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BOUGHT WITH THE INCOME
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SAGE
ENDOWMENT FUND
THE GIFT OF
1891
^..a^:^.:'2L.s..a.
iclVstLii
1357
Cornell University Library
TA
624.T87
A manual of underground surveying.
3 1924 004 585 588
Cornell University
Library
The
original of this
book
is in
the Cornell University Library.
There are no known copyright
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A MANUAL OF UNDERGROUND SURVEYING
Publidhed by the
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FIG.
1.— ILLUMINATING THE CROSS WIRES.
A MANUAL OF
UNDERGROUND
SURVEYING
BY
LOYAL WINGATE TRUMBULL,
Consulting Mining Engineer
E.M.
formerly Professor of Mining, University
of Wyoming; formerly United States Deputy Mineral
Surveyor for Colorado
;
WITH ILLUSTRATIONS
FIRST EDITION
— SECOND
IMPRESSION, CORRECTED
McGRAW-HILL BOOK COMPANY
339
WEST 39TH STREET, NEW YORK
6
BOUVEEIE StEEET, LONDON,
1910
E. C.
CiOPYBIGHT, 1908,
COPYBIGHT,
1910,
BY THE HlLL PUBLISHING COMPANT
BY THE McGeAW-HiLL BoOK COMPANY
TO
HIS
THIS
BOOK
IS
FATHER
LOVINGLY DEDICATED
BY THE AUTHOR
PEEFACE
The author has tried iii this work to meet the often expressed
wish of students, teachers, and practicing surveyors for a book
giving the best of American practice.
As a teacher the author
found it necessary to work up lectures upon mining surveying.
These have formed the basis of this work.
The author makes no pretense of presenting original material.
This book is frankly a compilation from various sources. Articles
printed in the various magazines and publications of the technical
societies have been drawn upon freely, as have also the catalogues
and literature of the different firms of instrument makers.
The descriptions of surveys, or methods of work, given by the
engineers who made them, are reprinted in full, as they were
printed in the publications to which credit is given. They represent best surveying practice, and fulfill the purpose as an object
lesson to the student better in their original form than would a
review or synopsis.
While much of the material given has appeared in print before,
much of it is new; written for this particular purpose by engineers
who are busy every day with the actual underground work. The
engineers of many of the largest mines of this country have kindly
furnished the author with detailed descriptions of the methods in
use at their properties. To these engineers we extend our sincere
thanks. Without their assistance this book could not have been
written.
Realizing fully that there are usually several equally good
of doing a thing, the author has tried to give a description of
ways
the several most-used and best ways of doing each thing, without
allowing his personal preference for any particular method to
prejudice
it.
The author wishes
to acknowledge his indebtedness to the
various instrument makers
who have
furnished cuts to illustrate
the instruments used in underground work. While unable to
thank by mention each engineer who has aided, encouraged, and
PREFACE
Vi
helped to write this book, the author wishes especially to thank
E. S. Grierson, chief engineer of the Calumet & Hecla; R. H.
Britt, manager of the Poorman; Mr. Howard Spangler, chief
engineer of the Portland; Mr. August Christian, chief engineer of
the Anaconda Copper Mining Co.; C. W. Goodale, chief engineer
Boston and Montana; Mr. Howard Eavenson, chief engineer
United States Coal and Coke Co. Mr. Lucien Eaton, superintendent of the Iron Belt Mine; Prof. Mark Ehle, Jr., of the South
Dakota School of Mines; Mr. James Underhill of Denver, Colo.,
and Prof. L. E. Young, director of the Missouri School of Mines.
Our thanks are extended also to the many authors and publishers
who have given their permission to reprint articles which have
been printed before.
This book is expected to be used only with students
Note.
have
an
understanding of Plane Surveying. No attempt is
who
made in this volume to teach ordinary surveying methods or
of the
;
—
theory.
While the work has been cross referenced to a consider-
able extent the reader
Where a
special
is
advised to
method or
make constant
piece of apparatus
use of the index.
is
explained by
another author in a quotation or special article the subject matter
been repeated in the general discussion
such method or apparatus. The index has been made especially
of such explanation has not
of
and complete
so that every item in the book upon any subject
be readily found. For this reason teachers will find it of
advantage to teach by subjects, rather than by chapter or
full
may
given number of pages.
The bibliography of each topic will be
found at the close of each chapter, and should be of use to both
teacher and student.
Loyal W. Trumbull.
DoWNiEviLLE, Calif., March, 1908.
—
CONTENTS
Chapter
....
...
Instruments
I.
—Attachments—Special
instruments — Bibliography.
Transit: Historical— Adjustments
—^Tapes—Repair of
Chapter
Meridian
II.
field
64
—Geographical
solar observation
Underground Practice
III.
.
Chapter
....
.
—Marking—Numbering—
Stations: kinds
ing in dark
^Setting
—Bibliography.
up
transit
—
—
—
92
—Sight-
Carrying the Meridian Underground
IV.
3
transits
...
—Solar attachment—Direct
solution —Bibliography.
Polaris
Chapter
PAGE
.
.
104
—
Traverse
One shaft
Wires
Weights
Three-wire method
Four-wire method Bent line -Vertical sights with ordinary transit
Measure of depth Bibhography.
—
—
—
Chapter V.
—
Secondary Openings, Survey of
.
.
119
—Stopes narrow— Stope-books—String surveys—Estimate of values— Volumes—Mine sampling— Bibliography.
Coal mines
Record of the Survey
Chapter VI.
Field notes
—Note-books— Side
book
of text-books.
—List
Chapter VII.
.
.
—
notes
Office
....
Uses of the Mine Maps
—
—
133
Laws regarding mine maps Uses of the topographical map
logical maps and sections
Old workings Assay maps.
Chapter
VIII.
Paper
—
Making the Map
—Scale—Platting of
—Coordinates—-Bibliography.
Chapter IX.
—
Map
—Geo;
angles
.
—Protractor—^Tangents—Chords
Filing
—
—
153
160
—
Models Erasures Ink and colors Blue-prints: Overexposed, to
write upon, waterproofing of Solution ^Tracing from blue-print
Vandyke prints Copying of drawings.
—
126
—Calculation-
books
—
vii
—
—
CONTENTS
Vlll
PAGU
Chapter X.
Bobe-hole Surveys
169
—^BibUography.
Photography
Chapter XI.
Methods op Various Engineers
175
—Iron mines of Wisconsin—Coal
mine, Wyoming—Calumet & Hecla—Poorman—Copper Queen—
Portland— Old Dominion—Anaconda— Boston & Montana—Coal
mine of West Virginia—Homestake—Vertical shaft
California
—
Detail description of procedure
in
Bent
line
survey
Chapter XII.
^To locate shaft.
United States Deputy Mineral Surveyor's Ex-
amination
224
Problems.
INDEX
.
247
ILLUSTRATIONS
PAGE
PIG,
1.
Illuminating the cross wires
2.
Transit
3.
Guard
4.
8.
Mining transit with top telescope
Mining transit with side telescope
Double opposite verniers on vertical circle
Interchangeable auxiliary used as side telescope
Interchangeable auxiliary used as top telescope
9.
Wye
5.
6.
7.
Frontispiece
4
for vertical circle
6
.
level
11.
Plate levels not perpendicular to vertical axis
Line of sight not perpendicular to horizontal axis
12.
Effect of error in second adjustment
13.
Effect of change of focus
10.
.11
....
....
....
...
.
.
16.
The
17.
18.
Telescope not parallel to level tube
The vertical axis not truly vertical
19.
Eccentricity of the telescope
20.
Eccentricity of the circle
21.
Eccentricity of the verniers
.
13
15
22
23
24
26
.
horizontal axis not perpendicular to the vertical axis
Prismatic eyepiece
23.
Mining transit
24.
Top
25.
Side telescope: isometric projection
26.
Transit with duplex bearings
27.
Lamp
28.
.
targets
.
....
30.
Brunton transit: reading horizontal angle
Brunton transit: reading vertical angle
Miners' compass
31.
Little
.
.
Giant tape splice
32.
Tape
33.
Polaris observation
34.
Solar apparatus
35.
Solar telescope attachment
36.
Solar screen
.28
.
29
31
33
.38
22.
telescope: elevation
.
13
...
14-15. Horizontal axis not truly horizontal
29.
7
9
riveting tools
40
42
46
47
49
50
52
53
55
55
56
58
58
65
66
68
.69
.
37.
Prismatic eyepiece and screen
70
38.
Sun's image on cross-hairs
71
39.
Star sphere
72
40.
Spherical triangle
75
ix
ILLUSTRATIONS
PAOE
76
FIG.
41.
Projection of star sphere
42.
Observation for meridian
Section of star sphere
Logarithmic cross-section paper
Logarithmic trigonometric paper
43.
44.
45.
46.
47.
48.
78
82
86
87
93
95
96
97
99
100
Underground stations
Plumb-bob string adjuster
Tunnel trivet
52.
Instrument bracket
Holding sight
Butte backsights
Tin-can backsight
53.
Plummet lamp and plumb-bobs
102
54.
Cross-wire reflector
102
55.
58.
Cast metal plumb weight
Plan of shaft station
Bent line survey
Double bent line
59.
Striding level
60.
Ordinary mine
61.
Surface
49.
50.
51.
56.
57.
62-66. Level
101
107
,
.
.
.110
113
114
115
144
map
map
144
maps
144
144
150
170
179
67-73. Vertical sections
74-75. Assay
maps
76.
Map
77.
Survey
78.
Sheets from stope-book
79.
Taking meridian from wires
80.
87.
Stope-book sketches for vein with one bend
Stope-book sketches for vein with two bends
Office map compiled from stope-book sketches
Specimen page of field notes
Map of workings of coal mine
Map of workings and proposed extensions
Inclined shaft survey by bent line
Horizontal plan of shafts and adit
88.
Vertical section of shafts
89.
Positions of wire
90.
Map
Map
Map
Map
81.
82.
83.
84.
85.
86.
91.
92.
93.
94.
of
proposed workings
line to stope
....
.
and adit
of placer location
of lode
claim
government section
of lode claim showing conflicting claims
Problems
of
....
195
198
199
202
204
205
207
209
214
219
220
222
224
230
231
232
239
A MANUAL OF UNDERGROUND SURVEYING
INSTRUMENTS
Surveying is the
art of
making measurements which determine
Mine surveying is
the relative position of two or more points.
the art of surveying underground openings,
i.
e.,
finding the relative
positions of points under the surface, or the position of points
underground relative to points upon the surface. The angles
and distances measured are usually drawn to scale upon various
planes and mine maps thus produced.
In mine surveying there are but few operations different from
those of plane surveying. The application of the same principles
to the different conditions, along with a greater degree of accuracy,
insures success underground.
'Donahue, in 'Colliery Surveying,' says: 'Surveying is
T. A.
the art of taking such measurements and observations of an object
as will enable a true proportionate representation to be drawn
on a plane surface. The principles upon which it depends are all
embodied in the science of geometry; so that surveying may be
said to be a practical application of geometry.'
Johnson, in his 'Theory and Practice of Surveying,' p. 431,
This should be
is an art, not an exact science.'
kept constantly in mind, and in every case that method which
says: 'Surveying
promises the
minimum
result should
be employed.
deviation from the scientifically correct
The Transit Theodolite
The instrument now almost
ment of angles is the transit
universally used for the measuretheodolite,
or
more commonly,
While other instruments are still used upon occasion
'transit.'
the transit is the engineer's standby. In times past various more
or less accurate, but now antiquated, instruments have served for
underground work.
As these are
of historical interest only, a
description of them will not be given.
3
A MANUAL OF UNDERGROUND SURVEYING
4
Other instruments which replace the transit for certain work,
it, will be described later.
Each engineer has his own preference when it comes to choosing
or act as an auxiUary to
FIG.
2.
— TRANSIT.
make and as to the attachments used. There
number of reliable makers, each putting good transits on the
market.
Whatever the make there are certain constructions
a transit, both as to
are a
INSTRUMENTS
5
which are generally admitted to be best for certain kinds
of
work.
For underground work, especially
in the metal
mines in rough
commonly known as a 'Mountain Transit,'
is favorite.
It should be mounted upon an extension tripod.
Not only is this a necessity in work underground, but it is a
wonderful convenience when traveling.
The horizontal circle is about 6 inches in diameter and is
country, a light transit,
graduated to read from 0° to 360° in both directions. A full vertical circle, brazed to the horizontal axis and protected by an
aluminum guard,
is
now commonly
Both
used.
circles
read to
minutes.
The telescope should magnify about twenty times, not more
than twenty-four times, erect image, and should focus upon points
at 4 feet distant.
A prismatic eyepiece is a convenience but not a
necessity.
An
auxiliary telescope
or
is,
ing to the kind of work to be done.
is
not, a necessity accord-
The transit should, however,
upon it so that the auxiliary
always have the connecting nipples
may be obtained and used at any later time, if necessary.
The telescope bubble should be long, for in most cases the
elevations will be obtained
by use
of the transit, either
ing them, as with the ordinary level, or
by means
by
carry-
of the vertical
angles.
Several of the
are illustrated.
makes
of transits
Some show an
Each maker usually
most used by mining engineers
auxiliary telescope, others do not.
any
Each publishes a small catalogue and
manual explaining his instruments. The user of a transit should
certainly have a copy of the catalogue published by the makers of
the instrument he uses, and the student can well afford to spend
furnishes either top or side telescope and
other attachments desired.
many
hours studying them.
To show
the variance in opinion regarding the best transit
for use underground, the following quotation
ing and Mining Journal of August 23, 1907,
is
from the Engineergiven:
must be of high enough grade to allow of good triangulation work, and not too sensitive for rough usage; light enough to
carry around the surface and on distant surveys in a mountainous
country, and the horizontal circle graduated to 20 seconds of
For average surface work, moderately high magnifying
arc.
powers are demanded; but the underground work will be at close
'It
A MANUAL OF UNDERGROUND SURVEYING
6
range and in poor light where small magnification is better. Taking
horizontal
all things into consideration, probably a 4- to 4i-inch
standards
U-shaped
circle reading to 20 seconds, full vertical circle,
mountain transit will outline the best instrument for the'
work. It should be procured from the best American manuSomething can be saved byfacturers, and will be expensive.
The U-standards and small
extras.
omitting some of the usual
This
in the usual place.
compass
with
a
circle will do away
habit,
I
befrom
largely
some,
by
disapproved
omission will be
the
attachment
to
an
compass,
as
the
of
fact,
matter
As a
lieve.
light
FIG.
transit, does
— GUARD
3.
not earn
its salt,
FOR VERTICAL CIRCLE.
and
is
a distinct disadvantage in the
correct construction of the instrument
itself.
The U-standard offers so many
advantages that its use is to be always recommended. It will
permit of lighter and at the same time more substantial construction.
It presents a better appearance and is less apt to get
decideclly valuable constructive
'
out of order.
Many would
hesitate to use a 4-inch horizontal circle
but the amount of such work is small, perextra care in repeating angles and of doing it on clear,
in triangulation work,
mitting of
still
days.'
As the transit is strictly a product
and as it is now used to the exclusion
except in rare or unimportant work,
short history of
who
its
it
of
American engineering,
of all other instruments,
has seemed proper to give a
To the student
invention and introduction.
wishes to study in more detail the history of engineering in-
FIG.
4.
— MINING
TRANSIT WITH TOP TELESCOPE.
A MANUAL OF UNDERGROUND SURVEYING
8
struments, we recommend the scholarly and detailed articles in the
Transactions of the American Institute of Mining Engineers.
The following short history
catalogue
of
Young &
of the transit
Sons, for whose
is
taken from the
permission to use
it
acknowledgment is gladly given:
The first
Invention and Introduction of Engineer's Transit.
1831.
was
It
a long
transit instrument was made during the year
instruments;
and
that
engineering
it
stride in the improvement of
—
'
should to-day retain
value of
'
its
The
found,
almost identical
its
first
form, proves the
introduction and the good judgment
of the inventor.
same work,
members of the
English theodolite, capable of performing the
if
we
are to credit the traditions of earlier
little favor with the American engiand inconvenient. Few cared to
workings
were
slow
Its
engineering profession, but
neers.
by reversing the theodolite
and trusting to the vernier readings; and as few
fancied the trouble of reversing telescope on its Y bearings, "end
trust the prolongation of a straight line
on
its
center,
for end."
Forgetfulness in fastening of clips resulted in
telescope, while
if
fall of
the
were too tight there was the danger of
clips
shifting the instrument in fastening, or
if
too loose, the telescope
Such were some of the discomforts attending use of the
theodolite, an instrument well fitted for many purposes, and whose
rattled.
peculiar merits
to
still
cause
many
of
our English brethren to cling
its use.
'
From
the theodolite the change was to the Magnetic Compass.
made to read full
independent of needle, was high in favor with many,
especially those surveyors who, from their local knowledge (and
some with naught besides), were selected to " run " the preliminary
This, in its simplest form, or in its modified form,
circle angles
lines of railroads.
By
dint of labor, these surveyors mastered the
intricacies of the vernier,
but could never be brought to doubt the
superior virtues of compass sights in seeing past a tree or other
With the transit the tree had to come down; they
would not undertake to say the staff on the other side of a tree
was in line of the cross web, but were sure they could make it
obstruction.
"just right" with the line of sights.
Nevertheless, though fre-
quently doing close work, the needle would play pranks that
produced much trouble and though to be commended for speed
on the preliminary, was rather too uncertain for location.
'In the year 1831, the first transit was made by William J.
;
INSTRUMENTS
9
Young.
It was graduated to read by vernier to 3 minutes, it
being in early days a favorite idea of inventors that graduations of
3 minutes could be easily read to one minute, and was less perplexing to use. The instrument had an out-keeper for tallying
the outs of the chain, and a universal or round
FIG.
was about 5
5-
— MINING
level.
The needle
TRANSIT WITH SIDE TELESCOPE.
inches, the telescope 9 inches, of low power.
standards were of almost identical pattern
The
now used by some
The center between plates was of fiat style, vernier on
and the plates moved upon each other
by rack and pinion. The plates and telescope detached from the
makers.
inside of the needle ring,
A MANUAL OF UNDERG^UND SURVEYING
10
tripod fastened,
we
when
believe,
attached,
by a snap dragon,
as
in later instruments.
'For whom the first transit was made, the records, as far as we
can find them, do not positively show; as well as it can be gathered
from them, and from other data, the first one was used on the State
works of Pennsylvania, but whether on the Mountain Division or
on the Inclined Plane of Columbia Railroad, is uncertain.
The distinguished engineers of the Baltimore & Ohio Railroad
'
and
also claim the use of the first transit;
we append
belief,
as illustrative of their
the following extract from Railroad Journal of
December, 1855:
'
"
The
transit
is
now
in
common
comparatively cheap instrument.
in Europe.
use in this country, and
Such, however,
In England, the old mode
is still
is
any other course
is
a
in vogue, to a great
extent, of laying out curves with the use of ordinates;
sure, indeed, that
is
not the case
we
are not
not an exception.
'"Some years since, Mr. Charles P. Manning, an accomplished
American engineer now the efficient chief of the Alexandria,
Loudoun & Hampshire Railroad went to Ireland, and on the
Limerick & Waterford Railway, initiated the method, so common
—
—
in this country, of laying out curves with the transit.
" The first instrument of this name was made by Mr. William
Young, the accomplished mathematical instrument maker, of
Philadelphia, for the Baltimore & Ohio Railroad Company, the
engineers of which made the first suggestions modifying the old
theodolite.
We have in times past used this instrument, which is
much like those made at the present time by the same manufacturer,
and is, if we are not mistaken, still in the field.
'"Since then, transits have been little improved, but have
been changed in the wrong direetion. They are generally much
heavier than formerly, containing as much brass and mahogany
'
J.
as one
man
can well stand under. This great weight is not only
but dangerous. Heavy instruments are much more liable
than light ones to get out of adjustment on transportation, even
useless,
They are not a whit steadier in the
wind; being generally made with clumsy tripods and large plates,
they expose a greater area to the breeze. If the feet of the tripod
be firmly planted, the instrument is rarely disturbed by the wind.
Besides this, a heavy instrument is much more liable to danger
from accident in a rough country."
in the ordinary field service.
IN.iTRUMENTS
'And the
11
following, fron"! same journal of January 5, 1856:
The First Transit Compass.
In our issue of the 15th of
December, 1855, in noticing the field book of C. E. Cross, C.E.,
we took occasion to state some facts concerning the first transit
compass, an instrument made by Young, of Philadelphia. We
have since then received an interesting letter from Mr. Charles P.
Manning, whom we mentioned as having initiated in Ireland the
American method of laying out curves. Mr. Manning disclaims
the honor in favor of Richard B. Osborne, Esq., an engineer who
received his professional education in the service of the Reading
—
'
"
FIG.
6.
— DOUBLE
OPPOSITE VERNIERS ON VERTICAL CIRCLE.
Railroad Company, under Messrs. Moncure and Wirt Robinson
(where he finally occupied the responsible position of chief of the
engineer department, during the early struggles of that corporation, in its
competition with
its rival,
the Schuylkill Navigation
Company), and from which road he went to Ireland, and took
charge of the location and construction of the Waterford &
Limerick Railway in 1846.
"Mr. Manning says further: 'I obtained from Mr. Young, and
sent to Ireland, probably, the first transit compass ever known in
that country or in England; and soon afterwards joined Mr.
Osborne as his principal assistant, for the purpose of aiding him
in the effectual introduction, at least upon that road, of the
American system of location and construction.'
'
" We were familiar with these facts when we made the statement
which Mr. Manning desires corrected. But our object was not so
'
A MANUAL OF UNDERGROUND SURVEYING
12
mention the party to whom the credit of introduction
was due, as to state a few facts immediately connected with the
Mr. Osborne introduced the instruhistory of the instrument.
much
ment
to
into Ireland, Mr.
Manning
initiated its use
among
the junior
assistants.
Osborne was the first to construct an iron bridge upon the
plan of Howe's Patent Truss, several of which he put upon the
Waterford & Limerick Railway; and, I believe, he also built and
'
" Mr.
placed upon the same road, the
first
eight- wheeled, double-truck
passenger and freight cars (American plan) that were ever used in
Great Britain.
'"Mr. Manning gives us a very entertaining sketch of the
first transit, made by Young, of which we remarked
we had in times past made use.
"
Twenty and odd years ago
when a mere boy
I saw that
history of that
that
'
—
'
—
instrument upon a lawyer's table, and afterwards in a court-room
— a dumb witness in behalf of the patentee.
Nineteen years ago,
after considerable service in tracing the center line of the
Wash-
&
Ohio Railroad, it was used in
making surveys for the extension of the last-named road, westward from Harper's Ferry, and your humble servant carried and
used it at that time in Washington County, Maryland, and in Ohio
County, Virginia.
""In the last seven years the instrument accompanied me as a
duplicate, and was occasionally used upon the location and construction of the Baltimore & Ohio Railroad, through the wilderness, west of Cumberland, and now rests upon its laurels in the
office of the Baltimore & Ohio Railroad Co., in Baltimore.
ington branch of the Baltimore
""It was
instrumental in setting the
peg that was driven
Ohio Railroad, west of
Harper's Ferry; and it was "hard by," and able to do duty, when
the last peg was set for completing the track of that road upon the
banks of the Ohio River.
for the extension of the Baltimore
first
&
""In all material points Mr. Young has never been able to
improve upon this original work of his hand, but in some of its
minor parts he has effected desirable changes such as the tangent
screws connected with the clamp of the tripod, the substitution of a
clamp and tangent screw for the old rack-and-pinion movement
of the two compass plates, the subdivision of degrees into minutes,
by an improved graduation of the vernier, etc., etc.
INSTRUMENTS
""The
original instrument
13
had an index
for counting the
number of deflections made
at one sitting;' also a small bubble upon
the exterior of the telescope, for the purpose of defining a hori-
zontal line, without resorting to the aid of its companion, the ordinary level; but these superfluities were soon thrown aside; and
one of its peculiar features was, and is, a vernier, graduated only
to three minutes.' "
'Mr. Manning but expresses the facts
all
when he says that in
The changes
material points Uttle change has taken place.
FIG.
7.
— INTERCHANGEABLE
AUX-
FIG.
8.
Used
as Side Telescope.
that have taken
circumstances
— INTERCHANGEABLE
place have been those called for
— modifications
acteristics of the transit,
AUX-
ILIARY.
Used as Top Telescope.
ILIARY.
by
peculiar
which, while retaining the char-
have approached more nearly to the
Transits in after years became
peculiarities of the theodolite.
divided into the two distinct classes. Flat Center, as
first
intro-
duced, and Long Center, with centers as previously used on
theodolite
;
but
for accurate
exception.
it
was not
for
many
years that the long center
work the best construction
now is the rule, and the
It
— became
flat
—
other than the
center the exception.
A MANUAL OF UNDERGROUND SURVEYING
14
'
Engineers of the present day, unaware of the actual difference
two styles, and unacquainted with the circumstances of
in these
early introduction of instrument, are apt to treat the flat center
with a disrespect
it is
far
from deserving.
'For the same strength, the
flat
centers are far the lightest.
Said an experienced and competent engineer to us, within a few
first requisite of a transit is lightness and portaJudged by these requisites, the flat center is the instrument of to-day. But he spoke for his own peculiar branch
railways; and while we are by no means ready to indorse this
opinion, we have no hesitation in saying that the circumstances
existing at the time of. first use of the transit were such that had
the instrument been constructed with the long center, its usefulness and general introduction would have been very much retarded.
The great peculiarity of the first-made transits was their ability
to stand hard usage, and non-liability to get out of order under
ordinary usage. The center is a broad metal plate
thick, which
it is impossible to bend or injure in any manner, except by wear;
the plates were thick, not easily bent, and the spring vernier, in
case of bending of plates, followed their motions and allowed the
days past, "The
bility."
—
—
made sufficiently accurate to continue work. The
rack and pinion had nothing that could break, while the tangents,
as then constructed, were equally simple.
If the standards, by a
readings to be
were bent so that the telescope would not revolve in a vertical
was such that with the ax as a screwdriver the standards could be loosened and a piece of paper inserted to correct them.
fall,
plane, the construction
In fact, the opinion of the writer, with means of observation
and the use of such an instrument, is, that a flat-centered transit,
rack and pinion, and spring vernier, cannot he made totally useless
by any accident short of absolute breakage of parts.
Not so, however, with the long center. There the least injury
'
'
to centers or plates ends the usefulness of the instrument for
work, and
it
can stand comparatively
its
rough usage without
little
receiving this injury.
'Of the good judgment of the
length of time that
still
doing duty
as rodman,
we
—
first
form
many of them have been
is
the best of evidence.
of construction, the
in use
— for some are
Twenty-five years ago,
followed and worked with a flat-center transit that
to us then looked old enough to retire
upon
its laurels.
So con-
INSTRUMENTS
stant had been
the edges of
—
—
use that its corners
of hard, hammered brass
standards, and other parts, had then been rounded
its
its
15
in carrying against clothing.
Ten years afterwards we followed
on the location of one of our main lines across the
mountains, where for a long time it had been the sole available
instrument; and one year ago it was in the shop for repairs, the
owner still believing that for railway work it had no superior.
This instrument was light, weighing between 15 and 16 pounds; had
behind
it,
FIG.
9.
— WYE
LEVEL.
seen at least forty years' service, a large part of the time in the
hands of
assistants,
and
in rough,
wooded country.
We
doubt
the possibility of a long-centered instrument leading an equally
long
life.
While in charge of some railway works, we kept in the office,
where there were several assistants, both styles of instruments,
'
and the
'It is
assistant's choice, in all cases,
was
for the flat center.
not our intention to argue any superiority in the
first
A MANUAL OF UNDERGROUND SURVEYING
16
not the equal, for accuracy and smoothness
of motion, of the long center.
Its day of universal application has
passed and its field of usefulness narrowed; but it yet has its
form
of transit.
It
is
and the engineer will do well in making selections to give it
fair consideration.
Our desire is simply to do it justice, and to
offer for it a slight defense to our younger engineers, who, having
never seen or used it, can know but little of its faults or merits.
'In the transit's early days, no express, on call, drove to the
door, receipted for the boxes, and relieved all anxiety, no matter
how many thousand miles away nor what obscure point was the
destination.
Instead of this they had in many cases to be
consigned to the top of the stage, or to the Connestoga wagon,
unless the destination was near the coast, when the sea became the
best route. Thus we find the following extracts, looking at ranfield,
dom
'
into the books of shipment:
" 1833.
August 13th. Sent, per ship Chester, to F. Beaumont, Natchez, care of Florchell & Co., New
" 1833.
August
Orleans.
W.
'There
is
no
16th.
Sent, per brig
G. Neil, for Boston
difficulty in
transit that nothing
much
&
Mohawk,
to Boston, to
Providence Railroad."
understanding
why
the call was for a
short of entire annihilation would
render necessary to send back, over
its
slow, long,
and uncertain
journey, for repairs.
'The spread
improvements in this country had, at
commenced, and with it the demand for the new
instrument increased rapidly. So great was this increase, and so
much did it outgrow the facilities of manufacture, that the inventor was compelled to send to England an order to have the
greater part of a limited number of transits made.
This was in
1835, and these were the first transits, or parts of transits, made in
England. About three dozen were thus obtained, the more particular parts being made here.
They proved far from remunerative; some few were passable, others more troublesome, requiring
alterations and repairs; while a fatal fault to a needle instrument
(iron in the metal) was found to exist in nearly a dozen.
'Of the latter, most were broken up; several remained in the
establishment in an unfinished condition until recently, one of
this time, fairly
of internal
INSTRUMENTS
the last being taken to adorn the
monument
17
of a civil engineer,
in Laurel Hill Cemetery, Philadelphia.
manufacture of the transit instrument was, for
with many difficulties. The art
of graduation had as yet made but little progress, and the introduction of the transit called for nearer approach to perfection.
The first graduating machines were extremely primitive, consisting
simply of a circular plate of about 18 inches diameter, upon which
degrees and half degrees were marked off, either by mechanical
subdivisions or from a similar plate. The one in the establishment of W. J. Young bears the name of "Adams, Maker, London,"
and consists of such a plate as we have described.
'Such were the means of graduation in 1820. Mr. Young
started, as soon as he commenced business, the construction of an
engine of 24 inches diameter, worked by the endless screw and
treadle and shortly after the introduction of the transit, commenced another of 26 inches diameter, for finer work, in which
a new and important principle of construction for these engines
was introduced. A few years afterwards, this same machine was
rendered automatic, and is yet doing active duty. About the
same time, Mr. Edmund Draper constructed a graduating engine
which, among those acquainted with it, has a high reputation for
'The
want
earlier
of conveniences, attended
;
accuracy.
As transits advanced to perfection, these advances in graduabecame necessary. That they were not made at once, but
were the result of almost a life of thought, work, and patience,
and source of expense, is evident from the fact that from 1821 to
1860, or but ten years before his death, W. J. Young was almost
constantly engaged upon the making or perfection of these engines.
'Another serious difficulty arose from want of opticians of
The first glasses used were imported principally from
ability.
England. With the slow communication across the ocean at that
period, it was long before an order given could be received; and
the purchase of all glasses to be found here of proper size and
What was more
focal length furnished but a short supply.
differed
in
size and length
that
the
next
supply
troublesome was
instrument,
inquiry
for
a
larger
or one of
When
an
from the last.
'
tion
came, the question which determined the
manufacture was the capability of making the
different construction,
practicability of its
telescope.
A MANUAL OF UNDERGROtJND SURVEYING
18
'
The
been brought nearer perfew
The decimal graduation of vernier
W. Miffin, C.E., proved a great ad-
transit instrument having thus
fection in graduation
more changes
and
optical performance, received but
in construction.
suggested at an early day by
S.
vantage in the turning off deflection angles for curves, and was
adopted by many, notably by the engineers of Pennsylvania Railroad, all of whose instruments were graduated in that manner.
'The
loose vernier
and
by the
was an improvement over the much-
arc, for vertical angles, applied
writer about the year 1850,
liable-to-be-injured full circle.
'The shifting staff-head, patented by W. J. Young, in 1858,
was another of those little improvements which increase the value
of the instrument much.
'The many varied uses to which, from progress of science in
this country, the instrument has been called, has brought forth
instruments of greater delicacy and different constructions, until
to-day, the finest transit of the conscientious instrument maker
is a splendid instrument, not surpassed in its performances by the
production of any other country.
'Of later minor improvements, some beneficial, some the exploded humbugs of bygone days, we are not now to speak. The
profession has other means of discovering them.
Our desire is
simply to keep from oblivion, the dates and circumstances of
introduction of the instrument which has played so important a
part in the ever memorable forty-five years of American railroad
construction, and which might, perhaps, be lost in the whirl which
has been crowding the railroad mind ever forward, leaving it no
time to look back to the earlier laborers.
Telescopes.
Telescopes placed upon transit instruments
within the past few years have a higher power than was formerly
placed upon the generality of these instruments.
'The general demand is for a high power; and those unacquainted with the subject consider the higher power the better
telescope.
The power of a telescope depends upon proportion of
focal lengths of object glass and eyepiece and while in theory any
power may be given to any telescope, in practice the extent is
limited by other points, such as effects of aberration, loss of light,
and size of field view. With the same object glass every increase
of power is followed by a decreased illumination, or a decrease of
light and a smaller field.
These results follow in obedience to
'
—
;
INSTRUMENTS
19
mathematical laws, and cannot be obviated.
certain proportions between
Science has given
power and length
of telescopes,
and
the best opticians of Europe, with their extended experience,
invariably follow these proportions.
'The practice in this country of late has been to force the
power beyond these bounds; the result is, that while under very
favorable circumstances the center of
somewhat better
definition,
it
will
field
of
view
will give
a
only do so under favorable
circumstances, such as clear atmosphere and strong illumination
of the object;
and that
either the field
must be much reduced
or objects out of immediate center will not be in focus.
In cloudy
weather, in lesser light of morning and evening, in the tremulous
condition of atmosphere arising from evaporation from the surface
of the ground, especially cultivated ground, these high
powers
all suffer.
'There are purposes, where great definition is so much an
all other telescopic requirements, in which
object as to supersede
these high powers are advisable; but the engineer should under-
stand that in using them that he loses on the other points, and
especially remember the exact focusing required of them; otherwise parallax produces a sensible error.
exact focusing of high powers
is
For rapid working the
a drawback, a change in telescope
being required for almost every small change of distance.
Com-
parison of two telescopes differing widely in power will illustrate
In the lower powers, in ranging a line, distances between
300 and 400 feet require little if any change, and the same of say
500 and 700, or 800 and 1200; but in higher powers every change
of a few feet, until practically parallel rays are reached, requires
separate focusing, and if not properly focused are liable to be less
this.
than the lower powers.
loss of light, even in the best high powers,
an impression of glass being "less distinct" on its
distinct
'The
though smaller objects are better defined by
its first use is one of cloudiness.
it,
is
what gives
first use,
for
the impression on
'Fortunately the particular use of engineering instruments
requiring definition on but one point at a time allows us to
make
other conditions of optically good glass subordinate to this one
of
power to a great extent.
'Inverting glasses are not more powerful, except that from the
small space occupied by the eyepiece, they allow for the same
A MANUAL OF UNDERGROUND SURVEYING
20
length of telescope a greater focal length of object glass, and thus
increase the power.
amount of light, or greater
The prejudices of American
illumination, and a much larger field.
engineers are against them, but in Europe their merits are almost
'They, however, have a
much
greater
universally acknowledged, and they are almost the only ones used.'
The Adjustments of the Transit ^
While every elementary text-book on surveying gives a descripit is thought best to include it in this work,
as the uses to which the transit is put underground are so varied
and the accuracy required so great.
The adjustments of an engineer's transit are of two kinds: (1)
The maker's adjustments, or those which reliable makers give the
instrument while it is in process of construction; and (2) the
field adjustments, or those which occasionally have to be verified
The latter are, as a matter of
in the field use of the instrument.
included
in
the
former,
since
makers always find it necescourse,
sary to verify all the adjustments, and deem it an essential requisite of a properly constructed and thoroughly tested instrument,
to send it from their hands only when in every respect accurately
adjusted for immediate use.
The Maker's Adjustments.
In order that the mathematical
conditions of the practical problem of angular measurements in
the field may be realized in the instrument itself, it is necessary
that the following points of construction and adjustment be
tion of the adjustments,
—
accurately attained:
1.
The
and
lenses of the objective
of the eyepiece
telescope truly centered in their respective
2.
The
of the
cells.
optical axis of the system of lenses coinciding with
the mechanical axis of the tube, in
all
the relative positions of
the objective and eyepiece, the lenses remaining always at right
angles to this axis.
3.
The
cross hairs, during each observation, in the
focus of the object glass
4.
The
vertical
common
and eyepiece.
cross hair
(all
other adjustments made) at
right angles to the horizontal axis of the instrument.
5.
The
line of sight at right angles to the horizontal axis, or
coinciding with the axis of collimation.
6.
The
axis of the telescope level lying in the
'
Based upon " Engineers' Manual," Queen
same plane
&
Co.
as the
INSTRUMENTS
line of collimation, or
21
not 'crossed' with respect to the coUima-
tion plane.
The axis of the telescope level parallel with the line of sight.
The horizontal axis of the instrument at right angles to
the axis of the alidade, or to the axis of the upper plate; and
7.
8.
hence
(all
other adjustments made) the line of sight always lying
in the plane
center
of,
which
The form
9.
is
at right angles to,
the horizontal graduated
and passes through the
circle.
of the pivots of the horizontal axis the equivalent
of true cylinders.
10.
11.
The V's or bearings for
The vertical graduated
these pivots, of equal form.
circle at right angles to
the hori-
zontal axis of the instrument.
12. The vertical graduated
with respect to the horizontal
13.
14.
The
The
circle
and
its
verniers truly centered
axis.
alidade, or upper, plate at right angles to
its axis.
axis of the alidade, or upper, plate coinciding with the
axis of the lower, or circle, plate.
15.
The
lower, or circle plate, at right angles to the
axis of both alidade
and
common
circle plates.
The graduations of the horizontal circle and of its verniers,
and concentric with the common axis of the alidade and
16.
true
circle plates.
17. The zeros of each set of verniers, or reading microscopes,
accurately 180° apart, as measured at the respective centers of
the graduated
18.
The
circles.
axis of each of the alidade levels at right angles to the
vertical axis of the instrument.
19.
The pivot of the compass needle coincident with the
vertical
axis.
20.
The
zeros of the compass graduations in the
same plane as
the line of collimation.
21.
22.
The magnetic needle perfectly straight.
The magnetic axis of the needle coinciding with the
axis
of form.
23.
The magnetic needle adjusted
for the magnetic dip of the
place of observation.
24.
The
axis of the suspended
plumb bob
coinciding with the
vertical axis of the instrument.
While
it
would be
difficult
and unnecessarily tedious to
set
A MANUAL OF UNDERGROUND SURVEYING
22
down every adjustment attended to by the maker, the foregoing
may be taken as a Hst of the more prominent ones. Other adjustments peculiar
to the accessories of the transit
and
to special forms
referred to in treating of these elsewhere.
be
The following practical methods
The Field Adjustments.
errors of an engineer's transit are
the
for detecting and correcting
given for use in the field. A full explanation of the nature of each
of the transit will
error
is
also
may
tion
made
—
in order that the
work
of detection
and
correc-
proceed intelligently.
— To
First Adjustment.
make
the axis of the plate levels
perpendicular to the vertical axis of the instrument.
—
Detection of Error}
Level the instrument carefully both
ways, care being taken to make each bubble tube parallel to a
pair of plate screws.
Turn the telescope through 180° by measur-
This measurement should be a direct
ing on the vernier plate.
angular measurement on the plate, and not a mere approximaIf the instrument is not
adjustment the bubbles,
tion.
a-^
_--=3
—^^^''^^^Sfa-a"
»
in
~
after this revolution, will
no
longer remain in the centers of
the tubes.
This displacement
of the bubbles
is
twice the true
error of the instrument.
a
if
a' (Fig. 10)
For
represent the
projection on a parallel verti-
— PLATE
LEVELS NOT PERPENDicuLAR TO VERTICAL AXIS.
FiG.
10.
cal
<,
o'
plane of the bubble tubes,
the Vertical axis of the in-
strument, the turning through
180° would bring a to a" and a' to a" ', the angles a" o' a and
a" ' o'
being respectively equal to ao' o and a' o' o. The line
KL
representing the
angle a'
o'
proper position of the bubble tube, the
a" will therefore be the double error, and cause twice
the displacement of the bubbles due to the true error.
Correction of the Error.
way back
— To
correct, bring the bubbles half
to the centers of the tubes
by
raising or lowering either
end of the tubes, screws being placed there for that purpose.
Then
level accurately by means of the plate screws.
This process should be repeated several times, as, without
extreme accuracy in this adjustment, any attempt to perform the
other adjustments
is
valueless.
"Aftef the other adjustments have been
used to check the plate levels
made
or, in fact, to set
up
the telescope level can be
by.
INSTRUMENTS
23
—
Second Adjustment.
To make the line of sight coincide with
the Hne of collimation, or to make the line of sight perpendicular
to the horizontal axis of the telescope.
Detection of the Error.
— The
direction of the line of sight
is
determined by two points; the optical center of the object glass,
and the intersection of the cross hairs. Of these the latter is
movable and is the part whose position is to be corrected.
Set up the instrument, level carefully, and sight (Fig. 11) to
some well-defined point, A. Reverse the telescope (i.e., turn it
over) and sight to B.
A and B should be as far distant as possible
from the instrument, since the apparent deviation and con-
FIG.
11.
— LINE
OF SIGHT NOT PERPENDICULAR TO
HORIZONTAL AXIS.
sequently the accuracy of the subsequent correction increases
H
B
should be taken equal to A H. If the
be not perpendicular to the horizontal axis of the
instrument EE', A and B will not be on the same straight line
with H. To determine whether this is so or not, turn the teleas the distance.
line of sight oo'
scope around on
its vertical
axis of the instrument
angle
OHE'
and
axis
now
of the old position corresponding to
and the angle OHE to OHE" '.
over on horizontal axis) its line
;
far to the left of the line Aoo' as
at C.
sight to A.
The angle aHO'
E"HE, since these
ment from B to C
The horizontal
E" E" ', the
occupies the position
Now
OHE"
in the
of sight will strike this
it
new,
reverse the telescope (turn
time as
did before to the right, that
is,
represents the doubled error, so also does
angles are equal.
represents the
But the
sum
total angular
of these angles,
and
moveis
con-
sequently four times the true error.
Correction
of
the
Error.
— To
correct,
with the telescope
pointed at C, place a stake at D, the distance D C being made
Move the cross-hair ring by means of
equal to one fourth B C.
the capstan-headed screws placed on the side of the telescope,
This operauntil the intersection of the hairs cuts the point D.
tion
is
accomplished by screwing both screws at the same time.
A MANUAL OF UNDERGROUND SURVEYING
24
the one in and the other out.
be remembered that an
It should
inverting or astronomical telescope does not invert the motion of
the cross-hair ring, and hence the screws must be turned so as to
move
the ring in the same direction as that apparently required
With the usual terrestrial or erecting
to produce coincidence.
must be turned so as to move the ring in the
from that which the error apparently requires.
If the line of sight
Effect upon Reading of Horizontal Angles.
not at right angles to the horizontal axis but makes any angle, say
telescope the screws
opposite direction
is
—
90°-c, the quantity,
tion error.
The
horizontal angles
c, is
the error of the line of sight of the collima-
effect of
is
such an error,
r
SS'
FIG.
In this
— EFFECT
12.
figure,
axis, while OZ',
adjusted sight
is
on measurement
of
MN
z
T"
OP ERROR IN SECOND ADJUSTMENT.
is
the horizontal axis,
OZ
is
the vertical
OP, and OS' are three positions of the inaccurately
axis or line of sight, which makes respectively
the equal angles Z'OZ,
that Z'PS'
c,
best seen from Fig. 12.
FOR, S'OT,
or
c,
with the plane
a parallel to the great circle
ZRT,
so
ZRT.
Let the sight axis be directed to a point P, whose altitude is
Then, if the sight axis were accurately collimated, P
would be projected on the horizon at S. But with the error c
PS=h.
in collimation
MTN,
it is
PR,
projected at S'.
very approximately equals
c.
as the arc of a parallel to
For any altitude
h,
the error
PR, projected on the horizon, is ST, or SS' is in excess of
the effect of the same error on a horizontal pointing.
For varying
c,
or
INSTRUMENTS
altitudes, therefore, the gi^'en error consists of
25
a constant part
S'T and a variable part SS'. Denoting ST by Z, S'T by
SS' by (c), we evidently have from the figure
c,
and
(c)=Z-c
and because PR may be assumed
and is the arc of a parallel to ST.
Z=c
and inserting
as approximately equal to c
sec h
this value in the previous equation,
(c)
=c
sec
h—c
(1)
we have
(2)
which allows the variable collimation error to be computed as a
c and the altitude h.
The following table, for various assumed altitudes and various
assumed values of c, will give a practical idea of the effect of collimation error upon measurements of horizontal angles \\ith the line
simple function of the assumed constant error
of sight directed to the given altitude.
TABLE SHOWING EFFECT OF AN ERROR c OF COLLIMATION ON
MEASUREMENT OF HORIZONT.IL ANGLES
A MANUAL OF UNDERGROUND SURVEYING
26
For, representing the collimation error due to two pointings
of different altitude, hi and ^2, by Ac, or, what comes to the same,
letting Ac = (c)i — (c)2, we have evidently from equation (2)
Ac = c
(sec hi—sech-i),
which, for hi=h2, becomes zero.
Third. The varying part, SS', of the projected collimation
error
is also,
for pointings of different altitudes, eliminated
when
determined by the principle of
reversion, or when the angle is first measured in one position of
telescope and then the telescope turned over on its horizontal
axis and round the vertical axis, the measurement again made,
and the mean of the two measures taken.
For if Ac is considered positive in one position of the telescope,
the angle between the two points
is
Far
Siglit
"Near Sight
FIG.
it
13.
— EFFECT
OF CHANGE OF FOCUS.
must be considered negative
entering with different signs,
of the measures for the
Fourth.
From
likely to exist
in the reverse position;
it is
eliminated
two positions
the table
it is
and hence
by taking the mean
of the telescope.
evident that the collimation error
low altitudes, negligible even in high-class
A = 10° the table shows the error
less than 10".
The table also shows the necessity for painstaking
collimation, or for proper methods of elimination of the error, when
work.
Even
is,
for
for c
= 10' and
the pointings of the telescope are of
any considerable altitude.
Not in Line of Collimation.
There is
also a small error introduced when both sights are horizontal.
Owing to the change _of focal distance when sighting on objects
When
Vertical
Wire
is
—
INSTRUMENTS
far
first
on a
and then near, the angle
far object the objective
is
c is
27
When
not constant.
drawn
far in
and
F
is
sighting
short, say
When sighting on a near object (modem
mining transits can be sighted on an object only 4 feet distant)
the objective is run clear out and F may be as much as, say,
for instance 8 inches.
10 inches.
be 10 minutes when sighting on a far
become 10" X ^^ = 8 minutes
when the object sighted is near and F, is 10 inches, or the real error
now, the angle
If,
object,
when
F=8
c
inches, then c will
of the reading of the angle
more
measured
is
10" — 8"
= 2".
This
is
shown,
clearly in Fig. 13.
= angular error for distant object.
= angular error for near object.
2^ = focal distance for far object.
c
Ci
i^i=focal distance for near object.
c
= ctg —
~
Ci=
ctg
—
d
d
is
constant;
ii-i.
d
F varies
inversely with distance of the object
sighted, but an angle decreases as
c
its ctg
increases,
i.e.,
decreases with nearness of object sighted.
— To make the of collimation revolve
Error. — Set up the instrument, and level care-
Third Adjustment.
in a vertical plane.
Detection of the
line
Sight to some high object. The top of a steeple is generally
most convenient. Depress the telescope and note carefully where
the intersection of the cross hairs cuts the ground. Turn the
fulh'.
instrument through 180° (this time only approximately) and,
reversing the telescope, sight to the same high point, depress the
tube again, and again note where the line of collimation strikes
The
the ground.
(Fig.
and
14).
fault to be remedied
BOA'
or
B'OA
line drawn through
them both.
The motion of the
P
that the horizontal axis
is
inclines the axis as represented
angles
is
not parallel to the plane of the plate bubbles
Turning thi'ough 180° brings the support A to A'
of the telescope
by the dotted
line A'B',
the
representing the doubled error, since the
parallel to the
bubble plane would bisect
line of collimation is represented in Fig. 15,
being the high point,
K
and
L
the two points on the ground,
A MANUAL OF UNDERGROUND SURVEYING
28
M
being the middle point which the cross hairs should cut
instrument were in adjustment.
AB by
the
— To correct, therefore, raise or lower
Correction of the Error.
one end of the axis
if
means
of a screw placed in the standard
for that purpose, until the line of sight revolves in the plane from
P
to
M.
The
reflection in a basin of
mercury
of the high point
K M L
FIGS.
14
AND
15.
— HORIZONTAL
AXIS NOT TRULY HORIZONTAL.
determine the point M, and the consequent error
be determined without the reversal of the telescope.
Instead of a very high terrestrial object a star may be advantagewill suffice to
KM
or
ML
ously used in this reflection method.
Error Introduced.
—
If
the horizontal axis of the telescope
is
not at right angles to the vertical axis of the instrument, but
makes an angle 90° — i,
i is
the error of the horizontal axis.
:
INSTRUMENTS
In Fig. 16
OZ
29
MN the
represents the vertical axis,
horizontal
OZ, or in correct position, and M'N' the
making an angle i with the correct position. The
axis at right angles to
horizontal axis
line of sight will therefore
move
in the plane
Z'PT
instead of the
z
FIG.
plane
16.
— THE
ZRT, and
HORIZONTAL AXIS NOT PERPENDICULAR TO
THE VERTICAL AXIS.
if
directed to P, the deviation
the horizon will be ST. Let ZZ'=i, ST=
= 90° — A., then from the figure we have:
(l),
PR projected on
TR = h, and RZ
Pi?=(i) cos/i;
also
or,
PR = i cos (90° -h)
PR = i sin h,
and hence,
or finally,
(i)
{i)
cos h = i sin h,
=i
tan
h,
(3)
from which formula the following table may be computed
TABLE SHOWING EFFECT OF AN ERROR i OF HORIZONTAL AXIS
ON MEASUREMENT OF HORIZONTAL ANGLES
,
A MANUAL OF UNDERGROUND SURVEYING
30
The
Practical Deductions from this discussion are:
The
First.
effect of the existence of
or of the violation of the oondttion
an instrumental error i,
be eliminated by
H^V, may
the method of reversion observation, already explained in the
practical deductions concerning the collimation error,
The
Second.
effect of the error i is also eliminated
c.
by taking
the difference of the readings for any two pointings of the same
For,
altitude.
we
if
represent the effective errors for the two
and A2 of an error i, by (i)i and
we have evidently from equation (3)
altitudes hi
(i)2,
A i=i
(tan hi
— tan
(i)2,
and A^ = (i)l —
/12)
which, for hi=h2, becomes zero.
Third. This error, i, is of much more serious influence on
horizontal angles than the collimation error.
Fourth. In a thoroughly tested and carefully adjusted instrument, and with altitudes less than 5°, this error need not be
feared, but with an instrument having any considerable error i,
or with pointings of a considerable altitude, the resulting error
on the horizontal angle is serious.
Fifth. It is to be borne in mind that in observations like those,
for example, required in making the third adjustment, the effective
(i)
error
(i),
varies as the tangent of the angle of depression as well
as of elevation.
— To make the axis of the telescope
Error. — Drive two stakes several hundred
Fourth Adjustment.
level parallel to the line of collimation.
Detection of the
midway between them and, using the
bring the long bubble to the center of its
tube.
Sight to a rod held on each stake. The difference of these
readings will be the true difference of height between the points,
feet apart.
Set up exactly
instrument as a
level,
no matter what the error
of the
instrument
may
be.
For
if
eo,
Fig. 17, represent the position of the telescope, the line of sight
will cut the
rod at A.
while the spirit level
the
new
D
and B.
D
same horizontal reading,
e'o' and will intersect
at C.
since
iS is
CD -^5 = true difference of height of
EF represents the proper position
For, since
of the telescope, then
and
indicates the
position of the line of sight will be
the rod set over
points
Turning the telescope around horizontally
W still
FD-EB = tr\ie difference of height of points,
midway between B and D,
the angles which eo and.
INSTRUMENTS
31
the two positions of the telescope, make with EF, being equal,
must be subtended by equal distances on the rod, or EA=FC,
hence adding to FD and EB, we have (FD + FC) -{EB + EA) =
e'o',
true difference of height of points (since this addition does not
affect the
as
balance of the equation), or true difference
we stated at firet.
Now, clearly, having determined the
of the points, the instrument
this accurateh'.
Correction of the Error.
of the stakes,
by
true difference of height
must be corrected so
as to
measure
— Now set up the instrument over one
measure the height
the stake, either
= CD — 4-B,
of the cross hair
above the top of
direct reference to the horizontal set of screws
A*^
,j^j^777T777777777777777n77777^t
T^7777777m777^i
FIG.
17.
— TELESCOPE
of the cross-hair ring, or
NOT PARALLEL TO LEVEL TUBE.
by looking through the
objective toward
a graduated rod held at a distance of about a quarter of an inch
from the eye end, and with a neat lead-pencil point marking on
the rod the center of the small field of view. Set the target on
the rod to this reading plus or minus the difference of height be-
tween the points, according as the point set up over is higher
Now sight to the rod thus adjusted
or lower than the second.
and beld on the second stake, and note if the cross hairs cut the
target in the center,
tube.
when the long bubble is in the center of its
by lowering or raising one end of the level
If not, correct
tube by means of nuts placed there for that purpose, until the
still remaining in the
desired intersection is-obtained, the bubble
center of the tube.
Here the height
point over which the instrument
is
above the
very approximately
of the cross hairs
set
up
is
A MANUAL OF UNDERGROUND SURVEYING
32
independent of any accuracy of adjustment. The entire error of
the instrument is therefore shown by its deviation from the true
reading as indicated on the rod, by the distance of the cross-hair
Now check up plate
intersection from the center of the target.
levels against telescope level.
Fifth Adjustment.
when
— To
Detection of the Error.
By
make
the vertical circle read zero
the bubble of the telescope level
— This
may
is
in the center of its tube.
be done in two ways:
(1)
by reversion.
Sight to some distinct point, note the reading
By Reversion.
on the vertical circle. Turn the instrument around horizontally
simple inspection;
—
(2)
half way, reverse the telescope,
One
and sight again to the same
half the difference of the readings
doubled by reversion.
is
the error,
it
point.
having been
— The
Correction of the Error.
either the vernier or circle
correction is made by moving
by loosening screws designed for the
purpose of permitting circular motion. 'The index error' may,
however, be simply noted, and each observation corrected by the
required amount. Inspection is the readiest method by which to
perform the above adjustment, but when the index error is small
and difficult of detection, doubling it increases the accuracy of the
correction.
be small and the vertical circle have but one
be corrected by first setting the circle so as to
read zero altitude and bringing the bubble of the telescope level
This error,
vernier,
may
if it
also
and then, by the method of the fourth adjustment, moving the cross-hair ring up or down so as to bring the line
to a zero reading,
of sight parallel to the axis of the telescope level.
—
—
To make the vertical cross hair truly
when the instrument is leveled.
Detection of the Error.
Set up the instrument and level carefully.
Suspend a plumb line from some convenient point. Bring
Sixth Adjustment.
vertical
the vertical cross hair into coincidence with
it, and note whether
the line and hair correspond throughout their entire length. If
they do not, the hair
ment be properly
is
out of adjustment, because,
leveled the
plumb
line will
if
the instru-
be perpendicular to
the plane of the bubble tubes.
The same
noting
if
error
may
be detected by plunging the telescope and
some point sighted to,
the vertical hair passes over
throughout
its
entire length.
Correction of the Error.
— To
correct the error the
cross-hair
INSTRUMENTS
ring
must be moved
ciroularlj'.
This
is
33
accomplished by loosening
the four screws of the cross-hair ring.
These screws penetrate
amount of play
enlargement of the space through which
the screw is inserted. When the screw is tightened the piece just
below the head of the screw is clamped fast to the telescope tube.
the ring a short distance, and are allowed a certain
by reason
sidewise
of the
When all four screws are loosened, however, it permits the ring to
be turned through a distance limited by the edges of the hole
through which the screw is inserted. The vertical hair alters its
direction with the turning of the ring.
Error of Deviation of the Vertical Axis of the Instrument from
the Vertical.
This is due either (1) to error in the condition
L J_T', that is, inaccurate adjustment of the level axis with respect
—
FIG.
18.
— THE
VERTICAL AXIS NOT TRULY VERTICAL.
to vertical axis; or, (2) to untrutlifulness
and lack
of sensitiveness
of the levels; or, (3) to inaccuracy of use of the levels in setting
up
the instrument.
OZ is the vertical, OZ' the vertical axis deviating
an angle ZOZ', which we designate v. If the axis of
sight is directed to P, this point will be projected to T instead of
to S; and if we designate AS by u and -IT by «', their difference
will be equal to the desired projection error, which we designate
In Fig. 18
from
(v);
OZ by
that
is ?t
— m' = (v).
The plane
of the circle at right angles
to the vertical axis will therefore take the position
stead of
AMBN,
equal to
v.
The
so that the angle
BOB' between
A'M'B'N'
the planes
is
line of sight being directed to P, the horizontal
.
A MANUAL OF UNDERGROUND SURVEYING
34
must take the position of M'N', at right angles to OT and
approximately to OS, whence the inclination to the true horizontal
We have now a triangle
plane is MOM', which we designate i'
LMM' right angled at M, whose side LM = AS, because AL and
SM each equal 90°. But the arc AS is the azimuth of the projected point P as measured from the point of greatest inclination
A, and this arc, or its equal LM, we designate u. In the right
spherical triangle LMM', LM = %i, L = v, and MM' = i', and hence
axis
.
i'
But an
error
{i')
inclination
in
i'
=v
sin u.
of the horizontal axis
measurement
produced a projected
of horizontal angles in which, according
to the previous article (3),
= i' tan h,
= v sin u tan
(d) = V sin u tan
{i')
and therefore
or
where («) represents the
on the horizon. For the
takes the form
{i')
effect of v, for
and the table
(4)
any pointing,
maximum value of
{v)=v tan
h,
h,
as projected
sin u, or I, the formula
h,
of the preceding section gives the values
of the
effective error.
The Practical Deductions from consideration of this error are:
The error v made in adjusting and setting up the instrument cannot be eliminated by reversion observations.
Second. If we suppose an angle measured between two points
of the same altitude we can find the expression for the maximum
value of the error A v. Let hi and ui be respectively the altitude
and azimuth (as measured from point of greatest inclination of
horizontal circle) of the first point, and /ig and ?<2, the same of
second point, and the difference between the effective errors (vi)
and (V2)be A v, that is, Av = (wi) — (^2) then from equation (4)
we evidently have
First.
;
Av=v
(tan hi sin ui
This value attains, for hi=h2,
— tan
its
/12
sin
112)
maximum
(5)
in relation to mi
and U2 when sin iti = — sin U2, or when Ui—U2= ± 180°. That is,
the error becomes greatest for hi=h2''when the angle measured
IXSTRUMEXTS
Ml
— 1*2
is
180°.
35
Under these conditions the above formula
(5)
becomes
Maximum Av =
Av
or the greatest error
v
tan
h,
from the error v in verticahty of
between two points of the same
arising
axis will, for a straight angle
altitude,
'2
be just double the values set down in the table as given.
is evident that for altitudes less than 5°, and with
Third. It
good
levels properly adjusted
and care
in setting up,
no appreci-
able error need be feared, even in high-class work.
A
be drawn from the foregoing disr, may be of practical use.
First. If we measure horizontal angles with an engineer's
transit whose coUimation error is c, error of horizontal axis i,
and whose vertical axis has a deviation of v from the vertical, the
few general
infei-ences to
cussion of the axial erroi-s
three effective erroi-s
(c),
c, i,
(i),
and
(v),
may combine
in a total (s), so
that for a single pointing
and
if
As
represent the total error
made
in measuring
an angle,
or for two pointings,
As= Ar+ Ai + At',
or reproducing their values,
As = c
(sec /ii— sec
+
of
v
Iio)
+
i
(tan /ii— tan Aa)
(tan hi sin iti— tan
/i2
sin
11-2)
(6)
Second. From this equation (6) it becomes e\-ident that it is
importance to choose points nearly of the same altitude if we
would by reversion eliminate all instrumental errors eliminable.
Third. Only the collimation error c and the error of the horizontal axis i can be eliminated b}' revei"sion.
Fourth. Since the error of verticality of axis v can become
larger than any other of the erroi-s, and can also have a more
serious result on the measurement of horizontal angles, it requires
special attention.
The error r, as already stated, depends not
only on care in the use of the levels in setting up, but on their
proper adjustment, and on their truthfulness and sensitiveness as
'
well.
The
Effect of the
Axial Errors on the Measurement of Angles
A MANUAL OF UNDERGROUND SURVEYING
36
of
Altitude.
— Having
devoted considerable space to the con-
sideration of the effect of small errors of direction of the three
principal axes upon the measurement of horizontal angles, we
speak of their effect on measurement of angles
This subject has been rather carefully investigated
of altitude.
by Dr. W. Jordan in his inimitable " Handbuch der Vermessungskunde," Vol. II, and we give here as a matter of considerable
interest the general result of a cumbrous mathematical discussion.
have now
For a
briefly to
fairly adjusted
altazimuth instrument, and for vertical
angles not exceeding 45°, the effect of the usual small errors
altogether inappreciable.
45°,
For angles
and when extreme accuracy
is
of
is
greater altitude than
required, greater care than
usual must be taken with the adjustments. It is to be noted,
however, that iiow we speak only of extreme accuracy and of
instruments reading vertical angles to seconds of arc.
error of the axes of 10' the
angle of 45°
is
sum
total of effective error
For a total
on a vertical
only 0.89", of 60° only 1.51", and for a total error of
it is only 7.86", and for 60° only 13.60".
30' for vertical angle of 40°
Therefore, even in the use of a fine geodetic instrument, the
three axial errors do not, with reasonable precautions, produce any
error in measuring angles of altitude less than 60°.
Of course,
in
the use of the engineer's transit, axial errors produce an entirely
inappreciable effect on measures of moderate angles of altitude,
and are not
in question.
however, be an entire misconception to suppose that,
do not have an appreciable influence in the
measurement of vertical angles, no errors are, therefore, to be feared
in such measurement.
The constant errors, such as the errors of
graduation and eccentricity of the circle, and particularly the
index error and the error of the level lying in the same plane as the
It would,
since the axial errors
are the ones requiring closest attention.
Their elimination
can be accomplished only by special methods of work and proper
instrumental adjustment and design.
circle,
—
—
Relative Value of the Adjustments.
For pure transit work
by which we mean the running of straight lines, the measuring of
horizontal angles, and the like
the first three adjustments are
the most important.
The fourth and fifth refer to the instrument
when used as an engineer's level, while the sixth, though classed
with the first three, is by no means essential. Indeed, this adjustment should be seldom made, inasmuch as its performance
—
INSTRUMENTS
is liable,
by moving the
37
cross-hair intersection eccentrically, to dis-
place the second and third, which have already been performed.
hair, however, become necesand third must be tested again so as to insure their
non-disturbance. The verticality of the hair, though not abso-
Should an adjustment of the vertical
sary, the second
lutely necessary for accurate work,
is exceptionally convenient for
determining the true- perpendicular when only a small portion of
a rod sighted to can be seen. Frequent tests of the vertical hair
are useful, but its adjustment is unwise unless followed by a readjustment of the instrument in regard to the line of collimation.
General Remarks on the Adjustments. It is well to note that
—
all of
these adjustments, except the fourth, can be performed
while the instrument
still
remains in one position.
being entirely independent of the rest
and indeed
may
be
The fourth
left until
the
last,
sometimes entirely omitted, as the use of the transit
as a level is comparatively rare, except in mine work where it almost always replaces the level.
The great fault of young surveyors is to blame inaccuracies in
is
work upon a faulty construction
of the instrument.
For
no excuse. Errors may arise from three causes: (1)
Errors- in, or damages to, the parts of the instrument; (2) insufficient adjustment, and (3) carelessness in setting up or in sightThe last are by far the most probable causes of inaccuracies
ing.
in work, and, if the adjustment be unsatisfactory, the surveyor
has no one to blame but himself, while errors in the instrument
can always be detected by the refusal of the instrument to respond
In the latter case, the
to repeated tests while being adjusted.
only remedy, beyond obtaining a new instrument, is to note
carefully what species of errors are likely to occur, and so to handle
the instrument as to avoid them as far as possible.
A wide and nearly level stretch of country is by all means
preferable for the performance of the adjustments.
The sights
taken, except those in the fifth and sixth adjustments, should be
as long as possible, so that the ensuing apparent error may be
their
this there is
greater.
After the surveyor has used his instrument for some time, he
be sufficiently competent to judge of its accuracy. Until
may
then the instrument should be tested at least once a week, if not
more frequently. If he should find the instrument one of accuracy and great permanency of parts,
less
frequent adjustments
A MANUAL OF UNDERGROUND SURVEYING
38
may
be made.
suffers a
ment
Adjustments should always be made
fall,
or
if
if
the instru-
the surveyor has reason to believe that a
severe jar has happened.
The foregoing methods, while essential to the proper testing
and use of the transit, are intended only as instruction in practical
field adjustments, and these do not take the place of the permanent adjustments given by makers, although they are to some
extent a test of the latter.
Having treated
The Errors of Eccentricity and of Graduation.
the axial errors, we still have to consider those errors which are
due to: (1) the eccentricity of the telescope; (2) the eccentricity
—
of the circle; (3) the eccentricity of the verniers,
and
(4) the in-
accuracies of graduation.
FIG.
19.
— ECCENTRICITY
OF THE TELESCOPE.
—
Assuming, in the first
of the Telescope.
no eccentricity of the circle or of the vernier,
be an eccentricity of the telescope on account of
The Eccentricity
place, that there
there
may
still
is
the line of sight not being mounted directly over the center.
Fig. 19 the eccentricity of the line of sight of the telescope
represented
by the
In
is
radius of a circle conceived as described about
the center, C, of the
circle.
All lines of sighting will be tangent to
Pi and P2 are two points to which the eccentrically
placed telescope is in turn directed, and between which it is intended to measure the angle. The angle a represents the true
this circle.
angle, while a'
and
a" represent the angles
positions of the eccentric telescope.
figure gives us the following relations:
A
measured with two
simple inspection of the
INSTRUMENTS
A MANUAL OF UNDERGROUND SURVEYING
40
circle; (2)
the error arising from the non-intersection of the center of
rotation by the straight hne joining the zeros of the verniers or microscopes, or the error of eccentricity of the verniers or microscopes,
due to their zeros not being exactly 180° apart, as measured at the
center of the circle;
(3)
errorsdue to faulty graduation;
due to inaccurate estimate
The
error of eccentricity of the circle
follows: In the
accompanying
FIG.
alidade,
2
AA'
C that of
(4) errors
in reading the verniers or microscopes.
Fig. 20, let
may be investigated as
C be the center of the
— ECCENTRICITY OF THE CIRCLE.
the circle, CC the eccentricity,
20.
e,
the effectible error, e of the eccentricity.
and A' A"
Let
AB
straight line joining the zeros of the verniers or microscopes;
the reading of vernier A,
B
of B,
or
be a
A
A' the true reading of vernier
A, B' the true reading of vernier B. Then assuming that by
careful centering of the instrument e has been made very small,
AA' may be regarded
CD;
E0° by E and 0°A', as already
stated, by A', or the angle EC A' by {E-\-A'), and representing
the radius C'A' by r and 206,265" by s we have, from the triangle
the arc
as equal to the perpendicular
and, therefore, representing the arc
CC'D, the following expression:
AA' =
—
sin
(E
+
A')
r
But since sin (E + yl') and
we may write
AA' =
sin
—
es
r
sin
(E + A) are sensibly the same
(E
+ A)
(1)
:
INSTRUMENTS
If
we now
alidade will
allow
B
to coincide with B' the vernier line of the
B'A" and the
in the direction
lie
41
central angle,
We
s.
effective error
due
A" A' = 2 ^A' = the
to the eccentricity of the circle will be the arc
have, therefore, finally the following ex-
pression for the error due to eccentricity of the circle
e
—
=
sin
+
(£
A)
(2)
r
This equation shows that for the direction EF, when sin
{E + A)=0, the error e becomes zero, and that for {E + A) =
±90°,
e
=—
;
which
is
the
maximum
r
value for the error due
*
to the eccentricity of the circle.
from (£; + il)=0° to (£ + A) = + 180°
a positive series of £ results, and from 0° to —180° a negative
Hence, if but ojie vernier is read in a given position
series of s.
of the telescope, the telescope then transited and directed to the
same object, and the same vernier read, the mean of the two
readings will eliminate the eccentricity. For it is clear that the
It
is
also evident that
each case make equal angles with the
and hence e have the same value with
In other words, since in equation (1) sin (£ + 4)
line of the verniers will in
line of zero eccentricity,
opposite sign.
will
be positive, and sin
EF
,
(£+4 + 180°)
negative,
values of opposite signs, and, therefore, in a
s will
mean
have equal
of values will
disappear.
We may
also
apply equation
(1)
to the readings A'
and B'
and write:
^'= A + -^sin
(£;
+
A)
(3)
(E
+
B)
(4)
r
5'
=S+
^
sin
r
By
we
taking the
mean
of these
two readings
as thus expressed,
get:
} {A'
+
B')
-\
{A
+ B)=
?^sin
r
(^
(A
+
5)
+
E) cos \ {A-B),
whence we see that the difference between the mean of the true
readings and the mean of the vernier readings decreases as {A — B)
approaches 180°; and when {A — B) exactly equals 180°. or when
the verniers are rigorously 180° apart, this difference is nil. The
mean of the readings of two verniers of microscopes which are
'
A MANUAL OF UNDERGROUND SURVEYING
42
180° apart, therefore, completely eliminates the error of the eccentricity of the circle.
In order to comprehend the effect of even a small displacement of
let us from equation (2) take the maximum value of £ or
the center,
«T
Maximum
e
=
—
2 es
r
and assume
e
= 0.0003
Maximum
in.
.
=
and
2
r
= 3.0
in.
Then we have:
X 0.0003 X 206265^ ^
4^ 25"
o
If e
had been as great as 0.003 in., the maximum
would have been 6' 52.5".
error of ec-
centricity
This fully illustrates the importance of three things:
Correct designs of the axes or 'centers' of the instrument;
(1)
(2)
E
FIG.
21.
— ECCENTRICITY
OF THE VERNIERS.
care in adjusting circle for eccentricity; (3) the reading of both
verniers or microscopes in the higher classes of work.
The error of eccentricity of circles, as here treated, is really
made up of two mechanical errors, viz.: (1) inaccurate centering
of the circle
on its
axis of center,'
'
and
(2) ellipticity of
the centers
'
Moreover, there arises in some designs of 'centers,'
a wear of 'centers' which produces a serious eccentricity and
themselves.
which cannot be remedied mechanically except by furnishing the
instrument with new 'centers.'
The Error of Eccentricity of the Verniers.
assumed that the zeros
— We have hitherto
of the verniers or microscopes are exactly
INSTRUMENTS
180° apart.
This-
may
what may be termed
of the verniers
is
43
not be the case; and
if it is
eccentricity of the verniers.
we have
not,
The
eccentricity
the perpendicular distance between the center of
the ahdade and the straight hne joining the zero of the verniers,
and
in Fig. 21 represented
is
duces
is
The
by CV.
effective error
a constant one, represented by the angle
error of eccentricity
variable one.
If,
s, is,
o.
The
it
pro-
effective
on the other hand, as already shown, a
then, the zeros of the verniers or microscopes
are not accurately 180° apart, but
make an angle of 180° + a so
moment out of question,
that, the eccentricity of the circle for the
B'
= A' + 180° + a;
(4) for
and we may then
from equations
find
(3)
and
the entire difference of reading between the two verniers, or
B-A-180° = 8.
d
=
a
+ ?-^{smE +
A).
(5)
r
Considering the alidade turned from
through the angles
90°, 180°,
four respective values of
A
do-
a
its
0° position respectively
and 270°, we would have
the following values of d:
+
'^^^
r
Bin
E
for these
A MANUAL OF UNDERGROUND SURVEYING
44
The objection to the use of the last two formulas for determining
s are that but two differences are employed, and hence errors
of observation and of graduation may make the result uncertain.
The only complete method for determining a and e, free from
complication with errors of graduation and observation, is to
determine a large number of d's for different direct and reversed
a and
positions of the ahdade, and" then treat the results of the observations according to the well-known
method
For
of least squares.
such treatment of the subject our readers are referred to standard
treatises
(11),
and
on practical astronomy and geodesy.
(12),
however, enable us for
derive fairly reliable values of a and
£
many
Equations
(10),
practical purposes to
by simply making four
sets
of observations, at intervals of 90°, of the differences of the vernier
or microscope readings.
The Errors
of Graduation.
— The errors
of graduation, unless
be investigated until the effect of
and of the vernier has been ascertained.
of the coarsest sort, cannot
eccentricity of the circle
After determining the value of the eccentricity of the circle and
computing its effect on the division whose graduation error is to
be found, the outstanding differences, allowing for the constant
deviation of the verniers from the required 180°, are to be attributed to graduation and observation errors. The errors of
graduation are divided into two classes: (1) Those which are of a
periodic character, and (2) those which are of an accidental charac-
The former depend upon slow changes
ter.
in the temperature
of the engine during graduation, or in the condition of the cutting
tool.
The
latter are not
dependent on known conditions, and
being as likely negative as positive, are classed as accidental.
is
It
usually found in well-graduated circles that the major errors
of graduation are of the first class
and may be expressed
as a peri-
odic function of the varying angle.
Instead of using the distance apart of the two vernier zeros
may be used as a
and read by means of
as the standard angle, the length of the vernier
test
when successively applied round the
the excess graduations of the vernier.
circle,
The
effect of the eccentric-
on
computed and duly allowed for before errors of graduation as such
can be noted. For a complete discussion of this subject we refer
the reader to the " Vermessungskunde " of Jordan, and to the treatises on practical astronomy of Chauvenet, Brunnow, and Sawitsch.
ity of the circle
the length of the vernier must, in this case, be
INSTRUMENTS
45
—
The foregoing discussion of
The Errors in Practical Work.
the axial and circle errors, aside from its value in suggesting points
of construction and adjustments of special importance to accuracy
of work, should also afford
The
many
a hint to the practical engineer.
limited space does not permit us to state either the special fea-
programmes of work which are
and eliminate all the errors.
this review of the errors than by
tures of instruments or the special
in the different cases required to avoid
And
we may not
yet
better close
drawing attention to se\'eral points of caution to be exercised in
the three most usual forms of work with the transit,
the
viz.,
measurement of vertical angles, the laying out of straight lines,
and the measurement of horizontal angles.
Vertical angles have their zero in the horizon, and this zero
must be physically determined by a level lying in a plane parallel
to the graduated circle on which the measurements are to be made.
This level, whether it be a plate level, the telescope level, or a
special level attached to the vernier arm, should not only (1)
lie
have a
sensitiveness comparable to the fineness of the reading on the
circle, and (3) should always, in an observation, be adjusted to
zero position of bubble, or else be read for the small deviation of
in a plane parallel to the measuring circle, but (2) should
the bubble.
If
the telescope level
used, the vertical angle
is
simply the difference of readings on the
of the bubble
and
circle for
is
the zero position
for the pointing.
from the
amount. Both
the error of adjustment of the plate level and the index error can be
eliminated by striking the mean of the measures of the angle taken
with the telescope, both in the direct and in the reverse, or transited
The
error of vertical axis, or the deviation of this axis
vertical,
may
affect the
measurement
position, provided the alidade
revolved
180°.
The
erroi-s
is
of
carefully releveled after being
eccentricity
reading both verniers or microscopes,
and two
to the whole
if
are
and,
For an
must be
relied on.
eccentricity
if
may,
for small angles, be considered constant;
the 'fourth adjustment' has been accurately made,
eliminated
zero
Transiting
verniers, however, require a complete circle.
arc of a circle with one vernier, the adjustments
The
and
by
eliminated
there be two.
by taking the
for the pointing.
nated by using an entire
The method
it is
difference of the readings for bubble at
The graduation
circle,
errors can only be elimi-
capable of being shifted on
of reiteration of the angle
may
its axis.
then be employed.
A MANUAL OF UNDERGROUND SURVEYING
46
Straight lines can be prolonged accurately only with good
instruments and the most careful attention. Here the secret of
the elimination of errors is so to arrange the programme of work as
to distribute the errors symmetrically with respect to the proposed
a circumpolar star
If
line.
meridian
it is
is
observed for the direction of the
therefore important that the observations, both as to
number and
character, be arranged symmetrically with regard
to the time of transit, or the time of elongation, as the case
If
the pointings for a line are
all
horizontal,
and the
be prolonged by transiting the telescope, or turning
it
may be.
line is to
over on
its
horizontal axis, the constant collimation error will enter with
double
its
value.
If
one of the pointings
is
at an angle, as in the
case of determining the direction of a circumpolar star, the errors
and
of collimation, of the horizontal axis,
may
vertical axis
all
enter the result.
of verticality of the
Particularly would the
error of verticality, due to the level at right angles to the line, be
and necessitate attention to the sensitiveness, adjustment,
and reading of the level lying in that direction.
serious,
A
by
line
may
secting
be prolonged so as to eliminate
up over the forward
setting
rear
point,
transiting
these errors,
all
point, leveling cross level, bi-
telescope,
locating the
required
and then revolving the alidade 180° and repeating the
operation, and taking the mean position between the two located
point,
points as the true required point.
Horizontal angles, including the horizontal straight angles
most frequently measured in practical
work, and the errors to which they are liable
just referred to, are those
have, therefore, been fully discussed.
Auxiliary Telescopes.
When the line of
sight is highly inclined, the main telescope
—
of the transit
becomes
terference with the
FIG. 22
—PRISMATIC
used at
all,
be used
if
but
^^'^^I'^l different
mount
EYEPiECE.
if
owing to
useless,
plates
in-
the transit.
of
devices are used to sur-
this obstacle.
When
the sight
is
downward, the main telescope cannot be
the sight be upward, the main telescope can
a prismatic eyepiece (Fig. 22) be inserted.
This
little
attachment is made by every engineering-instrument company
and is very handy for several purposes.
By means of it the
transit
man
looks along a line at right angles to the axis of the
INSTRUMENTS
47
telescope instead of longitudinal to
it.
This device does not,
however, furnish any aid for downward sights.
For this purpose, an auxiliary telescope must be used. These
are principally of two kinds; the top telescope attached above
FIG.
23.
— MINING
TRANSIT.
the main telescope, or the side telescope attached to the end of
the horizontal axis of the main telescope outside the standard.
The
solar
compass
may
be forced to do service as an auxiliary
A MANUAL OF UNDERGROUND SURVEYING
48
telescope, but its use
is
possess one.
The Top Telescope.
objectionable and but few mine surveyors
— The
top telescope (Figs. 4, 8, 23) is
by means of one or two bars
fastened rigidly to the main telescope
long enough to cause the line of sight of the top telescope to clear
the horizontal plates when the main telescope is placed in a vertical
These bars,' if two are used, are usually brazed to the
position.
shell by the manufacturer, and attached to the main
by means of nipples and coupler nuts. The manufacturers make all light mountain transits with the nipples so that
the top telescope may be used if desired, and old transits, if sent
top telescope
telescope
to the manufacturer,
The adjustments
may have
the attachments fitted to them.
of the top telescope are
manufacturer adjusts the top telescope during
very simple. The
making, so that
its
the axes of the two telescopes are parallel and in the same plane.
The positions of the objective and eyepiece can be changed only
by the manufacturer.
The only adjustments
user are those of the cross hairs.
in the same plane as that of the
for
the transit
First, the line of sight
main
must be
telescope; second, the lines
must be parallel, and third, the cross hairs must be truly
and vertical. The first is accomplished by sighting
upon a plumb-bob string with the main telescope and adjusting
of sight
horizontal
it coincides with
top telescope has a
the vertical cross hair of the top telescope until
the string.
special
The mounting
of the single-stem
arrangement for the adjustment to a vertical plane.
secure parallelism of the lines of sight of the
parallel horizontal strings are fastened
up
two
telescopes,
To
two
at a distance of 100 feet
or more, so that the perpendicular distance between the strings
is
equal to the perpendicular between the axes of the two telescopes.
The main
telescope
is
sighted
upon the lower
zontal cross wire of the top telescope
coincides with the upper string.
The
is
string
and the
hori-
raised or lowered until
it
cross hairs are brought into
true vertical and horizontal positions during the previous adjust-
ments by sighting on vertical and horizontal strings.
When sighting on a point with the top telescope the horizontal
angle is not affected, and is read direct from the horizontal circle,
but the vertical angle must be corrected.
In Fig. 24, R is the distance between the lines of sight,
md is the measured distance, va is the vertical angle as read
from the vertical circle and a is the amount by which it must be
INSTRUMENTS
49
corrected to give the true vertical angle. This angle a is evidently the angle whose sine is iZ/rw d. Therefore the true vertical
V A±R/m d. When
angle equals
the angle
zontal, the correction is to be subtracted,
FiG.
added.
This
is
24.
— TOP
easily
TELESCOPE:
is
below the hori-
when above
it
must be
ELEVATION.
remembered, for the sign
of the angle
is
also
the sign of the correction.
—
The Side Telescope.
The side telescope answers the same
purpose as does the top telescope. It clears the plates when
A MANUAL OF UNDERGROUND SURVEYING
50
pointed vertically.
zontal axis of the
Being screwed to an extension of the horitelescope, outside of the standard, it can
main
be attached only to instruments made for that purpose.
The adjustments of the side telescope are practically identical
with those of the top telescope. The maker fixes the position of
PIG.
25.
— SIDE
TELESCOPE: ISOMETRIC PROJECTION.
the auxiliary telescope so that the axes of the two are parallel
and in the same horizontal plane. The field adjustments are those
of the cross hairs only.i
by
sighting the telescopes
'
This
is
The lines of sight are made parallel
upon two plumb lines whose distance
not true of some auxiliaries recently put upon the market.
—
INSTRUMENTS
51
apart equals the distance between the centers of the telescopes.
in the same horizontal plane
The horizontal wires are made to lie
by sighting upon a horizontal line.
When
elevation
sighting a point with the side telescope
is
read direct from the vertical
circle,
its
angle of
but the horizontal
angle must be corrected.
In Fig. 25,
and
is
R
is
the distance between centers of the telescopes,
is the horizontal distance, vd the
the measured distance; hd
vertical distance, va the vertical angle, and a the amount
the angle, as read from the plates, must be corrected.
= ——
Sin a
but hd = md cos va
,
hd
Then
sin a
a
Or,
a
md
= sin"
by which
cos va
R
.1
md
cos va
= ^^—
Now^ = sin-i-^
md
cos va
Substituting this value for 6
a
As the
sine
and tangent
the formula a
is
= sin-i
= tg-i
md
,
as before.
cos va
of small angles are
—
md
may be
;
approximately equal,
used: and indeed,
if,
as
cos va
most commonly done, the distance measured be from point
main
sighted to the center of the end of the horizontal axis of the
telescope, the formula
is
theoretically correct.
be on the right side of the instrument, the
correction must be added to the angle read from the plates to secure
If the side telescope
if on the left side of the
must be subtracted. By sighting a point with, first,
the telescope upon the right side, and then again with it upon the
left side (by revolving and plunging) two angles are read which
are evidently each in error by the amount a, or the difference
between the two readings is 2 a. Halving this amount and
adding it to one reading, or subtracting it from the other, gives
the true bearing. The value of a can probably be obtained
the true azimuth of the point sighted;
instrument,
it
A MANUAL OF UNDERGROUND SURVEYING
52
with greater accuracy by this double reading than by the formula;
and
besides, the reversed reading eliminates
any error which may
be introduced by the nonadjustment of the instrument.
FIG.
26.
-TRANSIT WITH DUPLEX TELESCOPE BEARINGS.
INSTRUMENTS
53
Besides the ordinary top and side telescopes, some of the
instrument makers are putting an interchangeable auxiliary
telescope on the market. This screws on to a single standard
FIG.
27.
— LAMP
TARGETS.
above the main telescope as a top telescope, or upon the end of
the horizontal axis as a side telescope.
Besides the type mechanism for auxiliary telescopes as ex-
A MANUAL OF UNDERGROUND SURVEYING
54
many
plained above, there are nearly as
ments as there are makers
Transit with Inclined Standards.
transit
is
in the
the engineer
The
line
is
variations
and improve-
of surveying instruments.
arrangement
— The novelty in this mining
of the inclined
standards by which
enabled to range the telescope to a vertical
line.
without any additional telescope, while the
of collimation remains on a line passing through the center of
result is obtained
measured horizontal angles have
and no correction for offset is
necessary, avoiding the inconvenience and liability of error of
instrument; consequently
all
their vertices over a center point,
double telescopes.
By means
ment
of longer centers, a light counterpoise
of details the overbalance of telescope
Transit with Diiplex Telescope Bearings.
is
and arrange-
entirely destroyed.
— This transit
answers
all
the purposes of the ordinary transit and in addition can be used
to
make
highly inclined readings
by
setting the telescope into the
bearings of an additipnal pair of inclined standards (Fig. 26).
Mining Transits with Lamp Targets.
Mining transits are
—
furnished,
when
so ordered, to be used with mining
lamp
targets,
detachable above the leveling screws and interchangeable with the
instrument, so that in sighting forward the target is placed in
from tripod and moved into forlamp target is substituted on the one from
which the instrument (Fig. 27) is removed.
The target is the same height as the transit, measured from
the parallel plate to the line of sight, and being provided with
two spirit levels set at right angles and having both horizontal
and vertical motion, it is quickly set. to the proper angle of the
line of sight by means of the sight vane.
The face of the target
is made of milk-white glass (on which is painted a suitable figure)
and illuminated from the back by a bull's-eye lantern, which can
be thrown in and out of position as desired. It is essential that
position, the instrument taken
ward
lard
tripod, while
oil
be used with the lamp.
The use
of three tripods with interchangeable lamp targets and
head became very common in English collieries, and has
been used to some extent in the coal mines of this country. The
system has not met with favor among American engineers, how-
transit
ever.
—
The Brunton Pocket Transit.
This instrument has been
meet the requirements of mining engineers,
especially designed to
INSTRUMENTS
mine managers, and
adapting
the
it
geologists,
its
55
and peculiar features
and on
size
to preliminary surveys both underground
surface,
to
taking topography,
to
geological
field
work,
and, in short, to any purpose for which a light pocket instru-
ment
is
desirable
and where a moderate degree
of accuracy will
suffice.
This
neere
little
instrument
and deservedly
does not
own
so.
one, and,
ably in his pocket.
if
very popular among mining engi-
is
Hardly an engineer
he
is
It weighs only 8 oz.
to be met who
Brunton is prob-
is
in the field, the
and
is
2|
X
1
in.
in
dimensions.
Fig. 28 shows operator's view of instrument when using as a
compass for taking horizontal angles or courses. In the mirror
can be seen the reflected degree circle, needle, and level.
FIG. 28.
— READING
HORIZONTAL
FIG.
29.
— READING
VERTICAL
ANGLE.
ANGLE.
29 shows the operator's view, of the instrument when taking vertical angles.
In this operation, the lid is raised to an angle
of approximately 45° with the case the sighting bar is straightened
out until it is parallel with the face, its end being turned at right
angles as shown; then the station is sighted through the hole in the
end of the folding sight and the opening in the mirror, the vernier
lever being turned until the bubble tube is level, which can be
When the sight
plainly seen in the reflected image in the mirror.
instrument and
the
of
lid
the
raise
has been obtained, it is better to
Fig.
;
take the reading direct from the face than to attempt reading it in
the mirror, where the reversal of the figures might sometimes cause
an
error.
A MANUAL OF UNDERGROUND SURVEYING
56
Tapes
The narrow
ments, the
less
side
tape
wire
foot tape
hand a
measure-
all
work requiring any degree
of accuracy, the
were common, but the narrow
For most underground work the 100most convenient, but the surveyor should have at
now
is
for all extended measure-
for radiating stope
used.
is
Formerly tapes
flat
now used
is
measurements or
accurate linen or metallic tapes are sometimes
allowable, but for
steel
tape
steel
For the
ments.
is
I in., or wider,
a favorite.
200-, a 300-, and, for surface work, a 500-foot tape.
Besides
need a small 5- or 10-foot vest-pocket tape
for measurements falling between the 5-foot marks on the long
tapes and for measuring the H. I., H. P., etc.
The markings were formerly etched upon the steel ribbon.
these, he will, of course,
FIG.
This practice has given
or 10-foot mark.
notch upon
it is
stamped into
its
The
30.
way
it
is
COMPASS.
to a notched brass sleeve at each 5-
is easily found, even in the dark, the
permanent and readily found, and the number
sleeve
surface remains always legible.
sleeve are beveled so that
which
— MINER'S
it
The ends
of the
does not catch upon things over
drawn.
In the coal mines of the East a tape 310
ft.
long has been a
The extra 10 ft. is at the zero end, and is graduated to
feet and tenths.
The tape itself is graduated to 10 ft. The head
chainman holds the last 10-foot mark to the forward station, and
favorite.
INSTRUMENTS
57
the rear chainman then reads the additional feet and decimals
from the 10-foot portion of the tape back of the zero point.
In the metal mines, the tape is stretched between the two
points and the fractional part of a 5-foot division is measured with
the 5-foot pocket tape.
To mark
the point upon the tape op-
posite the point to which" measurement
being made, some engi-
is
upon the
neers use a small clip which snaps securely
simply mark the point with thumb and
tape.
Others
finger.
Where a long tape is being used, it is convenient to have a clip
handle which can be fastened to the tape at any point. By using
this the tape is easily pulled taut without the liability of kinking
which is present when the tape itself is taken hold of directly.
For much underground work, a reel is necessary. On the surface the reel is a nuisance, but underground it is often necessary
The reel problem
to keep a portion of the tape wound upon it.
is a live one, and the manufacturers of surveyors' apparatus have
The reel must
failed to meet it as they have other problems.
be strong, for it receives very rough usage, and it should be light.
The crank for winding up the tape should be long to give a good
leverage, and the handle upon the opposite side must be strong
and so placed that the reel balances well when winding the tape
it
The space
in.
for the tape
tape will not bind, and
when the
must be roomy enough, so that the
it from unwinding
a spring fitted to hold
down.
have
the mine blacksmith make their reels,
Many engineers
When the tape
larger than their tape.
reel
size
and others use a
a
this reason
size.
For
own
of
its
reel
into
a
will
not
fit
is dirty, it
it is
reel is laid
best to use a 500-foot reel for a 300-foot tape, etc.
wiped and oiled each
of course, be cleaned
—
The tape should,
night after using
it
in a
wet
place.
broken when handled carelessly,
mend them
in the field.
A sleeve
it
As the
steel tapes are easily
often becomes necessary to
of thin copper, cut
and bent
to
around the tape, a bottle of acid to clean the ends of the
It
tape, a little solder and a torch, and the trick is easily done.
requires practice, however, to make a neat job of it and have the
tape measure up correctly over the mended spot.
The engineer can well afford to carry a couple of patent tape
These do away with the necessity of a soldered
splices with him.
entirely.
splice till he is back in his office, or, in fact, do away with it
fit
closely
The ends
of the
broken tape are inserted
in a metallic sleeve
A MANUAL OF UNDERGROUND SURVEYING
58
and held by small screws turned down
upon them. These do not catch upon obstructions, and will
withstand the pull necessary to stretch the tape. Fig. 32 shows
a punch and set used for repair of
steel tapes by use of rivets.
(Fig. 31) of the right size,
No
the
FIG.
31.
— TAPE
attention need be given to
corrections
for
temperature
The
and sag on short tapes.
stretch on even a 300-foot tape is
SPLICE.
only nine-hundredths of a foot
30° increase in temperature.
for
The temperature underground seldom
is
many
degrees different
from the temperature at which the tape is standard. The sag
on an unsupported 500-foot tape may be upward of five-tenths of
a foot, and for that reason the long tape should be supported.
The effect of sag is offset by the stretch if the correct pull is known.
On
short tapes, neither
is
appreciable.
Johnson's 'Theory and Practice of Surveying' says: 'For an
accuracy of
1
in 5000, the tape
may
be used in
all
kinds of
by hand, the horizontal position and
estimated by the chainman. For an accuracy of
mean temperature of the tape should be known
weather, held and stretched
amount
of pull
1 in 50,000, the
FIG.
32.
— TAPE
RIVETING TOOLS.
to the nearest degree Fahr., the slope should be determined
stretching over stakes or on ground
the pull should be determined
by
whose slope
is
by
determined,
spring balance.'
While the errors due to temperature, sag, and stretch are too
small to be appreciable on 100-foot tapes, they must be calculated,
and the corrections made, where long tapes are used on important
work.
INSTRUMENTS
59
Repairing Engineers' Field Instruments
The writer has frequently noticed the lack
part of
ments.
many
engineers to
one
If
instrument,
is
make minor
of ability
on the
repairs to their field instru-
so unfortunate as to
fall
while carrying an
generally results in so damaging
it
^
it
as to render
it
At such times the man with
and a few simple tools can make at least
useless to the average assistant.
some mechanical skill
temporary repairs and thus save his employer considerable expense. In such an emergency an engineer who will not make
an earnest attempt to repair the damage is not deserving of an
Every engineer whose work takes him some
him a few tools, such as a
pair of flat pliers, a small file, large and small screw-drivers, a
spool of soft brass or copper wire, a pocket knife, also an extra
level vial, an ounce or two of plaster of Paris, and a bottle of
honorable
title.
distance from a city should keep with
liquid shellac.
The young engineer should be
familiar with the details of
construction of the instruments he uses, and
it is to be regretted
not given on this important subject.
The catalogues of most important makers give valuable informa-
that more instruction
tion regarding their
is
own
of general application,
instruments, and also
which
it
many
would be well to study
suggestions
carefully.
Suppose a transit has a fall the standards are probably bent,
and a level vial broken. Many men would start for town at once
under such circumstances, and possibly lose several days' time in
having repairs made, but remember that the successful engineer
is the one who does things and never admits that he is stumped.'
If you are of this kind, take the transit apart, lay the bent standard
on a fiat block of wood, and with another block of wood and a
hammer or mallet proceed to straighten it. This will not be an
:
'
easy task, but
it
'
'
can be done.
The
level
tube should then be taken
apart and cleaned out, the extra level vial inserted and blocked up
with a leaf from a notebook, taking care to get the marked or
convex side of the tube uppermost. If the level divisions are not
cut on the glass, look for a small file scratch near one end of the
vial; or if that is not apparent, put that side up which shows
inside signs of grinding.
'
Mix up a spoonful
of the plaster of Paris
Engineering News, January 25, 1906,
A MANUAL OF UNDERGROUND SURVEYING
60
with water and place a portion around each end of the glass. In a
few minutes this has hardened and the tube can be replaced.
"Whittle out a new one
Is one of the adjusting screws broken?
from a piece of hard wood, fastening that end also, if necessary
and possible, with a piece of copper wire.
Broken tripod legs are easily replaced with a piece of wood
and some string, or wire, held in place by shellac. You may not
make a neat job of your repair work, but don't mind that if you
are able to complete the work assigned you without loss of time.
The writer has in mind a man of considerable skill in certain
lines, who had 'accepted' an offer of a responsible position and
had been placed at work. As a result of a moment's carelessness,
an alidade ruler was slightly bent, and, without attempting to
repair it, he rushed to the nearest telegraph office and sent a
message to his chiel, reading: 'I have bent my alidade ruler.
What shall I do? The answer which came back was Straighten
This he easily did. At another time a levelman telegraphed:
it.'
:
'
'
'Cross wires broken; send another level,' although he
knew
that to
answer he redo so would
insert
new
wires,
disband your
can't
cross
was,
'If
you
ceived
party,' and with the possibility of discharge as a stimulant he
found that repairs were easily made. Still another levelman,
who could not catch his chief by telegraph, stopped the work of
his party and sent his Y-level nearly 1000 miles to an instrument
maker in order that the eyepiece might be centered on the crosswires.
He could have remedied that trouble in five minutes by
No error would have
the proper manipulation of a screw-driver.
been introduced into his work, even if the cross wires were not in
result in a delay of several days; the
the center of the
field of
view, so long as the usual level adjust-
man had not learned to distinguish
between a blemish and a fatal defect.
During the past year in certain instrumental work under the
writer's charge, an expense of over fifty dollars was incurred in
having new cross wires inserted by an instrument maker, not
ment had been made.
This
including the loss of time
Broken
to replace
by the various
parties.
cross wires are of frequent occurrence,
if
quiring his assistants to learn
how and
;
in order to aid
prepared a description pf the process, which, as
others,
is
and are easy
one knows how; consequently the writer
here given in
full:
it
may
is
now
re-
them he has
be of use to
INSTRUMENTS
A small bottle
61
of shellac dissolved in alcohol (preferably a thin
dry quicker) and a cocoon of spider web are
tools required are a pair of dividers, or a 6-inch
solution, as that will
needed.
The only
piece of soft iron, or copper, wire bent to a U,
available, a forked stick will answer.
and if neither is
The dividers, wire or forked
beeswax pressed around each
should have a small piece of
end to hold the web. A couple of small pointed sticks the size
of matches are useful.
The best cocoons for ordinary use are yellowish-brown, about
long; they may usually be found in dead or hollow trees, or
in.
j
under the bark of old stumps.- Good ones may often be found
under rocks, or in old barns or greenhouses. Occasionally single
webs, which may be used in an emergency, may be taken from
stick,
grass or bushes or limbs of trees; these are generally rough
and
but some of their defects may be removed by gently rubbing
them with a small stick. If a very fine web is needed, it may be
secured from a small white cocoon. A good cocoon will furnish
enough webs to last for years, and each chief of,party should have
one packed with the shellac in his instrument box. The best web
obtainable can be secured by making a spider spin one as he falls
from the end of a stick. A small spider will probably spin a fine
web, and a large spider a coarser web such webs are always smooth
and free from dust. If the spider is made to jump from the end
of the dividers, or forked stick, the web can be wrapped around the
ends and so be in position for immediate use.
Take the instrument which needs the new cross wires to a
place sheltered from wind and dust.
Unscrew and remove the
eyepiece slide without disturbing the object glass. Take out two
opposite capstan-headed screws of the four which hold the crosswire ring in its cell, and loosen the other two.
Using the latter
as handles, revolve the ring 90° and insert one of the pointed
sticks through the end of the telescope tube into a screw hole;
and, while using it as a handle, remove the other screws and take
out the ring. Clean the lines of the reticule ring from all old
shellac or dirt and lay it on a board or table with the marked side
up.
Draw some of the web from the cocoon, either with the
dirty,
;
fingers,
or with one
of
the moistened,
pointed sticks.
Keep
and working the tangled mass until an inch or two of single
web is drawn out. Attach the ends of the web to the dividers, or
wire, by winding them around the wax and pressing them in with
pulling
A MANUAL OF UNDERGROUND SURVEYING
62
web around the forked stick, fastening
Examine the web for defects by means of a pocket
magnifier, or the eyepiece from the telescope.
If the web is
satisfactory in size and quality, moisten it by dipping it in water
for a few seconds or by breathing gently on it a few times.
As
the wet web lengthens, take up the slack by opening the dividers,
or by bending the wire or stick, but do not attempt to stretch
the web more than about
in., from its original dry length.
Place the web (still on its holder) carefully over the reticule, allowing the holder to rest on the table, thus stretching the web
the fingers; or wind the
it
with shellac.
-j^g-
and move it about until it falls exactly in the center of
two opposite lines, using a magnifier to insure accuracy. Put a
small portion of the liquid shellac over each side of the web,
about -^ in. from the central opening of the reticule, and leave
undisturbed for 3 or 4 minutes, or until the shellac hardens.
While the shellac on one web is drying, another can be prepared.
slightly,
After
all
are set, replace the reticule in the telescope
the method used in removing
it.
When
by
reversing
in place the cross wires
should be on the side of the rig toward the eyepiece.
Instruments such as the prism level, dumpy levels, and transits,
not pro-iaded with wyes or similar devices for adjusting the cross
may be put in close adjustment by means of improvised
wooden, or metal, rings in the following manner:
For the prism level, the body of which has a close finish,
remove the object-glass cap and run the eyepiece slide part way
out as though focusing for a near-by object. Provide a Y of wood,
or metal, large enough to fit over the object-glass end of the
telescope where the cap usually fits.
Take a second Y of a size
wires,
suitable to enclose the eyepiece slide near the
main telescope
tube.
Fasten these Y's securely in an upright position and rest the
telescope in them, sight a distant point which the cross wires cut,
revolve the telescope in the wyes and adjust the cross wires in
the usual way. A final adjustment must be made for such instru-
ments as
this by the usual methods.
But prevention is always better than cure, and a great many
instrument troubles may be prevented by care in handling the
instruments, and by the frequent application of a little oil (a very
little will
answer) to spindles, leveling screws, tangent screws, and
An occasional cleaning with an oily rag will work
telescope slides.
wonders.
Never overstrain a screw; make
it
snug and no more.
INSTRUMENTS
63
The workman who takes good care of his tools, who learns to
do good work with the mean? available, is not the man who fills
He knows it is results that are wanted,
his report with excuses.
not excuses.
The atmosphere
is,
of a
mine
then, quite necessary that
is
generally
all
warm and
moist.
It
the surveyor's instruments be
warm room. Otherwise they will condense the moisture
atmosphere when taken underground, and the glass become
fogged and the metal parts rusted.
kept in a
of the
Bibliography.
— Surveyors' Instruments, Eng. and Min. Jour.,
Instruments,
vol. ix, p. 8, 1906; Transit
Tapes,
p. 1,
ibid., vol.
iii,
p. 95,
ibid.,
1891; Repair of Instruments, Eng. News, vol.
Imperfections and
Trans. A.
I.
M.
Improvements
of
Surveyors'
ibid., vol. vii,
i,
p. 25, 1906;
Instruments,
E., vol. vii, p. 308; Evolution of Instruments, ibid.,
vol.xxviii; Thornton's Miner's Dial, r6id.,xxxviii;
ibid., vol. viii, p.
iv,
August 25, 1904;
175; Hanging Compass,
Plummet Lamps,
39; Glass Stadia Rod, Jour. Franklin Inst., vol.
1868; Dialing Trouble and Treatment, Col. Guard, vol.
i,
1898; Adjustment of Surveying Instruments, Proc. Inst.
Surv.
(Transvaal),
vol.
ii;
p. 21,
Mine
Photographic Survey Instruments,
Trans. Soc. of Engineering, p. 171, 1899; Dip Needle, Lake Superior
Inst., August, 1904; Surveyors' Instruments, Mining Reporter,
M.
vol. ix, p. 29,
Reporter, vol.
1904; Repairing Engineers' Instruments, Mining
p. 8, 1906; Compass on Tripod, M. and Sci. P.,
ii,
vol. X, p. 15, 1904.
II
MERIDIAN
The
lines of the
survey of a property
may
be referred to the
Hnes of other Surveys by various methods. One very often used
is that of connecting by traverse with the survey lines of the adThe Government requires that this method
joining properties.
be used in connecting a claim survey with the public-land survey.
Where the lines of the adjoining property may be assumed as
correctly surveyed one can take the meridian directly
from them.
To observe the meridian instrumentally one has
choice of
three methods, namely, observation of the transit or elongation
of
some
star,
observation of the sun
by means
of a solar compass,
or direct sun observation with the ordinary transit.
To use the
method one must have a star almanac;
must have a solar attachment.
first
the second one
to use
PoLABis Observations
sometimes convenient to be able to take the meridian from
when one is without a star almanac to learn when
It is
Polaris at a time
Polaris
is
at elongation or culmination.
Observations are usually
elongation,
if
made upon
possible at both eastern
Polaris
when
it
is
at
and western elongation, and
the difference of the two observations taken as true north.
If one
but remember that the Great Dipper and Polaris are on opposite sides of the true north, one can instantly tell by a glance
at the heavens whether Polaris is near either elongation or culmina-
will
tion.
Now
the third star in the handle of the dipper, counting from
the outer end, whose
Polaris.
It does,
name
however,
is
lie
Alioth,
a
little
is
almost directly opposite
more than 180° ahead
of
meridian below the true north just twentyfour and a half minutes of time before Polaris crosses it above.
Polaris.
It crosses the
Also, of course,
it is
at one elongation just twenty-four
64
and a
half
MERIDIAN
minutes before Polaris
is
at the other.
65
If,
then, one sees both
Alioth and Polaris under the vertical wire of his telescope, he
knows
that in twenty-four and a half minutes Polaris will be in the true
meridian.
is
The same
applies to the horizontal wire
when
Polaris
at elongation (Fig. 33).
Folaria
/'
FIG.
33.
-
Pole.
— POLARIS
OBSERVATION.
Explanation of the Solar Attachment ^
'
In the engraving (Fig. 34) we have a graphic illustration of the
shown being intended to represent
solar apparatus, the circles
drawn upon the concave
those supposed to be
surface of the
heavens.
'When
hour
the telescope
circle will
is
set horizontal
by
its spirit level,
be in the plane of the horizon, the polar axis
point to the zenith,
and the
'
zeros of the vertical arc
From
'Gurley's Manual.'
and
its
the
will
vernier
66
A MANUAL OF UNDEEGROUND SURVEYING
will coincide.
shown
Now,
of the zenith.
we
incline the telescope, directed north as
descend from the direction
The angle through which
FIG.
on the
if
in the cut, the polar axis will
34.
— SOLAR
it
moves being
APPARATUS.
vertical arc, will be the colatitude of the place
instrument
supposed to be used, the latitude
by subtracting this number from 90°.
is
laid off
itself
where the
being found
MERIDIAN
When
'
the sun passes above or below the equator,
tion, or angular distance
can be set
67
from
it,
upon the declination
off
its
declina-
as given in the
arc,
and
its
"Ephemeris,"
image brought into
position as before.
'In order to do this, however,
the latitude
it is
necessary not only that
and declination be correctly
upon their removed in azimuth
set off
spective arcs, but also that the instrument be
until the polar axis points to the pole of the heavens, or, in other
words,
is
placed in the plane of the meridian; and thus the position
of the sun's
image
will indicate
not only the latitude of the place,
the declination of the sun for the given hour and the apparent
time, but
it will also determine the meridian, or true north and
south line passing through the place where the observation is
made.
'The interval between two equatorial lines, c c, as well as between the hour lines, b b, is just sufficient to include the circular
image of the 'sun, as formed by the solar lens on the opposite end
of the revolving arm.
Allowance for Declination.
Let us now suppose the observa-
—
'
made when the sun has passed the equinoctial point, and
when its position is affected by declination.
'By referring to the "Ephemeris," and setting off on the arc
the declination for the given day and hour, we are still able to
determine its position with the same certainty as if it remained
tion
on the equator.
'When the sun's declination is south, that is, from the 22d of
September to the 20th of March in each year, the arc is turned
downward, or toward the plates of the transit, while during the
remainder of the year the arc is turned from the plates.
'When the solar attachment is accurately adjusted and the
transit plates
made
perfectly horizontal, the latitude of the place
and the declination of the sun for the given day and hour being
also set off on their respective arcs, and the instrument set approximately north by the magnetic needle, the image of the sun
cannot be brought between the equatorial lines until the polar axis
is
placed in the plane of the meridian of the place, or in a position
parallel with the axis of the earth.
position will cause the
The
slightest deviation
image to pass above or below the
from
this
lines,
and
thus discover the error.
'From the position
of the sun in the solar system,
we thus obtain
68
A MANUAL OF UNDERGROUND SURVEYING
a direction absolutely unchangeable, from which to run lines and
.measure horizontal angles.
'This simple principle
of solar instruments,
FIG.
35.
but
is
not only the basis of the construction
the only cause of their superiority
it is
— SOLAR
TELESCOPE ATTACHMENT.
over instruments having the ordinary magnetic needle.
For
in
an
instrument having a magnetic needle, the accuracy of the horizontal angles indicated,
and therefore
of all the observations
made
depends upon the delicacy of the needle and the constancy with
which it assumes a certain direction, called the magnetic meridian.'
MERIDIAN
69
Direct Solar Observation
^
Of the applications of plane surveying to the survey of mineral
no one is more representative, or has been more greatly
perfected in the West, than the use of the sun to determine the
bearing of a given line. For many years bearings were determined
by the use of various solar attachments, but of late years the
method known as the direct observation seems to have almost
entirely taken their place.
While with great care any one of the
several solar attachments on the market will give fair or even good
results, they are all relatively expensive, fragile, and, with one
exception, easily thrown out of adjustment.
With the method
known as "the direct observation" no attachment is needed to the
'
lands,
ordinary transit provided with a vertical arc or
circle,
preferably
the latter, and no adjustment has to be considered other than those
necessary to use in every transit in mineral-land surveying.
FIG.
36.
— SOLAR
SCREEN.
'As the exact determination of the bearings of
lines is
more important in mineral-land surveying than
in
probably
any other
branch of engineering, perhaps, disregarding of course geodetic
work, it will be taken up in detail.
'To determine the beaTing of a line by direct observation, the
transit
line
is
set
up
as solidly as possible
whose bearing
is
to be determined
the upper plate set at 0° or,
;
the upper plate
corrected.
'
If
This article
if
carefully leveled.
The
may
the bearing
is
be considered 0° and
approximately known,
may be set at the assumed bearing to be afterwards
more convenient, the assumed bearing
is
reprinted,
by
of a line to
Land Surveying,'
by the Mining Reporter Publishing
permission, from 'Mineral
by. James Underhill, Ph.D., pubUshed
Company.
and
A MANUAL OF UNDERGROUND SURVEYING
70
some prominent object may be taken, and the first course required
on the survey deflected from this line. The upper plate is then
loosened and the telescope pointed at the sun. The sun may be
observed in various ways; for example, through a colored glass
placed over the eyepiece to which may be added a prism when the
FIG.
sun
is
37.
very high.
— PRISMATIC
EYEPIECE AND SCREEN.
This colored glass
may
be conveniently placed
and is thus always ready for
involves
the
method
attachment
of the colored glass,
As
this
use.
the
sun
is
high
some
when
personal
discomfort
as regards
and also
card,
sheet
of
brown
head,
a
paper,
or
better
the
the position of the
the
which
latter
does
away
with
the
glare
on
back of a notebook,
this
by
used.
On
surface,
preferably
held
may
be
white surface,
in the sliding cover of the eyepiece
.
MERIDIAN
71
the assistant, the cross wires are first focused, and finally the
sun is brought into the proper position by the aid of the tangent
screws.
'A Davis screen is a piece of apparatus attached to the telescope
same purpose as the card mentioned above, and its
use leaves both hands free to manipulate the instrument. Otherwise it is of no great advantage (Figs. 36 and 37)
to answer the
'
are
In regard to placing the sun with reference to cross wires, there
many
opinions.
FIG.
In most treatises we are instructed not to
D
c
38.— SUN'S IMAGE ON CROSS HAIRS.
sun as in Fig. 38a, but to place it in one quadrant, as in
can thus be observed more accurately. While this
is perfectly true, especially with inverting instruments, a correction for semidiameter of the sun must be made, and the operabisect the
Fig. 38b, as it
be somewhat confusing to the beginner. The
student is therefore advised at first to divide the sun into quadrants
tion
is
liable to
method of placing the
As an error of one
cross hairs tangent until proficiency is secured.
an error of one
causes
minute in placing the vertical cross wire
of
one minute in
error
an
minute in the resulting azimuth, while
by the two
cross hairs (Fig. 38a), leaving the
A MANUAL OF UNDERGROUND SURVEYING
72
placing the horizontal wire causes an error of several minutes in the
might be well to place the sun as in Fig. 38c. The reason
be seen on examining the examples which
follow.
The sun in very accurate work is sometimes placed in a
rectangle or other arrangement of cross wires, but in ordinary
work these are unnecessary refinements.
result, it
for this will readily
FIG.
39.
— STAR
SPHERE.
Another very exact method
of placing the sun in the direct
tangent to the cross wires first in the
northeast corner with the telescope normal, and then in the southwest corner with the telescope inverted. These are the best posi'
observation
is
to place
it
tions in the morning.
In the afternoon the other two quadrants had best be used in order that the sun may be moving in the
same direction with reference to the cross wires. The average of
MERIDIAN
73
the two vertical and two horizontal angles
is
the subsequent calculations and in this
way
the semidiameter of the sun
At
used in each case in
all
consideration of
two sets of such
no check.
'In an instrument provided with stadia wires care must be taken
not to confuse these with the horizontal cross wire. It is also
well not to assume that the stadia wires are each equally distant
from the horizontal cross wire.
If the stadia wires are correctly placed they should be 0° 34' 22"
apart, and each 0° 17' 11" from the center horizontal wire.
As the
sun's semidiameter varies round 0° 16' the stadia wires may be
used with advantage to place the sun with a very slight probable
is
avoided.
observations must be made, otherwise there
least
is
'
error (Fig. 38d).
We will assume that the sun has been bisected. The vertical
and horizontal circles are then read and noted, and an observation made with the telescope inverted, assuming that the first
observation was made with the telescope normal. By averaging
the two results all errors of adjustment or in leveling the instrument are obviated. As a check a number of observations may be
made on the sun, and the writer finds that two each, with normal
and inverted telescope, are sufficient. The observations should
not be made within two hours on each side of noon, nor when the
'
sun
is
too near the horizon, as the correction for refraction
is
then
too great.
'The direct solar observation depends on the solution of a
39^) whose sides are all known, and
whose angle between two planes is desired. These planes, as can
spherical triangle (see Fig.
be seen from the figure, are (one) observer, zenith, pole; and (the
other) observer, zenith, sun.
In our work we have first the
from pole to horizon or from zenith to equator;
and therefore the colatitude (90° latitude) for one side, or in other
words we have from pole to zenith; we have the declination, distance of the sun above or below the equator and therefore the codeclination (90° declination), that is from pole to sun, and we
finally get the altitude and thence the coaltitude (90° the altitude),
by the solar observation with the transit as described above. In
Fig. 39 the sun is shown by solid lines north of the equator and
latitude, distance
Redrawn from the Bulletin, Colorado School of Mines, January, 1901,
'Determination of the Meridian by the Direct Solar Observation,' Edward P.
Arthur, Jr., E.M.
'
A MANUAL OF UNDERGROUND SURVEYING
74
by dotted
lines
south of the equator, this also showing its posiThis triangle may be solved by any one bf the
tion before noon.
various formulas found in every treatise on spherical trigonometry.
'The best formula, however,
for the direct observation is that
derived by John G. McElroy, of Breckenridge, Colorado, and given
in the
Michigan Engineers' Annual
'
which
is
cos
Z= ±
cos
for 1889, p. 62, as follows:
T
;
/
cos a
tan
I
tan
a,
simply a modification of one of the fundamental equations
of spherical trigonometry.
'Before illustrating the utility of the formula and the facility
with which it may be logarithmically reduced, it will be proper,
for the sake of completion, to give the argutnent on which it rests.
To this end let P Z S, Fig. 40, be a spherical triangle, and k an
arc of the great circle
PS
drawn from Z perpendicular
to
P
S, or to
produced.
Then from the
=
cos s
and from the
cos
p
=
s
cos
p
x):
(1)
cos k cos X
k,
= cos
we
(z
D
cos
(2)
find
— x)
cos X
But from S Z
D,
—
S Z D,
triangle
Eliminating cos
cos
PZ
triangle
cos k cos (z
= sm2tan
S=
(3)
tan x cos p;
=
whence, tan x
x
cos
cos
S
(4)
p
Placing this in (3) there results
cos s
cos
or, cos s
'This
is
the
=
=
,
sin
cos 2 H
p
cos
p
cos z
above-mentioned
+
p
sin z
cos S;
cos
p
sin
p
sin z cos
fundamental
S
equation.
(5)
It
asserts that the cosine of either side of a spherical triangle equals
the product of the cosines of the other sides, plus the product of the
sines of those sides into the cosine of their included angle.
To
apply
to the derivation of our solar formula let us consider
which represents the four astronomical triangles PZS,
PZS', P'Z'S, and P'Z'S', projected on the plane of the meridian
it
Fig. 41,
:
MERIDIAN
FIG.
PNHZ.
40.
— SPHERICAL
75
TRIANGLE.
In A.M. observations, the azimuth angles at
Z
or Z'
be estimated from the north to the right; in p.m. observations,
will
from the north to the left.
We adopt the following notation
'
PP' = axis
of the celestial sphere.
P = the celestial north pole.
P' = the celestial south pole.
EQ = th.e celestial equator.
HO = the celestial horizon of which the poles are Z and N.
Z and AT = zenith and nadir of an observer in north latitude.
= zenith and nadir of an observer in south latitude.'
Z' and
£^2=1 = observer's latitude when at Z.
-BZ'= 1 = observer's latitude when at Z'.
A'^'
jS'=the sun
iS'
= the
when north
of the equator.
sun when south of the equator.
yS=the sun's north polar distance when north.
P
By James
Underbill, Ph.D.
MERIDIAN
85
serving the altitude of the sun with the transit, the azimuth
usually obtained at the present time by the following formula:
Z= ±
cos
^
cos a cos
in
tan a tan
is
I,
I
which
Z = azimuth required.
d = declination.
= latitude.
I
a = altitude of sun corrected
'The
first
term
of the
+
—
and the second term
second member
for refraction.
is
for north declinations,
for south declinations,
is
—
+
for north latitudes,
for south latitudes.
'As this formula can be transformed into
cos
Z= ±
sin
d sec a sec
Z
=F
tan a tan
Z,
be seen at once that any method of solution providing for
in the first term of the second member and
one multiplicati
Drinker's 'Tunneling,' p. 919.
2
Mines and Minerals,
vol. xxii, p. 248.
A MANUAL OF UNDERGROUND SURVEYING
106
number 20 copper wire with a 7i-pound iron window weight is
used. The Calumet & Hecla uses a number 22 steel piano wire
with an 11-pound weight.
The
equal strength, but
steel wire is smaller for
is
not so easily
The copper wire is not so apt to
the steel. A number 18 copper wire
obtainable, as a general thing.
remain bent or kinked as is
will sustain a 12-pound weight to a depth of 1200 feet, but for a
greater depth, or with a heavier weight, a larger copper wire, or a
steel wire, must be used.
Where a number 20 copper wire is not
strong enough, it is probably better practice to use steel.
To Lower Wires
In shallow shafts,
it is
the end of a wire and lower
in Vertical Shafts
practicable to attach a light weight to
directly off a reel.
This is impossible,
however, for anything but very shallow shafts, for the weight will
it
catch in the timbering.
Where a cage
is
installed, it is
convenient to attach the end to
the top of the cage and run the wire
When
off
the bottom
a reel at the surface as the
reached the end of the wire
cage
is
may
be attached to the side timbering and the cage hoisted clear
if
lowered.
desired.
It
is
best to have the reel at the surface where the
hoisting engineer can see
and the wire
fails
is
it,
for
to run freely,
if
it is
the reel
is
carried on the cage
almost sure to be broken before
man
can be signaled to stop. Several hundred feet of
down upon the top of the cage makes a most
troublesome tangle. After such an accident, the wire must be
the hoist
loose wire dropping
thrown away,
Where
may
for the kinks in
it will
never come out.
wires are to be lowered through very deep shafts,
it
be best to use a large wooden frame, pointed at each end and
large in the middle, to pull the
end down.
Such a frame, 10 or
12 feet long and 4 feet in diameter at the middle, cannot catch
on the timbering.!
A simple
shafts
is,
device which
we
find of great
advantage in plumbing
to have in the wires on the side toward the transit, three
from an ordinary trace chain. Cut the wires about 4J feet
above the end of the weight and fasten the three links between
links
these two ends.
'
Mines and Minerals,
vol. xxii, p. 247.
CARRYING THE MERIDIAN UNDERGROUND
107
This allows the wires to twist and turn as they please, and one
always be in such a position that you can sight
through it to the wire beyond, and feel certain that your transit
is on the proper line, and that you have seen both wires.
of the links will
A MANUAL OF UNDERGEOUND SURVEYING
108
lines
tangent to an
ellipse.
The centre
of the ellipse
is
the true
Other methods are described in Colliery
Engineer, September, 1895, p. 31 and in Engineering and Mining
Journal, January 12, 1893, p. 81.
position of the wire.
;
Two-WiBE System
Two
wires are most generally used where
to carry the meridian
down a
vertical shaft
becomes necessary
which has no underit
ground connections with any other opening.
The wires
are, of course,
hung
as far apart as
to secure the greatest length of base.
They
is
possible in order
are either
hung
in a
predetermined plane by lining them in with the transit as they are
placed, or after hanging them their plane is determined by setting
it, or by triangulation methods.
The same procedure is followed underground to take the meridian off the two wires.
Where it is convenient to set the transit
in the plane of the two wires, most engineers prefer to do so.
Where the underground statio;ns will not permit of this, the triangulation method must be used.
The distance between the two wires as measured at the bottom
must check that as measured at the top. In case the measurements do not check, the probability is that some obstruction in the
shaft causes one of the wires to hang out of plumb.
In case,
however, that a search fails to find any such obstruction, some
the transit up in
is necessary.
If the plumb-weights used are of
be that magnetic influences disturb them. Instances
of this kind have been proved.
If so, the substitution of lead
other explanation
iron, it
may
weights for the iron will cause the discrepancy in measurements to
disappear.
Sometimes, however, the wires fail to hang perpendicularly
on account of air currents in the shaft. Air rushing in from levels
on one side of the shaft may push one wire in toward the other.
If it is pushed directly toward the other, the distance apart of the
wires will be affected, but not their bearing.
It
is
known
that air rushing
up a shaft has a tendency to assume
a corkscrew motion instead of traveling in straight
lines.
Now
phenomenon will cause one wire to diverge from the true plane
in one direction and the other wire in the other direction.
Their
bearing, as determined from them at the bottom, will then evithis
CARRYING THE MERIDIAN UNDERGROUND
109
dently be different from their bearing at the top.
Their distance
apart will also be affected, as each wire will tend to
move from
true position along the tangent to a circle whose centre
lies in
its
the
plane of the two wires.
air, or splashing of drops of water, affects but
be that the bearing of the bottom ends of the
wires will be changed without affecting their distance apart.
As this can be in no way known, it is evidently the chief objection
If
the rush of
one wire,
it
may
to the two-wire system of plumbing shafts.
That the effect of air currents upon plumb-wires is considerwas shown by a survey ^ of the Tamarack Shaft No. 5, where
the divergence at a depth of 4,000 feet was a tenth of a foot.
able
The Three- Wire System
By
system three wires instead of two are used. The three
The position of each wire is found
by triahgulation at the top, and the meridian is calculated at any
point below from a triangulation to the wires. It is not necessary
nor customary to set the instrument up in the plane of two of the
wires when this method is used. It may be done, however.
The advantages of the three-wire system are those affording a
check upon work done. In the first place, if the three wires are
in the same relative positions when measured at the bottom that
they are at the top, it is unreasonable to suppose that air currents
could have twisted them about so that the meridian taken off
And, second, the three wires give three possible
will be incorrect.
With three
triangles which may be solved for check results.
wires it is always possible to set up the instrument so that two of
them will be in position to give a triangle of good shape. Where
the underground workings take off from the shaft in different
directions, this is no small advantage.
The objections to the system are: the extra wire to hang, the
use of one more compartment of the shaft for the third wire, and
the time required to make the extra observations. The advantages certainly outweigh the objections. The certainty that any
two wires lie in a true plane, rather than a warped surface is
advantage enough to warrant the hanging of the third wire, even
if it is not used in the taking off of the meridian at all.
this
wires are not in the same plane.
'
Mines and Minerals,
vol. xxii, p. 247.
A MANUAL OF UNDERGROUND SURVEYING
110
Four-Wire Method
^
We will
suppose that in the shaft through which the meridian
is to be carried, there are two hoistways, each 7X11 feet, with a 12inch bunting between, as shown in Fig. 56. Now the first thing
'
to be
known is, which side
up the transit. The
setting
\
of the shaft
is
the best adapted for
point to be marked in the mines will
/
CARRYING THE MERIDIAN UNDERGROUND
course, not accurate, but will be
the hangers.
At the point
111
found to be quite a guide in setting
a permanent station and carry
A make
the meridian thereto.
'
The hangers to be used can be made from strap iron, ^ inch
by 2 inches wide, and about 16 inches long or longer if
thick
necessary, but not shorter.
In one end of the iron have a jaw with a
'
fine
cut at the apex,
or a drill-hole just large enough to contain the fKire to be used for
plumbing; in the 12 inches opposite the jaw-end have three countersunk drill-holes through which to fasten the hangers to the top
of the shaft,
by
sheet-iron nails.
'In most shafts there
and the
is
a space between the ends of the cage
from 2 to 4 inches, so that
examine the wires after they
are hung, the holes in the jaw of the hanger should be set in such a
position that the wire passing through it will hang about midway
sides of the timbers, varying
in order to lower or hoist the cage to
in this space.
On the north side of the shaft, fasten the hangers permanently
over the chalk marks previously made, with the jaws pointing
'
toward the point A.
On the south side of the shaft, the outer end of the hanger can
be fastened temporarily.
'Having carried the meridian to, and set the transit on, the
station at A, take backsight, then foresight in the wire-hole of
the hanger C, and set the wire-hole of the hanger B on the same
Then, having recorded this course, foresight on the wireline.
hole of the hanger E and set the wire-hole of the hanger D on the
same line; record this course, and the meridian to be carried into
the workings below is established. Now measure carefully and
record the distances A to B, A to C, and B to C; then the distances A to D, A to E, and D to E, and finally the distances B
The necessity of this is for a twofold purto D and C to E.
pose; first, for establishing the point A at the bottom of the shaft,
and, secondly, for theoretical calculations in the office to prove
the work.
The transit party can now descend to the bottom of the shaft,
taking with them four buckets of oil, the weights or plumb-bobs
to be attached to the wires, and all the surveying instruments,
leaving a responsible party on the surface to handle the wires.
Having arrived at the bottom of the shaft, the cage may be
'
'
A MANUAL OF UNDERGROUND SURVEYING
112
hoisted about 3 feet above the landing, and several planks thrown
across the timbers on which to set the buckets of
oil.
The man
on the surface may be signaled to lower one wire and fasten securely on top, passing it through the wire-hole of the hanger; now
the weight may be attached and the wire adjusted to such a
length that when sustaining the full weight of the plumb-bob
the latter is sure to be free from the bottom of the oil bucket.
The weight may be then inserted in the oil, using care not to put
all of it on the wire with a jerk, but letting it go down slowly so that
the wire may receive the full strain gradually and not so suddenly
that it will snap in two. The same method may be followed until
the four wires are in proper position.
'After the wires have been hanging a few minutes with the
weights attached, the latter
Watch
the buckets.
may move
this carefully
to one side or the other of
and keep moving the buckets
hang perfectly free, then leave everything alone
become perfectly steady.
'If the wires have been placed midway in the space between
the ends of the cage and the sides of the shaft timbers, the cages
can now be hoisted and lowered, to allow an examination of the
until the weights
until the wires
wires, so as to be absolutely certain that there are
to prevent
them from hanging
free
and plumb.
no projections
Care should be
taken, however, to notify the hoisting engineer not to allow either
cage to approach either landing closer than 3 feet, or the cages will
tear off the hangers on the surface landing
and crush the weights
and buckets on the bottom landing.
'When
the wires have apparently settled one
find the point of intersection. A, of the
two
may
proceed to
lines at the foot of the
shaft.
'Stretch a string along the wires B C and D E, using care to
prevent the string from touching any of the wires, and with a plumbline mark on the bottom of the gangway the intersection and com-
pare with the same distances on the surface. If they compare
closely, one can rest assured that they are settling nicely, and
can proceed to carry the meridian from the wires to the desired
point.
'Set the transit at the intersection just found, backsight on
B C, foresight on the wires D E, compare the included
angl^and the distances with the same angle and distances on the
the wires
surface.
If
not exactly the same, then
move
the transit in the
.
CARRYING THE MERIDIAN UNDERGROUND
direction necessary to increase or decrease
tances, as the case
may
the
angle
113
or
dis-
be.'
By Bent Line
An
interesting string
a shallow vertical shaft
method
is
for carrying the meridian
Fig. 58 illustrates
July, 1901, p. 559.
FIG.
57.
down
described in Mines and Minerals of
— BENT
how
the various lines,
all
LINE SURVEY.
being in one plane, take the meridian from a comparatively long
base at the surface, and also give a long base below from which
the meridian
is
taken by setting a transit in
line
with the two
This device does not, however, give position of a
To get the position of a
point, simply the direction of the line.
plumb-lines.
point from which to measure, a single plumb-line must be lowered
from the horizontal string.
The description of an interesting survey by means of bent lines,
made by Prof, Mark Ehle, is given on page 212.
A MANUAL OF UNDERGROUND SURVEYING
114
By Transit Sights
Where a shallow shaft is the only opening by which the meridian
it may be convenient to establish a line by
can be carried below,
direct transit sight.
Either top or side telescope, inclined standard transit, ec-
DJA,
FIG.
centrically
used.
mounted
Ob,
,
58.
— DOUBLE
BENT
LINE.
telescope or ordinary transit telescope
may be
In every case extreme care must be used in getting the
instrument exactly level so that the vertical wire shall travel in a
truly vertical plane.
With the top
telescope, the line is
swung down and
points, as
marked. By turning
the plates 90° the vertical wire marks another vertical plane.
far apart as possible at the shaft bottom, are
CARRYING THE MERIDIAN UNDERGROUND
The
two planes
intersection of these
is
115
the plumb through the
centre of the instrument.
With a
side telescope, a plane parallel to,
from, the true plane
By
is
and equally distant
established on each side of the vertical plane.
swinging the plates 90° two more planes are established, which,
together with the
first
two,
make a square whose
centre
is
the
point directly under the centre of the instrument.
The ordinary
transit
^
when
set
up
in a leaning position gives
the line of a true vertical plane but not a plumb-point, except
as an angle of 90° from the horizontal position can be read on the
This
vertical circle.
however, not accurate enough for any-
is,
thing but the very crudest kind of work.
Vertical
Sights
necessary to
with Ordinary
make a
vertical sight
FIG.
hand,
it
may
59.
— When
it becomes
and no auxiliary telescope is at
Transit.
— STRIDING
LEVEL.
be done by leaning the plates of the transit so that
the line of sight,
when
vertical, will clear the plates.
made down a shaft, the transit is set up
with two legs shortened and resting close to the shaft edge. The
third leg is extended and securely anchored.
The instrument is
If
the sight
is
to be
then leaned over the shaft so that the plumb-line
will fall inside
the shaft.
When
the plates are
now
tipped toward the shaft by means of
swung
the leveling-screws, the line of sight can be
each side of vertical.
In order to have the
line of sight cut
horizontal axis of the telescope
First,
a vertical plane, the
must be made truly horizontal
the inclined position of the instrument.
in several ways.
several degrees
This
and simplest, a striding
level (Fig. 59)
may
till
in
may be accomplished
be placed upon the horizontal axis and the plates swung
the bubble is in the centre of its run. Second, the plates may
^Engineering and Mining Journal,
May
16, 1903, p. 749.
A MANUAL OF UNDERGROUND SURVEYING
116
be moved till the line of sight will follow a plumb-line through
about 45° of vertical angle; or, third, three points in a vertical
plane may be established with the instrument leveled, and the
instrument then inclined and centred in the determined plane.
In steeply inclined or crooked shafts
By Traverse of Shaft.
—
it is
often necessary to run a transit traverse.
This
is
done exactly
Extreme care and checks upon all
work will give accurate results. The work is slow and tedious,
however, and is to be avoided wherever any other method can be
Platforms must be built across the shaft to support instruused.
ment and men, and timbers must usually be securely placed to hold
station points.
As all these timbers must be removed from the
as in surface
work or
slopes.
shaft no stations are left to serve as a check at a later time.
Work
of this kind
is
dangerous, and special care
is
necessary
The author will carry a scar, made
by a candlestick dropped by an assistant from a temporary staging
60 feet above, to his grave. The transit man must also remember
that a misstep may land transit or man in the sump, perhaps
hundreds of feet below. At first he will probably be able to think
in the selection of assistants.
of little else, but familiarity always tends to
make one
careless.
Measuring Depth of Shafts
The
depth
is frequently measured to determine the
the same principle, a weighted wire is low-
hoisting rope
of a shaft.
On
ered into the shaft and measured as
agaiii, for
a check, as
it is
it
descends, also measured
withdrawn.
A
tape is stretched parallel to the wire, or rope, at the top, and
end-points marked on the wire. The wire is lowered the length
of the tape and again marked, and so on till the first mark reaches
its
the lowest part of the shaft to be measured. It
take the elevations off at the various levels by
is
usually best to
means
of instru-
ments sighted at a mark on the wire as it is lowered.
This method is good for shallow shafts, and a connection driven
between levels on two deep shafts may meet accurately where the
elevations have been determined by a measured wire in each case.
It
is,
however, true that a hoisting rope, or a wire,
is
very elastic
and stretches to a measurable extent. A wire 4000 feet long has
been known to stretch 15 feet upon the addition of .40 pounds
weight at the end, and to shorten 2 feet when this weight was suspended in oil. It is then quite evident that while concordant
CAHRYlNG THE MERIDIAN UNDERGROUND
results
may
be obtained by this method, the results are in error
by equal amounts.
For shallow
the wire would give a negligible
is
117
shafts,
amount
where the
elasticity of
of stretch, the
method
quick and good.
By another method the shaft itself is measured. This is done
by laying off successive lengths of the tape along the guide. One
man must stand upon the cage, or bucket, and place a mark upon
A second man works
from a seat clamped to the hoisting rope at the length of the tape
above the cage. He holds the upper end of the tape opposite
the mark made by the man at the lower end. He must do the
the guide opposite the zero end of the tape.
signaling to the hoisting engineer.
A 100-foot tape is most frequently used, but a longer tape, if
checked for length while hanging vertically, can be used and will
save time and chance of error, as the number of times it is laid off
is reduced.
To mark the end-points, the author has used the longThese can be pushed
spined large glass-headed library tacks.
wooden guide with the bare hand. The head of the tack is
not set close up to the wood and the tape can slide under it, so that
into a
the markings of the tape rest directly against the spine of the tack.
An
may be driven and the exact endhead with a centre-punch. The man
at the lower end should leave a candle-snuff burning near the endpoint to aid the upper man in finding it.
When measuring an inclined shaft, the measurements are usually made along the line of sight of the transit from one station
ordinary white carpet tack
point marked upon the
flat
Where the
driven upon a fixed angle,
it is
quicker and easier to stretch the tape directly upon the skip
rail.
to the next.
shaft
is
Bibliography: Transferring Meridian Underground.
ing Shafts on the Comstock, Eng.
and Min.
— Plumb-
Jour., vol. Iv, p. 81;
Plumbing Shafts in Montana, ihid., vol. Iv, p. 72; Plumbing Shafts
South Africa, ihid., vol. Ixxiv, p. 478; Plumbing Shafts by
in
Leaning Transit,
Mine,
ihid.,
ihid., vol.
Ixxv, p. 749; Plumb-lines at
Tamarack
April 26, 1902; Transferring Meridian Underground,
ihid., vol. Iv, p.
179; Plumbing Shafts at Hoosac Tunnel, Colliery
Eng., vol. xvi, p. 52; General
vol. xvi, p. 31;
Methods
of
Plumbing Shafts,
Wires of Plumbing Shafts,
Suspension of Wires,
ibid.,
vol. xiv, p. 92;
ibid.,
ihid., vol. xvi, p.
32;
Shaft Surveying for
Tunnels, Vose's "Manual of Railroad Engineering"; Shaft Sur-
A MANUAL OP UNDERGROUND SURVEYING
118
veying at Przibram, Proc. Inst, of C. E. of Eng., vol. civ; Crooked
Shaft by Plumb-line, School of Mines Quarterly, vol. xvi, p. 146;
Severn Tunnel Survey, S. M. Q., vol. iii, p. 272; Mine Surveying,
iii, p. 269; Wires for Shaft Surveys, ibid., vol. xi, p. 333;
Prevention of Vibration of Wires, ibid., vol. iii, p. 271; Plumbing
ibid., vol.
Shafts of Croton Aqueduct, Trans. A. S. C. E., vol. xxiii, p. 22;
Cincinnati Water-works Tunnel, Eng. Rec, vol.
li,
p.
234; Shaft
Survey Iron Mines of Penn., Trans. A. I. M. E., vol. vii, p. 139;
Sperry Method of Plumbing Shafts, ibid., vol. xxiv, p. 29; General
Methods of Shaft Plumbing, ibid., vol. xxi, p. 292; Underground
Connection, ibid., vol. xxiv, p. 25; Survey Measurements of Steep
Drivages, Col. Guard., September 24, 1897; Measure of Depth by
Wheel, ibid., April 20, 1898; Plumbing Shaft in Missouri, Mines
and Minerals, July, 1901; Tamarack Shaft Survey, ibid., vol. xxii,
247; Inclined Shaft Survey,
Survey, ibid., December, 1900;
p.
M. and
Sci. Press,
August
ibid., April,
A
25, 1906.
1900; Meridian of a
Quick Vertical Shaft Survey,
SURVEY OF ROOMS OR STOPES
The main transit traverses in the survey of a mine are carried
through the openings which are to be permanent; that is, the main
haulage ways and headings, and the shafts and levels. Those
openings which change in shape from time to time, and which are
often filled up, or caved, after being worked out, are measured
up by some method which is rapid, but not necessarily so accurate
These secondary openings are,
as are the main lines of the survey.
of course, connected with the main survey, and all are mapped
together.
sometimes carried along the
usually the rooms
breast,
are measured by taking a side-shot up every third or fourth room
and simply measuring the intervening rooms by tape through
the break-throughs nearest the face. See page 206 for instructions issued to surveyors by the United States Coal and Coke
In coal mines, a transit
especially in
line is
long wall work, but
Company.
In metal mines,
it is
sometimes necessary to measure, with
considerable care, the openings from which ore has been removed.
These measurements are frequently used as a basis upon which
tonnage is estimated, and also as a basis upon which contract
work is
The
paid.
Institute of Mine Surveyors (Transvaal) discussed ways in
which these measurements were best made on the Rand. These
papers occupy some fifty or sixty pages of their Transactions
(Vols. II and III), and are well worth study, but are too lengthy
to be reprinted in this volume. Any engineer who has to measure
up contract work each week or two, especially on ledges similar
to those of South Africa, can well afford to secure copies of these
volumes of the Transactions.
In this country, those mines which have very large ore-bodies
generally use the square-set
method
of timbering has
method
made
of timbering.
This regular
possible the use of stope-books of
119
A MANUAL OF UNDERGROUND SURVEYING
120
cross-section paper,
and the sketching
of the sets thereon instead
of the actual taping of the openings.
Narrow Stopes
is
In narrow stopes where the square-set system of timbering
it is customary to carry a transit-line up through a
not used,
chute or
manway, and then get the
outline of the stope-face
radiating lines to points on the face.
For
this
by
work, a pocket
compass is sufficiently accurate. The lengths of the
and the vei-tical distance between stope-walls are measured
transit or
lines
Where a stope is long, it may be best to carry
up the chute or manway nearest to one
then the whole length of the breast and down the last chute
with pocket tape.
an ordinary
end,
transit-line
to close on the nearest station of the regular mine survey.
If the surveyor is mapping the geology and the assay values,
he must, of course, be careful to note all such during the stope-
he is mapping the geology, he had best have the
foreman go through the stopes with him to point out
any changes in geology which have been noticed during the breaksurveying.
If
shift-boss or
ing of the ore.
The miners
in
each particular stope are usually
able to bring things to the attention of the surveyor
would
which he
of himself not notice.
Method of Keeping Stope-Books
'
'
For maintaining an accurate record of all work done in the
mines of the Butte district, a survey is run out on every level,
beginning at the shaft, to the face of each crosscut and drift as
the work advances, and is brought up to date once a month.
Notes and sketches are made showing the timbering, angles, sidesets, stations,
manways, and
these notes an accurate plan
chutes, with their numbers.
map
is
From
plotted in the office stope-
book, showing the level with the timbers as they actually stand
in the mine.
X 4i inches, and consists of
some convenient scale, each sheet
being divided into squares of 1 inch by heavier lines. A scale of 20
feet to the inch has been found to give good results, as it is large
enough to admit of plenty of detail and not so large as to be cumThe
field
stope-book
is
about lOJ
sheets of cross-section paper of
^
SURVEY OF ROOMS OR STOPES
Each square represents a
bersome.
line of intersection is
121
square-set, while a dot at the
used to indicate a post.
With such a
scale,
the book, on being opened, will represent on a double page about
400 feet in length of the vein, and
will be wide enough to permit of
two floors being plotted on the same sheet one above the other.
The sketch of the sill floor of each level is made in the field-book
for the work of 'taking up stopes underground.
Where the drift
timbering is regular, that is, where each side conforms to the
'
standard drift set for the mine, the posts of a set are simply
sketched in by a dot at each corner of the square but where con;
ditions are such that regular sets cannot be used,
indicate just where
and how each
it is
essential to
irregularity occurs.
The data give correct representations of all chutes and manways that have been run on all floors, in such a manner that their
true position with regard to the level and the stope can be known
at a glance.
The field stope-book thus compiled furnishes a
permanent record of the work in the mine, shows the manner in
which the development work was prosecuted, the date at which
it was done, and supplies the data for office maps and estimates
of the amount of ore extracted, cost of the extraction, and the
possible ore reserve.
(See descriptions and illustrations, p. 203.)
String Surveys
Instead of using a transit or pocket transit, the surveys of
secondary openings are frequently made by stretching strings
between points and then reading their course by ordinary compass, and dip by clinometer, or by use of the hanging compass.
Instead of using a compass, the strings
triangles
may
^
and the lengths
be calculated.
method
is
great.
of the sides
When
The
may
be stretched in
measured so that the angles
carefully done, the accuracy of this
triangles
must
not, however, contain
any
angles approaching 180°, or the point of intersection of the two
strings cannot be determined accurately.
•
2
Longdate Iron Mine, Engineering and Mining Journal, August 1, 1891.
Trans. A. I. M. E., August, 1900; and Eng. and Min. Jour., January 27,
1900.
A MANUAL OF UNDERGROUND SURVEYING
122
Estimating Values of Ore Deposits
While a coal mine
may
number
estimate of the
be measured up, and an almost exact
of tons of
marketable coal which
it will
produce may be made, it is impossible to do the same in the case
Coal producers must always take into account,
of a metal mine.
and make provision for, increase of wages, strikes, increased railroad charges, and varying prices of the coal produced. Besides
all
these, in metal mines, there is the uncertainty of continued
and
size of ore bodies with extended working.
attempts have been made to invent a formula which
shall give the net profit per ton of ore handled.
These are all
impractical.
Each mine or ore deposit is a case by itself. But in
almost every case, the framework upon which the examining
engineer hangs his observations, notes, assays, and geologic ob-
richness
Many
servations
is
a
map
The absolute
of the
mine survey.
necessity for an accurate
perhaps, only understood
by
the engineer
examine a large property, the mine maps
map
of the
who has been
of
mine
is,
called to
which have not been
at hand.
Volumes
For estimating the volumes of open-cut work, placer digging,
various methods and formulas have been devised.
S. Napier
Bell 1 describes quick methods which he has used.
By one he
takes the profiles of cross-sections, making one transit setting in
each section, and taking vertical angles to various points on the
etc.,
section,
measuring by tape or by stadia.
adjoining sections
give the volume.
The mean area of two
by the distance between them to
This method is rapid and is accurate enough for
is
multiplied
many purposes.
By another method
the topography of the surface
level readings (or inclined side-shots) to points
Each three
is taken by
on the surface.
assumed to be the angles of a plane
end of a vertical triangular
prism. The other end is any assumed horizontal plane.
By
calculating these vertical prisms over the whole area, the total
contents of the excavation prism are known at any time. The
triangle.
of these points are
This triangle
'
is
called one
M. and M.,
vol. xxvii, p. 42.
;
SURVEY OF ROOMS OR STOPES
123
any two consecutive surveys is,
removed during the
intervening time. This method is more accurate than the former
one, but takes considerably more time.
difference
between these
totals; at
of course, the cubic content of the material
Mine Sampling
While mine sampling is not a part of mine surveying, it so
is one of the additional duties of the mine surveyor that
it seems best to at least outline the work.
The engineer has the assay maps of the mine to keep up to
date, and usually marks the points from which systematic mine
samples are to be taken, even if he does not oversee the work of
breaking the samples, or even break them himself. The engineer
who does not carefully study and map the geology, and also map
the position of samples and resulting assay values, will usually
have to step down and out. Of course, in large properties where
mining geologists and special samplers are employed, the surveyor
pays no attention to these things, but in all except the largest and
most up-to-date properties, the surveyor must also be geologist,
mine sampler, and frequently assayer as well.
Theoretically, the sampling of a mine is a very simple operation
representative fragments of the ore are broken from the different
ore-bodies and assayed. The value per ton multiplied by the
frequently
number
of tons evidently gives the gross value of the ore in place.
Assuming certain
costs for
matter to figure the net
But
mining and reduction,
it is
a simple
profit.
work
from simple, owing to the
sample of any particular
body of ore. The ore-body may be exposed on one, two, three, or
four sides and, of course, the greater the proportion of exposed
area to the cubic content of the body, the more nearly representative of the whole mass will be the average of the samples; but at
best, only an approximation, be it ever so close, can be secured by
means of sampling ore in place in the mine.
Sample Interval.
The mine sampler must first decide upon
some particular sample interval, i.e., distance between points at
which samples are to be taken. This is different for each particular
mine; a coal vein need be sampled only at distances of perhaps
several hundred feet, while a narrow, rich, pockety gold vein must
practically the
is
far
difficulty of securing a truly representative
—
;
A MANUAL OF UNDERGROUND SURVEYING
124
be sampled at intervals of perhaps only 24 inches. Each ore deposit is a law unto itself, and in order to best determine upon the
sample interval, the engineer will probably have to study the geology of the deposit, have a few selected (commonly known as
grab ') samples assayed, and perhaps begin his sampling at multiple intervals; i.e., instead of sampling at every 5 feet at first, he
will sample at every 10 feet and later on sample at the alternate
5 points if the results from the assay of the 10-foot samples indi'
cate the necessity of closer sampling.
—
The method of actually breakMethod of Breaking Samples.
ing the sample varies with the physical shape and condition of the
material to be sampled. Whatever its shape or condition, a groove
must be cut clear across the exposed face so as to secure a proportionate part of each band of material.
If the material be soft like clay, a scraper will cut the desired
groove, and if brittle like coal, a small hand pick or prospector's
hammer may be
and hammer are
satisfactory; for harder materials a gad, or moil
For very hard material a moil struck by a
best.
heavy double-handled hammer may be necessary.
To catch the fragments as they are broken away from the face,
the most satisfactory method is to have a second man hold up a
candle or powder box so that all fragments will fly into it.
In case very large samples are to be broken,
to use a canvas sheet spread
method
on the
it
may
be better
This
floor of stope or drift.
however, open to the objection that the sample is so
by having fragments of high
grade thrown into it, or accidentally by having the richer, fine
is,
easily salted, either intentionally,
or brittle ore breaking from the back outside of the sample groove.
— The
size of a sample depends upon the width
sampled and the condition of the material. If the face
be of uniform structure so that the dimensions of the groove can be
kept uniform, a 5-inch by J-inch channel is probably large enough
but if the face be composed of alternating hard and soft bands, it
may be necessary to increase the size of the channel to 10 or 12
Size of Sample.
of the face
inches
by
3 inches in depth.
Reducing
—
the Size of the Samples.
Where the samples are being
taken for the mine and can be sent direct to the mine-assay office,
the samples are, of course, reduced in the office. Where the
samples have to be sent to some distance to be assayed, they
must be reduced upon the ground.
The small hand crusher
is
the
SURVEY OF ROOMS OR STOPES
125
most convenient and can usually be secured, but frequently the
rock must be crushed by other means. A heavy casting (old anvil,
or stamp die) laid upon a sheet of canvas serves as a convenient
base upon which the ore
band
of iron
is
with a handle
crushed by means of a hammer. A
is convenient for holding the pieces
while breaking them.
After breaking to the required
and forth
size,
the canvas
is
rolled
back
until the ore is fully mixed, the resulting pile of ore
and then bucked down to say
down, the sample may be sealed
in canvas or paper sacks and later bucked down at the assay office.
The samples should be numbered by means of paper, wood, or
metal tag inside the sack, and an identification (not the assay
number) marked upon the outside of the sack. This last is a safeguard against intelligent salting; if an occasional sack of barren
rock is included and it shows a metal content upon assay, one at
once suspects salting and governs himself accordingly.
The sampler must be always upon his guard against salting;
accidental, under all circumstances, and intentional, whenever
there is anything for anyone to gain thereby. The tricks and
schemes whereby salting is accomplished are very numerous.
They vary all the way from throwing high-grade into the sample
box as the sample is being broken, through the injection of gold
chloride through the sample sacks, to the secreting of gold buttons
in the sides of the crucibles which are used in assaying.
The work of the sampler is hard and tedious. It must be
carefully and intelligently done.
While the sampler can, and
should, have a miner to do the actual pounding of the moil, he
must be present constantly to see that nothing detrimental to the
securing of a true sample is done.
quartered or halved
100 mesh.
till
of small bulk
Instead of bucking
it
.
—
Bibliography : Secondary Openings.
Stope Measurements,
Eng. and Min. Jour., January 27, 1900; Measure of Stopes, Colo.
Sci. Society, December 3, 1894; Stope Measurements, Proc. I. of
Mine
p.
Surv., vol.
ii;
Cross Sections in
Rock
Cuts, A. S. C. E., 1890,
386; Examination of Mineral Properties, S.
Volumes, Mines and Minerals,
&
Min. Soc,
S. Africa,
M.
Q.,
vol.
iii;
Small Drifts and
Stope measurements Jour. Chem.
May, 1909.
Stopes, ibid., vol. xxi, p. 344.
Met.
vol. xxvii, p. 42;
VI
RECORD OF THE SURVEY
Field Notes
It should be recognized that
the purpose of helping the
notes are not taken for
field
memory
of the
party making them.
They should be complete, so that one entirely unacquainted with
the workings surveyed can
make a
correct
map from
fact, it is generally the case that the notes are
mapped by
office
men who have never
them.
In
worked up and
seen the workings.
Besides the actual record of courses, distances, angles, etc.,
there should be noted the position and dimensions of every object
affecting the
mine
in
any way.
system, drainage, power
lines,
This covers stables, ventilation
haulage,
rolls, faults,
thickness of
deposit and kind of rocks.
If one surveyor is taking care of several mines, he should have
a separate note-book for each mine. A careful and complete index
The notes of the day should be looked
will save time and trouble.
over carefully each night to see that no apparent errors go uncor-
rected.
The notes should be taken with lead
engineers never allow an erasure.
If
pencil,
a mistake
and many chief
is made, a line
should be drawn through the part in error and the note rewritten.
Erasing and rewriting is a fruitful source of error. A moderately
hard pencil should be used and the characters made small rather
than
large.
Above all things, do not be stingy with space in your note-book.
Use plenty of room, be extravagant even, rather than crowd your
work. And remember that a neat note-book is to be desired.
Many a young engineer owes his advance to a nicely kept notebook, and many another has failed of advance because his notebook did not recommend him.
The notes of the survey should, of course, be headed by the
name of the place in which the survey is made, together with the
126
RECORD OF THE SURVEY
Often, too, the
date.
names
name of
many ways
given, as also the
There are
127
engaged in the work are
of those
the instrument used.
of
keeping the notes themselves, each
engineer adopting a form which impresses him as the best.
The
mind is to record everything, and to do it in
such a way that any other engineer who examines the notes will
understand them readily. The notes cannot be made too plain.
point to be kept in
(For note forms, see pp. 191, 201.)
The forms differ from the forms used in surface work principally
in
having columns for vertical angle and distance, and for height
of point.
Columns are usually ruled
for the inserting of values,
coordinates, etc., which have to be calculated.
filled in
at a later time
These columns are
by copying from the calculation-book
or
ledger.
Note-Books
The ordinary
transit, or field-book
surveyors' supplies.
The pattern
maker, but any one
may
be used.
Some companies have note-books
of the
neat appearance and
is
by every
a
dealer in
with each
The right-hand page is best
ruled into small squares where sketching
and the headings
sold
is
of ruling differs
is
little
to be done.
especially ruled for them,
columns printed.
This gives the book a
a convenience, no doubt, for a
new man
working with any particular set
of notes for a time, a person never looks to see the headings of the
columns. He knows what each one is.
on the surveying corps; but
after
As regards size, the larger book has the advantage, so long as
small enough to slip into an ordinary pocket. On the other
hand, if a small book will carry the number of columns required,
and have each one wide enough to take its note without crowding,
One miist always avoid
there is no advantage in having it larger.
it is
crowding his notes.
Each book should have blank pages enough left at the front for
the complete indexing of all the notes in the book. Upon the
outside should be the number of the book, the dates between which
it
has been used, and the mine at which
it
was used.
When
filled
away, the number and mine name should be put upon
the back edge so that when lying or standing among others it
up and
may
be
filed
identified.
^The advantages
of the loose-leaf
'Loose-leaf records
system have been realized by
—Lee Eraser, Eng.
&
Min.
Jour., 12-25-09,
A MANUAL OF UNDERGROUND SURVEYING
128
mining companies are now
whether the matter has
Indeed,
using it.
further than common
carried
and
is
being
a
fad
not come to be
has
its advantages, howThat
it
permit.
convenience
sense and
note-books will
familiar
with
underground
all
one
at
ever, no
punched to be
double
and
are
usually
The
loose
leaves
question.
mine surveyors, and many
it is
held in covers
Hodson
1
much
like
of the large
to be questioned
the ordinary surveyors' field-book.
describes a system which
is
somewhat
L. C.
different.
He
says:
'
I have, tried
the following plan which seems to eliminate
Cards of the
difficulties.
size of
ordinary
filing
all
cards are ruled
columns for note-taking. Sheets of paper of the same size are
same way. These are placed in an envelope of oiled
paper, the front of the envelope being printed with the same form
For note-taking,
as the card, and bearing the same serial number.
the outside of the envelope is used, but copies are preserved on the
card and sheet by means of carbon paper. The clean card is filed
in a card-index cabinet and is not to be removed from the office,
while the sheet is kept in a loose-leaf note-book, which can be
carried whenever it is needed.
By good indexing and use of
different-colored cards for each class of surveys, all notes become
instantly accessible at all times, no matter what note-book happens
to be out of the office.'
in
ruled in the
Side Notes*
Side notes are those notes of the survey which are needed in
order to
draw a
correct
map
necessary in order to correctly
These include the pluses to
of the openings,
but which are not
map the traverse lines of the survey.
all
points to be noted, such as ore
chutes, upraises, winzes, side openings to rooms, etc.,
distance to the sides of the opening at
all
and the
points along the traverse
line.
The methods
of recording these notes are, of course, varied.
There are several different ways, first, in which the notes are taken,
and the method of keeping the side notes will, of course, depend
upon the method of taking them. The different ways of taking
may be roughly classified as: (1) The side notes of each sight follow the transit notes of that sight, and on the same page (2) they
;
'
'^
Iowa Engineer, May, 1907, p. 131.
System used in Bisbee, Ariz. M. & M., Oct. 1909.
RECORD OF THE SURVEY
are entered in the
129
same book on the opposite page
;
(3)
the transit
notes of the whole survey are followed by the side notes in the
same book; (4) each set of notes has a separate book.
The means of record are then classified as follows: (1) Sideshots recorded and no sketch made; (2) a sketch made as nearly
to scale and direction as is possible; (3) the red centre line of the
right-hand page is used to represent the transit line the lines to
each side of it represent the walls of the opening, and the distances are written in between.
The method without sketches is to be condemned except for
unusual openings, such as long tunnels without side openings. A
;
sketch
made
to scale
and direction
is
usually a failure as far as
being a true picture of the workings
is
concerned.
its
It will fre-
The
off the page, and has little to recommend it.
method is, then, the most satisfactory and is probably the
one most used at present.
Sometimes the notes of the survey consist entirely of sketches
quently run
last
(see p. 205).
When
carrying the transit notes on the left-hand page and the
sketch on the right-hand,
it
becomes convenient to use the railroad
surveyor's trick of beginning to record one's notes at the bottom
of the page and working up rather than vice versa.
Where this is
not done, the average noteman must turn his book around in order
to keep his sketch running forward.
Office Books
When
the field-notes are brought to the
into the ledger, or office note-book.
office, they are copied
This must show not only the
notes taken in the
field but also the calculated quantities.
The
heading of each survey must show the date of the field work and
by whom done,
the date of entry and by
whom
the calculations
were made, also the index numbers to show where the field-notes
and the calculation work are to be found. On page 130 is illustrated a double page of the ledger.
Calculation-Book
made in large books expressly for that
The heading shows the date, date of survey, and
All calculations are
purpose.
A MANUAL OF UNDERGROUND SURVEYING
130
eo
o
PL,
m
o
o
Q
<
W
W
O
«
1-1
o
PL|
.
'
RECORD OF THE SURVEY
reference pages of the ledger
men
131
field-book, also the names of the
Some system must be adopted so
and
doing the calculations.
that the exact part of the work wished
may
always be found in a
done by means
of logarithms and the calculation page shows a series of additions
work
is,
any course
is
particular part of the page.
and subtractions.
The first calculation
for
All
of course,
the reduction of the slope
The
distance to horizontal and vertical distances.
calculations
for this are as follows:
log slope dist.
log sin V. A.
log vertical dist.
vertical dist.
The next
=
=
=
=
log cos V. A.
log horiz. dist.
horiz. dist.
=
=
=
=
and latitude
to be calculated are the departure
local coordinates of the point sighted) of the course.
(or
This ap-
pears as follows:
log horiz. dist.
log sin bearing A.
log departure
East (or West)
These
=
=
=
=
coordinates added
local
log cos bearing A.
log latitude
North
(or
South)
(algebraically)
=
=
=
=
to the total
coordinates of the station of set-up, give the total coordinates of
the station sighted.
To
ically)
the elevation of the set-up station
the H.
I.,
Vert. Dist.,
mine
of the
is at,
is
added (again algebra-
P., to give the elevation of
Where the point
the station sighted.
system
and H.
of origin of the coordinate
or above, the surface, the vertical co-
ordinate of the stations grows larger as depth
the signs of
they are
if
H.
L.,
is
increased,
and
V. D., and H. P., are the opposite from what
the stations are carried as elevations (Figs. 24 and 25)
In making these calculations it saves time to have two men
work together to check each other. If one man simply repeats his
work
for a check, he
is
very apt to make the same mistake the
second time, and the error thus goes undetected.
The
office.
ledger
Any
The mapping
and calculation-book are never taken from the
notes required outside are copied into field-books.
is
done directly from the
ledger.
132
A MANUAL OF UNDERGROUND SURVEYING
After entering the notes in the ledger and making the calculaindexed to show to what pages in the ledger
tions, the field-book is
and calculation-book the notes have been
—
transferred.
Text-Boohs.
Ihlsing's 'Manual of Mining'; Lock's 'Practical
Gold Mining'; Underbill's 'Mineral Land Surveying'; 'Coal and
Metal Miners' Pocketbook'; 'Theory and Practice of Surveying',
Johnson; 'Principles and Practice of Surveying', Breed & Hosmer; 'Mine Surveying', Lupton; 'A Study of Mine Surveying',
L. E. Young; Gillette's 'Earthwork and Its Cost'; 'Mine Surveying', Broughs; 'Ore and Stone Mining', Foster; 'Colliery Surveying', T. A. O'Donahue; 'Ore and Stone Mining', C. LeN. Foster.
VII
THE USES OF MINE MAPS
'A PLAN which requires the presence of the person or persons
by whom it was prepared to explain it, or to supply information
which ought to have been on the plan, has its utility diminished
'The value of correct and comin proportion to the omissions.'
plete plans does not, in many cases at least, appear to be properly
appreciated.
It is no uncommon thing to see men blindly blundering about in mines, working deposits of complicated structure,
without even a plan of the workings to guide them, much less a
plan showing all the facts relative to geological structure, which
the manager should have constantly before him.' The working
plans are most important; others are secondary and taken from
them. 'In fact, without a detailed knowledge of structure, it
is as impossible for a manager to direct, with technical success, the
operations of a mine in complicated ground, as it is for a doctor
whose knowledge of anatomy is defective, to properly carry out
some complicated operation upon the human body.' ^
The importance of mine maps is not too well underMaps.
In no way can money be better spent than in making good
stood.
maps of a mining property of any size. The money so spent will
be repaid many times over. A map showing all workings is of the
greatest value, but in speaking of good maps we refer to maps
showing much more. A mine map should be constructed on the
same principle as a machine drawing, if the fullest benefit is to be
derived from it. A machine drawing, of course, is so full and
complete that any mechanic can construct that machine without
any explanation, or knowledge of its use, or without ever having
seen a similar machine. In order that a machine drawing should be
as complete as this, one drawing is insufficient, even in plan and
Detail drawings must be provided.
The same principles
section.
must be applied to mine drawings or maps. It may be stated
without any hesitation or fear of contradiction that a mine map
—
1
Mining
Reporter, vol. xlviii, p. 165.
133
134
A MANUAL OF UNDERGROUND SURVEYING
should be a pictorial representation of the details of work done in a
mine, not merely the
drifts, shafts, winzes, upraises,
Anyone who has had occasion
how
exceedingly small
is
to look
up
old
and
maps
stopes.
will
know
the practical information to be derived
from them. Even the date of the map may not be shown. Now
a mine map should show (1) The extent and contour of the working; (2) the shape and extent of the ore shoots, and the nature of
the ore found in them; (3) the geological features, such as variations in the wall rocks, faults, etc.
A complete .mine map must
consist of several maps.
These will be the main office maps,
showing the workings pure and simple; the superintendent's
working maps, on a scale sufficient for him to take them underground; assay maps, upon which are recorded the assays of all
mine samples, thus showing the value and trend of all ore shoots;
the geological maps, upon which are recorded the formations and
their changes, the nature and details of faults, and any other
geological facts deemed worthy of notice.
Ask any superintendent
or manager who is using such maps as to his opinion of their value,
and not one would give other than a most emphatic testimonial
as to the great importance of such maps to him in his daily work.
:
Now, many may demur
to the practical value of such
being so expensive to maintain, and
value they must be up to date.
all
maps
as
recognize that to be of
The answer is of course obvious.
two are saved, then the dollar investment
is a wise one.
Practical examples are better than academic
reasoning.
Let us give two
Pennsylvania and Great Britain.
Both, a number of years ago, required all mines to keep their maps
up to within a month. Mine owners vigorously protested. It
was found, however, after a few years' trial that in the coal and
iron mines the maps showed enormous losses of mineral.
The
maps not only showed where the losses occurred, but how they
occurred. The remedies were therefore suggested by the maps
themselves. The advantages were so great that the scope of the
maps is frequently extended beyond the requirements of the law.
If those laws were repealed to-morrow, the maps would continue
to be made.
Mining engineers know and appreciate the value of accurate
mine surveys and maps, and most mines have maps which will
answer all practical purposes, but there are mines without them.
A full set of maps must embrace level maps, and vertical longitudiIf
by spending a
dollar
—
THE USES OF MINE MAPS
135
nal and vertical cross-sections of veins which have
any consider-
able dip (see Figs. 60 to 73).
It is the practice to plot a general plan of the 'underlay'
a single sheet, showing each level in the mine, with
of
development, winzes,
indicated
and
by
all its
on
details
and stopes, each being
The idea of projecting plan
raises, cross-cuts,
characteristic marking.
on a single plane, as attempted occasionally,
and is never done by those familiar with the
principles of mine mapping.
The scheme of mapping each level
separately, each level map drawn to a certain datum, is an excellent one, and tracings of these several level maps may be made,
which admits of binding them together permanently or temporarily.
The lines showing the several levels may then be examined
simultaneously by placing the sheets one above another, and the
relative position of the workings on adjacent levels studied.
^ By plotting all the development work, and also the structural
is
vertical section
unsatisfactory,
geological features (such as changes in character of rocks through
which the workings
pass, the dip of the formation, all dikes inter-
secting the workings, cross-veins, seams, faults,
gether with their strike and dip) the
,
and gouges,
maps may be made
to-
to serve
The breaks in the vein, which occur on
any particular level, may be referred to levels above and below,
as may any other geological irregularities which may occur.
The
lack of just this sort of knowledge has sometimes resulted in
their greatest usefulness.
closing mines subsequently proved to be valuable.
Never, perhaps, is an accurate mine map appreciated so greatly
upon the reopening of a long abandoned property. Such mines
are usually flooded, and when new work is undertaken, as connecting with works of an adjoining property, or sinking a new
as
shaft to be connected with the' old workings, the element of danger
which attends such operations, owing to large volumes of water in
the old works, is reduced to a minimum. The manager knows
how far he is from the old levels or stopes, and can anticipate
imminent danger and provide against it.
Accurate maps are also of great service in searching for new
by their use a comprehensive idea of the entire vein
ore shoots, as
be obtained, for a glance at the map places the development
thousand feet, possibly, immediately under the eye,
and the relations of the various portions of the mine become
may
of several
apparent.
»
Survey
in Practical Geology.
Bui.
A.J.M.
E., Aug., 1909.
A MANUAL OF UNDERGROUND SURVEYING
136
Laws Affecting Mine Surveys
—
The requirements of the law with reference
maps vary somewhat in the different States, but those in
Pennsylvania.
to mine
^
the anthracite region of Pennsylvania are probably as rigid as anywhere, and are therefore given.
'Sec. 1. The owner, operator, or superintendent of every coal
mine or colliery shall make, or cause to be made, an accurate map
or plan of the workings or excavations of such coal mine or colliery
on a
scale of 100 feet to the inch,
which
map
or plan shall exhibit
the workings or excavations in each and every
seam
of coal, and,
the tunnels and passages connecting with such workings or excavations.
It shall state in degrees the general inclination of the
strata with
any material deflection therein
in said
workings or
excavations, and shall also state the tidal elevations of the bottom
of each
and every
shaft, slope, tunnel,
and gangway, and
of
any
other point in the mine or on the surface, where such elevation
be deemed necessary by the inspector. The map or plan
show the number of the last survey station and date of each
survey on the gangways or the most advanced workings. It shall,
also, accurately show the boundary lines of the lands of the said
coal mine or colliery, and the proximity of the workings thereto,
and in case any mine contains water dammed up in any part thereshall
shall
of, it shall
be the duty of the owner, operator, or superintendent
to cause the true location of the said
on said
map
dam
to be accurately
marked
or plan, together with the tidal elevation, inclination
and area of said workings containing water and whenever
any workings or excavations are approaching the workings, where
of strata,
such
dam
;
or water
is
contained, or situated, the owner, operator,
or superintendent shall notify the inspector of the
delay.
same without
A true copy of which map or plan the said owner, operator,
or superintendent shall deposit with the inspector of mines for the
district in which the said coal mine or colliery is situated, showing
the workings of each seam,
if
by the inspector, on a
One copy of the said map or
so desired
separate sheet of tracing muslin.
plan shall be kept at the colliery.
'Sec. 2. The said owner, operator, or superintendent shall as
often as once in every six months, place or cause to be placed, on
1
From 'Examination
Questions', p. 30, International Text-book Co.
ORDINARY MINE-SURVEY OR COMPOSITE MAP
From the Transacliom
vol.
of the
A.I. M. £,•
xxxvi, pp. 508-540.
FIG. 60.
•CAUE 40
—t
t^ M
9JA38
qAM 3TI8O1M00 aO Y3VHU8-akllM
•oa
.on
YflAHiaflO
.0t'S-80a .qq ,ivxj:ie .5«w
SURFACE MAP
SCALE 40
=1
t= 0>
3JA38
«IAM tOA^ftU^
40 FT. LEVEL
B
LCfiCND
J3V3J
.T^ 0*
OMadjj
120 FT. LEVEL
jgv3J .T^asr
1
60 FJ.
LEVEL
J3V3J .n oar
200 FT: LEVEL
J3V3J Tl OQS
VERTICAL SECTION ON LINE
1
am?-;
LCGFND
foot-waLl
ore
HANGING-WAUL
f
amj
i/io
moiToas jAOiXfiav
l'^^-
^s
^°'
.V8
\aji\
.i\
004
.Ol'i
aM3D3J
JJAIW-aMIOllAM
3P0
JJAW-TOOT
VERTICAL SECTION ON LINE
200 ft
2
leve^^^ CST^ \ C%.
C
FIG. 68.
V
S ai^lJ klO
--^^>.,
HOITaif JA0ITfl3
.fAl^'.'.^^^\^w\
o
.80
.oil
VERTICAL SECTION ON LINE
3
e
3HU no
yioiToaa jAOiTnav
—
I
S\3
Data furnished by
gineer.
and B.
may be
C.
W.
absolutely correct, the assistant
now
Goodale, manager, and Lee Hayes, chief en-
A MANUAL OF UNDERGROUND SURVEYING
198
standing at C, and reads the angles, measures
the distance, and checks the point on line at D. The two surveys
must agree, or the work must be done over. While the transit
takes the transit,
still
driven on the inside of the shaft at the same
elevation as the telescope the distance is measured down from the
known elevation of the station or tag at £ to a horizontal line
stands at C, a nail
is
;
from the
down
carried
From the nail in the shaft,
by tape measurement.
telescope.
the elevations are
the shaft
>h^^M^^=
FIG.
The
F is
FE is
transit
is
79.
— TAKING
MERIDIAN FROM WIRES.
E
and the angle between C and
assistant.
The course
from which can now be calculated the
now moved
to
read, doubled, and checked
the
known
course,
course between the wires
A
by the
B.
•
Meanwhile, on the level where the courses are sought, another
surveyor and assistant are 'taking off' the line from the wires by
exactly the same process as that described above. If only one
surveyor and one assistant work, they can be lowered through the
centre compartment.
Two
transits are, however,
always used for
no space for the transit at C, the compartment B is planked over and the wire suspended at G while the
transit is set at B.
This gives a distance of about 7 feet between
the wires. Two wires in one compartment have not given good
results and that method is not used.
this
work.
In case there
is
11897
L
D*E)
:
3rd Floor
(jin
D E
10-06
2nd Floor
A. 843
11899
D
7r
1st Floor
11899
if
—
.
\>-^
)
are
mapped f ron survey and
stopes Lre carried up abc ve
FIG.
80.
9
X
A.S28 Dr.E,
A.828 Dr.W.
Bill set
u
u
them.
— STOPE-BOOK
wn
Sill
SKETCHES FOR VEIN WITH ONE BEND.
:
A MANUAL OF UNDERGROUND SURVEYING
200
18 copper wire is used with 11- or 12-pound iron
These have been used through 1200 feet of depth.
The stations are marked by brass tags (I, Fig. 46) attached to
the timber or plug. The stations are numbered consecutively
from 1 to 99,999 or more. Several hundred tags are stamped at
once, then one 100 is used in one mine, another 100 in the next,
etc.
No duplicates are used. The tags are used by number in
order of survey, but with no reference to position in the mine.
The transit is set up under the plumb-bob. Angles are read to the
Number
weights.
and doubled for check. Loose-leaf notes are used. Following is a sample on page 201.
The heading shows the place of work, names, the surveyor and
'C. 10738 'gives page where the
assistant, followed by the date.
calculations were made; L. 5439' gives page where notes were
copied in the ledger. In the ledger are found courses, coordinates
and elevations, besides the written field notes.
The notes are in order from the beginning to the end of each
book, so that dates and station numbers are in order. Each place
in which a survey is made is indexed in the front of the book as
right,
'
well as in the ledgers.
shows the stope-book sketches for the level and three
above the level of a vein with one bend. The notes for the
survey lines on the sill floor are as follows
Fig. 80
floors
A
825 Dr. E.
Line for Timbers.
8/9/06.
Aber-Kane.
Vert.
H.I. Ang. R.
Transit
Courses
Ang.
Mag. and
True ^
Slope
and H.
Hor.
P
•Sf^
Debcbiftion
Dist.
Dist.
8286 B.
S.
8240
273° 24'
26.68
186° 48' S.32°68'E,
15.20 2.2 from
To
nail centre
last cap.
N. post.
9.50 2.3 from
N. post.
A
828 Drift
8240
108° 11'
W.
11/14/06.
S.
N.42°W.
216° 22' N.20°2'W.
timbers.
Abbr & Julian
To
10032 B.
Round
29.50
10032
E.
side centre cap.
To nail centre
E. side cap.
Bend
is
10032.
at No.
METHODS OF VARIOUS ENGINEERS
^
201
116111
FIG.
81.
— STOPE-BOOK
9686
SKETCHES OF VEIN WITH TWO BENDS.
METHODS OF VARIOUS ENGINEERS
Fig. 81
shows the field-book sketches
of a vein
203
and stope with
two bends.
Fig. 82
shows the
office
maps
as constructed
from the above
notes.
Field stope-books are on a scale of 20, 30, 40, and 50 feet to 1
inch.
The 30 or 40 is found best for most
4, 6, 8, and 10 spaces, or 16, 36,
the heavy lines.
divided into
inside
veins.
64,
Inches are
and 100 square
Steel tapes of 25-, 100-, and 250-feet lengths are used for
measurements. Maps are to the scale of 1 inch to 50 feet, drawn
upon paper 18x46 inches. This size represents a double page in
the large stope-books, in which all floors of all workings in the
mines are mapped.
Angles are platted by coordinates. The extensions of workings are tinted by water color; a different color for each year.
United States Coal and Coke
Cg.^
In ordinary flat work, the party consists of three men, but
on steep work, of five. The Y-level and 5i-inch engineers'
transit are the instruments used.
The meridian
is
determined by observation on Polaris, and
carried unde'rground through drift
The
by
traverse.
stations are spads (n. Fig. 46) driven into a coal or slate
a bored hole.
marked on
and on rib
marked by a
circle, a point on curve by a triangle and a bench-mark by a square.
The system of numbering is the same as that used in railroad
roof, or in
by white
Stations are
lead or Spanish whiting.
lines, i.e.,
roof
A transit-point is
48 -f 00.6.
is made under the plumb-bob, and sight is made on
plumb-bob string backed by a piece of white paper with lamp
behind it. The method of continuous azimuth is used.
Set-up
'
Survey methods furnished by Mr. Howard N. Eavenson, chief engineer.
27
26
27
26
27
S)
39
4th Floor
3rd Floor
28
28
:
METHODS OF VARIOUS ENGINEERS
The company
and specimen page
issues a letter
field-notes to its surveyoi-s.
205
This
is
given in
-f
full
(Fig. 83) of
as follows
+ +
+
i/A'
If
'm -
if
CT
•cA
•n/i
k1s.»»i
|8S|o
2
1
[I
(It
H
n
•u/: >L_li.
S
ij*
SI
*I
i|
If
SI
yjjjjjjjj.i.
ST
II
II
u
Ch
O
In
^iwjw.
5. !,/.,
^11
All
Booms
0]
.
No. ia=oo°oo'Kt.
thle Butt except
No. 18=73°19'lit.
FIG.
83.
— SPECIMEN
=
N. 42°ll'w.
K. 59°22'W.
PAGE OF FIELD-NOTES.
'United States Coal and Coke Company Method of
Recording Mine Suevey Notes
'Gary,
'In
room
notes,
draw a
of each survey, as at
A, B,
etc.,
W.
Va., August 19, 1903.
each room for face at date
and record survey letter for each
line" across
A MANUAL OF UNDERGROUND SURVEYING
206
The date of survey, with survey letter after it,
must be written at top of page (as A, July 5, 1922). Consecutive
letters, A, B, C, etc., are to be used for consecutive quarterly
surveys, beginning in each mine when first rooms are turned.
For intermediate surveys, use dates, and no letters. Note all
Enough
distances as being total from transit-point in heading.
measurements must be taken to show clearly the shape of the
excavation; they must be taken to side of heading at mouth of
rooms, to end of necks of rooms, to first point where rooms reach
full width, to near side of all cut-throughs, to faces of rooms at
date of survey, and in general, to all points where directions of sides
Allow sufficient space to show rooms and pillars
of rooms change.
room, as at A.
clearly, so that figures, dates, etc., are
In making draw-back
'
hatching;
thus:
line,
not obscured.
use a broken line and widely spaced
illlllllllllH
the
full
regular surveys, as at
mark
^.nd
back from the centre of heading on room
some date (or letter) for recording date
of
drawn
distance
pillar (see sketch)
draw-back
Use
.
line as for
C
'In heading notes, draw a line for face of heading, and
mark
Measure and record distances right and
left to the sides of headings and rooms at points not greater than
25 feet apart, and less where decided changes of width take place.
date clearly at this
line.
'These same notations, including lines for face, at date of
marked across headings and rooms must be used on all
survey,
mine maps.
The
letters are to
be at faces of rooms and are to
correspond with date of last survey as marked on map, and placed
January 4, 1923, A).
Dates instead of letters are to be used for faces of headings.
'AH rooms are to be turned by angles from transit-line in
after this date; thus: (date of last survey
headings, to be recorded in notes (see Fig. 100).
Records are to be made of both transit and
'
room
notes.
'Chief Engineer.'
1
Tapes
of 100
to the scale of
long as
may
1
and 300
Maps are made
upon paper 58 inches wide and as
The main lines are platted by co-
feet in length are used.
inch to 100 feet,
be necessary.
ordinates and extensions
by
steel protractors reading to minutes.
Blue-prints are taken quarterly.
Figs.
84 and 85, show maps of workings and workings projected
All headings, rooms, etc., are driven on line sights.
in advance.
'
Methods used
in
Rocky Mountain
collieries.
M.
& M.,
Sept. 1909.
;
.
.ussy!:- >-T--^n .. -^
y.)
No.
5
^..
-.
v
\;\\
p
.
r
Bum
y,-x.^
\\
.-^m
Headings
\i
ir~i-r
FIG. 84.
— MAP
OF WORKINGS OF COAL MINE.
A MANUAL OP UNDERGROUND SURVEYING
208
HOMESTAKE
At
the Homestake Mining Company's property, Lead, South
Dakota, the underground party consists of the transit man and
two helpers. The meridian is determined by Polaris or by direct
sun observations. The side telescope is used, but for vertical
The regulation plumbazimuth underground are employed.
Number 20 or 22 copper or brass wire is used. The azimuth is
taken off underground by setting the transit up in the plane of the
two wires and then lining in the plumb-line notches in spadS. To
hold the plumb wires steady, fifteen- or twenty-pound cast-iron
weights are immersed in cans of water, usually five-gallon oil cans.
Stations are plug and triangular-notched spads,and are not marked,
the notes and sketch being sufficient to identify them. The underground stations are not numbered, but surface stations each carry
a number.
sighting on short base
methods
line
it is
not relied upon.
for carrying
The set-up is generally made over a point (nail) carried to the
Where necessary, the instrument is set up under a plumb-
floor.
In low openings, the instrument
bob.
is
sometimes used without
tripod.
Deflection angles are read
and checked, and courses afterward
referred to azimuth.
Notes are kept on
Upon
blue.
4^x6
inch cards ruled 8 to an inch in light
these, a sketch of the
deflected angle
and length
Side notes are taken
work done is made and the
upon the sketch.
of course written
by
radiating side-shots to points around
are carried through the
headers and to shaft-stations and bench-marks made.
irregular
openings.
Levels
principal
Measurements are made with 100- or 400-foot steel tapes.
are to the scale of 50 or 100 feet to 1 inch and upon paper
Maps
X 100
inches in size. The principal courses are platted by
and departure, but unimportant side-shots by protractor.
Extensions of the survey are shown upon the map by dotting new
outlines and erasing the old lines of stope margin.
Blue-prints of
60
latitude
special sections are
taken as required.
Stopes are surveyed by counting square sets from some reference
point.
Regular cross-section paper, as near the scale of working
is used to sketch the sets and outline of
map
as can be procured,
each
floor of the stope.
FIG. 85.
— MAP
OF WORKINGS AND PROPOSED EXTENSIONS.
A MANUAL OF UNDERGROUND SURVEYING
210
No record of samples or assays is made on a map. This record is
kept by the Sampler in his record-book by name of stope or drift.
The inclination of the drill-rods in bore-holes is taken and
'
'
azimuth of bore found by plumbing points to the
are measured for depth.
A
The rods
floor.
Quick Vertical Shaft Survey '
'This article deals with the method I have used for fifteen years
making quick and accurate surveys of various vertical shafts in
Amador and other counties along the Mother Lode of California.
'The essential features of the method are the use of heavy
plummet lines and "bobs" hanging free while being set, but
in
securely fastened while observations are being taken.
illustrate the operation of this
that of
July
6,
method by
citing
I
can best
an actual
case,
my
survey of the Oneida vertical shaft in six hours on
1902. This main working shaft of the mine was sunk 1000
feet east of the outcrop
and intersected the
vein,
which dips to the
1900 feet, below the surface. The vein was then being worked
through six levels at 1200, 1500, 1700, 1800, 1900, and 2000 feet,
vertically below the collar of the shaft.
east,
'The adverse conditions under which this survey was made
A very wet shaft, through which water literally poured in
torrents; a shaft distorted and narrowed by swelling ground at
the 1800-foot level, and a shaft with an excessive number of working levels into each of which the survey had to be tied from one
hanging of the plumb-bobs and as quickly as was consistent with
good work, so as to interfere as little as possible with the regular
operation of the mine and the use of the shaft.
'To overcome these adverse conditions, two large-sized (numwere:
ber 12 gauge) soft-drawn iron wires were suspended in the centre
compartment of the shaft, with a 125-pound plumb-bob attached
to each, less than one foot below the 2000-foot level, the wires
from the surface with the bobs attached, through notches
At the 2000-foot station, opposite each wire, a template,
made from a piece of candle-box, was so placed and fastened with
a wire nail at one end that the free end could be swung or moved
to or from the wire in a horizontal direction practically in line with
sliding
in plank.
'
Written by
1906.
W.
E. Downs, for the
Mining and
Scientific Press,
August
25,
METHODS OF VARIOUS ENGINEERS
both wires.
loosely
By
211
the interposition of a small piece of
upon each template, with
its
wood
laid
end projecting over, and
in
contact with, the advancing side of the oscillating wire, the latter
was brought to rest after the retardation of a very few oscillations.
The position of rest was then carefully marked on the template.
As the oscillations diminished, the template was brought closer to
the wire until finally, when the latter was at rest, the template
was brought in contact with it and nailed in place. The wire
was then fastened to the template from underneath, in the position of permanent rest.
'Seven settings with a transit were made, one at each station
and one at the
collar of the shaft, all in the
same
vertical plane.
In each instance the instrument was set, by the "cut and try"
method, as near the nearest wire as the minimum focal distance
(about six feet) of the telescope would permit, with a lighted candle
beyond the farther wire. When in this position, the
be focused on either wire and accurately adjusted
The
to the exact plane of both; this was done in each instance.
slightest sidewise tremor of either wire, which neither lasted long
nor caused serious delay, was readily detected. From each setting wire nails wero accurately centred on line and driven into
solidly placed track ties, plugs, timbers, or planks, and steel-tape
measurements to the nearest hundredth of a foot made to locate
all in the same vertical plane.
them with reference to the wires
Subsequently, from these nails, courses were extended by deflection throughout each level and to the previously established surface
boundaries and all necessary measurements made, whereby the
in range
telescope
may
—
position of each point, or instrument-station, in the whole sys-
tem was determined with
reference to every other point.
these data the entire system
From
was accurately mapped and the
field-notes tabulated for future reference, so that the
survey could
be extended and mapped as development work progressed.
'
In this survey the horizontal distances between plummet-wire
centres were respectively: 2.43 feet at the collar, 2.44 feet at the
and 2.45 feet at the 2000-foot level. The divergence
downward is due to but one cause, which is purely
gravitational.
The mass of rock that would have to be in place
between the wires to have them hang parallel, or, more theoretically
1200-foot level,
of these wires
to converge
toward the centre
course the
wires
came
to
of the earth,
rest,
was absent, and
of
diverging slightly downward.
:
A MANUAL OF UNDERGROUND SURVEYING
212
Drafts and falling water in the shaft do not have any effect
upon
the sum total of this .divergence, although they do create tremors
and also operate to check the same.
In contrast with the hard-drawn piano-wire method of hanging
'
bobs of necessarily light weight in molasses or some other viscous
liquid, this method has no equal; it is quick and reliable, it has
proved so to my entire satisfaction in numerous instances where I
have made surveys for underground connections.
A plummet line of large-sized soft-drawn wire has two decided
advantages over one of small-sized hard-drawn wire; they are as
'
follows
'First.
In the process of hanging wire,
strains are absolutely
removed by
all
kinks and internal
stretching, leaving the wire
perfectly straight, a condition impossible with hard-drawn wire
wherein kinks and strains are left, subjecting the wire to local
wobbles nearly as great as the diameter of the wire itself.
'Second.
As external
disturbances, due to drafts and falling
water, are of a magnitude proportionate to the exposed surface of
the wire, and as the strength of a wire
is
proportional to the square
and therefore to the square of its exposed suralthough a hard-drawn wire is stronger per unit of
of its circumference
face, it is plain,
than a soft-drawn wire, that if the difference in
enough, a large soft-drawn wire is better adapted to
cross-sectional area
size is great
withstand said disturbances than a small hard-drawn wire. The
so-called advantage of being able to bisect a small-sized wire with
the vertical cross-hair of the instrument better than a large-sized
wire
is
first
advantage.
in practice a
myth, particularly when contrasted with our
'The bobs must be symmetrically made, preferably
of solid
shafting accurately turned in a lathe and centred with an eye at
one end to receive the plummet wire. This wire must be a continuation, when suspended, of the axis of the bob, so that there will
be no local wobbles in the wire when the bob revolves, which it will
do to a small extent.'
A Method
'
for the Survey of a
Some time ago
old mine workings,
Wet
Mine-Shaft i
the writer, while engaged in the survey of some
had occasion to devise a method
By Mark
Ehle,
Jr., in
for the carry-
The Aurum, March, 1906.
METHODS OF VARIOUS ENGINEERS
213
two adjacent levels via a short length of
same representing such features as to render
ing of a line between
inclined shaft, the
ordinary methods' of procedure inapplicable.
Reference to the
accompanying figure will make clear the conditions.
'The incline in question was the only available opening connecting the levels, and therefore had to be utilized. It had a
length of some eighty feet, between levels, and dipped at an angle
of about seventy-five degrees for the upper sixty feet, changing to
a somewhat flatter angle throughout the remaining distance. It
comprised one ladder and two hoisting compartments. The ladderway, while available for travel between levels, offered by its
arrangement, serious,
work
at hand.
if
not insurmountable, obstructions to the
The adjacent
hoisting
compartment was
half
having been used as an ore bin. The outer hoisting
compartment, though open, presented its difficulties in the form of
full of rock,
descending water, which, falling in large quantities from the hanging side, dropped to the other,
and
in rebounding, filled the lower
portion of the compartment with a heavy shower of descending
drops.
'The traverse having progressed to the station P (Fig. 86) in
made under this station, and by means
of an auxiliary top telescope, a sight on the point B was defined
by a pin-thrust through a plumb-line suspended from station H;
the pin being rendered visible by a background of illuminated oiled
paper, stretched over one end of a tin can, a candle flame within,
thus being protected from the falling water. In order to prevent
vibration of the line, due to the heavy drops of water striking
it, some strips of old tin roofing were placed as a protection throughthe upper level, a set-up was
out the greater portion of
A satisfactory
its
length.
B having
been obtained, the necessary
measurements of azimuth, slope distance, vertical angle, HI, etc.,
were taken. Going below, a set-up was now made under station H,
the transit being protected from the falling water by an improvised
tin roof.
Through an opening in this roof a backsight on the
plumb-line suspended from station P was attempted, but failed
'
utterly, as
sight
any opening
on
in the roof, large
enough to permit
of dis-
covering the plumb-line, admitted such quantities of water, in the
form of spray, that not only the objective was blurred, but the
cross-hairs
instrument.
were endangered by water entering the tube
To add
of the
to the difficulty, the din of the falling water
FIG.
86.
— INCLINED
SHAFT SURVEY BY BENT LINE.
METHODS OF VARIOUS ENGINEERS
215
vetoed all attempts at vocal communication up or down the shaft;
but by rappings on the old air pipe, which extended up the laddery/ay, a crude system of signals was arranged and used.
Having
a backsight by this method, the foland successfully used: A strong, waterproof fishing line was suspended from station P in such a manner
that it would in any event define a plane with the plumb-line
suspended from the same station. This silken cord was then passed
down the incline and carried out into the lower level, being tem'
failed to obtain
lowing was devised
porarily fastened to the old air-pipe running along the opposite
A twelve-pound plumb-bob having been suspended from the cord at the point M, the lengths of cord on either
were kept taut, and in any position, the lines of these
side of
lengths
defined a plane containing the point P above. This
two
plane was then shifted by moving the lower point of attachment
of the cord along the pipe to a point F which brought the lower
length of cord exactly under the plumb-line suspended from H.
Another small bob was now hung from a point G in the lower
The point of this bob was centred over the small cord
drift.
stretched below, which was then removed to one side.
'The setting of the plumb-line at G in the manner described,
side of the drift.
M
'
insured of
its
being in the same vertical plane of the plumb-lines
H
H
from
and P, and at once rendered a set-up under
unnecessary;
for, having the azimuth of the course A B, the azimuth of such a
course as C D becomes identical with it, and a set-up under station
D
gives
stations
'
By
all
other information regarding the relative positions of
H and G.
the use of so heavy a bob at
M,
all
vibration of the small
cord was absorbed, and no difficulty from this source was experienced.'
A
'
Mining Survey
^
A high degree of accuracy is often required in mine-surveying,
mining work may not be misdirected. The
underground connections by drifts or shafts located as
the result of surveys presents a crucial test of correctness not
usually involved in any other class of surveying.
In view of these
in order that expensive
making
=
ing,
of
Reprint of article
August, 1900).
by J.
F. Wilkinson, Trans. A.
I.
M.
E. (Canadian Meet-
A MANUAL OF UNDERGROUND SURVEYING
216
and description of a survey made
San Francisco shaft of the New Almaden
considerations, the present notes
in June, 1890, for the
quicksilver mines,
who
may
be of interest to members of the Institute
are surveyors.
'The purpose of this survey was to locate on the surface a
2-compartment shaft (3.5X7 feet), to connect with another vertical shaft, of practically the same size, which had been
sunk a number of years before from an adit-level about 240 feet
vertically below the surface, to a deeper, so-called 600-foot level.
It will be seen, of course, that the most important matter was to
secure an exact coincidence in vertical line, so that the resulting
continuous vertical shaft from the surface should have no offset or
irregularity at the point of junction between its two parts.
The
levels were of less importance; but, as the hoisting- works were to
be placed in position and the new shaft permanently timbered from
the start, its correct alignment was an essential requirement. The
important 'features of the work, therefore, were the methods used
in determining with certainty: (1) That the shaft was located in
the right place in a general way; (2) that the ordinary inaccuracies of linear and angular measurements were so reduced as to
vertical
insure correctness of location within certain defined
limits.
'
Instruments.
— The instruments used were
:
and allowable
a Buff and Berger
transit-theodolite, with a 6-inch horizontal plate, reading to 10
seconds; a Heller and Brightly Y-level; a Chesterman
graduated in tenths and hundredths of a foot; and
leveling-rods, graduated to thousandths of a foot.
steel tape,
New York
The leveling-rods and. tape were compared with a standard
measurement, and the correction for each was ascertained. In
'
of
the case of the tape, the conditions for the standard were, that the
pull should be 16 pounds; that the tape should lie horizontally on
the ground; and that the temperature should be 70° Fahr. (this
being the average temperature in the adit underground). Three
corrections were thus actually necessary for each tape-measure-
ment,
viz. to reduce to the standard to correct for the catenary
curve and to correct for difference in temperature.
'While the graduations on the tape were made to hundredths,
:
;
;
measurements, it was possible to estimate thousandths of a foot, thus making these readings correspond in
minuteness with those obtainable on the leveling-rods.
yet, in careful
—
METHODS OF VARIOUS ENGINEERS
'Of course, to do this underground,
very
fine fish-cord for
it
217
was necessary to use
plumb-lines; and, on the surface, measure-
ments were made between small headless wire nails in stakes
by means of the transit. Here the hypotenuse
was thus obtained, while the vertical component was obtained by
leveling; and from these the horizontal component was calculated
in the usual manner.
Underground measurements were made
on a practically horizontal plane, by means of marks on plumblines previously aligned by the transit, and leveled.
'To correct for the catenary curve, the weight of the tape per
previously aligned
was ascertained, and the correction was calculated by the
For a tape weighing 0.00725 pound per foot,
with a pull of 16 pounds (exerted in all measurements by means of
foot
usual formula.
spring-balances), the correction to be applied in 100 feet
foot,
and
is
0.00855
in 50 feet only 0.00107 foot.
'For temperature, the correction in 100 feet for a difference of
is 0.00069 foot.
Most of the measurements in the adit
1° Fahr.
were made at a temperature not varying appreciably from the
assumed standard. On the surface, however, the temperature in
some instances varied from the standard as much as 20° Fahr.
'In making the angular measurements, the greatest care was
taken; and, by the most approved methods
repeating angles,
reversing the telescope, reading both from right to left and from
—
to right, etc.
left
—
possible instrumental errors, unavoidable
all
and
pei-sonal errore of observation, were
were read at least twice and in some cases
as many as four readings of ten repetitions each were taken.
The
number of times each angle was read, and the number of repetitions
in each case, are shown in column 4 of Table I.
By the means thus
employed, the angular measurements were made certainly correct
errors of adjustment,
eliminated.
All angles
within one second.
;
—
In the preliminarj- survey, the mean of
tape-measurements was taken. For the surface line,
besides the tape-measurements, two sets of levels were also run.
As to the surface line (Monument M. to Monument S. F.) it may
be observed that neither monument was visible from the other;
'Preliminary Survey.
two
sets of
,
so that, in order to define the line, several settings of the transit at
intermediate points were necessary.
The
different
measurements
reduced, the calculations made, and the results obtained in this
the first complete^survey, are shown in Table I; and, for their
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A MANUAL OF UNDERGROUND SURVEYING
222
position of the originally located corner,
C
Wire Cor. Cj
(called
This was possible without fear of the wire touching
the sides of the shaft, for the reason that the shaft had been made
several inches wider and longer than the collar-set of the aditin the notes).
shaft.
To prevent
oscillation, the
plumb-bob was immersed
mixture
+''
in a
of molasses
and water.
Then,
having ascertained
that the wire hung
without
freely
touching the sides
any
of the shaft, or
other objeiBt, at any
point,
its'
position
was instrumentally
observed
both
at
the surface and the
08,200
4-W-
adit-level.
Soath
The
co-
ordinates thus ob-
tained are shown in
the tabulated notes.
^
f076-Ftt
The
>
difference
be-
tween the two
sets
of coordinations
is
the error of the survey,
and
is
shown
both the preliminary and the checkin
survey.
'
FIG.
89.
-POSITIONS OF
{
=
^'^^er
c,.
It
must be
said
that the conditions
under which the
survey was made
were most favorable for the surveyor. The two assistants employed were reliable and experienced in that class of work; and,
as no mining was being done in that part of the mine at that
time, there was neither tramming, blasting, powder-smoke, nor
changeable draughts to interfere with observations or distract
attention.
On the surface, the atmosphere was clear and the air
steady; and, during the first part of the survey, there was very
Natural Scale:
1
Foot
1
Foot.
METHODS OF VARIOUS ENGINEERS
little
ing
wind.
was
'In
A sufficient length of time
223
was allowed, so that nothundue haste.
slighted or overlooked on account of
summary
The means taken
review, the special features to be noted are: (1)
to insure the location of the shaft in the right
place (two independent surveys and check-calculations); (2) the
methods used to reduce the ordinary inaccuracies of survey within
allowable limits; and also the practical demonstration, here given,
of the accurate results attainable by the use of the usual surveying
instruments and measuring apparatus, as described, when the
most approved methods of observation are carried to the extreme,
and neither time nor care
is
spared to
make
the results as nearly
perfect as possible.
'Fig. 89,
drawn
to natural scale, illustrates the final result of
the surveys.
'In this figure, the circle numbered 1, and completely filled
with black, shows the position of Corner Ci Wire, as coordinated
from the adit-level by first survey ; the open circle, numbered 2,
that of Corner Ci Wire, as coordinated from the surface by first
survey; the half-black circle, numbered 3, that of Corner Ci Wire,
as coordinated from the adit-level by second survey; and circle
numbered 4 (open, with a heavy horizontal diameter), that of
Corner Ci Wire, as coordinated from the surface by second survey.
'By the location-survey the shaft was 0.007 foot too far south;
and 0.007 foot too far east; by the check-survey, it was absolutely
correct north and south, and 0.047 foot too far east.
'By averaging the two surveys, giving to the location-survey
twice the importance or "weight" of the check-survey (because
all of its measurements were made twice, while in the checksurvey some were made only once), we have the average error
of the survey; the shaft thus being 0.0047— feet too far south, and
0.0203-1- feet too far east.
'This applies to the other three corners, as well as to Corner
C
XII
EXAMINATION FOR COMMISSION AS
MINERAL SURVEYOR
This examination
in
U.
DEPUTY
S.
Colorado consists of problems in calcula-
tion of closing line in a twelve- or thirteen-sided placer, together
with calculation of area by Double Meridian Distance Method,
calculation of lode line to fit an irregular claim, calculation of ties,
and areas
an actual approved survey together
A problem on the
subdivision of a section of the public survey is usually added. The
applicant is also required to determine a correct meridian from
solar observation, and must do this with his own transit.
There
are, of course, other problems but they in no way differ from those
numerous examples that have been given and explained in the
course of this work. .A few examples will, however, be given in
detail to illustrate special cases.
One favorite problem which is
of considerable importance is the one first mentioned above and
intersections
in
with writing up a complete set of field-notes.
is
as follows:
Placer Calculations.
1 to 13 of
— Given: The courses and lengths of lines
a certain placer (Fig. 90).
It is desired to
amend
the
making Cors.
Nos. 2 and 12 identical
survey
with the corners of the
survey,
original
the
courses of lines 1-2 and
Cor. No.l
C
E
12-13
to
remain the
same, and the course
of line 13-1 to be S.
FIG.
90.
— MAP.
OF PLACER LOCATION.
33°
34'
placer
area of 35 acres.
to
E.,
the
contain
new
an
Required, the lengths of lines 12-13 and 1-2.
In figuring the missing course and distance of line 13-1,
reference should be made to the latitudes and departures of courses
224
EXAMINATION FOR A COMMISSION
1
to 13, included in
225
computing the area by Double Meridian Dis-
tances.
The sum
sum
is found to be 2235.61, and the
found to be 1401.16, which latter
of the north latitudes
of the south latitudes
is
subtracted from the north latitudes leaves a north latitude of
In like manner subtracting the sum of the east departures,
834.45.
2466.42, from the
sum
of the west departures, 2701.97, leaves a
west departure of 235.55.
log
log
834 45
235 55
.
.
log cot 15° 46'
=
=
=
2 9214003
log
log cos 15° 46'
=
=
2 9214003
2 3720831
867 07
=
2 9380554
.
.
.
5493172
Missing course
In the triangle
given as
S. 15° 46'
.
.
.
9 9833449
.
.
E. 867.07 feet.
ABC draw AC parallel to DE, whose course is
Line AB we have found to be S. 15°'46' E.
S. 33° 34' E.
867.07 feet.
=
log
834 45
226
A MANUAL OF UNDERGROUND SURVEYING
EXAMINATION FOR A COMMISSION
A=
70° 21'
33° 34'
C=
33° 34'
87° 19'
227
228
log
A MANUAL OF UNDERGROUND SURVEYING
984.092 =5.986070
EXAMINATION FOR A COMMISSION
The square
log
root of 1,094,678.12
1094668.12
=
is
229
found as follows:
1046.21
984.09
62.12
A MANUAL OF UNDERGROUND SURVEYING
230
Calculation of Lode Line
N. 30°E.
Given the boundaries of a
300'
claim, calculate a lode line paral-
the
to
lel
side
and the
lines,
points at which the lode line in-
end lines. No point
on the lode line to be in excess of 150 feet from either side
line.
Lode line to be 1500 feet
tersects the
long.
The boundaries
are
as
fol-
lows: Beginning at Cor. No.
thence E. 702
thence
S. 58°
E. 800
to Cor.
ft.
No. 3; thence S. 30° W. 300
to Cor. No. 4; thence N. 58°
800 ft. to Cor. No. 5; thence
702
ft.
ft.
to Cor. No.
place of beginning.
which shows
1,
neces-
conditions
S. 30°
FIG.
800
+
— MAP
W.
300'
OF LODE CLAIM.
a + 702 - c
1502 + a-c
c — a
=
=
=
end
drawn
is
The
parallel to the
lines in the triangle
sides are a, b,
and
1500
a sin 88°
sin 60°
-
a
=
2
o sin 60°
=
2 sin 60°
sin 60°
a sin 88°
^
2 sin 60°
_
sin 88°
sin 60°
=
0.86603
log
2
73206
log
1
sin 88°
sin 60°
=
=
.
99939
0.86603
13336
.
.
whose
c.
1500'
2
log
the
(See Fig. 91,
sarily greatly exaggerated.)
91.
ft.
W.
W.
to Cor. No. 6; thence N.
30° E. 300
side b
1,
to Cor. No. 2;
ft.
-
1.73206=
.
60°
sin
0.238698
= - 1 125025
12.99 =
1.113673
13336
.
EXAMINATION FOR A COMMISSION
231
In the triangle whose side a we have found to be 12.99, the
and c are found as follows:
sides b
sin 60°:
12.99
sin 60°: 12.99
log
=
=
12.99
log sin
32°
colog sin
60°
log
sin 32°:
?
sin 88°:
?
= 1.113673
= 9.724210
= 0.062469
7.95=0.900352
60°
=
=
=
1.113673
9.999735
0.062469
14.99
=
1.175877
12.99
log
log sin
88°
colog sin
log
==
1500
=
lode line.
687.01
812.99
A MANUAL OF UNDERGROUND SURVEYING
232
Multiplying the side
we
LD
(157.95)
by the
sine of the angle L, 60°,
get the distance of the lode line from line 5-6, which
is
136.80
feet.
&
FIG. 93.
— MAP
\,
W. 300
—
Give the boundaries of a section
determine the boundaries of the S. E. \ of the N. W.
Subdivision of Section.
(Fig. 92) to
88 30
OF LODE CLAIM SHOWING CONFLICTING CLAIMS.
the S. i of the N. E. \ and the N. E. \ of the S. E. J sections.
S.
86° 17'
E. 5735.7
3°33'30"W. 5439.2
N. 78° 43' 30" W. 2792.8
N. 89° 28' 30" W. 2759.46
N.
feet.
feet.
feet.
feet.
S.
1° 19'
E. 2812.1
feet.
S.
0°58'
E. 2817.4
feet.
—
General Figuring.
In Fig. 93 we have an example of a
problem given the writer in his examination for a commission as
EXAMINATION FOR A COMMISSION
233
United States Deputy Mineral Surveyor. Given the data shown
in the figure, calculate boundaries of St. Louis Lode (cutting off at
intersection of end line with Sur. No. 8556 Denver Lode), section
and conflicts in each case,
improvements. Then write up the notes, giving imaginary bearings from corners and imaginary dimensions to improvements. Do not exclude Surs. Nos. 8733 and 8853, New
York and Chicago lodes, and state why.
Following is a partial list of questions asked
South Dakota.^
in South Dakota:
1. I run 360 feet on a descent of 1 foot in 15 feet, thence 240
feet on an ascent of 11° from the horizontal, thence 400 feet on a
tie directly, ties to conflicting claims,
also ties to
—
'
1 foot in 16 feet, thence 250 feet up an ascent of 35°.
'Required total horizontal distance, also difference of level of
the initial and terminal points. State a full solution with sketch.
'2. From initial point I run S. 12° E. 650 feet, and am inter-
descent of
From
cepted by a pond.
sufficient to- clear
650-foot point I run S. 82° E., a distance
S. 28° W. 420 feet to flag on line in
pond, thence
advance of pond, then S. 12° E. 460 feet to terminal point.
'Required the length of line from initial to terminal point.
State a full solution with sketch.
'3. I run S. 38° E. and at 380 feet turn off a base N. 82° E.
feet, from the eastern extremity of which a flag on line in
advance of river bears S. 8° E.
'What is the distance of flag from initial point? State a full
520
solution of sketch.
Course No. 2 of Delta mining claim is broken into by a rock
To obtain the bearing
unfavorable
to accurate chainage.
bluff,
and length of this line, I run from one extremity on a random line
'4.
W.
to a
point which from the data so far obtained I find to be on
my
S.
28° E. 610 feet, thence N. 82° E. 260 feet, thence S. 12°
random
line;
thence I continue the
first
random 340
and arrive at a point from which the other extremity
No. 2 bears
feet further
of said course
S. 62° W., 110 feet distant.
the bearing and length of course No. 2? What angle
from the course S. 12° W. in order to line in with the
State a full solution with sketch.
first random?
5. The two extremities of a straight line forming a portion of
'What
do
is
I deflect
'
These questions were kindly furnished by
South Dakota.
I
Prof.
Mark
Ehle, Rapid City,
:
A MANUAL OF UNDERGROUND SURVEYING
234
the boundary of a mining claim are not conveniently accessible,
but a convenient base can be had, from each extremity of which
both extremities of said boundary can be seen.
'1st. Illustrate this
'2d. State the
condition with sketch.
measurements, both linear and angular,
which are absolutely essential to a solution.
and
'3d. State briefly the trigonometric solution
their
respective purposes, with their respective formulae.
'4th. Trace the process to a final resulting course
and
distance.
A numerical
'
6.
example
is
not asked.
State a convenient formula applicable to
what
is
known
as
a "broken base," using the number of minutes in the deflection
angle of the second component.
'
7.
Given the following consecutive courses of a mining claim
From
From
From
From
From
= S.
3, = N.
4, = N.
5, = ?
1, = N.
Cor. No. 1 to Cor. No. 2,
28° 40'
Cor. No. 2 to Cor. No.
70° 30'
Cor. No. 3 to Cor. No.
Cor. No. 4 to Cor. No.
Cor. No. 5 to Cor. No.
Required bearing
'1st.
of line
W. 503
W. 476
9° 35' E.
79° 50' E.
feet;
feet;
485 feet;
343 feet;
feet;
?
4-5 and length of
line
5-1.
'2d. If
the line 5
by actual survey
—
1 is
of all the sides,
N. 79° 55' E. 395
feet, state
it is
found that
a traverse show-
ing the closing errors; then
'3d. Balance the survey on the assumption that the
measurements have equal weights.
4th. Deduce the resulting courses and distances of the
'
closing survey for record.
'5th.
method
Compute the area
of D.
M. D.
of the figure so enclosed
State
full
by the
solution with sketch.
'8. An incline descends on a dip of 30°.
It is determined to
sink a shaft to intercept incline, the shaft, to be at a point 450
feet
from mouth
of incline; the
descending at a rate of
1
'How deep will the shaft be?
9. What is azimuth?
'
surface from
foot in 75.
mouth
to shaft
:
EXAMINATION FOR A COMMISSION
235
Observe Polaris at greatest elongation at a place in
Apparent of the star is 88° 44' 10".
'What is the star's azimuth?
State the formula and whole process.
'What are the two hour angles corresponding to eastern and
'
10.
latitude 45° 30' N.
'
western elongations respectively, counting from culmination, round
with the sun to 24 hours, and their equivalents in mean solar
time?
example the star is observed at eastern
magnetic bearing at that instant is N. 13°"20' W.
'What is the magnetic declination?
'Is it to be called East or West?
'11, If in the last
elongation and
'
its
State process
and reason
therefor.
Revised Statutes (2320) limit lode claims located
after May 10, 1872, to 300 feet on each side of the middle of the
vein at the surface; suppose you were called upon to make an
official survey of such a location under order from this office, and
found it to be 350 feet on each side of the middle of the vein at the
surface, and you found nothing in the location certificate to dictate
to the contrary, what would be your action in respect to such a
Suppose such a location was 200 feet on one
location? Why?
side of the vein and 400 feet on the other, what would your action
'12.
S.
Why?
be?
A lode claim located since May 10, 1872, shows a length
1529 feet along the centre of the vein at the surface. What
'
of
U.
13.
would be your action in this case? Why?
14. The boundaries of a lode location have the following
consecutive courses, namely:
'
W. 800
W. 600
80°W. 90
62° W. 200
'S. 42°
feet;
22°
feet;
'S.
'N.
'S.
feet;
feet;
'N. 22° E. 600 feet;
'N. 42°E. 800 feet;
'N. 62° E. 190 feet; thence to place of beginning.
'What would your action be on this location if required to
make an official survey? Why?
'15. I run N. 89° 56' W. on a random line between Sees. 30
and
31,
and at 73.20 chains
intersect the west
boundary
of
town-
A MANUAL OF UNDERGROUND SURVEYING
236
ship at a point 22 links north of the corner of Sees. 25, 30, 31,
and
36.
'
1st.
What
is
the course of the return or true Hne?
The
position of the J section corner?
'3d. State a short rule for obtaining the return course in
'2d.
these cases, applicable
when
the fallings are within limits,
and- apply to the above case.
'
16.
An
order to officially survey a mineral claim
is
issued to
you from this office under date March 12, 1900; said order is based
upon a location certificate dated January 10, 1899. Upon proceeding with survey, you find the location as marked on the ground
does not conform to the location as recorded, and upon informing
your client to that effect, he provides you with a certified amended
certificate of location dated March 30, 1900.
'What action would you take in the matter of survey?
17. Describe fully your instrument, stating its make, age and
condition; also its capabilities as to power, illumination and
graduation, and its attachments of convenience for safe and
'
accurate work.
'What measure
of length have you?
your telescope has a level, state briefly in writing, how
you would adjust it and the horizontal hair.
'
18. If
'19.
The usual method
transit for collimation,
may
for adjusting the vertical hair in a
or
may
not place that hair truly in the
In a well-constructed instrument the disbe small; in such case what sensible effect has this
centre of the telescope.
placement will
displacement upon observations, seeing that the motion of the
slide will not project this hair truly along the axis of the telescope?
'20. It is required that
direct solar observation.
you determine the true meridian by
You
will make the observation in the
who will then furnish you with a copy of
From the data then at hand you will
presence of the examiner,
the nautical almanac.
make
necessary calculations, handing in the same complete.
In Latitude 30° N. the sun's decHnation 20° S. with hour
all
'21.
angle 5 hours; the refraction in declination
to
is 8'
50".
Assuming no index error, which would be the correct reading
set off on the declination are, proper for the above date?
'22. In latitude 44° N. the hour angle of the sun 6 hours, I
'
:
EXAMINATION FOR A COMMISSION
start a line
due north by
solar;
but find after running a mile in the
course so started that I have set off
'What
is
the nature and
237
6'
amount
too
much
latitude.
of error in course thus in-
duced?
'
above the hour angle
If in the
and amount
is
3 hours,
what
is
the nature
of error?
If the latitude is correctly set off, but instead of a declination
of 10° S. I set off 10° 10' S., the hour angle of the sun being 3
'
hours,
what then
is
the nature and
amount
of the error thus
introduced?
'State,
if
you can, the
cases.'
differential formulae applicable to these
—
California.^
The customary manner of appointment in this
and the adjoining states is as follows:
The surveyor who wishes an appointment, makes application
'
to the Surveyor-General, detailing his qualifications.
This ap-
with the recommendation from some Deputy
Mineral Surveyor of good standing within that district, is then
forwarded to the Surveyor-General's office, and in due time the
appointment is made. The customary filing of the bonds completes the appointment of the U. S. Deputy.
'If the deputy desire an appointment in any other state or
territory, I have found that a recommendation from the Surveyorplication, together
General of the state in which the original appointment was made
all that was necessary to obtain a commission in any addi-
was
Of course new and separate bonds must
each state or territory in which commission is held.'
Oregon.^
The examination in Oregon is about as follows
tional state or territory.
be
filed for
'1.
rulings,
—
Fifteen or twenty questions
covering the
Land
Office
the proper markings for corners of government land
surveys, the methods of taking latitude
the
maximum number
and
mill site,
by
the sun and Polaris,
of acres allowed in quartz claim, placer,
kind of corners which
may
be set in making patent
surveys, and various details of procedure in executing such surveys.
Given the notes of a quartz claim (metes, bounds, and
and the location of the same, make out notes and preliminary
This requires the same
plat of same as if surveyed for patent.
'2.
ties)
Kindness of Henry J. Jory, Los Angeles, California.
G. Moulton, U. S. Deputy Mineral Surveyor, Grant's Pass,
Oregon.
-
2
From H.
:
A MANUAL OF UNDERGROUND SURVEYING
238
work
to be done that a
work
his office
Deputy would have
making out
to do in
of such a survey.
Given the plat of the locations of four claims forming one
group, and overlapping each other, with a section corner located
on one of the centre ones (this plat is furnished by the SurveyorGeneral), make out notes of a survey for U. S. patent of the
group, with plat, calculations, etc. The claims are given on the
plat furnished as longer than 1500 feet and wider than 600 feet,
'
3.
so there
limits
is
a test of ability in getting them within the required
and at the same time not leave any
An
instrumental examination.
fractions.
Applicant
is
required to
take a transit and determine latitude and meridian
by sun and
'4.
upon an established meridian, and also to report
number of points whose bearing
Polaris, checking
the courses from a given point to a
is
known.
'Parts 2 and 3 are severe tests of applicant's ability, and the
examination as a whole
aim
is
an exceedingly thorough one.
It
is
the
men of the state as
way a fair one and free
of the office to get the best available
and the examination is in every
from "catch" questions.'
While this is all the information that the writer has been able
to obtain on the subject of examinations for commission as U. S.
Deputy Mineral Surveyor, it is safe to say that in no state is the
examination more difficult than in Colorado or Oregon. If the
applicant is able to pass the examination in either of these two
states, the chances are that he will be able to pass in any state
where an examination is held.
deputies,
Problems
cal
^
The following are suggested in order to teach the student graphiand trigonometric methods for solving mine-surveying problems
Problems involving descriptive geometry to determine the
intersections of veins, the location of openings to cut intersections
of veins
In
and to locate openings when veins are faulted.
certain assumptions must be made:
all c9,ses
(a) Except in Problems 4 and
be a horizontal plane.
'From
L. E.
Young's
Engineer, May, 1904.
"A Study
of
8,
the surface
is
assumed to
Mine Surveying Methods,'
in
Iowa
EXAMINATION FOR A COMMISSION
239
Veins are assumed to be planes of uniform dip. Interassumed to be straight lines. Except in
(&)
sections of veins are
(6)
Problem 3, thickness of veins is not considered.
Shafts on veins will be straight but inclined.
(d) Except where the grade is specified, tunnels are assumed
of
(c)
horizontal, also drifts.
Dimensions of shafts and tunnels should not be considis, openings are considered to be straight lines.
(/) All inclined shafts to be the shortest possible except in
Problem 8.
(e)
ered
;
that
Problem
(a)
veins.
(Fig. 94)
Locate vertical shaft on line 'a-6' to cut intersection of
Find depths of shaft and distance on a-b from ' A '.
'
FIG.
(b)
1
At
Find pitch
94.
— PROBLEMS.
300' from 'A' on 'a-b'
of inclined shaft
'
is
a vertical shaft 200' deep.
and distance on
incline
from bottom of
shaft to intersection of veins.
Draw
to scale 1"
= 300'.
Take ground
line E.
and W.
Problem 2
(a) Locate vertical shaft to cut intersection of veins.
Find
depth of shaft and the distance and bearing point to sink, from o '.
'0' vertical shaft is sunk to cut vein EF.
From this
(6) At
'
'
A MANUAL OF UNDERGROUND SURVEYING
240
is sunk on EF to cut intersection of the three
Find depth of vertical shaft, also bearing and length of
point inclined shaft
veins.
incline, also the pitch of inclined shaft.
Draw
to scale 1" = 300'.
Take
Problem
(a)
ground
strike of 'a-b' as
line.
3
Locate by distance from 'o' point on 'a-b' to sink shaft.
This shaft inclined and the shortest possible to cut intersection of
veins.
Find length, pitch, and bearing of shaft.
(b) Call intersection 'r'.
Part bounded by 'xor' is ore.
Taking xor as mean section and 6' as average thickness, compute
No. tons of ore. Heaviness = 170 pounds per cu. ft. Find length
'
'
oi 'or' 'xr
Draw
'.
to scale 1" = 300'.
Take
strike oi'cd' as G.
Problem 4
(a)
Horizontal distance from tunnel
mouth
to outcrop of vein (elevation 11745'.9),
N. 30° E. and dips 63° to the
NW.
is
Tunnel
(elevation 9653'),
6000'.
is
Vein strikes
driven N. 25°
W.
Find length of tunnel to cut vein. What depth on
vein; will tunnel cut vein knowing that 1700' NE. from outcrop
elevation is 12345'. 9 and taking hillside as plane of the three
horizontal.
points given.
(b) Same as (a) tunnel on 2.5 per cent, grade.
Draw to scale 1" = 2000'0.0. Take G E and W.
Problem
5
(a) Locate vertical shaft on Royal to cut intersection of veins.
Find depth of shaft and distance and bearing of point to sink
from'O'.
(b) Locate incline on Lotus.
Find depth, etc. Same as (a).
(c) Locate incline on Minnesota.
Find depth, etc. Same as
(a).
Scale 1" = 300'.
Take
G EandW
through 0.
'
Problem 6
(a)
On
NW. from o an inclined shaft is sunk
the bottom of shaft a drift extends on vein
the Lotus 200'
300' in length.
From
'
'
'
EXAMINATION FOR A COMMISSION
W.
N. 75°
241
At what distance from shaft should a cross-cut be
and Minnesota. This cross-cut
started to cut intersection of Royal
Find length of cross-cut.
to be at right angles to drift.
Draw to scale 1" = 300'. Take
and
through '
W
GE
Problem
o.
7
Locate vertical shaft to cut intersection of veins.
(a)
bearing and distance from
Vertical shaft
(b)
bottom
'
o
sunk at x' to depth of shaft in
is run to cut the intersection
is
Find
'.
At
(a).
of shaft cross-cut
of veins.
Find bearing and length of cross-cut.
(c)
Incline started at x' to cut intersection of veins.
(d)
Locate inclines on: Gopher, Mt. Boy, and
intersection
from
Find
and bearing.
length, pitch,
Yuma,
to cut
Find lengths, distances, and bearings
veins.
of
'o'.
Draw to
scale 1"
N. 30°
x' is 300'.
= 300'. Take
W. from
'
o
GEandW through
'
o.
Point
'
'.
Problem 8
(a)
From
'
outcrop bears N. 10° E. and dip of vein is 45°.
the point o has an elevation 300' higher than o '.
o
'
800' lip the
hill
Find strike
of vein.
(b)
From
'
'
'
o
'
shaft
is
'
sunk on
From
vein.
on vein. Find point of intersection and
'
o
'
tunnel
lengtlis of shaft
is
driven
and tunnel.
Shaft perpendicular to outcrop.
Draw
to scale 1" = 300'.
Take G
Problem
E and W.
9
Find point to sink by bearing and distance from
Find depth.
Call point 'a;'.
intersection of veins.
(a)
(6)
At
'x',
vertical drill-holes are
600',
of 'o' 5100', S. 67° 45'
due west
o
'
to cut
7850' from 'o'
put down
cutting a fault plane at 1000',
It has
been determined that portion
1000' respectively.
above fault plane has
W.
'
moved perpendicular
easterly direction along fault plane 500'
to strike in a south-
Find point to sink as in
A MANUAL OF UNDERGROUND SURVEYING
242
(a)..
Faulting took place, then country eroded to present level
condition.
Draw
to scale 1" = 3000'.
Take G
Pboblem
(a)
E a.iidW through
'
o
'.
10
On intersection of Pilot and Mary inclined
On intersection of Orphan No. 1 and Orphan
shaft
is
down
No. 2 inclined
bad, we wish to
600'.
is down 550'.
As the air in both places is
an inclined upraise from one shaft to connect with the other;
this connection to be the shortest possible.
Locate points in both
Find length,
shafts so work may be carried on at both ends.
pitch, and bearing of the connection.
Reverse traces on Orphan
1 and 2.
Compare.
Draw to scale 1" = 300'. Take G E &ndW through o
shaft
start
'
Problem
A vein
dips 60°, an, entry
five-per-cent. grade.
What
is
is
drift
driven N. 40°
whose
on a three-per-cent. grade
strike is
N. 60° E.
W.
in the vein
12
is
driven N. 40° E. in a vein
13
vein dips 45° to the west and strikes N. 12° 30' E.
on the vein
is
on a
Required, the dip of the vein.
Problem
A
11
the strike of the vein?
Phoblem
A
'.
driven N. 16° 30' E.
A
drift
Required, the grade of the
drift.
Problem
14
A
vein dips 54° to the east and strikes N. 18° 45' W. What
the bearing of a drift on the vein driven on a 3-per-cent. grade?
Problem
The
is
15
strike of a vein dipping to the
SW.
75°
is S.
45° 15' E.
From a
given point of outcrop, elevation 3629.4' the mouth of a
tunnel bears S. 40° 10' W. and distant 3000' on a vertical angle of
—21°
08'.
The tunnel
is
driven straight, horizontal, and N.
EXAMINATION FOR A COMMISSION
243
12° 15' E.
(a) Required, the distance from the mouth of the
tunnel to the point at which it intersects the vein,
(b) Assume
the tunnel on a 2-per-cent. grade,
(c) "What is the shortest distance from the tunnel portal to the vein?
Problem
A vein
A second vein
(a.)
to be level)
vein
is
16
dips 55° to the northwest and strikes N. 35° 10' E.
N. 35° 10' E. and on the surface (assumed
distant from the (a) vein 800'. How far from the
(b) strikes
should a vertical shaft be put down to pierce the intersection of the veins (1) if (6) dips 30° to the northwest; (2) if (a)
(o)
dips 75° to the southeast
will
and
be the depth of shaft in
all
(6)
55° to the northwest.
Problem
,
A
What
cases?
17
vein dips 43° to the northwest, strikes N. 33° 15', elevation
At an elevation of 869.2' and distant from the
of outcrop 914.6'.
outcrop 1000', an inclined shaft dipping 75° and bearing N. 56° 45'
is sunk to intersect the vein,
(a) Required the depth to which
W.
the shaft must be sunk.
(6) Assume the pitch of the shaft the
same, but the bearing S. 89° 14' W.; what will be the depth of
shaft?
Problem
The
18
surface has a uniform slope of 10° to the north.
and west and dips 40° to the north.
A
vein
strikes east
(a)
How far north of the outcrop must one go to sink a vertical
shaft which shall cut the vein at a depth of 700'?
(6)
What
will
be the bearing of drifts on the vein driven from the bottom of the
(c) How far can they be driven
shaft on a 3-per-cent. up-grade?
so as not to approach nearer than 100' to the surface?
Problem 19
The vein described in Problem 18 is intersected at a depth of
by a vertical shaft. From the bottom of the shaft a slope
1000'
on
the'
vein extends due north 600'.
per-cent. grade to- the southwest
An
entry
from the bottom
is
driven on a 4-
of the slope for a
:
.
A MANUAL OF UNDERGROUND SURVEYING
244
distance of 4000'.
Required the depth of vertical shaft necessary
end of the entry with the surface?
in order to connect the
Problem 20
The horizontal distance between two
vertical shafts is 1000',
the difference in elevation of the collars of shafts
is
291.4'.
The
depth of shaft sunk from the higher point is 647.2' from the bottom
of this shaft a cross-cut (a) is driven towards the other shaft on a
The second shaft is 350' deep. Required
1-per-cent. grade, 436'.
the length and grade of cross-cut (b) from this shaft to meet the
;
breast of
(a).
Pkoblem
21
Suppose that the lower shaft described in 20 bears S. 19° 40' W.
and that the cross-cut (a) is driven S. 40° W. Required the direction, grade, and length of (6)
of the other
Phoblem 22
A
vein dips 60° to the south and strikes N. 70° E. Consider
500' distant from the
outcrop and at an elevation of 3601' a vertical shaft is sunk to
the outcrop of the vein as 3650' elevation.
intersect the vein.
From this shaft the mouth of a cross-cut
tunnel bears S. 60° E, 2000' on a vertical angle of -30°. The
tunnel is driven N. 33° W. on a 2-per-cent. grade to intersect the
vein.
Required the length of slope on the vein necessary to
connect the shaft and the tunnel.
Problem 23
Using the top telescope
(a)
Elevation
+
V. A.
M. D.
-H.
+ H.
I.
= 876.42'
= 52° 29'
= 76.49'
= 2.58'
Pt.=
=
M. D =
r
3.45'
.301'
Distance from axes of main telescope to point of sight.
Required V. D., H. D., and elevation.
EXAMINATION FOR A COMMISSION
(b)
245
246
establis
A MANUAL OP UNDERGROUND SURVEYING
.
.
INDEX
PAGE
Accuracy
of
German mine
sur-
veys
140
of platting methods.
.
.
of
.
.
156
survey for shaft.
215
Anaconda C. M. Co. of Butte
192
Air currents shown on maps. ... 138
effect of, upon
.
plumb wires
Angles reading
reading
of,
book
Calculation
at Old
109
178
appointment of sur-
California,
veyors in
Calumet and Hecla
.
.
map
map
Coal mine,
193
.
.
map
Assays, record
of,
on maps
Bent
line
98
platting
Conflicting claims
Contours, underground
141
144
Copying
168
113
shaft survey
212
164
165
upon
tracing from
166
to waterproof
165
Blue print solution, formula for
cloth
Blue printing, electric
Boreholes, instrument for
veying
photograph of
sur-
171
inte-
rior of
surveys
172
169
Boston and Montana Mines of
Butte, practice at
Brunton pocket
transit
234
of drawings
for
top
telescope
readings
for
48
side telescope
readings
51
Cross wires, renewing of
Direct
solar
observation
60
for
meridian
69
168
Drawings, copying of
165
166
164
;
157
148
surveys
to write
by
140
101
Blue prints, overexposed
163
162
144
Co-ordinates
100, 193
tin can
239
188
155
207
209
used on mine maps
208
Correction,
Backsights, Butte
workings
proposed ex-
maps
Areas, mineral, on topographical
Assay maps
of
applied to glass
Homes take
mines.
of
tensions
Colors for
.
by
Chords, platting
ion mines 192
mines
a survey
of
Calculations of placer claim
Domin-
Anaconda
129
232
184
226
of lode line
197
54
247
Eaton, Lucien, methods used by
Erasures
Errors, of first adjustment
175
162
22
of eccentricity of circle
40
of eccentricity of verniers 42
of second adjustment. ...
23
of third adjustment
27
of fourth adjustment. ...
30
.
of fifth
adjustment
of sixth adjustment
32
32
..
..
INDEX
248
Errors, of platting
PAGE
156
in azimuth
83
in
71
tions
45
work
226
ment Mineral Surveyors
Field notes
126
Pile for geological
142
maps
maps and
sec-
141
tions
Graphic solution of the direct
observation
•,
-•
•
84
methods used by 188
Grierson, E.
S.,
Hangers
plumb wires
.
185
153
141
134, 136, 138
of
abandoned mines
134, 137, 139
photographs of mine
Map, uses
Geological mine
.
mine
Maps, mine, should show
74
for direct observation.
Formula
160
in.
geological
sections,
159
maps
Filing of
187
a system of
Mapping, instruments used
Maps, the making of mine
filing,
Maps and
for U. S. Depart-
Examination
by
Map
making direct observa-
in practical
PAOB
Manly, Frank A., methods used
174
of the topographical.
.
140
133, 141
Maps, uses of mine
Map of workings of a California
207
mine
of proposed extensions of a
209
coal mine
175
Methods of various engineers
Meridian, carried underground,
for
Ill
Homestake mine
208
Illuminating the cross wires
101
Inclined shaft survey
212
Inks
Instruments, mapping
163
at Butte
carrying underground
taking
59
62
175
care of
Iron mines, methods used in ...
of,
under112
shafts..
.
.
by two wires
by three wires
by four wires
by bent line
185
repair of field
off
ground
through two
198
104
Polaris
113
observation
64
for
Lamp
affecting
mine surveys.
.
.
.
136
in Illinois
138
66
69
tion
136
in Permsylvania
Mine map, ordinary
144
models
161
in
England
140
Miner's compass
in
Germany
140
Mine sampling
Models of mine workings
123
Note-books
127
143
130
Ledger
Level sheets, geological
Lining
in
timber
line calculation
175
man's
in
shafts
56
161
142
rods for mine use
Lights, for instrument
Lode
.
81
Latitude
Laws
by solar observation.
by direct solar observa^
54
targets
104
108
109
110
use.
for taking geology.
102
in use in iron mine.
inclined
182
232
Logarithmic cross-section paper
85
Loose-leaf note-books
127, 190
Notes
side
.
184
126
128
on cards at Homestake
208
form of, used at iron mine 178
.
.
INDEX
249
PAGE
Notes, form
of,
used at Poorman
Plumb-wires, size and weight.
mine
189
used at Portland
mine
191
used at Anaconda 193
used by Boston
& Montana ... 201
used by U
S.
Coal & Coke Co 205
in form of sketches
188
.
.
more than one
in
104
shaft
to lower, in shaft
affected
by
.
.
106
air cur-
109
rents
Plumbing
PAGE
105
vertical shafts at iron
mine
shafts
181
by
t
wo-wir e
system.
.
.
108
three- wire
books
Old Dominion C. M.
Old workings
Office
&
S.
Co
129
system.
191
four-wire
147
system.
.
.
.
.
109
110
transit sights 114
Paper
for
maps
Party, surveying,
186
Calumet and
Hecla
Homestake.
.
.
Poorman
189
175
190
Iron Belt
Copper Queen
Portland
o
188
208
f
.
.
Photograph
.
.
.
.
192
203
methods
of
instruments
by protractor
by tangents
by chords
by co-ordinates
226
154
185
155
155
155
157
212
Plumb-bob, symmetrical
used in Wisconsin
iron mine
175
Plumb-line adjuster
weights
190
and screen...
46
70
90
240
Property lines
Problems
given in examination
in South Dakota.
235
Protractor, platting by
155
.
.
Record of the survey
Rooms, survey of
126
119
Sampling of a mine
123
99
107
maps
mine maps
142
Scale of geological
154
maps, at iron mine
187
in Pennsylvania. 136
in Illinois
138
Screen, in making direct sun obof
172
Placer calculations
64
.
197
Photography an aid to engineers. 173
Pillars, survey of boundary. ... 138
Platting,
.
190
191
of interior of bore-
holes
Portland mine of Cripple Creek.
Prismatic eyepiece
.
Cripple
Creek
Old Dominion.
Anaconda.
Boston
&
Montana...
U. S. Coal &
Coke Co.
Polaris observation for meridian
of
servations
71
government
233
Sections, vertical and longituSection,
18
dinal
Setting
up under a
Shaft, dangers of
98
station
working
in.
.
.
.
116
.
.
179
210
inclined
survey, a quick vertical
secondary
plumbing of
measuring depth
139
of
108
116
..
INDEX
250
PAGE
Side notes
&
at Calumet
Hecla.
.
Sighting in the dark
Size
and
scale of
maps
154
stope book
map from
mine
184
Solar compass
frequency required ...
136
laws affecting mine
136
Surveyors, competency of foreign
.
mine
U.
S.
Taking meridian
telescope attachment
screen
70
accuracy of
direct observation
69
tags
reel
used in iron mines
Tapping flooded workings
Telescopes
auxiliary
duplex bearings
eccentricity of
Queen
Anaconda.
.
.
Montana
192
.
.
.
200
.
.
Iron Belt.
.
.
side
Timber, lining in, in shafts
mine
203
Calumet
&
Hecla
188
Homestake. 208
.
Tinting
Title of
Top
survey of
String surveys
Subdivision of section
Survey, a mining
of railroad
191
iron
180
145
153
166
166
20
22
maps
Tracing cloths
Transit adjustments
first
second
23
27
30
32
32
third
203
120
119
fourth
121
relative
fifth
sixth
234
215
of a wet mine shaft .... 212
Surveying, definition of
in
from a blue print
Stope books, method of keeping. 120
used at Anaconda. 196
used by Boston &
Montana
used
mines
Tracings, for level-sheets
176
Portland.... 190
Stopes, narrow
maps
telescope
Old Dominion
38
48
49
182
164
154
top
190
Boston &
value
general
Transit,
140
of.
36
re-
marks
3
Surveying party. See Party.
Surveys, accuracy of German
surveys
56
58
57
57
57
57
176
147
18
46
54
splice
Station numbers at Copper
coal
155
handle for
235
93
92
94
95
98
95
marks
numbering of
setting up under
112, 198
by
care of
South Dakota, examination ques-
Stations, kinds of
wires
off
Tangents, platting
Tapes, steel
tions in
140
Deputy Mineral 226
66
68
Spads
PAGE
169
Surveys, borehole
188
202
204
Sketches, only for notes
in iron
128
188
99
upon
Brunton
with inclined standards
setting up the
37
54
54
98
INDEX
PAGE
PAGE
175
Vandyke paper
167
Ventilation shown on maps .... 138
Transit, used-in Wisconsin iron
mine
history of
compass, the
requirements
8
11
first
of,
251
for
mine use
6
U-standard
6
Vertical
sights
with
ordinary
transit
115
Volumes
122
Washes
163
Waterproofing of maps and blue
Transverse of two or more openings
102
of shaft
114
XJsesof mine maps. .133, 140, 141, 152
165
prints
Weights, heavy, for plumb-lines 210
White lines upon blue prints .... 165
212
Wires, best, for plumbing shaft.
.
.
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