UNIVERSITY OF CALIFORNIA
AT LOS ANGELES
GIFT OF
The RALPH D. REED LIBRARY
o
DEPARTMENT OF GEOLOGY
UNIVERSITY OF CALIFORNIA
LOS ANGELES, CALIF.
TREA.TISE
MINE-SURVEYING.
STANDARD WORKS
FOR THE USE OF
SURVEYORS, MINING ENGINEERS, AND METALLURGISTS.
TRAVERSE TABLES : computed to Four Places Decimals for every
Miuute of Ang e ur> to 100 of Distance. By RICHARD LI/VTD GURDEN, Authorised
Surveyor for the Governments of New South Wales and Victoria. THIRD EDITION-.
21s.
ORE AND STONE MINING. By C. LE NEVE FOSTER, D.Sc., F.R.S.,
Prof, of Mining, Koyal College of Science. With very numerous Illustrations.
COAL MINING. By H. W. HUGHES, F.G.S., Assoc. R.S.M. With 490
Illustrations. SECOND EDITION. 18s.
PRACTICAL GEOLOGY (Aids in). By G. A. J. COLK, F.G.S., Prof, of
Geology, Koyal College of Science, Dublin. With numerous Illustrations. SECOND
KDITION. 10s. 6d.
BLASTING AND THE USE OF EXPLOSIVES. By O. GUTTMANN,
A.M.Inst.C.K. With Folding Plates and Illustrations. 10s. 6d.
ASSAYING. By J. J. BERINGER, F.C.S., F.I.C., and C. BERINGEK,
F.C.S. SECOND EDITION. 10s. 6d.
ELEMENTS OF METALLURGY: The Art of Extracting Metals from
their Ores. By J. ARTHUR PHILLIPS, C.E., F.C.S., F.G.S., and H. BAUERMAN, F.G.S.
With numerous Illustrations. THIRD EDITION. 36s.
NEW METALLURGICAL SERIES,
W. C. ROBERTS-AUSTEN, C.B., F.R.S.,
Chemist and Assayer of the Royal Mint ; Prof, of Metallurgy, 'Royal College of Science.
1. INTRODUCTION TO THE STUDY OF METALLURGY. By the
EDITOR. THIUD EDITION.
2. GOLD. By T. K. ROSE, Assoc. R.S.M., B.Sc., Assistant- Assayer of the
Royal Mint.
3. COPPER. By THOS. GIBB, Assoc. R.S.M., F.I.C.
4. IRON AND STEEL. By THOS. TURNER, Assoc. R.S.M., F.I.C.
5. METALLURGICAL MACHINERY. By H. JENKINS, Wh.Sc., Assoc
R.S.M., Assoc.M.Inst,C.E., of tHe Koyal Mint
6. ALLOYS. By the EDITOR,
Other Volumes in Preparation.
LONDON: CHARLES GRIFFIN & COMPANY, LTD., EXETER STREET, STRAND,
MINE-SURVEYING IN THE MlDDLK AGES.
(Facsimile of a drawing in Agricola's de re Metallica, 1556.)
A TREATISE
MINE -SURVEYING.
BENNETT H. BROUGH,
ASSOCIATE OP THE ROYAL SCHOOL
ENGINEERS AND OP THE MINING INSTITUTE OP CORNWALL; POEMERLT I-
8TKCCTOR IN MINE SURVEYING AT THE KOTAL SCHOOL OP MINES.
FOURTH EDITION, REVISED.
With numerous Diagrams.
LONDON:
CHARLES GRIFFIN & COMPANY, LIMITED;
EXETER STREET, STRAND.
1894.
(AH Rights Reserved.)
s\
Geology
Library
TH
PREFACE.
,. No apology is required for any well-considered attempt to pro-
P. vide a manual of Mine-Surveying for the use of English readers.
v The absence of any general work on the subject has long been
a source of practical inconvenience alike to teachers and students.
The text-books recommended to candidates for the examination
in Mine-Surveying held by the City and Guilds of London
Institute, namely, Budge's Practical Miner's Guide, published in
1825, and Hoskold's Practical Treatise on Mining, Land, and
^ Railway Surveying, published in 1863, are too limited in their
scope, the former dealing only with the mines of Cornwall, the
^ latter only with those of the Forest of Dean; besides which both
works are out of print, and increasingly difficult to procure.
} The present work is intended primarily for students, and
3 embodies the substance of the course of instruction in Mine-
^ Surveying given at the Royal School of Mines. At the same
time, it will also, it is hoped, be found useful as a companion to
the standard works of reference on Land-Surveying.
In the plan of the book, the surveying of collieries and that
of metalliferous mines do not receive separate treatment. The
two have much in common, and the one may often advan-
^* tageously borrow a method from the other. Few mine-surveyors
in Great Britain appear to be acquainted with the methods
HX and instruments used abroad. This is the more to be regretted,
^ as no mine-surveys made in this country approach in accuracy
those of the collieries of Pennsylvania, or those of the metal-
liferous mines of the Harz. Attention therefore has been
directed to the recent improvements in foreign practice. With
the exception of a few diagrams borrowed from Professor
222016
Kankine's Manual of Civil Engineering, the figures elucidating
the text have been specially drawn for this book.
The Appendix of examination-questions and exercises for
plotting has been culled from recent papers set at the examina-
tions of the Science and Art Department, of the City and Guilds
of London Institute, of the local boards under the Home Office for
granting certificates of competency to Colliery Managers, and of
various Mining Schools. These will, it is trusted, be found of
use to such students as have not the advantage of regular
instruction in the subject. It must, however, be borne in mind
that the mere reading of a text-book will never make a mine-
surveyor. The most that a book can do is to help the student
to obtain a knowledge of the theory of the subject. The
mechanical manipulation of the instruments can only be learnt
under the personal supervision of a teacher, whilst the technical
skill requisite for carrying out subterranean surveys must be
obtained in the mine itself.
I have taken for granted on the part of my readers an
elementary knowledge of mathematics, such, for example, as
would enable them to pass the second stage of the Science and
Art Department's examination in that subject.
In the preparation of the work, I have received valuable help
from numerous friends at home and abroad. In particular, I
am indebted to Mr. H. W. Hughes, Assoc. R.S.M., F.G.S., for
several important additions to the text, and to Mr. A. Pringle,
M.A., B.Sc., who ably assisted me while the volume was passing
through the press.
BENNETT H. BROUGH.
THE ROYAL SCHOOL OF MINES,
LONDON, February, 18S8.
PREFACE TO THE SECOND EDITION.
THE First Edition having been exhausted sooner than was
anticipated, advantage has been taken of the opportunity of a
re-issue to correct a few errors that had escaped notice in the
former edition. References to some papers published during
the year have been inserted, and a frontispiece, copied from
Georgius Agricola's De re Metallica (Basel, 1556), has been
added. This illustrates the primitive method of connecting
the underground and surface surveys by means of a stretched
cord and two plumb-lines.
February, 1889.
NOTE TO THE FOURTH EDITION.
THIS Edition has been thoroughly revised. Descriptions of
appliances invented since the publication of the Third Edition
in May, 1891, have been inserted, and references to some im-
portant recent papers are given. The additions cover twenty-
four pages of text. Among them will be found notices of the
methods of surveying in South Africa, and of making the
preliminary surveys for wire ropeways and for hydraulic
mining ditches. A few diagrams have also been added.
January, 1894.
CONTENTS.
CHAPTER L
GENERAL EXPLANATIONS.
PAGE
Surveying, . . . . . . . . 1
Historical sketch, ....... 1
Importance of mine -surveying, . . . . 3
Mineral deposits, .... 5
Mining terms, . . . . 6
Measures of length, ....... 7
Angular measures, . . . . . . 8
Trigonometrical formulae, . . . . 9
CHAPTER H.
THE MEASUREMENT op DISTANCES.
Methods of measuring, . . . .11
(a.) The chain, . . . . . . .11
Chaining on slopes, . . . . . .13
Offsets, . . . . . . .15
Obstacles to measurement, ..... 16
Surveying with the chain only, . . . .18
Chain used in trigonometrical surveys, ... 20
(6.) Rods, ........ 21
(c.) Steel bands, 22
(d. ) Measuring wheel, ...... 23
(e.) Pacing, . 23
Accuracy of linear measurements, . . . . 24
CHAPTER III.
THE MINER'S DIAL.
Directive action of the earth's magnetism, .... 26
Historical sketch, ....... 26
CONTENTS.
PAGK
Description of the miner's dial, . 28
(a.) The magnetic-needle, ..... 2 q
(6.) Spirit-levels, . . . . ...
(c.) The tripod, JJJ
(1.) Taking underground observations with the dial,
Taking vertical angles, . . . . 33
Keeping the dialling book, . . . .
(2.) Surface-surveys with the miner's dial, , . *' og
(3. ) Colliery- survey s with the miner's dial, . " .
CHAPTER IV.
THK VARIATION OP THE MAGNETIC- NEEDLE.
Definitions, . J '..'.' . . 40
(a.) Secular variations, . . . . . 40
(6.) Diurnal variation, . .- . " . 42
Irregular variations, ..... 44
Determination of the true meridian, . . . .44
1. Method of shadows, . . .' ' . . . 44
2. Method of corresponding altitudes, .... 46
3. Determination of the meridian by means of the Pole star, . 48
4. Determination of the meridian by means of a map, . . 49
Setting out the meridian line, . . ... .49
Inclination of the magnetic-needle, ..... 50
CHAPTER V.
SURVEYING WITH THE MAGNETIC-NEEDLE IN THE PRESENCE OF IRON.
Influence of iron rails, . . , . . go
Local attraction in the mine, . . . 53
Surveying with the dial in the presence of iron, . . . 54
Dialling-book, . . . . . . . - J4
Errors in compass surveys, . . . . 57
CHAPTER VI.
SURVEYING WITH THE FIXED NEEDLE.
Vernier, . . .
Racking, . . *
CONTENTS. XI
PAGE
Various forms of dial, ....... 61
(a.) Lean's miner's dial, ...... 61
(b.) The Henderson dial, 62
(c.) Da vis's miner's dial, ...... 63
Dial-joint, . . . . . ... 64
(d.) Whitelaw's dial, 65
(e.) Thornton's dial, . . . . 66
Traversing underground, . . . . .- . 67
Surveying in inclined shafts, ...... 75
The vernier compass, . . . 75
CHAPTER VIE.
THE GERMAN DIAL.
Invention of the German dial, .*'.*. . . 78
Measuring station -lines, ...... 78
The clinometer, . . . . . . . 79
Use of the clinometer, . . , . ' . . . 80
The hanging-compass, . . . . . . .81
Surveying with the German dial, ..... 81
Plotting the survey, . .; .' / .* . . 33
Surveying with the hanging-compass in the presence of iron, . 85
Use of the German dial, ... 85
CHAPTER VIII.
THE THEODOLITE.
Historical sketch, . .'" .' / . ' . . 87
Description of the theodolite, . .* . . . . 87
The telescope, . ., . . . . . . 90
Various forms. (a.) Hoskold's transit- theodolite, ... 91
(b.) The Everest theodolite, ..... 91
(c.) The Hoffman tripod head, . .. ''.'.' . 93
(d.) American theodolites, . , . . . 95
(e.) Traveller's transit- theodolite, . . .97
Adjustments of the theodolite, . . . . .98
Measuring horizontal angles, . . . . . . 100
Repetition, . . . . . . .101
Measurement of vertical angles, ..... 102
The solar attachment, ....... 103
xii
CHAPTER IX.
TRAVERSING UNDERGROUND.
Use of the theodolite in the mine, . . . , . 107
Comparison of the theodolite and compass, . . . .118
CHAPTER X.
SURFACE-SURVEYS WITH THE THEODOLITE.
Triangulation, ........ 120
Computing the sides of the triangles, .... 123
Interior detail of the triangulation, . . . . .126
American mining claims, . . . . . . 1 27
Surveying in South Africa, ...... 132
CHAPTER XI.
PLOTTING THE SURVEY.
Scales, . . . . . . . . .134
1. Simply divided scales, . *. , . .134
2. Diagonal scales, . . . . . .135
3. Vernier scales, . . . . ' . . .13(5
Plotting scales, . . . . . . .137
Plotting with a protractor, . . . . . 1 38
Plotting by means of chords, . . . . . . 139
Plotting by rectangular co-ordinates, . . . . 1 40
Calculating scales, . . . . . . .148
Traverse tables, . . . V . . . 149
Combined surveying and plotting instrument, . . 149
Plotting colliery surveys in Scotland, _. ' . . 150
Calculating the co-ordinates of a triangulation, . . . 151
CHAPTER XII.
CALCULATION OF AREAS.
Measures of area, . . - _ . . . . . 154
Methods of calculating areas, . . > ... . . 154
1. Method of triangles, . , . . . .154
2. Method of ordinates, . , . . . .156
3. Mechanical method, . . . . . .158
CONTENTS.
Produce of coal seams, ...... -,0^
The calculation of ore-reserves, ..... ,
CHAPTER XIII.
LEVELLING.
Definitions and principles, ...... 164
The mason's level and boning staves, . . . , 154
The spirit-level, . . . . . . .165
(a.) The dumpy level, . . . . . .165
(6.) The Y-level, . . . ... .166
(c.) The Troughton level, ...... 166
The adjustments of the level, . . . . .166
(d. ) Cushing's reversible level, ..... 167
The levelling-staff, ...... 167
Mine levelling-staves, . . ' . . 169
Practice of levelling, . . . . . .171
Section levelling, ...... 175
Bench marks, ....... 180
(e.) The reflecting level, . . . . . .183
Sources of error in spirit-levelling, .... 183
Accuracy attainable in spirit-levelling, . . 183
Plotting sections, ...... 184
(/.) The water-level, ...... 185
Trigonometrical levelling, .... 187
The clinometer, . ..... . .190
Physical levelling, . . . . . . 191
Determination of the depth of shafts, . . , . .193
Contour lines, . . . . . . .196
Applications of levelling, % 197
CHAPTER XIV.
CONNECTION OF THE UNDERGROUND- AND SURFACE-SURVEYS.
Methods employed, ....... 201
1. By means of an adit level, ..... 201
2. By means of two shafts, ..... 201
3. By means of one shaft, . ... . . 205
4. By means of a transit instrument, .... 208
4a. The Severn tunnel method, ..... 210
5. By means of a transit-theodolite, . . . .210
6. By means of the magnetic-needle, .... 213
CONTENTS.
CHAPTER XV.
MEASURING DISTANCES BY TELESCOPE.
PA^K
Theory of telescopic measurement, . . . . .217
Calculations, . . . . . ., . 222
The protractor, . . . .., . . 222
The tacheometer, ....... 223
The staves, . . ( . . . . . 223
The field-work, . . .* . . . . 223
The topographical stadia, . . . . . . 225
The theodolite and stadia, ...... 226
Telescopic measurements in mine-surveys, .... 228
CHAPTER XVL
SETTING-OUT.
Ranging straight lines, ...... 230
Plotting the underground traverse on the surface, . . . 231
Setting-out railways to mines, ..... 231
Ranging curves, ". . . . . . .231
Cross-sections, . .' ; ; ."..'. . 235
Driving levels underground, . ; . . . . 235
Curves for engine planes, . . . . . 037
Setting-out tunnels, ....... 237
CHAPTER XVII.
MlNE-SuKVEYING PROBLEMS.
Determination of the direction and inclination of a mineral deposit, 246
Determination of a point at the surface directly above one under-
ground, ........ 250
Holing from one excavation to another, . . . .252
Sinking shafts from several levels, . . , . . 256
The cubical content of a mine-reservoir, . . . . 257
Determination of the strike and dip of the line of intersection of two
veins, .. .- . "'-..-. . 258
CONTENTS. XV
PArtE
The search for dislocated lodes, . . . . .261
Irregularities of seams and beds, ..... 263
Subsidence and draw caused by working coal, . . . 265
CHAPTER XVIIL
MINE PLANS.
Plan and section, ....... 270
(a. ) Metalliferous mines, . . . . . 270
(6.) Colliery plans, ...... 273
Surface plans, ...... 274
(c.) American colliery plans, ..... 275
Importance of correct sections, ..... 276
Uniformity of scale and conventional signs, .... 277
Preservation of plans, ....... 278
Practical hints for constructing mine plans, .... 279
Copying plans, ........ 282
(1.) Copying by tracing, ...... 282
(2. ) Copying on tracing paper, ..... 282
(3.) Pricking through, ...... 282
(4.) Copying by photography, ..... 282
Reducing and enlarging plans, ..... 283
Isometric plans of mines, . . . . . . 284
Relief plans and mine models, ..... 286
CHAPTER XIX.
APPLICATIONS OF THE MAGNETIC-NEEDLE IN MINING.
Exploring for iron ore, ...... 289
(1.) Brooks' method, ...... 293
(2.) Thaten's method, ...... 294
(3.) Tiberg's method, ...... 297
Use of the magnetic-needle in surveying bore-holes, ... 300
Employment of a powerful magnet in cases of uncertain holing, . 303
APPENDIX I.
PACK
Examination questions, ...... 307
APPENDIX II.
Bibliography, . . . . . .318
321
A TREATISE
MINE-SUE YE YIN G.
CHAPTER I.
GENERAL EXPLANATIONS.
Surveying is the art of making such measurements as are
necessary to determine the relative positions of any points on
the earth's surface. From such measurements a map, or plan, of
any portion of the surface may be drawn, and its area calculated.
All surveys are conducted upon nearly the same principles, the
difference consisting in the style of instruments used in the work,
and the amount of attention bestowed on the various details.
The branch of surveying specially applied to mining is known
as Mine-surveying or, locally, as "dialling" or "latching." It
consists in measuring, with a view to subsequent delineation on
a plan and sections, first, the underground workings of a mine,
and, secondly, the mine-buildings at the surface and the mine-
concession or royalty. Thirdly, it requires an accurate method
of connecting the underground- and surface-surveys. Trust-
worthy plans and sections are of value for giving a condensed
view of all the facts connected with the works and explorations
of a mine ; for affording data to assist in the further prosecution
of workings after temporary abandonment of the excavations ;
and for the avoiding of destructive and lamentable effects
such, e.g., as disastrous litigation respecting trespass on adjoining
royalties, loss caused by driving in the wrong direction, or irrup-
tions of water, quicksand, or firedamp, giving rise to loss of life
and property which have too often resulted from incorrect or
imperfect mine-plans.
Historical Sketch. The origin of mine-surveying must be
sought with that of mining in very early times. The oldest
mine-plan known is a papyrus, preserved in the museum at
2 MINE-SURVEYIXG.
Turin, depicting the workings of an Egyptian gold-mine. It
was drawn in the reign of the king Mineptah, 1,400 years before
the Christian era. Land-surveying was first practised in Egypt.
There the annual overflows of the Nile, and the consequent
deposit of mud, destroyed the land-marks of the different pro-
prietors, so that it became necessary to determine them by
measurement every year. The oldest evidence of the solution
of mathematical problems is afforded by a papyrus in the British
Museum, which is believed to have been copied, 1,700 years
B.C., from a much older work. It gives rules for the calcula-
tion of areas of triangles, trapezoids, and circles.
That the important mines of the ancient Greeks necessitated
the solution of mine-surveying problems is shown by the fact
that such problems are fully discussed by Hero of Alexandria
(B.C. 285-222), several of whose works are extant. The greatest
advance in survey practice made by Hero was his invention of
the diopter, a sighting instrument for surveying purposes. The
oldest instrument for measuring angles, like the cross-head which
is still in use, only permitted right angles to be set out. This
primitive instrument consisted of two straight-edges fastened
together at right angles, a pointed vertical staff being fixed to
the point of intersection. The two straight-edges were provided
at each extremity with sight vanes, from which plumb-lines were
suspended so as to enable the instrument to be levelled. With
Hero's improved instrument, any angle could be measured.
Indeed, it must be regarded as the origin of the highly perfect
theodolite of the present day. It consisted essentially of a beam
resting between two uprights on a pillar-like stand. The beam
was movable in both directions by means of spiral screws acting
on horizontal and vertical cog-wheels. It was hollowed out, and
contained a metal tube, at right angles to which were glass
cylinders at each end of the beam. The cylinders had special
covers made of metal plate, which could be raised or lowered
by means of screws. They were furnished with vertical and
horizontal slits for sighting. The instrument was thus a com-
bined theodolite and level. Two staves with sliding circular
vanes were used in conjunction with it.
From the beginning of the Christian era until the Middle
Ages, mining records are wanting. An ancient charter relative
to the mines of the Mendip Hills is in existence. Of this Mr.
Robert Hunt gives a fac-simile in his British Mining. It dates
from the reign of Edward IV., about 1480. It is a rude attempt
at plan-drawing, representing the " Myne deeps," as they were
then called.
The first writer who treated mining systematically, Georgius
GENERAL EXPLANATIONS. 3
Agricola, in his work De re Metallica, published in 1556, devotes
an entire section (Book V.) to mine-surveying. He states, as
has been frequently repeated since, that the ancient mine-
surveyors strenuously endeavoured to keep their art a secret.
In the Middle Ages they were in consequence superstitiously
regarded as sorcerers. The divining-rod was closely associated
with the practice of their profession, and in many cases that
hazel-twig was trusted more implicitly than the most scientific
surveying operation.
In 1686 appeared the first treatise on mine-surveying, the
Geometria Subterranea of Nicolaus Voigtel. This was followed by
the treatises of J. F. Weidler, 1726 (in Latin); and of H. Beyer,
1749, and von Oppel, 1749 (in German). These works, by
advocating the plotting of mine-surveys by means of rectangular
co-ordinates, lifted mine-surveying to a higher plane.
In Great Britain, instructions for making mine-surveys were
published by Thomas Houghton in 1681 for the Derbyshire
miners, by William Pryce in 1778 for the Cornish miners, and
by Thomas Fenwick in 1804 for the Newcastle colliers.
Importance of Mine -Surveying. When the enormous value of
mineral resources is considered, the high importance, from a
commercial point of view, of the art of mining is apparent. In
the United Kingdom alone, the annual value of minerals raised
has approached 60,000,000, the result of the labours of some
500,000 persons directly employed in their extraction. It thus
becomes a matter of the utmost importance that the extent and
character of the mineral deposits should be made known. This
can only be effected by careful and accurate surveys.
Mine-surveying, unfortunately, has not kept pace with the
advances made in other branches of surveying ; for it is to be
regretted that, in many cases, mine-surveys are still made with
instruments which have long been set aside as too inaccurate for
surveys aboveground, although the latter rarely present such
serious difficulties as are encountered underground. This is,
in part, due to the conservatism of miners, a conservatism which
has frequently led them to regard with contempt every kind of
knowledge except that learned underground. It is a fact, as
Mr. R. Hunt points out, that the untrained mind, as a rule,
treasures every truth as a mystery to be carefully guarded for
individual use only. Experience has often stored an individual
mind with valuable facts, which are rarely recorded. The miner
trusts to his memory, and, when he dies, the results of his
experience die with him. The son has to begin where the father
began, and this is repeated from generation to generation, so that
there has been no advance. These remai'ks apply more parti-
4 MINE-SURVEYING.
cularly to the miners of the county of Cornwall, where the mining
proverb, " Where it is, there it is," still holds its own.
Happily, a better system is beginning to prevail. Coal-mining
is now carried on with a high degree of skill. Colliery managers,
who formerly were generally ignorant of the theoretical principles
upon which practice is based, are now submitted to a severe
educational test before a certificate of competency is granted.
It is, however, to be regretted that a similar examination has not
been instituted for the agents of metalliferous mines. The
mining schools which have been founded in various districts offer
suitable opportunities for the necessary theoretical training, as
also do the local classes held under the Science and Art Depai't-
ment, and under the City and Guilds of London Technical Insti-
tution.
Another cause which has retarded the progress of mine-sur-
veying is the uncertain and speculative nature of mining. Casual
failures, caused by the want of easily accessible information, fre-
quently lead to the abandonment of highly promising mines.
Mining, though speculative, is not entirely the work of chance ;
and he who, avoiding vague and unsatisfactory speculations, con-
stantly stores up facts, and can grasp the extent and object of
mining works, is frequently enabled to avoid expenses and diffi-
culties, in which those who are without such data would soon be
involved.
In this connection, Sir Warington Smyth, in a lecture on
mining, says: " At the present time, few large collieries or metal-
liferous mines are conducted without the aid of a satisfactory
plan, but there are very numerous mines in which this depart-
ment is much neglected. Moreover, there is generally a want of
uniformity in system, an absence of details which should give all
the information that can be laid down on paper, a deficiency of
surface-objects by which the workings can at a future day be
referred to their proper position, and (what may sometimes lead
to the most fatal errors) a neglect of observation or notice of the
variation of the magnetic-needle, according to which mining plans
are almost invariably constructed. It is too often the case Avhen
mines are worked by companies, that the shareholders are so
regardless of what does not, as they conceive, lead to immediate
gain, that they grudge the moderate sums needful for the employ-
ment of properly qualified surveyors, and either wink at the total
neglect of plans, or leave them to be carried out by men already
sufficiently tasked or incapable, although they may dial with
accuracy, of representing on paper what they have measured."
As an example of an error involving great loss, serious danger,
and future grave embarrassments, it may be mentioned that,
GENERAL EXPLANATIONS. 5
according to Mr. P. \V. Stuart-Menteath, at an important mine in
Spain an incorrect survey caused an error of 65 metres to be made
in driving a main tunnel less than 200 metres in length. In
collieries, too, examples are not wanting. Thus, in 1875, at a small
colliery in Nottingham there was an accident owing to some old
workings. Trusting the old plans, which showed a barrier 100
yards away, the men worked into the old headings with disastrous
results. Another case is recorded by Mr. J. Dickinson in 1878,
when an inundation occurred by which two lives were lost, from a
former working being cut into without any bore holes in advance.
In this instance, there was a correct plan of the former work,
but by a mistake of the surveyor, a wrong direction was set out.
Mineral Deposits. For practical purposes mineral deposits
may be divided into tabular deposits, including mineral veins,
beds, and seams, and irregular deposits, including masses, stock-
works, and pockets. Tabular deposits are those in which two
dimensions predominate. The third smaller dimension, the per-
pendicular distance between the two bounding planes, is termed
the thickness. The adjacent rock on both sides of these two
planes is termed the country, the portion on which the deposit lies
is the foot-wall, and that covering the deposit is the hanging-wall.
With beds and seams, these are known as the floor and roql
respectively. The strike or course of a deposit is the angle formed
with the meridian by the direction of a horizontal line drawn in
the middle plane. Its dip is the inclination downwards measured
111 degrees from the horizontal. As the dip of veins is usually
great, it is sometimes measured from the vertical, and is then
termed underlie or hade. The portion of a mineral deposit occur-
ring at the surface is known as the outcrop, basset, or (U.S.) apex.
Mineral veins or lodes are defined by Dr. 0. Le Neve Foster as
tabular deposits of mineral, which have been formed subsequently
to the rocks by which they are surrounded. Usually, they
occupy fissures in the earth, frequently cutting across the planes
of stratification of the rocks. They may occur in eruptive or
in sedimentary rocks. Their contents vary, some parts containing
worthless vein-matter or gangue, others being filled with ore.
The productive portions are termed shoots or courses of ore,
bunches, or ore-bodies. Cross courses are veins coursing nearly
at right angles to the chief lodes of any particular mining district.
The characteristic feature of beds and seams is, that they are
members of a series of stratified rocks. They may be inter-
stratified deposits, or superficial ones, such as peat, bog iron ore,
gold placers, and tin stream-works. In the former case, they are
younger than the floor, and older than the roof. As stratified
deposits, they were originally deposited in a more or less hori-
MIXE-SURVEYING.
form, and follow all the contortions of their country rock.
The minerals occurring in bedded deposits are coal, anthracite,
lignite, iron ore, cupriferous-shale, lead-bearing sandstone, gravels
containing diamonds, or gold, or tin, sulphur, salt, clays, limestone,
gypsum, oil-shale, alum-shale, and slate. Miners often erroneously
speak of " veins " of coal or ironstone ; these, geologically, are
true " beds " or seams.
" Masses " are deposits of mineral of irregular shape, which
cannot be recognised as beds or as veins. Such, for instance,
are the red haematite deposits of Ulverston, the brown haema-
tite of the Forest of Dean, the iron ore deposits of Missouri,
the iron mountains of Gellivara and Taberg in Sweden, and
the pipes of diamond-bearing rock in South Africa. They
may be filled-in cavities or metamorphic deposits, such as the
zinc ore deposit of Altenberg, which is 260 yards long and 65
yards broad and deep. When the whole rock is permeated with
mineral matter, accumulated in minute veins, the deposit is
termed a stockwork. Examples of such deposits occur at
Carclaze and other places in Cornwall, and at Altenberg in
Saxony.
No classification of mineral deposits can be quite satisfactory
in all cases. A bed, for instance, even of coal may be so folded
and contorted as to lose its original tabular form, and to assume
the shape of an irregular mass.
Mining Terms. Many local as well as technical terms are used
in mining. The following are definitions of some of the objects
most frequently named on mine-plans : A shaft is a pit sunk
down from the surface. In the mining of stratified deposits, the
shafts sunk are usually perpendicular. In vein-mining, they
may be sunk perpendicularly to cut the vein, or they may follow
its underlie. 'Levels are horizontal excavations along the course
of a vein, or horizontal passages, by which access is gained to the
workings of the mine. A level driven from the surface, to draw
.off the water, is termed an adit level, or (U.S.) a tunnel. A drift or
gallery driven across the usual direction of the veins generally for
the purpose of. searching for a new vein, or of connecting two
known veins, is termed a cross-cut. The extreme end of any level
or cross-cut is called the forebreast or end. A slope is the working
from which the ore is extracted. Above a level, the working is
an " overhand " or back stope ; an " underhand " stope is the
working downwards from the floor of the level. A winze is a
shaft which connects two or more levels, but does not come to the
surface. A rise is an upright winze commenced from a level ; a
sump is a winze worked downwards. Surface workings include
open cuts, pits, and excavations of limited extent. A tract of
GENERAL EXPLANATIONS. 7
land let for mining purposes is known as a sett, royalty, conces-
sion, or claim.
In coal-mining, the pair of galleries driven from the shaft are
variously known as drifts, headings, levels, way-gates, gate-roads,
and roller-ways. The winning of the coal is effected in different
ways, following a variety of modifications between the two
extremes, namely, the "post and stall" system, otherwise known
as the " bord and pillar," or in Scotland as " stoup and room"
and the " long-wall " system. In the former a given district is
at first worked by narrow excavations, so that no considerable
fall from above shall take place ; in the latter, the whole of the
available mineral is removed in successive slices, and the roof
allowed to fall in.
Measures of Length. The standard measure of length in the
United Kingdom is the yard. In addition to the yard, the fol-
lowing units of length are used for surveying purposes :
The inch, one thirty-sixth part of the standard yard. The foot,
one-third part of the standard yard. The fathom of 6 feet or 2
yards. The chain of 66 feet or 22 yards; divided into 4 poles
of 5i yards, and 100 links of 7'92 inches. The statute mile of
1,760 yards or 5,280 feet or 80 chains, divided into 8 furlongs.
The standard yard is the distance between two fixed points on
a certain metal rod at the temperature of 62 F., and under the
mean atmospheric pressure. The British and United States
standards are identical.
To obviate the inconveniences of the innumerable units of
length used in different countries, attempts were made towards
the middle of the 17th century to introduce a natural unit, which
could at any time be again determined if the standard should be
lost. Two proposals were considered ; one being based on the
length of a pendulum vibrating seconds, the other on the magni
tude of the circumference of the earth. The former suggestion
was due to Huygens, who proposed to divide the length of a pen-
dulum vibrating seconds into three parts, and to term each part a
foot. This method was found impracticable, since the length
of the seconds-pendulum varies with the latitude at different
places ; thus, at London it is 39 '139 3 inches, whilst at New York
it is 39-1017 inches.
The second plan was therefore adopted that is, a fraction of
the earth's meridian was taken as the standard. For this pur-
pose, at the time of the French Revolution, the distance ffom
Dunkirk to Barcelona was determined. Both these places are in
the same meridian as Paris. The measurement was subsequently
extended to the Island of Formentera, and, from the length
determined, the distance of the pole from the equator was calcu-
8 MINE-SURVEYPNG.
lated to be 513074074 French fathoms (toises). The ten-
millionth part of this length (0-513074 toise) was termed the
metre, and was adopted as the French unit of length. In 1799,
two similar rods of platinum were constructed as standards,
having that length at centigrade. The given length of the
metre being thus determined, it ceased to be a natural measure.
With the present improvements in measuring-instruments, it is
possible for us to determine the circumference of the earth with
greater accuracy, whilst the length of the metre is fixed.
Indeed, it is now known that the metre was determined a not
inconsiderable fraction too small.
The French measures of length are multiples and submultiples
of the metre. The value of the latter in British measure is
3-2808693 feet, or 39-37043 inches. For mine-surveys the metre
is the unit now almost exclusively used in continental European
countries. It is also employed on Government surveys in the
United States.
Special units of length used for mining purposes in various
countries are the following :
Feet.
6-000
3-280
5844
7-000
6-222
6-372
6-576
6-300
6-558
6864
2-7S2
6-394
Angular Measures. The circumference of a circle is divided
into 360 parts ; each part being termed a " degree." The degree
is divided into 60 minutes, and the minute into 60 seconds.
This is known as the sexagesimal division.
The French centesimal division of the quadrant into 100
degrees, instead of 90 degrees, is rarely used except for surveys
with the tacheonieter. Each centesimal degree is divided into
100 minutes, each of 100 seconds.
British Fathom.
Fathom
1*000
Metre,
0-546
Swedish Famn, ....
0-973
Russian Sashon,
1-166
Austrian Klafter,
1-037
Bavarian Lachter,
1-062
Wiirttemberg Lachter, . .
1-096
Hanoverian Lachter, . .
1-050
Saxon Lachter, . . .
1-093
Prussian Lachter, . . .
1-144
Spanish Vara, ....
0-463
French Toise. ....
1-065
GENERAL EXPLANATIONS. i)
Trigonometrical Formulas. The following is a summary of the
principal trigonometrical formulae used in surveying :
The trigonometrical functions of a given angle may be defined
as the ratios to each other of the sides of a right-angled triangle
possessing the given angle. Assuming that A, B, represent
the three angles of a right-angled triangle, C being the right
angle, and that a, b, c represent the sides respectively opposite to
these angles, c being the hypothenuse ; then the trigonometrical
functions of the angle A are
a c
sin A = - : cosec A = -
c ' a
b c
cos A = - : sec A = r
c ' b
tan A = r : cotan A = -
b a
The following equations give the most important relations
amongst the trigonometrical functions of the angle A :
sin A =
cos A =
tan A =
cosec A =
sec A =
cotan A =
The complement
it to make a rig]
1
= VI -cos* A'
tan A
cosec A
sec A
cotan A
= x/1 - sin 2 A
sec A
1
cosec A
sin A
cotan A
1
sin A
cos A
1
cos A
= \/l + cotan 2 .
= \/l + tan 2 A
= \/cosec 2 A
gle is that angle
and
^ = ta^A
cosec A
cotan A
cos A
tan A
of an an
tit angle,
sin A
which must be added
sin (90 - A) = cos A ; cosec (90 - A) = sec A
cos (90 - A) = sin A ; sec (90 - A) = cosec A
tan (90 - A1 = cotan A ; cotan (90 - A) = tan A
10 MINE-SURVEYING.
The supplement 'of an angle is that angle which must be added
to it to make two right angles. Compared with the trigonometrical
functions of the angle A, those of its supplement are-
sin (180 - A) = sin A ; cosec (180 - A) = cosec A
cos (180 - A) = - cos A ; sec (180 - A) = - sec A
tan (180 - A) = - tan A; cotan (180 - A) = - cotan A
The formulae for the solution of plane triangles are deduced
from the principles that the sum of the three angles of a plane
triangle is equal to two right angles, and that the sides of the
triangle are proportional to the sines of the opposite angles. For
right-angled triangles the most useful formulse are
b = a sin B c = a cos B
b = c tan B c = b tan
b = c cotan C c = 6 cotan B
For oblique-angled-triangles, the most useful formulas are
, a sin B a sin
6 = . T- c = -
sin A
THE MEASUREMENT OP DISTANCES. 11
CHAPTER II.
THE MEASUREMENT OF DISTANCES.
Methods of Measuring. The straight lines which have to be
measured by the mine-surveyor may be horizontal, vertical, or
inclined. The measurement of horizontal lines is of the most
frequent occurrence. When a line inclined towards the horizon
has to be measured, the operation is, as a rule, performed with the
object of determining the horizontal and vertical projections of
the line. It is then necessary, in each case, to determine the
angle of inclination formed by the measured line and the horizon.
Lines are usually measured with chains, tapes, or rods, divided
into fathoms, yards, links, feet, or some other unit of measure-
ment.
(a.) The Chain. The instrument most frequently used in sur-
veying is the chain. In coal-mines and in field-surveying,
Gunter's chain is employed. It is 66 feet in length ; 80 chains
being equal to 1 mile. This length was chosen by the inventor,
Edmund Gunter, in 1620, with the object of facilitating the
computation of areas ; 10 square chains being equal to 1 acre.
The chain is composed of 100 links of iron or steel wire, each
bent at the end into a ring, and connected with the ring at the
end of the next piece by means of three rings. The chain is thus
prevented from becoming twisted or kinked. A. couple of swivels
are also inserted in the chain, so that it may turn round without
twisting. Every tenth link is marked by a piece of brass with
one, two, three, or four points, corresponding to the number of
tens that the brass represents, counting from the nearest end of
the chain. The middle, or fiftieth, link is marked by a brass
circle. A swivel-handle is provided at each end of the chain.
The wire used in the construction of iron chains is usually
No. 8 W.G.; that used for steel chains is No. 12, or No. 8 W.G.
The hundredth part of the chain is called a link, and is equal
to 0-66 foot or 7'92 inches. All calculations with chains and
links can thus be easily performed by means of decimals. The
following table will be found useful for converting chains into
feet and feet into links :
12
MINE-SURVEYINQ.
CHAINS INTO FEET.
FEET INTO LINKS.
Chains.
Feet.
Feet.
Links.
o-oi
0-66
1-00
1 515
0-02
1-32
2-00
3-030
0-03
1-98
3-00
4-545
0-04
2-64
4-00
6-060
0-05
3-30
5-00
7-575
0-06
3-96
6-00
9-090
0-07
4-62
7-00
10-606
0-08
5-28
8-00
12-121
0-09
5-94
9-00
13-636
For colliery use, the chain is sometimes made with ten links in
brass at each end, in order to prevent the compass-needle being
attracted.
It must be remembered that any error in the length of the
chain will cause erroneous measurement throughout the entire
survey. It should, therefore, be tested and adjusted before the
commencement of every survey, or at any rate from time to time.
This is best done by having a standard marked on a level path-
way or on the top of a wall, showing not only the accurate
length of the chain, but also the length of every ten links.
Standard 66-feet and 100-feet chains have been fixed by the
Government in Trafalgar Square and Guildhall, for the use of
surveyors in London. For rough colliery surveys, the chain
may be left half-an-inch longer than the true length, since it
is rarely stretched perfectly horizontally, or drawn out into a
perfectly straight line. If a line has been measured with an
incorrect chain, the true length of the line may be found from
the proportion : As the length of the standard given by the
incorrect chain is to the true length of the standard, so is the
length of the line given by the measurement to its true length.
Accompanying the chain are ten arrows or iron pins, which are
used in succession to mark the end of the chain in measuring a
line. They are a foot long, and are made of stout iron wire
THE MEASUREMENT OF DISTANCES. 13
sharpened at one end and bent into a ring at the other. A piece
of red tape is usually attached to the rings to render the arrows
visible from a distance. The chain is folded by taking it by the
50-link mark, and folding the two ends simultaneously, taking
care so to cross the links that the body of the chain when folded
may be smaller in the middle than at the ends. The chain is
opened by taking both handles in one hand, and throwing the
chain out with the other.
The chain is used by two persons, the leader and the follower.
The former having been supplied with the ten arrows, stretches
the chain in the required direction, while the follower holds one
end of it at the starting-point. An arrow is then driven perpen-
dicularly into the ground by the leader at the point where the
chain ends. He then proceeds onward, drawing the chain after
him, and repeats the same operation throughout the length of the
line ; the arrow last put down serving as the mark to which the
follower has to bring his end of the chain. The arrows are
taken up by the follower as he advances, until he has them all,
when they are returned to the leader to be used over again. The
arrows are thus changed from one to the other at every 10 chains'
length ; care being taken to note each change in the field-book.
At the end of the line, the number of changes added to the
number of arrows in the follower's hand, and to the number of
links extending from the last arrow to the end of the line, gives
the total length of the line measured. If the ground is so hard
that an arrow cannot be driven in, the leader marks the ground
and lays the arrow down. Eleven arrows are usually pre-
ferred. The eleventh is used to mark the end of the eleventh
chain ; another being substituted for it before the leader goes on.
During the operation, the follower has to see that the chain is
tight, straight, and unentangled, and to direct the leader so as to
enable him to place the arrow in the ground exactly in the
alignment.
In measuring lines in a colliery, the arrows are usually dis-
pensed with ; the end of each chain being marked with a piece of
chalk.
The chain used in metalliferous mines is 10 fathoms or 60 feet
in length, and is provided with brass marks at every fathom.
Each link of the chain is 6 inches in length. The chain is some-
times made entirely of brass. No advantage is gained by using
Gunter's chain in a metalliferous mine, since acreage has never
to be calculated, and measurements have to be made with such
precision that the inch is to be preferred to the link as a unit.
Chaining on Slopes. In chaining up or down a slope, the
distance must be reduced on the plan to the projection of that
14
MINE-SURVEYING.
distance on a horizontal plane. If the slope is gentle, the lower
end of the chain may be raised until the chain is level. To
Angle.
Degrees.
Slope.
Gunter's Chain.
Correction
in Links.
10-fathom Chain.
Correction
in Feet.
100-foot Chain.
Correction
in Feet.
3
1 iu 19-08
0-14
0-08
0-14
4
1 in 14-30
0-24
0-14
0-24
5
1 in 11 -43
0-38
0-22
0-38
6
lin 9-51
054
0-32
0-54
7
lin 8-14
0-74
0-44
074
8
1 in 7-11
0-97
0-58
0-97
9
lin 6-31
1-23
0-73
1-23
10
lin 5-67
1-52
0-91
1-52
11
lin 5-14
1-83
1-09
1-83
12
lin 4-70
2-18
1-30
2-18
13
1 in 4-33
2-56
1-53
2-56
14
1 in 4-01
2-97
1-79
2-97
15
lin 3-73
3-40
2-04
3-40
16
1 in 3-48
3-87
2-32
3-87
17
1 in 3-27
4-37
2-62
4-37
18
1 in 3-07
4-89
2-93
4-89
19
lin 2-90
5-44
3-26
5-44
20
lin 2-74
6-03
3-61
6-03
25
1 in 2-14
9-37
5-62
9-37
30
lin 1-73
13-39
8-03
13-39
The rate of slope (the ratio of the hypothenuse to the perpendicular) is
the cosecant of the angle of inclination. The rate of inclination (the ratio
of the base to the perpendicular) is the cotangent of the angle of inclination.
THE MEASUREMENT OF DISTANCES. 15
ensure the raised end being exactly above the right spot, the
chain may be raised along a vertical staff, or an arrow may be
carefully dropped, or, better still, a plumb-line may be employed.
The process is called stepping, and, on steep ground, may be
carried on by half-chains, or even shorter distances. A more
accurate method is to measure the angle of the declivity. The
cosine of this angle, multiplied by the measured hypothenuse,
gives the length of the horizontal distance.
The most convenient method is by means of a correction to be
deducted from each chain. This correction, being known, may
be applied mechanically during the chaining by pulling the chain
forward at each chain-length through a distance equal to the
required correction.
The preceding table gives the correction for each chain
measured on the slope.
In order to save calculation, many mining dials and theodolites
have the correction for declivity marked on the graduated arc on
which angles are measured.
Offsets are ordinates or transverse distances measured from
known points on a station-line to objects the position of which is
to be ascertained. Offsets, as a rule, are measured at right
angles to the chain. The length of the offset having been deter-
mined, the position of the object is fixed with reference to the
main line.
Offsets may be measured with an offset rod, 10 links in length,
painted black and white in alternate lengths, or, preferably, with
a measuring-tape. This is divided on one side into links and on
the other into feet and inches. It should be tested frequently,
particularly after use in a wet mine. It is not advisable to use
offsets more than a chain in length. When the offset does
not exceed this length, with practice the eye may be relied
upon to give a right angle with precision. The cross-staff
and optical square, recommended by some surveyors for erecting
perpendicular lines, are rarely necessary in mine-surveying
practice.
The optical square consists of two small mirrors placed in a
brass box at an angle of 45, thus reflecting an object through an
angle of 90. The unsilvered half of one mirror gives a direct
view of the object, whilst the reflected and true object can be
exactly superimposed in the observer's field of view when they
are at right angles to each other. The cross-staff has two pairs
of sights fixed at right angles to each other on the upper end
of a staff having a spike at its lower end for fixing into the
ground.
In taking offsets, the surveyor reads the tape at the chain.
1G
MINE-SURVEYING.
The ring of the tape is held at the point to which the offset is
required. The surveyor then turns the tape in
I a horizontal -plane until he obtains the shortest
measurement, and ascertains the link on the
chain where the offset forms a right angle.
In cases where additional accuracy is required,
oblique offsets may be used. From two points in
the chain, offsets are measured obliquely to the
object, and the triangle thus formed, when
plotted, shows the accurate distance of the object
from the station-line. When the object is the
corner of a building, such as D in Fig. 1, it is
convenient to make each of the offsets, if possible,
lie in a straight line with a face of the building.
Obstacles to Measurement. Obstacles some-
times occur in a long station-line, rendering it
impossible to chain along the line with accuracy.
In some cases it may even be impracticable to
range the line directly across the obstacle. These
difficulties may easily be obviated by the use of angular instru-
ments. It is, however, possible to use the chain alone.
When the impassable obstacle can be seen over, a ranging pole
is planted in the station-line at the further side D (Fig. 2) of the
obstacle. At two marks, A and D (the nearer and further
sides of the obstacle respectively), two lines, A B and D 0, are
ranged at right angles to the station-line. These perpendiculars
are made equal to each other, and the distance B is measured.
Fig.
Fig. 2.
Fig. 3.
Fig. 4.
This measured distance will then be equal to the required dis-
tance, A D.
In order to erect a perpendicular to a line at a given point,
Euclid's proposition (I., 47) may be applied in the following
way : Measure 40 links along the line, and let one end of the
THE MEASUREMENT OP DISTANCES. 17
chain be held at that point, and and let the 80-link mark be
held at the given point where the perpendicular is to be erected.
Then take the 50-link mark, and tighten the chain, drawing
equally on both portions of it. The 50-link mark will then give
the perpendicular required. It is advisable to repeat the opera-
tion on the other side of the line, so as to test the accuracy of
the result.
When the obstacle can be seen over, the length of the gap in
the station-line may be determined by setting out a triangle
ABC (Fig. 3) enclosing the obstacle. The triangle may be of
any form or size, provided that B and are in one straight
line with D, and that the angles are not very obtuse nor very
acute. The lengths A B, AC, B D, and D C are measured.
Then the inaccessible distance will be found either by plotting
the triangle and the point D in its base, or from the formula :
AD = //A^OD + AO^Bp,^.^
The figure of the obstacle may be surveyed by offsets from the
sides of a triangle. Let b and c, in Fig. 4, be points in the
station-line on opposite sides of the obstacle. From a convenient
station A, chain the lines A b, A c, being two sides of the triangle
A. be. Connect these lines by a line B C to form the triangle
ABC. Then the inaccessible distance is obtained from the
following formula given by Rankine:
be
This formula will apply if the points B and C are taken in the
prolongations of A c and A b beyond the station-line, as at B'
and C', or in their prolongations beyond A, as at B" and C". The
formula is greatly simplified if A B and A C are set off so as
to be respectively proportional to A b and Ac. Then the
triangles ABC and A b c are similar, B C is parallel to b c, and
the inaccessible distance b c is equal to B C -T-VJ
A. JL>
When the obstacle can be chained round, but not chained
across nor seen over, the inaccessible distance may be determined
by means of parallel lines. Thus in Fig. 5, from A and B two
points in the station-line on the nearer side of the obstacle, set
off the equal perpendiculars AC, B D, of length sufficient to
enable a straight line to be ranged parallel to the station-line,
and to be chained past the obstacle. Commence the chaining
18
MIXE-SURVEYI>'G.
of this line at D, in continuation of that of the station-line at B.
As soon as the obstacle is passed, set off the perpendicular E G
equal to A and to B D. Then G will be a point in the
station-line beyond the obstacle, and the inaccessible distance
B G will be equal to D E. By repeating the process, an addi-
tional point H in the station-line may be found.
The problem may also be solved by means of similar triangles.
At A (Fig. 6) two diverging lines A F and A E are ranged past
the two sides of the obstacle. In these lines, measure the
distances A D and A of two points D and C, which lie in
one straight line with B. Continue the chaining of A F and
A E, and make those distances respectively proportional to A D
and A 0. Measure D C, noting the position of B, and measure
,E F, in which line take the point G, dividing E F in the ratio
in which B divides C D. Then G will be a point in the station-
line beyond the obstacle. Other points may be found in a similar
manner. The inaccessible distance is equal to T-~
-A. vA
When the obstacle can be seen over, but neither chained
across, nor chained round, as in the case of a station-line inter-
rupted by a river or ravine, a pole must be ranged and fixed at
D (Fig. 7) in the station-line beyond the obstacle. B D being
the inaccessible distance, at B set out B perpendicular to the
station-line. At range G A perpendicular to D, cutting the
station-line at A. Measure A B, B C ; then B D is equal to
BC 2 -j-AB.
3P
Fig. 5. Fig. 6. Fig. 7.
Surveying with the Chain only. In this method of surveying,
the surface is to be divided into a series of imaginary triangles ;
THE MEASUREMENT OF DISTANCES. 19
the triangle being the only plane figure of which the form cannot
be altered, if the sides remain constant. The triangles should
be as large as the nature of the ground will allow, and as nearly
equilateral as possible. The sides of these triangles are first
measured, and a straight line is measured from one of the angles
to a point in the middle of the opposite side. This fourth line
is called a tie-line or proof-line, and is an efficient means of detect-
ing errors. Within the larger triangles, as many smaller triangles
and tie-lines are measured as may be required for determining
the position of all the objects included in the survey. The
directions of the lines forming the sides of these secondary
triangles are so pjaced that the offsets to be measured from them
may be as short and as few in number as practicable. Pickets
are placed in the ground at each angle of the triangles, the
general form and position of which are noted for reference in a.
hand-sketch, distinctive letters being written at each point of
intersection. The points of intersection of all straight lines, as
well as the angles of the triangles, are always points measured
to or from. They are called stations, and the lines connecting
them station-lines. Secondary stations are best marked by
whites, which are cleft sticks holding small pieces of white paper,
on which a number may be pencilled.
In carrying out a survey with the chain only, it is necessary
to attend to the following rules : Walk two or three times over
the ground in order to get a good idea of it, helping your memory
with a rough sketch. The first line should be made as long as
the place to be surveyed will allow, so that it may form a con-
venient base with which the other lines may be connected.
Select a suitable station on each side of the base-line near the
boundary of the work. To these stations, lines should be
measured from each end of the base-line, thus forming two large
triangles, one on each side of the base-line . On the sides of these
triangles, smaller triangles must be marked out, so as to cover
all the ground to be surveyed.
The rough sketch is usually made in the field-book a book in
which every step of the operations gone through in the survey
is to be carefully entered at the time. The field-book is ruled
with a column down the centre of the page. In this are set
down the distances on the station-line at which any offset is
made, and on the right and left of the column are entered the
offsets and observations made on those sides respectively of the
station-line. The middle column represents the chain. It is,
therefore, advisable to begin the entries at the bottom of the
page ; the chain and field-book being thus placed in the same
position at the station-line with respect to the surveyor, who
MINE-SURVEYING.
keeps his face directed towards the distant station. The crossing
of fences, roads, or streams is to be shown by joining lines in a
way similar to the form which they present on the ground.
The following example shows the manner in which the field-
notes may be entered in the survey of a triangular piece of
ground :
From B
687
to D, tie-line
802
to A
From D
O
956
to D
From C
1265
to C
800
to B, point for tie-line
From A
In booking, certain conventional signs are adopted for the
remarks that occur frequently. The commencement of a station-
line, for example, is represented by a small circle or a triangle,
and its termination by a line drawn across the page. A station
left in a line, to or from which another line is to be measured, is
usually represented by its number enclosed in a circle. A turn
to the right or left is indicated thus f ,~1.
Proper attention in keeping the field-book saves much time in
plotting, and guards against errors likely to arise from reference
to confused notes. In fact, notes ought to be kept so clearly
that a draughtsman should be able to plot the survey without
further instruction from the surveyor
In spite of its apparent want of accuracy, the method of
surveying with the chain alone gives, in the hands of an accom-
plished surveyor, very satisfactory results. At the same time,
though sometimes used for the surface-surveys of small collieries,
it is not considered sufficiently accurate for surveys of metal-
liferous mine royalties.
Chain used in Trigonometrical Surveys. Before compensating
bars were invented, steel chains were employed for base-
measurement in the Great Trigonometrical Survey of the
THE MEASUREMENT OP DISTANCES. 21
United Kingdom. In using the steel chain, a drawing-post
and a weight-post were used; a 56-lb. weight being always
applied to one end of the chain, whilst the other was fixed to
the drawing-post. The chain was made to rest in deal coffers
supported by trestles, in order to obtain a perfectly level surface,
and thermometers were placed at different distances in order to
ascertain the temperature of the chain, so that the base might
be reduced to its value at a given temperature. The chain was
100 feet long, and consisted of 40 links, each $ inch square.
(b.) Rods. When very accurate measurements were required,
deal rods were at one time largely used instead of the chain for
measuring long lines. They were, however, soon discarded in
exact operations, as experience showed that they were liable to
sudden and irregular changes in length from dryness or humidity.
Saturated with boiled oil, and afterwards covered with a thick
coat of varnish, well-seasoned wooden rods will be found suffi-
ciently exact for ordinary purposes. Such rods are usually
made of lance wood, and are 5 feet in length. They must be
placed in line very carefully end to end. They are rarely
placed directly on the ground, which, as a rule, is too uneven.
A horizontal line may be constructed along the base to be
measured, by means of a stretched cord.
On the Trigonometrical Survey of the United Kingdom, glass
rods were substituted for wood in the measurement of the
Hounslow base in 1784. Their ends were protected with metal
caps. The results obtained were perfectly satisfactory, measure-
ments with the glass rods and a check measurement with a steel
chain of perfect workmanship, giving results that differed by
little more than half an inch in the base-line of 27,404 feet.
Steel rods also have been found useful for geodetic measure-
ments.
For the measurement of the Loch Foyle base, an apparatus
was devised by Colonel Colby. In this he obtained an unalter-
able linear measure by using compensating expansions. Two
bars, one of iron, the other of brass, 10 feet long, were placed
parallel to each other, and rivetted at the centre, it having been
found by numerous experiments that they expanded or con-
tracted in the proportion of 3 to 5. The brass bar was coated
with some non-conducting substance, in order to equalise the
susceptibility of the two metals to change of temperature.
Across each end of these combined bars was fixed a tongue of
iron, with a minute dot of platinum so situated on this tongue
that, with every change of contraction or expansion, the dots at
each end always remained at the constant distance of 10 feet.
On the Continent, rods 3 to 4 yards in length are employed,
22 MINE-SURVEYING.
terminated by two points, and provided in the middle with a
builder's level and a handle. This apparatus is known as the
field-compasses, and is often used for filling in the details of a
survey.
(c.) Steel Bands. The most suitable instrument for measuring
lengths in mine-surveys is the steel band. It is more convenient
and less liable to inaccuracy than the chain. It is usually 100
feet, or 100 links, in length, with feet etched on one side and
links on the other. It is provided with a handle at each end,
and is wound on a steel or wooden cross. It is employed in
precisely the same way as the chain. Like that instrument, it
presents the advantage of rapidity; but it has the additional
advantage of representing a length of which the variations are
dependent only on the temperature, since it does not kink,
stretch, nor wear so as to change its length.
In surveying the anthracite mines of Pennsylvania, Mr. E. B.
Coxe * uses a measuring-tape made of a ribbon of tempered steel,
0-08 inch broad and 0-015 inch thick. It is 500 feet long, and
weighs 2 Ibs. 7| oz. At each tenth foot a small piece of brass
wire is soldered across the tape, the white solder extending
about an inch on each side of the wire. In the latter is filed a
small notch which marks the exact spot where the tenth foot
ends. The distances from the zero point of the tape are marked
upon the solder by counter-sunk figures. The white solder
enables the 10-feet notches to be found very easily, and the
counter-sunk figures, being filled with dirt, stand out upon the
white ground of solder. The tape is wound upon a simple
wooden reel, 10 inches in diameter, which can be held in one
hand and turned by the other. Two brass handles, which can
be detached, accompany the tape, and are carried upon the reel.
The advantages of the tape are (1) the greater facility in
measuring up and down slopes, or along the face of the coal ;
(2) greater accuracy in measuring from one station to another,
as the tape forms a straight line from one station to the other,
and there is no error from the use of arrows; (3) the tape
does not stretch appreciably. Its disadvantages are (1) it is
liable to break, unless carefully handled ; (2) it is necessary to
roll it up and unroll it again when the distances vary very
much. The tape, however, can be easily mended when it breaks.
For this purpose, a small sleeve of brass is made tinned inside,
in which the broken ends of the tape are slipped and then,
soldered by heating the sleeve with a red-hot poker.
There are three sources of error in the use of the steel tape,
* Trans. Amer. Inst. M.E., vol. il, 1874, p. 219.
THE MEASUREMENT OF DISTANCES. 23
(1) the extension of the tape by stretching; (2) the shortening
of the tape in consequence of its assuming the form of the
catenary curve; and (3) the contraction or expansion due to
change of temperature. The tape does not stretch to any
appreciable extent, and any error thus caused is compensated
by the shortening due to the formation of the catenary curve
by the tape. The true distance indicated by a 500-foot steel
tape, when subjected to the usual tension of 40 Ibs., is calculated
to be 499 -9 185 feet. With regard to the expansion caused by
change of temperature, a tape measuring 500 feet in length at
32F. becomes 500-6 feet in length at 212, so that a variation
of 60 causes a variation of only two-tenths of a foot in a 500-
foot tape.
The steel band is to be recommended for all important work
in mine-surveying, whilst the chain should be used for filling in
details, and where extreme accuracy is unnecessary.
(d.) Measuring- Wheel. The viameter, or measuring-wheel, is
sometimes used for measuring station-lines. The wheel is rolled
over the ground to be measured, and its motion is communicated
to a series of toothed wheels so proportioned that the index- wheel
registers their revolutions, and records the whole distance passed
over. On very even ground the results are fairly satisfactory.
(e.) Pacing. A line may be measured by pacing, with tolerable
accuracy. This method consequently is frequently employed on
explorations, preliminary surveys, and in levelling with the
aneroid barometer. In order to obtain accurate results, the
surveyor must accustom himself to an accurate pace. This may
be done by pacing a distance of 200 to 300 yards repeatedly,
until the same number of paces is always obtained. An instru-
ment, called a passometer, made in the form of a watcji may be
conveniently used for registering the number of paces, thus
precluding the absorbing attention required for accurately
counting a considerable number of paces. The distance may be
registered direct by a similar instrument, the pedometer, which
can be adjusted with facility to long or short steps.
The usual step is the military pace of 30 inches, 108 of these
paces per minute representing a velocity of 3 -07 miles an hour.
If no unfavourable conditions come into play, for example, slope
of the station-line or fatigue, a distance may be determined by
pacing accurately to within 2 per cent. The pace of the surveyor
should be re-measured from time to time, since after the age of
25 to 30 years, the length of the pace diminishes considerably
with increasing age.
On slopes, the pace is always shorter than on level ground.
Professor W. Jordan gives the following averages :
MINE-SURVEYING.
Rise.
Pace.
Fall.
Pace.
Inches.
30-3
Inches.
30-3
5
27-5
5
29-1
10
244
10
28-3
15
22-0
15
27-5
20
19-7
20
26-3
25
17-7
25
236
30
15-0
30
19-7
The relation between the height of the individual and the
length of his pace, may be seen from the following averages :
Height.
Pace.
Height.
Pace.
Feet. Indies.
5
Inches.
29-5
Feet. Inches.
5 8
Inches.
31-5
5 2
30-3
5 10
32-2
5 4
307
6
32-6
5 6
31-1
6 2
33-0
Accuracy of Linear Measurements. Professor F. Lorber, of the
Leoben School of Mines, has made a careful study of the accuracy
of linear measurements. From 6,000 measurements, he deduces
the following table showing the mean error of each method
employed. The error is proportional to the square root of the
length, according to the theory of probabilities. The moan error
m in measuring a line L by five different methods is as follows :
Two rods along a stretched cord,
Two rods, without cord, .
Chain,
Steel band, ....
Field-compasses,
Measuring-wheel,
Square root f L
multiplied by
m = 0-000535
TO = 0000927
m = 0-003000
m = 0-002160
ra = 0-002120
m = 0-003600
THE MEASUREMENT OF DISTANCES.
25
The mean error is thus approximately
1:2:6:4:4:7,
according to the method employed. Thus, a measurement with
rods along a stretched cord is six times as exact as a measurement
of the same line with the chain. From the results given above,
it is evident that measurements with rods along a stretched cord
are the most exact, whilst, with the exception of the measuring-
wheel, the chain gives the most untrustworthy results. The
steel band, too, gives results one and a half times more accurate
than those given by the chain.*
Normal errors, such as those due to defects in the instrument,
and errors in allignment, increase in proportion to the length.
For the various instruments, with the exception of the rods along
a stretched cord, where the normal error r is reduced to a
minimum, these errors are as follows :
Two rods, without cord,
Chain, ....
Steel band, .
Field- compasses, .
r = - 0-00008 L
r = + 0-00046 L
r = - 0-00032 L
r = - 0-00079 L
In the case of the chain only is the error positive ; that is to say,
the length measured is longer than the true length.
The rapidity of measuring is shown by the following averages :
MEAN SPEED
PEK MINUTE.
Absolute.
Per Assistant.
Rods .
2
Feet.
45
Feet.
2-2
Chain, ....
2
50
29
Steel band,
2
65
32
Field-compasses,
1
85
85
* Improved methods of chaining are described by W. M. Thompson,
Min. Proc. Inst. C.E., vol. xcii., 1888, p. 268.
26 JIINE-SURVEYlIfG.
CHAPTER III.
THE MINER'S DIAL.
Directive Action of the Earth's Magnetism. In determining
the linear direction of mineral deposits, and in acquiring in-
formation to aid in laying down on paper the position and
extent of mine-workings, the magnetic-needle has long been
employed.
The action of the earth on a magnetic-needle is directive, that
is, it determines the position of the needle with relation to the
cardinal points of the horizon, but causes no strain on the point
on which the needle is balanced. Thus, if a magnetic-needle is
supported at its centre of gravity, it assumes a certain direction ;
one pole pointing towards the north and the other towards the
south. The pole of the needle directed towards the north is
called the north pole or, more correctly, the north-seeking pole,
and that directed towards the south is called the south pole or
south-seeking pole. The magnetic force acts through rocks,
glass, and liquids as instantaneously and with as great intensity
as through the air.
Historical Sketch. To Flavio Gioja (1302-1320) is usually
assigned the credit of having first enclosed a magnetic-needle in
a box. The use of the magnetic-needle for surveying mines is
first described by Georgius Agricola in the fifth book of his De
re Metallicd, published in 1556. The compass there described is
of a very primitive character. It consists of a series of seven
concentric circles filled with wax of different colours; in the
middle is a depressed receptacle to contain the magnetic-needle.
An old compass of this type is preserved in the collection
of the School of Mines of Clausthal in the Harz. It bears
the date 1541, and consists of a wooden plate, ^ inch thick
and 6^ inches in diameter, in the middle of which is a small brass
compass-box, 2 inches in diameter. The whole is placed in a
circular receptacle in a wooden box, which may be closed by a
lid, and which is provided with a hole in its base, probably to
enable it to be placed on a stand. The compass has only a north
and south line marked, and round its raised edge a double ruler
revolves. The wooden plate has several concentric circular
THE MIXER'S DIAL. 27
depressions, filled with wax of different colours. When in use,
the instrument was so placed that the needle pointed to the
north, and the ruler revolved until it pointed in the direction,
the bearing of which was required. A scratch was then made
on one of the wax circles to indicate this direction. The laying
down of the results was effected by repeating the survey at the
surface, commencing at the mouth of the shaft. The object of
such surveys was merely to determine how near the under-
ground workings were to the boundary of the concession.
In the 17th century, mines were surveyed in this country in
a somewhat similar manner. Thomas Houghton, writing in
1G81, describes the method of surveying adopted in the Derby-
shire mines, as follows : "Having provided yourself of a Dial
in a square Box, or a long square Box, which is better ; and also
of a Two Foot Rule, and a String or Cord with a Plummet at
the End : first plum the Shaft : Now suppose you come to take
a Length forwards into the Drift at the Shaft Foot, having first
made a Mark there where the Plum fell, let a Boy hold one End
of the String therein, and bid another Man take the Plummet,
and go as far back into the Drift as he can, till the Plum he hath
in his Hand touches the Side; and stretching the String streight,
observe that it touches no where betwixt that End he holds in
the Mark, and the Plummet the other Man hath in his Hand,
(if it touches the Side bid him come nearer) then apply the Dial
to the Side of the String, and when the String and Dial lie
exactly streight together, take the Point the Needle stands on,
which suppose here to be 44 ; set down the Point, bid him make
a mark at the Plummet ; then pull back the String and measure
it, which suppose here to be 12 rules and 14 inches : Then go to
the Mark he hath made, hold one End of the String in it, bid
him go back into the Drift with the Plummet as far as he can,
till the middle of the String begins to touch the Side; then
stretching the String streight, observe that it touches no where
betwixt them that hold it, apply the Dial to the Side of it, and
take the Point the needle stands on."
The process was then repeated until the end of the level was
arrived at. The lengths and bearings thus obtained were pegged
out at the surface, and thus a mark was obtained above ground
exactly above that left at the end of the level underground.
" You must observe," says Houghton, " that your Rule and
String lie parallel with the Edge of your Dial, that is, equally
at both Ends ; or else you will miss in taking the true Point.
Under Ground the Dial is guided by the String; but above
Ground the String is guided by the Dial."
Even in the middle of the last century, dialling was carried
28 MINE-SURVEYING.
on with appliances of a very primitive character. " The instru-
ments used," writes Dr. W. Pryce in 1778, " are, a compass
without a gnomon or style, but a center pin projecting from the
middle of the compass to loop a line to, or stick a candle upon,
fixed in a box exactly true and level with its surface, about 6,
8, or 9 inches square, nicely glazed with strong white glass, and
a cover suitable to it hung square and level with the upper part
of the instrument : a twenty-four inch gauge or two-foot rule,
and a string or small cord with a plummet at the end of it : a
little stool, to place the dial horizontally: and pegs and pins of
wood, a piece of chalk, and pen, ink, and paper."
The author warns " those who take no account of the points or
angles of the compass, Jbut in lieu thereof, chalk the bearing of the
line they measure with, on the board the compass lies in ; for if
they are not exceedingly careful and precise in their operations,
they may commit almost unpardonable and irretrievable blunders :
yet formerly, before penmanship and figures were so generally
understood and practised among the common Tinners, as they
are at present, most of our Mines and Adits were dialled for
in this manner."
Towards the end of the last century, the dial was fitted with
sights, by means of which the direction of the station-line could
be taken with precision.
Description of the Miner's Dial. In its simplest form, the
miner's dial consists of a box of brass or wood, on the base of
which is fixed a brass ring divided into 360. The base of
the box within this ring is also graduated, but each division
contains 10, and the numbers proceed from the north and south
points to 90 on each side, thus dividing the inner circle into
four quadrants of 90 each. On a finely pointed pin fixed in the
centre of the circle, a magnetic-needle is freely suspended, so that
when the dial is placed in a horizontal position and the needle
unchecked, one end points towards the north. This north-seeking
end is distinguished by some mark. The instrument is supplied
with a glass cover, and also with a brass lid to protect it when
not in use. Perpendicular to the horizontal plane of the instru-
ment, are two brass plates, called sights, one at the north, and the
other at the south point. These sight vanes are divided into two
parts, the upper one on one side having a fine slit cut throughout.
The corresponding division of the opposite sight carries a plain
wire. In the lower divisions, the relative positions of the slit
and wire are changed. The compass-box is attached to a tripod-
stand by a socket fitting on to a corresponding plug ; an inter-
mediate ball and socket joint furnishing the means of levelling,
the instrument.
THE MINER'S DIAL. 29
(a.) The Magnetic -Needle. In shape, the magnetic-needle is
usually rhombic (Fig. 8) or rectangular (Fig. 9), or its height
may be greater than its breadth, in which case the edges are
bevelled (Fig. 10). Magnetic-needles of the rhombic form have
the advantage of lightness. It is,
however, not advisable to make the
needle pointed, as it retains its mag- Fig.
netism longer when the ends are
square. In the form shown in Fig.
9, the points are replaced by a fine
etched line, representing the mag-
netic axis.
The needle is drilled through in
the centre, and carries above the aperture a hollow brass cap,
lined with some hard stone conically hollowed out. Agate or
carnelian is usually employed for the purpose ; but ruby is best.
The cap must be as light as possible, and it must be firmly fixed
to the needle in such a way that its axis forms a right angle with
the axis of the needle. The interior of the cap must be accurately
conical. Caps made of brass, silver, or steel should be avoided,
as they cannot be polished so well as those of agate, and they are
very soon bored through by the centre pin. This pin is made of
good steel with a hard, smooth, round point, the angle of which
is not too great. The more pointed the pin and the more
obtusely conical the interior of the cap, the less is the friction
of the needle on its pivot.
The needle must be made of very hard steel, and so con-
structed that its geometrical centre line passes exactly through
the centre of the cap. It must be sufficiently magnetised, and,
when placed on its pivot, must assume a horizontal position. A
needle which is horizontal before being magnetised, will dip
after having been subjected to that treatment. It is, therefore,
necessary to make one end of the needle heavier than the
other.
In order to preserve the pin from unnecessary wear, and from
being broken off when the instrument is carried, a contrivance is
employed for fixing the needle. This consists of a slide, pressed
from outside, which raises the needle and presses it against the
glass lid of the dial. When required to be used, the needle
should be lowered carefully, so that it gently rests and does not
fall upon the centre pin.
Much depends upon the sensitiveness of the needle. A
sluggish needle is utterly useless. The needle may be tested by
bringing a piece of iron near it when at rest, observing whether
it returns exactly to its former position after a few oscillations.
30 MINE-SURVEYING.
The test should be made at several points round the dial.
The needle should not move when the dial is gently revolved.
All parts of the dial, with the exception of the magnetic-needle
and the centre pin, must be made of metal free from iron or
nickel. They may be tested by bringing them near a sensitive
magnetic-needle balanced on a centre pin fixed in a piece of
wood, and noting whether the needle moves, as each separate
portion of the dial is brought near it.
In making a survey with the dial, care must be taken that
nothing capable of attracting the needle is carried about the
person, such as penknives, keys, steel watch-chains, spectacles,
nickel-plated studs, or iron rivets in the magnifier used to read
the graduations. Watches in which the movements are made of
nickel, attract the needle almost as much as when the movements
are made of iron. The brims of felt hats are sometimes stiffened
by inserting an iron wire round the edge. The surveyor should
therefore examine both his watch and his hat before commencing
a survey. Sometimes the needle persistently sticks to the under
side of the glass. This is caused by the glass becoming electrified
from rubbing against the clothes, or from being cleaned with a silk
handkerchief. The electricity may be at once removed by
touching the glass with the moistened finger or by breathing on
the glass. An unsuspected source of error in magnetic-needle
readings has recently been discovered to arise from the magni-
fying glass used for reading the graduations becoming electrified.
The magnifier generally used for that purpose has a hard,
highly-polished, black frame, which is peculiarly liable to become
electrified, even by the mere carrying in the pocket, so that,
when brought near the magnetic-needle, it draws it sometimes
as much as half a degree from its true resting place.
In a good dial the centre pin of the needle should be exactly
in the centre of the graduated circle, and the needle should be
straight. If this is not the case, there will be an error of eccen-
tricity in every observation. The constant eccentricity, when the
centre pin and the ends of the needle are not in one vertical
plane, and the variable eccentricity, when the centre pin is eccen-
tric to the graduated circle, may be detected by the readings at
the two ends of the needle not agreeing. In both eases the
error may be corrected by reading both ends of the needle, and
by taking the mean of the two results. Cases of irregular eccen-
tricity are sometimes met with that is, when the point of
suspension of the needle in the cap is variable. Xeedles pre-
senting this error are useless.
(6.) Spirit-Levels. On the dial-plate are two small spirit-
levels, consisting of glass tubes slightly curved and nearly
THE MINER S DIAL. 81
filled with some limped liquid, a bubble of air being left. One
of the spirit-levels is parallel to the direction of the sights,
whilst the other is at right angles to it. They are so adjusted
that when the bubbles are in the centres of the tubes, the dial
is level.
Spirit-levels are usually filled with alcohol or ether. The
bubble, being specifically lighter than the liquid, always assumes
the highest possible position ; and if the tube has been ground to
a perfectly circular longitudinal section, the tangent to its inner
surface at the centre of the air bubble is a horizontal line.
(c.) The Tripod. The dial is usually supported on three legs,
shod with iron, and connected at the top in such a way that they
Fig. 10a. Fig. 106.
are movable in any direction, lightness and rigidity being the
qualities desired. Usually the legs are made with a screw-joint
32 MINE-SURVEYING.
in the middle, and a set of extra points is provided to screw on,
when the workings are low. The dial is connected with the
tripod by means of a ball and socket joint, which consists of a
ball at the end of a covered spindle fitting into a corresponding
cavity under the dial-plate. The ball turns in a socket, and can
be loosened or tightened at will. It thus admits of motion in
any direction.
In order to ensure accuracy, it is advisable in underground
surveys to use three tripods, one for the instrument and the
others for the lamp or candle. The latter is fitted in a special
holder (Fig. 10a) provided with two spirit-levels, and capable
of being levelled by a ball and socket joint and levelling screws.
One of the best forms of tripod is that made by Messrs. E. T.
Newton &, Son, of Camborne, who employ slotted legs with
thumb-screws for tightening them when any wear takes place
owing to the shrinkage of the wood under climatic influences.
For surveying over very irregular ground, these tripods (Fig.
106) are provided with sliding adjustable slotted oak legs, a
device that greatly economises time in levelling the instru-
ment.
(1.) Taking Underground Observations with the Dial. The
bearing of a line is the angle which it forms with the direction of
the magnetic-needle. To take the bearing of any line, set the
compass exactly over any point in the line by means of a plumb-
line suspended from beneath the centre of the dial ; level the
instrument, and direct the sights to an object at the other end of
the line. Then measure the line, and note the distance measured
in the dialling-book. The needle will thus have been allowed
sufficient time to come to rest. A second look along the line
may now be taken in order to test the accuracy of the observa-
tion, the eye being applied to the south sight. The number of
degrees to which the north-seeking end of the needle points is
then carefully noted. This method of taking an observation
with the north sight in advance is that generally employed. The
results are called fore-observations. Sometimes, however, it is
desirable to place the eye at the north sight, and look back in a
direction contrary to the order of the survey. Observations
taken in this way are called back-observations. The angle is read
from the north-seeking end of the needle, and entered in the
dialling-book as if it had been a fore-observation. This method
is employed in dialling a line from the centre of a shaft, where
the instrument cannot conveniently be set up. By using the
back-observation throughout a survey, taking back-observations
and fore-observations alternately, the instrument is moved only
half the number of times it would otherwise be.
THE MINER'S DIAL. 33
The lettering of the miner's dial differs in an important par
ticular from that of the mariner's compass or pocket geological
compass. When we face the north, the east point is on our right
hand, and the west on our left, and the graduated card of the
mariner's compass is marked accordingly. In the miner's dial,
however, the letters representing east and west are transposed.
The reason of this will be seen from Fig. 11.
Here the dial is represented with the east and
west points in their true position. The line of
sight in which the observation is taken lies
over the north and south line marked N S.
This is to be placed in any required direction,
and being fixed, the magnetic-needle is found
to rest, we will suppose, in the position indi-
cated by the dotted line A B, the north-
seeking end of the needle coming to rest at 24
distant from the north and south line. The
reading of this is not N. 24 W., as might at
first be supposed, but N. 24 E. The reason
is apparent on considering that the needle is
the only representative of the magnetic bear-
ing, If then a corresponding line D is drawn upon paper, the
end will represent the magnetic north. The line N S coincides
with a line in the direction of the road to be surveyed, which on
the plan will be represented by a line E F parallel to N S, and
this line of direction is clearly seen to be on the east side of the
magnetic meridian, forming with it an angle of 24
In order to prevent confusion, miner's dials are, as a rule,
graduated from right to left, the east and west points being trans-
posed. An illustration of the necessity of this change may be
afforded by imagining a watch in which the dial-plate moves from
left to right, whilst the hand remains immovable. It is evident
that the hours must count from right to left for the watch to
indicate the right time. Similarly, in the case of the miner's
dial, the magnetic-needle always points to the north, and may
consequently be compared with the fixed hand of the supposed
watch.
In some of the older patterns of miner's dial the letters are
not transposed, the east being on the right and the west on the
left. In using a dial of this kind, the letters must be mentally
reversed before the bearing is noted. The best method to adopt
for entirely avoiding all confusion is to disregard the lettering
of the dial, and read the azimuth or meridian angle, remembering
that 90 represents the east, 270 west, and 180 south.
Taking Vertical Angles. In the old type of miner's dial, the
3
34 MINE-SURVEYING,
brass cover protecting the glass fitted on in one position only.
The edge was graduated to 45 on each side of a zero-point, a
pin being fixed on the edge directly opposite that point. The
line joining the pin and the zero-point was at right angles to the
line of sight. Vertical angles were measured by turning the
instrument, by means of its ball and socket joint, until it was in
a plane at right angles to its proper position for taking horizon-
tal angles, the graduation of the cover being at its lower edge.
A plumb-line was then suspended from the pin in the upper edge
of the cover. This line coincided with the zero of the graduation
when the sights were horizontal. On turning them upwards or
downwards from that position, the number of degrees indicated
by the plumb-line was found to represent the angle of elevation
or depression.
Miner's dials are now made with a semicircular vertical arc
which may be fixed at pleasure across the central line of the
compass. It is provided with a movable limb carrying a hori-
zontal bar with a pair of sights. The semicircle is, as a rule,
divided into single degrees, marked from in the centre to 90
on the horizontal line on each side. Frequently a long spirit-
level is fastened to the bar of which
the sights are part. The sights are
directed to the object, of which the
bearing is required, and inclined the
requisite amount. The horizontal and
vertical angles can then be read.
This vertical arc is in general use
in metalliferous mines. In collieries
where the vertical angles required to
be measured are never excessive, a
side arc is usually employed. This
has the advantage of leaving the face
of the dial quite free. Fig. 12 illus- ^ig. 12.
trates the best form of side arc. In
the dial here shown the sights are carried by an outer ring
concentric with the dial. This arc was invented in 1850 by
John Hedley, H.M. Inspector of Mines.
The side arc with sights attached to it should be avoided. If
the sights are directed to the forward or back object when taking
a vertical angle, the bearing will be incorrect, as the deviation
from the true line on looking through the side-sights amounts to
half the diameter of the dial that is, the distance from the
centre of the dial to the line of sight.
Keeping the Dialling-Book. The survey is noted in the follow
ing manner :
THE MIXERS DIAL.
35
WORK AND REST MINE. ADIT LEVEL.
From perpendicular line in engine shaft 3/- W. and 2/- N. of centre.
Shaft (90) 14 by 7.
Xo.
BEARING.
DISTANCE.
OFFSETS.
REMABKS.
A
359 45'
fins. ft. ins.
12 2 6
K. L.
2/- 3/-
B
346 00'
13 4 10
3/6 2/9
C
332 21'
10 3
2/- 3/-
X. 2/6 S. 3/-
D
275 03'
502
4/- 5j-
E
254 06'
359
6/6 3/-
F
292 15'
32
4/2 6/-
G 2
184 00'
12
3/- 3/-
END Of X Cllt.
G
272 00'
16 6
3/9 3/9
H
264 06'
540
2/6 2/-
J*
K
232 00'
232 00'
359
100
2/- 2/6
2/6 2/6
Petf and nail, N. wall,
2/- N. of J.
EXD.
The above are the notes of the survey of the adit level of a
supposed metalliferous mine, the name of which was suggested
by Mr. J. Henderson, M.InstC.E., as showing the intermittent
nature of many metalliferous mines, which are so frequently
abandoned when the metal falls in price, and re-opened in
better times.
The survey is made in the adit level, and starts from a per-
pendicular line in the vertical engine shaft, which is rectangular
in section, 14 feet long by 7 feet wide. The dial is set up at A,
and a back-observation is taken to the perpendicular line, the
observer looking through the north sight of the instrument. The
bearing indicated by the north-seeking end of the needle is read
and entered as the first bearing. It will be found advisable to
write the degrees and minutes as if the latter were decimals ; in
this way any confusion between such numbers as 30' and 3 is
avoided. The length of the station-line is measured, and the
result, 1 2 fathoms 2 feet 6 inches, entered in the distance column.
The best form of book to use is an ordinary account-book, the
, s., and d. columns serving for fathoms, feet, and inches.
36 MINE-SURVEYING.
In plans of metalliferous mines, it is highly desirable to repre-
sent the variable width of the level after the ore has been
extracted, so as to clearly indicate the position of the various
courses of ore. Offsets should therefore be taken at the end
of each station-line at right angles to it. They are measured in
feet and inches, and, in order to necessitate as little writing as
possible an important matter in a wet mine may be written
in a way similar to the abbreviated mode of writing shillings
and pence.
At C the survey line leaves the cross-cut driven from the
shaft to the lode, and continues on the lode. As there is a
sharp turn at this point, offsets are measured to the north and
south, as well as to the right and left. At F a cross-cut is
driven south of the lode. The dial being set up at F, an
observation is taken to a candle at the end of the cross-cut.
The bearing is then read, and the distance, 1'2 fathoms, measured.
This line is a branch from the main survey line, and is dis-
tinguished by a small figure 2 attached to the letter that would
have been assigned to the station had it belonged to the main
line. With the dial still at F, an observation is next taken to
G, and the survey continued as before. At K, the end, or fore-
breast, is reached, and a permanent mark has to be left, from
which the survey may be continued at a future date. The mark
should not be placed at the end, where it is liable to be shattered
in the next blasting operation. The usual practice is to measure
a fathom back along the line of sight, and to insert a peg and
nail in the wall of the level, carefully noting its position for
future reference.
The offsets to the walls of the level are sometimes omitted,
the level being shown in the plan as a double coloured line.
In this case, care must be taken to keep the line of sight exactly
in the middle of the level ; otherwise an incorrect representation
of the workings will result.
(2.) Surface-Surveys with the Miner's Dial. For making the
surface-survey of a mine-royalty, the dial may be used in the
same manner as it is underground. There is, however, the
advantage that opportunities frequently occur of checking the
work during its progress by means of tie-lines.
The manner in which the results should be entered in the
field-book may be seen from the accompanying record of a survey
of a four-sided field connected with the shaft of a mine.
The measurements in this survey are made in links. The
dial was placed at A, and, when the instrument had been
carefully levelled, the sights were turned in the direction of the
shaft. An assistant having by this time placed a staff at the
THE MIXER'S DIAL.
FIELD RECORD OF SURVEY.
37
A
512
6
460
10 /
400
- _J
/ET
370
[10
250
1
V ^
130
5.
115 00'
120
100
1\
D
433
6 l
400
12 \
250
11 I
4.
130
17 /
220 00'
'
1
C
450
s I
340
17 \
260
31 \
200
35 1
3.
100
23 /
285 18'
7 I
B
496
ii i
400
\
290
35 \
24.
270
1
27 /
2.
200
27 i
30 00'
15 (
630
0A
1. Shaft to A
13 33'
016
38 MINE-SUKVEYING.
centre of the shaft, the sights were turned until the vertical
hair of the back-sight exactly cut the staff. This being a back-
observation, the observer looked through the sight at the north
end of the dial. When the needle had settled, the bearing
indicated by its north-seeking end was read, and entered as
13 33' in the field-book The distance from the shaft to A,
630 links, was then measured, and noted. The sights were
then directed to a staff held at B. This was a fore-observation,
and therefore the observer looked through the sight at the
south side of the dial, turning the instrument until the vertical
hair of the fore-sight exactly cut the staff. The needle was then
read, and the bearing, 30 00', entered in the field-book. The
distance from A to B, 496 links, was measured, and offsets
taken at the bends in the hedge along that line. The instru-
ment was then removed to 0, and a back-observation taken to
the staff still standing at B. This gave the bearing of line
No. 3, 285 18'. Line No. 4 was a fore-observation from to D.
In order to obtain the bearing of line No. 5, the instrument
was centred over the point at D, where the staff stood, and a
fore-observation taken to a staff held at the original station A.
In this way, by going round the boundaries, the outline of the
field is obtained. In extensive surveys, this would not be suffi-
cient ; a number of tie-lines would have to be measured in order
to check the survey during its progress.
In the field-book, the date of the survey should be inserted,
all the station-lines should be numbered, and the booking should
begin at the last line of the page, and be written upwards. In
this way, the notes follow the direction of the survey and offsets
to the right or left are noted on the corresponding side of the
page. All objects, whether hedges, houses, or ponds, or what-
ever offsets have been taken to, may thus be sketched in with
facility. The notes should be kept so clearly and accurately
that if necessary the survey may be plotted after the lapse of
years, without trusting to the surveyor's memory for its details.
(3.) Colliery Surveys with the Miner's Dial. In surveying a
colliery where safety-lamps are used, the surveyor must provide
himself with a safety-lamp made of copper or brass, entirely free
from iron, for reading the magnetic-needle. The method of con-
ducting the survey is essentially the same as that adopted at the
surface. Instead of the staves used in the surface- survey, lights
must of course be used as signals.
The usual method of surveying a colliery is to start from the
centre of the shaft and continue along one of the levels to the
face, thence through the workings to the other face, and finally
back to the starting point at the centre of the shaft. For all
THE M:NEM'S DIAL.
other roads that require to be surveyed, marks are left to return
to. In this way tie-lines are obtained, which are of great value in
checking the accuracy of the survey. The size and direction of
all faults must be carefully noted in the survey-book.
A colliery survey, when no offsets are taken, may be booked
in the way shown in the following example :
Station-Line.
Distance.
Chains.
Magnetic
Bearing.
Inclination,
Descending.
Shaft to A
4-58
98 25'
000'
AB
855
175 00'
9 50'
EC
1775
178 13'
11 15'
CD
7-59
256 57'
000'
DE
8-84
277 53'
0QV
EF
9-50
5 08'
r 15'
FG
14-46
8 08'
5 45'
GH
9-10
78 45'
000'
When offsets are taken, it is best to begin booking at the
bottom of the page and write upwards as in the example of a
surface-survey. Except against ribs and in main gateroads, off-
sets are seldom taken in a coal-mine, since the position of the
face has probably changed before the surveyor reaches the sur-
face. In the method of booking generally adopted, both bearings
and distances are entered in the ruled column, and the line drawn
across the page at the end of each draft, as shown in the
preceding field-record, is always omitted.
The accuracy of a closed survey made with the magnetic
needle may be tested by reducing the observed bearings to
included angles. To do this, from the fore-bearing, increased
by 180, the back-bearing is subtracted, the difference being the
included angle between the two lines. The sum of the included
angles should, with four right angles, be equal to twice as many
right angles as the polygon has sides.
40 MINE-SURVEYING.
CHAPTER IV.
THE VARIATION OF THE MAGNETIC-NEEDLE.
Definitions. A magnetic-needle when suspended finds its posi-
tion of rest in a line joining two fixed points on the horizon. At
certain places on the earth's surface, these points correspond with
the north and south points of the horizon ; but, as a rule, though
near, they do not coincide with these. A vertical plane passing
through the points on the horizon indicated by the needle, is-
called the magnetic meridian, in the same way as a similar plane
passing through the north and south poles is known as the true
meridian of the place. The angle formed by the magnetic and
true meridians is termed the declination or variation of the
needle.
A knowledge of the declination is of the utmost importance in
preparing mine plans, as this does not remain constant in the same
place, but is subject to continual, though slight, variations. These
variations are either regular or irregular. Under regular varia-
tions are included secular and diurnal variations.
(a.) Secular Variations. Observations of the amount and
direction of these variations have been made in all parts of the
world. The first observation appears to have been made in Paris
in the year 1541. The declination of the needle was at that date
easterly, and amounted to 7. In 1550 it was 8, whilst in 1580
it amounted to 11 30'. Thus, between the years 1541 and 1580
the magnetic meridian veered 4 30' further towards the east.
From 1580 the declination decreased, the magnetic meridian:
moving towards the west, until in 1666 there was no variation;
the magnetic and true meridians coinciding. Ever since that date y
the variation has been westerly, attaining its maximum of 22 in
1820, and then gradually decreasing, so that the magnetic meri-
dian is now gradually approaching the true meridian.
The magnetic history of Paris does not apply to London ;
every place, as far as has been ascertained, has a magnetic history
of its own. The following table shows the change in the position
of the magnetic-needle near London from the earliest observations
up to the present time :
THE VARIATION OP THE MAGNETIC-NEEDLE.
Date.
Declination.
Date.
Declination West.
Date.
Declination West.
1580
11 15' E
1817
24 36'
1871
20 10'
1622
6 00' E
1818
24 38'
1872
20 00'
1634
4 06' E
1819
24 36'
1873
19 58'
1657
000'
1820
24 34
1874
19 52'
1665
1 22' W
1858
21 54'
1875
19 41'
1672
2 30' W
1859
21 47'
1876
19 32'
1692
600'W
1860
21 40'
1877
19 22'
1723
14 17' W
1861
21 32'
1878
19 14'
1748
17 40' W
1862
21 23'
1879
19 06'
1773
21 09' W
1863
21 13'
1880
18 57'
1787
23 19' W
1864
21 03'
1881
18 50'
1795
23 57' W
1865
20 59'
1882
18 45'
1802
24 08' W
1866
20 51'
1883
18 40'
1805
24 OS' W
1867
20 40'
1884
18 32'
1806
24 15' W
1868
20 33'
1885
18 25'
1809
24 22' W
1869
20 26'
1886
18 17'
1812
24 28' W
1870
20 19'
1887
18 10'
From this table it appears that the magnetic-needle has required
300 years (1580-1880) to move an arc of 11 15' + 24 38' +
(24 38' - 18 58') = 41 33'. The average annual movement is
consequently 8'. The figures given in the table from 1858 are
the mean values of the magnetic declination as determined at the
Kew Observatory.
At Newcastle and Swansea the declination is about 1 45'
greater than at London ; afc Liverpool 2, at Edinburgh 3, and at
Glasgow and Dublin about 3 50' greater. At Yarmouth and
Dover the declination is about 40' less than at London.
The mean value of the magnetic declination for any particular
place in Great Britain, at which no magnetic observations are
made, can generally only be inferred from the map prepared in
42 MIXE-SURVEYING.
1872 by Sir F. J. Evans, Hydrographer to the Admiralty. This
is given in the Philosophical Transactions, 1872, vol. 162. Allow-
ance must be made for the change which has since occurred.
Values found in this way are approximations only.
In certain parts of the earth, the magnetic and true meridians
coincide. The irregularly curved imaginary line joining the
points where there is no declination is called the agonic line.
Such a line cuts the east of South America, and, passing east of
the West Indies, crosses the United States, passing just east of
Charleston, South Carolina, and just west of Detroit, Michigan.
It then passes through the North Pole, crosses Lapland to the
Caspian, cuts the east of Arabia, and passes through Western
Australia to the South Pole.
Isogonic lines are imaginary lines joining the places on the
earth's surface whose declinations are equal at any given time.
Maps on which such isogonic lines are shown are called declina-
tion maps, and a comparison of these in various years shows the
variation to which the declination is subject.
The great variation in the declination shows the necessity of
recording the date and declination of the needle on all mine-
plans, with a note stating whether the bearings given were
magnetic bearings, or were reduced to the angles, which the lines
would form with the true meridian.
The antiquity of the workings on an old undated plan may be
approximately ascertained from the meridian line shown on it.
Thus, if a plan is found to be constructed to a meridian with a
declination of 24 west, it is reasonable to suppose that it was
drawn about the year 1800, for, according to the table, the
declination in 1802 was 24 6' west.
(b). Diurnal Variation. On observing a magnetic-needle
throughout an entire day, it will be found that the variation
does not remain constant, but changes more, and in a different
way, than is demanded by the secular change. Observations at
London show that at about 8 a.m. the needle reaches its furthest
point east, and that at 1 p.m. it shows the greatest westerly
deviation from the mean magnetic meridian. The declination
then decreases until 10 p.m., when it remains stationary until
4 a.m. It then decreases again until 8 a.m., by which time it
has again reached its furthest point east. The needle stands at
its mean position a little after 10 a.m., and a little before 7 p.m.
The diurnal changes are much the same over the whole of the
northern hemisphere, though the amount differs.
The following table shows the diurnal variation for London
(Kew), Trevandrum, in Madras, and Hobart Town, in Tasmania.
Of these places, the first is a station in middle latitude (northern
DIURNAL VARIATION.
HOUR.
LONDON.
TBEVANDRUM. HOBART Tows.
Minutes.
Minutes.
Minutes.
12 a.m.
-5-13
-0-61
+ 1-35
1 p.m.
-6-19
-0-45
+ 3-50
2 p.m.
-5-81
-0-15
+ 4-55
3 p.m.
-4-28
+ 0-13
+ 440
4 p.m.
-2-60
+ 0-28
+ 3-35
5 p.m.
-1-26
+ 0-24
+ 2-00
G p.m.
-0-39
+ 0-13
+ 1-15
7 p.m.
+ 0-22
+ 0-04
+ 0-50
8 p.m.
+ 0-68
-0-05
+0-00
9 p.m.
+ 0-99
-0-08
-0-55
10 p.m.
+ 1-24
-0-06
-0-90
11 p.m.
+ 1-37
+0-01
-1-00
12 p.m.
+ 1-43
+ 0-09
-0-95
1 a.m.
+ 1-29
+0-13
-0-75
2 a.m.
+ 1-39
+ 0-15
-0-55
3 a.m.
+ 1-51
+0-09
-0-40
4 a.m.
+ 1-88
+ 0-02
-0-40
5 a.m.
+ 2-51
+0-01
-0-75
6a.m.
+ 3-07
+ 0-18
-1-30
7 a.m.
+ 3-58
+ 0-32
-2-15
8 a.m.
+3-80
+ 0-24
-3-25
9a.m.
+ 2-95
+ 0-06
-3-70
10 a.m.
+ 0-46
-0-22
-3-00
11 a.m.
-2-68
-0-50
-1-15
In this table deflections towards the magnetic east are reckoned positive,
deflections towards magnetic west negative.
44 MIXE-SURVEYING.
hemisphere), the second is an equatorial station, and the third a
station in middle latitude (southern hemisphere).
The diurnal variations are found to vary with the seasons of
the year. They are much greater in summer than in winter.
The cause of the variations is frequently ascribed to the influence
of sunlight. Other influences appear to be at work, as is shown
by the fact that the variations of the declination of a magnetic-
needle at a place on the earth's surface coincide with the varia-
tions observed simultaneously underground. This was found by
Professor Borchers to be the case at Clausthal, in the Harz, where
a magnetic observatory was erected at the Eleonore mine, 1,788
feet below the surface. Similar results were obtained at a mag-
netic observatory established, at a depth of 3,280 feet below the
surface, in the deepest mine in the world, at Przibram in Bohemia.
The slightest movements of the magnetic-needle observed at the
earth's surface occur at the same time and to the same extent
even at the greatest depths to which mining is able to penetrate.
Irregular Variations. The magnetic-needle is subject to violent
and irregular disturbances, which are sometimes considerable,
amounting in extreme cases to 1 or 2 degrees. These irregular
disturbances or magnetic storms appear to be coincident with the
appearance of the aurora borealis, earthquakes, and volcanic
eruptions. The cause of these storms has not yet been deter-
mined. Sabine, however, found that they are most frequent every
eleven years when the spots on the sun are most numerous.
Experience shows that places of the same longitude have similar
disturbances at the same time, that those on opposite sides of
the globe differing by 180 of longitude, have disturbances equal
in amount but opposite in direction, and that places situated 90
west or east of the disturbed regions have practically no dis-
turbance. Atmospheric storms have no effect on the needle.
Notices of the occurrence of magnetic storms are published by
the Superintendent of the Magnetic Department at Greenwich
in the mining journals, and deserve the careful attention of mine-
surveyors.
Determination of the True Meridian. In order to find out the
extent of the declination of a magnetic-needle, it is necessary to
determine the true meridian. For this purpose various methods
are employed.
1. Method of Shadows. This method is based on the fact that,
at equal distances of its passage across the meridian, the sun is at
equal altitudes above the horizon. Consequently at these times
it gives shadows of equal lengths.
A staff is planted vertically in the ground, and the ends of its
shadows are joined when they are of equal length. On joining
THE VARIATION OP THE MAGNETIC-NEEDLE.
45
these points to the projection of the axis of the staff, an angle is
obtained, the bisectrix of which is the true meridian. The obser-
vation may be made more accurately by describing a number of
concentric circles (Fig. 13) with the foot of the staff as centre,
Fig. 13.
and marking the points, a, b, c, d, d', c', b', a', where each of
them is touched by the shadow. The arcs thus obtained are
bisected, and the points of bisection are joined to the centre of
the circle. The line m m thus obtained is the meridian. This
method, though a fair approximation, is absolutely correct only
at the time of the solstices (June 21, December 22). It is the
oldest method known ; it was used by the early Christians for
determining the east for their churches.
The method is considerably improved by placing a thin metal
plate provided with a small aperture, at the top of the staff. The
latter is inclined so that the aperture is
perpendicularly above the centre of the
concentric circles. In the shadow of the
metal plate, a bright spot appears, the
centre of which can be found with con-
siderable accuracy. This method has been
used on a large scale by placing perforated
metal plates in the roofs of high buildings,
a notable example being in the dome of
the cathedral at Florence (1467, A.D.)
The shadow method may be applied on
a small scale by employing a vertical pin
placed in the centre of a number of concentric circles on a drawing-
board. A more con venieiit apparatus may be made of a brass rod
about 7 inches in length, provided at its lower end with a screw
and at the top with a very thin plate of brass about 2 inches
Fig. 14.
46 MIXE-SURVEYING.
long and 1| inch broad, so arranged that it forms with the pin an
angle of about 120. In the middle of the plate a fine hole is
drilled. The pin being screwed into a board, half an inch square,
near the edge, a portable instrument, Fig. 14, termed a gnomon,
is formed. This can be placed on a table or drawing-board in the
open air, and used in the manner described.
2. Method of Corresponding Altitudes. If a good theodolite
(see Chapter "VIII.) is available, the meridian of a place may be
determined in the following manner : The theodolite, after
careful adjustment, is set up at the point, the meridian of which
is to be determined, a station commanding a free view being
selected. Vernier I. of the theodolite is then brought to zero,
and the position of vernier II. observed. The limb is then
turned horizontally, and the telescope moved vertically until it is
brought to bear upon a fixed star of the first or second magnitude
several hours before its culmination. As soon as the star passes
the cross-wires of the telescope, the latter is clamped, and both
the horizontal and vertical circles of the instrument are read.
The telescope is then allowed to remain with its inclination
unchanged, and after a time the star will not be visible through
it. After its culmination, the star will, in the course of time,
have the same altitude that it had at the first reading. The
star is followed with the telescope, and at the instant it crosses
the wires of the latter, the horizontal circle is read a second time.
Assuming that at the second reading the telescope had the
same inclination that it had during the first reading, the direc-
tion of the meridian will be represented by half the sum of the
two readings on the horizontal circle. The limb being turned
horizontally until vernier I. gives the calculated angle, the axis
of the telescope will give the direction of the meridian. The
method is based upon the fact that a star at equal altitudes
above the horizon of a place is equally distant from the plane of
its meridian.
It is evident that the accuracy of the result depends upon the
perfection of the instrument employed. The best results are
always obtained by observing the star at various altitudes before
and after its culmination, and by reading the horizontal circle
each time with the telescope clamped at the corresponding
altitude. Both verniers should always be read, and the arith-
metical mean of the readings taken if they are not identical.
The direction of the meridian is thus obtained repeatedly, and
if there is no error, the result will be the same with each inclina-
tion of the telescope. If the results differ slightly from one
another, the mean must be taken ; with larger differences, the
observations must be repeated. As a check, the observations
THE VARIATION OF THE MAGNETIC-NEEDLE. 47
should be repeated on the following night with the telescope
inverted. The result should not differ from that obtained on the
previous night. If there is a slight difference, the mean of the
results of the observations on the two nights will give the direc-
tion of the meridian.
As an example of this method of determining the meridian,
some of the observations may be given which were made for
fixing the meridian for the magnetic observatory belonging to
the Clausthal mines. The determination was effected with an.
8-inch theodolite. The instrument was set up on a stone foun-
dation, and accurately levelled. The vernier I. was brought to
zero, and the position of vernier II. noted. With the upper
plate clamped in this way, the telescope v/as brought to bear on
a signal on the top of the tower of Clausthal Church. The
following observations were then made with the stars 13 and y
Yirginis :
ALTITUDE OP THE STAB.
READINGS ON THE HORIZONTAL CIRCLE
CALCULATED FROM THE POSITION
OP THE Two VERNIERS.
ANGLE FORMED BY THE
MERIDIAN AND TUB
DIRECTION OP
CLAUSTHAL CHURCH
Before the
Culmination.
After the
Culmination.
/3 Virginia)
18 20'
56 15' 37"
196 22' 05"
126 18' 51"
19 40'
58 15' 12"
194 22' 45"
126 18' 58*
21 00'
60 18' 52"
192 18' 50"
12G 18' 51"
21 40'
61 21' 42"
191 15' 20"
126 18' 31"
22 20'
62 25' 57"
190 11' 45"
126 18' 51"
(y Virginia)
15 20'
57 40' 32"
194 57' 25"
126 18' 58"
16 40'
59 40' 02"
192 57' 55"
126 18' 59"
17 20'
60 41' 47"
191 56' 15"
126 19' 01"
18 00'
61 43' 57"
190 53' 55"
126 18' 56"
18 40'
62 47' 07"
189 50' 05"
126 IS' 36"
48 MINE-SURVEYING.
The zero of the horizontal circle represented the direction of
Clausthal Church. The arithmetical mean of the results shows
that the meridian formed an angle of 126 18' 51" with the
direction of Clausthal Church. Observations made the next
night gave exactly the same results. The same number of obser-
vations were made on the two following nights with the telescope
inverted. The mean of all the results obtained during the four
nights gave 126 18' 49". It must be noted that in these obser-
vations the stars employed were not first sighted and the angle
of altitude then read. The vertical circle was clamped at a given
division, and the star then brought on to the vertical wire of the
telescope, and followed by means of the tangent screw of the
upper plate until it also passed the horizontal wire.
If the theodolite is set up on a fixed point, and if the terres-
trial object, the azimuth of which is determined, is also a secure
point, a further marking-out of the meridian is not absolutely
necessary. In the preceding case, however, it was thought
advisable to mark out the meridian by means of a large square
stone buried in the earth on a mountain in the vicinity. A hole
drilled in the surface of this accurately in the meridian served
for the reception of a signal staff.
The meridian may be determined during the daytime by
sighting the upper edge of the sun before and after mid-day, a
dark glass being placed before the objective of the telescope. A
correction has, however, to be made on account of the obliquity
of the ecliptic a correction that is not taken into account in the
shadow method. This method of determining the meridian is
not to be recommended, as the astronomical almanacks required
for making the correction are not always available. The cross-
wires, too, may be directed to a star with far greater precision
than to the sun.
3. Determination of the Meridian by Means of the Pole-Star.
Of the bright stars of the northern heavens, the nearest to the
pole is the first star in the tail of the Little Bear, or the Pole-
star (a Ursse Minoris). It is a star of the second magnitude, and
may easily be found by imagining a straight line to be drawn
through the stars /3 and a of the Great Bear, and continued for
about five times the distance from /3 to a, counting from a.
These two stars are known as the pointers.
The meridian may be determined by observing the pole-star
either when it is in the meridian, or when it is at its ex-
treme elongation. The pole-star is not situated exactly at
the north pole of the heavens, but is now about 1 15' from it.
Twice in each sidereal day (23 hours 56 minutes) It is in the
meridian.
THE VARIATION OP THE MAGNETIC-NEEDLE. 49
A very simple method of determining the meridian of a place
consists in sighting the pole-star, marked A in Fig. 15, when it
appears in the same vertical line with the star
Alioth in the Great Bear (t Ursa? Majoris). *
This may be done by watching for the moment,
when a suspended plumb-line will cover both
stars. They will then be approximately in the
meridian. The pole-star is exactly in the % a
meridian about 29 minutes after it has been j ^
in the same vertical plane as Alioth. In the ^ #
southern hemisphere a similar process may be ^ * y
applied to the stars a Crucis and j3 Hydri. %
The meridian may also be determined by ob- ' _. ._
serving the pole-star at its extreme elongation,
that is, when it is at its greatest apparent angular distance east
or west of the pole. At this instant, the horizontal projection of
the apparent movement of the star alters its direction, and the
motion of the star appears to cease for a short time. The greatest
and least horizontal angles made by the pole-star with any given
line when the star is at the greatest distances east and west of
the pole, are observed and the mean of the angles taken. This
will be the angle made by the given line with the meridian.
This method is rarely practicable with an ordinary theodolite, as
one of the obsei'vations must generally be made by daylight.
4. Determination of the Meridian by means of a Map. For
an approximative determination of" the meridian, a large-scale
map may be employed. The direction of the meridian is
shown by joining the degrees of longitude marked at the top
and bottom of the map. The angle formed by the meridian
and some line easy to determine on the ground, is measured on
the map. With the aid of this line, the angle is marked off
on the ground. The approximation thus obtained is at most 15
minutes.
Setting-out the Meridian Line. In every mining district it is
very desirable that all difficulty in ascertaining the true meridian
should be at once removed by the erection of two conspicuous
objects placed exactly on a meridian line, to remain for per-
manent reference. T. Sopwith, writing in 1822, urged that it
would be a work of enormous advantage to the prosperity of
mining districts to have meridian lines carefully set-out at
distances of 1 mile from each other, and tall posts placed on
these meridian lines at every mile in length, the undulating sur-
face of the country being truly reduced to a horizontal base,
so that these posts or stations should indicate squares of exactly
1 square mile.
50 MINE-SURVEYING.
The best method of permanently marking out the meridian is
to insert, to a depth of 3 to 5 feet in the ground, a hard stone,
6 to 8 feet long and 2 feet square. The portion of the stone pro-
jecting from the ground is faced, and the top plane is made at
right angles to the axis. To avoid as much as possible the action
of frost, it is advisable to give the stone a good foundation and
to fix it in cement. On the top of the stone a brass plate, a foot
square, is fastened, so that it is exactly horizontal, and on this
the direction of the meridian line is shown by a fine engraved
line.
When the direction of the meridian is to be shown by two
stones a distance apart, points must be marked on them exactly
in the meridian. For this purpose, it is best to drill holes into
which staves can be inserted
For practical purposes, a simple method of ascertaining the
annual variation is to take the bearing of some remote permanent
object, such as a church steeple, from a fixed point. The
bearing of this so-called line of orientation is recorded from
year to year, the difference in the readings giving the annual
variation.
This line is also of great value if several dials are used in the
same mine. In consequence of small errors in the construction
of the instruments, the bearing of one and the same line is
found to vary when determined with different dials. By
observing the line of orientation, the error of each dial may
be determined, and applied as a constant correction to all
subsequent readings.
Inclination of the Magnetic-Needle. If a magnetic-needle is
free to move vertically, it does not, at most places on the earth's
surface, rest in a horizontal position, but inclines more or less
from it. The angle between the needle and the horizontal line
is called the dip or inclination of the needle, provided that the
vertical plane in which the needle moves is the magnetic meri-
dian of the place. The dip varies at different places; at the
magnetic equator there is no dip, whilst at the magnetic poles
the needle stands vertically.
The dip is not of great importance to mine-surveyors in Britain,
as the needles of dials are carefully compensated when sold.
Surveyors going abroad with an English dial should be provided
with a small sliding balance for the needle, which may be
adjusted when necessary, should the dip prove at all trouble-
some.
Like the magnetic declination, the dip is subject to secular
variations. The following are results of observations near Lon-
don extending over a series of years :
THE VARIATION OF THE MAGNETIC-NEEDLE.
r.i
Tear.
Inclination.
Tear.
Inclination.
1576
71 50'
18SO
67 35'
1600
72 00'
1881
67 34.
1720
74 42'
1882
67 34'
1800
70 35'
1883
67 31'
1830
69 38'
1884
67 30'
1850
68 48'
1885
67 27'
1865
68 09'
1886
67 27'
The following are the values of the magnetic elements observed
at Greenwich during recent years :
Tear.
Mean declination.
Mean inclination.
1881
18 27-1'
67 34-6'
1882
18 22-3'
67 34-1'
1883
18 15-0'
67 31 -6'
1884
18 8-0'
67 30-0'
1885
18 IT
67 27-8'
1886
17 54-5'
67 27-0'
1887
17 49 !'
67 26 -4'
1888
17 40-4'
67 25-4'
1889
17 34-9'
67 24-9'
1890
17 28-6'
67 22-9'
1891
17 23-4'
67 21 -4'
52
MINE-SURVEYING.
CHAPTER V.
SURVEYING WITH THE MAGNETIC-NEEDLE IN THE
PRESENCE OF IRON.
Influence of Iron Rails. The method of surveying described in
the preceding chapter cannot be used in mines where magnetic
substances deflect the needle. On account of the increasing use
of iron and steel in mines in the form of rails, props, &c., the
number of mines in which the magnetic-needle is not affected is
extremely small.
Rails placed end to end on the ground become, in the course
of time, permanently magnetised, and if a magnetic-needle is
brought near the junction of two rails, it assumes a position
parallel to the two rails. Some interesting experiments to
determine the influence of iron rails on the magnetic-needle were
made by Professor Combes of the Paris School of Mines. He
found that the nearer the direction of the rails approached that
of the magnetic meridian the more highly polarised they became.
The following deflections were observed when a miner's compass
was brought near rails which were placed in the direction of the
magnetic meridian :
Distance from tbe Bails.
Height above
the Kails.
Azimuth Observed.
Inches.
19 ft. 8 ins. on one side,
58
80 00'
5 ft. 3 ins. on one side,
47
83 30'
Above the first rail, .
43
83 15'
Between the two rails,
43
83 30'
Above the second rail,
43
83 45'
6 ft. 6 ins. on the other side,
43
83 30'
SURVEYING WITH THE MAGNETIC-NEEDLE. 53
With the rails placed at right angles to the magnetic meridian,
the following angles were obtained :
13 feet 1 inch on one side, .... 329 45'
Above the first rail, 328 00'
Between the two rails, 330 00'
1 foot 10 inches on the other side, . . 328 30'
"When the compass was only 15 inches above the rails, devia-
tions amounting to 7 30' were observed.
Experiments made at Freiberg, in Saxony, by Professor Junge
confirm these results, and permit the following conclusions to be
drawn :
1. Iron rails identical as regards weight and dimensions may
act differently on the compass, the deviation caused by one being
sometimes double that by another. The influence of two parallel
rails on the magnetic-needle cannot be neutralised. It is not
sufficient, as so many miners imagine, to place the dial exactly
midway between the two rails.
2. The influence of the rails on the needle is increased by
sharp blows. Four blows on a rail with, a hammer was found to
increase by 2 the deviation produced.
3. The influence of the rails is greatest when they form an
angle of 45 to 67 30' with the meridian. The deviation then
decreases until the rail is at right angles with the meridian, when
the deviation is intermediate between the maximum and that
observed when the rails make an angle of 22 30' with the
meridian.
4. The influence is very considerable when the compass is as
much as 47 inches above the rails. In such a case with rails at
an angle of 45 with the meridian, deviations amounting to 3 25'
have been observed.
No experiments appear to have been made with iron or steel
sleepers. There can, however, be no doubt that their influence
on the magnetic-needle is at least as considerable as that of iron
rails.
The only practical conclusion that can be drawn from the
results obtained by Professors Combes and Junge, is that an
accurate survey cannot be made with the miner's dial in the
manner described in the preceding chapter, unless the rails are
taken up.
Local Attraction in the Mine. In many metalliferous mines,
local attraction, due to the presence of magnetic iron ore in the
lode, is very considerable. At Botallack mine, in Cornwall, for
54 MINE-SURVEYING.
example, the needle has been known to be deflected to the
extent of 60 from its proper bearing. Experience shows that
certain eruptive rocks, notably those of a dark colour with a base
of hornblende or augite, affect the needle in the same way as
magnetite or magnetic pyrites. In districts composed of magnetic
rocks, the dial cannot be employed, as is shown by observations
made at Ammeberg in Sweden, where at equidistant points
along a straight line, the following bearings were obtained :
3 5f', 3 4', 3 2', 3 1', 2 7f ', and 2 6'. To make a number
of observations along a straight line is the best method of
finding out if there is any local attraction affecting the needle.
The influence of magnetic deposits on the compass has been
utilised in Sweden and the United States in exploring for
iron ore.
Surveying with the Dial in the presence of Iron. With the
general employment of iron rails in mines, the question arises to
what extent may surveys be made with the ordinary dial with-
out fear of deflections of the needle giving rise to error 1 As a
matter of fact, the magnetic-needle may be used for the purpose
of obtaining the true bearings of the traverse lines in places
where attraction exists, provided that the mode of procedure is
slightly modified. The method is based upon the fact that the
deviation of a magnetic-needle remains the same, if the relative
positions of the dial and the attracting object remain unaltered.
All that is necessary is to note the back- and fore-bearing
at each station, however much the magnetic-needle may be
deflected. Then, if the needle is attracted on looking to the
back object, it is attracted to precisely the same extent on
looking forward, so that the difference of bearing of the two
lines is unaltered. Consequently, if a correct bearing of any
one line of the traverse can be obtained, an accurate survey may
be made.
Dialling-Book. The best form of dialling-book to adopt is an
ordinary account-book, the , s., and d. columns serving for
fathoms, feet, and inches. If the measurements are made in
links, only one column is required. The date column of the
account-book serves for the number of the draft. In the space
between the date and money columns, two lines are ruled, giving
three columns, which may be used for the back-bearing, the fore-
bearing, and the calculated true bearing.
The method of booking a survey is shown by the following
example of a closed traverse, surveyed in the presence of a
very large amount of iron. The bearings and distances were as
follows :
SURVEYING WITH THE MAGNETIC-NEEDLE.
No.
Back-Bearing.
Fore-Bearing.
Correct Bearing.
Fm,
Ft.
!,
A
...
3 36'
3 36'
6
4
1
B
3 36'
136'
136'
3
4
104
C
5 27'
327 44'
323 53'
5
3
54
D
319 15'
224 53'
229 31'
6
1
74
E
202 57'
156 44'
183 18'
6
I*
F
167 48'
165 03'
180 33'
4
1
8
G
166 15'
79 48'
94 06'
8
3
H
79 34'
349 04
3 36'
...
...
The instrument was set up at B, where there was no attraction,
and a back-bearing was taken. This was found to be 3 36'.
This bearing being correct, it was also entered as a fore-bearing
at A. A fore-bearing was then taken at B ; this was found to
be 1 36'. This also is correct, as there was no attraction when
the back-bearing was taken, and the dial was not moved to take
the fore-bearing. The instrument was then moved to C, and a
back-bearing to B taken. This should have read 1 36', the
correct fore-bearing from B to 0. It was, however, found to be
5 27', showing that the needle was considerably deflected from
its true position. Back- and fore-bearings were taken at each of
the following stations, and in each case the needle was found to
be seriously deflected. Consequently, before the survey could be
plotted, the correct bearings had to be calculated.
The bearings 3 36' and 1 36', being known to be correct,
might be inserted in the correct-bearing column. The back-
bearing at was found to be 5 27' instead of 1 36'. It was
therefore 3 51' too great, and as the dial was not moved, the
attraction remained the same, so that the fore-bearing at was
also 3 51' too large. The correct fore-bearing at 0, then, was
327 44' - 3 51' = 323 53'. The back-bearing at D, which
should be the same as this, was found to be 319 15', that is,
4 38' too small. The fore-bearing taken at the same station
under the influence of the same attraction must also have been
4 38' too small, so that its correct value is 224 53' + 4 38' =
229 31'. The back-bearing at E should be identical with this.
It was, however, found to be 202 57', that is, 26 34' too small.
The fore-bearing at the same station must also be 26 34' too
56
MINE-SURVEYING.
small. Its correct value, then, is 156 44' + 26 = 34' = 183 18'.
This should be identical with the back-bearing at F, which was
found to be 167 48', or 15 30' too small. The fore-bearing at
F is also 15 30' too small, and its correct value is 165 03' +
15 30' = 180 33'. This should be identical with the back-
bearing at G, which was found to be 166 15', or 14 18' too
small. The fore-bearing is also 14 18' too small, and therefore
the correct bearing is 79 48' + 14 18' = 94 06'. This should
be identical with the bearing at the last station, which was found
to be 79 34', or 14 32' too small. The fore-bearing at the same
station is also 14 32' too small, and therefore its correct value
is 349 04' + 14 32' - 363 36', that is, 3 36'. The last line of
this traverse is identical with the first, so that the first and
last bearings should be identical. Thus, in a closed traverse the
surveyor is able to check the accuracy of his work.
The following page from the dialling-book at a metalliferous
mine may be taken as an example for calculation :
No.
Back-Bearing.
Fore-Bearing.
True Bearing.
Fms.
Ft.
Ins.
A
245 12'
245 12'
9
3
6
B
245 12'
254 30'
254 30'
8
5
6
C
254 30'
164 45'
164 45'
9
5
8
D
164 06'
169 24'
170 03'
4
9
E
178 12'
161 00'
152 51'
5
8
F
157 45'
174 00'
169 06'
4
1
G
171 27'
186 42'
184 21'
4
4
6
H
183 39'
178 18'
179 00'
5
4
9
J
177 33'
221 00'
222 27'
8
2
7
K
221 00'
79 18'
80 45'
1
5
7
L
89 33'
80 00'
71 12'
2
1
5
M
71 12'
82 48'
82 48'
5
3
K
82 48'
84 24'
84 24'
3
5
1
o
84 24'
90 06'
90 05'
7
5
o
p
90 06'
91 30'
91 30'
5
3
SURVEYING WITH THE MAGNETIC-NEEDLE. 57
If the first and last bearings are not identical, and if the
difference does not amount to more than a few minutes, the
slight error, due possibly to the imperfections of the instrument
employed, may be to a great extent eliminated by dividing the
error by the number of station-lines, and adding the result to, or
subtracting it from, each bearing. Thus, in the example given,
if the observed fore-bearing at H had been 349 00' instead of
349 04', the final error would have been 4'. It would be
assumed that no error occurred in reading the first bearing.
The error in each bearing would consequently be about ^', and
the calculated bearings could have been corrected for this error by
adding |' in each case, that is to say, J' to the calculated bearing
of B, 1' to that of C, 14' to D, 2' to E, 24' to F, 3' to G, and 4'
toH.
In applying this method to colliery and surface-surveys, it
will be found advisable to book upwards in the usual manner,
noting the back-observation (B.O.) at each station. A tabulated
statement of the bearings may then be made, and the true
bearings calculated.
Errors in Compass Surveys. In all cases where the dial is
used for surveying in the presence of iron, the greatest care
must be taken in making the observations; otherwise very
serious errors may arise, especially in long traverses. This may
be illustrated by an example.
In making a survey in the ordinary way with the dial, any
error in the readings will cause the next draft to have a false
position when plotted. Assuming that a survey is made between
the points A and E, Fig. 16, and that the bearings are read
direct from the dial without
error, the plan of the traverse
will be cocrect, as shown by the
line A B C D E in the figure. If,
on the other hand, a mistake is
made during the progress of the
survey, and the bearing, NAB,
of the line A B incorrectly deter-
mined to the extent of the angle
jg. BAB' or a, then the following
drafts will have the same error.
B' will be the end point of the first draft when plotted, thus
giving a lateral error of B B'. The other bearings of the traverse
being correctly determined, on plotting, the lines B' C', C' D',
D' E' will be obtained. These lines must be equal and parallel
to the lines B C, CD, D E, and therefore B B' = C C' = D D'
= E E'. In other words, the lateral error B B' caused by the
58 MINE-SURVEYING.
incorrect determination of the bearing of the line A B is carried
uniformly throughout the traverse, whatever its length may be.
The magnitude of this error is found by trigonometry to be
SAB. sin |.
The magnitude of the error is entirely different when the dial
is used as an angle-measurer in surveying over iron. Again,
assuming that the bearing of the line AB has been incorrectly
determined to the extent of the angle a, the angle NAB' having
been read instead of the angle NAB, if now the dial is
employed for measuring the angles, the bearing of the next line,
B C, is obtained by adding or subtracting the exterior angle at
B, according as the line B C is to the right or left of A B. The
other bearings in the presence of iron may be assumed to have
been correctly taken. The bearing of the line AB being
incorrect, the bearing of the line B C will also be incorrect to
the extent of the angle a. Each of the following bearings will
be incorrect to the extent of the same angle, so that on plotting
the calculated bearings, the line A B' C" D" E" will be obtained.
The error a thus affects the whole traverse from A to E, and
increases in proportion to the distance apart of those points.
The length from A to E being represented by L, the lateral
error, E E" is equal to 2 L sin ^.
It is thus evident that a survey may be very inaccurate, when
the angles are not correctly measured. In applying the method
of surveying with the needle over iron, the surveyor should not
fail to make a check-survey, or reverse course of dialling, selecting
fresh points for his stations. Not only in this method, but in
all other surveying operations, it is highly desirable that the
mine-surveyor should adopt the practice of always checking and
verifying every part of his work.
SURVEYING WITH THE FIXED NEEDLE. 59
CHAPTER VL
SURVEYING WITH THE FIXED NEEDLE.
Vernier. In the improved forms of the miner's dial, the com-
pass-box is connected with the plate that carries it, in such a way
that it can revolve on this plate. Motion is given to it by
a circular rack and pinion worked from below. Modified in this
way, the instrument is known as the circumfer enter, or rack-
dial. When the rack-screw is turned, two marks, made opposite
to each other, one on the projecting portion of the compass-box,
and the other on the plate, will separate. Their angular distance
apart is measured by means of a vernier, which may be defined
as a contrivance for measuring smaller portions of space than
those into which a line is actually divided.
The principle of the vernier is as follows: If a line containing
n units of measurement is divided into n equal parts, each part
will represent one unit ; and if a line containing n - 1 of these
units is divided into n parts, each part will be equal to
units. The difference between one division in the former case, and
n 1 1
one in the latter will be 1 = of the original unit.
n n
Similarly, the difference between two divisions of the one, and
o
two divisions of the other, will be of a unit : between three of
n
3
the one, and three of the other, -, and so on. Hence, in order
to obtain a length of of a unit, a division of one scale has to be
made to coincide with one on the other scale, and the space
between the two corresponding arth divisions from the coinciding
divisions, on both scales will be the required length of - of a
unit.
The same reasoning applies if n divisions of the vernier are
made equal to n + 1 divisions of the limb. In this case, how-
Dl> MINE-SURVEYING.
ever, the vernier must be read backwards. There are thus two
kinds of vernier, called direct or retrograde, according as they
are read forwards or backwards from the zero points. Most
verniers in surveying instruments are of the direct type. In all
cases, the zero of the vernier scale marks the point on the limb,
the reading of which is required.
The difference between a limb division and a vernier division
is - of the value of a limb division. This difference is known
n
as the least reading of the vernier, and expresses the degree of
minuteness to which readings can be effected.
The circle divided to 30' is a common graduation for the
miner's dial. If 30 divisions on the vernier are made equal to
29 on the circle, each division on the vernier will be equal to
rm x 30
- o?r~ = 29', or 1' less than a division on the circle. The
vernier will therefore read to an accuracy of one minute.
As an example of more minute division, the sextant used in
marine-surveying may be cited. The limb of this instrument is
divided at every 10 minutes, and 59 of these parts are made
equal to 60 divisions on the vernier. The least reading in this
. n 10 1A/ ,
CaSeiS 60 = 60= 10 '
The rule for reading an instrument provided with a vernier is
as follows : Read the circle, in the direction of the graduation,
up to the line preceding the zero of the vernier. This gives the
number of whole units of the circle. The line on the vernier
coinciding with a line on the circle gives the number of fractional
parts of one unit of the circle to be added to the former
reading.
Racking. Provided with a vernier, the compass may be used
to measure angles in a horizontal plane, or azimuths, without the
aid of the magnetic-needle. This method of surveying is known
as fast-needle dialling or racking.
The word azimuth used without qualification, usually means
the number of degrees, minutes, and seconds by which the direc-
tion of a vertical plane passing through a station and a given
object deviates to the right of a vertical plane passing through
the station and the north pole. The relative azimuth of any two
objects may be measured at any given station; that is to say, the
angle by which a vertical plane passing through the station and
one of the objects deviates to the right of a vertical plane passing
through the station and the other object. An azimuth exceeding
180 denotes that the direction of the object to which it is
SURVEYING WITH THE FIXED NEEDLE.
Gl
Fig. 17.
measured lies to the left of the direction from which azimuths
are measured, by an angle equal to the difference between the
azimuth and 360.
The horizontal angle between any two directions is the
difference of their azimuths, if the
difference is less than 180. If
it is greater than 180, the angle
between the directions is the ex-
cess of 360 above the differ-
ence of the azimuths. Thus,
in Fig. 17, the dial being set
up at A, and A B having the
azimuth of 0, the azimuth of C,
an object to the right of A B, is
equal to the angle BAG. On the
other hand, the azimuth of D, an
object to the left of A B, is the
angle subtended by the arc b' d,
that is, the difference between the angle BAD and 360.
Various Forms of Dial : (a.) Lean's Miner's Dial. There are a
great number of different types of mining circumferenters adapted
for surveying without the use of the needle. They differ merely
in details of structure ; the essential parts are the same in all.
Fig. 18 represents Lean's dial, as manufactured by Mr. W. F.
Stanley of London. This form of dial is that most frequently
used in metalliferous mines. Like the. ordi-
nary miner's dial, it consists of a brass com-
pass-box attached to a tripod-stand by a socket
fitting on to a corresponding plug. In addi-
tion to the levels, sights, and magnetic-needle
of the ordinary dial, it has, above the main
plate, a divided vernier plate by which hori-
zontal angles may be measured indepen-
dently of the needle. The same graduation
thus serves for the vernier and for the needle.
The movement of the circle is effected by a
concealed rack and pinion, the head of which
projects from the under side of the main
compass-plate. The instrument is provided
with a vertical arc for measuring vertical
angles, and a telescope so that the instrument
may be used as a theodolite for surface-surveys. The vertical
arc and the telescope may be removed, and the sights used. The
latter are made to ibid down for convenience in packing. Under-
neath the compass-box is a pin to fasten the two plates together
Fig. 18.
62
MIXE-SURVEYIXG.
at 360, and a spring to throw the needle off its pivot so as to
preserve it when not in use.
(6.) The Henderson Dial is an improved form of the Lean dial.
,It is 6 inches in diameter, well divided, and graduated to the left.
This instrument is represented in Fig. 19.
In the construction of the sights, the use of horse hairs is
avoided, as they are continually getting burnt by a flaring candle
underground. In place of the ordinary horse-hair sights, the
split-sight is adopted. There is a narrow slit in each sight,
through which the object can be distinctly seen, and its bearing
determined with precision. On the other hand, if the vertical
hair is used, it covers to a certain extent the object, which should
be seen sharply denned.
Fig. 19. Henderson Dial.
The needle is mounted on a ruby instead of the ordinary
agate. Care must, consequently, be taken to throw off the needle
when not required, as the shock, caused by placing the tripod
SURVEYING WITH THE FIXED NEEDLE. 63
suddenly on the ground, is apt to crack the ruby, which, though
extremely hard, is brittle.
To the north-seeking end of the needle, an aluminium vernier
is fixed, the needle being counterbalanced at its other end. By
the aid of this contrivance, a bearing can be read to three
minutes, a degree of precision sufficient for general purposes.
The special feature of the dial is the attachment to the instru-
ment of two sets of folding sights, one revolving within the
other. The fixed sights are always in a line with the back
object in fast-needle surveying; whilst the inner or revolving
sights adjusted to the forward object give the angle of deviation
from the original direction. The sights are made to fold over so
as to be out of the way, in case the new line should too closely
approach the direction of the old one. From the joints of a dial
working loose, an imperceptible movement will sometimes take
place in the body of the instrument on turning it in a new
direction. There results, of course, an error in the angle obtained
when looking towards the forward object. In the Henderson
dial, however, the back object can be again sighted through the
fixed sights, and re-adjusted should any deviation be observed.
For taking vertical angles, a semicircular vertical arc is fixed
across the central line of the dial, when required. It is provided
with a movable limb, to which a vernier is attached, as well as a
horizontal bar carrying a pair of sights and a long spirit-level.
A folding shutter is fitted to each sight, with the object of pre-
cluding the possibility of the eye being directed to the wrong orifice.
This dial was invented by Mr. J. Henderson, M.Inst.C.E.,*
and is manufactured by Mr. Letcher, of Truro.
(c.) Davis's Miner's Dial. This improved form of Hedley dial
is the best instrument for colliery use. As represented in
Fig. 20, the dial combines all the
latest improvements of the Hedley
dial with the outside vernier of
the theodolite.
It consists of a compass-box 5
or 6 inches in diameter, divided
into 360 on the compass-ring, and
into four times 90 on the plate,
being at the north and south
points, and 90 at the east and
west points. The needle is
Fig. 20. mounted on an agate cap, and
when not in use is thrown off by
a spring. There are two spirit-levels at right angles to each
* Proc. Min. Imt., Cornwall, vol. L, 1883, p. 317.
64 MINE-SURVEYING.
other in the face of the instrument, protected by the glass cover
of the compass-box. The sights are the same as those of the
older form of Hedley dial previously described.
Underneath the main-plate, there is a circle or limb divided
into 360. A vernier attached to the outside of the compass-box
enables horizontal angles to be read with great precision. Being
placed on the outside circumference of the dial, the vernier is
more easily read than when placed inside the compass-box, and
the necessity of raising the head above the dial-face is obviated.
The upper and lower limbs of the instrument may be fixed
together at 360, if required, by means of a pin under the body
of the instrument. This dial, it will be seen, differs from the
Lean and Henderson dials, in that the vernier is not movable,
but remains rigid with the sights.
The Hedley form of side arc for taking vertical angles is
replaced by a fixed circular box If inch in diameter, with a
hand traversing a dial-plate divided into 90. This new form of
arc presents the advantages of always being in position, and of
being so compact that it does not interfere with the manipulation
of the screws under the body of the dial.
For surface-surveys, a telescope may be substituted for the
sights. The tripod on which the dial is supported is made of
mahogany, with a brass screw-joint at the centre of each leg.
For very shallow seams, it is necessary to have an extra set of
joints in the legs. All the joints in the legs are made inter-
changeable, and great rigidity is obtained by increasing the
diameter of the legs towards the centre.
The special feature of the Davis dial is the arrangement
by which bearings may be taken simultaneously with the
magnetic-needle and with the vernier, the latter automatically
checking the former. Thus any error arising from incorrect
reading or from local attraction is at once detected. The
graduations of the vernier ring and of the needle ring are
so arranged that the readings correspond. This is effected
by numbering the dial from the north from left to right, and
by numbering the vernier ring from the vernier also from left
to right.
Dial-Joint. The miner's dial is usually fitted to a slightly
conical spindle, having on its lower end a ball, which is confined
in a socket in such a way that it can be moved in any direction
in the operation of levelling the instrument.
For facilitating the setting up of the instrument, an American
invention, the Hoffman joint,* has been adopted in conjunction
* Trans. Amer. Inst. Min. Eng., vol. vii., p. 308.
SURVEYING WITH THE FIXED NEEDLE. 65
with the Davis dial. This tripod head combines the play of the
ball and socket joint and the accuracy and rigidity of the theo-
dolite parallel plates.
The ordinary form of tripod has the disadvantage that it is
almost impossible to level up a sensitive bubble, so that it will
remain in the centre of its run long enough to take a satisfactory
sight. On levelling the instrument and sighting, a second glance
at the bubble almost invariably shows that it has changed its
position, and it is necessary to level up again. This defect is
due to the fact that the levelling screws, when moved in or out
to a considerable extent, do not stand perpendicular to the plate
on which they rest, but on an inclined plane, so that, on turning
them, their points have a tendency to slide down the plane. In
this position, they spring, and turning them is apt to bind or
bend them.
Another imperfection in many tripod heads, is that the
plummet is attached to some point on the axis above or below
the centre of the ball and socket. In either case, the plummet,
after being set over a station, will, during the operation of
levelling up, travel away from the point in a degree pro-
portionate to the distance of the attachment of the plummet
from the centre of the ball, and the deviation of the axis from
the perpendicular at the time the instrument is placed over
the centre.
The Hoffman joint (Patent 1878, No. 2084) is free from these
defects. Fig. 21 shows the form supplied with the Davis dial.
It is claimed to possess the following advan-
tages over the ball and socket joint: 1.
The plumb-line is suspended from the actual
centre of the dial. 2. The rubbing-surface
is some ten times greater, and consequently
the joint is more rigid. 3. The joint is
manipulated with greater ease and rapidity.
A slight turn of the milled flange from right
to left liberates the two concentric hemi-
spheres. The dial is then levelled up, and
a slight turn of the flange from left to right
Fig 21 secures the joint. 4. Only one hand is
required to manipulate the joint. 5. The
total height of the Hoffman joint is 3 inches ; that of the ball and
socket joint 3| inches. The length of the centre is 2 inches,
that of the ball and socket is barely 1 inch. The Hoffman
joint is not heavier than the ball and socket joint.
(rf.) Whitelaw's Dial. In this instrument (Patent 1878, No.
1592) the compass and lower limb are of the same diameter
5
MINE-SURVEYING.
(Fig. 22). The vernier is attached to the outside of the compass-
box, and is placed close to the right of the line of sight, so that
readings can be taken by the surveyor directly after sighting the
object, without moving
aside. The graduated
lower plate is covered
by the compass-box ex-
cept at the vernier. A
circular spirit-level
placed inside the com*
pass-box serves for ap-
proximately levelling
the instrument before
final adjustment with
the long level suspended
below the vertical arc.
The special feature
of this dial is the
manner in which the
vertical arc is supported.
In order that the com-
pass graduation shall
not be obstructed, the
standards are entirely
dispensed with. In their
place is a movable semi- Fig. 22.
circular arc carrying the
bar with the sights, or telescope if required. This arc is at right
angles to the graduated vertical arc, and the axis, en which it
turns, corresponds with the east and west points of the compass-
box. Angles of elevation or depression up to 90 can be taken
simultaneously with horizontal angles. The dial is thus well
suited for surveying in metalliferous mines. It is manufactured
by Mr. W. H. Harling, of London.
(e.) Thornton's Dial. This dial is the patent of Messrs. A. G.
Thornton and Co., of Manchester. Its special feature is a
graduated semicircular folding arc for taking vertical angles.
This vertical limb is fixed by hinge joints to the edge of the
compass-box, and may be folded down "out of the way of injury
when the dial is being carried about in the mine. A groove is
cut in the vertical limb, in which slides the bridge carrying the
sights. The bridge may be fixed at any angle by a clamp-
ing screw, and to it a vernier is attached for reading vertical
angles. In order to ensure the rigidity of the hinged ver-
tical limb, a pin is provided to fix it securely, and when folded
SURVEYING WITH THE FIXED NEEDLE. 67
down it rests upon a ledge, and so relieves the hinged joints of
strain.
The compass-plate is 6J inches in diameter, and its edge is
bevelled ; the divisions are thus clearly seen, and readings can be
taken very readily. The dial is provided with a vernier within
the compass-box, and with two spirit-levels let into the com-
pass-face at right angles to one another. It is attached to the
tripod in the usual way by a ball and socket joint with clamping
screw.
Traversing Underground. A traverse is a series of consecutive
courses, the lengths and azimuths of which have to be determined.
With the vernier-dial or circumferenter, the mode of procedure
is as follows :
1. Three tripods should be provided, and two candles or lamps
on stands fitting on the tripods of such a height that when the
light is replaced by the instrument, the axis of the telescope
when horizontal shall be of the same height as the top of the
wick. Having placed a tripod with a lamp at station 1 (say,
the centre of the shaft), set up the second tripod with the
circumferenter at the second station, and send on the third
tripod with the other lamp on it, as far forward as the light can
be seen. With the pin of the circumferenter keeping the
vernier at zero, take a back-observation to the lamp at station 1.
Clamp the vertical axis of the instrument, carefully measure
the distance from station 1 to station 2, and enter in the
dialling-book the distance and the horizontal angle 00'. Then
take out the pin, unclamp the vernier, and take a fore-observation
to the lamp at station 3, moving the sights by means of the
rack-work. Clamp the vernier, measure the distance from
station 2 to station 3, and note the distance and the angle
indicated by the vernier.
Then take up the first tripod, and send it forward, with the
lamp on it, to a station beyond the third tripod, place the second
lamp on the second tripod and the instrument on the third
tripod, and observe the angle as before, by first bringing the
vernier to zero by means of the pin. In this way any number
of angles may be measured, a back-observation being in each
case first taken with the vernier clamped at zero. Thus, the
last course is always taken as the base-line for the following
angle.
This method of surveying is illustrated by the accompanying
notes of a survey of a portion of a Durham colliery :
OS
MINE-SURVEYING.
_J
365
L_
1
250
225
Dipper W. 3 ft.
1
1
I
100
1
No. 4.-131 15'
365
1
NO. 3-138 20' 1
90
N. headways, 20
yards.
305
from y-
Continued 63 links to face
of ridding.
Permanent mark left in
roof.
|
299
20 yds. E. bord and holed.
W. bord
Zl
W. bord
NO. 2. 343 45' '
(orN. 16 15' W.)
160
100
60
299
30 yds. E. bord and holed.
1
Permanent mark left in
roof and thill.
fl- 0j 1 340 00'
(or N. 20 W.)
305
From winding shaft.
Survey from winding shaft to north face, round west and east face to
pumping shaft, main coal seam.
SURVEYING WITH THE FIXED NEEDLE.
No. 1094 15'
30
Bord continued east.
J
No. 993 00' 1
200
100
200
L
20 yds. to rise hitch.
r
NO. 8255 32'
160
Continued 3 yds. to rise
hitch.
_l
212
L_
H
100
82
cz
20 yds. to hitch.
r~
No. 7.-87 20' 1
212
60
L
100 links to hitch, rise not
proved.
No. 6. 89 07'
412
Continued 150 links to
rise hitch, not proved.
330
202
110
in
in
No. 5-273 21'
412
i
70
MINE-SURVEYING.
1
Left permanent mark.
1
400
^rs
13
. ' H
1
315
300
225
160
115
f
E
1
No 13.-273 20'
400
1
Continued 20 yds. to face.
1
Permanent mark left.
1
1
160
1
H
110
105
1 crosses dip hitch of 2 ft.
6 ins. going east.
j
Headways continued 20 yds
NO. 12.-131 22'
160
1
to permanent mark left
some 20 years ago.
_J
412
L_
|
300
L_
HI
205
II
35 yds. to rise hitch.
HI
100
in
30 yds. to rise hitch.
No. 11-251 16' |
412
r
SURVEYING WITH THE FIXED NEEDLE.
End of
Water level.
NO. 14.-95 53'
O
327
220
170
100
327
survey.
to ceutre of pumping shaft.
Water level, narrow place.
The local mining terms occurring in these survey notes have
the following meanings : A bord is a passage driven across the
grain of the coal. A headway is a passage driven in the direc-
tion of the grain of the coal. A stenton is a passage between
two winning headways. The thill is the floor of the mine. A
hitch is a slight dislocation of the strata, which does not exceed
the height of the seam. Ridding is clearing away a fall of
rubbish. The face is the extremity of the workings.
The distances are measured in links, and, in order to avoid
confusion, the total distance is first given in each draft. The
first two angles were taken from the magnetic meridian. The
figures = denote that line No. 3 is from the distance 305, that
is, the end of line No. 1.
The angles taken with the circumferenter are reduced to angles
from one meridian by applying the following rule : To the first
meridian angle, add the next observed horizontal angle. If the
sum exceeds 180, deduct that amount from it. If the sum is
less than 180, add that amount to it. The result will be the
second meridian angle. Thus, the angles taken in the survey
given will be reduced to angles from one meridian in the
following manner :
Meridian, . . 00' + 1st angle 340 00' = 340 00' = No. I mer. angle.
00' + 2nd angle 343 45' = 343 45' = N o. 2 mer. angle.
No. I mer. angle, 340 00' + 3rd angle 138 20' =478 20'
478 20' - 180 00' = 298 20' = No. 3 mer. angle.
No. 3 mer. angle, 29820' + 4th angle 131 15' =429 35'
429 35' - 180 O0'=249 35'= No. 4 mer. angle.
72 MINE-SURVEYING.
No. 4 mer. angle, 249 35' + 5th angle 273 21' = 522 56'
522 56' - 1 80 00' = 342 56' = N o. 5 mer. angle.
342 56'+ 89 07' = 432 03';
432 03' -180 00' = 252 03'= No. 6.
252 03'+ 87 20' = 339 23';
339 23' - 180 00' = 159 23' = No. 7.
159 23' + 255 32' = 414 55' ;
41 4 55' -180 00' = 234 55' = No. 8.
234 55'+ 93 00' = 327 55';
327 55' - ISO 00'= 147 55' = No. 9.
147 55'+ 9415'=24210';
242 10' -ISO 00'= 6210' = No. 10.
313 26' -180 00'= 133 26'= No. II.
133 26' + 131 22' = 264 48' ;
264 48' -180 00'= 84 48' = No. 12.
84 48' + 273 20' = 358 08' ;
358 08' -180 00' = 178 08' = No. 13.
178 08' + 95 53' = 274 01' ;
274 01' -180 00'= 94 01' = No. 14.
2. There is a second method of traversing with the fast-needle,
in which the work is continued from the original base-line by first
taking for each line a back-observation with the vernier at the
angle last read. With the circumferenter at station 2, and lamp
tripods at stations 1 and 3, take a back-observation to the lamp
at station 1, the pin keeping the vernier at zero, as described in
the first method of traversing. Clamp the vertical axis, take
out the pin, and take a fore-observation to the lamp at station 3.
Clamp the vernier, and instead of now moving it back to zero,
let it remain in the position in which it was clamped, and set up
the circumferenter at station 3. Take a back-observation to
station 2 by unclamping the vertical axis, leaving the vernier
clamped. In this way any number of angles may be measured,
the survey being always continued from the same meridian.
This method, however, is not to be recommended, as any error
made in one observation is carried on throughout the survey.
The observed angles may be reduced to meridian angles by
adding the meridian angle of the first line in each case. The
observed angle and the meridian angle of any station-line being
SURVEYING WITH THE FIXED NEEDLE.
73
known, subtract the former from the latter, the difference is the
meridian angle of the first station-line. If the vernier angle
exceeds the meridian angle, add 360 to the latter in order to
enable the subtraction to be effected. The meridian angle of the
first station-line thus obtained is added to each subsequent
vernier angle, the sum in each case being the meridian angle
of the line in question.
For example, the following angles were taken with the rack
dial, the needle being thrown off except where true bearings were
taken at E, looking back to D and forward to F :
No.
Angles.
True Bearings.
Distance.
Remarks.
A
000'
...
Fins. Ft. In.
10 4 9
/ From 2 ft. W. of
\ centre shaft.
B
275 06'
...
732
C
2S2 12'
...
8 1 9
D
278 51'
730
E
286 00'
277 03'
359
F
292 00'
283 09'
929
...
G
296 00'
9 5 10
END.
At station E the angle and bearing are known. Consequently,
to obtain the bearing of line A the angle 286 00' must be sub-
tracted from the bearing 277 09'. The latter being smaller than
the former, 360 must be added, giving 360 + 277 09' = 637 09'.
This result less 286 00' is equal to 351 09', the bearing of
line A. The same result is obtained with line F. Thus,
(283 09' + 360) - 292 - 351 09'. The bearings of the other
station-lines may be easily found by adding 351 09' to the
observed angle in each case.
The work may be plotted, without any preliminary calcula-
tion, with the protractor and scale as if the survey had been made
with the magnetic-needle. The protractor must, however, be
graduated in the contrary direction to that required for a needle
survey, if the dial is a left-handed one.
3. When the dial is numbered from the north from left to
right, all calculation can be dispensed with ; the angles being
MINE-SURVEYING.
read direct from the magnetic meridian. The Davis dial is
graduated in this way. The horizontal circle of that instrument
being also graduated from left to right, the bearings can be taken
simultaneously with the loose needle and with the vernier, the
latter acting as an automatic check on the former.
In making a survey in this way, select some disused road,
where there is no iron present, and take its magnetic bearing
from stations at the beginning and end. If there is no attrac-
tion, the two results will be identical. Then with the dial set
up at the end station, clamp the vertical axis by tightening the
collar attached to the ball and socket, unclamp the vernier-plate
by slackening the clamping screw, and turn the sights by means
of the rack and pinion screw, until the vernier reads exactly the
same angle as the magnetic bearing just taken. This bearing is
used as the basis of the subsequent determinations of the angles
of the traverse. Clamp the vernier-plate, unclamp the vertical
axis, and by means of the loose collar direct the sights to the
lamp at the first station. If the readings obtained with the
needle and the vernier are identical, the dial is in adjustment, and
the whole of the underground workings may be surveyed from
this base-line. In taking a fore-observation, the surveyor must
turn the south side of the compass face towards himself, whilst
in taking a back-observation, his eye must be at the north sight.
The following is an example of a survey made by this system:
kt
Vernier Angle.
Meridian Angle.
Distance.
Bemarks.
A
30 05'
30 05'
Links.
550
From end df disused road.
B 2
315 58'
...
708
C 2
51 01'
...
597
...
D 2
274 58'
...
722
B
115 12'
...
658
From A again.
C
10 33'
...
618
D
301 18'
301 10'
467
...
The survey was commenced in a disused road, the bearing of
which was found to be 30 05'. The vernier reading was made to
correspond with that angle. Then with the instrument set up at
SURVEYING WITH THE FIXED NEEDLE. 75
A, a back-observation was taken to the lamp at the end of the dis-
used road, the vernier remaining clamped at 30 05'. The vertical
axis of the dial was then clamped, the vernier-plate undamped,
and a forward-observation taken to B 2 . The vernier was found
to read 315 58'. Clamped at this angle, the dial was moved to
B 2 , and the survey continued as before. The survey can be
checked at any point by liberating the needle. If the vernier
and needle readings differ, the amount of magnetic attraction is
the difference between the two readings.
The dial being graduated from left to right, 90 indicates
"West, and 270 East. In plotting the survey a protractor
graduated from right to left must consequently be used.
Surveying in Inclined Shafts. The vernier-dial is of great value
for surveying in inclined shafts containing iron pumps. The
survey should be commenced in a level free from magnetic
attraction. On the basis of the bearing thus determined, the
survey is continued to the shaft.
Should the surveyor be called upon to determine the bearing
of an inclined shaft, containing iron pumps, with a miner's dial
unprovided with a vernier, he may perform the operation with
a cross-staff, either a well-made brass instrument or an improvised
one made by drawing two lines at right angles on a board, about
6 inches square and 1 inch thick. The lines must be cut half an
inch deep with a fine saw. The instrument thus made is fixed
on a three-foot stand.
The cross-staff is set up in such a position that a candle in the
shaft can be seen through one pair of sights. In the line of sight
of the other pair, the dial is set up in the level out of the way of
magnetic attraction. In this way, the candle in the shaft and
the dial in the level form a right angle with the cross-staff* An
assistant must now look through the sights of the dial to a candle
held immediately above the cross-staff, and read the bearing
indicated by the needle. Being exactly at right angles to this
line, the bearing of the shaft may be at once determined. Thus,
assuming that the needle reads 282, if the underlie is northerly,
the bearing of the shaft will be 12; if southerly, 192.
The Vernier Compass. The vernier of the circumferenter may
be used for reading the magnetic bearing. In this method of
surveying, the compass-box is clamped with the needle lying
upon the zero or north and south line marked on the dial. The
sights being then directed to the object, the bearing is read
direct from the vernier to 3 minutes, or by estimation upon a
superior instrument to 1 minute. This method is very expedi-
tious, and gives most accurate results. At any point in the
traverse, a fast-needle observation may be made without difficulty.
7G
MINE-SURVEYING.
In working with the fast needle, it is advisable to invariably
start with a loose magnetic bearing, and, if practicable, to close
with one. Intermediate checks by the same means are desirable,
but not essential. In this way, the needle lies upon the zero
line at every set, except where local attraction prevails, of which
the amount and direction are shown by the needle's deviation
from that line. The result is that the traverse angles booked are
also magnetic bearings.
In order to show grounds for confidence in this method, the
details of an actual survey, made by Mr. W. F. Howard,* may be
quoted. The survey was made between the Speedwell and
No.
Vernier Bearing.
Horizontal
Distance.
Remarks.
1
N. 34 24' W.
Links.
134
f From Speedwell north or down-
\ cast shaft.
2
N. 58 35' E.
639
...
3
N. 45 41' E.
274
...
4
N. 37 29' E.
130
...
5
N. 840'W.
127
...
6
N. 15 02' E.
405
...
7
N. 17 57' E.
206
...
8
N. 11 35' E.
158
...
9
N. 35 37' W.
73
...
10
N. 18 20' E.
260
...
11
N. 18 14' E.
470
...
12
N. 69 42' E.
384
...
13
S. 27 45' E.
63
14
N. 69 32' E.
73
15
N. 71 57' E.
78
!To face of main ventilating drift
intended to hole into Nether-
thorpe shaft.
* Trans. N. Eiigl. Inst. M.E., vol. xx., 1870, p. 31.
SURVEYING WITH THE FIXED NEEDLE. 77
Netherthorpe shafts at Staveley, with the intention of effecting a
holing into the latter. The straight distance between the sLafts,
measured direct on the surface, was 31-13 chains, and the distance
between the shafts by the underground roads was 3543 chains,
making the total circuit 66 -56 chains, and requiring 16 sets
underground. The foregoing is a copy of the survey notes.
The survey was made with a 5-inch Davis dial, divided to half-
degrees, with a vernier reading to 3 minutes.
In this instance, the magnetic bearing and the horizontal
distance sought, from the face of the heading to the intended up-
cast shaft, was calculated to be N. 58 38' E., 190-5 links. It
was then determined to drive direct into the shaft, and the draft
was accordingly set out at the above bearing ; and the holing
proved this bearing and the calculated distance to be absolutely
correct.
78 MINE-SUKVEYING.
CHAPTER VII.
THE GERMAN DIAL.
Invention of the German Dial. The continental method of sur-
veying mines consists in suspending a compass and a clinometer to
a stretched cord representing the line of sight. The compass and
the clinometer are read, and the length of the line measured.
In this way, the length, bearing, and inclination of the station-
line are determined. Mine-surveys were conducted in the manner
described by Agricola until the invention of the German dial,
or hanging compass, by Balthasar Roessler, who died at Alten-
berg, in Saxony, in 1673.
Measuring Station-Lines. The cord is 50 fathoms long. It is
made of hemp, and wound round a wooden reel provided with a
handle (Fig. 23). This cord is stretched
from station to station. The length of the
portion stretched depends, of course, on
the distance of the stations apart. It
should, however, not exceed 8 fathoms, so Fig. 23.
as to prevent the formation of a catenary
curve. The screws (Fig. 24) to which the cord is fastened are
4 inches in length. They are firmly fixed into the timbering
p,
u
Fig. 24.
of the level. When the cord is stretched between the two points,
the length of the line is measured. For this purpose, the Hun-
garian surveyors employ a fathom-rod ; the Saxon surveyors use
a brass 5-fathom chain.
For surveys at the surface, or in mines where there is no
THE GERMAN DIAL. 7U
timbering to hold the screws, a trestle of the form shown in
Fig. 25 is employed. It consists of a beam 8 feet in length and
6 inches in diameter, with two short legs. It should be as heavy
as possible, and no iron must be used in its construction.
In the Harz mines, instead of the cord, a thin brass chain is
used. It is 10 metres in length, and is provided with a hook at
one end. Every metre is indicated by a brass tag. The chain
is wound on a reel, and used in the same way as the cord. The
advantages it offers are: 1, It weighs very little; 2, its length
can be read without any delay ; 3, the best place for hanging the
clinometer can easily be found ; 4, no further measurements are
required to determine the points where offsets have to be taken.
Its disadvantage is that it is liable to stretch, and must there-
fore be carefully examined and adjusted every time it is used.
The Clinometer is used for determining the inclination of
the stretched cord. It consists of a thin brass semicircle
Fig. 26.
(Fig. 26), 9 inches in diameter, provided with hooks for
hanging it on to the stretched cord. In the centre of the
circle is a hole, through which a black human hair is passed, and
fastened on the other side by means of wax. At the other end
of the hair, a small brass plumb-bob is fastened. The hair touches
the graduation of the semicircle, and enables the angle of inclina-
tion to be determined. The hooks open towards opposite sides, and
are provided with apertures through which a clamp may be in-
serted when the clinometer is suspended from a highly inclined
cord. The graduation begins at the centre of the semicircle
that is, perpendicularly below the centre from which the plum-
80 MINE-SURVEYING.
met hangs. It commences with 0, and goes to 90 on both
sides. Each degree is subdivided into four equal parts, so that
an angle can be read direct to 15 minutes. As a rule, the quarter
degrees are further divided by the eye into three equal parts, so
that angles can be read accurately to 5 minutes. In order to
facilitate the reading, the graduated side of the clinometer is
usually silver-plated.
Use" of the Clinometer. If a cord, about 10 yards in length, is
stretched horizontally, and the clinometer suspended from its
centre, the human hair, hanging vertically on account of the
weight of the plummet, will coincide with the zero of the gradu-
ation, provided that the cord is
stretched perfectly tight, and that
the clinometer is free from defects
of construction. If the cord is in-
clined at an angle BAG (Fig. 27),
the hair will not coincide with zero,
but will give the angle D H E,
which represents the angle of in-
clination of the cord. For since
AHD + DHE = a right angle, and AHD+BAC=a right
angle, AHD + DHE = AHD + BAG, therefore DUE =
BAG. The clinometer thus may be used for determining the
inclination of lines.
The cord when stretched forms a catenary curve, and con-
sequently the angle of inclination varies at different points in the
curve. There must, however, be a point where the cord is
parallel to the line joining the two end points, and there the
clinometer must be placed in order to obtain the true inclination.
The weight of the clinometer being neglected, the correct point
of suspension is slightly below the centre of the cord. But the
weight of the clinometer alters the inclination of the cord, as it is
not uniformly divided between the two hooks. The place where
the clinometer must be suspended, in order to give the correct
inclination of the cord, has been found by Professor A. von Miller-
Hauenfels. His rule is as follows: The clinometer must be
suspended at a certain distance above the centre of the cord.
For cords at an inclination of about 15, this distance is obtained
by multiplying the length of the cord by 0-004 for each degree ;
for greater angles, the length must be multiplied by O'OOS for
each degree. Thus, with a cord 12 metres in length inclined at
an angle of 20, the clinometer must be suspended at a distance of
6 '72 metres from the lower end. In practice it is found sufficient
to suspend the clinometer at the middle of the cord, when the
latter is but slightly inclined. With highly inclined cords, how-
THE GERMAN DIAL.
81
ever, it is advisable to suspend the clinometer half a yard from
the two ends, and to take the mean of the two readings, as the
correct angle of inclination. The error will thus not exceed a
few minutes in a cord 10 yards in length.
The Hanging-Compass. The compass-box is 3 to 4 inches in
diameter. It is graduated into 360, or, more frequently, into
twice 12 hours. The numbering commences at the ends of the
diameter marked north and south, the 12 o'clock line, and pro-
ceeds from right to left. At the 6 o'clock line, the east and west
points are transposed as in the ordinary miner's dial. In the
larger compasses, each hour is divided into 16 parts; in the
smaller ones, into 8 parts. Further sub-divisions may be esti-
mated with the eye. The compass is, as a rule, read in hours,
eighths, and sixteenths of eighths. One hour is equal to 15,
one-eighth is 1 51' 30", and one-sixteenth of an eighth is 7' 2".
In order that the compass shall assume a horizontal position
when suspended to the cord, it is constructed on the plan of a
ship's compass. When the compass is
fastened in the gimbals of the hanging
instrument, and suspended to the cord,
the 12 o'clock line is in the same vertical
plane as the axis of the cord, and the
compass hangs level at all times.
The original construction of Rossler's
hanging-compass is shown in Fig. 28, copied
from Voigtel's Geometria Subterranea, the
first treatise on mine-surveying ever
written. It was published in 1686.
An improved form of hanging-compass,
made by Osterland of Freiberg, is shown
in Fig. 29. The hanging ring of the old compass is here
replaced by two movable arms. In order to keep the centre of
gravity as low as possible, the
clamping of the magnetic-needle
is effected by a large screw
underneath the compass-box.
The compass and clinometer
fit into a leather case fastened
to a belt worn round the sur-
veyor's waist. A few hairs,
some wax, and a plummet must
always be carried in reserve.
29 Surveying with the German
Dial. In booking a survey
made with the German dial, the date, the name of the mine, and a
Fig. 28.
82 MIXE-SURVEYING.
description of the starting-point should first be noted. A fixed
point having been selected as a starting-point, intermediate points
are so chosen that they can be connected without hindrance by
cords 6 to 8 fathoms in length. These points are either in the
permanent timbering of the level, or in timbers temporarily
inserted for the purpose. At these points, cord-screws are fixed.
The loop at the end of the cord is placed over the first screw.
The cord is tightly stretched to the next screw, and having been
wound round it two or three times, is carried on to the next
again. Six to ten station-lines are thus obtained, and the survey
is commenced. A plummet is dropped from the first screw to the
floor of the level, and the perpendicular distance measured. The
length of the stretched cord is measured by placing the measuring
rod gently along it. The clinometer is then suspended from the
middle of the cord, and the rise or fall read. Lastly, the hanging-
compass is suspended to the cord near the end-point of the line,
care being taken that the north end of the dial is directed towards
the end-point of the line. The bearing of the cord is then read.
The mode of procedure is the same with the other lines.
The observations are noted in the dialling-book. In the
column for remarks, sketches of portions of the level are inserted,
showing the position of the offsets measured from the stretched
cord. The bearing and dip of any veins or cross-courses met,
should also be noted. As the end-point of the survey, a fixed
point should, if possible, be selected, and the distance from the
floor of the level measured. When great accuracy is required,
a reverse survey is made as a check.
When the survey is complete, the bases and perpendiculars
of the inclined lines have to be determined. The cord being the
hypothenuse of a right-angled triangle, its length must be
multiplied by the cosine of the angle of inclination, in order to
obtain the base of the triangle, that is, the plotting length of the
line. The perpendicular is obtained by multiplying the inclined
length by the sine of the angle of inclination.
The form of dialling-book adopted is given on next page.
In this survey, the distances were measured in metres. The
hanging-compass used was divided into half-degrees, which
were subdivided by the eye into tenths of degrees. The
clinometer was also read to tenths of degrees. The figures
obtained by calculation, in the " base " and " perpendicular "
columns, are usually entered in red ink. If the survey is to be
plotted trigonometrically or by means of the protractor, the
observed bearings are first corrected for the magnetic declination.
The following is an example of the method of booking recom-
mended at the Freiberg School of Mines :
THE GERMAN DIAL.
S3
CARL MINE, ALSACE. SURVEY OF ADIT LEVEL WITH
THE HANGING-COMPASS.
Begun at + on right Timber, at entrance to Level.
No.
Length.
Inclination.
BEARING.
Base.
PKEPESDICULAB.
Remarks.
Observed.
Corrected.
Rise.
Fall.
1-34
R. 90 -0
1-34
...
To +
A
7-36
o-o
240'9
228'9
7-36
...
B
5-41
R. 3-l
210'3
198 -3
5-40
0-29
...
C
6-33
F. r-2
210'2
198'2
6-82
0-14
...
D
4-81
R. 3-8
186 -6
174 -6
4-80
0-31
...
...
E
6-24
F. 0-4
202-8
190'8
6-24
0-04
F
4-68
R. l'l
173 -1
161'l
4-68
0-09
...
...
...
1-32
F. 90 -0
1-32
( To floor
| of level.
In the Harz, where a thin wire is used instead of a cord, the
station-line is, if possible, made 10 metres in length. The
trigonometrical calculations are thus greatly facilitated, especially
if logarithms are used. The form of dialling-book adopted when
the compass is divided into hours, is shown on the next page.
The right-hand page of the survey-book is reserved for sketches,
showing the position of the offsets taken.
Plotting the Survey. The survey may be plotted by means of
the compass that was used
underground. The plotting in-
strument (Fig. 30), consists of a
truly rectangular plate of brass,
10 inches long and 5 inches
wide, with a raised ring in the
middle for the reception of the
compass-box. The diameter of
the ring parallel to the long side
Fig. 30. of the plate is marked on its
surface by means of two fine lines. The compass-box is placed
in the ring, and clamped so that the 12-hour line coincides with
O
84
MINE-SURVEYING.
|
1
i
1
JS : 1 : 1 : i : 1 : :
E
1
pi
1
no (N <N O d CO O
j : 2 ! 2 : 2 j 2 = 2 : 2
s
1
ned Cord.
ggoogggoggoo^
(Nt-Or^OOOOOOrH
|
ination of
1!
J i
8 fc -1* S K S {* S ft b
rH CS
1
fe C4 fn rt, p4 fe f^ PM pj ^ (4
i
i
gtb rHI^C5OCSO5O5C36>O
3s
05 r 5 2 OOC3rtG0 '* 00 :
.
-i
----------- :
1
I
oscjt-ooiooooooj :
ft
B9 H & ^3 H ^ 69 H H G3 fiQ
o
*
<JWOfiHri<OK H:> l^i-^ 1 ^'
1
+ <JpqOflHrt(O r il^Wi J '
THE GERMAN DIAL. 85
these two lines. The upper edges of the rectangular plate are
bevelled, so as to diminish the shadow on the paper.
The paper, on which the plan is to be drawn, is fastened to a
horizontal table. The plotting-instrument is then placed on the
paper, and turned until the marked end of the needle points to
the north. A line is then drawn along the side of the plate which
will represent the north line of the plan. A point for commencing
the plotting is selected, and the instrument turned at that point
until the needle points to the bearing of the first line. A line
is then drawn along the side of the instrument, and the required
distance measured with a scale.
This method presents the advantage of plotting the survey
with the actual instrument used to make it, and consequently
with the same degree of approximation. But the errors due to
magnetic influences are not eliminated, as the conditions are not
the same as they were in the mine.
In a drawing office, too, there are
always iron objects that may affect the
needle. At the French collieries of
Decize in Nievre, a drawing office has
been built in which all the ironwork
has been replaced by copper, for the
purpose of employing this instrument
without inconvenience.
Surveying with the Hanging-compass
in the Presence of Iron. Numerous
attempts have been made to modify
Fig. 31. the construction of the hanging-com-
pass in such a way that it can be
used for surveying over iron. Perhaps the most successful is
the adjustable hanging-compass (Fig. 31), invented by Mr. Pen-
kert* of Beuthen. It is so arranged that it can be centred under
the point of junction of two cords, and thus the bearing of the
two lines can be taken from the same place. The instrument
is manufactured by A. Ott, of Kempten, Bavaria.
Use of the German Dial. The hanging compass in Germany
and France is being replaced by the theodolite ; but it is still
found useful in narrow workings. It is occasionally used in
America. Thus, in surveying the Longdale iron mine in
Virginia, Mr. G. R Johnson has found it a useful auxiliary.
The four main adit levels of the mine having been surveyed, and
their entrances connected by level and theodolite lines, it re-
mained to survey the stopes and workings in order to make a
* Berg. H. Ztg., vol. xxxix., 1880, p. 9.
86 MINE-SURVEYING.
complete map, and to test the accuracy of the foregoing work.
To do this with the theodolite and level was out of the question,
both on account of the roughness of the workings, and also
because they were much too small so small in places that a man
could scarcely crawl through them. The hanging compass was
consequently used with very satisfactory results, the ends of the
survey coinciding with the corresponding points determined in
the theodolite survey.
THE THEODOLITE. 87
CHAPTER VIII.
THE THEODOLITE.
Historical Sketch. In mine-surveys, where extreme accuracy
is required, the theodolite should be employed. There is, how-
ever, no occasion for it to be used exclusively, as the modern
vernier-dial is a form of theodolite, which from its simplicity and
compactness is better adapted for underground work than the
theodolite itself, and proved by severe tests to give highly
satisfactory results. For surface-surveying the dial is, however,
decidedly inferior to the theodolite.
The employment of improved instruments for measuring
angles underground in place of the compass, dates from the end
of the last century. In 1798, H. C. W. Breithaupt, of Cassel,
invented a mine-surveying instrument, resembling an astrolabium.
This was essentially a theodolite. It had a graduated horizontal
circle with verniers, a vertical arc, a sighting-tube, and a
compass. Two sets of legs were used with the instrument. In
the same year, Professor Guiliani, of Klagenfurt, invented a
mining theodolite, calling it a catageolabium. Mine-surveys, too,
were made at the end of the last century by the Polish General,
Komarzewsk, with a graphometre souterrain which he invented.
Since 1832, the theodolite has been used, more or less, in all
mine-surveys, where great accuracy is required. Theodolites
specially constructed for mining purposes are now made in great
numbers by the continental and American instrument-makers.
In Great Britain, however, the tendency has been to improve
the construction of the circumferenter, making it more and more
like the theodolite, so that with it results can be obtained as
accurate as those made with a German mining theodolite of the
same size.
Description of the Theodolite. The theodolite is the most
important, but at the same time the most complicated, instru-
ment used by the mine-surveyor. In general outline, it may be
described as a telescope mounted on a horizontal and a vertical
axis, in such a way that the horizontal and vertical rotation of
its optical axis may be measured.
88
MINE-SURVEYING.
There are many forms of theodolite, but there are certain
essential parts common to all. The cost of a theodolite being
considerable, the mine-sur-
veyor is, as a rule, not in a
position to have several of
different sizes. In purchas-
ing an instrument, therefore,
he must select one which will
fulfil all his requirements. It
must be sufficiently large to
give accurate results in tri-
angulation, and at the same
time it must be sufficiently
portable to be used in the
mine. In its construction,
all metal must be avoided
that will affect the magnetic-
needle. The horizontal circle
should be 5 inches in dia-
meter, divided into half-
degrees, and provided with
verniers reading to single
minutes.
The various parts of the
theodolite are shown in Fig.
32. The most important
part is the horizontal circle,
G, which has its edge bevelled
and graduated, the degrees
being numbered continuously
round it towards the right
up to 360. At the centre
of this circle is another cir-
cular plate, the vernier-plate
F, capable of rotation inde-
pendently of the horizontal
circle. On the vernier-plate
is engraved a line, the index
line, passing exactly through
the centre, the end-points, or
indices, extending to the
graduation of the horizontal
circle. The indices are provided with verniers, read by means
of the microscopes g, g, which are sometimes provided with plates
of ivory to reflect light on the scale. The horizontal circle and
THE THEODOLITE. 89
the vernier-plate together are sometimes termed the horizontal
limb, in which case G is called the lower limb. The instrument-
makers' names are (F) plate, and (G) limb.
On the vernier-plate are two uprights or supports, D, D, which
support the horizontal axis, C, of the vertical or altitude circle, E.
The latter is provided with two indices with verniers at the
opposite ends of a horizontal bar, read by the microscopes e } e.
The telescope A B is fixed directly upon the horizontal axis.
The horizontal circle is screwed by a flange to a brass vertical
axis, K, passing through the collar of a clamp, where it may be
fixed or loosened by the clamp screw, k. Below the collar, the
vertical axis works freely on a ball and socket joint at its lower
end. The ball and socket is placed between the parallel plates,
L, M, which are provided with four levelling screws, I. The
vernier-plate is provided with two spirit-levels, /,/, and a longer
spirit-level, c, is attached to the telescope. The whole instrument
is supported on a strong tripod stand.
The vertical circle is divided into four quadrants, the degrees
in each of which are numbered from to 90, as shown in Fig.
33. In the old-fashioned theodolite the verti-
cal limb is a semicircle. This is surmounted
by an oblong flat piece of brass, the stage, to
the ends of which are screwed the two forked
rests called Y's, by which the bell-metal collars
of the telescope are supported. Under the tele-
scope is a long spirit-level. A theodolite of
this kind is termed a plane theodolite, whilst
one with a complete circle as vertical limb is Fig. 33.
termed a transit theodolite. The advantages
presented by the latter form are the greater vertical sweep of the
telescope and the greater accuracy of the readings of the vertical
limb.
Connected with the horizontal circle and vernier-plate, there
are two screws, H, I, one of which, H, is a clamping screw and
the other a slow-motion or tangent screw. When H is loose, the
two plates, G and F, can be moved independently, but when the
screw H is tightened they can only be moved separately by
means of the tangent screw I. Beneath the horizontal plates,
there are two screws, k and i, one of which, k, is a clamping
screw and the other a tangent screw. When the screw k is loose,
the whole of the upper part of the theodolite above the screw
can be rotated in either direction, in which case the horizontal
circle moves upon the double conical axis upon which it rests.
On tightening the screw k, the upper pai-t can be moved only by
means of the tangent screw i. Two screws refer to the vertical
90
MINE-SURVEYING.
circle, a clamping screw and a tangent screw d. When the
clamping screw is loose, the
vertical circle can be moved
freely ; but when it is
tightened, the circle can be
moved only by means of
the tangent screw d.
As an aid to memory, the
screws may be divided into
three sets, each of which
consists of a clamping and
a tangent screw. The upper
set belongs solely to the
vertical circle ; the centre
set, H, I, belongs to the
horizontal circle F;' and
the lower set, Je, i, refers to
the entire portion of the
instrument above it.
The circular plates with
their accompanying sockets
are shown in section in Fig.
34. The upper plate carry-
Fig. 34.
ing the compass-box, &c., is screwed fast to the flange of the
interior spindle, the lower plate is fastened to the exterior socket,
which in its turn is fitted to and turns in the hollow socket of
the levelling head.
The telescope consists of two tubes, one sliding within the
other, with the object glass at the further end, A, of the outer
tube, and with an eye-piece at the nearer end, B, of the inner
tube. The object glass is achromatic, that is, made of two
lenses, one of crown and one of flint-glass, the curvatures of
which are suitably combined. The object glass forms between
the eye-piece and its principal focus an inverted image of the
object sighted, and the eye-piece, consisting of two condensing
lenses, acts as a magnifying glass, and gives a virtual and highly
magnified image of the inverted image thus obtained. Some-
times, especially in American instruments, the eye-piece is
made up of four plano-convex lenses. An erect image is thus
obtained. An erecting eye-piece, however, causes a considerable
loss of light, and is therefore not to be recommended. It
requires but little practice to get accustomed to the use of an
inverting eye-piece, and the brilliancy with which objects
appear, owing to the amount of light gained by dispensing with
two lenses, is very marked in comparison with the results
THE THEODOLITE. 91
obtained with an erecting eye-piece of the same power. The
telescope may be focussed by moving the inner tube by a rack
and pinion turned by the milled head, b (Fig. 32).
The rays proceeding from the object-glass form a cone of light.
In order to get a line from the point of the cone straight through
the optical centre of the object-glass, and on, without deviation,
to the object examined, recourse must be had to
the device of collimation. The collimator of a
theodolite telescope is a circular brass diaphragm,
with a hole about half an inch in diameter in its
centre. It has a rim on its edge, and in this are
the collimating screws, a, a. The hole is crossed
by three spider-webs or equally fine platinum Fi 35>
wires (see Fig. 35), one horizontal, A B, and the
other two, CD, EG, deviating slightly to opposite sides of a
vertical plane. The point F where the wires cross each other
should be exactly in the axis or line of collimation of the
telescope. It is adjusted to that position by the collimating
screws.
Various Forms. (a.) Hoskold's transit-theodolite is an instru-
ment of great perfection, specially adapted for mining work. It
differs from the ordinary transit-theodolite in the arrangement
of the upper plate, which is made to project over the lower
plate at the points where the upright supports are attached, so
as to enable a larger compass to be employed. Thus, a 5-inch
circle will carry a 4 \ -inch compass ; whilst in an ordinary
theodolite of the same size a 2 \ -inch compass would be used.
The Hoskold theodolite presents the further advantage that
the compass is not obscured by the appendages of the upper
plate. In order to enable short sights to be taken, a pair of
folding sights, like those of a miner's dial, are fixed to the top
of the telescope. The instrument is also provided with a
diagonal eye-piece, which enables the telescope to be pointed
vertically without any discomfort to the observer.
In this theodolite and some others, a second telescope is some-
times attached below the horizontal circle. This is used like
the outer pair of sights of the Henderson dial, to determine
whether the circle has been disturbed during the interval
between two observations.
(b.) The Everest Theodolite. This instrument differs con-
siderably from the ordinary transit-theodolite, though the
principles of its construction are exactly the same. It was
designed by Captain Everest, and was first made by Messrs.
Troughton & Simms in 1838. Instead of the upper parallel
plate, this instrument has three diverging arms (Fig. 36) with
92 MINE-SURVEYING.
. 35A. Hoskold's miner's transit theodolite.
THE THEODOLITE.
93
a vertical levelling screw supporting the end of each. Each
screw has a flange at its lower end, by means of which it is
held down to the plate forming the top of the staff head. The
chief advantage of this construction is that the three levelling
screws can be adjusted with one hand, whilst the adjustment of
four levelling screws requires both hands.
Fig. 36.
The vernier-plate is represented in the Everest theodolite by
four radiating arms, three with verniers, the fourth with clamp-
ing and tangent screws. The verniers are read with the aid
of an independently moving microscope. The mean of three
readings is thus obtained for each observation.
The telescope is permanently fixed to the horizontal axis by
means of a collar-like expansion at the middle of the bell-metal
axis, into which the telescope is fixed. Instead of a vertical
circle, the Everest theodolite has two opposite sectors of about
90 each, so as to be capable of measuring elevations and depres-
sions, as far as 45. The horizontal axis works in a Y-shaped
upright. The spirit-level is not attached to the telescope, but
to the index bar. The circular compass-box of the ordinary
instrument is replaced by a long compass-box placed above the
telescope, reading only a few degrees east or west of the magnetic
meridian. The spirit-level for the horizontal circle is attached
to a stage below the Y's.
(c.) The Hoffman Tripod Head. The theodolites made by
94 MINE-SURVEYING.
Messrs. J. Davis & Son are provided with the Hoffman tripod
head (see p. 64). Ever since the introduction of the theodolite,
efforts have been made to give it the same facility of levelling as
is possessed by the miner's dial. The ball and socket motion has
been frequently tried. The upper part of a theodolite is, how-
ever, much heavier than that of the dial, and requires more
binding power than can be obtained with an ordinary ball and
socket joint.
The great need for a tripod that can be easily manipulated is
apparent, as it rarely happens that there is a level surface on
which to set the theodolite, and much of the time in surveying
is employed in adjusting the levelling screws. It has been
pointed out that it is almost impossible to level up a sensitive
bubble so that it will remain in position long enough for a satis-
factory sight to be taken, and the difficulty of centering a plummet
over a station has also been shown. The latter defect has been
obviated by the addition of the sliding-head, which permits the
entire instrument, with its plummet, to be accurately placed over
a fixed point, after the operation has been approximately per-
formed by moving the legs.
The Hoffman tripod head,* as modified by Professor J. H.
Harden of the University of Pennsylvania, is shown in Fig 37.
Fig. 37.
On unscrewing the levelling screws, the plate forming part of the
socket of the small ball, the centre of which is the axis of the
instrument, and the point from which the plummet is suspended,
can be moved in any direction within the limits of the inside
opening of the screw cap. It will be observed that besides the
small ball and socket, there is an extra and larger ball and socket
formed by a part of the plate to which the instrument is fastened,
* Trans. Amer. Inst. Min, Eng., vol. vii., p. 308.
THE THEODOLITE. 95
and the part to which the levelling screws are attached. The
latter part always remains parallel to the screw cap of the tripod
head, on which the points of the levelling screws rest, so that
whatever position the instrument may assume in relation to the
tripod head, the screw will always act directly perpendicular to
both plates.
Under all conditions, the instrument moves upon a centre
common to the two balls, this being the point to which the
plummet is attached. It is therefore impossible for the plummet
not to be perpendicular to the axis of the instrument.
The advantages claimed for the Hoffman tripod head are as
follows : 1. A saving of one-half to two-thirds of the time usually
occupied with screwing and unscrewing as in the old plan. The
instrument can be levelled approximately without the use of the
screws. Less than half a turn is then necessary to bring the
instrument to a perfect level, the operation at the same time
clamping it. 2. The levelling screws are at all times perpendi-
cular to the plate to which they are attached, and to the plate
and screw cap on which they rest. 3. The levelling screws are
reduced in length, and their duty to a minimum, the instrument
being no higher nor heavier than before. 4. The shifting head
for plumbing over a fixed point an improvement common to all
first-class instruments is retained, and no extra screws are
required to clamp the instrument. 5. The levelling screws are
covered from dust, and at the same time are no obstruction to
the working of the instrument in any position in which it can
be placed.
Numerous other attempts have been made to apply the ball
and socket motion for levelling theodolites rapidly, and several
American devices of this kind have proved very successful.
Thus, Messrs. W. & L. E. Gurley, of Troy, have patented a
quick-levelling tripod, somewhat similar in principle to that of
Hoffman. The spherical surfaces are, in this case, concave, and
the friction of these surfaces may be increased or diminished at
will by means of spiral springs. Messrs. Buff & Berger, of
Boston, furnish their theodolites with a quick-levelling attach-
ment, which does not form part of the instrument proper, but
consists of a coupling, with a ball and socket joint, which can be
screwed between the instrument and the tripod.
(d.) American Theodolites. In America, the miner's dial is
very rarely used for mine-surveys. In all important work, the
transit-theodolite is alone used. This instrument is known in
America as the transit. The name theodolite is reserved for the
Y-instrument in which the telescope cannot be revolved on its
horizontal axis. The transit instrument which has no vertical
96 MINE-SURVEYING.
Fig. 37A. Theodolite of the American type, with Hoffman tripod head.
THE THEODOLITE. 97
circle and no spirit-level attached to its telescope is called the
plain transit.
An excellent transit-theodolite, manufactured by Messrs.
Heller & Brightly, of Philadelphia, is described by Dr. R W.
Raymond.* It is a small portable instrument specially adapted
for use in mine-surveying. The principal peculiarity is the rib-
bing and flanging of the parts requiring strength, so as to dispose
the minimum amount of material where it will secure the greatest
rigidity. The horizontal circle is 4|- inches in diameter, and is
read by two double opposite verniers, placed outside the compass-
box, the vernier openings in the plate being made very wide so as
to allow the easy reading of the graduations. There is a 3-inch
magnetic-needle, and its ring is divided to half-degrees. The
telescope is 7^ inches long, with an erecting eye-piece. A sensi-
tive level, 4J inches long, is attached to the telescope. The
tripod is furnished with a shifting head for precise centering.
Clamps and tangent-screw movements are supplied to the plates
and vertical circle. The graduation of the compass ring and of
the horizontal circle is continuous from to 360. The weight
of the instrument, exclusive of the tripod, is 5| Ibs. The
weight of the tripod is 3| Ibs. The height of the instrument
from the tripod legs is 7 inches, the extreme diameter of the
plates 5 inches. The instrument and tripod head are packed
in a box 7 inches square, arranged with straps to allow its
being carried over the shoulder, while the folded tripod legs
serve as a walking-stick. Such compactness and lightness
are very important for underground work. This also applies to
surface-surveys, especially in a country like America, where the
surveyor has often to carry his own instrument.
(e.) Traveller's Transit-Theodolite. A still smaller transit-
theodolite is manufactured by Mr. L. Casella, of London, for the
use of travellers. It has complete 3-inch circles, both vertical and
horizontal, with verniers reading to one minute. It can there-
fore be used as an altazimuth for determining time, latitude,
and azimuth, as well as for ordinary surveying purposes. Its
telescope is eccentric. It is provided with a diagonal eye-piece
and a reflector for illuminating the cross-wires. It is thus well
adapted for shaft-surveying. It is supplied with a dark glass
for solar observations, a finely divided level, and a compass. It
packs in a mahogany case, 6| inches by 5^ inches, and 4 inches
deep ; the whole weighing only 3| Ibs.
A light tripod stand is added. Many important surveys have
been made with the instrument with very satisfactory results.
* Trans. Amer. Inst. Min. Eng., vol. i., p. 375.
98 MINE-SURVEYING.
This instrument is also constructed with the telescope in the
centre, the supports being raised to allow it to revolve vertically.
By this arrangement, whilst the height is increased, the width is
reduced in proportion.
Adjustments of the Theodolite. Every time the instrument is
used, the observer must make the following adjustments:
1. Place the theodolite exactly over the station by means of a
plummet hung from a hook directly under the vertical axis. It
must next be levelled, that is to say, the vertical axis must be
placed truly vertical. The easiest way to do this is to make the
vernier-plate truly horizontal, by means of the spirit-levels, /, f
(Fig. 32). For this purpose, the vernier-plate is turned into
such a position that the two spirit-levels shall be parallel to the
two diagonals of the square formed by the four levelling screws.
Two opposite screws must then be turned simultaneously and
equally, but in opposite directions, until the bubble is brought
to the centre of the leveL The other screws are then turned in
the same way, until the bubble of the second level is brought to
the centre of its tube.
A more exact adjustment can be made by means of the larger
and more delicate level, c, attached to the telescope. For this
purpose, set the instrument approximately level, clamp the axis
of the limb by k, leaving the plate free, and move the latter until
the telescope is over two of the levelling screws. Then bring the
bubble to the middle of its tube by the tangent screw, d. Then
turn the vernier-plate, carrying with it the telescope, through
half a revolution, and if the bubble is not in the centre of
the tube, bring it half way back by the tangent screw, and the
other half by the levelling screw. Repeat this until the bubble
remains central with the telescope in either position. Then
turn the vernier-plate through 90, so as to place the telescope
at right angles to its former position, and repeat the process
until at last the bubble remains central during the complete
rotation of the telescope. If the instrument is correctly con-
structed, the vernier of the vertical circle should read 0'.
If the bubbles are not at the centres of the vernier-plate levels,
when the bubble remains central in the level attached to the
telescope, the vernier-plate levels are not truly perpendicular to
the vertical axis, and must be adjusted by means of the screws
at their ends. This adjustment is rarely required with a well-
made theodolite.
2. When the image of the object viewed, formed by the object
glass, either falls short of or beyond the place of the cross-wires,
an error arises, which is called parallax. Its existence may be
detected by moving the head from side to side when looking
THE THEODOLITE. -. 99
through the telescope, observing whether the image appears to
move. To correct this error, the eye-piece must first be adjusted
by means of the movable eye-piece tube, until the cross-wires
are seen clearly defined. Then direct the telescope to some
distant object, and by means of the milled-head screw, b (Fig.
32), at the side of the telescope, move the inner tube in or out
until the proper focus is obtained. When disregarded, parallax
gives rise to serious error.
3. In addition to the temporary adjustments described above,
there are certain permanent adjustments which should be tested
from time to time, but which in a well-made theodolite seldom
require correction.
The adjustment of the line of collimation consists in placing
that line accurately at right angles to the horizontal axis. To
effect this, direct the telescope to a distant object, making the
cross-wires bisect the object precisely. Then carefully lift the
telescope out of its bearings, and replace with the ends reversed.
Revolve vertically, and again direct the telescope to the distant
object. If the cross-wires still coincide with the object, the
line of collimation is perpendicular to the horizontal axis. If
not, move the cross-wires one-half of the deviation by turning the
screws holding the diaphragm, and correct the other half by
moving the tangent screw of the horizontal circle. Reverse the
telescope again, and repeat the operation until the adjustment is
perfect.
In the Y-theodolite, the line of collimation is adjusted by
bringing the intersection of the cross-wires upon some well-
defined distant object. The telescope is turned round on its
collars in the Y's until the level is uppermost. Then, if the
cross-wires do not continue to coincide with the object, half the
difference must be corrected by moving the cross-wires, and the
other half by moving the tangent screw of the horizontal circle.
4. The level attached to the telescope must be parallel to the
adjusted line of collimation. To effect this adjustment in the
transit-theodolite, the elevation or depression of a distant object
is taken. The instrument is then reversed, the telescope revolved
vertically, and again directed to the same object. The mean of
the two readings will be the true elevation or depression of the
object. Set the verniers to this mean angle, and again observe
the object, making the intersection by means of the screws
retaining the index in its horizontal position. Then, correct the
level by its own adjusting screws.
To effect the adjustment in the Y-theodolite, the clips for
securing the supports that hold the telescope should be thrown
open, and the bubble of the spirit-level brought to the centre of
100 MINE-SURVEYING.
the tube by means of the tangent screw attached to the vertical
arc. The telescope should then be lifted out of its supports, and
reversed. If the bubble does not remain central, correct half
the error by the adjusting screws connecting the level with the
telescope, and the other half by the tangent screw of the vertical
arc.
5. When the telescope level has been adjusted, and the vernier-
plate is truly horizontal, it is necessary to note whether the zero
of the vertical circle coincides with the zero of its vernier. If
it does, there is no index-error. If it does not, the amount of
error should be noted and applied as a constant correction to all
subsequent readings.
6. The adjustment of the horizontal axis exactly perpendicular
to the vertical axis is, as a rule, left to the instrument-maker. In
some theodolites, however, there are adjusting screws for the
supports of the vertical axis. This is usually the case in instru-
ments of American make. In order to determine whether the
horizontal axis is perpendicular to the vertical axis, direct the
intersection of the cross-wires to an object, the altitude of which is
considerable. Then turn the vertical limb, until the cross-wires
cut some other well-defined point near the ground. Revolve the
'telescope on its axis, and turn the vernier-plate 180. Then if, in
raising and lowering the telescope, the line of collimation passes
through the two objects, the adjustment is correct. If not, half
the deviation is to be corrected by the tangent screw of the hori-
zontal circle, and the other half by the adjusting screws of the
supports. The operation must be repeated until the adjustment
is correct.
The permanent adjustments described above should be made
with great care. Many valuable instruments have been injured
by students who were anxious to adjust them, but were un-
acquainted with the method. It is necessary to be quite certain
that an adjustment is required before a screw is touched.
Measuring Horizontal Angles. The theodolite, having been set
up so that the centre of the horizontal circle is perpendicularly
above or below the station-point, is carefully levelled. The
horizontal vernier-plate is then clamped at zero. The position
of the second vernier is noted, in case it does not read 180
exactly. The horizontal circle and vernier-plate clamped to-
gether are turned, until the telescope is directed to the left-hand
station. The horizontal circle is then clamped, and the cross-
wires are made to accurately bisect the point by means of the tan-
gent screw. The vernier-plate is then released, and the telescope
carefully moved, the lower supports only being touched, ur ,til the
right-hand object is bisected. The vernier plate is then clamped,
TIIE THEODOLITE. JQl
and the cross-wires are made to accurately coincide with the ob-
ject by means of the tangent screw attached to the vernier-plate.
The two verniers have thus described an arc on the horizontal
circle equal to the angle to be measured. This may be read
direct from vernier I. With vernier II. it is found by taking
the difference of its two readings. The mean of the results ob-
tained with the two verniers is taken as the correct angle.
Another method of measuring horizontal angles is to clamp
the horizontal circle in any position. Then, direct the telescope
to one of the stations, clamp the vernier-plate, and turn the tan-
gent screw attached until the cross-wires accurately bisect the
left-hand object. Read the angles indicated by the two verniers,
and note the mean of the two readings. Then release the
vernier-plate, and move the telescope until the right-hand
object is bisected. Clamp the vernier-plate, and make the cross-
wires accurately coincide with the object by means of the tangent
screw. Again read the two verniers, and note the mean of the
two readings. The difference between the first and second mean
readings will be the horizontal angular distance between the,
two points. Thus, as an example :
"- 4 / Vernier I. Vernier II. Mean.
The first reading . . 173 11' 353 11' 173 11' 00"
The second reading . 259 35' 79 34' 259 34' 30"
Correct angle, . . . * 86 23' 30"
The reason for reading the two verniers is to correct any error
due to eccentricity or incorrect graduation of the plates.
It is advisable to measure the angle a second time with the
telescope inverted. The errors occurring during the first
measurement also occur during the measurement with the tele-
scope inverted, but on the opposite side, so that the mean of the
two measurements gives a result nearly free from error.
Repetition. In measuring horizontal angles, when great
accuracy is required, the errors of graduation may be diminished
by the process known as repeating, an operation invented by
Tobias Mayer, of Gottingen, in 1752.
The mode of procedure is as follows : Determine the horizontal
angle between the points A and B in the usual way, the vernier-
plate being clamped at zero. Let the angular distance between
A and B be 30 10'. Now, leaving the vernier-plate clamped to
the horizontal circle, unclamp the vertical axis, and turn the
instrument back to A. Then clamp the vertical axis, release
the vernier-plate, and again direct the telescope to B. In this
way the reading will be repeated, beginning at 30 10' instead of
102
MINE-SURVEYING.
0'. Suppose the result now is 60 25'. Repeat again, start-
ing this time from 60 25', and suppose that the third result is
90 40'. Dividing this result by the number of readings, we
obtain, as mean result, 30 13' 20".
The operation may be repeated any number of times, care
being always taken to direct the telescope towards A by turning
the vertical axis, and towards B by turning the vernier-plate.
For each complete revolution of the vernier-plate, 360 must be
allowed. It is advisable to perform the operation with the
telescope inverted, and to take the mean of the two results
obtained with the telescope in its two positions.
The following is an example of repetition :
The horizontal angular distance between the two points
determined in the usual way was 102 45'. On repeating, the
following results were obtained :
No. of Repetitions. Eeadiug.
Ver. I. 51 00' 45" )
4 ! [
Ver. II. 231 00' 45" )
Ver. I. 153 45' 45"
Ver. II. 333 45' 45"
Ver. I. 256 31' 00"
Ver. II. 76 31' 00"
Mean.
411 00' 45''
Angle.
102 45' 11"
513 45' 45" 102 D 45' 09"
616 31' 00" 102 45' 10 T
With the telescope inverted, the followin
obtained :
No. of Repetitions.
4
Reading.
( Ver. I. 51 00' 15"
( Ver. II. 231 00' 15"
Ver. I. 153 45' 20"
Ver. II. 333 45' 30"
Ver. I. 256 30' 40"
Mean.
411 00' 15"
results were
Angle.
102 45' 04*
513 45' 25" 102 45' 05"
616 30' 35" 102 45' 06"
Ver. II. 76 30' 30 V
Mean = 102 45' 08".
Measurement of Vertical Angles. The instrument having been
carefully levelled, the telescope is directed to the object, the
elevation or depression of which is to be measured. The cross-
wires are made to accurately bisect the object by means of the
THE THEODOLITE.
103
tangent screw attached to the vertical circle. The angle is then
read from both verniers, and the mean of the two readings taken
as the correct angle. When great accuracy is required, the
determination should also be made with the telescope inverted.
The following is an example of the measurement of a vertical
angle in this way :
Vernier I.
Vernier II.
Reading.
12 45'
13 02'
13 06' 12 40'
Mean = 12 53' 15".
Mean.
12 53' 30*
12 53' 00"
The Solar Attachment is a contrivance that is fastened to the
telescope axis of American transit instruments for the purpose
of determining the true
meridian. The principle was
enunciated by W. A. Burt,
of Michigan, and applied by
him to the compass in 1836.
It has since come into gene-
ral use in the surveys of the
United States public lands,
the principal lines of which
are set-out with reference to
the true meridian.
The Burt solar compass
consists mainly of three arcs
of circles, by which can be
set off the latitude of a
place, the declination of the
sun, and the hour of the day.
Through the centre of the
hour arc passes a hollow
socket, containing the spindle
of the declination arc. This
is termed the polar axis.
When this axis is parallel to
the axis of the earth, the
vertical plane of the terres-
trial line of sight, as defined
by the slits in the vertical
sights of the compass, coin- p . qs
cides with the meridian.
Fig. 38 represents the solar apparatus placed upon the cross-bar
of the transit-theodolite. The form represented was patented by
104 MINE-SURVEYING.
Messrs. W. & L. E. Gurley, of Troy. The following is the manu-
facturers' description of this attachment : A small circular disc,
\\ inch in diameter, with a short round pivot projecting above-
its upper surface, is first firmly screwed to the telescope axis.
Upon this pivot rests the enlarged base of the polar axis, which
is also firmly connected with the disc by four capstan head
screws passing from the under side of the disc into the enlarged
base. These screws serve to adjust the polar axis.
The hour circle surrounding the base of the polar axis is
easily movable about it, and can be fastened at any point desired
by two flat-headed screws above. It is divided to 5 minutes of
time. It is figured from I. to XII., and is read by a small
index fixed to the declination circle moving with it. A hollow
socket, fitting closely to the polar axis, moves upon it, and may
be clamped at any point desired by a milled-head screw on top.
By its two expanded arms below, this furnishes a firm support
for the declination arc, which is securely fastened to it by two
large screws.
The declination arc is about 5 inches in radius. It is divided
to quarter-degrees, and reads by its vernier to single minutes of
arc, the divisions of both vernier and limb being in the same
plane. At each end of the declination arm is a rectangular
block of brass, in which is set a small convex lens, having its-
focus on the surface of a small silver plate fastened by screws to
the inside of the opposite block. On the surface of the plate,
two sets of lines are marked intersecting each other at right
angles. The two sets are termed the hour lines and the equa-
torial lines, as having reference respectively to the hour of the day
and the position of the sun in relation to the equator. The declina-
tion arm is also provided with a clamp and tangent movement.
The latitude is set off by means of a large vertical limb, below
the telescope, having a radius of 2^ inches. The arc is divided
to 30 minutes, and is figured from the centre each way in two
rows, from to 80, and from 90 to 10, the former series being
intended for reading vertical angles, the latter for setting off the
latitude. It is read by its vernier to single minutes. It has a
clamp screw inserted near its centre, by which it can be clamped
to the telescope axis in any desired position. The vernier of the
vertical limb is made movable by the tangent screw, attached so
that its zero is readily made to coincide with that of the limb
when the arc is clamped to the axis in adjusting the limb to the-
level of the telescope.
A spirit-level on the under side of the telescope, provided
with a scale, is indispensable in the use of the solar attachment.
When the telescope is made horizontal by its spirit-level, the
THE THEODOLITE. 105
hour-circle will be in the plane of the horizon, the polar axis will
point to the zenith, and the zeros of the vertical arc and its vernier
will coincide. In this position of the instrument, if the arm of
the declination arc is placed at zero, and one lens directed to the
sun, its image will be seen between the lines on the silver plate
of the opposite block, and will indicate its position in the heavens,
on an instrument placed at the North Pole of the earth at the
time of the equinoxes, or when the equator is in the plane of the
horizon. If the telescope is inclined, as shown in Fig. 37, the
polar axis will descend from the direction of the zenith. The
angle through which it moves, being laid off on the vertical arc,
and shown by its vernier to be (say) 40, will be the co-latitude
of the place where the instrument is supposed to be used. The
latitude itself is found by subtracting 40 from 90, making it
50. Now, if the declination arm remains at zero, and the lens is
again directed to the sun, its image will appear on the opposite
plate as before, the instrument being used at the time of the
equinoxes at a latitude of 50. When, however, the sun passes
above or below the celestial equator, its declination or angular
distance from it, as given in the Nautical Almanack, can be
allowed for and set off upon the arc, and the image brought into-
position as before.
In order to do this, it is necessary that the latitude and.
declination be correctly set off upon their respective arcs, and
that the instrument be moved in azimuth until the polar axis
points to the pole of the heavens, or, in other words, is placed in
the plane of the meridian. Thus the position of the sun's image
will not only indicate the latitude of the place, the declination,
of the sun for the given hour, and the apparent time, but also
determine the meridian line passing through the place where the
observation is made.
The latitude of a place that is, its distance north or south ot
the equator, measured on a meridian may be found by means
of the solar attachment in the following manner : First carefully
level the instrument by means of the spirit-level of the telescope.
Next clamp the vertical arc, and, by means of the tangent screw,
make its zero and that of the vernier exactly coincide. Then,
having the declination of the sun for 12 o'clock of the given day
as affected by refraction carefully set out upon the declination,
arc, note also the equation of time. The sun is sometimes faster
and sometimes slower than a clock adjusted to mean time, the
difference being termed the equation of time. Fifteen or twenty
minutes before noon, the telescope is directed to the north,
and the object end lowered until, by moving the instrument on
its spindle and the declination arc from side to side, the sun's
106 MINE-SURVEYING.
image is brought nearly into position between the equatorial
lines. Then bring the declination arc directly in line with the tele-
scope, clamp the axis firmly, and with the tangent screw bring the
image precisely between the lines, and keep it there with the
tangent screw, raising it as long as it runs below the equatorial
line that is, as long as the sun continues to rise in the heavens.
When the sun reaches the meridian, the image will remain
stationary for an instant. The instant is, of course, apparent
noon when the index of the hour-arc should indicate XII. The
latitude is determined by reading the vertical arc.
The angle through which the polar axis has moved, being
measured from the zenith and not from the horizon, the angle
read on the vertical limb is the complement of the latitude. The
latitude may, however, be read direct from the inner row of
figures on the arc, beginning with 90 at the centre and running
to 10 on either side.
A very important addition to the solar attachment, patented
by Messrs. W. & L. E. Gurley, is shown in the figure. It is
an arrangement for recovering the latitude of a solar transit-
theodolite without referring to the vertical arc, and generally for
setting the telescope at any desired angle in setting-out inclines.
It consists of a spirit-level, connected by a short conical socket
with the end of the telescope axis, to which it is clamped by a
milled-head screw, and made adjustable by a screw and spring
on opposite sides of the enlarged end of the level-tube. When
the milled-head screw at the telescope axis is released, the level
turns vertically upon the axis, and can thus be set at any angle
with the telescope.
The latitude being set off upon the vertical arc, as usual, the
level is clamped, and centred. The telescope may then be
released and used in running lines, until it is desired to recover
the latitude again. This is accurately done with the spirit-level
alone without referring to the vertical arc.
The declination of the sun given in the Nautical Almanack
from year to year is calculated for apparent noon at Greenwich.
To determime it for any other hour at any other place, reference
must be made not only to the difference of time arising from the
longitude, but also to the change of declination from day to day.
Thus, supposing that the observations are being made at a place
eight hours west of Greenwich, the declination given in the
almanack for Greenwich noon of any day, will correspond to
the declination at the place in question at 4 o'clock a.m., of the
same date. To this must be added algebraically the hourly change
in the declination, also given in the almanack. A table may thus
be prepared giving the declination for each hour of the day.
TRAVERSING UNDERGROUND. 10?
CHAPTER IX.
TRAVERSING UNDERGROUND.
Use of the Theodolite in the Mine. In making a surface-
survey with the theodolite, one line may be measured, from which
all the other distances may be calculated by making them sides
of a series of imaginary triangles, the angles of which are deter-
mined. This method obviously cannot be employed in the
narrow workings of a mine, and consequently recourse must
always be had to the method of traversing. A traverse is a
series of consecutive drafts, of which the lengths and bearings
or azimuths are determined. When the miner's dial is used,
the bearing of each course is determined by the needle inde-
pendently of that of the preceding course. When the theodolite
is used, the readings taken are the angles contained by each
successive line and the preceding one.
When the station representing the angular point is marked
on the roof of the level, the theodolite must be so placed that
the centre of its horizontal circle is exactly perpendicular below
that point. The accuracy of the survey depends to a very great
extent upon the manner in which this operation is performed.
When the angular points are to be permanently marked, brass or
iron hooks (Fig. 39) may advantageously be used. The station-
point is marked by a hole in the hook, through which
a plumb-line may be passed. The hooks are driven
into the timbering of the roof, or with hard rock or
masonry into wooden pegs driven into holes previ-
ously drilled for the purpose. For centering, a
plummet is employed, the point of which coincides
with the axis of the line. When the plummet is
steady, and its point is directly above the centre of
the horizontal circle, the instrument is centered. A
mark should be made on the spirit-level, or on the
telescope, to indicate the position of the centre of
the horizontal circle. In order to ascertain whether
this mark is accurately in the axis of rotation of
the theodolite, the instrument, having been care-
fully levelled, is rotated under the plummet. If the mark is in
108 MINE-SURVEYING.
the vertical axis of the theodolite, it will retain the same position
under the point of the plummet during the rotation. If not, it
will describe a circle, the centre of which is the true point to be
used for centering.
If the workings of the mine are so low that a tripod-stand
cannot be used, recourse must be had to an iron arm screwed
into the timbering or into a vertical prop, or to a thick board
firmly fixed horizontally across the level, as a support for the
instrument. A new theodolite stand, intended to replace the
ordinary tripod, was shown at the Budapest Exhibition in
1885. It is the invention of Professor Chrismar of the
Schemnitz School of Mines. It consists of a support fixed across
the level at such a height that the mine trucks can pass under-
neath it. A survey can thus be made without interfering with
the ordinary work of the mine. The instrument consists of two
hollow wrought-iron. pipes, one sliding within the other, in such a
way that the length may rapidly be increased or decreased. By
means of a steel wedge working in a screw, the stand may be
forced against the side timbers of the level with a pressure of as
much as 800 Ibs. without any part of the construction being
injured. The stand is prevented from rotating by providing it
at one end with three steel points. These stands can be used
from 35 inches up to 5 feet, and, with the lengthening bar sup-
plied, up to 6 feet 9 inches in width. The total weight of the
apparatus is 16 Ibs. The plate for the reception of the theodolite
is connected by a spindle with the outer iron pipe. This stand
has been adopted in the surveys of several of the Hungarian
mines with considerable success.
In using the theodolite underground, care must be taken to
avoid, as far as possible, short lines of sight. In the mine, the
cross-wires may be made to coincide with the object, and the
verniers may be read by artificial light, with the same precision
as at the surface. The unfavourable atmospheric conditions,
which so often interfere with the accuracy of surveys at the sur-
face, are not encountered underground. It cannot of course
be denied that, in subterranean excavations, difficulties have to
be overcome which never occur at the surface. For example,
great difficulties are met with in surveying with the theodolite
in very confined spaces, and particularly in shafts.
For long station-lines, a candle-flame is the best object to sight,
care being taken to shield it from draughts. With station-lines
less than 30 fathoms in length, it is advisable to sight a plumb-
line suspended from the angular point. This is distinctly seen
as a black line on a white ground, if a sheet of paper dipped in.
TRAVERSING UNDERGROUND. 109
oil is held behind it, and illuminated from behind by the flame of
a candle or lamp. A sheet of paper rendered transparent in this
way is visible at a much greater distance than a sheet simply
illuminated from the front side. When the air of the mine is
quite clear, a plumb-line can be sighted in this way at a distance
of 180 yards. Care must be taken that the paper is not held in
front of the plumb-line and the light behind, as, in this case, the
telescope will be directed not to the plumb-line, but to its shadow,
which also appears as a black line upon a white ground.
Weissbach advocated the use of a plummet-lamp, the flame of
which is accurately centered under the angular point. His lamp
has, however, not been adopted to any great extent, as it is
found to oscillate even with a moderate air-current. In collieries,
a safety-lamp suspended in the same way may be advantageously
used. A contrivance for turning the lamp on its longitudinal
axis must be provided, in case one of the rods outside the glass
cylinder obscures the flame. The flame of a safety-lamp burns
very uniformly, and is a very good object to sight. The lamp,
too, hangs very steadily on account of its weight.
In the anthracite mines of Pennsylvania, a plummet-lamp is
used in underground surveying. It consists of a brass lamp,
suspended by two chains, and terminated below in a conical
plummet. It is provided with a so-called compensating ring,
that is, a gimbal ring, surrounding and supporting the lamp,
which swings freely within it upon an axis. The two chains are
attached to this ring at the extremities of a diameter perpen-
dicular to the axis. Thus the point of suspension, the centre
of the lamp-flame, and the steel point of the plummet always
lie in a true vertical line, no matter how much the brass chains
may alter in length from the heating of the lamp or the wearing
of the links. A shield at the top prevents the flame from burn-
ing the string. These lamps are used in pairs for back and
forward observations.
The safety-lamp may be supported on a truly horizontal tripod-
rest, in which case it is advisable to use three tripods, a central
one carrying the theodolite, and two others carrying safety-lamps
in brass cups for back- and fore-sight respectively. Mr. W. F.
Howard advocates the adoption of coloured glasses, red and green,
for the object-lamps. Additional certainty is thus afforded from
the impossibility of mistaking other mining lights for the object.
For the same reason, H. Huabner* employs a plummet-lamp
with a red glass.
* Preuss. Zeitschr., vol. xxxii., p. 309, 1884.
110
MINE-SURVEYING.
In reading the graduations of the theodolite, a copper or brass
lamp should be used. The metal should be tested as to its free-
dom from magnetic substances. An oil lamp will be found more
agreeable to use than a candle. In fiery collieries, a small copper
or brass safety-lamp must be used. Unfortunately, all safety-
lamps give a poorer light than the open lamp or candle, and their
construction will not permit of the flame being brought near the
compass graduation and the verniers. A method of increasing
the illuminating power of safety-lamps, suggested by Mr.
Przyborski,* a Hungarian mine-surveyor, appears, therefore, to
merit attention. To one of the rods guarding the gauze exter-
nally, a powerful condensing lens is fastened by means of a double-
jointed arm. The lens can thus be brought into any position
that may be desired. Safety-lamps modified in this way have
been used for some time in the surveys of the Resicza collieries
in Hungary, with great success. Mr. E. B. Coxef in Penn-
sylvania has constructed a plummet-Mueseler safety-lamp for
surveys in fiery mines.
An ingenious device recently suggested by Professor Brathuhn,
of the Clausthal School of Mines, will probably come into general
use. To two of the rods outside the glass cylinder of the safety-
lamp (Fig. 39) a small plate is fastened by two screws. In the
Fig. 39a.
centre of this plate, opposite the flame, a tube is inserted, and
into this a bored cork fits. Through the bored cork passes a
curved glass rod, with a circular section O43 inch in diameter.
The light which passes in at the terminal surface is totally
reflected by the curved surfaces of the rod, and passes out at
* Berg. H. Ztg., vol. xliii., p. 49, 1884.
t Trans. Amer. Inst. M.E., voL iii., p. 39.
TRAVERSING UNDERGROUND. Ill
the lower end in full intensity. The free end of the glass rod,
which can easily be moved in its cork-holder, is placed over
the vernier, and a steady adequate light is obtained. Even in
mines free from gas it appears worth while to use a light
safety-lamp for theodolite work, as the flame is so steady and so
free from smoke.
A novel method of lighting has been adopted by Mr. Stanley,
who has adapted the prismatic compass of the military surveyor
for use underground. In this instrument the floating ring
attached to the magnetic needle is made of transparent celluloid,
and light is thrown under it from a small movable lamp by
means of a large prism. The floating ring is divided to half-
degrees, and the divisions can be very clearly read.
The electric light has been successfully applied to survey-
ing purposes by Professor Chrismar,* who, in his theodolite-
surveys of the Schemnitz mines, uses incandescent lamps as
objects to be sighted, and a smaller incandescent lamp for
reading the verniers. The electric current is obtained from an.
accumulator.
When the theodolite is used underground, it is necessary to-
illuminate the cross-wires. This is best done by reflecting light
into the telescope through the object-glass, in such a way that
the object can, at the same time, be sighted without hindrance.
For this purpose, a ring is fitted on to the object-end of the
telescope. To the ring is fixed at an angle of 45 a piece of
brass, silver-plated on the under side, with an elliptical hole in
the centre. The optical axis of the telescope thus passes approxi-
mately through the centre of the hole in the reflector. Two-
forms of reflector are shown in Fig. 40.
In one case there is an elliptical hole, in
the other there is a small ellipse of metal.
A light held near the reflecting surface
40. illuminates the cross- wires. Satisfactory
results can be obtained when the reflector
is made of white cardboard. For illuminating the cross-wires
very little light is required. The elliptical hole of the one
reflector must therefore not be too small, nor the small ellipse
of the other too large. In the theodolites made by Messrs.
Troughton and Simms, the cross-wires are illuminated by means
of a hole drilled in the supports, and a small mirror placed at an
angle of 45, in the axis of the telescope. The light is held near
the supports, instead of near the object-glass.
* Oesterr. Ztschr., 1886, p. 395.
112
MINE-SURVEYING.
Shades of white note-paper should be fixed to the vernier-
microscopes of the theodolite, and the light should be allowed
to fall on the back of them. In this way, the vernier can be
read underground with great precision. In some theodolites,
ground glass or ivory reflectors are placed above the verniers.
They are useful, not only in the mine, but at the surface on a
bright day when there is a difficulty in reading the vernier
owing to the glare of the silver surface.
The following is an example of the survey of a closed polygon
with the theodolite :
No. of Line.
Horizontal
Aug.es.
Meridian
Angles.
Measured
Distance.
Mag. iner. . .
000'
000'
Links.
1 off mag. mer.
121 27'
121 27'
1091
2 off 1 . . .
97 36'
39 03'
252
3 off 2 . . .
209 01'
68 04'
196
4 off 3 . . .
159 40'
47 44'
534
5 off 4 . . .
195 32'
63 16'
384
6 off 5 . . .
85 31'
328 47'
336
7 off 6 . . .
152 07'
300 54'
1055
8 off 7 . . .
103 34'
224 28'
771
9 off 8 . . .
104 03'
148 31'
154
10 off 9 . . .
262 58'
231 29'
605
1 off 10 . . .
69 58'
121 27'
proof line.
In traversing underground, the theodolite is set up at a
station, B, and after levelling, and clamping the plates, the
magnetic meridian is observed. The telescope is then directed
to a line suspended down the shaft at A. The vernier-plate is
then released, and the telescope directed to the forward station
at C. The first angle is entered in the survey-book as 00',
with the length of the line A B in the distance column. The
angle indicated by the verniers is read, and noted in the column
for horizontal angles. The distance, B C, is then measured, and
TRAVERSING UNDERGROUND. 113
noted with any remarks that may be necessary. Then, remove
the instrument to 0, level, clamp the vernier-plate at zero, and
direct the telescope to the back station, B. Release the vernier-
plate, and direct the telescope to station D. Read the angle,
and note it, while D is being measured. After reading the
horizontal angles, the vertical angles are read if required, and
noted as angles of elevation or depression. Proceeding in this
way, the conclusion of the survey is arrived at.
Before this traverse can be laid down upon paper, the hori-
zontal angles must be reduced to angles from the first line (in
this case the magnetic meridian) as meridian for the whole. The
rule for reducing the horizontal angles to plotting angles from
one meridian is as follows : Rule : To the first meridian angle
add the next observed horizontal angle. If the sum exceeds
180, deduct that amount from it. The remainder will be the
second meridian angle. To this, add the next observed angle
and proceed as before. When the sum of the meridian angle and
the next observed angle is less than 180, it must be increased
by 180. If, after deducting 180, the remainder exceeds 360,
it must be diminished by that amount, to give the required
meridian angle.
In the example given, the angles would be reduced to one
meridian in the following manner :
Meridian 00' + 1st angle 121 27' = 121 27' = No. I mer. angle
No. I meridian angle 121 27' +2nd angle 97 36' = 219 03'
219 03' - 180 00' = 39 03' = No. 2
(39 03' + 209 01') - 180 = 68 04' = No. 3
(68 04' + 159 40') - 180 = 47 44'= No. 4
(47 44' + 195 32') - 180 = 63 16' = No. 5
(63 16' + 85 31') + 180 =328 47'= No. 6
(328 47' + 152 07') - 180 =300 54'= No. 7
(300 54' + 103 34') - 180 =224 28' = No. 8
(224 28' + 104 03') - 180 = 148 31' = No. 9
(148 31' + 262 58') - 180 =231 29' = No. 10
(231 29' + 69 58') - 180 =121 27'= Proof
In working a closed traverse, the angles recorded form the
angles of the polygon. If the survey has been kept on the left
hand these angles will be interior ones, and a means is afforded
of testing the accuracy of the survey, as the interior angles of
the polygon together with four right angles should be equal to
twice as many right angles as the figure has sides.
The interior angles of a traverse may be found from the bear-
ings or courses by the following rules :
8
114 MINE-SURVEYING.
1. When the two lines lie in the first and second quadrants,
N.-E. and S.-E., or in the third and fourth quadrants, S.-W. and
N.-W., their sum is the interior angle.
2. When the two lines lie in the first and third quadrants,
N.-E. and S.-W., or in the second and fourth quadrants, S.-E.
and N.-W., their difference is the interior angle.
3. When the two lines lie in the second and third quadrants,
S.-E. and S.-W., or in the first and fourth quadrants, N.-E. and
N.-W., their sum deducted from 180 is the interior angle.
4. When the two lines lie both in the same quadrant, their
difference added to 180 is the interior angle.
For example. Let line 1 bear N. 63 16' E., and line 2 bear
S. 59 06' E., then the angle between the two bearings is
63 16' + 59 06' = 122 22'.
There is another method of measuring angles well adapted for
use in mines. It is, however, only practicable with a transit-
theodolite. The mode of procedure is as follows : Clamp the
vernier-plate at 00', unclamp the vertical axis ; direct the tele-
scope to the back object, and direct the line of collimation exactly
towards the object by the tangent screw of the vertical axis.
Revolve the telescope vertically. Unclamp the vernier-plate;
direct the telescope to the forward object; clamp the vernier-
plate, and direct the line of collimation exactly towards the
object by the tangent screw of the vernier-plate. Angles where
the vernier has moved in the direction of the graduation are
minus, or to be subtracted. When the vernier has moved in the
opposite direction, the angles are plus, or to be added.
This is the method of surveying adopted in the anthracite
mines of Pennsylvania. Mr. E. B. Coxe * works with the transit-
theodolite and plummet-lamps, with a single assistant, in the
following manner : He first selects the stations, marking the
places where spuds, or nails with a hole in the head, are to be
driven into the timbers. This is done before any instrumental
work is begun, as much labour can be spared, and very short
sights can often be avoided. When the stations have been
marked out, he goes to station 2 with the transit-theodolite, and
by means of the plumb-bob belonging to the instrument centres
his instrument exactly under the spud. His assistant in the
meantime takes the two plummet-lamps, suspends one from spud
No. 1, and the other from spud No. 3, and then comes back to
hold the light while the final adjustments are made and the
readings taken. Mr. Coxe sets the vernier at zero, and sights
back to lamp No. 1. He then reads the compass-needle, inverts
* Trans. Amer. Inst. Min. Eng., vol. i., p. 375; vol. it, p. 219.
TRAVERSING UNDERGROUND. 115
the telescope, and sights the lamp at station 3. Having read
the two verniers and the needle, he turns the telescope back,
sights No. 1, and turns the vernier-plate round nearly 180 until
he sights No. 3, when he again reads the two verniers. Thus he
obtains four readings of the deflection from the verniers, and a
compass reading as a check. If the readings are concordant, he is
sure that there is no mistake, and proceeds with the instrument
to No. 3. In the meantime the assistant brings the plummet-lamp
from No. 1 to No. 2, and then takes the lamp from No. 3 to
No. 4. The distances are measured with a 500-foot steel band.
A survey made by Mr. Coxe, in the anthracite coal region of
Pennsylvania, of a closed polygon with a periphery of 6 660 '19
feet gave the following results :
STATION.
ANGLE.
REDUCED ANGLE.
DISTANCE.
Bight.
Left.
1
004'
+ 004'
Feet.
664-97
2
047'
...
+ 51'
711-55
3
052'
- o or
408-60
4
033'
...
+ 32'
567-25
5
179 32'
- 179 00'
186-05
B
...
31 12'
- 210 12'
88-42
Bi
19 39'
-229 51'
389-50
B 2
...
9 36'
-239 27'
631-00
B 3
4 06'
-235 21'
381-25
B 4
35 55'
...
- 199 26'
752-50
B s
62 39'
...
- 136 47'
294-80
5
...
9 or
- 145 48'
527-20
4
86 27'
...
- 59 21'
464-85
3
44 17'
- 103 38'
210-05
2
5 51'
- 109 29'
382-20
116 MINE-SURVEYING.
The mode of procedure in the surveys of the anthracite mines
of Pennsylvania varies considerably in the different districts.
The excellent method adopted in the mines of the Pennsylvania
Eailroad has been fully described by Mr. R. van A. Norris.*
The surveying party consists of a theodolite-man, station-man,
backsight, foresight, and chain-man, with a fireman to attend to
the safety of the party. Three tripods are used, but the wicks
of the tripod lamps, which were found too large for accurate sight-
ing, are replaced by steel wire one-sixteenth of an inch in diameter
and three-eighths of an inch in height. The sights are taken to
the bottom of this wire, and measurements are taken along the
line of sight with a 300-foot steel tape, marked at every 5 feet.
The station-man keeps ahead of the party and fixes the stations
-by drilling a small conical hole in the roof and suspending a
plumb-line from an iron rod with a notched end fitting the hole.
' The point is then transferred to the floor. A better method is
to put a horse-shoe nail, with a hole punched in the end, into
a plug of wood driven into a hole in the roof, and then to suspend
the plumb-line from the ring and to set up the theodolite under-
neath. A still better method is to put a shoe-peg holding a small
loop of cooper wire in the hole.
Continuous azimuth angles are run, and the entries in the note-
book consist of the vernier reading on a continuous gradation
from to 360, and the quadrant reading or course. A needle
reading is taken roughly with a view to detect serious errors. At
the commencement of the survey, the vernier is set to the course
of the first line taken from the notes of a previous survey. The
error in a closed survey of fifteen or more lines is rarely found to
exceed three minutes. For levelling purposes, the vertical angles
are read very carefully, the sight-wire being so arranged that it
is just 0-5 foot below the centre of the instrument. The method
of booking adopted is shown on the next page. The error on
closing this survey is one minute. The horizontal distances,
elevations, and vertical distances are calculated in the office;
and the column headed " staff" gives the distance from the centre
of the instrument to the station in the roof. With this method
of surveying, it is possible to attain great speed, from forty to
fifty stations being considered a fair night's work. All main
stations are plotted from calculated latitudes and departures (see
Chapter XI.), and the stations in the workings are filled in with
the aid of the protractor.
* School of Mines Quarterly, vol. xi., 1890, p. 328.
TRAVERSING UNDERGROUND.
117
p
II
a *3
\*
s v
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a 1
11
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"QOt-C5 "!> " QO r- O
118 MINE-SURVEYING.
Comparison of the Theodolite and Compass. On account of the
great cost of mining works, the surveys for determining the
viirection, in which levels or tunnels are to be set out, are of such
importance that the greatest possible accuracy is demanded.
For this reason, the mine-surveyor ought to employ the instru-
ments and methods that will give the most accurate results, and
to use less perfect instruments only for unimportant or prelimi-
nary surveys. The compass is an imperfect instrument of this
kind. It is of great value in certain cases, especially for filling
in details. When, however, it is used for large and important
surveys, there is always a danger of meeting with great inaccu-
racies. The daily variation of the declination of the needle is
nearly 10 minutes. Disregarding the occasional irregular per-
turbations of the needle, it is obvious that errors of 10 minutes
or more may occur in the period between 8 a.m. and 1 p.m., when
the declination of the needle passes from' its minimum to its
maximum. With a radius of 100, the chord of 10' is 0-29.
Therefore, from the change in the direction of the needle, there
will be in a length of 100 fathoms a lateral displacement of nearly
three-tenths of a fathom.
The uncertainty of the readings of the compass is also a dis-
advantage. With compasses of the ordinary size, the needle
cannot be read more accurately than to one-fifth of a degree.
Thus, errors of one-tenth of a degree, or 6 minutes, are unavoid-
able. In a length of 100 fathoms, this error in the bearing gives
a lateral error of 0-174 fathom.
Magnetic storms and the influence of ferriferous rock masses*
in the neighbourhood may give rise to considerable error, often
difficult to detect while the survey is in progress.
With the theodolite very different results are obtained. With
a 6-inch instrument, the horizontal angle, even without repeat-
ing, may be determined accurately to 30 seconds. The chord of
this angle being 0-000145, in a length of 100 fathoms, the
lateral error will not exceed 0-0145 fathom. The accuracy of
the theodolite is thus 30 times as great as that of the compass.
The repetition of the angles not only ensures great accuracy,
but is also a valuable check on the results. If, for example, an
angle has been repeated four times, and if the second, third, and
fourth observations give results closely approaching the result of
the first observation multiplied by two, three, and four respec-
tively, it is evident there can have been no serious error. With
the compass, on the other hand, when a bearing is read repeatedly,
the conditions remain the same, and it is quite possible to have
exactly the same error each time.
In reading a bearing with the compass, the instrument must
* See paper by Prof. A. W. Rucker on " Eegional Magnetic Disturb-
ances." Proc. Eoycd Soc., vol. xlviii., p. 505, 1890.
TRAVERSING UNDERGROUND. 119
remain unmoved. The surveyor is therefore compelled to put
his eye, his head, and sometimes his whole body into a particular
position with reference to the instrument. With the theodolite,
however, there is no necessity for such inconvenience, as the
horizontal circle may be turned to any required position, without
changing the angle indicated by the vernier. The results are
therefore read with far greater precision.
The disadvantages of the compass pointed out in this compari-
son are not presented by the vernier form of that instrument.
The modern vernier-compass or circumferenter is practically a
theodolite, from its compactness and simplicity specially adapted
to underground surveying.
The theodolite of the usual size has the disadvantage of
want of portability, its weight being a great drawback to its
use underground. The telescope, too, cannot be used in mines
when the air is bad from powder-smoke.
120 MINE-SURVEYIXG.
CHAPTER X.
SURFACE-SURVEYS WITH THE THEODOLITE.
Triangulation. The surface-survey of a mine royalty may be
made with almost any degree of accuracy that may be required
by having recourse to a system of triangulation. A base-line is
measured with great accuracy, and, from its ends, angles are
taken to distant stations. The instrument is placed at each of
these new stations, and angles taken to other stations. In this
way, the ground is covered with a network of imaginary tri-
angles, all the angles of which have been measured. The length
of the base-line being known, the lengths of the sides of the
triangles may be calculated trigonometrically.
The first operation is the measurement of the base-line, a pro
ceeding requiring careful attention, as any errors will be multi-
plied in proportion to the extent of the survey. The base-line
should be measured upon a level piece of ground, and from both
of its ends the principal objects in the surrounding country
should be visible. The length of the base-line should be in
proportion to the extent of the survey. For mine-surveying
purposes, a base-line need never be longer than 300 fathoms.
The last triangle of the system should be selected in such a
way that one of its sides may be measured. This line is called
the base of verification. One base-line can then be calculated
from the other, and the calculated and measured results compared.
In this way the' accuracy of the survey may be tested.
The ends of the base-line should be marked by means of some
permanent object, such as a large stone sunk in the ground, or a
pile driven deep and concealed from casual observation. In the
level surface of the stone, a hole about 3 inches in depth should
be bored to mark the exact end of the line, and to serve for the
reception of a signal pole. Permanently marked in this way,
stations could be readily found at a future period.
The triangles should be as nearly equilateral as possible.
Special care must bs taken to avoid ill-conditioned triangles, that
is, triangles with any angle less than 30 or more than 150, as a
point is not definitely defined if the lines fixing it meet at a
SURFACE-SURVEYS WITH THE THEODOLITE. 121
very obtuse or very acute angle. The triangular points may be
marked by means of wooden pickets, 1 foot long and 4 inches
thick, driven into the ground. In these, holes should be bored
to a depth of 4 inches for the reception of the signal poles.
In measuring the angles, the telescope is first directed to the
left-hand object and then to the right-hand one, so that the
verniers move in the direction in which the horizontal circle is
graduated. If the telescope is directed to the right-hand object
first, the angle read must be subtracted from 360 in order to
give the interior angle required.
The three angles of each triangle should be measured, so that
the accuracy of the operations may be checked, by adding them
together, when they should amount to 180. In the case of the
great triangles occurring in geodetic-surveys, the total exceeds
180. The so-called spherical excess is due to the fact that the
triangle is spherical on account of the curvature of the earth.
Small errors made in measuring the angles may be corrected by
adding to, or subtracting from, each angle one-third of the total
error.
It sometimes happens that the level ground is of limited
extent, and not suited for the measurement
of the whole of a base-line. In such a
case the base-line is prolonged by ranging
lines in continuation of it, at one or both
ends, until a suitable length is obtained.
The lengths of the additional lines are cal-
culated from angular measurements, as
follows :
When the measured base, A B (Fig. 41),
can be conveniently extended in one direc-
tion only, towards H, select a lateral station
point, C, so that the resulting triangles,
ABC and B E, shall be well-conditioned, and if possible nearly
equilateral. Measure all the angles of these two triangles, and
calculate the length of the side B 0. Then choose a point E
in the line ranged in continuation of A B, and by means of the
side B C and the angles C E B, B C E, calculate the length of B E.
Check the result by selecting another lateral station, D, on the
opposite side of the base-line, and by solving the triangles,
A B D, D B E. The length of the line B E is thus calculated
from independent data. E H represents a farther prolongation
of the base-line, and F and G the lateral stations, which form
the triangles, by means of which its length is calculated.
A comparatively short base-line may be connected with the
sides of large triangles, without prolonging it and without
122 MI SB-SURVEYING.
introducing ill-conditioned triangles, by continually increasing
the sides of the triangle, as shown in
Fig. 42. A B is the measured base-line,
and C and D are the nearest stations.
In the triangles ABC, ABD, all the
angles and the side A B being known,
the other sides can be readily calculated.
Then in each of the triangles DAG and
DBG, two sides and the included angle pj g 40
being known, the length D may be
calculated in a variety of different ways which will check each
other. Taking D C as a base-line, choose a pair of stations, E
and F, at opposite sides of the base, and as far from each other
as is consistent with making CDF and C D E well-conditioned
triangles. Proceed as before to calculate the distance E F.
This will probably be sufficiently long to serve as the side of a
pair of triangles. If not, continue the process until a distance
sufficiently long is obtained.
The triangulation-survey of a mine royalty is based on the
same principles, operations, and methods as are adopted on the
trigonometrical surveys of countries. In such surveys, the
spheroidal form of the earth's surface has to be taken into
account, and the amount of accuracy required is much greater
than that required for any ordinary topographical survey. Thus,
on the Ordnance Survey of the United Kingdom, the average
length of the sides of the Primary Triangulation was 35 miles ;
the longest side was 111 miles. The angles were measured with
four large theodolites, two 3 feet in diameter, one 2 feet, and one
18 inches. With the exception of the theodolite 2 feet in
diameter, these instruments were constructed by Rarnsden at
the commencement of the trigonometrical operations in England
in 1798. They are now exhibited in the South Kensington
Museum, and are still in perfect condition.
In order to show how accurately the main triangulation was
conducted, it may be mentioned that in 1826, a base-line was
measured at Lough Foyle, in the north of Ireland, by means of
General Colby's compensated bars, and in 1849 the old base-line
on Salisbury Plain was remeasured with the same apparatus.
The length of the Salisbury Plain base was 6 -97 miles, and that
of the Lough Foyle base 7-89 miles. The length of the latter
base was calculated by a triangulation carried from the Salisbury
Plain base, and the difference between the calculated and
measured length of the Lough Foyle base was only 5 inches.
By means of secondary triangulation, the long sides of the
principal triangulation were reduced to lengths of 5 miles. The
SURFACE-SURVEYS WITH THE THEODOLITE. 123
angles were measured with a 12-inch theodolite. The stations
selected were, as far as possible, permanent objects such as
church towers.
The 5-mile sides of the secondary triangulation were reduced
by means of the Parish triangulation to lengths of 1 mile, or
less. In towns, the points were sometimes within as short a
distance as 10 chains. The angles were measured with a 7-inch
theodolite. Finally, the details were filled in by means of
ordinary chain-surveying.
Computing the Sides of the Triangles. For the solution of the
triangles when the base and the three angles are given, the
ordinary sine ratio is employed
sin A
a
sin B
sinQ
c
when, if c represents the base,
c sin A
or, using logarithms,
log a = log c + L. sin A - L. sin 0.
The sine of an angle A is equal to 1 -f- cosec A. Instead,
therefore, of subtracting L. sin C, L. cosec may be added ; the
formula then is
log a = log c + L. sin A + L. cosec - 20.
In the survey of the triangles shown in Fig. 43, the base-line
af was found on measuring to be 4009-5 links. The angles were
as follows :
Fig. 43.
I. fag 35 12'
IV. cgre5642'
a gf 104 43'
ec<78503'
afg 40 05'
c eg 38 15'
II. abg 52 58'
V. dee 57 20'
bag 67 50'
ced5301'
agb 59 12'
crfe6939'
III. cbg 36 47'
VI. eg f 53 33'
bge 85 49'
efg 84 17'
beg 57 24'
fe g 42 10*
124: MINE-SURVEYING.
The sides are calculated in the following manner :
To find side a g in Triangle I.
af:ag = sinagf: sin afg
log a, g = log af + L. sin afg L. sin a gf.
log 4009-5 = 3-6030902
+ L. sin 40 05' = 9-8088192
- L. sin 104 43' = 9'9855135
logcrp = 3-4263959
ag = 2669 '3 links.
If instead of subtracting the sine of the angle opposite to the
given side, its cosecant is added, the result will be as follows :
log 4009 -5 = 3-6030902
+ L. sin 40 05' = 9 '8088 192
+ L. cosec 104 43' = 10-0144865
logag = 3-4263959
To find side/gr in Triangle L
af'.fff = sinagf: sin fag.
log 4009 -5 = 3-6030902
+ L. sin 35 12' = 9 '7607483
+ L. cosec 104 43' = 10'0144865
log/2 = 3-3783250
fg = 2389-6
To find side a b in Triangle II.
logag = 3-4263959
+ L. sin 59 12' = 9*9339729
+ L. cosec 52 58' = 10 '0978419
log a b = 3-4582107
a .6 = 2872-2
SURFACE-SURVEYS WITH THE THEODOLITE. 125
To find side b g in Triangle II.
loga*/ = 3-4263959
+ L. sin 67 50' = 9'9666533
+ L. cosec 52 58' = 10 '0978419
log 60 = 3-4908911
bg = 3096-7
In the same way, the lengths of the other sides will be found
to be as follows :
Triangle III.
log b c = log bg + L. sin 85 49' + L. cosec 57 24' -20
b c = 3666-0 links.
log eg = logbg + L. sin 36 47' + L. cosec 57 24' -20
c g = 2201 links.
Triangle IV.
log c e = log c g + L. sin 56 42' + L. cosec 38 15' - 20
ce = 297 1-5 links,
log e g = log c g + L. sin 85 03' + L. cosec 38 15' - 20
eg = 3541 -9 links.
Triangle V.
log c d = log c e + L. sin 53 01' + L. cosec 69 39' - 20
cd = 2531 -7 links,
log d e = log c e + L. sin 57 20' + L. cosec 69 39' - 20
de = 2668-0 links.
Triangle VI.
log ef = log eg + L. sin 53 33' + L. cosec 84 17' -20
ef= 2863-3 links.
log/0 = log eg + L. sin 42 10' + L. cosec 84 17' -20
logegr
L. sin 42 10'
L. cosec 84 17'
=
3-5492413
9-8269098
10-0021653
fag/*
=
3-3783164
fg
=
2389-55 links,
12G MINE-SURVEYING.
a result practically the same as that obtained in the solution of
triangle I.
In some cases the two sides of a triangle and the angle con-
tained between them may be known, and it is required to find
the two other angles, and the third side. In this case, the sum
of the two sides is to their difference, as the tangent of half the
sum of the two unknown angles is to the tangent of half their
difference. Half their difference thus found, added to half their
sum will be the greater of the two angles required that is, the
angle opposite to the greater side.
Interior Detail of the Triangulation. The triangulation for a
survey being completed, the filling-in of the interior detail pre-
sents no difficulty. Roads, rivers, woods, &c., may be surveyed
by traversing with the theodolite or with the dial. For filling in
details, the prismatic compass is of great use. It is a hand
instrument consisting of a glass-covered circular brass box, 2|
inches in diameter, containing a graduated card or aluminium
ring, under or across which a magnetic-needle is fixed. The card
or ring is divided to half or one-third of a degree. The needle
and card are accurately balanced. Sights are attached to the
rim of the box. The farther sight has a fine thread stretched
along its opening in the direction of its length. The near sight
has a small slit below which is a reflecting magnifying triangular
prism, so placed that on looking through the slit the eye sees at
the same time the vertical wire of the farther sight and the needle-
reading, the divisions on the card appearing as a continuation of
the wire. The graduation of the ring begins at the south end of
the needle, and proceeds towards the right, round to 360. In this
way bearings are shown to the east of north. With this instru-
ment, when held in the hand, bearings may be read to within 30
minutes to 2 degrees. The instrument is thus suitable only for
preliminary and unimportant work. Mounted on a stand, the
instrument gives more satisfactory results.
The plane table* is an instrument which may be advantageously
used for filling in details where minute accuracy is not required.
It consists of a drawing-board mounted on a portable tripod
capable of being levelled, like the graduated limb of the theodo-
lite. It must also have a free horizontal angular movement, and
be provided with a clamp and tangent screw. The index on the
board consists of a flat straight-edge, either with upright sights
at its ends or with a telescope for determining the line of sight.
The use of the plane table is similar to that of the theodolite.
Instead, however, of reading off horizontal angles and afterwards
plotting them on paper, the angles are at once laid down in the
field on a sheet of paper strained on the top of the table.
* Consult J. Pierce's paper on the economic use of the plane table, Min.
Proc. Inst. C.E., vol. xcii., 1888, p. 187.
SURFACE-SURVEYS WITH THE THEODOLITE. I'll
Before the introduction of the theodolite, the plane table was
largely used for mine-surveying in Sweden, where the magnetic
nature of the iron ore deposits renders the compass useless for
surveying purposes.
American Mining Claims. Prospectors are usually without
suitable instruments to lay off their claims on the surface with
any degree of accuracy, and consequently the methods they em-
ploy are generally very crude. Before the patent or title from the
United States can be obtained, a very accurate survey of the
claim must be made with the theodolite by a deputy of the
United States Surveyor-General of Public Lands. These officers
are known as the United States Deputy Mineral Surveyors, and
are required to pass an examination.
Mining claims are of different dimensions according to the
local laws. The length is limited by the United States laws to
1,500 feet in the direction, or along the strike, of the vein. The
width varies in the different States ; it is usually 300 feet on
each side of the middle of the vein at the surface. The end lines
of the claims must be parallel, but the side lines need not be so.
This prevents more than 1,500 feet of a vein being included in
one claim.
When mineral discoveries are made on surveyed land, the sur-
veys must be so connected with the public survey that there will
be no difficulty in finding some fixed point or corner of that
survey. When discoveries are made on unsurveyed land, the
survey must be connected with permanent natural objects, such
as fountain peaks or rocks.
It is frequently found that two or more claims conflict or over-
lap. In such cases, priority of location determines the ownership
of the area in dispute. In making the plan, the United States
Deputy-Surveyors must deduct the area in conflict from the sub-
sequent claim. When the survey for patent is completed, the
claim must be marked by at least four stakes, one in each corner.
According to the instructions issued to the United States
Deputy Mineral Surveyors, all mineral surveys must be made with
a transit-theodolite with solar attachment, or with some other
instrument acting independently of the magnetic meridian. All
courses must be referred to the true meridian. The magnetic
declination must be noted at each corner of the survey.
In case the claim is situated in a district where there are no
corners of the public survey within 2 miles, the surveyor must
establish a permanent mineral location monument. This should
consist of a post 8 feet long and 6 inches square, set 3 feet in
the ground, and protected by a well-built conical mound of stone,
3 feet high and 6 feet in diameter at the base. All corners of
128 MINE-SURVEYING.
the claim must be established in a permanent manner, and the
corner and survey number must be neatly chiselled on the
sides facing the claim. In case the point for the corner is
inaccessible, a witness-corner must be established as near as
practicable to the true corner, with which it must be connected
by course and distance.
The claimant is required by law to show that 500 dollars' worth
of labour has been expended upon the claim by himself. The sur-
veyor must, therefore, give full details of all improvements made
upon the claim. A preliminary plan on a scale of 200 feet to an
inch must be filed with the field-notes. With the notes, too, a
report must be submitted stating in detail the observations and
calculation for the establishment of the meridian from which the
courses were deflected, in cases where the solar attachment was
not used. If any of the lines of the survey were determined by
triangulation or traverse, full details must be given of the
calculations whereby the results reported in the field-notes
were obtained.
The field-notes must be prepared in conformity with the accom-
panying specimen :
FIELD-NOTES*
OF THE SURVEY OF THE CLAIM OF THE " ARGENTUM MINING COMPANY 5 '
UPON THE SILVER KING AND GOLD QUEEN LODES, AND SILVER
KING MILL SITE, IN ALPINE MINING DISTRICT, LAKE COUNTY,
COLORADO. Surveyed by G. LIGHTFOOT, April 22 to 24, 1886.
Survey No. 4225 A Silver King Lode. Beginning at corner No. 1,
identical with corner No. 1 of the location. A spruce post, 5 feet lotig
4 inches square, set 2 feet in the ground, with a mound of stone marked
(1)4225 A, whence the W. corner Section 22, Township 11 S., Range
81 W. of the 6th principal meridian, bears S. 79 34' W., 1378-2 feet.
Corner No. 1, Gottenburg lode (unsurveyed), bears S. 40 29' W., 187 '67
feet. A pine, 12 inches in diameter, blazed and marked B. T. (bearing-tree)
(1) 4225 A, bears S. 7 25' E., 22 feet. Mount Ouray bears N. 11 E.
Hiawatha Peak bears N. 47 45' W.
Thence S. 24 45' W. (variation 15 12' E.), 1242 feet to trail coursing
N.-W. and S.-E., 1365'28 feet to corner No. 2. A granite stone, 25 by 9 by
6 inches, set 18 inches in the ground, chiselled (2) 4225 A, whence corner
No. 2 of the location bears S. 24 45' W. , 134'72 feet. Corner No. 1, survey
No 2560, Carnarvon lode, bears S. 3 28' E., 116'6 feet. North end of
bridge, over Columbine Creek, bears S. 65 15' E., 650 feet.
Thence N. 65 15' W. (variation 15 20' E.), 152 feet intersect line 4-1,
survey No. 2560, at N. 38 52' W., 231 "2 feet from corner No. 1. 300 feet
to corner No. 3. A cross at corner point, and (3) 4225 A chiselled on a
granite rock in place, 20 by 14 by 6 feet above the general level, whence
* For a copy of these notes, I am indebted to the kindness of Mr. 0. Carstarphen, U.S.
Surveyor-General, Colorado.
SURFACE-SURVEYS WITH THE THEODOLITE. 129
corner No. 3 of the location bears S. 24 45' W., 134 "72 feet. A spruce
16 inches in diameter, blazed and marked B. T. (3) 4225 A, bears S. 58 W.,
18 feet.
Thence N. 24 45' E. (variation 15 20' E.), 73'4 feet intersect line 4-1,
survey No. 2560, at N. 38 52' W., 396 '4 feet from corner No. 1. 150 feet inter-
sect line 6-7 of this survey. 237 feet to trail, coursing N.-W. and S.-E.
1000-9 feet intersect line 2-3, Gottenburg lode, at N. 25 56' W, 76 '26 feet
from corner No. 2. 1365 '28 feet to corner No. 4, identical with corner
No. 4 of the location. A pine post, 4 '5 feet long, 5 inches square, set 1 foot
in the ground, with a mound of earth and stone, marked (4) 4225 A, whence
a cross, chiselled on rock in place, marked B. R. (bearing rock) (4) 4225 A,
bears N. 28 10' E., 58-9 feet.
Thence S. 65 15' E. (variation 15 12' E.), 28 '5 feet intersect line 1-4,
Gottenburg lode, at N. 25 56' W., 285 '13 feet from corner No. 1. 65 feet
intersect line 5-6 of this survey. 300 feet to corner No. 1, the place of
beginning.
Gold Queen Lode. Beginning at corner No. 5, a pine post, 5 feet long,
5 inches square, set 2 feet in the ground, with mound of earth and stone,
marked (5) 4225 A, whence corner No. 1, of this survey, bears S. 14 54' E.,
37016 feet. A pine, 18 inches in diameter, bears S. 33 15' W., 51 feet,
and a silver spruce, 13 inches in diameter, bears N. 60 W., 23 feet. Both
are blazed and marked B. T. (5) 4225 A.
Thence S. 24 30' W. (variation 15 14' E.), 285 feet intersect line 4-1
of this survey. 315 feet intersect line 4-1, Gottenburg lode, at N. 25 56' W.,
237*78 feet from corner No. 1. 688 '3 feet intersect line 1-2, Gottenburg
lode, at N. 64 04' E., 12-23 feet from corner No. 2. 1438 feet to trail,
coursing N.-W. and S.-E. 1500 feet to corner No. 6, a granite stone, 34 by
14 by 6 inches, set 1 foot in the ground to bed-rock, with mound of stone,
chiselled (6) 4225 A, whence a cross, chiselled on ledge of rock, marked
B. R. (6) 4225 A, bears due north 12 feet.
Thence N. 65 30' W (variation 15 20' E.), 70'3 feet intersect line 3-4 of
this survey. 223 '37 feet intersect line 4-1, survey No. 2560, at N. 38 52' W. ,
567-28 feet from corner No. 1. 300 feet to corner No. 7, a cross at corner
point, and (7) 4225 A chiselled on a granite boulder, 12 by 6 by 3 feet above
ground, whence a cross chiselled on vertical face of cliff, marked B. R.
(7) 4225 A, bears N. 72 W., 56'2 feet. A pine, 14 inches in diameter,
blazed and marked B. T. (7) 4225 A, bears N. 10 E., 39 feet.
Thence N. 24 30' E. (variation not determined on account of local attrac-
tion), 38-43 feet intersect line 4-1, survey No. 2560, at N. 38 52' W.,
653 feet from corner No. 1. 165 feet to trail, coursing N.-W. and S.-E.
1043-73 feet intersect line 2-3, Gottenburg lode, at N. 25 56' W., 379-06 feet
from corner No. 2. 1432 '90 feet intersect line 4-1, Gottenburg lode, at
N. 25 56' W., 626-94 feet from corner No. 1. 1500 feet to corner No. 8,
a spruce post 6 feet long, 5 inches square, set 2-5 feet in the ground, with
mound of stone, marked (8) 4225 A, whence a cross chiselled on rock in
place, marked B. R. (8) 4225 A, bears S. 9 12' E., 15'8 feet. A pine,
20 inches in diameter, blazed and marked B. T. (8) 4225 A, bears N. 83 E.,
28 -5 feet.
Thence S. 65 30' E. (variation 15 16' E.), 300 feet to corner No. 5, the
place of beginning.
Area. Total area of Silver King lode, 9 '403 acres. Less area in conflict
with survey No. 2560, 0'124 acre, and in conflict with Gottenburg lode,
1 '363 acre ; total 1 -487 acres. Net area of Silver King lode, 7'916 acres.
Total area of Gold Queen lode, 10 '331 acres. Area in conflict with other
surveys, 4'022 acres, thus, with survey No. 2560, 0'034 acre, with Gotten-
130
MINE-SURVEYING.
bnrg lode, 2 '679 acres, with Silver King lode (exclusive of conflict of said
Silver King lode with the Gottenburg lode), 1'309 acres. Net area of Gold
Queen lode, 6 '309 acres.
The net area of the lode claim, including the Gold Queen lode and Silver
King lode, is 14 '225 acres.
Survey No. 4225 B Silver King Mitt Site. Beginning at corner No. 1,
a gneiss stone, 32 by 8 by 6 inches, set 2 feet in the ground, chiselled
(1) 4225 B, whence W. corner section 22, Township US., Range 81 W. of
the 6th principal meridian, bears N. 80 W., 1880 feet. Corner No. 1,
Claim. o
ARCENTUM MINING COMPANY
ALPINE MINING DISTRICT
Cotmty , Colorado *.
Fig. 44.
survey No. 4225 A, bears N. 40 44' W., 760'2 feet. A cotton-wood,
18 inches in diameter, blazed and marked (1) 4225 B, bears S. 5 30' E.,
17 feet.
Thence S. 34 E., 90 feet road to Wabasso, coursing N.-E. and S.-W.
208 feet right bank of Columbine Creek, 75 feet wide, flowing S.-W.
504'8 feet to corner No. 2, an iron bolt, 18 inches long, 1 inch in diameter,
SURFACE-SURVEYS WITH THE THEODOLITE. 131
set 1 foot in rock in place, chiselled (2) 4225 B, whence a cotton-wood,
blazed and marked B. T. (2) 4225 B, bears due east, 182 feefc.
Thence S. 56 W., 351 feet left bank of Columbine Creek. 394 "4 feet to
corner No. 3, a point in bed of creek, unsuitable for the establishment of
a permanent corner.
Thence N. 34 W., 15 feet right bank of Columbine Creek. 40 feet to
witness corner No. 3, a pine post, 4'5 feet long, 5 inches in diameter, set
1 foot in ground, with mound of stone, marked W. C. (3) 4552 B, whence
a cotton-wood, 15 inches in diameter, bears N. 11 E., 16 '5 feet, and a cotton-
wood, 19 inches in diameter, bears N. 83 W., 23 feet; both blazed and
marked B. T. VV. C. (3) 4225 B. 370 feet road to Wabasso, coursing N.-E.
and S.-W. 647 "2 feet to corner No. 4, a gneiss stone, 24 by 10 by 4 inches,
set 18 inches in the ground, chiselled (4) 4225 B, whence a cross, chiselled
on ledge of rock, marked B. R. (4) 4225 B, bears N. 85 10' E., 26'4 feet.
Thence N. 48 43' E., 125 '5 feet to corner No. 5, a gneiss stone, 30 by 8
by 5 inches, set 2 feet in the ground, chiselled (5) 4225 B.
Thence S. 34 E., 158 '3 feet to corner No. 6, a pine post, 5 feet long,
5 inches square, set 2 feet in the ground, with mound of earth and stone,
marked (6) 4225 B, whence a pine, 12 inches in diameter, blazed and marked
B. T. (6) 4225 B, bears S. 33 E., 63 "5 feet.
Thence N. 56 E., 270 feet to corner No. 1, the place of beginning. The
variation at all the corners is 15 20' E. The area of the mill site is 5 acres.
Expenditure of Five Hundred Dollars. The value of the labour and
improvements upon this claim is not less than 500 dollars. The said
improvements consist of:
The discovery shaft of the Silver King lode, 6 by 3 feet, 10 feet deep in
earth and rock, which bears from corner No. 2, N. 6 42' W., 237 '5 feet.
Value 80 dollars. An incline, 7 by 5 feet, 45 feet deep in coarse gravel and
rock, timbered, course N. 58 15' W., dip 62, the mouth of which bears
from corner No. 2, N. 15 37' E., 908 feet. Value 550 dollars. The discovery
shaft of the Gold Queen lode, 5 by 5 feet, 18 feet deep in rock, which bears
from corner No. 7, N. 67 39' E., 219'3 feet, at the bottom of which is
a cross-cut, 6 '5 by 4 feet, running N. 59 26' W., 75 feet. Value of shaft
and cross-cut 1000 dollars. A log shaft-house, 14 feet square, over the
last-mentioned shaft, value 100 dollars. Two-thirds interest in an adit,
6 '5 by 5 feet, running due west 835 feet, timbered, the mouth of which
bears from corner No. 2, N. 61 15' E., 920 feet. This adit is in course of
construction for the development of the Silver King and Gold Queen lodes
of this claim, and survey No. 2560, Carnarvon lode. The remaining one-
third interest has already been included in the estimate of 500 dollars
expenditure upon the latter claim. Total value of adit, 13,000 dollars. A
drift, 6 '5 by 4 feet, on the Silver King lode, beginning at a point in the adit
800 feet from the mouth, and running N. 20 20' E., 195 feet; thence
N. 54 15' E, 40 feet to breast. Value 2,800 dollars.
Other improvements consist of:
A log cabin, 35 by 28 feet, the S.-W. corner of which bears from corner
No. 7, N. 30 44' E., 496 feet. A dam, 4 feet high, 50 feet long, across
Columbine Creek, the south end of which bears, from corner No. 2 of the
mill-site, N. 58 20' W., 240 feet. An adit, 6 by 4 feet, running N. 70 50' W.,
100 feet, the mouth of which bears, from corner No. 5, S. 58 12' W.,
323 feet.
Instrument. The survey was made with a Young & Sons' mountain
transit-theodolite with solar attachment. The courses were deflected from
the true meridian as determined by solar observations. The distances were
measured with a 50-foot steel tape.
132
MINE-SURVEYING.
The first corner of the survey must be connected by course and
distance with some corner of the survey of public lands of the
United States, if the claim lies within 2 miles of such corner.
The United States public lands include all the territory north of
the Ohio River and west of the Mississippi River, not owned by
individuals previous to the date of cession to the United States
Government. All this territory has been laid out in rectangular
tracts bounded by north and south, and east and west lines, each
tract having a particular name. The reference lines consist of
principal meridians and standard parallels. The former may be
more than 100 miles apart. The standard parallels are 24 or 30
miles apart. In setting-out these lines, each mile is marked by a
Btone, tree, or mound, and is called a section corner. Every sixth
mile has a different mark, and is called a township corner. From
each of these, auxiliary meridians are set-out north to the next
standard parallel. The territory is thus divided into ranges, which
are 6 miles wide and 24 miles long. Each range is numbered
east and west from the principal meridian. The ranges, being
cut by east and west lines joining the corresponding township
corners on the meridian, are thus divided into townships each 6
miles square. Each township is divided into 36 squares called
sections, by meridians 1 mile apart, and by east and west lines at
the same distance from each other. The sections are divided
into half-sections and quarter-sections. The law requires that all
excesses or deficiencies, either from erroneous measurement or
from the convergence of the meridians, shall, so far as possible,
be thrown on the extreme tier of sections and half-sections con-
tiguous to the north and west boundaries of townships.
Surveying in South Africa. In the colony of the Cape of Good
Hope the legal unit of land measure is the Cape rood. The
Cape measures are as follows :
Measures of Length.
Measures of Surface.
f
Roods.
425-94
Feet.
Inches.
Morgen.
1
Sq. roods.
600
Sq. feet.
Sq. inches.
...
1
12
...
...
1
144
...
1
12
...
...
1
144
In order to convert British feet into Cape roods, multiply
by 0-08067, and acres into morgen, multiply by 0-47246. In
order to convert Cape roods into feet, multiply by 12-396, and
morgen into acres, multiply by 2-11654.
SURFACE-SURVEYS WITH THE THEODOLITE. 133
In ordinary survey work in South Africa, measurements of
distances by chain or steel tape are less frequently resorted to
than in Europe. The use of the chain is limited to the measure-
ment of base lines, from which the longer distances are derived
by triangulation. Base lines should be measured at least twice,
and the results should agree within an inch in 100 roods. The
triangulation is commenced from the base line, and the size of
the triangles increased as rapidly as possible without making
them ill-conditioned until their sides have an average length
sufficient to enable the surveyor to cover the area to be sur-
veyed with a set of comparatively large triangles. With this
main triangulation, all other points of the survey are connected
by minor triangulation. The vertices of the triangles are shown
by flags, the staves of which should be perpendicularly fixed in
the ground. The theodolite is invariably used for measuring
the angles.
134 MINE-SURVEYING.
CHAPTER XL
PLOTTING THE SURVEY.
Scales. Plotting a survey consists in representing on paper,
to a smaller scale, the lines and angles determined on the ground.
The operation of drawing lines, the length of which shall be some
fraction of that of the lines measured on the ground, is called
drawing to scale.
A scale may be defined as an artificial means of representing
any given dimensions. Thus, a fathom may be represented by a
straight line 1 inch long; then 2 fathoms would be represented
bv a line of 2 inches, 3J fathoms by 3| inches, and so on. Three
kinds of scales of equal parts may be distinguished 1, simply
divided scales ; 2, diagonal scales ; and 3, vernier scales.
1. Simply divided scales consist of any extent of equal divisions,
numbered 1, 2, 3, &c., beginning at the second division on the
left hand. The first of these primary divisions is sub-divided
into 10 equal parts, and from these sub-divisions the scale is
named. Thus it is a scale of 30, when 30 of these secondary
divisions are equal to 1 inch. If the primary divisions are taken
as units, the secondary divisions will represent tenths.
As an illustration of the method of constructing scales, let it
be required to construct a scale of 3 chains to the inch, to exhibit
18 chains. Draw a line 6 inches long, and divide it into 18 equal
parts. These are the primary divisions, each of which represents
one chain. Divide the first primary division into 10 equal parts;
each of these secondary divisions will represent 10 links. Next
draw a thicker line at a short distance below the first line, and
draw vertical lines between them to indicate the divisions of the
first lines. Place the zero at the line between the first and second
primary divisions, and then, from left to right, place in succession
the numbers 1, 2, 3, &c., at each primary division. Number the
secondary divisions from the zero from right to left, O'l, 0-2,
0'3, &c. With this system of numbering, lengths are taken
from the scale with greater facility. Thus, to take off 3 chains
25 links from the scale described, one point of the dividers
must be placed at the figure 3 on the scale, and the other point
PLOTTING THE SURVEY. 235
extended back to a place midway between the second and third
secondary divisions.
In cases where fathoms and feet are required to be shown, tha
first primary division is divided into 6 divisions representing
feet. If the scale is to show feet and inches, the first primary
division must be divided into 12 equal divisions, representing
inches.
A scale constructed in this way should be drawn upon every
mine plan. Paper, when exposed to atmospheric influences, is
found to expand or contract to a considerable extent. This is
especially the case with new paper, or newly-mounted paper.
The serious errors apt to arise from this cause are, to a large
extent, obviated by making a scale on the paper as an accurate
standard of measurement. This will expand and contract with
the paper, and thus afford a valuable indication of the state of
the paper.
The scales usually employed for the plans of metalliferous
mines are 4 or 8 fathoms to the inch, sometimes 5 or 10 fathoms.
For colliery plans, scales of 2 or 3 chains to the inch, or of 25-34:
inches to the mile, are the most usual.
In order to assist in giving a clearer idea of the relative pro-
portions of the scales used, it is desirable that they should be
expressed fractionally that is to say, that they should be so
named as to indicate the ratio the line drawn on the paper bears
to the line measured on the ground. Thus, a scale of 2 fathoms
to the inch is a scale of j^-, or, as it may also be written, 1 : 144,
since 1 inch represents 2 fathoms, or 144 inches of real length.
A scale of this kind is called a natural scale.
In the construction of the maps of the Ordnance Survey of
Great Britain, the following scales are used :
Towns, . . . 1 : 500, or 126 '72 inches to the mile.
Parishes, . . 1 : 2500, or 25 '34
Counties, . . 1 : 10560, or 6
The Kingdom, . 1 : 63360, or 1
In the scale adopted for the parish maps, largely used for
colliery plans, 1 square inch represents an acre.
2. Diagonal Scales. A diagonal scale of equal parts is con-
structed in the following manner: Draw eleven straight lines
parallel to each other and y^ inch apart. Divide the top line into
equal parts, these primary divisions being of any required length.
Through the points marking these primary divisions, draw
perpendiculars cutting all the parallels. Number the primary
136
MIXE-SURVEYING.
divisions from the left, 1, 0, 1, 2, 3, &c., as in the case of the
simply divided scale. Then sub-divide the top and bottom lines
of the first primary division into 10 equal parts. Number the
alternate divisions, 2, 4, 6, 8, from right to left along the
bottom line, and number the alternate parallel lines, 2, 4, 6, 8.
from the bottom upwards. Then draw lines, as in Fig. 45, from
the zero of the bottom line to the first division of the top line,
from the first of the bottom to the second of the top, and so on
until the scale is complete.
c
ft t
H
I
|
_ T
__
41 1
_
J
I
I I
_
1
I
j ]
1
10 8 6 4 Z |0 20 3(
Fig. 45.
The diagonal lines are all parallel. Consequently the distance
between any two successive lines, measured up any of the eleven
parallel lines which they intersect, is the same as the distance
measured upon the highest and lowest of those lines. The
distance between the perpendicular which passes through the
zero point, and the diagonal at the same point, is on the top
line, and equal to one sub-division on the bottom line. It is
therefore equal (Euclid, vi. 4) to one-tenth of a sub-division on
the second line, two-tenths of a sub-division on the third, and so
on. In this way, each of the diagonal lines, as it reaches each
successive parallel, separates farther from the perpendicular
through the zero point by one-tenth of the extent of a sub-division,
or one-hundredth of the extent of a primary division. Thus, by
means of a diagonal scale a distance can be taken off to two
places of decimals.
The general rule for taking off any number consisting of three
figures from a diagonal scale is as follows : On the parallel line
indicated by the third figure, measure from the diagonal
indicated by the second to the vertical indicated by the first.
3. Vernier Scales. The construction of the vernier scale is
similar to that of the vernier of circumferenters and theodolites
(see p. 58). In order to show how the principle of the vernier
is applied to the construction of scales, let it be required to.
PLOTTING THE SURVEY. 137
construct a scale of 6 feet to the inch to show feet and decimals
of a foot. Construct a scale of feet in the ordinary way, sub-
divided throughout its entire length. Above the first primary
division draw a line parallel to the scale and ending at the zero
point. From this point set off towards the left along the line
parallel to the scale a distance equal to 11 sub-divisions, and
divide this distance into 10 equal parts as shown in Fig. 46.
Fig. 46.
Eleven divisions of the scale being divided into 10 equal parts
on the vernier, each division of the latter represents Ai or l^j-
foot. Thus, the distances from the zero of the scale to the
successive divisions of the vernier represent 1 foot 1-tenth, 2 feet
2-tenths, 3 feet 3-tenths, 4 feet 4-tenths, 5 feet 5-tenths, 6 feet
6-tenths, 7 feet 7-tenths, 8 feet 8-tenths, 9 feet 9-tenths, 10 feet
10-tenths, and 11 feet.
The manner of using the scale is as follows : To take off a
distance of 16 feet 7-tenths, one point of the dividers must be
placed on the 7th division of the vernier, and the other on the
9th division of the scale. From to the 7th division of the
vernier represents 7 feet 7-tenths, and that distance subtracted
from 16 feet 7-tenths leaves 9 feet.
Plotting Scales. The most convenient scales of equal parts for
plotting are those of ivory or box-wood, which have a feather
edge along which they are divided, so that distances can be at
once marked off without the application of the dividers. In the
same way, the length of a given line can be at once read off.
Dividers should never be used to measure distances when an,
edge scale is available for the purpose. An ivory scale is soon-
spoilt by being dug into by the dividers.
Each plotting scale should be provided with a shorter scale for
the purpose of plotting offsets. The offset scale should be edge-
divided like the plotting scale. In plotting a survey, the plotting
scale is placed along the station-line with its zero point at the
beginning of the line. The offset scale is placed at right angles
to the plotting scale, and slid along the latter, until its edge comes
to the distance at which an offset was taken. The length of this
is then marked off from the offset scale by means of a needle.
The offset scale is slid along to the next distance, and the opera-
tion repeated. The points thus obtained are joined by straight
lines.
138 MINE-SUKVEYING.
Plotting with a Protractor. A semicircular protractor may be
used to lay down or protract angles. It consists of a semicircle
of horn, brass, or German-silver, divided to half-degrees. The
degrees are numbered from to 180 both ways. To lay off an
angle at any point of a straight line, the protractor must be placed
so that its straight side, that is, the diameter of the semicircle, is
on the given line, with the middle of the diameter, which is
indicated by a small notch, at the given point. With a sharp
pencil or a needle, a mark is made on the paper at the required
number of degrees, and a line is drawn from that mark to the
given point.
In using this instrument for plotting a survey, the straight
side must be applied to an assumed meridian line drawn on the
paper, the centre of the protractor coinciding with the point in
the meridian line selected for the commencement of the survey.
A line must then be drawn from the centre of the protractor
passing through the degree required. The length of this line
is marked off by means of a scale. Then at the end point
of the line a second meridian line is drawn parallel to the
first, and the protractor applied to this in the same way as before.
The meridians at each station may be drawn by means of a
T-square, the north and south lines on the paper being made
parallel to one of the sides of the drawing-board.
Fitted with a movable arm and a vernier, the semicircular
protractor may be read with great precision. Supposing it is
required to plot a line through a given point at a certain angle
with the meridian of a plan, a semicircular protractor fitted with
a vernier may be used, in conjunction with a 60 set-square and
a straight-edge. The arm of the protractor is set by the vernier
at the required angle, and at the same time the arm-line is laid
on the meridian of the plan. The set-square is then placed
against the protractor by the straight-edge, and slid along the
latter until its edge passes through the given point, when the
line drawn through that point will form the required angle with
the meridian. According to T. Welizki,* this method of plotting
is preferred by almost all Russian surveyors.
More accurate results are obtained with a full-circle protractor
of brass or of vulcanite. With this instrument, not only the
bearing itself but the corresponding bearing on the other side
should also be marked off. Then, if the line drawn from one
point to the other passes through the centre previously marked
on the meridian line, it is evident that the bearing is accurately
plotted.
* Zelt.f. Vermessungswesen, vol. xii., p. 252, 1883.
PLOTTING THE SURVEY. J39
Drawing meridian lines at each station is apt to give rise to
error, and always presents the inconvenience of having a number
of lines on the plan which have to be rubbed out. With a circular
protractor this unnecessary labour is avoided by placing the
instrument along a meridian line drawn near the centre of the
paper, and marking off in rotation the various bearings of the
survey. Confusion may be avoided by figuring on the paper by
the edge of the protractor the bearing, not the number or letter
of the draft, as is often done. The bearings having been thus
marked, the protractor is removed, and the lines are transferred
to their proper positions on the plan by means of a rolling parallel
ruler. This instrument necessitates the use of a perfectly true
drawing-board. It is provided with two rollers of exactly the
same circumference, firmly attached to the same axis. It is
made of ebony or of brass.
Elaborate circular protractors are made with a movable aim
provided with a vernier. Such instruments are usually made
with a glass centre, with two fine lines intersecting at the centre
point. The most perfect instrument for accurate plotting is the
folding arm protractor. This is provided with two opposite arms,
each with a vernier, and <& clamp and tangent motion for setting
the angles. The extreme end of each arm carries a point, which
by a gentle pressure may be caused to puncture a fine hole in the
plan. These instruments are usually 6 inches in diameter, and
divided on silver.
The most rapid method of plotting a survey is by means of a
cardboard protractor, as with this instrument there is no occasion
to figure the various bearings on the paper. The cardboard pro-
tractor, as used in the Ordnance Survey Office, is 12 inches in
diameter. The centre portion is cut out, and the north and south
line made to coincide with the meridian on the paper. The
parallel ruler is then placed at once on the required bearing, and
on the bearing directly opposite. The survey line is then drawn
in the vacant space inside the circumference. Much time is thus
saved, and the plan is kept clean, and not covered with pencilled
bearings. The results are very accurate, on account of the large
diameter of the protractor.
Plotting by Means of Chords. A traverse may be plotted
from one meridian, without a protractor, by means of a table of
chords and a parallel ruler. For this method, all that is required
is a table of sines, or, better still, of chords, and a good rolling
2-foot parallel roller. Since the chord of an angle is twice the
sine of half the angle to a radius of unity, a ready means is
afforded of protracting to any radius required. The meridian
angles, if they have been taken with the theodolite or from the
140 MINE-SURVEYING.
outer circle of the dial, must first be reduced to bearings ; the
rule for performing this reduction being as follows :
For angles between
and 90, enter in bearing column as N.E.
90 and 180, subtract from 180, and enter result as S.E.
180 and 270, deduct 180, and enter result as S.W.
270 and 360, subtract from 360, and enter result as N.W.
Having tabulated the chords of the bearings, describe a circle
with a radius of 1000 units (say 10 inches). This avoids the
necessity of multiplying the chord by the radius ; the decimal
point merely having to be moved 3 places to the right. Angles
can be laid down by this method as easily as with a 20-inch
protractor.
The circle is drawn in a convenient part of the plan, and the
meridian line drawn through it ; the north and south ends being
marked. If the bearing is N.E., the chord is measured off from
the north point, eastwards. Thus, for a bearing of N. 64 14' E.,
the point at which the scale reading 1063-2 intersects the cir-
cumference of the circle is noted, and the number of the station
is affixed. The north and south points on the circle are the
zero points to measure from, and from these points the chords
are measured off to the east or west as the case may be.
The following sample page illustrates the method of reducing
the survey notes.
Plotting by Rectangular Co-ordinates. This is the most accurate
method of plotting a survey, because the position of each station
is plotted without being affected by any errors committed in
plotting previous stations.
It consists in assuming two fixed axes, O X and Y, crossing
at right angles at a fixed point or origin, O, and in calculating
the perpendicular distances, or co-ordinates, of each station from
those axes. When the direction of the true meridian has been
ascertained, it is advisable to make one of the axes represent it.
Thus, in Fig. 47, let A O represent a hori-
zontal line surveyed. Through the starting
point 0, draw a north and south line, O Y,
and at right angles to this, through the same
point, an east and west line, O X, then the
angle Y O A will represent the bearing of
the line O A. The line O Y is taken as
abscissa axis, and the line O X as ordinate
axis. From the end point of the given line,
O A, the two perpendiculars A a and A a' are let fall to those
PLOTTING THE SURVEY.
141
SURVEY OF LONG- WALL WORKINGS AT A SCOTTISH
COLLIERY.
No. 10 Pit. From centre of shaft, 12 ft. x 6 ft. ; long side bearing S. 18 E,
No.
Meridian
Augle.
Bearing.
Chords
r 1000.
Distance,
Remarks.
Links.
A
298 00'
N. 62 00' W.
1030-0
116
...
B
299 30'
N. 60 30' W.
1007-5
47
...
C
320 00'
N. 40 00' W.
684-0
71
D 2
315 00'
N. 45 00' W.
765-3
...
bearing only, into air course.
D
227 30'
S. 47 30' W.
805-4
151
into stone drift.
E
228 00'
S. 48 00' W.
813-4
59
F
301 00'
N. 59 00' W.
984-8
86
...
G
297 30'
N. 62 30' W.
1037-5
45
...
H 2
20 00'
N. 20 00' E.
347-2
100
...
J 2
14 30'
N. 14 30' E.
252-3
45
...
K 2
42 30'
N. 42 30' E.
724-8
66
to face lying N. 68 W.
H
319 00'
N. 41 00' W.
700-4
103
J 2
16 00'
N. 16 00' E.
278-3
58
K 2
10 30'
N. 10 30' E.
183-0
45
...
L 2
10 15'
N. 10 15' E.
178-6
97
...
M 2
40 00'
N. 40 00' E.
684-0
43
...
N 2
55 30'
N. 55 30' E.
931-2
23
to face lying S. 30 E.
J
313 00'
N. 47 00' W.
797-4
95
...
K 2
20 00'
N. 20 00' E.
347-2
68
...
L 2
9 30'
N. 930'E.
165-6
117
...
M 2
8 00'
N. 800'E.
139-5
44
N 2
20 30'
N. 20 30' E.
355-8
35
f 10 links to face, lying N.
\ 58 W.
K
304 00'
N. 56 00' W.
938-9
101
L 2
13 30'
N. 13 30' E.
235-0
100
...
M 2
355 00'
N. 500'W.
87-2
99
to face running E. and W.
L
290 00'
N. 70 00' W.
1147-1
87
M 2
100'
N. 100'E.
17-4
64
N 2
348 00'
N. 12 00' W.
209-0
70
to face lying S. 65 W.
" M
278 00'
N. 82 00' W.
1312-1
49
...
N
266 00'
S. 86 00' W.
1363-9
29
O 2
349 00'
N. 11 00' W.
191-6
52
...
P 2
332 00'
N. 28 00' W.
483-8
28
to face lying N. 60 E.
261 00'
S. 81 00' W.
12988
94
P 2
2 00'
N. 2 00' E.
34-9
50
to face lying S. 89 E.
P
261 30'
S. 81 30' W.
1305'5
38
to end of level.
142
MIXE-SURVBYIXG.
axes. A a is termed the latitude and A a the departure of the
line A. The latitude of a point may be denned as its distance
north or south of some parallel of latitude. The distance that
one end of a line is due north or south of the other end, is called
the difference of latitude of the ends of the line, or, briefly, the
latitude of the line, or its northing or southing. Similarly the
distance which one end of a line is due east or west of the other
end is called the difference of longitude of the ends of the line,
or the departure of the line, or its easting or westing.
On regarding the right-angled triangles O A a and O A a in
Fig. 47, it will at once be seen that the latitude and departure
may be calculated from the length A and the bearing A O a'
or /3. Now a' A is equal to O a, and a O is equal to A a ; it is
therefore evident that -r-f^ = sin [3, and consequently A a'
= OA sin ft and Oa = OA sin j3. Similarly O a = O A
cos /3, and A a = O A cos j3. In other words, to find the lati-
tude of any line, multiply its length by the cosine of its bearing,
and to find its departure, multiply its length by the sine of its
bearing. If the foreward bearing of the line is northward, its
latitude is north and is regarded as positive. If the foreward
bearing of the line is eastward, its departure is east, and is
regarded as positive. West departures and south latitudes are
regarded as negative magnitudes.
In Fig. 47, let O Y represent the meridian, and let O A B
represent a mine road, the survey of which with the circum-
ferenter gave the following results :
*
Angle.
Bearing.
Distance.
A
o o (xy
32 15'
Links.
176
B
220 17'
72 32'
180
C
79 13'
331 45'
155
The vernier-angles must first be reduced to meridian angles
with the result given above. The reduced bearings must then be
calculated. They will be found to be as follows : A, N". 32 15' E.;
B, N. 72 32' E. ; C, N. 28 15' W. The latitudes and departures
may then be obtained from the formula?
Latitude
Departure
Distance
Distance
cos bearing,
sin bearing.
PLOTTING THE SURVEY,
143
The troublesome and tedious multiplication by natural sines
and cosines may be avoided by using logarithms. The calcula-
tions will then be as follows :
Departures.
A. log 176 = 2-245512
L. sin 32 15' = 9727227
Latitudes.
log 176 = 2-245512
L. cos 32 15' = 9-927230
1-972739
2-172742
Easting
9391
Northing
148-85
B.
log 180
L. sin 72 32'
Easting
= 2-255272
= 9979499
log ISO
L. cos 72 32'
Northing
= 2-255272
= 9-477339
2-234771
1-732611
54-02
= 171-70
C.
log 155
L. sin 28 15'
= 2-190331
= 9-675154
log 155
L. cos 28 15'
= 2-190331
= 9-944922
Westing =
1-865485 2-135253
73'36 Northing = 136-54
In making calculations with logarithms, it must be remembered
that in tables of logarithmic sines and cosines, the logarithm of
the assumed radius is 10 -000000. Consequently in the preced-
ing calculations, the log. radius 10 is deducted in order to give
the log. of the natural number sought.
The results of the calculation should be entered in four columns,
for northing, southing, easting, and westing respectively.
No.
REDUCED BEARING.
DISTANCE.
LATITUDE.
DEPAKTCKE.
N.
s.
E.
w.
A
N. 32 15' E.
Links.
176
148-85
93-91
...
B
N. 72 32' E.
ISO
54-02
171'70
C
N. 28 15' W.
155
136 -c4
73-36
339-41
265-61
73-36
144
MINE-SURVEYING.
Regarding the northing as positive and the southing as negative,
the algebraical sum of the latitudes is 339-41 links. The easting
being positive, and the westing negative, the algebraical sum of
the departures is 265-61 - 73-36 = 192-25 links.
Before the calculated co-ordinates can be used for plotting pur-
poses, the total latitudes and the total departures must be calcu-
lated. This is done by taking the algebraical sum at each station,
as follows :
No.
Total Latitudes from Station O.
Total Departures from Station O.
o-oo
O'OO
A
+ 148-85
+ 93-91
B
+ 202-87
+ 265-61
C
+ 339-41
+ 192-25
Having prepared this table, draw a meridian line through the
first station O, Fig. 47. Along the meridian, north latitudes
are set off upwards, and south latitudes downwards. East
departures are set off perpendicularly to the right, and west
departures perpendicularly to the left. Set off, therefore, along
the meridian in a northerly distance the latitude 148-85 links to
the scale required. This gives the point a. From that point,
set off perpendicularly to the right the departure 93-91 links.
The station A is thus fixed on the plan. Join the points O and A.
From O again sec off upwards 202-87 links to b', and from that
point set off 265-61 links perpendicularly to the right. This
gives the point B. Join the points A and B. From O again set
off upwards the latitude 339-41 links to c, and from that point
set off the departure 192-25 links. The last point C is thus fixed.
In this way any survey may be plotted with great ease and
rapidity, and with greater accuracy than is possible by any other
method.
The calculated co-ordinates are of great value for testing the
accuracy of a closed traverse. Obviously, when a surveyor makes
a circuitous survey returning to the starting point, he has gone
exactly as far to the north as he has to the south, and as far to
the east as to the west. Consequently, if his survey is correct,
the sum of the northings should be equal to that of the southings,
and the sum of the eastings equal to that of the westings.
An illustration of this is afforded by the survey of a closed
PLOTTING THE SURVEY.
polygon with a theodolite, the notes of which are given on p.
107. On calculating the co-ordinates, the following results are
obtained :
No.
KEDCCKD BEARINGS.
DISTANCE.
LATITUDES.
DJSPABTUBSS.
North +
i^outh -
East +
West -
1
S. 58 33' E.
Links.
1,091
569-5
931-3
2
N. 39 03' E.
252
195-5
158-8
...
3
N. 68 04' E.
196
73-1
...
182-0
...
4
N. 47 44' E.
534
358-9
...
395-3
5
N. 63 16' E.
384
172-5
343-1
6
N. 31 13' W.
336
287-1
...
...
1740
7
N. 59 06' W.
1,055
541-3
...
...
904-5
8
S. 44 8 28'W.
771
...
550-5
539-5
9
S. 31 29' E.
154
131-4
80-5
10
S. 5129'W.
605
...
377-0
...
473-0
...
1628-4
1628-4
2091-0
2091-0
If there should be a slight error, the latitudes and departures
must be corrected, before plotting, so that their sums shall be
equal in each case. This is done by distributing the error among
the lines in proportion to their length, the balancing being
effected by the following proportion : As the sum of all the
lengths is to each particular length, so is the total error in lati-
tude (or departure) to the correction of the corresponding latitude
(or departure). The correction has been made in the above
example. It may frequently be made by determining the error
per chain, without making the exact proportion.
The error of closure is the ratio of the length of the line joining
the first and last points of the survey of a closed polygon, to the
whole perimeter. Being the hypothenuse of a right-angled
triangle, of which the errors in latitude and in departure are the
other sides, the length of this line is equal to the square root of
10
146
MINE-SURVEYING.
the sum of the squares of those two errors. This divided by the
whole perimeter gives the error of closure. In mine-surveys, it
should not be more than 1 in 1,600, or 5 links per mile. In ordi-
nary surface-surveys it will average 1 in 300 or 27 links per mile.
A co-ordinate protractor, called a trigonometer by the makers,
Messrs. Keutfel and Esser of New York, has recently been intro-
duced in America. It consists of a plate 15 inches square (Fig.
48), divided into 100 equal squares by horizontal and vertical
lines. It is provided with an arm
fastened with its zero upon the zero
at one corner of the plate. It is
graduated, with the same division
as the plate, to read distances from
the centre outwards. On the sides,
the plate has angular graduations,
the zero joint being the centre of
the quadrant. By moving the arm
to the given angle, the latitude is
at once read off on the vertical scale
and the departure on the horizontal
scale, for the given length as read
on the arm. If, for instance, BAG
is the given angle, and A D the
given distance, D E and D F are
Fig. 48.
the co-ordinates. The readings are exact to within O'l per cent.
The instrument is also of use for calculating the bases and per-
pendiculars of inclined station-lines in mine-surveys.
Though described in 1886 by Mr. E. G. Gaertner* as a new
invention, this instrument was known two hundred years pre-
viously. It is, I find, described on p. 127, and figured on
plate 7 of Nicolaus Voigtel's Geometria Subterranea, published
at Eisleben in 1686.
Calculating Scales. For ordinary practical work the co-ordi-
nates may be determined with great rapidity by means of the
slide rule. On this rule, logarithms of numbers, sines, and
cosines are represented graphically in the form of scales. The
instrument consists of a rule, having on its face a groove cut
throughout its entire length, in which a second rule slides
smoothly. The bearing and length of a given line being known,
its departure is found by setting 1 on the slide to the length on
the rule, and against the sine on the slide will be found the
required departure on the rule. Latitudes are found in a
similar way, the cosines being read off by reading the shies
backwards. To avoid this operation, complementary figures may
be pencilled along the line of sines.
* Trans. Amer. Inst. M.E., vol. xiv., p. 180, 1886.
PLOTTIXG THE SURVEY. 147
No slide rules of English make can compare in accuracy and
portability with those made by Gravet, of Paris. One 26 centi-
metres long is accurate to one part in 500. Co-ordinates of the
lines occurring in mine-surveys may thus be determined accurately
to the first place of decimals. The back of the slide is divided for
sines, tangents, and logarithms, all of which can be read at the
back through special openings without removing the slide, or the
slide may be reversed. A sliding index, or cursor, is provided,
which adds materially to the power of the instrument. For
important theodolite surveys, the slide rule is not accurate
enough. For this work, however, it saves much time in calcu-
lating differences of logarithmic sines, <fec. The most acciu-ate
slide rule available is of the Grave"t type with the graduations
not on wood, but on celluloid, a white substance resembling ivory.
Careful tests of this instrument show that the average error in
calculating co-ordinates is O12 per cent. The errors are conse-
quently inappreciable when the survey is plotted to any of the
scales usually employed for mine-plans.
With the celluloid slide rule, and other rules of the Gravgt
type, the departure of a given line in the survey may be found
by placing the given angle, as shown on the line of sines against
the index at the back of the rule, and by reading off the number,
on the scale on the face of the slide, corresponding with the given
distance, as shown on the upper scale. The latitude is found in
a similar way, the cosine being used in place of the sine. In
this way results may easily be found without calculation, accurate
to the first place of decimals.*
In the Government Mining Offices on the Continent, cal-
culating machines are extensively used for computing the
co-ordinates of mine-surveys. The type of instrument generally
used is that invented by M. Thomas, of Colmar, in Alsace.
This instrument has recently been improved by Mr. Edmondson
and by Mr. Tate. Full descriptions of the three instruments are
given by Mr. C. V. Boys.f
Traverse Tables. Tables which show by inspection the
amount of the latitude and departure for any bearing and dis-
tance are termed traverse tables, because by their aid the
resolution of traverses is effected without calculation.
In order to be of any use to the mine-surveyor, such tables
must be calculated for every minute of bearing and to four places
of decimals. These conditions are fulfilled by the tables calcu-
lated by J. T. Boileau, by W. Crellin, and by R L. Gurden.
There are several other tables published, which, though well
arranged, are not sufficiently in detail for mine-surveying pur-
* Colliery Guardian, p. 587, 1889.
t Journ. Soc. Arts, vol. xxxiv., p. 384, 1886.
MINE-SURVEYING.
14 b
poses. For example, the traverse tables given in Chambers' s
Mathematical Tables are calculated only for every degree of
bearing to one place of decimals. Though valuable for problems
in navigation, they are useless for mining purposes.
The following example will illustrate the method of using
Boileau's tables, which are calculated for every minute of bearing
and to 5 decimal places for distances of 1 to 10 : Given the
bearing of a line, N. 32 15' E., and its length 1 chain 76 links,
required its latitude and departure. Seek the table headed 32,
and from the section 15', take out the latitudes and departures
separately for the hundreds, tens, and units, removing the decimal
point in each case as many places to the right as the figures in
each separated portion of the distance exceed those in the corre-
sponding numbers in the tabular distance columns. The distance
1 chain 76 links will be separated into 100, 70, and 6 links, and
the traverses for each will be taken out separately, thus :
Reduced Be i ring. Distance. Latitude. Departure.
N. 3215'W. 100 84-5727 53-3614
70 59-2009 37-3530
6 5-0743 3-2016
176 148-8479 93-9160
The most accurate traverse tables published are those com-
puted by Mr. R. L. Gurden, Authoi-ised Surveyor for the
Governments of New South Wales and Victoria. These tables
are calculated to four places of decimals for every minute of angle
up to 100 of distance, so that the sines and cosines for a distance
of 12 miles may be ascertained correctly to within half an inch.
In the example given above, the latitude and departure are
found with Garden's tables, thus
Reduced Bearing. Distance. Latitude. Departure.
N. 32 15' W. 100 84-5728 53-3615
76 64-2753 40-5547
176 148-8481 93'9162
Only one opening of the traverse tables is required. With
logarithms, on the other hand, the book has to be opened in four
places, two separate additions have to be made, and in taking out
natural numbers proportional parts have to be resorted to, in
order to find figures of the second place of decimals. The advan-
tage of these traverse tables over logarithms, both as regards
simplicity and economy of labour in calculation, is thus apparent.
In important undertakings it will be found advisable to calcu-
late the co-ordinates by logarithms, and repeat the calculation by
the traverse tables, so as to obtain an independent check and
verification.
PLOTTING THE SURVEY. 149
Combined Surveying and Plotting Instrument. Henderson's
rapid traverser is based on what is known as the plane-table
system of surveying. By its aid, underground or surface surveys
can be made, and the results laid down on paper with very great
rapidity. Unlike the plane-table, however, it is not intended
that the rapid traverser should be used for plotting the survey
in the field, this being done in the drawing-office, with the aid
of a parallel rolling ruler and scale.
The instrument consists of a circular metal table of about
10 inches diameter, mounted on an ordinary tripod stand, with
the usual adjusting screws. It is provided with a brass alidade,
with an ordinary sight at each end, revolving round a fixed
centre pin. Upon the face of the table a disc of celluloid is
screwed, and over this the alidade, by means of a groove, can
travel freely. The disc is divided into five or more concentric
rings marked on the celluloid, and the feather-edge of the alidade
is also divided by means of a rectangular notch at each ring, for
the purpose of pencilling on the disc the line observed. By
means of clamping screws, similar to those of the circumferentor,
the disc can be clamped to the stand, and the alidade, with
sights attached, to the table when required.
In traversing, the instrument is levelled and the alidade is
sighted back to the starting point of the survey. Both the
alidade and the table are then secured clamped. The direction
of this first line of the survey is marked with a finely pointed
H H pencil on the selected ring of the disc, at two points equi-
distant from the centre, and duly lettered or figured within the
notch cut in the feather-edge of the alidade. Three tripods are
used. Each of the two spare ones carries a candle-holder with
levels attached, a white card replacing the candle in surface
surveys. The alidade is next undamped, sighted to the forward
tripod, and clamped, the direction of the second line being
marked on the celluloid as before. The instrument is then re-
moved from its tripod and fixed, with the alidade still clamped on
the forward stand, and sighted back to the position it previously
occupied and clamped. This having been done, the alidade is
undamped, sighted to the next forward station, again clamped,
and the direction marked as before, the process being repeated
for the remainder of the traverse. The magnetic meridian is
taken at any convenient spot in the course of the traverse by
means of a trough compass placed temporarily against the back
edge of the alidade. The line thus given, pencilled on the disc,
establishes the orientation of the whole of the survey.
The sights of the alidade are graduated to give angles of
depression or elevation up to 25. Thus, the instrument suffices
150 MINE-SURVEYING.
for the majority of collieries, for the levels of metalliferous
mines, and for all ordinary surface surveys. Where greater
accuracy in vertical angles is required, as in inclined shafts,
a vertical semicircle is attached to the alidade, and the angles
read as with the theodolite.
In plotting the survey, the celluloid disc is unscrewed from its
circular table and placed with the north line, that has been
marked on it, in its proper position on the meridian line drawn
on the intended plan. A rolling parallel ruler is then applied
to each line of the survey in succession as shown on the disc,
and marked off on the plan. In a large survey, the disc may be
moved to any meridian line as required. For future reference,,
the disc itself may be preserved with the name and date of the
survey recorded on it, or, if necessary, the magnetic bearings
may be read off with the aid of a protractor and booked, when,
the celluloid disc may be cleaned for future use.
This instrument has been successfully used by the inventor,
Mr. James Henderson, in numerous surveys of Cornish mines,
notably at West Wheal Frances, at Redruth. In November,
1892, it was decided to put out a cross-cut south from the
174-fathom level so as to come under the perpendicular portion
of Bailey's shaft, which was perpendicular only as far as the
60-fathom level, and then went off to the south following the
underlie of the lode. After the cross-cut, which was 20 fathoms
in length, had been driven, a rise had to be carried up through
some 55 fathoms of ground to the bottom of the perpendicular
portion of Bailey's shaft. In order to do this, the relative
position of the two points was determined by surveying down
80 fathoms of the inclined portion of the shaft to the winze to
the 174-fathom level, the total distance of levels surveyed
amounting to 300 fathoms, and the number of stations required
being fifty-three. The perfect holing on October 17, 1893,
affords a guarantee of the adaptability of this instrument to
complicated underground surveys.
Plotting Colliery Surveys in Scotland. In the West of Scot-
land, a method of plotting colliery surveys, which differs from
that in vogue in other districts, is frequently employed. The
protractor used consists of a circular brass plate, 2 feet in
diameter, pivoted at the centre, so that it can rotate in a
horizontal plane. It is supported in a square mahogany frame,
the surfaces of the frame and of the protractor being flush. A.
brass or steel straight-edge is attached to one side of this square
frame. The drawing-paper is used in circular sheets, which are
fastened on the face of the protractor inside the graduated
circle. A sheet of paper is permanently glued on, and sheets
PLOTTING THE SURVEY. 151
may be attached to this by means of wafers as required. A
T-square replaces the parallel ruler used in other methods of
plotting with the protractor. It is brought to the diameter
of the protractor, and then the required bearing is brought
under the edge of the T-square by rotating the protractor. The
protractor is then held steady, while the T-square is moved
along the straight edge attached to the mahogany frame, in
order that a line may be drawn through a station point. A
day's survey having been plotted, a tracing is made and trans-
ferred to the main plan of the colliery.
Calculating the Co-ordinates of a Triangulation. In South
Africa, where triangulation is exclusively \ised for surveys of
mine concessions, it is usual to plot by co-ordinates. For the
calculations necessary, C. L. H. Max Jurisch's " Tables of
natural sines and cosines to seven decimal figures of all angles
between and 90 to every 10 seconds with proportional parts
for single seconds" (Cape Town, 1884), are chiefly used. The
problem occurring is as follows : Given the co-ordinates of two
points, P and Q, the angles of direction x P Q or x Q P, the dis-
tance P Q and by observation, the angles of the triangle P Q R ;
required the co-ordinates of R. From the given data the dis-
tance P R and Q R and their angles of direction a; P R and
a; Q R may be calculated.
Consequently
P R sin as P R = ;?/ - distance of R from P = A y
PRcosaPR = o;- distance of R from P = A x
Q R sin x Q R = y distance of R from Q = A' x
Q R cos x Q R = x distance of R from Q = A' x
y of P + A ?/ = y of R ; a; of P + A a; = cc of R
y of Q + A'y = y of R ; x of Q + A'# =i x of R
It is usual to calculate the co-ordinates of R from both equa-
tions, in order to have a check on the calculations. In these
equations, the co-ordinate drawn from any point parallel to the
vertical or y axis is briefly called the y of that point, and the
other co-ordinate is called the x of that point.
The following example, given by Leopold Marquard (" Co-ordi-
nate Geometry," Cape Town, 1882), will illustrate the manner in
which the calculations are made :
152 MINE-SURVEYING.
Lines.
Given AB =
BC =
CD =
DE
EF
FG =
Required the co-ordinates of A, B, C, D, E, F, G.
The line A B having been selected as x axis and B as the
origin, we have
Cape Roods.
= 41-26
Angles.
ABC =
+ 69 54'
= 37-98
BCD =
+ 134 44'
- 66-46
ODE =
- 47 12'
= 118-30
DEF =
- 87 03'
= 167-75
EFG =
+ 277 13'
= 148-55
0; aof A = + BA = + 41-26
2/ of B = ; a; of B =
Angle X B C = 69 54', to this is added B D = + 134 44',
and from the sum 180 is subtracted. When the angle of inter-
section of two lines and the angle of direction of one of them is
known, the angle of direction of the other is found thus : When
the two angles have the same vertex, their algebraical sum is
the required angle of direction, and when they have different
vertices, their algebraical sum, either diminished or increased
by 180, as may be most convenient, will be the required angle
of direction. Consequently
Angle X C D = 24 38'
Add C D E = - 47 12' and add 180.
Then X D E = 157 26'
Add D E F = - 87 03' and add 180.
Then X E F = 250 23'
Add E F G = + 277 13' and subtract 180.
Then X F G = 347 36'.
To determine the co-ordinates of C :
log B C (37-98) = 1 -5795550 log B C = 1 -5795550
logsinXBC (69 54') = 9-9727092 log cos XBC = 9-5361286
1-5522642 1-1156836
yof C = + 35-67 x of C = + 13-05
SURFACE-SURVEYS WITH THE THEODOLITE.
153
Similarly the co-ordinates of the other points will be found to
be as follows :
y
X
D
+ 63-37
+ 73-46
E
+ 108-77
- 35-78
F
- 49-24
- 92-10
G
- 81-14
+ 52-98
154
MINE-SURVEYING.
CHAPTER XII.
CALCULATION OF AREAS.
Measures of Area. The area of mine-royalties and of coal
wrought is usually expressed in acres. The statute acre is equal
to 10 square chains or 100,000 square links. It is sub-divided
either decimally or into 4 roods of 1,210 square yards, and 160
perches of 30^ square yards. One square mile is equal to 640
acres.
In order to reduce square links to acres, roods, and perches,
divide by 100,000 by cutting off five figures to the right hand.
The figures remaining to the left will be acres. Multiply the re-
mainder by 4 ; the whole-number remaining will represent roods.
Multiply the remaining fraction by 40 ; the figures beyond the
decimal point will be perches. The nearest round number is
usually taken ; fractions less than half a perch being disregarded.
The metric unit of land measure is the hectare of 10,000 square
metres. This is equal to 2-4711 acres.
Three methods of measuring
areas are employed : the method
of triangles, the method of ordi-
nates, and the mechanical method.
1. Method of Triangles The
survey of the ground having been
plotted, lines are drawn on the plan
so as to divide it into a number of
triangles, the area of each of which
is calculated. Thus, in order to
calculate the area of the polygon
A B D E F G (Fig. 49), measure
all the sides of the figure, and the diagonals AC, A D, A E, and
AF. Then if the lengths of the three sides of the triangle
ABC are denoted by a, 6, and c, the area of the triangle is
given by the formula
Js (s -a)(s- b) (s - c),
in which s represents the half sum of the lengths of the sides of
the triangle.
CALCULATION OF AREAS. 155
Assuming that the side BC is 120 links in length, AC 135
links, and A B 90 links, the area of the triangle is
^172-5 x 52-5 x 37-5 x 82-5,
or 5293-18 square links.
If logarithms are employed, the formula is
log. area = \ {log s + log (s a) + log (s V) + log (s c)}.
In the same way, the area of the remaining four triangles in
Fig. 49 are calculated. By taking the sum of the areas of the
five triangles, the area of the whole polygon is obtained. As a
check on the calculations, the lengths of the diagonals B D, BE,
BF, and BG may be determined. Five new triangles would
thus be obtained. The sum of these five areas should be the
same as the result of the first calculation. If there is a small
difference, the mean of the two results is taken as the correct
area. If the difference is considerable, the measurement must be
repeated.
Another useful formula for calculating the area of triangles is
the following :
ap
Area = -
in which a is any one of the sides of the triangle, and p a
perpendicular let fall upon that side from the opposite angle.
When two sides and the included angle are known, the area is
given by the formula
a b sin
Area = - ^ - '>
a and b representing the two sides, and the included angle.
When one side of a triangle and the adjacent angles are given,
. a 2 sin B sin
its area is equal to ^. 7^ - 7^.
2 sin (B + C)
The areas of figures with curved outlines may be found by the
method of triangles preceded by a process termed equalising
or giving and taking. This consists in drawing through the
boundary a straight line, leaving as much space outside the
straight line as there is inside it, as nearly as the eye can
estimate.
It is sometimes advisable to reduce a polygon to a single
triangle equivalent in area, as in the following example : In
156
MINE-SURVEYING.
the polygon A B C D E in Fig. 50, draw a line from A to C, and
with a parallel ruler draw a line B F parallel to A C cutting C D
produced in F. Join A F. Then the area of the quadrilateral
figure A F D E is equal to that of the original figure. The
Fig. 50.
triangles A B F, C B F being on the same base, B F, and between
the same parallels, are equal. Take away from each the common
triangle B H F, H being the point at which the lines A F and
B intersect ; the remaining triangles A B H, F H are equal.
But in the alteration of the figure, F H has been substituted
for A B H ; therefore, the area of the quadrilateral is > equal to
that of the original figure. Similarly, by drawing E G parallel
to A D, intersecting C D produced in G, and by joining A G, the
area of the triangle A F G may be made equal to that of the
quadrilateral figure A F D E, and consequently to the original
figure. Whatever may be the number of sides of the polygon,
a similar process will reduce it to a triangle having the same area.
2. Method of Ordinates. An axis A X is measured along the
greatest length of the track to be measured (Fig. 51). Offsets
are measured at right angles to that axis, sufficiently close
together to make the spaces between them approximate to
trapezoids. Let d be the distance along the axis between two
adjacent offsets or ordinates, and b, b', the breadths of the
figure at those ordinates. The area of the trapezoid is then
- ^ - , and the area of the whole figure is the sum of the
areas of the trapezoids into which it is divided.
for example. Let A X in Fig. 51 represent the chain from
which offsets were taken to a curved fence. The lengths of the
CALCULATION OF AREAS. 157
bg = 48, and 6 10 =
and the fence is
19.
The
area
included
bet\
50
x
(30 +
38)
=
3,400
50
X
(38 +
61)
=
4,950
50
X
(61 +
50)
=
5,550
50
X
(50 +
85)
-
6,750
50
X
(85 +
80)
=
8,250
50
x
(SO +
40)
=
6,000
50
X
(40 +
60)
-
5,000
50
X
(60 +
69)
=
6,450
50
X
(69 +
48)
=
5,850
50
X
(48 +
19)
=
3,350
Total . . = 55,550
Half this total, that is, 27,775, is the area in square links.
When the intervals between the offsets are all equal, as in the
above example, the calculation may be considerably simplified.
All the values of d being equal, the formula becomes
Area
/& i ' <
= f ~ + b + 6 2 + 1 3 + &c. +
that is to say, the area is equal to the sum of all the intermediate
offsets, and of one half the end offsets multiplied by the constant
interval between, them. Applying this formula to the above
example
Area = (15 + 531 + 9J) x 50 = 27,775 square links.
When the line determined by the offsets is curved, the area
may be calculated with greater accuracy by Simpson's formula.
This assumes that the lateral boundaries of the figure consist of
short parabolic arcs. An even number of equal distances must
be measured along the axis, when the formula is
Area = j b + b n + 2(6 2 + 6 4 + &c.) + 4(6 X + b 3 + &c.) 1 ^;
that is. the area is equal to one-third of the constant interval
between the offsets multiplied by the sum of the first and last
158
MINE-SURVEYING.
offsets, twice the sum of the even offsets, and four times the sum
of the odd offsets. Applying this formula to the example given,
Kf]
Area = (30 + 19 + 510 x 1104) ^f
o
= 27716| square links.
In calculating the area of a surveyed piece of land, it is
advisable to use exclusively the dimensions given in the field-
book. The process is, however, very laborious, and may
frequently be dispensed with by equalising boundaries and
taking measurements on the plan.
By means of rectangular co-ordinates, the area of a piece of
land may be accurately calculated without necessitating the
preparation of a plan. The general rule for finding areas by
this method is as follows : Multiply the total latitude of each
station by the sum of the departures of the two adjacent courses.
The algebraical half sum of these products is the area.
The total latitude of each station is found by adding the lati-
tude of the preceding course to the total latitude of the preceding
station. To find the adjacent departures, add the departures of
the two courses, one on each side of the station. The following
is an example of this method of calculation :
No.
A
Bearing
Distance
LATITUDE.
DEPAMCRB.
Total
Latitude.
Adjacent
Departures.
Double
Areas.
N.-f
s. -
E. +
w. -
N. 51 33' E.
18-14
22-85
...
...
29-18
B
S. 7307'E.
12-30
3-57
11-77
+ 18-14
+ 34-62
+ 628-00
C
S. 2037'W.
18-32
17-15
6-45
+ 14-57
+ 5-32
+ 77-51
D
S. 7845'W.
25-40
...
4-95
24-91
- 2-58
-31-36
+ 80-90
E
N.2326'W.
8-21
7-53
...
3-26
- 7-53
-28-17
+ 212-12
25-67
25-67
34-62
34-62
I
... | ...
998-53
The double area of the polygon is thus 998-53 square chains.
The area, therefore, is 499-26 square chains, or 49-926 acres.
3. Mechanical Method. Instruments for measuring areas on
plans are termed planimeters. The form most generally used
CALCULATION OF AREAS. 159
is the polar planimeter of Amsler, of which the general principle
is shown in Fig. 52. This is an instrument for measuring the
area of any figure, however irregular,
by the mere passage of a tracer round
about its perimeter. It consists essen-
tially of three parts, the adjustable
arm D, the polar arm B C of fixed
length, and the rolling wheel F,
which rests upon the plan. The wheel
is graduated and provided with a ver-
nier. The two arms of the instrument
are hinged together by a hardened
steel axis 0, and permit of an angular
52, motion of nearly 180. The rolling
wheel is mounted on a steel axis
parallel to the adjustable arm C D, that is, parallel to the
imaginary line joining the tracing point at D and the axis
C of the polar arm. The number of complete revolutions of the
rolling wheel are shown by a record disc driven by an endless
screw on the shaft E. At the end of the arm B is a loaded
disc which rests upon the table, and serves as a fixed support
for the instrument. In its centre at B is an upright pin forming
the turning point or pole of the whole instrument. At the end
of the adjustable arm, at the same distance from it as the axis E,
the tracing point D is screwed in vertically.
When the tracing point D is carried round the outline of any
figure, such as G H I, BO as to return to the point from which it
started, it can be proved* that the distance rolled by the edge of
the wheel F is equal to the area of the figure divided by C D,
and consequently that the area of the figure is equal to C D
multiplied by the distance rolled by the wheel F. In Great
Britain and the United States, the graduations on the circle
usually represent square inches of area on the plan.
This planimeter gives results sufficiently accurate for mining
purposes, and its cheapness and simplicity render it of great
value. When, however, a very high degree of accuracy is required,
it is found that the planimeter is seriously affected by the paper
on which the measuring-wheel revolves. This is particularly
noticeable with old plans that have been folded up for a length of
time. It is also noticeable when the operation takes place near
the edge of the paper, necessitating the wheel passing over that
edge.
In cases where the use of the polar planimeter appears imprac-
* For proof, consult the report on this instrument by Sir Frederick
Bramwell in Rep. of Forty-second Meeting of the Brit. Assoc., p. 401. 1872.
160
MINE-SURVEYING.
ticable, recourse must be had to the precision planimeters made
by G. Coradi, of Zurich. In these instruments, the so-called
suspended planimeters and linear rolling planimeters, the measur-
ing wheel does not travel on the plan itself but on a disc, which
is an integral part of the instrument.
The suspended planimeter is essentially a polar planimeter ; it
gives, however, results ten times more accurate than those given
by Amsler's instrument. The linear rolling planimeter is the
most accurate instrument of its kind yet invented. Instead of
revolving round about a pole, the rolling planimeter moves in a
straight line, on either side of which the area is determined.
The following table showing the mean error in planimeter
readings has been drawn up from the results of a series of experi-
ments made by Professor Lorber* of the School of Mines of
Leoben, in Austria :
A.REA.
THE MEAN ERROR IN A PASSAGE OP THB TRACER AMOUNTS
TO THE FOLLOWING FRACTION OF THE AREA:
In Square
Centimetres.
In Square
Inches.
With the Polar
Planimeter.
Unit of Vernier
10 sq. mm.
(O'OIS sq. in.)
With the Sus-
pended
Planimeter.
Unitof Vernier
(OWlsq'Tn.)
With the
Boiling
Planimeter.
Unit of Vernier
1 sq. mm.
(O'OOl sq. in.)
With the
Rolling
Plauimeter.
Unit of Vernier
0'5 sq. mm.
(0-0005sq. in.)
10
1-55
lin 75
1 in 625
1 in 625
1 in 1,000
20
3-10
1 in 148
lin 1,111
1 in 1,000
lin 2,000
50
775
1 in 355
1 in 2,500
1 in 2,000
1 in 3,000
100
1550
1 in 682
lin 4, 167
1 in 3,333
1 in 5,000
200
31-00
1 in 1,274
1 in 7,143
1 in 5,128
1 in 7,693
300
46-50
1 in 9,375
1 in 8,000
1 in 10,000
Produce of Coal-seams. The area of coal wrought in any par-
ticular seam may be estimated by dividing the plan into squares
of 10 acres each. It will be found useful to have a sheet of
tracing cloth, divided into 1-acre squares, drawn to the same
scale as the plan with which it is to be used. The side of a
square, of which the area is 1 acre, measures 316-228 links.
The squares should be drawn in black lines, and sub-divided into
quarter-acres by means of faint red lines. The area of coal
* Ze.it. des oesterr. Ingenieur- und Architektenvereins, part iv. 18S4.
CALCULATION OF AREAS. 161
wrought can be estimated with considerable accuracy by merely
placing the sheet of tracing cloth over the plan, and by counting
the squares covering the space on the plan representing that area.
The area of the coal wrought and the thickness of the seam
being known, the tonnage may easily be calculated, as the specific
gravity of the coal (1,250 to 1,500), with that of water taken as
1,000 for standard, is equal to the number of ounces in a cubic
foot.
The produce of coal-seams depends not only upon the specific
gravity of the coal (1*25 to 1'50), but also upon the system of
working, and the number of faults. According to Professor J.
H. Merivale, at a Durham colliery working the Harvey seam
3 feet 6 inches in thickness, 5,185 tons per acre were obtained
when working by the long wall system, and 5,052 tons when
working by the bord and pillar system. The yield per acre per
foot thick of the South Staffordshire thick coal by the various
methods of working is calculated by Mr. H. W. Hughes * to be
as follows: Square work, 1243 tons ; longwall (two divisions),
1398 tons; longwall (one division), 1155 tons.
A rough rule is to calculate the produce at 100 tons per inch
per acre, which leaves an ample allowance of some 25 per cent,
for loss of every kind. Another rule frequently used is to calcu-
late the produce at 18 cwt. to the cubic yard. This gives 120|-
tons per inch per acre or 1,450 tons per foot per acre.
The Calculation of Ore-Reserves. Having finished the survey
of a metalliferous mine, the surveyor is sometimes called upon to
calculate the quantity of ore-reserves in that mine. Various
methods are employed for this purpose. Indeed different sur-
veyors will not agree within wide limits as to the amount of ore-
reserves in the same mine. Sometimes the amount of ore in sight
will be considered to be a rectangular block limited by the out-
crop of the vein, the depth of the shaft, and the extreme points
of the levels, diminished by the amount extracted. Other sur-
veyors would avoid so excessive an estimate and take but one-
third of that amount.
The following method is recommended by Mr. J. G. Murphy,
an experienced American mining-engineer, as the fairest and
most trustworthy : Let it be required to calculate the ore-
reserves in a mine opened up on a vein with a mean cross-section
of 6 feet ; a cubic foot of the vein matter in place weighing
150 Ibs. The ore stopes are generally very irregular. In this
case, however, it may be supposed that the stope faces are 11
feet apart and 8 feet high. There is an inclined shaft, 10 feet by
* The Thick Coal of South Staffordshire, Sheffield, 1885, p. 17.
11
162 MINE-SURVEYING.
6 feet, following the dip of the vein, and 6 levels, each 7 feet by
6 feet, 100 feet apart. The lengths of the levels are
I. 200 feet west ; 150 feet east
II. 160 100
III. 120 400
IV. 100 140
V. 165 ISO
VI. 350 150
The longest level west is 350 feet and the shortest 100 teet.
Assume the bounding line of the area of available ore to be at
a distance west of the shaft,
The longest level east is 400 feet, and the shortest 100 feet.
The bounding line in this direction calculated in a similar way
will be at a distance of 250 feet from the shaft.
The inclined shaft has opened up the vein for 670 feet.
Deducting say 15 feet for the irregularity of the surface, the
quantity of ore in sight Avill be a rectangular block 655 feet deep,
225 + 250 or 475 feet long, and 6 feet wide, that is, 1,866,750
cubic feet.
From this quantity, however, must be deducted the quantity
of ore extracted, namely
Cubic Feet.
Inclined shaft, 655 x 10 x 6 = 39,300
Level I., 350 x 7x6 = 14,700
Level II., 260 x 7x6 = 10,920
Level III., 520 x 7x6 = 21,840
Level IV., 240 x 7x6 = 10,080
Level V., 345 x 7x6 = 14,490
Level VI., 500 x 7x6 = 21,000
Level I., stoped east (rough estimate), 3,400
Level I., stoped west, . . . 6,500
Level II., stoped west, . . . 7,000
Level III., stoped east, . . . 20,000
Level VI., stoped west, . . . 12,000
Total, 181,230
Or in round numbers, . . .182,000
CALCULATION OP AREAS. 163
This quantity, deducted from 1,866,750 cubic feet, leaves
1,684,750 cubic feet. Divided by 13J, the number of cubic feet
required for a ton, this gives 124,797 tons of ore in sight.
The quantity of ore discovered in a mine may be estimated
from its specific gravity and the average size of the vein. The
specific gravity of the ore, with that of water taken at 1,000 for
standard, is equal to the number of ounces in a cubic foot. Great
caution is necessary to determine the proportion of the vein
which may be considered solid ore.
A vein 6 feet square and 1 inch thick contains 3 cubic feet ;
therefore, in order to find the number of cubic feet per square
fathom of a vein, it is merely necessary to multiply the thickness
in inches by three.
The following example illustrates the method of finding the
weight of any ore per square fathom in a vein : What quantity
of galena will be produced per square fathom from a mineral
vein 6 inches in width? One quarter of the vein consists of
galena, the remainder of zinc-blende. One-twentieth must be
allowed for cavities in the vein.
The specific gravity of galena is 7*5, and a cubic foot of water
weighs 1,000 ounces ; therefore, a cubic foot of galena weighs
7,500 ounces. The vein being 6 inches thick, there are 18 cubic
feet in a square fathom. One quarter of that amount, or 4 -5
cubic feet, consists of galena. The weight of galena in ounces
is therefore
7,500 x 4-5 = 33,750 = 2109-375 Ibs.
From this, one-twentieth, or 105-468 Ibs., must be deducted,
leaving 2003-907 Ibs., or 17 cwt. 3 qrs. 15 Ibs., as the weight of
lead ore per square fathom.
164
MINE-SURVEYING.
CHAPTER XIII.
LEVELLING.
Definitions and Principles. Levelling is the art of determining
the relative distances of points from the centre of the earth.
One point is said to be above another when it is farther from
the centre of the earth, and the difference of distance from that
centre is called the difference of level between the two points.
The operation of finding how much one point is higher or lower
than another may be trigonometrical, geometrical, or physical.
Trigonometrical levelling necessitates the measurement of
lengths and angles. As an illustration, the simplest case may
Fig. 53.
Fig. 54.
be taken. In order to determine the difference of level between
A and (Fig. 53), or in other words the line A B, the angle
A C B, and one of the two lines A C and C B must be measured.
The height required is then found by trigonometrical calculation
from the two magnitudes measured.
In geometrical levelling, a horizontal line or plane is con-
structed, and the distance of the two points A and B (Fig. 54)
from this is measured directly by setting-up vertical staves.
The difference of the two readings on the staves is the difference
in level between the two points.
Physical levelling is based on the change of atmospheric
pressure at different altitudes. The most important instrument
for this method of levelling is the barometer.
The Mason's Level and Boning-staves. For geometrical level-
ling, there may be employed the mason's level, boning-stavcs,
or the spirit-level.
The mason's level is based on the principle of the plumb-line.
It is only used for levelling, when no other instrument can be
LEVELLING.
165
. 55.
obtained. To use the instrument, two pickets are driven into
the ground and adjusted until the plumb-line of the mason's
level shows that their heads are truly level.
The same operation is more rapidly performed by means of
boning-staves, which are simply 3-foot staves having a T-head.
Both these methods are very rough and inaccurate, and only
suitable for very short distances.
The Spirit-level is the instrument commonly used. The
spirit-level proper is a glass tube B 0,
Fig. 55, hermetically sealed at both
ends, partially filled with liquid. By
giving the tube a slight arched curva-
ture, the bubble may be made to rest
firmly in the middle, and by regulat-
ing the curvature, the travelling of the bubble may measure
small angular deviations from the horizontal line. The tubes
are ground on the inside so as to give a similar curvature to the
part of the tube under which the bubble travels.
(a.) The Dumpy Level The term spirit-level is also applied
to the levelling instrument, of which the spirit-level proper is
the essential part. The instrument most generally used in Great
Britain is the dumpy level, invented by W. Gravatt. It is
represented in Fig. 56. A is the spirit-level attached by screws
at a, a, to the telescope B C. The
small circle near the object end B
of the telescope represents a small
transverse spirit-level used to show
whether the cross-wire of the tele-
scope is truly horizontal. D D is a
flat bar or oblong plate fixed on
the top of the vertical axis E. To
this bar the telescope is attached
by adjusting screws rf, d. The
hollow vertical axis turns upon a
spindle fixed to the upper parallel
plate F, the spindle being con-
tinued downwards and being at-
tached to the lower parallel plate G
by a ball and socket joint. There
are four levelling-scre wsy, by which
the vertical axis is set truly vertical.
The lower plate is screwed on the tripod head H. The tripod
consists of three wooden legs like those of the theodolite. In
some instruments, a compass is carried on the top of the plate
d, d for taking the bearings of lines of trial sections.
56.
166
MINE-SURVEYING.
Fig. 57.
The telescope of the level is similar to that of the theodolite,
except that the diaphragm contains one horizontal
wire and two parallel vertical cross-wires, as shown
in Fig. 57. This levelling instrument derives its
name from its dumpy appearance, due to the large
aperture and short focal length of the telescope.
The latter is usually 9 to 14 inches in length.
(6.) The Y-Level. Of the different varieties of levelling
instrument, that termed the Y-level is preferred by American
engineers. In this instrument the telescope is mounted 011 Y's,
like those of the Y-theodolite.
A recent form of American Y-level, made by Messrs. Heller
& Brightly, of Philadelphia, is shown in Fig. 58. The telescope
rests 011 Y's, and is confined in them by clips fastened by binding-
pins. The telescope is 17 to 20 inches long. It has at each end
Fig. 68.
a ring of bell-metal ; by these it revolves in the agate bearings
of the Y's. and can be clamped in any position. The spirit-level
is attached to the under side of the telescope, and is provided at
its ends with screws for horizontal and vertical adjustment. The
level scale extends over the whole length, and is graduated into
tenths of an inch. A clamp and tangent screw are connected
with the axis for moving the bar and telescope.
(c.) The Troughton Level. In the Troughton and Simms'
pattern of fixed telescope level, the brass case of the spirit-level
is embedded in the top of the outer telescope tube. There are
no adjusting screws. These levels are made with telescopes of
10 to 26 inches in length.
The Adjustments of the Level are the same as those of the
theodolite. They are as follows: Temporary Adjustments: 1.
For parallax. 2. To place the vertical axis truly vertical by
LEVELLING. 167
means of the le veiling-screws. Permanent Adjustments: 3. For
collimation. 4. To make the spirit-level parallel to the line of
collimation. 5. To place the telescope and spirit-level perpendi-
cular to the vertical axis.
The adjustment of the line of collimation in the Y-level is
obtained by rotating the telescope on its collars. The parallelism
of the level to the line of collimation is obtained by reversing the
telescope end for end on its Y's.
The adjustments of the le veiling-instruments with fixed tele-
scopes are not so simple, but they are much more permanent.
In the dumpy level, the adjustment for collimation is made by
the instrument-maker before soldering the telescope tube to the
two blocks that support it. In this case, the adjusting-screws of
the diaphragm should never afterwards be disturbed. To make
the level and line of collimation parallel, a level piece of ground
is selected, and after levelling the instrument by means of the
le veiling-screws, it is directed to a staff held by an assistant at a
distance of about 10 chains. The difference between the height
read and that of the centre of the telescope above the ground is
noted. The instrument and the staff are then made to change
places, and the observation repeated. If the results agree, the
level and the line of collimation are parallel. If they do not, the
inclination of the telescope must be altered by means of the
levelling-screws, and the bubble then brought to the middle of
its tube by means of the adjusting-screws a, a (Fig. 56).
(d.) Cushing's Reversible Level. On account of the inconveni-
ence attending the adjustment for collimation in levelling-instru-
ments where the telescope is fixed, it occurred to Mr. Gushing,*
Inspector of Scientific Instruments to the India Office, to make
the eye-end and object-end of the telescope interchangeable.
For this purpose he fixes to the internal tube of the telescope a
gun-metal socket, which is turned and ground with a short
conical fitting and wide flange to receive the eye-end, with its
eye-piece and diaphragm. On the opposite end of the outer
tube, a precisely similar fitting receives the cell containing the
object-glass. Both ends are identical as regards the fitting,
though the object-end is necessarily rather longer than the eye-
end on account of its having to carry on the outside the cover or
dew-cap. The line of collimation is adjusted by reversing the
collimation stop, which in this level is a glass disc with lines
engraved upon it by a fine diamond, instead of the ordinary
cross- wires.
The Levelling-staff serves to measure the vertical distance
from the horizontal line formed by the axis of the telescope down
* Min. Proc. Inst. C.E., vol. lix., 1880, p. 278.
168 MINE-SURVEYING.
to the station on the ground. Formerly the levelling-staff con-
sisted of a wooden rod, furnished with a sliding vane or target,
which was raised or lowered by the staff-holder in response to
signals from the observer. Such staves are now rarely used.
The principal objection to which they are liable is that the
observer must depend on the staff-holder to read the height
observed, or if the latter is not sufficiently intelligent to perform
so important a duty, must himself go and read off the height of
the vane. In this way great loss of time is caused, and there is
uncertainty in the results, as the vane may possibly have shifted
in the meantime.
A very perfect staff of this kind, known as the New York
target rod, is largely used in the United States. It is graduated
to hundredths of a foot. To indicate where the horizontal line
cuts the staff, a target is used, the face of which is divided into
quadrants painted with two alternate colours. In the face, there
is an opening a tenth of a foot long, through which the figures
can be seen on the face of the rod. The right edge of the opening
is provided with a vernier, by means of which the staff can be
read to thousandths of a foot.
In order to avoid entrusting the reading of the staff to an
attendant, Mr. W. Gravatt invented a staff, the face of which
was graduated distinctly enough for the observer himself to
read off the figures through the telescope of his instrument.
The sliding vane is thus dispensed with, and the staff-holder has
nothing to do but to hold the staff vertical.
The levelling-staff usually consists of three parts, sliding one
within the other, and, when opened out for use, forms a staff 14
to 16 feet in length. It is made of mahogany soaked in boiled
oil, and painted with several coats of oil paint. The whole
length is divided into hundredths of a foot, coloured alternately
black and white, and occupying half the breadth of the staff.
The patterns of levelling-staves are very various. The form
shown in Fig. 59, invented by T. Sopwith, F.R.S., is that
most frequently used. In this the feet are represented
by large red figures, the tenths are shown by odd black
figures, and the hundredths are coloured alternately
black and white. Between the odd figures represent-
ing tenths, a black diamond is painted to indicate the
alternate five-hundredths. The top of every figure
represents its value. Of the black and white divisions,
the bottom of each black space represents odd hun- ^^.
dredths, the top even hundredths. The staff is usually ^- '
14 feet in length, and divided into 3 parts, which,
when drawn out, are held in position by a spring clip Fig. 59.
LEVELLING. 169
at the back. When closed, they form a staff about 5 feet 3 inches
in length, 3 inches wide, and 1 inch deep.
An important modification has been introduced in the gradua-
tion by Mr. A. G. Thornton, of Manchester. It consists in the
repetition at each 3 inches of the number of feet in small red
figures on the left of the staff. This improvement will be found
very advantageous, especially with short lines of sight, as an
exact reading can be taken on any part of the staff where the
cross-wire falls, without the necessity of raising or lowering the
staff. It is important that the staff be held truly vertical while
it is being read. To help the staff-holder in this, a small
plummet is suspended in a groove cut in the side of the staff, by
means of which its verticality can be determined in one direction.
The observer himself can detect by means of the two vertical
wires of the telescope whether it inclines in the other direction.
The plummet may be replaced by a round spirit-level, the
tangential plane of which is perpendicular to the back of the
staff.
The error caused by the staff being inclined is considerable.
Let h be the reading on the staff when it is held vertical, and ft'
the reading when the staff is inclined at an angle of 8 from the
vertical. Then -n = cos 8, and h' = s . Thus, if 8 = 2, and
n cos o
h = 4 feet, then h' = 4-002 feet
If necessity should compel the staff to be used without a
plummet or round spirit-level, it should be moved backwards
and forwards by the staff-holder ; the lowest reading will be the
most correct one.
A triangular piece of sheet iron, about one-tenth of an inch in
thickness, having the corners turned down, is used to rest the
staff on. The corners are pressed into the ground. By means of
this iron plate, the staff is kept on the same spot, and at the
same height from the ground, while the observer is reading the
back- and fore-sight. A chain and ring are attached to the plate
for the convenience of the staff-holder in lifting it from the
ground, and in carrying it from station to station.
Mine Levelling- Staves. For levelling underground, staves
may be employed similar in construction to those used at the
surface. They must, of course, be shorter. The best sizes are
a 9-foot Sopwith staff to close down to 3 feet 6 inches, or a
6 -foot Sopwith staff to close down to 2 feet 6 inches. The staff
is illuminated by means of a miner's candle or a safety-lamp.
Mr. Stanley has designed a staff, made in lengths of 18 inches,
like a folding rule.
170 MINE-SURVEYING.
Mr. G. J. Jee * has designed a useful staff for colliery work.
It consists of three lengths, sliding one into the other. The
bottom length is graduated upwards in the ordinary way, and is
3 feet in length. At the top of the first division of the staff is
attached a 2-inch band, which is graduated upwards, and forms
an accurate continuation of the scale on the lower division of the
staff. The band passes over a brass roller attached to the top
division of the staff, and thence is carried down and wound
round a brass drum, fixed just below the roller, to the top of
the same length of the staff, the band being kept in tension by
means of a box-spring attached on one side to the axis of the
cylinder. It is thus evident that when the second length of
the staff is drawn out, the band unwinds and gives a con-
tinuous reading up to 5 feet 8 inches, or to any intermediate
distance that the height of the roof will allow. In the same
way when the third length is drawn out, a continuous reading
may be obtained up to 9 feet, or to any intermediate distance
required. The weight of the staff is 5 IDS. It is manufactured
by Messrs. J. Davis & Son, of Derby.
The clumsy contrivances used in the St. Gothard tunnel
induced Professor M. Schmidt,t of the Freiberg School of
Mines, to devise a staff specially adapted for levelling in mines.
It consists of two staves, each 5 feet in length. The front one
is graduated, whilst the second acts as a pedestal. The two are
joined together by two clamps and screws, in such a way that
the graduated staff may slide along the pedestal for a distance of
4 feet. The graduated staff is backed with an iron plate drilled
with small holes, corresponding to its graduation. Into these a
steel pin on the pedestal works automatically with a spring,
whenever the graduated staff is drawn in or out. A pointer is
attached to the pedestal at a given height (e.g., 4 feet), when the
graduated staff is pushed home. When the latter is drawn out,
the reading, less the difference between the foot and the pointer,
added to the constant height, denotes the height of the line of
sight above the foot of the staff.
Attached to the side of the staff, is a portable reflector lamp
for illuminating the scale. It can be raised or lowered at will,
and its reflector is so placed that as much light as possible falls
upon the scale, whilst the flame itself is kept out of sight. In
mines where the ground is stony or soft, a cast-iron shoe with a
hemispherical steel head is placed under the staff.
For rough levelling in metalliferous mines, a levelling instru-
* Colliery Guardian, vol xxxviii., p. 576, 1879.
t Oesterr. Zeitsckr, vol. xxix., p. 295, 1881.
LEVELLING. 171
ment may be made out of an ordinary carpenter's level, fitted
with sights, and made to fit on the dial tripod. The staff used
in conjunction with this instrument may be made out of a piece
of planed deal, 3 inches in width, marked into lines representing
feet and inches by means of a piece of red-hot hoop iron. The
numbers of the feet may also be burnt-in in bold Roman figures,
every half foot being indicated by a longer line. The level
having no telescope, the reading of the staff has to be entrusted
to the staff-holder.
For very accurate levelling, Borchers' vane-rod is generally
used in the Continental mines. To enable this contrivance to be
used, all the station-points must be marked by small hooks fixed
into the roof of the underground road. The contrivance consists
of a steel rod, rectangular in section, 5 feet 5 inches in length,
provided at its upper end with a movable hook. The rod is
graduated into inches, the graduation proceeding from the inside
of the hook to the lower end of the rod. Up and down the rod
slides a sheet-iron circular vane or target, 8 inches in diameter,
which may be clamped at any height. At right angles to the
longitudinal axis of the rod, a line is scratched through the
centre of the vane. With their centres truly on this line, three
circular apertures are cut, two 0-4 inch in diameter, and one OO7
inch in diameter. In front of one of the larger openings a
piece of ground glass is fastened. To the back of the vane a
vernier is fastened with its zero coinciding with the horizontal
line scratched on the vane.
In levelling, the rod is hung from a hook in the roof of the
mine-road, and the vane placed at right angles to the line of
sight. For very short station-lines, the flame of a miner's lamp
is held behind the small hole, and the vane moved up or down
until the horizontal cross-wire of the telescope coincides with
the point of light sighted. For greater distances of 60 to 200
yards, the aperture covered with ground glass is used if the air
is clear; with still greater distances the uncovered aperture is
used. Very long station-lines are not to be recommended, on
account of the difficulty of communicating with the assistant.
This levelling-rod is exceedingly simple. It hangs perpendi-
cularly by its own weight, and, unlike wooden staves, it is not
affected by the water and dirt in the mine. At the same time
it presents the advantages of fine adjustment, exact reading,
and great rapidity.
Practice of Levelling. If it is required to determine the differ-
ence of level between two points not very far apart, this may be
done by simple levelling. For this purpose, the levelling-instru-
ment is set up midway between the two stations A and B, Fig.
172
MINE-SURVEYING.
60. With the bubble remaining unmoved in the middle of its
tube, the telescope is directed towards
a staff held vertically at A, and the
reading h noted. The staff is then held
vertically at B, and the telescope di-
rected towards it, the reading h' being
noted. The difference of level between
the two points A and B is then h h', and
B is higher than A when h is greater
than h'. The difference of level is thus
determined by two readings on the staff, one with the telescope
directed backwards towards the staff at A, and the other with
the telescope directed forewards to the staff at B, or, in other
words, by means of a back-sight and a, fore-sight.
In order to obtain the greatest accuracy, the instrument is set
up as nearly as possible midway between the two stations A and
B. The advantage of thus placing the instrument is that the
instrumental errors and the errors due to the curvature of the
earth and to refraction are neutralised.
Let the instrument be set up at in, Fig. 61, so that ma = mb,
and let a 6 be a horizontal line. Then if all the sources of error
act in such a way that the optic axis of the
telescope directed towards the staff at A
gives an angle, amd, with the horizon-
tal line, the cross-wires of the telescope
will not coincide with the point a, but
with the point d, and on directing the
telescope to the staff at B, the cross-wires
will coincide not with point b, but with c.
^-^-^
, 1
\
Fig. 61.
The same causes being at work in both positions of the telescope,
the angles amd and b m c must be equal. Because m a = m b,
ad = be. The difference in level is equal to h - h', that is (A a +
a d) (B b + b c). It is here assumed that the condition of the
atmosphere is the same with the fore-sight as with the back-
sight, and thus the refraction is the same in both cases.
The influence of the curvature of the earth's surface is depen-
dent on the radius of the earth, r, and on the length of the
station-line I. Imagine an arc of a circle to be described passing
through the telescope axis A, Fig. 62,
and with the centre of the earth as
centre. The arc will intersect the
staff set up at B in the point C. The
curvature in the figure is of course
very much exaggerated. The hori- Fig. 62.
zontal line passing through A, inter
LEVELLING. 173
sects the staff at the point D. Thus, A is the true horizontal
line, A D the apparent horizontal line, and C D the depression
of the true below the apparent horizontal line. Then the cor-
rection for curvature is C D, a third proportional to the
earth's diameter and distance between the level and the staff.
I 2
D is thus equal to . For a distance of 1 mile this correction
is 8 inches, or two-thirds of a foot. Two-thirds of the square of
the distance in miles will be the amount of the correction in feet.
The error C D is diminished by the refracting action of the air,
as the real line of sight is a curved line, in which light proceeds.
The curve being concave downwards, the point D is not seen at
the cross-wires of the telescope, but the point E. With a calm
dear atmosphere, D E is equal to 0-1348 C D, or 0-1348 .
The coefficient 0-1348 is the mean of the determinations of
several physicists.
The total error due to the curvature of the earth and to
refraction is thus ~ - 0-1348 - = " .. The earth's dia-
2r '2r r
meter being equal to 41,778,000 feet, the correction for curvature
and refraction per mile would be
0-4326 x 5280 2 + 20,889,000 = 0-577 foot = 6-92 inches.
At distances up to 10 chains, the errors produced by curvature
and refraction are so small that they may be neglected.
In crossing over a deep valley it is sometimes advisable to set
up the level at one of the points A and the staff at the other
point B, in which case the height of the centre of the instrument
above the ground must be measured. The difference of level d
will then be equal to the height of the instrument i above the
ground, less the reading on the staff h that is, d = i - h. If
the correction c for curvature and refraction has to be taken into
account the formula becomes
d = i - (h - c) = i - h + c.
If the instrument is placed at B, and the staff at A, the difference
of level is
d h' c i'.
The mean of these two values gives the difference of level
independently of all correction
li h i i'
174 MINE-SURVEYING.
"When the distance is too great or the ground too much
inclined for the difference of level to be determined by one
operation, recourse must be had
to compound levelling, a process
consisting of several simple
levelling operations. The differ-
ence of level of each two succes-
sive points is determined in the
way described. Fig. 63 gives Fig. 63.
an example of compound level-
ling. By setting up the levelling-instrument at the three
stations, the following values were obtained :
Back-Sight. Fore-Sight.
Feet. Feet. Feet
L AD = 6-71 BE = 3'92 Rise from A to B = 2'79
II. CF = 7-86 CG = 2-41 Rise from B to C = 5'45
III. HC = 2-84 DI = G-39 Fall from C to D = 3'55
17-41 1272 Rise = 4 -69
If the back-sight is greater than the fore-sight, the ground
rises. If the fore-sight is greater than the back-sight, the
ground falls. The rises being regarded as positive, and the
falls as negative, the algebraical sum gives as the result of the
levelling that D is 4-69 feet higher than A. The same result
is obtained when the sums of the back-sights and of the fore-
sights are taken, and the smaller sum subtracted from the
larger. Thus 17-41 - 12-72 = 4-69. The difference obtained
is difference in level between the end points. It indicates a rise
when the sum of the back-sights is the greater, and a fall when
that of the fore-sights is the greater.
This is the method of conducting a flying-level that is, a
levelling operation merely to determine how much one point is
above or below another. If, for example, it is required to deter-
mine what thickness of strata there is, at a certain point A at
the surface, above the present workings in the mine below it,
the depth of the shaft is measured, and levelling commenced
at the bottom of the shaft and continued to the point under-
ground directly below A. A flying-level is then made at the
surface from the shaft to A. The depth of the shaft being
known, the thickness of the strata at A can be calculated from the
rise or fall determined at the surface and underground. Thus,
if the shaft is 300 feet deep, and the point underground is found
to be 5 feet lower than the bottom of the shaft, whilst the point
LEVELLING.
175
A at the surface is found to be 40 feet higher than the top of the
shaft, the thickness of the strata at A will be 300 + 5 + 40 =
345 feet.
Section-levelling. When a section of the ground is to be drawn,
the distances between the several stations must be carefully
measured. The levelling-instrument should be placed as near as
possible midway between the two stations, and the levelling is
then conducted in the manner described. To facilitate the
plotting of the section, the vertical distances of the points are
calculated above an assumed level-line called the datum-line.
The observations are recorded in the levelling-bookNin the
following manner :
FORM OF RECORD I.
No.
Back-
Sight.
Fore-
sight.
Rise.
Fall.
Height above
Datum
5000.
Distance.
Remarks.
A
5-49
0-06
5-43
...
55-43
Chains.
1-50
B
4-32
2-24
208
57-51
470
C
8-40
1-52
6-88
...
64-39
9-12
D
3-21
7-42
...
4-21
60-18
10-36
E
1-41
6-50
5-09
5509
13-98
F
1-68
4-53
285
52-24
16-38
G
7-20
0-22
6-98
...
59-22
19-98
H
12 GO
9-51
309
62-31
24-98
J
9-51
0-33
9-18
7,1-49
29-18
K
5-02
4-18
0-84
72-33
32-78
L
5-08
4-02
1-06
...
73-39
36-36
M
6-01
3-07
2-94
...
76-33
40-68
N
0-82
4-00
2-82
79-15
45-73
7075
47-60
41-30
12-15
- 50-00
29-15
29-15
29-15
176 MINE-SURVEYING.
The starting-point is 50 feet above the datum-line, which in this
case was the level of the high-water mark at London Bridge.
The column headed " Height above Datum " contains the abso-
lute height of each forward station above the horizontal line
passing through the high-water mark. The numbers are ob-
tained by taking the algebraical sum of the rises and falls, the
former being considered positive, and the latter negative.
As a test of the accuracy of the arithmetical work, the columns
of back- and fore-sights should be added up, and the smaller sum
subtracted from the larger. The result should agree with the cal-
culated height above datum. Another test is afforded by adding
up the rise and fall columns, when if, upon subtracting the smaller
sum from the greater, the remainder is the same as that obtained
by the two other operations, there can be no doubt that the levels
have been correctly calculated. Thus, in the example given, the
height of N above the starting-point is 79-15 - 50-00 = 29-15
feet. The sum of the back-sights being 76 -75, and that of the
fore-sights 47 -60, the difference also gives 29-15 feet as the height
of N above the starting-point. Lastly, the sum of the rises is
41-30, and that of the falls 12-15, the difference being 29-15 feet
as before.
In order to make a correct section of a continuous surface, the
levels of a series of points may be determined with the instrument
at one station. The first and last observations are then the
principal back- and fore-sights respectively. Thus, in Fig. 64,
Fig. 64.
A is a station where the instrument is set up, and b A c is the
line of sight. The first back-sight is taken with the staff at the
starting-point B, of which the height above the datum-line is
known. The reading on the staff is B6, or 2-95 feet. The first
fore-sight is taken with the staff at C, giving the reading c, or
0-58 foot. Between the points B and C, several intermediate
sights are taken. The first intermediate-sight, taken with the
staff at the point marked 1, is at the same time a fore-sight to B,
and a back-sight to the point marked 2 ; 3 is a fore-sight to 2 and
a back-sight to 4, and so on with the other points. When the
level is carried on to a new station D, the assistant holds the
LEVELLING.
177
staff steadily at 0, at exactly the same point as it was for the
fore-sight from A. The first back-sight C c is taken, and the
process repeated until the fore-sight Ee, or 1-01 foot, is taken.
The staff is then held stationary until the levelling-instrument is
moved on to the next station.
The readings are recorded and reduced in the manner shown
in the following example :
FORM OF RECORD II.
No.
Back-
Sight.
Fore-
Bight
Kise.
Fall
Height above
datum
100 '00.
Distance.
Remarks.
1
2-95
3-99
104
98-96
Links.
35
2
3-99
4-90
...
0-91
98-05
90
3
4-90
3-99
0-91
...
98-96
125
4
3-99
3-08
0-91
99-87
165
5
3-08
107
2-01
101-88
220
6
1-07
1-88
0-81
101-07
245
7
1-88
5-00
...
3-12
97-95
295
8
5-00
5-52
...
0-52
97-43
335
9
5-52
1-23
4-29
101-72
400
10
1-23
0-58
0-65
...
102-37
420
11
8-20
7-30
0-90
103-27
455
12
7-30
6-50
0-80
...
104-07
515
13
6-50
2-08
4-42
108-49
580
14
2-08
1-81
0-27
...
108-76
635
15
1-81
1-01
0-80
...
109-56
740
...
59-50
49-94
15-96
6-40
-100-00
...
9-56
...
9-56
9-56
The first back-sight and last fore-sight of each line of sight are the
most important in point of accuracy. Any error made in taking
12
178
MINE-SURVEYING.
an intermediate sight affects that line only, whilst any error in
the back-sight or fore-sight is carried on throughout the section.
In order to correct for curvature and refraction, the first back-
sight and last fore-sight of each line should be at points as nearly
as practicable equidistant from the instrument.
In recording the readings in the levelling-book, a separate
column may be used for the intermediate sights. The readings are
reduced, and the computations checked in the manner shown in
the following example :
FORM OF RECORD III.
No.
Back-
Sight.
Intermediate.
Fore-
Sight.
Rise.
Fall.
Height above
datum
100-00.
Total
Distance.
1
2-95
3-99
...
1-04
98-96
Links.
35
2
...
4-90
...
0-91
98-05
90
3
3-99
...
0-91
98-96
125
4
...
3-08
...
0-91
99-87
165
5
...
1-07
...
2-01
101-88
220
6
1-88
...
0-81
101-07
245
7
...
5-00
...
3-12
9795
295
8
...
5-52
...
...
0-52
97-43
335
9
...
1-23
...
4-29
101-72
400
10
...
0-58
0-65
...
102-37
420
11
8-20
7'30
0-90
103-27
455
12
6-50
0-80
104-07
515
13
...
2-08
4-42
108-49
580
14
1-81
0-27
108-76
635
15
...
...
1-01
0-80
109-56
740
...
11-15
1-59
15-96
6-40
- 100-00
...
9-56
...
9-56
9-56
...
LEVELLING.
179
In this way a large amount of unnecessary addition is avoided.
There is a third method, known as the collimation method, of
reducing levels. It saves one column of figures, and is easier to
work out, as the distinction between rises and falls is not con-
sidered. The following is the form of record :
FORM OF RECORD IV.
Back-
Sights.
Inter-
mediate.
Fore-
Siglits.
Height
of Line of
Collimation
above Datum.
Height of
Surface above
Datum.
Distances.
Total
Distances.
0-15
...
...
206-04
205-89
Chains.
o-oo
Chains.
38-00
4-80
...
201-24
1-00
39-00
...
3-80
...
20224
1-00
4000
5-49
...
8-00
203-53
198-04
1-00
41-00
5-44
...
...
198-09
1-00
42-00
9-25
...
...
194-28
1-00
43-00
9-64
...
193-89
1-00
44-00
5-64
17-64
...
-12-00
...
...
12-00
...
...
"'.
A modification of this form of booking will be found advan-
tageous for levelling in mines. Only two columns are used for
entering the heights observed on the staff. The intermediate
and fore-sights are placed in one column, the latter being dis-
tinguished by being underlined. The reduced levels for the
"height above datum" column are obtained in the following
way: Add the back-sight to the reduced height for collima-
tion and subtract intermediate and fore-sights. On reaching a
fore-sight, the next back-sight is added to the reduced height at
that point, when the intermediate and fore-sights are subtracted
as before.
Should it be required to work out the levels backwards, the
rule is : Add the fore-sight to the reduced height for collimation
and subtract intermediate and back-sights.
On reaching the bottom of a page in the levelling-book, if there
is no necessity to move the instrument, the last intermediate
sight is booked as a fore-sight at the bottom of the page, and
180 MINE-SURVEYING.
again as a back-sight at the top of the following page. By so
doing, the same number is added to, and subtracted from the
collimation height, and consequently the reduced heights are
not affected. The accuracy of the calculations is ascertained in
the ordinary way, by adding all the back-sights and all the fore-
sights, and subtracting the smaller total from the larger one.
The advantages of this method, especially for underground
levelling, are apparent, as it necessitates the writing of fewer
figures. The form of record for this system, recommended by
Mr. H. W. Hughes, is shown by the extract from his levelling-
book of a South Staffordshire colliery given on p. 181.
Bench Marks. When a section has been completed, it is
generally necessary to check its accuracy by repetition. To do
this, it is advisable in levelling to follow the shortest route, and
to level at intervals to some known points on the exact line of
section. The points thus selected are usually bench marks.
These are fixed points of reference, the levels of which are known.
In the Ordnance Survey of Great Britain, the bench marks are
generally chiselled on some permanent stone slab, pillar, or wall.
The form of mark for them is the broad arrow /t\. In level-
ling on long lines of section, a bench mark is generally made at
every quarter of a mile, so that any error in the operation may
not involve re-levelling the whole line. By referring to the maps
of the Ordnance Survey, the heights may be found of the bench
marks above the datum-line (the level of mean tide at Liverpool).
In collieries it is the general practice to record the levels of
the works from some fixed datum near the shaft, as, for example,
the flat sheets at the top or bottom of the shaft, the delivery of
water from the high set of pumps, or some other fixed point.
Mr. J. A. Ramsay * proposes to take or continue the Ordnance
levels into the workings. In the Ordnance bench mark the
broad arrow points upwards to a horizontal line. To make a
distinction, it is suggested that as soon as the levels become lower
than the datum line or sea-level, the broad arrow should be
reversed. The levels obtained in this way may be written upon
the plan in plain figures at particular points on the main roads,
and, when necessary, may be continued into the face of the off-
workings.
Mr. Ramsay gives the accompanying extract from his level-
ling-book to illustrate the method he proposes of continuing the
Ordnance levels into the workings of a colliery. (See p. 182.)
* Trans. N~. Eny. Intt. M.E., vol. xx., 1870, p. 73.
FORM OF RECORD V.
181
Baok-
Siglit.
Fore and
Inter-
mediate
Sights.
Reduced
Heights.
Distance.
Remarks.
Feet.
Datum 100 feet below inset, distance
070
...
102-72
5,466
measured from pit shaft. Section
of coal. Coal, 3' 9" ; dirt, 0' 5" j
coal, 3' 2"; floor composed of clay.
2-98
100-44
5,500
floor of coaL
5-74
97-68
5,544
3" up coal.
0-13
" "-
5-08
92-73
5,600
floor of coal.
0-13
37
86-49
5,671
99 99
0-88
2-94
84-43
5,700
99 99
535
82-02
5,761
3" up coal.
4-55
~
4-96
81-61
5,800
5" below coal.
3-75
82-82
5,823
floor of coal.
4-00
foot of fault, rise about 9 yards, fault
4-30
82-52
5,900
hades 15.
0-18
86-64
5,966
5-18
~
1
0-30
91-52
6,015
4-50
0-16
95-86
6,048
5-29
0-05
101-10
6,078
}- crossing measures below coal.
3 -SO
0-01
104-89
6,111
6-58
o-oi
111-46
6,136
4-15
450
111-11
6,251
floor of seam.
2-35
113-26
6,348
1' 0" above bottom of coaL
2-75
112-86
6,402
0' 6"
4-48
-
4-46
112-88
6,517
floor of seam, road to left.
3-64
113-70
6,623
2" above bottom of coal.
3-93
~
3-11
114-52
6,781
floor of coal.
4-08
113-55
6,803
99 99
5-15
112-48
6,921
99 99
5-30
112-33
7,017
3" below coal.
Proof. Total fore-sights = 38 69; total back-sights = 48'30. Difference
(viz., rise) = 9'61, which, added to 102-72, the reduced height at 5,466,
gives 112-33, the reduced height at 7,017.
182
FORM OF RECORD VI.
No.
Back-
Sight.
Fore-
Sight.
Rise.
Fail.
Datum.
Dist.
Kemarks.
85 "90
f Ordnance B. M. on north -
l east corner of watch house
1
3-31
5-08
...
1-77
8413
...
2
402
11-00
...
698
7715
3
2-60
4-40
1-80
7535
...
The flat sheets on lip of pit.
Take Depth of the Pit with
100 feet Chain.
Depth, 518 ft. 11 in. = 518 91.
Less surface height above
datum.
...
518-91
44356
/ Flat sheets at bottom of pit;
J reversed Ordnance B.M.
J cut into stone walling,
V. side of pit.
Level down Cross-cut to make
Section for Engine Plane.
1
6-85
594
0-91
442-65
90
7'9 ft. high Hard post cover.
2
594
5-19
075
441-90
129
7'5 do. do.
3
5-19
5-04
0-15
441-75
165
SO do. do.
4
504
329
1-75
...
440-00
210
6'0 do. Blue metal cover.
5
3-75
5-05
1-30
441-30
276
53 do. do. timbered
6
2-53
5-54
...
3-01
444-31
354
f On the brow of large down-
J throw trouble, measure
) down, with straight edge
V and plumb-line
Dist. 6 ft. + 5* ft. + 3 ft.
+ 6 ft. + 6 ft". = 27 ft.
7
000
20-69
2069
465-00
381
f Down,4-33+4-45+3-39+3-32
t +520 = 20-69.
8
3-45
2-11
1-34
46366
425
f 4 ft. high Roof very jointy
\ and bad top coal left on.
9
3-97
2-34
1-63
46203
462
( 4-3 full height of seam, bad
\ roof, closely timbered.
10
2-89
388
097
463-00
507
4-6 do. do. do.
11
2-06
4-49
...
2-43
465-43
555
f 5'0 better roof, timbered in
I places only.
12
1-95
4-82
2-87
468-30
600
f 5'0 ordinary height of seam
( good roof.
13
3-15
4-15
1-00
469-30
657
5 do. do.
14
4-00
3-37
0-63
468-67
705
50 do. do.
15
4-73
3-03
1-70
466-97
780
5-0 do. do.
16
326
3'84
0-58
467-55
840
5-0 do. do.
17
2-76
4-71
1-95
469-50
8S5
5-0 do. do.
6152
87-46
8-86
34-80
25-94
25-94
LEVELLING. 183
(e.) The Reflecting Level. For rough surface levelling, the
reflecting level may be used. It consists of a small sighting-
tube, with a bubble-tube set above it. It is so arranged that
the bubble is seen through the bottom of its tube, and reflected
by a mirror into the sighting-tube. An instrument of this
kind, invented by Abney, is also useful as a clinometer. In
this instrument, the bubble-tube is fastened to an arc 2 inches
in diameter. In taking a level, the vernier, fastened to a bar
at right angles to the spirit-level, is set to the zero of the vertical
arc. On looking through the tube, the object observed will be
level with the eye when it is intersected by the bubble. The
results obtained are very satisfactory. Like all reflecting instru-
ments, this level is useless in the bad light of a mine.
Sources of Error in Spirit-Levelling. There are four sources of
error in levelling 1, Errors of observation; 2, instrumental
errors ; 3, errors from unstable supports ; 4, atmospheric
errors.
Errors of observation are mostly unavoidable, and arise chiefly
from the bubble not being carefully centred. Instrumental
errors are due to the instrument not being in adjustment, and
to the staff not being vertical. Errors from unstable supports
can only be eliminated by duplicating the levelling in the
opposite direction, and by taking the mean of the results. At-
mospheric errors arise from wind, tremulousness of the air
in clear sunny weather, and variable refraction due to sudden
bursts of sunshine on the line.
A waterproof cloth should be thrown over the level in case of
rain. Staves should be wiped dry after being exposed to the
rain, placed horizontally to prevent warping, and occasionally
compared with a standard length.
Accuracy Attainable in Spirit -levelling. Mr. W. Seibt arrives
at some interesting results, calculated from observations made
under ordinary conditions. His telescope of 18-inch focal length
had a magnifying power of 42, and an object glass of l-inch
aperture, besides a very sensitive spirit-level. The instrument
was always set up between the back and forward staves, and the
observations taken by one central cross-wire ; both ends of the
spirit-level being read at each observation. Observations were
only made in still clear weather ; the back- and fore-sights being
taken as soon as possible after one another. Each complete
observation occupied 6 minutes, and 24 pairs of observations
were taken at each station. Although the mine-surveyor is
rarely in a position to use an instrument as delicate as that
described, the results arrived at are of interest for the sake of
comparison.
184 MINE-SURVEYING.
The mean error m, in an observation consisting of a back- and
fore-reading, was found to be as follows :
At 50 metres (164 feet) + -28 millimetre (0 'Oil inch).
100 (328 ) 0-62 (0-024 ).
150 (492 ) 0-71 (0-028 ).
200 (G56 ) 0-91 (0-035 ).
The distance for observing should be limited by the capacity
of the observer and of his instrument. It will always be rightly
chosen when it is extended as far as the nature of the ground to
be levelled will allow, and on the other hand, when it is so short
that no trace of air movement is noticeable through the tele-
scope, and the graduation of the staff is presented as a perfectly
stationary and sharply-defined image. If this principle is acted
on, it is asserted that the mean error per kilometre should not
exceed 0*64 millimetre, as in extensive levelling operations the
line of sight does not usually exceed 100 metres.
At the second International Geodetic Conference it was de-
cided that the probable error in the difference of level between
two points, 1 kilometre apart, must not, as a rule, exceed 3 milli-
metres, and in no case exceed 5 millimetres. According to the
report of the United States Coast and Geodetic Survey, on the
line from Sandy Hook to St. Louis, 1009 miles in length, the
probable error per kilometre was 1-2 millimetre.
Plotting Sections. In order to plot a section from the reduced
levels as entered in the levelling-book, it is first necessary to
rule a straight line to represent the datum-line from which the
heights are calculated. Along this line the horizontal distances
between the points are marked off, and at each point a line is
drawn at right angles to the datum-line. Along the lines thus
obtained, the vertical heights are marked off, the figures given
in the "height above datum" column being used for this purpose.
In marking off on the datum-line each distance separately, any
error made is carried forwards. To remove this source of error,
it will be found advisable to add the measured lengths together
so as to obtain the absolute distance of each station from the
starting point.
As a rule, in plotting a section two scales are used, one for
the horizontal distances, and the other for the vertical heights
and depths. An exaggerated representation of the section is
thus obtained. By making the vertical scale much greater than
the horizontal one, the depths of cutting and embankment
required are shown with greater clearness than if both scales
LEVELLING. 185
are the same. The section shown in Fig. 64 is plotted on a
horizontal scale of 3 chains to the inch, and a vertical scale of
30 feet to the inch.
Sections of the main ways in collieries are usually plotted on
a horizontal scale of 2 chains to the inch, and a vertical scale of
20 feet to the inch. As a rule, the scale for the horizontal
distances should be the same as that of the plan with which it
corresponds.
Sections may be plotted with great rapidity by means of
Marquois scales. These consist of a right-angled triangle, the
hypothenuse of which is three times the length of the shorter
side, and two rectangular scales of equal parts, each with two-
scales, a so-called artificial scale placed close to the edge, and a
natural scale immediately within this. The divisions on the
artificial scale are three times the size of those on the natural
scale. The latter is a simply divided scale of equal parts, with
the divisions numbered from left to right. In the artificial scale
the zero is placed in the middle of the edge of the rule, and the
divisions are numbered both ways from that point to the two
ends of the rule. A pair of Marquois scales usually has scales of
30, GO, 25, 50, 35, 45, 20, and 40. The triangle has a short line
drawn perpendicular to the hypothenuse near the middle to
serve as an index.
To draw a line parallel to another, one of the rulers is laid on
the paper, and the short side of the triangle placed against it,
when parallel lines may be drawn by sliding the triangle up or
down.
To draw a line perpendicular to a given line from a given
point in it, the shortest side of the triangle is made to coincide
with the given line, and the ruler placed against the hypothenuse.
The triangle is then slid along the rule, until a line drawn
along the longest side of the triangle passes through the given
point.
With these scales the sight is assisted by the divisions on the
artificial scale being so much larger than those of the natural
scale to which the section is drawn, and any error on the setting
of the index produces an error of but one-third the amount in
the section.
For the purpose of receiving the plotting of sections, a special
kind of paper is prepared, on which faint lines are printed,
dividing it horizontally and vertically into one-twentieths of an
inch. By the use of this section-paper, much time is saved, as
no scale is required.
(/.) The Water-Level is a very simple instrument which, when
necessary, may take the place of a more elaborate levelling-
186 MINE-SURVEYING.
instrument. It requires no adjustment; it may be made by any
intelligent workman at very slight expense ; and in short dis-
tances no serious error can be made when using it. It consists
of a horizontal tube made of tin-plate or brass, terminated at
each end by a vertical glass tube in which the surface of a liquid
gives a horizontal line. By means of this line, the vane of a
levelling-staff is adjusted to the right height. The tube is made
so as to revolve on a light portable stand.
A water-level (chorobates) is described by Vitruvius (de Archi-
tectures, viii. 6), as used in the construction of the Roman
aqueducts. It consisted, not of a tube, but of an open trench
5 feet long, 1 inch wide, and 1J inch deep, cut in a plank 20
feet in length. It was adjusted until the water was at the same
height from the top at each end. The plank was provided with
legs accurately at right angles to it. They were of equal length,
and rested on the line to be levelled.
The water-level was in common use in the Derbyshire lead-
mines in the 17th century. The method of levelling then em-
ployed is described by Thomas Houghton, writing in 1681, as
follows:
" The Instrument for this purpose may be like the following
viz., a Water Stand, with one or more Channels, which the
Miner may make himself, upon an old seabon'd Joyce, cutting a
Mortess therein, a yard long, or more, as his own Discretion
directs, plaining the same very well and even."
The observer sights through a hole above the water channel,
at a staff 6 yards long ; the staff being moved until the top of
it can be seen. The instrument is then moved to the place
occupied by the staff, and the operation repeated, " till you have
finished the whole, and come to the Place where you intend to
begin your Sough [adit level] : then reducing your Poles into
Fathoms, compare them with the depth of your Mine, and thus
you may know whether it will lay it dry or no."
A modification of the water-level has recently been employed
with success by Dr. Luigi Aita, of Padua. His instrument
consists of two levelling-staves, in front of each of which a glass
tube, 7-87 inches long and O79 inch in diameter, slides up and
down. The two glass tubes are connected by an india-rubber
pipe, 30 yards in length. At one end of the india-rubber tube
is a stopcock, by means of which the connection between the two
glass tubes may be interrupted. When in use, one glass tube
and the india-rubber pipe are filled with a coloured liquid, the
staves are set up at the two stations, and the glass tubes raised
approximately to the same height at both staves. The stopcock
is then carefully opened, the fluid will stand at the same level
LEVELLING. 187
in both glass tubes, and its position can be read at both staves.
With this instrument a mile may be levelled in 6 hours. For
levelling in narrow, crooked, and partially fallen-in workings,
this instrument offers great advantages.
In mines where the seams are thin and inclined, the use of
the telescope-level is attended with great inconvenience. For
this work, Mr. T. L. Galloway and Mr. C. Z. Bunning* have
introduced a modification of Aita's water-level. The apparatus
consists of two glass tubes connected by an india-rubber pipe,
which may be of any convenient length from 10 yards upwards.
Each glass tube is attached to a scale graduated into feet, tenths
and hundredths in the same way as the ordinary levelling-staff.
The tubes are filled up to the centre of each scale with coloured
water. The scales being held vertically upon any sloping
surface and at any distance apart that the length of pipe will
admit, the difference of level between the stations at which the
scales are held will be represented by the difference of the
readings denoting the position of the coloured liquid in each
tube.
In order to remove the source of error arising from the
presence of air-bubbles in the liquid, a stopcock is fitted at each
end of the india-rubber pipe. These stopcocks being closed
under water prevent all oscillation while the apparatus is being
carried from station to station, so that there can be no possibility
of the intrusion of air-bubbles. Falls of stone, sudden bends in
the road, or timbering, obstacles so frequently interrupting the
line of sight in levelling underground, present no difficulty with
this apparatus, as it is obviously as easy to proceed over or
around any obstacle as to advance in a straight line. The
instrument has been used in mines under the most difficult
circumstances, and has been found to answer in all cases
exceedingly well, the saving in time being very consider-
able.
Trigonometrical Levelling. The trigonometrical method of
levelling is based on the solution of a right-angled triangle ABO
(Fig. 53), of which the base B C and the angle BOA are known.
The difference of level B A of the points A and C will be equal
to the base B C multiplied by the tangent of the angle BOA.
This method is less exact than spirit-levelling, because a small
error in the angle may give rise to a considerable error in the
difference of level.
Any instrument with a vertical limb may be employed for
levelling trigonometrically. A series of angles of depression and
* Trans. N. En<jl. Inst. M.E., vol. xxvii., p. 3.
188
MINE-SURVEYING.
elevation are taken along the line of section, the instrument
being sighted to a staff with a vane or a cross-piece fixed to it at
exactly the same height from the ground as the centre of the
axis of the telescope is. The staff must be held vertically while
the observer measures the vertical angle which the line of sight'
makes with the horizon. The instrument and staff are then
made to change places, and the vertical angle determined. The
mean of the two readings is taken as the correct result. The
distance must then be measured. As the distance is the
hypothenuse of a right-angled triangle of which the perpendicular
is the difference of level, the latter is obtained by multiplying
the measured distance by the sine of the angle observed.
The following is an example of the field record :
LEVELLING BY VERTICAL ANGLES WITH THE
THEODOLITE 1.
L
To
Inclined
lengths
in feet.
Vertical
angles.
Bise.
Fall.
Height above
datum 50-00.
Horizontal
lengths.
Total
distances.
2
1
471-0
7 21' R
60-24
...
110-24
467-09
467-09
2
3
192-5
311'R
10-68
...
120-92
192-19
659-28
4
3
313-5
515'F
28-68
92-24
312-18
971-46
4
5
340-0
147'F
10-57
81-67
339-83
1311-29
6
5
368-0
218'F
14-75
66-92
367-66
1678-95
70-92
54-00
50 00
16-92
16 '92
When the line to be levelled is marked out on the ground by
stakes set at a horizontal distance apart of 100 feet, the height
will be found by multiplying the horizontal distance by the
tangent of the angle of inclination. The form of record in this
case will be seen on next page.
In this section, in six stations a height of 145 feet has been
ascended in equal distances of 100 feet. With a spirit-level and
a 12-foot staff, the number of stations would have been doubled.
In order to simplify the calculations with this method of
levelling, Mr. A. Faul, of Baltimore, has computed a table of
LEVELLING.
189
LEVELLING BY VERTICAL ANGLES WITH THE
THEODOLITE 2.
From
1
To
Horizontal
Lenvths
measured
in feet.
Vertical
Angles.
Rise.
Fall.
Height alcove
Datum lOO'OO.
Remarks
100
945'R
17-18
...
117-18
1
2
100
715'R
12-72
129-90
3
o
100
9 30' R
16-73
...
146-63
3
4
100
10 15' R
18-08
164-71
5
4
100
330'F
6-12
158-59
5
6
100
845'R
15-39
173-98
7
6
100
830'R
1495
...
188-93
7
8
100
1000'R
17-63
206-56
9
8
100
1115'R
19-89
...
226-45
9
10
100
1230'R
22-17
248-62
11
10
100
145'F
3-06
245-56
...
...
154-74
9-18
- 100 00
145-56
145-56
heights* for all angles from to 22^, in minutes, for any
distance required. His object is to bring levelling by vertical
angles into more general use, and save the many stations re-
quired in spirit-levelling. The latter method is very tedious in
hilly countries where extreme accuracy is immaterial, especially
so in all preliminary surveys. The method of levelling by
vertical angles gives approximate results in the shortest possible
time.
Levelling may be performed by the theodolite by setting up
the instrument at the foot of a steep incline, with the line of
* A Short Treatise on Levelling by Vertical Angles with Tables of
Heights. New York, 1886.
190
MINE-SURVEYIXG.
collimation set at a known angle of inclination. Sights are then
taken, as if with a spirit-level.
Thus, suppose that the theodolite
is placed at A, Fig. 65, and that
b A C represents the inclined
line of sight. Then B b, c, and
the other vertical lines will re-
present the heights read off the
staff. The requisite data for
drawing the section are thus ob-
tained. This method saves time
in taking the levels of steeply
inclined ground.
When a proper levelling-instrument is not available, the line
of collimation may be placed horizontal, and the theodolite used
in the same way as the spirit-level.
The Clinometer. For exploratory work, where great accuracy
is not required, the clinometer is of great value, on account
of its portability. It resembles a jointed foot-rule, with an
inlaid spirit-level and sights on one arm, and a divided arc at
the hinge to indicate the angular degree of opening. It is set
level on a stand, and the hinge is opened until the object is seen
through the sights. The angle of inclination is then read.
Fig. 65.
Fig. 65A.
The best instruments of this kind are provided with a 2-inch
LEVELLING.
191
compass attached on pivots to the lower arm. The clinometer
should have a spirit-level attached to each arm, and folding
sights, and should screw on to a portable tripod, provided with
a ball-and-socket joint. In this form, the instrument is practically
a miner's dial, on account of its portability well adapted for
prospecting purposes.
In the clinometer, manufactured by Messrs. J. Davis & Son,
several improvements have been introduced by Mr. H. Louis.
The compass pivots are carried on a brass
arc capable of revolving in the lower por-
tion of the clinometer frame, so that the
compass can be placed horizontally and
read without regard to the position of the
lower limb. In this way, the dip and
strike of strata maybe read simultaneously.
The compass, too, may be reversed so that
the same end of the needle may be used
for all dial readings in running lines
up and down hill. A further improve-
ment consists in mounting the spirit-level
of the lower limb on a swivel, so that the
instrument may be levelled both ways
without being reversed. The clinometer
(Fig. 65A) is 6| inches in length, inch in
width, and 3 inches in depth. It weighs
1 Ib. 2 oz., and is mounted on a tripod (Fig. 65s), which is pro-
vided with a ball-and-socket joint, and which is 3 feet 10 inches
in length and 1 Ib. 8 oz. in weight.
Physical Levelling. The application of the barometer to
the measurement of heights is based on the fact that for a
constant temperature, the density of the air is proportional to
the pressure which it sustains. Since the atmospheric pressure
decreases as we ascend, it is obvious that the barometer will keep
on falling as it is taken to a greater and greater height.
The mountain barometer is an ordinary barometer tube, made
as portable as possible, and protected against external injury.
When in use, it is mounted on a portable tripod, and when not
in use, it is packed in a leather case. The mercury is contained
in a wooden cistern at the lower part of the instrument. A
screw compresses the mercury and forces it, when required, up
to the upper portion of the graduated tube. By means of a
vernier, the height of the column of mercury may be read to
the one-thousandth part of an inch. Attached to the barometer
p. ft*
192 MINE-SURVEYING.
is a thermometer, enabling a correction to be made for temper-
ature. This correction is necessary because the air and the
mercury are unequally expanded by heat.
The simplest barometric rule is as follows : Observe the
height of the barometer in inches at two stations. Then, as the
sum of the two readings is to their difference, so is 55,000 to the
difference between the height of the stations stated in feet.
For example. What is the difference in level between two
points at which the barometers read 30'014 inches, and 29-870
inches respectively ? The thermometers read the same at both
stations.
Difference in level = 55,000 x = 132-3 feet.
'
To correct for temperature, add T ^ of the result for each
degree, that the mean temperature of the air at the two
stations exceeds 55. Subtract the same amount if the mean
temperature is below 55. When the upper thermometer reads
higher than the lower, ^^ of the result must be subtracted when
the mean temperature of the air exceeds 55, and added when it
is below 55.
On the United States Geological Survey, a simple and direct
method of hypsometry is in use. In this method, proposed by
Mr. G. K. Gilbert,* three barometers are used instead of two.
Two of these are placed at points whose heights are known, the
third being read at the point to be determined. Prom the
reading of the two barometers at the points of known height,
the weight of the intervening air column is deduced, and, both
the weight and height of the column being known, its density is
computable. The density thus derived is then used in the
computation of the height of a second column of air between one
of the known points and the point to be determined.
Levelling by the barometer may be occasionally used for
taking flying levels in exploring a district. An approximation,
however, is all that can be obtained, even if the most elaborate
formulae are employed. The mountain barometer is a cumbrous
instrument. It must be more than 30 inches long, exclusive of
the cistern, and the mercury is always troublesome to transport.
On account of these disadvantages, for engineering purposes
the mercurial barometer has been to a great extent replaced by
the aneroid barometer invented by Vidi, and patented in Great
Britain in 1844. It consists of a circular box, the face of which
* Second Annual Report of the U.S. Geol. Surv., 1882, p. 405. In this
valuable monograph all the principal methods that have hitherto been
employed are fully described.
LEVELLING. IDS
is made of thin metal, rendered more elastic by being stamped
into concentric circular wave-like corrugations. The box is
nearly exhausted of air, and its elastic face supports the pressure
of the atmosphere, yielding to it with elastic resistance in
proportion to the amount of pressure. The movement is com-
municated to an index, and registered upon the dial. Aneroid
barometers are made of pocket-size, carefully compensated so as
not to be affected by changes of temperature, and with double
scales, one a barometrical scale of inches, the other a scale of
altitudes; that is to say, a scale of differences of altitudes for one
given pressure.
When specially constructed for mining use, the instrument is
graduated to represent 6 inches of the mercurial column, from
27 inches to 33 inches. This scale enables observations to be
made from 2,000 feet below sea-level to 4,000 feet above. The
finest divisions of the altitude scale represent 10 feet measurement,
which can be divided by a vernier, moved by rackwork adjust-
ment, to single feet. A lens, which rotates on the outer circum-
ference, enables the vernier to be read with facility. The
instrument is 4J inches in diameter, and is provided with a
leather sling case. In order to retain the sensitiveness of action
of the aneroid, it should be cleaned and adjusted every two or
three years by an instrument-maker.
The principle that the boiling-point of water varies with the
atmospheric pressure is sometimes applied for the measurement
of heights. The instrument used for this purpose, the hypsometer,
consists of a thermometer, surrounded by a double-telescopic
chamber, and suspended so that its bulb is above the surface of
some water in a metal boiler, heated by a spirit-lamp. It is thus
enveloped in steam when the water boils. This cheap and port-
able instrument for measuring heights is to be preferred, for its
simplicity and certainty, to the mountain barometer. Tables are
published by the maker, Mr. L. Casella, of London, giving
instructions for using the hypsometer.
Determination of the Depths of Shafts. In connection with
levelling operations underground, it is frequently necessary to
measure the depths of shafts. For this purpose, a wire with
weights at the end, or the winding-rope with the cage or the
kibble, is let down, and the length of the wire or rope measured
by means of rods. Or the depth of the shaft may be measured
direct by applying rods, chains, or steel bands to the timbering
of the shaft. Good results have been obtained by both methods.
It is, however, evident that the direct measurement is more
trustworthy, though more difficult and tedious, than the indirect
method. The measurement must be so contrived that the
13
194
MINE-SURVEYING.
starting- and end-points can be easily connected with the surface
and underground levellings.
The measurement by means of a wire is usually effected by
changing the vertical into horizontal measurement in the follow-
ing manner : From a small windlass (Fig. 66) erected at a
suitable distance from the shaft, the steel wire (piano wire) is
unwound, and passed over a pulley, which is placed over the
mouth of the shaft in such a way that the wire weighted with
10 to 30 Ibs. can without hindrance sink to the bottom of the
shaft. The starting- and end-points
are distinguished by threads tied on.
The depth is measured on letting
down and hauling up the wire, and
is done most conveniently with the
horizontal portion between the pulley
and the windlass. The wire is kept
in sufficient tension by the weight.
The elongation of the wire, caused
by its own weight and the attached
weight, does not interfere with the
accuracy of the result, as the wire is
measured in its stretched condition.
The method is very rapid ; at Firniiny,
near St. Etienne, a depth of 280 yards
has been measured in half an hour.
Experiments made at Firminy show
that the error with this method does not exceed one-fifth of
an inch per hundred yards of depth. Accurate results have
also been obtained at Schemnitz, in Hungary, by Professor
Chrismar, who measured in an hour a depth of 210 yards
accurately to within -j-Jj^n- of the measured length.
Local conditions may render it necessary to apply the measure
to the vertical part of the wire, in which case the operation is
somewhat more inconvenient, but in other respects similar to the
preceding.
Instead of the wire, the winding-rope may be used. In this
case, the measure is applied to the rope direct above the mouth of
the shaft. The results thus obtained are very similar to those
obtained with the wire. Thus, Borchers measured one and the
same shaft once with the wire and once with the winding-rope ;
the results being 129 fathoms 3 feet 3 inches and 129 fathoms
3 feet 3-54 inches respectively.
For the direct measurement of shafts, iron survey ing-chains r
steel bands, or specially constructed measuring-rods are employed.
The chain employed for measuring the depths of shafts must
. 66.
LEVELLING. 195
first be carefully tested. It is then let down the shaft at a suit-
able point, and suspended by the upper handle to a nail. A
second nail is driven within the lower handle, and touching it.
The chain is then removed, the lower handle being hung to the
second nail, and the process repeated as before. The depth thus
obtained must be diminished by the thickness of the nails included
in the measurement. It is therefore desirable to employ round
nails of uniform diameter. The chain, of course, must be allowed
to hang perpendicularly, and all obstacles, such as platforms, in
the shaft must be removed or bored through. Sometimes it is
impossible to measure the shaft in one straight line; a suitable
point must then be found in a line at right angles to the chain,
and the measurement continued.
With the steel band, shafts are measured in a similar manner.
This method has been employed with success by Mr. Graefe* in
the Stassfurt salt-mines for measuring shafts of considerable
depth. For this purpose, at a measured distance above the roof
of the cage, a seat is fastened to the winding-rope in such a way
that a miner can sit in it without danger, and apply the upper-
end of the steel band to the guides. The mine-surveyor stands
on the roof of the cage, and carries the lower end of the band.
Beside him stands a second workman, whose duty it is to give
the signal for raising or lowering the cage. In this way, after all
the preparations had been made, the Leopoldshall shaft was
measured three times in six hours with the following results :
First measurement, . . .1,095 feet 5 '80 inches.
Second ... 1,095 5"84
Third ... 1,095 5-84
In this case, the heights of 8 levels entering the shaft had also
to be determined.
In almost as short a time the Von der Heydt shaft, at Stass-
furt, was measured four times ; the heights of 7 levels entering
the shaft being determined at the same time. The results were
First measurement, . . . 1,152 feet 2'15 inches.
Second ... 1,152 2'07 ,,
Third ... 1,152 2'23
Fourth ... 1,152 2'11
The most accurate means of measuring the depths of shafts is
afforded by the measuring-rods constructed for this purpose by
Borchers, which are frequently employed in the continental
mines. The rods consist of a number of round steel bars 0-16 to
0-24 inch in diameter, and 1 to 4 yards in length. The ends are
* Berg. H. Ztg., vol. xlii., 1883, p. 4.
196
MINE-SURVEYIXG.
screwed, and may be connected by brass double screws, so that a
measuring-rod of any required length may be constructed. The
true end surfaces of the separate rods must be exactly at right
angles to the longitudinal axis, and the brass caps are provided
with an opening on both sides, so that the contact of the end
planes of two rods can be seen. The first rod is provided with a
hook, from the inner surface of which the counting commences.
On using these rods, the influence of temperature has to be taken
into account.
The measurement of the depths of inclined shafts presents the
greatest difficulties. In such shafts, Fig. 67, a plumb-line is
used, the points of suspension being
found by means of a spirit-level.
Such shafts are frequently tortuous in
inclination and in direction, in which case
they must be surveyed in the same way
as levels, the vertical arc of the dial being
employed in conjunction with a plumb-
line. It is an operation of great difficulty,
and one which in former times has given
rise to serious errors in the surveys of the
mines of Cornwall, Derbyshire, and the
Harz.
Fig. 67.
In surveying and levelling in the shafts of the Lehigh Valley
Coal Company, in the United States, a new form of plummet
has recently been adopted. It consists of a vertical core
12 inches long, with eight radiating flanges 9 inches high by
3 inches wide of i-inch metal. At the bottom there is a circular
disc acting as a web. This plumb-
bob weighs 20 Ibs., and has a surface
area of about 630 square inches. An
ordinary bob of equal weight would
have a surface of 90 square inches.
In a dry shaft, 500 feet deep, this
form of plumb-bob will settle, under
ordinary conditions, in about one
hour instead of in five or six hours,
as is the case with the older form.
Contour Lines on the earth's sur-
faceare lines traversingall the points
on the ground which are at a given
constant height above the datum
level. A contour line may also be
described as a horizontal section of the earth's surface, or as the
line -where the earth's surface is cut by a given horizontal surface,
Fig. 68.
LEVELLING. 197
or as the outline of an imaginary sheet of water covering the
ground up to a certain height. Fig. 68 represents the contours
of a hill.
Tracing contour lines consists in determining equidistant series
of points satisfying these conditions. The vertical distance
between successive contour lines on a plan depends on the figure
of the ground, and on the scale of the plan. Two methods of
tracing contour lines are employed (1) The regular method,
consisting in tracing the lines on the ground, and then surveying
them ; (2) the irregular method, which consists in collecting, on
the ground, data to enable the lines to be constructed on the plan.
On the Ordnance maps of Great Britain, on the scale of 6 inches
to the mile, contour lines are drawn at each 25 feet of height,
with principal contour lines, determined with greater precision,
at every 50 feet in the flatter parts of the country, and at every
100 feet in the hilly parts.
Mr. W. F. Howard advocates that colliery plans should exhibit
contour lines at regular and frequent intervals. In this way
the vertical throw of each fault, excluding the mere bending up
or down of the adjacent strata, which has often a tendency to
mislead, would be continuously shown though the fault should
be rarely penetrated. Contour lines are generally shown on the
plans of the anthracite mines of Pennsylvania.
Applications of Levelling. A branch of engineering, in which
the application of levelling is of great importance, is the setting
out of aerial wire ropeways. The importance of this mode of
transport in the development of mineral resources is known to
every mining engineer. As a case in point, the rich iron ores
of the Sierra de Bedar, in southern Spain, would probably have
remained untouched to this day but for an aerial wire ropeway,
9| miles in length, which connects the mines with the shore of
the Mediterranean, near the town of Garrucha, and which affords
cheap transport to the point of shipment. An ordinary railway
would have cost 100,000, whilst an aerial ropeway could be
built for about one-quarter of that sum, an outlay which left
a satisfactory margin for profits on the sale of ore.
In the older systems of ropeways, one endless rope is employed,
serving both as- carrying rope and hauling rope for the buckets.
Many examples of lines of this class can be seen in the Bilbao
iron ore district. The characteristic of the modern or Otto
system consists in the employment of two ropes a heavy fixed
carrying rope and a light travelling hauling rope, the buckets
being fitted with special devices for gripping the latter. With
ropeways of this class loads of 20 cwt. can be carried, so that as
much as 800 tons may be transported in a day of ten hours.
198 MINE-SURVEYING.
The most important Otto ropeway yet constructed is that for
the transport of iron ore at Garrucha. The line is divided into
four independent sections, the two first being driven by a 30
horse-power engine, and the two last by a 70 horse-power engine.
The greatest span of the line is 918 feet, the height above the
valley being 164 to 196 feet. The steepest gradient is 1 in 2,
and the tallest standard is 118 feet. The guaranteed capacity
of the line is 400 tons per day of ten hours. Since the com-
mencement of 1890, the line has been worked in two shifts of
eight hours, and no less than 900 tons per day have been trans-
ported to the coast. Despite many difficulties, the line was
surveyed, erected, and ready for work within ten months.
Another important Otto wire ropeway is that constructed for
the Sheba gold mine in the Transvaal. This is 2| miles in length,
and has a capacity of 150 tons per day of ten hours. The
maximum incline is 1 in 1'6, and the greatest span 1,480 feet.
In making the preliminary survey for an Otto wire ropeway,
there are several points to which attention should be paid. The
terminal points of the line should, whenever possible, be so
placed that the ropeway joining them shall be in a straight line,
as each turn increases not only the amount of construction neces-
sary, but also the cost of working, as it necessitates the erection
of a complete station. For lines of more than 3 J miles in length,
one or more intermediate stations must be erected, as greater
lengths than this cannot be worked with one hauling rope. At
the stations the line can form any desired angle. The points
selected for the supports for the bearing-rope should be marked
on the ground by wooden pegs distinctly numbered, and should
be shown in the section drawn. The supports should be 50 yards
apart, when 50 to 100 tons are transported in 10 hours, 40 yards
apart for 100 to 600 tons, and 35 yards apart for amounts above
600 tons in 10 hours. This rule may be neglected in crossing
roads, in which case one support should be a,t the side of the
road, and it may be neglected when this rule would necessitate
the support being placed in a narrow valley or hollow, in which
case, in order to avoid unnecessary height, the post may be
moved. For crossing valleys and rivers, spans of 350 yards may
exceptionally be employed, when supports are impossible or
would exceed 35 yards in height. In crossing roads, cross-
sections must be made in order to give the requisite data for
the erection of a protecting bridge, and cross-sections must be
taken at every point selected for a station.
Marshy sites must be avoided as far as possible ; but in cases
where this is out of the question, the surveyor must determine
the depth to the solid ground.
LEVELLING. 199
The hydraulic mining ditches of California afford some inter-
esting examples of levelling successfully conducted in the face
of great difficulties. Hydraulic mining consists in the disin-
tegration of auriferous gravel deposits by propelling a heavy jet
of water under pressure upon the bank, and in washing off the
gravel in sluices in which mercury is distributed. The gold
forms an amalgam, and remains caught. This method of mining
was introduced in California in 1856, although Pliny describes a
system of hydraulic mining in Spain, which resembled in many
respects the modern method. Hydraulic mining has given rise
to an extensive system of artificial reservoirs in the Sierra
Nevada for the storage of water, and to the construction of
artificial water-courses to convey the water thus stored to the
scene of mining operations. The setting out of these canals at
a grade of from 4 to 20 feet per mile, over deep gorges and along
precipitous cliffs, presents problems of great difficulty to the
mine surveyor. In many places it is impossible to find room
along the sides of the great canons for miles, to excavate a canal
or to rest a conduit or " flume," as it is locally termed. The
bracket flume of the Miocene mine is a marvellous example of
engineering skill. Here, in order to obviate the erection of a
trestle 180 feet in height, the water is conveyed in a wooden
flume 4 feet wide and 3 feet deep round a cliff 350 feet in
height. The flume is suspended upon brackets made of T-rails,
fixed into holes previously drilled in the vertical cliff. In
another place, in the line of this ditch, is a piece of breastwork
1,088 feet long and 80 feet high. Again, the Blue Tent Mine
has a ditch running for a distance of six miles along the face of
a cliff, over which the surveyors had to be suspended by ropes
1,000 feet above the bottom of the gorge, in order to establish
the line of the flume.
In other places deep gorges are crossed by means of inverted
siphons. The Cherokee ditch crosses a deep canon in this way,
the pipe sustaining a columnar pressure equal to 800 feet in
perpendicular height. In making the crossing, 12,000 feet of
38-inch pipes, -|-inch in thickness, were used. A few years ago
there were in California 6,000 miles of mining ditches, their
estimated total cost being 3,000,000. Some of them have been
built at a cost of 5,000 per mile. The cost, too, of keeping
them in repair is very considerable, as the hydraulic miner has
constantly to contend with the elements frost and flood, ice
and snow, wind and rain.
In the preliminary survey, to determine the best situation for
a long ditch, comparative observations should be made with
aneroid barometers, care being taken to determine the eleva-
200 MINE-SURVEYING.
tions, not only of the end points, but also of intermediate points,
from which different surveying parties can start on the subse-
quent setting out of the line. The necessary points being
established, the line is staked out, all stations being properly
numbered and pegs driven in to indicate the gradient. Accord-
ing to Mr. Bowie, the author of the standard work on this
subject, stations may be from 50 to 100 feet apart on ordinary
ground ; but very irregular country obviously demands shorter
intervals. Bench-marks should be placed every or | mile for
convenient reference. All details of tunnels, cuttings, and
depressions, which require pipes or flumes, should be worked
out in full, a work in which the hand-level can often be advan-
tageously employed. Complete notes should be made of the
character of the ground along the whole line.
In laying out mining ditches in California it is usual to
employ a light frame shaped like the letter A, made of |- by 1^
inch wood, and provided with a heavy plummet hanging on a
fine wire from a notch at the apex. The height of the frame is
usually 6 feet, and the base 10 feet. To commence, one end is
placed on a level piece of ground, and the other end is raised or
lowered until both ends are level, and the plumb-line marks the
same position on the cross-bar, if turned completely round. The
rade for the proposed mining ditch being decided upon, say
inch in 10 feet, a ^ inch piece of wood is placed under the rear
end of the frame, and the point indicated by the plumb-line is
marked on the cross-piece. One man then holds the frame,
while another lifts the front end until the plummet coincides
with the mark, he then drives in a peg in front. The rear end
of the frame is then placed exactly where the front end was, and
the process is repeated. In this way the ditch can be set out
with great rapidity. The only danger lies in getting the wrong
end foremost.
UNDERGROUND- AND SURFACE-SURVEYS.
201
CHAPTER XIV.
CONNECTION OF THE UNDERGROUND- AND SURFACE-SURVEYS.
Methods Employed. A correct survey of the underground
workings of a mine, and of the surface or royalty having been
made, it is necessary to determine accurately the bearing of
a line underground with a view to connect the two surveys.
For this purpose the following methods have been employed :
(1) By means of an adit-level or inclined shaft; (2) by means
of two shafts; (3) by means of one shaft with two suspended
plumb-lines; (4) by means of the transit-instrument; (5) by
means of the transit- theodolite ; (6) by means of the magnetic-
needle.
1. By Means of an Adit-level. When the mine is connected
with the surface by means of an adit-level, the connection of the
surveys is easily effected by continuing the underground traverse
through the adit-level to the nearest side of the triangle of the
surface-survey.
2. By Means of two Shafts. If both the shafts are vertical,
the connection of the underground- and surface-surveys is made
by means of two plumb-lines,
one suspended in each shaft.
The points of suspension are
joined to the surface-triangu-
lation by means of careful
measurements. In this way
the length and bearing of the
line joining the two plumb-
lines may be calculated by
means of rectangular co-ordi-
Fig. 69.
nates. A traverse is then made underground from one plumb-
line to the other, and from the data thus obtained the length
and bearing of the line joining the two plumb-lines is again,
calculated by means of co-ordinates.
Example. In two perpendicular shafts, plumb-lines are hung
at the points A and B (Fig. 69). From the surface-triangu-
lation it is found that the length of the line A B is 56-29
chains, and its bearing 118 36'. In the mine, a traverse was
made with the following results:
202
MIXE-SURVEYIXG.
From
To
Length,
Chains.
Measured
Angles.
Angles Re-
duced to one
Meridian.
LATITUDE.
DEPABTURB.
y.
s.
E.
w.
A.
I.
1-76
000'
000'
1-76
I.
II.
4-24
177 33'
357 33'
4-23
...
0-18
II.
III.
13-00
284 57'
102 30'
2-81
12-69
III.
IV.
16-75
177 56'
100 26'
3-03
16-47
...
IV.
V.
9-30
180 52'
101 18'
1-82
9-11
V.
VI.
8-28
158 33'
79 51'
1-45
8-15
VI.
VII.
3-74
184 53'
84 44'
034
3-72
...
VII.
VIIL
6-32
184 26'
89 10'
0-09
...
6-31
...
VIIL
IX.
6-12
93 53'
3 03'
6-11
0-32
...
IX.
B.
1-18
135 11'
318 14'
0-88
...
...
0-78
...
14-86
7-66
56-77
0-96
...
...
...
7-66
...
0-96
...
7-20
"~
55-81
...
With the co-ordinates 7-20 chains 1ST., and 55-81 chains E., the
length and direction of the hypothenuse may be calculated from
the formula: base 2 + perpendicular 2 = hypothenuse 2 , or tangent
of angle of bearing = -, r~^> an d the distance = latitude x
secant of angle of bearing. The hypothenuse in the above
traverse will then be found as follows :
log 55 -81
log 7'20
L. tan BAG
log 7-20
L. sec 82 39'
= 1-7467120
= 08573325
= 10-8893795 BAG
= 0-8573325
= 10-8930271
11-7503596 distance
56 '28 chains
UNDERGROUND- AND SURFACE-SURVEYS. 203
From this angle that is, the angle formed by the hypothenuse
A B and the first line of the underground-survey A I, and from
the bearing of the line A B determined at the surface (118 36'),
the bearing of the first station-line underground may be deter-
mined. In the above example, this is done by subtraction,
118 36' - 82 38' = 35 58'. From this may be deduced the
bearing of the other lines of the traverse. In the example, this
is done by increasing the reduced meridian angles by 35 58' in
each case. With the aid of these bearings, the co-ordinates of
the underground-traverse should be recalculated, and the results
balanced.
For suspending the plummet, a thin wire of iron or brass is
used. Hemp cords are useless for the purpose; because of their
torsion and contracting when wet. They present a greater
surface to the action of air-currents and water than thin wire, and
do not admit of such precise sighting. The plummet weighs 5 to
8 Ibs. It should not be hung on when the wire is let down the
shaft in case of accident from the wire breaking. A smaller weight
may be used when the wire is being let down, and at the bottom
of the shaft it can easily be changed for the required weight.
The plumb-line must, of course, hang perfectly free, without
coming in contact with the sides of the shaft. To ensure this
being the case, a lamp is slowly passed round the wire at the
bottom of the shaft. If, in whatever position it is placed, the
light can be seen from the top, the wire is clear.
The plumb-lines may be sighted without any difficulty in the
surface-survey, as the upper part of each wire does not move.
In the mine, however, the plumb-line has to be sighted at its
lower end, which continues to vibrate like a pendulum. The
motion may be reduced by allowing the plummet to dip into a
bucket of water, and by shielding the wire from air-currents and
falling water as far as possible. It is, however, impossible to
stop the vibrations altogether.
To lessen the motion of the plumb-lines, Mr. H. D. Hoskold
proposes the adoption of iron chains made from wire three-
sixteenths of an inch in diameter. The method would, however,
be inapplicable in a shaft of considerable depth.
In sighting a plumb-line with the theodolite, it is best to
follow it by means of the tangent-screw to the end of its vibra-
tion. There is then sufficient tiwie to read the vernier before it
reaches the other end of its course, as well as to intersect it in
that position with the cross-wires. This operation is repeated
several times, and the mean taken of all the results. When the
arc is very small, the mean may be estimated, and the cross-wires
set at that angle direct. The plumb-lines are rendered visible by
204 MINE-SURVEYING.
holding behind them a sheet of oiled paper illuminated by a lamp
from behind. This method of sighting a plumb-line is very
fatiguing, and necessitates great skill to read the vernier and
direct the telescope to the next extremity of the course, in the
comparatively short time in which the plummet completes its
swing.
These difficulties have been overcome by Professor Schmidt,*
of the Freiberg School of Mines. The plummets he uses are
hung to thick wire (O04 inch in diameter), and their weight is
considerable, being as much as 50 Ibs. They do not dip into
water, but are allowed to swing freely. At a short distance
above the bottom of the shaft, a horizontal finely-divided scale is
placed perpendicular to the line of sight of the telescope. The
swinging plumb-line is then observed with the telescope, and the
successive extreme positions are read and noted, the plumb-line
being purposely made to swing parallel to the plane of the scale.
The latter is illuminated by means of an ordinary miner's lamp
or candle.
From one or more series of double observations, the mean
position of rest of the plummet on the scale is calculated, and for
the subsequent survey the cross-wires of the telescope are made
to coincide with that calculated point. The calculation of the
position of rest is a very exact one. From two trials, one made
at a depth of 557 feet under favourable conditions, the other at
a depth of 1,722 feet under unfavourable conditions, Professor
Schmidt found that the mean error of one series of observations
was 0-12 inch, and the mean error of the result of a double
series was 0-08 inch. Under unfavourable conditions the
errors were 0-17 inch and 0'12 inch respectively.
In cases where it is required to connect the surface-survey
with the underground survey at several levels at different heights
in the shaft, it is desirable to fix the plumb-line. For this pur-
pose, Professor Schmidt f has invented a simple centering appara-
tus. On a perforated cast-iron plate, a prismatic centre-piece
may be slid in two directions at right angles to one another by
means of four centering screws. Above the latter are two scales
at right angles. The iron plate is placed so that one pair of
centering screws is in the line of sight of the theodolite-telescope,
the other pair being in the line of sight of a second small tele-
scope of low power. With this small telescope and with that of
the theodolite, the swingings of the plumb-line are observed, and
the position of rest calculated. The weight is then removed
* Saeclis. Jahrbuch., 1882, p. 145.
t Berg. H. Ztg., vol. xliii., 1884, p. 217.
UNDERGROUND- AND SURFACE-SURVEYS.
20-5
from the plumb-line, and a cap-screw placed on the wire. The
weight is then replaced, and screwed into the centre-piece of the
apparatus. With the aid of the two telescopes, and the centering
screws, the centre-piece can be brought into such a position that
the plumb-line is in its. calculated position of rest.
If either of the shafts used for connecting the underground-
and surface-surveys, is inclined, or if both are, the method is the
same, except that the shaft is surveyed by traversing instead
of by suspending a plumb-line.
3. By Means of one Shaft. When there is only one perpen-
dicular shaft, the underground- and surface-surveys may be
connected by transferring a short line from the surface to the
mine by means of two plumb-lines suspended in the shaft. The
bearing and length of this short line may be determined with
sufficient accuracy by connecting it with the surface-triangulation.
Then, if the underground-survey also includes the line formed
at the bottom of the shaft by the two plumb-lines hanging
vertically, the connection can be made from the known bearing
of that line. Thus, the survey is made at the surface and in the
mine in the same way, by constructing a triangle of which the
line joining the plumb-lines is a side.
The following details of the connection of the underground-
and surface-surveys effected in this way
may serve as an example : Fig. 70 is
a plan of a portion of a mine, in which
D G represents a line at the surface, con-
nected with the triangulation, and E F a
line of the traverse of the 135-fathom level
of the mine. In order to connect these
two lines, two plumb-lines A and B were
suspended in the perpendicular shaft, as
far apart as circumstances would allow.
The distance in this case was 0-9315 fathom.
The two wires were sighted from the point
G in the doorway of the mine-house, and
the angles B G D and A G D and the dis-
tances G B and G A accurately measured.
The triangle GAB was in this way com-
pletely solved, and the position of the line
A B formed by the two plumb-lines was
determined with reference to G D. The
theodolite was then set up at in the
135-fathom level, and with it were carefully
Fig. 70.
cross-cut at the
measured the angles B A = 32 08', AGE = 159 21', and
OEF = 269 31' 33", and the horizontal distances C B = 1-6373,
206 MINE-SURVEYING.
C A = 1-7169, and C E = 15-6563 fathoms. Since in the triangle
C B A the three sides were determined, it was unnecessary
to measure the angle BOA. This was, however, done as a
check. On calculation, the angle BOA was found to be
32 8' 10", C A B = 69 13' 15", and C B A = 78 38' 37". Of
the measured and calculated values of the angle B C A, the
mean 32 8' 5" was taken. The two other angles of the triangle
CAB were balanced so as to make the sum of the three angles
equal to 180. In this way the point G at the surface and the
point E in the mine are connected by known horizontal distances.
The angle which the line D G at the surface makes with the line
E F in the mine may then be easily determined.
The line D G being taken as the meridian, the line A B was
found from the surface-survey to form an angle of 23 12' 10"
with that meridian. Underground the angles formed by the
meridian and the various lines were
A C 69 13' 15" - 23 12' 10" = 46 01' 05"
C E 159 21' 00" - 46 01' 05" = 113 19' 55"
E F 113 19' 55" - 90 28' 27" ^ 22 51' 28"
In some cases the theodolite may be set up and centred at
the points A and B at the surface, but underground this cannot
be done with sufficient accuracy.
The accuracy of the connection depends on the correct deter-
mination of the angles A and B in the triangle ABC. These
angles usually have to be calculated from the known length A B
and from the sides A C and C B measured underground, as well
as from the angle C. This may be done by the ordinary sine
rule
~. a sin C . _, b sin C
Sin A = , sin B = .
In this formula, sin A is dependent upon the three magnitudes
C, c, and a. The length c and the angle C may be measured
underground with great accuracy, if Schmidt's method is em-
ployed.
The influence of an error in the length a on the angle A varies
considerably according to the form of the triangle. It is great
when the sides a and b are of equal length that is, when the
triangle A B C is an isosceles one. It is least when the triangle
has a very acute-angled form. The sines of angles near and
180 do not increase or decrease in proportion to a slight increase
or decrease of the angle. Conversely a small change in the sine
UNDERGROUND- AND SURFACE-SURVEYS. 207
has an inappreciable influence on the corresponding angle.
Consequently a small error in the length a has no effect on the
determination of the angle A, when the triangle is an acute-
angled one. If possible, then, the ordinary well-conditioned
triangle must in this case be avoided, and the theodolite placed
as nearly as possible in the continuation of the base-line.
By means of two plumb-lines, the connection between the
underground- and surface-surveys has been effected with con-
siderable success by Mr. E. Clark* in the brown haematite mines
belonging to the Glendon Iron Co. of Pennsylvania. The shafts
are usually 4 feet square, but, where an extensive plant of
pumping machinery is required, the size is increased to 8 feet by
6 feet. The depth of the shafts varies from 75 to 200 feet. The
principal difficulty in the survey of these mines has always been
the trouble experienced in connecting the underground-survey
with the surface-survey, on account of the small size of the
shafts, and the gradual movement of the ground pushing the
shaft out of the perpendicular.
The method adopted by Mr. Clark has been to establish a line
at the surface, and, by means of a straight-edge, wire, and plumb-
bob, to project that line to the bottom of the shaft, and there use
it as a base-line for the underground-survey. The line across the
shaft is marked in the timbers by nails, which may be permanent
and used in future surveys, if the earth about the shaft is suffi-
ciently firm. A straight-edge is placed against the nails, and
the assistant above lowers the plumb-bob by means of a reel and
annealed-iron wire of sufficient strength to hold the plumb-bob,,
which is of cast-iron, and weighs 10 Ibs. The two plumb-bobs,
are each received into a bucket filled with water at the bottom of
the shaft. Vibration may be lessened by mud thrown into the
bucket. When the plummets have become nearly stationary, a
theodolite is set up in line with the wires. This is done by
moving the instrument until the nearer wire coincides with the
vertical hair, and the second wire is concealed by the first ; or the
transit will be in line when the extent of the vibration of the
second wire to one side of the first is equal to the extent of the
vibration to the other side. The greater the distance between
the wires, and the farther the theodolite is from them, the more
accurately can it be placed in line. The average distance in 15
shafts surveyed in this way was 18 to 6 inches, this distance
being the base-line upon which the mine-survey was based. In
the coal-mines of Pennsylvania very good results have been
obtained by this method, with a base-line of 9 feet in length.
* Trans. Amer. Inst. M.E., vol. vii., 1879, p. 139,
208 MINE-SURVEYING.
4. By Means of a Transit-instrument. The most accurate
method of effecting the connection between the underground-
ancl surface-surveys is by means of the transit-instrument.
The transit-instrument is the standard instrument in every
astronomical observatory. It consists of a telescope formed of
two parts connected by a spherical centre-piece, into which are
fitted the larger ends of two cones, the common axis of which
is placed at right angles to the axis of the telescope, to serve as
the horizontal axis of the instrument. The two small ends of
the cones are ground into two equal cylinders or pivots, which
rest upon angular bearings or Y's, supported upon standards.
One of the pivots is pierced, and allows the light from a lamp to
fall upon a plane mirror, fixed in the spherical centre-piece, on
the axis of the telescope, and inclined to that axis at an angle of
45. Light is thus thrown directly down the telescope, and
illuminates the cross-wires.
The transit-instrument was first used to obtain the connection
between the underground- and surface-surveys by Mr. A. Bean-
lands,* in 1856. The first method he proposed was a purely
astronomical one. Having set up the transit-instrument with
its plane considerably out of the meridian and its telescope
pointed upwards, he observed the passage of several known stars
across the wires of the diaphragm in the usual manner. It was
found that at the surface the deviation of the plane of the
instrument from the meridian could thus be approximately
determined. Underground, however, with the telescope pointed
up a vertical shaft, it was found that the operation was attended
with such difficulty that it had to be abandoned. Instead of
observing stars, recourse was had to lights fixed at the top of
the shaft. The experiments were perfectly successful, and led to
the method identified with Mr. Beanlands' name.
As a matter of convenience is has been found advisable to fix
the transit-instrument at the top of the shaft, and to place
illuminated marks at the bottom as nearly as possible in the
same vertical plane as the instrument. The marks are illumin-
ated by the light of a lamp reflected upwards. They are placed
in such a position that they can also be sighted by a theodolite
placed in a line with them at the bottom of the shaft. If now
the cross-wires of the transit-telescope coincide with each of
these two points, it is evident that the horizontal line represented
by the marks coincides with the vertical plane of the instrument,
and is therefore parallel to the position of the telescope when
directed horizontally. In this way two lines are obtained, one
* Trans. N. Engl. Inst. M.E., vol. iv., p. 207; voL xx., p. 85.
UNDERGROUND- AND SURFACE-SURVEYS. 209
at the top of the shaft represented by the optical axis of the
telescope pointed horizontally, the other at the bottom of the
shaft represented by the line joining the centres of the marks.
If the two marks cannot be brought exactly to the centre of
the telescope, the apparent distance of each mark from the
cross-wires is measured by a micrometer, and the angular
deviation of the base-line from the plane of the transit calculated.
The bearing of the base-line is then deduced from that of the
instrument, and the connection between the underground- and
surface-surveys effected as in the previous case. By this method
the bearing of a line underground may be determined with a degree
of accuracy that has never been obtained with any other method.
As illustrations of the severe practical tests to which this method
has been subjected, the following examples may be given :
In 1857, Mr. Beanlands made a survey at Etherley Colliery
for the purpose of setting out a drift between the workings of
the George Pit, and a new sinking, the Dean Pit, half a mile to
the east. There was no connection underground between the
shafts, and it was therefore necessary to make a surface-survey,
and to connect it with the workings at both shafts. At the
George Pit, the connection was made by means of a very steep
and narrow day-drift, whilst at the Dean Pit, the transit-
instrument was employed, marks being left in each case for the
purpose of setting out the drift. The latter was worked from
both ends; the length being 700 yards. At the end of six
months a very accurate holing was effected, the deviation
between the two ends being 6 inches. If this deviation had
been due solely to the bearing, it would imply an error of 1
minute. It is, however, evident that it represents not only the
error of the bearing above and underground, but also of setting
out and working the drift. A more convincing proof of the
accuracy of this method of connecting the underground- and
surface-surveys could hardly be given.
The Pelton Colliery, near Chester-le-Street was worked, in
1864, by two adjacent shafts, 50 fathoms in depth. At a dis-
tance of 50 yards from the bottom of these shafts, an underground
sinking had been made to explore a lower coal-seam. It was
afterwards thought desirable that a shaft should be sunk from
the surface immediately above that already existing underground.
Mr. Beanlands made a survey for setting out the centre of this
shaft. The measurements were made with great care with a
levelling-staff, and the connection between the underground- and
surface-surveys was effected with the transit-instrument. The
shaft was set out from Beanlands' plan, and was found to corres-
pond with the lower shaft within 2 inches.
210 MINE-SURVEYING.
In shafts of very great depth the method has been employed
invariably with successful results. For example, in the Ryhope
Colliery, where the shaft is 253 fathoms deep, the bearing was
determined twice in different months, the difference between the
two results being only 1' 10".
As the method requires only one shaft with a clear view from
top to bottom, it can obviously be adopted in nearly every
colliery. Though a considerable time is necessarily spent in
erecting a platform for the transit, a bearing sufficiently accurate
for practical purposes may be obtained in a few hours.
4a. The Severn Tunnel Method. On account of the length of
the heading, the incessant jar of the pumping engines, and the
extreme wetness of the shaft, a plumb-line method was not
applicable in driving the Severn Tunnel. The length of the
proposed heading was 2 miles, and that of the available base-
line 12 feet. Consequently an error of -^ of an inch would
become 45 inches at the end of the two miles. To overcome the
difficulty, Mr. Richardson,* the engineer, devised the following
method : A large transit-instrument was firmly set up over the
shaft, and accurately in the vertical line passing through the
centre of the tunnel. This line was determined by two staves,
one on each side of the river. The heading having been driven
a short distance, a horizontal wire, 100 yards long, was stretched
at the bottom of the shaft. One end, A, was attached to the
side of the shaft furthest from the heading, the other, B, at a
point 100 yards along the heading. A length of 14 feet of wire
was visible from the top of the shaft when illuminated by an
electric light. The ends of the wire were passed over the V-
threads of horizontal screws, and stretched by means of weights
suspended from the ends. Thus, by turning either screw, a
very slight lateral motion could be imparted to the corresponding
end. The transit having been carefully levelled, the end A was
first sighted, and the corresponding screw turned until this
end was brought truly into the centre line. The telescope was
then directed towards the farthest point of the wire visible on
the other side of the shaft, and this point also brought into the
centre line by turning the screw at the end B, 100 yards distant.
The whole length of the wire thus was accurately directed into
the line of the tunnel. A base-line 100 yards in length, and
practically free from error, was thus obtained. Proof of the
accuracy of the method was afforded by the results obtained in
driving the tunnel. The headings were found to meet exactly.
5. By means of the Transit-Theodolite. In cases where the
shaft is of limited depth, and where a large and powerful transit-
* Engineering, vol. xxxiiL, 1882, p. 48.
UNDERGROUND- AND SURFACE-SURVEYS.
211
Fig. 71.
instrument it not available, the connection between the under-
ground- and surface-surveys may conveniently
be effected by means of the transit-theodolite.
The instrument is set up at the bottom of the
shaft. To enable its telescope to be pointed ver-
tically upwards, a diagonal eye piece must be
employed. This consists of a small right-angled
glass prism (Fig. 71), placed at the eye-end of the
telescope, in which the line of sight is reflected
from the plane of the hypothenuse vertically
upwards.
The mode of procedure is as follows : Having set up the
transit-theodolite at the centre of the shaft A (Fig. 72), it is
levelled, and the telescope directed to a small bright light placed
on the peg at B. Great care
must be taken to ensure the in-
strument being in perfect adjust-
ment so that the telescope shall
revolve in a vertical plane. The
vertical circle is then undamped,
and the telescope pointed up the
shaft in the same vertical plane
in the direction of the point a',
where a lamp-flame or a white
peg is brought exactly into the
line of sight. A permanent mark
is placed at a'. The telescope
is then directed towards the other
side of the shaft, and a mark
placed at V. In this way two
points are obtained at the sur-
face in the same vertical plane
The latter is carefully measured,
v^^//////////^
i
1
1 \
1
\ \
1
\\\
1
\\\
^
yj
//// j
!
-?HP
rrr-:rr /!Y
Fig. 72.
as the line A B underground.
and the distance thus found is measured off from A' to by
stretching a cord through the centres of the marks a and b. An
iron peg should be driven into the ground at C, with a hole made
in its centre for future reference. This hole is directly over
the centre of the peg previously driven into the floor of the
level at B.
With this method, Mr. H. D. Hoskold has obtained, with his
miner's transit-theodolite, very satisfactory results in the Dean
Forest mines. The method is well adapted for use in mines
where the shaft is of limited depth, and the workings not very
extensive. The shaft must obviously be of average width, and
not subject to any considerable dropping of water.
212
MINE-SURVEYING.
For connecting the underground- and surface-surveys, mining
transit-theodolites with eccentric telescopes are frequently em-
ployed in America and on the Continent. In these instruments
an auxiliary telescope is attached outside the standards to the
Fig. 72A.
prolongation of the horizontal axis of the principal telescope, or
that telescope itself is permanently mounted in a similar posi-
Fig. 72s.
tion. Sometimes the theodolite is made with an extra telescope
attached to the top of the central telescope, by means of coupling
nuts, which fasten it directly over the centre of the instrument,
and allow its ready removal without disturbing the adjustments.
UNDERGROUND- AND SURFACE-SURVEYS. 213
This method of arranging the supplementary telescope is
shown in tig. 72A. This form is that generally used in con-
junction with the American theodolite, shown in fig. 37A. The
auxiliary telescope is attached to the main telescope by two
pillars, which project beyond the edge of the horizontal plate
when the telescope is placed vertically. The method of placing
the auxiliary telescope eccentrically is shown in fig. 7 2s. In
this case, a counterpoise is fastened to the prolongation of the
axis. In both these attachments, the extra telescope is parallel
to the principal telescope.
The objection to the side-telescope is that a correction must be
applied to each reading of a horizontal angle equal to the tangent
of the angle, which is formed by the distance from the side-
telescope to the centre of the instrument, and the horizontal
distance between the stations.
In place of the diagonal eye-piece for sighting vertically up-
wards, an artificial horizon may be used. No special construction
of the telescope is then required, as it is
merely necessary to sight the image of the
flame (Fig. 73). The image and the flame
itself are in the same vertical plane, and the
image is seen at an angle of depression a
equal to the angle of elevation /3 that would
have been observed had the diagonal eye-piece
been employed.
The artificial horizon may be made of oil
mixed with lamp-black. The fluid is filtered
through linen, and carried into the mine in a
small bottle. When required for use, it is Fig. 73.
poured into a cylindrical brass vessel, care
being taken to protect the surface of the liquid from air-currents.
The artificial horizon will be found more convenient than the
diagonal eye-piece for surveying in highly-inclined shafts.
6. By Means of the Magnetic-Needle. When the mine has
only one shaft, the underground- and surface-surveys may be
connected by means of the magnetic-needle, provided that the
shaft is not sunk in magnetic strata. If the shaft is vertical, a
plumb-line is suspended in the shaft, and from this the under-
ground-survey starts. If the shaft is inclined, a traverse is made
down the shaft.
The method of employing the magnetic-needle consists in
determining the angle made by one of the sides of a triangle of
the surface-survey, as well as that made by one of the lines of
the underground traverse, with the magnetic meridian. The
lines are then connected by a survey made with the theodolite.
214 MINE-SURVEYING.
The accuracy of the method is increased by observing the mag-
netic bearings of two or more lines at the surface and under-
ground.
As the whole of the underground-survey depends on the
accuracy of the determination of the magnetic bearing of two
lines, it is advisable to use the theodolite for that operation.
The theodolite is provided with a magnetic-needle, which serves
to bring the telescope into the direction of the magnetic meridian.
As a rule, in theodolites, the diameter 0-180 is in the direction
of the telescope. It is, however, not absolutely necessary that
the optical axis of the telescope should accurately coincide with
that diameter, nor is a com-
pass with a complete gradu-
ated circle necessary. A
long narrow box, provided
with an index-line, Fig. 74,
suffices ; indeed, it has the
& * advantage of being less in
the way. The needle should
be as light as possible with thin points, and its centre of gravity
must not be too low down below the point on which it rests. A
magnifying-glass is used to see when the needle exactly coincides
with the index-line.
The tubular compass is very convenient for mine-surveying
purposes. It consists of a tubular case, the north end of which
is closed with ground glass, on which a fine scale is marked. By
means of a lens at the south end of the tube, this scale appears
slightly magnified. In front of the scale, swings the north-
seeking point of the needle, which is bent upwards, so that it can
easily be read with precision in the mine. This compass can
easily be adapted to any form of theodolite, as it is not necessary
to read it from above, but by looking through it in the same way
as a telescope.
With this compass, only one end of the needle is seen. To
obviate this disadvantage, Mr. Hildebrand* has devised a new
form of tubular compass (Fig. 75). In this, both ends of the
Fig. 75.
needle are seen at once, magnified ten times, the graduation also
appearing magnified to the same degree. The compass can easily
* Min. Proc. Inst. C.E., vol. xxxvL, 1886, p. 459.
UNDERGROUND- AND SURFACE-SURVEYS. 215
be read to a single minute in the mine, the light of a candle at a
distance of a yard being sufficient. The tube is rectangular, and
in it a magnetic-needle, 4'32 inches long, swings on a steel point.
Close by the south end of the needle is a glass micrometer, and
in front of that is a micrometer eye-piece magnifying ten times.
Between the south end and the centre of the needle is a small
telescope object-glass. By means of the eye-piece, the glass
micrometer and the south end of the needle are seen magnified
ten times, the magnified inverted optical image of the north end,
formed by the object-glass, being also visible. In other words,
by means of the eye-piece both the north and south ends of the
needle are seen passing before the glass micrometer. The latter
is divided into tenths of a millimetre, one division as seen
through the eye-piece consequently appearing equal to one milli-
metre. The middle line of the scale, the zero line, is lengthened
in both directions. When the needle is properly adjusted, the
images of the south end and of the inverted north end will appear
on that line. But if the needle gets out of adjustment, its centre
and its north and south points are no longer in the same plane,
and the two ends will not coincide with the zero line. The com-
pass must then be so placed that the two ends of the needle
appear at the same distance from the zero line. The north end
of the compass case is protected from dust by a glass-plate*, in
front of which is hinged a plate of ground glass, by means of
which the artificial illumination is assisted.
As the magnetic meridian is continually changing, it is
advisable that the observations at the surface and underground
should be made as nearly as practicable at the same time. The
best results are obtained when the bearings at the surface are
observed before and after those of the underground-lines.
If a considerable interval elapses between the observations,
the magnitude of the changes in the magnetic meridian must be
observed, and the error thus arising eliminated by calculation.
A knowledge of the absolute declination of the needle is not
indispensable. The most important point is to determine the
diurnal variation. This can only be done with sufficient
accuracy by means of a magnet suspended by a long thin silk
fibre, provided with a contrivance for observing the vibrations
by means of a telescope. Magnetic-needles supported on pivots,
as in the miner's dial, do not admit of sufficient accuracy.
Two contrivances are used for observing the vibrations of the
magnetic-needle (1.) Attached to a cylindrical magnet, sus-
pended by a silk fibre, at the north end is a glass plate with a small
photographic scale, and at the south end is a small achromatic
lens. The centre of the glass-plate is in the principal focus of
216 MINE-SURVEYING.
the lens, so that the line joining the middle division of the scale
is nearly parallel to the axis of the magnet. The scale is viewed
through the lens by means of a fixed telescope. The motion of
the magnet can thus be followed by observing the apparent
motion of the scale across the cross-wires of the telescope.
(2.) Another arrangement is to rigidly attach a mirror to
the magnet, so that the perpendicular to its surface is nearly
parallel to the magnetic axis. In this mirror, the image of
a fixed horizontal scale is observed by means of a fixed telescope,
and the angular motion of the magnet deduced from the motion
of the scale divisions over the cross-wires of the telescope. This
is called the mirror-method, and was first employed by C. F.
Gauss in the magnetometer constructed by him in 1830. The
magnetic observatory belonging to the Clausthal mines in the
Harz is arranged in accordance with this method. A Gauss
magnetometer is undoubtedly the best means of observing the
variation of the declination. The cost, however, puts it out of
the reach of most mine-surveyors.
A small magnetometer may easily be constructed of ordinary
surveying instruments. With a second theodolite or a levelling
instrument, the readings can be effected, and a scale can be
easily prepared. There is then only necessary a magnet with a
mirror. It is not absolutely necessary that the mirror shall be
perpendicular to the axis of the magnet. It may be attached at
any point of the magnet, suited to the station at which the
telescope is placed.
A portable magnetometer, on the collimation principle, in-
vented by Professor Borchers, has been used with great success in
the German mines. It consists of a magnet suspended by a silk
fibre, provided with a lens and scale, and enclosed in a glass case.
It is attached by a brass arm to the tripod head of the theodolite.
The use of a somewhat similar instrument has been advocated
by Mr. R. S. Newall.* In this, however, the needle is mounted
on a pivot instead of being suspended by a silk fibre. Attached
to the centre of the needle at right angles to its axis is a small
mirror, whilst a minutely graduated scale, consisting of a short
length, about 4 inches, of a circle 3 feet in diameter, is fixed
at the eye-end of a theodolite telescope, and so adjusted that
the degrees are reflected back to the eye by the mirror fixed
on the needle. In this way, the scale is magnified twice, and
may be easily read to a small fraction of a degree. The arm
carrying the telescope is attached to a circle graduated into 360,
and provided with sights, so that bearings may be taken in the
same way as with the ordinary miner' s-dial.
* Trans. N. Engi. Inst. M.E., vol. xx., 1S71, p. 108.
MEASURING DISTANCES BY TELESCOPE. 217
CHAPTER XV.
MEASURING DISTANCES BY TELESCOPE.
Theory of Telescopic Measurements. The indirect measure-
ment of distances by means of the telescope is based on the
solution of a triangle (Fig. 76).
Suppose the instrument to be at
A and a graduated staff at B ;
then the length A D will be
known, if the angle DAG and
the height D are known. Two Fi S- 76.
classes of instruments are em-
ployed. In one, the angle D A is constant, and the height of
the staff D varies with the distance. In the other, the height
of the staff is constant, and the angle D A variable.
The typical instrument of the latter class is that of Stampfer.
This consists of a telescope that may be moved 8 in a vertical
direction. Two divisions on a staff, held at a distance, are
sighted successively. These embrace a constant height 8. By
means of a micrometer screw it is easy to determine the angle,
through which the telescope has moved in passing from one
division to the other. Let a represent this angle, which is equal
to the number of turns n of the screw multiplied by a constant c.
The angle being small, it may be assumed that tan a = c n. The
distance required will then be equal to or . The
tan a en
constant c is determined by observations along a known distance,
and tables are constructed giving the distance for any number of
turns given to the screw.
The same principle is applied in Eckhold's omnimeter, an
instrument used in revenue surveys in India and in railway
surveys in America.
In American transit-theodolites, a so-called gradienter screw is
frequently attached to the horizontal axis of the telescope. It
consists of a tangent screw with a micrometer head, graduated
into 50 equal parts. As the screw is turned, the head passes
over a small silvered scale, so graduated that one revolution of
the screw corresponds to one space on the scale. Thus, the
number of whole revolutions made by the screw in turning the
218 MINE-SURVEYING.
telescope through a vertical arc can be ascertained from the
scale. When undamped, the telescope may be revolved ; but
when clamped, it can only be moved by the gradienter screw,
which thus takes the place of the ordinary vertical tangent
screAV. The micrometer head is so graduated that one revolution
causes the horizontal cross-line of the telescope to move over a
space of half a foot at a distance of 100 feet. The micrometer
head being divided into 50 parts, each division is equivalent
to one-hundredth of a foot in 100 feet. It is evident that, with
this screw, slopes can be established with great rapidity.
It is also useful for obtaining approximate distances, since for
any horizontal distance, the space on an ordinary levelling-staff ex-
pressed in hundredths of feet, included in two revolutions of the
screw, will be the number of feet the staff is distant from the
instrument. Thus, if the difference between two readings of the
staff is 2-854 feet when the telescope is moved vertically through
two revolutions of the screw, the staff is distant 285-4 feet.
On sloping ground, the staff is still held vertical, and the
distance read is too great. If a is the angle of elevation, the
true horizontal distance may be found by multiplying the space
on the vertical staff included in two revolutions of the gradienter
screw by j- cos 2 a J sin 2 a, in which h is the height above
a horizontal line subtended by one revolution of the gradienter
screw at a distance d, and n is the number of revolutions made
in any given case. The gradienter screw is usually so cut and
placed that when d = 100, n = 2, and h = \, the factor then
becomes
100 cos 2 a - | sin 2 a.
With the object of reducing the computation to a simple multi-
plication, Messrs. Buff & Berger, of Boston, U.S., supply with
their transits a table of factors calculated for vertical angles
of to 15.
Instruments in which the angle is constant, and the height of the
staff variable, are more important and more numerous. The origi-
nal instrument of this class is the stadia, invented by Wm. Green
in 1778. An early form of the instrument used in conjunction
with the stadia or staff consisted of a tube provided with three
parallel wires. In Fig. 76, let G, E, and F represent these wires ;
G being the axial wire, and E and F the end wires ; then the
constant angle a will be determined by the height G F, or i, and
the distance A G, or r, from the eye-piece to the wires. If AD,
the distance to be measured, is represented by d, and if s repre-
MEASURING DISTANCES BY TELESCOPE. 219
sents the height of the staff D C, intercepted by the wires G and
F, the equation obtained is d = s.
The stadia is no longer employed in this primitive form. In
Austria, however, a similar instrument is occasionally used in
levelling for railway sections. In this the tube is replaced by a
pair of sight-vanes, one of which has two parallel wires 0-03
metre apart, stretched across the aperture. The distance from
one sight to the other being O3 metre, the ratio - is equal to 10,
so that, in order to measure distances in metres with this instru-
ment, it is merely necessary to use a staff divided into decimetres.
As a rule, the distances to be measured are so great that a
telescope has to be employed ; in which case the formula is
d = s, as with the stadia tube ; r, however, is not constant, but
varies according to the proportion |- -j = ~f',f being the focal
length of the objective lens.
In the telescopes used in surveying, f is equal to 12 to 15
inches, and r varies as much as 0'24 inch for distances of 20 to
700 yards. Thus, for distances of 100 yards, the variation of r
in proportion to the focal length is very slight. It must, how-
ever, be taken into account, because r is used as a multiplier.
Various methods are employed for remedying the variability of
r. The telescope may be employed like the old stadia tube ; the
staff being graduated for a single distance, and no corrections
applied when the distance is greater or less than this. This
method can be used only when great accuracy is not required.
Early in this century, Reichenbach, a Bavarian engineer, pro-
posed a method that is still in frequent use. He eliminated r in
the equations - + -j = ~ and d = -r s, obtaining d - - s + f. The
value d, it is seen, is composed of two terms, one being propor-
tional to s and the other being the focal length/. The distance
measured from a point as far in front of the object-glass as the
focal length of that lens, is thus proportional to s. Then, if the
distance is to be reckoned from the centre of the instrument, a
constant, c, the distance from the centre of the instrument to the
object-glass, must be added. This may be made by the instrument-
maker equal to 0'5 f. The formula is then
d = 4 s+f+ c.
220 MINE-SURVEYING.
Ail distances will thus be reckoned from the centre of the instru-
ment, if the sum of the focal length and the distance from the
object-glass to the centre of the axis of the telescope is added to
the reading at every sight. For example, if the object-glass has a
focal length of 6 inches, and the micrometer wires are 6 inches
from the object-glass, 1 foot is the constant to be added to each
reading.
A staff may be graduated to read the distance direct. It is, how-
ever, useful only for measuring distances, and not for levelling at
the same time. It is preferable to use an ordinary levelling-staff
and a telescope, in which the instrument-maker has selected for,
some multiple of 100. Suppose, for example, that- - 100. The
distance from the centre of the instrument would then belOOs +
the constant. The calculation of distances is thus greatly
facilitated.
When the line of sight is inclined towards the staff, the space
intercepted is increased in the ratio of 1 to the cosine of the angle
with the horizon. Thus, the space s' for the staff perpendicular to
the horizon becomes s for the staff when vertical, and, by approxi-
mation, s' = s cos a. The inclined distance is then equal to 100 s
cos a + (f + c), and the horizontal distance is equal to 100 s cos 2
a, 4- (f+ c) cos a. But since (f + c) is, at most, equal to 2 feet,
and the angle a is so very small, c may be taken as equal to its
horizontal projection. The horizontal distance will then be equal
to 100 s cos 2 a + (/ + c).
In Germany it is usual to hold the staff perpendicular to the line
of sight. The inclined distance is then equal to 100 s + (f + c),
and its horizontal projection is equal to {100s + (/ + c)} cos a,
or, approximately, 100 s cos a + (f + c).
The most effectual method of remedying the variability of r is
that proposed by Porro, a Piedmontese officer, afterwards professor
at Milan, who in 1823 modified the construction of the telescope
in such a way as to remove all necessity for adding constants, and
the distances measured from the centre of the instrument are then
directly proportional to *. He introduced between the object-
glass and eye-piece a third lens, the focus of which coincided with
that of the object-glass. Consequently the rays after passing
through this third lens become parallel, whilst the sizes of objects
subtending the same angle at the centre of " anallatism," or un-
changeableness, are proportional to their distance from that point.
This point being placed in the vertical axis of the instrument, the
telescope is rendered anallatic. In other words, in consequence
MEASURING DISTANCES BY TELESCOPE.
221
of the interposition of the anallatic lens, the rays coming from the
end-wires to the staff, form an angle a with its vertex at O, the
centre of the telescope. The angle
cu is termed the diastimometric
angle, and O the anallatic point.
The angle varies with the distance
of the anallatic lens from the object-
glass. If this distance increases, u
decreases, and conversely, whilst
the distance remains constant, u is
invariable. It can easily be seen
that the distance from O, the centre
of the telescope, can be deduced
Fig. 77.
from the length A B intercepted by the wires. In fact the sides
of the diastimometric angle form with the staff virtual triangles,
O A B, O A' B'. These triangles being similar give
OPOP'
It is thus merely necessary to determine a simple constant, the
diastimometric ratio, and then to move the anallatic lens until
u coresponds to it. As a rule, k is taken as -g-^, in which case to
is equal to 0'32 centesimal degree. It follows that at 200 yards,
for example, the length of staff intercepted should be 1 yard.
The diastimometric ratio is represented by the expression 2 tan
^. The distance is then s + 2 tan ^.
The original instruments, tacheometers, made by Porro were
very favourably reported on by the Paris Academy of Sciences
and by a French Government Commission. Their extremely
delicate nature, however, prevented them from coming into
general use.
In 1856, M. Moinot, engineer to the Paris, Lyons, and
Mediterranean Railway, gave the tacheometer a form resembling
that of the larger modern theodolites. His instrument is based
on the same principle as that of Porro, but is much less delicate
and less expensive, while giving results of great accuracy. Like
Porro's original instrument, Moinot's tacheometer permits dis-
tances to be measured at the same time as angles and differences
in level. Its use has led to a new method of surveying for
railway purposes, termed tacheometry, which is quite as accurate
as the older method of longitudinal- and cross-sections. By the
advantages it presents of greater rapidity, and the small number
of assistants required, this method has undoubtedly contributed
222 MINE-SURVEYING.
to the development of railways, notably in mountainous districts.
The aim of tacheometry is to survey and level simultaneously a
tract of ground with the greatest possible accuracy in the least
possible time. In mountainous districts, it is a method of the
greatest value, since it dispenses with the chain and spirit level,
and thus the laborious, slow, and expensive processes of chaining
over bad ground and of levelling up and down hill, are avoided.
By means of a single observation, the distance, azimuth and
height are determined of every point visible and accessible from
a given station point. In this way, surveys are made in one-
third to one-fifth of the time that is required for the older
methods. Since its first application by Moinot in 1856, on the
line from Nice to Genoa, it has been employed in most of the
continental countries, excepting perhaps North Germany. There
Reichenbach's method is still used ; instruments being constructed
under the name of tacheometers, more or less similar to Moinot's
tacheometer, but without the anallatic telescope.
The tacheometer is so constructed that 2 tan ^ is equal to ^j.
The distance being equal to 200 s may be read direct from the
staff, if the latter is graduated in half-centimetres. Thus, if the
lower wire coincides with the division marked 100, and the
upper one with the division 110, the height s will be equal to 110
- 100 = 10 half centimetres, and the distance will be 10
metres.
In order to reduce the measured distance to the horizontal, the
work is always carried on with the staff held vertical, and the
angle of inclination of the optic axis is determined.
Calculations. For calculating the results of a tacheometer-
survey, the slide-rule may advantageously be used. The rule
contains scales of numbers, sines, and tangents. To these
Moinot has added a scale giving the values of sin 2 , the origin of
which is so placed that a single setting of the slide gives simul-
taneously the horizontal distance (s sin 2 <p), and the difference
of level. By means of these scales, the co-ordinates of points
observed from a single station with the tacheometer are rapidly
computed, without any direct measurements being made.
The Protractor designed by Moinot for plotting tacheometer-
surveys differs from the ordinary protractor, in that it gives at
the same time the direction and the distance of the point to be
determined on the plan. It is a semicircular protractor, of
transparent horn, or of thick paper, provided with a needle-
pointed pivot at its centre. Its straight-edge is graduated so
that distances can be measured off each way from the centre.
MEASURING DISTANCES BY TELESCOPE. 223
Angles are obtained from the graduated semicircle, reading from
a point marked on the plan.
The Tacheometer is nothing more than a theodolite with a
concentric distance-measuring telescope. It differs from the
theodolite in being furnished with an anallatic lens, and usually
in being graduated according to the centesimal method, the
circle being divided into 400 parts or degrees. Though not
indispensable for a tacheometer, this division is very convenient.
The angles are read more rapidly, on account of the simplicity
of the division into tens and hundreds, and since they are read
from two verniers, one at each end of a diameter of the circle,
errors are at once evident, the readings differing by 200.
Lastly, with the centesimal division, the slide-rule computations
are greatly facilitated. Tables of logarithms for the centesimal
method have been prepared by Callet, Borda, Plausolles, Laland,
and others, and have been in vise for many years. The best forms
of tacheometer are those made by Messrs. Troughton & Simms,
Mr. W. F. Stanley, and Mr. L. Casella.
The btaves used in tacheometry are always graduated with
sufficient distinctness to be read by the observers. Porro's staff
is triangular in section, and has three graduations with different
subdivisions according to requirements. For short distances,
the divisions are extremely fine ; for greater distances only
whole metres are marked in bold figures. Moinot's staff is
graduated in such a way that it can be used for short or for long
distances.
The staff should not exceed 12 to 16 feet in length, and
should be made of light wood. During the observation it must
be held perfectly vertical. It should therefore be provided
with a plumb-line, or, better, with a round spirit-level, the
tangential plane of which is perpendicular to the graduation of
the staff.
The Field-Work. Tacheometric-surveys are usually conducted
by a party of three, (1) the engineer to direct the work ; (2) the
observer at the instrument ; and (3) the recorder to book the
results. On level ground two staff-holders are employed, and
on irregular ground one or two more are necessary, in order to
prevent loss of time to the observer. For less important surveys
one observer and one staff-holder suffice.
When the instrument has been set up at a suitable point,
staff-holders are sent to all the points to be surveyed. To each
point a number is assigned, and noted in the field-book, and on a
sketch made at the same time. The telescope is directed
towards the staff, and the micrometer wires are read and noted
in the proper column of the field-book. The horizontal and
224 MINE-SURVEYING.
vertical angles are then read and noted. This operation is
repeated for all the points that can be seen from this station.
In this way, for every point three figures are obtained the
distance, and the horizontal and vertical angles. The point is
thus fixed by means of polar co-ordinates.
If the survey has to be connected with one previously made,
some data from the former work are necessary in order to make
the connection. Two points, if accurately determined, are
sufficient.
The instrument having been set up and levelled, the engineer
makes a reconnaissance of the ground to be surveyed, and gives
instructions to the staff-holder, who goes successively to all the
points selected by the engineer, and at each one holds the staff
steadily vertical until he receives a signal to pass on. The
observer at the instrument now makes the necessary observations,
which are noted in the field-book by the recorder.
When the ground to be surveyed is so extensive that two
stations are necessary, the engineer selects two points visible
from both stations. When the observation at the first station
is finished, the instrument is moved to the second, and the two
points are observed. The connection could, of course, be made
by means of one point only. It is, however, advisable to employ
two as a check on the accuracy of the work. When a number
of stations are required the method is similar. The method
described is that used by Porro.
Moinot employs the tacheometer in preliminary surveys for
railway lines in the following manner : Before the belt of
ground is surveyed, an extensive reconnaissance is undertaken,
and the main direction of the railway determined, so that the
survey may be limited to a comparatively narrow strip. On
account of the rapidity of the method there is no occasion to be
too anxious about limiting the width. A strip should always be
selected of sufficient width to allow if necessary a lateral dis-
placement of the line. A width of 400 yards is quite sufficient.
Marks are fixed 200 to 300 yards apart, and numbers are
assigned to them. For filling in details, points are chosen
wherever the ground presents any decided change of level. The
instrument is set up at a point so selected that connection can
be made with any existing survey or railway. The assistant
then gives a signal with a whistle or horn to announce that he
is ready. In the meantime the recorder has measured and noted
the height of the instrument, and the engineer has made a
sketch roughly to the scale of the plan to be prepared, showing
all the roads, rivers, boundaries, fields, and the station of the
instrument. As soon as he hears the signal, the engineer
MEASURING DISTANCES BY TELESCOPE. 225
indicates to each staff-holder his place, care being taken that only
one staff is ready at a time. The other staff-holder is still on
the road, or, if already at his post, he turns the narrow side of
the staff towards the instrument, and remains in this position
until it is signalled to him that the preceding reading is finished.
He then turns the graduation of the staff towards the instru-
ment, and by means of a signal directs attention to his position.
He then awaits the signal that he can pass on.
The assistant at the instrument has to read the upper and the
lower wires with each staff, and then the vertical and horizontal
angles, and to call them out in this order to the recorder, who
notes them in the field-book. The recorder enters the points in
order, as 1, 2, 3, &c. At every fifth or tenth point the assistant
gives a double signal, whereby the engineer, although at a
distance from the instrument, has a check on the accuracy of the
booking, seeing that he has entered the points in his sketch in
the same order.
In order to economise time, the engineer selects the points in
such a way that he comes finally in proximity to the point he
regarded as being most suitable for the next station. Here he
places a mark and sets up a staff, at the same time giving a
special signal to the assistant.
When the readings for this next station are finished, the
observations at the first station are complete, and the instrument
is carried on. In the meantime, the man who was holding the
staff at the new station returns to the preceding one just left by
the instrument. The recorder begins a new station in the field-
book, and at once enters the height of the instrument in its
proper column. A back-observation is now taken, and the
distance, height, and azimuth should coincide with the results
previously obtained.
By the aid of this method, Moinot has surveyed about 1,000
miles for railway purposes. The distances, when measured on the
ground with extreme care, have never differed from those shown
on the plan by more than one per thousand, and the longitudinal
section obtained by accurate spirit-levelling has never presented
any appreciable difference when compared with the results
afforded by the heights given on the plan.
The Topographical Stadia differs from the tacheometer in that
the micrometer is not applied to the telescope of a theodolite, but
to the alidade of a plane-table. The points are observed from one
station, the distances from this being reduced to the horizontal,
arid the heights calculated on the spot hy means of a special
slide-rule. The data thus obtained are at once plotted to the
scale required on a sheet of paper stretched on the plane-table,
15
226 MIKE-SURVEYING.
the height of each point being accurately noted. When the
height of a sufficient number of points is determined, contour
lines are traced with the ground in view. In fact, the ground is
practically sketched from nature.
On the United States Coast and Geodetic Survey, the plane-
table has been exclusively used for making topographical surveys;
the stadia, or telemeter as it is called on that service, being used
in connection with it. The stadia is graduated experimentally for
the particular instrument, and for the eye of the observer who
has it in use. It is simply a scale of equal parts painted upon a
wooden staff, about 10 feet long, 5 inches wide, and 1 inch thick,
so graduated that the number of divisions, as seen between the
horizontal wires of the telescope, is equal to the number of metres
in the distance between the observer's eye and the staff held
perpendicular to the line of sight.
American experience tends to show that the plane-table is
adapted to open country and long distances, where no contour
lines are to be determined, and where the stations are compara-
tively few, as well as where a multiplicity of detail is required.
Against the advantage of plotting the work in the field may be
placed the disadvantages of having no record but the field-sheet,
which is liable to be spoiled in a storm.
The Theodolite and Stadia. -The method of surveying with the
plane-table and stadia is being superseded in America by the use
of the transit-theodolite and stadia, a method introduced in 1864,
when it was officially adopted on the United States Lake Survey.
All that can be done with the plane-table may also be done with the
transit-theodolite. The plane-table can be used only for topo-
graphical work, and requires special practice, whilst the theodo-
lite for the stadia survey can be adopted in all cases where a
theodolite is required, and but little special training is required
in order to use it with the stadia.
The best instrument to employ is a theodolite reading to 30".
The micrometer wires should be fixed ; when adjustable, they are
not sufficiently stable to be trustworthy. The stadia is usually a
staff, 1 inch thick, 5 inches wide, and 14 feet long. In order to
graduate the staff, it is necessary to know what space on it cor-
responds to 100 feet (or yards, or metres) in distance. To deter-
mine this, it is best to measure off c + f in front of the plumb-
line, and set a point. From this point, accurately measure a
base-line of (say) 200 yards, on level ground, and hold the
blank staff at the end of this line. Have a fixed mark on the
upper portion of the staff, and set the upper wire on this. Then
let an assistant at the staff record the position of the lower wire,
as he is directed by the observer at the instrument. Eepeat the
MEASURING DISTANCES BY TELESCOPE. '227
operation until the mean gives a satisfactory result. If the base
was 200 yards long, divide the space intercepted by the two wires
into two equal parts, then each of these parts into ten smaller
parts, and finally each small space into five equal parts. Each of
these last divisions will represent 2 yards. Diagrams are then
to be constructed on this scale, in such a way that the number of
symbols can be readily estimated at the greatest distance at which
the staff is to be held. If, when tested by re-measuring the
base-line, the wire interval is found to have changed, the staff
must be re-graduated, or a correction must be made to all the
readings.
If the wires are adjustable, any unit scale may be selected,
and the wires adjusted to this. By this method, distances may
be obtained from levelling-staffs, where it is desirable that each
foot on the staff should correspond to 100 feet in distance.
In making a survey for the purpose of preparing a contoured
plan, a series of points should be determined with reference to
each other, both in geographical position and in elevation. These
points should not be more than 3 miles apart. The points of
elevation, or bench-marks, need not be identical with the points
fixed in geographical position. The latter are best determined
by triangulation.
A system of triangulation points being established, the angles
are observed and the stations plotted on the plan. For small
areas the plotting is best done by means of rectangular co-
ordinates. The survey may, however, be plotted directly from
the polar co-ordinates (azimuth and distance). For this purpose
the plan should have printed upon it a protractor circle, 12
inches in diameter, by means of which the lines can be plotted
accurately to 5'.
A line of levels is next run, bench-marks being left at con-
venient points. The topographical survey is then made, and
referred to this system of triangulation points and bench-marks.
The surveying party should consist of the observer, a recorder,
three staff-holders, and, if necessary, two axe-men.
The record in the field-book consists of (1) a description of the
point ; (2) the reading of the vernier ; (3) the distance ; (4) the
vertical angle. Two columns are left for reduction ; (5) the
difference of height corresponding to the given vertical angle
and distance ; (6) the true height of each point above the datum-
line. The right-hand page of the field-book is reserved for
sketching.
The only calculations necessary are to find the height of all the
points taken, with reference to the datum.-line, and sometimes to
correct the distance read on the staff for inclined sights. These
228 MINE-SURVEYING.
calculations may be performed by means of tables computed by
Mr. A. Winslow, of the State Geological Survey of Pennsylvania,
or by means of a diagram prepared by Professor J. B. Johnson,
of Washington University.
The only available information as to the accuracy of this
method of surveying is given in the report of the United States
Lake Survey for 1875. The entire stadia work of that year was
co-ordinated, and compared with the corresponding distances
obtained by triangulation. In this way 141 lines, on an average
1^ mile in length, were tested, the average error being 1 in 650.
The length of sight between the stations averaged 800 to 1,000
feet. The limit of error allowable in closing on a triangulation
was 1 in 300. No special pains were taken to make these lines
more accurate than others, since it was not known at the time
that the results were to be tested. The readings were taken to
the nearest metre ; the staves were graduated for a single dis-
tance ; and no corrections were applied when the distance read
was greater or less than this. The accuracy thus attained was
sufficient for the object of the survey. Had more care been
exercised in the work, the readings limited to 1,000 feet, and all
corrections applied, it would have been easy to bring the error
within 1 in 1,200.
This method was employed by Mr. W. B. Dawson,* for the
preparation of a map of the gold-field on the Atlantic Coast of
Nova Scotia, on a scale of 2 inches to the mile. The traverse
lines ran along the roads and principal streams, forming a net-
work of quadrilaterals, and were plotted by co-ordinates. The
instruments used in the survey were a Sopwith levelling-staff,
and a 6-inch transit-theodolite with a 4^-inch compass-needle.
The telescope was fitted with three horizontal spider lines,
unequally spaced, the larger interval corresponding to 100 feet
of distance for each foot intercepted by the staff. The smaller one
was only used for longer sight, and when the view was obstructed.
In five months of field work an area of 180 square miles was
surveyed, including nearly one hundred lakes from 7 miles long,
downwards, all the work being done by Mr. Dawson with one
assistant, and one or two men according to circumstances. Wet
days were devoted to the reduction of the observations. The
total cost of the survey was 16'75 dollars per square mile.
Telescope Measurements in Mine-Surveys. In mine-surveys
very accurate readings may be obtained on account of the
steadiness of the air. A transit-theodolite magnifying ten times,
with adjustable micrometer wires, was used in 1865 with great
* Trans. Amer. Soc. C.E., 1882, p. 397.
MEASURING DISTANCES BY TELESCOPE. 229
success by Mr. B. S. Lyman,* for surveying in an American
colliery. It saved much disagreeable groping in the mud to
count the links of a chain, and levels were taken at the same
time. The wires were placed so far apart that 1 foot of space
intercepted on the staff indicated a distance of 100 feet. The
figures on the staff were painted with red ink upon thin paper
that had been fastened to strips of common window glass by
transparent varnish. Then over the paper another coat of
varnish was poured, and upon this was placed another strip of
glass. The glasses, with the paper between them, were then put
into a narrow wooden frame, which formed one side of a long
box. This had neither top nor bottom, and its sides were so
hinged together that they folded over upon each other when not
in use. The back of the box had holes through it to supply air
to the lights, and either safety-lamps or candles were fixed to the
wood of the back. The box was made 5 feet in length ; but for
low mines one might be made much shorter. This staff lighted
inside makes telescopic measuring and levelling easy under-
ground, where chaining is particularly disagreeable.
To remedy the difficulty of getting sufficient light to read the
ordinary staff, Professor Johnson proposes to use two strips, one-
quarter of an inch wide, one of which is fastened with its top
even with the zero of the stadia scale, whilst the other is moved
to suit the position of the other wire. The reading of the top
edge of the upper strip then gives the distance, which is read off
by the staff-holder.
Tacheometry is specially adapted for geological-surveys, which
have frequently to be made in mountainous districts where
chaining is laborious and inaccurate, and where levelling up and
down the sides of the mountains is not to be thought of. The
Geological Survey of Pennsylvania has surveyed some 3,000
square miles by means of the transit-theodolite and stadia. In
the vicinity of mines and where land is valuable the work is
done with extreme accuracy, the length of the lines being limited
to 400 feet.f
* Journ. Franklin Inst., vol. lv., 1868, p. 385.
t For further information on this method of surveying, the student is
referred to Prof. J. B. Johnson's Manual of the Theory and Practice, of
Topographical Surveying by Means of the. Transit and Stadia, New York,
1885 ; and to B. H. Breach's paper on "Tacheometry, or Rapid Surveying,"
Min. Proc. Inst. C.E., vol. xci., 1888, p. 282, in which a bibliography of the
subject is given. Papers on this subject have also been written by
N. Kennedy, Mm. Proc. Inst. C.E., vol. xcix., 1890, p. 308, and by
W. Airy, ibid., vol. ci., 1890, p. 222.
230 MINE-SURVEYING.
CHAPTER XYI.
SETTING-OUT.
Banging Straight Lines. Setting-out, or the location of pre-
determined points, is defined as that branch of geodetic opera-
tions which is the converse of surveying and levelling, the latter
consisting in discovering the position of a series of actually-
existing points.
In ranging and setting-out a base-line for a surface-survey,
ranging rods, 5 to 7 feet in length, are used. They are usually
circular in section, and painted in lengths of 1 foot or 1 link,
black, white, and red alternately. When one colour cannot be
clearly seen, one of the other coloured portions can generally be
distinguished.
The rods are planted vertically in the ground, the vertically
being judged by the eye. When great accuracy is required, a
plumb-bob must be used. Its string is turned over the first and
second fingers of the hand, so that when it hangs vertically, the
rod may be placed parallel to it. The distance apart of the rods
varies from 66 feet to 300 feet.
For ranging straight lines of moderate length, the most con-
venient instrument is the transit-theodolite, because the telescope
may be turned completely over about its horizontal axis, so as to
range one straight line in two opposite directions from one station.
The error with this instrument should not exceed 10 seconds in
angular direction that is, about 3 inches in a distance of a
mile.
For straight lines of very great length, the theodolite is not
sufficiently exact. It is then advisable to use a transit-instru-
ment. In order that a vertical circle may be correctly described
by that instrument, it is necessary that the line of collimation
shall be precisely at right angles to the horizontal axis about
which it revolves, and that the pivots of that axis shall be pre-
SETTING-OUT. 231
cisely level with each other when they rest in their Y's on the
iron stand.
Plotting the Underground Traverse on the Surface. If it is
required to plot the traverse on the surface of the earth, a process
which in former times was in general use for determining the
position of the boundary of the mine, the first course, from which
azimuths were measured, must first be laid down in horizontal
length and direction, and its ends marked with stakes. The
position of the first station being thus determined, the second
station may be found by laying off from the first station, at the
proper angle, a horizontal distance equal to the length of the
course. In the same way, all the successive underground stations
may be marked out on the surface.
This process is tedious, and liable to error, and should conse-
quently only be employed when absolutely necessary. Instead
of repeating the traverse on the surface, the required distance
and its bearing should be calculated trigonometrically, and marked
out on the surface.
Setting-Out Railways to Mines. Railways to mines may easily
be set-out when the ground presents no great irregularities, the
best line for the railway being determined by levelling from the
starting-point to the mine. The line, of which a trial section
shows the fewest difficulties of construction, having been selected,
it is roughly marked out on the ground by strong pegs. The
entire line is then carefully levelled and an accurate section
drawn. From this the amount of cutting and embankment
necessary may be determined. The entire line is then set out on
the ground.
Two stakes are driven into the ground with their heads at the
intended formation level, at distances of about 50 feet apart, near
the commencement of a proposed cutting. The excavators are
then able to carry on the cutting at the proper rate of inclina-
tion by a process called boning. This consists in ranging a line,
of uniform inclination, from two points in it with T-shaped
instruments, called boning rods. Boning rods of the same height
are held vertically upon the two stakes driven into the ground,
and a third rod is held at some point along the intended slope ;
then, if the inclination is correct, the tops of the three rods
will be in line. If the third rod is too low or too high, it must
be raised or lowered until it is in line with the tops of the other
rods.
Banging Curves. Eailway curves are of frequent occurrence,
and even branch railways to mines, which are usually not of great
length, can rarely be made without them.
Acommonmethod of setting-out a railway curve of a given radius
232 MINE-SUEVETING.
oil the ground is by means of offsets. In Fig. 78, A and G are
the ends of the straight portions of the
line to be connected by a curve, being
the two points at which the curve falls
into the straight lines. Let AC, C E,
E G be the distances which it is desired
that the points found in the curve shall
be apart. Then measure, upon the
Fig 78. straight line A produced to D, the
distance C D equal to E, and join D
E. This distance D E is called the offset, and gives a point E in
the curve. Range a straight line through the points C E, and
upon it lay off the distance E F equal to E G, and join F G.
The point G will be the next point in the curve. Proceed in the
same way until the whole extent of the curve has been set out.
Let r be the radius of the curve, and d the distance AC, C E, or
E G, -which it is desired that the points found in the curve shall
be apart, then the value of the offset is
If C E and E G are two equal chords, the offset is
OE ' OP CE2
A B being a tangent to the curve at A, the value of the offset
from the tangent is
The values of D and E F will be found from the following
equations :
-DE 2 = D, and
For example. Let r = 15 chains or 990 feet, and the distance
d = 1 chain or 66 feet, the length of the first offset is ^ - jr^
SETTING-OUT. 233
= 2-2 feet. The distance to be laid off upon the line A
produced to give the place for this offset is >^/66 2 2'2 2 =
65-963 feet Again the length of the second offset is * A
yyo
= 4-397 feet, and the distance to be laid off upon the chord
66 x ^990 9'9^
produced to give the place for this offset is ^r ~
yyo
= 65-85 feet.
A rough method of setting out curves is to extend a line from
the tangential portion of the railway and measure an offset at
the end of each chain. The length of the offset is found from
the formula
792
Length in inches r . ^ . . . ,
radius ot curve in chains
in which 792 represents the number of inches in a chain.
For example. If the curve has the radius of 40 chains, the
length, in inches, of the offset at the end of the first chain is
792
T(T =
A more rapid and more accurate method of setting-out circular
curves is by means of angles at the circumference, a method first
described by Rankine in 1843. It is based on the theorem
(Euclid, III., 20) that the angle subtended by any arc of a circle
at the centre of the circle is double
the angle subtended by the same arc
at any point in the circumference of
the circle. In Fig. 79, A B is an arc
of a circle, C is a point in its circum-
ference lying beyond the arc. The
angle A C B is half the angle sub-
tended by A B at the centre of the
circle. When the point at which the
angle is measured lies upon the arc, Fig. 79.
as at E, it is the angle B E F = A E G
that is equal to half the angle at the centre of the circle. When
the point at which the angle is measured is one of the ends of
the arc, as at A, it is the angle DAB that is equal to half the
angle at the centre of the circle, expressed by a formula, the
angle at the circumference in minutes = ACB = FEB=.
D A B = half the angle at the centre
234 MINE-SURVEYING.
radius of circle
in which formula, the coefficient is the value in minutes of one
half of the arc that is equal to the radius.
The English practice of designating curves by their radii in
chains has but few advantages, as there are no acreage cal-
culations involved. It is preferable to express the radii in
hundreds of feet, or chains of 100 feet. This method is now
coming into general use. The American practice is to designate
curves by the number of degrees in the angle subtended at the
centre by an arc 100 feet in length. Thus, curves are named
one-degree curves, two-degree curves, &c., when the central
angle subtended by 100 feet is one degree, two degrees, &c. In
this method, which is one of great convenience, confusion is
created by terming the centre angle " the angle of deflection."
The value of this angle in degrees is 5729 '6 divided by the
radius in feet.
In setting out curves by means of angles at the circumference,
a 6-inch transit-theodolite is set and adjusted at a tangent point, as
A, and directed along the tangent to D. An angle equal to half
the degree of curvature is deflected from A D towards the side on
which the curve is to run. Of the two chainmen, the follower holds
his end of the chain at A, and the leader, keeping the chain
stretched, is directed by the observer at the instrument into
line with the axis of the telescope. In this way, the position of
the point E on the curve is fixed. From the line A E, the same
angle is set off, the instrument remaining at the tangent point.
The chainmen move forward ; the follower stopping at E, and
the leader moving the stretched chain around that point as
centre until the other end comes into line with the axis of the
telescope. A second point B on the curve is thus obtained. By
continuing the process of setting off angles equal to half the
degree of curvature, and causing them to subtend distances of
100 feet each, the entire curve is set-out. It is necessary that
the angle formed by producing the straight portions of the line,
should be known, in order to find the place on the ground from
which the curve is to start. As a rule, this may be taken at once
with the theodolite. If an obstacle x intervenes, a point y is
selected on one tangent, from which the distance y z to the other
tangent may be measured. The lengths x y and x z are then
found by solving the triangle x y z.
When obstacles prevent all the points from being se<>out from
one tangent point, the theodolite must be moved to the last
point set-out, having the last angle clamped on its upper plate.
SETTING-OUT. 235
The original tangent point being sighted with the vernier
clamped at that angle, by setting it off a new tangential direction
is obtained. By revolving the telescope, the tangent is produced
in the other direction, from which tangential angles may be set-
off to fix more points on the curve.
For example. If the radius of the circle is 19 chains or 1254
feet, and the distance required between the points in the curve
100 feet, the tangent angle to be set-off will be
1 Oft
1718-873 x /W = 137-07 minutes = 2 17' 4".
l.ZD'x
The method of setting-out curves assumes that the chord of an
arc is equal to the arc itself. The difference does not, however,
give rise to sensible error.*
Cross-sections. When each curve has been ranged, stakes,
branded with the distance from the beginning of the line, should
be driven in.
To ascertain the amount of excavation or embankment re-
qujred to form the railway, cross-sections must be taken at each
chain length at right angles to the longitudinal-section. The
slope at which it is desirable to form a cutting or embank-
ment depends on the nature of the ground. The usual slope is
1 foot fall in 1^ foot horizontal, or expressed by the ratio of
slope \\ to 1. Experience shows that fine dry sand will stand
at an angle of 35, dry loose shingle at 39, and compact damp
earth at 54.
Driving Levels Underground. In driving levels, it is usually
necessary that a certain inclination shall be maintained. The
miner must consequently be provided with suitable appliances in
order to enable him to fulfil the required conditions.
In metal mines, if the level has to be driven horizontal, the
easiest method is to conduct water into it. A dam is erected
just before the working end, and the level is so driven that
the water always maintains the same height. This method can,
however, only be applied when no water is given off from the
rock in the level, as with the slightest influx of water, the surface
is disturbed and ceases to be horizontal.
The inclination of the level may be checked by means of a
* For accounts of the methods of setting-out curves in cases where
extreme accuracy is required, the student may consult L. D. Jackson's
Aid to Survey Practice, London, 1880, pp. 208-288; J. C. Trautwine's
Field Practice of Laying out Circular Curves for Railroads, New York,
twelfth edition, 1886; W. J. M. Rankine's Civil Engineering, London,
sixteenth edition, 1887.
236
MINE-SURVEYING.
plumb-bob. The instrument usually employed (Fig. 80) is maae
of deal boards, 1 inch
thick. The foot-piece is
6 feet in length and 4|
inches broad. The vertical
piece is 3feetinlength,and
6 inches broad at the lower
end, tapering upwards
until, at the top, it is 4
inches broad. In addition
to the plummet, there is a
small spirit-level fixed to
the foot-piece to serve as
Fig. 80.
a check. The instrument is placed on the floor of the level, and
if the latter is being driven truly horizontal, the plummet will
hang in the hole made in the vertical piece for its reception,
and at the same time the bubble will be in the middle of its tube.
The main horse-roads in collieries should be driven with a
slight inclination towards the shaft, so that water may flow from
the workings to the sump. Experience has shown that an
inclination of 1 in 130, or a little more than | inch in the yard,
gives the most advantageous effect in drawing by horse-power
the loaded waggons towards the shaft, and the empty ones back.
Fig. 81.
'Care must be taken that this inclination is not exceeded, as, in
driving levels, there is always a tendency to rise too fast. For
maintaining the required inclination, a piece of board, J inch
SETTING-OUT. 237
thick, should be screwed to the foot at the end of the instrument,
which is nearer the shaft.
In order to test the inclination of an underground roadway
with an inclination of 1 in 5, Mr. W. Wardle uses the instru-
ment shown in Fig. 81. It is provided with two sole-pieces, the
bottom of the lower one being at a distance of 1 foot from that
of the upper one at one end, whilst at the other end it is brought
to a feather edge.
An ingenious clinometer, invented by Colonel G. P. Evelyn
(patent 1885, No. 1964), may be advantageously used for setting
out levels at any inclination. It consists of a curved tube filled
with water or dilute spirit, on which floats a small bubble of
compressed air. Adjacent to the tube, and concentric with its
outer periphery, is the graduated arc of a circle. When the air-
bubble is at the zero point of that arc, the base of the stand, in
which the tube is mounted, is horizontal, and any inclination
from the horizontal is shown in degrees by the position of the
bubble on the graduated arc. The tube is easily filled and
emptied, and the size of the bubble is regulated by a screw-cap
fitting over the cork.
To drive a level straight at a given bearing, plumb-lines are
suspended from points in the roof previously fixed by the dial
or theodolite. These lines indicate the direction in which the
level has to be driven, and should be placed 30 to 60 feet apart.
Curves for Engine Planes. Curves may be set out under-
ground by means of a theodolite on a short tripod, and candles or
lamps instead of ranging poles.
The direction in which curves for engine planes should be set
out is sometimes roughly ascertained by making a careful survey
and plan of the pillars and headings, through which it is required
to drive the curve. The survey is plotted on a large scale e.g.,
16 feet to an inch. The curve drawn on the plan is divided into
equal distances marked by points. The latter are then con-
nected by dotted lines. By means of a protractor, the bearing
of each of these lines is determined. For greater accuracy, off-
sets are measured at every 6 feet on each side of the lines to the
sides of the curve. In this way data are obtained from which
the curve may be set out.
Setting-out Tunnels. The centre-line of the tunnel having been
ranged on the surface of the ground, a series of shafts are sunk
from 100 to 200 yards apart along that line. In order to transfer
the ranging of the line from above to below the surface of the
ground, it is necessary to have two marks, consisting of nails
driven in the cross-timbers in the centre-line at the bottom of
each shaft as far apart as possible, to enable the line to be pro-
238
MINE-SURVEYING.
longed from the bottom of the shaft in both directions. To
determine the positions of the marks underground, a ranging-
frame is erected over the shaft. It consists of three half-timbers
framed as a triangle and supported at the angular point by stout
props. From the frame are suspended two plumb-lines, which
are ranged by a transit-instrument.
As this process cannot be satisfactorily used except in calm
weather, Mr. F. W. Simms introduced the following modifica-
tion: By means of the transit-instrument, the engineer ranges
two stakes in the centre-line at the surface, each being about 16
feet from the centre of the shaft, so as to be safe from
disturbance while the work is in progress. To mark the
exact position of the centre-line a spike (Fig. 82) is driven
into the top of each stake. The hole of each spike is
carefully ranged in the centre-line, a piece of white paper
being held at a short distance behind it, so as to render
it visible to the 'observer at the telescope. A string is
stretched centrally across the mouth of the shaft, and its
Fig. 82. ends are passed through the holes in the spikes. It is
then drawn tight and made fast. At each side of the
shaft a plank is fixed at right angles to the string, and so placed
that one side hangs over the shaft about 3 inches, so that a
plumb-line may hang from it without coming in contact with the
side of the shaft. A plumb-line being hung from each plank
directly under the cord marking the centre-line, the lower ends
of these plumb-lines represent two points in the centre-line at the
bottom of the shaft.
The approximate ranging of the heading connecting the lower
ends of the shafts is effected by means of candles, each hung from
the timbering in a sort of stirrup. The upper portion of the
candle-holder (Fig. 83) employed by Mr. Simms is made of thin
sheet-iron with a number of holes in it. The
lower portion is of iron wire, carrying a socket
for the candle. By means of the rack, the latter
can be raised or lowered to the proper level, and
being hung by a flat plate, it is prevented from
rotating.
The accurate ranging of the centre-line, when
the heading has been made, is effected by stretch-
ing a string between the marks already ranged
at the bottom of the shaft, and fixing, at intervals
of about 40 feet, either small perforated blocks
of wood carried by cross-bars, or stakes with
eyed-spikes driven into their heads, so that the
Fig. 83. holes may be ranged by the string exactly in the
straight line.
SETTING-OUT. 239
This method was employed by Mr. Simms for setting-out the
Blechingley and Saltwood tunnels on the South-Eastern Railway.
Both these tunnels were straight from end to end, as is generally
the case. Their centre-lines were ranged with a transit-instrument
of 30 inches focal length with an object>glass of 2f inches aper-
ture. In order to command a view of every shaft, the instru-
ment, mounted on a cast-iron stand, was set up on the highest
point of ground as near the middle of the tunnel as possible, and
raised above the surface by the erection of a temporary observa-
tory. This consisted of a building of larch poles, in the centre
of which was a brick pier 30 ieet in height for the support of the
instrument.
When the length of the tunnel is not very great, the transit-
instrument and temporary observatory may be dispensed with,
and the 6-inch or 5-inch transit-theodolite used with advantage.
This was done in setting-out the Clifton tunnel in 1871 to 1874.
This tunnel is straight, on an incline of 1 in 64. It is 1737J
yards in length. At a distance of 276 yards from the lower end
of the tunnel, where it approaches to within 140 feet of the
Blackrock Cliff, a side drift was opened from the face of that cliff
to the line of the tunnel. The tunnel was driven from this
drift, and from two shafts sunk 998 yards and 4'63 yards
farther on.
When the tunnels are of great length, and can only be driven
from the ends, the setting out is much more difficult than when
shafts can be sunk along the line. The direction of the axis of
the tunnel is determined by a traverse or a triangulation con-
necting the two ends. In very long tunnels, such as those of the
Alps, traversing is not sufficiently accurate, and recourse must
be had to triangulation, as was the case at St. Gothard. The
St. Gothard tunnel, the longest railway tunnel yet made, is nine
miles in length. Its construction lasted from September, 1872,
to February, 1880. The holing was effected on February 28,
1880, the length being 25 feet less than was expected. The
error in level was 1'97 inch, and the error in alignment was
12-99 inches. (Fig. 83a.)
The Mont Cenis tunnel was set out in the years 1857 to 1858,
without triangulation, with the aid of a high observatory. The
length of the tunnel was determined by triangulation, and the
line of levels was carried over the mountain. The tunnel is
upwards of six miles in length, and the junction was effected
without any error horizontally, and with only a foot of diver-
gence vertically.
Remarkably accurate results in tunnel alignment were obtained
240
MINE-SURVEYING.
SETTING-OUT. 241
in 1888 in the Croton aqueduct at New York. The points of
commencement of two headings were 6,400 feet apart, the one
being 270 feet and the other 353 feet below the surface. The
diameter of the heading was 16-5 feet. The direction was
obtained by means of two plumb-lines, 16-5 feet apart, let down
each shaft. When the two headings approached each other, the
final connection was made by two drills meeting in the same
hole from opposite sides of the rock, and after the blast had been
fired, it was found that the error in grade was - 014 foot, and in
alignment 0'09 foot.
In the construction of Division No. 6 of this aqueduct, Mr.
F. W. Watkins, the engineer in charge, found that the centre-
line wires were very difficult to distinguish, as the cross-hair of
the telescope and the two plummet lines appear so nearly alike.
He was, therefore, induced to devise an illuminated slit appar-
atus to replace the wires at the bottom of the tunnel. This
instrument consists of two vertical strips of brass (3 inches in
height) attached to separate horizontal bars moving in guides,
and provided with a tangent-screw motion, by which one or both
could be moved right or left and the vertical aperture between
them made as small as desired. One of these instruments was
screwed to a plank-bracket, close behind each plummet wire, and
so placed that the farther one could be seen through the tele-
scope in line just above the other. When these slits were
adjusted so as to be directly behind the plummet wires, the
latter were removed, and lights placed behind the slits. In
this way two fixed and illuminated points were substituted
for. the wires. The results of tests of the alignment effected
in this way show that the accuracy of the surveys was very
remarkable.
Taking cross sections for measuring the areas and quantities
of excavation in tunnel work is best done by measuring the
irregularities of the contour of the section by angles and dis-
tances from some point in the vertical plane through the axis of
the tunnel. For the Croton aqueduct tunnel, where sections
had to be made every 10 feet for over 30 miles of tunnel, a con-
venient instrument was designed by Mr. A. Craven. This
instrument, known from its yellow disc of varnished wood as
the sunflower instrument, consists of a light wooden tripod with
extensible legs, a shifting top, ball and socket joint, and levelling
screws. A vertical brass tube slides through the socket, and
carries at its top a wooden graduated disc, 18 inches in diameter.
An arm revolving on a central socket traverses the face of the
disc, and a wooden measuring rod, 14 feet in length, is placed
16
242 MINE-SURVEYING.
on this arm, and slid out to touch the surface of the tunnel, the
end of the arm at the same time indicating the angle from the
vertical. The measuring rod tapers from 2 inches to ^ inch in
width, and is graduated in feet and tenths from the smaller end.
In order to ensure the cross-section being taken at right angles
to the axis of the tunnel, the disc is provided with a small
sighting tube perpendicular to its face. The measurements are
recorded in the field-book, and the areas of the cross-sections are
determined by calculation, or by the planimeter.
When the difficulties of the task are duly considered, it is
probable that the accuracy of the work at the Hoosac tunnel has
never been equalled. This tunnel passes through the Hoosac
Mountain range in Massachusetts, and is 25,031 feet in length.
The tunnel was driven from the two ends, and also from a shaft
1,028 feet deep, sunk in the valley between two mountains in
the line of the tunnel. On the east side, the headings met at a
distance of 1,563 feet from the shaft, and 11,274 feet from the
eastern end, the lateral error being 0'025 foot and the vertical
error being 0'23 foot at the point of junction. Proceeding west-
ward, the tunnel extended 2,056 feet from the shaft before
meeting the excavation on the western side, which was 10,138
feet from the west entrance. The holing showed that the error
of alignment was 0'045 foot. The alignment in the central shaft
was obtained by two plumb-bobs 25 feet apart.
Curiously enough, the oldest piece of tunnelling of which there
is any written record was begun at the two ends, its construc-
tion being recorded in the oldest example of Hebrew writing
known. The inscription, now known as the Siloam inscription,
was discovered by some boys bathing in the Pool of Siloam, in
Jerusalem, in 1880. It is cut on a tablet 27 inches square at
the mouth of the tunnel, and, according to the translation of
Professor Sayce, reads as follows :
" [Behold] the excavation ! Now this is the story of the
tunnel : While the miners were still lifting up the pick towards
each other, and while there were yet 3 cubits [to be broken],
the voice of one called to his neighbour, for there was an excess
in the rock on the right. They rose up they struck on the
west of the tunnel ; the miners struck each to meet the other
pick to pick. And there flowed the waters from their outlet to
the Pool for 1,200 cubits, and [three-quarters] of a cubit was the
height of the rock over the heads of the miners."
From this inscription, it is evident that the tunnel was begun
from the two ends. And this view is confirmed by the results
of recent explorations. The Pool of Siloam is supplied with
SETTING-OUT. ' 243
water from the so-called Spring of the Virgin, the only natural
spring near Jerusalem, by this tunnel driven in the rock.
According to Major Conder's survey, the tunnel is 1,708 feet
long, or about 1,200 cubits of 18 inches. It does not, however,
run in a straight line, and towards the centre there are two
culs-de-sac, of which the inscription offers an explanation. We
thus see that the engineering skill of the day was by no means
despicable. Like the Mont Cenis tunnel, this aqueduct was
begun simultaneously at the two ends, and in spite of its wind-
ings the workmen almost succeeded in meeting at the middle.
They approached, indeed, so nearly to one another that the noise
made by the picks of one party of miners was heard by the
other, and the parting of rock was accordingly holed. This
accounts for the two false cuttings now found at the centre of
the tunnel, these representing the extreme points reached by
the two parties before they had discovered that instead of meet-
ing they were passing one another.
Though the inscription contains no indication of date, Pro-
fessor Sayce is of opinion that the tunnel was made in the reign
of Hezekiah, or possibly even in the time of Solomon.
With regard to the interpretation of the last line of the
inscription that " three-quarters of a cubit was the height of the
rock over the heads of the miners," it is remarkable that the
difference of height of the two channels at the point of junction
is just 13 inches, or close upon three-quarters of a cubit. Unfor-
tunately, however, the text is deficient just in the place where
the number occurs, and it may possibly indicate that the miners
knew the thickness of the rock above them. In this case,
the correct interpretation is probably 100 cubits, the average
thickness of rock above the aqueduct. Several marks, evi-
dently artificial, were discovered by Major Conder in the
tunnel square or triangular notches, measuring 1 inches
in "width. These appear to have been used, like the peg and
nail of the Cornish miner, to mark the end of a periodical
survey, or else to serve as a guide in setting the contracts to
the miner.
It is certainly remarkable that there should have been so
slight a difference in level between the two portions of the
tunnel. It would have been easy, by means of a plumb-line
or a rude water-level, to preserve the level of the channel floor ;
but' it is extraordinary that the two ends should differ by
only a foot in level, considering that they were started inde-
pendently.
In New South Wales, a very successful alignment was effected
244 MINE-SURVEYING.
by Mr. T. W. Keele * in the construction of the Nepean tunnel,
a conduit for supplying Sydney with water. The tunnel is
23,507 feet long, the bases at the east and west ends being
254 feet and 212 feet respectively, situated at the bottoms of
precipitous limestone gorges. There were six shafts, admitting
of only 12-foot bases, the depths varying from 210 - 5 feet to 324
feet. The length between shafts Nos. 2 and 3 was 4,341 feet,
the headings meeting at a point 3,018 feet from shaft No. 2.
The error in alignment was | inch, and in grade ^ inch. The
tunnel is 7i feet high and 9i feet wide, and is inclined at the
rate of 2J feet per mile.
The line was transferred from the surface to the bottom of
the shafts by plumbing. At the shafts brick pedestals were
erected, one on each side, on the centre line, and about 50 feet
apart, the tops being a foot above the shaft platform. Points
were then accurately established on each, and a steel wire, 0'02
inch in diameter strained, at its utmost tension, from point to
ipoint across the shaft. The process of plumbing down the shaft
was then proceeded with. An 8-inch transit theodolite on its
centering legs was then set up in one of the headings, and the
intersection of its cross-wires brought into coincidence with the
line as given by the plummets. After the instrument had been
adjusted to prolong the line into the heading, a hole was drilled
in the roof and a wooden plug inserted ; and on this the point
was obtained by sighting on to a plummet lamp, of the type
used in Pennsylvania, suspended from it. In order to give the
levels in the tunnel, the value of a bench-mark at the bottom of
a shaft was ascertained by measuring the calculated distance
.from the surface with a steel tape ; and the levels were run
into the headings. At intervals of 100 feet, hooks in pegs in the
-.sides of the tunnel, and opposite to each other at right angles to
the line, were so adjusted that strings stretched through them
were exactly 2| feet above the grade. The plummet lamps,
jbanging from the centre-pegs in the roof, being then lowered
until their lights were even with the horizontal strings, the axis
of the tunnel was determined, and the miners were provided
with both line and grade. All that they required to do was
to place a candle at the face in line with the lights from the
plummet lamps, and measure down 2 feet 9 inches to find the
grade of the invert. Bench-marks were established at intervals
of 500 feet, and were frequently checked.
The lengths of the headings and the results of the alignment,
when the junctions were effected, were as follows :
* Min. Proc. Inst, C.E., vol. xcii., 1888, p. 259.
SETTIXG-OUT.
245
Name of Heading.
Length in Feet.
Error in Inches.
In Line.
In Grade.
Inlet.
No. 5, West.
2054-0
1513-2
3
*
No. 5, East.
No. 4, West.
935-0 J
1970-0 )
3
Nil
No. 4, East.
2463-0 )
A, West.
425 -OJ
!
A
A, East.
No. 3, West.
496-0 )
1359 (
!
i
No. 3, East.
No. 2, West.
1323-4
3018-0
1
i
No. 2, East.
No. 1, West.
2385-0 )
2286-0 j
1
i
No. 1, East.
Outlet.
1126-5
2148-0
2|
^
After the tunnel had been pierced through, daylight at one
end was distinctly seen, without the aid of a telescope, from the
other, 4J miles away.*
* On tunnelling, consult F. W. Simms' Practical Tunnelling, 3rd ed.,
revised by D. K. Clark, London, 1877; H. S. Drinker, Tunnelling, New
York, 1878, F. Rziha, Lehrbuch der gesammten TunnellJauhmst, 2 vols.,
Berlin, 1867-72, with the authorities there cited, and F. W. Watkins, on
" Tunnel Surveying on the New Croton Aqueduct," Trans. Amer. Soc.
C.E., vol. xxiii., 1890, p 17.
246 MINE-SURVEYING.
CHAPTER XVII.
MlNE-SURVEYING PROBLEMS.
Determination of the Direction and Inclination of a Mineral
Deposit. Problems relating to the working of mines may be
solved graphically or numerically. Graphic solutions are the
most simple, but they require the plans on which they are based
to be of undoubted accuracy. Most problems are therefore more
conveniently solved by the ordinary methods of descriptive
geometry.
To determine the strike and dip of a vein that has been opened
by a level driven along it, two points are selected in the axis of
the level, either on the floor or on the roof. At these two points
two vertical props are set up, when the bearing of a horizontal
string connecting the two props will be the strike of the vein.
Instead of the stretched string, a rod may be held horizon-
tally.
The strike being determined, the direction of the dip may be
determined by setting off a line at right angles to the strike.
The dip may be measured with a clinometer.
A convenient instrument for determining the dip of mineral
deposits is the so-called gradometer, invented by Mr. W. Fairley.
It consists essentially of a 9-inch or 4-inch scale made to move up
and down a vertical bar. When the lower edge of the scale is
placed on the plane of which the dip is to be determined, and is
shown to be level by the spirit-level on the upper edge, the plane
is horizontal. When the plane is inclined, a slide, like that of
the slide-rule, marked on one side in degrees and on the other in
inches per yard, is taken out and passed through a slit at right
angles to the longitudinal axis of the scale. For measuring dips
above 45, a second slide is provided. The gradometer is of less
weight than a clinometer of the same length, and can be read
with greater facility.
If the strike of a deposit is known, its dip may be calculated
MIXE-SURVEYING PROBLEMS. 247
Thus if a line A E, Fig. 84, is drawn on the plane of the deposit
A B C D, and if through the point A, a
horizontal plane A F passes, then A B,
the line of intersection of the two planes,
is the line of strike of the deposit. From
any point G on the inclined line A E, let
fall a perpendicular G H to the horizon-
tal plane A F, and in the latter draw a
horizontal line A J, which is the line of Fig. 84.
strike of the inclined line AE. The
horizontal angle B A J is the difference in bearing between the
line of strike of the deposit and that of the inclined line ; whilst
the angle G A H in the vertical plane E A J represents the dip of
the inclined line A E. Let fall in the horizontal plane A F from
the point H a perpendicular line H K to the line of strike A B f
and join GK. Then GK is the line of dip of the deposit
ABCD, and the angle G K H in the vertical plane GHK
represents the angle of the dip of the deposit.
If the strike A B of the deposit is expressed by c, and the angle
B A J e, and the strike of the inclined line = a, then e = c a.
In the right-angled plane triangles A G H and A H K,
GH = AG sin b, and
HK = A G cos b sin e.
Then from the triangle GHK, the value of the required angle
of dip may be found from the formula
tanGKH
H K A G cos b. sin 9
_ tan 6
sin e
Conversely if the angle of dip d is known, the strike may be
found from the formula sin e = tan 6 . cotan d.
For example. 1. What is the dip of a seam coursing 127 30',
if a diagonal heading driven in the seam has a dip of 4,
and courses 90 or due east and west ? The angle e is
= 127 30' - 90 00' = 37 30'. The dip d is then found from
the equation
tan 4
248 MINE-SURVEYING.
Employing logarithms, this gives
Ltan 4 = 8 '8446437
L sin 37 30'= 9-7844471
Ltand = 9-0601966
Thus d = 6 33' 10".
2. Example. Determine the strike of a seam dipping 8, in
which a diagonal heading is driven, dipping 5 and coursing 60.
In this case
tan 5
sine =
tan b
Employing logarithms, this gives
Ltan 5 = 8-9419518
Ltan 8 = 9'1478025
Therefore e = 38 30'.
The strike c required is found from the equation c = e + a,
thus
c = 38 30' + 60 00' = 98 30'.
The strike and dip of a seam may be determined if three
points in it are given. Thus if three bore-holes, not in a straight
line, have been sunk to the floor of a seam, as shown in the plan,
Fig. 85, H M T, the problem is solved as follows : Measure the
depths of the three bore-holes from the same
assumed horizontal plane at the surface. In
this case, T represents the deepest, and H the
*V- ^ x ,'''' \ highest point of the deposit. Imagine per-
\ A \ pendiculars to be erected to H M at the
points H and M, and on them laid off the
heights H H' and M M', representing the
heights that the floor of the seam at the
bore-holes H and M is above the floor at
the bore-hole T. In this way, H' M' repre-
sents the line of inclination of the seam
between H and M. That line is produced
until it cuts the line H M produced at N.
Thus a point in the seam is determined, which is situated at the
same level as the bottom of the bore-hole T, and T N is the line
of strike of the seam.
MINE-SURVEYOG PROBLEMS. 249
The line H N is found, from the similar right-angled triangles
H H' N and M M' N, to be equal to
TT -NT ^ H' H M . .
= HH'-MM > .:*';*
From the bore-holes, the strike of H T and the angle N H T are
known, and as H N is found from equation 1, in the triangle
H N T there are two sides and the included angle known, con-
sequently
H N + H T : H N - H T = tan (T + N) : tan i (T - N) (2.)
From this, the angles T and N are found, as half their sum is
known. From the given strike H T and the angle T, the strike
of the line T N may be deduced.
In order to determine the dip of the deposit, imagine a line
H O drawn from H perpendicular to the line of strike T 1ST, then
TT (~\
in the right-angled triangle HOT, -=y--^_ = sin T, whence it
follows that H O = H T sin T.
At the point H erect a line perpendicular to H 0, and along
it lay off the height HP, being the height which the floor of the
seam in the bore-hole H is above that in the bore-hole T. Then
the line obtained O P is the true line of dip, and the angle
HOP represents the angle of dip of the deposit. Thus tan.
TT P IT P
H O P = ~, or, by substitution, tan H P = -r-
Expressed by general formulae,
- TTI
a sin V
d a' . TTT
jr- sm W
tanV= d ,
in which S is the angle of dip of the bed, V the angle between the
strike of the bed and M H, a the distance from M to H, a the
distance from M to T, W the angle in a horizontal plane between
250 MINE-SURVEYING.
M H and M T, d the difference of the depths of the bore-holes M
and H, and d the difference of the depths of M and T.
For example. in Fig. 85, H T = 150 yards, H M = 112 yards,
and M T = 100 yards, measured horizontally. The angle
M H T = 41 48' 37". T is the deepest bore-hole, and the floor
of the seam in the bore-hole M is 32 yards, and in the bore-hole
H 73 yards higher than in the bore-hole T. It is required to
determine the strike and dip of the seam, when T H courses
172 30'.
From the first equation given,
ITQ -I -I n
H N = 'o 'o = 199-41 yards.
Now, T + N = 180 - 41 48' 37"= 138 11' 23", and half T + N
= 69 5' 41 - 5". From the second equation
T-N 199-41-150 A
* -i- - 199-414-150 ' tan 69 5 41 ' 5
40.4.1
= 34941 tan69 " 5 '"' 5 "
From this, half T-N is found by logarithms to be 20 18' 55".
Half T + N being 69 5' 41-5", T is equal to 89 24' 36-5", and N
is equal to 48 46' 46-5".
As the strike of T H is 172 30', and as T N lies to the right
of T H, the strike of the latter is
(172 30' + 89 24' 36-5") - 180 = 81 54' 36-5".
The angle of dip H O P is found from the equation
tan H O P
150 sin 89 24' 36-5"
By the aid of logarithms, the angle H P is found to be
25 57' 7".
The strike of the seam, as found above, can be set out at the
surface in the usual way.
Determination of a Point at the Surface directly above one
Underground. If it is required to determine the position of the
MINE-SURVEYING PROBLEMS.
251
end of a level, it will be found advisable to calculate it trigono-
metrically instead of by plotting the traverse at the surface.
The rectangular co-ordinates of the underground-survey are
calculated, and the distance and bearing of the end from the
shaft found from the formulae :
departure ,
tan of bearing = -, and
distance = latitude x sec of bearing.
For example. In order to calculate the bearing and distance
of the end of the level from the centre of the shaft in the survey
of the Work and Rest mine, the record of which is given on p. 34,
the latitudes and departures must first be calculated, with the
following results :
WORK AND REST MINE. REDUCED SURVEY NOTES.
No.
Distance.
Bearing.
LATITUDE.
DBPABTUKB.
N.
8.
E.
W.
A
Feet.
74-50
N. 15' W.
74-49
...
0-32
B
82-83
N. 14 00' W.
80-37
.
...
20-03
C
63-00
N. 27 39' W.
55-80
29-23
D
30-16
N. 84 57' W.
2^5
30-04
E
23-75
S. 74 06' W.
6-50
...
22-84
F
192-00
N. 67 45' W.
72-70
...
177-70
G
96-50
N. 88 00' W.
3-36
...
...
96-44
H
34-00
S. 84 06' W.
...
3-49
33-82
J
23-75
S. 52 00' W.
14-62
...
18-71
...
...
...
289-37
24-61
429-13
MINE-SURVEYING.
The total latitude is 289-37 - 24-61 = 264-76 feet, and the total
departure is 429*13 feet. The distance from the shaft to the
station-point J at the end of the level is found from the formulae :
.. . 429-13 ,
tan of bearing = , and
distance = 264-76 sec. of bearing.
The calculations are performed most quickly by means of loga-
rithms, thus
log 429-13 = 2-632588
log 264-76 = 2-422852
10+ 0-209736 = L. tan 58 20*
L. sec 58 20' = 10-2798601
log 264-76 = 2-422852
12-7027121 - 10 = log 504 -32
To determine the position of the point at the surface correspond-
ing to the end underground, it is merely necessary to set-out
from the shaft a horizontal distance of 504-32 feet at a bearing of
58 20' or K 58 20' E.
This problem is of great importance for the determination of
the position of the underground workings in reference to the
boundaries of the concession or royalty.
Holing from one Excavation to another. The usual problem
relative to holing consists in determining the length and direction
of the axis of a gallery joining two given points. The problem
may be solved graphically or numerically. In the former case
the plans employed must be rigorously exact. In the numeri-
cal method, the length and bearing are deduced from the co-
ordinates of the end points.
For example, In the survey between the Speedwell and
Netherthorpe shafts at Staveley, of which the record is given on
L75, the latitudes and departures of the 15 drafts underground
m the Speedwell downcast shaft to the face of the main ven-
tilating drift, intended to hole into Netherthorpe shaft, were
calculated with the following results :
MINE-SUKVEYING PROBLEMS.
253
REDUCED SURVEY NOTES.
No.
Bearing.
Distance.
LATITUDE.
DEPARTURE.
N.
S.
E.
w.
A
N. 34 24' W.
Links.
134
11-14
...
7-63
B
N. 58 35' E.
639
33308
...
545-32
...
C
N. 45 41' E.
274
191-42
196-04
...
D
N. 37 29' E.
ISO
103-16
...
79-11
E
N. 840'W.
127
125-55
...
19-13
F
N. 15 02' E.
405
391-14
...
105-05
G
N. 17 57' E.
206
195-97
...
63-48
...
H
N. 11 35' E.
158
154-78
...
31-72
J
N. 35 37' W.
73
59-34
42-51
K
N. 18 20' E.
260
246-80
...
81-78
...
L
N. 18 14' E.
470
446-40
147-05
M
N. 69 42' E.
384
133-22
...
360-15
N
S. 27 45' E.
63
55-75
29-33
...
N. 69 32' E.
73
25-52
...
68-39
...
P
N. 71 57' E.
78
24-17
74-16
...
...
2441-69
55-75
1781-58
69-27
The total latitude amounts to 2441-69 - 55-75 = 2385-94 links,
and the total departure 1781-58 - 69-27 = 1712-31 links.
The direct bearing and distance measured at the surface from
the Speedwell downcast shaft to centre of Netherthorpe shaft,
intended upcast, were N. 37 02' E., 3113 links, representing
2485-06 links north latitude, and 1874-89 links east departure.
The positions from Speedwell shaft, in terms of latitude and
departure, were consequently as follows :
254 MIXE-SURVEYING.
N. Latitude. E. Departure.
Netherthorpe shaft, . . . 2485 '06 1874-90
Face of heading, . . . 23S5'94 1712-31
99-12 162-59
Now, tan of bearing = departure -4- latitude, and distance = lati-
tude x sec of bearing, therefore the distance to be holed is found
as follows :
log departure = log 162-59 = 2-211093
log latitude = log 99'12 = 1-996161
L tan of bearing = 10 + G'214932
The bearing is therefore N. 58 38' E.
log latitude =log 99-12 = 1 '996161
L sec 58 38' = 10-283568
log distance = 12-279729 - 10
The distance is therefore 190-43 links.
Having thus calculated the bearing and horizontal distance
from the face of the heading to the intended upcast shaft, Mr.
Howard determined to drive direct into the shaft, and the drift
was accordingly set-out at the calculated bearing and distance.
His survey and calculations were proved by the holing to be
absolutely correct.
If it is required to determine the inclination and distance of
the axis of the heading uniting the two given points, and the
co-ordinates of those two points referred to three axes of
rectangular co-ordinates are x y z and x y' z' respectively, the
distance d, the bearing /3, and the inclination a, may be found
from the formulae
d = J(x - x'f + (y - y'f + (z - z')*
tan /3 = - * ~ X ',
y - y
z - z'
= J(x - xj + (y - 2/')2 + ( - zj
Attention must be paid to the signs of the co-ordinates, which
always indicate the position in space of the axis considered.
A remarkable example of successful holing is afforded by the
Ernst- August adit level in the Harz. This great adit, one of the
longest in the world, was commenced in 1850 and completed on
MINE-SURVEYING PROBLEMS.
255
22nd July, 1864 ; it has a total length of 25,956 metres. It was
driven from the bearings and distances calculated from the
results of a survey made with extreme accuracy by means of the
theodolite and spirit-level from a number of points. The results
of the holings were as follows :
ERNST- AUGUST ADIT LEVEL.
Length
Surveyed.
EKBOB ON HOLING.
In Direction.
In Level.
1. Holing in Regenbogen mine,
Fathoms.
310
Inches.
0-2
Inches.
0-15
2. Holing between the mouth of the
adit at Gittelde, and the Fahlen-
berg shaft,
880
0-3
0-40
3. Holing between the Meding shaft
and the George shaft,
2,700
1-5
0-40
4. Holing between the Hiilfe Gottes
shaft and the mouth,
2,760
1-0
0-23
5. Holing between the George shaft
and the Knesebeck shaft,
1,580
1-5
0-60
6. Holing between the Knesebeck
shaft and the Hiilfe Gottes shaft,
1,430
1-1
0-14
7. Holing between the Schreibfeld
shaft and the Haus Sachsen
shaft,
1,890
1-5
0-37
8. Holing between the Meding shaft
and the Ernst- August shaft,
3,960
1-2
0-09
9. Holing between the Ernst- August
shaft and the Haus Sachsen
shaft,
1,190
0-7
0-06
To drive a tunnel through a hill, the line of the tunnel is set
out over the hill, and carefully levelled from the commencement
at the foot of the hill. When it is thought that the level of the
starting-point has been reached, or, in other words, when the rises
are equal to the falls, an assumed mark is placed, and the levels
accurately calculated. The assumed mark is then moved up or
down the height by which the rises and falls differ, to give the
256 MINE-SURVEYING.
exact position of the floor of the tunnel on the farther side of
the hill.
If the levelling is effected by the theodolite instead of by the
spirit-level, the total of the calculated bases of the various drafts
gives the length of the tunnel.
Sinking Shafts from Several Levels. Similar problems to those
relating to galleries are presented by shafts which have to be
sunk from several levels. If the shaft to be sunk is near an
existing shaft, the problem is comparatively simple, as it is then
merely necessary to drive headings from that shaft at different
levels until their ends reach the axis of the shaft to be sunk.
The conditions are not always so favourable ; the shaft to be
sunk may be at a considerable distance from any existing shaft.
In such a case, points are selected at each level of the mine-
workings, as near as possible to the shaft to be sunk. From
these points headings are driven to the axis of the shaft. The
length and direction of these headings may be calculated from
surveys made at the various levels of the mine. It is, of course,
necessary that the surveys shall- be made with extreme accuracy
with the theodolite.
This method was employed in the Harz for sinking the Konigin
Marie shaft, the first perpendicular shaft sunk in that district.
In 1851 it was decided by the Government authorities to drive a
deep water-level at a depth of 120J fathoms under the Ernst-
August deep adit, by which the mines of the Upper Harz were
then drained. The new deep water-level was intended to serve
as a great common water-reservoir for the mines of the district.
From this level, which is 324 fathoms below the surface, and 116
feet below sea-level, the water is raised to the Ernst- August adit.
For the reception of the engine for raising the water, it was
decided to sink a new perpendicular shaft, the Konigin Marie
shaft, which should also be utilized for raising the ore from
several mines.
In order to expedite as far as possible this important work,
the shaft had to be sunk from several levels. It was sunk from
the surface to the deep George adit, a depth of 146 fathoms, and
at the same time commenced at a level 202 fathoms below the
surface, and at another 270 fathoms below the surface.
Careful surveys having been made at each level, the shaft was
set-out from the points obtained from the calculated co-ordinates.
The different holings were successfully effected in 1866.
The accuracy of the work was then tested by suspending a
plumb-line in the shaft, and determining the position of the shaft
at the three levels. The plumb-line at the surface was exactly
in the centre of the hoisting compartment of the shaft, at a
MIXE-SURVEYIXG PROBLEMS.
257
distance of 40 inches from each of the lon<
from each of the short sides.
sides, and 70 inches
Designating the shaft as A B D, the distance of the plumb-
line from the sides at the different levels was as follows :
At the surface, .
At the 146-fathom level,
At the 202-fathom level,
At the 2;0-fathom level,
AB CD
Inches. Indies.
40-0 40-0
41-5 38-5
42-6 37-4
408 S9'2
70-0
71-0
70-0
68-6
BT)
Indies.
700
690
70-0
71-4
From these results it follows that the deviation of the shaft
from the vertical was as follows :
At the 146-fathom level,
At the 202-fathom level,
At the 270-fathom level,
1-0
o-o
1-4
1-5
2-6
0-8
Thus, the Konigin-Marie shaft presents a brilliant illustration
of accurate mine-surveying.
The Cubical Content of "a Mine-Reservoir may easily be deter-
mined by the aid of a levelling-instrument. The cubical content
must be calculated so as to ascertain the quantity of water which
the proposed reservoir will hold. In shape, a mine-reservoir
resembles most closely a truncated pyramid. It is therefore
supposed to be cut, at given vertical distances, parallel to the
surface of the water. The cubical content of the reservoir is
then determined from the area of these horizontal sections and
their vertical distance apart.
When a suitable site for the reservoir has been selected, and
the height of the dam fixed, the highest level (1, Fig. 86) of the
water is marked by a stake
fixed, into the dam. The
water-line of the reservoir
is then determined by find-
ing with the spirit-level a
number of points lying in
the level of 1. All these
points are then marked by
numbered stakes. Some 2
to 3 yards vertically below
the first stake, a second
stake is fixed into the dam. Fig. 86.
The contour of the reservoir
at this level is then determined by the spirit-level, and marked
258
MINE-SURVEYING.
by numbered stakes. In a similar way, contours of the reservoir
at lower water-levels are determined and marked out. The
contours marked out by the numbered stakes are then surveyed
by means of the dial, the prismatic compass, or the plane-table,
and laid down on a plan to a large scale. From this plan, the
areas, the cubical content of the reservoir is calculated by means
of the formula V = ^ h (B + ^B b + 6), where A is the vertical
height and B, b the area of the ends.
For example. In the mine-reservoir, shown in Fig. 86, five
horizontal sections were determined at vertical distances of
1-000, 1-050, 1-000, and 0-875 fathoms apart. The vertical
distance from the fifth and last section to the bottom of the
reservoir was 0-375 fathom. Each of the five water-levels were
distinguished by numbered stakes, so marked that all belonging
to one section had the same number. The five horizontal sections
were then surveyed with the compass, and plotted on a suitable
scale (1 : 1,000). The cubical content was then found to be
41814-13 cubic fathoms as shown in the following table :
CUBICAL CONTENT OF A MINE-RESERVOIR.
Level.
Area.
Vertical Distance of
Levels Apart.
Cubical Content.
1
Square Fathoms.
21843-31
Fathoms.
i-ooo
Cubic Fathoms.
18931-11
2
16161-29
1-050
13362-90
3
9577-30
1-000
6825-46
4
4404-34
0-875
2500-50
5
1553-25
0-375
194-16
Bottom.
o-oo
...
...
...
...
41814-13
The cubical content of a dump-heap is found in a similar
manner.
Determination of the Strike and Dip of the Line of Intersection
of Two Veins. It is important to determine the position of this
line, as it is frequently found to be a line near or along which a
run of rich deposit is likely to be met with. It is also of value
MINE-SURVEYING PROBLEMS. 259
in solving problems relating to the dislocations of veins. Rules
for determining by means of spherical trigonometry the strike of
the line of intersection are given in the treatises on mine-survey-
ing by Yon Oppel (1749), Kaestner (1775), and Lempe (1782).
The simplest trigonometrical solution to the problem is that
given by A. Rhodius.*
The problem may be solved by construction. Let a b' and
b" c (Fig. 87) be the lines of strike, at a given level, of the two
lodes dipping at angles of a and of.
In order to determine the line of
intersection, the perpendiculars
i k and I m are let fall in the direc-
tion of the dip of the lodes, and
made the bases of right-angled
triangles, the hypothenuses of
which are inclined at angles of a
and a! respectively, the perpen-
dicular being the same (h) in both
cases. The lines k n and m o are
then drawn parallel to a b' and b" c, and continued until they inter-
sect in the point e. Then e is a point of intersection of the two
lodes at a level which is deeper than the point of intersection b,
by a distance h, and consequently b e is the line of intersection
of the two lodes. The strike of this line can be measured with
the protractor.
By constructing a right-angled triangle with its base equal to
the line of intersection, be, and its perpendicular equal to h,
then the angle at e represents the angle of inclination or dip of
the line of intersection. This angle may be measured with the
protractor.
The preceding construction is generally to be recommended.
The problem may, however, be solved by means of plane trigono-
metry. The following is the solution given by Rhodius : If
b e, as in the first solution, represents the line of intersection of
the two veins a b' and b" c, then e q and e r, lines parallel to i k
and lm, are lines at right angles to the strike of the veins. The
angles which e q and e r form with the line of strike b e of the
line of intersection being indicated by x and y respectively, the
following equations are obtained :
eq = h cotan a; er = h cotan a', . . (1.)
e q = b e cos x ; er b e cos y, . . (2.)
* P reuss. Ztechr., vol. xiv., 1806, p. 119.
2GO MINE-SURVEYING,
and
But
Substituting u + v for x and 11, - v for y, so that u = half x + y
and v = half a; y, the equation 7 becomes
sin (a! + a) cos u cos v
sin (a' a) sin u sin v
= - cotan \ (x + y) cotan | (a; - y).
. sin (a + a') , .. , .
.-. cotan 1 (a; - y) = _ tan -J (a; + y)
cos x ,g an
i4.)
(5.)
(6.)
(7.)
e r cotan
cotan a + cotan
a cos y*
a! cos a? + cos y
cotan a
cotan a cotan
cosy '
a cos x cos y
cotan a
cotan a + cotan
cos y '
a cos x + cos y
cotan a - cotan
cotan a + cotan
of cos x - cos v/'
a' cos a sin a' + sin a cos a'
cotan a cotan
a' cos a sin a sin a cos a'
sin (a' + a)
sin (a' a)
sin (a - a )
In this, 5 represents the value of the angle a be, included by the
lines of strike of the two lodes, so that J 3 = 90 - (ac + y),
.and (# + #) = 90 - $ & The angle 3 is known, and x and y
are found from these two equations.
The angle of dip -^ of the line of intersection is calculated in.
the following way : h be tan -^, therefore,
h h cos x
tan -, = =- =
be eq er
= cos a; = cosy ^ g .
cotan a cotan a' ' ''
In order to employ this formula, the value of the angle x or y
MINE-SURVEYING PROBLEMS. 261
must first have been determined. The angle of dip is found
more conveniently from the formula
sin a sin a' . n , ,
tan 4* = 2 7 T, sm i 5 cos * (a - y).
sin (a + a)
-F0?' example. The strike of a lode is 101 15', and its dip
80 towards south; the strike of a second lode is 170 37i',
and its dip 75 towards west ; required the strike and the
dip of the line of intersection of the two lodes.
By applying the formulae given, the former will be found to bo
62 27J', and the latter 74 15' 26".
The Search for Dislocated Lodes. In following a lode, it
frequently happens that a cross-course is met, and, after driving
through it, the lode is not to be found on the other side. In
such cases it is said to be dislocated or heaved. The two inter-
secting veins seldom form an intersection at right angles ; more
commonly one is inclined to the other. In Cornwall, of 272
cases of intersection, recorded by Mr. W. S. Henwood,* 22'7 per
cent, were intersected but not heaved, 26-2 per cent, were found
by driving to the left hand, and 51 -1 per cent, to the right hand ;
63-5 per cent, were found by driving on the side of the greater-
angle and 12-9 on the side of the smaller angle. The average
distance of dislocation was 16 '4 feet.
The first clear views on the subject were put forward in.
1810 by Schmidt, who stated that dislocations were to be ex-
plained by a sinking of the hanging-wall of the dislocator.
Schmidt's rule, as modified by v. Carnall, is as follows :
If the dislocator is struck on its hanging-wall, it must be
passed through, and the driving continued in the hanging-wall
of the dislocated lode. If the foot- wall of the dislocator is
struck, it must be passed through, and the driving continued
in the foot-wall of the dislocated lode. For obtuse angles of
dislocation, the rule is reversed. The angle of dislocation is the
angle formed by the line of intersection of the two veins, and
that portion of the line of strike of the dislocator which enters-
into the foot-wall of the lode.
On Schmidt's theory, Zimmermann in 1828 based his rule,
which is more convenient to use, as it makes no exception of the
obtuse angle. His construction is as follows :
At the point D (or E), Fig. 88, in which the dislocator A is
cut, erect, on the line of strike and towards the inside of the dis-
locator, a perpendicular line D L (E L') lying in a horizontal plane.
Determine the position of the line M N (M' N') in which the
* Trans. B. Geol. Soc., Cornwall, vol. v., 1843.
262
MINE-SURVEYING.
planes of the dislocator and of the lode intersect. Prolong the
line to N (M') towards the opposite selvage making it D N"
(E M'). Observe to which side the perpendicular D L (E L')
deviates from, the line of intersection when it is directed towards
the opposite selvage, and after passing through the dislocator,
seek the dislocated portion of the lode on the side towards
which the perpendicular D L (E L') falls.
Fig. 88.
The construction is very simple. The line of intersection of
the lode and the dislocator is determined by the method de-
scribed. It is then merely necessary to erect a perpendicular at
the point D (or E). If the line of intersection is to be determined
by plane trigonometry, formula 8 is employed.
For example. On driving along a lode, d c, from d towards c,
Fig. 89, it is found that the lode ends at c, having been dis-
located by a fissure a b. The fissure has a strike /3 of 118 7J',
and a dip a' of 55 towards
, A , "-vx. the south-west, and the lode
\ ^vx, h& s a strike /3 of 150, and a
.^j \..__^>._, ..<-- di P of 82 3U ' towards the
north-east.
The first problem is to
determine the line of inter-
section of the two veins.
The point of intersection i
being found by the process
previously described, c i re-
presents the strike of the
line of intersection. By
erecting a perpendicular c k at the point c, it is evident that
Fig. 89.
MINE-SURVEYING PROBLEMS. 9Q3
tlie lost vein I in will be found, after tlie dislocator has been
passed through, by driving from c in the direction c b.
If the line of intersection is to be determined by means of
plane trigonometry, by employing formula 8, the required line
of intersection will be found to have a strike of 145 6' 23".
If recourse is had to spherical trigonometry, the calculations
are more simple. With c as the centre of a sphere, the sphei'ical
triangle A B C is described, in which the side AB(=p = /3
/3') is in the horizontal plane A c B, A C is in the plane of the
fissure a b, and B G in the plane of the lode c d. Again, c D is
the horizontal projection of the line of intersection S c C, and
C D an arc perpendicular to A B, and from the two right-angled
triangles A C D and B C D,
(1.) tan y sin x tan a, and
(2.) tan y = sin (<f> x) ' tan a.
From these two equations, it is found that
tan a!
cotan x = : + cotan p.
tan a sin
Numerical values being substituted,
cotan x = . co on? 550 0.*^ + cotan 31 52 i'
tan 82 30 sin 31 52
.-. x = 26 58' 53"
Now, the strike of the fissure ab is 118 7|'; therefore, the
strike of the line of intersection S c C = 118 7' + 26 58' 53" =
145 6' 23".
If, in the example given, it was found necessary to drive
11 yards from c towards b, in order to reach the lost lode at I,
the sinking H of the hanging-wall of the dislocator, must,
according to Zimmermann, have amounted to
_ 11 -sin 31 52^"
~ cos 55" cos 31 52 i" + cotan 82 30' sin 55
= 9-76381 yards.
Irregularities of Seams and Beds. Bedded deposits are
frequently found to be interrupted by faults, causing a cutting-
off of the bed, and a displacement of it up or down. A fault of
this kind is termed a hitch or trouble'; if on a very large scale,
a dyke. In order to represent the direction of the displacement,
the fault is known as an up-throw or down-throw.
The alterations in position of stratified deposits undergone
264: MINE-SURVEYING.
since their deposition, may be divided into three classes
(1) Faults caused by folding of the strata; (2) throws or faults
caused by fissures ; (3) displaced faults. Faults of the first and
third class are only met with in folded strata ; faults of the
second class also occur in horizontal strata. All these faults
give rise to dislocation of beds and seams, and rules have been
formulated, like those for lodes, for ascertaining the direction in
which to search for the displaced bed or seam.
Folded faults are, as A. Heim first showed, merely the final
result of folding. In many cases, the progressive steps may be
observed in the strike of the same fault. The mode of formation
of such faults must therefore be considered, not as an hypothesis,
but as an absolute well-established fact. Thus, at the Maiisfeld
Mine near Langendreer, a folded fault is very apparent in a
certain cross-cut, whilst 162 feet further north it becomes a
simple folding. Folded faults can only occur in beds and seams,
but not in veins, for these, being filled-up fissures, are of more
recent age than the country rock, and its foldings. With faults
of this kind, the same seam is frequently met several times at
one level. If a fault is recognised as belonging to the folded
class, the direction in which to search for the displaced seam
may easily be decided by means of a sectional sketch .
Throws or fissure faults, are those which have arisen entirely
through the slipping down of the strata on the hanging-wall of
the dislocator. The rule for ascertaining the direction in which
to search for the displaced seam is as follows: If the dislocating
fissure is met on its hanging-wall, the displaced seam must be
sought in the direction of the hanging- wall of the strata after the
fissure is passed through. Conversely, if the fault is dipping
from you, you must proceed downwards. Zimmermann's con-
struction is applicable to dislocated seams as well as veins.
The third class of faults were first observed by Professor
Koehler in the Westphalian coal-fields, and subsequently in the
lodes of the Harz. tinder the term displaced faults (Verschie-
bungen) are to be understood those dislocations, in which a part
of the previously folded or vertical strata, with the seams
contained therein, was torn away, by the force that caused the
folding, from another part of the strata, and slid or pushed away.
In such cases, the seams and the strata appear curved in the
direction of the movement, and gradually thinned out, though
no folding is to be observed, as is the case with folded faults.
In addition, the plane of disruption exhibits traces of the
movement in the form of slickensides and striations.
These displaced faults may thus be easily distinguished from
other faults. A fault having been recognised as belonging to
MINE-SURVEYING PROBLEMS. 9(55
this category, the displaced portion of the seam may be found by
crossing the plane of disruption, and seeking the shifted portion
of the deposit on the side towards which that plane is inclined.*
Subsidence and Draw. Interesting problems are presented by
the surface subsidence caused by the removal of coal in the
mine. By means of very accurate levelling, Mr. J. S. Dixon t
made a valuable series of observations at Bent Colliery on the
subject of the subsidence and draw from working the coal ; the
facts disclosed upsetting many old rule-of-thumb ideas on the
subject. In order to arrive at correct conclusions in an inquiry
of this kind, the best way is to select a line for a section on the
surface, and peg it off, or have some other means of fixing levels
that can be tested from time to time.
The line selected at Bent was at right angles to the advancing
workings, and as nearly as possible on the level course of the coal.
Pegs were put in at first every 100 feet, and afterwards every 50
feet. The Ell coal at this colliery was worked by the pillar-and-
stall method up till the middle of 1831, when the removal of the
pillars was commenced. It was, however, some time before this
operation reached the line along which the section was taken.
The excavation was 5 feet 6 inches in height, and the superin-
cumbent strata were allowed to fall and fill it up. The strata
are of a firm nature, and the surface is mostly boulder clay.
The original level of the surface before the pillars were
removed is shown by the figures in the table on p. 242. The
pillars were removed for a distance of 240 feet back from the
solid coal on January 21, 1882, and no subsidence of the surface
had ensued. On May 27, 1882, the levels showed the maximum
subsidence to have been T80 feet at peg 1650, 145 feet back
from the face, and the draw, that is, the disturbance at the
surface beyond the point of excavation, 60 feet outwards from a
point perpendicularly above the working face. On November
14, 1882, the face was 610 feet from the solid, and the subsidence
from the original level was as shown in the table. On April 15,
1883, the face was 750 feet from the solid; on November 27,
1883, it was 1060 feet distant; and on October 23, 1884, the
removal of the pillars had been completed for some months, and
the face was 1230 feet from the solid. The levels were again
* On the dislocations of veins, beds, and seams, consult S. C. L. Schmidt,
Theorieder Verschiebungen dlterer Gange, Frankfurt, 1810 ; C. Zimmermann,
Die Wiederausrichtung verworfener Gange, Lager und Flotze, Darmstadt,
1828; R. von Carnal!, Karstens Archiv., vol. ix., 1842, p. 3 ; H. Hoefer,
Oestr. Ztschr., 1881., p. 168, translated by R. W. Raymond, Trans. Amer.
Inst. M. E., 1882 ; R. Dannenberg, Ueber Verwerfungen, Saarbrucken, 1883;
G. Koehler, Storungen der Gange, Flotze, und Lager, Leipzig, 1886.
t Trans. Mining Inst. Scotland, vol. vii., 1886., p. 224.
263
MINE-SURVEYING.
taken, on June 17, 1885; the workings being in the same
position as they had been for about a year. On December 4,
1885, it was found that the subsidence had practically ceased,
and the draw had not altered.
SUBSIDENCE AT BENT COLLIERY.
PEG.
ORIGINAL
LEVEL OF
SUEPACE.
SUBSIDENCE FBOM ORIGINAL LEVBL AT
1881.
14th Nov.,
1882.
5th April,
1883.
27th Nov..
1883.
23rd Oct.,
1884.
17th June,
1885.
4th Dec.,
1885.
600
640-6
...
...
...
0-25
0-35
0-45
650
648-9
...
...
...
0-35
0-60
0-60
700
657-2
...
...
...
0-77
0-94
0-94
750
664-6
...
...
1-18
1-27
1-40
800
667-5
...
...
0-23
1-37
1-75
2-00
850
673-1
...
0-63
1-50
2-24
2-34
900
675-6
...
1-13
2-57
2-74
2-82
950
676-0
...
...
1-61
2-97
3-14
3-22
1000
677-1
...
2-10
3-27
3-49
3-60
1050
677-3
... -
2-43
3-32
3-64
3-75
1100
678-8
050
2-80
3-52
3-80
4-00
1150
679-7
0-70
2-93
3-57
3-81
3-92
1200
680-6
1-20
3-52
3-52
3-52
1250
680-9
0-60
1-60
3-08
3-45
3-45
3'45
1300
6792
0-40
2-00
3-03
3-42
3-42
3-42
1350
677-9
1-60
2-25
3-00
3-27
3-27
3-27
1400
677-5
1-60
2-45
3-83
3-17
3-17
3-17
1450
680-8
2-30
2-90
3-42
3-42
3'42
3-42
1500
680-1
...
3-05
3-05
3-05
3-05
3-05
1550
677-1
2-90
3-20
3-20
3-20
3-20
3-20
1600
675-5
3-00
3-00
3-00
3-00
3-00
3-00
1750
672-8
2-80
2-80
2-80
2-80
2-80
2-80
1850
663-4
1-70
1-70
1-70
1-70
1-70
1-70
1950
648-6
0-60
0-60
0-60
0-60
0-60
0-60
2000
649-7
0-04
0-04
0-04
0-04
0-04
0-04
MIXE-SURVEYING PROBLEMS. 267
The conclusion arrived at is that subsidence from the removal
of coal in this case attains its maximum towards the centre of
the excavated space, and gradually decreases in each direction.
The maximum subsidence was 4 -00 feet, and the average from
peg 1,000 to peg 1,600 was 3-76 feet, or 73 and 68 per cent,
respectively of the height of the excavation. The wave of maxi-
mum subsidence regularly followed the working face at an
average distance back of 186 feet, or 1 foot horizontal for each
3^ feet perpendicular. The permanent lengths of the draw may
be taken as 100 feet (Nov. 14, 1882) on the one side, and 83 feet
on the other (Oct. 23, 1884). At these points, the depth to the
coal was 650 and 646 feet, representing a draw of 1 horizontal
for each 6*5 feet perpendicular, and of 1 horizontal for each 7 '78
test perpendicular respectively.
The coal at Bent, it should be noted, dips at right angles to
the line of section at an inclination of about 1 in 20.
The question is one of great importance to mine-surveyors in
relation to the effect, on the surface, of mineral workings, and
to the area of coal that should be left to prevent damage to
buildings. It is consequently highly desirable that similar
investigations should be made in other coal-fields.
From a careful study of the subsidence occurring in the Saxon
coal-field, R. Hausse,* of the Zaukeroda Colliery, has arrived at
some interesting results. The direction of the plane of fracture
occurring on the breaking of undermined strata is determined by
the angle of fracture that is, the angle made by the plane of
fracture with the horizontal plane. Then if <p is the angle of
fracture, and j8 the dip of the strata, the following equation is
obtained :
1 + cos 2 13
tan <p =
sm
Then, if (3 is equal to 0, this equation becomes tan <p = oo, and
<p = 90; in other words, in horizontal strata the plane of fracture
coincides with the line of gravity. When j8 = 90, the equation
again becomes tan <p oo, and <f> = 90 ; that is to say, in vertical
strata, the plane of fracture coincides with the line of gravity.
By means of the formula, the angle of fracture may be calculated
in any case from the dip of the strata. In this way the following
results are obtained :
* Saechs. Jahrbuch, 1886, p. 111.
268 MINE-SURVEYING.
When/3 = then = 93 00'
10 85 10'
20 80 30'
30 76 10'
40 73 00'
45 71 40'
50 70 5tf
60 71 00'
70 74 00'
80 80 50'
90 90 00'
To show how these theoretical results compare with results
actually obtained in practice, the following example may be
cited : For supporting the Siemens' glass works at Doehlen in
Saxony, a safety pillar of 16 yards horizontal breadth was left,
and, in addition to this, the last stall up to that pillar was
packed with gob to a horizontal breadth of 16 yards. Assuming
that a dense gob-packing is compressed to - 6 of its original
volume by the pressure of the superincumbent strata, the
gob-pillar, for purposes of safety, represented a coal-pillar of
16-0 x 0-6 = 9-6 yards in breadth. Consequently the coal- pillar
and the gob-pillar together had the same effect in supporting the
buildings as a coal-pillar of 16'0 + 9*6 = 25*6 yards in breadth.
Notwithstanding the pillars, the surface was found to have sunk
considerably.
The thickness of the coal seam was 4 yards. It dipped 12
towards "the west, and had a perpendicular depth from the
surface of 180 yards. Calculated from this depth and the width
of the 25-6-yard pillar, the angle of fracture <p is found to be as
follows :
cotan?>
The dip /3 of the strata being 12, the theoretical formula gives
tanp = i + fr 312 ?!.;^ 84-20"
sin 12 cos 12
or 2 20' greater than the result obtained practically.
The theory of subsidence is ably discussed by Gallon,* who
* "Lectures on mining delivered at the School of Mines, Paris," by
J. Gallon, translated by W. Galloway and C. Le Neve Foster, vol. ii.,
London, 1881, p. 304.
MINE-SURVEYING PROBLEMS. 269
lays down the following proposition: If the coal has been
removed over a certain area, and the space filled up in a seam
worked by the methods adopted in Belgium and Northern
France, the subsidence of the roof on the filling-up causes
fractures along the perimeter of the area at right angles to the
plane of stratification. The subsidence of the ground within the
cylindrical space indicated by those fractures continues gradually
without sensible diminution in amount quite up to the surface,
whatever may be the depth of the mine.
270 MINE-SURVEYING.
CHAPTER XVIII.
MINE PLANS.
Plan and Section. For the representation of mine workings
a plan and a vertical section are required. The plan is a
projection of the mine workings on a horizontal plane ; the
section is a projection of the workings on a plane running
parallel to the main longitudinal direction of the mine. With
complicated and irregular mines, one section is not sufficient. In
such a case, several sections have to be made in given directions.
(a.) Metalliferous Mines. Four drawings are necessary in
order to represent a metalliferous mine (1) the ground plan ;
(2) the working plan; (3) a longitudinal section ; (4) a transverse
section.
The ground plan gives a general representation of the whole
concession. It may be on a scale of about 3 chains to the inch,
and on it the boundary of the property of every land owner
should be distinctly marked, and all the lodes indicated. The
working plan gives a general view of the underground workings,
as they would be seen from above if the ground was transparent.
This plan should be drawn on a large scale, 4, 5, 8, and 10
fathoms to the inch being scales used for the purpose. The
longitudinal section is drawn on the supposition that a section
of the ground is cut away, and that a side view of the mine is
exposed. All the vertical shafts, the stopes, the dip of the ore-
courses, and the surface-line with elevations of the mine
buildings, will be correctly shown. The levels, diagonal shafts,
and winzes will have a false appearance. The levels will appear
perfectly straight however crooked their course may be, the
diagonal shafts and winzes will appear perpendicular, and the
cross-cuts will be represented as open doorways. The transverse
section is of great value, as it shows the dip of the ore-courses.
In the transverse section, the view is taken at one end of the
workings, at right angles to the longitudinal section. Thus, the
inclination of the shafts and winzes sunk on the lode is shown.
The levels driven on the lode will be represented as open
doorways; the cross-cuts are correctly shown; and all variations
in the dip of the lode may be seen from the surface to the
bottom of the mine.
MINE PLANS.
271
Fig. 90. Plan and Longitudinal Section of a Metal-Mine.
272
MINE-SURVEYING.
When the lode is very flat, as at the Cornish mines of \Vheal
Jane and Wheal Kitty, the section is made along the lode. In
this way a true idea is given
^/////////y//////A \MW////W//7?7 of tlie g round worked ; but
an erroneous one with re-
gard to depth. This
method of projecting the
section is necessary to en-
able the ground stoped
away to be shown, as when
the lode is so very flat,
the back of one level in
a vertical section would
touch the floor of the next.
As a rule, lodes are so
vertical that a perpendi-
cular plane may be taken
for the section.
The workings of a metal-
liferous mine are repre-
sented in Figs. 90, 91, on
a scale of about 20 fathoms
to the inch. The mine has
an adit-level and below
that, 10-, 20-, 30-, 40-, and
50-fathom levels. The adit
is north of the shaft. The
engine shaft contains the
pumps which lift the
water from the sump or
Fig. 91. Transverse Section.
lowest point of the shaft to the adit-level, which comes out
to the surface on the adjacent hill side. This shaft was
sunk vertically to intersect the lode at the 10-fathom level,
a cross-cut being driven to the adit. Then, instead of con-
tinuing vertically, necessitating the driving of cross-cuts to the
lode, the shaft follows the latter. The shaded portions shown
in the longitudinal section represent the projection of the ore
masses, removed by stoping. In practice, such portions are not
shaded but coloured purple for tin, green for copper, blue for
lead, &c. Between the 10- and 20-fathom levels a mistake arose,
the winze and rise did not meet owing to an error of the
dialler.
It will be found advisable to colour all the levels on one lode
the same tint. Formerly it was the general practice to colour
each level a different colour, the adit-level being blue, and
MINE PLANS. 273
the levels below it red, green, yellow, violet, and brown in.
succession.
No scale is prescribed by law for the plans of the British
metalliferous mines. The variety of scales used presents great
difficulties with regard to the comparison of the plans of different
neighbouring mines. In many districts, the plans are prepared
in a slovenly and unsatisfactory manner. This is notably the
case in the Derbyshire lead mines. There, according to Mr.
A. H. Stokes, H.M. Inspector of Mines for that district, the
majority of the mines have no plans whatever. Even at the
larger mines which have plans, they are very roughly drawn
and rarely indicate the extent to which the ore has been worked.
The variable width of the levels is not shown, the latter being
represented by a coloured line. The position of the best and
most profitable parts of the mine, that is, the width to which
the ore has been extracted, is shown as an ordinary narrow
heading. In. fact, the plans are not true representations of the
mine, but merely represent the length of underground tramways.
Sections of the mine are seldom made.
(b.) Colliery Plans. By the Coal Mines Regulation Act, 1887,
the owner, agent, or manager of every colliery is compelled to
keep, in the office at the mine, an accurate plan of the workings
of the mine up to a date not more than three months previously,
and the general direction and rate of dip of the strata, together
with a section of the strata sunk through, or if that be not
reasonably practicable, a statement of the depth of the shaft,
with a section of the seam. Every such plan must be on a scale
not less than that of the Ordnance Survey of 25 inches to the
mile.
Representing collieries on a plan is a much more simple
operation than representing metalliferous mines. The workings
are projected on a horizontal plane. The coal withdrawn is
coloured dark, and the direction of the air-current indicated by
arrows. The intake air-current is coloured blue, and the return
air-current red. The water-courses may be coloured green,
drowned waste also green, and faults bright red shaded off on
the dip. Main doors may be indicated by a D in blue, main
stoppings by blue lines, and caution-boards by a C in red. The
heights of the different points above the level of the shaft-bottom
should be shown in red figures, and those below the level of the
shaft-bottom in blue. The signs shown in Fig. 92 are employed
on colliery plans.
When two or more seams are worked one above the other, and
are shown on the same plan, they are distinguished by means of
colour.
18
274 MINE-SURVEYING.
ftrtftio/i ei Air (arrvnt sAotm I/MS
JJtjy of Mine
ast-' tfhaft. ....... .
ff/' J?/wjy-jwS. ....
/(op/tin fr
JPoors j
Wovefe/i
Ca/tra-ff
Fault* ,-- .,
Fig. 92.
Admirable illustrations of the manner in which colliery plans
should be executed are afforded by the plans which accompany
the annual reports of H.M. Inspectors of Mines.
Surface Plans. The surface plan of a colliery or metalliferous
mine requires great distinctness of detail. If the scale of about
25 inches to the mile is adopted, the conventional signs used on
the maps of the Ordnance Survey should be employed. If the
scale is lai-ger, care must be taken to give the conventional signs
such dimensions as will accord with the scale of the plan.
Buildings are coloured crimson lake for houses, and dark grey (a
light wash of indian ink) for outbuildings. The mine buildings
may be distinguished from other buildings shown on the plan
by having a darker tint of red. In representing objects on the
plan, their natural colours are sometimes adhered to ; in other
cases a conventional colour is used. Thus, for grass land, a flat
MIXE PLANS. 275
tint of green (Hooker's No. 1) is employed; it is made of gam-
boge and indigo. Cultivated land is represented by a flat tint of
burnt sienna. Adjoining fields are slightly varied in tint,
furrows sometimes being indicated by coloured strips. Lakes and
rivers are coloured light blue (cobalt), with a darker tint on each
side. Marshes are represented by the blue of water, with hori-
zontal spots of grass green. Roads are coloured with a light
wash of burnt sienna, or yellow ochre. Hedges are represented
by green clots for bushes, brick walls by a red line, and woodeni
fences by lines of a neutral tint. In large scale plans, the~
Cornish hedge, some 6 feet in width, is shown by two lines the
true distance apart, with a wash of neutral tint along each side.
In all cases the shadow is put in. The boundaries of the mine -
concession are indicated by strips of colour.
When the underground workings are drawn on the surface-
plan, in the latter there should be no more colouring than neces-
sary. It will be found sufficient to colour the roads, buildings,
and water.
(c.) American Colliery Plans. In Pennsylvania the law requires
all anthracite colliery owners to prepare maps of all workings on
a scale of 100 feet to an inch for the use of the mine-inspector.
This scale is rather too large for convenient use, and consequently
most of the working maps used for reference are constructed on,
a scale of 200 or 300 feet to the inch. These maps generally
show all the important surface features, buildings, streams, roads,
and railways, as well as the underground workings. The latter
are commonly drawn in blue, red, or green ink. When several
beds are worked, the workings are shown by different colours
a device especially necessary when the workings on one seam are
above or below those opened on another bed. In addition to the
general map showing all the workings, separate maps showing
the workings on each seam are usually made. The survey-lines-
are plotted with a vernier-protractor, or a protractor of very
large size, and the results checked by latitude and departure cal-
culations. Tracings or blue-prints of the workings are supplied
from time to time to the viewer. When not in use the plans are
stored in large fire-proof vaults. The survey-notes are copied
into office record books for future reference. With the exception
of the work done by the U.S. Coast Survey, no other surveys in,
America can compare in accuracy with those of the anthracite
mines.
The sharp foldings of the carboniferous strata of the an-
thracite region of Pennsylvania, have made the study of the
structural geology of that region one encompassed with great,
difficulties. The necessity of having some definite information
27G
MINE-SURVEYIXG.
regarding the structure of the coal beds, before successful mining
operations can be prosecuted, induced Mr. C. A. Ashburner* to
introduce in 1880 a new method of representing on surface
maps the underground structure of the coal beds, from which
could be ascertained the situation of the outcrops of the beds,
the position of the synclinal and anticlinal axes, their depths in
special coal beds below the surface of the ground, and the dip of
the bed from the crest of the anticlinal to the bottom of the
synclinal. This was accomplished by contour-curve lines drawn
along the floor of the coal beds. The contours were obtained
from elevations determined in the areas where the coal beds
were mined, and from exploring the shafts,
A p bore-holes, and surface exposures in the
areas where no extensive mining had been
done. In areas where no underground
exploration had been made, the positions of
the contours along the floors of the coal beds
were deduced from surface exposures and an
extension of the structure from explored
areas.
Importance of Correct Sections. The im-
portance of keeping an accurate section of
a mine is shown by a serious accident that
occurred at Pantgwyn mine. On February
17, 1885, while three men were at work
sinking a new shaft, water broke in suddenly
and unexpectedly, and drowned them. The
exact nature of the casualty will be best
understood by means of Fig. 93, representing
a cross-section of the mine. ABC is the
old pumping and winding shaft, sunk perpendicularly for the
first 20 fathoms, and then following the dip of the vein. In
1884, owing to the stoppage of some neighbouring mines, the
pumping engine at Pantgwyn was unable to cope with the water,
which gradually filled the workings. The owners then resolved
to sink a new perpendicular shaft D E, and provide it with
more powerful pumping machinery. It was intended that the
new shaft should strike the Pantgwyn lode in virgin ground
below any of the existing workings, which were to be drained
gradually by percolation of the water through the porous vein-
stone. In February, 1885, the new shaft had reached a perpen-
dicular depth of 62 fathoms from the surface. The old shaft
was then supposed to be in the position indicated by the dotted
Trans. Amer. Inst. M.E., vol. ix., 1881, p. 50.
MINE PLANS. 277
lines, and the distance between the two shafts at E was reckoned
to be 40 feet. On examining the shaft as soon as it had been
cleared out, the Government Inspector of Mines, Dr. C. Le Neve
Foster, found that the thickness of the barrier was only 9 feet ;
the section of the mine being incorrect. It naturally appeared
to him very strange that such an error should have been made
in a small survey of recent date, with two shafts less than 50
yards apart at the sin-face, until he ascertained that the inclina-
tion of the shaft had never been measured below the 40-fathom
level. The drivages at the 55-fathom level and the 70-fathom
level had been deliberately laid down on the plan just as if the
shaft had been correctly dialled. The primaiy cause of the
accident was, without doubt, 'the want of a correct survey. In
reporting on this accident, Dr. Le Neve Foster points out
specially that it was not a case of approaching old workings, whose
exact position was unknown, or imperfectly known, owing to
the abandonment having taken place before there was any
statutory obligation as regards the keeping of plans ; but here
was a new shaft, started by the same company and the same
agent, within 50 yards of their own workings, which had been
discontinued only a few months before.
Uniformity of Scale and Conventional Signs. In Belgium and
in France the law demands that all mine plans shall be laid
down on a scale of 1 : 1000. The surface plan is prepared on the
same scale as that of the underground workings In Prussia,
the scale imposed varies in the different mining districts from
1 : 500 for metalliferous mines up to 1 : 1600 for collieries. In
Austria, the scale for mine plans is usually 1 : 720. For com-
parison, it may be added that the scale for colliery plans in
Great 'Britain must not be less than 1 : 2500. Previous to 1888
the smallest scale allowed was 1 : 1584. In Ameri'ca, the scale-
imposed in Pennsylvania for the anthracite mines is 1 : 1200.
The usual scale prescribed in the various States for the prelimi-
nary plan of a metalliferous mine-claim is 1 : 2400.
It is desirable to have not only a uniform scale, but also uni-
formity in the conventional signs used in the plans. With this
aim, typical mine plans have been published in Belgium by Mr.
J. van Scherpenzeel-Thim ; in Germany by Professor Schmidt,,
of the Freiberg School of Mines ; in Hungary by Mr. Pech, the
director of the Schemnitz mines, and in Sweden by Mr. G. Nor-
denstrorn. In Prussia the law demands uniformity in the-
drawing of mine plans, and special rules are issued by the Govern-
ment for the purpose. Unfortunately, there is a great want of
uniformity in British mine plans in the various mining districts.
If plans were always drawn after the same model it is evident
278 ' MINE-SURVEYING.
that the working would be more uniform, and that each new
mine-manager would be enabled to decipher more readily his
predecessor's work. The owners, and other persons interested in
mineral property, would thus be able to gain a clear understand-
ing of the plans, and successive generations would profit by the
stores of information thus recorded. Uniformity of system in
the plans, too, greatly facilitates the construction of general
maps of mining districts.
Preservation of Plans. So long ago as 1797 the importance of
a systematic mapping of mines was urged at Newcastle by Mr.
Thomas, and since that date the value of such a system has
frequently been dwelt upon for the purpose of diminishing the
probability of the recurrence of fatal accidents in collieries, and
of prolonging the duration of the coal resources of the United
Kingdom. It is always a matter of regret that faithful records
of all underground work in important mining districts have not
been carefully preserved. The importance of the preservation of
such records was strongty urged by Mr. T. Sop with in 1844. In
the United Kingdom plans of all abandoned mines are now
carefully preserved. The Coal Mines Regulation Act (1887)
requires that where any mine or seam is abandoned, the owner
of the mine or seam at the time of its abandonment shall, within
three months after the abandonment, send to a Secretary of
State an accurate plan showing the boundaries of the workings
of the mine or seam up to the time of the abandonment, and the
position of the workings with regard to the surface, and the
general direction and. rate of dip of the strata, together with a
section of the strata sunk through, or if that is not reasonably
practicable, a statement of the depth of the shaft, with a section
of the seam. Every such plan must be on a scale not less than
that of the Ordnance Survey scale of 25 inches to the mile, or
on the same scale as the plan used at the mine at the time of its
abandonment.
At the Home Office the mine plans are preserved, rolled in
cylindrical lacquered tin cases, closed with a lid, on which a
number is painted. The cases are placed side by side on shelves,
so that their numbers can be at once seen. At Freiberg a similar
plan is adopted. This method is very cumbrous. A better
method is to keep the plans without being rolled or folded in
portfolios. At Przibram, in Bohemia, the plans are kept in a nest
of drawers, each drawer forming the frame of a plan placed
between two sheets of glass.
Sopwith entirely dispensed with the large and unwieldy rolls
of paper on which the workings of collieries and metalliferous
mines are usually projected, by drawing the plans on imperial
MINE PLAXS. 279
drawing paper. Each sheet was divided into squares of 20
inches, forming an area of 400 square inches. An inch margin
was left at the top and bottom of the sheet, and 3 inches at one
side for binding a series of plans into a volume. At the other
side a margin of 1 inch was left, with a column 5 inches wide for
the insertion of written descriptions, scales, titles, references,
and other explanations of value as permanent records, with
which the plan itself ought to be encumbered as little as possible.
In this way, plans are kept perfectly flat, and their accuracy is
not affected by the tension of the paper caused by frequent
rolling. Eolled plans, on the other hand, soon become so
cracked and defaced, as greatly to impair the clearness and
accuracy of the plotting, whilst their bulk is a hindrance to
frequent inspection and to the plotting of new workings.
Practical Hints for Constructing Mine Plans. The paper on
which the plan is drawn should be the best hard drawing-paper.
If plans are required on canvass, the paper should be mounted
and carefully dried before the plan is begun, in order that the
contraction in drying may not alter the lines. To mount the
paper, a piece of linen or calico, rather larger than the plan is
required to be, is placed on a tilted table with a flat surface. A
strip, l]s inch wide, at the edges is glued, and pressed on the
table, the linen being at the same time pulled tight. With large
sheets, two persons pulling at opposite sides are required. The
paper is then placed with its right side on the linen. Its back
is then pasted until the paper becomes quite limp with the
moisture soaked in. The paper is lifted up carefully, and
placed with the pasted side on the linen, and pi*essed from the
centre to the edges. The rubbing-down may be done with the
hand or with a cloth; in either case a sheet of clean paper is inter-
posed. Paper thus mounted may be drawn upon nearly as well
as when stretched on a board. To give an edge for the T-square,
if required, a straight edge may be temporarily nailed on.
If several sheets of drawing-paper have to be joined end to
end, the edges to be joined should be reduced to half their
thickness. This may be done with a knife or with sand-paper.
In mounting and joining drawings, a great deal depends on
the paste employed. It must be sufficiently liquid and contain no
lumps. To prepare it, a small portion of good starch is com-
pletely dissolved in as small a quantity as possible of cold water,
and to this solution boiling water is poured with continual
stirring of the starch-paste thus formed.
Plans may be varnished by applying several coats of isinglass
size, allowing each to dry before applying the next, and finishing
with a coat of Canada balsam diluted with oil of turpentine.
280 MINE-SURVEYING.
The lead-pencil used for plan-drawing should not be veiy hard
nor very soft. The degree of hardness marked H H is the most
suitable. The quality may be tested by holding the point in a
candle-flame. Good pencils suffer no change in this experiment,
whilst bad leads burn away to ash with a sulphurous odour. It
is best to use two pencils; one with a flat or chisel point for line
drawing, and one with a point in the shape of a perfectly acute
cone for sketching.
Short lines should be drawn with the rolling parallel ruler.
The plotting scale should never be used for this purpose.
Straight edges, \ised for drawing long lines, may be tested by
drawing a line along the edge of the ruler, then laying the ruler
on the other side of the line, with the ends exactly upon it, and
drawing a line in the same manner. If the straight-edge is true,
these lines will exactly coincide ; if not, the error is rendered
apparent by being doubled.
For inking-in plans, Indian ink is always employed, as it does
not corrode the steel points of the instrument and preserves its
colour unchanged. The best ink, as imported from China, has a
finely granular texture and a conch oidal iridescent fracture.
When rubbed with water on a slab, it is not gritty, and smells
like musk. Inferior ink smells like camphor, and the worst ink
smells like soot and glue. The latter is useless for plan-drawing,
as it runs when other colours are passed over it. Indian ink
is prepared for use by rubbing it with water on a perfectly
smooth slab or saucer. It should only be rubbed backwards
and forwards, as, for some unexplained reason, rubbing it round
and round hardens it. The preparation must be perfectly black ;
but after it has become black, further mixing renders it viscous.
For removing pencil lines and for cleaning the paper, native
india-rubber, vulcanised india-rubber, or stale bread may be
employed.
The drawing instruments should be of the best workmanship,
as accurate results cannot be obtained with imperfect instru-
ments. Very few instruments are required, a pair of compasses
with a steel drawing-pen and a pencil-leg to fit, and a drawing-
pen being all that is required for plan-drawing. Bow-compasses
are unnecessary. A pair of turn-in compasses constitutes a set
of instruments sufficient for most mining purposes.
The best compasses are those which are sector-jointed. The
greatest care should be taken to clean steel drawing-pens every
time they are put away, and common ink should never be used
in them. It will be found desirable to have two of these instru-
ments, one for fine lines and another for thick lines. When the
proper opening for fine lines has been found, it is thus unneces-
MINE PLANS. 281
sary to change it, as the pen can always be cleaned by passing a
piece of paper between the nibs.
The most useful colours for mine plans are for surface boun-
daries and underground workings, crimson lake, indigo, cobalt,
Prussian blue, burnt sienna, gamboge. Purple, green, and other
tints may be obtained by mixing. Opaque colours, such as ver-
milion, red lead, and ultramarine, should be avoided. The end
of the cake of colour is moistened, and rubbed with a drop of
water. . This is afterwards diluted to the proper tint. The art
of laying-on a flat tint consists in allowing the coloured water to-
flow uniformly over the paper. This is done by applying, with a
large camel's-hair brush, kept always moderately full, a tint
across the upper part of the portion of the plan to be coloured,
and by continuing it downwards from right to left and left to
right alternately, never letting the edge dry. The drawing-
board should be inclined towards the draughtsman, and the paper
is moistened with water before the colour is applied if the portion
to be coloured is irregular. A little prepared ox-gall used with
the colours obviates the difficulty which often arises from the
smoothness or greasiness of the paper. It is, however, almost
impossible to use it too sparingly. In drawing the outlines, care
should be taken that there is always a piece of clean paper
between the hand and the drawing, in order to prevent any
greasiness of the paper.
Neat and distinct lettering is very essential in all plans. It
frequently happens that a perfectly accurate plan is absolutely
spoiled by a badlv printed title. The formation of letters
requires long practice. Lines drawn in pencil to be afterwards
erased, will be found useful as guides. No style of lettering is
more effective than the Egyptian or block letters, in which every
line is of the same width. By the aid of copper stencil plates a
great saving of time is effected. The lettering should be in lines
parallel to the bottom of the plan ; except the names of lodes,
rivers, and roads, of which the general course should be followed.
The plan may be enclosed in a rectangle by a border, which
usually consists of two parallel lines, one heavy and the other
finei-. The simplest border is the best, and time should not be
wasted over ornamental corners to embellish the plan.
The plan is usually drawn so that the top of the paper repre-
sents the north. Whether this is the case or not, a meridian-
line should always be drawn. The north point is sometimes
drawn in the form of an ornamental star. When it represents
the magnetic meridian, the abbreviation mag. mer., with the date
and declination, should be written by the side of it. A scale
should invariably be drawn on the plan, with a description of
it written above.
282 MINE-SURVEYING.
Copying Plans. Plans may be copied by means of geometrical
methods employed to detei-mine the points of the plan by
intersections or by co-ordinates. The operations are, however,
very tedious. In preference to geometrical methods, there are
several mechanical methods which should be employed.
1. Copying by Tracing. A large sheet of glass is fixed in a
wooden frame, and inclined at an angle of 25 before a window
or a lamp. The plan to be copied is covered with drawing-paper,
and placed on the pane of glass. The lines of the original can
thus be traced with facility.
2. Copying on Tracing-Paper. A sheet of tracing-paper or
tracing-cloth is fastened with drawing-pins over the plan to be
copied. The lines are then copied in indiaii ink, a set square
being used for ruling the straight lines. The tracing is mounted
011 white paper, and colour is then applied. If tracing-cloth is
used, it will be found advisable to apply the colour to the back
of the tracing.
In copying plans on tracing-cloth, considerable difficulty is
experienced, owing to the greasy nature of the surface, in.
getting the ink to run freely. This can easily be obviated by
sprinkling the surface of the cloth with finely-powdered chalk
or pipeclay.
3. Copying by Transfer. The transfer-paper used for this
purpose, is made of very thin paper, one side of which is
rubbed with black-lead powder, smoothly spread with a cotton
rag. The transfer-paper is placed with its prepared face down-
wards on the clean paper. Over it is placed the plan to be
copied, and all the lines are gone over with an agate point, or
other blunt-pointed instrument. If the original cannot be
treated in this way, a tracing of it must be employed. In this
way, a copy of the original plan is obtained in black lines, which
may be afterwards inked in.
4. Pricking-Through. In this method, the clean paper is fixed
on a drawing board, and the plan over it. All the angular points
in the latter are then pricked through with a veiy fine needle.
The points obtained on the clean paper in this way are joined
up, and the plan inked in.
5. Copying by Photography. Photographic processes present
the advantages of rapidity and fidelity of reproduction. The
apparatus necessary includes thin bluish tracing-paper, printing
frames of thick plate-glass hinged at the back, with a piece
of thick soft felt for equalising the pressure exerted by the
springs or clamps, a developing bath, non-actinic arrangements
(yellow window blinds by day, and a ruby lantern by night),
and cases for storing paper. Drawings on ordinary paper may
MINE PLANS. 283
be copied if exposed to light sufficiently long. Instead of springs
or clamps on the printing frame, use may be made of Street's
pneumatic frame, with an air cushion, inflated by blowing, press-
ing uniformly over the whole surface of the frame.
The process most commonly used is the cyanotype sensitising
process, invented by Sir John Herschel. White lines are
produced on a blue ground with a solution of 140 grains of
ferric ammonic citrate, 120 grains of potassic ferri-cyanide, and
1' oz. of distilled water. The solution should be kept in a stone-
ware vessel. This process depends upon the actinic action of
light reducing the ferric salts to the ferrous state under certain
conditions, one of which is the presence of organic matter, such
;is the size contained in the paper. The ferrous salt then com-
bines with the potassic salt to form insoluble Prussian blue.
In these processes a sheet of paper, a little larger than the
tracing to be copied, is fixed on a board, and with a sponge
a thin uniform coating of the liquid is applied as rapidly as
possible, and allowed to stand in non-actinic light until perfectly
dry. The tracing is placed against the glass of the printing
frame, and at the back of the tracing the prepared sheet is
placed. The frame is then exposed to light until the prepared
sheet becomes of a dark olive-green colour. The sheet is then
removed from the frame, and thoroughly washed in pure water
for a few minutes until it assumes the required shade of blue.
On the Ordnance Survey, Willis' platinotype process is em-
ployed. It gives white lines on a black ground, and is based on
the reducing action of a ferrous salt, when exposed to actinic
light, on platinum chloride. The sensitising solution is com-
posed of 60 grains of potassic-platinous chloride, 60 grains of
ferric oxalate, and 1 oz. of water. The exposure lasts until the
paper acquires a dull orange tint. It is then developed in non-
actinic light by floating it for 4 seconds in a solution of 130
grains of potassic oxalate and 1 oz. of water at a temperature of
150 to 200 F. When properly developed, the print is washed
for 10 minutes in 1 part of hydrochloric acid with 60 parts of
water, and finally washed in relays of fresh water, for 15
minutes.*
Reducing and Enlarging Plans. A plan may be reduced or
enlarged, by taking from the original a fraction of the dimensions
as required. For this purpose proportional compasses, or scales,
may be employed. A very rapid method of reducing or en-
larging plans consists in covering the original with a network of
* Eight other processes for the actinic copying of engineering drawings
are described by Mr. B. H. Thwaite. Jlin. Proc. Inst. C.E., vol. Ixxxvi.,
1880, p. 312. '
2c-t MINE-SURVEYING.
squares, and the copy with a network of squares having their
sides smaller than those of the original squares in the proportion
in which the plan is to be reduced. The details may then be
sketched in by the eye. This method may also be used for
copying plans on the same scale.
Plans may be reduced by mechanism by means of instruments
called the pantograph and eidograph. The pantograph is made
in various forms. It always consists essentially of four brass
rulers, E D, D B, F G, and G C, Fig. 94, jointed
together at F, D, C, and G, so as to form a
parallelogram. The two sides D C and D F are
extended to double their length. The side F G
and the branch F E are marked from D with
successive divisions, F P being to D P always
in the ratio of F A to D T. Small sockets for
holding a pencil or tracing point are placed at
Fig. 94. -P anc l T. The point A is made the centre of
motion and rests on a fulcrum weight. From
the property of similar triangles, the three points A, P, and T
must range in the same straight line, shown by the dotted line
P A T, which is divided at A in the ratio required Thus, while
the point T is moved over the lines of the plan, the point P will
trace out a similar figure reduced in the proportion of T A to
A P or of D F to F P, the proportion required.
The eidograph is more complicated in construction. Although
not so frequently used as the pantograph, it is superior to that
instrument, within the range of its working powers, which may
be considered to be limited to reducing between the lull size of
the original and one-third of the size. Its great merit is that
within its range it reduces accurately in all proportions ; for
instance, it will reduce in the proportion of 9 to 25 as readily as
1 to 2.*
Plans may be enlarged by any of the methods given for
reducing them. It is, however, always better to make a fresh
plan from the original notes.
Isometric Plans of Mines. The kind of drawing adopted for
representing the interior of mines, and the vertical surfaces of
sections of strata, is that which supposes the eye of the observer
to be placed in a direction exactly perpendicular to every part of
the plane represented. In this way, two drawings are necessary
the ground plan and section. By means of isometric projection,
these drawings may be embodied in one, in which all the lines of
the projection may be measured by a uniform scale.
* A full description of this instrument is given in W. F. Stanley's
" Alatliematical Drawing Instruments," London, 1866.
MINE PLANS. 285
A solid body, the chief planes of which are at right angles, the
cube for instance, is to be so placed that the three planes which
meet together at one corner are equally inclined to the hori-
zontal plane, that is the plane of projection. The three lines
which meet at that corner will then be projected so as to form
three equal angles of 120 each, and will be the plans of the
three edges of the cube. The plans of the opposite edges will
be parallel to these, and hence it follows that in isometric projec-
tion all angles which are in reality right angles are projected into
angles of 120 or 60.
In making an isometric plan of a mine, three lines must first
be drawn, making angles of 120 with one another, for the plans
of three edges of the solid, in which it is imagined that the
mine is enclosed. An isometric scale must then be constructed,
so that the isometric lengths of the required edges may be
found. When found, these are measured on the lines drawn from
their plans, and the drawing is completed by parallels.
It is known that the relation of a line to its isometric projec-
tion is as ^/3 to ^/2. To construct an isometric scale, two lines
must therefore be drawn in this ratio. For this purpose, a line
1 unit in length is taken, and at one end of it a perpendicular
is erected of the same length, and the ends joined. The hypo-
thenuse of this right-angled triangle will represent N /2 (Euclid
I., 47). If from one end of this line representing ^2 a perpen-
dicular 1 unit in length is erected, and this triangle completed,
the hypothenuse will represent ^3. Two lines are thus ob-
tained representing J2 and ^3 in the required relation for the
scale, and if the real lengths of the edges be measured along x /3
and perpendiculars dropped from their ends to ^2, the parts
thereby intercepted will be the isometric plans of the required
edges. *
in making an isometric plan of a mine, it is desirable that a
north and south line may form one side of the supposed isometric
square that i-egulates the drawing, the cross-lines being of course
east and west. The survey must be plotted by means of the
calculated latitudes and departures, the distances being set off
along the edges of isometric squares. This method is of great
value for elucidating questions of stratigraphy and for solving
problems relating to the intersection of lodes. The necessity of
referring every object to an isometric plane, however, renders its
application to all the minute details of extensive subterranean
workings not only tedious and difficult, but also less explanatory
than the ground plans and sections in common use.*
* Some excellent isometric plans of mines are given in T. Sopwith'a
Treatise on Isometrical Drawiny, London, 2nd ed., 1S3S.
286 MINE-SURVEYING.
Kelief- Plans and Mine Models. Instead of use being made of
isometric projection for representing the three dimensions of
mine-workings on a plan, it is frequently necessary to construct
a relief-plan or model of wood, plaster, glass, or wire.
When a plastic material, such as cl.ay, wax, or putty, is used,
metal or wooden pins are driven into the base or level datum
plane of wood, the top of the pins giving the elevations required.
A contour plan, of the same horizontal scale as that selected for
the model, is first spread upon the base-board. The pins are then
driven firmly through the contour lines into the board, the tops
left standing at a sufficient distance from the latter, to represent the
height of the various contour lines, according to the vertical scale
adopted for the model. After the pins are all properly set, the
plastic material is worked into position over and thoroughly
covering the pins. This process was employed in the construc-
tion of a model, exhibited at the Paris Exhibition of 1878, repre-
senting the No. 8 seam of the Loire collieries, which is intersected
by an inextricable network of faults of different ages. The model
was constructed for the instruction of mine-deputies, who find it
difficult to follow the dislocation caused by these faults, more
especially the dislocations of faults by faults of different age.
This method was also employed by Mr. C. A. Ashburner in
the construction of an interesting model of th6 Panther Creek
Coal Basin, Pennsylvania, showing the shape of the floor of the
bed. After the construction of contours in explored areas, the
most important aid to the determination of the geological struc-
txire of the coal beds in areas where surface exposures cannot be
obtained, is the construction of a model with the vertical and hori-
zontal scales the same. The first area so mapped in Pennsylvania
was the Panther Creek Basin, one of the most complicated basins
of the anthracite district of that State. Many of the difficulties
were not understood until a model was made of the floor of the
Mammoth coal bed, the thickest and most valuable bed mined in
Pennsylvania. A map was first made on a scale of 800 feet to
the inch, upon which contour lines were shown along the floor of
the Mammoth bed, 50 feet vertically apart, in the areas worked
and explored. In the areas included between the two classes,
theoretical contour lines were drawn on the map, in accordance
with the dip of the exposed strata. Thus, the final model, made
in wood and wax, not only formed a graphic representation of
the structure of the strata in a highly plicated district, but also
proved of great value in the definition of its geological structure,
and in the deduction of many conclusions affecting the amount
of coal contained in this coal basin, and the proper methods to
pursue in its ultimate mining.
MINE PLANS. 287
The method adopted by Mr. T. Sopwith in the construction of
his well-known models was as follows : A square representing a
portion of the mining district, one mile in extent, is divided into
64 squares by parallel lines a furlong apart. Sections along the
eighteen lines are drawn and cut out in pasteboard or in thin
plates of copper. These are then joined crossways by half-
lapping, that is, by cutting each section half-way down, where it
crosses another section cut in the same way on the other edge.
The model of hollow squares thus formed is placed on a plane
surface, and the spaces are filled in with wood or plaster, carved
or moulded, so as to represent the surface. The model of part of
the lead-mining district of Alston Moor, in Cumberland, exhibited
in the Museum of Practical Geology, in London, was constructed
by this method by Mr. Sopwith. The model shows the thick-
ness and dip of the limestone, sandstone, and clay beds. The
mineral veins are seen on the sides of the model dipping in
nearly a vertical direction through the various strata.
Probably the best method of constructing relief plans is that
adopted by Mr. M. Moulton in 1876 for a map of the State of
New Hampshire. The map was 16 feet long, the highest eleva-
tion being 6| inches above the datum. From a copy of the map
of the State on tracing-cloth, the datum sea-level line and the
contour line next above it were transferred through the cloth on
to a layer of wood, |- inch in thickness, of the same size as the
map. The outside line was drawn in blue and the inside in red.
The outer contour was then cut round with a fret-saw, thus
breaking off the wood outside the sea-level line. The pedestal
on which the map was to be fixed then received the first layer of
wood. The next layer was then prepared for sawing, as in the
first case, the outside line being the first 500-foot contour and
the inside or red line the next above. This having been cut out
with the saw, it was nailed and glued to the first layer, its
position being fixed by the red line on the latter. Throughout
the work the red lines served as guides by which each successive
layer was properly placed. After three layers were fixed, the
steps were carved off to produce smooth slopes at angles corres-
ponding to those of the map. Each successive group of three-
layers was treated in the same way.
A complete view of the nature of a mineral vein and of the
excavations upon it, is given by a model constructed by
Mr. T. B Jordan, in the Museum of Practical Geology. The
workings of each successive stage of 10 fathoms, are laid out on
a scale of 10 fathoms to the inch on a horizontal frame of light
wires crossing at intervals representing 10 fathoms, and the
portions of the vein which have been worked between the levels
288 MINE-SURVEYING.
are shown in their true position. Hence, on looking down from
above, the eye may trace all the benclings of the lode, and can
appreciate the comparative richness and poverty of different
parts. The model represents the Holmbush mine, in Cornwall,
a mine of a complicated chai'acter from the occurrence of work-
ings on cross-courses as well as on lodes. The excavations made
are represented in colours, while the solid ground is left blank.
The workings on each vein are distinguished by a special
colour. Although affording a perfect view of the general ar-
rangement of a mine, this method is too cumbrous and expensive
to be generally employed.
An excellent method of constructing mine models is illustrated
by three models of Austrian salt mines exhibited in the Museum
of Practical Geology. These models are constructed to a uniform
scale of 400 feet to 1 inch. The irregularities of the surface of
the ground are represented, and central, transverse, and longi-
tudinal sections are drawn on the sides of each model. On
removing the tops of the models, representing the surface, the
workings on the different levels are seen plotted on plates of
glass, fixed at the proper height, one above the other. The
colours of the workings shown on the glass plates, correspond
with those of the named levels on the longitudinal sections. An
outer line, drawn in discontinuous bars, shows the extent of the
deposit of salt at each level.*
At the Stockholm School of Mines, the students are trained in
the representation of mine workings on sheets of glass. The
advantage of the method is the power of simultaneously repre-
senting the underground workings and the surface.
In addition to the practical value and advantage of mine
models to the geologist and miner, such models will frequently
be found of great advantage in suits at law, in settling mining
claims and damages in dispute, when ordinary plans are un-
availing, f
* The method of working these mines is fully described by Mr. H.
Bauerman in A Descriptive Catalogue of the Geological, Mining, and
Metallurgical Models in the Museum of Practical Geology, London, 1865.
t On the construction of models, see A. E. Lehman, Trans. Amer. Inst.
M.E., vol. xiv., 1S86, p. 439; 0. B. Harden, ib. voL x., p. 264; L. M. Haupt,
The Topographer, New York, 1883.
MAGNETIC -NEEM.E IN MIX1XQ. 289
CHAPTER XIX.
APPLICATIONS OP THE MAGNETIC-NEEDLE IN MINING.
Exploring for Iron Ore. In exploring for magnetic iron ores,
the magnetic-needle affords valuable aid, and has been employed
for that purpose in Sweden and in the United States.*
The theory of its use is based upon the fact that certain
minerals deposited in the earth become magnetic by induction
under the influence of the earth's magnetism, and that, conse-
quently, the two poles are fixed in the direction of the magnetic
meridian, or, more exactly, in the direction of the magnetic
inclination at the opposite ends of the deposit. It is well known
that there are substances, such as steel and magnetite, exhibiting
polar magnetism ; that is to say, they retain the magnetism once
acquired even if the inducing force ceases to act. Other sub-
stances, such as soft iron and magnetic pyrites, exhibit simple
magnetism ; in other words, they are magnetic only so long as
the induction remains.
The intensity of the magnetism exhibited by deposits of mag-
netite varies greatly, and is frequently so slight that only
delicate instruments and practised observers can detect it ; in
other cases the needle is affected at considerable distances. It
must, of course, be remembered that a given magnetic force
affects the needle to exactly the same degree through 100 feet of
rock as through the same distance of air.
If the magnetic north pole of the earth is regarded as negative,
and the south pole as positive (in the northern hemisphere), the
upper end of a vertical mass of ore will be negative, and the
lower end positive. Consequently, if a magnetic-needle is
brought near the upper or negative pole of the deposit, the north-
seeking or positive end of the needle will be attracted. When
the point of observation is very near the ore pole the needle will
dip downwards. The lower or positive pole of the ore mass,
being usually situated at a considerable depth, will not affect the
* See paper on the " Use of the Magnetic-Needle in exploring for Iron
Ore," by B. H. Brough, Journ. Iron and Steel Inst., 1887, p. 289.
290 MINE-SURVEYING.
observation. Other deposits, coursing in a more or less easterly
and westerly direction, are less affected by induction ; the poles
being situated in the long sides of the deposit. Frequently
the deposits are faulted and broken. In this case the separate
portions behave like fragments of a broken bar magnet, the
adjacent ends exhibiting opposite polarity. In exploring for
ore, then, if, on advancing from south to north, the free needle
is first attracted and then repelled, a fault in the deposit is
indicated.
To explore for ore the ordinary miner's dial may be employed.
If a straight line is followed with the instrument, the needle will
remain directed towards the same point of the dial; or, in other
words, will remain in the magnetic meridian as long as it is kept
sufficiently far away from iron and magnetic ore masses. But if
these are approached, the needle will gradually be deflected.
The only case in which there will be no deflection is when the
attracting deposit is approached along the meridian passing over
its upper pole. It follows that in magnetic surveys the meridian
line must first be found, and fixed in the field or on the plan.
For this purpose at least two straight lines are set out in the
magnetic east and west direction, from 30 to 50 yards apart.
These lines will at some point cross the meridian line. If the
dial is set up at one end of a line of this kind, at a considerable
distance from the magnetic mass, there will, of course, be no
attraction. On approaching the meridian the needle will be
gradually attracted, and at a certain distance the maximum
attraction will be reached. On approaching nearer it will become
smaller, until, at the ore meridian itself, it will be inappreciable.
The angles of deflection observed at the various stations are
noted on pegs driven into the ground, and also in the field-book,
or on the plan. Following the same straight line to the other
side of the zero point or, what is the same thing, to the other
side of the ore meridian the same attractions are exhibited, but
in reversed order ; the needle turning back to the meridian.
If similar observations are made along the second east and west
line it is easy to fix the ore meridian by joining the two points
where there is no deflection. These points are midway between
the two points of maximum deflection. This passes over the
upper pole of the deposit, and if the pole is approached along the
meridian line, the dip of the north-seeking end of the needle will,
as a rule, be greater the nearer it comes to the pole. This
method is, however, not adapted for fixing the position of the
pole exactly. This may be done by determining the isogonic
lines that is to say, by joining the points where the needle has
the same deflection.
MAGNETIC-NEEDLE IN MINING. 291
Tn order to obtain one or more parallel isogonic lines on both
sides of the ore meridian, it is necessary to set out a number of
lines pai-allel to the ore meridian, and from 10 to 30 yards
apart. At the points where these lines intersect the east and
west lines, the angles of deflection must be observed, and isogonic
lines constructed by joining the points of equal deflection. The
needle being drawn so much out of its horizontal position that
its free play is hindered, it must be weighted and balanced by a
piece of wax. If, now, from some point of intersection in the
network of squares made on the field of observation, a line is
drawn in the direction of the deflection of the magnetic-needle,
it will cut the isogonic curve at a second point, and, eventually,
the ore meridian. The two points, where the isogonic line is cut,
are joined ; the joining line is bisected, and at the point of
bisection a perpendicular is erected ; then, perpendicularly under
the point where this cuts the meridian, is the upper ore pole,
and at this point it will eventually be found best to sink the
shaft, so as to be certain of cutting the ore mass. The ore
meridian, it must be noted, need not always be a straight line.
In cases where a better instrument was not available, excellent
results have, in this way, been obtained with the ordinary pocket-
compass, held in the hand.
For preliminary magnetic surveys, no instrument is better than
the Swedish compass. In this instrument, the needle, besides
revolving in a horizontal plane in the usual manner, can also
turn in a vertical plane to an angle of about 60 with the horizon.
The needle is horizontally suspended in a brass case on a long
vertical brass pin by means of a long glass cap. The brass ter-
minates above in a short steel point, on which the glass cap
rotates. At the bottom of this is a brass stirrup, provided with
fine holes, through which pass the horizontal pins supporting the
needle. To enable the needle to dip, there is a long slot cut
along the middle of it. The compass-box can be suspended by
means of three strings passing through three small rings fastened
120 apart on the outside of the box. It can thus be easily
carried in the hand. Graduation is not usual, and, indeed,
unnecessary. Only the cardinal points are marked, as in using
it deviations from the horizontal position alone have to be
noticed. This compass was invented in the last century by the
celebrated Swedish miner, Daniel Tilas, and is still in general
use. The dip of the needle is estimated merely by the eye, and
is not actually measured.
The miner's or dip-compass was invented in the United States
in 1866, and was adopted by the Geological Survey of New
Jersey in the systematic explorations for magnetic iron ore in
292
MINE-SURVEYING.
that State. In this instrument the magnetic-needle is suspended
so as to move readily in a vertical direction ; the angle of incli-
nation being measured upon the divided rim of a small compass-
box. The needle cannot move horizontally. The construction of
the instrument is shown in the accompanying figure. When in
use, the ring is held in the hand, and the compass-box, by its
own weight, takes a vertical position.
It must, of course, be held in the
plane of the magnetic meridian, which
can be determined by holding the in-
strument horizontally. In this way it
serves as an ordinary pocket-compass.
Messrs. W. & L. E. Gurley, of Troy,
New York, make several different
forms of this instrument. One form
has a 3-inch needle ; its case has the
two sides of glass. Another form has
a brass back and cover, and a 2 i -inch
needle. Fig. 95 represents an im-
proved compass by the same makers.
It is a modification of the Swedish
compass, and has a needle 3 or 4 inches
long, resting upon a vertical pivot, so
as to move freely in a horizontal plane,
and thus place itself in the magnetic
meridian ; while being attached to the
needle-cap by two delicate pivots,
one on each side, it is free to dip. It
Fig. 95. is usually provided with brass covers
on both sides.
With the dip-compass, whether Swedish or American, perfectly
trustworthy results can only be obtained when the observer is
acquainted by long experience with the peculiarities of his instru-
ment. Compass explorations being in many cases the sole source
of income, it can easily be understood that a skilful operator will
be inclined to keep his mode of procedure secret. Consequently
the uninitiated are apt to believe that the operator must be
specially gifted ; and frequently the supernatural properties
formerly ascribed to the divining-rod are transferred to the com-
pass. This excess of faith in some is accompanied by scepticism
in others. For this, unfortunately, there are good grounds ; the
compass being so admirably adapted for dishonest purposes.
Thus, Mr. T. B. Brooks mentions an American prospector whose
compass-needle in the vicinity of an ore mass always showed a
dip of 90 when facing west, and the true dip due to local attrac-
MAGNETIC-NEEDLE IN MINING. 203
tion when facing east. The former position, it is said, was very
successfully used in selling iron ore grounds, and the latter in
buying them. Similarly in Sweden a powerful magnet inserted
in a walking-stick has been successfully employed to give a large
dip to the needle when it was thought desirable to mislead the
purchaser.
As a rule, surveyors assume that the most ore must occur where
the dip-compass shows the greatest inclination, or is perpendicular.
This assumption, however, is erroneous. The place where the
needle is attracted most by a vertical ore bed is not directly
above, but to the north of, the south pole of the deposit. For, if
the magnetism of the earth is powerful enough, there must be
somewhere north of the ore pole a point at which the horizontal
components of the magnetism of the earth and of the ore bed are
equally powerful, but acting in opposite directions. At this,
point the horizontal forces neutralise each other, and then the
vertical forces of the magnetism of the earth and of the ore bed,
tend to bring the needle into a vertical position.
The evidences afforded by the needle often lead to error. An
unimportant pocket of ore near the surface may have as great an.
action on the instrument as a larger ore mass situated far below
the surface.
It is thus seen that in exploring for iron ore with the magnetic-
needle, a purely scientific method is necessary. The compass
should be employed for preliminary work, in order to save time
and labour ; but before a shaft is sunk, recourse should be had
to a more accurate method. Improved methods, available for
the purpose, have been devised by Brooks, Thalen, and Tiberg.
1. Brooks' Method. Mr. T. B. Brooks,* of the Geological
Survey of Michigan, in exploring for iron ore, determined with
a pocket-compass variations east or west ; the bearings of a
standard line being taken as in ordinary surveys. The inclina-
tions or dips were observed on the dip-compass held in the hand
in the plane of the meridian. Sometimes observations were
made with the compass held at right angles to this position, that
is, facing north and south. The instrument was always held in
the hand and levelled by its own weight. The intensity of the
magnetic force for the three positions of the compass was
measured by the number of oscillations made by the needle in a
unit of time, usually taken at a quarter of a minute. No attempt
was made to eliminate the earth's attraction by neutralising it
with a magnet while the observation was being made, nor by
computation ; and the great amount of friction in the compass
* Geological Survey of Michigan, vol. i., 1873, chap. viii.
294 MIXE-SUEVEYIXG.
renders the number of oscillations only an approximation to the
number that would be obtained with a delicately mounted
needle. Mr. Brooks has, however, done excellent work with
this method in the Marquette region and in New York and
New Jersey. He also describes another method of working,
which he calls magnetic triangulation. The mode of procedure
is as follows: Remote from any magnetic rocks, neutralise, by
means of a bar magnet, the earth's influence on the needle of a
solar compass. The needle will then stand indifferently in all
directions. If the compensated instrument is set up near the
magnetic pole to be determined, the needle will point as nearly
towards the local pole as its mode of mounting will permit.
The operation being repeated at two other points near the
magnetic pole, the three lines must intersect in one point,
which will be directly over the pole of which the position is
.sought. By using a dip-compass in a similar manner, data to
determine the depth would be obtained. The fact that several
local poles often influence the needle at each station renders this
method difficult in practice ; a place must be sought where but
one strong pole exists.
2. Thal6n's Method. Professor R. Thalen,* of the University
of TJpsala, employs a modification of Weber's portable magneto-
meter, or of Lament's theodolite. In its simplest form, Thalen's
instrument consists of a compass-box 3^ inches in diameter,
divided into degrees or half-degrees. At right angles to the
diameter, passing through the zero point of the graduation, an
arm extends horizontally. This serves as a sight in setting out
lines in the field, and receives the bar magnet for the deviation
measurements. A deflection of the needle is caused by means of
this magnet, the longitudinal direction of which is parallel to the
arm, and the distance of which from the needle always remains
unaltered. On the other side of the compass-box there is a
socket, into which a rod of soft iron can be placed perpendicularly
for inclination measurements. This iron rod, like the magnet,
effects a deflection of the needle. The instrument rotates about
a vertical axis, and is provided with a spirit-level and levelling
screws. In order to simplify the apparatus still further, the
compass-box may be fastened to a rectangular board, the edges
of which can be used as sights ; whilst the board itself receives
the bar magnet, which is fixed by screws or springs in the
position that is determined once for all. As support for the
instrument, an ordinary surveyor's plane-table may be employed.
The observations with the magnetometer consist for the most
* Jernkontoreta annaler, voL xxxiv., 1879, p. 17.
MAGNETIC-NEEDLE IN MINING. 295
part of deviation measurements, for which two different methods
may be employed. In one method the instrument is placed so that
the needle is directed to the zero point, the bar magnet having
been removed from its place. Directly the magnet is replaced,
the needle will deviate from its original position, the angle of
deviation being read from the graduated circle. In the second
method the instrument is turned, while the magnet is in its
place, until the needle points to zero. The bar magnet is then
removed, and, when the needle has come to rest, the angle is
read. In this method, under similar conditions, the angle obtained
will be greater than in the former method. Of the two methods,
the latter, or sine method, is the more delicate ; but it requires
more time than the former, as the instrument has to be re-
adjusted at every observation with the magnet and iron rod.
This method has the disadvantage of not being applicable in the
extreme north of the ore field, where the magnetism of the
ore bed is powerful. In the former, or tangent method, the
instrument remains \inmoved during both measurements. The
disadvantage, however, is that the so-called constants of the
instrument vary with the angle of deviation. This does not
matter if the results are to be arrived at geometrically, since it is
then merely necessary to join the points where the same angle
is obtained, quite regardless of the magnitude of the angle and of
its corresponding constant. If the position of the ore is to be
determined by calculation, the sine method must be employed.
Where no ore is present, the needle is acted upon by two
forces, one of which is due to the fixed magnet, and the other
to the horizontal component of the earth's magnetism. These
two forces acting simultaneously, the needle takes up a position
in the direction of their resultant. Then if a is the angle of
deviation, and H the component of the earth's magnetism, the
following formulae are obtained :
for the tangent method : H tan a = K t ,
for the sine method : H sin a = K 2 ,
in which Kj and K 2 are constants, so long as the size and position
of the magnet remain unaltered. If these constants are known,
the actual value of H may be found from the magnitude of the
observed angle by either of the methods. If the constants are
unknown, only the relative value of H may be found When
observations are made near an iron ore field, in both formulae H
must be replaced by R, the resultant of the horizontal component
of the earth's magnetism and the magnetism of the deposit. The
formulae then become
R, tan a = K 1 , and R sin = K 2 .
296 MINE-SURVEYING.
When the deviations are caused by the soft iron rod instead of
by the magnet, somewhat similar formulse are obtained ; but the
magnetism of the iron rod being due to induction, its intensity is
proportional to the variations of the vertical components of the
earth's magnetism. It follows that the constant K of each formula
in this case must be replaced by a m'agnitude that varies with the
magnetism of the rod. Observations with the iron rod indicate
the inclination of the earth's magnetism ; whilst observations
with the bar magnet serve for determining the horizontal com-
ponents of the same terrestrial force. Consequently, by combin-
ing the two methods, it is possible to find out the vertical com-
ponents of the magnetic force.
In order to survey an ore field, it must first be divided into
squares with sides 100, 50, or 25 feet in length. Then at every
angle of these squares, the deviation must be observed with the
magnet and iron rod. Similar observations must be made on
ground free from iron, and so far distant from the ore field that
the influence of the ore is not felt. It is also advisable to deter-
mine the magnetic declination for each point of observation.
This may be done by directing the sights along one of the lines
that have been set out, and reading the bearing, after the fixed
magnet and iron rod have been removed. Observations must
also be made along the magnetic meridian north of the supposed
ore pole to determine where the north-seeking end of the free
needle changes its direction from north to south, or whether it
invariably points towards the north.
When these determinations of declination, horizontal intensity,
and inclination have been carefully made, and the angles ob-
tained noted on paper divided into squares, lines are drawn for
each of the three series of observations, exhibiting equal declina-
tion (isogonic lines), equal intensity (isodynamic lines), and equal
inclination (isoclinic lines). This is done in each case by
joining the points by which equal angles were obtained. The
curvature of the lines is drawn as naturally as possible, care
being taken to avoid sharp bends. The curves of inclination
and intensity thus constructed are closed, and have an approxi-
mately circular or elliptical shape, provided that a single isolated
ore mass is being dealt with. They are grouped round two
points. The one at the north is where the greatest angle of
deviation was found, whilst that at the south is where the
smallest angle was obtained. Between these two groups of
curves is an open curved line representing the neutral angle.
In this neutral line the intensity is the same as if no ore was
present. The straight line joining the points where the greatest
and smallest angles were obtained passes over the centre of the
MAGNETIC-NEEDLE IN MINING. 297
ore mass, and indicates the dii-ection of the magnetic meridian
of the ore field. Directly beneath a point in this line, in a
vertical ore bed, the greatest mass of ore occurs. The rule that
most generally holds good in searching for iron ore is, that the
ore mass is to be found immediately beneath the point where the
magnetic meridian cuts the neutral line.
The isogonic lines consist of concentric ovals placed, as a rule,
symmetrically on both sides of the meridian. From the shape
and position of these curves useful indications may be obtained
regarding the position of the ore pole, and the shape of the
deposit.
3. Tiberg's Method. In exploring for iron ore, Mr. E. Tiberg
uses a dip-compass, 3 J inches in diameter, and half an inch deep.
The axis of the needle is at right angles to the plane of the box,
and rests upon two agate supports. The needle can thus move
freely when the compass is placed horizontally or vertically.
The instrument differs from other dipping needles in that the
centre of gravity of the magnetic-needle is a little below its
horizontal axis when the compass is in a vertical position.
The needle is compensated for the vertical force of the
earth's magnetism by a piece of wax fastened to its south-
seeking end.
The instrument is provided with a spirit-level for horizontal
adjustment, and with a ring, by means of which it can be sus-
pended vertically. The sighting instrument, used in conjunction
with the dip-compass, is a brass plate about a foot in length, pro-
vided at one end with four square flanges to receive the dip-
compass for horizontal measurements. At right angles to this
square, there is a groove in the plate with a sliding receptacle
for the bar magnet required for horizontal measurements. Four
folding sights are attached to the plate in such a way that their
lines of sight form a right angle. The instrument, consequently,
can be used as a cross- head. Two special sights are added for
levelling operations, and the instrument is provided with a
circular spirit-level.
The observations for vertical measurements are made at the
surface with the plane-table or by hand. The inclination instru-
ment is fastened to the plane-table, levelled, and turned until
the needle points to 90. The instrument is then raised with
the ring at the top, and placed at right angles to the magnetic,
meridian, and the angle indicated by the needle observed. The
same operation has to be done by hand if the plane-table is not
available. When the ore appears to be deep, or when the
horizontal intensity is powerful, recourse must be had to the-
plane-table.
298 MINE-SURVEYING.
The formula for calculating the vertical intensity G is
G = K. tan v,
in which v is the angle given by the needle that is, its deviation
from the horizontal and K a constant varying in different in-
struments from 0'75 to 14 of the earth's horizontal magnetic
force. Lines of equal vertical intensity may thus be constructed.
In magnetic plans it is usual to employ a blue colour for positive
intensity, and a red colour for negative intensity. The accuracy
attainable with this method is from 0'2 to 0-1 per cent, of the
earth's magnetic force in central Sweden. With the plane-table
250 to 300 observations may be made per day, and 450 to 500 by
hand. For each ore field surveyed the needle must be compen-
sated afresh, and a preliminary magnetic survey made. The
field is then divided into squares, with sides 40 feet in length.
The base-line is as nearly as possible in the middle of the field,
and parallel to the direction of the strike of the deposit. In
making the survey, observations are made every 10 feet, and in
some cases every 5 feet, in the immediate vicinity of the ore, and
every 20 to 40 feet or more when farther distant from the ore.
The general rule is to make as many observations as may be
required to indicate what the appearance of the curves will be.
Heights are estimated by the eye, or by a preliminary levelling
with the sighting instrument, and the more important topo-
graphical details are noted.
The maximum of intensity is generally presented by the point
where the ore is nearest to the surface. It may also be situated
between two adjacent deposits in which case the intensity
decreases, at first slowly, or not at all, and then comparatively
rapidly. The distance to the centre of a vertical ore bed may be
taken as at least 0'7 of half the breadth of the north-polar
attraction. This rule is, however, not very trustworthy. The
vertical distance of the plane of observation from the upper ore
pole is equal to the horizontal distance of the point where the
needle deviated most from the horizontal from that where J of
the greatest intensity was found. It is also equal to lg of the
distance of the point where the needle dipped most from that
where half the maximum was found. The latter rule is the best.
Sometimes these calculations enable an opinion to be formed
of the relative values of two similar ore beds. For two deposits
of a similar character, situated at least 30 feet beneath the
surface, it may be assumed that the deposit, for which the
product of the greatest intensity and the polar distance is the
greater, contains the larger quantity of ore for the same length of
deposit. If the polar surfaces of the two beds are limited this
product must be replaced by the square of the polar distance.
MAGNETIC-NEEDLE IN MINING. 299
A good idea of a deposit may be formed from the appearance
of the curves of intensity. Regular, long extended, elliptical
curves, enclosing a long but narrow district of greatest intensity,
always indicate a regular lenticular mass. An asymmetrical
bend in the curves indicates parallel deposits. More circular
curves may indicate a segregation of ore if the intensity decreases
regularly. Irregular curves indicate more or less irregular
deposits.
In exploring for courses of ore in the mine, a base-line is
marked out in the level, and observations made every 10 feet at
least. At each station three observations have to be made :
(1) To determine the direction of the total horizontal intensity
by means of the sighting instrument, the deviation of the
magnetic-needle from the base-line being observed. (2) To
determine the magnitude of its force by means of the bar
magnet. (3) To determine the vertical intensity by means of
the inclination instrument. Vertical measurements must also
be made at the top and floor of the level, and for this pin-pose
the instrument may be held in the hand. On neutral ground at
the surface, the horizontal force of the earth's magnetism and the
direction of the earth's magnetic meridian must be determined.
The results of all the observations are represented on paper,
along the base-line, as arrows showing the horizontal forces of
the magnetism of the ore at the points of observation. If all or
part of the arrows are directed towards the same point, there the
ore may be assumed to be. The ore would be at the level at
which the observations were made, if the vertical intensity is
negative. When the arrows approach in front or behind, the
plane of observation is above or below the magnetic centre of the
ore. When the vertical intensity is positive, the ore may be
above or below the plane of observation, always assuming that a
more or less vertical ore mass is being dealt with.
By applying this method Mr. Tiberg has discovered important
deposits of ore at the Swedish mines of Langban and Sikberg.
To illustrate the value of the magnetic-needle in exploring for
iron ore, it may be mentioned that, according to the statistics
given by Prof. Smock,* there were 115 mines in 1868 in the State
of New Jersey, whilst in 1874 the number had increased to 200.
All these ore localities were first made known by the use of the
magnetic-needle. In fact, the annual production of the State
had been increased 50 per cent, by the addition of new producing
localities found by the compass. It should also be stated that
in many cases there are no visible surface indications of ore.
* Trans. Amer, Inst. H.E., vol. iv., 1876, p. 353.
300 MIXE-SURVEYIXG.
Use of the Magnetic-Needle in Surveying Bore-holes. It has
been assumed that the diamond drill always bores a perfectly
straight hole, even though passing through rocks of different
hardness. Actual experience reveals an entirely different state
of things, the deviations sometimes being so great as to render a
bore-hole misleading. An ingenious plan of correctly ascertaining
these deviations has been devised by Mr. E. F. Macgeorge,* an
Australian engineer. His plan consists in lowering into the
bore-hole clear glass phials filled with a hot solution of gelatine,
each containing, in suspension, a magnetic-needle, free to assume
the meridian direction. The phials are encased in a brass pro-
tecting tube, and let down to the depth required, being allowed
to remain for several hours until the gelatine has set.
The construction of the phials or clinostats can be seen from
Fig. 96. The clinostat is a true cylinder of glass made to fit
accurately within the brass guide-tube. At the lower end it
terminates in a short neck and bulb, within which a
magnetic-needle is so held by a glass float as to stand
upright upon its pivot in every position of the phial,
and thus allow the needle to assume the meridian freely
without touching the sides of the bulb. Passed through
an air-tight cork and screw-capsule at the upper end is
a small glass tube terminating in another bulb above and
with its open lower end inserted in a cork which enters
^ the lower neck of the phial, thus preventing the escape
.p. g6 of the needle and float in the lower bulb. The upper
bulb contains a very delicate plumb-rod of glass con-
sisting of a fine rod terminating in a plumb of glass below
and a diminutive bulbous float of hollow glass above. It
is carefully adjusted to the .specific gravity of the gelatine in
which it is immersed, so as to insure the rod being truly
vertical whatever the position of the phial and bulb may
be. When the gelatine is fluid the plummet hangs freely
perpendicular, whilst the needle in the lower bulb assumes the
magnetic meridian. When, however, the phial is at rest in any
position, the contents solidify on cooling, and thus hold fast the
indicating plummet and magnet in solid transparent material.
On withdrawal from the bore-hole the phials can each be replaced
at the same angle at which they cooled, and when the phial is
revolved upon the part where the magnetic-needle is seen em-
bedded in the gelatine, until the needle is again in the meridian,
the phial is manifestly in the same direction, both as regards
inclination and azimuth, as it was when its contents were con-
gealed, and thus the gradient and bearings of the bore-hole can
Engineering, vol. xxxix., 1885, pp. 260, 334.
MAGNETIC-NEEDLE IN MINING.
301
be determined. By repeating the observations at intervals of
every 100 feet, the path of the bore-hole can be accurately mapped.
The inclination and azimuth at the time of cooling is deter-
mined exactly by the recording instrument, or clinometer, which
is a modification of the theodolite. The phial, with its congealed
contents, is placed in a sheath of brass tubing (Fig. 97), attached
Fig. 97.
to a movable arm carrying the index of a vertical arc. The
upper bulb of the phial is brought into the field of two cross-
visioned microscopes, carried with the arm round the vertical
arc, which are kept truly in the same plane at every angle of
inclination by a parallel motion. Upon the object-glass of each
microscope vertical lines are drawn. The phial is revolved in its
sheath, and the arm is moved along the arc by the tangent screw
xintil the embedded plummet is made perpendicular from each
point of view. The phial is now at the angle of inclination at
which its contents solidified, and its lower bulb will be found
nearly in the axis of the revolving arm, and about an inch above
302 MINE-SURVEYING.
the centre of a horizontal revolving circular mirror, having a
system of parallel lines engraved across its face. Reflected in,
the mirror will be seen the image of the embedded needle, which,
of course, pointed north before it was fixed by congelation in
the bore-hole. If now the mirror is revolved until the number
270 of the graduated circle is opposite the marked end of the
needle, and until the reflected image of the needle is parallel with
the engi*aved lines, an index at the side of the graduated mirror
frame will give the exact angle between the needle and the verti-
cal plane of revolution of the phial, which is, in fact, the magnetic
bearing of the inclined phial and of the bore-hole it occupied at
the time of the application of the test.
This method was first applied at the Scotchman's United Mine
at Stawell, in Victoria, and was so effectual as to enable the bore-
hole to be found 37 feet away from its supposed position at a
depth of 370 feet, a deflection that increased to the large amount
of 75 feet at a depth of 500 feet. An exploratory level failed to
find the bore-hole at its theoretical position, assuming the drill
to have gone straight down. The subsequent search works lasted
for more than a year, and cost altogether 3,663. Had the
method been available at the commencement, the level driven
would have cost only 1,352, and the saving effected would have
been no less than 2,311.
Similar experiences have been met with in a number of other
bore-holes in the mining districts of Victoria, and the conse-
quence is that mine-proprietors are beginning to distrust the
diamond drill altogether. Yet, if accurately surveyed, the most
crooked bore is quite as useful as the straightest ever imagined
by drill-makers. In view of these facts, the Victorian Govern-
ment has contracted with the inventor to test all approved bores
which have passed through auriferous rock.
By means of the clinograph, as the inventor terms his appara-
tus, a bore may be straightened when so deflected as to endanger
the safety of the drill ; for, suppose a bore-hole to have deflected
suddenly, the depth of the point where the most serious deflec-
tion took place can be found. Then, if an india-rubber washer
is forced down to 20 feet below this point, and liquid cement run
in until it reaches some feet above the point of deflection, and
allowed to set, then the drill may be again lowered and started
gently, until it has started fairly in its corrected path, when the
usual speed of boring may be resumed.
A less satisfactory method for ascertaining the inclination and
direction of bore-holes was suggested by G. Nolten.* In the
* Preu**. Zeitschr., vol. xxviii., 1879, p. 176; Translation by C. Z. Bun-
ning and J. K. Guthrie in Trans. iV. Eng. Inst. M.E., vol. xxix., p. 61.
MAGNETIC-NEEDLE IN MINING. 303
instrument employed, the amount of deviation is etched upon
glass by hydrofluoric acid ; whilst its direction is found by means
of a compass-needle, clamped by the aid of a stop-watch, after
sufficient time has been allowed for settling. Notwithstanding
the great imperfections of this instrument, its use in Germany
has revealed some startling deviations of bore-holes. For example,
in a bore-hole at Dienslaken, bored with a rotating drill, the
deflection amounted to 47 at a depth of 750 feet. The bore-
hole, undertaken by the German Government, at Lieth, in
Holstein, was but little better than the preceding ; but, by a
lucky accident, the deflection of 3 at 984 feet gradually changed
to the opposite quarter of the compass at 1,640 and 2,624 feet,,
and concluded with a deflection of only 1 at 3,280 feet.
Employment of a Powerful Magnet in Cases of Uncertain
Holing. In 1846 Professor Borchers, of Clausthal, first proposed
to employ a powerful magnet in cases of uncertain holing from
one excavation to another. Since that date, he has improved the
method in many ways, and has frequently employed it in practice
with great success. In order to ensure a successful holing, the
ends of the two levels must not be more than 20 yards apart.
The apparatus employed consists of a powerful magnet, with a
specially constructed protractor, a compass, and a small auxilary
magnet.
The powerful magnet consists of six magnetised steel bars 4
feet in length, enclosed in two wooden boxes, provided with
water-tight lids. One of these boxes contains only one magnet ;
whilst the other box contains the remaining five, separated from
one another in the middle and at the ends by pieces of card-board.
In the centre of its upper side, the larger box is provided with a
pivot, which fits into an aperture in the smaller box. On this
i : .-^1
Fig 98. Fig 99.
pivot, the small box can be rotated, and the north pole of the
magnet inside can thus be made to correspond with the south
poles of the magnets in the large box. Consequently, a portion
of the magnetic force of the latter is neutralised. The powerful
magnet must be fixed in such a way that it can be pointed in
various directions, without altering the position of its centre.
304:
MINE-SURVEYING.
For this purpose, is employed a brass protractor, Figs. 98, 99,
which can be screwed on to a thick board. At the centre of the
protractor, a brass plate revolves, and between the turned-up
edges of this, the principal magnet may be placed. At right
angles to the longitudinal axis of the magnet, an index line is
engraved. Provided the rock barrier is not more than 6 yards
across, an ordinary compass, with a sensitive needle, may be
employed. For greater distances, the compass-needle must be
suspended by a silk fibre. Under these circumstances the steel
pivot is removed from the compass, and a case screwed on to the
plate, as shown in Fig 100. The sides are covered with glass to
protect the needle from air currents. The upper end of the glass
tube, containing the silk fibre, is provided with
a contrivance for centering the needle. The
latter is somewhat longer than the diameter
of the compass dial, and does not require to
be centered with mathematical accuracy, pro-
vided that both ends are read, and the mean
of the two readings taken. The auxiliary
magnet is a small magnetised bar 12 to 18
inches in length.
The mode of procedure is the following:
At the end of one of the levels, the protractor
is firmly fixed in such a way that its north
and south line is in the magnetic meridian.
At the end of the other level, the compass
is set up, as nearly as possible at the same
height as the protractor, and placed so that the needle indi-
cates north. The needle must then be rendered astatic. To
effect this, the auxiliary magnet is placed in the direction of the
north and south line of the compass, on the side away from the
principal magnet in the other excavation, and moved backwards
and forwards until the force attracting the needle is neutralised.
"When these preparations are complete, the principal magnet,
with the small box above it, is placed on the movable plate of
the protractor, and brought approximately into the direction of
holing. The powerful magnet then acts on the astatic needle of
the compass, and causes it to take up a direction determined by
a law enunciated by Gauss. But as the needle is not perfectly
astatic for all directions, what attracting force remains must
be again neutralised for the position taken up under the action
of the powerful magnet. This is done by revolving on its pivot
the small box above the principal magnet, until the north pole of
the magnet it contains corresponds with the south poles of the
other magnets. The action of the large magnet is thus
Fig. 100.
MAGNETIC-NEEDLE IN MINING. 305
diminished. Then if the compass-needle is not perfectly astatic,
it will alter its position, as the attracting force of the principal
magnet increases or diminishes. If a change in the position of
the needle is observed during the action of the weakened magnet,
attempts must be made to bring the needle back to the position
it occupied when the principal magnet acted with full force, by
moving the auxiliary magnet very slightly. The upper bar of
the large magnet is then turned back to its original position, and
it is ascertained whether the compass-needle alters its position.
If this is the case, the process must be repeated until the needle
gives the same bearing with the full force and with the
diminished force of the large magnet.
From the bearing of the needle and the direction of the lai-ge
magnet, the direction of holing may be determined by con-
struction, in the following way : A B C (Fig. 101) is a right-
angled triangle, with the right-angle at C ;
A being the centre of the large magnet,
the longitudinal axis of which is in the
direction of the hypothenuse A B. At G
is the astatic-needle, which, attracted by t
the large magnet, takes up a position in
the line C D. The direction of this Fig. 101.
line is determined by the eqxiation
A D = A B. Strictly speaking, the magnet N S should be
very small. For practical pm-poses, however, this law may be
applied without any appreciable error.
The question now arises, in what way should this law be
applied. A geometrical method is inconvenient in the mine; and,
consequently, it is desirable to calculate the angles (BAG)
and /3 (A C D), that is, the deviation of the direction of holing
A C from the position of the magnet N S, and from that of the
compass-needle C D. A, B, and are situated on the circumfer-
ence of a circle, the centre of which is E. In the triangle DEC,
the angle D E is equal to a + /3 ; and, since the triangle AEG
is isosceles, the angle A C E is equal to the angle C A E ; there-
fore, the angle D C E is equal to a /S. The ratio of the sides
D E and E 0, however, is 1 : 3, and 1 : 3 = sin (a - j8) : sin (a + /3);
therefore,
sin (a - /3) = ^ sin (a + jS).
Suppose, for example, that the bearing given by the protractor
of the large magnet was 154, and that given by the compass
125 15'; the difference is then 28 45' = + /3. Now,
sin 28 45' = 0-48099 ; one-third of which is 0-1G033, which is
the sine of the angle 9 14'. Consequently,
20
306 MINE-SURVEYING.
+ = 28 45'
- ft = 9 14'
therefore, = 19 and /3 = 9 45'. The direction of holing A B
is, therefore,
125 15' + 9 45' - 135 0'
154 0' - 19 0' = 135 0'
This calculated bearing has to be subtracted from 180", since
the north and south line of the compass always remains in the
same position throughout the process ; the needle being revolved.
The direction in which it would be necessary to drive would,
consequently, be
180 - 135 - 45.
Instructions for carrying out the operations required at the
large magnet are given by means of previously arranged signals
by the observer at the compass.
A powerful magnet was applied with success in a somewhat
similar manner in 1885 by Mr. A Haddon* in seeking a bore-
hole, that had diverged from the vertical, at the Holyrood
Brewery, Edinburgh. After the bore-hole had gone down 200
feet, it was considered necessary to connect it by a level with a
neighbouring well 18 feet 3 inches distant. The miner entrusted
with the work having failed to find the bore-hole, Mr. Haddon
procured four 8-inch bar-magnets, placed end to end, and secured
between two laths of wood. These he lowered into the bore-
hole with the south pole downwards, and, by noting the deflec-
tion of a compass-needle at different points in the mine, he found
that the bore-hole was 8 feet from its expected position.
* Engineering, vol. xxxix. , p. 31 .
307
APPENDIX I.
EXAMINATION QUESTIONS.
The following examination questions will be found useful to those students
who have not the advantage of regular instruction in mine-surveying,
affording them a means of personally testing their knowledge :
1. Give the length of a link, and of a chain. How many chains are there
in a mile, and how many acres in a square mile ? (Colliery Managers'
Examination, Bristol.)
2. In chaining over sloping ground, how do you correct for the inclina-
tion ? Give a simple rule when the inclination is expressed either in angular
measure or as a gradient, e.g., 1 in 6, 1 in 15. (City and Guilds of London
Institute, Examination in Mine-Surveying, 1885.)
3. Describe the miner's dial, and note the improvements recently intro-
duced into its construction. (Royal School of Mines, Examination in Mine-
Surveying, 1884.)
4. Give a copy of a page of a survey-book recording an imaginary under-
ground-survey. How may you approximately ascertain the date of the
workings of an old undated plan ? (Colliery Managers' Examination, West
Lancashire, 1S87.)
5. Describe the Henderson dial, and state its supposed advantages over
the rack instrument. (R.3.M., 1833.)
6. Give a short description of the miner's dial, with its usual appliances,
especially when it is used as a theodolite, the needle being thrown off.
(City Guilds, 1880. )
7. Describe a Guuter's or land measuring chain. (City Guilds, 1881. )
8. What is meant by the term true meridian ? Describe a simple method
for approximately determining it. (City Guilds, 1885.)
9. State the present deviation. In what manner is the deviation usually
found to vary from year to year, also in travelling from one locality to
another at a considerable distance ? (City Guilds, 1885.)
10. Sketch on paper the following bearings of a survey : N. 82 E., 68
links ; S. 51 E., 95 links ; N. 63 E., 78 links ; N. 20 E., 97 links ; N. 35
W., 87 links ; N. 87 W., 140 links ; S. 52' W., 140 links ; S. 48 E., 85
links. (Colliery Managers, Derby. )
11. Explain the traverse tables. (Colliery Managers, South Wales.)
308
MINE-SURVEYING.
12. Suppose you were driving towards an old waste, which is shown on
a plan 20 years old, explain the precautions to be taken as regards the
meridian. (Colliery Managers, Derby.)
13. You are required to traverse over a level in which rails are laid
down. How would you proceed to use an ordinary miner's dial under the
circumstances, the dial being without a rack, but supplied with two sets of
legs ? The only true bearing was one taken in a cross-cut north, at a dis-
tance of, say, 5 fathoms off the main level, where the traverse is being
made ; this cross-cut occurring; about half way in the traverse. Rule a sup-
posed page of your underground book suited to this surpose, and give, say,
six drafts or bearings all supposed to be affected by the attraction of the
rails, the polarity of the whole being governed by the true bearing in the
cross-cut north. If time will permit, insert distances and prove your work
by plotting. (City Guilds, 1883.)
14. Explain by writing and sketching how to make a loose needle survey.
(Yorkshire College, Leeds, 1886.)
15. The three sides of a triangle measure 144, 192, and 240 links respec-
tively. Find the area of the triangle in square yards, and the angle
opposite to the shortest side. (City Guilds, 1885.)
16. What is the area in statute acreage of a triangular field whose sides
measure 2420, 186ft, and 2005 links respectively ? A sketch may be given,
but not to scale. Logarithms are recommended for the calculation. (City
Guild*, 1883.)
17. Explain by writing and sketching how to make and book a fast
needle survey. (Yorkshire College, Leeds, 1886.)
18. The area, in acres, roods, and poles, is required of an irregular field,
which was surveyed by running one line through it from end to end (A to
B), with offsets taken as under :
No plan to be drawn.
150
B
15-50
182
13-00
12-48
175
11-59
55
9-80
183
2SO
8-65
202
3-93
92
1-50
75
145
0-45
A
Length of line, 15 '50 chains. (City Guilds, 1883.
APPENDIX I.
309
19. Give a general description of the theodolite, and explain the method
in which you would use it iu making an underground-survey. (City Guilds,
1887.)
'20. What are the special advantages and disadvantages in the use of the
ordinary miner's compass as compared with the theodolite ? (City Guilds,
1887.)
21. Lay down the underground-survey given on page 38, on the scale of
3 chains to an inch. Trigonometrical calculations may be used. (City
Guilds, 1887.)
22. Find the horizontal distance and direction of the Station H from the
shaft. Also the approximate difference of level between these points. (Citi/
Guilds, 1887.)
23. Work out the following series of levels, showing the height, above the
Station A of each point taken :
Distance.
Back-Sight.
Intermediate.
Fore-Sight.
A
12-63
...
...
0-40
9-16
1-00
7-43
...
1-50
531
...
2-00
4-06
3-50
2-16
...
4-50
9-06
042
5-50
7-50
...
6-50
6-15
...
8-00
3-60
900
2-12
1050
10-15
0-75
11-20
8-70
...
13-00
4-45
...
14-60
3-23
(City Guilds, 1887.)
310
MINE-SURVEYING.
24. Explain by writing how to level and plot a section. ( Yorkshire
College, Leeds, 1886.)
25. Find the quantity of coal in 1 acre of a seam of the following
section : Top coal, 2 feet 4 inches ; band, feet 10 inches ; bottom coal,
1 feet 8 inches ; total, 4 feet 10 inches, taking the specific gravity of coal at
1"25. (Colliery Managers, Newcastle-on-Tyne.)
26. Find the quantity of coal in an acre of a seam 5 feet 6^ inches thick,
taking the specific gravity at 1'25. (Newcastle on-Tyne.)
27. If pillars are left 30 by 21, and winnings 32 by 26, what percentage
is got in the first working? (Colliery Managers, Newcastle-on-Tyne.)
28. How much coal might be expected to be available in an area of 150
acres of a 4-feet seam, allowing one-fifth for faults and waste ? (Science and
Art Department, Examination in Alining, 1884.)
29. The solid contents of a lode are in volume per cent. :
Galena, 30
Zinc-blende,... ... ... ... ... 15
Iron pyrites, ... ... ... ... 20
Quartz, ... ... ... ... ... 35
What is the weight per cubic fathom of the stuff and of its different con-
stituents ? (S. and A. D., 1884. )
30. A copper lode is 14 inches thick, containing copper pyrites and
fluorspar in the proportion of 2 parts of fluorspar to 1 part of copper pyrites.
What is the weight of a square fathom of the lode, allowing one-thirtieth
for hollows? (Richard.)
31. A level 7 feet high is driven on a tin lode 8 inches thick, of which
one-tenth is oxide of tin, the remainder being quartz. How many tons
of tin stuff will be obtained per fathom in length, if the lode is quite solid ?
(Rickard.)
32. In working to the full rise of a seam of which the inclination is 1 in
12 you meet with a rise fault of 10 yards. What will be the length of a
rise tunnel to be drawn at the inclination of 1 in 6 between the seam at the
low side of the fault, and the seam on its rise side, supposing the fault to be
vertical? (Colliery Managers, West Lancashire, 1887.)
33. Plot on a scale of 8 fathoms to the inch the following under-
ground traverse, taken with the ordinary miner's " left-hand" dial :
.
Bearing.
Distance.
A
355 30'
fms. ft in.
10 4 9
From centre of pp. shaft.
A at crossing of East level.
B
...
84 26'
732
C
92 04'
8 1 9
C AtxcutN.
"D^
342 09'
730
D 2 END do.
D
96 05'
359
END.
(City Guilds, 1883.)
APPENDIX I.
311
34. Describe the ordinary method of using the theodolite in making an
underground-survey. Also any special method which may be adopted
where great accuracy is required. (City Guilds, 1887.)
35. Lay down the following underground-survey on the scale of 2 chains
to an inch :
Distance, Chains.
Vertical Inclination
Horizontal Angles.
Shaft to A
1-90
0'
A = 145 15'
AB
6-75
4 35'
B = 177 3(X
BC
4-30
3 13'
C = 213 54'
CD
9-77
0'
D = 97 20'
DE
3-90
6 46'
E = 130 13'
EF
6-13
0'
F = 167 3(X
FG
3-01
2 20'
The horizontal angles are those on the left hand of a person travelling in
the direction of the survey, and the magnetic bearing of the line F G is 30
east of north. (City Guilds, 1887.)
36. The difference of level of two points several miles apart is required
with great exactness, and a levelling-instrument of high power is used for
the purpose.
Under what circumstances would it be necessary to allow for the spherical
form of the earth, and in what manner would you make the proper correc-
tions ? (City Guilds, 1887. )
37. A colliery waggon way is laid down in a straight line from A, near the
shaft, to a point B, in a direction 40 east of north, and is to be extended to
join a main line of railway towards the east, running due north and south.
The distance from B to the main line is 30 chains, measured due east, and
the junction is to be made by a curve 60 chains radius.
Show how the waggon way must be set out, and find what length of line
will be required beyond the point B.
In setting out the curve from the straight portion of railway, what offset
must be made at the end of the first chain ? (City Guilds, 1887.)
38. It is intended to sink a shaft on the end of a level driven from
Pendarves' shaft, and the following is the survey by J. Budge from the
centre of the shaft to the eastern end of the level :
312
MINE-SURVEYING.
No.
Bearing.
Distance.
A
357 00'
fins. ft. ins.
730
from centre of shaft.
B
82 45'
406
C
81 30'
300
D
90 00'
8 1 1
E
102 00'
500
F
96 45'
430
G
105 00'
245
H
85 00'
330
J
77 45'
227
K
351 00'
440
END.
As absolute accuracy was required a reverse or proof course of dialling
as made from the end back to the shaft, with the following results :
No.
Bearing.
Distance.
A
171 30'
fins. ft. Ins.
4 2 10
from eastern END.
B
259 00'
230
C
265 15'
3 1 6
D
283 15'
320
E
279 30'
843
F
268 45'
720
G
263 00'
420
H
260 15'
348
J
177 45'
7 1 10
centre of shaft.
Calculate the distance and bearing, from Pendarves' shaft, of the point at
the surface at which the new shaft must be sunk.
APPENDIX I. 313
39. Sketch and describe a hanging compass, state in which way it is
tested and repaired, and describe the manner of its application. (Tokio
University, Japan, 1879.)
40. Give a short description of the German dial, and what you consider
to be its merits or demerits as compared with the English miner's diaL
(City Guilds, 1880.)
41. Describe the continental method of surveying mines by means of the
hanging compass, giving sketches of the instruments employed. (R.S.M.,
1886.)
42. What methods have been used to determine the deviation of bore-
holes from the vertical? (Science and Art Department, 1887.)
43. At the Scotchman's United Mine, Stawell, and in various other
places, it has been found that bores made by the diamond drill have
deviated so seriously from their initial direction as to imply errors amount-
ing to from 30 to 75 feet in bore-holes of 500 feet. Describe a method of
making a survey of such bore-holes, and assuming the errors to have been
detected, how is it possible to straighten a bore which has been so deflected
as to endanger the safety of the drill ? (R.S.M., 1885.)
44. How should the compass be used in exploring for iron ores? (R.S.M.,
1887.)
45. Two parallel lodes were discovered at the surface, which was level,
30 yards apart underlying south, the south lode making an angle with the
horizon of 65 degrees, the north lode of 52 degrees. Eequired the per-
pendicular depth from the surface to their point of intersection ; and how
far south of the south lode would the centre of a perpendicular shaft have
to be placed to come down to the same point? Illustrate by a sketch, not
necessarily to scale, but a scale is recommended in order to roughly test the
accuracy of the calculations. (City Guilds, 1883.)
46. Illustrate in colours the following parts of a finished plan, scale 8
fathoms to the inch : A road 25 feet wide bounded on each side by a hedge
or bank 6 feet wide, showing a gateway, with a cross hedge or two. also a
house 30 feet by 20 feet abutting on the road, with a pond adjoining open
to the road, but with the hedge continued round its other sides. The pond
not to be less than 58 feet long and 25 feet wide, and of an oval but
irregular shape. A shaft 10 feet by 6 feet to be shown in one of the fields,
surrounded by a burrow or rubbish heap which is to be sketched in with
pen and indian ink. The whole drawing to be about 1 foot in length.
(City Guilds, 1883.)
47. Without the application of a protractor, lay off the following angles
from the same base, viz. : 20, 30, and 62 degrees, using a table of natural
eines for the purpose. Describe the process. (City Guild*, 1883.)
48. In the triangle ABC, the angle A = 37 45', B = 72 15', and the
side A B = 437. Find the sides AC, B C, and the perpendicular distance
from C to A B. (City Guilds, 1887.)
49. In the triangle ABC, the side A B = 365, A C = 180, and the angle
B = 25 30'. Determine the angles A and C, and the side B C. (City
Guilds, 1887.)
50. What do you understand by the word traversing ? Where is this form
of surveying necessary ? How would you use an angular instrument in the
314
MINE-SURVEYING.
operation, and how would you check the accuracy of the plotting of the work
by trigonometry ? (City Guilds, 1883.)
51. Describe the true meridian, as compared with the magnetic meridian.
How does the adoption of the latter affect plans made from compass
observations and added to, as in mine plans, from year to year ? (City
Guilds, 1882.)
52. It is desired to know the exact distance and bearing of an imaginary
line between the centre of a perpendicular shaft A and a point B in a level
underground, over which it is intended to sink another perpendicular shaft,
the dialling of the level commencing from A. Sketch the supposed drafts
underground, marking each with its length and bearing, and proceed to
describe the best and most accurate method of laying down, at the surface,
the line required, and the position of the proposed new shaft over B. (City
Guilds, 1881.)
53. Describe the ordinary process of levelling, stating any precautions
required to ensure accuracy. (City Guilds, 1885.)
54. Work out the following series of levels and plot in the form of a sec-
tion. Horizontal scale 1 chain to the inch, vertical scale 20 feet to the
inch. Datum-line 50 feet.
Distance.
Back-Sight.
Fore-Sight.
Chains.
0-70
Feet.
1-30
Feet.
8-85
1-50
8-85
2-30
245
13-96
5-40
3-60
5-40
0-52
4-05
12-62
8-80
5-40
8-80
1-12
7-00
2-32
7-05
9-40
1-33
9-96
10-20
3-34
5-87
11-35
5-87
9-10
-(City Guilds, 1885.)
55. Plot, on a scale of 2 chains to an inch, the following survey :-
APPENDIX I.
315
Chains.
Bearing.
Inclination.
Itiae.
A
2-50
119 45'
...
B
7-47
137 16'
3 5V
C
13-03
141 32'
...
D
3-40
196 50'
...
E
6-50
189 24'
9 36'
F
11-66
266 36'
7 30'
G
5-25
272 22'
(City Guilds, 1885.)
56. A straight draft is required to be driven of uniform inclination
between C and G. How must it be set out from each end ? (City Guilds,
1885.)
57. Describe the method of using the transit-theodolite in order to
measure horizontal and vertical angles with great precision. (City Guilds,
1885.)
58. Explain the principle of the vernier, and describe the manner in
which you would construct a vernier for a circle to read 30 seconds, when
the arc is divided into quarter degrees. (R. S. M., 1884.)
59. flow may the underground- and surface-surveys of a mine be con-
nected? (Jt. S. M.,I8S7.)
60. In a 20-fathom level driven on an east and west lode, underlying
north, a winze has been commenced bearing due north, and it is determined
to pitch a rise against it in the 40-fathom level ; the 30-fathom level not
having been driven far enough east for the purpose. How would you
determine the exact point in the 40-fathom level to start from ? (R. S. M.,
61. Calculate trigonometrically the bearing and distance of C from the
centre of the shaft in the following traverse :
No.
Angle.
Bearing.
Distance.
Bemarks.
A
000'
351 29'
fms. ft. in.
10 4 8
From centre of shaft.
B
90 21'
...
932
C
175 12'
12
END.
(R. S. M., 1SS6.)
316
MINE-SURVEYIXG.
62. Lay down, on a scale of 1 chain to the inch, the survey given on
age 36, representing a four- sided field connected with the shaft of a mine,
lalculate the area. (City Guilds, 1885.)
63. Plot the following survey, by W. Rickard, of a Cornish mine :
From pp. line in Williams' shaft at the 60-fathom level.
No.
A
Bearing.
Distance.
Inclination.
Inclined
Length.
Remarks.
176 00*
fin. ft. in.
326
...
fm. ft in.
B
77 3<X
4 1 9
...
...
...
C
82 45'
533
...
...
D
97 15'
329
to Vivian's winze.
E 2
4 15'
F.75 45'
10 5 6
F 2
285 W
729
...
...
G 2
263 00'
633
...
...
to Williams' shaft.
H 2
171 W
...
R.74' 11'
536
Up shaft to pp. line.
E
79 15'
636
...
...
...
F
57 00'
729
...
...
G
H
65 30'
183 00'
246
529
...
...
At x cut drive to
regain the lode.
On lode.
J
94 45'
646
...
...
to John's rise.
K 2
182 30'
...
R.67 30'
11 3
Up rise to 50 fm. level.
L 2
84 15'
549
...
...
...
M 2
75 30'
628
...
...
to Mitchell's shaft.
K
79 15'
854
...
...
END.
64. State the nature of the dislocations or heave* of lodes, their probable
origin, their appearance vertically and on a horizontal plane ; and the
various rules that have been recommended for regaining the severed portion.
(JR.S.M. Examination in Mining, 1879.)
65. A, B, and C are three bore-holes ; the depths of which from the same
horizontal plane to a seam of coal are respectively 100, 106, and 108 yards.
APPENDIX I. 317
From A to B is 100 yards, and from A to C 120 yards. The angle in a
horizontal plane between A B and A C is 30. What is the direction of the
dip of the seam, and the angle of dip ? (Mtrivale's Notes and Formulae.)
66. Name the permanent adjustments of the transit theodolite, and state
how they are made. (Edinburgh University, 1S88.)
67. Explain fully the process of setting out a tunnel in the driving of
which a number of shafts have to be employed. (Edinburgh, University,
1888.)
68. Suppose you were required to take levels along an underground
roadway in order to plot a section showing both roof and floor, state what
instruments you would use and how you would proceed. (Colliery Managers,
West Lancashire, 1887. )
69. State approximately the declination of the magnetic needle for the
year 1 888, and the average annual variation. How is the declination found
to vary in amount as you travel northwards or eastwards? (City Guilds^
1888.)
70. Describe the Hedley dial. (City Guilds, 1888.)
71. Explain what is meant by the true meridian. How may the true
meridian be determined by simple observations of some well-known stars ?
(City Guilds, 1888.)
72. Describe the method of measuring horizontal angles with the theodolite
by the process of repetition, and point out the special advantages of thi
mode of using the instrument. (City Guilds, 1888.)
73. Explain the method of reducing and plotting a survey by rectangular
co-ordinates. What are the advantages of this method as compared with
the ordinary mode of plotting with the scale and protractor ? (City Guilda,.
1889.)
74. What is meant by the term "error of collimation " as applied to a
transit-theodolite ? How may this error be detected and rectified ? Assum-
ing that a considerable error of collimation is allowed to remain uncorrected,
in what manner will it affect the measurement of an angle? Can the
instrument be used in such a manner as to neutralise this error? (City
Guilds, 1889.)
75. It is required to determine the position of a distant point, C, in the
workings of a colliery, with reference to the surface. For this purpose a
survey is made with the theodolite above and underground, from the shaft
A to C, and also to a second shaft B, by which means the underground and
surface-surveys are connected. Show how you would carry out the survey
so as to obtain the most accurate result.
Give your idea as to the degree of accuracy attainable by this method ;
and how far it will depend upon the relative positions of the points A, B,
and C, and the nature of the surveys between these points. (City Guilds,
1889.)
76. Describe the slide rule. (City Guilds, 1890.)
77. A line is measured on a imiform slope of 1 in 17. What allowance
per chain must be made for the inclination ?
APPENDIX II.
BIBLIOGRAPHY.
The following is a list of the principal treatises published on mine-survey-
ing :-
AGRICOLA, G. "De re metallica libri duodecim," folio. Basel, 1556.
HOUGHTON, T. "Kara avis in terris, or the compleate miner," 12mo.
London, 1681.
VOIGTEL, N. "Geometria subterranea," folio. Eisleben, 1686. Also 1692,
1714.
WEIDLER, J. F. "Institutiones geometriae subterranse," 8vo. Wittenberg,
1726.
JUGEL, J. G. " Geometria subterranea," 4to. Berlin, 1744. 2nd Edition,
Leipzig, 1773.
BEYER, A. " Grundlicher Unterricht vom Bergbau nach Anlaitung der
Markscheidekunst," 4to. Altenburg, 1749. 2nd Edition, 4to.
Edited by C. F. Lempe, 1785.
OPPEL, F. W. VON. " Anleitung zur Markscheidekunst," 4to. Dresden,
1749.
DUHAMEL, J. P. F. G. "Geometric souterraine," 4to. Paris, 1787.
FENWICK, T. "A Theoretical and Practical Treatise on Subterraneous
Surveying," 8vo. Newcastle-upon-Tyne, 1804. A reprint of this
work is published with additions by T. Baker.
HECHT, D. F. " Lehrbuch der Markscheidekunst," Svo. Freyberg, 1829.
BUDGE, J. "The Practical Miner's Guide," Svo. London, 1825. 2nd
Edition, 1845.
HANSTADT, J. N. L. VON. "Anleitung zur Markscheidekunst," 4to.
Pest, 1835.
WEISBACH, J. "Die neue Markscheidekunst," 2 vols., 4to. Brunswick,
1851-59.
ADRIANY, J. " Leitfaden seiner Vortrage iiber Markscheidekunde, " Svo.
Vienna, 1852. 2nd Edition, 1861.
BEER, A. H. " Lehrbuch der Markscheidekunst," Svo. Prague, 1856
HOSKOLD, H. D. "A Practical Treatise on Mining, Land, and Railway
Surveying," Svo. London, 1863.
SARRAN, M. E. "Manuel du ge"ometre sou terrain," 2 vols., Svo. Paris,
1868.
MILLER- HAUENFELS, A. VON. " Hohere Markscheidekunst, " Svo. Vienna,
1868.
BORCHERS, E. "Die praktische Markscheidekunst," Svo. Hanover, 1870.
LINTERN, W. "The Mineral Surveyor and Valuer's Complete Guide,"
12mo. London 1872.
LIEBENAM, A. " Lehrbuch der Markscheidekunst," Svo. Leipzig, 1876.
BRATHUHN, 0. " Lehrbuch der praktischen Markscheidekunst," Svo.
Leipzig, 1884.
VILLET, F. " Trait pratique du lever des plans souterrains," Svo.
St. Etienne, 18S5.
APPENDIX II. 319
The following works contain chapters on Mine-Surveying :
PRYCE, W. "Mineralogia cornubiensis, " folio. London, 1778 (pp. 202-213).
HAUSMANN, J. F. L. " Reise durch Scandiuavien," 5 vols.,8vo. Gb'ttiiigeu,
1811-18. [An account is given of the methods of surveying mines
in Sweden, vol. v., pp. 115-126.]
VILLEFOSSE, A. M. HERON L>E LA. " De la richesse mine'rale," 3 vols., 4to,
with folio atlas. Paris, 1819.
SOPWITH, T. " A Treatise on Isometric Drawing," 8vo. London, 1834.
WILLIAMS, B. " Practical Geodesy," 8vo. London, 1842.
COMBES, C. "Trait de 1'exploitation des mines," 3 vols., 8vo, with 4to,
atlas. Paris, 1844.
DEGOUSEE, J. " Guide du sondeur," 2 vols., 8vo. Paris, 1847.
PONSON, A. T. "Traite' de 1'exploitation des mines de houille,"4 vols.,
8vo, with folio atlas. Lie"ge, 1852. 2nd edition, 1870.
BAUERNFEIND, C. M. " Elemente der Vermessungskunde, " 2 vols., 8vo.
Munich, 1856. 5th edition, 1876.
RICKARD, W. "The Miner's Manual of Arithmetic and Surveying,
containing the usual Calculations Employed by the Miner," 8vo.
Truro, 1859.
GILLESPIE, W. M. "A Treatise on Levelling, Topography, and higher
Surveying," 8vo. New York, 1871.
ANDR, G. G. "The Draughtsman's Handbook of Plan and Map Drawing,"
4to. London, 1874.
HYSLOP, J. "Colliery Management," 2nd edition, 2 vols., 8vo. London,
1876.
DA VIES, C. "Elements of Surveying and Levelling." Revised by J. H.
van Amringe, 8vo. New York, 1883. The chapter on Mine-
Surveying was revised by J. G. Murphy.
HABETS, A. "Cours de topographic," 8vo. Liege, 1883.
HUNT, R. " British Mining,' a Treatise on the Metalliferous Mines of the
United Kingdom, " 8vo. London, 1884.
CHANCE, H. M. " Report on Coal Mining. Pennsylvania Second Geological
Survey," 8vo. Philadelphia, 1885.
JOHNSON, J. B. "The Theory and Practice of Surveying," Svo. New
York, 1886. The chapter on Mine-Surveying was written by
C. A. Russell.
WARLLE, W. " Reference Book on Practical Coal Mining," Svo. London,
1887.
STANLEY, W. F. "Surveying and Levelling Instruments," Svo. London,
1890.
PELLETAN, A." Traite de Topographic,'' 8vo. Paris, 1893.
INDEX.
ABNEY'S level, 183.
Accuracy obtainable in spirit-level-
ling, 183.
, , of linear measurements, 24.
Adit level, 6.
Adjustments of the level, 166.
,, of the theodolite, 98.
Agricola, G., 3. 26.
Aita, L., 186.
American mining claims, 127.
transit, 95.
Amsler's planimeter, 159.
Anallatism, 220.
Aneroid barometer, 192.
Angular measures, 8.
Apex, 5.
Arrows, 12.
Artificial horizon, 213.
Ashburner, C. A., 276, 286.
Azimuth, 59.
BACK-OBSERVATIONS, 31.
Balancing, 147.
Ball and socket joint, 31.
Barometer, aneroid, 192.
mountain, 191.
Base-line, 120.
Base of verification, 120.
Basset, 5.
Pauerman, H., 288.
Beanlands, A., 208.
Bearing of a line, 31.
Bed, 5.
Bench-marks, 180.
Bibliography, 318.
Boning staves, 164.
Borchers, E., 303.
,, measuring rods, 194.
, , portable magnetometer, 216.
,, vane rod, 171.
Bord, 70.
Bore-holes, strike and dip of a seam
found from, 248.
surveying, 300.
Bowie, A. J., 200.
Boys, C. V., 149.
Bramwell, Sir F., 159.
Brathuhn, O., 110.
Brooks, T. B., 293.
Brough, B. H., 229, 289.
Bunning, C. Z., 187, 302.
Burt's solar compass, 103.
CALCULATING machines, 149.
,, scales, 149.
Calculation of areas, 154.
Gallon, J., 268.
Candle-holder, 238.
Cape rood, 132.
Casella's theodolite, 97.
Chain, 11.
,, only, surveying with the, 18.
,, used in trigonometrical sur-
veys, 20.
Chaining on slopes, 13.
Chains converted into feet, 12.
Chords, plotting by, 142.
Chorobates, 185.
Chrismar's, O., Ill, 194.
Chrismar's theodolite stand, 108.
Cii-cumfererlter, 59.
Claim, 7.
Claims, survey of, 127.
Clark, E., 207.
Clinograph, 300.
Clinometer for bore-holes, 300.
for exploratory work, 1 90.
,, German, 79.
G. P. Evelyn's, 237.
Clinostats, 300.
Coal mines regulation act (1887), 273,
278.
Coal-seams, produce of, 160.
Colby's compensating bars, 21.
Colliery surveys with the dial, 37.
with the rack-dial, 67.
, , with the theodolite, 1 1 2-
Collimation, 99.
322
Collimation method of levelling, 179.
Colouring plans, 281.
Combes, C., 52.
Compensating bars, 21.
Computing the sides of triangles, 123.
Concession, 7.
Conder, Major, 243.
'Connection of underground- and sur-
face-surveys, 201.
Contour lines, 196, 257.
Conventional signs for mine plans, 277.
Co ordinates, plotting by, 142, 151.
Copying plans, 282.
Correction for chaining on slopes, 14.
Corresponding altitudes, 45.
Country, 5.
Course, 5.
Coxe, E. B., 22, 114
Craven, A., 241.
Cross-course. 5.
Cross-cut, 6.
Cross-sections, 235.
Cross- staff, 15.
Croton aqueduct, 241.
Curvature of the earth's surface, 172.
Curves for engine planes, 237.
Curves, ranging, by means of angles
at the circumference,
233.
by means of offsets, 231.
Cushing's reversible level, 167.
DATUM line, 175.
Davis' s dial, 63.
Dawson, W. B., 228.
Declination of the magnetic needle,
40.
Depth of shafts, 193.
Diagonal eye piece, 211.
,, scales, 137.
Dial joint, 64.
Dialling book, 35.
,, ,, for surveying in pre-
sence of iron, 54.
,, definition of, 1.
Dickinson, J., 5.
Diopter, 2.
Dip, 5, 246.
Direction of mineral deposits, 246.
Direct vernier, 60.
Dislocated lodes, 261.
Distance-measuring by telescope,217.
Distances, measurement of, 11.
Diurnal variation of the magnetic
needle, 42.
Divining rod, 3.
Dixon, J. S., 265.
Down-throw, 263.
Drawing-plans, 279.
Drift, 7.
Driving levels underground, 235.
Dump heap, cubical content of, 258.
Dumpy level, 165.
Dyke, 263.
EARTH'S magnetism, directive action
of the, 26.
Eccentric telescope for transit-theo-
dolite, 212.
Eccentricity of magnetic needle, 30.
Eckhold's omnimeter, 217.
Eidograph, 284.
Electric light for surveying purposes,
111.
End, 6.
Enlarging plans, 283.
Equalising, 155.
Errors in compass surveys, 57.
,, spirit-levelling, 183.
Evelyn's clinometer, 237.
Everest theodolite, 92.
Examination questions, 307.
Exploring for iron ore, 289.
FACE, 71.
Fairley's gradometer, 246.
Fast-needle surveying, 59.
Faults, 263.
Feet converted into links, 12.
Field-book for chain surveys, 20.
Field-compasses, 22.
Fixed-needle surveying, 59.
Floor, 5.
Flying levels, 174.
Follower in chainin2, 13.
Foot-wall, 5.
Forebreast, 6.
Fore-observations, 31.
Foster, C. Le Neve, 5, 268, 277.
GAERTNER, E. G., 148.
Galloway, T. L., 187.
Galloway, W., 268.
Gangue, 5.
Gate roads, 7.
German dial, 78.
Gilbert, G. K., 192.
Giving and taking, 155.
Gnomon, 45.
Gradienter screw, 217.
Gradometer, 246.
Graefe, M., 195
Gravatt's level, 165.
staff, 168.
Gurden, R. L., 150.
Gurley's solar attachment, 104.
Guthrie, J. K., 302.
HADE, 5.
Hanging compass, 78.
wall, 5.
Harden, J. H., 94.
0. B., 288.
Hausse, R., 267
Heading, 7.
Headway, 71.
Hedley's dial, 34.
Henderson, J., 35.
dial, 62.
,, rapid traverser, 149.
Kenwood, W. S., 261.
Hero of Alexandria, 2.
Hildebrand's compass, 215.
History of the miner's dial, 26.
,, mining- theodolite, 87.
surveying, 1.
Hitch, 71, 263.
Hoffman joint, 64.
,, tripod head, 93.
Holing from one excavation to an-
other, 252.
Holing use of magnet in, 303.
Hoosac tunnel, 242.
Horizontal circle of theodolite, 88.
Hoskold, H. D., 203, 211.
Hoskold's transit theodolite, 91.
Houghton, T.,27, 186.
Howard, W. F., 76, 109, 197.
Huebner, H., 109.
Hughes, H. W., 180, 161.
Hunt, R., 2.
Hydraulic mining ditches, 199.
Hypsometer, 193.
ILL-CONDITIONED triangles, 120.
Illumination of cross-wires of theo-
dolite, 111.
Inclination of colliery roads, 236.
,, magnetic-needle, 50.
Inclined shafts, surveying in, 75.
Index-error, 100.
Interior angles of a traverse, 112.
Intermediate sights, 176.
Intersection of two veins, 258.
Iron ore, exploring for, 28 ( J.
EX. 323
Iron rails, influence of, 52.
,, surveying in the presence of. 54.
Irregular deposits, 5.
,, variations of the magnetic-
needle, 44.
Irregularities of seams and beds, 263.
Isogonic lines, 42.
Isometric plans of mines, 284.
JACKSON, L. D., 235.
Jee's levelliug-staff, 169.
Johnston, J. B., 228, 229.
G. R., 85.
Jordan, T. B., 287-
W., 23.
Junge. A., 53.
Jurisch, C. L. H. M., 151.
KOEHLEE, G., 265.
LATCHING, definition of, 1.
Leader in chaining, 13.
Lean's dial, 61.
Least reading of a vernier, 60.
Lehigh Valley Coal Co., 196.
Lehman, A. E., 288.
Lettering of the miuei-'s dial, 33.
,, on plans, 281.
Levelling, 164.
-book, 175, 177, 178, 179,
181, 1S2.
-staff, 167.
Levels of a mine, 6.
Limb of theodolite, 89.
Lighting verniers, 110.
Linear measurements, accuracy of,
24.
rolling planimeter, 160.
Local attraction in the mine, 53.
Lodes, 5.
Long compass-box, 214.
Long-wall, 7-
Lorber, F., 24, 160.
Lyman, B. S., 229.
MACGEOROE, E. F., 300.
Magnet used in cases of uncertain
holing, 303.
Magnetic meridian, 40.
-needle, declination of, 41.
,, ,, for exploring for
iron ore, 289.
,, shape of, 29.
Magnetometer, 216.
Map, determination of meridian by. 49.
324
INDEX.
Marquard, L., 151.
Marquois scales, 185.
Mason's level, 164.
Masses, 6.
Measures of area, 154.
length, 7.
Measuring-tape, 15.
-wheel, 23.
Meridian line, setting-out, 49.
Merivale, J. H., 161.
Miller- Hauenfels, A. von, 80.
Mine models, 286.
Mineral deposits, 5.
Miner's dial, 28.
Models of mines, 286
Moinot's tacheometer, 221.
Morgen, 132.
Moulton, M., 287.
Murphy, J. G., 161.
NATURAL scale, 135.
Newall, R, S., 216.
Newton's tripod, 31.
New York target rod, 168.
Nolten, G., 302.
Norris, R., 116.
OBLIQUE offsets, 16.
Obstacles in chaining, 16.
Offset rod, 15.
Offsets, 15.
Oldest mine plan, 1.
Omuimeter, 217.
Optical square, 15.
Ordnance bench mark, 180.
,, survey, 122.
Ore-reserves, calculation of, 161.
Orientation, line of, 50.
Osterland's hanging compass, 81.
Outcrop, 5.
PACING, 23.
Pantograph, 284.
Parallax, 98.
Passometer, 23.
Pedometer, 23.
Penkert's hanging compass, 85.
Physical levelling, 191.
Photography, 282.
Pierce, J., 126.
Plane-table, 126.
Plane theodolite, 89.
Planimeters, 158.
Plans of American collieries, 275.
colleries, 273.
Plans of metalliferous mines, 270.
Plate of theodolite, 89.
Plotting-scales, 139.
,, sections, 184.
,, surveys, 134.
,, with the German dial, 83.
,, the underground traverse on
the surface, 231.
Plumb-bob, 107, 190, 236.
Plummet lamp, 109..
Point at surface directly above one
underground, 250.
Pole star, determination of meridian
by, 48.
Porro's lens, 220.
tacheometer, 221.
Post and stall, 7.
Preservation of plans. 278.
Prismatic compass, 111, 126.
Prolongation of base-line, 121.
Protractor, 140, 222.
Pryce, W., 28.
Przyborski, 111.
QUICK levelling tripod, 95.
RACK dial, 59.
Racking, 60.
Railways to mines, setting-out, 231.
Ramsay, J. A., 180.
Ranges, 132.
Ranging rods, 230.
,, straight lines, 230.
Rankine, W. J. M., 235.
Rapid traverser, 149.
Raymond, R. W., 97, 265.
Record of colliery survey, 39.
,, ,, with fixed
needle, 68.
,, surface-survey with the
dial, 37.
Reducing plans, 283.
Reflecting level, 183.
Relief plans, 286.
Repetition, 101.
Reservoir, cubical content of, 257.
Retrograde vernier, 60.
Rhodius, A., 259.
Ridding, 71.
Rise, 6.
Rods, 21.
Roessler's hanging compass, 81.
Rolley ways, 7.
Roof, 5.
Royalty, 7.
325
SAYCE, Prof., 242.
Scales, 134.
,, for mine plans, 277.
Schmidt, M., 170. 204.
Schmidt's rule, 261.
Scotland, plotting surveys in, 150.
Seam, 5.
Section corner, 132.
Secular variations of the magnetic
needle, 41.
Seibt, W., 183.
Sett, 7.
Setting-out, 230.
Severn tunnel, 210.
Shadow-methyl of determining the
true meridian, 44.
Shaft, 6.
,, surveying, 75.
Shafts, depth of; 193.
, , sunk from several levels, 256.
Siloam inscription, 242.
Simply divided scales, 134.
Simms, F. W., 238.
Slide-rule, 149, 222.
Slope, ratio of, 235.
Slopes, chaining on, 13.
Smock, J. G., 299.
Smyth, SirW. W., 4.
Solar attachment, 103.
Sopwith, T. , 285, 287.
Sopwith's staff, 168.
South Africa, surveying in, 132, 151.
Southern hemisphere stars, 49.
Spherical excess, 121.
Spirit-level, 165.
Spirit-levels of the miner's dial, 30.
Split-sight, 62.
Stadia, 218.
,, and theodolite, 226.
Stampfer's distance-measurer, 217.
Stanley, W. P., Ill, 169, 223, 284.
Station-lines, 19.
,, measuring, 78.
Stations, 19.
Steel band, 22.
Stenton, 71.
Stepping, 15.
Stockwork, 6.
Stokes, A. H., 273.
Stope, 6.
Stoup and room, 7.
Strike, 5.
Stuart-Menteath, P. W., 5.
Subsidence and draw, 265.
Sump, 6.
Surface-plans of mines, 274.
Surface-surveys with the dial, 35.
theodolite, 120.
Surveying, definition of, 1.
,, with the chain only, 18.
Suspended planimeter, 160.
TABULAR deposits, 5.
Tacheometer, 223.
Telemeter, 226.
Telescope, 90.
Telescopic measurement of distances,
217.
Telescopic measurements under-
ground, 228.
Thaten, R., 294.
Theodolite and compass compared,
118.
levelling with, 187.
surveys in Pennsylvania,
114.
Thill, 71.
Thornton's dial, 66.
staff, 169.
Thwaite, B. H., 283.
Tiberg, E., 297.
Tie-line, 19.
Topographical stadia, 225.
Township corner, 132.
Tracing, 282.
Transit-instrument, 208.
,, theodolite, 89.
,, ,, for connecting
surveys, 210.
Trautwine, J. C., 235.
Traverse, 67.
tables, 149.
Traversing underground, 67, 107.
Trianglation, 120.
Trigonometer, 148.
Trigonometrical formulae, 9.
levelling, 187.
Tripod of the miner's dial, 31.
Trouble, 263.
Troughton's level, 166.
True meridian, 40.
,, determination of, 44.
Tubular compass, 214.
Tunnel, 6.
,, driven through a hill, 255.
Tunnels, setting-out, 237.
UNDERLIE, 5.
Units of length, 7.
Up-throw, 263.
326
VARIATION of the magnetic-needle,
40.
Veins, mineral, 5.
Vernier, 59.
,, compass, 75.
plate of theodolite, 88.
scales, 138.
Vertical angles, measurement of,
33.
Viameter, 23.
Vitruvius, 186.
Voigtel, N., 148.
WAKDI.E, W., 237.
Water-level, 185.
Watkins, F. W., 241.
\V ay-gates, 7-
Weissbach's plummet lamp,
Welizki, T., 138.
Whitelaw's dial, 65.
Whites, 19.
Winslow, A., 228.
Winze, 6.
Wire ropeways, 197.
Y-LEVEL, 166.
ZIMMERMAN'S rule, 262.
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Discharge through Orifices Gauging Water by Weirs Flow of Water
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London Hydraulic Power Company Birmingham Hydraulic Power System
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BROWNE (W. R.), Student's Mechanics), 5
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PAGE
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THE DESIGN OF STRUCTURES:
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POCKET-BOOK; Or, Synopsis of Animal Classification. Comprising
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and Tables. By Dr. Emil Selenka, Professor in the University of
Erlangen. Authorised English translation from the Third German
Edition. In Small Post 8vo, Interleaved for the use of Students. Limp
Covers, 45.
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HKNSIVR and SUCCESSFUL attempt to present us with a scheme of the natural arrangement of
the animal world." Edin. Med. Journal.
" Will prove very serviceable to those who are attending Biology Lectures. . . . The
translation is accurate and clear." Lancet.
LONDON: EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS.
GAS, OIL, AND AIR ENGINES:
A Practical Text - Book on Internal Combustion Motors
without Boiler.
BY BRYAN DONKIN, M.lNST.C.E.
With numerous Illustrations. Large 8vo, 2 is.
GENERAL CONTENTS. Gas Engines: General Description History and Develop-
mentBritish, French, and German Gas Engines Gas Production for Motive Power-
Theory of the Gas Engine Chemical Composition of Gas in Gas Engines Utilisation of
Heat Explosion and Combustion. Oil MotOPS : History and Development Various
Types Priestman's and other Oil Engines. Hot-AiP Engines : History and Develop-
ment Various Types : Stirling's, Ericsson's, &c., &c.
"The BEST BOOK NOW PUBLISHED on Gas, Oil, and Air Engines. . . . Will be of
VERY GREAT INTEREST to the numerous practical engineers who have to make themselves
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PRACTICAL EXPERIENCE, combined with HIGH SCIENTIFIC AND EXPERIMENTAL KNOWLEDGE,
and an accurate perception of the requirements of Engineers." The Engineer.
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NEWS to all who desire reliable, up-to-date information. . . . His book is MOST TIMELY,
and we welcomed it at first sight as being just the kind of book for which everybody inter-
ested in the subject has been looking. . . . We HEARTILY RECOMMEND Mr. Donkin's
work. ... A monument of careful labour. . . . Luminous and comprehensive. . . .
Nothing of any importance seems to have been omitted." -Journal of Gas Lighting.
INORGANIC CHEMISTRY (A Short Manual of).
BY A. DUPRE, Ph.D., F. R. S., AND WILSON HAKE,
Ph.D., F.I.C., F.C.S., of the Westminster Hospital Medical School
SECOND EDITION, Revised. Crown 8vo. Cloth, 75. 6d.
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"There is no question that, given the PERFECT GROUNDING of the Student in his Science,
the remainder comes afterwards to him in a manner much more simple and easily acquired.
The work is AN EXAMPLE OF THE ADVANTAGES OF THE SYSTEMATIC TREATMENT of a
Science over the fragmentary style so generally followed. BY A LONG WAY THK BEST of the
snail Manuals for Students." Analyst.
HINTS ON THE PRESERVATION OF FISH,
IN REFERENCE TO FOOD SUPPLY.
BY T. COSSAR EWART, M.D., F.R.S.E.,
Regius Professor of Natural History, University of Edinburgh.
In Crown 8vo. Wrapper, 6d.
LONDON : EXETER STREET, STRAND.
io CHARLES GRIFFIN & CO. '8 P UBL1CA TIONS.
SECOND EDITION, Revised. Royal Sv0. With numerous Illustrations and
13 Lithographic Plates. Handsome Cloth. Price 30^.
BRIDGE-CONSTRUCTION
(A PRACTICAL TREATISE ON):
Being a Text-Book on the Construction of Bridges in
Iron and Steel.
FOR THE USE OF STUDENTS, DRAUGHTSMEN, AND ENGINEERS.
BY
T. CLAXTON FIDLER, M. INST. C.E.,
Prof, of Engineering, University College, Dundee.
"Mr. FIDLEB'S SUCCESS arises from the combination of EXPERIENCE and
SIMPLICITY OF TREATMENT displayed on every page. . . . Theory is kept in
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as to students of Bridge Construction." ("TAe Architect" on the Second
Edition.')
" Of late years the American treatises on Practical and Applied Mechanics
have taken the lead . . . since the opening up of a vast continent has
given the American engineer a number of new bridge -problems to solve
. . . but we look to the PRESENT TREATISE ON BRIDGE-CONSTRUCTION, and
the Forth Bridge, to bring us to the front again." Engineer.
" One of the VERT BEST RECENT WORKS on the Strength of Materials and its
application to Bridge-Construction. . . . Well repays a careful Study."
Engineering.
"An INDISPENSABLE HANDBOOK for the practical Engineer." Nature.
" An admirable account of the theory and process of bridge-design, AT ONC*
SCIENTIFIC AND THOROUGHLY PRACTICAL. It is a book such as we have a right
to expect from one who is himself a substantial contributor to the theory of
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Industries.
"A SCIENTIFIC TREATISE OF GREAT MERIT. " Westminster Review.
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appeared no one more ABLE, EXHAUSTIVE, or USEFUL than Mr. Claxton
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LONDON: EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS.
ORE & STONE MINING,
BY
C. LE NEVE FOSTER, D.Sc., F.R.S.,
PROFESSOR OF MINING, ROYAL COLLEGE OF SCIENCE; H.M. INSPECTOR OF MINES.
In Large 8vo. With Frontispiece and 716 Illustrations. 345.
"Dr. Foster's book was expected to be EPOCH-MAKING, and it fully justifies such expec-
tation. ... A MOST ADMIRABLE account of the mode of occurrence of practically ALL
KNOWN MINERALS. Probably stands UNRIVALLED for completeness." The Mining Journal.
GENERAL CONTENTS.
INTRODUCTION. Mode of Occurrence of Minerals: Classification: Tabular
Deposits, Masses Examples: Alum, Amber, Antimony, Arsenic, Asbestos. Asphalt,
Barytes. Borax, Boric Acid, Carbonic Acid, Clay, Cobalt Ore, Copper Ore, Diamonds,
Flint, Freestone, Gold Ore, Graphite, Gypsum, Ice, Iron Ore, Lead Ore, Manganese
Ore, Mica, Natural Gas, Nitrate of Soda, Ozokerite, Petroleum, Phosphate of Lime
Potassium Salts, Quicksilver Ore, Salt, Silver Ore, Slate, Sulphur, Tin Ore, Zinc Ore.
Faults. Prospecting: Chance Discoveries Adventitious Finds Geology as a
Guide to Minerals Associated Minerals Surface Indications. Boring: Uses of
Bore-holes Methods of Boring Holes: i. By Rotation, ii. By Percussion with Rods,
iii. By Percussion with Rope. Breaking Ground: Hand Tools Machinery-
Transmission of Power Excavating Machinery: i. Steam Diggers, ii. Dredges,
iii. Rock Drills, iv. Machines for Cutting Grooves, v. Machines for Tunnelling
Modes of using Holes Driving and Sinking Fire-setting Excavating by Water.
Tin
holes Underground \V orkings Beds Veins Masses. Haulage or Transport:
Underground: by Shoots, Pipes, Persons, Sledges, Vehicles, Railways, Machinery,
Boats Conveyance above Ground. Hoisting or Winding: Motors, Drums, and
Pulley Frames Ropes, Chains, and Attachments Receptacles Other Appliances
Safety Appliances Testing Ropes Pneumatic Hoisting. Drainage: Surface Water
Dams Drainage Tunnels Siphons Winding Machinery Pumping Engines
above ground Pumping Engines below ground Co-operative Pumping. Ventila-
tion: Atmosphere of Mines Causes of Pollution of Air Natural Ventilation-
Artificial Ventilation : i. Furnace Ventilation, ii. Mechanical Ventilation Testing
the Quality of Air Measuring the Quantity and Pressure of the Air Efficiency of
Ventilating Appliances Resistance caused by Friction. Lighting : Reflected
Daylight Candles Torches Lamps-Wells Light Safety Lamps Gas Electric
Light. Descent and Ascent : Steps and Slides Ladders Buckets and Cages Man
Engine. Dressing: i. Mechanical Processes: Washing, Hand Picking, Breaking
Up, Consolidation, Screening ii. Processes depending on Physical Properties :
Motion in Water, Motion in Air Desiccation Liquefaction and Distillation
Magnetic Attraction iii. Chemical Processes: Solution, Evaporation and Crystal-
lisation, Atmospheric Weathering, Calcination, Cementation, Amalgamation Ap-
plication of Processes Loss in Dressing Sampling. Principles of Employment
of Mining Labour : Payment by Time, Measure, or Weight By Combination of
these By Value of Product. Legislation affecting Mines and Quarries:
Ownership Taxation Working Regulations Metalliferous Mines Regulation Acts
Coal Mines Regulation Act Other Statutes. Condition of the Miner : Clothiag
Housing Education Sickness Thrift Recreation. Accidents : Death Rate of
Miners from Accidents Relative Accident Mortality Underground and Above-
ground Classification of Accidents Ambulance Training.
" This EPOCH-MAKING work . . . appeals to MEN OF EXPERIENCE no less than to
students . . . gives numercus examples from the MINING PRACTICE of EVERY COUNTRY.
Many of its chapters are upon subjects not usually dealt with in text books. ... Of
great interest. . . . Admira.b\y'M\itlreLted."J>(rz-undJ L ftit/enmannis<:AeZeitung.
" This SPLENDID WORK." Oesterr. Ztickrft. fur Berg- und Hiittenviesen.
LONDON: EXETER STREET, STRAND.
12 CHARLES GRIFFIN <k CO.'S PUBLICATIONS.
SECOND EDITION (for 1895). Shortly.
Cloth, for Office use, 8s. 6d. Leather, for the Pocket, 8s. 6d.
GRIFFIN'S ELECTRICAL PRICE-BOOK.
FOR THE USE OF
Electrical, Civil, Marine, and Borough Engineers, Local
Authorities, Architects, Railway Contractors, &e., &e.
EDITED BY
H. J. DOWSING,
Member of the Institution of Electrical Engineers ; of the Society of Arts ; of the London
Chamber of Commerce, &>c.
GENERAL CONTENTS.
PART I. PRICES AND DETAILS OF MACHINERY AND APPARATUS.
PART II. USEFUL INFORMATION CONCERNING THE SUPPLY OF
ELECTRICAL ENERGY; Complete Estimates; Reports, Rules and Regu-
lations, Useful Tables, &c. ; and General Information regarding the carrying out
of Electrical Work.
" The ELECTRICAL PRICE-BOOK REMOVES ALL MYSTERY about the cost of Electrical
Power. By its aid the EXPENSE that will be entailed by utilising electricity on a large or
small s:ale can be discovered. . . . Contains that sort of information which is most often
required in an architect's office when the application of Electricity is being considered."
Architect.
"The value of this Electrical Price-Book CANNOT BE OVER-ESTIMATED. . . . Will
save time and trouble both to the engineer and the business man." Machinery.
GRIFFIN (John Joseph, F.CS.) :
CHEMICAL RECREATIONS: A Popular Manual of Experimental
Chemistry. With 540 Engravings of Apparatus. Tenth Edition. Crown
8vo. Cloth. Complete in one volume, cloth, gilt top, 12/6.
Part I. Elementary Chemistry, 2/.
Part II. The Chemistry of the Non-Metallic Elements, IO/6.
GURDEN (Richard Lloyd, Authorised Surveyor
for the Governments of New South Wales and Victoria) :
TRAVERSE TABLES: computed to Four Places Decimals for every
Minute of Angle up to 100 of Distance. For the use of Surveyors and
Engineers. Third Edition. Folio, strongly half-bound, 2i/.
%* Published with Concurrence of the Surveyors- General for New South
Wales and Victoria.
" Those who have experience in exact SURVEY-WORK will best know how to appreciate
the enormous amount of labour represented by this valuable book. The computations
enable the user to ascertain the sines and cosines for a distance of twelve miles to within
half an inch, and this BY REFERENCE TO BUT ONE TABLE, in place of the usual Fifteen
minute computations required. This alone is evidence of the assistance which the Tables
ensure to every user, and as every Surveyor in active practice has felt the want of such
few knowing of their publication will remain without them." Engineer.
LONDON: EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS. 13
Griffin's Standard Publications
FOR
ENGINEERS, ELECTRICIANS, ARCHITECTS, BUILDERS,
NAVAL CONSTRUCTORS, AND SURVEYORS.
Applied Mechanics,
Civil Engineering,
Bridge-Construction, .
Design of Structures, .
Sewage Disposal Works,
Traverse Tables, .
Marine Engineering,
Stability of Ships,
The Steam-Engine, .
Dynamos,
Gas, Oil, and Air-Engines,
Boiler Construction,
Management,
Fuel and Water (for
Steam Users),
Machinery and Millwork,
Hydraulic Machinery, .
Metallurgical Machinery,
Useful Rules and Tables
for Engineers, &c., .
Electrical Pocket-Book,
Electrical Price-Book, -
RANKINE, BROWNE, JAMIESON, 22, 5, 16
PROF. RANKINE, . 22
PROF. FIDLER, . . 10
S. ANGLIN, ... 3
SANTO CRIMP, . . 7
R. L. GURDEN, . . 12
A. E. SEATON, . . 29
SIR E. J. REED, . 24
RANKINE, JAMIESON, . 22, 16
R. E. CROMPTON, . 8
BRYAN DONKIN, . 9
T. W. TRAILL, . . 30
R. D. MUNRO, . . 18
/ SCHWACKHOFER AND )
\ BROWNE, . {
PROF. RANKINE, . 22
PROF. ROBINSON, . 26
H. C. JENKINS, . 25
PROFS. RANKINE AND ) ^n
JAMIESON, . J
MUNRO AND JAMIESON, 19
H. J. DOWSING, . . 12
Graphic Tables for Con-
version of Measurements, PROF. ROBT. H. SMITH, 28
Marine Engineers' Poeket-
Book, .... SEATON AND ROUNTHWAITE, 29
Nystrom's Pocket-Book, DENNIS MARKS, . . 19
Surveyors' Pocket-Book, CRIMP AND COOPER, . 6
LONDON: EXETER STREET, STRAND.
14 CHARLES GRIFFIN A CO.' 8 PUBLICATIONS.
In Large 8w, with Illustrations and Folding-Plates. loj. 6d.
BLASTING:
A Handbook for the Use of Engineers and others Engaged in
Mining, Tunnelling, Quarrying, &c.
BY OSCAR GUTTMANN, Assoc. M. INST. C.E.
Member of the Societies of Civil Engineers and Architects of Vienna, and Budapest,
Corresponding Member of the Imp. Roy. Geological Institution of Austria, &rc.
GENERAL CONTENTS. Historical Sketch Blasting Materials Blasting Pow-
der Various Powder-mixtures Gun-cotton Nitro-glycerine and Dynamite
Other Nitro-compounds Sprengel's Liquid (acid) Explosives Other Means of
Blasting Qualities, Dangers, and Handling of Explosives Choice of Blasting
Materials Apparatus for Measuring Force Blasting in Fiery Mines Means of
Igniting Charges Preparation of Blasts Bore-holes Machine-drilling Chamber
Mines Charging of Bore-holes Determination of the Charge Blasting in Bore-
holes Firing Straw and Fuze Firing Electrical Firing Substitutes for Electrical
Firing Results of Working Various Blasting Operations Quarrying Blasting
Masonry, Iron and Wooden Structures Blasting in earth, under water, of ice, &c.
"This ADMIRABLE work." Colliery Guardian.
"Should prove a vade-mecum to Mining Engineers and all engaged in practical work."
Iron and Coal Trades Review.
WORKS BY GEORGE H. HURST, F.C.S.,
Member of the Society of Chemical Industry ; Lecturer on the Technology of Painters'
Colours, Oils, and Varnishes, the Municipal Technical School, Manchester.
PAINTERS' COLOURS, OILS, AND VAR-
NISHES : A Practical Manual. With Numerous Illustrations. Price
I2s. 6d.
GENERAL CONTENTS. Introductory THE COMPOSITION, MANUFACTURE,
ASSAY, and ANALYSIS of PIGMENTS, White, Red, Yellow and Orange, Green,
Blue, Brown, and Black LAKES Colour and Paint Machinery Paint Vehicles
(Oils, Turpentine, &c., &c.) Driers VARNISHES.
" This useful book will prove MOST VALUABLE. We feel bound to recommend it to ALL
engaged in the arts concerned. " Chemical Nfivs.
" A practical manual in every respect . . . EXCEEDINGLY INSTRUCTIVE. The
section oil Varnishes the most reasonable we have met with." Chemist and Druggist.
"VERY VALUABLE information is given." Plumber and Decorator.
" A THOROUGHLY PRACTICAL book, . . . constituting, we believe, the ONLY English
work that satisfactorily treats of the manufacture of oils, colours, and pigments." Chemical
Trades' yournal.
" Throughout the work are scattered hints which are INVALUABLE to the intelligent
reader. " Invention.
GARMENT DYEING AND CLEANING.
A Practical Book for Practical Men. With Numerous Illustrations.
GENERAL CONTENTS. Technology of the Textile Fibres Garment Cleaning
Dyeing of Textile Fabrics Bleaching Finishing of Dyed and Cleaned Fabrics-
Scouring and Dyeing of Skin Rugs and Mats Cleaning and Dyeing of Feathers
Glove Cleaning and Dyeing Straw Bleaching and Dyeing Glossary of Drugs
and Chemicals Useful Tables.
LONDON: EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS. 15
COAL-MINING (A Text-Book of):
FOR THE USE OF COLLIERY MANAGERS AND OTHERS
ENGAGED IN COAL-MINING.
BY
HERBERT WILLIAM HUGHES, F.G.S.,
Assoc. Royal School of Mines, Certificated Colliery Manager.
SECOND EDITION. In Demy Svo, Handsome Cloth. With very Numerous
Illustrations, mostly reduced from Working Drawings, i&s.
"The details of colliery work have been fully described, on the ground that
collieries are more often made REMUNERATIVE by PERFECTION IN SMALL MATTERS
than by bold strokes of engineering. ... It frequently happens, in particular
localities, that the adoption of a combination of small improvements, any of
which viewed separately may be of apparently little value, turns an unprofitable
concern into a paying one." Extract from Author's Preface.
GENERAL CONTENTS.
Geology : Rocks Faults Order of Succession Carboniferous System in Britain.
Coal : Definition and Formation of Coal Classification and Commercial Value of Coals.
Search for Coal : Boring various appliances used Devices employed to meet Difficulties
of deep Boring Special methods of Boring Mather & Plait's, American, and Diamond
systems Accidents in Boring Cost of Boring Use of Boreholes. Breaking Ground;
Tools Transmission of Power : Compressed Air, Electricity Power Machine Drills Coal
Cutting by Machinery Cost of Coal Cutting Explosives Blasting in Dry and Dusty
Mines Blasting by Electricity Various methods to supersede Blasting. Sinking:
Position, Form, and Size of shaft Operation of getting down to " Stone-head " Method of
proceeding afterwards Lining shafts Keeping out Water by Tubbing Cost of Tubbing
Sinking by Boring Kind - Chaudron, and Lipmann methods Sinking through Quicksands
Cost of Sinking. Preliminary Operations : Driving underground Roads Supporting
Roof: Timbering, Chocks or Cogs, Iron and Steel Supports and Masonry Arrangement of
Inset. Methods of Working : Shaft, Pillar, and Subsidence Bord and Pillar System-
Lancashire Method Longwall Method Double Stall Method Working Steep Seams-
Working Thick Seams Working Seams lying near together Spontaneous Combustion.
Haulage: Rails Tubs Haulage by Horses Self-acting Inclines Direct-acting Haulage
Main and Tail Rope Endless Chain- Endless Rope Comparison. Winding: Pit
Frames Pulleys Cages Ropes Guides Engines Drums Brakes Counterbalancing
Expansion Condensation Compound Engines Prevention of Overwinding Catches at pit
top Changing Tubs Tub Controllers Signalling Pumping: Bucket and Plunger
Pumps Supporting Pipes in Shaft Valves Suspended lifts for Sinking Cornish and
Bull Engines Davey Differential Engine Worthington Pump Calculations as to size of
Pumps Draining Deep Workings Dams. Ventilation: Quantity of air required
Gases met with in Mines Coal-dust Laws of Friction Production of Air-currents
Natural Ventilation Furnace Ventilation Mechanical Ventilators Efficiency of Fans
Comparison of Furnaces and Fans Distribution of the Air-current Measurement of Air-
currents. Lighting: Naked Lights Safety Lamps Modern Lamps Conclusions
Locking and Cleaning Lamps Electric Light Underground Delicate Indicators. Works
at Surface; Boilers Mechanical Stoking Coal Conveyors Workshops. Preparation
of Coal for Market : General Considerations Tipplers Screens Varying the Sizes made
by Screens Belts Revolving Tables Loading Shoots Typical Illustrations of the arrange-
ment of Various Screening Establishments Coal Washing Dry Coal Cleaning -Briquettes.
"Quite THK BEST BOOK of its kind ... as PRACTICAL in aim as a book can be . . .
touches upon every point connected with the actual working of collieries. The illustrations
are EXCELLENT." Athenieiun.
" A Text-book on Coal-Mining is a great desideratum, and Mr. HUGHES possesses
ADMIRABLE QUALIFICATIONS for supplying it. . . . We cordially recommend the work."
Colliery Guardian.
"Mr. HUGHF.S has had opportunities for study and research which fall to the lot of
but few men. If we mistake not, his text-book will soon come to be regarded as the
STANDARD WORK of its kind." Birmingham Daily Gazette.
*+* Note. The first large edition of this work was exhausted within a few months of
publication.
LONDON: EXETER STREET, STRAND.
1 6 CHARLES ORIFFIN & CO.'S PUBLICATIONS.
WORKS BY
ANDREW JAMIESON, M.lNST.C.K, M.I.E.E., F.R.S.R,
Professor of Electrical Engineering, The Glasgow and West of Scotland
Technical College.
PROFESSOR JAMIESON'S ADVANCED MANUALS.
In Large Crown 8vo. Fully Illustrated.
1. STEAM AND STEAM-ENGINES (A Text-Book on).
For the Use of Students preparing for Competitive Examinations.
With over 200 Illustrations, Folding Plates, and Examination Papers.
TENTH EDITION. Revised and Enlarged, 8/6.
" Professor Jamieson fascinates the reader by his CLEARNESS OF CONCEPTION AND
SIMPLICITY OF EXPRESSION. His treatment recalls the lecturing of Faraday." Athenttum-
" The BEST BOOK yet published for the use of Students." Engineer.
" Undoubtedly the MOST VALUABLE AND MOST COMPLETE Hand-book on the subject
that now exists." Marine Engineer.
2. MAGNETISM AND ELECTRICITY (An Advanced Text-
Book on). Specially arranged for Advanced and " Honours " Students.
3. APPLIED MECHANICS (An Advanced Text-Book on).
Specially arranged for Advanced and " Honours" Students.
PROFESSOR JAMIESON'S INTRODUCTORY MANUALS.
In Crown &vo, Cloth. With very numerous Illustrations and
Examination Papers.
1. STEAM AND THE STEAM-ENGINE (Elementary Text-
Book on). Specially arranged for First- Year Students. FOURTH
EDITION. 3/6.
" Quite the RIGHT SORT OF BOOK." Engineer.
" Should be in the hands of EVERY engineering apprentice." Practical Enginttr.
2. MAGNETISM AND ELECTRICITY (Elementary Text-
Book on). Specially arranged- for First-Year Students. THIRD
EDITION. 3/6.
" A CAPITAL TEXT-BOOK . . . The diagrams are an important feature." Schoolmaster.
"A THOROUGHLY TRUSTWORTHY Text-book. . . . Arrangement as good as well
can be. . . . Diagrams are also excellent. . . . The subject throughout treated as an
essentially PRACTICAL one, and very clear instructions given." Nature.
3. APPLIED MECHANICS (Elementary Text-Book on).
Specially arranged for First-Year Students. SECOND EDITION. 3/6.
" Nothing is taken for granted. . . . The work has VERY HIGH QUALITIES, which
may be condensed into the one word ' CLEAR.' " Science and Art.
A POCKET-BOOK of ELECTRICAL RULES and TABLES.
FOR THE USE OF ELECTRICIANS AND ENGINEERS.
Pocket Size. Leather, 8s. 6d. Tenth Edition, revised and enlarged.
(See under Munro and Jamieson.}
LONDON : EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS.
" The MOST VALUABLE and USEFUL WORK on Dyeing that has yet appeared in the English
language . . . likely to be THE STANDARD WORK OP REFERENCE for years to come."
In Two Large 8vo Volumes, 920
pp., with a SUPPLEMENTARY
Volume, containing Specimens
of Dyed Fabrics. Handsome
Cloth, 45s.
MANUAL OF DYEING:
FOR THE USE OF PRACTICAL DYERS, MANUFACTURERS, STUDENTS,
AND ALL INTERESTED IN THE ART OF DYEING.
E. KNECHT, Ph.D., F.I.C.,
Head of the Chemistry and Dyeing Department
the Technical School, Manchester; Editor of "The
Journal of the Society of Dyers and Colourists ; "
CHR. RAWSON, F.I.C., F.C.S.,
Late Head of the Chemistry and Dyeing Depatment for
the Technical College, Bradford ; Member of Council
ot the Society of Dyers and Colourists ;
And RICHARD LOEWENTHAL, Ph.D.
GENERAL CONTENTS. Chemical Technology of the Textile Fabrics-
Water Washing and Bleaching Acids, Alkalies, Mordants Natural
Colouring Matters Artificial Organic Colouring Matters Mineral Colours
Machinery used in Dyeing Tinctorial Properties of Colouring Matters
Analysis and Valuation of Materials used in Dyeing, &c., &c.
" This MOST VALUABLE WORK . . will be widely appreciated." Chemical News.
" This authoritative and exhaustive work . . . the MOST COMPLETK we have yet seen
on the subject." Textile Manufacturer.
" The MOST EXHAUSTIVE and COMPLETE WORK on the subject extant." Textile Recorder.
" The distinguished authors have placed in the hands of those daily engaged in the dye-
house or laboratory a work of EXTREME VALUE and UNDOUBTED UTILITY . . . appeals
quickly to the technologist, colour chemist, dyer, and more particularly to the rising dyer
of the present generation. A book which it is refreshing to meet with." American Textilt
Record.
LONDON: EXETER STREET, STRAND.
i8 CHARLES GRIFFIN & CO.S PUBLICATIONS.
ELECTRO-METALLURGY (A Treatise on):
Embracing the Application of Electrolysis to the Plating, Depositing,
Smelting, and Refining of various Metals, and to the Repro-
duction of Printing Surfaces and Art- Work, &c.
BY WALTER G. M'MILLAN, F.I.C., F.C.S.,
Chemist and Metallurgist to the Cosfipore Foundry and Shell-Factory; Late Demonstrator
of Metallurgy in King's College, London.
With numerous Illustrations. Large Crown 8vo. Cloth 10s. 6d.
GENERAL CONTENTS. Introductory Sources of Current General Condition
to be observed in Electro-PlatingPlating Adjuncts and Disposition of Plant-
Cleansing and Preparation of Work for the Depositing- Vat, and Subsequent Polishing
of Plated Goods Electro-Deposition of Copper Electrotyping Electro-Deposition
of Silver of Gold of Nickel and Cobalt of Iron of Platinum, Zinc, Cadmium,
Tin, Lead, Antimony, and Bismuth ; Electro-chromy Electro- Deposition of Alloys
Electro-Metallurgical Extraction and Refining Processes Recovery of certain
Metals from their Solutions or Waste Substances Determination of the Proportion
of Metal in certain Depositing Solutions Appendix.
" This excellent treatise, . . . one of the BEST and MOST COMPLETB
manuals hitherto published on Electro-Metallurgy. " Electrical Review.
"This work will be a STANDARD." Jeweller.
"Any metallurgical process which REDUCES the COST of production
must of necessity prove of great commercial importance. . . . We
recommend this manual to ALL who are interested in the PRACTICAL
APPLICATION of electrolytic processes." Nature.
SECOND EDITION. Enlarged, and very f idly Illustrated. Cloth, 4s. 6d.
STEAM ~ BOI LE RS:
THEIR DEFECTS, MANAGEMENT, AND CONSTRUCTION.
BY R. D. MUNRO,
Chief Engineer of the Scottish Boiler Insurance and Engine Inspection Company.
This work, written chiefly to meet the wants of Mechanics, Engine-
keepers, and Boiler-attendants, also contains information of the first import-
ance to every user of Steam-power. It is a PRACTICAL work written for PRAC-
TICAL men, the language and rules being throughout of the simplest nature.
" A valuable companion for workmen and engineers engaged about Steam
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THE STABILITY OF SHIPS.
BY
SIR EDWARD J. REED, K.C.B., F.R.S., M.P.,
KNIGHT OF THE IMPERIAL ORDERS OF ST. STANILAUS OF RUSSIA ; FRANCIS JO6KPH O
AUSTRIA ; MKDJIDIE OF TURKEY ; AND RISING SUN OF JAPAN ; VICE-
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SCIENTIFIC AND TECHNOLOGICAL WORKS. 25
dlriffhi's P^tliuriral juries.
STANDARD WORKS OF REFERENCE
FOR
Metallurgists, Mine-Owners, Assayers, Manufacturers,
and all interested in the development of
the Metallurgical Industries.
EDITED BY
W. C. ROBERTS-AUSTEN, C.B., F.R.S.,
CHEMIST AND ASSAYER OF THE ROYAL MINT ; PROFESSOR OF METALLURGY IN
THE ROYAL COLLEGE OF SCIENCE.
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1. INTRODUCTION to the STUDY of METALLURGY.
By the EDITOR. THIRD EDITION. 125. 6d.
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SECOND EDITION, Revised and Enlarged.
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HYDRAULIC POWER
AND
HYDRAULIC MACHINERY.
BY
HENRY ROBINSON, M. INST. C.E, F.G.S.,
FELLOW OF KING'S COLLEGE, LONDON ; PROF. OP CIVIL ENGINEERING,
KING'S COLLEGE, ETC., ETC.
TKHttb numerous TKfloo&cuts, anfc Sijtg=nfne plates.
GENERAL CONTENTS.
Discharge through Orifices Gauging Water by Weirs Flow of Water
through Pipes The Accumulator The Flow of Solids Hydraulic Presses
and Lifts Cyclone Hydraulic Baling Press Anderton Hydraulic Lift
Hydraulic Hoists (Lifts) The Otis Elevator Mersey Railway Lilts City
and South London Railway Lifts North Hudson County Railway Elevator
Lifts for Subways Hydraulic Ram Pearsall's Hydraulic Engine Pumping-
Engines Three- Cylinder Engines Brotherhood Engine Rigg's Hydraulic
Engine Hydraulic Capstans Hydraulic Traversers Movable Jigger Hoist
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Shop Tools Tweddell's Hydraulic Rivetter Hydraulic Joggling Press
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Centre Crane Wrightson's Balance Crane Hydraulic Power at the Forth
Bridge Cranes Hydraulic Coal-Discharging Machines Hydraulic Drill
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with Variable Power Hydraulic Machinery on Board Ship Hydraulic Points
and Crossings Hydraulic Pile Driver Hydraulic Pile Screwing Apparatus
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to Gunnery Centrifugal Pumps Water Wheels Turbines Jet Propulsion
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fort Packing Power Co-operation Hull Hydraulic Power Company
London Hydraulic Power Company Birmingham Hydraulic Power System
Niagara Falls Cost of Hydraulic Power Meters Schcinheyder's Pressure
Regulator Deacon's Waste- Water Meter.
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LONDON: EXETER STREET, STRAND.
SCIENTIFIC AND TECHNOLOGICAL WORKS. 27
GRIFFIN'S METALLURGICAL SERIES.
THE METALLURGY OF GOLD,
BY
T. KIRKE ROSE, D.Sc., A.R.S.M., F.C.S.,
Assistant Assayer of the Royal Mint.
LARGE 8vo, HANDSOME CLOTH, ILLUSTRATED. 21s.
LEADING FEATURES.
1. Adapted for all who are interested in the Gold Mining Industry, being
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3. The MAcARTHCR-FoRREST CYANIDE PROCESS is fully described for the
first time. By this process over 2,000,000 of gold per annum (at the rate of) is
now being extracted, or nearly one-tenth of the total world's production. The
process, introduced in 1887, has only had short newspaper accounts given of it
previously. The chapters have been submitted to, and revised by, Mr.
MacArthur, and so freed from all possible inaccuracies.
4. Among other new processes not previously described in a text-book are
(1) The modern barrel chlorination process, practised with great success in,
Dakota, where the Black Hills district is undergoing rapid development owing
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SCHWACKHOFER and BROWNE:
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A MANUAL OF
MARINE ENGINEERING;
COMPRISING THE DESIGNING, CONSTRUCTION, AND
WORKING OF MARINE MACHINERY.
By A. E. SEAT ON, M. Inst. C. E., M. Inst. Meeh. E.,
M.InstN.A.
GENERAL CONTENTS.
Part I. Principles of Marine
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Part II. -Principles of Steam Valves, &e.
Engineering.
eulations for Cylinders,
Pistons, Valves, Expansion
Part IV. -Propellers.
Part III. -Details of Marine i Part V.-Boilers.
Engines : Design and Cal- Part VI. Miscellaneous.
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BY
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AND
H. M. ROUNTHWAITE, M.LMech.E., M.I.N.A.
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30 CHARLES GRIFFIN <k CO.'S PUBLICATIONS.
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In Large 8vo. Fully Illustrated.
A TEXT-BOOK OF PHYSIOS:
COMPRISING
PROPERTIES OF MATTER; HEAT; SOUND AND LIGHT;
MAGNETISM AND ELECTRICITY.
J. H. POYNTING, J. J. THOMSON,
SC.D., F.R.S., AN J) U.A., F.B.S.,
Late Fellow of Trinity College, Cambridge ; Fellow of Trinity College, Cambridge; Prof.
Professor of Physics, Mason College, of Experimental Physics in the University
Birmingham. of Cambridge.
MTION, Rented and Enlarged. Pocket-Site, Leathtr, alto/or Office Uie, doth, 12*.
BOILERS, MARINE AND LAND;
THEIR CONSTRUCTION AND STRENGTH.
A HANDBOOK OF RULES, FORMULAE, TABLES, &c., RELATIVE TO MATERIAL,
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ffor tbe TUse of all SteamsTIlsers.
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WORKS BY DR. ALDER WRIGHT, F.R.S.
FIXED OILS, FATS, BUTTERS, AND WAXES:
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