan or =546.7 =T. 1000 × 0.9 = 0.7 m.
NA for 6.795 km. = 2.4 + 0.7 = 3.1 m.
(h—h’)
h = 1.4
h’= 3.3.
h—h’= –1.9
Substituting in the f
H = 693.7 - 546.7 -H
rmula, we have
1 + (−1.9) = 1241.6 meters = Altitude of “B.”
:
3.
5. SPIRIT LEVELING
Instruments.-Spirit leveling is so called because it makes
use of a spirit level attached to a telescope, or other device for
defining a line of sight, to make the line of sight level. The
term “differential leveling” is applied to the operation of
obtaining the difference in altitude between two stations by
means of a spirit level.
The instruments in general use for spirit leveling are:
1. Engineer's Complete Transit or Theodolite.
2. The Wye Level.
3. The Dumpy Level.
4. The Hand Level.
Since the Engineer's Complete Transit is the instrument
almost exclusively used by the Battery Commander in the field
work connected with his problems, the discussion will be con-
sidered to apply to it alone, although the Theory of Spirit
Leveling applies equally well to the otherinstruments mentioned.
Theory.—There are two steps in leveling for any single
set-up:
(1) To find how far the plane of sight is above a point of
known altitude. This is the backsight rod reading.
(2) To find how far a given station is below the plane of
sight. This is the foresight reading.
The repeated applications of these two steps constitute a
“level circuit” or “line of levels.”
Consider the case shown in Fig. II.

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LEVELING 127
(1) The instrument is set up and carefully leveled as has
been previously described. Care must be taken to see that the
line of sight, when level, will strike on the rod held on the
B.M. In case of doubt this should be verified by directing the
telescope toward the B.M. and centering the telescope bubble
before centering the plate bubbles. A sight through the tel-
escope will then indicate whether the instrument is too high or
too low. This simple precaution frequently saves much time
and annoyance.
(2) Sight on the level rod held on the B.M. Carefully
center the telescope bubble and read the rod.
(3) Verify the centering of the bubble. If it has moved,
repeat the reading of the rod.
(4) Record the rod reading and compute the H.I.
The rodman now goes ahead to the next point, either a
station or a T.P. If it is a T.P., he must be directed where to
Set it so that the instrument man can read the rod.
(5) Proceed as before with the telescope sighted on the rod
at the forward point.
(6) Record the rod reading and compute the altitude.
This completes the two steps. The level circuit is con-
tinued by a repetition of the foregoing.
From the foregoing discussion it is seen that it is not neces-
sary to have the altitude of the starting point referred to sea
level datum unless the altitude of the station is desired with
respect to the same datum. For purpose of obtaining dif-
ference in altitude only, any datum may be assumed for the
starting point. -
Notes.—In order to avoid confusion it is necessary to adopt
Some suitable system of recording the notes. The system may
vary for different cases but a satisfactory method is shown
below, which represents the field notes of the level circuit
shown in Fig. III.
These notes show the method of recording a rod reading on an
intermediate station as “A.” In some level circuits, as for pro-
file leveling or cross sectioning, the intermediate readings may
be more numerous than the readings on B.Ms. or T.Ps. But
ordinarily in different leveling there are very few intermediate
readings and these are taken to establish altitudes for possible
future reference. Such intermediate stations, if they are
permanent, then become B.Ms. It is a good plan to draw a
ring around the most important altitudes for convenience in
picking them out and to distinguish them from altitudes of
128 ORIENTATION FOR HEAVY (COAST) ARTILLERY

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|EXTRACT FROM FIELD NOTE BOOK
T.Ps. All Bench Marks and important stations should be so
carefully described that they can be found at any time without
difficulty. This is an important point, frequently neglected.
Level Rods.-There are two types of leveling rods. (1)
Target rods, having a sliding target which is set by the rodman
on signals from the levelman, and (2) self-reading or direct
reading rods, read directly by the levelman. The self-reading
rod is probably the most popular. However, the target rod
presents less chance for mistake and in a circuit of very accurate
levels the target is always used. Most direct reading rods are
also provided with a target.
Error of Closure.—As in the case of a transit traverse a
circuit or running of levels should always be checked either on
the starting point or on some other point whose altitude is
known. Errors are to be expected. The error of closure of a
level circuit run with a transit in good adjustment, with careful
methods and sights ranging about 75 m. should not exceed
E=.006 VS, where E = error of closure in meters. S = number
of instrument set-ups. -
f
LEVELING 129
6. ERRORS
1. Instrumental Errors.-These are practically confined to
errors of adjustments. They may be entirely eliminated by
making the lengths of backsights and foresights equal.
2. Mistakes in Manipulation.—
(a) The bubble may be incorrectly centered.
(b) If the observer rests his hands on the tripod he may
CallSé all eIſI’OI’. -
(c) The leveling rod must be held plumb or perpendicular
to the line of sight. When “short rod” is used, the rodman
can easily balance the rod on the station and hold it steady.
When “long rod” is used, or for readings over 2 m. it is usually
advisable to “wave the rod.” The rodman stands directly
behind the rod, facing the instrument, he leans the rod, first
toward the instrument, then away from it, the top describing
an arc about .6 m. long. The instrument man selects the
lowest reading on the rod.
(d) Dirt or any accumulation, as of snow or ice on the foot
of the rod, introduces an error.
3. Mistakes in Reading the Leveling Rod.—Reading 8 for 9
or vice versa, transposing figures, etc. Each observer must
learn his own peculiarities in this respect.
4. Errors in Sighting.—Coarseness of the crosswire, grad-
uations of the rod or form of the target and the eyesight of the
levelman all have to do with such an error. In using the
transit as a level instrument it is a common mistake to use one
of the stadia wires for the horizontal wire. Long sights should
be avoided. 75 m. is long enough with the average instrument.
5. Errors due to Change in Position of Instrument or Rod.—
These may be avoided by setting up on firm ground and taking
the foresight immediately after taking the backsight. Small
wooden stakes driven diagonally into the ground and using the
high corner make satisfactory turning points. Loose stones
should not be used. Turning points should be carefully
selected with regard to the next set-up. Be careful in walking
around the instrument not to jar or disturb it.
6. Errors Due to Natural Sources.—Unequal expansion of
different parts of the instrument, change of length of level rod,
curvature of the earth and refraction of the atmosphere are
included under this head. They are usually inappreciable and
are ignored in ordinary work, but are taken into account in
precise leveling.
130 ORIENTATION FOR HEAVY (COAST) ARTILLERY
7. Mistakes in Recording and Computing.—Transposing
figures, recording foresight as backsight or omitting a fore or
backsight entirely are among the common mistakes. A con-
venient check on the computing is obtained by the following
rule: Add all backsights together; add all turning point fore-
sights, including the foresight on the closing point, together;
the difference between these sums should equal the difference
between the altitudes of the starting and closing stations.
8. Personal Errors.-These are not serious in ordinary
work, but must be considered in precise leveling.
CHAPTER VIII
MERIDIAN DETERMINATION
MECHANICAL SOLUTIONS
ELEMENTS OF ASTRONOMY AND TIME
OBSERVATION ON THE SUN
OBSERVATION ON Polaris
OBSERVATION ON A STAR AT EQUAL ALTITUDEs
OBSERVATION ON RNOWN TERRESTRIAL POINTs
i
In the preparation for artillery fire on the Western Front it is
essential that battery positions be accurately known. After a
battery position has been selected the coordinates of the di-
recting gun, and usually of all guns, and the Y-azimuth of
each aiming line must be found. In some cases these can be
obtained by solving the three point problem, either mechani-
cally with a plane table or mathematically with a transit, or by
running a traverse from a known point on a known line. In
Some cases, however, there may be but one datum point avail-
able and a survey must be run from that point to the battery
position, and the survey oriented or “tied in” by an astro-
nomical observation to determine the True North. Further,
such an observation may be necessary as a check on other work.
The line in which the plane of the Meridian intersects the plane
of the horizon is called the “North and South Line” or the
“True Meridian.”
1. MECHANICAL SOLUTIONS
There are four simple and rapid approximate methods of
Meridian determination in general use which, for want of a
better name, are called “Mechanical Solutions.” By their
use general directions can be found quickly, which is often
valuable in a strange country, or True North can be found
within a degree, which is sufficiently accurate for some pur-
poses, such as in making rough sketches.
(a) If the declination of the compass is known True North
can quickly be determined from Magnetic North, with an
accuracy of one or two degrees, or even closer, depending on the
accuracy of the compass. This was covered fully in Chapter
III.
132 ORINETATION FOR HEAVY (COAST) ARTILLERY
(b) If the hour hand of a watch is pointed at the sun, a
line bisecting the angle between that hour hand and 12 o'clock
points South. (See Fig. I.) If the sun is shining general
directions can thus be found very quickly.
*2.
Fig. I.-DIRECTIONS FROM SUN AND HOUR HAND OF WATCH
(c) Another method is to fasten a sheet of cardboard at the
upper end of a vertical board attached to the south edge of a
table, exposed to the sun's direct rays. (See Fig. II.) Prick
a small hole in the cardboard, through which a Sunbeam can
fall on the table. For half an hour before and after noon, put
a pencil mark on the table every five minutes at the center of
this Sunbeam. These successive marks will form a curve
concave northwards. With a point on the table directly
beneath the hole in the cardboard as a center, and any con-
venient radius strike an arc that will intersect the path of the
Sunbeam twice. A line perpendicular to the chord connecting
these two intersections is a True North and South line. By
this method True North can be determined to within one
degree.
(d) At night directions can be found quickly by looking
for the North Star (Polaris), which is always within two

MERIDIAN DETERMINATION 133
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Fig. II.-APPROXIMATE NORTH FROM PATH OF SUNBEAM AT NOON
degrees of the plane of the Meridian; the relative positions of
the fixed stars is always the same, although they apparently
revolve around the Earth from East to West, and a knowledge
thereof is valuable, especially in case Polaris is obscured by
clouds.
2. ELEMENTS OF ASTRONOMY AND TIME
The Great Dipper (Ursa Major) is the most important of
the constellations and is easy to find. The “pointers” of and
8 point to Polaris at all times as the Dipper circles the Pole,
the bowl of the Dipper being towards Polaris (see Fig. III).
About the same distance on the other side of Polaris is Cassi-
opeia, a group of five stars forming an irregular letter W, its
upper part being toward Polaris. As the Latitude of any
place is equal to the altitude of the Pole, when the Dipper and
Cassiopeia are on either side of Polaris (East and West) the
altitude of Polaris will give a reasonably correct figure for the
latitude of the place of observation. When they are above or
below Polaris, a compass reading on Polaris will give the decli-
nation of the compass to within its least reading. There are
many other constellations which should be known, but which
have to be omitted here. These are given in the “Training
Manual in Topography, Map Reading and Reconnaissance,”
by Major George R. Spalding, published by the Govern-
ment Printing Office, and in various textbooks on practical
astronomy. -
However, in the preparation of artillery fire True North
must be known to within one minute and sometimes even


134 ORIENTATION FOR HEAVY (COAST) ARTILLERY
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/ Š
* / S
&T,
‘’s V. §
*> \
zººs Sk —%
*>
Fig. III.-CONSTELLATIONS NEAR POLARIS
closer. That accuracy can be obtained by astronomical
observations with a transit or theodolite. A knowledge of the
elementary principles of astronomy is essential to a clear
understanding of astronomical observations. Therefore, con-
sider briefly the Motions of the Earth, the resulting apparent
motions of the stars as seen from the Earth, and time.
Motions of the Earth.-The Earth has two motions, both of
which are counter-clockwise motions of revolution: It re-
volves around its own polar axis and it moves around the Sun
in an elliptical orbit. (Fig. IV.) The Earth's axis is not per-
pendicular to the plane of its orbit, but is inclined at an angle
of about 66% thereto; for our purposes its positions at all
points in its orbit can be considered as parallel. Therefore,
when the Earth is in one-half of its orbit, the Sun is below the
plane of the Equator and when in the other half of its orbit,
above the Equator. This causes the different seasons of the
year. The angular distange of the Sun above or below the
Equator, measured from the Earth, and called the Sun's
declination, is used in solar observations.
Sidereal Time.—The length of time it takes the Earth to




MERIDIAN DETERMINATION 135
*( & )
-
*
*
s
º
º
-
*
*
*
z*
f
\
\
W
*
N.
a
f t \
Sº,
Fig. IV.-MOTIONS OF THE EARTH
make one complete revolution (360°) around its own axis is
constant and is called a “Sidereal Day.” This is 23 hr.
56 min. 4 Sec. of standard time (the time our watches keep).
The rotation of the Earth around its own axis is the most
uniform motion in nature. The Earth makes one complete
circuit of its orbit in a year, during which it makes 366.2422
revolutions around its own axis. Thus, there are 366.2422
sidereal days in a year. As both motions of the Earth are
counter-clockwise, one revolution is apparently lost in a year,
and the sun crosses a Meridian one time less than the number
of revolutions of the Earth. In Fig. IV:
Arc ABCA =360° = 1 rotation around Axis
= 1 Sidereal Day, -
=23 hr. 56 min. 4 sec. Standard Time.
Arc ABCAB =361°= = 1 Apparent Solar Day.
Arc MNOPM = 1 Year=366.242 Sidereal Days,
=365.2422 Mean Solar Days.
Apparent Time.—The length of time between two successive
transits of the sun across a Meridian is called an “apparent
solar day.” As the motion of the Earth around its orbit is not
uniform, but varies inversely as the distance to the Sun, the
length of time between successive transits of the Sun will
depend on the position of the Earth in its orbit. This will


136 ORIENTATION FOR HEAVY (COAST) ARTILLERY
be better understood by examining Fig. V, the shaded areas
being equal and representing equal lengths of time. The
average “apparent solar day,” or the average time between
successive transits of the Sun, is called the “mean solar day.”
Four times a year apparent solar time is the same as mean
solar time; during two of the intervening periods it is slower,
and during the two alternate periods it is faster. Standard
time, kept by our watches, is based on mean solar time. The

Earth's Or \bºt
!ſ Suva
*: zzzzzzzzzzzzzzzz ZZZZZZZZZZZZZZZZ
Fig. V.-VARIATIONS IN EARTH's ORBITAL VELOCITY
American Ephemeris gives for each day in the year an “equa-
tion of time,” which added to or subtracted from mean solar
time as the case may be, gives the corresponding apparent
solar time at any instant. All calculations are based on mean
solar time. When observations are made on the Sun, Sun time
(apparent solar or true time), computed by the equation of
time from mean time, is used.
The Year.—A year contains 365.2422 mean solar days, or
365 days, 5 hrs., 48 min. and 46 sec. of mean time. In order
to take up the extra 5 hrs., 48 min., 46 sec., an extra day,
Feb. 29, is inserted in the calendar every fourth year (Leap
Year) and omitted every hundred years.
The Solar System.—The solar system consists of several
planets (the Earth, Mercury, Venus, Saturn, etc.) which
revolve around the Sun, and the various satellites, such as the
Moon, which revolve around the planets. The position of the
MERIDIAN DETERMINATION 137
planets and the Moon at any time, as seen from the Earth,
depends on the combination of their motions and the Earth's
motions, necessitating awkward calculations in case obser-
vations are made on them.
The position of the Sun, however, as seen from the Earth,
depends only on the Earth's motions, and by observations of
the Sun, Latitude, Longitude, azimuth and correct time can
be computed with comparative ease.
Fiaced Stars.-Similarly the positions of the “fixed stars”
(practically all the stars except the planets and comets) depends
solely on the Earth's motions, because they are at such infinite
distances that their own motions are imperceptible, and by
observations on them the same data can be obtained as from
Solar observations. Because of the great distance to these
stars, the Earth's motion around its orbit has little effect on
their positions and can often be disregarded and a sidereal day
can be defined as the interval of time between successive
transits of a star across a Meridian. As there is one more
sidereal day than there are mean solar days in a year, a sidereal
1
day is 3 min., 56 sec. shorter than a mean solar day, 365,2422
X24 hrs. Therefore, a star crosses the Meridian 3 min.,
56 sec. earlier each day, and in stellar observations this time
difference must be considered.
Time and Longitude.—Time depends on longitude. When
it is 12 o'clock noon at Greenwich (0° longitude) it is 6 P.M. at
90° E., midnight at 180° and 6 A.M. at 90° W. longitude.
The following table gives the relation between mean Solar
time and longitude:

Mean Solar Time Longitude Mean Solar Time Longitude
Interval Interval Interval Interval
24 hours 360° 1 minute 15'
1 hour 15° 4 seconds 1’
4 minutes 1° 1 second 15"
Standard Time.—Thus, each point on the Earth's surface
has its own mean local time, depending on its longitude, all
points on the same meridian having the same mean local time.
With the growth of railroad travel these small time differences
became very inconvenient, and the United States was divided
into four somewhat irregular “Time Belts.” Standard time
138 ORIENTATION FOR HEAVY (COAST) ARTILLERY
is the same for all points in each belt and is the mean local
time of a central Meridian in that belt. Standard time in
adjacent belts differs by just one hour.
Under the recent “daylight saving” Act of Congress Stand-
ard time is advanced one hour during the Summer months
(April to September, inclusive), Standard time then being one
hour faster than the mean local time of the Standard Meridians.
In England and France Standard time is Greenwich mean
time (Greenwich is near London) with a similar daylight saving
plan in Summer. The following table gives Standard time
data:

- STANDARD TIME
Longitude Meº cal
Summer Winter
Greenwich. . . . . . . . . . . 0° Noon 1 P.M. Noon
Eastern. . . . . . . . . . . . . . 75° W. 7 A.M. 8 A.M. 7 A.M.
Central. . . . . . . . . . . . . . 90° W. 6 A.M. 7 A.M. 6 A.M.
Mountain. . . . . . . . . . . . 105° W. 5 A.M. 6 A.M. 5 A.M.
Pacific....... . . . . . . . . 120° W. 4 A.M. 5 A.M. 4 A.M.
Celestial Sphere.—To an observer, the Earth seems station-
ary and the Sun and stars appear to revolve around it from
East to West, which is the reverse of what actually happens.
The Earth seems to be the center of a hollow sphere, the Sun
and stars being on the inner surface. This imaginary sphere,
called the “Celestial Sphere,” is a very useful conception and is
the basis of most astronomical observations. (See Fig. VI.)
Its axis is the Earth's axis produced; its equator is the Earth's
Equator produced. The zenith is a point on the Celestial
Sphere directly above the observer. The Horizon is the inter-
section of the horizontal plane through the observer with the
Celestial Sphere. In this Celestial Sphere everything is
measured as an angle, either between imaginary lines, or be-
tween imaginary planes. The distance between the Equator
and the zenith, and the altitude of the Celestial Pole both
equal the observer's Latitude. The altitude of the Sun or a
star above the horizon depends on the time of day. The
declination of the Sun or a star—its angular distance North or
South of the Equator—depends on the time of year (the posi-
tion of the Earth in its orbit).
Astronomical Triangle.—The spherical triangle between the
Pole, the zenith, “Z,” and a star (or the Sun, “S”) is called
MERIDIAN DETERMINATION 139
452-----
Q2--T --~~
N.
N
N
`s
Nº Sl
S __\* 3
§ -’ S.
§ 2^- ~
S}/ 2' $2. ©
S// Sº S.
/ - J’
(VH * * - - - * - - - amº ºf A -- * * * *-* - sº º
/D/ $ /V
-
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// 2.
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i
Fig. VI.-CELESTIAL SPHERE
the “Astronomical Triangle” or the “PZS Triangle.” (See
Fig. VI.) The curve UQBZPN is a Meridian, NREAUWH
the Horizon, EDQW the Equator, and RSBH the Sun's path.
The observer is at the point “O.” The side NP = Z NOP =
Latitude, “Q.” The side AS = ZAOS = Sun's altitude, “H.”
The side SD = Z DOS=Sun's Declination, “D.” One side,
PZ, is the Co-Latitude (90°–Latitude); another, PS, is the
polar distance, “P” (90°–Declination), of that particular star
(or the Sun); the third side, SZ, is the co-altitude (90°–alti-
tude) at the instant of observation. These sides are measured
as angles between imaginary lines from the observer to the
vertices of the triangle. The angle at the zenith (PZS) is the
azimuth of the star (or Sun); the angle at the Pole (ZPS) is
called the hour angle; from it sidereal time, in the case of a star,
or apparent solar time, in the case of the Sun, can be deter-
mined. The angle at the zenith is the same as the angle in the
plane of the horizon between the Meridian and a plane through
the observer, the star and the zenith. The hour angle is the
same as the angle in the plane of the Equator between the
plane of the Meridian and a plane through the observer, the
Pole and the star. The PZS triangle has six parts—three
angles and three sides—all measured as angles. If any three

140 ORIENTATION FOR HEAVY (COAST) ARTILLERY
parts are known, the triangle is determined and any of the
unknown parts can be computed. In Meridian observations
on the Sun and some stars, the three sides of the PZS triangle
are found, and in Meridian observations on Polaris two sides
(PZ and PS) and the hour angle are found; from either set of
observations the angle at the zenith, the azimuth of the Sun
or star, can be computed.
3. OBSERVATIONS ON THE SUN
If all three sides of the PZS triangle are known, the angle at
the zenith can be found by means of a formula, which is the
method used in Solar Observations. The data necessary is the
Latitude and the Sun's altitude and declination at the instant
of observation. The altitude is measured with a transit and
the exact time recorded; the corresponding declination is found
in an Ephemeris, and assuming that the Latitude is known, all
necessary data is at hand. The transit must have a smoked
glass eyepiece or else the image must be clearly focused on a
sheet of paper held back of the eyepiece.
Detailed Procedure.—In order to determine the azimuth of
a line by means of an observation on the Sun, the instrument
should be set up over one of the points marking the line, and
carefully leveled. If the vernier of the vertical circle is not
adjustable, the amount and sign (+ or –) of the index error
should be recorded. Clamp the upper plate at zero, then
bring the vertical crosswire on the reference stake, and clamp
the lower plate. The colored shade glass, if one is used, is then
screwed on to the eyepiece. The upper clamp is then loosened
and the telescope turned toward the Sun. The Sun's disc
should be sharply focused before beginning the operations.
In making the pointings on the Sun great care should be taken
not to mistake one of the stadia wires for the middle wire.
The Sun's image is then brought consecutively in the upper
º
gº)
FIG. VII
POSITION OF SUN IN PLACING WIRES
FOUR QUADRANTS TANGENT TO SUN
2.
2)

MERIDIAN DETERMINATION 141
left, lower right, upper right, and lower left quadrants formed
by the horizontal and vertical crosswires. (See Fig. VII.)
As the Sun's diameter is about 32', the crosswires cannot be
placed at its exact center, but they can be placed tangent to
two edges of the Sun at once. Thus, by taking four observa-
tions, one with the Sun in each quadrant of the crosswires, the
result is the same as if one observation had been made on the
Sun's center. By keeping one crosswire tangent, to the Sun,
and letting the Sun creep up until it is tangent to the other
crosswire also, exact readings can be taken.
In each case clamp both horizontal and vertical motions,
and with the slow motion screws bring both crosswires tan-
gent to the two sides of the Sun. At the moment of contact
record the time, the vertical and the horizontal circle readings.
Point again at the mark and read both verniers as a check.
Then reverse the telescope and repeat the operation. The
mean of the horizontal angles will be the angle between the
reference mark and the mean position of the center of the Sun.
The mean of the vertical angles will be the angular altitude of
the center of the Sun. The observations should be made as
rapidly as possible (as is consistent with accuracy) with the time
intervals between the pointings approximately equal.
Refraction.—On account of refraction astronomical bodies
appear to be higher than they really are. Hence, all vertical
angles found by astronomical observation should be reduced
by subtracting the correction for refraction. Below about 20°,
the correction for refraction is very uncertain and hence any
observation depending principally on altitudes should be taken
only after the Sun or star is from 20° to 30° above the horizon.
The correction for refraction varies with the temperature,
height of barometer, etc. The following mean values for a
temperature of 50° F. and barometer reading of 29.9 inches are
taken from “Hayford's Geodetic Astronomy.”
MEAN REFRACTION CORRECTIONS

Altitude Correction | Altitude Correction Altitude Correction
0° 34' 08" 16° 3' 20" 40° 1’ 09"
5° 9' 52" 17° 3' 08" 45° 0' 58"
10° 5' 19” 18° 2. 57*. 50° O' 49"
11° 4' 51" 19° 2' 48" 55° 0' 40"
12° 4, 27” 20° 2' 39" 60° 0' 34"
13° 4' 07” 25° 2' 04" 70° 0' 21"
14° 3'49" 30° 1'41" 80° O’ 10”
15° 3' 34" 35° 1'23" 90° 0' 00"
142 ORIENTATION FOR HEAVY (COAST) ARTILLERY
If observations are taken too near noon the altitude of the
Sun is changing too slowly and the astronomical triangle is
poorly proportioned for definite results. Hence, the best time
for observations is from 8:00 to 10:00 A.M. or from 2:00 to
4:00 P.M.; they should never be taken within an hour of noon.
In the computations an Ephemeris of the Sun is needed, and
in using the tables great care should be taken not to confuse
“mean” and “apparent” times. In the following example
the computations have been made with the United States Land
Office Ephemeris. The tables on pages 2–13 give the declina-
tions of the Sun for Greenwich apparent (or true) noon, and
equations of time to be applied to apparent to get mean time.
If the observer's watch time of observation has been corrected
to Greenwich mean time, this equation is applied to that time
to get apparent (or true) time of observation; and the decli-
nation given for Greenwich apparent noon is then interpolated
for apparent time of observation.
If the American Nautical Almanac had been used, the
tables would have given the declinations for Greenwich mean,
noon. Consequently, no equation of time would be applied
but the declination would have been at once interpolated for
watch time of observation corrected to Greenwich mean time.
Formula.—The formula for azimuth is taken from Hay-
ford's Geodetic Astronomy and no proof is here given.
Let D = Declination of Sun.
H = Altitude, corrected for refraction.
Q = Latitude. 0.
P = Polar distance of Sun = 90°–Declination.
A = Azimuth of Sun from North, measured clockwise
in the morning, and counter-clockwise in the
afternoon. §
s-ºn tº
/sin (S–H) sin (S-Q)
Then tan 9/3A = v cos S cos (S-P)
Computations.—The calculations may be summarized in
nine steps as follows:
1. Correct average watch (Standard) time of observation
to Greenwich mean time.
(First, correct for watch error, if any; second, correct for
difference in watch time between station and Greenwich. If
Standard time is used, the Greenwich mean time is found by
adding the Longitude, in hours, of the Standard Meridian to
MERIDIAN DETERMINATION 143
which it refers if West of Greenwich, subtracting if East.)
2. Find Greenwich apparent time of observation (after
Greenwich noon) by applying equation of time from the
Ephemeris.
Note.—If the Ephemeris gives the Sun's declination at
Greenwich mean noon the equation of time must not be used.
The correction for the number of hours since noon, i.e., the
change in declination since noon will be determined from the
time elapsed at the moment of observation since mean noon
instead of that since apparent noon. 4
3. Find declination of the Sun at nearest Greenwich
apparent noon from the Ephemeris.
4. Correct this declination (3) to declination at instant of
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Fig. VIII,-SKETCH SHowING POSITIONS OF SUN, MARK, TRUE AND
LAMBERT NORTH

144 ORIENTATION FOR HEAVY (COAST) ARTILLERY
observation, by applying the difference for 1 hour from
Ephemeris multiplied by the number of hours intervening (2).
5. Find polar distance of Sun. This is 90-declination (4).
(It is important to fix in mind the algebraic signs corresponding
to North and South declinations, viz.: North = +; South = —.)
6. Correct observed altitude for refraction. This is always
subtractive. (From table of mean refraction corrections.)
7. With the corrected altitude = H; Latitude = Q; and Polar
distance = P, substitute in the formula:—
/sin (S–H) sin (S-Q)
Tan 3%A = V/ cos S cos (S-P)
Angle A = angle from North to Sun, clockwise in the morn-
ing, and counter-clockwise in the afternoon.
8. Find angle from North to mark. (By applying angle
between Sun and mark to angle “A” found in (7).)

9. Find Y-azimuth of line from station to mark. (By
correcting (8) for convergence.)
FIELD NOTES.
HoRIzoNTAL -
Point Telescope ANGLES - Mean Angle | Altitude #º
Wernier AWernierB & sº tº a.º. tº lº &
Mark | Normal 0°0' | 180°0' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9|- | Normal 46°37' 226°37' 46°37' 46°37' 23°23' 4— 4–00
||8 Normal 46°18' 226°18' | 46°18' | 46°18' 22°36' 4— 5–20
- Normal 46°30' 226°30' | 46°30' | 46°30' 22°55’ 4— 6–30
Oſ- Normal 47°26' 227°26' | 47°26' | 27°26' 22°1' 4— 8–30
Mark | Normal 0°0' | 180°00' | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Means = | 46°42'45"| 22°43'45"| 4– 6– 5
Mark | Inverted | 180°00' | 0-0 |.........l.........l.........l.........
0|_ Inverted 228°10' | 48°9' 228°9'30"| 48°9'30" | 21°52' 4–12–20
TÉ Inverted 227°53' || 47°53' | 227°53' || 47°53' 21°04' 4–14–00
-- Inverted 228°07 || 48°07' 228°07' | 48°07” 21°22' 4–15–10
n- || Inverted 229°00' 49°00' 229°00' | 49°00' 20°28' 4–17–00
Mark | Inverted | 180°00' 0°0' l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Means = | 48°17'23"| 21°11'30" 4–14–38
= 47°30'04"| 21°57'38"| 4–10–21
4 h. 10 m. 21 S. = average watch (Standard) time of observation.
º 1 m. 30 S. = watch error.
4 h. 11 m. 51 s. = corrected Standard time of observation.
+5 h. 0 m. 0 s. = difference in Standard time between Ft. Monroe and
Greenwich.
MERIDIAN DETERMINATION 145
1. 9 h. 11 m. 51 S. =Greenwich mean time of observation.
– 10 m. 17.9 s. =equation of time to be applied on Mar. 11th (from
Ephemeris).
2. 9 h. 1 m. 33.1 s. = Greenwich apparent time of observation, after Green-
wich apparent noon.
3° 55' 0.5" = Declination of Sun at Greenwich apparent noon
Mar. 11th. (Declination is South and decreasing;
from Ephemeris.) º
8' 51.1" = correction for number of hours since Greenwich appar-
ent noon. (From Ephemeris, difference for 1 hr.
Mar. 11th = 58.84". 9 h. 1 m. 33.1 S. = 9,026 hrs.
9.026×58.84" =8' 51.1".)
3.
4, 3° 46' 9.4" = Declination at time of observation. .
90° 00' 00" As declination is South, its algebraic sign is – ; hence
+ 3° 46' 9.4" 90°–(a negative declination) =90°,+that declin-
- ation.
5. 93° 46' 9.4" = Polar distance of Sun.
21° 57' 38" = observed mean altitude. - -
– 2' 26" = correction for refraction and is always subtractive.
(Found from table of mean refraction correction.)
6. 21° 55' 12" = altitude of Sun, corrected for refraction.
Corrected altitude = H = 21° 55' 12"
Latitude =Q=37°00' 02"
Polar distance = P = 93° 46' 09"
2|152° 41' 23"
S = 76° 20' 41"
S–H = 54° 25' 29"
S— Q=39° 20' 39" Formula:
sin (S.–H) sin (S.–Q)
/
S– P = 17° 25' 28” - Tan 3% A = V/ cos S cos (S-P)
9.910279 = log sin (S–H)
9.802074 = log sin (S-Q)
0.626941 = colog cos S
0.020400 = colog cos (S-P)
2 : 0.359694
.179847 = log tan 3% A 56° 32' 18" = % A *
113° 4' 36" = angle A=angle from North to Sun, counter-clockwise because
observed in the afternoon.
+ 47° 30' 04" =mean angle between Sun and mark.
7
8. 160° 34' 40" = angle from North to mark, contra-clockwise.
– 48' 00" = correction for deviation to West from Lambert North.
(MI — Mo) ×sin Lat. = 1.3×sin 38°=.8=48'.
(Origin of Lambert grid on Ft. M map, Long. 75°, Lat. 38°.)
159° 46' 40" = angle from Lambert North to mark, counter-clockwise.
360° 00’00” — 159° 46' 40" = 200° 13' 20".
9. 200° 13' 20" =Y-azimuth of line to mark, clockwise.
200° 13' 20" =200.22° or =222.4699. (See Fig. VIII.)
Example (French Method of Computation).--The French
Ephemeris gives they declination of the Sun for Greenwich
mean noon each day, giving it to the nearest tenth of a minute,
146 ORIENTATION FOR HEAVY (COAST) ARTILLERY
and the correction to be applied thereto for time (or Longitude)
intervals. Therefore in using these tables no correction is
necessary for apparent time, and the Sun's declination at the
instant of observation can be found directly by adding the cor-
rection for the elapsed time to the declination at Greenwich
mean noon. In another table is given the refraction correc-
tions to be applied to the observed altitude.
The following example is based on observations made in
France and is computed using the French Ephemeris. The
computations are quite similar to those when the American
Ephemeris is used.
Observed data:
10–16–17 Lat., 48° 40'. Long., 4° 13' E”
Sun to right of mark. Watch, 2 m. 00 s. slow'
Mean deflection angle 144° 04' 25"
Mean observed altitude 16° 37' 00"
Mean time of observations 2 h. 55 m. 30 s. P.M.
Computations:
2 h. 55 m. 30 s. = mean watch time of observations.
+ 2 m. 00 s. = watch correction.
2 h. 57 m. 30 s. =Standard time (Greenwich) of observations.
8° 46'.7 =South declination of the Sun at Greenwich mean noon,
Oct. 16, 1917. (From French Ephemeris.) -
+ 2'.8 = correction for elapsed time. (From French Ephemeris.)
8° 49'.5 =South declination of Sun at instant of observation.
16° 37'.00 = observed altitude. e
— 3’.22 =refraction correction. (From French Ephemeris.)
16° 33’.78 = corrected altitude (H).
48° 40'.00 = corrected Latitude (Q).
98° 49'.50 = Polar distance (P).
2|164° 03'.3
82° 01'.6 = S
colog cos S = 0.857:885
S–H = 65° 27'.8 log sin (S–H) = 9.958892
S– Q = 33° 21'.6 log sin (S.–Q) = 9.740272
S— P = 16° 47'.9 colog cos (S-P) = 0.018939
2.575.988
% A = 62° 44'.4 Log tan 3% A = .287994 e
A=125°28'.8 = Angle from North to Sun, counter-clockwise, because
in the afternoon.
360° 00'.0
234° 31'.2 = Azimuth of Sun.
—144° 04'.4 = (Sun to right of mark.)
90° 26'.8 = Azimuth of Line.
+ 2° 40'.8 = Deviation to West from Lambert North.
92° 07'.6 = Y-azimuth of Mark.
MERIDIAN DETERMINATION 147
4. OBSERVATION ON POLARIS
Orbit of Polaris.-Polaris, the “North Star,” is very near
the Pole, its polar distance being about 1° 07', and it is there-
fore frequently used for the determination of True North.
To an observer on the Earth it apparently revolves around the
Pole counter-clockwise in a slightly elliptical orbit. (See
Fig. IX.) When it is directly above the Pole, it is said to be
at Upper Culmination; when it is directly below, at Lower
Culmination; when it is directly west of the Pole, at Western
Elongation, and when directly East at Eastern Elongation.
It makes one complete revolution about the Pole every Sidereal
Day, or every 23 hrs. 56 min. 4 Sec. of mean time. Its position
in its orbit is expressed by the smaller angle between it and
Upper Culmination, that angle being measured in hours
instead of degrees. That is called the “Hour Angle” and
means the elapsed time since the last Upper Culmination, if
Polaris is West of the Pole, or the time that must elapse before
the next Upper Culmination, if Polaris is East of the Pole.
This hour angle can never be over 11 hrs. 58 min. (half the time
of revolution).
The “American Ephemeris,” published by the General
Land Office in Washington, gives for each day in the year the
4/20er &/22/72//o/7
§
§ § §
S S
SN SS
S. S
S | S
S. S
§ §
§ §
Š [[]
4-42/72-S/3/27s
Alower &/77/naffo/7
Fig. IX.-APPARENT ORBIT OF POLARIS

148 ORIENTATION FOR HEAVY (COAST) ARTILLERY
time of Upper Culmination of Polaris at Greenwich and the
corresponding Declination, which varies by about 50" during
the year, also in another table, the azimuths of Polaris at
certain hour angles, declinations and latitudes.
Observations at Culmination.—If an observation is made on
Polaris at the exact instant it is at either culmination, and the
transit is then depressed and a point marked on the ground,
that point is directly North of the instrument. This observa-
tion is simple and no calculations are necessary, but a slight
error in the time of observation will cause an appreciable error
in the line, because Polaris is moving rapidly East or West at
culmination. Moreover, clouds may hide the star at that time,
or culmination may come at an inconvenient hour (2 A.M.)
Therefore such observations are seldom made.
Observations at Elongation.—When Polaris is at Elongation
its motion is practically vertical for about 20 minutes—down-
ward at Western Elongation and upward at Eastern—and a
small error in time has no appreciable effect on the results.
Several different readings of the angle between the star and a
given line can be taken during this 20 minutes and accurate
results obtained. Then by looking up the azimuth of Polaris
at Elongation, in an Ephemeris, the true azimuth of the line
can be computed. Observations of Polaris at elongation are
frequently made, but the same objections of inconvenient time
and possible invisibility hold true as at culmination.
Observations at any Time; Hour Angle Method.—Observa-
tions at either culmination or elongation are special cases; the
general case is to make the observation at any time, and then
compute the hour angle at that instant and the corresponding
azimuth of Polaris. If the general case is understood either of
the special cases can readily be used if desired.
The Hour Angle Method consists in measuring the angle
between any given line, whose Y-azimuth, computed from the
observations, and Polaris at any instant (or depressing the
telescope and setting a stake in line with Polaris) and then
finding (from an Ephemeris) the hour angle and declination of
Polaris at that instant. Knowing them and the Latitude,
two sides (PZ and SP) and the included (hour) angle of the
PZS triangle are known and the azimuth of Polaris at that
instant can be computed. (See Fig. X.)
MERIDIAN DETERMINATION 149
Fig. X.-ORBIT OF POLARIS
ZPNO = Plane of Meridian. Z = Zenith.
P = Celestial Pole. S = Polaris. O = Observer.
SHB = Orbit of Polaris. Z.P = 90°– Lat.
SP=Polar Distance. ZZPS = Hour Angle.
ZPZS = Z NOM = Azimuth.
Small errors in the Latitude have almost no effect on the
azimuth, and it can usually be estimated with sufficient accu-
racy from a map, because one minute of Latitude subtends a
distance of about a knot (6080.7") on the Earth's surface, and
the location is usually known much closer than that. In
observations on Polaris it is not necessary to solve the triangle,
however, because that has been done for a large number of
cases and the results tabulated in the Ephemeris, so that it is
only necessary to interpolate for the proper values.
Observations.—Set your watch accurately—to the second—
at Standard time before the observation, and as soon as possible
afterwards compare it with Standard time, and estimate its
probable error, if any, at the instant of observation. Set your
transit on the line whose azimuth is desired, sight on some
other point on that line, lock the lower plate and read both
verniers. (If the verniers are first set at 0° this is simplified.)
Loosen the upper plate and point the telescope at Polaris.
To facilitate this, first set off your Latitude on the vertical arc,
and then point the telescope at Polaris by sighting over it.
(See Fig. X.) A slight movement of the tangent screw will
then bring Polaris into the field of vision and on to the vertical
crosswire, which must be illuminated by a lantern or flash-
light. When Polaris is on the crosswire record the exact time
and the vernier readings. Plunge and reverse the instrument
and sight on Polaris, again recording the time. Then sight on

150 ORIENTATION FOR HEAVY (COAST) ARTILLERY
the line and record vernier readings. Compute the mean of the
two deflection angles. If great accuracy is desired, repeat two
or three times, but work up each set of observations separately.
Computations.—The computations necessary to determine
the azimuth of Polaris at the instant of observation can be
divided into seven steps, viz.:
1. From an Ephemeris or Nautical Almanac, find the time
of the nearest Upper Culmination of Polaris and its corre-
sponding Declination.
2. Correct (1) for the Longitude of the place of observa-
tion; the correction is .16 min. for each 15° Longitude
15
(#x3 min. 56 sec. = .16 min) if West of Greenwich, the
correction is subtracted, because the time of Upper Culmina-
tion is earlier there than at Greenwich; if East of Greenwich
it is added. This gives the time of Upper Culmination at point
of observation in local mean time.
3. Correct the time of observation (Standard time) to
local mean time, first correcting for any watch error.
4. Find the hour angle (the time interval between (2)
and (3).
5. With this hour angle, declination and Latitude, find in
an Ephemeris the corresponding azimuth of Polaris.
6. Compute the correct azimuth of the line.
7. Compute the Y-azimuth of the line.
Eacample
Date, March 11, 1918. Observation at Fort Monroe, Va.
Latitude, 37° N. Longitude, 76° 18' W.
Mark was West of Star Watch, Correct Standard time.
FIELD NOTES
Deflection
Point Vernier A | Vernier B Mean Angle Time
Mark. . . . . . . . . . O°0' | 180°0' 0°0' . . . . . . . . . . . . . . . .
Star. . . . . . . . . . . 120°39' 300°39' 120°39' 120°39' 7–31–40 P.M.
Star. . . . . . . . . . . 300°40' 120°40' 120°40' 120°40' 7–37–20
Mark. . . . . . . . . . 180°0' 0°0' 0°0' | . . . . . . . . . . . . . . . . .

Means 120°39'30" 7–34–30

Mark. . . . . . . . . . 0°0' 180°0' 0°0' . . . . . . . . . . . . . . . . . .
Star. . . . . . . . . . . 120°38' 300°38' 120°38' 120°38' 7–44–56
Star. . . . . . . . . . . 300°38' 120°38' 120°38' 120°38' 7–47–30
Mark. . . . . . . . . . . 180°0' 0°0' 0°0' | . . . . . . . . . . . . . . . . .
Means 120°38' 7–46–13
MERIDIAN DETERMINATION 151
Computations of the First Set of Readings
1. 2 h. 16.4 m. P.M. = nearest Upper Culmination (Mar. 11) from Ephemeris,
page 4. (Note—Declination 88° 52'22.4".)
— .8 m. = correction for difference in Longitude from Greenwich
(.16m, for each 15° Longitude;+if East; —if West.)
2 h. 15.6 m. = Upper Culmination at point of observation in local
mean time.
2, 7 h. 34 m. 30 s. = average watch time of observation.
— 5 m. 12 s. = correction to local mean time. Longitude of observa-
tion=76°18' =76°.3.
76.3—75 (Standard Meridian) = 1.3.
4 m. X1.3 = 5.2 m. = 5 m. 12 s.
3. 7 h. 29 m. 18 s. =local mean time of observation.
–2 h. 15 m. 36 s. = local mean time of Upper Culmination at point of
observation.
5 h. 13 m. 42 s. = mean time hour angle. =5 h. 13.7m.
As stated before, the azimuths of Polaris have been com-
puted for a large number of hour angles, declinations and
latitudes and the results tabulated in the Ephemeris, pub-
lished by the U. S. General Land Office, the tabulation appear-
ing on pages 14 and 15. The back azimuth (360°– azimuth)
when Polaris is West of the Pole is the same as its azimuth at
the same hour angle when it is East of the Pole. Therefore the
table only gives the azimuth. This is a complete and con-
venient table from which the azimuth corresponding to any
hour angle, declination and Latitude can quickly be found by
interpolation, but at first glance it looks complicated. As
soon as it is understood, however, the necessary interpolations
are simple. At a given Latitude the azimuth varies with the
declination and hour angle, but the same azimuth will hold for
several different combinations of declination and hour angle,
Similarly for the same declinations and hour angles at another
Latitude, another azimuth will hold true. The variations in
the azimuth caused by variations in Latitude or Declination
are small, while the variations caused by changes in the hour
angle are large. Therefore the table was compiled so as to give
certain azimuths for each 2° of Latitude, the azimuths vary-
ing by about 2 minutes, and opposite them the corresponding
hour angles for each 10 Seconds of declination. In using this
table it is necessary to interpolate three times: First, for the
hour angle corresponding to the proper declination; second, for
the azimuth corresponding to the proper Latitude; and third,
for the azimuth corresponding to the proper hour angle. In
this example the declination was 88° 52'22.4", the Latitude 37°
and the hour angle 5 hr. 13.7 min. A portion of the table in
which these values lie, separated so as to permit easy inter-
polation below.
152 ORIENTATION FOR HEAVY (COAST) ARTILLERY

Declination Latitude
Tissº-527-20Tssº-527-22. Tssº-307|36. Tº as TT
# 5 — 2.6 5 – 3.2 A 5- 5.1 || 81.4 82.5 B | 83.6 L
: 5 — 13.7 83.33’ C #
É| 5–15.0 5–15.8 A 5-13.4 || sº sº. 5 B sag 3
The table gives certain hour angles for declination of 88° 52'20" and 88° 52' 30",
and the corresponding azimuths for Latitudes 36° and 38°. The first interpol-
ation, A, is between the two pairs of hour angles for the hour angles corresponding
to the given declination. The second interpolation, B, is between the two Lati-
tudes for the azimuth at the given Latitude; the new azimuths are correct for
any of the three combinations of hour angles and declinations on their respective
lines. The third interploation, C, is between these two azimuths found in B, to
find the azimuth corresponding to the given hour angle with reference to the hour
angles found in A. The result, 83.33, is the azimuth of Polaris at an hour angle of
5–13.7, a declination of 88° 52'22.4" and at Latitude 37°, i.e., at the instant and
place of observation.
In an Ephemeris of the Sun and Polaris used by the A. E. F. in France the
Azimuths of Polaris have been computed for a constant declination of 88° 52' 20"
between Latitudes of 478 and 60s and for every 10 m. of hour angle. The inter-
polation to obtain the azimuth of Polaris is somewhat simpler than that required
in the Land Office Tables, but a small correction must be made when the declin-
ation differs from 88° 52'20". These corrections are placed in a condensed table
following the table of azimuths. The following problem illustrates how the
tables are used:
Date of observation = Aug. 25, 1918. Declination = 88° 52' 05".
Latitude = 54.59. Hour Angle =4h 23m.
INTERPOLATION
LATITUDES
Hour ANGLE
* 54.0° 54.5g 55.08
4h. 20m. . . . . . . . . . . . . . . . . . . . 1° 33’.7 1° 34'.6 1° 35'.5 --
4h. 22m. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1° 34'.9 | . . . . . . . #
4h. 30m. . . . . . . . . . . . . . . . . . . . 1° 35'.4 1° 36'.4 1° 37'2 |:

The azimuth, 1° 34'.9 corresponds to a hour angle of 4h. 22m. and a declin-
ation of 88° 52' 20" but the true declination is 88° 52'05". In the table of cor-
rections under azimuth of 1° 34'.9 and opposite 88° 52' 05" is found + 0.4' ap-
plying this to the azimuth, 1° 34'.9, the corrected value is 1° 35'.3.
5. Azimuth =83,33' = 1°23'20" equals azimuth of Polaris at Latitude of ob-
- serving station. (Star was West of North because observation was after
nearest upper culmination.)
6. 1°23'20" = azimuth of Polaris.
120° 39' 30" = mean deflection angle, mark to star. (Mark was West of star.)
MERIDIAN DETERMINATION 153
122° 2'50" = angle from North to mark (counter-clockwise).
48' 00" = correction for deviation to West for Lambert North.
(M-Mo.) ×sin Lat. e. (76.3–75) ×sin 38° =.8°=48' 00".
©iºn ; * grid on Ft. Monroe map Long. =75°
at. - 38°.
121° 14' 50" = angle from Lambert North to mark (counter-clockwise).
7, 360° 00' 00"
— 121° 14' 50"
238° 45' 10" =Y-azimuth of line to mark, clockwise. = 265,2818. (See
Fig. XI.)
Without listing the computations for the second set of readings the result
obtained is 265.3819.
Taking a mean of the two we have 265.377& Y-azimuth, from Lambert
North to mark, measured clockwise.
Zamber/
/Vo/7/?
77°C/e
e /Vor//?
Aºo/a/75 |
2d-/*23'20"
/*TS 49%.00"
\\
A9
0.4%
38 231 a.
Fig XI.--SKETCH SHOWING POSITIONS OF MARK, T.N., L.N., AND POLARIS
\


154 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Eacample, (French Method of Computation).-The French
“Tables Extraites. de la Connaissance des Temps” give in one
table the hour angle of Polaris in sidereal time at Greenwich
mean noon each day (“Polarie avance sur le Soleil moven”).
It must be corrected for the difference in Longitude (16 min.
for 15°) to get the hour angle at local mean noon. In the fol-
lowing example this correction is so small that it can be neg-
lected. This hour angle of Polaris at local mean noon, plus
the elapsed sidereal time (which is the elapsed mean time plus
a correction), gives the hour angle of Polaris at the instant and
place of observation; measured clockwise from upper culmi-
nation, from 0 hr. to 24 hrs.
Another table gives the azimuth of Polaris corresponding
to each even degree of Latitude, and each 10 min. of hour angle.
The former varies from 10° to 65° and the latter from 0 hr. to
24 hrs. The azimuths in this table are computed for a mean
declination and no corrections are given for a variation therein.
Consequently, the results may be 30" in error. However, this
may be neglected for most practical purposes.
The following example is based on observations made in France and is com-
puted using the French Ephemeris: -
Observed data:
Date, October 11, 1917. Lat. 48° 40' N. Long. 4° 13' E.
Mean deflection angle, 88° 50' 37". Mean time, 4.33.21 P.M.
Mark was East of star. Watch, 1 m. 30 s. slow.
Computations:
4. h. 33 m. 21.s. Mean watch time of observation.
+ 1 m. 30 s. Watch correction.
4 h. 34 m. 51 S. Standard (Greenwich) time of observation.
+ 16 m. 50 s. Longitude correction (−4° 13' = 16 m. 50 s. variation).
4 h. 51 m. 41 s. } Local mean time of observation, or elapsed mean time since
4 h. 51.7 m. local mean noon. -
+ 0.8 m. Cºº for sidereal time.
4 h. 51.7 m.
(*# *x8.98 m. = 0.8 m. )
4 h. 52.5 m. Elapsed sidereal time since local mean noon.
11 h. 46.3 m. Hour angle of Polaris at Greenwich mean noon, Oct. 11, 1917,
from French Ephemeris.
4.21
0.0 m. Longitude côrrection (# X.16 = 0.04 m)
11 h. 46.3 m. Hour angle of Polaris at local mean noon, Oct. 11.
+4 h. 52.5 m. Elapsed sidereal time since local mean noon. º
16 h. 38.8 m. Hour angle of Polaris at instant and place of observation.
The following table contains the proper data on the azimuth of Polaris, taken
from the French Ephemeris and arranged for easy interpolation:
MERIDIAN DETERMINATION 155
Hour ANGLE
LATITUDE -
16h. 40m. 16h. 38.8m. 16h. 30m.
48° 1° 35'.1 | . . . . . . . . . . . 1° 33’.4
48° 40' 1° 36'.3(A) 1° 36'.1 (B) 1° 34'.6(A)
49° 1° 36'.9 | . . . . . . . . . . . 1° 35'.3
The first interpolations (A) are for the azimuths corresponding to the bracket-
ing Latitudes, at the bracketing hour angles; the second interpolation (B) is
between the two values thus formed to determine the azimuth at the proper
hour angle. It should be noted that for hour angles less than 12 hrs., Polaris is
West of North, and for hour angles over 12 hrs., it is East of North.
88° 50' 37" = Mean deflection angle. Mark, was East of Star.
1° 36' 06" = Azimuth of Polaris (Star was East of North).
90° 27' = Azimuth of mark, measured clockwise from the True North, to
nearest minute, which is as close as it can be computed reliably
unless a correction is made for the proper declination of Polaris
2° 41' = Deviation to the West for True North.
93° 08' =Y-azimuth of line.
5. OBSERVATIONS ON A STAR AT EQUAL ALTITUDES
True North can also be readily obtained by the method of
“Equal Altitudes.” A star that is above the horizon all the
time is called a “Circumpolar Star,” and if observations are
made on it when it is at the same altitude on both sides of its
orbit, True North is halfway between the two readings. The
Fig XII.-OBSERVATIONS OF STAR AT EQUAL ALTITUDES
ABE = Orbit of the Star. P = Pole.
Z BOD = Z AOC = Altitude. O = Observer.
ZDON = Z CON = Azimuth. Z = Zenith.

156 ORIENTATION FOR HEAVY (COAST) ARTILLERY
observations cover a period of Several hours but neither an
Ephemeris nor exact time is necessary. For convenience it is
best to take the observations when the star is below the Celes-
tial Pole. If an observation is taken on a star in the lower left
hand quadrant of its orbit, reading both the horizontal angle
to a given line and the vertical angle, and a few hours later a
second observation is taken when the star is at the same alti-
tude in its lower right hand quadrant, the azimuth of the line
is the mean of the horizontal angles. (See Fig. XII.) Greater
accuracy can be obtained by making several pairs of observa-
tions and computing the mean result.
6. OBSERVATION ON RNOWN TERRESTRAIL POINTS
On the Western Front a transit is usually set up with its
zero on some prominent landmark. The Y-azimuth of this
arbitrary line (zero reading of the transit) is called V.,. If the
coordinates of both the transit point and the W. point are known
the Y-azimuth, V., can be quickly computed, but unless the line
is very long (say 20 kilometers or more) the probable errors in
the coordinates, which are known only to the hearest meter,
will cause a slight probable error in the Y-azimuth.
Arithmetic Mean.—With this arbitrary setting of the transit
the angles to several visible known points can be measured.
This is called making the “Round of the Horizon.” From the
coordinates of the transit point and each such point its Y-azi-
muth (V) can be computed, and from each value of V and the
corresponding transit reading, an independent value of V, can
be computed. These values will vary slightly, because of
errors in the coordinates. It is impossible to tell which
individual result is the more accurate, but it is evident that
their mean value is more reliable than any single value, its
accuracy increasing with the number of points considered,
because the errors in the coordinates of a number of points,
each known to the nearest meter, tend to balance. This is the
same principle that is used in computing the center of impact
in gunnery; a single shot may be anywhere in the 100 per cent.
zone; from three shots a fair value for the center of impact can
be found; and from five shots a closer value.
In computing the mean value of V., from a set of readings
on several known points, any result which differs widely from
the others should be discarded, because it is evidently in error.
MERIDIAN DETERMINATION 157
For instance, suppose that the following five values for Vo were
obtained from angles to five known points, viz.:
A–17° 31' 30"
B–17° 31' 45"
C–17° 31' 25"
D–17° 34' 15"
- : E–17° 31' 20"
The extreme variation in the five values is 2' 55" (between
D and E), but if D is omitted, the extreme variation is 25"
(between B and E). It is evident that there is a material error
in the D value and it should be discarded. The mean of A, B,
C and E is 17° 31' 30", which can be considered as an accurate
determination of We, correct to within 5".
Weighted Mean.-The mean value found above is called the
arithmetic mean. If the distances from the transit point to
the various known points are nearly equal, the probable error
in each value of V, is the same and the airthmetic mean can be
used. However, if the distances vary, particularly if one
distance is several times as great as another, the probable error
in the longer distances is less than in the shorter distances, and
this should be considered in computing the mean value of Wo.
The simplest way is to assign each value a weight in proportion
to its length, multiply each value by its weight, find the sum of
the products, and divide by the total weight. The result is the
“weighted mean.” Usually only seconds need be considered.
The following is an example of this method:

Line Length Weight. Vo Product
A 3384 3 * 17°–31’ – 30" 907
B 4550 4 17°–31’—45" 180"
C 2537 2 17°–31’—25" 50”
D 4838 omit 17°–34’ — 15" • e
E 2114 1 17°–31’ – 20” 20"
10 340
Weighted Mean = 17°–31’–34"
Arithmetic Mean = 17°–31’ –30"
The difference between the arithmetic mean and the weighted
mean is small (in this example only 4"), but the weighted mean
is the more accurate. By the method of least squares a mean
value can be estimated that is even closer than a weighted'
mean, but the method is long and its use is only justified when
extreme accuracy is desired and there is plenty of time. Either
158 ORIENTATION FOR HEAVY (COAST) ARTILLERY
an arithmetic or a weighted mean value for V., determined as
above, is usually sufficiently accurate.
In the following example a transit, graduated clockwise, is
at a known point, P, and the angles from the V. line are read to
three other known points, A, B and C. (See Fig. XIII.) In
the following table v represents the angle found by using the
formula given under Quadrillage: tan v = Ax/Ay or log tan v
=log Ax-log Ay.
Fig. XIII.-DETERMINATION OF MEAN VALUE OF Vo
|
To find the Y-azimuth, V, of a line to a station after determin-
ing the angle, V, it is necessary to plot the line and the angle, v,
and by inspection determine the relation between v and V.
The following formulae cover the possible relations:
W = v; W = 180° ==v or W =360°–v.

MERIDIAN DETERMINATION
159
Eacample:
Given—
Point X—Co-ordinate—Y Transit Readings
A. . . . . . . . . . . . . . . . . . . . . . . . 381,121 191,618 12°–30’–00"
B. . . . . . . . . . . . . . . . . . . . . . . . 384,045 193,392 85°–51’ –00"
C. . . . . . . . . . . . . . . . . . . . . . . . 383,115 192,110 59°–33’ –30"
P. . . . . . . . . . . . . . . . . . . . . . . . 383,676 190,486
Find Vo Ǻ
TABULATED CoMPUTATIONS
Quantity A B C
383,676 383,676 383,676
381,121 384,045 383,115
AX 2,555 369 561
190,486 190,486 190,486
191,618 193,392 192,110
Ay 1,132 2,906 1,624
Log Ay. . . . . . . . . . . . 3.407391 2. 567026 2.748963
Log Ay. . . . . . . . . . . . 3.053846 3.463296 3.210586
Log tan v. . . . . . . . . . 9.753.545 9. 103730 9. 538377
V. . . . . . . . . . . . . . . 66°–06’—15" 7°–147 – 12" 190°–03’—26"
V computed. . . . . . . . 293°–53’—45" 367°–14' – 12" . 34°–56’—34"
Reading. . . . . . . . . . . 12°–30’—00" 85°–51’–00" 59°–33" —30"
Vo. . . . . . . . . . . . . . . . 281°–23'-45" | 281°–23'-12" | 281°–23'-40"

Vo =Vcom. – Reading.

Line Length Weight Vo Product,
PA. . . . . . . . . . . . . 2750 3.5 28.1°–23’—45" 158
PB. . . . . . . . . . . . . 2950 4.0 28.1°–23’ — 12" 48
PC. . . . . . . . . . . . . 1700 2.5 281°–23’ –04" 10
Total. . . . . . . . . . . . . . . . . . . . . . . 10. 0 844°– 10’ —01" 216
Arithmetic Mean . . . . . . . . . . . . . . . . . . . . . . . . 281°–23’ —20" 22
Weighted Mean. |. . . . . . . . . . . . . . . . . . . . . . . . 28.1°–23’ — 22" s s a
Rnowing the Y-azimuth W., of this arbitrary line, Lambert
North or True North can easily be found, and the correct
value of the Y-azimuth of any line radiating from that station,
based on the mean value of V., can be computed. A mean
value of V, based on several observations to distant points is
very reliable.
CHAPTER IX
TRANSIT TRAVERSE
METHODS OF RUNNING TRAVERSES
FORMS FOR FIELD NOTES
COMPUTATIONS
ADJUSTMENT OF COORDINATES AND ALTITUDE
PLOTTING THE TRAVERSE
:
The transit may be used in making a traverse instead of
a plane table, the essential difference being that the obser-
vations taken with the transit are more precise and are re-
corded in a note book together with rough sketches as a
guide, the computation and plotting being done at any time
and place convenient. Transit traverses can easily be made
with a precision of less than 1 per cent. error and are invar-
iably used in preference to the plane table traverse when very
precise locations are desired. Having triangulation stations
already established, the position of any point in the area
covered by the triangulation system can be located by run-
ning transit traverses which should begin and end at a trian-
gulation station. If only one triangulation station is near,
the traverse should be run to the unknown point and made
to close by returning to the same station by a different route.
The transit is used to measure the horizontal angles at
the intersection of adjacent courses; the vertical angle, or
slope, of each course; to lay down and prolong the straight
lines forming the several courses; and to measure each course
if stadia measurements are used.
Having this data, the remainder of the work—which may
be done at any time and place convenient—consists of
(1) computing and adjusting the error in the horizontal
angles, (2) giving the corrected Y-azimuth of each course
and aiming line, and adjusting the error of closure,
(3) reducing the actual length of each course to its horizontal
projection; (4) computing, from this corrected data, the coor-
dinate components of each course; and (5) plotting or tabu-
lating the results of these computations. These computations
cannot be made unless the field notes show (1) the length of
each course, (2) the angle at all the intersections of adjacent
TRANSIT TRAVERSE 16.1
courses, (3) the angle from some one course to a line of known
direction, and (4) the coordinates of some point on the traverse.
Lacking any one of these, the notes are incomplete and of little
value. To this extent notes should be made complete before
the field work is completed. Additional field data for checks
is always desirable and often extremely valuable.
The several methods of running a traverse, as indicated in
the following discussion, are usually named from the manner
in which the angles are read. In this connection it should
be borne in mind that each course must also be measured,
usually by one of the three following methods: (a) stadia,
(b) tape, or (c) computed trigonometrically. Stadia measure-
ments are quickly and easily made, but with a probable error
of one in 400, under ordinary conditions. When time and the
terrain permit, tape measurements are much better than
the stadia, being much less liable to gross errors as well as
more precise than stadia measurements under all ordinary
conditions. Computed courses are most precise, but require
the use of a triangulation system on a small scale, which
would be advisable only in case of very rough country, ob-
struction, or the need of a very precise survey.
It should also be observed that in all this work pertaining
to the computation of firing data, the angular measurement is
much more precise than the accompanying linear measure-
ment. The explanation is that an error of one or two meters
in the location of a gun position is of no importance as com-
pared with a small error in direction for a 10 kilometer range.
1. METHODS OF RUNNING TRAVERSES
Direct Angle Traverse.—This method consists simply in
measuring the angle at each station directly from a back-
sight on the preceding station to the station ahead. If de-
sired the angle may be doubled, tripled or repeated any num-
ber of times. If the limb on the transit is graduated clock-
wise the stations of the traverse should be occupied in counter-
clockwise order, to simplify the reading of limb and vernier.
Care must be taken not to read the exterior angle at a re-
entrant angle, as Sta. C, in Fig. I.
In Fig. I let A represent a triangulation station and D a
directing gun whose position is to be determined. The tran-
sit is set up at A, the angle to AB from some reference line of
known Y-azimuth is read, and the distance to station B is
determined by reading a stadia rod or by tape measurement.
!
162 ORIENTATION FOR HEAVY (COAST) ARTILLERY
O
Gwri Pºsſfor " º
A A
77-ſarau/zhon
Staffor
Fig. I.-DIRECT ANGLE TRAVERSE
The transit is taken to B and the interior angle between the
courses AB and BC is measured and the distance to C is
determined. C is occupied in a similar manner. To check
the work the traverse is made to close by returning to A by
another route which in this case includes one additional
station, E.
Method of procedure at each station.
(1) Set up and level transit over stake marking the station.
(2) Using the upper motion, clamp vernier A at 0°.
Wernier A is under the eyepiece end when the telescope is
in the normal position. Vernier B is used only as a check.
(3) Direct telescope on preceding station with lower
motion and clamp. (This is called backsighting.) At the
first station read the direct angle between the line to the for-
ward station and a line whose Y-azimuth is known in order to
have the data for computing the Y-azimuth of the courses of
the traverse. -
(4) If using stadia measurement read and record the
intercept on the rod and the corresponding vertical angle.
(5) Loosen upper motion and direct telescope on forward
station with upper slow motion and clamp. (Foresighting.)
(6) Read and record vernier A. In very accurate work
the angle should be measured by repetition, that is, the angle
should be added on the limb several times and the mean of
the readings used.




TRANSIT TRAVERSE 163
(7) Read and record stadia intercept and vertical angle
to the forward station.
Deflection Angle Traverse.—This method is being used
almost exclusively for artillery work in France at the present
time and particular emphasis will be placed on it in this
Chapter. By taking certain precautions it can be made
very precise. Instead of measuring the interior angles, as
in the direct angle method, the angle between any course
extended and the next course is determined. The same
courses shown in Fig. 1 will be used for an illustration of this
method and also for the two methods which follow. When
using this method the stations should be occupied in the same
order, clockwise or counter-clockwise, as the numbering of
the graduations of the 0°–360° circle on the limb of the tran-
sit. This simplifies reading the angle on the limb. Read
always on the 0°–360° circle, never on those graduated by
quadrants. In the field notes record always and only the
figures actually read, indicating whether the angle is Right
or Left. All reductions and computations should be made
later and not as a part of the field notes, which should never
be erased or changed in any way after leaving the station at
which they were taken. •
Deflection angles may be read either by the simple or
double reverse method. Simple deflection angles are read
but once with the instrument, being quickly read but liable
to error both from mistakes in reading and poor adjustment
of transit. Double reverse reading tends to prevent personal
errors, compensates for poor instrument adjustment, and gives
a more precise value because of the repetition of measure-
ment. The latter is the standard method for precise traverse.
Simple deflection angles—Procedure at each station:
(1) Set up and level transit over station.
(2) Using upper motion, clamp vernier A at 0°.
(3) With telescope normal, using lower motion, clamp
the transit with the line of sight on the preceding station.
At the first station read the deflection angle between the
forward station and the orientation line.
(4) Loosen the upper motion, plunge the telescope,
direct it toward the station ahead using upper motion only,
read and record vernier A. This completes the angle read-
ing; loosen the lower motion, leaving the upper motion clamped.
(5) If using stadia measurement, with telescope normal,
read rod intercept and the vertical angle and record.
164 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Orlantoſh Y,
rtantof ion • *
i.' rú
Fig. II.-DEFLECTION ANGLE TRAVERSE
Double Reverse deflection angles—Procedure at each station:
(1) Set up and level transit over station.
(2) Using upper motion, clamp vernier A at 0°.
(3) With telescope normal, using lower motion, clamp
the transit with the line of sight on the preceding station.
At the first station read the deflection angle between the
forward station and the orientation line.
(4) Loosen the upper motion, plunge the telescope, direct
it toward the forward station, using upper motion only, read
and record vernier A.
(5) Leaving upper motion clamped, loosen lower motion,
and direct telescope (still inverted) toward the preceding
station, using lower motion only, and clamp.
(6) Loosen the upper motion, plunge telescope (back to
normal) and direct it toward the forward station, using upper
motion only, read and record vernier A. -
This completes the angle reading, giving two values,
which should check closely. Any even number of repeti-
tions, as four, six, etc., may be obtained by repeating the
above cycle of operations. Length and slope of courses are
then measured as described for the Simple Deflection Angle
Traverse.
Azimuth Traverse.—In this method the transit is oriented at
each station and the angles made by the transit lines with true





TRANSIT TRAVERSE 165
north are measured. A traverse can be run by measuring
Y-azimuth, the only difference being that the angles are meas-
ured from Lambert north instead of true north. The angles
are not measured with the same precision and certainty as
when using the double reverse method, but the field work is
more quickly and easily done, and can be roughly checked
at any time by means of the compass. The method is mainly
used on short traverses where time is a greater consideration
than precision. The first and closing stations may have refer-
ence points of known Y-azimuth, or orientation may be
obtained from solar or Polaris observations.
Procedure at each station:
(1) Set up and level transit over station.
(2) Lower motion should be loose; upper motion clamped
with vernier A reading the same as when looking forward
from the preceding station.
Fig. III.-AZIMUTH TRAVERSE
(3) With telescope inverted, direct it to preceding sta-
tion, using lower motion. This orients the limb; that is,
with telescope normal, vernier A gives azimuth for any point-

166
ORIENTATION FOR HEAVY (COAST) ARTILLERY
ing of the telescope.
The instrument may be oriented at
the first station of a traverse by setting on vernier A the
Y-azimuth of any line from the first station to a given point
and with the lower motion direct the inverted telescope on the
given point, then clamp the lower motion.
(4)
Loosen upper motion, plunge telescope back to nor-
mal, direct it to forward station using upper motion and read
and record vernier A. This reading is the azimuth of the
course, looking forward. Read always and only on 0°–360°
circle on the limb. -
COMPARISON OF METHODS OF ANGLE MEASUREMENT
ADVANTAGES DISADVANTAGES
DIRECT | 1. Stations may be occupied in 1. Liability of error in reading
ANGLES any order. exterior instead of interior
2. Error in one angle measure- angle at a reentrant angle.
ment does not affect others. |2. Angle as read cannot be used
3. Must be used when telescope directly in computing Y-azi-
cannot be plunged. muth of course.
4. Probably the most simple 3. Lack of adjustment of transit
method for those not well ac-l causes errors.
quainted with transit.
SIMPLE | 1 and 2. Same as preceding. 1. Cannot be used on telescopes
DEFLECTION 3. Computation of Y-azimuth too long to be plunged.
ANGLES more simple than with direct|2. Practically all errors of ad-
angles, as the angle read justment affect results.
actually measures the change
in direction.
4. By reading on 0–360° circle,
| R. and L. designations are
unnecessary.
DOUBLE | 1, 2, 3 and 4. Same as preceding. 1. Cannot be used on telescopes
REVERSE |5. Eliminates practically all the too long to be plunged.
DEFLECTION errors due to lack of adjust- 2. Manipulation somewhat con-
ANGLES ment of transit. . fusing to those not familiar
6. Repetition gives both a check with transit.
and added precision. -
AZIMUTH | 1. Reading gives azimuth, direct.|1. Stations must be occupied in
ANGLEs 2. Notes and computations much order.
simplified. - 2. Angles cannot easily be read
3. Compass reading may be used by repetition.
to check azimuth of line. 3. Setting of plates must be
checked before reading any
angle.
4. Errors in one angle affects all
work which follows.
5. Errors of adjustment of transit
affect results.
BEARINGs | 1. Field work quickly and easily 1. Results liable to have great
done under adverse conditions.
2. May usually be done with
disabled transit.
errors, being neither consistent
nor dependable.
–ºf–
TRANSIT TRAVERSE 167
Before running a traverse give careful consideration to
the necessary precision of the results required, study the
terrain and select the method best suited. Give due con-
sideration to both time and precision, which will usually be
the controlling factors in selection. What is gained in accu-
racy will be lost in time and vice versa. The terrain will
usually determine whether the distances will be measured
by tape or stadia. If time is available and the ground is not
particularly rough the tape should be used, but if speed is
essential or the terrain is very hilly the stadia is preferable.
2. FoEMs FoR FIELD NOTES
It is a universally accepted principle that field work is
usually of no value unless all the various readings and other
data are carefully and systematically recorded according to
some suitable form, exactly as they are read from the instru-
ments. The question of the particular form is of much less
importance than the keeping of it. Those forms here given
are considered suitable for the work under discussion, but
when the method is changed the recorder should give con-
siderable thought to devising suitable changes to fit the new
conditions. A sketch showing the approximate length and di-
rection of each course, and their relations to any reference points
and lines, will be found helpful in clearing up any uncertainty
in the notes or in the manner in which readings were taken.
“Full and complete descriptions of all road crossings or
intersections, kilometer posts, boundary stones or other
permanent monuments should be made in the notes as the
line progresses; in fact one should endeavor to place his tra-
verse so that each line run may constitute a permanent record
not only in the notes but upon the ground as well. To this
end all stations wherever possible should be on hubs securely
placed, marks on stones or nails in roots of trees. Any por-
tion of a line run may be very useful in some future work and
save valuable time in retracing, as well as avoid a multiplicity
of astronomic observations which are generally more or less
tedious on account of atmospheric conditions.
“Above all, keep notes and descriptions in a legible and con-
cise manner so that they may be readily interpreted by any
other field party, and, what is equally important, so that the
computer will not be at sea in seeing at a glance what has really
been done. A neat sketch, supplemented by a word picture is the
best possible medium for conveying information of this type.”
FIELD NOTES-DIRECT ANGLE TRAVERSE
e Horizontal STADIA Rod READINGS 100 Times
Sta. Line Angle Vertical Intercept REMARKS
(Vernier “A”) Angle - +0.30 m.
Upper Middle Lower -
A A—AT O° To A sta. T.
A A—B 81° 10' — 19 15’ 3.31 1.91 0. 50 281.3 |281.55 =tape measure
Mean — 19 15' 281.6 m.
B B-A 0° +1° 15' 2.916 1. 52 0.10 281.9
B B–C 83° 51’ +3° 0' 2.02 1.26 0. 50 152.3 Sta. B =stake-Hinail at S. end of bridge
Mean +3° 1' 152. 4 m.
C C—B 0° –3° 2' 2. 522 1.77 1.00 152.5
Sta. C =stake-Hinail at lone oak, near
C C–D 209° 19' +0° 46' 1.905 1.08 0.25 165.8 creek
Sta. =stake, point or location over which transit is placed.
Line =line along which telescope is directed.
Horizontal Angle =reading of vernier “A.”
Vertical Angle =reading on the vertical circle when middle horizontal crosswire of telescope cuts stadia \rod at same reading as height of
telescope above top of station stake.
Stadia Rod Readings=readings of horizontal crosswire intersection on stadia rod held on station indicated.
#
w
100 ×iº. +0.30 m. = total rod intercept, checked by middle wire, multiplied by 100, and instrument constant added, giving slope length
OI (3OUli SE.
Remarks=any pertinent data not noted elsewhere.
ź

FIELD NOTES-SIMPLE DEFLECTION ANGLE TRAVERSE
Def V I STADIA ROD READINGS º Times
- & ~ : Avº ( ; A 27 eflection ertica ntercept REMARKS
Sta. Line Vernier “A Angle Angle +0.30 m.
e Upper | Middle | Lower
A A—AT 0° 0' To A Sta. T
A A—B 335° 49' 24° 11'L — 19 15' 3.31 1.91 0. 50 281.3 281.55 = tape measure
Mean — 19 15' 281.6 m.
B B—A 0° 0' +1 15' 2.916 || 1 , 52 (). 10 281.9
B B–C 26.3° 51’ 96° 09/L +3° 0' 2.02 1.26 0. 50 152.3 sº ºstake-ºnal at S. end of
}ridge
Mean +3° 1' 152.4 m.
C C–B 0° 0' –3° 2' 2. 522 | 1.77 1.00 152.5 |Sta. C =stake-Hinail at lone oak,
near creek
C C–D 29° 19' 29° 19'R. +0° 46' 1.905 1.08 0.25 165.8
Vernier A =reading of “A” vernier on 0°–360° graduations, horizontal limb.
Deflection Angle=angle from preceding course produced, to the forward course. Value and direction both deduced from Vernier “A”
readin
gs, knowing direction of graduation of horizontal limb and remembering that deflection angle is always less than 180°.
an essential part of field notes, but included here to show how it is obtained from vernier “A” readings.
Other columns are same as form for Direct Angle Traverse.
Not
Ž

FIELD NOTES-DOUBLE REVERSE DEFLECTION ANGLE TRAVERSE
© Mean STADIA Rod READINGs 100 Times
Sta. Line Vernier “A”. Differences | Deflection | Vertical Tape Intercept REMARKS
Angle Angle Measure +0.30 m.
Upper | Middle | Lower
A A–AT | 247° 14' s To A Sta. T
A A—B 223° 03' 24° 11’ — 19 15' | 281.55 m. 3.31 1.91 0. 50 | 281.3 281.55 =tape meas.
A | A–B | 198° 52' 24° 11’ | 24° 11’L | – 19 15' - 281.6 m.
B B-A 113° 41' +1° 15' 2.916 1. 52 0, 10 || 281.9
- Sta. B = stake-Hnail
B B–C 17° 33’ 96° 08' +3° 0' | 152.00 m. 2.02 1.26 || 0 , 50 | 152.3 at S. end of bridge
B B–C | 28.1° 23' | 96° 10' | 96° 09'L | +3° 1' 152.4 m.
C C–B 312° 04' –3° 2' 2. 522 1.77 1.00 152.5 Sta. C=stake-Hrail
at lone oak, near
C C–D 341 ° 24′ 29° 20' +0° 46' | 165.75 m. 1.905 1.08 0.25 | 165.8 creek
C
C–D 10° 42’ 29° 18' 29° 19'R.
Vernier “A” =readings of “A” vernier on 0°–360° graduations, horizontal limb. The initial setting for the backsight is not 0°, but the
upper motion is clamped at any position, the telescope directed at the backsight using lower motion, and vernier “A” read and
recorded. Measuring the angle then proceeds as previously described.
Differences = difference between successive readings of vernier “A.” Each difference gives one value of the deflection angle, and its direc-
tion; and they should check closely, which guards against errors of reading, etc. Limb of transit assumed to be graduated clockwise.
Mean Deflection Angle=the mean of the Differences column, giving a more precise value than any one difference and compensating for the
usual errors of transit adjustment. The repetition may be carried along to four or six times for greater precision, if desired.
NoTE.—If the accuracy desired requires that the angles be measured by the double reverse method all distances should be taped to maintain
the same degree of precision between the lengths and directions of the courses.
§

FIELD NOTES-AZIMUTH TRAVERSE
STADIA Rod READINGs 100 Times
Sta Line Azimuth Vertical Intercept REMARKS
e (Vernier “A”) Angle +0.30 m.
Upper Middle Lower
A AT—A 316° 47' Azimuth from A sta. T = 316° 47'
A A—B 292° 36' — 19 15' 3.31 1.91 0. 50 281.3 281.55 =tape measure
Mean — 19 15’ 281.6 m.
B B—A +1° 15' 2.916 1.52 0.10 281.9
B B–C 196° 27' +3° 0' 2.02 1.26 0. 50 152.3 Sta. B =stake-Hnail at S. end of bridge
Mean +3° 1' 152.4 m.
C C–B +3° 2' 2. 522 1.77 1.00 152.5
Sta. C=stake-Hnail at lone oak, near
C C–D 225° 46' +0° 46' 1.905 1.08 0.25 165.8 creek
Mean
Azimuth = angle from true north, measured clockwise, to each course in its forward direction.
Azimuth of line from sta. T to sta. A would
have been previously determined as 316° 47'. 'Vernier “A” is set to this reading, telescope plunged and set on sta. T, orienting the
transit.
Other columns same as preceding forms.
Sighting to B, telescope normal, then gives azimuth of line A-B.
s

172 ORIENTATION FOR HEAVY (COAST) ARTILLERY
3. CoMPUTATIONS
Having the complete field notes and field sketch of a transit
traverse, the desired information—usually consisting of the
coordinates of the gun position and Y-azimuth of a reference
line from it—may be computed at any time. Unlike the field
work, which would never be done twice exactly alike, the
computation should give identical results by all computers,
using the same field notes. Field work is then a matter of
precision while computations are either accurate or inaccurate,
the latter being of no value. It is desirable to keep this dis-
tinction in mind, because no computation may be used until
checked, and checking is impossible unless each computer is
accurate. For this reason all computations are made with
logarithms of not less than five places, and care in the work
will usually give checked results more quickly than any attempt
at speed.
The successive steps in the computation of a traverse, of
which the previously given field notes are a part, will be shown
in detail in the remainder of this chapter. The computations
are given on Fig. V, which represents a typical computation
form suitable for this work. The detailed explanation of this
form is given in the subhead, “computation of coordinates.”
Adjustment of Angular Error.—The sum of all the interior
angles of any irregular closed figure, as a closed traverse, is
found by multiplying the number of sides, less two, by two
right angles (180°). This method is used to check the angles
of a closed, Direct Angle Traverse. For example, Fig. I
shows a closed traverse of five sides. The sum of the interior
angles should be (5–2) times 180° = 540°. If the sum is
approximately 540° the field work is probably free from
angular errors, the difference between the actual sum and 540°
being a measure of the precision of the angle measurements.
This difference should usually be apportioned to each angle
equally. Thus, if the sum actually were 540° 10', each angle
should be reduced by 2'. The reason for this is not that
each angle was probably read 2' too small, but that some
one angle may be 10' in error, or two angles may each be 5'
in error, and in the absence of any definite knowledge of the
error the best adjustment will be to apply the same correction
to each angle. Occasionally, Some particular angle may
be known to be liable to error, justifying the placing of all or
a large part of the adjustment at this angle; but usually the
TRANSIT TRAVERSE 173
uniform adjustment is preferable. If the adjustment is more
than 2' per angle additional field work to reduce the error is
necessary. For precise traverses the adjustment should
be well within 1' per angle. Note that no adjustment is
made of any angle measured from a line of known Y-azimuth,
and which is not one of those angles whose sum is checked
against the theoretical value.
The sum of the deflection angles of a closed deflection
angle traverse should be 360° since the transit makes one
complete revolution in a closed circuit. If the stations are
occupied in clockwise order, deflection angles to the right will
be plus, while those to the left will be negative, the signs
being considered in computing the sum. The divergence of
thus sum from 360° is the total angular error. This is appor-
tioned equally to each angle. If the sum for a 5 course tra-
verse were 359° 50', the error would be 10'. The adjustment
would be 2' per angle, and it would be added to plus angles
but subtracted from negative angles. -
A traverse may not close on itself, but at a point of known
coordinates on a line of known Y-azimuth, starting from some
similar location. The algebraic sum of its deflection angles
should equal the difference of Y-azimuth of the two known
lines. The error is apportioned equally among the angles,
as for a closed deflection angle traverse. For example, Fig. IV
L.M.
§ N N A Tº
§l &#3 | \ friargv/affon &
- § ſº §§ D 3% who/, *N
!—s §§§ 2\!
§ § Z
§ &
~! §
&//
:
§
G
GUAW sº
Posſrow | *š.
º
/
3. º- fior sºsºs"
3.
Fig. IV.-ANGULAR TRAVERSE
shows a traverse of four courses, running from Station A on
line AX to the gun position, G, and closing at Station B on
line BY. Lines AX and BY and Stations A and B might
belong to a triangulation system previously established.

174 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Sum of deflection angles is:–
+ 48° 10' – 97° 18' Y-azimuth of Line BY = 201° 08/
+ 54° 16' — 27° 50' Y-azimuth of Line AX = 160° 20'
+ 63° 40' — 125° 08' Difference of Y-azimuth = 40° 48'
+ 166° 06'
Sum = +166° 06’—125° 08' = +40° 58'.
Errors in traverse angles equals difference of 40° 48' and
40° 58', or 10'. The correction, or adjustment, will be 2'
per angle, subtracted from plus angles and added to negative
angles. The corrected angles are indicated in parentheses
on Fig. IV, and are those accepted and used for the computa-
tion of Y-azimuth and coordinates.
Computation of Y-azimuth.-In order to determine the
coordinates of an unknown station by running a traverse to
it from a station whose coordinates are known, it is necessary
that the Y-azimuth of courses be accurately determined.
This can be done if the Y-azimuth of any one of the courses is
known. If the traverse starts from a triangulation station it
is very likely that the Y-azimuth of some line through the sta-
tion has previously been determined by one of the three accu-
rate methods given in the Chapter on Meridian Determination.
If this is the case it is only necessary to read the angle between
the line of known Y-azimuth and the first course in order to be
able to orient the traverse. If there are no lines at the initial
station of the traverse whose Y-azimuth are known the Y-azi-
muth of the first course will have to be determined by a solar
or Polaris observation or by computing a Terrestrial Y-azimuth,
otherwise the traverse will be worthless.
Having the adjusted angles of a traverse and the Y-azimuth
of any one course, the Y-azimuth of each course may be readily
computed. While a line may have two Y-azimuths, differing
by 180°, a traverse course is always assumed to point in the
direction the traverse was run.
In Fig. IV, the Y-azimuth of AX is assumed to have been
previously established as 160° 20'. The Y-azimuth of each
course would be computed as follows:
Sta. A, Y-azimuth of course AX = 160° 20'
Sta. A, direct angle right +48° 08'
Sta. A, Y-azimuth of course AC = 208°28'
Sta. C, deflection angle right = +54° 14'
TRANSIT TRAVERSE 175
Sta. C, Y-azimuth of course CG = 262°42'
Sta. G, deflection angle right = +63° 38'
Sta. G, Y-azimuth of course GD = 326°20'
Sta. D, deflection angle left = – 97° 20'
Sta. D, Y-azimuth of course DB = 229°00'
Sta. B, deflection angle left = — 27° 52'
Sta. B, Y-azimuth of course BY = 201° 08'
The final computed Y-azimuth of any series should check
with its previously determined value, thus checking each of
the intermediate computed values.
Reduction to Horizontal.—Tape measurements are usually
made so as actually to measure the horizontal projection of
the slope distance covered. Trigonometrically computed dis-
tances are always horizontal. Stadia measurements give slope
distances, from which the horizontal and vertical projections
are computed or obtained directly from stadia reduction
tables. These reductions must be made, as illustrated by an
example in connection with the explanation of these stadia
reduction tables in the Chapter on Linear Measurements, be-
fore the traverse can be plotted or computed. The horizontal
projection is then used to compute the coordinates while the
vertical projection is the increment of altitude of each course
Computation of Coordinates.—Computations are made on
a ruled form, illustrated by Fig. V, after the field measure-
ments have been adjusted and entered in their proper col-
umns, each column being explained as follows:
Sta.-Indicates the position of the transit during all the
measurements shown in the same horizontal space.
Line.—Indicates the pointing of the telescope for all
measurements on the same horizontal line on the field form
or computation sheet.
Deflection Angle.—In this column are placed the adjusted
deflection angles. The angles shown are the same as given
in the field notes, but they will not be the same if a correction
is to be applied as explained in Adjustment of Angular Error.
Y-azimuth, V.—This is the Y-azimuth of each course, in the
forward direction, computed by applying the deflection angles
in the preceding column to the Y-azimuth of the preceding
course, explained in Computation of Y-azimuth, and Fig. IV.
Vertical Angle.—In this column is entered the mean of
the two values of the vertical angle along each course, copied
from the field notes direct.
176
ORIENTATION FOR HEAVY (COAST) ARTILLERY
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TRANSIT TRAVERSE - 177
Distance, Stadia or Tape.—In this column, opposite each
course, is entered the mean value of the two stadia measure-
ments along the course. If the course is measured with tape
the horizontal projection has usually been measured and in
which case the value may be entered directly in the following
column.
Horizontal Distance, D.—This is the horizontal projection
of the slope length of each course, computed from the stadia
measurement as explained in Reducation to Horizontal. It is
helpful to note in the preceding column the amount deducted
from the slope distance. This horizontal distance D is the
distance used in all coordinate computations, or for plotting
the traverse.
Altitude Increments.--This is the vertical projection of
the slope length of each course. When stadia measurements
are used this Altitude Increment is obtained directly from
reduction tables, as explained in Reduction to Horizontal. If
tape measurements are used, the altitude increment = dis-
tance D, multiplied by the tangent of the vertical angle of
the course. The sign of the value obtained will be plus for
an ascending course, and negative for a descending course.
Care should be observed that the value obtained is placed in
the column of the proper sign. This sign will be the same as
the sign of the vertical angle. -
Coordinate Computations.—Having the horizontal length,
D, and the Y-azimuth, V, of each course, the difference of the
X and Y coordinates of the beginning and end of each course
is computed. The difference of X coordinates is called dx,
and difference of Y coordinates is called dY. These differ-
ences, called increments, are computed from the following
relations:
- dX=D sin W; dY = D cos V
dX is the projection of the course on the X axis and dY
is the projection on the Y axis, as shown in Fig. VI. V is
the Y-azimuth; but the sine and cosine of Y-azimuths greater
than 90° must be taken with the proper sign, and the angle
actually looked up in the tables is in every case the smaller
angle between the Y axis and the course in the forward direc-
tion, as shown in Fig. VI. For example, for a course of Y-
azimuth between 0° and 90° the Y-azimuth itself is used; if the
Y-azimuth were 100°, the angle used in computing dx and dY
would be 80°; if the Y-azimuth were 225°, 45° would be used,
and if 320°, 40° would be used.
178 ORIENTATION FOR HEAVY (COAST) ARTILLERY
L. N.
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+d Y | +dy
270. 90
X . \ — dx +d){ /
– d Y | – d’Y /
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Fig. VI.--COORDINATE INCREMENTS AND Fig. VII.-SIGNS OF INCREMENTS
ANGLES OF COURSES WITH Y AXIS IN FOUR QUADRANTS
The signs of the resulting values of dx and dY must be
carefully observed. If d X extends toward the right it is
positive, while to the left is negative. If d Y extends upward
its sign is positive, while downward is negative. Another
quick method of determining the signs is by the use of Fig.
VII. For Y-azimuths between 0° and 90° both increments
have plus signs; for Y-azimuths between 90° and 180° dx wil
be + while d'Y is —, and so on.
The method of making these computations is shown on
Fig. V which shows that at Station A, course AB has a
Y-azimuth of 292° 36' and a horizontal distance of 281.46
meters. In the first column under “X Coordinate Compu-
tations” is placed the logs of the quantities. First is the log
sin of the angle used, which is the smaller angle from 292° 36'
to the Y axis. This is 67° 24′ which, for the quick reference,
may be noted in small figures as shown. To the log sin
67° 24' is added the log D, which is 2.4494167. The sum of
these logs is the log d) for the course. In the tables the
corresponding distance d x is found to be 259.85, and its
sign as determined by any of the rules just given is negative.
259.85 is therefore entered in the dx column headed —. The
value of d'Y is similarly obtained, using log cos in place of log
sin, the same angle, 67°24', being used.
4. ADJUSTMENT OF COORDINATES AND ALTITUDE
Computations of the dx and dY increment of each course
having been made and entered in their proper columns of the
computation form illustrated by Fig. IV, the algebraic sum

TRANSIT TRAVERSE 179
of the dx values of the courses between any two stations
gives the difference of X coordinates of those stations. Simi-
larly for the Y coordinates. Therefore, with a closed trav-
erse, the initial and closing station being the same, the
algebraic sum of the dN increments should be zero, and the
same for the d'Y increments. That is, the sum of the + d x
values should equal the sum of the – d.X values. Assuming
the computations to be accurate, the difference of these totals,
called the error of closure, is a measure of the precision of the
field work. -
Before using a traverse having errors of closure, some
attempt must be made to correct or adjust the several meas-
urements so as to eliminate these errors in field work. If
the error of closure is large, the field notes and computations
should be checked carefully for some misinterpretation of the
notes, or mistake in computation, to make certain that the
error is due to the field work. If the error proves to be in
the field work, and is large, the only satisfactory procedure
is to check the field work. If the error of closure is small
it is compensated for by adjusting the computed value, so as
to eliminate the error. Occasionally this adjustment may be
applied to only one, or a few of the field measurements which
are known to be faulty. Usually the more reasonable and
satisfactory method is to assume the field work to have been
done with uniform precision and adjust all the measurements.
A standard and accepted method consists in apportioning
to the d\, d\ and altitude increment of each course its part
of the total error, in the proportion of the length of course
to the total length of traverse. -
This adjustment is more easily understood by referring
to the computation on Fig. V. To find the correction that
must be applied to each course multiply the total error of clo-
sure by the length of the course and divide by the total length
of all the courses. The error of closure of d x increments is
indicated as +1.21 (linear unit is meter). To adjust the
2
course A — B, apply, 1145.07% 1.21 = 0.30 to the dN increment
of the course. The sum of the +d), increments being the
larger, all – d.X increments are to be increased, while +d)K
values are decreased. To the – d.X increment of course A–B,
which is 259.85, is added 0.30, making the adjusted increment
260.15. If each d x value is adjusted in this manner, the sum
of the adjusted --d Y values will equal the sum of the adjusted
180 ORIENTATION FOR HEAVY (COAST) ARTILLERY
—d X values. The d'Y increments are adjusted in the same
manner. The method of distributing the error in the sum of
the plus and minus increments of altitude is similar to that
used in balancing the coordinate increments. The correction
that must be applied to each increment is found by multiply-
ing the total error by the length of the course and dividing by
the total length of all the courses.
If the traverse is not a closed circuit, but runs from one
triangulation point to another the dN, dY and altitude incre-
ments are adjusted by exactly the same method, so as to make
the algebraic sums of the increments indicate the same dif-
ference of coordinates and altitude between the initial and
closing stations as are known actually to exist.
As a traverse always starts from a triangulation station
whose coordinates are known, the coordinates of any station
on the traverse can be determined by adding algebraicly to
the coordinates of the first station the dxs and dYs to the
station whose coordinates are wanted. Example, in Fig. W
the coordinates of the gun position are:
X = 4000–260.15 – 43.20 – 118.95 = 3577.70
Y = 6000+ 108.77–145.44 – 115.28 =5848.05
The altitude of the gun position is found in a similar manner:
Altitude = 500—6.18—H·7.99-H2.19 = 504.00
5. PLOTTING THE TRAVERSE
The traverse may be plotted by several different methods,
at various times during the course of the work, with varying
degrees of precision, depending upon the use to which the
plot will be put. -
A rough and approximate sketch should be made at the
time the field work is done, for the purpose of adding clearness
to the notes and indicating the general direction and extent
of the traverse. A plot to a small scale of the completed
field notes should be made before computing the traverse,
as an aid in making these computations and applying the
adjustments. When the computations are adjusted and com-
pleted, the final and official plot of the traverse is made, with
care consistent with the results required. It may be made on
the battle map direct, on the firing board, or on any other
map used for location purposes. Occasionally, with a short
traverse the plot may be made with scale and protractor, laying
off the adjusted angles or Y-azimuths and horizontal distance,
TRANSIT TRAVERSE 181
D, of each course. A more precise and preferable method is
to plot each station by its coordinates as computed from the
adjusted increments of the computation sheet. This requires
the grid system to be drawn before plotting begins.
Fig. VIII shows a plot of the computations on Fig. V.
The coordinates of the initial station being known the coordi-
nates of any other station are computed by applying to the
coordinates of the initial station the algebraic sum of the
increments of each course between the stations. Thus in
the plot shown Station B is 260.15 m. to the left and 108.77 m.
above Station A. Applying these values to the coordinates
of Station A gives the coordinates of Station B, and similarly
for the other stations.
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It is desirable to give the coordinates of each station on
the plot. While it may also be convenient to indicate the
Y-azimuth and length of each course, these figures should be
enclosed in parentheses, or encircled, as they are slightly in
error due to the adjustment corrections applied to the incre-
ments in adjusting the traverse. -


CHAPTER X
INTERSECTION
1. REDUCTION TO CENTER AND SWING
2. U. S. METHOD OF INTERSECTION
3. FRENCH METHOD OF INTERSECTION
1. REDUCTION TO CENTER
The method of determining the coordinates and distance to
an unknown point has been explained under triangulation.
It will be remembered that it was necessary to set up a transit
at each end of a base line of known length and read the hori-
Zontal angles to the unknown point. In France there are many
points located over the entire battle area whose coordinates are
known. The distance between any two of these known
points can be determined and used as a base line. Setting up
a transit at each end of the base line and measuring angles to an
unknown point gives the necessary data for determining the
coordinates of the unknown point. In many instances, how-
ever, points whose coordinates are known are towers, trees, etc.,
and cannot be occupied. In such cases the transit is set up
near the known point which cannot be occupied and angles
measured to the unknown point and also to known points.
Each angle read must now be reduced so that it will be the
same as if the transit had been set up over the known station.
For this reduction it is necessary to know:
a. The angle measured at the instrument between the
center of the signal and the first distant station to the right of
it as viewed from the instrument. -
b. The distance in meters from the instrument to the cen-
ter of signal.
c. The approximate distance from the signal occupied to
the various signals sighted. As these distances are very large
in comparison with the distance from the instrument to the
signal they may be computed from the uncorrected angles, or
measured from an accurate map where stations can be located
closely.
INTERSECTION 183
The formula for computing the Swing, in seconds, for any
line may be put in the following simple form:
Si a sin Y a sin Y
In or = − Or o = −.
d d sin 1"
(sin o. = o sin 1" for very small angles)
o: = angle of Swing.
a = distance from off center station to signal.
d = distance from signal to distant station.
ºy = angle between signal and distant station.
Fig. I.-REDUCTION OF CENTER

184 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Example:
At a station S, four other stations, A, B, C and D, were sighted. (See Fig. I.)
A round of the horizon was made, including a sight on the signal; the angles as
noted below are from the field notes.
Stations sighted Angles Reduction to Angles Reduced to Center
Center
Station A to B 45° 36' 30.00" + 4.91 45° 36' 34.91"
Station B to C 40° 33' 14.00" — 0.46 40° 33' 13.54."
Station C to D 97° 10' 16.00" — 15.92 97° 10' 00.08"
Station D to A 176°40' 00.00" +11.47 176°40' 11.47"
The angle as measured between center of signal and the first station to the
right, station A, is 23° 07' 10", and distance from instrument to center of signal is
1.43 m.
. The logarithms of distance, in meters, from station S to the other stations
sighted, as computed with the anudjusted angles or measured from a good map,
were found to be:
Station S to A = 4.29846
Station S to B = 4.40804
Station S to C = 4.43266
Station S to D = 4.36725
The computation may be put in the following form:

Stations A B C D
Angle Signal to. . . . . . . . . . . 23° 07' 10" | 68° 43' 40" | 109° 16' 54"| 206° 27' 10"
log 1.43 m. . . . . . . . . . . . . . . 0.15534 0.15534 0.15534 0.15534
colog sin 1". . . . . . . . . . . . . . 5.31443 5.31443 5.31443 5.31443
log sin angle. . . . . . . . . . . . . . 9,59400 9.96935 9.97493 9.64881
Colog distance sta. S to . . 5.70154 5.59196 5.56734 5.63275
Log corrections. . . . . . . . . . . +0.76531 +1.03.108 || --1.01.204 || –0.75133
Correction in sec. . . . . . . . . . +5.83" +10.74" +10.28" —5.64"
It should be especially noted:—
(a) That the sign for any correction is the same as that
for the sine of the angle. The sign of any correction will
therefore be positive from 0 to 180°, and negative from 180
to 360°. *
(b) The correction for any angle will be the difference
between the corrections for the two lines bounding it, always
taking the lines in order of Y-azimuth.
(c) The general rule is to change the sign of the first cor-
rection, in order of Y-azimuth, and add algebraically to the
second. The sum will give the correction in seconds to be
applied to the angle.
INTERSECTION 185
The corrections may be conveniently tabulated as below.

Sides Angle Corrections Sum
A and B ASB —5.83-H10.74 +4.91" Proof
B and C BSC — 10.74-H 10.28 —0.46" +4.91 0.46
C and D CSD | – 10.28— 5.64 — 15.92" + 11.47 15.92
D and A DSA +5.64-H 5.83 | +11.47" + 16.38 = 16.38
If a line takes a plus correction for the side of one angle it
will readily be seen that this same line will take the same minus
correction for the adjoining angle. It is therefore well to
check the work by seeing that the positive and negative cor-
rections balance. -
These corrections are then applied to their appropriate
angles as will be noted in the “reduction to center” column
above. -
As the horizon was closed to 360° before reduction to center
it should remain so after the corrections have been applied.
This formula and method may be used also when a station
is occupied and a point sighted where the signal and station
mark bear a similar relation to each other as the instrument
and signal does in this problem. This reduction is known as
“swing” and is the correction necessary to change the point-
ing from the signal or point sighted to the station mark.
Whether the computed swing is to be added or subtracted
from a given angle will be readily seen from the sketch showign
the conditions which exist between the station occupied, the
signal sighted and the station mark or center of station.
2. U. S. METHOD OF INTERSECTION
On account of the extreme accuracy required in determining
the coordinates of points to be used by the Heavy Artillery it
is not sufficient simply to determine the coordinates of an
unknown point by triangulation from a single base line. The
work must be checked by determining the coordinates by a
different method or by using another base line and computing
them again by the same method.
In this chapter the method of locating a point by inter-
section from two base lines will be discussed. For con-
venience the two connected base lines will be taken up although
it will readily be seen that the method is applicable to two or
more independent base lines. By using a plane table the
186 ORIENTATION FOR HEAVY (COAST) ARTILLERY
unknown point can be located by intersection if the plane table
is set up and accurately located at two or more stations that
have previously been plotted. (See Chapter on “Plane
Table.”). In this case the coordinates would have to be read
from the map and unless the map is drawn to a very large scale,
which would be impossible, the coordinates as scaled would
be of no value except as a rough check on the mathematical
determination that will now be given.

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Fig. II.-FIGURE FOR PROBLEM
It is assumed that the unknown point H (see Fig. II) is
visible from three stations, K, L, M, whose coordinates are
known. With a transit the angles a, b, c and d are measured
by occupying the three known stations. The length and
Y-azimuth of “r” and “s” are calculated from the coordinates
of K, L and M.
Angle “e” = 180°– (a+b); “f” = 180°-c-H d)
From the Law of Sines: dº -
In triangle KLH.
r sin b
KH = —:
S11) 62
INTERSECTION 187
In triangle LHM.
In triangle KJH.
Angle HKJ = Y-azimuth (VI) of r— Za.
HJ = AXs = P(H sin HKJ; and JK = AY = KH cos HKJ. (1)
In triangle HNM.
Angle NMH = 180°–[Y-azimuth (V.) of s-- Zd
HN = AXm = HMsinNMH, and NM = AYm = HMcosNMH. (2)
Two sets of coordinates can now be obtained from equa-
tions 1, 2:
From equation (1) Xn = Xk-H AX,
Yh = Y,+ AY,
From equation (2) Xn = Xm – AXm
Yh + Ym-H AYm -
The arithmetic mean of the X and Y coordinates of the
point H will be taken as the coordinates of H.
Eacample:
Given the coordinates of three points, K, L, M, as follows:
R L M
X = 110750 115500 118250
Y = 80500 - 82500 81750
. A transit is set at the three points and the following angles measured to a
point, H. (See Fig. II.) -
Angle a = 23° 34' 30"
b = 128° 36'
C = 89° 29' 8"
d = 57° 31' 32"
Required the coordinates of the point H.
Chapter II deals with the computations of Y-azimuth and the distance
between two points whose coordinates are known; therefore the computations
to determine r, s, and Y-azimuth of KL and LM will not be given:
r = 5154 meters; S = 2851 meters
the Y-azimuth of KL = 67° 10'; the Y-azimuth of LM = 105° 15' 8".
e = 180°–a–b f = 180°– c – d
a = 23° 34' 30" C = 89° 29' 8"
b = 128° 36' = 57° 31' 32"
152° 10' 30" 147° 0' 40"
179° 59' 60” 179° 59' 60"
C = 27° 49' 30" f = 32° 59' 20"
KH =! sin b MH =5 sin c
sin e sin f
log 5154 = 3.712144 log 2851 = 3.454997
log sin 128° 36' =9.892940 log sin 89°29' 8" = 9.999932
colog sin 27° 49' 30" = .330895 colog sin 32° 59' 20" = .264021
- log RH = 3.935979 - log MIH = 7.319000
188 -ORIENTATION FOR HEAVY (COAST) ARTILLERY
ZJKH =Y-azimuth of KL– Za ZNMH = 180°–Y-azimuth of LM — Zd
Wr = 67° 10' Ve = 105° 15' 8" -
a = 23° 34' 30" d = 57° 31' 32"
43° 35' 30" = Z.JECH 162°46’40”
179° 59' 60”
ZGLH = Y-azimuth LM — Zc 17° 13' 20" = Z NMH
Ve = 105° 15' 8"
C = 89° 29' 8"
15° 46' 0" = Z GLH
In A JRH In A MNH
A Xk = 5950.06 A Xm = 1550.27
log AXk =3774522 log = AXm =3.190407
log sin 43° 35' 30" =9.838543 log sin 17° 13' 20" =9.471407
log KH = 3.935979 log MH = 3.719000
log cos 43° 35' 30" =9.859902 log cos 17° 13' 20" =9.980078
log AY =3.795881 log AYm = 3.699078
AYK = 6250.00m AYm = 5000.24m
X =X,+AX =110750 -
- 5950.06 116700.06m
Xh =Xm — AXm = 118250 -
1550.27 116699.73
2|233399.79
116699.90
Yh = Yk+ AYK = 80500
6250 86750.00
Yh =Ym + AYm =81750
5000.24 86750.24
2|173500.24
86750.12
(Adopted Coordinates of H)
X = 116699.90
Y = 86750.12
3. FRENCH METHOD OF INTERSECTION
Statement of the Problem.—Having sighted an unknown
point from several points whose coordinates are known, to
compute the coordinates of the unknown point.
The method is to find an approximate point by a graphic
plot, and then to compute the data required to construct a plot
on a large scale around the approximate point. From this
large scale plot the exact location of the point can be obtained.
To Find the Approacimate Point.—On drawing paper divided
into squares, plot the known points on a scale of 1:20000.
With a protractor draw the lines representing the sights from
each known station to the unknown station. The Y-azimuths
of these sights may be found by astronomical observations or
by determining a terrestrial Y-azimuth as explained in the
INTERSECTION 189
Chapter on “Meridian Determination.” The coordinates of
the intersection of the sights as read from the plot will be
used as the coordinates of the approximate point.
Compute the Y-azimuths of the lines joining the known stations
to the approacimate point, using the coordinates at the approx-
imate point as read from the map and the coordinates of the
known station.
Find the difference “do” of the computed Y-azimuths and
the true Y-azimuths. Use the formula d()=.W – Woomputed,
where W is the true Y-azimuth obtained by one on the methods
mentioned above and “V computed” is the Y-azimuth com-
puted from the coordinates of a known point and the coordi-
nates of the approximate point.
Compute the data necessary to construct a plot on a large scale
around the approacimate point. This plot will be made up of the
loci which should intersect at the true point, that is to say, the
lines representing the sights made to the point. These lines
may be drawn knowing;
a. Their distance from the approximate point.
b. Their direction. &
The distance from the approximate point to the line which
represents the sight is given by the formula:
Q = D sin d0; where D represents the distance computed
from coordinates from the approximate point to the station
from which it has been sighted.
If the angle d0 is very small q = D sin 1' (d0). e
Let S = sensibility of the line = displacement of the line for
a variation in d0 of one minute.
then, S= D sin 1'; and q = Sq0.
The direction of the line which represents the sight has
already been obtained. It is the true y-azimuth of the sight.
To construct a large scale plot (for example 1:100) around
the approacimate point. Assume the approximate point at the
origin of the axis of x and y, and draw the lines which represent
the sights. The direction of the sights and the distances from
the approximate points are known.
Take q in the proper direction, noting that the line is to the
right or left of the approximate point (viewed from the known
station) according as the true Y-azimuth is larger or smaller
than the computed Y-azimuth. As a rule the lines represent-
ing the sights will not intersect exactly at a common point,
but a small triangle of error will remain.
In locating the true point take into account the sensibility
190 ORIENTATION FOR HEAVY (COAST) ARTILLERY
of each line, S = q/d0 and also give less weight to a line from a
station whose coordinates may be doubtful and at which the
different values of Vo are inconsistent.
After the true point is plotted, scale from the plot the differ-
ence of coordinates from the approximate point and add these
differences with the propersigns to the approximate coordinates.
Note.—The plot is accurate, whatever may be the distance
from the approximate point to the true point, if the formula
q = D sin d0 is used. However, for differences of (d0) smaller
than three grades, the formula q = D sin 1' d0 may be used.
Eacample:
445000

%7
Kea, & / / N
3 / - - >
Z —
/ _T
44/ e / ~e? LT 4.
§ AC
§440000 R. § R. S. NS §
Ti-kº
443
442
s
Fig. III.-PLOT OF POINTS ON A 1:20,000 scALE
F The point H has been sighted from three known stations, K, L and M. (See
Pig. III.) -
Station Coordinates
Vo Reading on H
X y
L 29,010 441,344 31.1.181 g 96.775g
M 32,423 442,474 297.457g 38.837g
K 26,608 440,566 8.440g 31.480g
Plot the points L, M, K, on coordinate paper to a scale of 1 to 20,000 and
construct the approximate location of H. The coordinates of this point as
scaled from the plot are found to be
X approx. = 29,395 m.
Y approx. =444,417 m.
INTERSECTION 191
Using these coordinates and the coordinates of L, the length and Y-azimuth
of LH, approximate, are calculated.
LH approx. = 3098 m.
Computed Y-azimuth of LH approx. = 7.9358
Vo-HReading = W
31.1.181+96.775 = 7.9568
V computed = 7.935
d0= 021g = 2\.1
S = D sin 1\ = 3098 sin 1\ =
q=S d0=.5×2".1 =
MH approx. =3598 m.
V computed of MH =336.31&
Vo-HReading = W
297,457+38.837 =336.294&
V computed =336.319
.5 m.
1.0 m.
-ms-
d0= .025g = 2\.5
S = D sin 1 =3598 sin 1'= .56 m.
q=S d0= .56×2.5 = 1.4 m.
KH approx. = 4754 m.
V computed =39.882&
Vo-H Reading = W
8.440+31.480 = 39.920&
V computed = 39.882
d0= .038g = 3\.8
S = D sin 1\ = 4754 sin 1\ = 0.7 m.
q =S d0= 0.7×3.8 = 2.8 m.
y
24/79/ox.
!. /
N N N sº / -
`s / - -
| N 2 77ve ſax -t/0
TSS-Ao/7/lay --27
Z | SQ
V | >
/ G||
/ Jazz/€ /:/00
Fig. IV.-LARGE SCALE PLOT


192 ORIENTATION FOR HEAVY (COAST) ARTILLERY
In Fig. IV the origin is taken as the approximate point and the line L is drawn
to the right of the origin since the true Y-azimuth is greater than the computed
Y-azimuth. It is drawn at an angle of 7.9568 (Y-azimuth of sight from L) with
the y axis and at a distance of q = 1.0 m from the origin. As the scale is 1 to 100
the distance on the plot will be 1.0 cm.
In a similar manner the data is computed for the sights from K and M and
the lines representing these sights are drawn on the plot. The lines instead of
intersecting at a point form a small triangle of error ABC. In locating the point
dotted lines are drawn parallel to the sights L, K, M inside of the triangle of
error and at distances from them proportional to the sensitiveness, S, of the
respective sights.
The intersection of the dotted lines is taken as the true point. Measuring
the distances of the true point from the x and y axis on the large scale plot the
increments to be added algebraically to the coordinates of the approximate point
are found to be dx= +1 and dy = -2.7
Approximate Point x =29395.0 y =444417.0
dx= +1.0 dy = —2.7
True Point X = 29396.0 m. Y = 444414.3 m.
(XHAPTER XI
RESECTION
1. TRIGONOMETRIC SOLUTION
2. U. S. METHOD
3. RELEVEMENT
In case three or more points that can be seen from any given
unknown point have been plotted on a plane table, the unknown
point can be occupied and its position located on the plane table
by Resection, as described in Chapter VI. Because of the
small scale necessary in plane table work of this character and
the errors inherent in small scale graphic solutions, the coor-
dinates of a point as determined by plane table are not reliable
closer than 10 or 20 meters. This is not sufficiently accurate
for the heavy artillery, and in general the plane table can only
be used to check results obtained by more accurate methods.
If a transit is set up at the unknown point and the angles
between lines to three or more known points are accurately
measured, the position of the unknown point can be accurately
computed, its accuracy depending on the care taken in measur-
ing the angles, the accuracy of the coordinates of the known
points, and the care used in the computations. This is called
the “Three Point Problem,” or “Resection.” It is merely the
reverse of Intersection. In Intersection, only two known
points are necessary, but in Resection three are required, unless
the true orientation is known.
There are several methods of making this determination,
but only the three mentioned at the beginning of this chapter
will be considered here. All of these methods are based on the
relations brought out under the heading “Graphic Solutions,”
and illustrated in Fig. IX, at the end of Chapter VI. These
relations are as follows: The angle measured at the unknown
point between lines to two known points determines a circle
passing through those three points (two known, one unknown).
The angle between lines to the two known points is the same
at any point on that circumference and is one-half the central
angle subtended by the chord joining the two known points.
If the plane table or transit is oriented, only two known points
need be used; otherwise three are necessary, and more are
often used. The unknown point is at the intersection of the
circles drawn through two or more pairs of known points.
194 ORIENTATION FOR HEAVY (COAST) ARTILLERY
The so-called “Trigonometric Solution” is easy to under-
stand, but is rather long. The “U. S. Method” is more
difficult to understand, but somewhat shorter, and in case the
three point problem is to be solved frequently, it is the better
method. Both of them are mathematical solutions. “Releve-
ment” is a French method which combines the plane table
graphic Solution and some features of the mathematical solu-
tions, and is particularly adapted for use with quadrillage.
In any case, if the unknown point is on a circle through the
three known points, the problem is indeterminate, and if it is
too close to that circle, the solution is not accurate.
1. TRIGONOMETRIC SOLUTION
Given three visible known points, A, B and C (see Fig. I),
and an unknown point, P, which is occupied with a transit,
three possible cases may arise, viz.: 1. When the unknown
point is inside the triangle formed by the three known points;
2, when it and the known point C are on the same side of the
line AB; and 3, when they are on opposite sides. The fol-
lowing solution is the same for all three cases:
Case-// Case-///
Fig. I.-TRIGONOMETRIC SOLUTION
1. Plot the points A, B and C from their coordinates and
estimate the position of P. Draw a circle through A, B and
P. Draw the lines PA, PB, PC, AD and BD, D being the
second intersection of PC with the circle. (See Fig. I.)
Z DAB = Z DPB = or
Z DAB = Z DPB = 3
As angles having their vertices in the circumference of a
circle and subtending the same arc are equal.
2. In A ADB; AB, o, and 8 are known. Compute AD
and BD by using law of sines.

RESECTION 195
DA BD AB AB
Sin 3 Sin & Sin ADB Sin (180–a–3)
3. In A ADC:
Z CAD = Z BAC = a
AC and AD are known.
Compute ZACD using tangent formula:
AC+AD tan J/3 (ZADC-H ZACD)
AC–AD T tan J/3 (ZADC — ZACD)
4. In A ACP:
AC, ZAPC and ZACP are known.
Compute AP or CP using law of sines:
AP CP AC
Sin ACPTSin CAPT Sin 3
5. Compute the coordinates of P from A or C knowing
AP Or PC.
6. Check by solving BDC and computing the coordinates
of P from C or B.
EXAMPLE OF A THREE-POINT PROBLEM SOLVED
TRIGONOMETRICALLY
194, ooo
193, Ooo
192, O Oo
191, Ooo
19 C), C C C,
39 i., ooo 3ea, Ooo 383, oco 3 8 a., Coo
Fig. II.-ILLUSTRATION OF EXAMPLE

196 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Given: Required
A B C P
X 381,121 384,045 383,115
y 191,618 193,392 192,110
ZAPC = 3 = 47° 3’.5
A BPC = 0 = 26° 17'.5
X y X y
B =384,045 193,392 B=384,045 193,392
A=381,121 191,618 C=383,115 192,110
AK = 2,924 BIK = 1,774
- log BK = 3.248954
log AK = 3.465977 |.
log tan BAK = 9.782977
Z BAK = 31° 14'44"
g log AK = 3.465977
log cos BAK = 9.931942
log AB = 3.534035
AB = 3420. 07
X y
C =383,115 192,110
A =381,121 191,618
AM = 1,994 CM = 492
log CM = 2.691965
log AM = 3.2997.25
log tan CAM = 9.392240
Z CAM = 13° 51' 36”
log AM = 3.299725
log cos CAM = 9.987167
log AC = 3.312558
AC = 2053.80
..º.
In A ADC
ZBAFC = 31° 14'44"
Z CAM = 13° 51' 36"
ZBAC = 1792.3' 08"
o, = 269 17' 30"
ZDAC = 43°40'38"
180° 00' 00"
ADC-HDCA = 136°19'22"
J% (ADC-HDCA) = 68 09'41"
AD+-AC=4667.02
AD = 2613, 22
AC = 2053.80
AD —AC = 559.42
In A ADC -
AD+AC tan 9/3 (ADC+DCA) |
AD-AG-tan J. (ADCEDCA)
CL = 930 BL = 1,282
log BL = 3. 107888
log CL = 2.968483
log cos CBL = 0. 139405
Z CBL = 35°57'30"
log BL = 3. 107888
log cos CBL = 9.908187
log CB = 3. 199701
AB = 1583.80
In A ABD: ZADB = 180°– (a +3)
Cy = 26° 17. 30"
6 = 47° 03' 30"
Z ADB = 106° 39' 0"
180° 00' 00"
AB = AD – BD
sin ADB - sin 8 sin o.
log AB = 3.534035
log sin ADB = 9.98.1399
3. 552636
log sin 6 = 9.864540
log AD = 3.417176
AD = 2613. 22
3. 552636
log sin o. = 9.646346
log BD = 3. 198982
BD = 1581. 18
In A BDC -
Z ABL = 58° 45' 16"
Z CBL = 350 57' 30"
ZABC = 229.47° 46"
6 = 47° 03' 30"
ZDBC = 69° 51' 16"
180° 00' 00"
BDC+DCB = 110° 08' 44”
J% (BDC+DCB) = 55° 04' 22"
CB+BD = 3164.98
CB = 1583.80
BD = 1581. 18
CB – BD = 2.62
In A BDC
CB+BD tan 3% (BDC+DCB)
CBEED ~tan Já (BDCEDCB)
RESECTION 197
log tan M. (ADC+DCA) = 0.397128 log tan 4 (BDC+DCB) = 0.155948
log (AD–AC) = 2.747738 log (CB – = 0.418301
3.144861 0. 574.249
log (AD+AC) = 3.669040 log (CB+BD) = 3.500236
log tan Vá (ADC–DCA) = 9.475821, log tan 3% (BDC —DCB) = 7.074013
}% (ADC–DCA) = 16° 39' 08" }% (BDC — DCB) = 0° 04'05"
}% (ADC+ACD) = 68 09'41" % (BDC+DCB) = 55° 04' 22"
ZACD = 84° 48'49" Z BCD = 55°00' 17"
180° 00' 00" 180°00' 00"
ZACP = 95 11’ 11” Z BCP = 124 59' 43”
In A ACP In A BCP
ZACP = 95° 11’ 11” Z BCP = 124° 59'43"
ZAPC (3) = 47° 03' 30" ZCPB (a) = 26°17'30"
ZCAP = 37° 45' 19° Z CBP = 28°42'47"
180° 00' 00" 180° 00' 00"
AC CP AP CB___CP BP
sin 6 Tsin CAPTsin ACP sin of Tsin CBP sin BCP
log AC = 3.312558 log CB = 3. 199701
log sin 6 = 9.864540 log sin o. = 9.646346
3.448018 3. 553355
log sin ACP = 9.998.218 log sin BCP = 9.913516
log AP = 3.446236 log BP = 3.466871
3.448018 3. 553355
log sin CAP = 9.786958 log sin CBP = 9.681624
log CP = 3.234976 (check) log CP = 3.234979
Coordinates of P from A Coordinates of P from C
ZCAP = 37° 45' 19" Z CBL = 35°57'30"
ZCAM = 13° 51' 36” ZCBP = 28°42'47"
Z MAP = 23°53'43" ZPBL = 7° 14'43"
- Ay = 1131.79 Ay =2906. 56
log Ay = 3.053762 log Ay = 3.463380
log sin MAP = 9.607526 log cos PBL = 9.996509
log AP = 3.446236 log BP = 3.466871
log cos MAP = 9.961102 log sin PBL = 9.100774
log Ax = 3.407338 log Ax = 2.567645
Ax = 2554.68 - Ax = 369. 53
X y X y
A 381,121 191,618 B 384,045 193,392
A+ 2,554. 7 – 1,131.8 A — 369.5 — 2,906.6
P 383,675.7 190,486.2 P. 383,675.5 190,485.4
Coordinates of P
& Mean Values
x=383,675.6
y = 190,485.8
198 ORIENTATION FOR HEAVY (COAST) ARTILLERY
2. U. S. METHOD
The trigonometric relations that exist between the different
triangles have been reduced to certain formulas that can be
used to solve the three point problem. The derivation of these
formulas is given below, being taken from Artillery Notes
No. 11. Standard computation forms have been designed to
furnish a convenient record and to facilitate the work. On the
following pages is an example of this method, the initial data
being the same as that used in the example of the Trigonometric
solution. A comparison of the two will show that the U. S.
Method is somewhat shorter, but because of the complicated
formulas, is difficult to remember. On the other hand the
trigonometric solution can easily be worked out for any given
problem. -
From the final position of the unknown station P the
Y-azimuths of the lines from P to the known points can be
computed. They can also be found from the angles used in
the computations and the Y-azimuths of the lines joining the
known points. -
Additional known points may be sighted and an extra check
thus obtained on the solution. If the coordinates of P as
obtained from two or more solutions based on different known
points (when more than 3 points are used) differ only slightly,
the mean value should be taken, but if they differ widely there
is probably an error in the initial data of the computations.
In case there is any doubt as to the accuracy of the coordinates
of any of the known points, additional points should be sighted
and the mean value determined. Where the lengths of the
lines joining the known points vary widely a weighted mean
should be used. -
Fig. III.-PROOF OF FORMULAS

RESECTION 199
Derivation of Formulas.-
Let Angle CAP= q. Let G = b + q'
{{ {{ CBP = q.' = 360°– o – 8– (ACP + BCP)
“ Line AC =b =360°–ACB — (a+8)
{{ « BC = 8,
Note.—In third case the angle ACB is the exterior angle at
C. It must always be considered as the angle inside the
quadrilateral ACBP.
sin 6 CP sin q _CP
From the law of Sines, te = TT all CI T.
sin 6 b SII) Cy 8,
CP b sin d a sing,' a sin (G — p) a sin G cos? — a sin b cos G
sin 3 T sin a sin a - sin o.
Considering the second and last expression
b sin q sin o. = a sin G sin 3 cos p – a cos G sin 8 sin (b
Dividing by sin q
b sin o. = a sin G sin 8 cot p – a cos G sin 8
b sin o-Ha cos G sin 3
a sin G sin 8
. . . COt G, . cot G (b sin o-Ha cos G sin 3)
Multip lying by cot G cot G a sin G sin 8 -
ſ b sin o. a cos G sin 8 }
l cº a sin G sin st º G a sin G sin 6
- b sin o.
I. cot q = COt G a sin 8 cos G+1 ſ
In similar manner
/ a sin 3 l
II. cot º' = cot G lbsin a cos G+1 ſ
sinſ 180°– (q)+3)] AP
Solving, cot q =
Cot G
From the law of Sines, in AAPC; º =
Sin 6 b
b sin [180°– ©
III. AP–ººl * * similarly, in ABPC;
IV. BP=* sin (180°-(º-Fo)
SII) Cy
Eacample:
This example is worked out with the above formulas and arranged according
to a standard computation form.
Given
A { x=381,121
y = 191,618
B { x=384,045
y = 193,392
C [ x=383,115
M..........] ſ APC = 8 = 47° 3'.5
Obser ved { BPC = 0 = 26° 17.5
200 ORIENTATION FOR HEAVY (COAST) ARTILLERY
To Find for point P
X =
y =
Draw a figure representing the three points, lettered from left to right A, C,
B, respectively, as seen from the point P, the position occupied. The side AC,
letter b, and the side CB, letter a. The angles APC and CPB letter 8 and of
respectively, and angles CAP and CBP letter q and q, respectively. Through
P and C draw lines parallel to the X-axis, and through A and B lines parallel to
the Y-axis. The intersection of the lines through C and B, letter K, through
C and A, letter M.; through A and P, letter T; and through P and B, letter W.
B
|
3520OO
Fig. IV.-ILLUSTRATION OF EXAMPLE
Ye = 1921.10 Xe = 3
Ya = 191618 XA = 381.121
AM = 492 MC = 1.994
In A MAC; AM=492
Mº-º:
MCA = ***.
tan MC
log AM = 2.691965
(—) log MC =3.299725
log tan MCA =9.392.240–10
MCA = 13° 51’.6
MAC = 76° 87.4
- AM
sin MCA
log AM = 2.691965
(—) log sin MCA =9.379405–10
log b =3.312560
b = 2053.8
Y, -193392 x = 384,045
Ye = 192.110 Xe = 383.115
BK = 1.282 CK = 930
In A KCB; CK=930
#-12sº
tan KCB = ****
an KC CK
log BK =3.107888
(—) log CK=2.968483
log tan KCB = .139405
KCB = 54° 2'.5
IKBC = 35° 57.5
BK
** sin KCB
log BK =3.107888 .
(—) log sin KCB =9.908187–10
log a =3.199701
a = 1583.8

RESECTION
201
ZACB = 180°-EMCA +KCB or +ACB+KCB = 220° 10'.9
ZACB must always be taken inside quadrilateral ACBP.
NoTE.—The proper signs must be determined from the figure.
G =q-i-p' =360°–(3+a+ACB)=66°28'.1
— eat ſ b sin o. l
I. cot q = cot G{#s ſ
log b =3.312560
log sin a = 9.646346–10
log b sin o. = 2.958906
log a = 3.199701
log sin 3 =9.864539–10
log cos G =9.601251–10
log a sin 8 cos G = 2.665491
log b sin o. = 2.958906
(—) log a sin 3 cos G = 2.665491
b sin o. \ -
los (; H = 2
Og a sin 3 cos G ſ 934.15
b sin o. -
a sin 6 cos a = 1.9652
(+) 1.0000
ſ b sin o. \ =n=
lasing cos a-Fl j =q 2.9652
log q = .472054
log cot G =9.638958–10
log cot q = .111012
II, cotº-cot G (Hºrs
cot ºp' = cot b sino, cos G
log a =3.199701
log sin 3 =9.864539–10
log a sin 8 = 3.064240
log b =3.312560
log sin o. =9.646346–10
log cos G =9.601251–10
log b sin of cos G = 2.560157
log a sin 8 = 3.064240
(—) log b sino, cos G = 2.560157
log {
a sin 6
b sin of cos G
a sin 3
b sin of cos G=3.1921
(+) 1.0000
} = .504083
ſ a sin 3 l /
-*-*. -: = 4. 2
insii. 5t" j q' = 4.1921
log q' = .622432
log cot G =9.638958–10
log cot * = .261390
b 1 q = 37° 45'.3 tºº. 42'.8
- 9 — e 180°– (d.'
III. AP=" tº [ ; fºre |IV. BP=tº [ ** +o)]
180°– (p+8) = ZACP =r 180°– (p’-Ho) = ZBCP =r'
= 95° 117.2 = 124° 59'.7
log b =3.312560 log a =3.199701
log sin r =9.998.218–10 log sin r" =9.913391–10
colog sin 6 = . 135461 colog sin o. = .353654
log AP = 3.446239 log BP = 3.466746
AP = 2794.1 BP = 2920.2
In A APT \ In A WPB \
_ ſ 180°-EMAC==q, \ ſ 180°-i-KBC+q,'
ZPAT* = { or-i-MAC+q, ſ T Z WBP+ = { or-i-KBC+q,' ſ
S = 66° 67.3 S’ = 7° 14'.7
AT = AP cos S BW = BP COS S'
log AP=3.446239
log cos S = 9.607521–10
log AT = 3.053760
AT = 1131.8
TP = AP Sin S
log AP = 3.446239
log sin S = 9.961084–10
log TP=3.407323
TP = 2554.6
*Xa--TP=XP =381,121+2554.6
=383,675.6
log BP=3.466746
log cos S' =9.996519–10
log BW =3.463265
BW = 2905.8
PW = BP Sin S'
log BP=3.466746
log sin S' =9.100758–10
log PW=2.567504'
PW =369.4
*Xb==PW =XP =384,045–369.4
=383,675.6
1)
ſ
202 ORIENTATION FOR HEAVY (COAST) ARTILLERY
*Ya==AT = Y, - 191,618–1131.8 *Yi,4-BW = Y p = 193,392–2005.8
= 190,486.2 +. = 190,486.2
Mean Xp =383,675.6
Mean Yp = 190,486.2
*When + occurs in a formula the proper sign to use must be determined from
the figure for each special case.
3. RELEVEMENT—FRENCH METHOD
As in intersection, the French have developed a method of
resection, called Relevement, which is a combination of the
graphic plane table solutions and the accurate mathematical
Solutions. It attains the accuracy of the latter, but requires
less work, and is well adapted for use with quadrillage because
it reduces the effect of errors in the coordinates of the known
points. It permits any number of known points to be brought
into the solution, thereby strengthening the result and attain-
ing to some extent the accuracy of a least square adjustment.
The description of relevement is necessarily long, but if it is
clearly understood it can be used quite rapidly. When more
than three known points are used it is shorter than either of
the mathematical solutions.
Field Work.-A transit is set up at the unknown point with
its line of sight, when the verniers read zero (W, line), directed at
one of the known points or at any random object. The
telescope is directed at each of the known points in turn and the
verniers are read. Each of these readings measures the angle
between the line to the corresponding point and the V, line.
Computations.—The known points are plotted on a small
scale (say 1:20,000) and the unknown point is located graph-
ically by means of the various transit readings. Its coor-
dinates are scaled from the plot, but are only approximate.
The point they represent is called the “approximate point.”
From its coordinates and those of the known points the Y-azi-
muths of the rays from it to the various known points are
computed. From these approximate Y-azimuths and the cor-
responding transit readings a mean value of the Y-azimuth,
V, is deduced. From this and the transit readings the Y-azi-
muths of the probable rays to the true point are computed.
The vicinity of the approximate point is plotted on a large
scale, showing these probable rays to the true point. They
form a “Chapeau” of error. By changing V, slightly the
chapeau is reversed or eliminated and the true point found.
The detailed procedure, divided into nine steps is as follows:
1. Determine graphically the approacimate coordinates of the
RESECTION - 203
unknown point. This is done by plotting the known stations
from their coordinates on a sheet of coordinate paper, using a
scale of 1 to 20,000 (1 mm. = 20 m.). The sheet should be
divided into 5 cm. Squares representing 1000 m. squares on the
ground. With a transit set up at the unknown point measure
by repetition the angles between the lines to the known points.
Using extreme care locate the unknown point on the map by
one of the graphical solutions of the three point problem.
Scale the distances of the unknown point determined graph-
ically to the nearest grid lines and in this way determine its
approximate coordinates. The approximate point thus ob-
tained is called X.
2. Compute the approacimate orientation. The Vo of the
transit at the unknown station is determined by one of the
following methods. However, the orientation of any line
through the unknown point may be determined, for if the
orientation of one line is known the Y-azimuth of any line
through the same point can be determined by measuring with
the transit the angle between the two lines.
(a) By compass. This is very inaccurate and should be
used only in case of an emergency.
(b) By computing the Y-azimuth of the line from the un-
known point to the most distant known point. This will
give a result sufficiently accurate for a computation by Releve-
ment provided the known point is 1000 m. to 2000 m. distant.
(c) By observation on the Sun or Polaris. Making an
observation on Polaris is the most accurate method known for
determining the Y-azimuth of a line, but on account of atmos-
pheric conditions or for lack of time this method is often
impracticable. Due to the inaccuracy of the methods em-
ployed in making a solar observation the value of V, thus
obtained may be in error from 1 to 3 minutes.
(d) By observation on known terrestrial points. This
method, which is explained below, is more accurate than the
method involving a solar observation, provided the values of
V, shown in the calculations agree closely. However, with
inconsistent values of V, the Y-azimuth determined by solar
observation should be used. A method of computing V, from
a point whose coordinates are known is given in the chapter on
“Meridian Determination,” and the method of computing an
approximate V., from a point whose coordinates are only ap-
proximately known will be found very similar to it.
It is always possible to compute an approximate orientation
204 ORIENTATION FOR HEAVY (COAST) ARTILLERY
by computing the Y-azimuths of the lines joining the approxi-
mate point to several distant known points, using the formula
Vo-V computed—Reading. A clear conception of the mean-
ing of V, may be had if the transit is understood to be directed
on some distant known point on the horizon with the vernier
set at zero. With the lower limb clamped, the V, is the Y-azi-
muth of the line of sight when the vernier reads zero. In
other words it is the Y-azimuth of the zero line on the lower
limb of the transit. V computed is the Y-azimuth of the lines
connecting the approximate point to the known points, com-
puted from their coordinates. This method of calculating a
Y-azimuth is given under “Cartography of French Maps.”
“Reading” refers to the reading of the vernier when the tele-
|
l
§
Š
s
Q5
-Q
N--> ~J N
C N \
3- \ \
\, \
\, \ \
\, \ \
/ \ |\ \
\
/ \\\\\
/ \ \ \
/ \ \ \ \
/ \ \ A \, \
/ \ \ \ \ \
| \ \ \ \ \
| \ i l
| | | | | |
| ! i ! :
| | | | | |
l | | | |
l | | | | |
\ | | | | |
\ | | | | |
/ !
\ / / ! / |
/ / / / /
09 / / / /
T / / / /
Aſ
/X / /
/ \\ / /
º//
© @A /
/
^{9 2’
O
Fig. V.-DETERMINATION OF APPROXIMATE Wo


RESECTION 205
scope is directed at a known point, or in other words it is the
angle between the V, line and the line to the known point
sighted on. (See Fig. V.)
XO is the V, line. Suppose the telescope is directed to the
point M, the reading on the vernier would then be the angle
OXM, which, added to the Y-azimuth of V, would give the
Y-azimuth of XM. Or, if the Y-azimuth of XM has been com-
puted, by subtracting the value of the angle OXM (Reading)
we obtain the Y-azimuth Vo. The Y-azimuth of V, may in
this way be computed using each point separately. The dif-
ferent values found will differ slightly and the mean of these
values of Vo will be taken as the true value.
The approximate determination of Wo from the approximate
coordinates of the transit point is illustrated in the following
example taken from a French Bulletin:
The known points sighted, with their transit readings and
coordinates are as follows:
Point Reading a – Coordinates — y
Cote = ( 50.399 44,875 461,187
Malmy = M 106.50g 49,989 464,141
Acacia = A 365.10 51,507 459,580
Berzieux = B 39.69g 48,688 462,438
The first step is to plot these points accurately on as large
a scale as practicable. This has been done in Fig. V and the
transit point located by a graphical method. Its coordinates
as scaled from the diagram are x = 50,707, y = 463,785.
These may be several meters in error, but can be used for an
C M A B
44,875 49,989 51,507 48,688
50,707 50,707 50,707 50,707
AX —5,832 –718 —800 –2,019
461,187 464,141 459,580 462,438
463,785 463,785 463,785 463,785
Ay –2,598 +356 –4,205 — 1,347
Log Ax 3. 76582 2.85612 2.90309 3.30514
Log Ay 3.41464 2. 551.45 3. 62377 3. 12937
Log tan v 0.351.18 0.30467 9.27932 0.17577
V 73. 320g 70. 6969. 11 .969g 62. 545g
V 273. 320g 329, 304% 188. 031 g 262.545&
Reading 50.39% 106. 50g 365. 10g 39.69%
Approx. Vo 222.930g 222.804& 222,931 g 222. 855g
206 ORIENTATION FOR HEAVY (COAST) ARTILLERY)
Approx. Vo = V com – Reading
Mean value of Approx. Vo =222.88%
approximate determination of V, which is similar to the deter-
mination in the method given in the chapter on “Meridian
Determination,” when the coordinates of P were accurately
known. The computations above:
In this case, because the scaled coordinates of P have a
large probable error, a corresponding error will appear in each
value of V, that is based thereon, and it is not worth while to
take a weighted mean. The arithmetic mean, 222.88%, is
more reliable than any individual value, although it may be
20 minutes in error. -
3. Compute Y-azimuths of Limes to Known Points.-The
Y-azimuths of the lines to the known points are found by the
formula:
V =Vo-H Reading
XB = Wo-HReading to B =222.88+ 39.69 = 262.578
XC =Vo-HReading to C =222.88-|- 50.39 =273.27%
XM =Vo-H Reading to M =222.88--106.50 =329.38%
XA =Vo-HReading to A =222.88-|-365.10 = 187.98%
(A Y-azimuth of 587.98% is the same as 587.98–400 = 187.98%.)
4. Compute Data Necessary to Plot Vicinity of Approacimate
Point on a Scale of 1 to 100.
In Fig. V the lines XB, XC, XM and XA are known as
reverse sights if considered as being drawn to the unknown
station. From plane table work, we know they would inter-
sect at one point which would be the point sought, provided all
coordinates and the orientation were accurate. This condition
is not to be expected and instead a figure called a “chapeau"
will be formed by the reverse sights, varying in size depending
on the accuracy of work, being very small if the errors in the
work are small. Using a scale of 1 to 20,000 (1 mm. = 20 m.)
in plotting the points, the reverse sights may appear to inter-
sect in a point on the map, which point, in reality, may be
10 to 20 meters distant from the actual location of the approx-
imate point. By constructing a large scale map (1 to 100),
the location of the point of intersection of the reverse rays can
be determined within .1 or .2 of a meter.
In drawing a map of this size it will be impossible to plot
the known stations and only a small area around the approx-
imate point can be shown. To construct this map it is neces-
sary to know the following:
(a) The distance “q” from the reverse sight to the
approximate point.
(b) The Y-azimuth of the reverse sight.
RESECTION 207
(c) The position of the reverse sight with reference to the
approximate point, that is, whether it passes to the right or
left of the approximate point. *
(a) The Distance “q.” This distance depends on the angle
d0 between the line from the approximate point to the known
station and the reverse sight, and the length of the reverse
sight. (See Fig. VI.)
S$
N.
SS
SS <3 §
SS3- S
N &
SS *~
N. ^
N Qly
SS < §
N
SS a/O $ Ş
N S. |
SS \
`N \ 9
\\ \ (ſ
N \
C/?doeavs -º
>~a
_2^
_2^ d'O
_2~ 2^
_2^T 2^
~~ /
_2~ 0 2^
* 0 <x?
1. 3&a/O
2^
2^
2^
2^
2^
49 2.
2^
,”
,”
2.
Z
O//7/72/.5%fs
Areve/3e Sø//'s *se sºmeºs ºsmºs ºmºmº sº ºmº =º
Fig. VI.-CHAPEAU OF ERROR
This distance is determined by the formula q = D sin d0,
where D is the distance from the approximate point to the
known station either computed from coordinates or carefully
scaled from the 1:20,000 plot, and d0 the difference between

208 ORIENTATION FOR HEAVY (COAST) ARTILLERY
the computed Y-azimuth of the line from the approximate
point to the known station and the Y-azimuth of the reverse
sight. -
(b) The Y-azimuth of the reverse sight is the Y-azimuth
found by formula, V of reverse sight = V,-H Reading (to station).
This Y-azimuth is considered from the unknown point to the
known point, and is actually the back Y-azimuth of the reverse
sight.
(c) Position of Reverse Sight.—The reverse sight is drawn
on the right or left side of the approximate point according as
the Y-azimuth of the reverse sight is larger or smaller than the
computed Y-azimuth of the line from the approximate point to
the known point.
5. Construct Large Scale Plot Around Approacimate Point.—
The reverse sights are drawn as though they had been taken
from the known stations. Let the approximate point be at
the origin of the x and y axis. Lay off the different values of
“q” in the proper direction so they will be perpendicular to
the reverse sights (see Fig. VII) and then draw the lines
representing the reverse sights.
* * C
N-
*- -
|--
£º
\
{
Approximate
Forzf
S.
*
*
`S
s
º
YS
Vº w - ſ 2^
A/PS/ Z! <! A vº 20
<!
NS N ^jºe. \
S 2.
W .
C/7aaeace
F'ig. VII.-LARGE SCALE PLOT


RESECTION 209
Evample: Consider the reverse sight from C in the problem given above.
Given coordinates of X as measured from the map to be x = 50,707; y = 463,785
and coordinates of known station C (44,875; 461,187). From these the length
of the line CX is found to be 6385 m.
V of reverse sight = Vo-HReading.
- =222.88–H50.39 = 273.27g
V computed from coordinates =273.32%
d0=273.27g — 273,329 = —5\
qe = D sin d() = 6385 sin 5’ = 5.01 m.
Since the Y-azimuth of the reverse sight is less than the computed Y-azimuth
the reverse ray will be drawn to the left of the approximate point. The Y-azimuth
of the reverse sight is 273.278. Rinowing these three conditions the line C can be
drawn. Repeating the conditions, we have the reverse sight from C drawn to
the left and 5.01 cm. distant from the approximate point, and making an angle
of 273.278 with the y axis. In a similar manner the reverse sights from B. M.
and P are drawn.
Station V of reverse sight —V computed = d0
B 262.57g —262.545g = +2.5\
C 273.27g –272.320g = —5.0"
M 3.29.38g —329.3049 = +7.6\
A 187.98g — 188.031& = —5.1\
q = D sin d()
B q = 2427 sin 2.5 = 0.95 right
C - q = 6385 sin 5.0% = 5.01 left
M q = 801 sin 7.6\ = 0.96 right
A q = 4281 sin 5.1\ = 3.43 left
The reverse sights do not intersect at a common point for
the reason that the computed orientation of V, is not the true
orientation. A small figure of error will be formed exactly in
the same manner as in making a location with a plane table in
the field when the orientation is slightly in error. In Fig. VII
the figure of error is composed of two triangles, 123 and 345.
(The arrows on the reverse sights indicate their direction.)
6. Change the orientation of V, by a round number of
minutes (5 or 10) in the direction which reduces the figure of
error made by the reverse sights. By increasing V, the Y-azi-
muth of each reverse sight is increased, that is to say, the new
sight may be drawn to the right of the one first drawn. A
simple examination of the first figure of error shows in what
direction it is necessary to rotate the lines representing the
reverse sights so as to eliminate the figure of error, or in other
words, in what direction the initial V, should be changed. For
a variation of 1 in V, each reverse sight is displaced by an
amount equal to its sensitiveness, S. * *
The sensitiveness of a reverse sight is computed in the fol-
lowing manner: The formula, q = D sin d0 has already been
explained, “q” representing the distance of the reverse sight
from the approximate sight and d0 being a small angle ex-
pressed in minutes. The sines of very small angles are very
nearly proportional to the angles and since D is a constant
“q” can be assumed to be proportional to the angle d0. Now
210 ORIENTATION FOR HEAVY (COAST) ARTILLERY
write the formula q = D sin 1 (d0). D sin 1 is a constant and
is called the sensitiveness “S” of the reverse sight. Its value
can be expressed D sin 1 = q/d0. In the example given above
qe was found to be 5.01 m. and the d0 was 5*, therefore the
sensitiveness of the reverse sight from C is equal to 5.01/5
or 1.00. This means that since a difference in the two
Y-azimuths of 5 gave a difference of 5.01 m. a change in V,
of 1 will give a change of 1 m. in the position of the reverse
sight from C. The sensitiveness of each reverse sight is com-
puted and written on the line representing it.
Q
Station S = D sin, 1 = dO
- 0.95
B S=2.5- = 0.38 10S = 3.8
{ 5.01
C S=50 = 1.0 10S = 10.0
, 0.96 & — 1 2
M S=#6 =0.13 10S = 1.3
.43
A S –? 1 = 0.38 10S = 3.8
The examination of the chapeau (figure of error) shows
approximately the number of minutes it is necessary to change
V, in order to eliminate the chapeau. We should be changed
by a round number of minutes (for example 10, and in any
case at least 5) near, or preferably more than the number of
minutes necessary to eliminate the chapeau. In this way new
reverse sights can be drawn which will give a very small
chapeau of error or one which is inverted as a result of shifting
the orientation slightly more than would have been necessary
to exactly eliminate the chapeau of error (in the same manner
as is done in the Inverse Triangle of Error solution of the three
point problem with the plane table). Then draw (dashed
lines so as not to confuse the figure) the new reverse sights
parallel to the first and a distance (for example, 10S) in the
direction which will eliminate or invert the chapeau. Indicate
on these lines the points from which they represent new reverse
sight. (See Fig. VII.)
In Fig. VII, V, was increased 10' and each reverse sight will
be found moved to the right and parallel to its first position
and distant 10S centimeters from it. B' is parallel to B and
3.8 cm. to the right. C' is parallel to C, 10 cm. to the right,
and similarly with the other two sights.
7. Draw the lines representing the segments. Consider the
segment AB, that is, the segment of a circle containing the
stations A and B in which the angle between the reverse sights
RESECTION 211
A and B can be inscribed. The original reverse sights from
A and B, based on the approximate orientation V, intersect
at 5. The new reverse sights from the same points, based on
the orientation Vo-H 10' (for example) intersect at 6 (see Fig.
VII). The two points 5 and 6 lie on the segment of the
observed angle AXB. A small portion of this segment may be
represented by its chord and in this case the segment may be
represented by the line 56, which should be drawn in red or in a
fine black line. (This is exactly the same as joining the
corresponding vertices of the two triangles of error in the
Inverse Triangle of Error solution of the three point problem
with the plane table.)
The sensitiveness of the segment is the displacement of the
segment for a variation of 1 in the angle of the segment. The
point R, intersection of the first reverse sight from B with the
second reverse sight from A, corresponds to a variation of 10
in the angle of the segment AXB. The sensitiveness of this
segment is then 1/10 of the distance “h” from R to the seg-
ment 5 6. - -
Now draw the remaining segments by taking the known
points in pairs. Select those segments which intersect at
angles nearest to 100 grades and which have good sensitiveness
(small values for h). In Fig. VII all segments have been dis-
carded except MC, AB and CB. The segments will probably
not intersect at a common point but will form another triangle
of error. In Fig. VII this triangle is EFG.
8. Select the True Point in the same way as in the compu-
tation by French “intersection” of the coordinates of a point,
taking into account the sensitiveness of the segments, and
drawing dotted lines parallel to the sides of the triangle EFG
formed by the segments. These parallels are drawn inside of
the triangle of error and at distances from the sides propor-
tional to the sensitiveness of the segment. In Fig. VII, the
dotted line “Z” is parallel to MC and at a distance from it
proportional to the sensitiveness of MC, which is h’/10.
The dotted line “y” is parallel to AB and at a distance from it
proportional to hy10. The distances h and h' are determined
by measurement on the large scale plot. The line “x” is
parallel to CB and at a distance from it proportional to the
sensitiveness of CB. In this instance the sensitiveness has to
be estimated as C’ and B, also C and B', intersect beyond the
limits of the plot. In actual practice when there are a large
number of segments the true point, P, is adopted at the center
212 ORIENTATION FOR HEAVY (COAST) ARTILLERY
of the area formed by the intersections of the greater number of
segments, thus making it unnecessary to determine the sensi-
tiveness of the segments. Measure from the large scale plot
the difference of the coordinates between the approximate point
and the adopted point, adding the values with the proper sign
to the coordinates of the approximate point. The differences
in coordinates of the adopted point in Fig. VII are dx=2.3 m.
and dy= −3.4 m. The coordinates of the approximate point
are :
x = 50,707. y = 463,785.
The coordinates of the adopted point will be
x = 50,707+2.3 = 50,709.3 m.
y =463,785–3.4 = 463,781.6 m.
9. Compute the Round of the Horizon at the Adopted Point.—
Compute the Y-azimuths of the lines joining the adopted point to
the known points which have been sighted (distant points only).
From the Y-azimuths V of each line and the reading made on
the transit the Y-azimuth W, of the transit is found (V, = V —
reading). Thus, a series of values of V, is found, which should
be nearly the same. The agreement between the different
values of V, is a check on the precision of the operation. Take
the mean of the values of Vo, giving to each a weight propor-
tional to the distance of the point from which it has been
computed, eliminating doubtful points and those close by.
The true Y-azimuth of each sight is then found by adding the
reading to the mean value of Wo. See method of computing
terrestrial Y-azimuth in chapter on “Meridian Determination.”
NOTE.—The relative position of the approximate point and
the true point has no influence on the final determination if
the distance between them is not more than 20 or 30 meters.
If this distance is too great, the chosen point will be percep-
tibly inaccurate, and the values of V, will show considerable
variation. In this case the chosen point should be taken as a
second approximate point and the operation repeated.
The computations necessary in solving a Resection Prob-
lem by Relevement will be considerably shortened if the angles
between the lines to the known points are reduced to mils.
By expressing dO in mils the distance “q” can be determined
without the use of logs, since it is simply the number of mils
multiplied by one thousandth of the range. This relation
between mils and the distance “q” is not exactly accurate, the
error being about 2 per cent., but this will not affect the final
result by an appreciable amount.
RESECTION
213
Jo
Below is given a problem worked out on a convenient form
with the angles reduced to mils and the computed Y-azimuth
of the longest ray used as a basis of the approximate orientation.
£4––
Jø/2//07
SS }//0x
s
*N_
/ Q ſº § § //7/
Fig. VIII.-LARGE SCALE PLOT (SECOND EXAMPLE)
CoorDINATES READINGS
Point X Y Degrees Mils
B. L. (A) | 389592.6 191261.4 0° 0' 0" O
F. P. 383459. 1 189916.6 134° 28' 20" 2390.61
O. P. C. 38.4045. 1 193392.0 275° 48' 20" 4903. 20
ID. R. 384.175. 6 191067.3 29.2° 40' 20" 5203. 06
Approximate Point X = 384070
Y = 190660





214 ORIENTATION FOR HEAVY (COAST) ARTILLERY
*

Point (A) B. L. F. P. O. P. C. D. R.
X 389592.6 383459. 1 38.4045.1 384.175. 6
X of Approx. Pt. 384070. 0 384070. 0 384070.0 384070. 0
AX 5522.6 610.9 24.9 105.6
Y 191261.4 189916.6 193392.0 191067.3
Y of Approx. Pt. 190660.0 190660.0 190660.0 190660.0
AY 601.4 743.4 2732.0 407.3
Log AX 3. 7421436 2.7859.701 1. 396.1993 2.0236639
Log AY 2. 7791634 2.8712226 3.4364807 2.6099144
Log Tan v 0.9629802 9.9147475 7.9597186 9.4137495
V 1489. 52 700.67 9, 29 258.4
V computed 1489.52 3900. 67 6390. 71 258.4
V obs. = V com. * O.
of A+-Reading 1489.52 3880. 13 6392.72 . 292. 58
d0 (+Mils)* 0 —20. 54 +2.01 +34. 18
Scaled Dis. from
Approx. Pt. = D 5560.0 965. 2715. () 425 - 0
D - 46 14.43
4.- P__
d0 1000-S 5.56 .97 2.72 .43
1—Change Orientation by +3 Mils (1 to 5)
Reverse sight 16. 68 R. 2.91 R. 8.16 R. 1.29 R

meters R or L
*NotE-do is positive when V obs, is greater than V com. and negative when
V obs is less.
Approx. Point, if minus draw it to the left.
When dO is positive draw the reverse sight to the right of the

X Y
Approx. Point 384. 070. 0 190.660.0
Increments — 12.4 +12.4
Adopted Point 384.057.6 190.672.4
CHAPTER XII
TOPOGRAPHIC RECONNAISSANCE
VISIBLE AND INVISIBLE AREAS
DETERMINATION OF DEFILADE
MAXIMUM RANGE
MINIMUM RANGE
DEAD AREAS
MEDIAN LINE OF FIRE
CHARTS SHOWING POSSIBILITIES OF FIRE
SUMMARY
The governing condition in the choice of a battery posi-
tion is such that the tactical mission assigned to the Artillery
may be fulfilled. The batteries must be able to deliver
effective fire on given points, considering the direction, range
and site. In determining the battery positions, the means
of access, and the several means of information, observation
and command must be considered.
In the choice of battery positions, the following general
principles apply:
(a) In the ordinary case the higher command assigns
either specific targets by coordinates or target areas. In
emergencies, targets may be assigned by higher command,
or fire requested on them by observers, the targets being
designated by approximate coordinates.
(b) The higher command fixes the areas where the artil-
lery must be placed.
(c) Inside these areas the different commanding officers
determine their several emplacements according to the fol-
lowing principles: -
(1) If the mission of the battery is not fixed in detail
from the start, as large a field of fire as possible should be
given them.
(2) If the mission of the batteries is absolutely deter-
mined from the start, which is the exception, the greatest
protection consistent with the fulfillment of their mission
should be given to them.
(3) The concealment of the emplacement from the view
of terrestrial observers, and if possible of aerial observers.
(4) The rendering of liaison and command easy.
216 ORIENTATION FOR HEAVY (COAST) ARTILLERY
(5) The arrangement for ammunition supply and hous-
ing of personnel, so that both will be under the best possible
conditions. -
(d) Observing stations should afford a good view of the
targets and have sure communication with the battery.
Preparatory to occupying a position, the Battery Com-
mander and the Orientation Officer must study the situation,
considering the mission of the battery, the limitations imposed
by higher command, the possibilities of the armament and
the nature of the terrain. This study is best affected by a
careful examination of the map, followed by a reconnaissance
on the ground. - -
In this chapter, various topographical operations required
i the map reconnaissance will be discussed. No attempt
will be made to prescribe any order in which the various
steps should be taken up, or to classify them according to
their relative importance, as different situations present
such a variety of considerations that no fixed rules can be
made. The map itself will give fairly accurate results in
these operations, but the results must be checked on the
terrain.
1. VISIBLE AND INVISIBLE AREAS
The choice of an observation station and the factors which
influence such choice is a tactical operation and will be con-
sidered elsewhere. However, this choice will depend to a
great extent upon the results obtained in determining the
parts of the enemy territory visible and invisible from any
point chosen as a possible observing station.
By Profiles.—If a regular contour map is at hand (for
example, a battle map based on large scale Surveys) the
location of visible and invisible areas may be determined
with considerable accuracy by plotting on the map itself.
This plotting will be less accurate if the relief of the map
is inaccurate. In any case this work should be considered
only a first approximation which must be verified by direct
study on the ground. The method of determining graphi-
cally the visible and invisible areas consists in making sections
of the ground based on contours along vertical planes radiat-
ing from the point of view. These sections are constructed
on a sheet of cross-section paper. For horizontal distances
the scale of the map itself is used, but the vertical scale should
be increased (for example, 5 millimeters may represent 10
TOPOGRAPHIC RECONNAISSANCE 217
meters difference in level) because of the greater accuracy
in determining the necessary intersections, as will be seen
later. The horizontal lines should be numbered according
to their corresponding contour lines.
- /
ZºZ///4
/,
/
c
ſ % -- 3/ Vºž/ % %//
st tº 2 - 9. y 3% gº /%fº%
%
Figs. I and II.--—CONSTRUCTION OF VISIBILITY CHART
It is unnecessary to construct the profile through the
entire extent of the vertical section. For a profile analagous
to that shown in Fig. I the work may be confined to the
parts of the profile indicated by the full lines. The dotted
parts need not be drawn. A first glance at the map shows
that there are four successive ridges—A, B, C, and D. (See
Fig. I.) Begin by constructing the profile of the upper part
of the ridge A. Then from the point of view O draw the
tangent OA to this profile. The point of contact A is the
boundary between a visible and invisible area. All parts
of the ground beyond A and below this line are invisible.
By consulting the map it is seen that the culminating point
of the ridge D is certainly above OA. This point is num-
bered 350 on the map, and at the distance of the ridge B the
line OA intersects with the profile at 345. It is easily seen
that the ridge B will overtop the line. Construct its profile.
The point B, the intersection of this profile with OB, is a







218 ORIENTATION FOR HEAVY (COAST) ARTILLERY
second boundary between the visible and invisible areas.
The point of contact C of the tangent OC is the third point.
Finally, it is seen without any construction that the ridge D
is below the OC line. It need not be constructed. The
various points defining visible and invisible spaces are trans-
ferred to the map by their horizontal distances from the
vertical through the point O. The boundaries between the
visible and invisible areas are determined by plotting similar
points along the planes radiating from the point of view and
connecting these points with a smooth curve. Care should
be exercised in connecting these points. It must be remem-
bered that the inner limit of an invisible area always follows
a ridge line and that the outer limit is usually on a direct
slope. The result obtained should be similar to Fig. II. It
may however be necessary to construct short intermediate
profiles to determine the limits of the areas in such instances
as points “A” in the figure.
On the Terrain.—Having done the preliminary work on
the map, proceed to the observation station and endeavor,
by direct observation, to give more precision to the boun-
daries, the observations being based on measurements of
angles or bearings. Look for all prominent points which,
by accurate location in direction alone, may serve to correct
the positions of the boundaries—the disappearance of a
ridge behind a nearer ridge, the intersection of a boundary
with a line of the planimetric detail, such as a road or an
edge of a wood, or with a line of the enemy's defensive works,
such as a trench or a communication trench. Then study
with field glasses, or with observation telescope, every part
of the ground seen between two successive boundaries. Note
whether if, on the contrary, it includes secondary ravines
forming small defiladed zones that have escaped notice in
the preliminary study of the map. Mark off the parts of
the ground that are rendered invisible by natural or arti-
ficial masks, such as woods, hedges, villages, or screens.
Finally, in areas where the ground is invisible look for tall
objects which may emerge above the ridge that masks them
(summits of woods, tops of trees, roofs of houses, steeples,
etc.). Identify them carefully and mark them on the map.
It is only after having made this study completely and thor-
oughly that the observer can decide definitely on visible and
invisible areas. The different zones may be distinguished
by hachures or by conventional tints; for example:
TOPOGRAPHIC RECONNAISSANCE 219
1. Parts visible, no tint.
2. Parts hidden by the form of the ground itself, flat black.
3. Parts that would be visible but for the interposition
of a mask between the observer and the area, blue.
4. Objects which are situated in an invisible area but
whose tops are visible, red.
2. DETERMINATION OF DEFILADE
Necessary Defilade.—The suitability of any point as a
battery position will depend, especially in the case of small
and medium calibre batteries, upon the amount of defilade
from enemy observation of that position. With the larger
calibre batteries this factor is not so important because of
the other considerations which usually outweight it, but with
any type of battery it should be considered. If the position
is defiladed the amount of this defilade should be known in
meters and compared with the amount required to hide the
flash and smoke of that particular type of battery. If the
position selected has not sufficient defilade, another which
has (other considerations being equal) should be selected or
steps taken to provide the required amount by artificial means.
The defilade necessary for different guns varies consider-
ably and depends upon the caliber and especially upon the
lengths of the guns and the angles of elevation at which they
are fired. The following will give a few approximations of
the height to which the flash and smoke can rise above the
muzzle of the piece. The smoke has a bluish appearance
when seen against a dark background and a yellowish appear-
ance when seen against a background of the sky.

Height of the Height of the
Flash Above Visible Part of
the Muzzle the Smoke Above
the Muzzle
Guns of minor caliber (75 mm. to 120 mm.)
and short pieces. . . . . . . . . . . . . . . . . . . . . . 3 to 5 meters | 5 to 8 meters
Guns of intermediate caliber and of inter- . . .
mediate length. . . . . . . . . . . . . . . . . . . . . . .] 5 to 8 meters | 10 to 15 meters
Long guns of intermediate caliber. . . . . 8 to 12 meters | 15 to 20 meters
Large caliber guns (320 mm., 400 mm). 10 to 20 meters | 20 to 30 meters
—s
Roughly speaking, the flash extends two gun lengths
beyond the muzzle and the visible part of the smoke four gun
lengths beyond the muzzle.
220 ORIENTATION FOR HEAVY (COAST) ARTILLERY
The amount of defilade of the roads of appraoch to the
battery position should likewise be known. When an ap-
proach is not completely defiladed, determine precisely the
part which is not defiladed and designate the points of th
enemy Zone from which it is seen. -
Determination from Maps.-Having determined the points
in the enemy territory which appear most dangerous the
amount of defilade of a position or an approach road with
respect to these points may be determined by means of pro-
files between them. In constructing these profiles the hori-
Zontal scale of the map is preserved but the vertical scale is
C
_ – " T
*
*
* ~ ... *
* - - - - - - "
Fig. III.-TERRESTRIAL DEFILADE
exaggerated as considered before. It must be understood
that in making these profiles only the dangerous crest C
(Fig. III) and the friendly crest B (which forms the defilade
for the battery) and the point A, for which the defilade is
being determined, need be profiled. The amount of defilade
h is measured on a vertical line through A. from the surface
of the ground (or from the level of the muzzle of the gun
when firing at its maximum elevation, as the case may be)
to the intersection of the vertical line with a line drawn tan-
gent to the crests C and B. In measuring h the vertical
scale of the profile must be considered.
The construction is the same if considering defilade from
balloon observation. Construct a profile of the position,
the friendly crest and the balloon at its proper distance and
height. Draw a line from the balloon tangent to the crest
B and measure the defilade as before. It is not always neces-
sary to actually plot the position of the balloon on the pro-
file. The same result can be obtained by determining the
angle which the line of sight from the balloon and tangent
to the crest makes with the horizontal, and constructing this
line on the profile. The tangent of the angle will be the
difference in level of the crest and the balloon divided by
the distance between them, both values being in terms of
the same unit. In laying off this angle the “tangent method”

TOPOGRAPHIC RECONNAISSANCE 221
is used, that is, find the tangent of the angle B, say 1 on 15,
lay off 15 units on the horizontal, AD, from the crest (Fig.
IV), and at D lay off 1 unit times the exaggeration of the ver-
tical scale, on a vertical line, to C. The line drawn through
C and B will represent the line of sight from the balloon tan-
gent to the crest.
*
* ~
* ~
* * =
--"
• *
* * *
-----------" "
Fig. IV.-BALLOON DEFILADE
Eacample of Determination of Vertical Eataggeration.
Scale 1:20,000 5 cm. = 1 km. 1 cm. = 200 m.
Vertical scale 1/5 cm. = 5 m. 1 cm. = 25 m.
- 200
Vertical exaggeration = 25 - 8.
Determination on the Terrain.—It is always useful to
measure directly on the terrain, the defilade of your position.
This is generally done as follows: From the position A or
from the crest B which defilades the position the inclination
{ { } }
o” of the tangent AB is measured. (See Fig. V.)
Fig. V.-CoMPUTATION OF DEFILADE
Measure from the crest B the angle of site “8” at which
the heights of enemy crests are seen from the crest B. This
angle of site can be calculated by finding the difference of
altitude between the crests B and the enemy crests and the
distance between these crests, tang equals H/D. The defilade
is measured by the angle which the line AB makes with the
tangent CB prolonged. If C is higher than B (that is to say


222 ORIENTATION FOR HEAVY (COAST) ARTILLERY
if it is positive) this angle is o – 3. If C were lower than B,
the angle would be a-H 3. If d is the distance from battery A
to crest B (measured on the map or estimated on the terrain),
and if he is the difference in altitude between the battery and
the crest we have the defilade:
h = ho-d tan 8
= d tan o – d tan 8
= d tan (o:-3) (approximately).
The formula may be used in any of the above forms accord-
ing to the data at hand. It must be remembered that if the
angle 8 is negative the sign of the last term becomes positive.
The calculation is the same for a balloon. The angle of
site 8 (Fig. IV) (which is now almost always positive) at
which the balloon is seen from the crest B measured from
this crest or else calculated from the estimated altitude and
distance of balloon from crest B. The formula then becomes:
h = d tan (o. – 3) (approximately).
In flat country it is better to get as near as possible to
the screen; however, the minimum angle which can be used
for fire on close targets limits this proximity.
Practically it may be said that when placed immediately
behind a screen the defilade is equal to the height of this
screen. Particularly in a wood, a gun firing through the
opening between trees without having any trees cut down
before it has defilade which is equal to the height of the trees.
3. MAXIMUM RANGE
The first requisite of a battery position is that from it
the target can be hit in any kind of weather. This results
in establishing the sector in which the position of batteries
must be placed. It is sufficient to place on the map a circle
whose center is the most distant part of the target and whose
radius is the maximum range of the gun under the worst
weather conditions. The choice of positions is primarily
limited to the region included by this circle and the boundary
of the sector assigned for location. It is well whenever
possible to choose a position such that the targets lie well
within the maximum range of the gun because of the greater
amount of dispersion which obtains when firing at the maxi-
mum range. Having definitely decided upon the battery
position, a circle, with a radius equal to the maximum range
of the gun (reduced for adverse weather conditions) and
TOPOGRAPHIC RECONNAISSANCE 223
with the battery position as a center, is drawn on the map
to show the area with regard to maximum range which can
be reached from that position.
4. MINIMUM RANGE
The minimum range at which a battery can fire from a
given position may result from the materiel itself. Gene-r
ally, however, local circumstances determine the minimum
range by establishing the minimum angle at which it is pos-
sible to fire, that is to say, the angle below which the projec-
tile would strike the crest of hills of trees which mask the
battery. If it is found that a position has been chosen from
which short range targets cannot be reached because of the
minimum range produced, it may be necessary to select a
position farther from the mask or to select another for which
the minimum range is less. -
The map can only give indications as to the minimum
angle for such a position. The angle must always be corrected
on the terrain itself. This study of the map is made by means
of cross sections or profiles of the terrain.
Make a profile with an exaggerated vertical scale of the
intersection of the mask (HH') and if the plane of fire through
the battery G and any possible target. (Fig. VI.) If the
crest is wooded, the height of the trees must be considered
or may be estimated (at an average 15 meters).
7–4
_-T 23S ſº § 2. ~~~~ Y ~
...” ſ º *.
e” A/ We S.S
º' | :- N.
- § | É- NS
Zº ! º W. Wvº - SN
; Nº. E. N A
ſº ! ET22 % º N 7–
º Sºlº Zi à Pºcº -
*...* | * * ^ Wºº, ºse º:
G 2%iº // I //o//zo/772/ SºśWºź. Z.
Z | w/ `--> 7.
Fig. VI.-MINIMUM RANGE
Draw the tangent GH to the face of the mask. Let GL
be the horizontal through the gun muzzle. Measure angle
H'GH, keeping in mind the vertical exaggeration of the profile
/ H/
Tan H'GH = GH’’ - G
When the crest of mask is a considerable distance from


224 ORIENTATION FOR HEAVY (COAST) ARTILLERY
the gun, this angle would not give a sufficient angle of eleva-
tion to clear the mask, since the trajectory is a curve and the
projectile falls below the line of departure and would strike
the ground near the crest. Therefore, determine the range
to the restricting contour, look up the angle of elevation
for this range, and add this angle (HGB) to the original
angle. The projectile fired at the resulting elevation H'GB
will just clear the mask.
Look up in the range table, the range corresponding to
the angle of elevation H'GB. This range is measured on
the horizontal plane through the muzzle, therefore lay off that
range GT on GL. If the surface of the ground as shown
by the profile is above the level of the muzzle of the gun,
as in the figure, it is obvious that the projectile will strike
the ground at a range less than GT, and if lower, at a range
greater than GT. Therefore at T construct TT" at an angle
with the horizontal equal to the range table angle of fall for
the range GT. This is done by the tangent method as before
described. Then T', the intersection with the profile, is
approximately the point at which the projectile will strike
the ground, and will be correct within the limits of the accu-
racy of the map and the projectile. For guns using a high
angle of fire, and consequently having a steep angle of fall,
it is not necessary to consider the difference in level between
the muzzle of the gun and the ground at the point of fall.
In constructing the angle of fall the vertical exaggeration of
the profile must be considered.

225 * - 27.5"
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225 2. > 4- CO 225
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Fig. VII.-EXAMPLE OF MINIMUM RANGE
Example.—Vertical Scale 1/5 centimeter=5 meters. Horizontal Scale 5
centimeters = 1 kilometer (1 : 20,000). Range table of 155 mm. gun and profile
with battery at G. To determine minimum range along profile: Draw GH
tangent to profile. Angle of site of the restricting contour =
Difference of Level G & H 250 – 200 100 mil
- IIll IS.
Range X,001 501 x 001
TOPOGRAPHIC RECONNAISSANCE 225
But to clear mask it is necessary to increase this angle by the angle of eleva-
tion for 501 m. = 6.2 (from Range table by interpolation). Therefore the angle
of elevation = 100+6.2 = 106.2 mils, which gives range of 4958 meters and the
slope of fall = 1 on 6.7. Lay off GT =4958 meters. The point T would be the
point of fall of the projectile on a plane level with G. Now at the vertical scale
1 cm. =25 m. and at horizontal scale 1 cm. =200 m. the vertical exaggeration
=200/25=8. Therefore to plot a slope of 1 on 6.7 it is necessary to multiply
1 by 8.0 and draw TT', as shown intersecting the profile at T', at 4846 m. from
battery which is the actual minimum range of the gun from the position G along
the line on which the profile was constructed.
If the battery is to be located in a wood as in Fig. VIII
the profile gives an indication of the distance “ac” which
must be cleared of trees in order to fire at a given angle, “o.”
iº
O.
Q.
Fig. VIII.-CLEARING NECESSARY FOR BATTERY LOCATED IN WOODS
This clearing will always be important for positions of
the battery (like the position “a”) where the trajectories
graze the face of the hill. At the same time, the profiles of
the terrain show the advantage which exists in certain cases
where it is possible to avoid this cutting of trees by placing
the battery at the base of the counter-slope as at the posi-
tion “b.”
From the Terrain.—In checking on the terrain the results
obtained in determining the minimum range from the map,
an instrument for measuring vertical angles, i.e. a transit, .
theodolite, or even the gun itself, using the bore of the gun
as a telescope, is set up in the gun position and the angle
HGH" (Fig. VI) is measured. The remaining operations are
the same as before.
5. DEAD AREAS
It is absolutely indispensable to know the formation of the
terrain surrounding the target in order to see if the target can

226 ORIENTATION FOR HEAVY (COAST) ARTILLERY
be reached and from what position the battery can render the
most efficient fire. Every point on a counter-slope for which
the declevity, measured in the direction of fire, is greater
than the angle of fall, is protected from fire. For any par-
ticular profile, the portions of the surface in dead angles may
be determined as follows:
Figs. IX and X-PROFILES TO DETERMINE DEAD AREAS
In Figs. IX and X, being given the profile ABC with the
point “A” chosen by inspection to be in the neighborhood
of the point of tangency of the trajectory with the crest which
is the battery edge of the dead angle. Let R = the range
of A from battery and AA’ tangent to the trajectory as deter-
mined by its angle with the horizontal (1). This angle (i)
with the horizontal can be found as follows:–
Let HA be the horizontal through A. Then the angle of
site HAG =
difference in height of gun and A
range X.001
Let a = range table angle of fall, measured with regard
to GA. Then in Fig. IX, i= a – s; and in Fig. X, i= @-Hs.
That is i-angle of fall minus the angle of site with its proper
sign, the angle of site being positive when the gun is below and
negative when it is above the target.
Draw HAA' = angle i. Draw BB' parallel to A' A tangent to
slope at B, intersecting slope at C. The space BC is dead
space within which a target could not be reached. It is neces-
sary to exaggerate the vertical scale but care must be taken
to represent angles not by the multiple of the angle but by the
= S (in mils).

TOPOGRAPHIC RECONNAISSANCE 227
multiple of the tangent of the angle. The effectiveness of fire
on counterslopes is a subject treated in Gunnery.
Aſsumed 77 ya/a/7a Co/7sfracfor Poinf
275" A 275"
250 25O
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Fig. XI.-CoMPUTATION OF DEAD AREA
Example.—Given profile AC, with A assumed point of tangency at 4500 m.
from 155 mm. gun Range Table. Vertical Scale = 1/5 cm = 5 meters. Hori-
Zontal Scale 5 cm. = 1 kilometer. Vertical Exaggeration = 8.0. Angle of site
_280–200 - * il l
(s) T4500×100T = 18 mils. Angle of fall (a) at 4500 m. = 128.3 mils. Angle of
fall with regard to Horizontal i = a -s = 110.3 mils =Slope of Fall = 1 on 9.2.
At A construct AC a slope of 1 on 9.2 giving regard to the vertical exaggeration.
Draw a line parallel to slope of fall at 4500 m. and tangent to the profile at
B, 4630 m. (scaled) from the gun position. C the intersection with the profile
is the limit of the dead area at 5050 m. from battery.
Dead areas may be readily determined mechanically by
the use of a ruler on which ranges and corresponding trajec-
tory contours have been plotted to the map scale used in con-
structing the map. The objections to the use of the ruler
are that it gives an error due to this fact that the angle of
site is disregarded and that different rulers have to be con-
structed for each combination of powder and projectile and
map scale being used. - -
6. MEDIAN LINE OF FIRE
During the reconnaissance on the terrain, the map is
constantly oriented by means of a compass. For example,
the map will be fixed on an oriented plane table corrected
for declination and the two limits of the field of fire will be

228 ORIENTATION FOR HEAVY (COAST) ARTILLERY
traced thereon. This precaution permits the choosing of
positions in wooded country which will allow individual guns
to profit by the clearing between trees to fire on given targets.
The oriented map permits, also, the staking out upon the
terrain of the directions of gun platforms which will be, in
general, the bisectors of the chosen fields of fire. These
bisectors are called directrices.
In determining the directrix of the platform for a gun hav-
ing but a small horizontal field of fire to the right and to the
left of the directrix, the drift of the projectile must be kept
in mind. This correction is particularly important for mor-
tars and howitzers. It will be necessary then to shift for the
mean range of the targets.
The directrix that must be staked out on the terrain for
guns of limited horizontal field of fire can be obtained by
constructing on tracing paper sectors representing at different
map scales 1/80,000, 1/50,000, 1/20,000, the terrain covered
from the same position. To accomplish this a curve AB is
constructed which represents the points of impact of the gun
firing in a fixed position AD with different ranges. (See
Fig. XII.)
º
Q
This curve may be deduced from the range table values
of the drift for each range. The line AD representing the
directrix of the platform, the curve AB is turned to the right
and to the left through an angle “of” equal to the possible
horizontal traverse on either side of the directrix. The sur-
face limited by the two curves thus obtained and the maximum
and minimum range represents the terrain that can be covered
from A with the directrix AB when the atmospheric conditions
are normal. It is useful to draw on the same figure the curves
limiting the field of fire if a lateral wind of 10 meters per sec-
Ond is blowing. Those curves are also deduced from the
Fig. XII.-FIELD OF FIRE







TOPOGRAPHIC RECONNAISSANCE 229
range table. If the gun fires different reduced charges, each
field of fire may be shown in a different color, and will be out-
lined somewhat as follows: (See Fig. XIII.)
Fig. XIII–FIELD OF FIRE FOR DIFFERENT CHARGEs
This tracing paper placed on the map, the point A coincid-
ing with the position of the battery and the shaded sector
covering the target, will give the direction which it will be
necessary to give the stakes on the terrain to determine the
direction of AD.
Draw on the battle map the median line of fire decided
on, and measure its axial bearing or its Y-azimuth with a pro-
tractor. In laying out this line of the ground for materiel
with a large field of fire, it is sufficient to set up at the gun
position an instrument with a magnetic needle, orient it, and
have set out a sufficient number of stakes in the direction
determined by the axial bearing of the median line. The
Peigne compass, the compass goniometer, or the plane table
with leveling alidade may be used. However, for guns with
a limited field of fire, the Y-azimuth of the median line must
be accurately measured from the map and a transit, oriented
to read Y-azimuths, used to determine the direction of the
stakes set out.
7. CHART SHOWING PossIBILITIES OF FIRE
When the battery position has been definitely decided
upon or occupied, a chart must be made showing the area it
can cover under normal conditions, that is a chart showing
the lateral limits of the field of fire, the maximum range, the
minimum range and dead angles. This will be of great value
to the battery commander in determining at a glance whether
or not any particular target can be fired upon. The battalion
commander must have a similar chart, compilations of the
battery charts, showing the zone of action of the battalion,
by means of which he assigns targets and gºritrols the fire




230 ORIENTATION FOR HEAVY (COAST) ARTILLERY
upon them. The tactical use of the group is also determined
by means of a similar chart showing the zone of action of the
grOup.
Construction.—This chart is prepared by drawing upon
the map or a sheet of tracing paper (1) the lateral field of
fire, (2) a circle representing the maximum range as before
described, (3) the outline of the minimum range and (4) the
outlines of the dead areas. These latter two are determined
by investigating for minimum range and dead angles along
Several planes radiating from the battery position in the field
of fire, plotting the points thus found and connecting them
with smooth curves in a manner similar to that described in
the preparation of the chart showing the visible and invisible
areas. (See Fig. XIV). The minimum range and corrected
minimum range is plotted on the profile of each ray as deter-
mined in the foregoing, and these points transferred to the
map on their respective rays. The points thus obtained are
joined by easy curves whose general form is determined by
the direction and form of the restricting contour, considera-
tion being also given in the case of the corrected minimum
range to the form of the terrain where points of impact would
occur with the gun set at the minimum range.
The dead areas de and flº are determined on each profile
as described in preceding parts of this mimeograph. The
inner and outer limit points plotted on the rays from which
the profiles were constructed and these joined by curved lines
whose form between points is determined by considering the
form of the terrain shown by the map contours. When this
interpolation might lead to error in badly broken or contorted
areas additional profiles must be made and points plotted.
The dead areas, minimum range area, etc., are now tinted or
hachured on the map. The maximum range line is drawn
by inscribing an arc whose radius is the maximum range of
the piece reduced to the scale of the map and whose center
is the gun position.
By roughly constructing similar charts for all possible
battery positions during the reconnaissance, the possibilities
of fire from these positions can be readily compared and will
aid in the final selection of a position. The battery positions
other than the one finally decided upon may be used as places
to which one or more guns can be moved in order to get more
effective fire uxon targets which cannot be effectively reached
from the primary position.
TOPOGRAPHIC RECONNAISSANCE
231
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Fig. XIV.-CHART SHOWING POSSIBILITIES OF FIRE





282 ORIENTATION FOR HEAVY (COAST) ARTILLERY
8. SUMMARY
The selection of a battery position is of the greatest impor-
tance and a choice can only be made after the gravest con-
sideration and a careful review of all the available maps, con-
Sultation with those who have been in that locality for a
considerable period, and a searching reconnaissance of the
terrain.
Initial Selection.—The area in which a position must be
selected is defined on the map by:
(a) Being within the sector assigned by the higher com-
mand. -
(b) Having all the targets or the enemy area assigned
within the maximum range of the battery. This may be
defined by drawing upon the map arcs of circles whose radius
is the maximum range of the battery under adverse conditions
and whose centers are the most distant targets or outer limits
of the enemy area assigned. The final battery location must
be within all these arcs.
(c) Having all targets at a sufficient range so that the
angle of fall may be greater than the counter-slope on which
any target may lie. This may be defined, first, by drawing
on the map lines radiating from the various targets in the
direction of the assigned sector; second, by plotting points on
these rays representing the gun positions of minimum range
permitting the angle of fall to be greater than the target's
counter-slope; third, by connecting these points with smooth
curves. The final battery location must be outside of all the
lines so constructed.
(d) Having the battery placed within an area defined by
the direction in which it is best to fire in order to give the
greatest value to each shot owing to the dispersion of your
fire being greater longitudinally than laterally.
In Fig. XV the minimum range lines ABC are determined
by contours surrounding Ti, and EBD are determined by con-
tours surrounding Tº. Thus EBC defines the minimum
range at which both targets may be fired upon without hav-
ing the mask of either form a dead area containing the target.
Likewise the maximum range arcs were drawn—FGH
with T, as a center and JG I with T, as a center. The defin-
ing line FGI is therefore the maximum range limit for both
when considered together.
The direction of most effective fire for each target defines
TOPOGRAPHIC RECONNAISSANCE
233
\
WA
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: º
WT-> a 2- ) T
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«
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Fig. XV.-CHART OF AREA IN WHICH A BATTERY MAY BE LOCATED
an area (cross-sectioned in the figure) in which a position
should be selected to get the most effective fire upon both.
Secondary Selection.—Having ascertained the area in which
your battery must be placed the selection of a position within
this area may be made on the map but must be verified on the
terrain. The influences governing such a selection may be
classified under two general headings Selective and Limiting.
Under the head of Selective would fall:
(a) Ease of Access.-A position selected near a road has
advantages due to, (1) the ease with which the guns may be
brought up or taken out, (2) the easier transportation of Sup-
plies, (3) the lessened fatigue of the men in their daily marches
to and from their living quarters, and the ease with which



234 ORIENTATION FOR HEAVY (COAST) ARTILLERY
materials for building emplacements may be brought up and
the ease in disposing of the earth excavated in the emplace-
ments along the sides of the road. The lack of roads or paths
from the nearest highway to the emplacement, thus disclosing
its position to the aerial observer, is of great advantage.
(b) Defilade.—To get a sufficient defilade to hide the battery
and the flash, Smoke or dust therefrom from terrestrial or bal-
loon observation and to secure natural ramparts requiring the
enemy to use a greater range than he would otherwise, with
its consequent greater dispersion in his counter battery firing.
(c) Proper Concealment.—A position must be selected when
it is possible to erect artificial masks that blend in with the
surrounding scenery and does not give the enemy the infor-
mation as to the battery position through their evident arti-
ficiality. These artificial masks may be shrubbery, curtains,
nets, etc., and their value depends not only upon their ability
to conceal the battery and its working but their seeming
natural. Woods may be used to advantage if it is unneces-
sary to cut away trees and thus disclose your location. The
edge of a woods is therefore more generally selected, orchards
may be used for smaller caliber guns or large guns if the open-
ings between the trees are sufficient. Second and third line
trenches provide excellent cover for smaller guns, and ruined
villages have the advantages of allowing the work of con-
struction of emplacements to proceed with little fear of the
enemy discovering the displacement of earth, or the piling of
materials in the general disorderly appearance of such places
and the ease in maintaining camouflage discipline under these
conditions. -
Under the head of Limiting would fall:
(a) Minimum Range.—The minimum range or elevation
that must be used to reach the targets or area assigned without
moving too far from the defilade to neutralize its advantages.
(b) Proximity.—The proximity of cantonments, supply
depots, other batteries, enemy reference points, enemy targets,
or friendly command or adjustment observation posts must
be avoided, as fire may be drawn upon them by the battery or
by them to the battery. -
(c) Low Ground or Depressions.—Low ground is to be
avoided as it is largely impossible to provide shelters for your
men in this kind of terrain. Depressions and low lying land
are also to be avoided owing to the settling of gas in the low
plains and the consequent difficulties of dispersing it. A low
TOPOGRAPHIC RECONNAISSANCE 235
depression getting to a large extent the disadvantages of all the
enemy gas delivered to such points as drain into the depres-
SIOI).
(d) Avoidance of Main Roads and Means of Communica-
tion.—One emplacement near means of communication to
more advanced troops may draw unnecessary fire to the road
causing delay and difficulty in supplying the needs of the for-
ward trenches and as these roads are systematically shelled
by the enemy an emplacement near them receives much fire
therefor.
Various Factors.—It is necessary to consider the nature
of the ground to see if a firm foundation may be secured for
gun platforms, and the possibility of digging in to secure
adequate protection; to consider the drainage afforded the
emplacement by the slope and nature of the terrain, it being
desirable to secure a position into which the water shed by
the surrounding terrain will not flow and to secure drainage
for the shelters themselves to relieve them of rain water and
Seepage. It is necessary to be among surroundings that
will make flash burns easily hidden.
The means of liaison and command must be considered
carefully as the location of observation stations for command
or adjustment of fire may have a direct bearing on the location
of the battery and where the selection of positions for such
stations are limited and the positions for the battery largely
unlimited the position of the battery will be governed by their
necessary location.
From a careful study of the battle map information can
be obtained about the location of railroads, roads, streams,
and forests, all of which has more or less influence on the
Selections of a battery position.
The choice of a position for an observation station is gov-
erned largely by the enemy area visible from the station as
it is readily concealed owing to its comparatively small size.
236
ORIENTATION FOR HEAVY (COAST) ARTILLERY
EXTRACT FROM RANGE TABLE–155 MM. GUN, CHARGE 8.85 KG.-
SHORT FUSE—M. V. 596 M. S.
Range | Angle of Angle of Slope of | Range | Angle of Angle of Slope of
in Elevation | Fall Fall in Elevation | Fall Fall
Meters Mils p Mils a | 1 On Meters | Mils p Mils a | 1 On
500 6.2 6.8 150. 1 4300 86.4 118.6 8.55
600 7.6 8.5 120.1 4400 89.4 123.3 8.22
700 9 . () 10.2 || 100.0 4500 92.4 128.3 7.90
800 10.6 11.9 87.4 4600 95.4 133.3 || 7.60
900 12.2 13.6 75.0 4700 98.4 138. 3 || 7.32
1000 13.8 15.3 66.6 4800 101.4 143.5 || 7.06
1100 15.4 17.2 59. 1 4900 104.4 148.5 6. 81
1200 17.0 19.1 53.3 5000 107.5 153.7 6. 57
1300 18.6 21.0 48.5 5100 110. 7 159. 3 | 6. 34
1400 20. 2 22.9 44.5 5200 114.0 164.9 6. 12
1500 21.9 24.9 40. 9 5300 117.3 170. 7 || 5.91
1600 23.6 27. 1 37.6 5400 120. 6 176.6 || 5. 71
1700 25.4 29.3 34.8 5500 124.0 182.5 5. 52
1800 27.2 31.5 32.3 5600 127. 5 188.6 5. 34
1900 29.1 33.7 30.2 5700 131.0 194.6 5.17
2000 31.0 36.0 28.3 5800 134.6 200. 7 || 5.01
2100 33.0 38.6 26.4 5900 138.2 206. 7 || 4.86
2200 35.1 41.2 24.7 6000 14.1.8 213. 1 4.71
2300 37.2 43.9 23.2 6100 145.5 219.0 4.58
2400 39.3 46.6 21.9 6200 149.2 225.2 4.45
2500 41.4 49.3 20.7 6300 153.0 231. 1 || 4.43
2600 43.6 52.4 19.4 6400 156.9 238. 1 || 4 - 20
2700 45.8 55.6 18.3 6500 160.8 244.8 || 4.08
2800 48.0 58.8 17.3 6600 164.8 251.3 || 3.97
2900 50.2 62. 0 16.4 6700 168.9 257.6 3. 87
3000 52.5 65.2 15. 6 6800 173.0 264. 1 || 3.77
3100 54.8 68.7 14.8 6900 177. 1 270.9 3.67 .
3200 57.1 72. 1 14. 1 7000 181.2 278.2 3. 57
3300 59.4 75.9 13.4 7100 185.4 285.0 | 3.48
3400 61.8 80.0 12 7 7200 189.6 291.4 || 3.40
3500 64. 2 84.0 12. 1 7300 194. 0 298.0 3.32
3600 66.6 87.6 11.6 7400 198.5 305.8 || 3.23
3700 , 69.3 91.5 11.1 7500 203.0 313. 1 || 3.15
3800 72.0 95.8 10.6 7600 207.5 320.8 || 3.07
3900 74.7 100.5 10. 1 7700 212. 0 327.7 3.00
4000 77. 6 104.5 9. 71 7800 216, 6 335.0 2.93
4100 80. 5 109.0 9.31 7900 221.3 341 .. 5 2.87
4200 83.4 .7 8.92 8000 226.0 349. 4 || 2.80


CHAPTER XIII
THE FIRING BOARD
1. PURPOSE
2. DESCRIPTION
3. CONSTRUCTION
4. USE
5. PARALLAX PROTRACTORS
1. PURPOSE
Assuming that the position of the gun and the Y-azimuth
of the reference direction have been satisfactorily determined
and that the position of the target on the map is known by
its coordinates, the artillerist has at hand the data that he
requires; but if he plots these positions on the ordinary un-
mounted map, errors and inconveniences result, which can
only be eliminated by the use of a firing board.
The sources of error result from:
(1) The difficulty of making accurate measurements of
range of Y-azimuth on an unmounted map, especially if the
gun, aiming point, and target are on different sheets.
(2) The distortion which, however true to scale a map
may be when first printed, is bound to arise owing to the ex-
pansion and contraction of the paper according to the state of
the atmosphere.
The errors arising from these sources are far from negligible.
They increase with the range and should be eliminated so far
as possible. They are minimized by the use of firing boards.
Field of Use.—A firing board is considered more necessary
for guns having a wide field of fire than for those of limited
fire. It is not considered as essential for the heavy artillery
guns as for the field artillery, for heavy artillery has time for
computations. However, no battery commander should feel
that his firing data problem is solved completely until the
firing board has been made.
Our Coast Artillery is familiar with plotting boards which
graphically determine ranges and azimuths to targets, and the
French planchette de tir and the British artillery board are
plotting boards which are designed to serve similar purposes.
238 ORIENTATION FOR HEAVY (COAST) ARTILLERY
The Firing Board (Planchette de Tir) is used on the Western
Front in the Heavy (Coast) Artillery:
(1) To graphically check the trigonometric computa-
tions of range and Y-azimuth. -
(2) To graphically determine range and Y-azimuth when
an emergency demands haste.
(3) To visualize the relative positions of gun and target
on the map and thus assist in computations.
2. DESCRIPTION
The Firing Board consists essentially of a flat rigid surface
on which gun and target positions are accurately indicated.
A drawing paper, sometimes backed with linen, is mounted
on a base little affected by dampness or temperature changes.
This base is usually zinc on a wooden back or frame. The
quadrillage covers the entire probable field of fire. A sheaf
of Y-azimuths in the angular system for which the aiming
instruments are graduated radiates from the gun position.
When a target is plotted, the distance between it and the gun
position can be scaled for the range and the Y-azimuth can
be read from the sheaf with a protractor for subdivisions
of sheaf. Fig. I is a photograph of a firing board with its
construction lines. - •
Scales.—The scale of the quadrillage of the firing board
is usually made the same as that of the battle map used.
The most common for heavy artillery is 1/20,000. For long
ranges, say 20 km., a scale of 1/40,000 is used. •
Accuracy.—With a carefully prepared board, on a scale
of 1/20,000, it should be possible to read the range to within
10 m., which is sufficiently close. It should be possible to
read Y-azimuth to 1 mil. *.
3. CONSTRUCTION
(1) Prepare Board.—Tack a sheet of zinc to the wooden
backing. A drawing board may be used without the backing.
For purposes of demonstration a beaver board slab may be
used.
(2) Mount the Drawing Paper.—It should have a good
surface for taking ink. A good “stretch” can be made as
follows: (Use drafting room paste.) Cover one side of the
paper with a thin layer of paste free from lumps. Turn it
over and place it lightly on the board. Put a second sheet
THE FIRING BOARD 239

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Fig. I.-FIRING BOARD
on top to protect it. Start at the center pressing the paper
to the board, working toward the edges in every direction
(using a draftsman's triangle or something similar). This
works the excess paste, bubbles, etc., out from under the
paper and stretches it evenly. The excess paste can be
removed from the edge by a cloth. Allow the mount to dry. -
(3) Draw the Quadrillage on the Board, first with a hard
pencil, kept well sharpened; and after the work has been
checked trace the lines with ink.
a. Draw the major axis ab approximately in the middle
of the paper.
b. Draw the minor axis cd perpendicular to ab, approxi-
mately in the center, by determining at least four points
240 ORIENTATION FOR HEAVY (COAST) ARTILLERY
from A and B as centers. (Fig. II.) A and B and the radii
should be so chosen that the four points will be about equally
spaced and the outer ones be near the edges of the board.
It is absolutely essential that these axes be at right angles.

A
A3
b
\
Fig. II.-FRAME LINES FOR QUADRILLAGE
c. Draw arcs with centers on the axes. The radii for
the arcs from each axis should be multiples of the distance
between the lines of the quadrillage and the arcs should be
tangent to the proposed outer lines of the quadrillage.
(Fig. II.) For a 1 to 20,000 quadrillage, the distance be-
tween lines is 5 cms, representing 1000 m. The radii should
therefore be multiples of 5 cms. -
- d. Draw tangents to these arcs. They will be parallel
to the axes. (Fig. II.) *.
e. Commencing at the axis cd, by means of a carefully
graduated ruler, determine points at 5 cm. intervals on the
axis ab and its two parallels. Join successively the sets of
three points lining the paper parallel to cq.
f. In the same way the paper may be lined parallel to ab.
g. Place the numbers on the quadrillage representing
THE FIRING BOARD - 241
the metric coordinates of the portion of the battle-map to
which the firing board corresponds.
(4) Check the Quadrillage.—It is indispensable that the
quadrillage be precise.
a. Draw a diagonal through two intersections. It should
pass through all other possible intersections. Draw several
such diagonals.
b. With a millimetric ruler measure the lengths of the
sides of the squares in the different parts of the firing board.
The error should not exceed .2 mm. in a 5 cm. square.

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Fig. III.-LOCATION OF GUN POSITION
(5) Locate Position of the Gun on the Firing Board.—It is
necessary to plot points with the greatest possible precision.
Use a millimetric ruler.
Let the point M be located by its coordinates x = 58,242 and
y = 25,231.
1 mm. is equivalent to 20 m. on the ground. Therefore
12.1 mm. represents 242 m. Draw a line parallel to the
242 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Y-axis at a distance of 12.1 mm. from the 58,000 line by plot-
ting three points a, b, and c. Point M will lie on this line.
(Fig. III.)
Similarly draw line def parallel to the X-axis at the proper
distance, 11.5 mm., from the 25,000 line. -
The intersection of these lines determines the point M.
Locate the different pieces of the battery or the different
positions likely to be occupied by mobile artillery in the same
IQ3,Illſleſ".
If the square is too small, incline the ruler so that the 0
and 5 are in coincidence with the sides of the squares. (See
Fig. IV.)
Fig. IV.-SCALING ON QUADRILLAGE OF WARYING WIDTHS
If the square is too large, place the ruler parallel to the
lines of the quadrillage, leaving equal intervals between the
sides of the square and the 0 and 5 marks respectively. This
is an approximation. (See Fig. IV.) -
(6) Draw Sheaf of Y-azimuths for every 100 mils or 50
decigrades. -
a. Through the directing gun position draw two lines
parallel to the x- and Y-axis; these lines represent Y-azimuths
of 0 and 1600 mils.
b. In several squares located 45° from the square con-
taining the directing gun, plot points in the same relative posi-
tions and in the same manner as the directing gun was plotted
in its square. These points lie upon the ray of 800 mil
Y-azimuth which may be drawn by connecting the points with
a straight edge. (Fig. V.)
c. Bisect each of the two 800 mil angles by the compass
method. (Fig. VI.) Lay off OA = OB along the sides, and

"RHE FIRING BOARD - 243
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Fig. V.-LAYOUT OF 800 MIL. RAY
with A and B as centers, draw arcs of the same radius, which
determine by their intersection the points M and N upon the
bisector of the angle AOB. A. and B and the radius should be
so chosen that M will be at about the outside limit of the sheaf
and the directing gun, M, and N will be about equally spaced.
Fig. VI.—METHOD OF BISECTING AN ANGLE

244 ORIENTATION FOR HEAVY (COAST) ARTILLERY
d. By bisection draw rays for every 100 mils in this quad-
rant. Sheafs in other quadrants are constructed similarly. It
is only necessary to construct a sheaf to cover the field of fire.
If the decigrade is used as the angular unit, draw the 500
and 1000 decigrade rays. The 250 and 750 rays are con-
structed by bisection. With the directing piece as a center,
draw a circumference with a large radius, and divide each of
the 250 decigrade arcs into 5 equal parts. These are points
lying upon rays drawn at intervals of 50 decigrades. Each
ray must be determined by at least two points. These rays
must be drawn sufficiently long to surround the targets.
If it is desired to avoid dividing the angles by compass,
construct a protractor of large radius (50 to 75 cm.) on heavy
paper, and mark the 100 mil or decigrade divisions upon it.
Protect the center of the protractor by a re-entrant angle.
In every case, before marking a graduation on a firing board
verify the position of the protractor by coincidence with the
800 and 1600 radii which must always be drawn in advance.
The protractor must be very accurately constructed. The
bisection method is more accurate.
A diagonal scale similar to the one placed on Coast Artillery
plotting boards can be used in place of the sheaf and pro-
tractor and has been adopted by the British Artillery.
One of the best methods of laying out an angle is called
the tangent method. It is trigonometric and based on the
fact that in a right triangle the base times the tangent of one
angle equals the perpendicular (the side opposite). Lay off
on the given side of the angle a convenient length and at the
end of this base erect a perpendicular extending toward the
required side of the angle. Multiply the natural tangent of
the required angle by the base (a base of ten units is very con-
venient). Lay off this distance on the perpendicular and join
the point thus located with the vertex of the angle. When
the angle is greater than 45° the tangent becomes too long
and the complementary angle is plotted.
4. USE
The steps by which range and Y-azimuth are determined
from the firing board may be summarized as follows:–
(1) Location Targets by Their Coordinates.—Take a piece
of tracing paper which is divided into quadrillage squares
of the same scale as the battle map. Place this tracing paper
THE FIRING BOARD
2
4
5
over the target so that the lines coincide with the grid lines of
the battle map and make a sketch of the target. Superimpose
this sketch upon the firing board making its coordinate lines
coincide with the proper grid lines. By pricking through the
tracing paper, the desired points are located on the firing board.
Points are often transferred from the battle map to the
firing board by the use of an amberoid or metal angle, grad-
uated along its inner edge in subdivisions of the grid. (Fig.
VII.) These angles must have their edges graduated in the
same scale as the map. If the coordinates of the target are
accurately known, it may be plotted on the firing board by
the more accurate method described for plotting the gun
position.

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Fig. VII.-AMBEROID OR METAL ANGLE
(2) Measurement of Range.—The range, determined from
the firing board for each gun, is the distance from the gun
to the target measured in mm. multiplied by the scale of the
board. Before making this measurement, the graduations of
the ruler should be checked with those of the board. To do
this lay the ruler parallel to the X or Y axis, whichever is more
nearly in the direction of fire. Make one of the large divisions
of the ruler which approximates the range coincide, with the
grid line on the board nearest the target. Check back along
the ruler to its zero, seeing that the proper divisions coincide.
246 ORIENTATION FOR HEAVY (COAST) ARTILLERY
If the zero division fails to coincide with its corresponding
grid line, mark the amount of the error on the ruler, to the
right or left of the zero as the case may be, and use this mark
as the Zero in measuring ranges to targets in the proximity
of the target for which this check was made.
(3) Measurement of the Y-azimuth of Target.—The Y-azi-
muth of the line from directing piece to the target is deter-
mined first. Lay the protractor on the firing board with
its center at the directing piece position. Turn it so the outer
radii coincide with the radii of the sheaf between which the
target lies. Read on the protractor the amount to be added
to the Y-azimuth of the radius of the sheaf passing to the left
of the target.
The Y-azimuth for the other pieces is that of the directing
piece corrected by the parallax. This question is taken up
in Gunnery. To determine it from the firing board, place
the center of the protractor on the target and the zero radius
on the directing piece. Read the parallax angle for each
piece. For pieces to the left of the directing piece, add the
parallax to the Y-azimuth of the directing piece. For pieces
to the right subtract the parallax.
(4) Determination of the Angle for the Sight.—The Y-azi-
muth thus determined is added or subtracted (a simple sketch
will show which) to the Y-azimuth of the gun-aiming point
line will give the angle which when corrected for drift, etc., is
applied on the gun sight.
Catalog of Targets.-The form below is a record of the
coordinates, altitudes, ranges D, and Y-azimuths V, for tar-
gets for a mobile battery. From this data a bombardment
can be undertaken at any time.


- Coordinates Number of Piece
Target Altitude
X | Y D. P.

P
2
3
4.
=
–
–
=
Cross-roads. . . . . . . . . . . .
Steeple of village of. . . . .
PP-R
=
–
–
ºR=R
-
–
=
THE FIRING BOARD 247
The firing board is also used for measuring range and
direction for shifting fire. Such a problem is a change from
reference target to an objective. (This is a gunnery question.)
Typical Eacample
Given—
Directing gun X =383,475 Y = 190,389
Target X =381,250 Y = 196,735
Y-azimuth of Line gun to aiming point = 27°31'
=489.17 mils.
(Degrees are used because tables are available.)
Firing Board. Scale 1 to 20,000
Y-azimuth sheaf for every 100 mils.
Find–Trigonometrically and graphically by Fir ng Board.
1. Y-azimuth (gun to target) =V.
2. Map range = D.
3. Angle (target-gun-aiming point).
Graphic Triºri. Computations
- d
(1) (1) cot V=Iy
dX=381,250–383,475
=2,225
dY = 196,735–190,389
=6,346
–2225
cot V = 6346 - — .3506
W = 340° 40'.73 = 6056.64 mils.
W = 6057.5 mils
(2) 1 to 20,000 means that 1 cm =200 m dX
Line (gun-target) scales 33.63 cm. (2) * Sin TV
D=200Xscale reading
=200X33.63 = 6,726 m. — 2225
(3) Angle T-G-A. P. = Y-azimuth (gun (3) Angle T-G-A. P.
to A. P.) +6400–Y-azimuth =489.17+6400–6056.64
(gun to target). =832.53 mils,
=490–H6400–6057.5
=832.5 mils
It is therefore seen that the graphic s...' fion was very good for the range
checked exactly and the Y-azimuth within 1 mil, with the trigonometric com-
putations. -
British Artillery Board.—The system of map coordinates
is called a grid. It is based on lettered squares 6000 yards
on a side subdivided into numbered squares 1000 yards on
a side. Each square is divided into four by dotted lines.
This grid is the same as the one used on British Battle Maps
and is described in Chapter II. It is drawn on the artillery
board in a manner similar to that described above for the
firing board. (See Fig. VIII.)
248 ORIENTATION FOR HEAVY (COAST) ARTILLERY
-$–|—º -:
—º
|-S |^s
S | SO
t-- {
Fig. VIII.-BRITISH ARTILLERY BOARD
The British draw a diagonal scale in the proper angular
System in place of the sheaf and protractor and use a perma-
nent amberoid range Scale graduated in yards according to
the scale of the board, pivoted at the gun position for reading
the range. The gun arm swings over the diagonal scale and
angles between the different positions of the range scale can
be read direct. The construction of the diagonal scale is the
same as in our Coast Artillery practice. -

THE FIRING BOARD 249
5. PARALLAx PROTRACTORS
Parallax protractors, sometimes called objective protractors,
are designed to measure small angles only (100 to 200 mils).
The radii extend the entire length of the protractor. The pro-
tractors are frequently used in graphical work, especially for
the following purposes:
1. On Firing Boards, scale 1/20,000, for the measurement
of the parallax of the target subtended for the battery front,
of the angular front of the target as seen from the battery,
and of the elements necessary for a shift of fire.
-2. In organizing a system of ground observation for the
construction of maps and sketches on a 1:5,000 scale and for
the plotting of points of impact.
3. In the organization of the fire from an epi or emplace-
ment battery, for determining the parallax of an aiming point
plotted on a large scale map (1:2,000). -
The following description of protractors is given on the
assumption that they are graduated in mils although decigrades
may be used equally well.
(a) Transparent Celluloid Protractor. (Fig. IX.)—This
protractor is used for measuring on a firing board or a battle
map, scale 1:20,000, either the front of the targets as seen
from the battery and the elements necessary for a shift of fire,
by placing the center at the battery, or the parallax of the
target subtended by the battery front, by placing the center
at the target.
Fig. IX.-TRANSPARENT CELLULOID PROTRACTOR
The radii are drawn at 5-mil intervals. The two outside
radii are graduated in range on a 1:20,000 scale. The pro-
tractor ordinarily in use allows the measurement of ranges up
to 17 kilometers (or 8.5 kilometers if used on a scale of 1:10,000).
(b) Non-transparent Protractor. (Fig. X.)—This protrac-
tor is used for drawing on a large scale map radii from a point

250 Ol?IENTATION FOR HEAVY (COAST) ARTILLERY
outside the map. Having drawn a radius from its Y-azimuth,
for example, and knowing the distance of a point P on the
radius from the center, the map is placed upon the protractor
with the radius already drawn coinciding with the axis of the
protractor. It is then moved along this axis until the point P
falls upon the proper graduation of the axis of the protractor.
Greater accuracy is obtained by putting a ruler on top of the
map along the axis. Then, holding the map in this position,
there remains only to draw the radii 10 mils on either side of
the radius already drawn, by joining the points laying on the
same radius of the protractor.

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Fig. X. —NON-TRANSPARENT PROTRACTOR
This method may be used to good advantage in making
objective sketches on a 1:5,000 scale. The protractor should
be 5 meters long if it is to be used for drawing a sheaf of Y-azi-
muths on a 1:2,000 map from an aiming point 10 kilome-
ters distant.
(c) Transparent Protractor of Tracing Paper.—This pro-
tractor, which differs from the preceding one only in the mate-
rial of which it is made, is used for measuring angular deviations
upon a large scale map which does not include the center.
The same method as indicated above is used, except that the
protractor is placed on the map instead of under it.
If it is to be used for measuring the parallax of a distant
(10,000 meters) aiming point on a large scale map (1:2,000),
it must be 5 meters long.
CHAPTER XIV
PANORAMIC SEQETCHES
ESSENTIAL FEATURES
ANNOTATIONS AND CONVENTIONAL SIGNS
CONSTRUCTION
PRINCIPLES OF PERSPECTIVE
:
1. ESSENTIAL FEATURES
Purpose.—The panoramic sketch supplements very satis-
factorily the battle map. It is of particularly great service
in training artillery observers, either non-commissioned or
commissioned officers or other intelligent men who keep
watch on the battle field. When a flash appears on the
terrain, the observer refers it by eye to neighboring objects
and when it re-occurs he obtains its exact location on the
horizon. The gun which has thus revealed itself will be
located accurately, by the assistance of other observation
stations. This method of making a note on the sketch, with
date and time, is the best and simplest method of recording
the results of daily observations. It also enables observers
to keep track of new works prepared by the enemy, etc. The
sketch should be kept constantly up to date.
It has another advantage; in case of relief, the new artillery
officer will by this means inherit all the experience of his
predecessor, and can undertake his work without any period
of transition or of feeling about.
It is also advantageous for the battery commander to
have at his station the panoramic sketches made at his many
observation stations. He should endeavor to identify on
the ground any objects shown on these sketches that are
likely to be used as reference points by auxiliary observers
in fire for adjustment or in designating targets.
Under the present conditions of warfare the observer
should neglect none of the means available in order to under-
stand the ground before him, that he may be able to direct
fire accurately on a definite point visible from the principal
observation station.
Types.—Panoramic sketches assume various forms, rang-
252 ORIENTATION FOR HEAVY (COAST) ARTILLERY
ing from very complete and detailed panoramas, executed
at leisure down to rudimentary perspective sketches made
by the orientation officer during a rapid reconnaissance prior
to making the selection for a battery position.
In open warfare the only artillery sketch to be used is the
rough panoramic sketch which may be supplemented if neces-
sary, by small plan sketches. On the other hand, in warfare
of position it is possible and necessary to make a very accurate
and detailed sketch on a large scale and in some cases the
sketches are colored to bring out special features.
A panoramic sketch will not attain its purpose unless it
fulfills the following conditions:–
It must be simple and leaving aside all esthetic considera-
tions, indicate only that which is essential. -
It must be accurate and should therefore be prepared on
a definite scale. It must be controlled by measurements of
horizontal and vertical angles. Graduations of horizontal
and vertical angles should be ruled upon it. Regard for
accuracy requires the use of thin, well defined lines, continuous
lines and of clear uniform tints, with none of the hazy outlines
and half tints that constitute the charm of artistic landscape
drawings.
It must be plain, plainer than the reality itself, and must
bring out at the first glance the details that are of interest
to the artillerist, which have been obtained only after a patient
examination of the sector.
It is very evident that these conditions are not all com-
bined in photographs. Nevertheless, photography may be
used with advantage to facilitate the preparation of a pano-
ramic sketch, as it furnishes at once a detailed framework
supplementing that obtained by measurements of horizontal
and vertical angles. The use of a photograph to supplement
the control in the preparation of a panorama should always
be preceded by a thorough and minute study of the sector
made at the observation station with the help of the map and
of optical instruments. It is only in this way that a judicious
selection of details can be made from the photograph, so as
to bring out those that will be needed and to eliminate those
that would be useless, or even troublesome.
Having made a round of the horizon and thus identified
features that are clearly seen, endeavor to discover others
by their direction and location on the map. Determine
exactly the directions of those that are not visible by means
I?ANORAMIC SEKETCHES 253
of the directions of those that are. Thus, for example, the
map shows that between villages A and B there is a highway
winding around the wood. Endeavor to discover by the
use of optical instruments where this road enters the villages
A and B. Try to find it between the two villages. Perhaps
certain parts at least can thus be discovered. Perhaps more
of it is visible, and the edge of the wood which it skirts may
be recognized. Again between one ridge and another the
map shows a valley. Endeavor to distinguish the two ridges
one from the other, etc. Other examples are shown in Fig. IX.
2. ANNOTATIONS AND CONVENTIONAL SIGNS
Annotations are the remarks which assist to identify and
locate the feature, and are placed on the sketch, but should
be so placed as not to obscure the drawing. They consist
of the horizontal angle in mils., the vertical angle, and the
distance measured on the map or measured with a telemeter,
of the principal points in the region of the targets. (See
Fig. IX). They should therefore be kept separate and placed
in the upper or lower part of the drawing. They should be
written horizontally on a line higher or lower, according as
the feature indicated is farther or nearer in the order of the
several distances represented. If necessary use reference
letters; also a few reference lines, lightly and clearly drawn,
each ending in an arrow touching the feature. Between
the annotations showing visible features, indicate the prin-
cipal features screened from sight, as shown by the map.
(villages, brooks, railroads, etc.). Do not forget to state
precisely the point of view, which should be indicated below
and to the left of the sketch.
It is desirable to apply distinctive names at once to those
objects on the ground which may serve as reference points.
t should be borne in mind that these names will be used later
to designate these features and it may happen that the man
who uses the name later, i-one, for example, with the infantry
—may not occupy the same point of view.
Conventional signs should be used to represent these
features so that they can easily be identified and will appear
the same on all sketches.
Fig. I shows trees near and far; when a tree is near its
outline is well defined, and the hatching is close and heavy.
When further away its outline becomes more even and the
254 ORIENTATION FOR HEAVY (COAST) ARTILLERY
CLITTLITTTTTſūſī.
FIG.. II
A Q & ſº
FIG. I.
Fºr Wood. FIG. III Wood wVeaſ:
Figs. I to VII.-CONVENTIONAL SIGNS
hatching is far apart and light. As the tree is further away
it becomes Smaller and has less hatching until when very dis-
tant it has no hatching.
L Fig. II is a near hedge, if further away its size and density
of shading decrease.
Fig. III represents the edge of woods, it must be remem-



PANORAMIC SKETCHES 255
bered that in winter there is no foliage and the edge becomes
indistinct, hence the trunk only of the extreme left and right
hand tree should be used as the reference marks in locating
the wood on the sketch.
Fig. IV represents a village; it is unnecessary to show more
than one house in fair outline, all other houses may be shown
by their roofs only. The village need not be portrayed in
its exact likeness.
Fig. V shows a church steeple and roofs topping and behind
the horizon. Features such as these assist to locate features
not visible but obtained from the map. -
Fig. VI shows successive ridges, and a road bordered by
trees. Ridge lines never cross each other, the further ridge
line stops at the nearer ridge line. They should be hatched
with few lines drawn in direction of slope.
Fig. VII represents bridges, one crossing a river, one cross-
ing a brook and the other crossing a valley. Roads are repre-
sented by lines converging at the distance. Most objects are
shown as they exist only in miniature; excessive detail of
objects only serves to destroy and not improve their iden-
tification.
3. CONSTRUCTION
The equipment necessary to produce a good panoramic
skétch is as follows:
Pencils, with hard and soft leads.
Paper, thumb tacks and a drawing board.
A pencil eraser, and sharp pen knife.
Field glasses.
A transit, theodilite or battery commander's telescope.
The Scale of the drawing will vary as the size of the paper
and of the amount of terrain to be sketched. No definite
scale can be set down on account of the variation above
mentioned, but some of the determining factors in the selec-
tion of a scale will be discussed.
There are two scales to be considered, one a horizontal
scale representing horizontal angles the other a vertical scale
representing site. The two scales make a grid on the paper
to assist in making the sketch.
The horizontal scale is as a rule 10 centimeters for 100
mils. or even more (the horizontal scale should always be
converted into mils. and so plotted) vertical lines from the
256 ORIENTATION FOR HEAVY (COAST) ARTILLERY
top to the bottom should be drawn and as many as may
be necessary according to the scale used. (See Fig. VIII.)
The center of the scale should indicate 1600 mils., the lesser
on the left, the greater on the right, this is done to avoid
using plus and minus or right and left. The horizontal
scale in Fig. VIII is 10 cm. equals 50 mils. The paper is
ruled with horizontal lines spaced according to the vertical
scale adopted. In Fig. VIII the vertical scale is 4 cm. = 1°.
The zero of the scale should be at the horizon. The vertical

1500 1525 1550 1575 1600 1625 1650
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Fig. VIII.-GRID ON PANORAMIC SKETCH
scale must be selected to suit the terrain to be sketched.
Flat country will require a large scale to bring out the features
while mountainous terrain will require only a small scale.
Experience will soon teach the officer the most desirable ver-
tical scale to use under different conditions.
PANORAMIC SKETCHES 257
The grid being drawn on the paper the main features
are now considered. Main features of military importance.
are as follows:— -
Land marks: (churches, stacks, steeples, etc.).
Ground forms, hills, ridges, spurs, valleys, ravines.
Obstacles, rivers, stream lines, marshes.
Roads, hedges, railroads.
Positions held by the enemy or liable to conceal him:
woods, hedges, fences, walls, embankments, cuts, hills, ravines,
etc. - -
Villages, towns, groups of buildings.
Features of the foreground in the immediate vicinity of
the sketches usually should not be included in the sketch.
Having decided on the main features a strong feature
near the center of the terrain is decided upon as the near
reference point, it should be such that it is visible at all times
irrespective of the climatic conditions except of course in very
heavy fogs. The instrument is set so as to read 1600 mils., .
200 grades, or 180 degrees depending on the graduations and
the upper plate clamped, the main reference point is then
sighted on and the lower plate clamped. The upper plate
clamp is then loosened and the instrument is ready to read
horizontal angles.
The round of the horizon is now made reading the hori-
Zontal and vertical angle to a prominent point on each of the
main features. These points should be plotted at once
(see Fig. VIII, A, B, D, E, etc.) and the main features drawn
in. The angular coordinates of the point E are: horizontal
angle = 1615 mils. and vertical angle = 0°. For the point
K h.a. = 1560 mils. and v.a. = 1° 30'. It is well to note that, as
the vertical scale is considerably larger than the horizontal, if
readings were taken at the top and base of houses, trees, etc.,
and so plotted the features would be distorted, a square house
or large heavy tree would appear very narrow and high, there-
fore after locating objects by their base they should be drawn
in proportion so that they can be identified. (See Fig. IX.)
Filling in may now be accomplished. Having the main
features which we wish to have accurately located as a frame
work, the other features are located in their proper position
using the frame work as a guide, these others should be
sketched in free hand with bold, free strokes. These features
can be filled in after all main features have been read and
plotted. Begin in the distance and fill in towards the fore-
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PANORAMIC SKETCHES 259
ground. Use faint, thin lines for features in the distance.
Use heavy lines for features in the foreground. These give
the appearance of depth to the drawing.
Do not draw a line aimlessly so that it will have to be
erased, but notice the actual position of the feature with
reference to those which were selected as control features.
The sketch should now be finished up, the necessary data
put on the lower left hand corner and the directions north
and south inserted. Annotations should be completed if
not put in detail at first, the crests drawn in and all connec-
ting lines on the sketch between features inserted and the
hatching completed. The sketch should now be a very com-
plete and accurate duplica of the terrain. Fig. IX shows a
completed panoramic sketch.
4. PRINCIPLES OF PERSPECTIVE
Features nearby appear larger than those in the distance.
The horizon, as the term is used in perspective, is on a level
with the eye.
Each set of horizontal parallel lines has its own vanishing
point on the horizon at which these lines converge on the
drawing. Thus parallel horizontal lines directly to the
front converge at the center of the horizon as it appears on
the drawing. Those parallel to the top of the paper, appear
parallel to the horizon on the drawing. Sets of parallel
horizontal lines between these two directions converge at
the proper point on the horizon to indicate their direction.
Parallel lines sloping downward converge at a point below
the horizon.
If these principles are not understood or are not applied
the drawing will not convey the right impression of the ter-
rain pictured.
CHAPTER XV
ORIENTATION FOR RAILWAY ARTILLERY
PRINCIPLES OF RAILROAD CURVES
TYPES OF EPIs
SURVEYS OF EPIs
GRADUATION OF A CURVED EPI
RESURVEY OF OLD TRACKS
:
General.—This chapter considers only the more simple and
fundamental principles of railway location, explaining only
those essential details of the survey of tangents and simple
curves, and the resurvey of curves already constructed, which
are necessary for the computation of position, altitude and
direction at any point along a track. No attempt is made to
take up the subject of economic location or construction of
railways, types of construction or rolling stock, or maintenance.
The methods of procedure here outlined are by no means the
only ones, but are both simple and sufficiently precise for the
class of work which may have to be done by the artillery under
actual field conditions.
Any railway survey work which the artillery may have to
do in the field will probably consist of nothing more com-
plicated than location surveys of short pieces of connecting
track and of firing tracks (epis) on locations already approxi-
mately determined; or of resurveys of track already con-
structed but either in poor condition or of which the records
are not available. It is highly improbable that these lines will
consist of anything but pieces of straight track connected by
simple curves, in which case the survey and computation will
require only a knowledge of simple curves in addition to the
ability to handle a transit traverse. -
For further details it is suggested that reference be made
to the following standard works: . -
1. “Military Railways,” Professional Papers No. 32, Corps
of Engineers, U. S. Army.
2. “Railroad Construction,” by Walter Loring Webb. (John
Wiley & Sons.)
ORIENTATION FOR RAILWAY ARTILLERY 261
3. “Railroad Curves and Earthwork,” by C. Frank Allem.
(Spon and Chamberlain.)
4. “American Civil Engineer's Pocket Book.” (John Wiley
& Sons.)
1. PRINCIPLES OF RAILROAD CURVES
(a) Methods of Survey.—When a new railroad location is
to be made the general route is first determined, usually by a
rough reconnaissance of the ground or a study of reliable
contour maps, if they are available. General topographic
features usually control the practical routes.
The second step is usually running a deflection angle transit
traverse survey along or close to the accepted general route
for the purpose of preparing maps and profiles to be used in
making a more detailed study of the lay of the ground. Several
such traverses may be run in order to select the most desirable
of several possible routes.
The third and final survey is called the location survey, and
consists of a transit line run on the center line of the track and
perpetuated by substantial stakes placed 100 feet apart on
straight track, and 100, 50 or 25 feet apart on curves, together
with such other stakes and marks as are necessary for the actual
work of construction. Continuous measurement is made from
the beginning of the road, and careful and permanent record is
made of all angles and distance so that the location of any
point on the line may be either plotted or calculated from any
other point. In other words the actual survey line, midway
between the rails, constitutes a continuous traverse in which
the angles are replaced by curves which connect adjacent
tangents. Having this traverse, the computation of position,
altitude and direction at any point on the track is entirely
similar to the computation of a transit traverse, except for the
computation around the curves. The curves themselves, as
far as the survey and computations are concerned, are actually
polygons formed by 100 feet chords of the theoretical curve of
the center line, and hence, each curve actually is a traverse of
a number of equal sides and equal angles, so that at the last
analysis a railroad survey is only a transit traverse and is
computed as such.
(b) Types of Curves.—There are four general types of
curves in railroad work. Only the first one explained will
probably ever be used by the artillery, although an acquaint-
ance with the others is desirable.
262 ORIENTATION FOR HEAVY (COAST) ARTILLERY
1. A simple curve is one of constant radius, connecting
two pieces of straight track, which are invariably called
tangents in railroad work.
2. A compound curve is a curve which connects two
tangents, as in the case of a simple curve. The curve itself
differs in that a portion at each end is usually a simple curve of
one radius while the central portion is a simple curve of a
shorter radius.
3. An easement curve is one in which the connection
between a simple curve and a tangent is made by using a
section of special curve of constantly changing radius in order
to ease the shock due to the change for high speed trains.
4. A reverse curve is actually not a type of curve, but
rather the use of two curves of any of the three preceding
types, turning in opposite directions so as to form an “S”
shape. The two curves should be separated by a short piece
of tangent, for practical reasons.
/
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s! NAPLE CURVE CONMPOUND CURVE
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EASEMENT CURVE SIMPLE REVERSE CURVE
Fig. I.-TYPES OF RAILROAD CURVES
(c) Simple curves being curves of constant radius are
simply arcs of circles. Fig. II shows the names of the Several
parts, being the standard notation on railroad work.


ORIENTATION FOR IRAILWAY ARTILLERY 263
Definitions: -- -
Tangents are the sections of straight track which, if produced,
would intersect at the P.I. (Point of Intersection). The line
here spoken of and considered is the survey line, being midway
between the rails. All points described as being on the track
lie on this line. tº
Radius, R, is the distance from the survey line to the
Center, C, of the circle of which the curve is a part.
\.
Center
Fig. II.-STANDARD NOTATION FOR SIMPLE CURVES
Point of Curvature, P.C., and Point of Tangency, P.T., are
the points where the curve joins the tangents.
Tangent Distance is the distance from P.C., or P.T., to the
P.I. &
Long Chord is the straight line distance from P.C. to P.T.
Chord, or Unit Chord, is a 100-foot chord of the curve, in
the English system of measurement. -
Sub-chord is a chord shorter than unit chord, used at be-
ginning or end of a curve when there is not an even number
of unit chords included in the entire curve.
Length of Curve, L., is the sum of the chords, not the theo-
retical measurement on the arc of the circle.
Total Angle, or Central Angle, or Deflection Angle is called

264 ORIENTATION FOR HEAVY (COAST) ARTILLERY
A (delta) and is the deflection angle between the tangents
at the P.I.
Degree of Curve, D*, is the angle at the center subtended by
wnit chord. -
Fundamental Relations between the parts are such that any
two being known the others may be computed. From the
nature of the problem in the field, the tangents are usually
located on the ground, and A is determined by measuring the
angle between them. One other quantity must be known or
assumed. Topographical conditions may determine the Tan-
gent Distance, or the External Distance. In the absence of
such limitations the degree of curvature may be limited by
the allowable sharpness of curve. American practice is to
assume a desirable degree of curvature, D*, as the other known
quantity, and compute the others. European practice is to
assume a radius and, knowing A, compute the others. In
any case the following relations of simple trigonometry. always
apply:
half the Unit Chord
Radius=" e Unit Chor
sin Dº/2
Tan. Dist. = RadiusXtan A/2.
Long Chord=2XRadiusXsin A/2.
2
3
e J 1 l
4. External Dist. = Rad. 1 ſ . = R.exsec A/2.
5
- l cos A/2"
Middle Ordinate = Rad. (1–cos A/2) = R. vers A/2.
Many tables have been prepared by means of which the
other quantities may be read directly when any two are known.
While these tables are indispensable to a railroad engineer on
precise location work, for the needs of the artillery it is con-
sidered certain that the use of these tables by others than
experienced engineers, is more than likely to lead to confusion,
error, and false security. If the fundamental relations are
thoroughly understood the following methods will be suffi-
ciently precise for any problems likely to be encountered,
no tables being needed.
The radius of a 1° curve (D’= 1°) is actually 5729.65 feet;
approximately 5730.0 feet, which should be remembered.
Then the radius of a 2° curve would be approximately *.
2865 feet; of a 10° curve would be 573.0 feet, and so on, from
which all the other quantities may be computed directly,
knowing A. Or, if A and any other quantity are known, D?
ORIENTATION FOR RAILWAY ARTILLERY 265
may be computed by the formulas given, and the radius
º º * 5730. te
obtained from this relation, R = Dº The actual radius of a
10° curve is 573.69 feet, which gives some measure of the
approximation, sufficiently precise for any problem except
actual location on permanent railroad lines.
A closer approximation may be made by the use of a table
of functions for a 1° curve, for various values of A, computed
on the basis of its actual radius, 5729.65 feet. Values for other
degrees of curvature are then obtained by proportion as
explained in the preceding paragraph. The additional pre-
cision is usually of little consequence, and the “Engineer Field
Manual of U. S. Army” gives functions of a 1° curve of radius
5730.0 feet, evidently considering this sufficiently precise for
any field work liable to be encountered.
Ordinary track will seldom be of sharper curvature than 6°,
but firing tracks, epis, usually are constructed somewhat
sharper and of some even radius, as 150 or 200 meters, corre-
sponding to a curvature of 12° to 10° in the English system.
Metric Curves.—When the metric system of measurement
is used, as will probably be the case in foreign service, the unit
chord on railroad surveys will be 20 m., angular measure still
being degrees and minutes. The degree of curve will then be
the angle at the center subtended by unit chord of 20 m. The
result is that a curve of the same degree of curvature as in the
English system will, on the ground, be an absolutely similar
figure, but of about two-thirds the size. That is, a 6° metric
curve will be exactly like a 6° curve in the foot system reduced,
to Scale, to about two-thirds its actual size. Each 20 m.
unit chord on the metric curve subtends 6° at the center;
each 100-foot chord on the foot measure 6° curve does like-
wise. There will be the same number of chords in each case
and all other lines will be similar, and all dimensions in meters
will be 1/5 of the similar foot-measure distances, since the
similarity of chords holds for all other linear dimensions.
The angular values, however, since the figures are similar,
will be identical for the two curves.
(d) Vertical Curves.—At points where the grade of a rail-
road changes, the change should be “eased off” by a curve
in the vertical plane. This is a problem for main line railroad
construction and maintenance rather than for more or less
temporary and hurriedly constructed firing tracks. A standard
266 ORIENTATION FOR HEAVY (COAST) ARTILLERY
method is here indicated, although its use may never be
required. - *
Assume a summit at which grades of 2 per cent. and 0.5
per cent. intersect, as shown in Fig. III. The change of grade
is 2.5 per cent. Multiplying by 100 m. (200 m. for sags) gives
| liº-º-º-ºp
|
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| co-be |
Fig. III.-LAYOUT OF VERTICAL CURVE
the approximate length of curve, 250 m. in this case. Always
use some even hundred meters, say 300 m. Then A and B,
300 meters apart, indicate ends of curve, the intermediate
distance being divided into 50 m. spaces. Draw chord AB
and make CD equal half the distance CE. Make the inter-
mediate offsets from the tangents proportional to the square
of the distance from the points A or B, as indicated on the
figure. --
(e) Turnouts.--When one track branches off from another
the special construction involving switch and frog by which
this is accomplished is called a “switch,” or more properly
a “turnout.” If a simple curve branches from a straight
track this turnout will not start exactly at the P.C. of the
simple curve and follow it but will introduce a compounding
of the curve. Owing to the fact that there is no standard
method of constructing turnouts—variation due to gage of
track, class of construction, materials available, etc., affect-
ing any particular turnout—the layout of the work and its
construction requires either an engineer or a construction
foreman of considerable experience, and precludes the possi-
bility of profitably discussing the subject in this chapter.
As far as the artillery is concerned, running in simple circular
curves will give all the data required for the firing data calcu-
lations, and if the artillery should be called upon to construct
a turnout, the theoretical point of intersection of the tracks
may be shifted to fit materials and conditions at hand, without
affecting the firing data as far as the epis are concerned.



ORIENTATION FOR RAILWAY ARTILLERY 267
2. TYPES OF EPIs
The preceding discussion of railroad curves is general and
applies to any material; but the types of epis illustrated by
Fig. IV refers particularly to the French 32 cm. Railroad
Materiel. The French 32 cm. Railroad gun is slightly larger
in caliber than our 12" Seacoast guns and is of about the same
length and weight. It fires as a howitzer using angles of
elevations from 32° to 40°. With a maximum powder charge
of 115 pounds, the gun throws an 850 pound projectile some
22,000 yards. The total weight of the gun and carriage is
162 tons. The car rests on two ten-wheeled trucks, each
arranged to rotate completely. The total length of gun
carriage, including car buffers is, 25.9 meters, or about 85 feet.
The truck travels and fires on the standard gage track (4'8%"),
the firing track being a curve of either 150 or 200 meter radius.
The gun normally is laid in a direction tangent to the epi.
Pointing in direction is accomplished by moving the car around
the track. After each shot the piece is brought back to firing
position by two windlasses placed on the forward truck. The
French allow five minutes for placing in battery, after which a
shot can be fired every three minutes. A firing track and
platform are provided for each piece. -
In the French Railway Artillery the battalion is the tactical
unit, and consists of two batteries of two guns each. There-
fore, firing tracks are arranged in groups of four. These could
be arranged in numerous ways, but on the Western Front three
standard layouts have been developed. These are: 1. Single
spurs. 2. Pairs. 3. Tong shaped (En Tennaille).
Single Spurs.-The first method is to run four similar,
independent firing tracks from one lead or approach track.
When possible all four epis are made identical; i.e., the radii,
central angles, distances between tracks and arcs of fire are the
same for all tracks, because those features simplify the calcu-
lation of firing data. However, such standardization is not
essential and if the terrain is rough, each track is located
independently. This feature—the possibility of locating the
tracks independently of each other—is the main advantage of
the single spur layout, because it can be used in many locations
where the other layouts can not.
In Pairs.-There being two guns in a battery, it is advan-
tageous to locate the four tracks in two concentric pairs, one
268 ORIENTATION FOR HEAVY (COAST) ARTILLERY
line of centers
C
opproach track
EN TENNAILLE
Fig. IV.-TYPES OF EPIs

ORIENTATION FOR. RAILWAY ARTILLERY 269
pair for each battery, because this simplifies administration and
the calculation of firing data.
If both pairs turn in the same direction the tracks are said
to be arranged “in pairs”; if they turn in opposite directions,
the arrangement is called “En Tennaille.” The usual radii
for each pair of tracks are 150 meters for the inner and 200
meters for the outer, each pair being concentric and therefore
parallel. Fifty meters between the tracks seems unduly
large, but it is necessary to protect each gun from the other's
blast and to minimize the chance of injury to both guns by
one German shell. Tracks arranged “in pairs” take about
the same ground area as in the “single spur” layout and, like
the latter, are arranged in several ways, depending on the
topography and approach tracks, although it is not quite as
flexible.
En Tennaille.—The third standard plan, “En Tennaille,”
gives a tong-shaped layout. In the first two methods the
tracks turned in the same direction, being called right or left
handed, depending on whether they turn to the right or left as
you face the field of fire. In this layout they turn in opposite
directions, each pair being concave towards the other. If the
pairs have a common center, then, being diametrically opposite
arcs of two concentric circles, this arrangement takes a rela-
tively large area—approximately 400 by 600 meters—but
administration and the calculation of firing data is simpler than
in any other plan. Therefore, when the necessary space is
available, this layout is usually installed. The area required
is materially reduced, with a slight loss of convenience in com-
puting firing data, by overlapping centers.
The best types of layout is selected for each site; it is
properly designed and built by the regular Railway Battalions.
During the progress of construction work the center, or centers,
of the firing tracks are accurately located on the ground, and
marked by a permanent monument—a large stake, a rail or a
Stone.
It is highly probable that other material and condition will
require layouts differing from any of those here illustrated,
and it may be the problem of the artillery to adapt the form of
their epis to the material with which they are equipped, and to
their particular organization. A knowledge of simple curves
and methods of laying them out and of the accompanying
computations should go far toward simplifying this work.
270 ORIENTATION FOR HEAVY (COAST) ARTILLERY
3. SURVEYS OF EPIs
When a new firing track is to be constructed and made
ready for use the work naturally divides into three steps:
(a) The center line of the track is located, surveyed and
staked out upon the ground, and tied in to the system of
coordinates.
(b) The coordinates and altitude of the center of the epi,
and the Y-azimuth of at least one natural reference line from
the center, must be computed from the field notes.
(c) Computations, charts and reference stakes or marks
must be computed and arranged so that the range, angle of
site, and direction from any point on the epi to possible targets
in the field of fire may be quickly and easily obtained, and
be instantly available for aiming and laying the material.
Survey of Epi.—The operations actually performed can
probably be more clearly explained by means of a typical
problem: -
Let Fig. V represent a portion of a map on which A and B
show the location of triangulation stations, line R–R indicates
roilroad” P
~ —V-93° £Z'--
* *
* -
Fig. V.--SURVEY OF SINGLE EPI

ORIENTATION FOR. RAILWAY ARTILLERY 271
a railroad already constructed and available for artillery use,
and the dotted rectangle outlines the approximate position of
a suitable piece of ground upon which orders have been given
to construct an epi having an effective field of fire between
Y-azimuths 350° and 25°.
Survey and Location of Tracks.-Upon examining the
area between the present railroad and the location selected for
the epi a line is found which would be suitable for an approach
track. It is located on the ground by temporary stakes and
with a transit the line is produced to its intersection with the
present railroad at P.I. The intersection angle at P.I. is
measured and found to be, say, 30°. Conditions on the
ground might be such that it was desirable to keep the curve as
close to P.I. as possible, because of a hill or swamp to the north
of this point, and a 6° curve is selected, being as sharp a curve
as allowable for an approach track. The rad. of a 6° curve
5730
is ax;=191 m. The tan. dist. = R. tan A/2= 191 tan 15°=
51.18 m.
Measuring back from P.I. a distance of 51.18 m. gives the
P.C. of the curve, and measuring ahead 51.18 m. on the line of
the approach track locates the P.T. Permanent stakes should
be placed at all these controlling points.
By going to A, setting up the transit, backsighting at B, and
turning the angle to P.C. the Y-azimuth of the line A–P.C. is
found to be 5° 0'. The length is measured also, giving the
first course of the traverse which will eventually connect the
center of the epi with the triangulation system. At P.C. the
deflection angle from the backsight at A to P.I. is measured,
giving the Y-azimuth of the railroad already constructed. The
Y-azimuth of the approach track is then computed from the
angles turned, and indicated on Fig. V, being 60° 0'.
The limiting Y-azimuths of the field of fire have been given
as 350° to 25°. An allowance of 10° each way may well be
made to allow for adjustment of fire, making limits to be used
340° and 35°. Any epi curving to the left will evidently
Satisfy the latter figure, actually giving a limiting Y-azimuth
of 60° instead of 35°, and the curve must be continued until its
tangent has a Y-azimuth of 340°. This requires an intersection
angle, A, for the epi of 60° to 340° or 80°. A radius of 150 m.
will probably be selected. This value, with A=80°, determines
all the other dimensions of the epi. Tan, dist. = R tan A/2=
150 tan 40°=125.87 m.
272 ORIENTATION FOR HEAVY (COAST) ARTILLERY
The problem of locating the epi then consists of producing
the line of the approach track to a point on the general location
of the epi, where, on turning an angle of 80° 0' to the left, and
continuing 125.87 m. on the new line to the P.I., the latter
point will fall inside the further limit of the area selected.
This will probably be a cut-and-try process on the ground.
When the P.C., P.I. and P.T. are satisfactorily located and
staked out, the length of approach track between P.T. and P.C.
is measured, and, if possible, the center, C, of the epi is located
from P.C. and permanently marked, and the angle measured
at C from P.C. to at least one permanent landmark, preferably
to several of them. This completes the location work except
the actual staking out of the curves. -
Laying out a Curve. Deflection Angle Method.—We know
from Geometry that the acute angle between a tangent and a
chord is equal to one-half the central angle subtended by that
chord. Also, the acute angle between two adjacent chords
is equal to one-half the total arc subtended by those chords.
Then if it is desired to lay out a D’ curve from a known point,
P.C. (Fig. VI), one would proceed as follows:
pº
P]. stake A
Fig. VI.-DEFLECTION ANGLE LAYOUT

ORIENTATION FOR. RAILWAY ARTILLERY 273
A transit is set up at the point P.C., and an angle = D*/2
turned to the right from the tangent produced to P.I., establish-
ing the direction of the chord to the first stake. A distance of
20 m. (unit chord) is then measured, by tape or chain, along
this line from P.C., thus establishing the first stake. With the
transit still at P.C., an additional angle = Dº/2 is turned off
from P.I., establishing the direction to the second stake.
The 20 m. chain is then stretched from the first stake and the
further end put in the line of sight of the transit, which locates
the second stake. Thus the points 20 m. apart are located,
The final deflection angle to the P.T. is A/2. If it is desired
to locate points 10 m. apart the deflection angles increase by
D°/4. This assumes that the curve is measured on the arc
and the method is practically correct for a curvature of less
than 12°. This is called the method of “deflection angles.”
This deflection angle method is general; the curve may be
located from either the P.C. or P.T., or, after an intermediate
stake is set, the transit may be moved up to this stake and the
location work continued from this point by turning off angles
of D*/2 from the tangent to the curve.
To apply this method to the particular epi of our example,
first compute the degree of curvature, D*, from the formula:
D° 3780, f tri >
T 5XR OI’ Iſlet,TIC curves,
5730 5730 a. O © O /
= 5:150–755–7°.64=7° 38'4.
A table of Stations and Deflections is then prepared for
convenience, as follows:
Station Total deflection from
(or stake) tangent
P.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0° 0'
P.C.-H. 1. . . . . . ". . . . . . . . . . . . . . . . . . . . . . . . . . . 3° 49'.2
2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7° 38'.4
3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11° 27'.6
4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15° 16'.8
5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19° 06'.0
6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22° 55'.2
10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38° 12'.0
10+9.42 m. (+1°48'). . . . . . . . . . . . . . . 40° 00'.0
Setting the transit over P.C. stake, sighting with vernier A
set at 0° on the limb, along the line to P.I. and clamping the
transit in this position, prepares the transit for turning off the
274 ORIENTATION FOR HEAVY (COAST) ARTILLERY
deflection angles to successive stakes set at the unit chord,
20 m., intervals along the curve. There will seldom be an
even chord length at the end. The total angle, A, divided by
the D* gives the number of full chords and the fraction of a
chord to close on the P.T. This fractional part of the full
chord deflection, being 1° 48' in this case, and the same frac-
tional part of the unit chord, being 9.42 m., should close on P.T.
Coordinates, Altitude and Y-azimuth of Reference Line at
the center of the epi. The field work now completed locatets
the limits of the epi upon the ground, and its center, and con-
nects the center to triangulation stations by means of a transit
traverse. This allows the coordinates and altitude of the
center and Y-azimuth of the reference line from the epi center,
to be computed. The traverse should be closed from the center
to some triangulation point, to check the work before accepting
the results of the computations. Also, meridian determina-
tions at the epi center are necessary, to check the computed
Y-azimuth of the reference line.
These computations of the coordinates of the center of the
epi can be made even if the point on the ground is inaccessible.
In this case, however, it would be better to compute the data
for the P.C. or P.T. All the orientation can actually be made
from the latter points, and if the center is inconveniently
located on the ground it need not be occupied.
Range, Angle of Sight, Y-azimuth to a target of known
location, from any point on the epi, may be computed from
the data given above.
Range.—The coordinates of the center of the epi have been
computed. From these values, the coordinates of any point
on the curve are easily deduced from the length and Y-azimuth
of the radius to that point. Having coordinates of points on
the curve and coordinates of the target, the map range is
computed.
Angle of Site is a function of range and difference of altitude
of gun and target. The altitude of the center having been
computed from the field work, the altitude of any point on the
curve is deduced from the length and slope of the radius to that
point. The altitude of target is either taken from the map or
determined by trigonometric leveling if it is visible. The
difference of altitude of gun and target is thus determined,
which, with the map range, gives the angle of site.
Y-azimuth of Gun-Target Line.—The Y-azimuth of one or
more reference lines from the center of the epi to permanent
ORIENTATION FOR RAILWAY ARTILLERY 275
landmarks has been determined by the transit traverse, or
meridian determinations, or both, preferably. Having this
data an aiming line of any desired Y-azimuth may be laid down
with the transit and staked upon the ground; or the Y-azimuth
from any point on the curve to the reference point may be
measured or computed; or the position of points on the curve
may be marked, the tangents of which will have certain
Y-azimuths.
4. GRADUATION OF A CURVED EPI
Purpose.—For sliding material, firing from a curved epi,
the epi must be graduated in Y-azimuths of the tangents.
This graduation is intended only to determine the approxi-
mate position of the gun for each target and is made in even
one or two grade intervals. The operation described below
may be performed either before or after the exact topographic
preparation of the initial firing data and consists in deter-
mining the coordinates of a reference point, R, and the direc-
tion of various reference lines from that point. The point
R should be located at some distance from the rails, prefer-
ably near the center of the epi or, if this be impracticable, at
150 to 250 meters outside the epi. The point being marked
on the terrain by a stake, the epi is graduated in Y-azimuths
of the tangents in the following manner:-
Use of the Theodolite.—The theodolite is set up at the point,
R, and oriented by the reference lines, if these have been deter-
mined, or by the compass. From R. (Fig. VII) sights are
taken on stakes 1, 2, 3, placed at intervals of 20 or 30 meters
along the track. This gives the Y-azimuths of the lines R1,
R2, R3, etc.
The theodolite is next set up exactly on the line R1, one or
two meters outside the outer rail, and is oriented by back
sighting on R. Several sights reading Y-azimuths of even
grades are taken on the outer rail (Fig. VIII), thereby deter-
mining the chords ab, a'b', etc.
It is assumed that the Y-azimuth of the tangent to the
epi at the center of the arc ab is the same as that of the chord
ab. The center of the arc is determined with a tape and is
marked with paint on the outer rail. The corresponding
Y-azimuth is stenciled on the web of the rail and on the
nearest tie or, preferably, on a stake beside the track. The
first secant ab, should be at least half a grade from the tangent
276 ORIENTATION FOR HEAVY (COAST) ARTILLERY
/
~/
—º 4. A’
3.
| Geº/7fer--G)
\
Fig. VII.-FIRST STEP IN GRADUATING AN EPI
†
Fig. VIII.-Y-AZIMUTHS OF TANGENTS

ORIENTATION FOR. RAILWAY ARTILLERY 277
to the rail, so that the line of sight will mark distinctly the
extremities of the chord.
The telescope is then turned one or two grades at a time away
from the tangent and other points of graduation are deter-
mined. If the curve is irregular three or four sights only
should be taken because the approximation introduced in
assuming the parallelism of the chords and the tangents become
too inaccurate.
The same operation is repeated for each of the alignments
R2, R3, etc., care being taken to always set up the instrument
at the same distance from the outer rail in order to obtain a
Series of regularly distributed points. Interpolation between
points may be made if there are any gaps.
If a survey of the epi is to be made at the same time, the
lengths of R1, R2, R3, etc., should be measured.
5. RESURVEY OF OLD TRACKs
Perhaps the most frequent use of railroad surveying by the
artillery will be in connection with the taking up of battery
positions on tracks already constructed. Such tracks might
be in poor condition or damaged; the records destroyed or lost,
reference marks gone, or some similar condition exist which
might very likely require a resurvey to determine the necessary
firing data. Returning to Part 3 of this chapter, the same
suggested methods of field work and data required will apply
in this case. The only difference is that the track is already
located and constructed on the ground, and it must be meas-
ured and staked again so that it may be repaired and the
data recomputed.
Relocating the curves is the first field work to be done.
New and permanent stakes should be set at P.C. and P.T. of
each curve, and at the intermediate stations, all on the center
line of track, and also at P.I. and center if these points are
accessible. If a curve is in fairly good condition, on level, open
ground, and the center is accessible, by the use of a transit
perpendiculars may be erected at the center of a number of
chords measured on the rails. These perpendiculars are radii
of the curve and would intersect at the center if the curve and
the measurements were perfect. Unless the track is in bad
shape, or the curve rather flat, the points of intersection of the
radii will be closely enough grouped to locate the center with
sufficient accuracy. On curves of small degree of curvature
the radius is so long that the method is not practical. Having
278 ORIENTATION FOR HEAVY (COAST) ARTILLERY
the center located the radii to P.C. and P.T. are determined by
perpendiculars to the tangents. This locates the P.C. and
P.T. stakes and the curve is then determined by the meas-
ured radius and central angle.
A quick and convenient method of measuring an old curve
is by using the deflection angle method previously described
for the survey of new curves. A transit is set on the center
line of track a short distance on the curve side of the apparent
P.C., so as to be certain that it is on the curve instead of the
tangent. With the lower motion clamped in any position, take
readings on the horizontal limb to successive points set at unit
chord lengths along the curve. The differences of successive
readings are half the degree of curvature. Sufficient readings
should be taken so as to give a consistent average, which is
doubled and used as D*. The lines of the tangents may be
produced to the P.I. and the intersection angle measured,
which, with D*, determines the curve. Tan. dist. is then
computed and laid off on the ground, establishing the P.C.,
P.T., and the center is located if desired. The P.I. need
not be reached in order to measure A, and lay off the tan. dist.
Various trigonometric solutions will get around this difficulty.
Another quick, but approximate, method consists of
measuring the middle ordinate subtended by holding the ends
of a string or tape.20 m. long against the head of a rail. The
middle ordinate in cm. divided by 4.36 gives the curvature in
degrees (Dº). That is, the middle ordinate of unit chord is
4.36 cm. for each degree of curvature. The only certain way
of doing this is to average a large number of measurements
made on both the inner and outer rails. One other value,
as A, is necessary, which allows all the curve data to be com-
puted and staked on the ground.
Another approximation of D* consists of stretching a string
of tape between two points on the gage side of the outer rail So
as just to come tangent to the gage side of the head of the inner
rail. The radius is then found by dividing twice the gage of the
track into the square of half the chord formed by the string.
Having determined the data concerning the curves by any
of the preceding methods, the curves and tangents are staked
out as explained for new track, which gives alignment for
repair and reconstruction and also furnishes measurements for
the transit traverse from some established point to the center
of the epi. The location and firing data is then computed anew
the same as for new construction.
CHAPTER XVI
ERRORS IN MAPS AND FIELD WORK
1. SOURCES OF ERROR
2. CLASSIFICATION OF ERRORS
3. ELIMINATION OF ERRORS
4. MAXIMUM ERRORS
5. TABLES
6. PROBLEMs
The general subject of errors and its application to a
particular field is difficult of explanation. The comprehen-
Sion of its importance and significance requires study and
experience. The layman may think that, because the instru-
ment he uses reads to very small quantities, the results ob-
tained are very accurate. On the other hand the engineer
who has had experience realizes that there are innumerable
Sources of inaccuracy which may introduce errors of varying
size into the results. The engineer studies each particular
Series of determinations he is to make, eliminates as far as
possible all sources of error, and then makes all possible cor-
rections. The subject cannot be taken up exhaustively here.
It is hoped that the elementary discussion will convey the
fundamentals for continuing the study and applying it in the
field. .
1. SOURCES OF ERROR
It is impossible to obtain exact or absolute values for any
measurement. The difference between the measured value
and the true or exact value would be the true error. This
cannot be obtained since the true value of the measurement
cannot be obtained. It is possible however to get a value
for the maximum error to be expected in any measurement
and therefore an estimate of the precision of the measurement.
This determination is the subject of the discussion. A clear
distinction must be made between error and discrepancy.
Because two measurements of the same quantity differ only
very slightly, it must not be assumed that they are very
accurate. The difference between them would be a discrep-
ancy. The error might be almost any amount depending upon
the true value of the measurement. -
280 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Natural Sources.—The first of three main groups of sources
would include temperature, wind, refraction of light, action
of gravity, and obstacles to measurement. The observer
has no control over them.
Instrumental Sources include imperfections in the construc-
tion of instruments and in their adjustment; also expansion,
contraction and other possible changes in the instruments.
Personal Sources include imperfections of human sight
and touch and actual mistakes.
2. CLASSIFICATION OF ERRORS
1. Mistakes have their source in the mind of the observer
and are due to carelessness, inexperience, and mental confu-
sion. Examples.—Mistakes in reading a tape or vernier;
wrong record of number of tape lengths; turning the wrong
tangent screw; sighting on the wrong station; and arithmetical
mistakes in the computations. When mistakes are very
Small it is possible to fail to distinguish them from accidental
GI’I’OI’S.
2. Constant errors occur from well understood causes
and may be eliminated. They are due to such things as
temperature, Sag and pull of a tape, imperfect graduation and
adjustments of the instruments. Example.—A tape }% cm.
too long because of high temperature; this would be a constant
error, for under the same conditions, i.e., the same temper-
ature, the tape will always be 3% cm. too long. If a measure-
ment is repeated a number of times under precisely the same
conditions, the constant error is the same for each measure-
ment both in sign and magnitude, and is therefore cumulative.
It is not reduced by taking the mean of all measurements.
Under changed conditions the tape might become too short,
i.e., low temperature; then the sign would have changed.
This illustrates how a constant error from a given source
may be plus or it may be minus, but under the same conditions
cannot be plus or minus.
3. Accidental Errors are those which remain after mis-
takes and constant errors have been eliminated. They are
as likely to be plus as minus and of varying magnitude, and
are therefore compensating, while constant errors under the
same conditions always have the same sign and the same
magnitude. These errors may be said to be due to imper-
fections in human sight and touch which render it impossible
to make exact readings; to know when a crosswire exactly
bisects a signal; to handle instruments delicately; impercep-
ERRORS IN MAES AND FIELD WORK 281
tible changes in the instrument itself; and indeterminate
variations in pull of tape, etc. Example.—An observer makes
an error of 34 cm. in determining a length by a tape; this is
as likely to be plus as minus and is an accidental error. If
he repeats the measurement, he is liable to make a similar
error which is as likely to be plus as minus. The accidental
error of the mean is likely to be less than the accidental error
of any one measurement. Theoretically in the mean of an
indefinitely large number of observations, that part of the
total error due to accidental errors would entirely disappear
while that part due to constant errors would still remain.
Relative Importance of Errors.—In general it may be said
that constant and cumulative errors are more important
than accidental and compensating, and that the more meas-
urements there are of a quantity the less the mean is affected
by the accidental errors. Any error that is large enough to
be appreciable should usually be avoided or corrected. How-
ever, appreciable is a relative term and an error which is
appreciable under certain conditions is inappreciable under
others. Errors so small that they would of "en be ignored
in plane surveying would be considered of great magnitude in
geodetic surveying.
3. ELIMINATION OF ERRORS
Mistakes.—There is no excuse for the existence of mis-
takes in final results. They are discovered by systematic
checks consisting in comparing results with known conditions.
Checking work is an essential part of all surveying.
Constant Errors.-These are prevented or eliminated partly
by systematic methods of field work, partly by calculation
and correction. Errors due to imperfect adjustment of
instruments can be eliminated for example by the method of
double reverse; plunging the telescope for vertical angles;
reading both verniers eliminates errors due to eccentricity
and graduation. Variations in the length of a tape due to
temperature, sag and pull may be calculated and corrected for.
Accidental Errors.—These cannot be eliminated but they
follow a mathematical law, the law of probability, according
to which they may be greatly reduced by comparing the
results of a series of measurements. As stated before the
true accidental error cannot be determined but the maximum
error to be expected can be ascertained. From this, the
282 ORIENTATION FOR HEAVY (COAST) ARTILLERY
most probable value of the quantity itself can be determined.
The greater the number of measurements in the series, the
less the maximum error to be expected.
The law of probabilities is applied to the question of
the most probable value and the error in the “Method of Least
Squares.” It will not be taken up as the artillery officer will
probably not have occasion to use it.
4. MAXIMUM ERRORS
The purpose of the topographical work is the determina-
tion of the initial firing data. The question therefore is what
is the effect of the surveying on the firing data. The total
error in the firing data cannot be ascertained either in amount
or direction. The maximum error to be expected can be
determined from the errors to be expected in each of the
surveys which form a part of the determination of the firing
data; it can never be less than the greatest error in any one
of the single parts.
For the remainder of the discussion, it is assumed that
the determination of the errors in each of the surveys is under-
stood. The tables give approximate values of errors for
different methods and instruments; their application to firing
data is given below.
The errors in firing data due to the topographical work
can be said to be included in two general classes. *
1. Distance.—A distance is determined between two
points. The error will be due to the errors in the determina-
tion of location of the two points.
2. Direction.—The error in direction of a line will be due
to the errors in the determination of the locations of the points
at the ends of the line, or will be the error in the direct deter-
mination of the direction (i.e., astronomic observation). In-
cluded in this class are errors in deflection angles which are
the sum of the errors in the direction of the two lines form-
ing the angles. - -
Error in Distance.—A line is determined by the points
at its ends. The locations of these points are not absolute.
In Fig. I assume that P' and B' represent the determined
locations of a gun and a target respectively. Assume that
the gun has been located within a distance PP' of the absolute
position, which absolute position would then be within a
circle of radius PP' and center P'. Similar conditions can
ERRORS IN MAPS AND FIELD WORK 283
Fig. I.-ERRORS IN DISTANCE
be assumed at the target B". The absolute position would
be within a circle of radius B'B which represents the maxi-
mum error to be expected in the determination. It is easy
to see that the absolute length of the line might be PB or pb
which would be the greatest and the shortest possible lengths
or it might be the length P” B" representing a line joining
possible positions of the gun and target within the small
circles shown in the Figure. It can readily be seen that the
greatest possible variation of the determined length P'B'
from the maximum or minimum possible absolute lengths
would be the sum of the errors PP' and BB' in the determina-
tion of location of the gun and target (the error would also
be represented by the sum of Pºp and B'b). To summarize,
the maximum error to be expected in the determination of
the length of a line (the range gun to target in this case),
would be the sum of maximum errors to be expected in the
determination of locations of the ends of a line (the gun and
target).
Error in Direction.—This will be considered under three
headings. : -
1. Direct determination.—It is readily seen that the
error in direction of a determination by astronomical obser-
vation or observation on several terrestrial points (V.), is
the error in the determination itself increased, in case of the
latter by the initial errors in the location of the observed
points. &
2. Location of points.-If the direction of a line is com-
puted from the locations of the ends, i.e., from their coordi-

284 ORIENTATION FOR HEAVY (COAST) ARTILLERY
nates, the maximum error depends on the errors in the loca-
tions and on the distance between the points.
In Figs. II, let P and P' represent the absolute and deter-
mined positions of the gun and R and R' the corresponding
positions of the aiming point.
zºº
// ( / )
sy / Ap
//
</
*—zy
Fig. II.-ERRORS IN DIRECTION
In Fig. II A, assume for the purpose of discussion that
the gun has been located absolutely, and that the aiming
point has been located within a distance RR' of its absolute
position. As before, the absolute position would be some-
where within a circle of radius RR'. In the worst condition
it would be located on the circumference at R, and the maxi-
mum error to be expected in the computed direction of the
line PR' would be angle 8.
In Fig. II B, assume for the purpose of discussion that
the aiming point has been located absolutely and that the
determined gun position P' is within a maximum error of the
absolute position represented by P'P. It can then be seen
that the maximum error to be expected in direction would
be angle 6'. The directions are Y-azimuths from Lambert
north.
In Fig. II C, it is assumed that neither the gun nor the
aiming point have been located absolutely, and that PP"
and RR' represent the maximum errors to be expected in
the location of each. The absolute positions lie within the
circles shown. The worst condition would be found if the
absolute locations were on the circumferences, and on oppo-
site sides of the determined positions as shown in the sketch.
It is easily seen that the maximum error to be expected is


ERRORS IN MAPS AND FIELD WORK 285
the sum of the maximum errors due to the inexact location
of the two points as discussed in connection with Figs. II A
and II B. The absolute direction may be either greater or
less than the computed direction by this amount.
3. The distance between points.-The angle at one end of
a line subtended by the short distance representing the error
in location of the other end, varies inversely as the length
of the line.
* sº.
f f \
. |
/
Fig. III.-RELATION OF ANGULAR ERROR TO DISTANCE
In Fig. III, let P represent a gun position, R' and R'
represent the positions of aiming points, determined with an
equal degree of accuracy. The maximum error is represented
by R' r" which is equal to R" r". It is seen that the angle
subtended by the error of the farther aiming point is much
less than that subtended by the nearer.
The angular errors discussed above are the parallaxes of
the aiming point and gun, and the value in mils would be
the error in location R’r' in meters divided by the distance
PR' in kilometers.
To summarize, the error in the direction of a line computed
from the coordinates o' the ends of the line is the sum of the
parallaxes of the ends of the line (as stated before the parallax
includes the error in location of the point and the length of
the line). -
Errors in Deflection Angle.—Direction in artillery work
is used to obtain a deflection angle to be set off on the sight-
ing instrument. This deflection angle is the difference in
direction between two lines. The maximum error to be ex-
pected in it is therefore the sum of the maximum errors to
be expected in the direction of each line. In applying the
angle to the gun, the error to be expected in the sighting
apparatus must be added to the maximum error to be expected
in the determination of the angle.

286 ORIENTATION FOR HEAVY (COAST) ARTILLERY
Combination of the Distance and Direction Angles in a
Practical Problem.—The following is taken from the Manual
for the Orientation Officer.
Fig. IV.-ERRORS IN DISTANCE AND DIRECTION
In Fig. IV, P', B', R' represent the determined positions
of a gun, target and aiming point respectively. The abso-
lute, or true positions might be P, B, and R. The determined
range would be P'B', whereas the absolute range would
be PB. The deflection angle would be R'P'B', whereas the
absolute deflection angle would be RPB. The line PB is
prolonged in both directions and P'b' is drawn parallel to it.
P'R" is drawn parallel to PR. Pºp and B'bb’ are perpen-
dicular to the line PB.
The determined range P'B' would differ from the abso-
lute range PB by pp-HBb nearly. Under the worst condi-
tions the error in the location of the target would be in the
prolongation of the line PB, as discussed in connection with
Fig. I, and Bb would be equal to BB’; also pIP would be equal
to P'P. The maximum error to be expected in the range
would therefore be BB'--PP', or the sum of the errors to be
expected in the location of the gun and the target.
The error in the deflection angle R'P'B' would be the
difference between it and the absolute angle RPB (or R"P'b').
This difference is the sum of the errors in direction of the

ERRORS IN MAPs AND FIELD work 287
line P'R' to the aiming point and the line P'B' to the target.
The error to be expected in the direction of the line to the
aiming point is angle o, assumed to be a direct determination.
The error in the direction of the line to the target would be
tº e b'b-H bR’
angle 8 (in mils) = P/E7 (b'b = Pºp)
P'p-Hb B' (meters)
- T P'B' kilometers)
As before, under the worst conditions B'b and P'p would
be equal to PP' and BB'. Angle 3 in mils would be
- PP'+BB' (meters)
P'B' (kilometers)
The error in the deflection angle would be a +3.
5. g TABLES
A series of tables giving approximate errors in results
obtained by different methods and different instruments
are included here. They can be used in determining the
probable errors in topographic determinations and in decid-
ing upon the methods and instruments to be used to obtain
the desired degree of accuracy in any determination. It
must be understood that the errors given are only approxi-
mate but with average carefulness and experience any one
should be able to do work within these limits of accuracy.

TABLES OF COMPARATIVE ACCURACIES.
TABLE I—MAPs.
POINTS OF THE
MAP GENERAL CONTROL | PoinTS OF PLANIMETRIC DETAIL
Battle Maps—All Accurate within the Accurate within about 10 meters,
scales. limits of plotting— except in case of blunder, or where
about 0.2 mm. the detail is photographically en-
larged from the 1:80,000 map. In
latter case errors may be as large
as 100 meters. . -
1:800,000 General|Accurate within the Errors may be as large as 100 meters.
Staff Map. limits of plotting. * * * * * *
1:50,000 Black and Accuracy same as 1:80,000 G. S. M., from which it is a
White Map. photographic enlargement,
1:50,000 Colored Based on surveys at 1:10,000 and 1:20,000. More accurate
Map. than either of the two preceding.
288
ORIENTATION FOR HEAVY (COAST) ARTILLERY
TABLE II—INSTRUMENTS FOR MEASURING DISTANCEs.
INSTRUMENT
MAXIMUM ERROR
TO BE ExPECTED
—a-
REMAIvks
Pacing.
Telemeter.
Stadia.
Steel Tape.
1 in 50.
1 in 150.
1 in 300.
1. in 5,000.
1 in 10,000.
1 in 100,000.
1 in 300,000.
|Over rough ground, sand, brush,
etc., and on slopes, the error is
even greater.
For a two-meter base. The error
decreases as the base increases.
For ordinary work with sights of not
over 100 or 150 m. 1 in 1,400 is
possible with very accurate instru-
ments and the most skillful work.
Fair accuracy for work of average
speed without using spring balance
or thermometer or eliminating sag.
Probable accuracy for heavy artil-
lery field work.
Very good work. (See Chapter V,
for a table of conditions which will
give an accuracy of 1 in 10,000
using 100-foot steel tape, and for
a discussion of the requirements
for an accuracy of 1 in 10,000 to
1 in 50,000.)
Excellent.
Possible.
***.
TABLE III—INSTRUMENTS FOR MEASURING ANGLEs.
MAXIMUM ERROR
INSTRUMENT TO BE ExPECTED REMARKS
Compass. 15' = 5 mils. (Approx.) |Large and uncertain errors are
Clinometer (Vertical
angles only).
Plane Table, with
open sight alidade.
Plane Table, with
telescopic alidade.
Compass Goniom-
eter.
Transit (similar to
the French Jobin
Theodolite).
1°.
15' = 5 mils.
7' = 2 mils.
1 mil.
20" or 30" = . 15 mils,
caused by local attraction, mag-
netic storms, and unknown varia-
tions in local declination. Slight
errors are caused by sluggishness
of the needle and lack of coin-
cidence between the geometric
axis and magnetic axis of the
needle.
Error in sighting. Add the plotting
error which is 0.3 mm. for each
. multiplied by the scale of the
plot.
(A French instrument, practically
equivalent to a panoramic sight
with compass attachment.)
Some transits read to 20" which can
be considered the probable varia-
tion from the absolute value owing
to difficulty of estimating co-
incidence of graduations. Other
transits read to a minute. The
reading is therefore within one-
* minute or 30" of the absolute
V3 IU16.
ERRORS IN MAPS AND FIELD WORK
289
TABLE IV—SURVEYING METHods AND CALCULATIONs.


METHOD
Intersection.
Resection . (Three-
point and Releve-
ment).
Traverse (linear).
Traverse (angle).
Y-azimuth by Astro-
nomic Observa-
tion. On Polaris
On the Sun.
Terrestrial Y-azi-
muth—by transit.
By Compass Goni-
Ometer.
By Plane Table and
Compass with tele-
scopic alidade.
Same, with open
sight alidade.
Orientation by Com-
pass using tabular
magnetic declina-
tion.
MAxIMUM ERROR
To BE ExPECTED
REMARKS
3 meters for transit—
10 meters for plane
table.
3 meters for transit—
10 meters for plane
table.
av'n.'
8 Vn."
1' or 0.3 mil.
3’ or 1 mil.
3’ to 4" or 1 mil.
3 mils.
15' or 5 mils. ,
25' to 30' or 8 mils.
20 mils or more.
The total error in location of the
point is the error in the determina-
tion itself plus that due to the
locations (coordinates) of the
points used in the determination.
If three points only can be occupied
the U. S. is probably more accurate
than the French method.
Greater accuracy is attainable when
a larger number of points are used.
Formula for maximum error in the
position of the last point. “a” is the
maximum error to be expected in
any one course, and “n” is the
number of courses in the traverse.
With a transit and tape the error
in determination should be less
than 1%, with a plane table 2%.
Formula for maximum error in the
direction of the last line, 8 being
the maximum error to be expected
with the instrument for each angle
measurement and “n” the number
of angles.
The total error in direction is the
error in the determination itself
plus that in the direction of the
initial line.
Considered to be the most accurate
method of those used by the
Heavy Artillery Officer.
Solar observation presents more
difficulties and therefore is more
liable to error than observation on
Polaris.
-NotE.-In plane table work, in addition to the above tabulated errors the
error in the drafting (so called plotting error) must be considered.
290 ORIENTATION FOR HEAVY (COAST) ARTILLERY
TABLE V–ERROR IN ANGLES OF A TRAVERSE.
INSTRUMENT AND
METHOD of ORIEN- CY ºy o-y 8 (2-3) –1|N
TATION OF THE 23?
DESIRED LINE
mils mils mils] mils. ' \
Plane table and com—
pass with points of
general control. 49
Open sight alidade 8 |27' 50" I 7 5 | 15' 30" | ** —
Plane table and com-
pass with points of
50
general control. - 16
8
4
5
1
5
Telescopic alidade 30" 1 || 4 || 2 || 7 |13\
Compass goniometer
with points of gen-
eral control. . . . . . 3 1 2 1
2
Transit with points - - 25
of general control. 1 || 3'.36|| 6′.3 . 5 . 15|.5' | 1 || - “’ — 1 = 5.5| 5
5
Transit with astron- 0
omic observation. .5| 1'.7 | 3".1 5 0 . 15| .5' | 1\ |-RTE
NOTE.—o, is the maximum error to be expected in the direct orientation at
the point. Values are taken from Table IV.
ºy is the maximum error to be expected in the Y-azimuth of the known line
which might be used to orient the angle traverse.
8 is the maximum error to be expected in any one reading of the instrument.
o: —y is the angular error which should not be exceeded in the traverse in order
that the direction determination by it should be more accurate than the direct
determination.
N is the number of courses in the traverse that should not be exceeded in
Order that the traverse determination be the more accurate.
6. PROBLEMS
It is impossible to do justice to the subject of errors in
topographical work in a simple written discussion. Experi-
ence on the part of the officer is the only way in which he
can realize the importance of the subject. Several problems
are included with the idea of indicating how the subject could
be approached in a particular instance.
1. The location of a point A has been determined by the three point problem,
using points of the general control. From A the directing gun of a battery has
been located by a traverse of four courses, about 300 meters in total length, run
with transit and tape. The transit was oriented at A on points of the general
control. An aiming rule was installed and oriented by astronomic observation.
It is desired to fire on a target whose position is determined from a battle map.
The approximate range is 4000 meters. What are the maximum errors to be
expected in calculating the range and deflection?
Error in position of A 3. m. (Table IV).
Error in position of gun relative to A, in distance,
300X1/5000 = .06 m. (Table II).
ERRORS IN MAPS AND FIELD WORK 291
Error in direction:
due to orientation 1. ... mils (Table IV).
due to traverse, .15X V8 = .42 mils (Table III, IV.)
Total 1.42 mils.
1.42 mils at 300 meters .426 m.
Disregard the .06 m., as it is less than .426 m.
Error in position of gun 3.426 m.
Error in position of target 10. m. (Table I).
, Total range error 13.426 m.
Error in orientation of aiming rule .5 mils (Table IV).
Error in direction of gun-target line,
*184264%-34 mil
Total deflection error 3.9 mils.
II. In the same problem a traverse was run by a slightly different route of
five courses, but the same approximate total length, with a plane table and
telescopic alidade, as a check on the previous work. The table was orientated
at A on points of the general control, and the work was plotted at 1:10,000.
The distances were paced. The position of the gun so found fell about 6 meters
from that determined by the transit and tape.
Error in position of A 3. m. (as above).
Error in position of gun relative to A, in distance, º
300X1/33 =9.1 m. (Table II).
Error in direction,
*due to orientation 5 mils = 1.5 m., at 300 m.
due to reading angles 2 V10 = 6.32 mils = 1.9 m., at 300 m.
due to plotting 3 V 5 = .67 m., at 1:10,000 = 6.7 m.
Total 10.1 m.
(Disregard the 9.1 m., as it is less than 10.1 m.)
Error in position of gun 13.1 m.
As the difference between 13.1 and 3.426 is greater than the discrepancy
H.". the two results, i.e., 6 meters, we may consider the second to have checked
the first.
*(NoTE.—In a plane table traverse of five courses there are ten sighting
operations, but only five lines to plot.)
III. The maximum errors in range and deflection for firing on an auxiliary
target, A, were determined to be 20 meters and 5 mils, respectively. The approx-
imate range was 10,000 meters. It is desired to fire at a target, T, 200 meters
from A. The maximum error in the location of the gun, G, is 10 meters. What
are the maximum errors to be feared in the range and deflection calculated for
firing on T” -
Error in position of T due to transfer,
10X 10,000 -: .2 Iſl.
.2 m. at 10,000 m. = .02 mils.
Error in range to T; 20 m.-H.2 m. = 20.2 meters.
Error in deflection to T; 5 mils—H.02 mils = 5.02 mils.
IV. The question may arise whether to determine the
direction of a line directly, or to run an angle traverse from
the end of another line of known Y-azimuth. It will depend
upon the number of courses necessary in the traverse. As-
sume that o is the maximum error to be expected if direct
orientations were used; y is the maximum error in the known
!): ORIENTATION FOR HEAVY (COAST) ARTILLERY
line; and 8 is the maximum error to be expected in a single
reading of the angle measuring instrument. The permis-
sible angular error in the traverse would be o – Y. The num-
ber of courses which might be used in the traverse can be
represented by N. The maximum angular error to be ex-
pected in the traverse would be 3 V2(n+1). If there were
N courses in the traverse there would be (N+1) stations at
which the instrument would be set up; in measuring the
angle at each station two readings of the instrument would
be made, one for each side of the angle. Therefore there
would be 2(N+1) separate readings of the instrument.
Whether this exceeds o–y depends upon the value of N.
The value of N is derived as follows:
8 V2(N + 1) < (a — y)
2(N+1) <º
9
(o. — y)*
N < 23? — 1
Knowing the value of o and Y, and 8 for the instrument and
method used, the value of N can be determined. Table V
gives the values of N for different methods and instruments.
("HAPTER XVII
DUTIES OF THE ORIENTATION OFFICER
GENERAL
RECONNAISSANCE
SURVEY WORK
OBSERVATION SERVICE
ORIENTATION RECORDS
LIAISON
DISTRIBUTION OF INFORMATION
1. GENERAL
As stated in the Introduction, under normal conditions
the orientation officer performs certain fairly definite duties,
yet, like the normal atmospheric conditions assumed in
range tables, the normal seldom exists, and all battery officers
—lieutenants as well as captains—must be able to handle this
work. An orientation officer—or a battery officer doing
orientation work—may be compared to the resident engi-
neer on construction work: he is an executive who must plan,
supervise and check the work of locating points, lines, direc-
tions, and levels. To do this he must train enlisted men to
be proficient in all the various phases of the work, and to
train them requires a more thorough knowledge on his part
than would be required merely to do the work himself.
The orientation officer must have considerable basic technical
knowledge. He must understand maps: their construction,
projections, meaning, accuracy and triangulation systems. He
must know quadrillage, plane trigonometry and logarithms;
Surveying instruments and methods; practical astronomy and
its uses; plotting, drafting and sketching; the materiel with
which his batteries are working, its power, range, accuracy
and limitations. In addition to this technical knowledge he
must know his own environment, i.e., the tactical situation,
the terrain in which his batteries are working: its hills, valleys,
streams, roads, railroads, fields, woods, towns, telegraph and
telephone lines, drainage and weather conditions, not only
behind his own front lines, but behind the enemy's as well;
further, he must use this knowledge for the benefit of his a
294 ORIENTATION FOR HEAVY (COAST) ARTILLERY
battalion. He can secure much information of this character
from maps, photographs and sketches, but the information so
obtained must be supplemented by personal reconnaissance.
2. RECONNAISSANCE
Map Study.—There are certain fundamental considerations
in the selection of positions for batteries and observatories in
which technical skill is not required, but in which good judg-
ment is essential. These considerations are ease of access,
possibilities of concealment, surroundings, character of the
ground, and drainage. The value of a given position with
respect to these considerations can to a great extent be deter-
mined from a careful study of the maps. Similarly, map study
will determine visibility, defilade, maximum and minimum
range, dead areas, and possibilities of fire. These points were
taken up in detail in Chapter XII. Thus, by means of map
study alone, the character and possibilities of a tentative
battery position can be closely approximated.
Study of the Terrain.-These factors can be considered and
a tentative decision can be made from a study of the maps
but in all cases they should be verified by an actual recon-
naissance of the terrain. Map study is invaluable: it can
minimize, but can seldom entirely replace field work. In
a reconnaissance a plane table, or sketching board, and com-
pass, supplemented possibly by a small camera, are the logical
tools. The methods used in such work were briefly discussed
in Chapter VI. More detailed data on reconnaissance and
sketching methods will be found in the Engineer's Field
Manual. -
3. SURVEY WORK
The survey work is conducted with a view to obtaining the
following data: -
(a) The position of the directing piece observation stations
and targets. -
(b) The altitudes of the guns and targets in meters above
sea level. -
(c) The Y-azimuths from the directing piece to reference
points and targets.
Position of the Directing Piece.—In order to avoid the
inaccuracies of the drawing of maps, the position of a piece
is generally determined with a transit by reference to the
geodetic points which constitute the framework of the map.
DUTIES OF THE ORIENTATION OFFICER 295
The coordinates of the piece are determined by calculation
following one of the usual topographic methods; intersection,
resection, or traversing, or by a combination of some of those
methods.
The choice of methods will be guided by (1) the desire to
avoid errors and consequently to limit the operations to those
which connect them with the nearest possible points, and
(2) by the necessity of providing the indispensable checks,
never less than one. -
Since the directing pieces occupy sheltered positions it will
often be impossible to obtain their positions directly from the
geodetic points. In fact, it will usually be necessary to have
recourse to a traverse which should start from a known point
or one determined by the three-point problem or by intersec-
tion, and should close on the same point or on another known
point. Each case offers a different problem which should be
carefully examined with a view to limiting the number of
operations to a minimum. Long traverses and distant inter-
sections are also to be avoided.
An oriented transit is always kept oriented as an approxi-
mately accurate check on the operations. If these are based
on regularly established geodetic points, positions may be
located with a Jobin theodolite to within 3 meters. The
results may not be quite so accurate if the work is based on an
old survey which has not been revised since the outbreak of
W8,I’.
The same methods may be used with a plane table and
telescopic alidade. If the size of the plane table and the dis-
tances to the known points permit, the scale of 1:10,000 is
used for three-point problems, intersections and resections.
The scale of 1:2,000 is always used for traverses. If the
geodetic control is accurate, these scales will permit of an
accuracy to within 5 or 6 meters. A scale of 1:20,000 will
involve errors of 10 or 12 meters even in simple operations.
In cases of insufficient triangulation or of insufficient time
the position of the piece may be determined by reference to
the planimetric details of a map. Instruments and topo-
graphic methods are necessary in order that the map may be
used with certainty and precision. The details of the map
are verified, care being taken in their identification, and the
exactness of the map is checked. For this latter purpose one
or two points are occupied with a plane table and the directions
and distances to neighboring details on the terrain are com-
296 ORIENTATION FOR HEAVY (COAST) ARTILLERY
pared with those given on the map, and a traverse is run
through the points to be verified. Three or four such points
having been checked, the position of the piece is connected
with at least two of them. The principal methods are:
(a) Traverse: Start from one of the determined points, pass
through the directing position, and close on another point.
(b) Three-point problem: Occupy a station near the gun
position at which a three-point location can be made, and
determine the position of the piece by direction and distance
(polar coordinates).
(c) Intersections.—From three determined points take
sights on the gun position.
(d) Combinations of these methods are good.
The position of the directing gun may also be determined
by transferring the required points from the battle maps to
a plane table sheet by their coordinates which are measured
to within one-tenth of a millimeter by a double decimeter
rule. The field work should be done on a scale of 1:2,000, of
1:5,000, or of 1:10,000, for, while these scales do not increase
the precision at the starting points, the graphical errors are
reduced. In addition to this plot, another plot should be
made on a 1:20,000 scale to bring out the errors which may
be made in sighting on the more distant points. If the battle
map is fixed on the plane table by thumb-tacks or by pasting
along the edges. The transfer of points is avoided, thereby
permitting more rapid work, but it is necessary to work on
the scale of the battle map used.
Altitude of the Directing Piece.—A special topographic oper-
ation for the determination of the altitude of the directing
piece is often unnecessary for, with a good battle map, it is
usually safe to locate the position on the battle map by its
coordinates and to determine its altitude by interpolation
between the contour lines. Longitudinal profiles of railways
or epi surveys may sometimes be used but frequently the
origin of elevations for these are assumed arbitrarily and this
origin must therefore be known.
Where available maps are not sufficiently accurately con-
toured, a leveling operation is required. A traverse, as short
as possible, is then run from a point of known elevation through
the position to another point of known elevation, and the
slopes between successive stations are measured. The start-
ing point may be a bench mark of known elevation, a point
whose elevation is given on a reliable map, or a station whose
DUTIES OF THE ORIENTATION OFFICER 297
elevation is determined by measuring the Zenith distances of
near-by geodetic points of known elevation. In this last
case, the height of the rod target and that of the instrument
must not be disregarded and the correction for apparent level
must be applied. -
Lacking other methods the altitude may be determined
approximately by comparing the barometric reading of the
position with that of a point of known elevation. The bar-
Ometer falls, on the average, one millimeter for a rise of 11
meters.
Having determined the altitude of the directing gun the
altitudes of the other guns is usually determined by running
lines of spirit levels using the directing gun as a bench mark.
The elevations on the battle map are, in general, more
accurate than those obtained by the other methods given
above. -
Reference Direction.—In laying the directing piece in direc-
tion use is generally made of a line of predetermined Y-azimuth
called a reference direction. Those reference directions may
be represented by right lines emanating from the gun position
itself or from a near-by point, R, called a reference point whose
coordinates are known. A reference direction may also be
represented by an alignment on the terrain which passes near
the battery (straight road, canal, etc.).
If the reference directions emanate from the gun they
constitute lines of sight, that is, lines from gun to aiming
point. In this case there will be required for each position:
(a) A reference direction on a distinct and distant point
(single tree, steeple, chimney, etc.) which will be used as an
aiming point during the day, and
(b) A reference direction on a near-by point (picket,
painted line on a tree, etc.) which will be used as an aiming
point at night or in case of fog and to which a signal lantern
may be attached.
If the reference directions are to emanate from a point R,
the point is chosen, if possible, near the battery and in view
of all the pieces. An angle-measuring instrument is set up
at R and oriented on, the reference direction, and laying is
accomplished by reciprocal sighting on this instrument. The
point R is distinctly marked on the terrain by a picket or
a stake.
The straight alignment of a railroad, a long and straight
road, a straight wall, etc., in the vicinity of a battery may be
298 ORIENTATION FOR HEAVY (COAST) ARTILLERY
used. In this case laying is accomplished by reciprocal sight-
ing on an instrument set up and oriented on this alignment.
The determination of the Y-azimuth of the reference direc-
tion necessitates topographic operations in order that it may
be drawn accurately on the plane table, or the battle map.
The use of the coordinates of the reference point and of the
distant reference mark (or of gun and of aiming point) is not
sufficiently accurate although, on occasion when the reference
mark is very distant and the coordinates are accurately
known, it may have to be used. The following methods are
used almost exclusively: - -
(a) Astronomical.—By means of a well-adjusted transit,
the Y-azimuth of the reference direction can be determined to
within 1 mil by—
(1) Observation on Polaris at its maximum elongation.
(2) Observation on Polaris at any time (preferably at
dusk) using a watch whose error is less than one minute. -
(3) Observation of the altitude of the sun or of any star
of the first magnitude, at any favorable time, using a chro-
nometer. - -
(4) By time observations, if the conditions permit keeping
the time within a margin of about 5 seconds.
(b) Geodetical.—An angular traverse is made with the
fewest possible sides by means of a transit This should start
from a known geodetic point or from a three-point station.
On a good general control and a well located initial station,
an accurate angular traverse of 3 or 4 sides with the transit
will give an accuracy to within 1 mil. The precision will be
even greater if the angular traverse has but a single side.
(c) Topographic.—With a transit set up at a known point
and sights made to known signals, a terrestrial Y-azimuth may
be computed and carried to the gun position with an angular
traverse.
This same operation may be done graphically with a plane
table by setting it up over a known point and orienting it by
sights on other known points. The orientation in this case
should be carried to the gun position by means of an angular
traverse of not more than three sides.”
The Y-azimuth of the reference direction is measured on
the plane table by a large zinc protractor. If the gun posi-
tion can be sighted directly from the initial station, the error
will not exceed 2 or 3 mils. If there are one or two inter-
mediate stations, the error will be 3 or 4 mils. Operations
DUTIES OF THE ORIENTATION OFFICER 299 °
based on a good battle map give results of about the same
degree of accuracy.
(d) Use of the Compass.-The amount of magnetic decli-
nation given on the maps should never be used in instrumental
determination of direction for the results so obtained would be
only approximate. All instruments should be oriented with
due correction for the declination of the region where they are
used. Precautions must always be taken to avoid local
magnetic attraction. -
Compilation of Data.-After the batteries and observa-
tion stations have been located considerable work still remains
to be done, especially in compiling the data in a form con-
venient to use. A firing board (called Planchette de Tir and
Artillery Board by the French and English respectively)
must be made for each battery and kept up to date. Visi-
bility Charts, Possibilities of Fire Charts, and Panoramic
Sketches must be finished. Additional reference points and
aiming lines must be determined, and the various contingencies
of combat must be met.
Alternate Positions.—Once the enemy discovers a battery
it must move immediately or be destroyed. Therefore,
alternate positions must be prepared into which a battery
can move on short notice and for which all orientation data
has been prepared so that the battery can recommence fir–
ing with a minimum delay.
Preparation for an Advance.—An Orientation Officer's work
does not stop here, however. He must keep the possibility
of an advance in mind and constantly study the terrain behind
the enemy's lines; both on the maps and from the observation
stations, with a view to the selection of suitable advanced
battery and observatory positions. He must determine the
location and altitude of numerous reference points behind the
enemy’s lines, using intersection and trigonometric leveling,
So as to facilitate rapid orientation in new positions when the
battalion moves forward.
When the enemy is retreating more opportunities for
effective artillery fire are offered than at any other time, but
unless a battery can move forward rapidly and open accu-
rate fire at once from predetermined new positions, these
opportunities may be lost. Conversely, the orientation
officer studies the possibilities in case of an enemy advance.
When an attack is to be launched, artillery is concen–
trated on the designated sector, often at night, and must
300 ORIENTATION FOR HEAVY (COAST) ARTILLERY
open fire at once. To permit this all necessary data must be
prepared beforehand, transmitted to the proper officers, and
every precaution must be taken to insure its clear under-
standing and proper use. This comprises one of the most
important duties of an orientation officer.
4. OBSERVATION SERVICE
The observation work of the group is distinctly separate from
that of the battery; the former covering a larger and more
diversified field in detail while the latter is a combination and
general observation. By virtue of his broad knowledge of the
terrain and of conditions within the group, the orientation
officer is the logical man to organize and supervise the group
observation service. His work of organization includes the
Selection and location of observation sites, the establishment
of initial and reference Y-azimuths, the preparation of pano-
ramic views and plans of the observation stations, and the
instruction of the observers in their routine and special duties.
If observation stations have been established by the indi-
vidual batteries, the orientation officer may be called upon to
verify the survey work, since a considerable degree of accuracy
is necessary.
Under instruction from the battalion commander, the orien-
tation officer centralizes and coordinates all information gath-
ered by the various observation stations and other sources.
He studies and compares photographs relating to the battery
objectives and transmits a summary of his results and findings
to the Intelligence Service and to each of the batteries.
In a reconnaissance preparatory to an offensive, observation
sites suitable for use in the course of the successive phases of a
forward movement are considered and selected in so far as
possible. The scouts who will be intrusted with keeping that
portion of the battalion observatory work in order are care-
fully instructed and drilled by the orientation officer. These
scouts are informed as to their respective missions during
reconnaissance and during the installation of observation
stations and the organization of service. The orientation
officer instructs them in advance as to map details of the
entire region with which the observation stations may deal,
indicating probable sites. This instruction is conducted in
conjunction with terrestrial observations of the ground under
consideration.
DUTIES OF THE ORIENTATION OFFICER 301
5. ORGANIZATION RECORDS
Fire organization records, as maintained by the orientation
officer, are collected and filed by him at the battalion head-
quarters and embody information of battery emplacements,
fields of fire, objectives, and observation stations, their out-
looks, and allied items. These records serve as notes for the
battalion commander's reference, which he may pass on to
his successor, thereby simplifying the transition from one
commander to another, and as guides for reinforcing batteries
arriving to assist the battalion at any time. The records are
broad and clear, preferably diagrammatic and devoted to
those general aspects especially important to the group com-
mander. They thus include the location of batteries, their
possibilities and fields of fire, the location of principal objec-
tives, the various means of observation, and a plan of con-
centration or extract therefrom. This plan of concentration
may be clearly formed by mounting a battle map on a board
or wall and representing each battery emplacement by a pin,
attached to which is a colored thread indicative of the caliber
and range of the particular battery. It is thus obvious whether
or not an objective is within range of various batteries. A
more graphic method is to cover a battle map with tracing
paper with a 2.5-mm. quadrillage and to lay off the limita-
tions of the field of fire for each battery, considering maximum
and minimum ranges and dead spaces. Then within each
square is inscribed the number of each battery within whose
effective field of fire the square lies. This method affords a
means of making up artillery concentration plans with
minimum of difficulty. --
6. LIAISON
This service cannot be organized to the best advantage from
the personnel of the batteries; the orientation officer is best
fitted to conduct it, as well as being in a position to benefit
most by any resultant information. He therefore dispatches
this duty himself or employs the scouts best adapted to the
work. The nature of the work always depends upon the
immediate situation and upon orders from the battalion com-
mander. Information of great value concerning enemy first
line positions may be derived from neighboring infantry units.
By visiting the observation stations of adjacent batteries at
frequent intervals, information, sketches, and panoramic
views of considerable utility may be obtained.
302 ORIENTATION FOR HEAVY (COAST) ARTILLERY
This service results not only in information of particular
benefit to the battalion, but also tends toward complete col-
laboration and the necessary cooperation between the bat-
talion and adjacent infantry and artillery units.
7. DISTRIBUTION OF INFORMATION
The orientation officer is in a position to transmit essential
information to the Intelligence Service; this information is
embodied in a Bulletin of the Service and in that form is
distributed throughout the units concerned. To each battery
he supplies, in addition, photographs which may prove of
interest, particularly those showing the results of their own
fire. He also distributes battle maps, correction sheets of
the topographic service, various instructions, and extracts
from the Bulletin of the Intelligence Service completed and
explained, if necessary, by data obtained within the group.
The orientation officer, in general, sees that the topographic
and observation materiel are maintained in good condition
and in sufficient quantities.
He habitually considers himself, for the moment, as a por-
tion of that unit with which he is in touch. He informs them
to the full extent of his knowledge as to the situation of the
group and of the neighboring units; he communicates to them
all pertinent orders and instructions which concern them.
In addition to the prescribed definite duties, the orientation
officer should be of constant assistance to the group com-
mander. He lives near the latter and should be well informed
upon all that happens within the group, not only as to its
personnel but what it has done and is expected to do in the
contemplated operations. The telephone service is closely
connected with his observation services, as is the radio service;
the ordnance and munitions have a direct bearing on the
bombardments which he assists in carrying out. He should
be thoroughly in touch with these services and cheerfully render
them any service in his power. -
When an advance is imminent, the orientation officer is
most active in assisting the group commander with the prepa-
ration of the ground for the advance and in rendering aid along
topographic lines to the batteries, helping them to dispatch
their functions with expedition. It is thus apparent that the
orientation officer is in close touch with the entire activity of
the group, and occupies a position of relatively large impor-
tance therein. ; , --, ...
* is . J
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.*.*. . . . . . . * *...--
DEC 2, 1922
AJNIV, Cº. ºi.
| BRARY
iii'ſ OF MICHIGAN
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3 9015 O6525 7209



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