font
ague,
C.8
THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES
ROBERT W. WEBB GEOLOGY
The
RALPH
LIBRARY
DJfcEED DEPARTMENT OF GEOLOGY UNIVERSITY OF CALIFORNIA LOS ANGELES, CALIF.
DEPT., U.C.U
ROBERT W. WEBB GEOLOGY
DEPT., U.C.LA.
All Naval and Military Books, wheresoever Published, are kept in Stock, and can
be supplied without delay, by
EDWARD STANFORD, Naval and Military Publisher and Bookseller, 26
&
27,
Cockspur Street, Charing Cross, London, S.W.
CATALOGUE POST FREE.
MILITARY TOPOGRAPHY ILLUSTRATED
BY PRACTICAL EXAMPLES
OF A PRACTICAL SUBJECT
BY
MAJOR-GENERAL W.
MONTAGUE,
E.
C,B,
,
p. s. c.
LATE GARRISON INSTRUCTOR; INTELLIGENCE DEPARTMENT, ETC.
WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON
MDCCCXCIII
All Riijhts reserved
CONTENTS.
INTRODUCTION
PAET
I.
ELEMENTARY. 1.
To
find the distance
elevation being
from a
2.
Example
of resection
3.
Example
of intersection
hill, its
hill, its
height and angle of
known
13 .
.
;
by
bearing being given
.
4.
To
5.
Method
6.
To
7.
Plotting from a
.
.
to be used
known when the
in the contours
of a point, its
"
13
its
known
H
.
;
E, one .
.
14
......
15
not normal
.
15
.
16
find the height of an object, distance
depression being
.
also to find the height of a
distance arid angle of elevation being
also to fix the position of a point
fill
.
.
.
scale
is
and angle
where several valleys unite
.
of
section line," also to fix the position
HE
and one bearing being given
562963
.
16
CONTENTS.
6
8.
"
Form
lines" used to
mark a change
in slope on a hill-
side 9.
17
Example
of the principal terms used in
Topography
in
connection with the ground 10. Intersection
18
also to find heights, the
;
elevation being given
.
and angle of
.
.
PART
HE
.
.
.
18
II.
THE FIELD-BOOK. 11.
12. 13.
To sketch hilly country by a traverse To plot a traverse line across hilly country To plot from a field-book, and to find the .
... .
.
RF
.
16.
17.
To
18.
20.
To To To
21.
To
22.
The use
1 5.
23
plot a winding road, and the hills on either side
.
plot a hill from contours noted in a field-book
.
fix
hill
and traverse the .
initial
.
up
hill
a valley,
and plot the
the scale not
and a valley
plot the traverse of a road winding
traverse
25
26
......... ...
plot a road crossing a
24
contour of an isolated
.
.
plot a road winding
normal
19.
22
of the
sketch
To To To
14.
21
initial
up a
hillside
.
27
28 29
contour of a hilly 30
feature plot in the head of a valley from notes in a field-
book
31 of
country
"
Reference Points
"
when
plotting hilly
32
CONTENTS,
PART
7
III.
FORM LINES. 23.
"
Section lines lines
24.
"
to of
"
"
Section lines
"
of slope "
Form
and
25.
Example " Form lines " showing small
2G.
To
and " Form
....
to give the height of a hill,
show the change
lines
.
.
.......
tween contours
find the height of a hill
34
features which occur be-
by
a
"
....
R
35
Section line," a good
exercise in plotting in contours
PART
33
36
7 .
ADVANCED SKETCHES.
...... ......
27.
Intersection and resection
28.
To assume a datum, and
29.
Intersection,
30.
Example
31.
Conventional signs, and the value of the points of the
32.
To
33.
Fixing a point by alignment
34.
To
35.
To
36.
To
sketch
find
is
find the
to be executed resection,
and use
R F
of
the
38
VI
40
in contouring
40
in contours
where several watercourses join
calculate the height of a hill
.
fall
of a
44
........ ....
heights
fractional. fill
41
42
from the
stream calculate
38
formula to
compass fill
37
on which the
in a sketch
when the angle
from scanty data
of elevation
is
44 45
CONTENTS.
8 37. 38.
To survey an inaccessible position To find the scale on which a portion vey
is
.... of a
46
combined sur-
to be executed
47
PART
V.
SECTIONS. '
39. 40.
41.
To draw the section of a hill To draw a section of a hill from notes taken To draw the plan of a hill from its section
NOTES TO DIAGRAMS
.
.
.
.
.
.
...
carelessly
.
51
52 53
55
INTRODUCTION.
THE
following exercises are intended to assist beginners in Military Topography to overcome the difficulty they constantly meet with on finding that the
study of a most practical and out-of-doors subject is conducted at a table in a class-room, and that the ground,
and
its slopes, its features, its hills, its valleys,
streams, which they are told to depict, disin a mass of rules and formulae. In each of appear these exercises the student is introduced to a small its
portion of the ground, will assist
him
is
given just so
many
to understand its features,
cient points to enable
him
data as
and
suffi-
to sketch it correctly.
Each example is intended as a practical guide to some rule or formula, and to point out its use to the
when on the actual ground. In the theoretical or indoor study of Military Topography a frequent cause of perplexity with
sketcher
beginners
is
to
mix up the
scale of the plan with
10
INTRODUCTION.
the slopes of the ground, and it is not always easy to convince them that there is no connection between
No matter what the scale of our plan the hard-and-fast mathematical truth remains that the two.
is if
slope of 1, we shall have to take fifty-seven paces before we are one pace lower than our starting-point, and that if the slope changes to 2 or 3, we shall have to complete one-
we
set out to pace
down a
same
half or one-third of the
we have The the
"
got
down our one
fifty-seven paces before
pace.
no doubt, is owing to the use of normal system," in which the distance to be difficulty,
measured
vertically
the scale.
between contours varies with
To a man who has once mastered the
subject, of course,
no such
difficulty
can occur
;
it is
only with beginners it is possible, and it is mentioned here because these examples are intended for their benefit.
It is also a trouble to beginners to find themselves
so often face to face with that perfectly intractable 19.1,
which appears
We
out of place. figures,
but
it
is
to
have jostled the original
know
the change
is
made
.",7.:;
to save
at the expense of sacrificing unity.
Tme, we shall walk down our 1 slope for 19.1 yards before we shall find ourselves one foot below our starting-point,
and the
figures
and the reason
for
adoption are clear enough to the ordinary surveyor; but I have found that the original rule has far more hold on the student's mind, and that their
INTRODUCTION.
1 1
an end when he is taught that in one unit vertically he must measure drop fifty-seven units horizontally down a slope of 1.
all difficulty is at
order to
In working out these examples do not be in a hurry, do not try to make a pretty picture and get the thing done in each example is wrapped up the ;
more standard rules or forimportant to learn and to underAbove everything accuracy must not be
application of one or
mulae which stand. sacrificed
to
it is
pictorial
effect;
when the sketch
is
inspected the dividers will be applied to the various distances shown, and marks of approval will be in proportion to the difference between those on the sketch and those on the original.
Another
Look out
hint.
for
your triangles
!
Ee-
member
that the solution of most of the problems in Military Topography depends upon that of a right-
angled triangle.
always easy
and
sides are given,
First find out your triangle not this found look out which of the
and
if
there are two such, the third,
representing the x of the
puzzle,
is
easily forth-
coming. Again,
when
"
section lines," or traverses
following
which changes of height occur, mark each change in order by the formula, by which the exact vertical height is found and a secure starting-point is gained in
for further progress.
the slopes
Do
not be content to step
up or down with the
scale of horizontal
equivalents on your protractor, that
is
well enough
1
INTRODUCTION.
2
rough out-of-door work when no examiner with his dividers will have the last word
for adepts, or for
in the matter.
In the following examples, those in Part I. deal with elementary problems in intersection, resection, the use of the formulae to ascertain heights and disThose in Part II. tances, and plotting easy ground.
show how to book, more
down in the fieldwhen taken across uneven
plot the notes jotted
especially the ordinary field-book problems are not given here as those in the text-books are always " In Part III. " form lines and " section available.
ground
lines
"
:
are
worked out and
their use fully explained.
Part IV. takes the learner on to more advanced ground, the sketches being framed to include in each
example most of the foregoing rules. Lastly, in Part V. two examples of sections are given, which are quite simple, but require considerable care to render with accuracy. The plans have been executed as they would have been had they been finished in the field, sufficient accuracy only being aimed at to enable the officer requiring
ground
them
to read
the configurations
of
the
represented for military purposes. \V.
E.
MONTAGUE.
13
PART
I.
I.
A, B, C, are hill-tops overlooking a lake which lies and bearing from that central point
in their centre,
15, 135, 255. Their summits are respectively 70
respectively
ft.
above datum level
;
ft.,
130
the lake being 30
ft.
ft.,
90
above
the same point. Slopes taken to each hill-top from the lake are
1|, 4, 2
respectively.
Plot the above.
Scale
TTTT^IT.
normal contours.
II.
A B S.
is
a
hill- top
100
ft.
above datum
level.
and C are under-features on a spur stretching A distance of 500 yds. hill.
from the main
MILITARY TOPOGRAPHY.
14
between is
40
D B
;
ft.
A
and B, and
lower than the
B
and C
hill to
;
each imder-feature
the X. of
it.
another under-feature of the same height as from it bearings were taken to B 300, to C 240. is
The
between
col
those between
B
A
B is B and
and
and C, and
Plot the above at 6
in.
65
ft.
below
A
;
D, 45 ft. below 15. to the mile, normal con-
tours. III.
A
stream winds through a valley in a direction bearing 215 for a distance of 1000 yds., its average fall
*V
A, B, C, are hill-tops on either side. From the head of the stream the bearing of A is 245, the angle of elevation 4, slope concave and ;
from the mouth
of
the stream
C being 60. From A the bearing of C From C the bearing of B
it
bears 357, the
bearing of
The angle stream is 4.
C and B
of elevation of
are each 40
ft.
is
120.
is
33.
B
from the head
of tin-
higher than the head of
the stream.
The
col
between
B and C
Plot the above at 6 tours.
is
in. to
55
ft.
above
sea-level.
the mile, normal con-
ELEMENTARY.
15
IV.
A
stream
rises in a valley at a point
the sea, into which
A
and
B
ft.
60
ft.
above
flows in a direction due S.
W. and
are hill-tops
of the stream,
40
it
E. of the source
each 250 yds. distant from
it,
A being
lower than B.
The angle of depression from distant, is 4.
From B
A to
the sea, 670 yds.
a spur stretches southwards to the coast
;
two under-features, connected by cols C and D, each one 40 ft. lower than the one to the N. The angle of depression from B to them 3. on
it
Plot the above at 6
in. to 1 mile,
contours normal.
V.
A
is
a hill-top
which sends a spur due
S. to
the
sea.
B is an under-feature on it, distant from A 382 yds., and 60
ft.
above the sea-level.
The angle of elevation from B to A is 3. The col which connects B with the main hill of B. ft. below, and 180 yds.
is
36
K
Contour the above, scale 12 intervals 12 ft.
in. to
1 mile, vertical
MILITARY TOPOGRAPHY.
16
VI.
A, B,
Two
A and
C
are hill-tops.
streams rise midway between
A
and C, and
B, uniting at a point D, 300 yds. S. of A, and
continue in that direction at a
fall of
TV.
Bearings from
A to A B Angles
..
B,
155.
C,
222. 280.
C, through D,
of elevation
D D D The heads
to A,
6.
B, 6. C,
4.
of the streams are
30
ft.
below
B and
C.
Contour the above at 12
in. to
the mile, contours
normal.
VII.
From
the extremity of a cape projecting into the sea you pace due N. up a slope of 2 for a distance of 300 yds. to a small plateau 50 yds. across. You
continue to pace
down the northern
knoll, still going N., the angle of
same
as before, for
same direction on
143
level
yds.,
slope of this
depression the
and continue in the
ground
till
the hills
A
and
ELEMENTARY.
B
W.
bear E. and
elevation
to
A
of
17
your position
being 4,
marked on the Ordnance
B
to
map
6
the angle of
;
the latter
;
as 60
ft.
is
above sea-
level.
From to
A
the centre of the knoll bearings were taken,
30,
to
B
327.
Plot the above, scale 12
in.
to the mile,
normal
contours.
VIII.
Being desirous to plot and contour an isolated hill you proceed to the summit, which is formed by a plateau stretching 300 yds. N. and E.
and W.
your
initial
lay out
"
and 150
S.,
yds.
The edge of this plateau you take as contour, and from a central point on it
section lines
"
A, B, C, bearing respectively
40, 160, 280.
You then
pace
down each (
Line A,
{
as follows
238 yds. at 6 Atro
I
slope.
O
II
_
5
it
ft Cl Ct
AO
II
**
:
4
II
(I
O
II
II '
2
716
1 i
n
Plot in the above, scale 4 contours.
B
in.
ii
to 1 mile,
normal
MILITARY TOPOGRAPHY.
18
The summit
of
an island 100
ft.
above the sea
forms a plateau about 350 yds. across, the S.E. edge broken inwards by the head of a valley in which is a stream which joins the sea at an average
An
under-feature, 20
ft.
connected with the main
fall of
TV.
below the summit and
by a
hill
col
45
ft.
above
sea-level, bears from a central point on the plateau
157, the angle of depression to it 1. Slopes on and W. 10. the E. of the main hill 2|, on the
K
Plot the above at 6
in. to
a mile, normal contours.
X.
A
and
B
are hill-tops on an island.
C and
D
are under-features.
Bearings from
A to A
B, 107
B B
D, 135; 2. C,
The sea
C,
;
distance,
500 yds.
68. 760
i.
is
1200
yds. S. of B.
190
,t
400
..
200
i.
W.
D. of
A.
N. of C.
ELEMENTARY.
The and 70
col ft.
between
A and B
is
230
1
yds. distant
9
from
below the former.
Angles of depression from B to D, 3.
A
B,
1.
B
it
C, 3
D
M
the sea, 7.
Plot the above at 6
in. to
.
a mile,
normal contours.
21
PART
II.
THE FIELD-BOOK.
XI.
The following traverse was taken across some low hills plot and contour a plan from the entries, scale ;
>
normal contours
Forward angle 60.
A to B
:
MILITARY TOPOGRAPHY.
22
xrr. 628 481
Fall
evel.
441
Rise
2.
299
Fall
3'.
7.1
closing angle on (T) 270
9;
Level.
180"
ffl)
330
Level.
310
Rise 8.
238
Level.
198
Level
158
Fall
50
stream's source,
;
fall -fa-
7.
Level.
90
(n) Level.
Rise 7. Rise 5
s .
Rise 3\ Rise.
2.
Rise 2
;.
stream 150 yds. 90.
Plot the above entries in a field-book; scale 12 inches to 1 mile, normal contours.
23
THE FIELD-BOOK. XIII.
50^
to
A
180.-
800 360
spur 203*
150 125
140
260 100 49"
to
A 134"
(n) 560
slope
4'.
150 136
(T)
A
tract of hilly country three-quarters of a mile is
square
to be represented
on a plan three inches
square.
The from
and a ridge stretching
features are a plateau
it,
both 250 feet above datum level; an under-
with the main hill by a col, a a in and is a stream. which Angle of spur, valley from the of the depression extremity ridge to A 2|, feature, A, connected
to the col
320 yds.
distant,
6.
The above traverse was made ridge
commencing
in the
Sketch the above to
of the plateau
N.W. corner
scale,
and
of the ground.
normal contours.
MILITARY TOPOGRAPHY.
24
XIV. 1800
100
1650
1300
angle of elevation
B3
angle of elevation
700
150'-:
360"
'4*
Plot the above traverse
of
D 2.
an unenclosed road
winding through a valley between B, C, D, hill-tops, from sea-coast to sea-coast, the highest point upon it
45
feet
and
D
above the is
sea.
B
is
20
feet higher
than C,
10 feet higher than B.
Scale 6 inches to the mile, normal contours.
THE FIELD BOOK.
25
XV. 608 417
-t
341 150 33*
1310 slope 3
100)
slope 7
1210
1019 637
382 7
Plot the above traverse of a footpath crossing an Scale TTTSW? normal contours.
isolated hill.
What contours
What
are the angles of the slope between the ?
is
the general gradient of the path in going
up and coming down the
hill
?
MILITARY TOPOGRAPHY.
26 rl
^
THE FIELD-BOOK.
27
XVII.
32.3
215 337
C
(Hi)
480 36"
(it)
286 337
(l)
Plot and contour the above entries in a field-book of a road
winding up a valley to a pass between two
hill-tops.
Scale 12 inches to
1 mile,
YI. 15
feet.
28
XVIII. [.
MILITARY TOPOGRAPHY.
THE FIELD-BOOK.
29
XIX 1146
955
860
765
620
526
382
286
60
(T)
Plot the above entries in a field-book of the traverse of a road winding from the coast
up the
side
1, and put in the contours vertical interval on the right of the road
of a hill, general slope at
10
ft.
normal
scale.
;
MILITARY TOPOGRAPHY.
30
XX. Coast 328*, slope
T
5
133"
180.
270, slope
-
3T
10"
Plot the above entries in a field-book of the initial
overlooking the sea, and fill in the contours to the sea-level on the south scale 4 inches
contour of a
hill
;
to 1 mile,
normal contours.
THE FIELD-BOOK.
XXI.
Crest
31
32
XXII.
MILITARY TOPOGRAPHY.
33
PART
III.
FORM LINES. XXIIT. A, B, C are hill-tops on a ridge to the N. of and Streams rise under A parallel with the sea-coast.
and
in the cols
at the
head
on either
side,
and
the sea
fall into
of
sandy bays. a point S at the head of one of these bays, is 360, distant here 100 yds. across, the bearing of
From
A
1020 yds. Bearings from
A
to B,
266
;
angle of depression, 1
;
distance,
;
distance,
760 yds.
A to C, 78^
;
angle of depression, 1|
760 yds. Cols between
A and B, 420 yds. u A C, 525
from it
c
A ii
;
;
slope,
5.
4
e .
MILITARY TOPOGRAPHY.
34
General slopes to the sea south of
and 2
The
B and
of C,
."
respectively.
central
bay
is
about 600 yds. across at
its
entrance.
The following
"
section lines
"
were taken
:
A to F, bearing, 202. A to D, 190 yds. slope, 5. D E, 1050 1. ;
..
E
A to G
F
M
on the
sea,
350 yds.
G, bearing, 137 to
H
ii
f
382 yds. slope, 3. dist., 382 yds. slope, 1. ;
;
;
115
the sea, bearing,
Scale, 6 in. to 1 mile,
3.
slope,
dist.,
;
H, bearing, 164
K oil
;
198;
2.
..
1.
slope,
normal contours.
XXIV.
A its
a hill-top 90 ft. above sea-level, and from " " section lines were taken to the coast, as
is
summit
follows
AB 3.
AD 6.
:
H, bearing, 180. B to H, slope, 2. E G, bearing, 135.
D
to E,
82 yds.
;
A
to B, 190 yds.
;
slope,
A to D, 134 yds.
;
slope,
slope,
7.
E
to G, slope,
8.
AF
K, bearing, 230. A to F, 115 yds. 8. F to K, slope, 10.
;
slope,
FORM
35
LINES.
Plot and contour the above under the following O conditions
:
Scale of plan, 12
Contours at 12 Calculate
the
in. to 1 mile.
ft.
vertical interval.
E and F
of heights o
above high o
water.
XXV. From
the top of a spur the following section lines
were taken
A A
1.
2.
:
General slope, 5. to B, 760 yds., slope, 4. 380 yds., depression, 1
A
(300 yds., N. and
C
A
3.
A
to
yds., depression,
slope,
A
to B,
290
2|. 1275
f
;
to
level,
3.
yds., slope,
C
C
;
D
B
knoll,
200 yds. ;
C
to
to C,
knoll,
;
D,
380
300 yds. fall to D, 5 for 135 yds. 5 for 1070 yds. to
;
;
General slope, The points D are on the datum 5.
yds.,
290 yds.
fall to C,
;
knoll,
50
yds., depression 2
yds., slope, 2. level, 300 yds.
A
C
level,
;
D, 380 yds., slope, 4. B B, 380 yds., slope, 2.
fall to C,
4.
to
to
255
A
S.)
B
level.
Plot and contour the above, scale ^TI^TT* normal contours.
Calculate the heights of the three knolls.
MILITARY TOPOGRAPHY.
36
XXVI. A, B,
C
are hill-tops on an island.
Bearing of
B
Bearings of
from A, 17
A
and
B
;
distance,
350 yds.
respectively from C, 252,
305. Angle
of depression "
From C
a
coast, as follows
yds,
4; E
The
from C to A, 3 to B, 2. " is taken due E. to the ;
section line
to F,
:
C
175
to
D, 110
yds.,
yds., 6
;
D
to E,
180
3.
coast-line is indented
by bays stretching inA and B, A and C, between midway is The head of the bay between A and
land to points
B and
C.
1'.
formed by a
The
sea
is
cliff
20
ft.
high.
200 yds. north of B, and 100 yds. south
of A.
south of C, 8. Slope north of C, 10 Plot and contour the above at a scale of 12 ;
the mile, normal contours.
in.
to
37
PART
IV.
ADVANCED SKETCHES.
XXVII.
A 2270
down a
stream, after winding yds., joins the sea
eral direction,
A and
C
From
the
;
its
valley for about
average
fall
yy^
;
gen-
153.
are hill-tops,
mouth
from a point 40
ft.
The bearings
of
B
an under-feature of C.
of the stream,
A bears
292, and
higher up 201.
C from
A and
from the stream's
source are 24 and 85.
From B source,
The
A
is
240
750 yds. south
of
A.
the bearing of
;
of the stream's
309. sea
From
is
A the
the clinometer:
following angles were observed with to B, depression, 1; to a rock in
38
MILITARY TOPOGRAPHY.
the sea marked on the chart as depression, 1
;
to C, elevation,
H
mile distant,
1.
Plot and contour the above at a scale of 4
in.
t<>
the mile, normal contours.
XXVIII.
A tract of hilly country about 1800 yds. square. A lake,, about 150 yds. across, lies in the centre of three hills, ABC. A stream leaves it on the S.E., average
fall,
TV.
From the centre of the lake A bears 314, B bears and from the shore the distance 70, C bears 225 to A is 900 yds., to B 800 yds., to C 1100 yds. ;
The angle
of elevation
from the lake to
A
is
5,
but the slope is only 3 for the first 380 yds. is 100 ft. higher than B, which is 175 ft. lower
A
than C.
Between ft.
A and
B, and
A
and C, are
cols each
100
higher than the lake. Plot the above to scale so that the distance be-
tween the shore of the lake and the hill-top C shall occupy 2| in. on the plan. Contour the plan on the
normal
scale.
XXIX.
A
lake, its shores irregular, thrusting themselves
into the valleys between the six hills A, B, C, D, E,
ADVANCED SKETCHES. F,
which enclose
it
;
cols,
25
39
above the lake, con-
ft.
necting the hills one with another.
Distance from
A
to B,
Depression to lake.
Bearing of to B, 50
A A
600 yds.
5
from
A
(same level as D).
C, 106 C, 205
5
D, 310 D, 255
10
E E E
A, 186
8
E,
F, 133 B, 98
6
F,
F
A, 255
i
B
B, distant 190 yds.
C (same
level as B).
D, distant 230 yds. 190
5
..
127
,.
Plot and contour the above at the same scale as that of a combined survey of which
it is
to
form a
part.
On lost
arriving on the ground
your note-book in
You can
only
call to
on the normal
You
are
you which the
mind
that
it
find that
scale
was
you have
was entered.
to be contoured
scale.
able
to
ascertain
the position of five
consecutive contours by marks left on the ground,
the slope at that point being 5, and the distance
between the whole
you
find to be
of the
152 yds.
marks on measurement
40
MILITARY TOPOGRAPHY.
XXX.
A
stream
rises
under a
hill
A, which
is
1250 yds.
N. of an inlet of the sea into which the stream flows.
A
A
section line from
yds., 6
B,
4
slope; 480 yds.,
distance to the sea, 2
bearing 180
The remaining
slope.
slope.
an tinder-feature
A, bears from
of
700 yds. angle of depression, connecting it with A is 18 ft. below B. distance,
C
288
gives
;
2.
it
213
The
;
col
an under- feature of B, and bears from it 180 The distance, 800 yds.; angle of depression, 1|. is
;
col connecting it
From C From
with
to the coast,
B
due
is
S.,
30
ft.
above the
the slope
is
sea.
7.
A
a narrow ridge runs in a direction 140 for 600 yds., when it opens out into a plateau, covered
with heath,
general direction 180 for 600 yds. it is 300 yds. across at its widest part. Slope from its southern crest to the sea, 10. its
;
Plot the above, scale 6
contours at 20
ft.
in. to 1
mile,
and
fill
in the
vertical interval.
xxx
r.
A
stream flowing in a direction from N.N.W. joins At 1), where it the sea, having an average fall of ^ .
ADVANCED SKETCHES.
41
100 yds. wide, gradually narrowing to 50 yds. 300 yds. from its mouth. Here it is crossed by an iron bridge over which a road leads to enters the sea,
it is
the church at a gradient not exceeding 3 another road follows the right bank of the stream up the ;
on one side of
valley, a line of telegraph
the
W.
stream where
of the
it
On
it.
enters the sea
is
a
small village.
The
into cliffs
D
from
A D
is
22
and
70
B
is
ft.
marshy, but
The church, on a depression to D, 4.
high.
angle of
;
is
75
ft.
500 yds.
W.
hill
A, bears
which bears from
The
4.
stream
col
between
A
below A.
a point 1340 yds.
94 and
rises E. of the hill
angle of elevation,
;
B
40
is
an under-feature of B, a
From of
W.
coast
of
A
up the stream the bearing
134. head of another
of this point is the
valley through which a stream flows
stream at the village, average sides covered with oak-trees. Plot the above at 6
fall to
to join the first
D
in. to 1 mile,
J^, the valley-
and
fill
in the
contours at the normal intervals.
XXXII.
A
hill
A
is
due W.
of another hill B, each
above a small lake which
lies
between them.
120
ft.
MILITARY TOrOGUAPHY.
42
A its
stream leaves the lake on the
course due S.
A point H streams join bears from
From B
;
its
average
fall
S.,
and continues
V
5
on the stream marks where two smaller from the
it
A
155, from
hills to the eastward,
a spur stretches in a direction 150
under-features
and
B 204.
C and I) on
it,
;
two
connected by cols with
15
and with each other; a distance of 350 yds. between B and C, and C and D; angle of depression from B to both,
3.
Streams
rise
below these cols and join
the main stream at H.
From and
B
the lake-shore the angles of elevation to
are 5
and 7.
becoming
first,
The
A
steeper as they ascend.
Plot the above, scale 6 it
slopes of
A
are gentle at
in. to
1 mile,
and contour
according to the normal system.
XXXIII.
A
lake,
S., lies in ft.
about 400 yds. E. and W. and 200 N. ami the hollow of some hills, at a height of 90
above datum A, B,
ridge
;
and
D extreme
points of a
K a knoll, its summit circular, about
;
across
level.
E are hill-tops C
;
F and G
on either side of
80 yds.
streams which rise under the cols
B and
flow into the lake.
stream leaves the lake on
its
Another
southern side at a point
ADVANCED SKETCHES.
M with a uniform
full of yV,
43
and a fourth stream quits
the basin at H, flowing S.W.
M
is
in the direct line
between
I)
and K, 700 yds.
distant from D.
B, 275.
Searings fram D, C,
G, 300.
360,
Bearings from K.
distant 900 yds.
2.
E, 256.
E,
K, 282. A, 302.
H, 240. Angles of
B, 321. F,
K K
314.
G, 346.
to B,
elevation.
2.
A, 3.
M
E, 4.
Searings from A.
Angles of depression.
H, 173.
K to M, 2. Bearings from E,
D
C.
B B
227.
K, 239. A, 273.
E
Plot the above, at 6 contours at 20
ft.
in. to
..
Y, 2f.
M
G, 2.
11
H, 8
1 mile,
vertical interval.
M,4.
M
.
and put
in the
44
MILITARY TOPOGRAPHY.
XXXIV.
A
stream rises at
A
midway between two
B
and C, east and west of it, and each 100 slopes from A to B and to C, 4.
Two narrow
B and
spurs start from
hill-tops
ft.
higher
C, falling
1
;
.1
1000 yds. to F and E, and bearing respectively from B and C 140 and 160. The sea is 300 yds. S. of E, the coast rising in a for a distance of
cliff
40
ft.
The sea
high.
is
600 yds. E.
The stream has an average direction 157
for
500
V
fall of T
where
I'..
A
in a
meets the northern
yds., till it
slopes of the knoll D,
of
from
it
divides, one half
flowing S.E. into the sea a distance of about 1400 yds., falling in that length 50 ft.; the other half circling
W. and
D
round
S.
till
it
loses itself in the
marshy ground on the coast 200 yds. S. of D. From the summit of D the bearing of C is 317, of
B
25
;
the angle of depression to the point where
the stream divides,
Hot
5.
the above at a scale of T u!*ff> an d contour
it
on the normal system.
XXXV.
A
stream
rises
on the
S. of
crest of a small plateau
and flows down a valley
250
and 20
ft.
ft.
below the
above the sea-level,
in a direction bearing
210
ADVANCED SKETCHES.
45
730 yds. at an average fall of ^. Here a second stream joins it from the N. and W., the ground at this point marshy, and the two united flow round the
for
slopes of the hill
A
till
they join the sea about 400
yds. S.E. of that hill.
From
the
A
being 50
where the streams unite the
point
two
bearings of
ft.
A
hills
B
and
B
and 30
ft.
are 126
and 278,
higher than the ob-
The bearing from the same point to the col between A and B is 215, distant 200 yds. angle of elevation, i. From this col the angles of elevation to A and B are 2 and 1 respectively. server's position.
;
The sea
is
325 yds.
S.
of A,
and 360
yds. S. of
B.
At
a point on the main stream 180
sea an under-feature
angle of elevation,
The
C
ft.
above the
bears 312, distant 400 yds.
;
|.
B
and C
below B, and the col connecting the under-feature C with the plateau is 20 ft. below C. col
between
is
Plot the above at a scale of 6
20
ft.
in. to 1
mile,
normal
contours.
XXXVI. B
is
an elevation at the head of a valley in which is 1000 yds. S. of a
a stream flowing easterly, and hill-top A.
is
46
MILITARY TOPOGRAPHY.
C
an under-feature of A, the bearings from 73 and 139.
is
it
to
A and to B The
A
stream
source 80
B
from
is E. and W., and at 220 yds. from that height. in the valley between A and B, its
direction of the sea-coast
B
a point S. of
is
rises
above the
ft.
sea,
33, and flows S.W.
A
141, bearing from it enters the sea S.
till
of C.
A
From
and from
B
the angles of depression to
the source of this stream are 2
From
A
40
below
400
ft.
and 1.
the angle of depression to
A
yds. across
;
is
in
C
is
1.
a spur forming a plateau about it is a lake, a stream leaving it
on the E. and flowing down a valley in that direction another stream rises under the col between A ;
and C, and enters the sea main stream.
at the
Plot the above at a scale of 4 in the
same point
in. to 1
mile,
as the
and
fill
contours at the normal intervals.
XXXVII. From
the mainland you wish to
make
a survey of
an island to which you cannot gain access because of
a channel, called the
"
half-mile water," on account
of its width.
On an
old chart, not
drawn
to scale,
you
find the
ADVANCED SKETCHES. Thus the
heights given.
hill
47
from which you intend of the two ft.
marked 300
to conduct the survey is
;
peaks on the island, that on the N. is marked 90 ft., that on the S. 70 ft., the col connecting them 30 ft. In appearance the island consists of these peaks, the slopes to the sea on the
W.
on the E.
steep, those
very gentle, stretching out into two low points, which them a bay.
enclose between
The slope the base a
on which you stand
of the hill
cliff
about 100
ft.
From
high.
the following observations are taken
the
10, summit is
:
Bearings to
Northern shore Southern
of island,
n.
N. peak S.
64.
n
118.
n
75. 109.
peak
91.
Col of depression to
Angles Eastern extremity of N. peak, 2|. n
S.
ii
peak, 2f.
Plot the above at a scale of 4 fill
in the contours according to the
in. to 1 mile,
normal
and
scale.
XXXVIII.
An
irregular
ridge,
heads of two valleys,
indented on the
lies to
S.
by the
the N. of and parallel to
48
MILITARY TOPOGRAPHY.
the sea-coast, which here stretches E. and "W extremities of the ridge
marked by
cairns
;
the
C and D.
A
and B, knolls below the ridge towards the coast, both the same height, angle of depression from B to the sea,
Two yds.
3. streams rise under the ridge at points 180
and 380
from C, and flow southwards,
yds.
uniting towards the E. of A, and then falling
S.
till they join the sea. General slope of the watersheds, 2.
again
A line
200 yds. apart, folthese are marked X and Y,
of telegraph, the poles
lows the coast; two of the former "W. of Y.
Bearings.
C
to
A B B
an old
C,
333.
D,
to
map
was attached.
50.
A, 360. B, 327.
A,
45.
B,
5.
of elevation
The plan of
95.
0,350.
Y to Y X X Angle
D,
from
B
to C,
.
be executed on the same scale as that of the
On
same ground it,
to
which no
scale
however, you find that the
ADVANCED SKETCHES. distance between
A
and
the ground you find distance
as
you
nature of the
Hot
it
it
B
is
1.6".
49
On
arriving on
impossible to measure this
intended,
owing
to ,the
broken
hills.
the above on the required scale, and contour on the normal system.
51
PART
V.
SECTIONS.
xxxix. Draw
a section of a hill from the following data Scale for horizontal distances, TITBITvertical
it
M
Vertical interval, 12
A
T |- T
4 in 200 yds. of 6 ft. in 100 yds.
to B, rise of
B
C, rise
C
D, level for 80 yds. E, rise of 38 ft. in 200 yds.
D E
,.
F
G
.
ft.
F, fall of 15
ft.
G, rise of 18 r,
H
H,
rise of
I, fall
33
down
I
n
K, level
K
n
L, rise of 25
for
down
ft.
for
ft.
for
a slope of 3.
225 yds. 150 yds.
slope of 6
for
150 yds. ft.,
slope
^T
-
300 yds.
52
MILITARY TOPOGRAPHY.
L
to
M,
fall of
it
N,
fall
M
30
down
for
ft.
75 yds.
slope of 2
for
220 yds.
XL.
You make of
the following notes of a detached hill
which you wish to take a careful section. Commencing on the W., the angle of elevation
from datum level
you come
is
where
2.
You pace up
this slope
till
changes to 4, but have for" " your paces, but a reference point on an adjacent hill gives your height at 78 ft. above datum. Before leaving the point where the slope to
it
gotten to count
changes you take the angle of elevation to the top the
hill
and
find it is
of
5.
You now pace up the slope of 4 for 352 yds., when the slope again changes and continues at this which you find by be 200 ft. above datum.
fresh angle to the top of the hill,
another
"
"
reference point to is a small plateau about 50 yds. across, and the slope on the E. to the datum is uni-
The summit
form at 6.
Draw
a section of the
conditions
under the following
hill
:
Scale of horizontal distance, n
Normal
vertical
scale of contours.
n
53
SECTIONS.
XLT.
Draw last
10
;
tion
a plan of the hill
example. on the S.
due
slope, 7
which
in section in the is
uniform at
is
the slopes which enclose the valley in
it lies
slopes of
shown
the N. the slope
a watercourse running in a direcfrom a point 20 ft. below the summit ;
S. ;
On
bearing about S.E. and S.W. at uniform
4.
Scale the
same
as that of the section.
55
NOTES TO DIAGRAMS,
i.
SIMPLE exercise in finding the size
taken from intersect
HE
by the formula.
The
immaterial, as the slopes would be its shore at points where the three bearings
of the lake
is
it.
II.
Easy example of resection to
fix
the position of D.
III.
head of the stream being found by A can be found, the distance and The position of B is found by slope being also given. calculating the HE between it and the head of the stream, and marking where this distance cuts the bearing taken to B from C.
The height
the
fall
of the
given, that of
IV.
An
HE
easy example of finding the heights, the slope and
The cols should be taken The fall of the intermediate to contours. heights stream and slope from to the coast can be assumed. of one
(A) being given.
at
D
56
MILITARY TOPOGliAI'IIV.
V.
The
scale not being normal, it
must be drawn on the
sketch.
VI.
An
exercise in finding the height of hills by the forof plotting in contours where several valleys
mula, and unite.
VII.
N
The point which
the
"
section line
"
followed arrives at
Find the II K above the sea. of B from this level (slope and VI given), adjust your compasses to this distance, and when they cut the bearing of B from the knoll, being placed at right angles to the of the knoll
is
15
ft.
"section line," the position of B is fixed. The line thus it being produced to the right iixes the position of A, when its height can be found by the formula. fixing
VIII.
An
example of "form lines" marking the change of " " on a section line that on A occurring at 2^ slope contours, on B at 2J contours, and on C at 3| contours from the highest contour. IX.
An
example of
filling-in a small space
with several
a plateau, a valley, a col, an To produce a satisfactory under-feature, and a spur. sketch the head of the valley must make a considerable indentation in the plateau at the named point. conventional signs
e.g.,
NOTES TO DIAGRAMS.
57
X.
Easy exercise in
None
the formula.
they
may be
plotting, and calculating the VI by of the summits are on contours, so "
indicated
form
by
lines."
XL An easy example of traversing in a hilly country; the traverse should close on D. XII.
The
entries
mark the contours on "
a "section line" "
up
to the top of the hill at II, a form line marking one If the work is done carefully the final station station. will close on I.
XIII.
The scale is found by comparing the size of the plan with the area of the ground to be sketched, f of a mile is to be represented by 3 in. e.g., 4 in. to the mile.
The cated
plateau not falling on a contour by a "form line."
The lowest part above datum
of the
must be
indi-
ground shown will be 90
ft.
level.
XIV. The positions of B and D are found by finding the HE from the points on the traverse line from which the angles of elevation are taken, setting the compasses to this distance and marking where they cut the bearings
MILITARY TOPOGRAPHY.
58
None of the points marked on the trim-inon contours, so care must be taken to find the exact height of the spot whence the heights of U and J) are taken. The col between C and 3) is taken in tinsketch at 45 ft. from
I.
line are
XV.
An example of contouring a road, the sketcher noting The slopes are 1, 1|, 1, a station at each contour. 2, and 2, 2, 5, 2. The general gradient by calculating the height over the distance.
is
found
XVI. The
initial
contour
taken 25
is
ft.
below the highest
point so as to show more exactly the general shape of the hill. It is traversed with great care and "section lines" taken
down
the principal features.
XVII. The added
scale not being normal, a scale of slopes
must be
to the plan.
XVIII.
An
example of a road carried up a slope at a gradient than the slope. The height of I station must be assumed at above 0, otherwise the river when crossed by the road will be a minus quantity. The shape and less steep
size of the ridge are
only roughly shown by the bearings, it lend themselves to several
and the contours W. of modes of rendering.
NOTES TO DIAGRAMS.
59
XIX. The
zigzag lines represent the windings of the road, " " section lines taken down the hill at
the arrow-heads are right angles to
the traverse line.
contours on the traverse
line,
First
mark
the last will be
off
the
60
ft.
The road
in one instance only cuts one of these, so in calculating the slopes care must be taken to allow for the " " fraction of a contour from whence the section line starts.
XX. The
irregular line represents the initial contour,
its
height above the sea found by the distance and slope The height of the knoll viz., 120 ft. given from IV is found in the same manner.
XXI. The by the
drawn and its height determined which can be assumed at any height
crest line being rise
from
I,
above datum level, the lowest point of the stream found from IV.
is
XXII.
An
example
of
the use of
"
reference points."
At
III three points are found to be on the same level as The height of III is not known, but the observer. that of the N. bridge can be found by the fall of the
stream to be 120 ft., and as that is one of the points on the observer's level, it follows that III is at 120 ft.; and B, and station I. also the col between
A
MILITARY TOPOGRAPHY.
60
XXIII.
An
" example of form
"
used to denote a change found by working up fmm F the intermediate heights at E and D, also that of A, being found by the formula. The heights of G and H should be found in the same way. of slope. the sea at
The height
of
lines
A
is
;
XXIV. "
" form lines Easy example of marking a change of The intermediate slope. points B, I), E, and F should have their respective heights calculated by the formula ; the distance to the sea from B, E, and F can be found in the same manner. As the scale is not normal it must be added to the sketch.
XXV. "
" example of form lines showing features intermediate between contours which otherwise would not The height of A is obtained from section line appear.
An
A
5.
XXVI.
An
exercise in
" " form lines to indicate a change of
The height of C is found by the slopes and disslope. " tances given by the section line," then the heights of A and B can be found. Care should be taken to show the indentations in the coast-line.
NOTES TO DIAGRAMS.
61
XXVII.
An
example of intersection and resection. The height being found from the rock in the sea which is assumed to be ft., the other heights follow. of
A
XXVIII. The scale is found by making a length of 2| in. on the plan, equal to 1100 yds. on the ground. The lake must be assumed at a sufficient height above datum The
level to allow for the fall of the stream size of
the plan will be nearly 4
in.
on the S.E.
square.
XXIX.
An
example of intersection and
of the hills found by the formula.
resection, the heights The lake is taken as
datum.
XXX. "
" form lines example of marking a change of of The and slope, slightly more difficult contouring. " " height of A is found by the section line to the sea. The
An
cols
should be placed so as to make the contours of the
main valley
fit
in neatly.
XXXI.
An
example of the use of conventional
signs,
and
of
calculating the value of the points of the compass in N.N.W. is the second point from N, each degrees.
62
MILITARY TOPOGIIAI'IIV. r
point being WOlth llj
from culated from lit-
]).
:$:57
I
The
;
the bearing <>f tin- sin-am of the streams must lx: cal-
fall
).
XXXII.
A
more advanced example
several valleys meet. The distant will be the point H. are found
marking
by calculating the
of filling in contours larger
the lake
nx in-
A
The
HE
where
the
and 11 positions of from the lake-shore and
this distance along the bearings
from
it.
XXXIII.
of
The bearing 282 taken through D its distance is 700 yds. E. ;
should be
left till
M gives the of
M.
direction
The
the surrounding contours fix
K
knoll
its
shape.
XXXIV. The
distance of
B and C
from
A
is
found by the
1
1
!'..
A
the height of slope and VI being given by calculating the fall of the stream to the sea in the S.E. corner. ;
The knoll
D
is
found by resection, and requires care in
filling in the contours.
XXXV. The point where the streams unite must be its height noted. The main stream
found and
carefully
two below the plateau. An example of working with fractions of a degree. A good deal of the position of the contours is left to the draughtsman. half contours
rises
KUbLKl W. VVbbD OGY DEPT 63
NOTES TO DIAGRAMS.
XXXVI. The 90-foot contour forms the edge of the plateau, the position of the lake on it has always seemed to be the difficulty of the example.
XXXVII. Aii example of surveying an inaccessible object. The western slopes of the island can be assumed, in the sketch 12 is taken. The eastern extremities of the island are found
by calculating the the hill on the mainland.
HE
from the top of
XXXVIII. To of
find the scale,
make an independent
triangulation
A and B from the base XY at any convenient scale
;
this
RF
gives the distance between them in yards, when the can be found and the sketch made on that scale, begin-
The heights of ning as before from the base XY. B are found by the slope from B to the sea.
A and
XXXIX. There is no difficulty in this problem, only care must be taken to mark the exact spot between contours where The vertical the vertical distances cut the uprights. scale is the GO on the Marquoise Scale. If properly worked out the slope ending at N" should be on the same level as A. The highest point is 122 ft. above
datum
level.
64
MILITARY TOPOGRAPHY.
XL. The
horizontal distance for the initial slope is found From this point ft., and the slope 2.
by the height, 78
the distance to the top of the hill is found in the same way. The intermediate point, to which the slope is 4, is found by calculating its height, the horizontal distance
and slope being given, and adding the result to tinThe scale for height of top of the first slope, 78 ft. vertical heights will be found to be 12| on the 50 Marquoise Scale.
XLT.
A
datum
line
must be drawn
of the
same length as
that of the section, the points on it which the contours cut being dotted off on a slip of paper and transferred to this datum line for the plan, care being taken to number
The them according to height. the summit can then be dotted
slopes N.
traced round the central hill-top. section of a plan reversed.
It is merely to take a
I'Kl.NTKD
in,
and S. of and the contours
BV WILLIAM IH.ArKWOOD ANFI SONS
-..
Seal?.
Toseo:
VI.
20 feet.
Scale,
-nrhnr.
W. 20feet.
TEE.
too
rentes.
VI.
20 feet
iv:
Scale
wb:
W.
ZO feet.
V.
Scale..
3'
of Horizontal,
72*80-
W. 12 feet.
VI.
Scale,. -TT&O
VL 10
feet,
Scale,
s-iao:
VI.
W feet.
Scale
/3-zfor
VI 3Ofi>?t
IX.
Scale,
Tsfar.
VI.
20 feet
H
VT
20 feet.
xir.
7^ "to J
Contours
XIII
Scale,,
is a 40.
VI.
30 fee>.
.8
-5
Scale.
JvAr
VI.
20 feet.
Scale,,
ins-go
Vf.
Z0 feel..
Scale
VI /(/>,.(
60
xrx:
Scale.
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3Ofiet
XXI
fe:
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20 feet.
4
JKXLV.
Scale.
VI.
IZfeet.
JT
Scale,
.*
of ff.E?
6*
7*
'
IO
Scale
3
inches to /mile,.
VI
W feet
XKV:
Scale
s^ao
VI.
W feet.
230 60
VI.
30 feet
Scale
TSlhfo.
VI.
3O feet,.
XXIX.
Scale
-jihnr.
VI.
JO feet
v
24-0
Scale
Tojsa
W. 20 feet.
160
Scale
TTO n 20 feet.
A. 22
Scale
Ttrfea
VI.
20 feet.
236
Scale.
7of6
W.
20 feet.
A
Scale.
Tzr&zr
VJ.
20 feeL
Scale
-nrhio.
VI
20 feet.
XXXV
Scale,
-n&rv
VI.
30 feet
1
300
Scale
7j**v.
VI.
30 feet.
XXXVTT
A
XXXVI11
Scale,. -*&*.
VI.
36 a* 72
60 48
36 21 13
ScoZe-
fossa.
IXXXIX.
V \
V \ \
\ H nt.Qurs
L
M:
zoo too
160
120
'00
80 SO
745
352
Scale
Ts
Cor
XL.
637
'25 of an.
W
XLI.
UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book
DEC 2 7
QTR
is
DUE
on the
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OCT1
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