LIBRARY

UNIVERSITY OF CALIFORNIA.

A PRACTICAL TREATISE ON

MINE SURVEYING

BY THE SAME AUTHOR
Third Edition, Revised and Enlarged

MINING

An Elementary Treatise on the Getting of Minerals

With 596 Diagrams and Illustrations

Crown %vo, gs. net

LONGMANS, GREEN, AND CO.

LONDON, NEW YORK, AND BOMBAY

VENTURE COLLIERY.

BLACK VEIN,

REFERENCE.

Fences on, Surface, - Line of fault, irv coal

Footpaths ^-. BoJLor faulty cooJU

Cart-tretcTcs si-^-.-_-.-_-r Coal/wor'JceGisTtizdecL

Underground, Rocucis in, Coa.1/ ==.

ScaJLe, 10 Chains to 1 Iruch,

(As this is only a portion of the

IERY PLAN.
the boundary of the estate is not shown.)

Frontispiece.

A PRACTICAL TREATISE

MINE SURVEYING

ARNOLD LUPTON

MINING ENGINEER, CERTIFICATED COLLIERY MANAGER, SURVEYOR,

MEMBER OF THE INSTITUTION OF CIVIL ENGINEERS,
MEMBER OF THE INSTITUTION OF MECHANICAL ENGINEERS,

MEMBER OF THE INSTITUTE OF MINING ENGINEERS,
MEMBER OF THE INSTITUTE OF ELECTRICAL ENGINEERS,

FELLOW OF THE GEOLOGICAL SOCIETY, FELLOW OF THE SOCIETY OF ARTS, ETC-,

LATELY PROFESSOR OF COAL MINING AT THE VICTORIA UNIVERSITY

(YORKSHIRE COLLEGE, LEEDS), AND SOMETIME

EXAMINER IN MINE SURVEYING TO THE CITY AND GUILDS OF LONDON INSTITUTE

WITH ILLUSTRATIONS

OF THE

f UNIVERSITY J

LONGMANS, GREEN, AND CO.

39 PATERNOSTER ROW, LONDON

NEW YORK AND BOMBAY

1902

AH rights reserved

PREFACE

THIS book has been prepared with the intention of assisting
students in learning the art of Surveying. The author, during
the twenty-one years of his Professorship in the Mining Depart-
ment of the Yorkshire College, had to teach a great many
students the elements of this art, and for that purpose put
together various notes. As a former Examiner in Mine Survey-
ing to the City and Guilds of London Institute also, the author
gained a considerable insight into the needs of students. He
has added to his own experience as a practical surveyor by
reading a number of books on surveying and papers published
in the transactions of various scientific societies both in this
and other countries.

Where it has been thought advisable to reproduce extracts
or drawings from these, acknowledgment will be found in
the text.

Whilst primarily the object the author has had in view
has been the preparation of an elementary text-book, he has
endeavoured to make the book of value as a reference book to
the more advanced parts of the subject, and the chapters dealing
with Trigonometrical Plotting, Hypsometry, Method of finding
the True North, Metalliferous Mine Surveying, Photographic
Surveying, Prospecting with the Magnetic Needle, etc., have
been included with this purpose in view.

The reader should endeavour, as far as possible, to get
practical experience of the instruments and in the method of
using them, and the author would recommend such of his
readers as have not done so to view the collection of surveying
instruments at the South Kensington Museum, London.

182313

vi PREFACE.

The author would like to acknowledge the uniform courtesy
shown to him by those members of the Government Depart-
ments (Koyal Observatories, Greenwich and Kew, the Ordnance
Survey Office, the Meteorological Office, etc.) who have supplied
him with various information, and also his thanks to the various
makers of surveying instruments herein described.

The tables of Logarithms, Antilogarithms, Squares, Sines,
Cosines, Tangents, etc., which form a portion of the appendix,
are taken from a work on Elementary Physics by Mr. John
Henderson, D.Sc. (Edin.), A.I.E.E., F.K.S.E., to whom the
author is indebted for permission to reproduce them.

In conclusion, the author wishes to state that professional
engagements might have entirely prevented him from com-
pleting this work had it not been that among his assistants he
numbered some experienced surveyors, and he thinks it fair to
acknowledge the valuable assistance he has had from them,
especially from Mr. Herbert Perkin. He would also like to thank
those of his friends who have undertaken the revision of various
parts of the work.

Any corrections or additions which suggest themselves to
the reader will be gratefully acknowledged.

AENOLD LUPTON.

G, DE GREY ROAD, LEEDS,
July, 1901.

CONTENTS

CHAPTKK

I. NEED AND ADVANTAGES OF ACCURATE PLANS, ETC.

II. THE MEASUREMENT OF DISTANCES . . . ... ,. . 5

III. METHOD OF SURVEYING ON THE SURFACE BY MEANS OF CHAIN

AND POLES . /. ' ' i . ,-s 18

IV. INSTRUMENTS FOR MEASURING ANGLES 43

V. INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES .... 85

VI. GEOMETRY, TRIGONOMETRY, LOGARITHMS 96

VII. SURFACE SURVEYING WITH THE THEODOLITE ., 112

VIII. UNDERGROUND SURVEYING 129

IX. METHODS OF PLOTTING AN UNDERGROUND SURVEY .... 149

X. METALLIFEROUS MINE SURVEYING . . . 181

XI. METHODS OF CONNECTING SURFACE AND UNDERGROUND SURVEY 188

XII. LEVELLING . . . ..." 201

XIII. CONSTRUCTION OF PLANS 255

XIV. MEASUREMENT OF MINERAL TONNAGES CALCULATION OF CON-

TENTS OF PIT-HILLS CALCULATION OF EARTHWORK, ETC. . 279

XV. SURVEYING BORE-HOLES 288

XVI. MISCELLANEOUS 307

XVII. PROSPECTING FOR MINERALS BY MEANS OF THE MAGNETIC

NEEDLE 349

XVIII. METHODS OF FINDING TRUE NORTH, OR GEOGRAPHICAL MERIDIAN 356

viii CONTENTS.

PAGE

APPENDIX

EXAMINATION QUESTIONS VARIOUS 371

CITY AND GUILDS or LONDON INSTITUTE 375

SURVEYORS' INSTITUTION EXAMINATION PAPERS . . 386

THE LAW AND MINE SURVEYING ... 391

ATTRACTION or THE MAGNETIC NEEDLE BY IRON . . . . . . 393

MATHEMATICAL TABLES . . . . . . 396

INDEX . 409

MINE SURVEYING

CHAPTER I.

NEED AND ADVANTAGES OF ACCURATE PLANS, ETC.

MINE surveying is necessary for two reasons : In the first place,
a map or plan, and section, are necessary to guide the miner in
his daily work, so that when the workings have extended over a
considerable area, it may be seen at a glance which parts of the
mineral have been got and which remain to get ; in what direc-
tion the roads go, how far apart they are one from another ; how
machinery can be best arranged for underground haulage ; how
the ventilation of the mine may be most economically conducted ;
and how the drainage may be effected. The plan should also
show the direction of faults, and where the mineral has been
found good, or where inferior or unworkable. The section will
show the inclination of the bed or vein, and the height above or
depth below any given datum- line. Contour-lines on the plan give
the same information for the whole mine. In the second place,
the plan of the mine (see Frontispiece) is required to show the
position of the underground workings with regard to objects and
boundary-lines on the surface. To take mineral from under-
neath the land without the previous sanction of the landowner
may be treated as felony, and, if it is done through accident or
inadvertence, may be punished with a heavy fine. It is, there-
fore, of the highest importance that the owner or tenant of the
mine should not only have an accurate plan of the boundary of
the estate under which he has a licence to work, but an equally
accurate plan of the underground workings, drawn upon the
same paper (or other drawing material) that is used for the
plan showing the boundaries, fences, buildings, roads, streams,
and other notable objects above ground. A mining plan is

MINE SURVEYING.

therefore, generally speaking, incomplete unless it is also a
plan of the land above ; and a mining surveyor is therefore
not competent for the entire production of a mining plan unless
he understands land surveying as well as mine surveying. It
frequently happens, however, that the plan of the surface is
made by a land surveyor, and the plan of the mine by a mine
surveyor; and this combination often produces very accurate
results. In some respects it is better that the whole of the plan
should be made by one surveyor, who is responsible for the
accuracy of the combination of underground and surface work,
and in this case that person should be the mine surveyor, as he
is the man who possesses the additional knowledge of the mine
which is necessary for a proper survey.

Meridian Line, Even in case the mine surveyor is relieved
from the work of land surveying by having an accurate map of
the estate put into his hands, he cannot delineate upon it the
workings of the mine unless he has some knowledge of land
surveying, because he will require to mark upon the plan a
meridian line to which his underground survey must be referred.
This meridian line may be drawn north and south in the
geographical meridian, or line of longitude ; or it may be drawn
in the direction of the magnetic pole, or it may be some other
line which is marked out both on the surface and in the mine
below, in the same vertical plane. None of these lines can be
correctly marked upon the surface plan without some knowledge
of land surveying. It is, therefore, necessary that the mine
surveyor should be instructed in the art of land surveying.

Every art in which it is possible to achieve perfection has a
fascination for the human mind, and surveying is one of these
arts.

Degree of Accuracy attained. The accuracy with which the
survey may be made is only limited by the skill and care of the sur-
veyor, provided he has the opportunity of using the most suitable
instruments which are made; and, as a general rule, the surveyor
obtains the accuracy necessary for his purpose. It is, however,
perhaps also true that, as a general rule, he is not much more
accurate than is necessary. Thus, in a mine of large extent,
the workings of which are neither near a boundary nor near to
some important building which must not be disturbed, an error
of half a chain in the position of any part of the workings is by
no means uncommon.

NEED AND ADVANTAGES OF ACCURATE PLANS. 3

Reasons for Great Accuracy. On the other hand, when
approaching some important building, or when approaching a
boundary which must not be passed under a heavy penalty, and
which must yet be reached because the owner of the mine does
not wish to sacrifice any portion of the mineral which is his,
then minute accuracy is often attained. In some metalliferous
mines great value attaches, perhaps sometimes reaching 1000,
to a single square yard of ground, and in such a case it is
necessary that the plan should be so accurate that no rival skill
can detect an error.

If the owner of a mine inadvertently crosses the boundary,
and gets mineral to which he has no right, he may be obliged to
pay in damages nearly the whole market price of the mineral,
possibly ten times the royalty ordinarily payable, so that in the
case of a seam of coal, he might be fined to the extent of two or
three shillings per square yard for every yard in thickness.

In order to avoid crossing the boundary, there are only two
courses one is to leave a considerable margin of the mineral
inside the boundary, and the other is to have a plan of extreme
accuracy, and to mark out the limits of workings underground
upon this plan from day to day. To leave a wide margin of
coal or other mineral ungot, unless it is required for the purposes
of a permanent barrier, involves a corresponding loss and waste
of mineral.

An accurate plan is also necessary for engineering reasons.
It may be necessary to drive an underground road or tunnel
from one pit to some other pit, and a serious loss may result if
the mark aimed at is not hit in the centre.

For reasons of safety an accurate plan is much to be
desired. Abandoned workings may be full of water, and if
the plan of these abandoned workings does not show them all
and in a correct position, the workings from some new mine
may inadvertently break in upon accumulations of water, and
thus lead to fatal, and financially disastrous results. It is,
therefore, in the highest degree desirable that mine surveyors
should habituate themselves to the making of accurate plans,
because a habit of carelessness, once acquired, is difficult to
throw off when minute accuracy is necessary.

It is, however, not the surveyor who requires to be impressed
with the importance of an accurate plan, it is rather those who
have to pay for his services, and they do not always see where

4 MINE SURVEYING.

they get any return for an expenditure on carefully made maps
and plans. It thus happens at some collieries that hundreds
of pounds are annually wasted which would be saved by the
employment of a careful surveyor, not merely to make a plan of
the roads after they are driven, but to set out the roads in the
right direction. The cause of this waste is easily explained :
without an accurate plan, showing the existing workings, faults,
and inclination of the seam, it is impossible to lay out the roads
so that the shortest length of road may suffice ; hence an
unnecessary number of roads, and these roads crooked, are
often made. Also, even if the roads are correctly schemed, they
will not be made in the direction intended unless the workmen
are guided by marks carefully fixed by the surveyor. Each
yard of road in the mine costs so much to make, varying accord-
ing to circumstances in coal-mines N from 2s. to 20s., and in
metalliferous mines and cross-measure drifts from 10s. to 10 ;
it also costs so much to maintain, and then there is the cost of
transit. Thus in a mine raising 300,000 tons of coal a year,
the cost of making and maintaining roadways of all kinds, and
of haulage, may, combined, easily amount to 20,000 a year.
If the length of the roadways is 5 per cent, longer than necessary,
the cost will be increased in a corresponding degree, or to the
extent of 1000 a year. In many cases the costs are on a
higher scale, and, of course, the loss from unnecessary lengths
of road is correspondingly increased.

It is absolutely certain that the money spent on the produc-
tion of accurate plans and contours, and sections giving every
engineering and geological detail, is repaid many times over
(tenfold to a hundredfold) every year in the ordinary course of
working.

CHAPTER II.

.,, THE MEASUREMENT OF DISTANCES.

CHAINS, TAPES, POLES, MEASURING-WHEELS.

THE instruments generally used by the mine surveyor are as
follows :

Measuring-chains. Gunter's chain is that usually employed
for land surveying and in coal-mines.
This chain (see Figs. 1 and 2) is 66 feet
long, or the eightieth part of a mile. It
is divided into 100 parts, called "links."
100,000 square "links," or 10 square
chains, equal 1 acre. The chain is con-
structed either of iron, steel, or brass
wire. If made of steel wire, it is about
T V inch in diameter. A chain-length
is composed of a hundred pieces of wire,
which have a loop at each end, and are
6 inches in length. These pieces are
united by three short links, about f inch,
internal measurement, made of flat wire. Fia 1 '~ Gu c n h t ^ n 8 measurin s-

Swivel

to 3O 4O

FIG. 2. Gunter's measuring-chain (enlarged view).

These three short pieces and the long pieces make up a length
of nearly 8 inches, or exactly 7 '92 inches. At each end of
the chain the 6-inch piece is shortened to about 4 inches ;

6 MINE SURVEYING.

then comes a small link, and then a brass handle, making up
the total length of 7*92 inches. Measuring from the outside
of the handle for a length of 10 links, the end of the tenth
link is in the centre one of the three small loops connecting
two 6-inch pieces. Attached to the centre loop is a small brass
tag, with one prong, which indicates a length of 10 links from
the end of the chain. Measuring 10 links further, another
brass tag is similarly attached to the chain ; but this second tag
has two prongs. At the end of the next 10 links is another
brass tag, which has three prongs ; at the end of the next 10
links is a similar brass tag, with four prongs ; the end of the
next 10 links is the centre of the chain, and has a simple
round-ended brass tag. Each end of the chain is constructed
in the same way, measuring from the outside of the handle to
the centre, so that the same tag may count 40 or 60, according
as it is before or after the centre, 30 or 70, 20 or 80, 10 or 90.
At 25 links from each end of the chain, instead of the three
simple loops connecting two 6-inch pieces, there is one loop and
two swivel-jointed loops, so that if the chain has got twisted it
may be untwisted. The swivel-joint also marks the length of
25 or 75 links. At the centre of the chain is another swivel
link ; this is marked by the round-ended tag above mentioned.
Sometimes 10 links at each end of the chain are made of
brass, so that the end of the chain may be held near a magnetic
compass without attracting the needle. If the chain is made of
brass or iron wire instead of steel wire, it is about inch thick.
For ordinary mine surveying it is desirable to have a good
strong chain.

Engineers often use a chain 100 feet long, divided into links
of 1 foot in length. Where a section is being levelled, it is
convenient to have the lengths in feet, because the altitudes
are measured in feet. The use of 100-foot chains is making
headway, and has much to recommend it. Whenever the term
"link" is used, however, Gunter's link of 7'92 inches is the
one referred to. In the Cornish mines a chain 10 fathoms,
or 60 feet, in length is used, the chain being divided into 120
parts, each 6 inches in length, and marked with a tag every
6 feet (i.e. every fathom).

Tapes. A 66-foot painted tape, divided on one side into feet
and inches, and on the other into links, is very convenient for
measuring offsets, and the width and height of roads. The best

THE MEASUREMENT OF DISTANCES. 7

kind of tape is the " metallic " tape, made with fine brass wires
interwoven with vegetable fibre.

Steel Tapes. Where great accuracy is desired, steel tapes
may be used. The steel tape, being one continuous ribbon of
metal, is less liable to stretch than the chain. One side is
marked with feet and inches, and the other with links. Steel
tapes have to be carefully used, in order to avoid breaking,
and must be cleaned after use, or the marking will become
obliterated by rust.

Sometimes a tape much longer than 100 links is used. Mr.
Eckley B. Cox, of Drifton, Pennsylvania, showed the writer a
steel tape 500 feet in length. This tape was very light, about
^ inch broad and T V inch thick. Every tenth foot was marked
with a piece of brass wire soldered on with white solder, the
number of each mark being shown by figures on the solder.
The tape is carried on a reel, from which the required length
may be unwound. One end of the tape is held at one station,
and the distance to the other is read off upon the tape to the
nearest 10-foot mark ; from this mark to the station the length
is measured by a 6-foot staff marked in feet and decimals of a
foot. By the use of this long tape, the entire length of a line
can be measured at one operation to the hundredth part of a
foot, and the errors due to marking off chain-lengths on rough
and uneven ground are thus avoided.

When measuring large tracts of outlying country, where
portability and lightness are of great importance, what is known
as a compound steel band chain is often used. It consists of
two or more separate steel bands, each one chain long. These
can be joined together by swivels and hooks, and used in lengths
of one, two, or more chains.

The first chain of each set is divided into links in the usual
manner ; but the other chains are not subdivided. The bands
are wound up on a steel cross.

Measuring-poles. For measuring short lengths poles are
often used, divided into links by painting alternate lengths of
one link black and white. The divisions of the pole are some-
times in feet for architectural purposes; and for measurements of
extreme accuracy, the divisions are subdivided into tenths. As
a general rule, poles are only used for measuring offsets to the
line measured by the chain. For this purpose a 10-link (or, in
the alternative, a 10-foot) pole is most convenient. In some

8 MINE SURVEYING.

cases the base-line for a trigonometrical survey has been
measured along a line, carefully levelled for the purpose, by
means of poles laid end to end, so as to avoid the errors due to
the inaccuracy of chains or tapes.

Measuring-rods have been so constructed that the length
is uniform for all temperatures. These are made by using a
rod compounded of two side by side, one brass and the other
iron, which have an unequal expansion. At each end is a
cross-piece, projecting on one side, with a centre-mark so
placed that the centre-marks maintain an equal distance during
variations of temperature. .-+

Pacing. Distances are sometimes measured by pacing.
With a little practice a surveyor may learn to step a yard, and
in this way to measure distances with an error not greatly exceed-
ing 5 per cent. The ordinary pace is much shorter, being, say,
30 to 33 inches. There is a great difficulty, however, in count-
ing the paces, as it is difficult to maintain concentrated atten-
tion. Paces may be counted by means of a pedometer, an
instrument which registers the movements of the body made in
walking, thus counting the paces.

A man may educate himself to take a pace of even length
uphill and downhill, the natural tendency being to take a long
pace downhill and a short pace uphill. To maintain, however,
uniformity of pace, a man of average height should adopt a pace
not exceeding 2 feet 9 inches ; and then, with practice, he may
maintain this for the whole day both uphill and downhill.

Measuring-wheel. A measuring- wheel may also be used,
with a counter to record the number of revolutions. The wheels
of any carriage, whether propelled by steam, horse, or hand-
power, or an ordinary bicycle or tricycle fitted with a counter,
will do. The circumference of the wheel being known, say 10
feet, the distance traversed will be the number of revolutions
multiplied by 10 feet. Of course, this will only give the dis-
tance with approximate accuracy, but for many purposes, such
as a preliminary geological survey, this accuracy might be quite
sufficient. For still less accurate measurements, there are other
means, such as the speed of a steamer on a river or lake.

Accuracy of Steel Tape. For any purposes required by the
mining engineer, a steel tape is sufficiently accurate. The
expansion of steel between the temperature of freezing and
boiling water is rather more than 1 in 1000, say 1*2 ; and the

THE MEASUREMENT OF DISTANCES. 9

expansion in length for 1 is about 6'4 parts in a million, and
for 50 is about 3'2 parts in 10,000, or, say, one part in 3125.
In temperate regions a variation of 50 is as much as is to be
expected ; in England this is an extreme variation. Suppose
the steel tape to be tested and found correct at a temperature
of 50 , 1 then for a variation of 10 either higher or lower, the
variation would be about 6'4 parts in 100,000, or, more correctly,
1 in 15,625. Where extreme accuracy is required, this correc-
tion should be made. To enable it to be done more readily,
Mr. W. F. Stanley of London makes a patent band chain
handle adjustment, in which, by means of a screw, the chain or
band can be lengthened or shortened as desired. A scale on
the handle also enables adjustment to be made for variation in
temperature during the performance of the work.

A steel tape *37 inch wide and "01 inch thick, 66 feet long,
when laid out on a pavement, requires a pull of about 4 Ibs.
to draw it straight over the slight inequalities of the pave-
ment. A total pull of 8 Ibs. will stretch it T V beyond the
mark made at the 4-lb. pull. A total pull of 12 Ibs. gives a
total stretch of a bare eighth ; a total pull of 16 Ibs. gives
a stretch of a good eighth ; and a total pull of 20 Ibs. stretches
the chain fV beyond the mark made with the 4-lb. pull. The
steel tape is not suitable for rough usage, and is therefore
only used for the main lines of an important survey, and for
those details which it is necessary to mark on the plan with
extreme accuracy, or for measuring the base-line of a trigono-
metrical survey on the surface.

For the ordinary work of a mining survey a strong chain is
the best measuring instrument.

Testing a Chain. Before beginning a survey, and frequently
during the survey, it is necessary to test the chain, to see that it
is the right length. The importance of this will be understood
when the reader considers that if the links of a chain are joined
by three rings, then there are eight wearing surfaces for each
link, or 800 in a chain-length. If each should wear the y^
part of an inch, this means that the chain is lengthened by 8
inches. For the purpose of testing, a flat piece of pavement or
piece of level ground beside a straight wall should be carefully
measured with a pole or foot rule, and a chisel-mark put on

1 Messrs. Chesterman claim that their steel tapes are practically accurate at
62 Fahr., and say the expansion is about -008 inch in 100 feet for each degree.

io MINE SURVEYING.

every tenth link ; the chain is then drawn tight over or against
these marks. If any section of the chain is too long, it is
shortened by taking out a loop ; if any section is too short, it is
lengthened by putting in a loop ; the two ends of the piece of
wire forming the loop are not welded together, so that the link
can be easily opened with a chisel and closed with a hammer. A
few hours' work with the chain over rough ground, where the
chain has to be pulled tight to draw it into a straight line, or to
set it free from some obstruction against which it has caught,
may be sufficient to stretch the chain an inch or more. A care-
fully tested steel tape is a very convenient instrument for testing
the accuracy of a chain in the absence of any more certain fixed
measure.

Method of Chaining. When measuring on the surface with a
chain, the method is as follows : The line to be measured
having been marked out with poles, the chain is managed by
two men the leader and the follower. The leader takes one end
of the chain, and draws it in the direction of the pole towards
which he is steering; the follower holds the other end of the
chain at the peg or mark where the line begins. The leader
carries ten arrows ; these arrows (see Fig. 3) are pins made of

iron wire about y\ inch m diameter, pointed
!$O *' /s '~ 1 a ^ one en ^ an( ^ f rme( l m ^o a ring 2 inches

in diameter at the other end, and may be
FIG. 3. Arrow. any convenient length from 13 inches to

20 inches ; to render them more conspicuous,
a piece of coloured ribbon is tied at the top of each. The
follower directs the leader to the right or left until the chain
is drawn tight in an absolutely straight line for the next pole ;
the leader then places an arrow at the end of the chain, and
lets the chain lie upon the ground until directed to drag it
forward. In case there are two marks in the requisite line
behind the leader, he can put himself in direction by turning
round so as to face the follower, and then moving the chain till
he has placed it in a line with the guiding poles or pegs. Whilst
the chain is lying on the ground, offsets can be taken to any
building or other object to the right or left, or the distance of
any fence, ditch, pathway, etc., that is crossed by the chain
may be exactly noted. On receiving a signal, the leader drags
the chain forward another length, putting a second arrow in the
ground. When signalled forward again, the follower takes up

THE MEASUREMENT OF DISTANCES. n

the first arrow and advances to the second arrow, and so on ;
thus the number of chains measured is always the same as the
number of arrows in the hands of the follower. When the tenth
arrow has been placed in the ground, the leader drags the chain
forward and lets it lie upon the ground in its proper position
until the follower has picked up the tenth arrow and handed the
whole ten to the leader, who must never receive from the follower
less than ten arrows. Any breach of this rule will probably
lead to confusion. In order to mark the end of the chain when
the leader has no arrow in his hand, he must make a mark with
a wooden peg. After receiving from the follower the ten arrows,
he puts one down beside this peg, thus marking the end of the
eleventh chain.

Measuring Rough Ground. In measuring over hillocky ground
and through fences, copses, etc., it is necessary to draw the chain
straight between the arrows, otherwise the length will measure
greater than it really is. In order to make it straight (that is,
nearly straight), it is necessary to pull tight, though violent
pulling is unnecessary and injurious.

In measuring up or down a bank, the length of the slope
being greater than the horizontal distance, the measured length
will be too great for a plan. In order to measure the correct
horizontal length for a plan, it is usual, when measuring
downhill, for the follower to hold his end of the chain on the
ground, and for the leader to fix a pole vertically in the
ground at some convenient length, and then to hold the chain
on a level with the starting-point against this staff, and read
the length ; the horizontal distance is thus measured in steps
(see Fig. 4). This method is only adopted for very short slopes,
or in case the surveyor has no instrument for measuring the
inclination.

In the case of a long uniform slope, the length of the slope
is measured by drawing the chain straight down it, the angle of
the 'slope is taken with a suitable instrument, and the length of
the slope as measured is reduced by calculation to the true
horizontal distance before putting the length on the plan.

It is sometimes a good practice to put a wooden peg into the
ground at the end of every tenth chain, from which measure-
ments can be taken at some later period of the survey.

Taking a Line through Obstructions, The measurement of
a line is often hindered by some obstruction, such as a stone

ML\E SURVEYING.

wall. In this case it is necessary to measure up to the stone
wall, which is say 48 links distant from the last peg, the thick-

FIG. 4. Measuring in steps.

ness of the wall is found by measuring on to the top to be say
3 links, making the distance through the wall 51 links. The
follower then, taking hold of the fifty-first link, holds it against
the foot of the wall, and directs the leader as before where to
fix the end of the chain.

In a country containing many trees, it is often difficult to
set out a line which may not lead into the trunk of a tree. In
such a case there are three courses to be adopted : the first is
to cut down the tree ; the second is to end the line at the tree ;
and the third (see Fig. 5) is as follows : Measure at right angles

C A Q S

FIG. 5. Obstruction to survey-line.

to the line an offset (A to B) longer than the width of the
obstruction, and at 2 chains back measure another offset
(C to D) of equal length, and at 4 chains back a similar offset
(E to F) ; three poles set up at the end of these offsets will be in

THE MEASUREMENT OF DISTANCES. 13

a straight line parallel with the main line. This line is then con-
tinued for a distance of 6 chains past the obstruction, and three
offsets, PQ, RS, TU, set out from this parallel line in the
opposite direction to the three original offsets ; three poles set
up at the end of these three offsets at Q, S, U, will be in a
straight line, and a continuation of the original line. The
same course may be adopted if the original line runs into a
building.

Chaining Underground, When chaining in the mine, arrows
are not usually employed, because the ground is too hard for
them to pierce ; the end of the chain is usually marked on
stone or rail with a piece of chalk, and the number of the
chain written by the side of the mark ; the leader chalks on a
piece of stone the figures 1, 2, 3, 4, 5, etc., up to 10, or marks
(/, //, ///, ////, /////, //////, ///////, etc.), and then begins again. It is,
however, seldom that the lines in an underground survey reach
a length of 10 chains.

This system of marking the length leads to many errors ;
the attention of the leader and follower and surveyor may be
called off, and the number of chain-lengths forgotten; and it
would save many errors in measurement if the system of arrows
adopted by surface surveyors was copied in the mine. Instead
of an arrow, a simple ring of metal would suffice ; the end of
the chain would be marked by the chalk as usual, and the ring
of metal laid down beside it would form an automatic counter
of the number of chain-lengths, the leader starting with 10 rings
in his possession, and the follower, taking the rings up, will
know the number of chain-lengths by the number of rings he
holds. At the end of each line the follower would give up
his rings to the leader, who would always start with ten rings.
So many of the lines measured in mining surveys are, however,
less than 1 chain in length, and the length so seldom exceeds
5 chains, that mining surveyors as a rule have not thought it
worth while to adopt such a system ; but the writer's experi-
ence leads him to think that it would lead to a considerable
saving of time. It rarely happens that the end of any line to
be measured corresponds exactly with the end of the chain ;
therefore, except in these rare cases, the chain should be drawn
forward past the dial or mark indicating the end of the line,
and then the exact distance to the mark read off upon the chain.
If this rule is always observed, it will be conducive to accuracy

14 MINE SURVEYING.

of measurement, as the chain will always be read from the
follower's end.

Surveying-poles. These are used for marking out the line to
be measured, and generally vary in length from 10 to 15 links ;
a 12-link pole is a very convenient length. It is generally made
of pine (see Fig. 6), about 1-J- inch diameter at the base, gradu-

Blcuck

Red, White

FIG. 6. Surveying-pole.

Black

ally tapering to f inch at the top ; the base is shod with iron ,
about 9 inches in length, ending in a point ; with this iron
point a hole can be made, even in hard ground, in which the
pole can be fixed.

It is necessary that the pole should be perfectly vertical, as
it frequently happens that only the top of it can be seen over
hedges or other obstructions ; therefore, if the top is not over
the point, the line will not be set out straight. Fig. 7 shows a
surveyor in the act of fixing a pole in line
with two other poles. The surveyor, desiring
to mark out a line, fixes two poles in the
desired direction, at a convenient distance
apart, say 20 to 50 yards; he then fixes a
third pole in the same line at a further
distance of say 20 to 50 yards ; if these poles
are in a straight line, when standing behind
one pole at a distance of say 10 yards, and
closing one eye, the other two poles should
be invisible. A fourth pole is now fixed in
the same line. The first pole can now be
taken out and placed in advance, forming the
fifth mark ; then the second can be taken up
and placed in front, forming the sixth mark,
and so on ; by means of these four poles a
straight line of any length can be marked out across the
country. If three poles are always in the ground, it will be at
once evident if one of them has got moved.

In practice a good deal of care is required to keep the line
quite straight, as it is not always easy to fix the poles perfectly
plumb, or they may be blown on one side by the wind, or may

FIG. 7. Fixing a
pole.

THE MEASUREMENT OF DISTANCES.

be inaccurately fixed to the extent of half an inch. If the third
pole is 60 yards in advance of the first pole, and half an inch out
of its correct position, that is a deflection of 1 in 60 X 36 X 2,
or 1 in 4320. 'This deflection in a small survey might not be
very serious, but the deflected line may be deflected still further
in the same direction, and the error of 1 in 4000 may soon be
increased to 1 in 1000.

For setting out long and important lines, the eye of the
surveyor is often assisted by the telescope mounted on a theodolite
stand. With a good instrument and great care almost perfect
accuracy may be maintained in poling out a line. Sometimes
small flags about a foot square are fastened to the top of the
poles to make them more conspicuous. The poles are all painted
black, red, and white in alternate lengths of 1 link (or 1 foot),
so as to make them more easily visible, and this also fits them
for use as measuring-poles.

For special purposes, as, for instance, for use in a large
trigonometrical survey, poles of extra
length and strength are used; these
are maintained in a vertical position
by means of guy ropes (see Fig. 8)
fastened to pegs in the ground, or to
weights. Sometimes a pole is fixed
on a wooden frame.

It happens very frequently that it
is necessary to range a straight line
between two fixed points, neither of
which is visible from the other, or, if
visible one from the other, it is in-
convenient to go to either of them so
as to range out the line from the
beginning; but whilst one of these
points is invisible from the other,
they are both visible from an elevated
piece of ground between them. The
surveyor and his assistant proceed to
this intermediate position, and, each

, , , .

holding a pole and standing about

. 8. Pole fixed by guy ropes.

50 yards apart, face each other, placing themselves as nearly
as they can guess in a line between the two fixed points,
A and B (Fig. 9). The surveyor at D', looking towards A, motions

16 MINE SURVEYING.

the assistant at C' into the line AC'D' ; his assistant at C'

looking towards B, motions the surveyor into the line BD"C'.

As the surveyor is moved towards the line BDC, the assistant

D , has to be moved at the same

C '_..- -' & ' H ' time towards the line ACD,

^--- --.'.'-- ~.-'-to--"- : ~- : '~ :: *"&--- -Q and this movement is con-

* D B tinned until the two lines ex-

FIG. 9. Setting out a straight line between ,.i * ;! -i/u A^PID
two points nSt visible from each other. actlv coincide, then AC D B

form one straight line.

With a little practice this operation can be performed in two or
three minutes.

Where great accuracy is required, a theodolite may be used
to check the positions C and D, first erecting it at D to ascertain
if C is in the straight line ACD, and then erecting it at C to
ascertain if D is in the straight line BDC ; a central position
E may be marked out with a peg, and a centre line accurately
fixed; a transit theodolite may then be fixed over this and directed
towards A ; when the telescope is reversed the cross-hairs should
be upon the station B.

Although four poles are sufficient with which to mark out a
line, it is usual to have more, perhaps seven or eight, in one
line. With six or seven poles standing in a line there is less
chance of a divergence from the original direction, because
although three poles are sufficient if there are no accidents, still
if two of these should be accidentally knocked a little on one
side, the direction would be lost. As each pole is pulled up, a
peg is put into the hole to mark the place, so that the line may
be easily found another day. The kind of peg that is used
varies according to the circumstances of the case ; sometimes a
small twig cut from a hedge is the best kind of mark, as it is
not likely to attract attention ; on other occasions a piece of
wood about 18 inches long and 1J- inch square, pointed at one end
and flat at the top, may be driven in. For a permanent station
it is, however, necessary to have a stake which cannot be easily
withdrawn, say 3 feet long and 4 inches square, driven down
till the top is but little above the ground, with a cross-mark
nicked in the top to show the line of survey. Pegs of this kind,
however, should not be put dpwn in a place where they will
interfere with agricultural work, such as mowing-machines, but
should be placed by the side of a hedge or ditch, where they
will be no impediment and attract no notice.

THE MEASUREMENT OF DISTANCES.

TABLE SHOWING THE EQUIVALENT VALUES OF VARIOUS
MEASUREMENTS.

LINEAL MEASURE (LENGTH).

Mile.

Chains.

Yards.

Feet.

Links.

Inches.

1760

5280

8000

63,360

0125

100

792

000568

04545

4-545

000189 i -01515

333

1-515

000125

7-92

0000158

00126

0278

0833

126

SQUARE MEASURE (AREA).

Acres.

Roods.

Perches.

Sq. yards.

Sq. feet.

Sq. inches.

160

4840

43,560

6,272,640

1 40 1210

10,890 1,568,160

00625

025 1

30i

272J 39,204

0002( 66

000826

0331

9 1,296

000023

0000918

00367

111

144

000000159

00000064 -0000255

000772

00694

/ 27,878,400 sq. feet.
1 square mile = ] 3,097,600 sq. yards.

640 acres.

Acres X '0015625 = sq. miles.
Sq. yards x '000000323 = sq. miles.

10 sq. chains = 100000 sq. links 1 acre.
46,656 cub. inches = 27 cub. feet = 1 cub. yard.

NOTE. The above tables will be found to comprise many of the data needed
by the surveyor. To use the tables : Suppose it is required to convert yards into
links. On referring to the table we find 1 yard is equal to 4'545 links, so by multi-
plying yards by 4-545 we get the equivalent distance in links. Other units of
measurement may be converted in a similar manner.

CHAPTEE III.

METHOD OF SURVEYING ON THE SURFACE BY MEANS OF CHAIN

AND POLES.

FOR the purpose of making a survey on the surface of an estate
of moderate size, say 1000 acres, it is not necessary to have
expensive instruments. A score of straight poles, a good
G-unter's chain, ten arrows, an off-set staff or tape, and some
pegs to mark the stations, are all the instruments required ; a

compass and theodolite may
be very useful and advan-
tageous, but they are not
absolutely necessary.

The method of making a
survey with chain and poles
may be explained in the fol-
lowing manner : Let Fig. 10
be the plan of an estate on
level ground, of triangular
form ABC. From the point

A, B is visible; fix a pole
at A and another at B, and
measure the distance A to

B. From the point B, C is
visible ; fix a pole at C, and

From the point C, A is visible ;
The measurements are entered

A to B, length 600 links
B to C, 900
C to A, 800 .

Line

FIG. 10. Simple surface survey.

measure the distance B to C.
measure the distance C to A.
in a book, thus

Line No. 1
No. 2 ...
No. 3

The survey is now complete, and, if the lines have been measured

METHOD OF SURVEYING ON THE SURFACE. 19

accurately, these three measurements are sufficient for the
production of an accurate plan.

It will be seen that A, B, and C are angles, and that the
figure measured is a triangle (from Lat. trcs, tria, three, and
angulus, an angle, meaning a figure with three angles). The
length of each side has been measured, but not the angles; so
that if only two of the sides had been measured the lines could
not be drawn on paper in their correct position as regards each
other. Having got the lengths of the three sides, however,
they can be plotted with the aid of an elementary knowledge of
geometry.

Plotting a Triangular Survey. The method is explained by
reference to Fig. 10. The line No. 2, being the longest, is
drawn on the paper, and the length marked by means of the
s<?ale (Fig. 54). The scale is 12 inches in length ; each inch
represents a length of one chain, or 100 links. The scale may
be made of cardboard, boxwood, ivory, or metal. It is generally
made of boxwood or ivory, the length of which is not appreciably
affected by temperature ; each inch is divided into ten parts,
each part representing 10 links. A needle-pricker is used to
prick out the ends of the line, the prick-hole being surrounded
with a little ring sketched with the pencil. The compasses
(Fig. 55) are now opened, and by means of the scale set to the
length of line No. 3. (800), and with their aid the arc WX is
drawn from the point C. The compasses are now adjusted to
the length of line No. 1 (600), and from the point B the arc
YZ is drawn; this intersects the arc WX at the point A. By
means of a straight-edge the lines CA and AB are now drawn,
and the plan is complete.

To test the accuracy of the drawing, the scale should be
laid on the line AB, which should measure 600, and on the line
AC, which should measure 800. If the lines, when measured,
are found incorrect, it shows that the compasses have not been
set to the right length.

Booking a Surface Survey. If the survey is plotted by the
person who measured it on the ground, there is no diffi-
culty; if, however, it is measured by one person and plotted
by another, the notes of the survey as above given are not
sufficient, because the point A, instead of being as shown,
might be on the other side of the line BC, as shown by the
dotted lines. It is therefore necessary that the surveyor

MINE SURVEYING.

should make some sign in his note-book of the direction in
which he turns, and the way of booking the above survey would
be as shown in Fig. 11. In this the angles are sketched by the
surveyor looking the way he is going. The longer side of the
angle represents the direction in which he is going, the shorter
side represents the direction of the line which he is leaving,
and, in plotting the lines AB and CA with the compasses, they
must be drawn on that side of the base-line
which will give the angles corresponding to those
sketched in the field-book. If the bearing of
each line is noted, this would do instead of
sketching the angle.

For the purpose of plotting lines 1 and 3 on
the proper side of the base-line No. 2, it is not
necessary that the bearing noted should be
accurately observed; it would be sufficiently
near if the note is made north-west or north-
east, south-west or south-east, as the case may
I A. IV. be. This approximate observation of the bearing
\y| can, of course, be made immediately by a glance

towards the sun if it is shining, or, failing that,
by the aid of a magnetic pocket-compass. The
bearing noted in the pocket-look is that of the
point toivards which the surveyor is moving when
measuring the line.

I N The survey above described is the simplest

\J possible kind of land survey, and at the same

time it is a type of every species of surface
survey. No piece of ground can be enclosed in
less than three straight lines. No line can be
measured on a curve; therefore every piece of
ground must be measured by straight lines.
Solution of Triangles. Plane triangles are composed of six
parts, namely, three angles and three sides, and when three
parts (one of ivhich must be a side) are given, the other parts can
be determined. There are four cases : (1) Measuring the three
sides; (2) measuring two sides and the angle enclosed; (3)
measuring one side and the angles at each end ; (4) measuring
two sides and the angle opposite one of them.

In the system of surveying now under consideration, the sur-
veyor has no instruments for measuring angles, and therefore

S.E.

Line 3 CtoA

Co
90O

Line 2 BtoC
Bo

600

Ao
LineJ AtoB

FIG. 11. Sur-
veyor's notes of
Fig. 10.

METHOD OF SURVEYING ON THE SURFACE.

the first method that of measuring the three sides is the
only one open to him, and every part of the estate he measures
must be divided into triangles, of which each side is measured,
and, if it is carefully done, a plan may be made of almost
perfect accuracy.

It is, however, inevitable that mistakes should be occasion-
ally made in the following ways : (1) by the lines of poles not
being set out perfectly straight ; (2) by the measurements made
with the chain having some accidental error ; (3) by accidental
mistakes in the position of pegs or other marks, and in booking
or plotting the survey.

Tie-lines. In order to detect such mistakes, it is necessary
to measure tie-lines. With a proper system of tie-lines it is
impossible for any error to escape detection (except where
details are filled in by
unchecked offsets). Ee-
ferring to Fig. 12, the
triangle ABC is the plan
of an estate, the sides of
which have been measured
and found to be as follows :

AB, 550; BC, 620; and

AC, 600. A tie-line is
then run from A to D,
measuring 485. The
length BD is also mea-
sured, 298. By this means
the large triangle ABC

is divided up into two smaller triangles, ABD and ACD. In
plotting the survey, the large triangle ABC is first plotted,
then the distance BD is marked off on the line BC ; the distance
AD should then measure 485. If it does not measure exactly
485, it shows that there is some mistake in the measurements,
and they must be measured over again until the error is dis-
covered. If, on the other hand, the line AD does measure
exactly 485, it is strong evidence that the survey has been
accurately made.

It is, however, just within the bounds of possibility that, by
a combination of errors of measurement, a plan might be pro-
duced that was not correct, notwithstanding the tie made by the
line AD. Such a combination of errors is in the highest

FIG. 12. Surface survey, showing the use of
tie-lines.

22 MINE SURVEYING.

degree improbable; but if absolute proof is required, another
tie-line must be measured. It is also better to have two tie-
lines for another reason: in case an error should have been
made, it is useful to know which of the measurements is most
probably wrong ; and the more tie-lines that are made, the more
quickly and certainly can the exact position of the mistake be
detected. To make a second tie-line, measure on the line AC
the length A to E, 290 ; then measure the length B to E, 500.
When the lines 1, 2, 3, and 4 have been plotted, then on the
line AC measure the length A to E, If the distance BE
measures 500 on the plan, it is conclusive evidence that the
survey and plan are correct. There is, however, other evidence.
The lines AD and BE intersect at the point F, and the dis-
tances BF 328 and DF 161 should be noted in the survey-book.
By subtraction, the lengths EF and AF are then known. The
large triangle is now divided into seven triangles and one trape-
zium, of each of which the measurements are known. If all
the measurements, as scaled on the plan, agree with those in
the note-book, it is incontestable evidence that the plan is abso-
lutely accurate ; and this proof of accuracy is obtained merely
by measuring two tie-lines.

The student who is unfamiliar with the practical difficulties
in the way of making an accurate plan may possibly be inclined
to think that the sketch in Fig. 12 shows an unnecessary
number of tie-lines; but that is not the case. In ordinary
practice a good surveyor makes so many tie-lines that the pos-
sibility of accidental error is entirely eliminated ; and if the
plan is wrong, the fact that an error existed somewhere must
have been discovered when plotting. Most of these tie-lines are
measured, not merely as tie-lines, but as lines of survey neces-
sary for the location of fences, buildings, rivers, pits, or other
objects, the position of which must be correctly marked upon
the plan.

Offsets. In the preceding examples it has been assumed that
the boundary-lines to the estate, in the form of a triangle, were
perfectly straight lines, and coincided with the lines measured.
In practice, however, it seldom happens that a fence or wall
continues straight for any considerable distance, and, in order to
survey this fence or wall, it is necessary to set out and measure
a straight line beside it ; this line proceeds to the end of the
fence, or until it turns away in another direction. For the

METHOD OF SURVEYING ON THE SURFACE.

second fence, or for the altered direction of the first fence,
anotHer line has to be set out and measured ; this is shown in
Fig. 13, which is a copy of a portion of a field note-book. The
thick lines here indicate the fences, and the thin lines those
which are marked out by the surveyor's poles. Line 1 is
shown 980 links long. At the beginning it is seen^ that the
fence is 6 links to the left hand ;
at 400 links along the line the
fence is 7 links to the left hand,
and it is observed that between
these two points the fence is
perfectly straight. These two
measurements to the left, 6 and
7 links respectively, are called
" offsets." An offset is always
measured at right angles to the
survey-line from which it starts,
and in order that they may be
correctly measured, it is essential
that the surveyor should be able
to mark out a line at right angles
by pointing a pole from the sur-
vey-line to that part of the fence
which is at right angles to the
place where he is holding the
pole. If the offsets are merely
intended to show gentle curves
in a hedge, it will not be of any
appreciable importance whether
the line of the offset is measured
at an angle of 70 or 90 from
the survey-line. If, however,
the offset is intended to denote
the correct position of the corner
of some building or other land-
mark, it is, of course, of the utmost importance that it should
be correctly set out at an angle of 90.

A competent surveyor cannot fail to mark out a short offset,
not exceeding, say 15 links, with sufficient accuracy for the
ordinary landmarks in a survey. Should the offset, however, be
longer, every important mark should be fixed by triangulation.

FIG. 13. Portion of surveyor's field
note-book.

24 MINE SURVEYING.

On referring to Fig. 13, it will be seen that the fence ceases to
be perfectly straight beyond 400 links, therefore offsets have
to be taken at 500 and at 550 links; at 600 links the line
passes a building, the end of which forms a portion of the
boundary. The position of this is ascertained by the offsets.
At 930 the line crosses another fence ; at 950 there is an offset
of 10 links to the left to the first fence ; at 980 the line ends ;
there is an offset of 11 links to the first fence and to the fence
corner. No. 1 line comes to an end because the boundary
fence turns sharply to the right. It is therefore necessary to
set out No. 2 line in the direction the boundary now takes.
The fence is rather crooked, and the offsets are therefore closer
together than was necessary on No. 1 line ; and at 40 links
from the beginning of the line the fence bends to the left,
forming a bay.

Unless the exact line of this fence is a matter of importance,
the surveyor would take the inner points of the bay by mea-
suring the offsets at 44 and 60 links, and these offsets are
only 24 and 23 links long respectively ; and, indeed, it is not
an uncommon thing to measure an offset 40 or 50 links in
length ; but the surveyor cannot expect to set out an offset of
that length with precise accuracy without the aid of some
instrument.

Degree of Accuracy of Offset depends on Scale of Plan.
In plotting a plan, however, on a scale of say 2 chains to
an inch, the thickness of an offset line represents a distance
of 2 links ; and therefore precise accuracy in measuring
the exact shape and position of every little twist in a hedge
would be wasted, because it would be impossible to repro-
duce this accuracy on a 2 -chain plan. If, however, the plan
were to be plotted on a larger scale, say 2 inches to 1 chain,
or on a larger scale still, as for building purposes, then the
measurements must be taken with extreme accuracy, because
any defect will appear on the plan. For such a purpose
the position of the corners of the bay must be accurately
found out by triangulation, and the tie-lines shown in the
figure; 27 and 28 links long respectively, must be measured
(for such measurements a tape is generally used), and from the
main offsets branch offsets are measured, as shown by the
figures 1 and 2, so that the exact shape of the fence may be
ascertained.

METHOD OF SURVEYING ON THE SURFACE. 25

Note-book not to Scale. It will be observed that in Fig. 13
the line 2 is only shown for a length of 72 links, and line 1,
980 links long, occupies little more space on the paper. That
is because the figure does not represent a plotted plan, but a
sketch in the surveyor's book. It is necessary that every
measurement should be clearly shown ; thus where the offsets
are few, the measurement on a line of great length only occupies
a small space in the field-book ; on the other hand, where the
offsets are many, a line of short length may occupy several
pages.

It will also be observed that the number of offsets to be
taken will not only depend on the nature of the fences, but on
the scale of the plan on which they are to be marked.

Survey-lines. The student will now understand that one
of the chief purposes of a survey-line is that of a base from
which to measure offsets to the fences, buildings, etc., and that
this base must be sufficiently near to the objects which he
desires to put upon the plan to enable him to set out
right-angle offsets to them by the eye. This being so, his
knowledge of the system by which the land in Great Britain
and Ireland is divided into small fields by hedges and walls,
which are generally crooked, will suggest to him that, as a
general rule, it will be necessary to run a survey-line by the
side of every fence, whether this fence be merely a division
betweeen two fields or the boundary of a road, railway, or
estate. It is also necessary to run a line past every building,
and frequently two, three, or four lines have to be run to fix
with the necessary precision and certainty the position, shape,
and dimensions of some building of only moderate importance.

How to survey an Estate. Fig. 14 shows the plan of a small
estate divided into ten fields by walls, hedges, and fences; it
contains two pit-shafts, colliery buildings, a chapel, and a
school. The surveyor is instructed to make an accurate plan
of the surface. The owner of the property or his agent
points out to him the boundary-lines, indicating in each case
whether his boundary is the centre or side of a ditch, or the
centre of a hedge, or the side of a wall. The surveyor makes a
rapid hand-sketch, similar to the plan in Fig. 14 (but neces-
sarily rough and disproportionate), and is now in a position to
begin the survey. His first step will be to mark on the sketch
the lines which he intends to measure. The longest line which

of Cficusis.

FIG. 14. PJan of a small estate.

METHOD OF SURVEYING ON THE SURFACE. 27

can be measured forms, as a rule, the best base-line ; this, he
finds, is from south-west to north-east, and is marked No. 1 on
the plan ; No. 2 line is set out beside a boundary fence, also Nos.
3, 4, 5, 6, 7, 8, 9, 10, 11, 12. These twelve lines suffice for the
delineation of the boundaries, but additional lines are necessary
for the internal fences and buildings, and lines 13 to 33. are set
out. These lines are set out, not with special regard to the
construction of triangles, but to their convenience as lines from
which to take offsets to the fences, etc. It is, however, found
that a complete system of triangulation is made if some of the
internal lines, as first sketched out, are prolonged a little. Thus
line 13, starting at the point a, and proceeding to b, may be
prolonged as indicated by the dotted line to the point c ; line

17, beginning at the point d and proceeding to e, may be
prolonged, as shown by the dotted line, to the point /; line 15,
beginning at y and ending at h, is prolonged to i; lines 10,

18, 19, and 26 are also prolonged, as shown by their dotted
extensions. If all these lines are correctly measured, an
accurate plan of them may now be produced, and, by means of
the offsets, the fences and buildings may be correctly put down.
Out of all the 33 lines above mentioned, No. 1 is the only one
which has not been set out along a fence, and which serves no
other purposes than those of a base-line and a tie-line.

Estate divided into Triangles, At first sight the student will
fail to see that most of the estate has been divided into triangles,
but on careful examination he will detect a good many, which
are marked on the plan A, A, A, etc. ; there are, in fact,
nine triangles, of which, however, only Nos. 1 and 2 are of large
dimensions.

Hypothetical Triangles, In addition, however, to these nine
triangles that have really been laid out across the fields, there
are a number of other triangles which may be legitimately
completed by a hypothetical line which can be measured off
the plan formed by plotting the former triangles. Thus take the
corner x formed by the junction of lines 11 and 12 ; it is the
apex of a hypothetical triangle, the other two corners of which
are at o and c. o is the starting-point of all the measure-
ments, and is therefore the point first marked upon the plan ;
c is fixed on the plan as the apex of the triangle A, formed
of portions of lines 1, 10, and 13. These two points being fixed,
it is easy with a scale to measure the distance o to c, which

28 MINE SURVEYING.

is the base of the hypothetical triangle of which x is the apex.
In order to put x on the plan, the compasses would be set to
the length ox (line 12), and from the centre o an arc would
be described ; the compasses would then be set to the length ex
(line 11), and another arc described, intersecting the previous
arc at the point x.

To take another instance, point / is the apex of a hypo-
thetical triangle of which the other corners are at g and d ; the
point d is on the base-line ; the point g has been fixed on the
plan by means of the triangle A, formed by the lines 1, 2, and
15. With the compasses set to the length gf (line 3), and from
the centre g, an arc is described ; then with the compasses set
to the length df (line 17), and from the centre d, another arc
is described, cutting the previous arc at the point/. In this
way the hypothetical triangle gdf is completed. In a similar
manner smaller hypothetical triangles at the north-eastern
corner of the estate may be set out.

The whole of the boundary-lines are now fixed by these
triangles, and the accuracy of the work is checked by the
internal lines, which can now be drawn in their right places
without any further use of the compasses.

Tie-lines, It will, however, be advisable to run some other
lines across the estate, merely as check-lines ; thus, from // to
x a tie-line (No. 34) might be run passing through the No. 1
pit ; this not only gives additional certainty to the points g and
x, but to the position of the pit, which is of the utmost im-
portance in a mineral plan. The advantages of this tie-line do
not end there, the point x being fixed by it independently of
point c ; the position of point c can be fixed from the point x,
and its accuracy thereb} 7 confirmed. Other tie-lines should be
measured ; for instance, on line 11 the position of the fence
corner p is only fixed by the measurements at the meeting of
lines 26 and 11. On line 12 the position of the fence corner q
is only fixed by the measurements at the intersection of line 27,
and therefore neither of these points has been ascertained with
absolute certainty. A tie-line may therefore be run from d to
p (line 35) ; this gives additional security, not merely to the
point p, but to line 24 and to point d itself. A short tie-line
(No. 41) from q to the line 34 will check that position. Other
short tie-lines may also be measured, as 36 and 37 near the
school-house and chapel, 38 to fix the position of No. 2 pit, 39

METHOD OF SURVEYING ON THE SURFACE. 29

near the southern boundary,
and 40 at the back of the
colliery workshops. By
these forty-one lines and
their offsets the survey is
completed, and it is impos-
sible that an important error
can escape detection. The
figure now shows a total of
thirty-four triangles.

Intersection of Lines. It
is in the highest degree im-
portant that the crossing or
intersection of two lines
should be carefully noted,
and the careful performance
of this work is characteristic
of a good surveyor; it fre-
quently involves a good deal
of trouble, and therefore it
is frequently neglected by
the hasty or careless sur-
veyor. The base-line is
touched and crossed by the
following lines : Nos. 2, 12,
39, 28, 32, 13, 14, 34, 26,
36, 20, 15, 17, 35, 37, 23,
22, 6, 21, 10, 31, and 8. It
is not sufficient, however,
to mark on the base-line
the distance at which these
lines cross or intersect ; but
it must also be noted at
what length on each of the
crossing or touching lines
the intersection or meeting
takes place. This is shown
on Fig. 15, which is copied
from the surveyor's note-
book.

Entry of Intersections and

No. 1 Base Line from S.W. to N.E.

FIG. 15. Surveyor's field notes, from which
Fig. 14 has been plotted.

30 MINE SURVEYING.

Stations in Note-book. In this note-book the student will read
the figures (540) = Y ; this means that at 540 on the base-line,
line No. 28 starts, and is *on the right hand of the base-line.
Also (1010) = - 6 T y- ; this means that at 1010 on the base-line,
line No. 13 crosses it at 665 links from its starting-point,
iff-o = (2530) ; this means that at 2530 on the base-line, line

No. 15, which is on the left hand of the base, reaches it at a
distance of 1660 from the beginning of line 15.

The peg from which the measurements start is driven firmly
into the ground, and its position is also fixed by a measurement
to the corner of the field, shown in Fig. 15. The surveyor notes
that he intends to start No. 2 line on the left-hand side from the
same point ; he notes that another line will join this peg from
the right-hand side ; but he has not yet given the line a number,
and the note -ff 9 - (that is, 2000 in line No. 12) on the right-
hand side of the page has been added at a later period of the
survey after line No. 12 had been set out and measured, and
was found to be 2000 links in length from its beginning up to
the starting-peg of No. 1 line, where it ended. At 540 a peg
was put down as a convenient place for starting another line,
which was subsequently found to be No. 28 ; at 846 a second
peg was put down as a convenient place for starting a line,
which was subsequently found to be No. 32 ; at 1010 a third
peg was put down as a convenient place for the intersection of
another line. As the surveyor measures the line, he leaves
pegs (noting the distance) at suitable places for the starting,
ending, or intersection of other lines ; the numbers of these
lines he, perhaps, cannot foresee at the time. Space must be
left in the note-book for figures which have to be added after
the intersecting or touching lines to which they refer have been
measured.

Keferring to the intersection of line 34, it must be under-
stood that the place of intersection, 1345, was not noted when
the line was first measured, and for this reason that the exact
position of the intersecting tie-line could not be foreseen.
When, however, line 34 was run and <3ame across the base-line,
poles were fixed in some of the stations previously left on the
line, so that the exact point of the intersection of the two lines
could be established ; then a measurement was taken from a
station previously measured on the base-Kne, as, for instance,

A35*35

\60 80^- --

35 470

1500
60 1340

50 1200

BEARING N30W

28 790

Linefrom, ~fjy to ^ Line from

V */

FIG. 16 (1). Surveyor's field notes, from which Fig. 14 has been plotted. Lines 2 to 41.

538

@
30 360

20 140

Line from

530

Line from-^ to A

55 250

FIG. 16(2). continued.

Line from ^

Line @ from to

Line ( 6 J Continued

L919

Line (10) from-

Line (o) from to

FIG. 16 (3). continued.

,-
32

-P- _P_

Line (12) from

^toA

373 32

1242

1170

1840

1470

1840

FIG. 16 (4). continued.

41 540

31 422
351

23 211

Line (15) from

2250

770

1388 80

850 46

500 40

Line @ Continued

609

(15)

@1170
=

x~x 3020 1170

Line(l7) from -^jr to ~^r

FIG. 16 (5). continued.

IVERS!

52 (389) =

1497

529

481

301 15

309 1311

Line

624) 220

Line (23) from

220

'<>

921

312- 46

282^
252,

^ 200 921

Line from to

395

435

300

(10)

250

3510

100

448

Line (21) from ^ to ^
7)

Line (20) continued

FIG. 16 (6). conti nued.

Line@ from gg to

511

(40)

(300)
120

2320

_ 963

line from

1028

1550

Line from to

Line

480
continued

FIG. 16 (7). continued.

618 =

545

(28)

570

467

1032

NO. 2 PIT
---57

1799

J54_

WINDING ENGINE HOUSE ^

NO.l PIT.

'61 928

61 852

. 756

780

550 M 56

WINDING ENGINE HOUSE *& - 618
N0.2 PIT.

1169 65]

Line (2?) continued

732

772 )] fro.i PIT

480

371 N0.2 PIT

Line (32) from -7^- to ^~

375

from

535

420

319

789

FIG. 16 (8). continued.

. 673

709

300

322

94
333 . 300

_ 420

"35

Line (39\Tie from JL to _*20_

250 N0.2 PIT

Line(37)Tiefrom^to-^

83 =

1311

Line

METHOD OF SURVEYING ON THE SURFACE. 39
FIG. 16 (9). continued.

to ML

34) (12)

NOTE. In order to save space, and also for convenience and rapidity of booking,
the starting and finishing points and junction of one line with another are ex-

770 419 ^

pressed as fractions ; e.g. " Line (16) from /^\ to ^ '' means that line (16)

starts from a station left at 770 links along line (?), and ends at a station 419 links
in line (is) ; the number of the line being enclosed in a circle and appearing as
the denominator of the fraction.

To indicate a station, its length as read off from the chain line is enclosed in a

circle; eg. the length (609) in line (15) is a station, line (g) crossing at this point
(1350) links from the starting-point (i.e. of line (14)).

the station at 1010. In measuring from this to the intersection
of line 34, two hedges are crossed, and the survey-line No. 14,
so that there is little possibility of a mistake in identifying
the station from which the measurement was taken. In the
same way the position of the station 1550 on the base-line,
where No. 26 ends, is found by remeasuring a portion of the
base-line.

The same care has to be taken in crossing other lines, as,
for instance, the tie-line No. 34 crosses lines 14, 1, 13, 29, 33,
32, and 27 ; and the position of the intersection of all these
lines must be noted with the same care as was taken in noting
the intersection on the base-line. By this careful noting of
intersections, the detection of any error in the survey is a
certainty ; and not only that, but the place of the error is
quickly discovered, and the length which has been inaccurately
measured or incorrectly entered in the note-book can be
measured over again, otherwise the surveyor might have to
waste a great deal of time in remeasuring lines that had been
accurately measured the first time.

Complete Note-book. Figs. 15 and 16 give the whole of the
survey-book from which the plan Fig. 14 has been plotted, and

40 MINE SURVEYING.

the student is recommended to plot this survey without referring
to Figs. 14 and 17 until he has finished. Fig. 17 shows the
order in which the triangles are plotted.

Railway Surveying. The mining engineer has frequently to
set out railways for mineral traffic, and every surveyor ought
to understand how to survey the country where it is proposed
to make a railway. Fig. 18 shows a piece of country through
which it is proposed to make the line which is shown by the

FIG. 17. Showing the order in which the survey-lines given in Figs. 15 and 16

are plotted.

thick black curve, and it is necessary to make a plan of the
fields, etc., through which it passes. The main lines of the sur-
vey are marked 1, 2, 3, 4, 5, 6, 7, 8. It will be seen that the
proposed line of railway starts in a direction north-west, then
turns to north-east, and again to south-easfc; and the piece
of ground surveyed is a strip about 12 chains wide, follow-
ing the curve of the railway. By the careful measurement
of the triangles, line 4 is accurately placed in relation to

METHOD OF SURVEYING ON THE SURFACE. 41

line 1, and line 6 is accurately placed in relation to line 4, and
the survey may thus be continued for a good many miles with
great accuracy. It is essential that all parts of the survey
should be connected by two or more lines, so that all the

FIG, 18. Preliminary railway survey.

measurements are checked. The lines Nos. 1 to 8 are the main
lines ; numerous other lines run alongside the fences and com-
plete a network of triangulation that eliminates all chance of
undetected errors.

42 MINE SURVEYING.

When the student has once mastered the principles on which
the plans Figs. 14 and 18 are made, he understands the whole
theory of an ordinary surface survey of an estate; and practice,
combined with the requisite physical and mental faculties, only
is required to make him a competent land surveyor.

CHAPTEE IV.

INSTRUMENTS FOR MEASURING ANGLES.

IT is characteristic of the man of science to use every means at
his command for testing the accuracy of his observations.
Keferring to Fig. 18, plan of a railway survey, it is obvious that
if the bearings of some of the main lines were taken, that is
to say of lines 1, 4, and 6, they would be a check upon the
accuracy of the triangulation, especially if it were continued for
a long distance, say 10, 20, or 100 miles. For this reason
surveyors commonly use a magnetic compass to take the bearings
of their main lines. With this information they can quickly
correct any very serious blunder that might have been made
either in the measuring or in the plotting of the survey.

Magnetic Compass. The construction of the magnetic compass
is based on the well-known fact that a very light steel bar, like
a knitting-needle, which has been magnetized, will, if balanced
at its centre on a fine point, turn so that one end points to the
north and the other end to the south ; whichever way the needle
is placed originally, it is always the same end which seeks the
north, that end is therefore called the north end (meaning the
north- seeking end) of the needle, and the other end the south
end of the needle. The direction in which the needle points
is not, however, towards the north pole (i.e. towards the pole
star), but it is towards the magnetic pole. To an observer in
England this magnetic pole is west of the true or geographical
north pole. A person standing at Greenwich and looking due
north would have the magnetic pole a little to the left of his
line of sight. The difference between magnetic and true north,
or the angle between the magnetic meridian and the geo-
graphical meridian, is called magnetic declination.

Declination of the Needle. On the 1st of January, 1901, the
magnetic needle at Greenwich pointed in a line about 16 26'
west of the true or geographical north. The magnetic pole is
constantly moving its position. Three hundred years ago the
magnetic north in England was east of true north ; it moved
gradually westward until the year 1818, when the needle near

44 MINE SURVEYING.

London pointed about 24 38' west of the north pole. Since
then it has been gradually returning eastwards. The move-
ment in England is now approximately at the rate of 6' to 8'
a year, or roughly 1 in 8J years. Apparently the present rate
of movement is rather slower than the average of the last 36
years, which has been fairly regular, averaging during that
period about 8 minutes a year in the neighbourhood of London. 1
Variation of the Declination. The declination of the needle
from the true north is not the same for all places ; thus whilst
the declination may be 16 26' west at Greenwich, and about
the same at Worthing in Sussex, and Newmarket in Cambridge,
it would be about 17 34' at Torquay, or Kidderminster, or
Leeds, or MiddlesborOugh, and 18 35' at Pembroke, or Conway,
or Barrow, and 19 30' at Glasgow. The lines of equal declina-
tion (or isogonic lines) for the British Isles are shown on a map
published annually as a supplement to the Colliery Guardian. 2
A somewhat similar map on a reduced scale is shown in
Fig. 19. This map has been prepared by reference to the
elaborate paper by Professors Riicker and Thorpe, published in
the Philosophical Transaction*, 1890. The isogonic lines drawn
on this map represent average declinations ; there are a great
many local variations due to various causes, such as the mag-
netic character of the rocks, of which no account is taken in
the diagram. The direction of these lines is north-easterly, and
a person travelling along one of these lines, say from Torquay
in Devonshire to Leeds in Yorkshire, and using the magnetic
compass, would find the same decimation from the true north
along the whole line, but in journeying from London to Liverpool
there would be a change in the declination every mile. By way
of illustrating the use of this map, a surveyor in the Warwick-
shire Coalfield will find that the isogonal marked 19 in 1886
passes through that district, and that the declination in January,
1901, was 17 15'. A surveyor in the Liverpool district is on
another isogonal, marked 20 in 1886, and 18 15' in 1901. Half-

1 Everyday there is a slight movement, known as the diurnal variation. Accord-
ing to Professor H. Stroud, M.A., D.Sc., the needle reaches its westerly maximum
deviation at 1 p.m., and its maximum easterly at 10 p.m. (in the southern hemi-
sphere east and west must be interchanged). This variation is about 10 minutes,
or a sixth of a degree. For ordinary bearings this slight variation may be neglected,
but when fixing the north point on a plan, or in other cases where extreme accuracy
is desired, account must be taken of this variation. The reader is referred to the
paper by Professor Stroud, in the Proceedings List Mining Engineers, vol. vii. p. 268.

2 May be obtained from the Colliery Guardian office, 49, Essex Street, Strand, W.C .

INSTRUMENTS FOR MEASURING ANGLES. 45

II 10 9 6 7 6 S 4- 3 2 101 2

FIG. 19. Magnetic chart for the British Isles, showing the lines of equal magnetic
declination, as laid down by Professors Riicker and Thorpe in 1886. The
dotted lines were obtained by joining up the points where equal declinations
were found ; the full lines show the average or mean lines. The figures
printed at the ends of the curves are the declinations as appended by Professors
Rttcker and Thorpe in 1886. The present declination can be obtained approxi-
mately at any time by deducting 7 minutes per year for every year since that date.

46 MINE SURVEYING.

way between these two isogonals, that is, in the neighbourhood
of Crewe, the decimation in January, 1901, was a mean between
17 15' and 18 15', that is to say, 17 45'.

If a person were travelling along a line of latitude from east
to west in England, the declination would increase as he went
westward at the rate of about 1 in 100 miles on the south coast,
and in the latitude of Berwick at the rate of 1 in about 70 miles.
If instead of travelling from east to west, he were to travel (in
England) from north to south, that is to say, along a line of
longitude, the variation would be about 1 in 300 miles in the
longitude of London, and 1 in 200 miles in the longitude of
Falmouth and Milford Haven. If he were to travel north-west,
as from London through Oxford and Cheltenham to Aberyst-
with, the variation would be on the average at the rate of 1 in
rather more than 80 miles, and travelling from Whitby to Carlisle
the declination would change at the rate of about 1 in 70 miles.

If the traveller should get on board a ship and sail round the
world, he would find that in some places the declination is west,
in others east, and that in some places there is no declination,
that is to say, the needle points in the direction of the geographical
north.

For the guidance of mariners and others, maps are prepared
which show the declination of the needle in all parts of the
world that have been explored by civilized man. A reduced map
prepared from the Admiralty chart corrected up to 1900, is
shown in Fig. 20. 1 In whatever locality a surveyor may find
himself, the Admiralty chart will show him the decimation of
the needle, and the local rate of variation. He can, however,
always ascertain the declination of the magnetic needle from
the geographical meridian by observation, provided he knows
how to mark out a line due north and south. For particulars
of the various methods of finding the true north, the reader is
referred to the chapter dealing with that subject.

In the magnetic compass the surveyor has an instrument
with which he can observe how far any line which he may have
marked out varies in direction from a line drawn towards the
magnetic north, or, as it is usually called, the magnetic meridian ;
if he is able to observe the angle that each line makes with the
magnetic meridian, he can easily calculate the angle that each
line makes with the other lines, thus he can calculate the angles

1 The Admiralty charts may be had from the agent, 31, Poultry, London, E.C.

INSTRUMENTS FOR MEASURING ANGLES.

O5
00

>-.

c bo

2.2
"S Q
2 o

^ a

O s

48 MINE SURVEYING.

at the intersection of lines 1 and 4 in Fig. 18, and of lines
4 and 6, and can thus check the accuracy with which these lines
have been laid down on the plan.

Mariner's Compass. Before proceeding to further detail as
to the method of using the magnetic needle, it will be well to
describe some of the numerous forms of magnetic compass.
The mariner's compass is the form most generally known, and
of greatest use, because by means of it all the fleets of the
world are steered across the ocean.

The novice, looking at a mariner's compass (see Fig. 21),
might fail to learn that it had anything to do with the magnetic
needle, because no needle is visible. The magnetized steel bar
(or needle) is covered with a card, and, being supported at its
centre on a sharp-pointed pivot, is free to revolve, and the card,
being attached, moves with it; the instrument is enclosed in
a brass case with a glass window, so that it is sheltered from

the wind; the compass-holder is
suspended in brass hoops (gim-
bals), so that the horizontal posi-
tion of the card may not be
disturbed by the motion of the
ship. Inside the box or case are
two marks above and in a line

FIG. 21.-Mariner's compass. with the ce ~ ntre of * n e card, and

on opposite sides of the card :

these two marks are placed in a line parallel with a line drawn
through the centre of the vessel. If, then, the ship is pointing
towards the magnetic pole, these two marks will coincide with
the direction of the magnetic needle ; if the ship is turned to
the right of the magnetic pole, these two marks will be pointing
in a line north-east of the magnetic meridian ; and if the ship
is turned the other way, it will point north-west of the magnetic
meridian.

In order that the direction in which the ship is pointing
may be ascertained without delay, the card is divided by marks
called "points;" there are thirty-two points in the circum-
ference, eight in each quadrant, so that each point is an arc of
11 15'. Thus : north, north by west, north north-west, north-
west by north, north-west, north-west by west, west north-west,
west by north, and west begins or ends another quadrant. The
other quadrants are similarly divided, and the outer rim of the

INSTRUMENTS FOR MEASURING ANGLES.

card is divided into 360. The direction in which the ship
travels is seen by reading on the card the position of the fixed
marks in the box ; one mark represents the bow of the vessel,
and the other the stern ; the bow mark is red. The card of the
mariner's compass is shown in Fig. 22.

FIG. 22. Card of mariner's compass.

Prismatic Compass. A somewhat similar compass, called the
prismatic compass (see Fig. 23), is used by land surveyors, but
a light divided circle (generally made of aluminium) is often
substituted for the card over the needle ; it is also fitted with
sights : one sight, A, has a slit ; the opposite sight, B, has an
opening, down the middle of which is stretched a hair or other
fine thread. This slit and hair are placed in the direction of
the line of survey, and the bearing is read by a pointer in the
box, which is in the same line as the sights. The instrument is
made so that the bearing may be read whilst it is held in the
hand. In such a case it is necessary to read the bearing at the
same instant that the sights come into the line. That this may be

MINE SURVEYING.

done, a reflecting prism is placed just below the top of the slit A.
By means of this prism the marks on the graduated circle are
reflected into the eye, and the mark which coincides with the
line of sight is the bearing. This method, of course, only
suffices for rough approximations to the bearing. Where
accuracy is required, the compass must be placed on a stand,
and in some cases this stand is made of a single stick, the
pointed end of which is placed in the ground, and on the upper
end is a ball-and-socket joint, by means of which the compass
can be levelled.

In some cases a tripod stand is used, and this is suitable for
underground work. In order that the correct bearing may be

read, it is necessary that the circle
should be marked as if the north
end of the needle were the south
end. Suppose the observer is look-
ing towards a staff, light, or other
mark north of him, the north end
of the needle will, of course, be at
the opposite side of the compass-
box to the observer ; therefore the
observer can only read the south
end. If this end is marked "south,"
the observer would be apt to book
that reading, and afterwards imagine
that he had proceeded in a southerly
direction. To avoid such an error,

FIG 23. Prismatic compass.

the reading he observes should give him the direction in which
he is moving, and therefore the letter N should be placed at the
centre of the southern semicircle, and the letter S at the centre
of the northern semicircle, and the east and west marks should
be put in their correct positions relatively to the north and
south marks, that is to say, the letter E will be at the side
which is really the west, and the letter W at the side which is
really the east.

Graduation of Circle. The division of the circle into points
as used by the mariner is not required by the surveyor. The
circumference is divided into degrees only, each degree being
the three hundred and sixtieth part of the circumference.
Counting from the N. end of the card, which is 0, and pro-
ceeding, say, towards the E. mark, the first quadrant, up to 90,

INSTRUMENTS FOR MEASURING ANGLES.

is called north-east ; the second quadrant, from 90 to 180, is
south-east ; the third quadrant, from 180 to 270, is south-west ;
the fourth quadrant, from 270 to 360, north-west. In order,
however, to facilitate the plotting, it is a common plan to count
both ways, from both the south and the north ends ; thus from
north to west the degrees may be figured (on an inner ring of
figures) from to 90, and from north to east also from to
90 ; from south to west in the same way the figures go from
up to 90, and the same from south to east ; so that the bearings
are always read so many degrees from the meridian line, say 40
north-west or 40 north-east, as the case may be ; or, if the
observer is proceeding in a southerly direction, he might be
going 30 south-west or 30 south-east, meaning that the bearing
is the direction of a line proceeding from the centre pivot of the
compass through a mark on the circumference 30 from the
meridian line. The compass is made in various sizes from 1J
inch diameter up to 6 inches ; the common size is about 2J
inches. The weight of the card or metallic circle on the needle
is, however, some objection to the use of this form of compass.

FIG. 24. Hedley dial with outside vernier.

Dial Joint.

iiiiiliiii i li

Vernier Clamp

HlUed head to turn, Vernier

FIG. 25. Details of Hedley dial with outside vernier.

INSTRUMENTS FOR MEASURING ANGLES. 53

Miner's Dial. The dial is the instrument generally used
by mining surveyors for taking bearings and angles. It differs
from the two preceding forms of compass in this important
respect that the card or graduated circle is stationary, and
the needle swings clear of it. One of general utility is shown
in Figs. 24 and 25. Dials are made in various sizes, from a
small pocket one, up to one carrying a needle 18 inches long
(these large ones being for special work only). For general
work the most usual size has a needle about 4^ inches long ;
occasionally a 6-inch needle is used.

In France the needle is usually a thin flat bar, wide at the
centre, and the sides gradually converging to a point at the
extremities (a, Fig. 26). In 'England it is common to use a
needle rectangular in cross-
section, and nearly the same
thickness throughout. Just
at the middle it is a little
wider, and near the ends it
is drawn down to a fine edge
(6, Fig. 26). Sometimes,

instead of drawing the end / [ - Q \

down to an edge, a line is
marked on the top to repre-
sent the middle of the needle
(c, Fig. 26). A piece of
agate (stone) is securely fixed

in a brass cap Screwed into FlG 2 6.-VarietiTs of compass needle,
a hole drilled through the
middle of the needle from top to bottom, and in this agate a
conical hole is drilled from the under side nearly through ; this
agate rests on the sharp point of hard steel of the pivot that
carries the needle. The agate is hard enough to resist the
cutting effect of the steel point. The needle is free to revolve
round the point in a horizontal plane. It is essential that the
friction on the point should be reduced to a minimum, as the
magnetic force is very small, and is insufficient to overcome
any but the smallest frictional resistance.

The needle has to be so weighted that, when magnetized, it is
evenly balanced on the steel point or pivot; a small piece of brass
clipping the needle firmly, but capable of sliding along it,
enables the balancing to be done accurately.

54 MINE SURVEYING.

In course of years a needle is apt to lose its magnetism,
and requires to be remagnetized. This may be done -by taking-
out the needle and unscrewing the cap. The north pole of a
strong permanent bar magnet is then stroked down the needle
from the centre to the south end. The needle is then turned
round, and the south pole of the magnet is stroked from the
centre to the north end of the needle. The needle is then
turned over, and the process repeated on its under side.

It is important that the agate cap of the needle, and the
steel pivot on which it works, should be kept free from dust.
The pivot should also be kept sharp, so as not to interfere with
the free movement of the needle.

The top of the needle is level with the upper surface of a
graduated circle which is fastened on to the dial-plate, and
this upper surface is about J- inch above the bottom of the dial.
The graduations are carried down the vertical side of the circle.
This circle is divided into degrees, and if the end of the needle
is not opposite one of the divisions, the surveyor has to estimate
as nearly as he can the fraction of the degree beyond the last
mark, thus : -, J, f, ^, --, f , and -J ; the bearing being, say, south-
east 21| or , as the case may be.

Many surveyors do not profess to read to eighths on a dial
of this size (4i-inch needle), and would only book quarters, as
21|. It is, however, possible, with a well-marked dial and a
well-made and properly magnetized needle, to read to even one-
eighth of a degree, which means that, supposing the bearing is
booked by the surveyor as 21J, it is possible that he may be
deceived, and that the real bearing is 21^ or 21f ; but the error
need not be more than % either way.

E. and W. reversed. In the ordinary dial (Figs. 24 and 25)
the letter E is put on the west side, and the letter W on the
east side of the dial-plate or graduated circle. The graduations
are read by the help of two systems of figuring. The outer set
of figures are marked 10, 20, etc., up to 360. These figures go
from north to east, and continue round the way the sun
travels ; thus W. is at 90, S. at 180, and E. at 270. The
other system of figuring is on the inside ring, and refers to
the quadrants, as 10, 20, 30, up to 90. Thus, counting from
the north to the right hand are 10, 20, 30, etc., N.W. ; starting
from the north to the left hand are 10, 20, 30, etc., N.E.;
starting from the south to the right hand are 10, 20, 30, etc.,

INSTRUMENTS FOR MEASURING ANGLES. 55

S.E. ; and starting from the south towards the left-hand are
10, 20, 30, etc., S.W.

Mode of using the Dial. There are two sights on the dial in a
line with the north and south marks on the dial-plate. These
are shown in Fig. 25, and consist of folding arms hinged at the
point i, so as to fold down when not in use. Each sight has in
it a broad opening and a slit, and down the centre of the broad
opening is stretched a hair. The observer takes a sight by
placing his eye at the slit, and moving the sights until the hair
in the opening opposite is exactly in the centre of the object
to which he is sighting. When taking inclinations, the circular
holes shown are sighted in a similar manner. In using the
dial the north (or N.) sight is always turned in the direction
the surveyor is going. If he happens to be sighting a station
behind him, then the south (or S.) end of the dial is turned
towards this station ; if he happens to be going in a direction
magnetic north, the north end of the needle will point exactly
to 360 or of the graduated circle over the letter N ; if he
happens to be going north-east, the line of sight will be to the
right hand of the north end of the needle.

To read the bearing, the surveyor looks at the north end of
the needle, and reads the bearing against which it points, say
21 N.E. ; but, whichever way the surveyor goes, he must bear
in mind to turn that end of the dial which is marked N. (for
north) in the direction in which he is going, and to read
the bearing from the north end of the needle. The north end
of the needle is indicated by a mark upon it ; it sometimes
consists of a notch, and sometimes of a brass cross-bar.

Hedley Dial. The kind of dial most commonly used, and
perhaps the most convenient form that is made, is known as
the Hedley dial, and it is this form of dial which is illustrated in
Figs. 24 to 28. The distinctive feature of this dial is that
the sights are not fixed on the dial-plate, but to a separate
ring outside, carried on bearings on each side of the centre dial-
plate ; the circle carrying the sights can thus be moved up and
down through an arc of about 60 either way, so that a sight
can be taken up or down a very steep place. Attached to the
instrument is a semicircle for measuring vertical angles, the
arm J (Fig. 24) is fixed to a projecting end of the axis which
carries the movable ring to which the sights are attached. The
semicircle is fastened by two studs to this ring, and is therefore

56 MINE SURVEYING.

inclined to the same degree as the line of sight, when it is taken

FIG. 27. Face of dial, showing Halden's method of measuring inclinations.

through the small round eye-hole and the cross-hair of the

opposite sight. The arm
J always remains in a ver-
tical position as long as
the surface of the dial is
kept level, and a pointer
at the end of the arm en-
ables the angle of elevation
or depression to be read.

The semicircle is gra-
duated in quadrants, zero
being at the centre, and
the graduations extending
to 90 each way. There is
a clamping-screw at the
lower end of the arm J, by
which the sights can be
clamped at any desired
angle of inclination.

Messrs. Halden make a
dial with an improved arc

for measuring vertical angles. Instead of an external attachment,

FiG.'.27A. Caeartelli's dial, showing semicircle
for measuring inclinations.

INSTRUMENTS FOR MEASURING ANGLES. 57

which may get broken, the graduated arc is on the base of the
compass-box, the traversing finger working on a centre near the E.
point of the dial (see Fig. 27) . Another form of inclinometer is
shown in Fig. 2?A. This is made by Messrs. Casartelli, and con-
sists of a graduated brass semicircle, in the same line as the sights,
which folds down on one side of the dial-box when not in use.

Dial with Inside Vernier. The dial is generally so made that
it could be used for measuring angles if the needle was taken
away, or if, owing to the presence of iron or other magnetic
metal or rock, it cannot be used. One form of this is shown in
Fig. 28. On the inside of the dial-box is fastened an index or

FIG. 28. Hedley dial with inside vernier.

vernier, the on the vernier being in the same line as the dial-
sights. The dial-box is so made that it can be moved round
independently of the dial-plate. If the dial-plate is firmly
clamped and the sights moved to the east or west, the mark on
the inside rim of the box moves with them, and the angle of
movement can be read on the graduated circle.

The use of the vernier is that fractions of degrees may be
accurately read. The ordinary dial vernier reads to 3', or ^
part of a degree. The dial-plate is graduated and figured as
already described. When using this dial for taking bearings
with the needle, the mark in the centre of the vernier must be
over the north or zero point of the graduated dial-plate (as

58 MINE SURVEYING.

shown in Fig. 28), and it can be kept in this position by means
of a brass pin, which is put up through the bottom of the
dial-box and the dial-plate. When it is desired to use the
vernier for taking angles, this brass pin is pulled out and
the clamping-screw slackened. The sights are moved by means
of a milled head on a pinion, the teeth of which fit into a rack
on the inner side of the dial-box. By means of this pinion the
sights can be easily moved to the required extent.

Outside Vernier. In another, and in some respects superior,
form of this dial (Figs. 24 and 25) there are two graduated
circles : one inside the dial-box, e (Fig. 25), to be used for
taking bearings with the needle; and the other outside the
dial-box, / (Fig. 25), to be used when taking angles without
the needle. This outside graduated circle is immovably fixed
to the vertical axis, while all the other parts of the dial above
it can revolve (by the action of the rack and pinion). The outer
graduated circle is covered by a brass rim outside the compass-
box, which conceals it from view, except at one place where
this rim is partly cut away so as to expose the graduations for
a length of say 30.

On the movable dial-box is fixed the vernier h (Fig. 25),
on which is a centre-mark. For the sake of convenience in
reading, this vernier is not exactly under either of the sights,
but is a little on one side, and at the beginning of a survey
the centre-mark of the vernier is placed opposite the zero
on the graduated external circle. If the dial-sights are then
looking north and south, any movement to the east or west
will be measured in degrees and minutes by the movement of
the mark on the vernier from the zero point.

The advantages of this form of dial are first, that the outer
graduated circle and vernier can be easily read ; second, that
the sights are always in a line with the north-and-south line on
the dial-plate, and therefore the needle can always be swung
and a true bearing observed (in case there is no attraction),
whereas with the dial with inside vernier a loose-needle bearing
could not be read until the ring carrying the sights had been put
back into its original position, with the centre-mark of the
vernier opposite the north-and-south line of the dial.

It is essential that the dial should be placed level, and for that
reason two spirit-levels, at right angles to each other, are generally
placed on the body of the dial (as shown in Figs. 24 and 25).

INSTRUMENTS FOR MEASURING ANGLES,

The spirit-levels may also be placed on the limb to which
the sights are attached (as shown in Fig. 28), and, although
more liable to get broken in this position, they do not interfere
with the swinging of the needle.

Dials are generally made of brass, but aluminium dials are
now being made, and are preferred by some on account of their
great lightness.

Dial-joint. The dial is generally carried on a tripod stand,
to which it is attached by a coupling, having a ball-and-socket
joint (see Fig. 25). Above the ball is a strong brass pillar, a,
which fits into a socket, b, which may be screwed on and off
from the under side of the dial. The dial and socket are free
to revolve round this pin or vertical axis, but can be fixed in
one position by means of a clamping-screw, c. Below the ball
is a clamp, d, by means of which the vertical axis can be
tightened in the required position, and by which it can be
slackened to admit of adjustment. This ball-and-socket joint,
and the upper swivel movement, generally give satisfaction if
they are kept in good order, but it is necessary that they should
be cleaned from time to time and used with care. Some sur-
veyors of great experience condemn this joint because of the
insecure attachment of the dial by a screw, which may lead to
an inaccurate survey, and also because of the absence of any
convenient mode of levelling the head of the tripod holding the
lamp-cup.

There are, however, other modes of attachment. The
ordinary parallel plates, such as
are used with the theodolite
(Fig. 37), may be substituted
for the ball-and-socket joint.
There is also the Hoffman joint,
made by Davis of Derby (see
Fig. 29). By turning the milled-
head screws a, a from left to
right, the two concentric balls
B and D are liberated, and the
dial can then be approximately
levelled up ; on turning the

Screws in the opposite direction, FlG " 29- Hoffman levelling-joint.

the joint is clamped, and the final adjustment may be made
by turning opposite screws in reverse directions just as required.

MINE SURVEYING.

Another variety of levelling-joint (shown in Fig. 2?A) has
a ball held between two plates which can be tightened or
slackened by turning a thumb-screw. On the top of the ball is
a strong brass pillar, fitting into a socket fixed on the under side
of the dial ; in the socket is a clamping-screw. Each tripod has

FIG. 30. Bullock's levelling-joint.

fixed to it the levelling-joint. Two lamp-cups, fitted with cross-
levels, are used to hold the object-lamps, and by means of these
levels the brass pillar is set, so that when the dial (as in fast-
needle work) is moved and placed upon it, its face will be level.

INSTRUMENTS FOR MEASURING ANGLES.

Some surveyors who have used most kinds of dials strongly
recommend the joint above described.

Bullock's ball-and-socket joint is shown in Figs. 30 and 30A.

FIG. 30A. Bullock's le veiling-joint.

On reference to the figure, it will be seen that three adjusting
screws, a, converge on to a cone, b, to which is attached the
ball ; then, by tightening or slackening these screws, the top

MINE SURVEYING.

may be thrown to any reasonable angle, and so enable the
operator to obtain an accurate adjustment. One advantage of
this joint is that when all the screws are touching the cone, the
top cannot be thrown out of adjustment.

Dial-legs. The tripod head is carried on three legs, usually
about 4 feet 6 inches long; when these legs are spread out,
the dial is at a convenient height to read ; for low roads shorter
legs are used. The long legs are often jointed in the middle, so
that by unscrewing the lower half the legs remain about 2 feet
3 inches in length. These legs may be jointed again, for thin
seams or very low places in the roads, for which places legs 12
or 15 inches in length are used. Telescopic legs are sometimes
made, and are convenient in low, narrow, and rough places. It
is important that the legs should be attached to the tripod head
in such a manner as to preclude the possibility of slackness,
whilst they must not be too stiff for convenient use. The three
kinds of head commonly employed are shown in Figs. 31, 32,

FIG. 31. Ordinary
dial tripod.

FIG. 32. Improved form of
dial tripod.

FIG. 33. Theodolite tripod.

33. In Fig. 31 the legs get slack if they are kept long in a
dry place, but they can be tightened by soaking the joints in
water, which causes the wood to swell. In Fig. 32 the split end
of the legs can be tightened over the brass projection by means
of the thumb-screw. In Fig. 33, which is the method adopted
in the tripod stand for theodolites, the joints can be tightened
or slackened as much as desired by turning a nut upon a
screw. This seems to be the strongest and best method.

Lamp -cups. In fast-needle dialling two lamp-cups are
usually employed. These are shown in Fig. 25, and consist of
shallow cups of suitable diameter to receive the lamp. One of
the cups is provided with levels, and this is always used in
fixing the front legs ready to receive the dial.

INSTRUMENTS FOR MEASURING ANGLES. 63

Various Dials. Many modifications of the dial are made. In
one of these a telescope is substituted for the simple slit and
hair-'sight, the sights being made detachable, so that the tele-
scope may be taken off and the ordinary slit and hair-sights
substituted, as shown at A and B (see Fig. 34). The telescope

FIG. 34. Hedley dial with telescope.

is advantageous for work where extreme accuracy is required,
because the lamp, candle, or other mark can be clearly seen,
and the meridian line of the dial turned precisely on the centre
of the light, whereas with the slit and hair an error amounting
to the thickness of the hair or the width of the slit may be easily
made. The possible error, however, from this source, if the hair
is properly fixed, is not more than 1 in 1200, or less than ^V
of a degree, so it is only for special cases, either where very
long sights are taken or where special accuracy is required,
that the telescope is useful.

It is obvious that a single telescope is, in some respects,
not so convenient as the ordinary sights, which are made
double for looking either backward or forward, and where the
telescope is supported in the manner shown in Fig. 34, it is
necessary to take it out of the holders and reverse it for the
back sight.

Dial with Eccentric Telescope. In surveying without the
needle or " fast needle," as it is called the angle can be read

64 MINE SURVEYING.

with great accuracy by means of the outside vernier ; but if the
needle is used there may be some difficulty in reading it, in
case the line of sight should correspond with the magnetic
north, as the needle will then lie immediately below the tele-
scope. This difficulty is got over by placing the telescope on
one side of the dial instead of over the centre, as shown in
Fig. 35. There is, however, a drawback attending this form,
because the line of sight through the telescope is not directly
parallel with the direction of a line from the centre of the dial
to the lamp. This, however, may be got over by placing the

lamp to be looked at at an
equal distance away from the
mark, and on the same side of
the mark.

The plan of having the
telescope on one side has not
only the advantage of leaving
the top of the dial quite clear
and taking up less headroom,
but has the further advantage
of permitting the telescope to

be moved through a complete
FIG. 35.-Dialith eccentric telescope gQ ag fo j k

(Kindly lent by Messrs. W. F. Stanley & Co., Ltd.)

backwards or forwards, up or

down, as required, or at any intermediate inclination. When
the telescope is fixed on one side of the centre, it is called
eccentric. This eccentricity of the telescope need not be taken
into account when reading the degrees on the vertical circle ; it
is only when measuring a horizontal angle or transferring a
horizontal line of sight from a plane on another level either
above or below, that the eccentricity has to be considered.

In dialling "loose needle " (that is, using the needle to read
the bearings) for ordinary purposes, the eccentricity need not
be considered, because the error in reading, whatever it may
be in the back sight, is corrected in the fore sight. In fast-
needle work, however, the eccentricity has to be considered.
The surveyor must so arrange the lamp or other object viewed
through the telescope that it is exactly as far from the centre
of its tripod stand as is the telescope from the centre of the
dial, and the object viewed must be on the same side of the
centre of the stand as the telescope. Any failure to attend to

INSTRUMENTS FOR MEASURING ANGLES.

this may lead to very serious errors. This liability to error has
discouraged the use of this form of instrument.

By the use of an
eccentric lamp-holder, the
line of sight from the tele-
scope to the lamp is
exactly parallel to the line
from the centre of the dial
to the centre of the tripod
stand which is in the line
of survey, and therefore
the eccentricity of the tele-
scope leads to no error.

Combined Mining Dial,
Level, and Theodolite. This
instrument, which has only
recently been brought out,
is shown in Fig. 35A.

The chief feature is the
method of supporting the
telescope in cranked gim-
bals, thus enabling a sight
to be taken vertically up-
wards or downwards.

For fast-needle work, two outside verniers are used, reading
to single minutes. The vertical circle has a clamp and tangent,
and is also divided to read to
minutes.

Hanging Compass. An old-
fashioned kind of compass,
which is still used in some
places, is shown in Fig. 36,
In this case the compass-box,
instead of resting on a tripod
stand, is suspended by a cord
in such a manner that the box
is always level, and the needle
free to revolve. The cord is FIG. 36. Hanging compass.

Stretched from end tO end Of (Kindly lent by Messrs. W.F.Stanley^Co., LM.^

the line of which the angle has to be taken, and the reading of
the compass-needle shows the bearing of this cord.

FIG. 35A. Combined raining dial, level, and

theodolite.
(Kindly lent by Messrs. W. F. Stanley & Co., Ltd.}

66 MINE SURVEYING.

The following recommendations, in addition to those already
made, may be of use to purchasers of dials :

(1) There should he two verniers where very accurate work
is required.

(2) The plate which carries the vernier should he clamped
with a proper grip, and not merely by the point of a screw.

(3) The dial should not be attached to the stand by a screw
which may unscrew unknown to the surveyor.

(4) Spirit-levels should have a white backing.

Vernier. Called after the inventor Pierre Vernier. This is
a small movable scale running parallel to the fixed scale on the
dial, theodolite, protractor, barometer, etc. The use of the
vernier is to facilitate the reading of the exact, position of some
mark which elides upon the scale or close to it. For instance,
in the case of a dial the centre mark is indicated by an arrow-
head which moves round the circumferentor when the sights of
the dial are moved, as in fast-needle dialling. There is a similar
mark indicated by an arrow-head on the plate that revolves
above the graduated circle of the theodolite. In the case of a
barometer, the moving mark is the top of the column of mercury.
This mark may be placed exactly opposite one of the marks of
the graduated circle in a dial or theodolite, or on a straight
barometric scale, in which case no vernier is required ; but if
the mark comes to some position between the graduations, then
the vernier is useful in reading the exact position between the
two divisions of the scale. In the case of a dial, the sliding
scale or vernier is fixed to that part of the dial which revolves
round the graduated circle, and the arrow-headed mark is
generally in the centre of the vernier, say 20 divisions on the
vernier corresponding to 19 divisions on the graduated circle.
If the divisions of the graduated circle are equal to one degree,
then the divisions of the vernier are each equal to -?/g of a degree,
so that when the centre mark on the vernier is set opposite one
degree of the circumferentor, the nearest division of the vernier
to the right or left of the centre mark will be -$ of a degree
short of reaching to the corresponding mark on the graduated
circle. If, therefore, the arrow-mark is moved 5 \ f of a degree to
the right, the next division on the vernier to the arrow-mark
will coincide to the corresponding mark on the graduated circle.
If the arrow-mark should be moved -./$ of a degree, the second
division of the vernier will be in line with the corresponding

INSTRUMENTS FOR MEASURING ANGLES. 67

division upon the graduated circle, and so on; therefore, in
order to read the exact distances that the arrow-mark is from
the degree from which it has moved, it is necessary to look for
the line on the vernier that happens to coincide with one of the

Reading 67 51'.

Reading 281 12

FIG. 36A. Vernier readings.

divisions of the graduated circle. If that division is 6 from the
arrow-head, then the arrow-head is ~$$ of a degree past the degree
on the graduated circle from which it has been moved. Since
the degree contains 60 minutes, the twentieth part of a degree

68 MINE SURVEYING.

is three minutes, and therefore if the sixth division on the
vernier scale corresponds with a line on the graduated circle,
the arrow-head is 18 minutes past the degree. It will he seen
that the principle of the vernier is that the space between any
two divisions on the vernier scale is a small fraction less than
the space between any two divisions on the fixed scale, and
therefore if one division line on the vernier scale is exactly
opposite a line on the fixed scale, to bring the next line on the
vernier scale opposite the next line on the fixed scale it 'must be
moved through the small fraction above named. It should
be noted that the divisions on the vernier scale may be spaced
farther apart than those on the fixed scale. An illustration of
three readings of the vernier is given in Fig. 36A.

Theodolites. The principle of theodolite construction is
similar to that of the improved Hedley dial, with outside
graduated circle shown in Fig. 34 ; but the details of construc-
tion are very different, as may be gathered from Fig. 37. In
the theodolite a telescope is always used, and mining theodo-
lites are generally constructed as transit instruments; that is
to say, the telescope can be turned all round in its bearings,
so as to look either forward or backward. The telescope is
generally carried on a vertical framework, a (Fig. 37), attached
to and standing above the horizontal compass-box I at a
sufficient height to allow the telescope to be reversed. The
graduated circle c, for measuring vertical angles, is fixed on one
of the telescope trunnions, while a pointer, d, carrying verniers
is fixed to the framework. This circle can be clamped by
means of the screw x. On the plate to which the telescope
framework is attached are two verniers, e, c, at opposite sides ;
below this plate is another carrying the horizontal graduated
circle /, which can be clamped to the vertical axis of the
instrument by the screw h. The upper plate can also be
clamped to the lower plate. Spirit-levels are placed on the
telescope and on the upper horizontal plate. A 5-inch theodolite
will read both vertical and horizontal angles to 1', and an 8-inch
theodolite to -' ; a 12-inch theodolite will read to 1". Mining
theodolites are seldom bigger than 6 inches : the 5-inch is big
enough for convenience (a 5 -inch transit theodolite weighs from
12 Ibs. to 14 Ibs. without the legs). By a 5-inch theodolite is
meant one in which the horizontal graduated circle is 5 inches
in diameter. With this instrument, the compass-needle, being

INSTRUMENTS FOR MEASURING ANGLES.

underneath the framework carrying the telescope, is not easily

observed ; it is therefore only occasionally used for taking the

"bearing of a base-line, or for noting the approximate direction

of lines ; the chief use of the instrument being for measuring

FIG. 37. Transit theodolite.

the angles, both vertical and horizontal, made by one line with
the next.

Another variety of theodolite construction is shown in Fig.
37A. The standards carrying the telescope, which are usually
made in separate parts screwed together, are here all in one
solid casting. The axis and standards are also in one casting,
so that displacement of the axis is impossible.

70 MINE SURVEYING.

Instead of the ordinary compass-needle, a trough compass
is sometimes substituted, shown in Fig. 38 (and shown in
position in Fig. 3?A). In this narrow box or trough the compass-
needle is only free to revolve a few degrees on either side of the

FIG. 37A. Stanley's theodolite.

meridian, and it is merely used for fixing the theodolite in the
magnetic meridian, this line serving as a base from which
the bearings of the other lines can be calculated. Considerable

FIG. 38. Trough compass.

accuracy may be obtained in fixing the instrument in the
magnetic meridian, because it is possible to see a very slight
divergence of the needle from the N. and S. marks on the
compass-box.

INSTRUMENTS FOR MEASURING ANGLES.

Another kind of compass (Fig. 39) was made for the author,
useful only for the purpose of setting the telescope in the
meridian ; it is fixed below the bottom plate of the theodolite.
In this case the needle is very short only 2 inches and is
not suspended at the centre, but near to one end, the short end
being thick and balancing the longer end, the thin end of which
conies opposite a nick in the tube when the instrument is
turned in the magnetic meridian, and the position of the needle
is accurately observed by means of a microscopic eyepiece.

FIG. 39. Improved form of trough compass.

Theodolites are generally made with parallel plates (see #, g,
Fig. 37), by which the instrument can be levelled. A Hoffman
head or other form of ball-and-socket joint, however, is some-
times used, which also has four adjusting screws. The ball-
and-socket joint enables the instrument to be levelled whilst
the tripod stand is on very irregular ground. With the parallel
plates alone there might be some difficulty in adjusting the
instrument.

Use of Theodolite Underground. For the purpose of illumi-
nating the cross-hairs of the telescope, which, owing to the
darkness of the mine, would be otherwise in-
visible, one of the trunnions is made hollow, a
lens being screwed into the outer end. Oppo-
site this glass is fixed the bull's-eye of a small
oil-lamp, the light from which passes down
the hollow trunnion till it meets a reflector,
consisting of a polished steel face about
T V inch in diameter, placed within the telescope,
by which the light is reflected on to the cross- FlG- 40. Lamp for
hairs.

For use in mines containing fire-damp, the
small lamp for illuminating the cross-hairs
must be enclosed in gauze, similar to that used for safety-
lamps, and also shielded against the effects of strong currents,
so as to comply with the conditions of the Mines Regulation
Act (see Fig. 40).

illuminating the
cross-hairs of theo-
dolite.

MINE SURVEYING.

In the absence of the hollow trunnions, the cross-hairs may
be seen by the light of a lamp held near the object-glass.

Sextant. This is an instrument for taking angles either in a
vertical or a horizontal plane. It is used in surveying new
countries, and for nautical and military surveying (Fig. 41).
To measure the angle at the intersection of two lines, the tele-
scope is directed upon an object in line No. 1. By means of a

movable reflector fitted on the instru-
ment and connected to the vernier,
another object, in line No. 2, is at the

FIG. 41. Sextant. FIG. 42. Box sextant.

(Kindly lent by Messrs. W. F. Stanley tfc Co., Ltd.')

same time brought into the same line of vision ; the angle
through which the reflector is moved is measured by the vernier,
and the angle between the two objects is read on the graduated
arc. Small sextants, called box sextants (Fig. 42), are often
made about 3 inches in diameter, so arranged that they can be
conveniently packed in a pocket- case. The instrument is carried
in the hand, but, owing to the fact that two objects are brought
simultaneously into the line of vision, the angle formed by
the two lines of sight may be read with some approach to
accuracy. 1

Henderson's Rapid Traverser. Mr. James Henderson has
recently patented a very simple instrument (see Fig. 43) for
measuring and recording the angles of a survey. It consists of
a circular metal table, on the top of which is fixed, by means
of several small brass screw-nuts and bolts, a thin disc of cel-
luloid or other suitable material, about 10 inches in diameter.

1 For description of the sextant and mode of using, the reader is referred to
Hints to Travellers, published by the Koyal Geographical Society, also Surveying
Instruments, by W. F. Stanley.

INSTRUMENTS FOR MEASURING ANGLES.

Fixed on to the upper surface of the table and above the
celluloid disc, by means of a centre-pin passing through, is a
cross-bar, called an alidade, one side of which is bevelled. At
each end of this cross-bar is a sight similar to the ordinary dial
sight. By means of the usual clamping-screws, the table

FIG. 43. Henderson's rapid traverser.

carrying the celluloid disc can be clamped to the stand, and
the alidade, with the sights attached, can also be clamped to
the table, when required. The disc is divided into five concen-
tric rings, slightly scratched or grooved on the celluloid ; and
the bevelled edge of the alidade is notched out so as to afford to

MINE SURVEYING.

each ring on the disc a certain length of bevelled edge, each
length being distinguished by a number.

The object of these concentric rings is not only to permit
separate surveys to be accomplished on one disc, but to avoid
overcrowding of direction-lines in any particular spot on the

FIG. 44. Henderson's rapid traverser, showing quadrant.

disc. The semicircle for reading angles in a vertical plane
with ordinary sights or telescope can be attached when required
(see Fig. 44). The instrument is based on what is known as
the plane-table system of surveying ; unlike the plane table,

INSTRUMENTS FOR MEASURING ANGLES. 75

however, it is not intended that the rapid traverser should be
used for plotting the survey in the field, but this is done
afterwards, in the office, with the aid of a parallel ruler and
scale.

The table is levelled by means of two spirit-levels, one of
which is fixed on the alidade, and the other a small portable
one which is carried in the pocket.

The magnetic meridian is taken, at any convenient point in
the course of the survey, by means of a trough-compass placed
temporarily against the back edge of the alidade. The actual
direction of the lines of sight is indicated by making a pencil-
mark on the disc, and at the conclusion of the survey the disc
is taken off and the directions of the lines ruled off it on to
the plan.

For future reference the disc itself may be kept, or else the
magnetic bearings of the lines can be read off by means of a
protractor and entered in the field-book, when the celluloid
disc can be cleaned with soap and water or indiarubber, and so
made ready for a future survey. The discs are now being made
of enamelled zinc instead of celluloid.

Tacheometer (see Fig. 45). This is an instrument used for
measuring distances without a chain or tape. The ordinary
tacheometer is similar to a theodolite, the only radical difference
being in the telescope, in the diaphragm of which are fixed
marks which can be directed to a graduated staff, such as a
levelling-staff. The further the staff is from the instrument, the
greater number of feet or inches will be seen between the two
marks in the telescope. These marks may be made either
of cobweb, like the ordinary hairs in the diaphragm of the
theodolite, or of fine metallic points (in the later forms of instru-
ment, lines engraved on a glass diaphragm are substituted for
these hairs or wires) ; and they are placed at such a distance
apart that the vertical height of an object between those
two lines or points is some fraction, say 1 per cent., of the
horizontal distance from the observer to the object. Thus if
the vertical height on the graduated staff between the two points
is 1 foot, the staff is 100 feet distant ; if the vertical height is
10 feet, the staff is 1000 feet distant. According to the kind of
work which it is intended to do, these points can be placed
nearer together or further apart. The accuracy with which
measurements can be made in this way depends upon the power

FIG. 45. Tacheometer (Troughton and Simms).

INSTRUMENTS FOR MEASURING ANGLES. 77

of the telescope and of the microscopic eye-piece, and also upon
the fineness of the points or cobweb used. Where it is possible
to chain, the surveyor will, of course, employ this method in
preference to the tacheometer, if great accuracy is required;
but where, owing to the roughness or impassability of the
ground, the measurement cannot be taken in this way, the
tacheometer is of great use, and also for approximate measure-
ments it is convenient.

With a telescope of moderate power (magnifying, say, fifteen
diameters), and for distances not exceeding 500 feet, tacheo-
meter-measurements, on a bright day, should be correct to 1 per
cent. ; for shorter distances, say under 300 feet, the error should
not exceed J per cent. ; with a more powerful telescope the
error may be much less. Some engineers have claimed that the
error has never exceeded 1 in 2000 ; but for such a degree of
accuracy a very fine instrument and great care in using are
necessaiy.

It is stated by surveyors of experience that a telescope mag-
nifying fortyfold will read a staff to ^tro foot at a distance of
660 feet ; and, supposing the arrangement of hairs in the dia-
phragm is such that 1 foot on the staff represents 100 feet hori-
zontal distance, this means a possible error of J foot in 660, or
an error of 1 in 1320. There is no doubt that with a good tele-
scope great accuracy may be obtained with the tacheometer.

Measurement of Distances with Ordinary Theodolite. It is
possible to measure distances with the theodolite without the
aid of two cross-hairs or other marks, by simply measuring
the vertical arc subtended by a staff of given length. To
measure lengths in this manner, direct the horizontal hair to
the bottom of the staff or to some fixed mark above the bottom,
and then, by means of the tangential screw, direct the hori-
zontal hair to the top of the staff or some fixed mark, say 10
feet above the lower mark. Having read the angle, the distance
can be calculated. Assuming that the staff is held vertically,
and that the ground is level, the 10 feet will represent the chord
of the arc. If the angle measured, for instance, was 1, the
natural chord is 0'017453 ; then the distance may be found by
the following sum : 0-017453 : 1 : : 10 : 572*96. This method
is not so handy as that with two hairs, because the calculation
is longer, and it involves two readings with the telescope, and
there is, perhaps, an additional chance of error ; still, it is one

78 MINE SURVEYING.

that may be easily used in the absence of a tacheometrical
attachment to the theodolite.

It follows, then, that when using a 10-foot staff, an error of
one minute in the reading at a distance of 573 feet would mean
an error of V f * na ^ distance, or nearly 10 feet. The ordinary
5-inch theodolite is only graduated to read to minutes ; but
there is no reason why an error of one minute should be made
in the reading. The error in the reading should not exceed
half that ; and it is not necessary that there should be any
material error. The longer the staff, the less will be the error
for a given length ; but it is evident that for the accurate
measurement of long lengths it is necessary to have a theodo-
lite graduated to read to 10". With such an instrument and
a 10-foot staff, the error, instead of being 1 per cent., will be
reduced to \ per cent., or 1 in 600.

In comparing the accuracy of tacheometer-measurements
with that of ordinary chaining, it should be borne in mind that
over rough ground, whether on the surface or in the mine, an
error of half a link to the chain is very easily made, unless the
surveyor gives the most careful personal attention to the laying
out of the chain.

Some tacheometers are constructed on a slightly different
principle. Instead of fixed points or cross-hairs at the dia-
phragm, between which is seen a length of a graduated staff,
varying in exact proportion with the distance the staff is from
the object-glass, a staff of fixed length is used, and at the dia-
phragm is a slide carrying a cross-hair, which can be raised or
lowered by means of a screw until the whole length of the staff,
or of two very clear marks on the staff, are included between
two cross-hairs. The movement of this slide depends on the
distance the staff is away; the further the staff is from the
object-glass, the less the movement of the slide. This move-
ment is measured by the turns of a screw, on the head of which
is a scale ; the distance corresponding with any given move-
ment of the screw is marked upon the scale, so that no calcula-
tion has to be made.

In taking the observation, the two cross-hairs are so placed
that one entirely obscures the other, and are directed towards
one of the marks on the staff; the telescope is then clamped,
and the requisite movement of the micrometer screw is made.

Many tacheometers are so made that the distance as read

INSTRUMENTS FOR MEASURING ANGLES. 79

on the scale requires no correction; in others a correction is
necessary, owing to the fact that the distance measured by a
tacheometer of the simplest kind is from the principal focus of
the object-glass, whilst the distance required is from the centre
of the instrument at which the angles are measured ; therefore
the distance, as read off the staff, has to be corrected by the
addition of a constant quantity equal to the sum of the focal
distance of the object-glass, and the length from the object-glass
to the centre of the theodolite. Thus, in using the theodolite
with the fixed points, it is observed that the length of the
graduated staff between them is, say, 2 feet ; if the points have
been adjusted so that the factor for length is 100, then the
distance is 2 x 100 = 200 + the length between the object-
glass and the centre of the telescope (say 6 inches) -f the focal
length (say 12 inches), or the required length is 201*5 feet.
If the lengths are required in links, the staff should be graduated
in links and decimals.

Tacheometer Measurements in Hilly Country. When the
tacheometer is used for measuring lengths on a level country,
the staff will, of course, be held in a vertical line. If, however,

FIG. 46. Tacheometrical measurements in hilly country.

the ground is steeply inclined, then some consideration is
necessary. In the first place, the telescope may be fixed quite
level, and the staff held vertical, in which case the distance
measured will be the horizontal length between the telescope
and the staff (Fig. 46) ; of course, in this case, the length
measured is limited by the height of the staff for the back
sight, and the height of the telescope above the ground for
the fore sight. In the second place (see Fig. 47), the telescope
may be directed in a line parallel with the inclination of the
ground, and the staff held at right angles to the inclination of

MINE SURVEYING.

the ground ; then the distance measured will be the length of
the slope and not the horizontal distance, which would have to be
calculated by means of an observation of the angle made by the
telescope with a horizontal line. In the third place (Fig. 48),
the staff may be held vertical, and the telescope inclined at

FIG. 47. Tacheometrical measurements in billy country.

the same angle as the average slope of the ground, in which
case the length measured will be greater than the length of the
slope, and a correction will have to be made, owing to the
greater length of the staff visible between the cross-hairs.
Perhaps the best practice on steep gradients is to hold the staff

FIG, 48. Tacheometrical measurements in hilly country.

at right angles to the incline ; for moderate inclines the errors
due to not holding the staff exactly in the correct position are
very slight when this method is employed.

For further information on the subject of tacheometry, the
reader is referred to Mr. T. G. Gribble's excellent book on
Preliminary Survey (Longmans, Green and Co.).

Prismatic Stadia-telescope. 1 An ingenious modification of
the ordinary stadia-telescope (tacheometer) is to use a glass

1 Robert H. Richards, Boston, America, Inst. M.E. Montreal Meeting, February
1893 ; also Glen Summit Meeting, October, 1891.

INSTRUMENTS FOR MEASURING ANGLES. 81

prism or wedge. A ray of light passing through a prism is
deflected, the amount of deflection depending on the angle
enclosed by the two sides of the prism at their apex if prolonged.
If, therefore, half the object-glass of a telescope is covered with
a prism, and a graduated staff is observed, the figures on one
side will be seen in their correct position ; on the other side
they will be seen out of place, owing to the deflection caused by
the prism. Thus, if with the uncovered half of the object-glass
the cross-hairs of the telescope appear to cut the figure 3,
with the covered half the cross-hair may appear to cut the
figure 5, showing that the deflection of the rays of light caused
by the prism is measured by 2 feet on the staff if the staff is
distant 100 feet. This deflection is equal to an angle of about
1 9'. If, therefore, the staff were moved to a distance of 200
feet from the telescope, the deflection, being at the same angle,
would cover 4 feet of the staff; and if the staff were moved
to a distance of 300 feet, the deflection would cover 6 feet of
the staff, and so on.

This angle of deflection being ascertained, it follows that
the distance at which the staff is held from the telescope can be
calculated from the amount of deflection as read on the staff.
Thus

If the figure read with one half of the

telescope is 3, and with the other half 4, the distance is 50

3 5 100

>, ' ,, 3 ,, ,, 6 ,, 150

8 7 200

3 8 250

,, ,, 3 ,, ,, 9 ,, 300

and so on, every foot of deflection on the staff representing
50 feet of distance from the telescope, every T V foot representing
5 feet ; T ^ foot, 0'5 foot ; and T ^VTF foot, 0'05 foot.

Mr. Kobert H. Kichards has tried various telescopes in
which the deflection of the prism varies from 1 foot of staff in
100 feet in length, to 3 feet of staff in 100 feet in length. The
greater the deflection, the greater the accuracy with which the
amount of it can be read ; on the other hand, the greater the
deflection, the longer the staff required for any given distance.

Mr. Pdchards considers a telescope magnifying thirty dia-
meters suitable for reading the staff at a distance of 1000 feet,

MINE SURVEYING.

and for distances up to 2500 feet, with a specially constructed
sliding target staff. For a sight of 1000 feet and a prism de-
flecting 1 per cent., a staff about 12 feet long is required.

Mr. Richards also recommends the use of what he calls the
optical vernier. This may be understood by reference to Figs.
49 and 50. This is a staff about 6 inches wide, and a height
necessary for the distance it is intended to read ; it is painted

half white and half black.
On the upper left-hand side
is a vernier painted in white ;
the rest of the left-hand side
of the staff is black, and the
main scale is painted in
black opposite this.' It is
divided into lengths repre-
senting 50 feet of horizontal
distance, which are num-
bered 1, 2, 3, 4, 5, 6, etc. ;
this means six fifties, or
300 feet. Each fifty is
divided by five equidistant
diamond points, represent-
ing 10 feet. The vernier is
also divided so that five
points shall cover a space
equal to four points on the
main scale. The main scale
is seen through the un-
covered half of the telescope,

SELF-READING TARGETS
AS SEEN BY THE EYE

SELF READING TARGET AS
SEEN THROUGH THE PRISM

in connection with

a prismatic stadia

telescope.

4-V.p vprm'pv

^11^ Vtililltil

FIG. 49. staff used FIG. 50. Method of prism. The prism deflects
reading ditto. the vernier, and it is thrown

, .,

down opposite some figure
on the main scale.
In Fig. 50 the zero of the vernier is apparently past the
third point below 4 ; 4 means 4 times 50, or 200 ; the three
points on the main scale are each 10 feet, therefore the distance
is 230 + a fraction of 10. The second point of the vernier from
zero is exactly opposite one of the points on the main scale ;
each point of the vernier counts 2, therefore the fraction is
T V x 10, or 4 feet. So that the total distance is 234. The

INSTRUMENTS FOR MEASURING ANGLES.

heights on the main scale, representing 50 feet of distance, have
been found by experiments with the prism.

Tape Target. At distances greater than 1000 feet, the figures
on the staff cannot be read, and Mr. Eichards recommends a
tape target, the distance being read by the assistant carrying
the tape. This target is shown in Fig. 51. The telescope' is
directed towards the centre of three diamond points on one
target ; the other target is moved along the tape, in accordance
with signals given by the surveyor, until its
deflected image becomes opposite to the
image seen through the uncovered portion
of the object-glass ; the two centre diamonds
of each set of three correspond when the
targets are set at the correct distance apart ;
the two outer diamonds do not correspond,
and the distance of their points apart
should be equal for each pair, as shown in

TAPE-TARGETS AS SEEN BY EYE

FIG. 51. Tape with
movable targets.

TAPE TARGETS BEING
READ BY THE PRISM.

FIG. 52. Method of reading movable
targets.

Fig. 52. The assistant reads the distance on the tape, and books
the figure, and perhaps signals the reading to the surveyor.

All the systems of tacheometry above described necessitate
the use of a staff on which the graduations can be read through
a telescope, or on which are movable marks which can be read
by an assistant who adjusts the marks in accordance with signals
received by flags or otherwise from the surveyor.

It is, however, very convenient to use a range-finder, with

84 MINE SURVEYING.

which the surveyor is independent of any markings upon a staff.
The ordinary method of triangulation with the theodolite from
a measured base is a kind of range-finding, and for exact work
it is the best method known.

For approximate calculations, such as are used sometimes
by military engineers, a tape or cord of given length may be
carried by two observers, each carrying a box sextant, and
reading simultaneously the angle formed by the base-line and
the object whose distance they wish to ascertain.

Range-finder. An ingenious adaptation of the prism has
been devised by Professors Barr and Stroud. In this instru-
ment the measured base is a short tube, 3 feet long, held by the
surveyor in his hand, or fixed on a tripod. The tube is held at
right angles to the line of sight (see Fig. 53). It contains the

g./ fl"

5e -^

FIG. 53. Barr and Stroud's range-finder.

equivalent of two telescopes, one at each end of the tube or
base, with the requisite optical appliances for seeing the two
fields of view in juxtaposition one over the other. Eays of light
from the object viewed enter through openings, V.^ V 2 , at
each end of the tube, and are reflected at right angles along the
axis of the telescope by means of the reflectors H^ H 2 . The
observer places his right eye at the eye-piece K 2 , and, by means
of the arrangement of prisms at J, sees two images of the
object, one above the other, but not in line with each other. By
the movement of an achromatic glass prism, M, of small
angle along the axis of one of the telescopes, the two images
of the object whose range is required are brought into exact
alignment, when the position of the prism furnishes a measure
of the range, which is read off by the left eye on a scale, B,
attached to the prism, and moving with it. The surveyor has,
therefore, no calculations to make, but simply sets his instrument
upon the object, such as a staff, church, house, tree, fence corner,
candle, lamp, etc., and then, after adjusting the two images of the
object in exact alignment, reads the distance as written on the
instrument. A similar instrument has been adopted in H.M Navy,
and is now installed on most of the battle-ships and cruisers.

CHAPTEE V.

INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES.

IN considering the use of instruments for plotting angles, it will
be well to refer to the plan of an estate shown in Fig. 14. On this
plan the bearing of No. 1 line is marked " North 10 East," which
means that the direction of the line from the starting-point is
going towards the north-east, and the exact bearing is 10 east
of north ; the bearing of No. 2 line is also given as N. 30 W., and
line No. 12 is S. 74 W. If these lines are laid down according
to the bearings so marked, and for the lengths measured, they
will take up their correct position as regards each other, and it
will not be necessary to use the compasses for the purpose of
plotting them. If, however, the lines have been already plotted
from the measurements only, the bearings can be used as a
check on the accuracy of the survey and of the plottings, because
the relative positions of the lines, as shown by the bearings,
will be the same as that shown by the triangular measurements.

One use, therefore, of an instrument for taking these bearings
is to check the accuracy of the survey ; the second use is,
perhaps, more important, and that is to ascertain the direction
of the survey-lines with regard to the magnetic meridian, and
for most mineral plans it is necessary to have the magnetic
meridian, or "north point," as it is commonly called, marked
with extreme care.

In the production of a plan, two distinct classes of instru-
ments are necessary. These are, first, the instruments pre-
viously described for measuring lengths and angles on the
ground, and second, the instruments for drawing or plotting
upon paper the above-mentioned lengths and angles.

Scales. The instrument for drawing the lengths is called
the scale : it consists of a straight piece of hard material, either

86 MINE SURVEYING.

ivory, wood, metal, or cardboard; it is generally a little more
than 12 inches long, and is divided into equal parts to suit
the purpose required. For an ordinary English mining plan
it is usual to have a scale of chains, the measurements being
taken with the Gunter's chain. Thus it may be desired that
1 chain in length shall be represented by a length of 1 inch
on the plan ; then the scale will be divided into inches. If,
however, this would produce too big a plan, -J inch may be used
to represent 1 chain, and the scale will therefore be divided into
half-inches, or it may be divided into thirds, fourths, fifths,
sixths, eighths, or tenths of an inch, each division intended to
represent 1 chain. The most common scale for mining plans
is that in which % inch represents 1 chain, commonly called a
2-chain scale, which means that 1 inch on the plan is equal
to 2 chains measured in the field or mine.

In the Coal-Mines Eegulation Act of 1887 it is mentioned
that the scale of a colliery plan must not be less than 25'344
inches to the mile (which is equivalent to 3157 chains to
1 inch). 1 This seems to give sufficient latitude as to the size
of scale to be adopted ; in many mines a scale of 3 chains to
1 inch is used; in others, a scale of 1 chain, and sometimes
half a chain to the inch.

Having divided the scale into chain-lengths, each chain-
length is then subdivided into tenths, each tenth representing
10 links. The surveyor, in plotting a length more than 10
and less than 20 links, must divide the space by his eye, as
smaller graduations are not generally used. The edge of the
scale is bevelled, so that the dividing marks on the edge of
the scale touch the paper. It is found convenient to have on
the opposite edge of the scale to that on which the chain-scale
is divided, a feet-scale. This is a scale in which sixty- six divisions
on the feet-edge measure the same distance as 100 divisions on
the opposite or chain-edge. This enables the scale to be used
for taking off measurements in feet from a plan which has been
plotted in links. The use of feet and links on the same scale,
however, often leads to confusion and error.

Another scale is also used, called an offset scale. It is
generally 2 inches in length, graduated in the same manner as

1 The exact wording of the Act of 1887 is as follows: "Every such plan must
be on a scale of not less than that of the Ordnance Survey of twenty-five inches to
the mile, or on the same scale as the plan for the time being in use at the mine."

INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES. 87

the long scale, but the divisions begin and end exactly at the
ends of the scale. It is used in the manner shown in Fig. 54,
to mark off lengths at right angles to the lines drawn on the
plan. The scale is laid down on the paper along the line

FIG. 54. Scale and offset.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

representing the survey-line ; the offset scale is then placed so
as to measure lines at right angles, and is moved along the
scale to the division representing the required distance on the
survey-line ; the length of the offset can then be marked off by
means of the shorter scale.

In constructing a plan, the scale is usually drawn upon it,
and thus, if any serious shrinkage of the paper takes place,
measurements may be made by means of this scale.

Ivory is much liked for scales, because of the clearness of
the lines, but boxwood is cheaper and less easily broken ; metal
is not much used, partly, perhaps, because of its greater tendency
to expand or contract with variations of the temperature.
The expansion of brass between freezing point and boiling
point is -o- of its original length, which is equal to Tr w part
for each degree of temperature, or to the expansion of o-^Tr part
for a rise of 40 in temperature, that is to say, the scale would
expand 1 inch in a length of 2250 inches, or ^V part of an inch
in a length of 100 inches. This amount of expansion is not
very serious, especially as the temperature of a drawing office
in England does not usually vary as much as 40 ; it is seldom
that drawing is done in an office of a less temperature than
50 or a higher temperature than 65, hence the expansion
would be only that due to 15, or ^V inch in a total length of
100 inches ; therefore the expansion of brass does not seem to

88 MINE SURVEYING.

be a sufficient reason why it should not be used. A more
practical objection is that metal scales soil the drawings.

Ordnance Maps. The survey of the United Kingdom was
commenced by order of the Government about the year 1784.

The survey has been published in maps of various scales,
viz. 1 inch to the mile, or -yihnr; 6 inches to the mile, or
TTrhnr; and 25'344 inches to the mile, or TT/OTT- Town plans,
on scales of 10| feet to a mile and 5 feet to a mile, are also
published of the principal towns. On these maps are shown
the various boundaries of the counties, unions, parishes, etc.
The first two series show the contour-lines, and are particularly
useful for the purpose of deciding as to the best route to adopt
for lines of railway, and the positions of shafts, buildings, etc.
They also show the lines of latitude and longitude.

The oVoij scale maps can be obtained either plain or with
the buildings and rivers coloured. The fields are all numbered,
and the area of each field in acres is either printed on the map
or can be obtained for each parish, published in book form.

A plan made by mounting the various sheets of the -r^Vo-
map covering the royalty is sometimes used on which to mark
underground workings. By application to the Director-General
of the Ordnance Survey Office, Southampton, however, tracings
from the original plotted plans can be obtained, and these are
much more accurate for this purpose, as the printed maps often
shrink a good deal. Owing to this latter fact, measurements
from the Ordnance plans should be made with the printed scale
given on each sheet.

Geological maps are also published on the 1-inch and 6-inch
scales, and give a great deal of valuable information as to the
faults, dip of the measures, and other geological features of the
country.

Compasses. Compasses are generally used to set off the
distances from the base-line as previously explained ; these
are shown in Fig. 55. They are made in various sizes, ranging
from 2J inches to 9 inches long. There are points at the end of
each limb, needle-points are the best ; one limb is jointed, so
that the needle-point can be taken out, and a pencil, a, or pen, b,
substituted ; one or more lengthening pieces, c, can be added to
this limb, so as to increase the length that can be set out.
When this length is insufficient, beam compasses are used.
These are formed with a beam, or piece of wood, and are shown

INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES. 89

in Fig. 56. At one end of this beam is fastened a screw-clip, a,
carrying a point at right angles to the beam, and about 2 inches
long. A similar clip, b, carrying a pencil is slipped on to the
beam, and is moved along till the required distance from the
point fixed at the other end is obtained. It is then clamped,

FIG. 55. Compasses.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

and an exact adjustment for length is made with an adjusting
screw on the point-holder; then, with the fixed point as the
centre, a circle may be described with the pencil-point. Several
beams of say 2, 4, and 6 feet in length are kept for use with
these compasses.

Straight-edge. For the purpose of ruling a straight line

FIG. 56. Beam compasses.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

from one point to another, a straight-edge is used ; a metal
straight-edge is the best, not being liable to warp. Steel
straight-edges require to be kept bright, and are sometimes
nickel-plated. Though not absolutely necessary, it is a good
thing to have bevelled edges to the ruler.

Parallel Ruler. A parallel ruler (Fig. 57) is much used by
mining surveyors ; it is generally made of metal, as a considerable

90 MINE SURVEYING.

weight is advantageous ; it consists of a bar from 2 inches
to 3 inches wide, and from -/^ inch to y'V inch in thickness,
with bevelled edges, and varying from 6 inches up to 2 feet in
length. In this bar are cut two holes within a short distance

FIG. 57. Rolling parallel ruler.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

of each end ; on the upper side of the bar are fixed two rollers,
fixed on a long spindle, the ends of which are carried in
brackets ; the lower sides of the rollers project a little way
through the bar, so that the bar may roll along. Each of these
rollers is the same diameter, and is roughened with longitudinal
cuts to prevent it from slipping. These rollers being the same
diameter, if there is no slipping, the two ends of the bar will
move at the same rate and the same distance when rolled
along over the paper. Thus, if the ruler is held in a given
position, and a line drawn, and it is then carefully rolled
across the paper, and another line drawn, the two lines will
be parallel one to the other.

Fig. 58 shows another form of parallel ruler, known as the

sliding-bar parallel ruler,
but for the purposes of a
mine surveyor the rolling
parallel ruler will be found

FIG. 58.-Sliding parallel ruler. to be the . m st efficient.
(Kindly lent by Messrs. W. F. Stanley and <>., d.) Drawing-pencil. 111 plot-

ting a survey the lines are

drawn with a hard-lead pencil cut to a fine point. Pencils are
made in varying degrees of hardness, the most useful being that
marked H.H. The Koh-i-noor pencil is highly recommended.

Pricker, Distances and stations are generally marked off
the scale with a needle-pointed pricker, the point of the needle
making a much finer and more permanent mark than the point
of the pencil. In this way a length may be marked on the
2-chain scale with an error not exceeding 1 link ; thus if the
actual distance measured was 8 chains 55 links, the prick-

INS TR UMENTS FOR PL TTING LENG THS AND A NGLES. 9 1

mark made with the needle might possibly be 8 chains 54 links
or 8 chains 56 links, but, in either case, it would be within a
link of the correct distance.

Set-squares. A large set-square is useful 1 for marking out

FIG. 59. Set squares.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

lines at right angles to one another ; such lines are required
for plotting lengths ascertained by trigonometrical computation ;
the larger this set-square, the greater the degree of accuracy
with which the cross-lines can be drawn. The draughtsman
is recommended to use one not less than 12 inches long on each
of the square sides. The two
most usual forms of set-square
are shown in Fig. 59.

Protractor. For plotting
angles a graduated circle
marked in a similar way to
the dial, called a protractor, is
used (see Fig. 60). 1 These may
be made of brass, and vary
from 8 to 12 inches in dia-
meter ; the 8-inch protractor
is graduated to half-degrees,

FIG. 60. Brass protractor.
{Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

and the 12-inch protractor to
quarter-degrees, smaller frac-
tions of a degree having to be
estimated ; the protractor being so much larger than the dial,
the fractions of a degree can be estimated with greater

1 For plotting circle readings of the needle, the numbers on the protractor
should count the reverse wav of those on the dial.

9 2

MINE SURVEYING.

accuracy, and therefore there should be no serious errors in
plotting from this cause.

It is, however, difficult with an 8-inch protractor to divide a
degree without some error, which may very likely amount to
^; the thickness of a needle-prick is about J on an 8-inch
protractor, so that for very accurate work a simple 8-inch pro-
tractor is not sufficient. By using a 12-inch protractor the
accuracy is increased in the proportion of 2 to 3 ; but for very
accurate work a protractor fitted with a vernier with, folding
arms, clamp, and tangent-screw is sometimes used (Fig. 61).

FIG. 61. Brass protractor with folding arms.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

By means of the vernier the arms may be adjusted to 1',
that is to say, to the sixtieth part of a degree. At the end
of each arm is a sharp pricker, which can be pressed down to
mark the paper. If this instrument is well constructed and
properly used, the angles can be marked out with great
accuracy.

It is, however, a common practice to use a cardboard pro-
tractor (Fig. 62). The graduated circle is printed on to a stout
card, and is generally 12 or 15 inches in diameter. The
divisions are made to read inward from the circumference,
instead of outwards as with other protractors, the centre space
of the card being entirely cut away.

In using cardboard protractors it is not necessary to prick
off the angle, as the parallel ruler can be placed upon the
protractor at the right angle, and then rolled to the required

INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES. 93

place, provided, of course, that the work is within the circum-
ference of the protractor. For plotting underground surveys,
where the lines are usually short and close together, these
protractors are very convenient.

A modified form of cardboard protractor has been designed
by Mr. R. F. Percy, 1 and is shown in Fig. 63. It is made of

FIG. 62. Cardboard protractor.

thin pasteboard. Parallel north-and-south lines are, with the
greatest care and accuracy, drawn at intervals of 2 or 3 inches,
and at the ends of all these parallels, on the left at the north
edge, and on the right at the south edge, divergences of 1 and
fractions of 1 are indicated (Fig. 63). The part within the

1 Transactions Fed. Institute of Mining Engineers, vol. xiii. p. 585.

MINE SURVEYING.

divided circle is, as usual, cut away, and the plotting is executed
within that space.

The parallel meridians allow the protractor to be placed
exactly where it is needed, very few meridian-lines being required

\_J

FIG. 63. Percy's form of cardboard protractor.

on the plan. The divergences marked at the ends of the parallel
lines will allow the protractor to be twisted for declination, so
as to bring the meridian to the date of the survey.

Drawing-pens. Fig. 64 shows a drawing-pen; it has two

STANLEY LONDON

FIG. 64. Drawing-pen.

(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

pointed blades, kept apart by a spring ; the distance apart can
be adjusted by turning a milled-head screw. It is supplied
with ink by means of a brush or pen, and when used should
be held nearly upright between the thumb and forefinger. After
being used some time, the nibs become blunt, and will require
sharpening on an oil-stone ; this is an operation requiring some
skill and practice.

Curves. For drawing curved lines, such as railway curves,
it is found useful to have ruling-edges made of pear wood or
cardboard. These are cut to arcs of circles with radii varying
from 1 to 250 inches, and are sold in sets.

Weights and Pins. To hold the plan while working at it,
drawing-pins may be used, but these injure the plan. Lead or
iron weights are more commonly used by mine surveyors ; they
are of oblong form, and covered with cloth or leather so as not
to soil the paper.

INSTRUMENTS FOR PLOTTING LENGTHS AND ANGLES. 95

Colours and Brushes. For inking-in the finished plan, Indian
ink is used. This is generally sold in hexagonal or octagonal
sticks, and is ground into liquid ink by rubbing with water
upon some kind of palette. The rubbing is continued until a
line drawn with the ink dries quite black. Lines drawn with
the best ink, however, are liable to run when colour is washed
over them, so the lines should be as fine as possible.

Liquid Indian ink may be obtained which overcomes this
defect, but it is hardly so good to draw with as the stick ink.
Water-colours are used for colouring drawings ; they are
supplied in cakes, and are ground in the same way as Indian
ink.

The best kind of brushes for colouring are those made of
sable hair.

Drawing-paper. It is important that the best drawing-paper
should be used for mining plans. That known as Whatman's
is very good. The sizes in which sheets of drawing-paper can be
obtained are

Demy 20 inches by 15| inches

Medium 22f ,,17

Boyal 24 19^

Imperial ... 30 ,, ,,22

Double elephant ... 40 ,, ,, 27

Antiquarian 53 ,, ,,31 ,,

Mounted plan paper can also be obtained in continuous rolls
in widths varying from 27 inches to 60 inches, or paper can be
mounted to order to make a plan of any size. For a large
permanent plan the best paper mounted on strong brown
holland will cost as much as 5d. to Sd. a square foot. The
thickness of the paper and holland together varies from about
T V inch up to about ^ inch ; ^V inch makes a very good plan.

Tracings. Copies of drawings are usually made on tracing-
paper or tracing-cloth, which are transparent. These may be
obtained in continuous rolls the same as the drawing-paper.

CHAPTER VI.

GEOMETRY, TRIGONOMETRY, LOGARITHMS.

BEFORE proceeding to consider the method of surveying on the
surface by means of angles, or of underground surveying which
is always done by means of instruments for measuring angles,
it will be necessary to consider the relations of the sides and
angles of a triangle to each other, which are ascertained by the
science of Trigonometry.

A slight knowledge of Geometry is also necessary. The
definitions given below are taken from Euclid's Elements.

Fig. 65 shows a circle ; the point A, from which it has been
described, is called the centre of the circle.

The diameter of a circle is a straight line drawn through

the centre, terminated both ways
by the circumference (BC, Fig.
65).

The radius of a circle is a
straight line drawn from the
centre to the circumference (AB,
Fig. 65).

The circumference of a circle
is the line described by the pencil
of the compass when it is re-
volved round a point.

A chord is any straight line
drawn across the circle from cir-
cumference to circumference, not
passing through the centre (DE, Fig. 65).

An arc is that part of the circumference of a circle which lies
between the two ends of a chord (DFE, Fig. 65).

An angle is formed when two straight lines, not in the same

FIG. 65. Circle : diameter, radius,
chord, arc.

GEOMETRY, TRIGONOMETRY, LOGARITHMS.

straight line, meet together. The unit adopted in measuring
angles is the degree. The circle is divided into 360 degrees
(written ) ; each degree is subdivided into sixty equal parts, called
minutes (written ') ; and each minute is subdivided into sixty
equal parts, called seconds (written "). The circle is also
divided into four equal parts, called quadrants, each containing
90 degrees (CAP, BAF, BAG, CAG, Fig. 65).

The measure of any angle (CAM, Fig. 65) is the number of
degrees covered by the arc CH.

A right angle encloses 90 degrees ; a straight line at right
angles to another straight line is said to be a perpendicular
(Pig. 66, (1)).

An obtuse angle contains more than 90 (Fig. 66, (2) ).

(2)

(3)

(4)

(6)

FIG. 66. Angles and triangles.

An acute angle contains less than 90 (Fig. 66, (3) ).

A triangle is a figure contained by three straight lines. An
equilateral triangle has three equal sides, and three equal angles
(Fig. 66, (4) ) ; an isosceles triangle has two sides equal (Fig. 66,
(6) ) ; a right-angled triangle is that which has one of its angles
a right angle (Fig. 66, (5) ).

A square has four equal sides, and all its angles are right
angles.

A rectangle has all its angles right angles, but not all its
sides equal.

A trapezium is a plane figure contained by four straight
lines, of which no two are parallel.

Parallel straight lines are those which, if produced both ways,
would never meet.

98 MINE SURVEYING.

The following theorems are also taken from Euclid, and
should be thoroughly mastered :

(1) When a straight line meets another straight line, the

angles formed are together equal
to two right angles. Eef erring
to Fig. 67, the two angles ABC
and ABD together equal two
right angles, or 180, so that if

_^_^ we know the number of degrees

D B C in one angle, we can find the

FIG. 67. Elementary geometry. magnitude of the other by sub-
traction.

(2) If two straight lines cut one another, the vertical or
opposite angles are equal. Thus in Fig. 68 the angle AEC

FIG. 68. Elementary geometry.

equals the angle DEB, and the angle AED is equal to the angle
CEB ; and the four angles are together equal to 360 ; therefore,
if one angle is known, the other three can be calculated.

(3) If a straight line,
EF, fall on two parallel
straight lines AB and CD,
the angles AGH and GHD

B are equal, the angles EGB
and GHD are equal, and
the two angles BGH and

D GHD are together equal to
two right angles (see Fig.
69).

(4) The angles at the
base of an isosceles triangle

FIG. 69. Elementary geometry. (see Fig. 66, (6) ) are equal

to one another.

(5) The three angles of a triangle are together equal to two
right angles, or 180 ; therefore, knowing the two angles, we can
get the third by subtraction.

GEOMETRY, TRIGONOMETRY, LOGARITHMS.

(6) Any two sides of a triangle must be together greater than
the third.

(7) In any right-angled triangle, the square which is described
on the side opposite the right angle is equal to the sum of the
squares described on the sides containing the right angle.
Fig. 70 shows a right-angled triangle ; then AB 2 = AC 2 -f BC 2 .
Suppose AC is 80, BC is 100; then to find AB

AB 2 = (80) 2 + (100) 2 /. AB = 128-1

In the same way, we can find AC or BC, if we have the other
two sides of the triangle given.

B wo <- D

FIG. 70. A right-angled triangle.

B C

FIG. 71. Elementary geometry.

(8) If one side of a triangle be produced, the external angle
is equal to the sum of the two opposite internal angles. The
angle ABC is equal to the sum of the angles DAB and ADB
(Fig. 71).

(9) In every triangle equal sides subtend (or are opposite
to) equal angles, the greatest side subtends the greatest angle,
and the least side -the least angle.

Practical Geometry.

(1) To bisect a line AB (Fig. 72) ; that is, to divide it into
two equal parts. From A and B, with any radius greater than
the half of AB, describe arcs cutting each other in c and d.
From c draw a straight line to d, and it will bisect the line AB.

(2) To draw a line perpendicular to a given line AB at a
point C in the line (Fig. 73).

From C, with any radius, cut the line AB in c, c ; from c, c,
with any radius greater than half cc, describe arcs cutting in d ;
draw the line Cd, and it will be perpendicular to AB.

100

MINE SURVEYING.

(3) To draw a line perpendicular to a given line AB, from
a point C above or below the line (Fig. 74).

FIG. 72. Method of bisecting a line.

FIG. 73. To draw a perpendicular line.

The description and letters of the last problem apply to this
figure also.

(4) To draw a line perpendicular to a given line AB, at its
extremity (Fig. 75).

A B

FIG. 74. To draw a perpendicular line. FIG. 75. To draw a perpendicular line.

From B, with any radius, describe an arc having its extremity
c in the line AB.

From c, with the same radius, cut the arc in d ; and from d,
with the same radius, cut the arc in e.

From d and e, with the same radius, describe arcs cutting
in/.

Draw the line /B, and it will be perpendicular to the line
AB at its extremity.

GEOMETRY, TRIGONOMETRY, LOGARITHMS.

101

(5) Through a given point C to draw a straight line parallel
to a given straight line AB (Fig. 76).

A' B

FIG. 76. To draw a parallel line.

From any point B in the line AB describe an arc CA, and
from the centre C, with the same radius, describe the arc BD,
and make the arc BD ^

equal tq^the arc AC.

Then the line joining
CD is parallel to the line
AB.

(6) To construct a
triangle, its three sides
being given (Fig. 77).
Let the sides be 50, 75,
and 60. Draw a line
AB, and mark off the

length AC equal to 50 on
the scale; then, with centre
A and radius 75, draw an
arc, and from the centjre C, with the radius 60, draw another

A 50 c B

FIG. 77. To construct a triangle, three sides
being given.

Then join AD and CD, and

arc, cutting the first arc in D.
ACD is the required triangle.

(7) To construct a triangle
when two of its sides and the
angle between them are known
(Pig. 78).

Let the two sides be 30 and
40, and the angle included 45.
Then draw a straight line AB,
and mark off a length AC equal
to 40, and, by means of a pro-
tractor, make the angle CAD equal to 45, and make AD equal
to 30. Then, by joining DC, the triangle is completed.

A 40 C B

FIG.- 78. To construct a triangle, two
sides and the included angle being
given.

102 MINE SURVEYING.

Trigonometry deals with the relative measures of the sides
and angles of triangles.

Let ABC be any angle (Fig. 79), then in one of the lines

containing the angle take any
point D, and from D draw DE
perpendicular to AB. Then we
have formed a right-angled
triangle BDE, and the side DE is
called the perpendicular; the side
BD, which is opposite the right
B E A an gi e> i s called the hypotenuse,

FIG. 79. Relations between sides -i ji * DC , P <,]]*,] th p

and angles of a triangle. ancl tne S1Cle Dt 1S callea tne

base.

From these three sides we can form six ratios or fractions
as follows :

(1) BE = Perpendicular ^ EBQ
BD hypotenuse

/r\ BE base

(2) = r- ,, ., cosine ,, ,,
BD hypotenuse

/0 \ ED perpendicular

By inverting the above three ratios, we obtain three more,
as follows :

(4) _r- > = '- is called the cosecant of the angle ABC
' D E perpendicular

/ e \ BD hypotenuse

(5) ~ = -^^ secant

/\ BE_

These trigonometrical ratios are always the same for the
same angle, but are different for different angles.

In some cases these ratios i.e. sine, cosine, etc. may be
represented in magnitude by single lines.

For instance, referring to Fig. 80, suppose the circle to have
been drawn with a radius of 1

Then the sine of the angle ABC is = F P = FD

and the cosine ,, ^ = = FB

oLJ

GEOMETRY, TRIGONOMETRY, LOGARITHMS. 103

and the tangent of the angle ABC is ^ ^ =
cotangent 1
secant
cosecant 1

= AC

HE_HE_
HB~ F
BC = BC =
BA " i
BE = BE =
HB i

It will be seen that by referring all these ratios to a radius
of 1, we are able to measure their values for any angle. Thus
in Fig. 80 the angle ABC is drawn 60, and if the line FD be

measured with the same scale that
AB was drawn with, it will be
found to be 0'866 ; therefore the
sine of 60 (to radius 1) is 0'866.
In the same way the other ratios
can be arrived at.

\30

90?"

B-

FIG. 80. Trigonometrical functions.

-- 6 OO Links - ->

FIG. 81. Use of trigonometrical ratios.

Tables of these ratios may be got in which the values of the
natural sines, cosines, etc., have been worked out for all angles.

The word "natural sine" is used to distinguish it from the
logarithmic sine. The natural sines are the actual values of the
ratios, while the logarithmic sine is the logarithm of that ratio.

EXAMPLES. (1) Let Fig. 81 represent a triangular field. The base EB is
known to be 6 chains, also the angle EBD 30; then to find the side ED.

We know that ^^ = tangent of EBD- On referring to our book of tables,

EB
we find the natural tangent of 30 is 0-5773503.

Then = 0-5773503; but EB = 6 chains = 600 links. Then ED =

600 x 0-5773503 = 346-41. An*.

Since the angle HEB = the angle ABC.

IO4

MINE SURVEYING.

In a similar manner, by working out the equation ~~ cosine 30, we can

find the other side BD-

(2) At a point 100 yards from the foot of a building, I measure the angle of
elevation of the top, and find that it is 23 15' : what is the height of the
building ?

Let Fig. 82 represent the pro-
blem ; E D is the unknown height.
The length BE is known to be
100 yards, and the angle EBD
to be 23 15'.

FIG. 82. Use of trigonometrical ratios.

Then ^g = tan 23 15'.

From the table of tangents we
find that tan 23 15' = 0-4296339.

.*. ED = 100 x 0-4296339
= 43 yards (nearly)

which is the required height.
Of course, both these problems could have been solved by plotting ; but unless
the scale had been very large, the results would not have been nearly so
accurate.

Logarithms.

Logarithms are used to facilitate calculations.

The logarithm of a number is the power to which an invari-
able (or constant) number, called the base, has to be raised to
equal the given number.

In common logarithms the base is 10, and the power to
which 10 has to be raised to produce any number is the logarithm
of that number. Thus

10 X 1, or 10 1 = 10 /. 1 = log. 10
10 x 10, or 10 2 = 100 /. 2 = log. 100
10 X 10 x 10, or 10 3 = 1000 /. 3 = log. 1000
10 X 10 x 10 X 10, or 10 4 = 10000 .'. 4 = log. 10000
and so on.

It is proved by algebra that 10 = 1

and O'l or T \, = 10' 1

and 0-01 or T J = 10 ~ 2
0-001 or T(5 V (T = 10-
and so on.

= log 1

- 1 = log. 0*1

- 2 = log. O'Ol

- 8 = log. O'OOl

Thus we see that the logarithm of a number greater than 1
and less than 10 is a positive decimal ; and the log. of a number

GEOMETRY, TRIGONOMETRY, LOGARITHMS. 105

between 10 and 100 is greater than 1 and less than 2 ; that
is to say, will be 1 + a decimal, and so on.

We see also that the logarithm of any number between 1 and
O'l is negative, and would lie between and 1, and can be
written - 1 + a decimal ; and the log. of a number between
O'l and O'Ol can be written - 2 + a decimal; and so on.

A logarithm consists of two parts the integral, or whole-
number part, which is called its characteristic , and the decimal
part, which is called the mantissa.

The mantissa of the logarithm may be found in a table of
logarithms, but the characteristic is found as follows :

(a) If the number whose logarithm is sought is greater than
unity, the characteristic is always one less than the number of
figures it contains ; thus

The logarithm of 43758 = 4*6410575

4375-8 = 3-6410575

43-758 = 1-6410575

4-3758 = 0-6410575

etc.

(b) If the number is less than unity, the characteristic is
minus or negative, and is found by adding one- to the number
of cyphers between the decimal point and the first significant
figure; thus

GO O)

Log. 0-43758 = 1-6410575

0-043758 = 2-6410575

0-00043758 = 4'6410575

Many good tables of logarithms can be obtained ; the author
often uses Chambers's, 2 which, in addition to giving the loga-
rithms of all the numbers from 1 to 108000, contain an excellent
explanation of their use, from which some of these illustrations
are taken. 3

I. To perform multiplication by logarithms.

Add the logarithms of the factors, and the sum will be the
logarithm of the product.

1 c = characteristic ; m = mantissa.

2 Chambers's Mathematical Tables, published by W. & R. Chambers.

3 Babbage and Callet's Tables give logarithmic sines, cosines, etc., worked out
to 10 seconds.

OF THE-

( UNIVERSITY

106 MINE SURVEYING.

EXAMPLES. (1) Multiply 9999 by 999.
Log. 9999 = 3-9999566
999 = 2-9995655

Sum = 6-9995221, which is the log. of 9989001. Am.

(2) Multiply 0-03902, 59-716, and 0-00314728.
Log. 0-03902 = 2-5912873
59-716 = J.-7760907
0-00314728 = 3-4979353

Sum = 3-8653133, which is the log. of 0-007333533. Ans.

II. To perform division by logarithms.

From the logarithm of the dividend subtract that of the
divisor, and the remainder will be the logarithm of the quotient.

EXAMPLES. (1) Divide 371-49 by 52-376.
Log. 371-49 = 2-5699471
52-376 = 1-7191323

Difference = 0-8508148, which is the log. of 7-092752. Ans ,

(2) Divide 241-63 by 4-567.

Log. 241-63 = 2-3831509
4-567 = 0-6596310

Difference^ 1-7235199, which is the log. of 52-90782. Ans.

III. To raise a number to any power by logarithms.
Multiply the logarithm of the given number by the index of

the power to which it is to be raised, and the product will be the
logarithm of the required power.

(1) Find the cube of 30-7146, written thus : (30'7 146) 3 .
Log. 30-7146 = 1-4873449

4-4620347, which is the log. of 28975-75. Ans.

(2) What is the value of 9-163 4 ?

Log. 9-163 = 0-9620377

3-8481508, which is the log. of 7049-38. Ans.

IV. To extract any root by logarithms.

Divide the logarithm of the given number by the index of the
root to be extracted, and the quotient will be the logarithm of
the required root.

(1) Find the cube root of 12345, written thus : V 12345.

Log. 12345 = 4-0914911.
3)4-0914911
1-3638304, which is the log. of 23-11162. Ans.

GEOMETRY, TRIGONOMETRY, LOGARITHMS. 107

(2) Find the fourth root of 0-0076542.

Log. 0076542 = 3 8838998
= T-4709749

To divide a negative characteristic, add such a quantity to the characteristic
as will make it divisible without a remainder, and prefix an equal number to the
decimal part of the logarithm. Thus, in the example, add 1, and you get
4 + 1-8838998 -r- 4 = T-4709749, which is the log. of 0-295784. Ans.

In calculations in which sines, cosines, etc., occur, and
logarithms are to be used, then the logarithmic sine, cosine,
etc., must be used. They can be obtained from Chambers's
Tables.

The logarithmic sine is obtained by finding the logarithm of
the number representing the natural sine, and adding 10 to its
characteristic.

For example, if the reader refers to his book of tables, he will
find that the natural sine of 30 is 0-5000000. The logarithm
of 0'5 is 1 '6989700, but to avoid the inconvenience of the
negative characteristic, 10 is added, and so we arrive at log.
sine 30, which is equal to 9'6989700.

In using log. sines, cosines, etc., the 10 which has thus been
added is always deducted again, as in the following example :

To find ED, page 104, Example 2.

ED = 100 x tangent 23 15'
v ] og. ED = log. 100 + log. tan 23 15' - 10
= 2 + 9-6330985 - 10
= 1-6330985, which is the log. of 42-964
" ED = 42-964. Ans.

The Solution of Triangles. In every triangle there are six
parts, viz. three sides and three angles.
If any three of these parts are given,
one of which must be a side, the remain-
ing parts can be found, the process
being known as the " solution " of the

triangle.

It will be at once seen that this
information is of great service to the
surveyor, who is able, by observing the

angles of his triangles, to calculate

AT. i 4.1- j.u -j j j.i FIG. 82A. Solution of

the lengths of the sides, and thus triangles.

check the measured distance. In cases

also where it is not practicable or necessary to measure one of

io8 MINE SURVEYING.

the sides, its length can be calculated from the other known
parts of the triangle.

In order to shorten the formulae, the three angles of the
triangle will be referred to as A, B, and C, and the three sides
opposite them a, b, and c, respectively (see Fig. 82A).

Case 1. Given the three sides a, b, and c, to find the angles.

Let s = half the sum of the three sides.

Then ton

- a)

These formulae will give us the angles A and B. The angle
C = 180 - A - B.

EXAMPLE. The three sides of a triangle are : a = 750 links ; I = 835 links ;
and c = 679 links. Find the angles A, B, and C.

Here S = 75 + 8 -! 5 + 679 = 1132

A /( 6) (s - c)

then tan w = * / i ~-^ ^ '

2 'v s(s a)

1132 835) (1132 -679)
1132(1132-750)

297 x 453
lT32~~x~382
= \/0-31 11321.

= 0-5577921, which is the natural tangent of the
angle 29 9' 9"

~ = 29 9' 9"

and the angle A = 58 18' 18"

T> /

"2 = \/

tan

8(8 -

/(U32-750)(1132-i;7I>

1132(1 132 -835)

/ 382 x 453
V H32 x 291

453

~Wl
- V6-5I47053

= 0-7174290, which is the natural tangent of the
angle 35 39' 24-5"

2 = 35 39' 24-5"

and the angle B = 71 18' 49"

and C = 180 - 58 18' 18"-7118' 49"= 50 22' 53"

GEOMETRY, TRIGONOMETRY, LOGARITHMS. 109

Case 2. To solve a triangle, having given two angles and

a side.

In any triangle the sides are proportional to the sines of

the opposite angles.

a b c

S " ~

shTA " sin B ~ sin C

Let A and C be the given angles and b the given side. Then
the angle B = 180 - A - C.
To find the sides

a b

sin A ~~ sm B
_ b sin A
~slrTF
from which we get the side a.

_
sin C ~ sin B

6 sin c

.-. c = s D
sm B

from which we get the side c.

EXAMPLE. In a triangle ABC, the angle A = 50, the angle C = 66, and
the side a is 1000 yards. Find the remaining sides and angle.

The angle B = 180 - 50 - 66 = 64
To find the sides

sin A sin B
1000 &

' sin 50 " sin 64 6

1000 x sin 64
' l ~ sin 50

_ 1000 x 8987940

0-7660444
898-7940

_
0=7660444

-i c
and -f-fi

sin C sin B

& sin c
c = -^ ?s-
sin B

1173-29 x sin 66

c =

sin 64
_ 1173-29 x 09135455

0-8987940
= 1192*5

i io MINE SURVEYING.

Case 3. Given any two sides b and c, and the angle A between
them, to find the remaining side and angles.

The angles (B + C) = 180 - A, from which we get (B + C),
and tan - = j - cot ^, from which we get (B - C) ; and

<L "T~ C A

(B + C) + (B - C) = 2B, thus we find the angle B ; and C
= 180 - A - B, from which we get the angle C. We have now
got all the angles, and can find the remaining side by Case 2.

EXAMPLE. The two sides of a triangle are 135 yards and 105 yards, and the
angle between them is 60 : find the remaining side and angles.
Let A be the angle ; then I and c are the sides.

The angles (B + C) = 180 - A

= 180 - 60 = 120

,B-C\ b-c , A
tan (---)= ^ cot - 2 -

- 135 ~ 105 cot 30
135 + 105

= <& x 1*7320508

= 6-21650635, which is the tangent of 12 12' 59'
/. B - C = 24 25" 58"
and B + C = 120
their sum = 2B = 144 25' 58"

/. B = 72 12' 59"
and C = 180 - 72 12' 59" - 60

= 47 47' 1"
To obtain the side a

then

_ __

sin A ~~ sin B

a 135

0-8660254 0-9522168
and a = 122-7

Case 4. Given two sides and the angle opposite one of them, to
find the remaining side and angle.

Let the two given sides be b and c, and the given angle B.

then since r , = -. ^

sin C sm B

. . c sin B
/. sm C = j

When C is found, A = 180 -B-C.

b sin A
ItoB-

In must be noted, however, that when the angle B is acute,

GEOMETRY, TRIGONOMETRY, LOGARITHMS. in

and the side I is less than ihe side c, there are two solutions to

the angle C. This will be understood on reference to Fig. 82s,

in which B is the given angle

and c one of the given sides ;

the other given side fc may

be in either of two positions

AC or ACi, thus forming

two triangles ABC and

ABCi. The angle ACB

being the supplement of the

angle ACiB, both would have

the same sine, and therefore

either of these triangles would

be permissible.

In practical work, however, there will be no doubt as to
which value to take, as the surveyor generally knows the shape
of the triangles he is working on.

It is impossible within the limits of this work to go at greater
length into the subject of Trigonometry, but the reader is
referred to one or other of the standard works on the subject. 1

1 Elementary Trigonometry, by J. Hambliu Smith, published by Longmans ;
Trigonometry for Beginners, by J. B. Lock, published by Macmillan Co.

CHAPTEK VII.

SURFACE SURVEYING WITH THE THEODOLITE.

IN order to make the plan of a large estate with accuracy, or of
a small estate with extreme accuracy, or of portions of an estate
across which lines cannot be measured at will as, for instance,
where the ground is occupied with buildings, as in a town it
is advisable to use an instrument for taking angles. A transit
theodolite is generally used. There is nothing in the theory
upon which the theodolite is designed to make it more accurate
than a miner's dial ; but theodolites are generally used by
persons requiring extreme accuracy, and the instruments are
therefore made with great care. A 5-inch theodolite is an
instrument of very convenient size for an ordinary land sur-
veyor's use, and is graduated to read to angles of 1'. The larger
the horizontal circle of the theodolite, the greater the degree of
accuracy with which the theodolite can be read, thus a 12-inch
theodolite reads to 1" ; a 6-inch theodolite may be constructed
to read to angles of 20" ; 8-inch theodolites are graduated to
read to 10". For very important work special theodolites have
been made up to 36 inches' diameter, reading to ^ of a second.
The larger instruments are only required for very large surveys,
such as the Ordnance Survey of the United Kingdom, or for
very important railway surveys, where a long tunnel is projected
to pierce a mountain, as, for instance, some of the tunnels
through the Alps. The size of the instrument to be used
depends on the nature of the work in hand. It may easily be
calculated that the sine of an angle of 1", to a radius of 100 miles,
is equal to about 2 feet ; and the sine of an angle of 1' for a radius
of 100 miles is equal to 153'59 feet. It is evident, therefore,
that for the accurate fixing of places at a distance of 100 miles
by means of the theodolite supposing it to be possible that a

SURFACE SURVEYING WITH THE THEODOLITE. 113

sight of this length could be taken it would be necessary to
have one reading to seconds or fractions of a second ; but for
fixing a point at a distance of only 1 mile, an instrument reading
to minutes or fractions of a minute would have a corresponding
accuracy.

Fig. 83 shows a plan of an estate in which the principal
distances are to be ascertained by means of the theodolite. The
first step is to select some piece of ground on which a line of
100 yards or more in length can be measured over a smooth
and level surface. It does not matter where this piece of ground

FIG. 83. Survey of an estate by triangulation from measured base, with

theodolite.

is, but the nearer it is to the centre of the estate the better ;
it might, however, be on one side or even outside the estate.
It should also be in a good position for obtaining sights to
numerous parts of the estate to be surveyed. Having selected
this ground, let the base-line AB, say 2000 links in length, be
measured. It is essential that the measuring should be done
with extreme accuracy ; this may be effected by using a care-
fully tested chain, or a steel tape. In order that the steel tape
may be used with accuracy, the direction of the line should be

ii4 MINE SURVEYING.

first carefully marked out by means of pegs or otherwise, and
the distance approximately measured with a chain or common
tape ; then, at the end of every chain-length, a piece of smooth
wood, or stone, or slate must be placed in the ground ; so that,
in measuring with the steel tape, the end of every chain-length
can be carefully marked with a fine-pointed pencil. If the line
is not perfectly level, the inclination must be measured, so
that the length as measured may be reduced by calculation to
that of a horizontal line. The temperature at the time of
measurement should also be noted, so that corrections may be
made for expansion or contraction if necessary. At each end
of the base-line is fixed a permanent mark. This may consist
of a wooden peg, say 4 inches square, driven firmly into the
ground, the top of which is cut level and smooth, so as to
receive the mark indicating the end of the line. The peg A
may be fixed before the measurement of the base-line is begun ;
the peg B should not be fixed until the point has been accurately
marked. After it has been driven in, and the top levelled and
smoothed, the base-line must be remeasured, and the end of the
desired length marked precisely on the peg. As it will be
necessary to fix the theodolite over each of these pegs, it may
be advisable, in case the weather is wet, or likely to become
wet, and so make the ground soft, to fix in the ground three
pegs or blocks of wood or stone, each equidistant from the
centre-mark, and each at the same level. The tripod stand can
then be fixed on these three supports without any fear of its
yielding, and the centre of the tripod will thus be brought over
the centre-mark at the end of the line. A plumb-bob must be
used, in order that the tripod may be accurately fixed in the
correct place.

Having thus carefully measured the base-line, the theodolite
is fixed first at one end and then at the .other, observations being
taken to all the points or stations which are visible ; these are
then fixed without any further measurements, although, for the
purpose of what is called "filling in," it will save time to use
the poles and chain in the way described in Chapter II. It will
also be desirable to measure certain other distances, checking
the accuracy of the distances obtained by calculation.

It would save time, of course, to use two theodolites, one
fixed at each end of the base-line, i.e. at A and B ; but it is not
everybody who possesses two of these instruments. If only one

SURFACE SURVEYING WITH THE THEODOLITE. 115

theodolite is obtainable, two tripod stands may be used with
advantage, one fixed at A, and the other at B, and the instru-
ment moved from one to the other, so saving the time other-
wise lost in correctly centering the instrument over these points.
Stations fixed by Angles. It is now necessary to fix a number
of other stations, for instance, C, D, E, F, G, H, I, J, K, L. At
each of these places a pole is fixed, and the angle made with
the base-line is read by means of the theodolite. The stations
are so chosen that no angle shall be less than 30 or more than
120. Stations C, D, E, and F are fixed by reading the
angles CAB, CBA, DAB, and DBA, also the angles EAB,
EBA, FAB, and FBA. It will be seen that in the triangle
CAB one side, AB, and the angle at each end are known,
and therefore the remaining sides and angle can be calcu-
lated (see p. 107), and the position of the point C found ;
the positions D, E, and F can similarly be fixed with
great accuracy. The places G, H, I, J, K, and L are not
absolutely fixed, only one observation being made from the
nearest end of the base-line. The theodolite may now be
moved to the station C, and the calculated distance CD used
as a base-line for further observations; the angle ACL is now
taken, fixing the point L, and a further sight is taken to the
point M, the angle DCM being read; the position N is then
observed, the angle DCN being read, and the station O by
reading the angle D C O ; the position H will also be fixed by
reading the angle ACH. The theodolite may now be moved to
D, and the position M fixed by reading the angle CDM; N is
fixed by reading the angle CDN ; J is fixed by reading the angle
JDB ; and G is fixed by reading the angle GDB. A new station
is projected at P. The theodolite may now be moved to M, and
the position O fixed by reading the angle CMC; a new station
is projected at Q by reading the angle QMO ; the station R is
projected by reading the angle OMR, and S by reading the
angle SMN. The theodolite may now be moved to N, and
station Q fixed by reading the angle QNM, and the station
S fixed by reading the angle SNM, P fixed by the angle
PND, and checked by the angle SNP; station T is pro-
jected by the angle SNT. The theodolite may now be moved
to S, and the station T fixed by reading the angle TSN. The
accuracy of the station Q is tested by reading the angle QSN,
also the accuracy of the station P by reading the angle NSP.

ii6 MINE SURVEYING.

Triangles. In this way the whole estate may be covered with
a series of triangles, and no single station should be placed at a
greater distance than is convenient for accurate sighting of the
staff, this distance depending on the power of the telescope. The
stations at the end of the system of triangulation, as, for
instance, the stations S and T, may be quite out of sight of the
original base-line AB. At every station all the reasonable
angles should be observed, and by this means every station will
be observed several times and the accuracy of the work tested.

Where the direction of a line of fence corresponds with the
direction of a line connecting any two stations, the length can
be measured with a chain in the ordinary way, offsets being
taken to the fence ; the measured length should agree with the
calculated length, and form a check upon the accuracy of the
work.

Great care is necessary in fixing the stations, the angle of
which is to be read. The common method of marking a station
is to fix a surveying-pole in the ground at the required spot,
and, after its position has been recorded, to mark the place by
means of a peg driven into the ground. This peg may be round
and of the same diameter as the pole, in which case it will fit
into the same hole; the centre of the hole is marked by a
cross on the top of the peg, and with care considerable accuracy
may be attained by this method ; but errors are liable to creep
in, owing to the staff not being fixed quite vertically, and to the
peg not being driven quite into the centre of the hole. Where
possible, observations should always be made to the bottom of
the pole, in which case the fact of the pole being placed a little
out of truth will not lead to any error.

It would be possible to overcome these errors by fixing the
positions of the stations by means of pegs in which a hole was
bored to receive the pole.

Tripod stands could also be used for sighting to, which could
be accurately fixed up over each station.

One objection, however, to the use of a tripod stand in place
of a pole is that in a level country it might be rendered invisible
by hedges and walls of moderate height, whereas the top of an
ordinary surveying-pole can be seen over these obstructions.
Another objection is the cost and weight of such a contrivance,
which therefore preclude its use except for very special purposes.

In the course of a day's work, a surveyor might wish to

SURFACE SURVEYING WITH THE THEODOLITE. 117

observe twenty stations, and not to disturb the poles in any one.
Where the distance is considerable, a slight error in fixing
the pole may not be observed. Suppose, for instance, that
the centre of the pole at D (Fig. 83), as observed from A and
B, is 1 inch distant from the centre of the mark on the peg at
D, over which the theodolite is subsequently placed ; if the
distance BD is 5 chains, this will be an error of 1 inch in 3960,
equal to an error of about 1 minute, and such an error, of course,
must not be deliberately risked. Therefore, after placing the
station peg at D and marking the centre, the pole should be
held vertically over the mark, in order to see if it corresponds
with the station as observed, and if it does not correspond, the
observations must be repeated. If, however, the length BD,
instead of being only 5 chains, had been 12 chains, an error of
1 inch would only be about 22 seconds, and might be neglected
in a survey of this size.

When a survey-line crosses a stone wall or wood fence, it is
a good plan to make a notch at the junction ; by so doing the
line is much more easily found on subsequent occasions.

The position of such objects as church spires, mill chimneys,
and corners of large buildings may be fixed by observations with
the theodolite, thus checking the "filling-in" process done by
means of the chain.

The method of triangulation above described is similar in
principle to that adopted in the Ordnance Survey of the
British Isles, the whole of the stations being fixed by triangu-
lation from two principal base-lines, one on Salisbury Plain,
about 7 miles long, and the other on the shore of Lough Foyle
in Ireland, about 8 miles long ; l but for this survey specially
large instruments were used theodolites 3 feet, 2 feet, and
18 inches in diameter. According to Mr. Bennett H. Brough,
the exact 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 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.
The sides of some of the principal triangles measured here from
80 miles up to 111 miles in length ; the principal triangles were
divided into secondary triangles with sides 10 to 15 miles in
length, and these again into tertiary triangles with sides

1 Ordnance Survey of the United Kingdom, by Major Francis P. Washington, R.E-

ii8 MINE SURVEYING.

averaging \\ mile in length. It is within these last that the
chain surveyors work. For the smaller triangles smaller
theodolites were used.

The theodolite is often used, not as the chief means of fixing
the station, but as a check upon the accuracy of the measure-
ments made with the chain, and to facilitate the ranging of
a long line of poles. With regard to the ranging of poles
in the manner already described on p. 14, Chapter II., there
is a possibility of the line becoming crooked, owing to the
poles being fixed imperceptibly out of the true line, and so
causing a gradual, but in the end considerable, divergence ; this
may be caused by the poles being blown by the wind or other-
wise caused to lean on one side after being truly fixed. If,
however, the line is ranged with the aid of a theodolite fixed on
some level piece of ground, any slight divergence from the true
line, when passing across a field in a hollow or hidden from view
by high hedges, is at once corrected with the aid of the telescope
as soon as the line reappears in the line of sight. The angles
that the main lines make one with another are also observed, as
shown in Fig. 84, where thirteen theodolite stations are shown
at which the angles of the various lines are observed. In the
large triangle ABC there shown, the three angles are measured
as well as the three sides ; if, however, one of the sides has been
measured, the lengths of the other two sides could be calculated ;
but as all three sides are measured, the accuracy of the measure-
ments can be checked by calculation, and therefore, if the work
is honestly done, it is impossible for an error to escape detection,
that is to say, it is impossible that the fact of an error existing
somewhere shall escape detection, though it may take a little
trouble to ascertain exactly where the error occurs. It is evident
that one fine day's work with the theodolite will accomplish
more in the way of checking the accuracy of a triangulation
already made with chain and poles than five days' work of actual
measurement with the chain across the fields.

Use of the Theodolite over Rough and Impracticable Ground.
It frequently happens that it is impossible to measure the
sides of triangles in the way shown in Fig. 84, because of
obstructions consisting of rivers, woods, precipices, and build-
ings ; in such cases the use of a theodolite or similar angle-
measuring instrument is necessary, as the distance between
various stations, visible from some position of advantage outside

120

MINE SURVEYING.

the line to be measured, can be accurately fixed by triangulation
from some base-line of known length. In towns it is, generally
speaking, impossible to run diagonal lines, or to take sights
from corner to corner of the rectangles formed by the streets ;
it is, however, possible sometimes to fix the theodolite on
elevated positions or buildings, and so take observations to
the principal stations in the survey of a town ; but for the
filling-in of the streets, the accurate reading of the angles
formed by one street with another is the only means of making
a correct plan. The surveyor, in fact, traverses a number of

;C f

FIG. 85. Town surveying with the theodolite.

rectangular or polygonal figures, and the accuracy of his work
can be proved by the plan so obtained agreeing with stations
found by the main triangulation, which has been conducted from
some rising ground overlooking the town.

Fig. 85 shows a plan of a few streets which it is necessary
to survey. The points A and B are two of the principal
stations, the positions of which have been fixed from rising
ground outside the town. From these two points, and from
intermediate stations between them, angles are taken between
the line AB and other lines running up the centre of the streets
to the points C, D, E, F. The point F being also a principal

SURFACE SURVEYING WITH THE THEODOLITE. 121

station, the accuracy of the intermediate survey is thereby
checked.

Angles are likewise taken at the intersections of the cross-
streets. The lines between the various stations are then
measured, off-sets being taken to all buildings ; and from the
angles and measurements taken it will be possible to plot the
survey thus made.

It does not often happen that the mining surveyor has to
prepare a plan of the whole of a large town ; but it not infre-
quently happens that he requires an accurate plan of part of a
town or village through which he cannot easily range diagonal
lines of survey.

Use of Miner's Dials, etc., on the Surface. The dial is often
conveniently used for many of the purposes for which the theo-
dolite is better applied. The theodolite, being an expensive and
cumbrous instrument, is not infrequently left at home when the
dial will serve the purpose in view ; for instance, the boundary
of an estate may be traversed with the dial, and angles read as
in Fig. 84, and the bearings of each line may be taken with the
loose needle. In this way the accuracy of the chaining is
checked, and it may be fairly argued that the instrument which
is sufficiently accurate for underground work is sufficiently good
for the surface, and this, with certain limitations, is true, if the
dial is a good one and the distances are not long. For filling in
a few fields, buildings, rows of houses, and for taking the bearings
of main lines, the dial is a very convenient and useful instrument.

It must, however, be borne in mind that the ordinary miner's
dial only reads angles to 3', and that an error of 3' is equal to
8*7 in 10,000; but it is not necessary to make such an error,
it need not be more than one half, or say 4*3 in 10,000, which
in round figures is equal to an error of 31 links in a mile.
Where greater accuracy than this is necessary, the dial cannot
be used for measuring angles.

In preferring, however, the use of the theodolite and of the
chain and poles for surface work, the mining engineer is guided
by the thought that by means of these instruments he can make
a plan which is practically correct without an error of even half
a link in a mile, and therefore he will not incur the risk of an
error of 3^ links to the mile except for those portions of the
underground survey where he is compelled to trust to the
accuracy of his reading of the magnetic needle.

122 MINE SURVEYING.

Magnetic Meridians. With the exception of a few mines
where some magnetic ore is worked, every mining plan has
marked upon it the magnetic meridian, and in the vast majority
of mines the underground survey is made with the magnetic
needle ; therefore the correct fixing of the meridian is of the
very highest importance. For this purpose, when a new survey
is being made, the bearings of all the main lines should be
taken with the greatest possible care by means of the same dial
that has been used for the underground survey. Of course,
before using the dial, it should be carefully examined to see
(1) that the needle swings freely and has sufficient magnetiza-
tion to cause it to overcome any friction there may be on the
pivot, and seek the north without undue delay; (2) that the
needle is quite straight, and that both ends read the same, it
being evident that if the needle is quite straight and the gradua-
tion of the circle quite accurate, the readings of the two ends of
the needle will agree ; (3) that the lines of magnetic force in the
needle are parallel with its centre-line drawn lengthwise. The
first two can be at once seen, and if the needle or graduated
circle is wrong, another needle or circle must be obtained. Any
error due to No. 3 can only be ascertained by comparing the
bearing of a certain line with the bearing given by another
needle ; therefore, for an important survey, the magnetic needle
on the dial or theodolite should be compared with several other
instruments. If the same instrument is used for both surface
and underground surveys, the error due to No. 3 may be
neglected.

It has been already said that the ordinary 4J-inch compass
needle can only be read to about ^ of a degree ; it follows,
therefore, that the meridian, as laid down from one reading of
the needle, may possibly be misplaced to the extent of \ of
a degree. Perhaps the most accurate way of observing the
bearing of a line is to turn the sights of the dial until the point
of the needle corresponds with some mark on the graduated
circle either the zero mark or the degree nearest to the bearing
of the line. It is easier to observe whether or no the point of
the needle corresponds exactly with the division on the scale,
than to estimate with precision, without the aid of a vernier, the
proportional part of a degree to which the needle points. If,
however, the dial is clamped with the needle pointing to some
mark on the graduated circle, the sights can then be moved

SURFACE SURVEYING WITH THE THEODOLITE. 123

through the fractions of a degree necessary to bring them into
the line of observation, and the fraction of a degree can then
be read with the vernier, of which the readings are say to 3',
the error in the vernier being not more than one-half of that,
that is to say, H'. The exact fixing of the needle upon one of
the marks in the graduated circle may be done by means of a
magnifying-glass or microscopic eye-piece, and when a surveyor
has the advantage of broad daylight, there seems no reason why
there should be any error ; at any rate, the error need not ex-
ceed oV of a degree, thus the sum of the errors from one reading
would be, say, 4J-'. The observation of the bearing in this way
should be made, say, three times, and the average taken, and if
the bearings of six different lines are each read with an equal
amount of care, and the error in any single case is not more
than 4^', it follows that if the meridians laid down from these
six observations differ from each other, they can only differ to
the extent of 4^', and a mean may be almost perfectly accurate,
or at any rate it is probable that the error may be greatly
reduced, and amount to say only 2', or an error of six links
in 10,000.

To overcome any possible error from the diurnal variation
of the magnetic needle, the meridian should be taken at the
same time as the survey was made in the pit.

The writer has seen in Germany a station on the surface
near a mine for observing the daily fluctuation of the needle.
A magnetic needle was delicately suspended in a dark chamber,
and a ray of light was reflected by a mirror on the needle on to
a graduated arc of large diameter ; the slightest movement of the
needle, being at once apparent, could be easily recorded. In a
similar way the variation of the needle is obtained at Greenwich,
but in this case photographic records are obtained.

Having once laid down the magnetic meridian on the plan
in the careful manner above described, it should not be altered
unless an equal amount of care is used. Perhaps the simplest
way of correcting the meridian is to compare the magnetic
declination, as ascertained at the Eoyal Observatory at Green-
wich from year to year ; thus, in the year 1900 the magnetic
decimation was 16 32' at Greenwich, and in the year 1901 it
was 16 26', so the meridian as laid down on the mining plan
might be corrected to an equal amount. For the ordinary
extensions, however, of a mining survey it is not generally

124 MINE SURVEYING.

considered necessary to correct the meridian every year ; it
should, however, be done at least once in two years.

The common way of correcting the meridian is to fix two or
more pegs in some conveniently situated field on a line, the
bearing of which has been accurately observed and recorded on
the plan ; upon a subsequent occasion the dial can be fixed in
the direction of these marks, and any variation in the needle
observed. It must, however, be noted that whilst this is useful
for the purpose of checking meridians, the minute accuracy of
the process depends, first, on the care with which the original
bearing of the line was observed ; second, the accuracy with
which the pegs were fixed in that line ; and third, upon the
immovability of these marks, and the care exercised in fixing
the instrument over them.

Some surveyors advocate the marking on the plan of the
geographical north and south meridians or lines of longi-
tude. The geographical meridian, of course, never changes,
and the magnetic meridian can always be obtained for the
purpose of plotting the survey by setting off the correct decli-
nation.

It must be remembered that great care must be exercised
in altering the meridian by means of marks upon the plan,
because, when a plan has been used some years, it is possible
that, owing to shrinkage or bending or breaking of the paper,
marks upon the plan may become a little misplaced. If, in the
case of an existing plan, it is sought to ascertain the true mag-
netic meridian, it can only be done by ascertaining the bearing
of lines between various points on the surface which are marked
on the plan, and it must be borne in mind that, although the
plan may be on the whole an exceedingly accurate and excellent
one, it is quite possible that, owing to difficulties of draughts-
manship and slight extensions or contractions of the paper, or
slight errors in the original survey, any particular part may
be inaccurate to the extent of 5 or 10 links or more, and it
is important to observe that this may cause a very serious
error in fixing the meridian. Suppose the length of the line
observed be only 5 chains in length, and the two stations as
marked on the plan were each only 5 links out of their true
position in opposite directions, this would make an error of
direction of 10 links in a length of 500, or 1 in 50, which is
equal to an error of 1 9'. If, however, the distance, instead of

SURFACE SURVEYING WITH THE THEODOLITE. 125

being only 5 chains, was 50 chains, the error would be propor-
tionately less ; it is therefore important that the marks on the
plan between which the line of bearing is observed should be a
long distance apart, but, in order to reduce the probable error,
the bearing of several other lines must be observed, both ends of
which are quite distinct from the first line. Supposing the plan
to be on the whole accurate, and that five or six lines are taken,
each 20 chains in length, it is probable that the errors in the
position of one line as marked on the plan will balance those of
another, and that the meridian obtained as the average of the
observations will be fairly accurate.

Position of the Shafts. It is, of course, necessary to fix with
extreme accuracy the position of the shafts, and their position
should be indicated, not merely by an accurate delineation of
them as circular or rectangular pits, as the case may be, but by
the intersection of lines as shown in Fig. 84. All the principal
survey-lines should be drawn on the plan in thin lines of some
colour, say red or blue, and the length of each line written upon
it ; particularly should this be done in reference to the lines
intersecting the centre of the shafts.

It is a common plan to rule only one magnetic meridian
upon the plan, and that is commonly ruled through the centre
of the downcast shaft ; upon this line should be written the
words, "magnetic meridian," and the date upon which it was
observed ; but the writer thinks that it would, perhaps, be better
practice, upon the construction of a new and carefully made
plan, to rule several parallel magnetic meridians. It is easy
upon a new and unused plan to rule parallel lines, but some
years later, when the underground workings have extended to
portions of the estate perhaps 30 inches distant from the original
meridian, it is not so easy to rule the new meridian strictly
parallel to the one ruled through the shaft. Of course, the
meridian first ruled has by that time become antiquated, but
the new meridian can be drawn through each of the old
meridians, the variation being the same in each case, either
from observations made upon the variation from some fixed
marks on the surface, or by adopting the variation as given by
the Astronomer Eoyal.

In addition to making a plan showing correctly every object
upon the surface, the surveyor should mark on it the position
of lines of sewers, or drains, the property of any sanitary

126 MINE SURVEYING.

authority, also the position of lines of gas and water-pipes.
The lines of fences shown are supposed to represent the centre
of the hedge or wall, unless there is a ditch, in which case the
line shown on the plan should be the centre of the ditch, but
the position of the hedge should also be noted by a little mark
upon the line, as shown at h (Fig. 84). If a wall is the
boundary of a property, it is generally all upon one side; in
that case the line shown upon the plan will be the side of the
wall that represents the boundary. In the case of a river
dividing two properties, the boundary-line is generally in the
centre of the river; in the case of a public road dividing two
properties, the boundary-line of the minerals is generally the
centre of the road; but this is not always the case, and the
correct boundary-line of the mineral property may have to be
determined by reference to the title-deeds.

Reduction of Lengths for Inclination. As before mentioned
(p. 11, Chapter II.), it is necessary, in chaining, to measure the
horizontal distance between various stations for the purposes of
producing a plan in which all the objects are shown upon the
same horizontal plane. Where the measurements are obtained
with the chain or tape, this can be done in the manner referred
to, by ranging a series of vertical poles in the line to be measured,
and holding the chain or tape as nearly as possible level when
measuring the distance from pole to pole. For the purposes of
ordinary accuracy, it is not necessary that this chain or tape
should be absolutely level, because at moderate inclinations the
differences between the length of the line as measured on the
slope, and as measured strictly level between the two poles, is
very slight; thus at an inclination of 2-J- the difference is
rather less than 0*1 per cent. This, of course, would be a serious
matter for long lengths, or for the very accurate fixing of some
particular point, but for the ordinary filling-in of a survey it is
sufficiently accurate. This method of measuring should only
be resorted to either in the absence of instruments for taking
the inclination or for the case of short slopes, banks, or terraces.

One of the chief uses of the theodolite is to facilitate the
taking of the vertical angle formed by the slope of the line to be
measured, and a line in a horizontal plane ; in order that the
true horizontal distance may be calculated. The method of
reduction generally adopted may be explained with the aid of
Fig. 86. Here the distance measured on the slope is, say, 1562,

SURFACE SURVEYING WITH THE THEODOLITE. 127

the angle of inclination is 2. It is evident that the horizontal
distance is equal to the cosine of the angle, if the slope is
considered as the radius, and the vertical height of the upper
end of the slope above the lower end is equal to the sine of

FIG. 86. Keduction to horizontal distance of lengths measured on a slope.

the angle. On referring to a book of mathematical tables,
it appears that the natural cosine of 2 is 0*9993908, and the
natural sine is G'0348995; therefore the length measured on
the slope has to be multiplied by the decimal fraction represent-
ing the cosine ; thus if the length had been 100, the cosine
would be 99*939; if it had been 1000, the cosine would be
999-39 ; in this case the decimal fraction has to be multiplied
by 1562, and the actual cosine, which is the horizontal distance,
is 1561*0484296, and the length of the sine is obtained by
multiplying the decimal fraction by 1562 ; therefore the actual
sine or altitude is 54-5130190.

In taking the inclination with the theodolite, the vertical
circle is clamped with the vernier at zero, and the telescope is
fixed horizontally by means of the levelling- screws ; the telescope
is then undamped, and fixed upon the station of which the
altitude has to be observed, the vernier reading gijjing the angle
of inclination. It is important that the cross-hairs of the
telescope shall be fixed upon a mark which is the same height
above the ground as the centre of the telescope, and for that
purpose a cross-bar or piece of paper should be fixed upon the
pole at the proper altitude.

Average Inclination of Slope and Steep Undulations. It must be
borne in mind that with the theodolite the average inclination

Cosine 997J641 tOOO = 997 S64I

FIG. 87. Reduction to horizontal distance of lengths measured over undulating

ground.

of a slope is measured ; this may be a moderate inclination,
say 4, as shown in Fig. 87. Here, supposing the length of the
straight line measured down the average slope along a line

128 MINE SURVEYING.

stretched tight from top to bottom, to be 1000 links, then the
reduced length is equal to 1000 links multiplied by the decimal
fraction representing the natural cosine of 4, which is 0'99-75641,
or the reduced length is 997*5641 links.

But in this particular case the average slope is compounded
of a number of shorter slopes, some of which are very steep, as
shown in the following table :

Length measured Inclination

on the slope. in degrees. Cosine.

No. 1 ... 80 ... 4 ... 0-9975

No. 2 ... 100 ... 28 ... . 0-8829

No. 3 ... 100 ... 20 ... 093969

No. 4 ... 50 ... 27 ... 0-8910

No. 5 ... 50 ... 14 ... 0-97029

No. 6 ... 50 ... 28 ... 0-8829

No. 7 ... 100 ... 8 ... 0-99026

No. 8 ... 100 ... 15 ... 0-9659

No. 9 ... 80 ... 15 ... 0-9659

No. 10 326-3 4 0'9975

Total 1036-3 Total 997'62

Here it will be observed that the total length measured along
the undulations is 1036*3, and therefore it would be very mis-
leading to reduce the length so measured by the reduction due
to the average inclination for 4 ; it is necessary to measure the
inclination of each slope, unless the method described in
Chapter II. of measuring in horizontal steps is adopted.

The student will gather from this example that one short bit
of steep incline, say 28 in 100 links, may cause a greater error
in measurement than a gentle slope such as 2 would cause in
1 mile.

For the purposes of precise accuracy in a large survey, it is
necessary to take the inclination of the gentlest slopes, but it
is far more important to be careful in the chaining of short
pieces of rough ground ; and, where perfect accuracy is required,
it is necessary to stretch the chain, or steel tape, or steel wire
from station to station, the precise inclination of this wire being
observed.

Measurements can be obtained with great accuracy by the
system of triangulation shown in Fig. 83, as by this method all
the errors due to the roughness of the ground are eliminated,
except so far as they may affect the shorter lines between the
main stations.

CHAPTER VIII.

UNDERGROUND SURVEYING.

IN the collieries of Great Britain the shafts are generally sunk
vertically, in which case the centre of the shaft at the bottom
should be vertically below the centre of the shaft at the top ;
but it sometimes happens that the shaft has got a little twisted
in sinking, and therefore, in starting the survey of a new
colliery, it is necessary to hang a plumb-line down the shaft,
in order to transfer the centre-mark from the surface to some
beam at the bottom of the shaft, and when this has once been
carefully done, it is desirable to make a written record of it
upon the plan (see Fig. 84). If the shaft is not vertical, the
bearing and inclination must be taken in the same manner as
any other highly inclined passage.

Surveying with Miner's Dial or Compass. The following is the
method of making an ordinary colliery survey with the Hedley
dial shown in Fig. 24. Assuming that there is no iron or
other substance to attract the needle from the meridian, the dial
is placed in the centre of the road of which the direction is
required. A mark is fixed in the centre of the shaft, say a
lamp ; if this lamp cannot be conveniently fixed in the centre
of the shaft, it may be moved nearer to or further away from
the dial, but it must be placed on some part of a straight line
which passes through the centre of the shaft and the dial.
The distance at which the dial is placed from the mark, or the
length of the sight, is, generally speaking, as far as the nature
of the case permits. Supposing the road to be straight for a
considerable distance from the shaft-bottom, the dial may be
placed, say, 5 chains from the mark ; but the distance must not
be so great as to prevent the surveyor seeing the lamp clearly
through the slit of the sight, or holding convenient communication
with the other members of the party who are making the
measurements and fixing the lights under his direction. The
dial and lights should always, where practicable, be fixed in the

130 MINE SURVEYING.

centre of the roadway to be measured, and then the line of survey
will correspond exactly with the direction of the roads. When
this is not done, offsets must be taken to the side of the road.

The dial being now fixed and levelled, the ball and socket-
joint, or other arrangement for levelling, is clamped; the
needle is undamped ; the sights are turned upon the candle or
lamp to be observed ; the surveyor looking through the slit, and
cutting the lamp-flame with the vertical hair. As soon as the
needle is steady, the bearing can be read. The dial should be
so placed that the side of the graduated circle which has the
letter N engraved on it is turned in the direction in which the
survey is proceeding ; that is to say, in this case, in the direction
from the shaft towards the dial. If the north end of the needle
now points exactly to the zero mark under the letter N on the
graduated circle, the direction of the line is due (magnetic)
north ; if, on the other hand, the north end of the needle points
to the graduation at 180, or to the zero mark under the letter S,
the direction of the line is due south ; if the needle points to the
90th degree, the direction of the line is due west ; and if it points
to the 270th degree, or to the zero mark under the letter E, the
direction of the line is due east ; if the needle points to the 45th
degree between the letters N and W, the direction of the line is
north 45 west; if it points to 20, it is north 20 west; if it
points to some place between 20 and 21, say a quarter of the
distance from 20, the direction is north 20| west. The bearing
so observed is booked as No. 1 bearing. A light is now fixed at
a point further along the road, and the sights of the dial are
turned upon this, care being taken that the sight which is on
that side of the graduated circle on which is marked the letter N
is turned towards this light, because that is the direction in
which the survey is proceeding. The bearing is then read in
the manner described for No. 1 bearing, and is booked as No. 2
bearing. The measurements are now taken, a Gunter's chain
being generally used. If it is desired to note the exact width
and every slight bend in the sides of the road, then the chaining
may be done on a line kept straight from the dial to the light,
by ranging lamps or candles in the line, in the same way as
poles are ranged in a line on the surface, and offsets can be
taken to right and left of this line. The length at which roads
branch off is also noted. When the measurements have been
made, the surveyor proceeds with the dial and legs past the

UNDERGROUND SURVEYING.

forward light along the road which he is surveying, till he has
got a convenient distance, or till he comes to some turn in the
road which would hide the light from his view if he went
further ; he again fixes the dial in the centre of the road, and,
sighting back to the light he has left, takes No. 3 bearing, and
sends a light forward for No. 4 bearing; then the measure-
ments of these two lines are taken. In this way the surveyor
proceeds throughout the mine. He will, perhaps, survey back
to the shaft by another road, and his last sight may be taken
to the identical spot 011 which the first light was placed ; in

Z N

iw z N

FIG. 88. Graphic method of buokiug a survey.

NOTE. A, Station left in previous quarterly survey. Eoads driven 15 links wide.
All measurements in links. X , Station left for next quarterly survey.

that case there is what is called " a tie." During the course
of the survey, the surveyor will probably leave marks opposite
the centre of some of the roads branching out to the right .or
left, from which he can start to survey the branch road. In
" loose-needle " surveying only one set of legs is required, and
this is used for the dial, the lamp or candle to which the sights
are taken being put on the floor of the mine.

Booking. There are several ways of booking or recording the
bearings and measurements. One is shown in Fig. 88. This
may be called the graphic method : the note-book contains a
sketch ; very little attempt is made to make the sketch according
to scale, but it shows the turns of the road, branch roads, etc.,

Jt!7fi**79i*

N67E

? 5

N 49

<>/ Slant

N5I W

"? 3

BorcL

65 irv 1

N50W
A^ / from A

Borct

N 24 W

N 66 E~l

(R)

N64%E
N 1O, from

N 66'/4E

from 4-5 in 7

FIG. 89. Written moihocl of booking a survey.

UNDERGROUND SURVEYING. 133

and to some extent facilitates
plotting. The same survey may
be booked in consecutive writing,
as shown in Fig. 89; or, again,
75 ^Bor-ct- in the form of a table which may

be printed so that the columns

From, 70 aionq Main Lewi onl ^ have to be filled U P; An

instance from another mine is

shown in Fig. 90. These three
methods, the graphic, the written,

, . and the tabular, have their dif-

A ferent advocates ; but the ex-

Nr6fro m 78 in /5.. perienced surveyor may use all

Fro. 89A. Written method of bookins

Fig. 91 is the plan plotted from

the survey notes given in Figs. 88 and 89. Fig. 92 is the
plan plotted from the bookings given in Fig. 90. The method
of plotting is given in Chapter IX.

Fast-needle Dialling with Dial with Outside Vernier. It
happens very frequently that, owing to the occurrence of iron
or other source of attraction, the needle cannot be used near
the bottom of the shaft, and perhaps the only place in which
a correct bearing can be obtained is in some old road or in some
working place from which the rails can be removed. When
this is the case, the survey may be made in one of two methods.

No. 1 method : The surveyor proceeds at once to the old
road or other place where he can obtain a loose-needle sight ;
this is, perhaps, a quarter of a mile from the pit-bottom.
He there fixes his tripod stand firmly, levels the dial, and
lets the needle swing ; he then looks forward in the direction
in which he intends to proceed, and observes the bearing.
This forward light is fixed upon a tripod stand similar to the
dial-stand, which is placed at a convenient point on the line to
be surveyed, the lamp being placed in a cup which has been
carefully levelled; the cup should be of such a diameter as just
to contain the lamp without difficulty ; in this way the centre
of the lamp is made to coincide with the centre of the stand.

The dial is now moved forward and placed on the stand
previously occupied by the lamp ; the lamp-cup and lamp being
removed and placed upon the stand from which the dial has been
taken ; a third tripod with cup and lamp is sent forward along

J34

MINE SURVEYING.

the road to be surveyed and fixed at a convenient distance. The
dial being now in a place where there is attraction, the needle
is no use, and may be clamped ; hence the term "fast-needle."
The vernier circle is now undamped, and the zero mark on the
vernier fixed at a mark on the external graduated circle corre-
sponding with the loose-needle bearing last read, thus if the
bearing was N. 89 30' W., the vernier is put to N.W. 89 30',
and is clamped in that position. The sights are now fixed upon
the light where the dial was previously, and the bearing as read
on the vernier circle is, of course, the same as previously, that

Number
of sight.

Distance.

Inclination.

Bearing.

Remarks.

Measured Plotte.1.

(1)

355

350 10 rise

N. 50 E.

Commenced in A slant at

bottom of No. 11 gate, and

left mark to return to.

At 160, No. 10 gate, to the

left ; at 330, No. 9 gate, to

the left.

(2)

200

N. 50 E.

From 355 in (1), down A

slant to coal-face.

(3)

140

S. 70 E.

From 200 in (2), down coal-

face to old goaf at right of

slant.

(4)

183

N. 80 W.

From 200 in (2), along face

to left of slant.

At 180, No. 9 gate.

(5)

256

250

N. 89J W.

From 183 in (4), along coal-

face.

At 132, No. 10 gate.

(6)

200

S. 70 W.

From 256 in (5), along coal-

face to edge of goaf.

398

385

15 fall

S. 1| E.

From 256 in (5), down No. 11

gate to mark left in A

slant at commencement of

survey.

FIG. 90. Tabular method of booking a survey.

is, N.W. 89' 30'. The vertical axis of the dial is securely
clamped, the vernier circle is then undamped, and the sights
directed, by means of the milled head on the pinion, upon the
forward light, bearing in mind that the sight upon that side of
the dial where the letter N is marked is always turned in the
direction in which the survey is proceeding ; then, having fixed
the sights upon the forward mark, the vernier is read, say,
N.E. 314. The vernier circle is then securely clamped, the
vertical axis is undamped, the dial is removed from the tripod,

UNDERGROUND SURVEYING.

135

the lamp and lamp-cup from the tripod behind are brought
forward and put in the place of the dial, the dial is taken

Links too o i 2 3 t- Chains

Scale - 2 Chains to one Inch

FIG. 91. Plan plotted from the survey notes given in Figs. 88 and 80.

forward and substituted for the lamp and cup on the forward
tripod, and levelled. The back sight is now taken to the stand

Links

o i

Scale = 2 Chains to one Inch.

+ Chains

FIG. 92. Plan plotted from the survey notes given in Fig. 90.

136

MINE SURVEYING.

where the dial was last fixed, and the vertical axis is clamped
with the sights on this line, the bearing on the vernier circle
reading, of course, as before, N.E. 314. The vernier circle
is now undamped, a tripod with lamp and cup are fixed
forward, and the sights turned on to the forward light, and the
bearing is read by the vernier, say N.E. 314 30'. The survey
is continued throughout in this manner.

If, during the course of a survey, the dial is fixed at some
station where there is believed to be no attraction, the needle
may be undamped and the bearing of the needle read. This
should agree with the bearing shown by the vernier ; if it does
not agree, it is a proof either that there is attraction, or that
the survey has been inaccurately made; if it agrees, and if
there is no attraction, it is a proof that the angles have been
accurately taken. The more loose-needle sights that can be
obtained in a fast-needle survey the better, because by this
means the accuracy of the work is proved.

No. 2 method : Instead of the preceding mode of beginning

the survey, another, which
is perhaps in some re-
spects more accurate, may
be adopted. Fixing the
dial similarly where there
is no attraction, the needle
is undamped, and the dial
turned until the north end
of the needle corresponds
with the zero mark under
the letter N on the gra-
duated circle. With the
help of good lights the
needle may be adjusted to
this mark with great ac-
curacy, with an error of
say not exceeding 1' ; but
to attain this degree of
accuracy, the surveyor
must take great pains.
The vertical axis of the
dial is now clamped and
the needle again observed, to make sure that it still points to

N3I4E
(N46E)

Fm. 93. Method of booking a fast-needle
survey.

UNDERGROUND SURVEYING. 137

N. ; the vernier, of course, also corresponds with zero on the
outside circle. The vernier circle is now undamped, and the
sights directed, by means of the racking pinion, on to the forward
mark, and the bearing read as before, say N.W. 89 30'. The
survey and bookings then proceed as before. The booking of
this survey (by the graphic method) is shown in Fig. 93.

There is no difference between the booking of a fast-needle
survey and a loose-needle survey, except that it is a good prac-
tice to book the angle of the quadrant as well as the angle of
the circle, as this forms a check upon the accuracy of the
bookings. The outer graduated circle on which the vernier
works is divided continuously from to 360, and is not sub-
divided into quadrants, so that the angle of the quadrant has to
be obtained by a mental calculation, as follows :

Angles as read on circle.

Quadrant.

Quadrant angle.

Between and 90
90 and 180
180 and 270
270 and 360

N.W.
S.W.

S.E.

N.E.

Same as circle-reading
Subtract circle-reading from 180
Subtract ] 80 from circle-reading
Subtract circle-reading from 360

The quadrant angles are shown 011 the bottom of the dial-
box and act as a check on the calculation.

The practical difference between the making of a fast-needle
survey and a loose-needle survey is that the dial has to be fixed
twice when using the fast needle for once that is required in
using the loose needle, because the back sight in the fast- needle
survey is required as a base-line from which to measure the
angle of the forward sight, whereas in the loose-needle process
the magnetic meridian always forms the base, and bearings can
be read both of back-sight and fore-sight from the same station.

Fast-needle Survey with Dial with Inside Vernier. Many dials
are made without the outside graduated circle and vernier, the
vernier being inside, moving round the circle wit-h the sights
as shown in Fig. 28. If with this kind of dial the vernier is
moved from the zero, the sights are out of position, and the
vernier must be restored to the zero mark before taking a loose-
needle bearing. The process of fast-needle surveying with this
dial is as follows : Placing the dial, as in the last instance, on
a tripod stand where there is no attraction, the needle is
undamped, and, when it has settled, the dial is turned on the

138 MINE SURVEYING.

vertical axis (the vernier being at zero) until the zero on the
graduated circle is opposite the north end of the needle. The
sights are now in the magnetic meridian ; the vertical axis is
then clamped and the sights turned, by means of the racking
pinion, upon the forward mark, reading N. 89 30' E. It will
be remembered that in the survey last described the bearing
was put down as N.W., but this time the bearing read by the
vernier is N.E., that is because the vernier is fixed on the same
circle as that used for the needle, and for convenience in reading
the needle (in loose-needle surveying) the east and west have
been transposed on the circle. Having read the bearing thus,
N.E. 89 30', it is booked as N.W. 89 30'. The surveyor now
moves the dial to the forward stand, placing a lamp where his
dial was fixed ; looking back towards this lam]) and clamping
the vertical axis, the bearing still reads, according to the dial,
N. 89 30' E. He now turns the sights to the forward light,
which reads N. 46 W., and is booked N. 46 E. He now
clamps the vernier circle, unclamps the vertical axis, and moves
the dial on to the forward legs, and fixes the sights in the
direction of the back sight before he unclamps the vernier screw
to take the forward sight. He proceeds with the survey as in the
previous instance, but with this difference, that he always books
the bearings as read from the vernier with the E. or W. reversed.
If he arrives at some place where there is no attraction, he can
loosen the needle, the north end of which should then come to
rest at under the letter N on the graduated circle ; if it does
not, it is a sign that there has been some mistake in taking the
angles.

Fast-needle Survey without Loose-needle Base Dial with
Outside Vernier. Another method of proceeding with the fast-
needle survey is to fix the dial in the road which it is desired
to survey, notwithstanding that there is attraction, and turn
the sights towards a mark in the centre of the shaft or other
station forming the beginning of the survey. The vernier circle
being clamped at 0, this line is booked as due north, or 0.
The forward sight is taken to a lamp fixed in a cup on the
tripod stand. To take this sight, the vertical axis having been
first clamped upon the back sight, the vernier circle is undamped
and the sights turned upon the light ; the angle is then read on
the outside circle, say N.E. 350 or N. 10 E., and this bearing
is booked. The vernier circle is then clamped, and vertical axis

UNDERGROUND SURVEYING. 139

undamped, and the dial moved forward and the sights fixed
again in the line of the last sight, reading, of course, the same
bearing. The vertical axis is now clamped, the vernier screw
undamped, and the sights turned upon the forward light, the
bearing reading on the outside circle say N.E. 840 or N. 20 E.
The survey is continued in the same way, the first sight that
was observed being taken as the meridian line.

When some portion of the mine is reached where there is
no attraction, the sights are fixed upon the back sight, which
has been recorded say N.W. 20 ; the needle is released, and the
real bearing of the line in which the sights are clamped is shown
by the needle-point ; thus the bearing, as read on the vernier
circle, is N.W. 20, whereas the actual bearing as shown by the
needle is S.W. 50, or 130 on the circle, showing a difference
between the real bearing and the bearing so far recorded in the
survey, of 110. The bearings hitherto recorded in the note-
book may now be all corrected by the addition of 110; thus
the first bearing, instead of being N. or 0, is really S.W. 70 in
the quadrant, or 110 on the circle ; the next bearing, instead of
being N.E. 10, or 850 in the quadrant, is S.W. 80, or 100 on
the circle; the next bearing, instead of being N.E. 20, or 840
on the circle, is due W., or 90 on the circle.

Having now got the true bearing, the vernier circle is
adjusted to it, and set at S. 50 W. or 180 ; the forward sight can
then be read say 140, or S. 40 W. ; the same bearing, of course,
will be given by the loose needle. The dial is now moved to
the forward station, where there is attraction ; the vernier plate
has been clamped at S. 40 W. ; the sights are now fixed on the
tripod previously occupied by the dial, and the forward bearing
read with the vernier, say S. 80 W., or 150, and the survey con-
tinued in the manner described for fast-needle dialling (p. 188,
Fig. 98).

This process is sometimes modified as follows : The whole
survey is made with the fast needle, using the first sight as
a base-line, and calling that north, without any reference to
the actual direction, as in the instance above given, no loose-
needle sight being taken until the end of the survey (loose-needle
sights may be taken during the progress of the survey at places
where there is 110 attraction, to obtain the bearing; for this
purpose a diversion may be made into some place where there
is no iron), which is, say, at the face of the workings or the end

140 MINE SURVEYING.

of the level from which rails or other iron have been removed.
The needle is now released, and the true bearing of the last
sight observed, which is say N. 30 E. in the quadrant, or 330,
on the circle ; whereas the nominal bearing, as recorded by
the fast-needle survey of the same line, was N. 50 W., or 50 in
the circle, showing a difference of 80 between the two bearings,
or 280 following the graduations on the circle. The first
bearing taken in the survey may now be corrected to that extent,
and, instead of reading north, will now read 280 in the circle, or
N. 80 E., which is the correct bearing.

In plotting this survey, the bearings will be plotted as
originally recorded, using the direction of the first sight as the
meridian line. The real magnetic meridian will now be ruled
upon the paper across the starting-point, which is say the centre
of the shaft, the meridian being ruled at an angle of 80 (or
280) from the first sight or nominal meridian. A careful tracing
is then made, and is fixed over the plan of the estate, the centre
of shaft on tracing and plan being coincident, placing the real
meridian parallel with the meridian line of the plan. In a
similar way, the meridian may be plotted from the intermediate
or check-bearings mentioned above.

Fast-needle Survey without Loose-needle Base Dial with Inside
Vernier. When using the dial with inside graduated circle,
the process is as follows : The first sight is recorded as north,
the vernier being at zero ; the vertical axis is now clamped, the
vernier undamped, and the sights turned upon the forward
light ; the bearing which with the other dial was read with
the vernier N.E. 10, or 350, now reads with this dial N.W.
10, or 10 in the circle, and is booked N. 10 E. The vernier
is now clamped, the vertical axis undamped, and the dial
moved to the forward tripod, and the sights directed back to
the station on which the dial was previously fixed ; the vertical
axis is now clamped, the vernier, of course, still reading N.W,
10. The vernier circle is now undamped, and the sights fixed
on the forward light, reading N.W. 20, or 20 in the circle,
-instead of N.E. as with the other dial, and this bearing is
booked as N. 20 E. The survey is continued in this way, the
bearings being booked E. when the vernier reads W., and vice
versa, until a place is reached where there is no attraction.
The dial, having been fixed at this place, and the bearing as
taken by the fast-needle process having been observed with great

UNDERGROUND SURVEYING. 141

accuracy, the vernier is turned to and there clamped ; the
vertical axis being undamped, the sights are now turned upon
the back light, and the actual bearing with the loose needle is
observed, the actual bearing is say, as in the instance given on
p. 139, S. 50 W., or 130 in the circle ; whereas the bearing, as
recorded by the vernier, was N. 20 E., and the bearing as
booked N. 20 W., or 20 in the circle. There is thus a difference
of 110 in the readings, and the readings hitherto taken may
now be corrected by adding 110. The vernier is now undamped,
and is fixed at S.E. 50, or 230 on the graduated circle; the
sights are now turned again upon the back sight, when the
loose needle should point to the north, or on the graduated
circle ; the vertical axis is now again clamped, the vernier circle
undamped, and the forward sight taken ; the loose needle still
points to the north ; the bearing is read with the vernier, and
the survey is continued as in the method given on p. 138.

Large Surveys. It is frequently the case that the survey of
a mine or district of a mine has to be interrupted, and recom-
menced the next day or after an interval of days or weeks. If
the survey is made on the loose-needle plan, there is no difficulty
or disadvantage attending the interruption ; the place where the
survey ends may be marked by means of a hole drilled or cut in
the side or in the roof, or may be simply recorded by measure-
ments from some fixed place, such as branch roads, and the
exact position of the light taken by offsets, as shown on the
sketch (see Fig. 94). The survey can be continued at any time

36 ->

FIG. 94. Station in underground survey fixed by measurements.

by placing a light at this place, which can be refound by measure-
ments, and then proceeding to observe the bearing of the forward
lines.

In the case of a fast-needle survey, however, the last line of
which the bearing has been noted being the base-line from which
the bearings of the continued survey have to be taken, it is

142 MINE SURVEYING.

essential that the exact position of the instrument and of the
lamp last observed should be marked with great care. This,
however, is rather a difficult and unsatisfactory operation. The
ordinary workings and roadways of a mine are not suitable
places for accurate and permanent marks ; the roof, floor, sides,
and timber are liable to continuous movement, and might move
an inch or two in the night ; the probability or otherwise of
such a movement may, however, be known to those who are
constantly in the mine, and know whether that part is quiet or
subject to movement. In order to diminish and to discover
errors due to inaccurate marks, at least three places on the line
of survey should be marked. As long as these three marks
preserve their original relative positions, the chances are very
much against any error due to the movement or inaccurate
placing of the marks. The distances from mark to mark should
also be as long as possible ; thus if the distance were 100 links,
an error of 1 inch in the position of a mark would amount to 1 in
792, or about 4^ minutes, whereas if the distance were 5 chains,
the error would be proportionally less, or about 1 minute.

A common plan of fixing a mark is to drill a hole in the roof ;
into this a wooden plug is driven, and into the wooden plug is
driven a nail or hook, from which a lamp may be hung by a
string, care being taken to see that the lamp-flame is vertically
below the hook. Three marks may all be fixed in the same
line, and the distance from the dial measured. On restarting
the survey, lamps are hung from each of the three marks, and
if they are in one straight line as originally fixed, the surveyor
may have confidence that there has been no disturbance. He
then fixes the dial under the forward mark, and adjusts the
vernier to the reading of the bearing as recorded in his note-
book. He then clamps the vernier, unclamps the vertical axis,
and turns the sights on to the back light ; then clamping the
vertical axis, he unclamps the vernier circle, and takes the
forward sight in the ordinary manner, continuing the survey as
if there had been no interruption.

Theodolite. Where extreme accuracy is required (and in
every large mine it is required), the theodolite is often substi-
tuted for the dial. The process of surveying is the same as that
used with the Hedley dial with outside vernier, and the booking
is done in the manner shown in Fig. 93. In the theodolite as
generally made the compass needle cannot be conveniently

UNDERGROUND SURVEYING. 143

read, and is therefore only used for obtaining the meridian.
Where a trough or tubular compass is used, the needle only
swings freely when in the magnetic meridian. If the survey is
begun at some place where there is no attraction, the telescope
is turned towards the magnetic north, the utmost care being
taken to see that the needle is swinging freely, and that the
direction of the telescope is parallel to the meridian line ; the
vertical axis of the theodolite is then clamped, the vernier plate
is undamped, and the telescope directed towards the light on
the line of survey of which the bearing has to be observed,
whether that is a backward or a forward light. The bearing
is now read from the vernier, and is recorded both as the
bearing of a quadrant and as the degree of the circle, thus :
N.E. 40, or 40 on the graduated circle.

It will be noted that the graduated circle of the theodolite
reads clockwise, and that, therefore, when the telescope is turned
from north eastwardly, the bearings as read advance from
to 40, 50, and upwards ; whereas on the outside circle of the
dial, shown in Fig. 24, the graduations read the reverse of
clockwise, and when the dial is turned N.E., the figures read
from 360 backwards, as 850, 340, etc. On the other hand,
when the sights are turned W., the figures advance, as 10, 20,
30, etc. ; the reverse of this being the case with the theodolite.
Some confusion is therefore apt to arise in the mind of the
surveyor who first uses a dial of which the vernier circle is
graduated the reverse of clockwise, and then uses a theodolite
graduated clockwise. The remedy for this appears to be that
the mining surveyor using an outside-circle dial should have
the inner circle read from the needle, graduated the reverse of
clockwise, and the outside circle graduated clockwise.

The advantages to be gained by the use of a theodolite, as
compared with an ordinary dial, are as follows : (1) More
accurate sighting of the stations, owing to the use of a telescope ;
(2) more accurate reading of the angles owing to the use of a
more finely graduated circle and vernier, read by means of a
microscope ; (3) longer sights, due to the use of a telescope ;
(4) greater accuracy in fixing the marks, also due to the use
of a telescope ; (5) greater accuracy in observing the inclination,
due to the long level on the telescope, and to the finely
graduated vertical circle and vernier read with the aid of micro-
scopes ; (6) use of the theodolite for levelling, either as an

H4 MINE SURVEYING.

ordinary level, the vernier fixed on the vertical circle at 0, or
by taking angles, the latter process being sufficiently accurate
for most mining purposes, and very much more rapid than the
ordinary process of levelling ; (7) the measurement of lengths
by using the instrument as a tacheometer ; (8) the possibility
of taking sights upwards at any degree of elevation, and down-
wards with a depression of 60.

A special eye-piece is supplied with the instrument, to be
used when taking sights vertically upwards, or nearly vertical ;
this enables the theodolite to be used for sighting up vertical
shafts, and marks can be placed on the surface or at some
intermediate level above the theodolite in the same vertical
plane as some line of underground survey.

Surveying with Prismatic Compass. This instrument, shown
in Fig. 23, may be used instead of the ordinary miner's dial for
loose-needle surveys. Of course, for work having any pretence
of accuracy, it must be fixed on a tripod stand.

Surveying with Henderson's Rapid Traverser. This instru-
ment, shown in Figs. 43 and 44, has one notable convenience,
which is that the survey can be just as conveniently started
where there is attraction and the needle cannot be used, as
where there is no attraction. Eeferring to Fig. 95, the instru-
ment is fixed up at A, and levelled, and the sights turned

FIG. 95. Method of surveying with Henderson's rapid traverser.

to the centre of the shaft O and clamped. By means of a
pencil the line of the fiducial edge is marked in two places
on the fifth ring, and the direction of the survey indicated
by an arrow-head ; No. 1 is written in the corresponding
notch of the. alidade. The alidade is now undamped and the
sights turned towards the forward light at B and clamped;
the line of the sight is again marked on the fifth ring and
marked No. 2. If, however, No. 2 line should nearly coincide

UNDERGROUND SURVEYING. 145

with No. 1 line, then it should be marked on the fourth ring.
The fiducial edge being clamped on this sight, the instrument
is lifted off the tripod, a lamp and lamp-cup are substituted
for it, and the instrument is placed on the forward tripod B,
in place of the lamp and cup previously there. The sights
are turned on to the back light at A ; the vertical axis being
then clamped, the sights are now undamped, and turned on the
forward light C and again clamped, and the direction of the
sight marked on the fifth or fourth ring, or, in case the direction
should be nearly the same as in the lines 1 and 2, on the third
ring, so as to avoid confusion ; this line is marked No. 3. The
instrument is now moved to the forward tripod at C, and here,
as there is no attraction, the bearings can be taken. The sights
are turned upon the back light B ; the vertical axis is again
securely clamped, the sights are then undamped, and a trough
compass is placed on the disc beside the alidade. The trough
compass (see Fig. 38) is a compass needle in an elongated
rectangular box, the sides of which are parallel to the meridian
on the graduated arcs. One of these parallel sides is accurately
placed against the thick side of the alidade, which is then
turned until the needle of the compass points exactly in the
meridian line ; the alidade, of course, is then in the same line,
and this line is ruled with a fine-pointed pencil across the
whole width of the disc and by the thick side of the alidade.
All the bearings previously drawn on the disc now appear in
their correct relation to the meridian line. The survey may be
continued in the same way as it was begun, and all the bearings
afterwards marked will also be in correct relation to the meri-
dian line. If any other place is met with where there is no
attraction, the compass can be again applied, and if the
meridian first marked on the disc was accurately shown, and
the survey has since proceeded with accuracy, the second
meridian line will correspond with the first.

This method of surveying is similar to the fast needle in
this respect, that the instrument is placed at each end of each
line, the first line being used as* a base from which to measure
the angle made by it and the second line.

The instrument may be used to make a loose-needle survey
in the following manner (see Fig. 96) : The instrument is set
up as before at A, and the vertical axis clamped ; the sights
are then undamped, and by means of the trough compass the

146 MINE SURVEYING.

meridian is marked on the disc ; the sights are then turned on
the back light at O, and the bearing No. 1 ruled by means
of the fiducial edge, as in the preceding example; the sights
are then turned on the forward light I, and the bearing No. 2
marked as before. The instrument and tripod may now be
lifted up and carried forward beyond the light I, and fixed at
the place B. The sights are then undamped and moved till
the alidade is parallel with the meridian, as marked on the
disc, and clamped ; the trough compass is now placed on the
disc with its side against the alidade, and the vertical axis is
then turned until the needle points in the meridian; the

x cr~
FIG. 96. Loose-needle surveying with Henderson's rapid traverser.

vertical axis is then clamped, the sights undamped and turned
on the light I, and the bearing No. 3 marked in pencil against
the fiducial edge. The sights are next turned on the forward
light 2, and the bearing No. 4 marked. The survey may be
continued in the same way. By this method the instrument
is only set up once for two bearings.

The reader will notice that in using this instrument no bear-
ings are recorded in the note-book, only lengths corresponding
to the numbers of the sights, and, with regard to the booking of
the numbers and lengths, he may adopt either of the three
methods used for the dial, that is, the graphic, the written,
or the tabular.

The Henderson traverser may have as a separate attachment
a vertical semicircle with small telescope, by which inclina-
tions can be read and sights taken vertically. There is also
an arrangement by which moderate inclinations can be read
without the use of the graduated semicircle; this consists of
a slide h, which can be moved up or down the vertical limb
through the openings of which the sights are taken, the eye
being fixed at an opening at the top of the other vertical limb
as shown in Fig. 97 ; the slide is moved up or down till it

UNDERGROUND SURVEYING.

147

becomes in line with the light that is being observed. The
position of this slide marks the angle which the line of sight
makes with the horizontal line.

For the purpose of levelling the disc, a loose spirit-level is
used, which may be carried in the waistcoat pocket. In plotting
the survey, the celluloid disc is removed from the instrument
and placed on the paper, where it serves as a protractor ; the

FIG. 97. Method of measuring inclinations with Henderson's rapid traverser.

directions, being already marked on it, have only to be ruled off
by means of a good metal parallel ruler. An example of an
actual survey is given in Chapter IX. on " Methods of Plotting."
Surveying with Suspended Dial. In some mines, especially in
metal-mines, many of the passages, whether called shafts, drifts,
rises, or winzes, are so highly inclined that an ordinary dial
can scarcely be fixed. If the passage is so short and straight
that a sight can be taken through from one level to another, the
steepness of the road constitutes no difficulty, at least it does
not when working with the theodolite or dial, unless the inclina-
tion is more than 60; but where the passage is crooked so

148 MINE SURVEYING.

that it cannot be surveyed without placing the instrument in
it, the suspended dial is often used. A strong linen cord is
attached to a bar or prop fixed at either end of the length to
be surveyed, and upon this the dial is suspended by two hooks,
as shown in Fig. 36. The dial hangs level, and the needle
shows the bearing of the cord. The length is then measured
with a chain or tape, and the next length above or below is
then observed in the same manner ; the vertical angle must at
the same time be observed with equal care, and this is accom-
plished by having the vertical circle round which the compass
box rotates graduated in degrees.

It is, however, comparatively seldom that this method
becomes absolutely necessary,. because the length of these steep
roads is not generally very long between the levels, and the
direction can be observed by looking down from the level above,
and looking up from the level below.

CHAPTER IX.

METHODS OF PLOTTING AN UNDERGROUND SURVEY.

THE usual method of plotting an underground survey is with
the protractor, parallel ruler, scale, needle-point, and pencil.
Protractors are described in Chap. V. and shown in Figs. 60-62.
Plotting with. Metal Protractor. The surveyor, having drawn
a line to represent the meridian, places the protractor upon
some part of the line which is a little distance from the part of
the plan on which he wishes to plot the beginning of his survey.
By means of weights, he fixes the protractor so that and 180
are on the meridian line, the being towards the north.
Having made a prick-mark at the centre of the protractor,
he takes the needle-point and pricks off No. 1 bearing against
the edge (see Fig. 98) ; with his pencil he draws a dotted line
away from this prick-mark, being the prolongation of an imagi-
nary line from the centre of the protractor to the prick-mark.
At the end of this short dotted line he writes the number of the
sight and the bearing ; he then pricks off No. 2 sight, marking
the paper in a similar manner, and so on till he has pricked
off all the sights of the survey or of that portion of the survey
which falls within a convenient distance of where the pro-
tractor is placed. If the survey is extensive, he will rule
another meridian line, exactly parallel to the first, on a portion
of the paper over which the survey will extend. He then fixes
the protractor on this new meridian line, and pricks off the
remaining bearings, or as many as relate to that portion of the
survey which lies near the protractor. If necessary, he may
rule a third and fourth meridian, and mark off the bearings in a
similar manner. He now takes the parallel ruler and, placing
it on bearing No. 1, moves the ruler to that part of the paper
on which he wishes to commence plotting, and rules a line ; the

MINE SURVEYING.

beginning of it is marked with a prick-mark, and the end of it
is pricked off on the line by means of a scale ; he now fixes the
parallel ruler in the direction of bearing No. 2 as pricked oft'

N60 C 40'W (7^

N8&20'W.(D-

S7640'W."' ^
&

FIG. 98. Method of plotting with brass protractor.

FIG. 99. Draft of survey plotted from the bearings given in Fig. 98.

from the protractor, and, rolling the ruler to the end of line
No. 1, he draws line No. 2 from the prick-mark at the end of
No. 1 line, and marks off the length with a scale and pricks it

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 151

off ; and so on through the whole of the survey. The draft of
the plotted survey is shown in Fig. 99, and the finished plan in
Fig. 100.

In marking off the bearings with the protractor, it is a
common plan to make a mark on each side of the protractor ;
thus, if the bearing was N. 50 W., it would be numbered, and
the direction N.W. written in pencil at the end of the dotted line.

FIG. 100. Finished plan plotted from bearings given in Fig. 98.

Another prick-mark would then be put opposite to it at S. 50 E.,
and the same number attached to it as to the first prick-mark.
Making these two marks gives a longer base by which to set the
parallel ruler, and the written bearing on the N.W. side reminds
the surveyor of the direction in which the line is proceeding.

Plotting with Cardboard Protractor. The cardboard protractor
(as shown in Fig. 62) is often preferred to the metal pro-
tractor. This is fixed upon a meridian with the zero towards
the north and 180 towards the south; a line is then ruled
across the meridian in the direction east to west, that is to
say, from 90 to 270, so fixing the centre of the circle. The
parallel ruler is then placed with one edge at the centre-mark
and the same edge at the degree of the bearing, say 1ST. 50 W.,
and is then rolled to the required position. When using the

152 MINE SURVEYING.

cardboard protractor the meridian is ruled on that part of
the plan on which the plottings are to be made, so that the
lines may all be laid down within the circle. If the parallel
ruler is sufficiently long, it may be stretched right across the
circle, say from N. 50 W. to S. 50 E., and this is the best plan
and the one most commonly adopted. As the plotting proceeds
the protractor can be moved from time to time along the
meridian or to a fresh line ruled parallel to the first.

Owing to the large diameter of the paper protractor, the
fractions of a degree are easily observed, and, with care, this
method of plotting the bearings is very accurate, and no prick-
marks are made on the paper.

Vernier Protractor. The protractor shown in Fig. 61 is
used where minute accuracy is necessary in plotting the bear-
ings, as, for instance, in setting out a bearing, which proceeds
for a great length in one straight line. The method of plotting
is the same as that just described with the metal protractor.
The vernier is set to the required bearing, and then this is
pricked off by the needles fixed in the folding arms, the
bearing being pricked off on each side of the centre so as to
increase the length over which it is marked on the plan.
Supposing the instrument to be accurately adjusted, so that the
prick-marks on each side, when united by a line drawn through
the centre, are in the same straight line (a test which can be
easily made), the bearings can be marked off as accurately as
they can be read by the theodolite vernier, but the points of the
needle by which they are pricked must, of course, be fine for
accurate work.

Errors of Plotting. In plotting by the methods just de-
scribed, the errors that may creep in are of a very obvious kind.
With an 8 inch protractor the size of a prick-mark with an
ordinary needle varies from i, which is very small, to ,
which is an ordinary size ; a pencil-line may be drawn much
finer, and, if a hard and carefully sharpened pencil is used,
may be drawn to about ^V in thickness. Eoughly speaking,
however, it may be said that with an 8 -inch protractor the
bearing cannot be pricked off with a mark less than in width,
and that even with the utmost care there may be an error of
half that, or T y .

Great care is required to fix the parallel ruler over the
centre of the prick-marks, and the draughtsman is generally

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 153

sufficiently satisfied if he can be sure that the parallel ruler is
over both prick-marks without using a magnifying-glass to
ascertain that it is over the centre of the prick-marks. In
rolling the ruler the pressure must be applied midway between
the two rollers, so as to prevent any slipping of one roller. If
the rollers have exactly the same diameter, the ruler will keep
its edge parallel to the line from which it started ; if one roller
is a little larger than the other, or has upon its circumference
any dirt accidentally increasing its diameter, the ruler will not
keep its edge parallel to the starting-line. The accuracy of
the rolling may be tested by ruling two lines, the second line
12 inches or more distant from the first ; then turning the
ruler end for end, set it parallel to the first line, and roll it to
the second line ; if the edge of the ruler exactly coincides with
this line, it shows that the rollers are each of the same size,
and also that they are fixed concentrically on the axis. It is,
however, difficult to get a parallel ruler that is perfectly accu-
rate, and it is not uncommon to find that in rolling a distance
of 8 inches it changes its direction to the extent of 4', and of
course such a ruler is no use for accurate work. The error
may be reduced, however, by setting up on the plan, by means
of scales, a number of parallel meridians not more than 12
inches apart, so that the ruler will not have to be moved any
great distance ; and the error can be still further eliminated
by ruling the bearings first with one edge of the ruler and then
reversing it and ruling the bearings with the other edge, and
taking the mean.

The length of the lines is also subject to errors due to the
practical difficulty of correctly marking off the distance. The
diameter of a fine prick-mark on a 2-chain scale is about 1J
links, and the diameter of a clear prick-mark on a 2-chain
scale is about. 2 links. It is thus evident that two different
draughtsmen may plot the same survey so as to show a consider-
able difference at the end ; and if, after plotting the survey, the
surveyor finds that it does not tie in, it may be quite easy for
him,, knowing in which direction lies the apparent error, by
going over his plotting, to eliminate it.

All these errors may be reduced in amount in the following
way : By using (1) larger protractors or a vernier protractor ;
(2) a very fine needle-point; (3) a very finely pointed pencil;
(4) an accurately rolling parallel ruler. If the scale to which

154

MINE SURVEYING.

the plan is plotted is a large one, the measurements will be
plotted more accurately ; but any errors made in marking off
the bearings from the protractor will be increased.

In making a plan, the surveyor first plots the skeleton
outline as shown in Fig. 99. When satisfied with that, he
rules in the details as shown in Fig. 100 ; this gives the width
of the gate-roads, strait^work, banks, and, if desired, the
position of overcasts, stoppings, and other ventilating arrange-
ments, though these are not usually shown on the working plan,
but are put on another plan kept especially for ventilation, the
arrangements for which, except in the case of permanent
overcasts and some of the stoppings and separation doors, are
liable to continual alteration.

Ogle's Protractor. Where it is possible to fix the paper on to
a drawing-board and to use a T-square, the protractor shown in

FIG. 100A. Ogle's form of protractor.

Fig. 100A can be advantageously employed. It consists of an
outer frame, a, with a true edge to work on the T-square ; inside
this frame is a graduated ring, I, capable of being rotated ; and

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 155

inside this is another ring, c, also free to rotate. To use the
protractor, the N and S marks on the ring b are placed parallel
with the meridian line on the plan, and the ring is then clamped;
the required bearing can then be set off by moving the inner
ring c to the required angle.

Trigonometrical Plotting. 1 The mechanical errors of plotting
may be altogether eliminated by adopting a system of trigono-
metrical computation, by which the latitude and longitude of
every station in the mine are found, and recorded in a survey-
book. The positions on the plan may be sketched in by hand
or put on by scale, according to circumstances, and the distance
between any two parts of the plan may be calculated from the
information contained in the survey-book, and also the bearing
of any proposed new road between any two places on the survey.
To facilitate the drawing of the plan, it is made on paper ruled
in squares, thus forming lines of latitude and longitude. In
France it is a common thing to have the plan made upon a
number of separate pieces of paper or cardboard, each piece say
about 2 feet square ; these can be pieced together, as shown in
Fig. 101, as required. In England, however, the practice is
almost universal of having the whole of the survey on one large
piece of paper. If the size of this becomes unwieldy, the
plan is divided into several districts ; in this case a smaller
scale plan is used, containing the whole of the mine for
occasional reference, so that the engineer may see at a glance
the relative positions of different parts of the mine, whilst
using the large scale plan for details. The trigonometrical
system of computation, where used in England, is generally
used for checking some main stations when, owing to particular
circumstances, greater accuracy than usual is necessary. The
system, however, of ascertaining the latitude and longitude of
every station has many advantages, especially where the area
under one management covers a large extent of country, and in
fixing the boundaries between different concerns. Wherever
there is a Government survey the lines of latitude and longitude
shown on the Ordnance maps should be adopted, the measure-
ment to the shaft being taken from three or four of the nearest
station marks.

1 A short but excellent treatise on this subject, entitled, " Practice in Under-
ground Surveying, etc.," by the late Mr. W. F. Howard, A.I.C.E., of Chesterfield, is
contained in the Proceedings of the North of England Institute, vol. xx., and in the
Chesterfield and Derbyshire Institute, April 13, 1878.

156

MINE SURVEYING.

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 157

This method of plotting is applicable equally to surface and
underground surveying. It is usual, in England, to calculate
the position of every station in links and to two decimal places.
If the calculations are properly checked, there can be no error,
and the relative positions of any two places on the surface, or
any two underground places, or of one place on the surface and
another place underground, can be stated to two decimal places
of a link for distance, and with equal accuracy for bearing,
always supposing, of course, that the measurements taken in
the survey and the angles observed are perfectly accurate. By
this system, therefore, the errors of plotting are entirely
eliminated.

On reference to Fig. 102 the method of computation will be
explained. Five points on the survey are A, B, C, D, and
E, of which A is the beginning. The bearing AB is N. 50 W.,
the length 850 links; the bearing BC is N. 33 20' W., and
the length 731 ; the bearing CD is N. 41 35' 20" E., and the
distance 762'2; and the bearing DE, S. 38 30' E., and the
distance 280. If we assume that the point A is the point of
origin, and has longitude and latitude, what are the
positions of B, C, D, and E ?

In ordinary technical parlance in England it is usual to
speak of distances measured from longitude to longitude as
" departures," and of distances measured from latitude to lati-
tude as "latitudes." In France the geographical terminology
is maintained, and the distances measured from longitude to
longitude are referred to as " longitudes ; " but as in English
books the word " departure " is constantly substituted for
"longitude," the student must understand that they are con-
vertible terms: the "latitude" means the distance measured
N. or S. along the meridian, and the " departure " means the
distance measured E. or W. at right angles to the meridian.

To ascertain the latitude and longitude of B, the dis-
tance AB may be regarded as the radius of a circle of which
a portion is shown, xyz\ the meridian line AM is drawn through
another radial line, and from B a perpendicular is let fall on
to the meridian at s. The line Bs is the departure of the line
AB, or distance measured between lines of longitude, and is the
sine of the angle at A to radius AB. The line As is classed
under the title of latitudes, and is the distance from latitude to
latitude of the line AB, which is the cosine of the angle at A

fcr:

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 159

to the radius AB. The position B is obtained as follows by the
use of a table of natural sines and cosines : The sine of 50 to
radius 1 is 0*76604 ; this, multiplied by the actual radius, which
is 850, gives the actual length of the sine Bs, 0*76604 x 850
= (a) 65113, and the cosine of 50 to radius 1 = 0-64278, and to
radius 850 = 0-64278 X 850 *= .(b) 546'37 ; therefore the longi-
tude or departure of B is a = 65113, and the latitude is b
= 46-37.

In the same way we proceed to calculate the longitude and
latitude of C. The line x'y'z is the arc of a circle with radius
BC, Cs' is a perpendicular let fall from C to the meridian
BM', the line Cs' is the sine of the angle at B, and the line
Bs' is the cosine. The natural sine of 33 20' to radius 1 is
0-54951, and to radius 731 is 0'54951 x 731 = (a 1 ) 401-69.
The natural cosine to radius 1 is 0-83548, and to radius 731 is
0-83548 x 731 = (b') 610-74. Then the distance a' is the de-
parture or longitude of C, and the distance b' is the latitude
of C, taking B as the point of origin.

We now rule the meridian CM", and let fall the perpen-
dicular Ds", and draw the arc %"y"z". Ds" is the sine of the
angle at C, and Cs" is the cosine. The natural sine of the
angle 41 35' 20" to radius 1 is found if using Chambers's
Tables, in which the natural sines are only calculated to
minutes in the following manner :

Natural sine 41 36' is 0'6639262

41 35' is 0-6637087 0*6637087

60 |_a0002175 0-0000724

0-00000362 0-6637811

0-0000724
Natural sine 41 35' 20" to radius 1 = 0*6637811

It will be seen that the natural sine of 41 35' is 0-6637087.
To this there has to be an addition for the 20" ; the amount of
this addition is found by taking the proportional part of the
difference between the sine of 41 35' and the sine of 41 36'.
The sine of 41 36', as shown above, is 0-6639262, and the
difference is 0*0002175 ; this, divided by 60, gives the addition
for 1" = 0-00000362, and this again, multiplied by 20, gives the
addition for 20", which is 0*0000724 ; this, added to the fraction
already found for 41 35', gives the exact natural sine of 41 35' 20"

160 MINE SURVEYING.

= 0-6637811. The greater the number of degrees in the arc
of a quadrant, the greater the sine and the less the cosine.

To find the cosine for the above angle, we proceed as
follows :

Natural cosine 41 35' = 0:7479912 0*7479912
41 36' = 0-7477981 Q-Q000642
60 | 0-0001931 0-7479270
0-00000321

0-0000642
Natural cosine 41 35' 20" to radius 1 = 0*7479270

In the above sum the natural cosine of 41 35' is first found
as shown above, then the natural cosine of 41 36'; this is
subtracted from the first figure, and is the difference for 1'.
Dividing this by 60, we have 0*00000321, the subtraction for
1"; multiplying this by 20, we have 0*0000642, the subtraction
for 20" ; subtracting this from the fraction for 41 35", we have
the natural cosine of 41 35' 20" to radius 1 = 0*7479270.

Multiplying the sine above found by the actual radius 762-2,
we have 0-6637811 X 762*2 = a", 505'93 ; and multiplying the
natural cosine above found for radius 1 by the actual radius,
we have 0-7479270 x 762-2 = actual cosine b", 570-07. The
departure of D is thus a" = 505*93, and the latitude b"
= 570-07, taking C as the point of origin.

Applying the same method again to the line DE, we rule
the meridian DM"', and draw the arc x'"y'"z"' with radius DE.
Let fall the perpendicular Es'"; then E$"' is the sine of the
angle 38 30', and Ds'" is the cosine. The natural sine of
38 30' to radius 1 is 0*62251, and the natural cosine is Q'78261,
and the natural sine to radius DE is 0-62251 x 280 = a 1 ",
174-3, and the natural cosine is 0-78261 x 280 = b'", 219*13.
Therefore the departure or longitude of point E is a'" = 174*3,
and the latitude is b'" = 21913, taking the point D as the point
of origin.

If these points B, C, D, E are all referred to the starting-
point A, their positions can be shown in the tabular form given
on p. 161.

In that table the position north of each of the stations
B, C, D, and E is shown in the total column under the letter N.

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 161

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162 MINE SURVEYING.

The position west of each of the above stations is shown in
the total column under the letter W., and the amount that any
one station is further north or south from any other station can
easily be obtained by comparison with the figures, and the
amount that any one station is east or west from any other
station can also be obtained in the same way.

In ascertaining the relative positions of any given station
and the starting-point, the following method can be pursued :
All the latitudes or distances measured on lines parallel to the
meridian going north as far as the station whose position has
to be found are added together ; all the distances going south
are also added together ; that total which is less is subtracted
from the larger total, and the position of the station is thus
found either north or south of the starting-point. Similarly, all
the distances between the starting-point and the station whose
position has to be found which have been measured at right
angles to the meridian, called departures, or lengths going in a
westerly direction, are totalled ; all those going in an easterly
direction are totalled, and the less sum subtracted from the
larger ; the distance of the station east or west of the starting-
point is thus found. These positions are shown in the total
columns, Table I., the figures in which have been obtained by
means of this process of addition and subtraction. It is there
seen, for instance, that station D is 172718 links north of A,
and 546'89 links west of A.

Suppose that it is desired to know the distance in a straight
line from A to E, and the bearing of the line. Fig. 102 shows
that E is b + I' + b" - b'" north of A, and is a + a - a" - a'"
west of A. Then, for the sake of clearness, make a sketch as
shown in Fig. 102, draw the line AE, from E drop the perpen-
dicular Es"" ; then As"" may be considered the radius of a circle
x""y""z"". AE is the secant of the angle EAM, and E s "" is the
tangent of the same angle

the actual tangent = ^ ^ Q{
the actual radius

Es""
.-. ( ,,,, = natural tangent of radius 1

.-. a + a ' " ^1' I fr"' = natural tangent of the angle EAM
B72-59 . 247 067

1508-05

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 163

Looking down the table of natural tangents, this is found to
correspond with the angle 13 52' 40", and the bearing AE is
therefore N. 13 52' 40" W. The natural secant of the angle
13 52' 40" to radius 1 is 1-0300681. Multiplying this by the
radius As"", we have the actual secant 1 '0300681 x 6 + If + I"
- I 1 " = 1-0300681 X 1508-05. Therefore the distance AE is
1553-39.

When the student has gone over the above figures with his
Mathematical Tables, and has also to satisfy himself that the
calculations are correct drawn out the measurements to scale
and the angles with the protractor, and has repeated the
operation several times, he will have mastered the elements of
trigonometrical plotting.

If paper ruled in square sections is used, no scale is required
for plotting the latitudes and departures. Where the survey is
made with a Gunter's chain, the paper should be divided into
squares the side of which equals 1 chain on the scale to be
adopted in plotting the survey ; if the scale is 2 chains to
1 inch, the squares must each measure half an inch (or 1 chain)
on each side ; these squares are again subdivided into 100
smaller squares, measuring 10 links on each side. This sub-
division, however, is rather small, and the surveyor may have
to be content with squares measuring 20 links on each side,
and must measure the subdivisions, as required, with a scale.
The divisions of the chain-squares should be in stronger lines
than the subdivisions.

The survey shown in Fig. 102 and given in the above table
is shown again in Fig. 103, plotted on sectional paper, scale
4 chains to an inch. In actual practice, however, the lines on
the sectional paper are lithographed in some light colour, say
brown or yellow, which is not likely to be confused with any
part of the plan.

Another method of plotting is by means of a drawing-board
and T-square, or by a straight-edge and set-square. The
meridian is ruled on the paper by means of the straight-edge.
The straight-edge is fixed on the paper by weights, and the
latitudes are pricked off on the line from the starting-point
or origin, and the departures are ruled off by means of the set-
square. The set-square is moved along the straight-edge to the
required distance or latitude ; the departure is then ruled, and
the distance pricked off with the scale. For departures on the

i5 4

MINE SURVEYING.

other side of the meridian, the straight-edge is moved to the
other side of the meridian line, and the process repeated.

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In case the distance from the first meridian line to the place

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 165

on the survey is longer than the set-square, a new meridian can
be ruled parallel to the first by means of a set-square or parallel
ruler, the parallelism of the two meridians being tested by
measurements with the scale. In this way a more accurate
drawing is made than by using the ordinary sectional paper.

A sketch made upon ordinary sectional paper is sufficiently
accurate for most purposes, and is perfectly accurate for all
lengths measured in the meridian and at right angles to the
meridian, because the lengths can be measured off the plan by
counting the divisions on the paper, which, by the assumption
made in plotting, are the correct length, so that all lengths
measured in these directions are perfectly accurate, except such
errors as may arise in scaling between the divisions ruled on
the paper. If, however, the length of a diagonal is required,
some error in this length may arise from unevenness in the
ruling.

The way to measure any length not in the meridian or at
right angles to it is to take the distance with a pair of dividers,
and then mark that distance on the paper in a line parallel
to the meridian, and count the divisions. If, however, the
divisions as ruled are not exactly square, or if the squares are
not all the same size, this measurement of the diagonal will not
give the exact result, and the exact length would have to be
obtained by calculation, which can easily be done, as the lati-
tude and longitude of each of the two points are known, but
will take some time.

If, however, the lengths are accurately set out by scaling in
the second method of plotting just described, the diagonals can
be accurately scaled ; and, indeed, the scaling of the line con-
necting any two points is often coincident with an actual survey-
line, and the agreement between the two measurements is a
check upon the accuracy of the plan.

Logarithmic Computation. Instead of using natural sines
and cosines and ordinary numbers for multiplication, surveyors
commonly prefer to adopt the aid of logarithms. A short
explanation of the nature of logarithms has already been given,
and, in addition to this, a sufficient explanation is generally
given at the beginning of a book of Mathematical Tables to
enable the student to make use of the logarithmic system, even
without understanding it.

The method of using logarithms is shown in Table II.

1 66

MINE SURVEYING.

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2 .

I I I I

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W O Q

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 167

In this table the fourth column contains the logarithms of
the distance. Thus No. 1 distance (AB, Fig. 103) is 850 links.
On referring to a table of logarithms of numbers, and under the
column headed "number," the figure 850 will be found, and
opposite to that will be found the logarithm, which is 9294189.
As in this particular survey extreme accuracy is not required,
it will be sufficient to take the first five figures, 92941 ; but
taking mto account the remaining figures, it will be more exact
to call the fifth figure 2, and the logarithm may therefore be
written 92942. This logarithm is the same for 850 and 8500,
as can be seen by looking for the log. of 8500 ; and it would be
the same for 85,000, 850,000, or any higher sum the result of
multiplication by a power of 10 ; it is also the same for 85, 8'5,
0*85, 0*085, 0-0085, or any smaller sum obtained by the division
by any power of 10. In order that the logarithm shown in the
table may be distinguished as the logarithm of 850, it is neces-
sary to add a figure which is called the characteristic. For
850, the characteristic is 2, and the log. of 850 is 2'92942 ; the
log. of 8500 would be 3'92942 ; of 85,000, 4'92942, and so on.
The number in the characteristic is one less than the number of
figures before the decimal point of the natural number. If the
length had been 85, the log. would be 1*92942 ; if the number
were 8*5, the log. would be 0*92942 ; if it were 0"85, the log. would
be T92942 ; if it were 0'085, the log. would be 2*92942 ; if it were
0-0085, the log. would be 3*92942. In every case where the
number consists of integral figures, the characteristic of the
logarithm represents one less figure ; and where the number is
a decimal fraction, the characteristic has the sign written
over it, and is one more than the number of cyphers after the
decimal point in the number.

If it is desired to multiply two numbers together, this can
be done by adding their logarithms, the number corresponding
to the logarithm so found is the number that would have
been obtained by multiplication in the ordinary way. Thus to
multiply 850 by 769, add the two logarithms 2*9294189 and
2-8859263 ; the addition gives 5-8153452. The table of loga-
rithms is then referred to, to find the decimal part of the
logarithm. Taking for the present no account of the charac-
teristic, 8153453 is found, which is near enough for all ordinary
purposes, and take the number corresponding, which is 65365,
the last figure being the number at the head of the column.

1 68 MINE SURVEYING.

The characteristic, 5, of the logarithm shows that there are
six figures before the decimal point, and the answer is therefore
653650.

If, instead of multiplying 850, we were to divide it by 769,
the process would be to subtract one logarithm from the other ;
thus 2-9294189 - 2*8859263 leaves 0-0434926. To find the
number corresponding to this logarithm, we look down the
columns for the decimal portion ; we find the logarithm 0434802,
and the number corresponding to this is 11053. Subtracting
the logarithm so found from that which is given, we have a
difference of 124 ; in the table of differences under 394 (the
difference for one) we find the number 118 (the nearest number
lower than 124) and opposite to this the figure 3, and that gives
us the sixth figure; the difference between 118 (the figure in
the column of differences) and 124 is 6 ; multiplying this by
10, and again looking in the column of differences, we find 1 as
the figure opposite 39 ; this is the seventh figure. The number
now found is 1105331. On reference to the logarithm, it is seen
that the figure of the characteristic is 0, the number corre-
sponding to that logarithm has therefore one integral figure ;
therefore the decimal point comes after the first figure, and
the actual number is 1-105331.

Continuing the description of Table II. ; having written
down the logarithms of the lengths, the logarithmic sines and
cosines of the angles are written down in the next column.
Thus the log. sin of 50 is 9'8842540, and the log. cos 9'8080675.
It is not always necessary to write out the decimals to seven
places ; for small surveys five places are generally sufficient.
The student will notice the enormous number represented by
the characteristic 9 ; this is because the logarithmic sines are
calculated to an assumed radius of 10000000000.

The length of the sine is found by adding the logarithm of
the length to the logarithmic sine of the angle; thus 9*88425
+ 2-92942 = 12-81367. It is evident that this represents a number
vastly in excess of the real length. Whenever logarithmic sines
and cosines are used, it is necessary, before the logarithms so
found can be reduced to natural numbers, to subtract 10 from
the characteristic. Subtracting 10 from the above figure, we
have the logarithm of the sine 2-81367 ; on referring to the
table of logarithms, we find the number corresponding to this
is 651*13; and therefore the actual length of the sine or

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 169

departure is 651*13, which is placed under the column of
departures under the letter W., as the direction is westward.

The latitude is found by adding the logarithm of the cosine
to the logarithm of the length ; thus 9'80806 + 2'92942
= 12-73748. Subtracting 10 from this, we have the logarithm
2*73748 ; the corresponding number is 54637, and the decimal
point comes after the third figure ; the cosine is therefore
546'37, which is placed under the column of latitudes under
the letter N., as the direction is northward.

It must be noted that in Chambers's Tables the logarithm
is not given for any variation in the angle of less than 1' ; in
Babbage and Callet's Tables the logarithms are given for all
angles to 10", the sine and tangent are also given for 1" up to
5, and the cosine and cotangent for 1" between 85 and 90.

A great deal of time spent in calculating may be saved by the
use of traverse tables. These are tables in which the latitude
and departure (longitude) have been already calculated out for
certain lengths. Suppose, for instance, that the lengths for
which the calculations are made are from 1 to 100 inclusive,
then, if the actual length is less than 100, the latitude and
departure can be read off the table ; if the length is 'more than
100 and less than 200, the latitude and departure for 100 are
taken from the table, then the latitude and departure for the
remainder also taken and added to the other figures; if the
distance is several hundreds, then the latitude and departure
as found for 100 must be multiplied by the number of hundreds,
and the latitude and departure for the remaining part of the
length less than 100 taken from the table. Traverse tables,
however, are not much use to the surveyor unless they are
calculated to angles of 1' ; this has been done by E. L. Gurden. 1

The following example shows the mode of using these tables.
Bearing N. 20 10' E., distance 164 :

Departure

Bearing. Distance. Latitude. (or longitude).

N. 2010'E. ... 100 ... 93-87 ... 34'48

64 ... 60-076 ... 22-06

164 ... 153-916 ... 56-54

Traverse tables are, however, sometimes used which are not
calculated for every length up to 100. For instance, in Mr.
H. T. Hoskold's Treatise on Surveying, the latitude and departure

1 Traverse Tables for the use of Surveyors and Engineers, by Richard Lloyd
Gurden, 3rd edit. (Chas. Griffin and Co., Ltd., London).

1 70 MINE SURVEYING.

are calculated for 1, 2, 3, 4, and 5, or for any of these figures
multiplied by 10, 100, 1000, 10,000, or 100,000. Using such
tables as these, the above latitude and departure is set out as
follows :

Departure

Bearing. Distance. Latitude. (or longitude).

N. 20 10' E. ... 100 ... 93-87 ... 34'475

50 ... 46-934 ... 17-237

10 ... 9-387 ... 3-447

4 3-755 1-378

164 153-946 56-537

Table III. (p. 171) shows the survey given in Tables I. and
II. worked out by means of traverse tables.

Inclination and Reduction of Lengths. In the preceding
examples of underground surveying, booking, and plotting, no
notice has been taken of the inclination of the mine. It is, of
course, obvious that this is of the utmost importance ; where
minute accuracy is required, the inclination of every bearing
must be observed. Where good and carefully adjusted levels
are attached to the instrument, these observations of inclination
serve two purposes first, that of ascertaining the proper reduc-
tion of length for the plan, and second, that of ascertaining the
levels in all parts of the mine. The accuracy of this levelling
process, of course, depends upon the nature of the instrument
used and the care exercised by the observer. With a good
theodolite sufficient accuracy may be obtained for most practical
purposes, but not for all purposes. With a 5-inch theodolite, which
only reads to minutes, an error of 3 in 10,000 may be expected,
and this error would be too much for many purposes, for instance,
such as setting out a water-level ; but for the ordinary contour of
a mine and setting out roads for the purposes of haulage, the
accuracy attainable with the theodolite would be quite sufficient,
and for rough approximations careful levelling with a good dial
is very useful.

For the purposes of reducing the length, minute accuracy in
reading the vertical angle is not generally required. For the
angle of 1 the natural cosine is 0*9998477 ; if the measured
length was 10,000, the cosine or reduced length would be
9998-477. It is, however, seldom that a length of 10,000 is
dealt with in one measurement in a mining survey, as the minor
inequalities are of more importance in considering reductions of
length, as already explained in p. 128, so that it is very seldom

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 171

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172

MINE SURVEYING.

that an inclination of less than 1 involves an appreciable
reduction in the measured length.

The steeper the inclination, however, the more important it
is to observe the inclination with accuracy ; for instance, refer-
ring to Table IV., if the length of the slope (or radius) is 1000
and the inclination 1, the reduced length (or cosine) is 999*84,
and for an inclination of 1|, the reduced length (or cosine) is
999-65, or a difference of 019, while for 70 the reduced length
is 342-02, and for 70^, 333'80, showing a difference of 8'22.
Therefore, whilst at moderate inclinations it may be sufficiently
near to read the vertical angle to J, at steep inclinations it is
necessary to read to minutes in order to obtain the reduced
length correctly.

TABLE IV.

REDUCTION OF LENGTH MEASURED ON THE SLOPE TO HORIZONTAL DISTANCE FOR
ANGLES FROM 1 TO 70, AND THE DIFFERENCE FOR |.

Length measured
on slope.

Angle of
inclination.

Reduced length
(cosine).

Difference
for* .

1000

999-84

1 ftlQ

1000

999-65

/ \J 1 *7

1000

984-80

\ 1-55

1000

10*

983-25

/ J. tJtJ

1000
1000

20
20

939-69
936-67

j 302

1000
1000

866-02
861-63

j 4-3i

1000
1000

766-04
760-40

j 5-64

1000

642-78 . i P7 ,

1000

50J

636-07 i j

1000
1000

500-00
492-42

} 7-58

1000
1000

342-02
333-80

J 8-22

For the purpose, however, of obtaining the variation in level
with precision, the less the inclination the greater the accuracy
with which the angle must be read. Whilst the reduced length
is represented by the natural cosine, the variation in level is
represented by the natural sine- Taking the length of slope as
before at 1000, and the angle at 1, the altitude or depression
(sine) for 1 is 17'45, and for 1 30', 2617, showing a difference
in level of 8'72 feet for a variation of i (see Table V.) ; at 70
the altitude is 939*6926 ; at 70J, 9421550, showing a variation
of 2-4624.

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 173

TABLE V.

VERTICAL RISE FOB A CONSTANT LENGTH MEASURED ON THE SLOPE WITH ANGLES

VARYING FROM 1 TO 70, AND THE DIFFERENCE FOR J.

Length measured
on slope.

Angle of
inclination.

Vertical rise
(sine).

Difference
for i.

1000
1000

17-45
26-17

8-72

1000
1000

17364
182-23

8-59

1000
1000

342-02
350-20

8-18

1000
1000

30
30

500-00
507-53

7-53

1000
1000

642-78
649-44

6-66

1000

766-04

) - ~

1000

771-62

}

1000

866-02

\ d.-<Vl

1000

60^

870-35

}

1000

039-69

} O.QK

1000

70J

942-64

In taking his observations, the surveyor, of course, will bear
in mind what, part of the mine it is which he desires to delineate
on the plan, and of which he desires to show the relative levels.
As a general rule, the part shown on the plan is the floor or
rail-level, and he must take care that all his observations to
obtain the inclination or level must be made to marks equi-
distant from the floor ; thus, if the level of the eye-piece of the
theodolite or dial is 4 feet from the floor, he must take care
that the mark to which he directs the sight is at precisely the
same altitude above the floor, otherwise he will be led into error.
For this purpose, when surveying with three tripods, it is better
that they should each be of the same height, and that the lamp
or mark-holder should be of such a height above the tripod as to
bring the flame or other mark to the same height above the
tripod as the centre of the telescope of the theodolite or the
cross-hairs of the dial. When in the course of surveying an
assistant is sent forward to fix a mark on a tripod, the exact
height the mark will be above the ground cannot be known with
certainty, as the legs may be extended to suit irregularities in
the surface, so that the level of the lamp may vary a few inches
above or below the average height. In most cases this is
immaterial, but when the lamp is set over some permanent fixed
station, the exact altitude of which has to be determined, then

174 MINE SURVEYING.

the height from the lamp or other mark to the ground-level
should be measured and compared with the height of the mark
above the ground level of the other stations in the survey.

Table VI. (see p. 175) shows the survey made to ascertain
the inclination of a road in the mine, and the relative level of
different stations.

The plotted section is shown in Fig. 104 ; if it is desired to
show the roof of the road on the section, the height must be
measured at each station.

In the above table, the measured lengths are under column 1
the angles of inclination under columns 2 and 3. When the angle
observed shows that the roadway is rising in the direction in
which the observer is proceeding, the angle is entered in
column 2, under the heading " elevation ; " and when the angle
observed shows that the roadway is falling in the direction in
which the surveyor proceeds, the angle is entered under column 3,
under the heading " depression." Assuming that the surveyor

FIG. 104. Section showing altitudes of stations shown in plan, Fig. 102
(see Table VI.).

prefers the use of logarithms for his calculations, column 4 (a)
shows the logarithms of the lengths ; column 5, the logarithmic
sine (b) ; column 6, the log. cosine (c) ; column 7 is the reduced
length obtained, a + c 10 =/; column 8 is the elevation,
a + b 10 ; column 9, the depression, a -f- b 10 ; column 10
is the elevation in links ; column 11, the depression in links ;
column 12 is the total elevation above datum, or total depression
below ; and column 13, the reduced length in links.

It is convenient to measure all heights above some fixed or
imaginary level. For surface-work surveyors commonly take
Ordnance datum, which is the level of the old Docks Sill at
Liverpool ; for underground work it is frequently necessary to
take another datum, which the surveyor will choose according
to circumstances. Suppose, for instance, that the bottom of the
shaft is 1000 feet below Ordnance datum, and some of the work-
ings are 300 feet below the bottom of the shaft, his datum might
be 2000 feet below sea-level, in which case the plates at the pit-
bottom from which he began his survey would be 1000 feet above

METHODS OF PLOTTING AN UNDERGROUND SURVEY. 17$

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METHODS OF PLOTTING AN UNDERGRbUND SURVEY. 179

datum, and all the other stations would be more or less than
1000 feet. In plotting the survey, all the altitudes will be
measured upwards from a datum line drawn at the bottom of
the paper. But it might be equally convenient to use the
Ordnance datum ; then, the bottom of the shaft being 1000 feet,
all the other stations will be more or less than 1000 feet below
Ordnance datum.

In preparing the section shown in Fig. 104, the reduced

FTG. 109. Disc of Henderson's rapid traverser, with protractor and vernier for
reading off bearings.

lengths are marked off on a horizontal line, at each station a
vertical line is ruled, and the altitudes above or below datum
marked off.

Horizontal and Vertical Angles measured at the same Time. Of
course, when the surveyor has fixed his instrument, he will take

i8o MINE SURVEYING.

the horizontal and vertical angles at the same time, and thus
make sure that the stations observed for the plan and section
coincide, and he will therefore make a note in his book of the
vertical angle of elevation or depression. He may keep his book
either in the graphic, written, or tabular form. In case he
adopts the latter mode, a convenient form of book is shown in
Fig. 105. From this note-book the office survey-book (shown in
Fig. 106) is filled up : the sheet to carry these thirty- one
columns to be 2 feet to 2 feet 6 inches, otherwise the written
figures will be too small.

Method of plotting Survey made with Henderson's Rapid
Traverser. Fig. 107 shows the disc of the traverser, which has
been removed from the table of the instrument. A meridian
line having been drawn on the plan, the disc is placed on the
paper over this line, and held in position by weights. With
the aid of a rolling parallel ruler, the sight numbered 1 is now
ruled off, reference being made to the note-book to find the
length. No. 2 sight is then ruled from the end of No. 1, the
arrow-heads giving the direction in which the line has to be
drawn. When the lines have all been plotted, and proof
obtained that the survey has been accurately made, the offsets
and other measurements can be filled in.

One objection raised to the Henderson rapid traverser is
that it is necessary to keep the disc, because it is the only
record of the survey. In Fig. 109, however, is shown an
arrangement by which the bearings of the lines can be read off
by means of a protractor, and filled into the note-book.

CHAPTEK X.

METALLIFEROUS MINE SURVEYING.

THE surveying of metalliferous mines is conducted with similar
instruments and on the same s .e. _
principles as the surveying of
coal-mines. In metalliferous
mines, however, the work-
ings more commonly lie in
seams of steep inclination,
so that the cross-cuts which
in a coal-mine are nearly
level, in a tin-mine are nearly
vertical. The shafts are
generally inclined, and the
inclination is not regular,
following the vein. This
causes a special difficulty in
the preparation of an accu-
rate plan.

Instruments, For ascer-
taining the bearing of these
inclined shafts, it is neces-
sary to have an instrument
capable of reading any de-
sired angle in a vertical
plane, and for this purpose
a transit theodolite is com-
monly used. Where the
angle of inclination, however,
does not exceed 60, a Hedley
dial may serve the purpose,
and under circumstances
explained in p. 65 the
suspended dial may be used.

FIG. 110. Hand sketches made by surveyor
in field-book.

The suspended dial, however,

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METALLIFEROUS MINE SURVEYING. 183

is only useful where there is no attraction, and therefore is
very often inapplicable.

The measurements are usually taken with a 100-ft. chain.
Formerly a chain 10 fathoms in length was used ; every fathom
being marked, and the links 6 inches long.

Table VII. shows the note-book of a survey in a metalli-
ferous mine, commencing at the surface and proceeding down
an inclined shaft to the 100-fathom level, along the 100-fathom
level, and up a rise to the 90-fathom level, and on this level
back to the shaft ; then up a rise to the 80-fathom level, and
on this level back to the shaft, and across the shaft to the
bottom of No. 2 shaft, up No. 2 shaft to the surface, and back
to the starting-point.

Method of Surveying. The survey is usually made by the
"fast-needle method," and before commencing, the true bearing
of a line from the peg or B.M. at the top of the shaft to some
distant object is obtained with great accuracy, and forms a
base for all future surveys.

In starting the survey, the vernier of the theodolite is set to
the bearing of this line and clamped ; the telescope is then directed
so as to sight the distant object, and the whole instrument is
then clamped on this line. The zero line is now N. and S., and
the survey is proceeded with in the manner already described.

Eeferring to Table VII., columns 1 to 10 are filled up from the
observations made in the mine during the course of the survey;
the columns headed "Horizontal angles" give the direction of the
lines of survey, and the columns headed "Vertical angles " give
their inclination from the horizontal. At necessary points the
surveyor will take offsets to the hanging wall (which is the wall
above the vein) and to the foot wall (which is the wall below the
vein) ; these measurements are shown in columns 8 and 9.

In addition to filling up the columns 1 to 10, the surveyor
will make sketches showing the numbers and relative positions
of the different stations ; these sketches are shown in Fig. 110,
and are used to facilitate the plotting.

The reader will by this time understand that the principle of
plan-making is to represent all measurements in a horizontal
plane ; thus if a shaft is inclined, its length as shown on the plan
will be less than the length actually measured, and will be equal
to the cosine of the angle of inclination multiplied by the mea-
sured length. Similarly, in making a section, the measurement

1 84

MINE SURVEYING.

on a vertical plane will be less than that measured on the
slope, and will be equal to the sine of the angle of inclination

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Table VII. give these reduced measurements as obtained from

Vertical Section

FIG. 112.

Mean Stride of Reef N4 5 ^
1C

FIG. 111.

FIG. 111. Plan of workings in metalli
FIG. 112. Vertical section of ditto.
Fia. 113. Transverse section of ditto.

FIG. 113.

' 80 Faih Level
' '90 Falh. Level
' '/OO fatk Level

Transverse Section

SurreyLines

Dial Stations. /.~.5

Sui

SCALE &inch= 100 feet.

line plotted from the bookings in Table VII.

METALLIFEROUS MINE SURVEYING.

185

Traverse Tables; the method of calculating them by logarithms
is shown in Tables VIII. and IX.

Ill

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showing the top of the shafts and the direction of the levels.

1 86 MINE SURVEYING.

Fig. 112 is a longitudinal section of the same mine plotted
as if all the workings were in one vertical plane, all the inclined
lengths being reduced to vertical distances, in the same way
as in a plan the length measured on the slope is reduced to a
horizontal distance.

Fig. 113 is a transverse section of the mine across the No. 1
shaft, showing the surface and entrance to the levels.

These three figures include more than is contained in the sur-
vey, as there are old workings which are taken from another plan.

Fig. 114 is a longitudinal section in which the lengths
measured on the slope of the vein, and also the lengths
measured along the levels, are drawn without reduction; so
that if the plan were, so to speak, made to natural scale, it
could be laid down upon the vein following the sinuosities of the
levels. This section is useful as a kind of working plan on which
the lengths of level or shaft driven by the workmen can be shown
exactly as paid for, although its use might lead to confusion
with regard to the relative positions of the stations shown on
this working section, and the stations in some other vein or
adjoining mine. Practically all four drawings are necessary.

Method of Plotting. The plan is first plotted at the lower
edge of the paper, from the horizontal angles in column 4 or
the bearings in column 11, using the horizontal measurements
given in column 13 (calculated in the shafts and winzes, and
measured in the levels), the measured offsets given in columns
8 and 9 also being plotted. The directions of dip and mean
strike of the vein are at right angles to one another, and the
plan is usually plotted with the mean strike line approximately
parallel to the bottom edge of the paper. To obtain the vertical
projection (Fig. 112), station 1 is projected from the plan at
right angles to the mean strike ; No. 1 shaft is then plotted
according to the measurements given in column 12. At the
points determined for the respective levels, horizontal lines are
drawn, and the ends of the levels and positions of the winzes
are projected from the plan. Shaft No. 2 is plotted upwards
from station 9, according to figures calculated and observed.

The transverse section is plotted from the observed figures
only. Station 1 is plotted at the same height as station 1 in the
vertical section ; the angles of inclination of the vein are then
marked off with the protractor, and the length as measured on
the slope is marked off, and if the work is correctly done the

METALLIFEROUS MINE SURVEYING.

[87

corresponding levels in both vertical and transverse sections
should be on the same horizontal line.

In the longitudinal section (Fig. 114) the observed figures
are also used. The levels are ruled horizontally, and their

lengths laid off as the sum of the measurements made along
them. It will be seen in the plan that the levels curve about
a little, and, owing to this fact, the winze No. 2 N.W. appears
distorted in the longitudinal section.

CHAPTER XL

METHODS OF CONNECTING SURFACE AND UNDERGROUND SURVEY.

WHERE the compass needle can be used, the general method of
connecting the underground and surface surveys is by its means
as already described, and for most purposes this is sufficiently
accurate. Where, however, there is attraction, or in case
there is no attraction, but the magnetic needle is not considered
sufficiently reliable, some other method has to be devised.

Shafts some Distance apart. Where there are two shafts at
some distance apart, the underground survey may be connected

FIG. 115. Connecting surface and underground workings by the two shafts.

with the surface survey in the method shown in Fig. 115. In
this case the centres of the shafts have been accurately fixed
on the surface survey, and by means of a plumb-line have
been accurately transferred to the bottom of the shaft and
carefully marked. A fast-needle survey is then made of the

UNIVERSITY

.
CALIF

CONNECTING SURFACE AND UNDERGROUND SURVEY. 189

mine, beginning at the centre of one shaft and ending at the
centre of the .second shaft. This is plotted, then carefully
traced on stiff but transparent paper or cloth. This tracing is
then fixed on the surface plan by means of the two shafts, and
the workings, as shown on the tracing, transferred by a style
and marking-paper to the plan. Another method is to plot
the underground fast-needle survey from a hypothetical meri-
dian line, such as the first sight in the survey. When the
underground survey has been plotted and the position of the
second shaft fixed, the bearing of a straight line connecting
the two shafts may be calculated by trigonometric computation,
as shown on p. 158, Fig. 102, line connecting the stations A
and E ; but the actual bearing of a straight line connecting
the two shafts has been ascertained by observation of the
magnetic needle on the surface ; this actual bearing differs,
say 100, from the bearing as calculated from the hypothetical
meridian. All the other bearings obtained by the fast-needle
survey can now be corrected to the same extent, and the
survey plotted as if it had been made by the loose needle. In
case, however, the magnetic meridian has not been ascertained
on the surface, either by reason of attraction or want of a
compass, or because it is considered to be too variable, then
the geographical meridian may be set out, and the bearing of
a straight line between the shafts ascertained by means of a
theodolite or circumferentor. The bearing of this same line,
as calculated on the underground survey from the hypothetical
meridian, is then compared with the true line, and is found to
vary, say 100. The hypothetical bearings of the underground
survey can now be corrected to a like extent, and the under-
ground survey plotted in its correct position on the surface plan.

In case these shafts are, as above suggested, a long distance
apart that is to say, long in reference to the total size of the
survey, as, for instance, the distance between the two shafts
being half a mile and the furthest workings from either shaft
two miles this method of connecting the surface and under-
ground presents no special difficulty.

Underground Survey Shafts near together. If, however, the
shafts are close together, say from 10 yards to 60 yards apart,
as is commonly the case in coal-mines, then it is evident
that a base-line drawn through these shafts is a very short one
upon which to erect the whole of a large survey, and special

i go MINE SURVEYING.

care 'has to be taken to avoid mistakes. For instance, the
bearing of a line drawn through the centre of the shafts cannot
be ascertained by means of a pencil, protractor, and parallel
ruler from the plan ; but it is necessary to carefully set up marks
over the centre of the shafts, and to produce this line across the
estate, or a considerable part of it, and to connect the line so
produced with a number of the principal stations of the surface
survey, carefully ascertaining the bearings of various lines.
It will, of course, be unnecessary to repeat this operation if it
has been already done in the construction of the plan and the
bearing of a line through the centre of the shafts recorded,
the line being set out with the most absolute precision, and the
angle made by this line and the other main surface-lines noted
and recorded. In setting out this line an ordinary wooden staff
is much too thick to sight to, and it is better that a wire centre-
line should be suspended from a frame above each shaft. The
theodolite, set in a line with these wires, will connect their
direction with the surface survey ; at the same time, these
wires hang down to the bottom of the shaft, and by means of
a theodolite the underground survey is made connecting the
two wires.

The survey connecting these two centre-lines should take
the best and shortest road, so as to reduce the possibility of
error. Where there is no road straight from one shaft to the
other, it generally happens that there is a cross-road connecting
the main intake and return at no great distance from the shafts,
and in this case the survey may only require the setting up of
the instrument two or three times. Not only must the angles
be read with the most minute accuracy, so as to ensure that no
error exceeding a quarter of a minute shall creep in, but the
lengths must be measured with a carefully checked steel tape,
and the measurements recorded to the decimal of an inch. The
relative positions of the two shafts may then be accurately
calculated from the hypothetical meridian, both as regards
hypothetical bearing and distance. If this calculated length
agrees with the actual distance as measured on the surface,
the accuracy, to some extent, of the underground survey is
confirmed. The hypothetical bearing between the shafts is now
compared with the actual magnetic bearing as observed on the
surface, or with the actual geographical bearing; the hypo-
thetical meridian can thus be corrected, and the workings

CONNECTING SURFACE AND UNDERGROUND SURVEY. 191

plotted upon the plan of the surface in their true position. It
must, however, be impressed on the student that this calcula-
tion merely eliminates errors of plotting, and does not eliminate
any error arising from want of accuracy either in marking
out the line drawn through the centres of the shafts on the
surface, or in connecting the plumb-lines by the underground
survey.

Where Two Shafts are connected by a Straight Level on the
same Level as the Workings. Where the two shafts are con-
nected by a straight and level passage, it is comparatively easy
to ascertain the bearing of an underground road. Keferring
to Fig. 116, we will assume, as in the previous cases, that

JW2 Shaft JT91 Shaft

QC'IDTZJ:

FIG. 116. Taking an observation between two shafts.

a wire with a heavy plumb-bob is suspended in each shaft,
and that the direction of the line connecting these wires is
accurately shown on the surface-plan and the bearing ascer-
tained. The theodolite is now placed at a, Fig. 116, midway
between the two shafts, and in a straight line between the
two wires. Since all four doors cannot be opened at once,
the position a has either to be guessed at or ascertained by
preliminary survey. When the theodolite has been set up,
it is turned upon the wire in No. 1 shaft, the intermediate
doors being open; these doors are then shut, the telescope
reversed and turned towards No. 2 shaft, the doors being open ;
the distance of the line of sight from the suspended wire
is then measured. If this is 1 foot, and the theodolite is
exactly half-way between the two wires, it follows that the

192 MINE SURVEYING.

position of the theodolite is exactly 6 inches out of the centre-
line. The theodolite is then moved approximately 6 inches, the
telescope is then set upon the wire in No. 1 shaft, then reversed,
If in looking towards No. 2 wire the line of sight is found to be
not straight for No. 2 wire say -J- inch out the theodolite
must be moved T V inch, and then carefully fixed upon No. 1
wire. The telescope is again reversed, and this time the line
of sight should exactly hit No. 2 wire. If, however, it does not
hit No. 2 wire, the operation must be repeated until the position
a is fixed exactly in a straight line between No. 1 and No. 2
shafts. In order that the theodolite may be fixed with the
required accuracy, it is necessary that it should be on a stage
where it can be moved by means of screws. A movable stage
permitting of a movement of say 1 inch is sold by optical instru-
ment makers, but one suitable for occasional use could be easily
constructed by a carpenter. The theodolite being now in the
right position, the tripod can be fixed at b in the porch beyond
the plumb-bob in No. 1 shaft, and very carefully adjusted so as
to be exactly in the line connecting the two wires ; the theodolite
is now moved from a and set up at b, a mark having been left at
a made with precise accuracy under the centre of the vertical
axis of the theodolite. The telescope is now directed to this
mark at a, and should be in the same line as before. In order
to make sure, however, that no error has crept in in the fixing
of the mark a, or in the erection of the tripod at b, a through
sight should be taken past a to No. 2 wire. In order to get
this sight, it is necessary that there should be an opening
through all four doors at the same time. This, however, is
impracticable as a general rule, on account of the ventilation,
especially if the colliery is ventilated with a furnace, or if the
upcast is heated with steam, because, even if the furnace were
put out, the heat of the shaft would remain some days. If the
colliery, however, is ventilated with a fan, there would not be
so much wind when the fan was standing. Nevertheless, the
current due to natural ventilation would probably be such as
to shake the wires, so that it is in the highest degree inadvis-
able to open all four doors at the same time. The best plan
would be, having clamped the telescope in the right direction,
to proceed to cut holes in each of the four doors in succession
sufficiently large for the line of sight, the diameter of these
holes being say 2 inches to 3 inches, the correct position of the

CONNECTING SURF A CE AND UNDERGROUND SUR VE Y. 193

holes being fixed by the surveyor looking through the telescope
so that all four holes are in precisely the same line. In order
that there may be no difficulty in cutting these holes, the
theodolite stand at b has been fixed at such an altitude that the
line of sight will not cross any iron bands or stiffening bars on
the doors, and a drill suitable for boring a hole of the required
diameter made beforehand. When all the four doors are closed,
the current of air through the holes will not be excessive, and
they can be screwed up as soon as the operation of the surveyors
is completed.

In case it should be difficult to fix a tripod at b, it may be
necessary to erect a timber platform to receive the instrument,
with a traversing-table capable of movement by screws to the
extent of an inch or two, on which in the first instance the
mark, and in the second instance the theodolite, can be fixed.
Having thus fixed the theodolite at b in the direction ba, the
mark in the main tunnel at c can then be sighted, and the
angle abc observed. Since the bearing of the line ab is known,
the bearing of the line be can be easily calculated. The theo-
dolite is then transferred to c, and the survey continued from
the base be in the ordinary manner, and plotted from the
meridian, either magnetic or geographical, marked on the plan.
Permanent marks should be made in the lines ab and be.

In the Case of only One Shaft. It sometimes happens that
there is only one shaft. In coal-mines, of course, this is only
the case when opening out a new mine. It also sometimes
happens that where there are two shafts, one of them is not
available for the surveyor's use, either by reason of a furnace or
buildings over the pit-top making it difficult and expensive to
fix a centre-line visible by the surveyor on the surface and at
the pit-bottom. In this case the line of survey has to be con-
nected with the surface by observations made in one shaft only.

Wires in One Shaft. As in the case of two shafts, so in the
case of one shaft, the line may be transferred to the bottom by
means of wires. Where the distance between the wires is small,
as in the case of one shaft, it is essential that these wires should
be thin and perfectly steady. As steel is the strongest material,
it is best to use a thin steel wire, and to hang a heavy plumb-
bob at the bottom. The diameter of this wire should be,
say -jV inch, and the weight of the plumb-bob at the bottom
should be, say from 10 Ibs. to 40 Ibs. according to the quality

194 MINE SURVEYING.

of the steel. The plumb-bob should be attached to the wire
when at the bottom of the shaft, so that the breakage of the
wire will entail no danger, because the wires are not qualified
to hold this heavy load for long, and would break with a little
jerk. By the use of a heavy weight, the wire is stretched per-
fectly straight, and is able to resist the effect of the air-current ;
the weights themselves must be protected from the air-current
by being placed in buckets of water, oil, or tar, or in a box, the
wires passing upwards through a hole sufficiently small to
prevent an air-current getting into the box. The wires above
the pit-top must be securely fastened to a steady frame, and, if
there is a wind, must be protected from this as much as possible.

Before the position of the wires at the bottom of the shaft
can be observed, it is necessary to wait until the plumb-bobs
have finished swinging. The wire and plumb-bob may be
likened to a long pendulum. When a pendulum in the latitude
of London swings from left to right, if it is 391383 inches in
length, the swing will occupy exactly one second ; thus, if the
pendulum is lifted by hand and then allowed to drop, it will
be 1 second proceeding away from the hand and 1 second
coming back, or 2 seconds in making the return journey.
The time required for a swing is proportional to the square root
of the length of the pendulum ; thus if, instead of being 39'1383
inches in length, it were 391*383, the period of the swing would
be multiplied by the square root of 10; if the length of the
pendulum were 39138*3 inches, the duration of each swing would
be 1 second x v/1000, or 31 '623 seconds, or the swing and return
would occupy 63*246 seconds, or a little more than a minute.

Taking the case of a mine 1000 feet in depth, or 12,000
inches, we should find the duration of the swing as follows :
Y/39'1383 : \/12000 : : 1 second : x, and the period of the swing
would be 17*5 seconds, and the return swing 35 seconds. When
a pendulum is first started, it is easy to notice that it is not
stationary because of the length of the swing ; as, however, the
length of the swing decreases, it is not so easy to notice whether
it is swinging at all, and the longer the pendulum is the greater
the care required to make sure that the pendulum is stationary.
This can only be ascertained by placing a scale beside the
pendulum when it appears to be quite still, and then to observe
whether the pendulum increases or decreases its distance from
the fixed scale and moves along the scale or keeps at one fixed

CONNECTING SURFACE AND UNDERGROUND SURVEY. 195

point The surveyor, of course, will satisfy himself that the
plumb -bob and wire are swinging quite clear of impediment.
In order that the plumb-bob may be stationary, it is essential
that there should be no vibration in the frame at the surface to
which it is attached, therefore the machinery at the pit-bank
must not be working ; also it must not be too windy, or else
the exposed framework, though solid in appearance, will slightly
rock with the wind ; if there is any continuously moving ma-
chinery in the shafts, such as pumps, care must be taken that
the frame suspending the wires is not in any way subject to
vibration from this machinery, but takes its support indepen-
dently from the solid ground. A very rapid current of air may
also cause the wires to swing, and it may, therefore, be neces-
sary to slacken the ventilation at the time when the observation
is being made.

If the circumstances are such as to permit the above-named
conditions to be fulfilled, the surveyor has now got a means of
connecting the underground and surface surveys with sufficient
accuracy for most purposes. The greater the distance between
the wires, the greater the accuracy ; but there are often serious
practical difficulties in the way of utilizing the entire width of
the shaft for this purpose. Suppose, however, that the distance
between the wires is 100 inches, and the thickness of the wires
is ^V inch, if sufficient care is used, a surveyor may fix his
theodolite on the surface in a line with these two wires in the
following manner : Firstly without any instrument he looks past
the wires and fixes a mark in some convenient place in a line
with these wires, and as near to them as possible without being
too near to focus, say 30 feet from the nearest wire, the instru-
ment is then fixed over this mark on a traversing-table, so that
it can be brought exactly into the line of the two wires. The
surveyor can now range a line of poles in the same direction
as these wires, and connect this line with the rest of the survey,
and carefully establish its bearing in regard to the geographical
or magnetic meridian. The degree of accuracy with which this
can be done may be estimated in the following manner. If the
theodolite on the traversing-table, being at a distance of 30 feet
from the front wire, is so fixed that the second wire is com-
pletely hidden behind the first wire, then it might be possible
to move the second wire to the extent of 0*00431 inch before it
became visible on either side ; this divergence in a length of 100

1 9 6

MINE SURVEYING.

inches is equal to 1 inch in 23,202 inches a degree of accuracy
which is sufficient for the most part. But this error may be
eliminated by placing the theodolite on the other side of the
wires and repeating the observation. The line as now poled
out on the surface should agree with that poled out by the first
fixing of the instrument. In the same way, the underground
survey may be connected to these wires ; by sighting past the
wires the theodolite may be placed with approximate accuracy
in the same line. By means of the screw, the traversing-table
can then be moved until the theodolite is precisely in the line
of these wires. Having clamped the instrument on this line,
the vernier clamp can be loosened and the telescope turned in
the direction of the next sight, the angle read, and the sur-
vey proceeded with as usual, and plotted from the meridian.
If, when the telescope is first set up at the pit-bottom in
line with the wires, the vernier is set at the angle of the
bearing as observed on the surface, then all the subsequent
readings will be correct readings, and will not require further
correction. In case, however, the correct bearing has not been

ascertained, the bearings
recorded can afterwards
be corrected. The sur-
veyor will, of course, make
permanent marks at the
pit-bottom showing the
direction of the line
through the wires.

By Means of Transit
Instrument. In view of
the difficulty in steadying
the wires, many surveyors
prefer to use a theodolite
or other transit instrument
for transferring a line of
survey from the shaft-bot-
tom to the surface, or vice
versa. Taking the former

case, the surveyor finishes his survey at the bottom of the shaft
as shown in Fig. 117. Placing his theodolite over the last mark
at the bottom of the shaft, he clamps the vertical axis with the
telescope in the line of the last sight cd; he now points the

FIG. 117. Transit theodolite transferring line
of sight underground to surface.

The original diagram of the one on page 196 of this
book, exhibiting a mode of connecting underground
workings to the surface by sighting with a Transit
Theodolite up a shaft, is to be found at page 84 of the
work upon Mine Surveying, published by Mr. H. D.
Hoskold, in 1863.

196 MINE SURVEYING.

inches is equal to 1 inch in 23,202 inches a degree of accuracy
which is sufficient for the most part. But this error may be
eliminated by placing the theodolite on the other side of the
wires and repeating the observation. The line as now poled
out on the surface should agree with that poled out by the first
fixing of the instrument. In the same way, the underground
survey may be connected to these wires ; by sighting past the
wires the theodolite may be placed with approximate accuracy
in the same line. By means of the screw, the traversing-table
can then be moved until the theodolite is precisely in the line
of these wires. Braving clamped the instrument on this line,
the vernier clamp can be loosened and the telescope turned in
the direction of the next sight, the angle read, and the sur-
vey proceeded with as usual, and plotted from the meridian.
If, when the telescope is first set up at the pit-bottom in
line with the wires, the vernier is set at the angle of the
bearing as observed on the surface, then all the subsequent
readings will be correct readings, and will not require further
correction. In case, however, the correct bearing has not been

ascertained, the bearings
recorded can afterwards

_, . Tor transtemng a

survey from the shaft-bot-

IIG. 117. Transit theodolite transferring line

of sight underground to surface. tom to the SUriace, or I'ice

versa. Taking the former

CONNECTING SURFACE AND UNDERGROUND SURVEY. 197

telescope to the top of the shaft, using the right-angle eye-piece
for convenience. He may now place a mark as at a upon some
framework, either in or over the shaft, and another mark at b ;
these two marks will then be in the same vertical plane as the
last line of sight in the pit, and a line may afterwards be
produced from these marks by means of a theodolite, or a fine
wire stretched over them, or otherwise.

Another method, shown in Fig. 118, is to place the theodolite

vtTTT^fpr-iTj.

FIG. 118. Transit theodolite transferring line of sight on surface underground.

on a frame over the pit-top and fix the telescope in some con-
venient direction, as nearly as can be judged in the direction of
the underground level or tunnel along which the survey will
have to be continued. A line is poled out on the surface in this
direction and connected with other stations on the survey with
every accuracy; the theodolite is now turned so as to look
straight down the shaft. With an ordinary theodolite and
ordinary tripod stand this cannot be done, because the vertical
axis of the instrument is precisely under the telescope. One of
two things is, therefore, necessary : the theodolite must be
constructed with a telescope at the outer end of the horizontal
axis, so that its plane of rotation is outside the graduated circle,
or else the telescope may be taken off the bearings of the
theodolite and placed on other bearings carried on a plate with
a circular hole in the centre, through which the surveyor can
look downwards. The instrument the surveyor is then using

198 MINE SURVEYING.

is not a theodolite at all, but simply a transit telescope, and this
is all that is required. If this telescope revolves in a truly
vertical plane, or revolves truly on the centre-line of its axis in
any plane, whether strictly vertical or not, a line drawn through
any two stations in that plane will have the same bearing as
a line drawn through any other two stations in the same plane,
providing both the stations (if the plane is not vertical) are on
the same level in each case. It will, however, be well to take
care to level the axis of the telescope very carefully, so that it
will revolve in a strictly vertical plane, and then any difference
in level of the stations will not affect the bearing.

Having fixed the telescope in the most suitable direction, and
marked out the line on the surface, the surveyor now directs his
line of sight to the bottom of the shaft, and fixes two marks in
the same direction as the line marked out on the surface. With
a telescope of ordinary power and a shaft several hundred feet in
depth or more, the only mark that could be clearly distinguished
would be some point very brightly illuminated, as, for instance,
the flame of a lamp. A special lamp may be constructed, with
a narrow wick-tube only T V inch in diameter, and, of course,
a correspondingly small flame. The position of this lamp may
be adjusted by placing it on a frame, movable by means of a
screw. There must, of course, be two such lamps. When the
lamps are fixed in position, the surveyor can take his theodolite
down the pit, and fix it in a line with these two flames, and
continue the survey in the way previously described when using
wires.

The accuracy with which 'this work can be done depends to a
great extent on the power of the telescope used, and the accuracy
with which the telescope revolves in its bearings. To ensure
sufficient accuracy, a special transit instrument should be used
in the case of deep mines and very important surveys. When a
powerful telescope is used, it is not necessary to direct it 011 to
a lamp-flame ; a brightly illuminated mark may permit of more
accurate adjustment, and will not be moved by the wind ; this
mark should be a dark line on a white board, or a white line on
a black board. The limelight, or other bright light, might be
used to throw a brilliant illumination on to these marks, whilst
every other part is sheltered from the illumination. In this
way a survey of the deepest mine may be accurately connected
with the surface.

CONNECTING SURFACE AND UNDERGROUND SURVEY. 199

In an interesting paper contributed to the Federated Institute
of Mining Engineers, Professor Liveing gives the result of his
experience with the transit method. 1

He usually found it advisable to make the connection obser-
vation in the downcast shaft, because the air is there clear, and
has a fairly uniform temperature, which is a matter of great
importance, as avoiding irregular refraction.

At the shaft-bottom he fixes two short battens, A and B
(Fig. 118A), and upon these is placed a horizontal bar of pine.
The middle point of this bar
should be placed perpendicularly
below the centre of the transit
instrument, and the bar is placed
in the direction of the main road
from the shaft-bottom.

Upon this bar, at equal dis-
tances from the centre-points,
are screwed two small wooden
boxes, the top of each is inclined
at 45, and has a square opening
across which two fine copper
wires are stretched diagonally
forming a cross. The thickness
of these wires must vary with the
depth of the shaft and the power
of telescope employed. With a telescope with a 2J-inch aper-
ture, wires of No. 20 B.W.G., about 0*035 inch thick, answer well
for pits not exceeding 200 yards in depth.

In the lower part of this box is fixed a mirror, which reflects
in an upward direction the light of a lamp placed opposite an
opening in the side of the box. These two boxes are placed
upon the bar as far apart as the width of the shaft will permit.
The observation from the surface to those marks should be
repeated at least six times, and the mean of the results
taken.

The wire crosses can be observed both from the surface and
from the underground level.

Professor Liveing records an instance in which he had to
make the connection observation in the case of a shaft 500
yards deep, and where the cross-wires could not be placed more

1 Transactions Federated Institute of Mining Engineers, vol. xyiii. p. 65.

FIG. 118A. Arrangement of marks at
bottom of shaft.

200 MINE SURVEYING.

than 8 feet apart. In this case he replaced the cross-wires
by two small electric lamps, each having small arched filaments,
and these were so fixed that the planes of the filaments were
in the vertical plane joining them, and their axes were inclined
at an angle of 45, so that observations could he taken to them
both from the surface and from the main road underground.

CHAPTER XII.

LEVELLING.

Dumpy Level. To ascertain the relative levels of different
points, the instrument usually employed, called a level, is a
telescope, on the top of which are fixed two ordinary spirit-
levels (see Fig. 119), one long level, 6, fixed parallel to the axis

FIG. 119. Dumpy level.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.')

of the telescope, and also a cross-level, a, at right angles to it.
When the instrument is in correct adjustment, and the spirit-
levels have been adjusted by the levelling-screws so as to bring
the bubbles into the centre, the line of sight past the crossing
of the hairs is a level line.

At one end of the telescope is a diaphragm, /, containing the
webs, and an eye-piece, e, which can be drawn out of the tube
so as to focus on to the hairs in the diaphragm.

Underneath the telescope a compass box and needle are
sometimes placed, provided with a prismatic reader, g, so that
the bearing of lines being levelled may be taken.

The level is screwed on to a tripod similar to that of the

202 MINE SURVEYING.

theodolite ; when circumstances do not permit the use of a
tripod, the level may be placed on a piece of wood or any other
flat surface, feet (d, d) being often provided on the base plate
for this purpose. The level shown in Fig. 119 is the type
known as the "Dumpy."

The levelling-screws may be either three in number, as
shown in Fig. 119, or four, as shown in Fig. 120. In levelling
an instrument with three screws, the telescope is first placed
parallel to two of them and levelled. It is then turned a quarter
of a revolution ; that is to say, one end of the telescope is placed
over the other screw, and it is levelled in this direction. The
operation is repeated until the telescope is perfectly level. In
levelling an instrument with four screws and parallel plates,
the telescope is placed in a line with two opposite screws and

FIG. 120. Y-level. A, clamp for vertical axis; B, bubble-tube; C, screw to adjust
the diaphragm; L, clamp for compass needle; M, milled head screw to adjust
the limb carrying the telescope ; PP, pins to secure telescope in the Y's ;
T, tangent screw for accurate fixing of the telescope.

levelled. It is then turned in line with the other two screws
and levelled. The operation of levelling is performed by
turning opposite screws in opposite directions to each other.
It is generally considered that the three-screw arrangement is
quicker.

If the cross-level already referred to is in accurate adjust-
ment, and is a good length, it is, of course, unnecessary to turn
the level ; but the usual practice is as described.

Y-Level. Another form of level, known as the Y-level, is
shown in Fig. 120. In this type of instrument the telescope
is supported in Y bearings, and can be taken out and reversed.
There is only one level tube, which is parallel to the length

LEVELLING.

203

1L-

of the instrument, and for this reason it is not so quickly

levelled as the dumpy level, as it has

to be first levelled in one direction, and

then turned a quarter of a revolution

and levelled in this direction, to get the

instrument truly horizontal.

The advantage of the Y-level, how-
ever, lies in the fact that, as will be
seen later on, it is capable of being
easily and accurately adjusted.

Levelling-staff. The level is used in
conjunction with the levelling-staff,
which is generally about 16 feet in
length for surface work, and of much
shorter length for underground work.
The staff, as used on the surface, is
generally a wooden tube (see Fig. 121)
about 3 inches wide .and 2 inches thick,
inside which slides a similar but smaller
tube, inside which again slides a
wooden lath. On the face of the staff
is painted a scale of feet, tenths and
hundredths, the measurements starting
from the lower end. Sometimes the
figures on the scale are reversed, as
shown in Fig. 122. By this means the
reading on the staff is seen in its
natural position (this can also be
accomplished with the ordinary staff by
the use of a special eye-piece, but this
reduces the light).

Most surveyors prefer the staff with
the figures the correct way up ; a little
practice soon enables the surveyor to
see them correctly although really in-
verted by the telescope.

Pit Levelling-staff. The staff used
in the mine may be made of special
length to suit some particular seam.

A i ne i i ., FIG. 121. Levelling-staff.

A stan has been made by Linsley, of

Newcastle, consisting of a piece of wood 3 feet long and about

204

MINE SURVEYING.

2J inches wide by f inch thick, at the back of which slides a
lath which, when drawn out, gives a staff 6 feet high. The
lower part of the staff has the scale painted on, but the sliding
lath carries at the top a roller, on which wraps a tape If inch
in width, on which the scale is painted. The roller contains
a spring, which rolls up the tape. As the lath is extended,

FIG. 122. Levelling-staff with
figures reversed.

FIG. 123. Jee's pit levelling-staff.

the tape is unwound and the scale is always in its correct
position. A similar staff, called Jee's pit levelling-staff, is
manufactured by Messrs. John Davis and Son, of Derby, and
is illustrated in Fig. 123.

Mode of using the Level. The instrument is fixed on a
tripod stand and carefully levelled, so that it may revolve in a

LEVELLING. 205

horizontal plane ; the staff is held on sonie mark which is
the base or starting-point of the survey. The level cross-hair
of the telescope appears to cut this staff at some mark which
reads say 1*27 feet; the staff is then taken forward to another
station, and the telescope again directed upon it, when the cross-
hair appears to cut the staff at say 14*56 feet, showing a difference
in level of 13*29. It is thus obvious that the ground at the
first station was 1*27 feet below the level of the cross-hair of the
telescope, and the ground at the second station was 14*56 below
the level of the cross-hair, and therefore the ground at the
second station is 13'29 feet below the ground at the first station.
The staff is left standing at the second station, and the level is
moved forward beyond the staff ; it is then levelled and directed
upon the staff, when the reading is say 0*74 ; the staff is then
moved to the third station, and read, say 15' 62. It is again
obvious that the ground at the second station was 0*74 below the
level of the cross-hairs, and that the ground at the third station
was 15'62 below the level of the cross-hairs, the difference being
14*88. The staff is again left standing whilst the level is moved
forward to the next station, and so on.

When once the telescope has been fixed, it may be convenient
to take the relative levels of a number of stations within view.
The first sight that is taken is called the back sight, and the last
sight that is taken before moving the level is called the fore
sight, and all the other sights are called intermediate sights.
The staff is always left fixed at the station to which the last
fore sight was taken, whilst the level is being'moved and fixed
ready to take another back sight.

Tables X. and XI. are pages from the surveyor's note-book,
showing levellings.

The first column in Tables X. and XI. shows the distance from
the starting-point (that is to say, the place where the staff was
first set) to each station ; the measurement in each case is to
where the staff is placed, as that is the point of which the level
is observed.

In the second column the back sights are placed. The first
position of the staff is always a back sight, and therefore the
first back sight is at the starting-point, or at in the distance
column. The fore sight is the last position of the staff before
the level is moved to another place, and the second back sight
is taken to the staff, where it stood when the first fore sight

206

MINE SURVEYING.

LEVELS TAKEN AT

TABLE X.

FOR NEW ROAD, OCT. 4, 1898.

Total
distance.

Back

sight.

Intenne- Fore
diate sight, sight.

Rise. Fall.

Reduced
level.

Remarks.

Links.
i 13-27

100-00

( Back bight on peg A .
JSee survey-book No.

|9,p.l5,24/Sept./1898.

8-15

5-12

105-12

8-97 i

4-30

104-30

127

9-20

1-09

12-18

112-18

163

6-37

2-83

115-01

249

4-85

4-35

116-53

('Same level as door-sill

308

10-26

1-06

11 1 19 1 f woodman's cottage,
' ) 10 yards west of pro-

(.posed road.

354

1-87

14-75

5-55

106-63

396

4-15

2-28

104-35

430

4-66

2-79

103-84

( Same level as top of

467

9-39

7-52

99-11

/lower hinge hook of

(gate in quarry-field.

553

13-24

11-37

95-26

624

13-87

12-00

94-63

(Fore sight on peg B
\(see above).

24-34

29-71

24-34

5-37

LEVELS TAKEN AT

TABLE XI.
FOB NEW ROAD, OCT. 4, 1898.

Total
distance.

Back
sight.

Interme-
diate sight.

Fore
sight.

Rise.

Fall.

Reduced
level.

Remarks.

Links.

13-27

100-00

Back fright on peg A.

8-15

5-12

105-12

8-97

0-82

104-30

127

9-20

1-09

7-88

112-18

163

6-37

2-83

115-01

249

4-85

1-52

116-53

308

10-26

5-41

111-12

354

1-87

14-75

4-49

106-63

396

4-15

2-28

104-35

430

4-66

_ .

0-51

103-84

467

939

4-73

99-11

553

13-24

3-85

9526

624

13-87

063

94-63

Fore sight on peg B.

24-34

29-71

17-35

22-72

24-34

17-35

5-37

537

Total fall from A to B, 5'37 feet.
Fig. 124 is a section plotted from this page.

LEVELLING.

207

was taken ; and for that reason the back sight of the second
position of the level is shown in the tables on the same line,
and opposite the same distance, as the fore sight of the first
position. Similarly the subsequent back sights are placed in
the same line as the distance and fore sight of the preceding
position.

The student will see, on reference to Table X., that after the
three columns of staff-readings come two columns, one headed
"rise," the other "fall; " if the back sight reading is a larger

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Q

DatumLine

163 24-9 JOS 3S4- 396 4-3O 4-67 53 624-

Vertical scale 40 feet to 1 inch. Horizontal scale 1 chains to 1 inch.

FIG. 124. Section plotted from levels given in Tables X. and XL

figure than the fore sight, the difference comes in the rise column ;
if the fore sight reading is a larger figure than the back sight
reading, the difference comes in the fall column ; the readings
in the intermediate column are compared with the back sight.
In Table XI. the calculations are done in a different manner,
the intermediate sights being treated as back sights and fore
sights. The next column is headed "reduced level," which
shows the relative altitudes of the various stations, and also
their altitude as compared with the datum ; at the head of this
column is placed a figure at the discretion of the surveyor, the

2o8 MINE SURVEYING.

figure to be sufficiently large so that the fall below that level
shall not reduce the original figure to less than 1 ; thus if the
surveyor thinks that the total fall of the section he is about to
level will not be more than 70 or 80 feet, he would put at the
head of the column 100 ; then if the levelling shows that the
ground is falling, the amount of fall is deducted from 100 ; but
if the observations show that the ground is rising, the amount
of rise is added to 100. By putting this figure 100 at the head
of the column, the surveyor is relieved from the necessity he
would otherwise be under of putting the minus sign before the
figures in this column when the level of the ground fell below
the level from which the survey was started. If the total fall
is over 100, the surveyor might substitute 200, 300, or 1000.

To test the accuracy with which he has done the additions
and subtractions, he will add up at the bottom of each page
the total of back sights and the total of fore sights, also the total
rise and the total fall ; if the back sights show a larger total than
the fore sights, he will subtract the latter from the former, and
the difference will show the total rise. He will then subtract
the total under the " fall " column from the total under the
"rise " column, and the result should agree with that obtained
by the subtraction of the fore sights from the back sights ; this
difference should also be the same as that between the bottom
and the top figures in the column of reduced levels. This is
shown in the case of Table XL But in the form of booking
given in Table X., the student must remember, in adding up
the columns of rise and fall, to omit the figures in these columns
that are obtained by means of the intermediate sights, as they
do not affect the total rise and fall.

Elimination of Errors of Adjustment. Whilst the surveyor
should always use instruments that are in correct adjustment
so far as he knows, it is usual, in levelling, so far as possible
to use the instrument in such a manner as to eliminate errors
that might arise owing to the spirit-level not being precisely
parallel to the line of sight or axis of the telescope; thus if the
position of the level is midway between the back sight and fore
sight, then the error in one reading is corrected by a precisely
similar error in the other reading (see Fig. 125). In this case
the level is out of adjustment, so that the back sight reads 3*64,
whereas the correct reading should have been 3*45 ; the fore
sight reads 6'31, whereas the correct reading should have been

LEVELLING.

209

612; but the difference between the two incorrect readings,
2'67 feet, is the same as that between the two correct readings,
so that there is no error in the result. When, however, it is
remembered that the height of the telescope, as commonly used
on the surface, is only about 4 feet, and the length of the staff is
16 feet, it is obvious that, when surveying on an incline, the fore

l?[G. 125. Level out of adjustment ; errors eliminated by fixing level equidistant.

sight may be four times as long as the back sight, and that if the
length of the fore sight is restricted in order to keep the two sights
of equal length, a great deal of time will be lost. The length
of the sights, however, may be nearly equalized by putting the
instrument on one side of the line of survey, as shown in Fig.
126. Here the slope of the hill AB is 1 in 20, and therefore,
if there is a difference of

level of 14 feet between **$

the upper position of the
staff A and the lower posi-
tion of the staff B, the dis-
tance on the line of sur-
vey will be 280 feet. If
the level were put on this
line, it would only be
about 60 feet from the
upper station, and about
220 feet from the lower
station. If, however, the
position of the level is
moved to a distance of 240 feet to one side of the line, the length
of the back sight will then be about 250 feet, and that of the
fore sight about 320 feet, so that the length of the back sight to
the fore sight is about as 3 to 4, and the error that might have
occurred had the telescope been in the line of survey is reduced

Staff
B O

$L$&

220

FIG. 126. Equalizing length of sights.

210 MINE SURVEYING.

to one-third, and therefore will be insignificant, unless the
instrument is very seriously out of adjustment, which ought
not to be the case.

Bench Marks. The student will remember that the staff,
when once placed for the fore sight and the reading taken, has
not to be moved until after the level has been again fixed and
the reading taken ; should the staff be accidentally moved, the
surveyor will have to go back to his last fixed station. It is
a good plan to leave marks at convenient places, such as
walls, flagstones, gate-posts, buildings, or bridges, which he will
be able to recognize, and the exact level of which has been
recorded in his note-book, as shown in Tables X. and XI.
In case of any error, or having to continue an unfinished
survey, these marks are convenient stations from which to
start another series of levels, and also in case the line of
survey should return to the starting-point or cross itself, the
accuracy of the levels can be checked if a second reading is
taken at one of the original marks.

As in surveying, so in levelling, the surveyor cannot consider
his work complete until he has proved the accuracy of it, either
by levelling the same line twice, or by levelling in a circuit
returning to his original station, or by levelling from one mark
the altitude of which has been fixed by a previous survey (such
as the Ordnance Survey) to another mark of which the altitude
has been fixed.

Adjustments. From time to time the surveyor should test his
level, to see that it is in proper adjustment.

Adjustment of Telescope to Vertical Axis. The line of collima-
tion of the telescope of a level or theodolite is the line which
passes through the optical centre of the object-glass and the
intersection of the cross-hairs in the diaphragm. This line
should be at right angles to the vertical axis, so that when the
vertical axis of the instrument is truly vertical, the line of
collimation will be horizontal. In the case of the dumpy level
(shown in Fig. 119), the adjustment of the telescope at right
angles to the vertical axis is made by the maker, the telescope
being rigidly attached to the vertical axis.

In order to test the accuracy of the adjustment, make or find
two firm places at a convenient distance apart (say 200 feet),
each exactly level with the other. Place the telescope half-way
between these places, and in a straight line with them, and

LEVELLING. 211

level it. Take the reading of the staff at each of these marks.
If the vertical axis is at right angles to the telescope, then the
two readings will be the same ; if the two readings differ, the
vertical axis is out of adjustment, and this will involve some
loss of time in levelling the bubble-tube for each sight instead of
only once for each time the level is set up.

In the case of the Y-level (Fig. 120), where the telescope is
movable and the supports are capable of adjustment by means
of screws, the adjustment is made in the following manner : A
distant object (such as a levelling-staff) is sighted, and the
position of the cross-hairs upon this object marked precisely ;
the telescope is then taken out of its Y's and turned end for
end, and replaced and rotated through an arc of 180 on the
vertical axis. If the horizontal cross-hair is still on the same
mark, the telescope and vertical axis are at right angles ; if not,
the attachment to the vertical axis must be adjusted by means
of the screw M (Fig. 120), so as to move the telescope to bring
the cross-hairs half the distance between the two marks on the
staff.

To make the Spirit-level Parallel to the Line of Collimation.
The spirit-level is attached to the telescope by means of screws
at each end, or sometimes by means of a hinge at one end and
screws at the other. By moving these screws, one end of the
bubble-tube may be raised or lowered in relation to the other
end. The level should be strictly parallel to the line of colli-
mation. This parallelism may be tested in the following
manner : The telescope is fixed at a, half-way between the
stations b and c, the distance from a to b being say 60 yards,
and the staff is first read at b and then at c, the position of the
staff at each reading being carefully noted and being on some
hard and immovable place. The level is now moved to the
place c, about six or seven yards from the station b ; the staff is
then read again at the two former stations b and c. If the
difference in the readings is the same as when the level was
half-way between the two stations, it is a sign that the bubble
tube is parallel to the line of sight ; if it is not the same, it is
a sign that the bubble tube is not parallel. Suppose that in the
first reading, when the level was equidistant between b and c,
the difference in levels of the two stations appeared to be 1*2
foot, and that if when the level was at e, the difference in the
readings of the two stations was 1*4, then the bubble-tube must

212 MINE SURVEYING.

be adjusted so that upon again bringing the bubble into the
centre of the tube with the levelling-screws, the difference
between the readings b and c is precisely 1*2, which is the real
difference in level, because, in the first observation, the level
being midway between the two stations, errors due to the
bubble-tube not being parallel to the telescope were eliminated,
because the error was equal in both readings.

The method of adjusting the bubble-tube is first of all to
alter the inclination of the telescope as it stands at station e by
means of the levelling-screws till the readings of the staff in a
line with it show a difference between the two stations b and c
of 1'20. We know that the line of sight is then level. The
bubble-tube must now be adjusted by the screw or hinge attach-
ment to the telescope till it appears level.

Adjustments Preliminary to taking Sights with the Level.
In using the level there are some adjustments which have to
be made continually. In the first place, the tripod must be
firmly fixed, and, if the ground is soft, the legs pushed down so
that they are not likely to sink before the observations are
completed ; the brass head of the tripod must be fixed by the
eye approximately level ; the levelling- screws should be all about
the same length through the upper plate, in order not to put a
strain on the threads of the screws.

The telescope is now directed upon the staff, and the adjust-
ment for focus and parallax is made. The object-glass is on a
sliding tube, which can be moved in and out by means of a rack
and pinion. The nearer the object is to the telescope, the further
the object-glass has to be moved outwards (this is the adjust-
ment for focus). In order that the cross-hairs may be distinctly
seen, the eye-piece, which slides in and out, has to be adjusted
(this is the adjustment for parallax). When both the eye-piece
and the object-glass are correctly adjusted, the cross-hairs seem
clearly and steadily fixed upon the staff in one place, even
though the observer's eye may be moved from side to side or
up and down ; unless this is so, different readings will be taken
according to the position of the eye, and consequently errors
may be made. The bubble must now be brought to the centre
of the tube by means of the levelling-screws, so that the
telescope can be turned in any direction without moving the
bubble, in the manner described at the beginning of this chapter.

Correct Method of holding the Staff. It is important that the

LEVELLING. 213

staff should be held in a strictly vertical line, otherwise there is
an error in the apparent altitude proportionate to the difference
between the radius and the cosine of the angle from the vertical
at which the staff is held; thus, if the staff is sloping back-
wards at an angle of 10, and the reading is 10 feet, the real
height will be 9'848, or an error of T W of a foot; a staff,
however, that is 10 out of truth is obviously not vertical to the
most inexperienced eye. If the inclination of the staff is 5
from the vertical, and the reading is 10 feet, the real height
would be 9'96, or T ^ of a foot less. Any person standing on
one side of a staff can see at once if it is more than 2 out of the
vertical, and that amount of inclination will not seriously affect
the accuracy of the reading. Sometimes a little spirit-level is
fixed to the back of the staff, so that the man holding the staff
may see by the position of the bubble when he is holding it
vertically. The surveyor can tell by the vertical cross-hair if the
staff is leaning to the right or left, but he cannot tell whether
it is leaning to or from him. Sometimes the man holding the
staff is instructed to swing the upper end of it to and from
the surveyor. The vertical position of the staff is given by the
lowest reading.

It is exceedingly important that the man holding the staff
should not carelessly move it after the reading of the fore sight
has been taken. A plan adopted by an old railway surveyor to
impress this on the mind of the labourer holding the staff, was
to give the man half a crown to place on the ground at the
station, the staff on the top of it ; as he is not likely to leave
the half-crown behind, he is not likely to move the staff without
picking up the coin a movement which would probably be
observed.

In taking sights of a chain and upwards in length, the
surveyor can read the height of the cross -hairs on the staff in
feet and decimals. If, however, the staff is close to the level,
the length of the staff within focus may be too short for him
to read the feet, and he may require the staff lifted up to enable
him to see the number of feet below the decimal which he has
already read. He ought to carefully note the decimal before the
staff is lifted, if it is the back sight ; and, if it is the fore sight,
after the staff has been replaced on the ground. There is no
difficulty about instructing the man to lift the staff, as a rule,
because the surveyor is close to the staff. In the case, however,

214

MINE SURVEYING.

of a mine where there is no free space above the staff to permit
of its being lifted, it is common for the man holding the staff
to put his hand about the level of the cross-hairs, and then to
read the red figure, which is the number of feet below his hand,
or, what is better still, to keep his hand on the staff until the
surveyor can come to read the figure him-
self, which involves very little loss of time,
as the staff is only a few yards away from
the level. With the staff shown in Fig. 127
this procedure would be unnecessary, as the
feet-reading is shown three times in every
foot-length.

Curvature of the Earth. Owing to the
curvature of the earth's surface, objects as
viewed through the telescope of a level,
appear lower than they really are. For
instance, if we suppose that the earth is
perfectly circular (a perfect sphere without
any hills or valleys), and that we have a
level carefully adjusted so as to give a
level or horizontal line of sight, then, if
a staff is held some distance away from
the level, it will give a higher reading
than if held near the level, making it
appear that there was a fall. As a matter
of fact, both the points at which the staff
was held would have the same level, as they
would be the same distance from the earth's
centre.

Thus the greater the length of the sight,
the greater the correction to be added to
the apparent level to obtain the actual
level.

Befraction caused by the Atmosphere.
Light always travels in a straight line unless
diverted by the media through which it
passes. In passing through the atmosphere, the ray of light is
refracted (or bent) in such a manner that the object viewed
appears higher than it really is.

Correction for Curvature and Refraction. Molesworth's pocket-
book gives the following useful rule and table :

FIG. 127. Staff with
intermediate foot read-
ings.

LEVELLING.

215

D = distance in statute miles.
C = curvature in feet = -|D 2 (approximately).
C - B = curvature less refraction = fD 2 (approximately).

.D.

C-R.

D. C.

C-R.

Feet.

0-66

0-57

24-00

20-57

96-0

82-0

2-67

2-29

32-67

28-00

130-0

112 ;

6-00

5-14

42-67

36-57

170-0

146-0

10-67

9-14

54-00

46-30

216-0

185-0

16-67

14-29

06-67

57-14

266-7

228-6

The feet given in the above table (under the heading E)
have to be added to each sight which is long enough to require
correction.

A little reflection will make the effect of the curvature of the
earth perfectly clear. When the levelling-instrument is erected
on the tripod stand ready for use, with the proper adjustments
made and the bubble-tube perfectly level, the vertical axis of
the instrument is then a continuation of a radial line drawn
from the centre of the earth to the circumference. The line of
sight of the telescope is a line at right angles to this vertical
axis, and is therefore comparable to the tangent of a circle of
which the radius is the distance from the centre of the instru-
ment to the centre of the earth. The levelling-staff, which is
sighted through the telescope, being held vertically, is pointing
towards the centre of the earth, and is really a continuation of
a straight line drawn from the centre of the earth through the
circumference to where it meets the line of sight of the telescope.
This straight line from the centre of the earth is comparable to
the secant of the angle at the earth's centre. That part of the
staff which is between the surface of the earth and the line of
sight is that part of the line which, added to the radius, makes
up the full length of the secant. This part of the secant, how-
ever, in dealing with arcs of only a few seconds or even a few
degrees in size, is practically identical in length with the versed
sine of the arc, and the length of the tangent in arcs up to 3
differs by only a small fraction from the length of the sine. So
for the purpose of considering the effects of curvature, the length
from the level to the staff may be taken as either the tangent
or the sine of the angle subtended at the earth's centre, which-
ever is more convenient, and the distance as measured on the

216 MINE SURVEYING.

levelling-staff from the line of sight to the ground, may be
recorded as the versed sine. For arcs of less than 10 the versed
sine varies approximately as the square of the number of
degrees, or of the number of minutes or seconds in the arc
respectively. The distance from the level to the staff is pro-
portional to the size of the angle it subtends at the earth's
centre, and that is why the correction for curvature varies
as the square of the distance. It is easy for the student to
satisfy himself what the correction should be. For example,
assume the radius of the earth to be 4000 miles, and the length
of sight to be 10 miles, say from the side of one mountain and
across a valley to the side of another mountain. Then the sine
or tangent is ^%Q = 0*0025, which is the natural sine of an arc
of about 8J minutes. The versed sine of this arc is 0*000003,
that is to say, the versed sine is 0*000003 of the radius of the
earth (4000 miles), and is equal to 63 '36 feet ; so that the mark
sighted to on the mountain, at a distance of 10 miles, is 63 feet
further from the centre of the earth, or, in common parlance,
63 feet higher than the eye of the observer at the telescope.

The above calculation has to be corrected for refraction, as
previously mentioned. The refraction of light rays is the
change in their direction when they pass from one medium to
another, as, for instance, when they pass from air into water,
or when they pass from a layer of air of one density to another
layer of different density. The effect of refraction is to make
bodies appear higher than they really are, and the effect of the
earth's curvature is to make them appear lower than they really
are. The effect of refraction is much less than that of curva-
ture. Eefraction varies as the square of the distance, and for
1 mile is 0*105 foot. Eeferring to the table previously given,
it will be seen that in the case of a sight 1 mile in length,
the correction for curvature and refraction is 0*57 feet. For
\ mile the correction would be about one-fourth of the above
figure, and for J mile about one sixty-fourth of the above
figure, or rather less than 0*01 foot. With an ordinary 14-inch
level it is difficult to read the staff with accuracy at a greater
distance than 220 yards, at which distance the correction would
be insignificant. For this reason, when levelling in the ordinary
way, any correction of this kind can be entirely disregarded.
But supposing that the surveyor could read the staff with a
powerful telescope with minute accuracy, the amount of the

LEVELLING. 217

correction is so small that it would be a waste of time under
ordinary circumstances to take any notice of curvature. Sup-
pose, for instance, that a line was levelled continuously down-
hill for 15 miles, with the back sights about 26 feet long, and
the fore sights about 126 feet long, the total correction would
only amount to about 1 foot. The surveyor will, of course, bear
in mind that if he takes back sights and fore sights of equal
length, the error due to curvature and refraction will correct
itself, and, if the surface is undulating, the errors due to the
uneven lengths of the sights will correct themselves.

Confusion has often arisen in the minds of people from
the natural and prevailing idea that a line at right angles to
a vertical line, and which for ordinary practical purposes is
a level line, is necessarily a level line for geographical purposes.

When the sea is calm, the surface is level ; but it follows the
curve of the earth. In the same way, the surface of a canal is
level ; but it also follows the curve of the earth, so that any
number of lines drawn from the surface of the canal to the
centre of the earth at any points in the canal, are all of the
same length, the water being held in this position by the attrac-
tion of gravitation.

Borchers' Vane Rod. In some mines the vertical measure-
ments are taken from the roof, and not from the floor. Mr. B.
H. Brough, in his book on Mine Surveying, describes a staff
known as Borchers' vane rod, which is a steel rod having a
hook at the upper end. The rod is suspended from hooks fixed
in the roof, and hangs vertically by its own weight; it is
graduated, measuring from the centre of the hook at the top
downwards. A circular disc or target of sheet iron slides up
and down this staff; a line is scratched across the centre of
the target at right angles to the staff, and on this line are
three holes ; two of the holes are 0'4 inch diameter, and in one
of these is fixed a piece of ground glass ; the other hole is 0'07
inch. The surveyor sights to a lamp held behind the disc
opposite the small hole if he is near, and opposite one of the
larger holes if he is some distance off. The assistant moves
the disc up and down the staff, until the illuminated opening
is bisected by the cross-hairs of the level, when the assistant
reads the height below the roof. By this system of suspending
the staff, it is always vertical, and where the road happens to be
level and free from smoke or vapour, long sights may be taken,

218

MINE SURVEYING.

owing to the clearness with which the illuminated hole can be
seen.

Levelling over Rough Ground by Means of Straight-edge and
Spirit-level. For rough work, or very awkward ground such
as a thin seam, the telescope is sometimes dispensed with,
and the surveyor uses an ordinary mason's spirit-level, with
a straight-edge of convenient length, say from 6 to 12 feet,
according to the steepness of the incline (see Fig. 144). One end
of the straight-edge rests on the ground, rail, or sleeper ; the
other end is lifted up in contact with a vertical graduated rule or
staff, until the bubble comes to the centre of the spirit-level on
the straight-edge, when the altitude of the end of the straight-
edge above the ground is read on the foot rule or other vertical
graduated staff. The straight-edge is then moved down the
hill, and one end placed on the spot where the vertical staff
was held, and the operation repeated. This method of work

admits of great accuracy,
and it is obvious that
the accuracy attained is
in exact ratio to the
care employed, provid-
ing the straight-edge is
really straight, and the
spirit-level is accurately
constructed.

Water-level. A water-
level, designed by Messrs.
T. L. Galloway and C.
Z. Bunning, has been
used. 1 This is a modifi-
cation of instruments of
considerable antiquity.
The apparatus, as con-
structed by these gentle-
men, shown in Fig. 128,
consists of two glass
tubes connected by an

indiarubber tube of any convenient length, according to the
steepness of the roads it is intended to level, say 10 to 20 yards.
Each glass tube is fixed in a stand, and has attached to it a

1 North of England Inst. M.K, vol. xxvii. p. 23.

FIG. 128. Water-level.

LEVELLING. 219

scale graduated into feet and hundredths ; coloured water is
put into the tubes, so that when the stands are both on the
same level the water will be half-way up each glass tube ; if
one stand is now placed at a lower level, the water will rise in
that tube and sink in the upper one, and the difference between
the height of the water in the tubes shows the difference in
level ; thus if the water in the upper glass tube reads 0'54, and
that in the lower glass tube reads 3'72, the difference in level
is 3*18. A stop-cock is provided near the bottom of each glass
tube, which is shut whilst the apparatus is being carried from
station to station.

When carefully used, this instrument is capable of giving
accurate results, and it is handy for getting over rough places.

FIG. 128A. The gradient telemeter level.

.The Gradient Telemeter Level, This ingenious instrument is
intended to act both as a telemeter and as a level. Its con-
struction may be gathered by reference to Fig. 128A. The
gradient of any piece of land is ascertained by inclining the
telescope to the same slope as the ground, and the distance is
measured with the aid of a levelling- staff. The angle of inclina-
tion, covered by a given length of staff when observed twice,
gives a measure of the distance.

The value of the instrument lies in the exceedingly ingenious

220 MINE SURVEYING.

manner in which these operations are performed, and in the
rules and tables which are supplied with the instrument.

On reference to the drawing, it will be seen that the instru-
ment is carried on a tripod, has three levelling-screws, and a
horizontal graduated plate.

This horizontal plate revolves on a vertical axis, and carries
with it the whole of the instrument. Inside this vertical axis is
a second axis, which is attached to that part of the instrument
which is above the horizontal plate. This upper part carries
a compass by which the direction of the telescope can be ascer-
tained; it also carries an ordinary Y-level. Attached to the
compass-box is an index or arrow-head, A ; and by means of
the screw G the upper part of the instrument can be clamped
to the horizontal plate H. When proceeding to use the instru-
ment, the arrow A is clamped at zero, and the telescope is
levelled in the ordinary manner, and turned in the direction of
the staff. If the staff is within sight, the level of the station
can be read in the ordinary way. If the staff is too low or too
high, then it will be necessary to unclamp the screw G, and
turn the horizontal plate round until the telescope is inclined
(being carried on an inclined axis) to such an angle that the
staff can be read.

If the horizontal plate is turned until the reading on the staff
is the same as the height of the telescope above the ground, then
the figure on the horizontal plate opposite the arrow-head is the
gradient of the slope. If by turning the horizontal plate two
observations are taken to the staff, so that the readings differ by
5 or 6 feet, a simple calculation enables the distance of the staff
to be found.

The instrument that will measure the distance in this simple
manner, and also give the gradient, and can be used as an ordi-
nary level and give compass-bearings, seems to be very useful. 1

Levelling by Angles. As already stated in Chapter IX.,
pp. 170 to 180, the relative altitudes of the stations in the line
of survey can be ascertained by reading the vertical angle with
the theodolite, or, more roughly, with the dial or clinometer.
The method may be understood by reference to Fig. 129.
Here the theodolite is fixed at the top of a long but moderate
slope, and at the foot of a steep incline. The line of collimation

1 Further particulars can be ascertained from the pamphlet, which can be
obtained from the maker, Mr. L. Casella, 147, Holborn Bars, London, E.G.

LEVELLING.

221

is fixed perfectly level with the vernier of the vertical circle
at zero ; the telescope is now directed to a staff at the bottom
of the hill, on which is a cross-bar the same height above the
ground as the telescope ; the angle of depression read, 4 34',
is the slope of the incline, and the distance measured is the
hypothenuse of a triangle of which the horizontal distance is
the base and the vertical elevation is the perpendicular, or the
measured distance may be considered the radius of the arc, and

Station/

FIG. 129. Levelling by angles.

the vertical distance is the sine and the horizontal distance
the cosine. Half-way between the bottom of the hill and the
instrument is a depression ; the levelling-staff is held in this
depression, and the height read, which is 12*56 ; the height
of the theodolite was 4'4, therefore the depression is 8*16 below
the line of sight. This depression can, therefore, be drawn on
the plotted section. The telescope is now directed to the staff

Vertical angle.

From

Inclined length.

R = rising.

Staff-readings.

F = falling.

Feet.

0004-40 2704-40

Station 1

Station 2

Feet.
550

4 34' K.

1204-90 4206-00
1907-00 5504-40

2308-00

IOO4'OO 1904-40

490

15 14' K.

1502-00 490-4-40

1753-00

270

6 7' F,

Uniform slope

950

3 17' F.

' V

FIG. 130. Mode of booking when levelling by angles.

higher up the hill, and the angle read, which is 15 14'. There
are several knobs and depressions of the ground on this line which

222

MINE SURVEYING.

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LEVELLING.

223

are measured by reading the depth below the line of sight. The
instrument is now moved forward further up the hill, and fixed
within sight of the last staff, and the operation repeated.

In levelling by means of angles the sight may be very long,
and, therefore, corrections for curvature may be required.

The mode of booking is shown in Fig. 130, and the
calculations in Fig. 131, and the plotted section in Fig. 132.

The intermediate staff-readings have not been plotted on
Fig. 132, as it is drawn to too small a scale.

DATUM
LINE

200 +00

600

800 1000 1200 14-00 1600 1800 2000 2200

FIG. 132. Section plotted from Figs. 130 and 131. The lower line represents the
surface as plotted with both horizontal and vertical scales of 500 feet to 1 inch;
the upper line as plotted with a horizontal scale of 500 feet to 1 inch, and a
vertical scale of 100 feet to 1 inch.

The figure shows two sections, each plotted from the same
datum. The smaller section is plotted to a natural scale ; that
is to say, the altitudes and the horizontal lengths are both
plotted on the same scale, viz. 500 feet to 1 inch. The large
section is plotted to a distorted scale, the horizontal scale being
500 feet to 1 inch, and the vertical scale 100 feet to 1 inch.

It is usual to plot sections of the surface, taken for the

224 MINE SURVEYING.

purpose of a proposed road or railway, on a distorted scale, in
order that irregularities of the surface may be clearly shown.
For such a section a horizontal scale of 2 chains to 1 inch, and
a vertical scale of 20 feet to 1 inch is convenient, and a similar
ratio for larger or smaller scales.

For sections made for geological or mining purposes, a
natural scale is to be preferred, as a distorted scale presents
a confusing and therefore a misleading picture.

Measuring Altitudes by Traversing in a Vertical Plane, The
use of the bubble-tube on the theodolite may be dispensed with
if, instead of merely reading the angle of depression or elevation
from the horizontal as ascertained by the spirit-level, the angles
are observed as a traverse in a vertical plane using the first line
of sight as a base. In this case the theodolite is fixed at b,
looking back to the station a ; the relative levels a and b have
been previously carefully ascertained by ordinary spirit-levelling,
and therefore the angle of depression can be calculated. If the
instrument has a bubble-tube in proper adjustment, the angle
as observed will be the same, after setting the line of collima-
tion level with the vernier at zero, and directing the telescope
to a point the same height above station a that the telescope is
above b. The telescope is now reversed on the horizontal axis,
and the fore sight observed to the station c, the angle of eleva-
tion being read, the cross-hairs being fixed on the staff at the
same height above c as the telescope is above b. The theodolite
is now moved forward to c and fixed over the station, and the
staff is held up at b ; the telescope is directed so that the cross-
hair cuts the staff at the same height above the station b as the
theodolite is above the station at c, though not necessarily at
the same height as when the theodolite was at b and the staff
at c. The vernier is now fixed at the angle of elevation read
when the theodolite was at b looking towards c ; if the instru-
ment has been levelled, the cross-hairs in the telescope should
now coincide with the point b, but if not, the telescope may be
brought down on to the object b by means of the two screws
that move the arc to which the vernier circle can be clamped.
The vernier circle is now undamped, and the telescope reversed
and fixed on the upper station d, and the angle read. In this
way, the use of the spirit-level on the telescope is merely a
check, and is not essential. This plan, however, is not to be
recommended in preference to the use of the spirit-level at

LEVELLING.

225

each station, because any mistake made in the reading of any
one angle is multiplied by the entire length of the survey,

whereas if the spirit-level is used every time the instrument
is set up, and all the angles measured from the horizontal at
each station, the errors in reading from that station are

226 MINE SURVEYING.

confined to the distances measured from that station to the next.
In a traverse of this kind the correction for curvature and
refraction must be made as if the whole length of the traverse
was one sight.

Calculation of Heights from Observed Angles, the Horizontal
Distance being known, The altitudes of various stations, the
distances of which from the instrument can be determined by
reference to some plan, can also be conveniently obtained
approximately by the theodolite, as in Fig. 133. Here the
theodolite is fixed at a, a known spot on the plan ; b, c, d, and
e are also marked on the plan ; the angles of elevation may
thus be read, say, b, 6 10' ; c, 14 5' ; d, 15 50' ; e, 22 10'. The
lengths ab'\ ac', ad', and ae', which are known from the plan, may
be considered as radii of the corresponding arcs, and the vertical
altitudes bb', cc, dd', ee' are tangents, the value of which is found
by multiplying the natural tangent of the angle by the corre-
sponding radius, thus

Angle of elevation of 6 = 6 10' nat. tangent = 0-1080462 x 100 = 10-8 feet
e=14 5' =0-2508734x150= 37'63
d = 15 50' = 2835999 x 220 = 62-39
' e = 22 10' ,, = 0-4074139 x 425 = 173 15

For long sights the correction for curvature must be made
(see p. 214).

The method of levelling just described with the theodolite
can be done with other instruments of less precision, as, for

FIG. 133 A. Abney's level.

instance, by means of the dial with a vertical semicircle or
circle, by means of the box sextant, by the clinometer, or by
an Abney's level.

Abney's Level. An illustration of Abney's level is given in

LEVELLING. 227

Fig. 133A. It consists of a tube, c, provided with eye-piece, a, and
cross-hairs, I. Attached to the tube is a graduated semicircle, d,
and at the centre of this is an axis carrying a small bubble-
tube, c', which can be revolved ; an index with vernier shows the
inclination. Across half of the sight-tube is a reflector, adjusted
at an angle of 45, so that when the bubble is in the centre of
its run, its reflection is seen by the eye of the observer. It will
thus be seen that if a sight is taken to some object, and the
bubble-tube is moved till the bubble appears in the centre,
the vernier will record the angle of elevation or depression of
the object sighted.

Advantage of Levelling by Angles. The advantage of levelling
by angles is only where the inclination is considerable ; if the
inclination is such that sights of 5 to 10 chains can be taken
with the ordinary level, no time is gained by taking the angles ;
but where the inclination is such that the length of sights is
reduced with a 16-feet staff to a couple of chains, the levelling
process demands a good deal of time, and where as is not
infrequently the case, especially in mines the length of sights
is reduced to less than half a chain, the levelling process is
a very slow one indeed. The speed of levelling by angles is,
except for very steep roads, independent of the inclination, but
is limited by the uniformity of the incline ; the altitude of
a uniform slope of any length within the clear vision of the
telescope can be measured with the theodolite. This renders
this mode of levelling particularly useful for geological purposes,
and for preliminary surveys where minute accuracy is not
required. It must be borne in mind that the longer the sights
the larger the errors likely to be made.

Using Theodolite for Ordinary Levelling. The theodolite can
be used in the same way as an ordinary level by clamping the
vertical circle at zero and bringing the bubble level in the
usual way with the screws on the parallel plates or tripod.

Contouring. Contour lines are marked upon some of the
maps of the British Ordnance Survey. A contour line is so
called because it is a level line which, like a canal, follows the
contour of the surface. A contour line may be marked out on
the surface of the ground in the following manner : Let the
level be fixed at any point, say a (Fig. 134), and let the staff be
held at the point b upon a peg, the top of which is nearly level
with the surface of the ground, and which is, say, 225 feet above

228 MINE SURVEYING.

the sea. The cross-hairs read the figure 10'2 on the staff.
The staff is now moved in the direction of the point c, which
is distant, say 1 chain. 'The assistant holds the lower end of
the staff close to the surface of the ground, and walks up and
down hill as directed by the surveyor until the cross-hair of the
telescope is in line with the figure 10 2 on the staff ; the ground
is here 10'2 feet below the level of the telescope, and therefore
it is at the same level as the top of the peg b. A peg may be
driven down here. The staff is then moved to another point,
d, and the place is found where the cross-hair of the telescope

FIG. 131. Method of contouring.

reads 10*2, as before, when another peg is put down. In this
way as many pegs are put down as are within sight of the
telescope on the same level. A survey may subsequently be
made of these pegs, and their positions marked on the plan ;
a line drawn on the plan from peg to peg will be a contour
line. The surveyor, having carried this line as far as it is
required, will then level up the hill, say 25 feet, and fix a peg
at w, 25 feet above the peg b ; he will then proceed to range
a line of pegs, m, n, o, etc., which are on the contour line 250
feet above the sea.

In the same way, contour lines may be shown on a mining
plan, but since the view of the surveyor in a mine is confined
to the narrow road in which he stands, the only method of
contouring is to take levels of each road and mark them in
writing in the way shown in Fig. 135. Here every change of
level of 10 feet is marked with a dot, and the altitude shown in
figures, the figures giving either the depth below some station,
such as the shaft-top, or else the Ordnance datum is used,
the. correct distance of the shaft-bottom above or below Ordnance
datum having first been carefully obtained.

All the marks of equal altitude may now be connected by
lines. It is obvious that where the seam is steep these lines

LEVELLING.

229

%.}'

230

MINE SURVEYING.

will come close together, and where the seam is flat they will
be a long way apart. The universal practice of contouring
would result in many economies.

-XI

CM
CM

N
CO

O
CO

O
I/)

CM
CM

o
o

DATUM LINE 1OO ft. above

FIG. 136. Plan of surface, showing contours and section plotted from same.
Horizontal scale, 6 inches to 1 mile ; vertical scale, 1 inch =100 feet.

The surveyor should know how to draw a section from a

LEVELLING.

231

contoured plan. Fig. 136 shows a plan of the surface with
the surface contours in dotted lines; a line is marked across
the plan, and the corresponding section showing the changes in
level is also drawn.

levelling by Barometer. The barometer is of great use to
explorers, enabling them to ascertain the approximate altitude
of any place above the sea-level. The theory of barometric
levelling may be best understood by reference to Fig. 137. In
this case a section is shown of part of the earth's surface with
the atmospheric covering. The thickness of the air, though
liable to occasional variation, is usually fairly constant at all
seasons of the year, and the weight of the air at the sea-level
is on the average about 14'7 Ibs. to the square inch, or nearly

FIG. 137. Theory of barometric levelling. The shading represents
the atmosphere.

15 Ibs. This is equal to the weight of a column of mercury
1 inch square and 30 inches high. (Mercury weighs (at 32 F.)
0'491 Ib. per cubic inch.) Owing to atmospheric disturbances,
the thickness of air over any particular place is occasionally
reduced about 10 per cent., or say down to 28 inches, and
occasionally increased to nearly 31 inches. A very low reading,
however, seldom lasts long, the ordinary variation in Great
Britain at sea-level not exceeding 3 per cent., or say the
barometer is between 29 and 30 inches, the average height of
the barometer at sea-level being, say, 29'95 inches.

On ascending, Atmospheric Pressure falls; descending, Atmo-
spheric Pressure increases. It is evident that if the observer
ascends a hill, he will have a certain weight of air below him
varying with the elevation he has attained, and since the total
weight of air is constant, the weight of air above him must
be correspondingly reduced. If, therefore, he can ascertain the
weight of air above, he can, by subtraction from the total weight,
obtain the amount of air below him; this is the method of
barometric levelling. At each station, the altitude of which
is required, the observer measures the weight of air above, then

232 MINE SURVEYING.

subtracts that quantity from the total weight of the atmosphere
at sea-level, the difference being the weight of air between the
station of the observer and sea-level.

Explanation of Barometer. The barometer is simply a weigh-
ing-machine applied to weighing the atmosphere. The weight
of a column of air is equal to the pressure of a column of
equal size over the area of the base of the column ; thus if
a column of air the height of the atmosphere and 1 inch
square has a pressure of 15 Ibs., then 15 Ibs. is the weight of
a column of air of which the cross-section is 1 square inch
and the height is equal to the height of the atmosphere ; thus
in ascertaining the pressure of the air we ascertain its weight.

The mercurial barometer (see Fig. 138) consists of a long
tube, say 36 inches long, one end of which is sealed, and the
other bent round and enlarged to form a cup,
The tube is placed vertically with the top of the
cup upwards ; the cup is filled with mercury, or
quicksilver, as it is sometimes called. By a pro-
cess which it is not necessary here to describe,
all the air has been removed from the tube, but
the air is present on the surface of the mercury
in the cup, and presses it down. As the tube
is curved, the mercury, as it goes down from the
cup, must rise up the long vertical leg, and it
continues to rise until the weight of mercury in
the tube above the level of the mercury in the
cup has a pressure per square inch equal to
the pressure of the atmosphere per square inch.

It will be understood by the student that up
to the level of the top of the mercury in the cup,
the mercury in the tube and the mercury in the
cup balance ; above that level on the cup side
there is no mercury, and on the tube side there
FIG isJT Sim le * s no atmosphere ; therefore the mercury in the
barometer. tube has to balance the atmosphere. The cup is
made very large as compared with the tube, in
order that a great variation in the height of the column of
mercury in the tube may take place with a very small variation
in the. height of the mercury in the cup. As already stated, at
the sea-level 30 inches of mercury (29*95 inches in England)
balance the atmosphere on the average. At a higher level,

LEVELLING. 233

say 1000 feet, the column of air above the cup is less, con-
sequently the pressure of the air on the top of the cup is less,
and a less column of mercury is required to balance this
pressure ; the mercury therefore falls to the extent of the weight
of the 1000 feet of air which are below the cup. This weight,
if the barometer reading at sea-level is 30 inches, and the tem-
perature 52, will be equivalent to a pressure of about 0*541 Ib.
per square inch, equal to a column of mercury about 1*1 inch
high, and the barometer therefore will read 30 inches I'l inch,
or about 28*9 inches. Therefore, if the barometer reads 28*9,
the observer knows that there is a weight of air below him equal
to I'l inch of mercury, which, if the temperature is 52, and the
barometer at the sea-level 30, is equal to a column of air about
1000 feet in height.

It is, however, necessary to correct the above calculation
by the consideration that the column of air 1000 feet high will
not have the same density throughout ; thus, whilst 1 cubic foot
at the sea-level would weigh 0*077 Ib., 1 cubic foot at the
1000-feet level would weigh 0*0753 Ib., and the average weight of
a cubic foot of .air in the whole distance would be the mean
of these two figures, or 0*07615 Ib., and the weight of a column
of air 1000 feet high and 1 foot square at the base would be
76*15 Ibs., dividing this by 144, we get the weight of a column
of air 1 inch square at the base, which is about 0*529 Ib.

Assuming the mercurial column at the sea-level to be 30
inches, then the fall of the column at the 1000-feet altitude will be
found by the following rule of three sum : 14*7 : 0*529 : : 30 : x.
Here x = 1*08 inch.

In a similar manner, we can calculate the amount the
barometer will fall for any other elevation more or less than
1000 feet, and also for any depression. The student will
readily see that here is a means of calculating the height
that a barometer is raised or the depth that it is depressed
by the corresponding fall or rise of the mercurial column;
thus, should he walk up a mountain and observe that the
barometer has fallen from 30 inches when he was at the
base to 28'92 inches at the top, he knows that the height of
the mountain is 1000 feet, that is to say, assuming that the
temperature of the air is the same as in the previous observa-
tions, namely, 52. Should, however, the temperature be
different, then the height will not be 1000 feet, but it will

234 MINE SURVEYING.

be more or less than 1000 feet, because 1000 feet of air at
42 weigh more than the same volume at 52, and, of course,
would have a greater effect upon the mercurial column ; thus,
in calculating the height of a hill or the depth of a pit, it is
absolutely necessary always to take the temperature of the air,
not only at the upper and lower stations, but at intermediate
places, so as to arrive at the mean temperature of the air.

The correction for temperature must be made in accordance
with the following ascertained rules. If air having a temperature
of F. is heated to a temperature of 1 F., it will expand T -l ,,
of its volume, and if it is heated to any other temperature,
say 100, the expansion will be in the same ratio, or ]
of its volume. If a volume of 459 cubic feet of air at is
raised to a temperature of 1 (pressure constant), it will occupy
a volume of 460 cubic feet ; if it is raised to a temperature
of 100, it will occupy a volume of 459 + Hir * 459 = 559 -
In this way the relative volumes of the same weight of air for
any difference in temperature can be at once ascertained by
adding the observed temperature to 459. Thus taking four
temperatures 0, 32, 41, 71 the volumes would be 459, 491,
500, and 530, and the relative densities will be in the inverse
ratio ; thus the weight of 1000 feet of air at 32 : weight of
1000 feet of air at 41 : : 500 : 491 ; and again, the weight
of 1000 feet of air at 32 : weight of 1000 feet of air- at
71 : : 530 : 491.

As freezing-point is a temperature that can be easily verified,
the expansion of air for an increase in temperature of 1 F. is
often spoken of as the -^y part of its volume at freezing ; it would
be quite as convenient to say that the expansion of air was T thr
part of its volume at 41 for every increment of 1, 500 being a
much more convenient figure for division than 491 or 459.

Supposing that, in observing the barometer on the hill
referred to, the temperature was found to be 60 at the bottom
and 58 at the top, or an average temperature of 59, or 7
higher than the previously assumed temperature of 52, then
the air will, of course, have expanded : at 52 temperature the
volume of the air will have expanded from zero -$, making
a volume of 511 ; if the temperature rises to 59, the expansion
will be -^Y of its volume at 52, increasing the volume to 518.
The density of the air is inversely as the temperature, thus the
density of the air at 59 : the density of the air at 52 : : 511 : 518;

LEVELLING.

235

then the height of the column will be increased in the same
proportion : 511 : 518 : : 1000 : 1013-70 feet. If, however, the
temperature, instead of being increased from 52 to 59, had
been decreased to 41, the density of the air would have been
increased in the ratio of 500 to 511, and the height of the column
would have been decreased in the same ratio, that is to say,
511 : 500 : : 1000 ; 978-47 feet,

Compensated Barometers. The mercury itself is affected by
temperature ; thus a column of mercury 30 inches high and 70
temperature weighs much less than a column of mercury 30
inches high and 32 temperature, therefore the barometric
readings must be corrected for temperature. Mercury expands
with great regularity, the expansion between freezing-point and
boiling-point, that is, between 32 and 212 F., or a rise of 180,
is 0*018153, about -V, or, taking a column 30 inches high,
ff inch, and the expansion for 18 would be -f w inch ;
thus between freezing-point and 50 temperature, the baro-
metric column would rise -/ T inch, whilst the atmospheric
pressure remained constant. For a rise of 1 the expansion
would be 0*0001, or T oihMr; for a column 30 inches high the
expansion for 1 would be x^VW or 0*003 ; thus, the correction
for every rise of temperature of 1 above the standard is approxi-
mately a reduction of ^-3- for every degree,
that is to say, assuming the standard tem-
perature to be 52, and the actual tempera-
ture 53, and the barometric reading 30-003
inches, this reading must be corrected to 30
inches. If, however, the actual temperature
were 51, and the barometric reading was
29*997, this reading must be increased by the
addition of 0*003, which would make the correct
reading 30 inches.

Some mercurial barometers have a means
of correction for temperature by adjusting the
height of the mercurial cistern for various
temperatures ; this, however, is not usual. A
carefully made barometer generally contains
the mercury in a glass cup, which allows of
the level of the mercury within being seen. The bottom of the
cylinder is made of flexible leather, DB, and can be raised or
lowered by the screw C (Fig. 139). At the top of the cup is an

FIG. 139. Arrange-
ment for adjusting
the height of the
mercury in the cis-
tern of a barometer.

236

MINE SURVEYING.

ivory pointer, A, and before taking an observation, the level

of the mercury is care-
fully adjusted to this
mark, which corresponds
with zero on the scale,
and the correction for
temperature is made by
calculation.

Portable Barometer.
In order that the baro-
meter may be portable,
the flexible diaphragm
is raised by the screw
until the mercury is
pressed to the top of the
cup, the opening to the
atmosphere being closed;
by the same operation
the long glass column is
also filled with mercury,
so that there is nothing
to shake about. The
barometer is fixed in a
strong wooden or metal
tube, and a light tripod
stand is carried by which
it can be suspended in
a vertical position (see
Fig. 140). 1

Aneroid Barometer.
The most portable form
of barometer is called an
aneroid. In this case,
instead of the mercurial
tube, there is a metallic
box from which the at-
mosphere has been par-

F, G . HO,- J-ortable barometer. tiaU y exhausted; the

cover of the box either
itself forms a spring, or a metallic spring is attached to the

1 The illustration shows Negrctti and Zambra's mountain barometer.

LEVELLING. 237

cover and prevents it from collapsing. When the pressure of
the atmosphere increases, the box-cover is pressed in ; when
the pressure of the atmosphere decreases, the spring causes the
box-cover to come out. By means of multiplying-gear, the move-
ment of the box-cover is shown by a pointer on a dial-plate.
These instruments may be made to work with great nicety and
regularity ; but they must be carefully tested from time to time
. by means of a mercurial barometer. The instrument is made
in sizes from 2 inches diameter up to about 5 inches diameter ;
if the case is made of aluminium, the latter size is quite portable,
and is suitable for levelling operations, either on the surface or
in the mine, in cases where an error in level of say 10 or 20 feet
is not material.

With a well-tried 5 -inch aneroid, levellings may be taken to
within 10 feet of the correct level, and if the levellings are
repeated four or five times, the error may be reduced from
10 feet to 2 or 3 feet, or even less ; but it must be remembered
that whilst in some cases the levelling with the aneroid is
correct to a foot, in other cases, even with the best aneroid,
there may be an error of 10 feet, and therefore this instrument
must not be used where great accuracy is required.

Fixed-scale Barometer. It is convenient for the surveyor to
have an approximate rule always ready, either in his head or
in his note-book, and for this purpose a scale may be calculated to
suit the average temperature. English aneroids are usually
fitted with a scale showing the altitude in feet above the sea-level
for any given barometric pressure with an average atmospheric
temperature of 50.

50 is rather more than the average temperature of the air
on the surface of the earth in the latitude of Yorkshire, taking
the average of winter and summer, the actual average at Brad-
ford being 49'3. 1 At Greenwich the mean average temperature,
according to Glaisher, is 49'2; Dresden, 47*3; Moscow, 38*5;
Eome, 59'7 ; Jamaica, 79. 2

The mechanism of the best aneroids is compensated for
variations of temperature in the instrument itself, so that the
reading will be the same, whether it is inside a warm room or
out of doors in the frost, provided that the atmospheric pressure
is the same in each case. When the atmospheric temperature

1 Table published by Messrs. J. McLandsborougli, M.I.C.E., etc., and A. E.
Preston, M.I.C.E.

2 Box on Heat.

2 3 8

MINE SURVEYING.

happens to be 50, no calculation at all is necessary in levelling
with this instrument (that is, with the altitude scale attached as
named above), except the subtraction of the lesser height from
the greater, to show the difference in level ; thus, if station A
reads 324 feet on the barometric scale, and station B 560 feet on
the same scale, the difference in level is 560 824 = 236 feet.

The difference of atmospheric pressure, however, between
two different stations is less at high temperatures than it is
at low ones, consequently the scale needs correcting. The
variations of altitude shown by the fixed scale at a less tem-
perature than 50 are too great, and at higher temperatures are
too small. Fig. 140A shows the correction.

FIG. 140A. Diagram giving correction for mean temperature.
(From Gribble's Preliminary Survey.)

It will be seen that with the mean temperature at 53 no
correction is necessary. With the mean or average temperature
as 85, the reading on the scale of the aneroid must be multi-
plied by T07 in order to get a correct altitude.

Levelling by Boiling-point Thermometer. The temperature
at which water boils in an open vessel is dependent on the
pressure of the atmosphere, so that when the atmospheric
pressure is less, the temperature of boiling water, or the
temperature of steam at the atmospheric pressure, is also less ;
and inversely, when the pressure increases, the temperature at
which water boils, or the temperature of the steam at atmo-
spheric pressure, is also greater. Thus, whilst under the ordinary
atmospheric pressure water boils when it is heated to 212,
if this water is put into a receiver in which the atmospheric

LEVELLING.

239

pressure is reduced by means of an air-pump to say 5 inches
of mercury, then it will boil at a temperature of 134. On
the other hand, if water is put into a well-made steel boiler,
and subjected to a pressure of ten atmospheres, it will not boil
until a temperature of 357 F. is reached. This quality of
water (and other liquids) has been utilized for the purpose of
measuring the atmospheric pressure, numerous experiments
having determined the exact temperatures at which water
vaporizes for a great number of pressures.

Table XII. 1 shows the temperature at which water boils,
that is, the temperature of the steam given off by the boiling
water, for pressures varying between 17 inches of mercury and
31 inches of mercury.

TABLE XII.

TEMPERATURE AT WHICH WATEB BOILS FOR PRESSURES VARYING BETWEEN 17 INCHES
OF MERCURY AND 31 INCHES OF MERCURY.

Pressure iu Boiling- ; Pressure in Boiling-
inches of point. inches of
mercury. Fahr. mercury.

17-048 185

21:038

18-000 187-5

21-530

18-512 188-8

22-033

19-036 190-1

22-498 1

19-490

191-2

23-019

20-037

192-5

23-502 i

20-511

193-6

24-012 i

Boiling-

Pressure in

Boiling-

point.

inches of

point.

Fahr.

mercury.

Fahr.

194-8

! 24492

202'1

195-9

25-000

203-1

197-0

i 25-517

204-1

198-0

! 26-043

205-1

199-1

: 26-523

206-0

200-1

27-012

206-9

201-2

27-507

207-8

Pressure in i Boiling-
inches of point,
mercury. Fahr.

28-011
28-521
29-040
29-508
30-041
30-522
31-010

208-7
209-6
210-5
2 LI -3
212-2
213-0
2138

Calculation of Altitude by Boiling-point Thermometer. In order
to ascertain the difference of altitudes corresponding with any
difference of pressure or with any difference in the temperature
of the boiling-point, the following rule, given by Theodore G.
Gribble, is useful : 2

Rule. Let B = temperature of boiling-point in degrees F.
deducted from 212 ; H = height of station above sea-level ;
K = 540 for a mean temperature of intermediate air of 53, and
varying as explained below. H = KB + B 2 .

EXAMPLE. Boiling-points, 211-37, 210-14; the nxeari temperature of the
atmosphere, 82 F. : required the difference of elevation.

H = 540 x 1-064 x 63 + 0-63 2 = 362-37
H' = 540 x 1-064 x 1-86 + 1 86 2 = 1072-14

Ans. Difference in feet 709'77

1 From Hints to Travellers.

2 Preliminary Survey (Longmans, Green, and Co.).

240

MINE SURVEYING.

In the above example, K is 540. If the mean temperature
had been 53, no correction would be necessary ; the mean
temperature, however, is 82, consequently K must be increased,
and the multiplier is found from Fig. 140A to be T064,
which is the correction made on account of the temperature of
the air ; the figure 0'63 is the difference between 212 arid
211-37 ; and 0'63 2 is the square of this difference ; the figure 1'86
is the difference between 210'14 and 212.

The boiling-point thermometer is often constructed for use
with a spirit-lamp and small portable boiler
and telescopic tube, the whole of the apparatus
fitting into a circular tin case 6 inches long
and 2 inches diameter. The mode of using is
shown in Fig. 141.

Method of Levelling by means of Barometer
or Boiling-point Thermometer. A single obser-
vation of the barometer or boiling-point ther-
mometer does not give the altitude of any
station that may be observed ; it only gives the
pressure of the atmosphere at that particular
time, and this, as is well known, may vary from
hour to hour and day to day. All that can be
known from the observation of these instruments
is the comparative pressure of the atmosphere
at different places ; thus if the surveyor starts
from the sea-level at 6 a.m., observing the
barometer (or boiling-point thermometer), and
also recording the temperature of the atmo-
sphere, he may proceed up or down hill, observ-
ing the barometer at every change of inclination,
noting the station and atmospheric tempera-
ture ; returning in the afternoon by the same
rou te, he may again observe the instruments
at the same stations as in the morning.
If it is apparent that the atmospheric pressure has been
constant all day, the relative levels of all the various stations
can be calculated from the observations made. It might, how-
ever, not improbably happen that on returning at night to the
starting-point of the morning, the barometer reading is, say
\ inch lower than in the morning ; it is obvious that all the
readings made will have to be corrected for this variation in the

FIG. 141. Boiling-
point thermometer.

LEVELLING. 241

total atmospheric pressure, and the surveyor, if working single-
handed, may have means for facilitating this correction. For
instance, if, at noonday, having finished his outward journey, he
observes the barometer, then, remaining at the same place for
one hour, he observes the barometer again, he will see if it
is stationary. If it has fallen, say T V inch, he will note the
circumstance; again, on the return journey, he will note that
the barometer shows continuous signs of falling as compared
with the observations made in his outward march. In order
to judge of the rate at which the barometer is falling, the
hour of each observation should be noted. In this way the
surveyor will ascertain whether the fall in the atmospheric
pressure of \ mc ^ which has occurred during the day is in
consequence of a regular decline or a sudden drop. If it is a
regular decline, the corrections in the readings can be easily
made ; suppose the decline to be at the rate of T V inch per hour,
then the readings as observed must be increased by T V inch for
every hour that has elapsed since the first reading ; if, however,
the fall has occurred suddenly, say during the last hour, then
all the readings taken up till then require no correction.

Levelling with Two Observers with One Fixed and One Movable
Barometer. If in the case above described a barometer had been
fixed at the starting-point, and an assistant left there, he would
have observed at every hour, or at more frequent intervals,
the pressure and temperature of the atmosphere ; and the sur-
veyor would have been able to correct all his observations by
the rise and fall of the barometer as read by his assistant. Thus,
if at 6 a.m. the stationary barometer reads 30 inches, and if at 8
it reads 29'95 ; and at 10, 29'9 ; at 12, 29*85 ; at 2 p.m., 29*9 ; at
4, 29*95 ; and at 6, 30 ; the surveyor will correct his barometric
readings as follows : Suppose his reading at 8 a.m. was 29, he
will correct it to 29*05 ; if at 10 a.m. his reading was 28*50, he
will correct it to 28*60 ; if at noon his reading was 28, he will
correct it to 28*15 ; if at 2 p.m. his reading was 27*50, he will
correct it to 27*60 ; if at 4 his reading was 28 '50, he will correct
it to 28'55, and at 6 p.m. his reading will need no correction.
For any intermediate observations he will make a correction on
the assumption that the variation of pressure has been going
on at the same rate between the hours observed.

Levelling with Two Observers and Two Portable Barometers.
A still better method of levelling is for the assistant to follow

242 MINE SURVEYING.

the surveyor on his route. Before starting, two barometers
and thermometers are compared, and the watches of the sur-
veyor and his assistant set to read the same time. The
surveyor now starts, and on reaching the station whose altitude
he desires to measure, he plants a staff or makes a mark that
can be easily recognized by his assistant ; the assistant, who
remains at the starting-point, observes his barometer, ther-
mometer, and watch at the same time that the surveyor makes
his observations ; if they are within sight, the time for reading
can be fixed by the waving of a flag; if they are not within
sight, the time for reading must be made simultaneous in some
other way : if the distance is not too great and the other con-
ditions suitable, communication may be made by the discharge
of a gun, otherwise the readings must be taken at times agreed
upon, the assistant always reading his barometer at the stations
left by his leader. In this way the observations of the pressure
and temperature at the upper and lower of each pair of stations
are recorded simultaneously, and the difference in level can
therefore be calculated without regard to those changes in the
atmospheric pressure or atmospheric temperature which might
occur in the interval if the upper and lower readings were not
simultaneous.

It may be difficult to effect the readings of the two barometers
in all cases simultaneously ; therefore, to prevent errors that
might otherwise arise, the leader should fix main stations, say
every quarter of an hour, so that the assistant will be at the
last main station at the moment that the leader is recording his
barometer at the advanced main station, the readings at the
intermediate stations being taken at approximately the same
time. In this way, as much accuracy is obtainable as can be
expected from the instruments used, the care of the observers,
and the accuracy of their calculations.

Levelling with Three Barometers. Where the difference in
level of two stations is known, a barometer may be fixed at each
of these stations, and, the height being known, the density of the
air can be calculated. With a third barometer, readings are
taken at stations the altitudes of which are unknown, but which
can be calculated from the known density of the air as recorded
by the two barometers at the fixed stations ; thus, two barometers
being observed, say every hour or oftener, any changes in the
density of the air will be noticed, and the altitude of the other

LEVELLING. 243

stations calculated from the density ascertained at the hour of
reading.

This method of levelling dispenses with the observation for
the temperature of the atmosphere or for the moisture of the
atmosphere, and also with corrections for gradient, if the two
base stations are in the vicinity of the new stations. This
method of hypsometry is fully described in a very valuable paper
by Mr. G. K. Gilbert. 1

The rules adopted for the calculations are as follows : There
are three stations, lower, upper, and new, denoted by L, U, and
N. The height of U above L is found exactly by spirit-levelling,
and constitutes the base B ; the height of the new station which
is required is the height above the lower station ; this height is
called A, Barometric readings are now taken at all three
stations, and the height of the base B may be calculated approxi-
mately on the assumption that the air is dry and has a uniform
temperature of 32 ; this approximate height is called B. The
height of the new station A may also be calculated from the
barometric readings on the same assumption, and this approxi-
mate height is called A ; then the actual height of the new
station A may be found from the following rule of three sum :
Approximate height (B) of the base-line : true height (B) of the
base-line : : the approximate height (A) of the new station :

true height (A) of the new station; whence -5 = T-' ^ n *^ s

Jj A

way we find the true height (A) of the new station.

Let A represent the true height of the new station N above L.
a ,, uncorrected height of the new station

N above L.
I ,, barometric reading at the station L.

>j ^ )t )) ?> > u

?/ N

>}' 3J J) )) )) -^

B represents the actual height of the base ; then

log I - log n

Cl = JD ; 7 ^

log I log u
This is what Mr. Gilbert calls the logarithmic term of the

1 Published in the second Annual Report (1880-81) of the United States
Geological Survey.

244 MINE SURVEYING.

formula, and he gives the following example : Barometric read-
ing, station L, 29'879 ; station U, 23'336 ; station N, 27'475 ;
altitude, B, 6989 feet.

log I = log 29-879 1-47537

log n = log 27-475 = 1-43894
log u = log 23-336 = 1 '36803

log 7 - log n = 0-03643
log I _ log u 0-10734

log 0-03643 = 2-56146
log 0-10734 1-03076

Difference = 1-53070
log B = log 6989 = 3-84441

Sum (log a) = 3-37511
a = 2372-0 feet

This result, however, has to be corrected by what Mr. Gilbert
calls the thermic term ; and the full formula, as given by Mr.
Gilbert, is as follows :

/ -n v i L\ -D log I ~~ 1 n i A(B A)
A (m English feet) = B Q J =^-+ -^>

N _ log / - log n , A(B - A)
A (m metres) = B r : ^ + -r^no,,

log / - log n 149349

in which last formula A is the correct height.

In calculating the thermic term )QQ OOO > A may be taken

as equal to a, the unconnected height, to facilitate calculations,
and it will be sufficiently near for most purposes.
Applying this to the figures above given

A(B _-_A) _ 2372(6989 - 2372) _
'490000 490000

we get a correction of 22*4 feet to be added, making the total
altitude A 2372 + 22'4 = 2394'4.

In order to save calculating this thermic term, Mr. Gilbert
gives a table of its value for altitudes of A of 10,000 feet above

LEVELLING. 245

and 5000 feet below the lower station of the base, and for a
vertical base varying from 1000 to 10,000 feet. 1

It must be noted that if A is a vertical distance below U, it

.....it , A x (B - A)

becomes a minus quantity in the formula, and 400000

A X (B 4- A)
is equivalent to v } ; but the value of A as ascertained

~t 7 \J \J \J \J

by logarithmic term is also a minus quantity, so that the thermic
correction has to be added.

When the new station is higher than the upper station U,
B A becomes negative, and renders the thermic term negative,
so that the correction due to the thermic term has to be sub-
tracted from the altitude calculated from the logarithmic
term.

If N is^below U, the height is minus, and the correction, being
also minus, is added.

Where minute accuracy is not required, the thermic term
may be disregarded, and the altitude calculated from the

formula a = B, ^ ~ , g n . The correction for the thermic

log I - log u

term varies from up to about 2 per cent. When A and B are
equal, and on the same level, there is no correction, and the
required correction increases as the difference between A and B
increases. Thus if B is 1000 feet and A is 100 feet above L, the
correction is +0'2 feet, or per cent. ; when A is 500 feet, the
correction is 0*5 feet, or T V per cent.

Temperature of the Atmosphere. This is difficult to ascertain,
owing to the difficulty of placing the thermometer in a place free
from the effects of radiation from hot or cold objects. Thus a
thermometer placed in the shade at 8 a.m. near a north wall
might give the reading less than that due to the temperature of
the air owing to the coldness of the wail which had been cooled
down during the night ; again, a thermometer placed in the
shade near to a south wall might give a reading higher
than that of the temperature of the air due to radiation from
the wall which had been heated by the sun's rays. In the same
way, a thermometer placed in the shade near to the ground
may be cooled by radiation to the earth, which is cold owing to

1 The reader is referred to Mr. Gilbert's paper for this table, as it is too large to
insert here.

246 MINE SURVEYING.

the coolness of the night, or the thermometer may be raised
above the temperature of the air by the radiation from the
earth, which has been heated by the sun's rays.

But the difficulty of obtaining the temperature of the air
within 4 or 5 feet of the ground is by no means the only
difficulty or the chief difficulty. What is really required is the
temperature of the air above the ground for a height of several
hundred or several thousand feet, and a surveyor walking along
the surface of the ground has no chance of measuring this.
Walking up a hillside (see Fig. 142), the surveyor measures the
temperature of the air within say 4 feet of the ground, the
ground, having been greatly heated by the sun's rays, has
warmed the air ; the average temperature from A to B is say

FIG. 142. Variation in temperature of air.

65, while the average temperature A to C is unknown ; but
this is the temperature which is really required. On a cloudy
day and on a windy day the temperature AB is likely to
approximate to the temperature AC ; on a calm, bright day
the temperature AC will be much less than the temperature
AB. In clear weather the temperature of the ground during
the sunshine is much greater than that of the air, and during
the night is much colder than the air; but it is probable
that the average temperature day and night AB approximates
to the average temperature day and night AC.

According to observations made in Switzerland, and calcu-
lations made by Plantamour, Eiihlmann, and others, quoted
by Mr. Gilbert, the average range of temperature in the body

LEVELLING. 247

of the air in Switzerland is, in summer, 4 F. between the
early morning and noon, and in winter less than 2 F., whilst
near to the ground the range of temperature of the air varies
from 10 to 20 at the seashore, and from 20 to 35 in the
interior of continents between the hottest and coolest periods
of the daytime.

It follows, therefore, that where there is a great variation
in the atmospheric temperature between the night and day, it
would be better to take the mean temperature of the 24 hours
than to take the temperatures observed in the daytime, though
a more correct result would be obtained by making a correction
for noon or sunrise, according to the figures above quoted for
Switzerland.

These corrections must be applied to the mean temperature
of the air as ascertained by readings day and night ; thus, if
the observations are made in January, and the mean tempera-
ture of the air near the ground day and night is say 37'5, this
might be taken as the temperature of the air at sunrise, and
the temperature at noon as 39*5. If the observations were
taken in August, and the mean temperature of the air day and
night were 62*5, this temperature should be corrected by the
addition of 4 for observations made in the warmer part of
the day.

The difference of altitude between stations A and B may,
however, be taken by a series of readings, A, d, d 1 , d 2 , d 3 , d*, and

FIG. 143. Method of taking barometrical observations to avoid error due to

temperature.

so on ; the height from A to d is say 100 feet, and it is evident
that the temperature of the air in this stratum will more nearly
approximate to the temperature of the air near the ground

248 MINE SURVEYING.

than will the temperature of the air in stratum AC. which is
1000 feet high.

One method of obtaining the temperature of the air is given
by Nansen (First Crossing of Greenland], who tied the ther-
mometer to a string, and then whirled it in a circle in the air,
thus forcing it into such contact with numerous particles of air
as to minimize the effect of radiation either from the sun or
from snow, and obtained with great accuracy the temperature
of the air, within say 8 feet of the ground.

It is comparatively easy to obtain the temperature of the
air in a mine. If the surveyor proceeds say 20 feet down the
downcast shaft, where there is a rapid current of air, the effect
of the sun's rays or of frosty skies will be but trifling; a
thermometer held in the air-current will probably give the
temperature of the air, and the temperature of the air here
given will be approximately the temperature of the air outside
in the sunshine. Assuming, of course, that the velocity of the
air is considerable, say 500 feet a minute or more, a thermo-
meter held in the air will give approximately the temperature of
the air, unless it is held in view of a fire.

The surveyor must be cautioned that, on the surface, the
observation of the temperature of the air is the most difficult
observation he has to make ; as regards the temperature of the
barometer there is no difficulty.

Rule for calculating the Difference in Height of Two Stations
from Barometric and Thermometric Readings. Mr. Gribble gives
a very convenient rule and a useful table of constants by which
the surveyor can calculate the altitudes

H = difference of height in feet between stations.
S = sum of barometric readings.
D = difference of barometric readings.
K = a constant for each degree of temperature from zero to 102.

KxD

As above said, K varies with the temperature of the air, that
is to say, the average temperature of the column of air between
the two stations. This average or mean temperature * is found

1 In case the variation of level is rapid and great, the readings at each station
are averaged to give the day and night temperatures, so as to get the real
temperature of the air column.

LEVELLING.

249

by adding together the readings of the thermometer taken at
the two stations and at equidistant intermediate places, and
dividing their sum by the number of readings. Thus, if the
reading at the lower station is 50, and at the upper station 60,
their sum is 110; this, divided by 2, gives 55, the average

TABLE XIII.
VALUE OF K IN FORMULA H

KxD

Degrees of
mean tempe-
rature. Fahr.

Degrees of
mean tempe-
ratuie. Fahr.

Degrees of
mean tempe-
rature. Fahr.

48753

528 13

56757

48869

52929

56873

48985

53045

56989

49101

53161

57105

49217

53277

57221

49333

53393

57337

49449

53509

57453

49565

53625

57569

49681

53741

57685

49797

53857

57801

49913

53973

57917

50029

54089

58033

50145

54205

58149

50261

54321

58265

50377

54437

58381

50493

54553

58497

50609

54669

58613

50725

54785

58729

50841

54901

58845

50957

55017

58961

51073

55133

59077

51189

55249

59193

51305

55365

59309

51421

55481

59425

51537

55597

59541

51653

55713

59657

51769

55829

59773

51885

55945

59889

52001

56061

60005

52117

56177

60121

52233

56293

60237

52349

56409

100

60353

52465

56525

101

60469

52581

56641

102

60585

52697

temperature. Or again, if the lower reading is 50; reading
one quarter of the way, 48 ; reading half of the way, 45 ;
reading three quarters of the way, 43 ; reading at the upper

250 MINE SURVEYING.

station, 40 ; then the sum of the readings = 50 + 48 + 45^
-f 43 + 40 = 226 ; this, divided by 5 = 45'2, the average
temperature. In Table XIII. the column of mean temperature
is the average temperature so found.

It will be seen that the value of K varies from 48753 at
F. to 60585 at 102 F. This shows the importance of the
temperature-readings; this, of course, is an extreme range.
At 50 temperature the value of K is 54553 ; at 60, 55713,
showing a variation of 2 per cent, in the value of K for a
change of 10.

EXAMPLE. If the barometric reading at the upper station was 25-5 inches

S = sum of readings
D = difference

55-5
4-5

Temperature at upper station
lower

50
65

115

for 57

= 55365

Mean temperature

57-5

K for 58
2

K for 57-5

= 55481
| 110846

55423 x 4-5

,55-5
H = 4493-7

55423

If we assume a mean temperature of 50, then H =
5455|x D . if D = ! and s = 60> the upper rea ding being 29'5

and the lower reading 30'5, then H = f VV~ = 909-21. Let
us assume that D = 1 and S = 59, that is to say, that the upper
station reads 29, and the lower station 30, which is a very usual
set of readings, then H = ^y^ = 924'62.
Or again

D = 1 S = 68 H = *$p = 802-25

67 s.*$p = 814-22

66 *$pa = 826-56

65 AAM = 839-27

64 *^a = 852-39

63 ^p = 865-92

62 &4$p = 879-88

61 JU^L8 = 894-31

60 Z4fip = 909-21

59 JiJjip _ 924-62

58 -4i = 940-56

LEVELLING. 251

D = 1 S = 57 M/VISL = 957-07

56 M^p = 974-16

55 *^p = 991-87

54 jujya =-1010-24

This table gives the difference in height corresponding to a
difference of 1 inch in the barometric readings for a mean
temperature of 50 F. at different altitudes. It will be seen
that the less the pressure that is to say, at great altitudes,
1 inch of pressure represents a much greater altitude than
at great depths. The height due to a difference of pressure of
less than 1 inch can be easily calculated ; thus, if the difference
in pressure is 1*4 inch, and the upper station is 28*6 inches,
we take the altitude due to a difference of 1 inch of pressure
between 29 and 30 inches; then > of the altitude due to a
difference of 1 inch between 28 and 29 inches. To correct
for temperature, if the temperature exceeds 50, we increase
the altitude for every 1 F. above 50, 2 per 1000, or 1 in
500. Thus, if the altitude as calculated without the correc-
tion for temperature was 500, and the temperature was
found to be 51, the real altitude would be 501 ; if the
temperature were found to be 60, the real altitude would be

2 x 10
500 + - - = 510. If, on the other hand, the temperature

should be found to be 49, the column must be reduced by 2 per
1000, so that a 500-feet column, as calculated without correc-
tion for temperature, would be really 499 ; if the temperature
were 40, the 500-feet column should be corrected to 490, and
so on.

Measurement of Vertical Shafts. The determination of the
depth of a vertical shaft may be done in one of several ways. A
rough way is to let a cord down the shaft ; holding the lower end
at the bottom, pull it tight, mark the top of the shaft, then,
drawing the cord to the surface, measure it; this is inaccurate,
owing to the stretching of the cord and the contraction that may
follow from wetting.

A more accurate mode is to let a wire down the shaft, with a
weight at the end. The wire should be unrolled from a barrel,
and, as it is lowered, it should be measured on the surface in
convenient lengths of say 50 feet, the wire being stretched by
the weight all the time. The wire should also be remeasured as
it is rolled up.

252 MINE SURVEYING.

Another method is to measure the winding-rope in con-
venient lengths by means of a steel tape or other accurate
measure as it is being wound up and lowered down.

A fourth method is to measure the shaft-guides or other
smooth continuous surface. If the guides are of wood, a nail
may be driven in at the surface and a chain or steel tape
suspended ; at the bottom of the chain a second nail is driven in,
and the chain lowered down and suspended from this second
nail. If the second nail is driven in just below the last ring, so
that the end of the chain just touches the top of the nail, it is
evident that from the top of the first nail to the top of the second
nail will be the extreme length of the chain minus the thickness
of the ring at the top end of the chain by which it is suspended.
When the chain is suspended by the second nail, and a third
nail driven in just below the chain, but so that the last link can
just touch it, it is evident that the length from the top of the
second nail to the top of the third nail will be the length of the
chain minus the thickness of the top ring of the chain by which
it is suspended ; therefore, the length as recorded will be greater
than the actual length by the thickness of this ring multiplied
by the number of times the chain is suspended, therefore the
recorded length must be reduced by that amount. If the chain
or measuring-tape used is accurate, the measurement obtained
in this way will be accurate.

The measurement is facilitated by a contrivance described
by Mr. B. H. Brough. At the length of a chain or other measure
above the cage, a seat is fastened to the winding-rope, on which
a miner can sit and hold the upper end of the chain or steel
band to marks made on the guide. The cage having been
lowered down the shaft the length of the measure, the surveyor
applies the lower end of the chain to the guide, and marks the
place carefully ; the cage is now lowered down the chain-length ;
the miner holds the top end of the chain to the first mark, whilst
the surveyor makes the second mark below ; this operation is
repeated throughout the whole depth of the shaft. Instead of a
chain or tape, rods may be used.

There should be no serious error in the measurement of a
shaft, and with care a shaft 1000 feet in depth may be measured
with an error of less than \ inch.

Measurements of Inclined Shafts. Whilst the measurement
of vertical shafts is thus simple and easy, the measurement of

LEVELLING.

253

the depth of inclined shafts is often very tedious, and resolves
itself into a process of levelling with straight-edge and spirit-
level (see Fig. 144). In this case a straight-edge is fixed level
by means of a prop of some kind. For accurate work the
end of the straight-edge which is raised above the ground
should be clamped to a vertical rod when it has been carefully
adjusted by the level ; from the end of the straight-edge a
plumb-line is dropped to the ground, and, on some bar or mark
firmly fixed, the exact position of the centre of the plumb-line is
marked with great care, and then the length from the straight-

FIG. 144. Method of measuring inclined shafts.

edge to the ground is measured, the measurement being taken
to hundredths of an inch. The straight-edge is now lowered
and fixed on the mark made by the plumb-bob, and the opera-
tion repeated. A set square may be attached to one end of the
straight-edge, and the vertical rod fixed against this, dispensing
with a plumb-line. The vertical rod should have a scale marked
on it, and it should be erected on a smooth stone, brick, or bar,,
on which the straight-edge can be placed afterwards, or has
been placed previously.

If the shaft twists, it must be surveyed, although the direction

254 MINE SURVEYING.

is of no importance for ascertaining the depth ; the straight-edge
used being of a convenient length, the horizontal measurement
of each set is known. A dial may be attached with clips to the
straight-edge, and the bearing of each position noted. This, of
course, can only be done in case there is no attraction, so that
the loose needle can be used.

CHAPTEE XIII.

CONSTRUCTION OF PLANS.

As already stated, English mining plans are generally drawn on
large sheets of paper capable of containing the whole survey.
The kind of paper used is that which is generally described by
the makers as "best antiquarian," and is mounted on brown
holland. A sheet of the required size has frequently to be made
specially to order, and is prepared by pasting together a number
of sheets of the size made by the paper-manufacturer; where
one sheet joins another the edges are pared down to a bevel, so
that when the two edges are placed one over the other, the
thickness is the same as one sheet; the two pieces are then
united by a suitable paste. At the corners where four sheets
join, great care has to be taken to make a sound junction
without having a lump. A sheet of paper thus mounted should
be made months, if not years, .before it is wanted, the surveyor
keeping a stock in his office in a chest in the centre of the
room, that is to say, not against a wall which might be damp.
Mounted plan-paper can also be obtained in rolls up to 81
inches in width, and the length required for a plan cut off. The
plan, when made, is rolled up and put into a drawer when not
in use. As dust generally finds its way into the drawers, it is
necessary, to prevent dust from getting inside the roll, to cover
the ends with paper. The plan is often kept in a case of tinned
iron painted on the outside, with a hinged lid and fastened with
a padlock ; in this case the plan may be safely carried without
fear of injury; without such a case the plan would soon get
damaged in transport. If carefully used, the plan may serve
for a generation without being much the worse. When the
plan is confided to the charge of assistants who do not feel
the responsibility of the cost of replacing it, it is frequently

2 5 6

MINE SURVEYING.

damaged by being bent over the edges of tables in such a way as
to break the paper or seam it with cracks ; it is soon made black
by being exposed to the dust, and by being rubbed with dirty
articles. A plan when laid out on the table should be kept down
by leaden weights covered with leather (usually weighing about
2 Ibs.), the edges of which are rounded. The weights should be
always dusted before using, and the table dusted before the
plan is laid down. When working on the plan, it should be
covered up with clean paper, except that part which has to be
exposed for work, and if the draughtsman finds it necessary to
rest his arms upon the paper, he should lay down a sheet of
clean paper underneath his arms or other portion of his body
that may be pressing on the paper.

In order to bring that part of the paper on which he is
working within his reach, it is frequently necessary to draw the

FIG. 145. Improved drawing-table.

plan near the edge of the table. For this purpose the table is
fitted with a beading reaching to a depth of say 3J inches from
the top, and the corner of the edge planed off until the section
of the edge with the beading below is a semicircle. If any
segment of a circle less than a semicircle is used, there will be
a sharp edge, and in bending the plan over that edge it may get
injured. If the draughtsman leans against the plan drawn over
the table, he will soon dirty and injure it ; he must therefore
cover up the plan at this part with paper or calico.

Drawing-tables may be made with an outer bar, against
which the draughtsman rests, as shown in Fig. 145.

Miscellaneous Notes on the Preparation of Plans. To make
plain those parts of the plan from which the minerals have

CONSTRUCTION OF PLANS.

257

been extracted, it is usual to colour it with water-colours.
Colouring is apt to lead to shrinkage of the plan, and should
therefore be done as sparingly as possible, although the sur-
veyor must remember that colouring may be essential to the
utility of the record. It may be in some cases advisable to keep
a skeleton plan of the workings with no colouring, by which to
preserve the accuracy of the main stations, and to correct from

>' s -

i^iitfSL

ps*

FIG. 146. Delineation of buildings, fences, etc.

time to time the working plan, which has been distorted by
colouring and comparatively rough usage.

The advantage of a large plan, showing the relative position
of all the different workings connected with one concern, is
obvious, conveying forcibly and at once the whole situation to
the mind of the engineer ; on the other hand, the exact

2 5 8

MINE SURVEYING.

j * , -* * * \_- L

1DDDI
1DDDI

distances and bearings can generally be better ascertained by

calculations contained in the office survey-book.

The survey is laid down in fine pencil-lines, and afterwards
inked over ; the surface is invariably
drawn in Indian ink, walls, buildings,
hedges, etc., being indicated in the way
shown in Fig. 146.

Underground workings in the Mid-
land Counties of England are generally
inked in with pink lines (crimson lake) ;
those parts from which the mineral has
been entirely excavated, washed lake ;
faults are frequently shown with dotted
blue lines ; and other conventional
symbols are shown in Fig. 147. It is
sometimes convenient to indicate each
year's, half-year's, and quarter's survey
by a different colour; at other times
the written date and a shaded line are
considered sufficient (see Fig. 148). If
several seams of coal are shown upon
the same plan, a different colour should
be used for each seam, in which case
the half-year's workings in each seam
can be indicated only by the dates
written on the plan. There must, of
course, be a separate plan for each
seam ; but it is very convenient to show
all the workings also upon one general
plan, to facilitate the true understand-
ing of the situation. The north point

FIG. U7. Usual methods of gnou ^ ^ e indicated by an arrow of an

delineating underground .

workings, etc. (i) Arrows ornamental kind at one corner of the

indicating air - currents ; j / p- 14Q j Thig arrow ig not
(2) air-crossing, overcast

and undercast; (3) pillars to be used in plotting, but merely to

$^ffij3tf tt K indicate approximately the direction;

pit-shaft'; (8) regulator; the real meridian line is represented by

round aUltS ""* faulty a long thin line drawn with the aid of a

steel straight-edge across the plan. If

it is the magnetic meridian, the date is written against it.

Copying Plans. Plans can be most easily and quickly copied

CONSTRUCTION OF PLANS.

259

on tracing-paper or tracing-cloth. Tracing-paper is the more
pleasant to work on, but is easily torn ; tracing-cloth makes a
permanent copy, but is
liable to be much dis-
torted by colouring. A
cloth tracing, however,
often makes a good
working plan for rough
usage, and is service-
able, and when folded
into a leathercasemaybe
carried about the mine.
When the smooth or
greasy nature of the sur-
face makes it difficult
to draw upon, a little
prepared ox-gall mixed
with the ink or colour
obviates the difficulty ;
powdered chalk also is
sometimes useful when
rubbed over the surface.
Glass Table for tracing
through Thick Paper.
Plans drawn on un-

FIG. 148. North point. Method of showing
coal worked during the quarter.

mounted paper may be traced on to drawing-paper, by placing
the plan and the sheet on which it has to be traced upon a glass.
In order to get the light through this glass, it should be placed
in a frame near a window, and light from below thrown upwards
through the glass by a reflector; the reflector may be made
either of looking-glass or of white paper. The surface of the
paper on which the draughtsman is working should be shaded
by a blind. If the work is done at night, a brilliant illumina-
tion of reflected gaslight can be used, or better still, electric
lamps may be placed immediately under the glass.

Transferring. British mining plans being generally made on
mounted paper, sufficient light will not pass through to enable
them to be traced on to thick paper, in which case they may be
transferred. The usual practice is to make a tracing on thin
paper, then to place the tracing over the new mounted paper,
and, between, to place a transfer paper specially made of very

2 6o MINE SURVEYING.

thin paper, one side of which is blackened with black lead. By
means of a steel point (style) and a flat ruler, a fine line may be
traced on to the paper below. Great care is required in doing
this. If a blunt point is used, the line transferred will be too
thick; if a fine point is used, it is apt to cut the tracing. If
accidental pressure is put on to the tracing-paper, a black mark
is left on the plan below, which may make the survey-lines
indistinct, though it may afterwards be cleaned off.

Pricking through. Another method is to place the original
plan over the new sheet of paper, carefully fasten it down with
weights or drawing-pins, and then to prick through to the plan
below, and subsequently join the prick-marks by pencil-lines.
This method is very accurate, but requires great care in the
subsequent pencilling in, which has to be done by the aid of
continual reference to the original plan.

Copying by Photography. Architects and engineers reproduce
copies of their plans by the action of light on sensitized paper.
A tracing of the drawing is made on very transparent tracing-
paper or cloth (dead-black lines for the drawing, and vermilion
or burnt sienna for dimension lines). The sensitized paper
covered with the tracing is placed in a frame and exposed to the
light ; the point of sufficient exposure is indicated by various
changes in the colour of the sensitized paper; the sensitized
paper is then immersed in a bath (either of water or acid,
depending on the process used) and washed till the lines on the
tracing appear upon the paper, owing to the circumstance that
these lines have shielded the paper from the action of the light.
According to one process, the lines appear white on a blue ground ;
by another process they appear black on a white ground.

The sensitizing solution for the ferrotype or blue process, in
which white lines are given on a blue ground, may be easily
made as follows :

Solution A : Citrate of iron and ammonia, 100 grains ;
water, 1 ounce.

Solution B : Ked prussiate of potash, 70 grains ; water,
1 ounce.

These solutions will keep indefinitely before mixing, but after
mixing they should be used at once or left in the dark.

To prepare the paper, mix equal quantities of A and B, and
apply to one side of the paper with a sponge. The sponge
should be as full as it will hold of the solution, which should be

CONSTRUCTION OF PLANS. 261

liberally applied to the paper for about two minutes. Then
squeeze out the sponge and wipe off all the solution from the
surface of the paper, care being taken to use the sponge lightly
without abrading the surface. The paper, which is now of a
bright yellow colour on the prepared side, should be hung up to
dry in the dark.

Reduction and Enlargement of Plans. It is frequently necessary
to enlarge or reduce a plan. It is not, as a rule, advisable to
make a plan on a large scale from an original plan drawn on
a small scale, because any error in the original plan will be
multiplied as much as the plan is enlarged, and an error im-
perceptible on the small-scale plan may become important on
the large-scale plan, therefore a large-scale plan should, as a
general rule, be made from the original survey notes by replotting
the survey on the required scale. In reducing a plan any errors
in the original will be also reduced.

A common mode of reducing or enlarging a plan is to treat
the original plan as if it were the works, mine, or estate, that
had to be surveyed, and to make a survey of it by drawing
triangles, measuring offsets, etc., and then reproducing these
triangles, offsets, etc., with the aid of a smaller scale 011 another
piece of paper. The surveying of the original plan, and the
reduction, may be accomplished with the aid of two scales say
the original plan is on a scale of 2 chains to an inch, and the
reduced plan is to be on the scale of 6 chains to an inch, then
the lines are measured with the 2-chain scale, and plotted with
the 6-chain scale. If the original survey notes are available,
however, it would no doubt be more accurate and expeditious to
plot them afresh.

Enlarging or Reducing by Photography. Another method of
reducing and enlarging plans is by means of a lens and camera
obscura. This may be done by the ordinary process of photo-
graphy. Thus, supposing the plan to be 6 feet square, it might
be photographed on to a plate 12" X 12", or of any other
dimensions to suit the camera of the observer.

If the size of the negative is too small for the required plan,
an enlargement may be produced by placing the negative in an
enlarging camera, inside which is . a lens which enlarges the
view and prints it on a larger piece of paper at the other end
of the camera.

This process of reduction by photography may be done with

262

MINE SURVEYING.

great accuracy if sufficient care is taken. It is essential that
the plate on which the negative is formed should be parallel to
the drawing which is being photographed, and it is desirable
that the camera should be opposite to the centre of the plan.
The lines on the plan to be photographed must not be too fine,
otherwise the lines on the reduced plan become too thin to be
clearly visible. A line -^-^ i ncn i n width is perfectly clear, but
if that line were reduced by photography to one quarter of that
width, it would be too fine for ordinary distinctness ; if, there-
fore, it is proposed to reduce the plan to one quarter its original
size, and if it is decided that the minimum thickness of lines
on the reduced drawing should be T ^ inch, the lines on the
original plan must not be less than y^ inch in thickness.

The reduction or enlargement of plans by photography is not
usually practised by the mining engineer, because the cost and
trouble of procuring and arranging the apparatus is more than
the saving in labour to be gained by the process. It is also
necessary that the plan to be photographed should be all in
black and white. The system, however, is suitable for the illus-
tration of a report of which say a dozen or more copies are
required.

Pantagraph. This instrument, Stanley's improved form of
which is illustrated in Fig. 149, is used for the mechanical

FIG. 149. Pantagraph.

copying of drawings, either upon the same scale or upon a
reduced or enlarged scale. It consists of four arms jointed
together in pairs. On one of these arms is a tracer, and on
another a pencil-holder, and by means of scales engraved on

CONSTRUCTION OF PLANS.

263

the instrument the relative positions of these can be so arranged
that the figure drawn by the pencil bears a definite proportion
to that which is followed round by the tracer.

A similar instrument, called the eidograph, illustrated in
Pig. 150, is said to be superior to the pantagraph ; it is,

FIG. 150. Eidograph.

however, much more expensive, and for that reason some
firms 1 send the instrument out on hire for temporary purposes.
Proportional Compasses. Proportional compasses may be used
instead of or in addition to the scales. These compasses, as
shown in Fig. 151, consist of two straight bars pointed at each

FIG. 151. Proportional compasses.

end. Each of these bars is slotted to about two-thirds of its
length, a slide fits into each slot, and a pin with a milled head
passes through both slides ; each bar is graduated with cross-lines
marked from 1 up to 10. If the slide is fixed at 1, and the bars
twisted round the centre pin, the points at each end will remain
equidistant ; if the slide is fixed at 2, the points at one end will
open twice as far as the points at the other end ; if the slide is
fixed at 3, the points at one end will open three times as far as
the points at the other, and so on. Another side of the bar
is graduated | , -, | , and f ; thus if the slide is fixed at f, the

1 Amongst others Messrs. Halden and Co., 8, Albert Square, Manchester.

264

MINE SURVEYING.

points at one end will move 4 inches, while the points at the
other move only 3 inches. This instrument is very convenient
for marking off lengths on reduced plans.

CNJ

co o>

.. \
\ \

I
1

Enlarging or Reducing by Sectional Paper. To facilitate the
surveying of one plan and the plotting of another, it is a common
practice to divide each plan into squares ; thus the 2-chain plan

CONSTRUCTION OF PLANS. , 265

will be ruled into squares, measuring J inch on each side, and
the paper for the 6-chain plan into squares \ inch on each side ;
or, if this latter size is found inconveniently small, the 2-chain
plan may be ruled into squares 1 inch on each side, and the
6-chain plan into squares \ inch on each side. The plan may
now be reduced by sketching with a fine-pointed pencil (see
Fig. 152).

In order to save the labour of ruling the squares, and also to
avoid the disfigurement of the plan, tracing paper with sectional
lines ruled in fine blue ink is sometimes used. The mode of
reduction would be as follows : Over the 2-chain plan a tracing
divided into 1-inch squares is placed; a tracing divided into
^-inch squares is now placed over a piece of white paper, and
the reduced plan sketched on it by hand. The plan so made
may be subsequently transferred to a piece of paper ; or, instead
of that, the section lines for the reduced plan may be ruled on
the paper, and the sectional tracing-paper merely used for the
large plan.

For many purposes drawing-paper ruled with fine blue
sectional lines is exceedingly useful. This is not generally used
for mining plans, partly owing to the disfigurement of the
paper by the sectional lines, and partly owing to the difficulty
of procuring extreme accuracy in the ruling of these lines ;
but in many other cases this sectional paper is extremely
convenient.

The Opisometer (Fig. 153) is an instrument for roughly
measuring distances on plans which, owing to their sinuosities
would require the expenditure of a great deal of time with an
ordinary scale. It consists of a small wheel with a milled edge,
which revolves upon a screw for an axis. The screw moves
through the arms which carry it, being propelled by the move-
ment of the wheel, and a scale is attached, showing the distances
corresponding to any movement of the screw.

Relief Plans and Mine Models. Models of mines, showing the
configuration of the surface and the veins of minerals, or seams
of coal, faults, etc., are very useful and instructive, but are
exceedingly expensive. They are chiefly used for educational
purposes, and for displaying in exhibitions and museums. In
so far, however, as they represent actual mines, they must be
prepared from data which can all be put on to plans and
sections ; and the effect of a model can be given to a great

266

MINE SURVEYING.

extent by a skilfully prepared drawing, the cost of which is
insignificant in comparison with the cost of a model.

In the construction of a model, rocks are generally repre-
sented by wood, painted, to represent the different strata, seams
of coal, or veins of mineral. If machinery
is shown, this is also generally of wood,
painted where necessary to represent
iron ; real brass may be used to repre-
sent portions of the machinery made of
that metal. Fig. 154 is prepared from a
photograph of a model in the museum at
South Kensington.

Calculation of Area and Quantity of
Coal worked. One of the most important
uses of a mineral plan, particularly in
connection with collieries, is the calcula-
tion of the extent of mineral got in cubic
feet, cubic yards, cubic metres, or in
areas of square feet, square yards, square
metres, or acres and decimals, or acres,
roods, and perches.

Royalty. In Durham, Northumber-
land, Wales, and other parts, the lessee
of a colliery pays to the lessor a royalty,
as it is called, of so much per ton. The
derivation of the word " royalty " is pro-
bably derived from the fact that the
minerals, as also the land, in former days
belonged to the king. In the United
Kingdom, the land, and with the land the
minerals, is now generally the property
of private owners, such ownership being
either absolute, as when the land is held
in fee simple, or limited, as when the
owner has only a life interest, having to
transmit the estate to heirs. The owner
of a life interest of an estate, while the
law does not permit him to destroy the surface for his own
immediate gain, is permitted to get, or grant to others a licence
to get, as much of the mineral as he can during his lifetime.
The term of a mineral lease granted on an entailed estate

268 MINE SURVEYING.

cannot exceed 60 years, except by special leave of the Court of
Chancery.

The minerals reserved to the British Crown at the present
time are only gold and silver, and those lying underneath
Crown lands, as, for instance, the coal and ironstone in the
Forest of Dean ; the tin, lead, and copper in the Duchy of
Cornwall; the minerals in the Duchy of Lancaster; and the
minerals underlying the foreshore on our sea-coasts, that is to
say, the minerals underlying that portion of the coast which is
covered by the tide, and extends to a distance of three miles
from the shore, except in cases as, for instance, the estuary
of the Eiver Dee where the king has made a grant of these
minerals to a subject.

This royalty is often a fixed sum, as, say 6r7. a ton, or Is. 4d.
per chaldron (a chaldron being 53 cwt.) ; or it may be one price
on large coal and another price on small coal, say 6rf. per ton
on lumps that pass over a screen, the bars of which are 1 inch
apart, and 3d. a ton on the slack which falls through these bars.
In some districts, as, for instance, in North Staffordshire and
North Wales, the royalty is a fixed proportion of the total value
of the mineral sold, as, for instance, one-eighth, one-tenth, one-
twelfth, etc. In other parts of the country, as, for instance, in
Yorkshire, Derbyshire, Nottinghamshire, Leicestershire, War-
wickshire, etc., an acreage royalty is paid, the royalty being,
say 100 an acre on each seam. If several minerals are worked
together in one working, as, for instance, ironstone, coal, and
fire-clay, there will be a separate royalty on each, say 50 an
acre on the ironstone, 50 an acre on the coal, and 50 an
acre on the fire-clay. Sometimes the royalty is so much per
acre for a given thickness of coal, say 30 per acre per foot
thick, so that if the seam were 5 feet thick, the royalty would
be 150 per acre, the thickness of the seam being ascertained
each time the mine is surveyed.

Measuring Acreage by Division into Triangles. In calculating
the area got, the ordinary process is as follows : The area of
coal to be measured (which may represent the whole extent that
has been worked, or only the area got in one half-year) is divided
into trapeziums and triangles, the edges of the area being
straightened by give-and-take lines ; the trapeziums are divided
into triangles by diagonals, and from the apex of each triangle
of the base a perpendicular is let fall (see Fig. 155). Each of

CONSTRUCTION OF PLANS. 269

the triangles and trapeziums is numbered 1, 2, 3, etc., the base of
each triangle is measured, the diagonal of a trapezium forming
the base of two triangles; the perpendicular of each triangle
is also measured. The area is equal to the base multiplied by
the perpendicular divided by 2. The area of a trapezium is equal
to the diagonal multiplied by the sum of the two perpendiculars
divided by 2. Thus, referring to the figure, the area of
triangle No. 1 is equal to 1000 (the base) x 200 (the perpen-
dicular) -+- 2 = 100,000 ; and the area of No. 2, which is a tra-
pezium, is equal to 1000 (the diagonal) X 156 4- 200 (the

FIG. 155. Scaling by triangles and trapeziums.

perpendiculars) -f- 2 = 178,000 ; therefore the sum of the areas
1 and 2 = 100,000 + 178,000 = 278,000. If the measurements
are in links, we thus have an area of 278,000 sq. links.

The area of an acre is 100,000 sq. links, so that to turn
the square links into acres we must divide by 100,000. The
process of division by 100,000 is exceedingly easy, consisting in
simply putting the decimal point before the fifth figure from the
right-hand end of the number ; thus, in dividing 278,000 by
100,000, we put the decimal point before the 7, which is the fifth
figure from the right-hand end of the number, and we have the
answer 2*78000 acres. To turn 2*78 acres into acres, roods, and
perches, we multiply the decimal part by the number of roods in
an acre ; there are 4 roods in an acre, so we multiply 0'78by4,
and the result is 3'12 roods. To turn the decimal of a rood into
perches we must multiply by the number of perches there are in
a rood, which is 40 ; 0*12 x 40 = 4*8 ; therefore the number of
perches is 4'8 ; the total acreage is therefore 2 acres 3 roods
4*8 perches. It is, perhaps, mainly on account of the ease with
which square links can be reduced to acres that the use of the
100-link chain is so popular with mining surveyors.

2/0

MINE SURVE YING.

If the foot chain were used, then the area measurements
might have to be calculated in square feet. To reduce square
feet to acres, they must be divided by 43,560, the number of
square feet in an acre.

It must, however, be borne in mind that, in the scaling of
the plan, it is immaterial whether it has been made by the
measurement of links or of feet, because the measurements can
be taken off the plan by means of a scale of links, even though it

FIG. 155A. Scaling of coal worked during half-year.

was plotted from a scale of feet, just as the engineer can take
from a plan plotted from measurements in links any distance he
desires in feet by a scale prepared with that object. Scales are
often made to read feet on one side and links on the other.

In order to avoid scoring a plan with scaling-lines, it is usual
to place a piece of tracing-paper over the plan, and to make a
very careful tracing with fine lines of the areas to be measured,

CONSTRUCTION OF PLANS. 271

and upon this to draw, with a fine-pointed pencil, give-and-take
and dividing lines, and then to ink these in, writing upon them
the measurements. These scaling tracings are copied in a book,
and form a useful and permanent record of all the measure-
ments made. The advantages of this system of measurement
for the purposes of reference, and the ease with which the
scalings and calculations can be checked by assistants, commend
the system so strongly to the practical surveyor that it is likely
to hold its own as long as the system of acreage royalties prevails.

The method of scaling up an area of coal worked is shown
more fully in Fig. 155A. The triangles and trapeziums into
which the area is divided are numbered 1, 2, 3, etc. ; and the
lengths of the base and perpendiculars are marked on the lines.

The entry in the scaling-book for this area would be as
follows :

Colliery. Scaling of Freehold Coal worked during the Half-year

ending June 30, 1900.

(1) 400 x 150 = 60000

(2) 415 x (190 + 240) = 178450

(3) 440 x (138 + 198) = 147840

(4) 450 x (130 + 110) = 108000

(5) 420 x (20 + 178) = 83160

2)577450

288725
Deduct faulty coal (340 x 20) = 6800

3-27700
40

11-08000
2 acres 3 roods 11 perches at 100 per acre.

2 acres at 100 per acre

3 roods at 25 per rood

11 perches at 12s. 6d. per perch

0-08

281 18 6

The above is the usual way of getting out acreages and
royalties, but it is evident that a better and quicker way is to
take the acres and decimals thus

272 MINE SURVEYING. -

2-81925 acres at 100 per acre
100

281-92500
20

18-510
12

6-120 281 18s. Qd.

Statute Acre and other Acres, The term " acre," as applied to
the measurement of land, is generally understood to refer to the
statute acre of 160 perches, which was established by law about
the thirteenth century. There are, however, different acres in
various parts of this country (see Table XIV.), but the use of
these varying measures is rapidly giving way to the statute
acre, and they will soon be quite obsolete.

TABLE XIV. 1
LIST OF VARIOUS ACRES.

1 Statute acre contains 4840 sq. yards.

1 Scotch acre contains G150'4 (48 Scotch acres equal nearly Gl

statute acres)
1 Irish 7840 ,. (100 Irish acres are nearly equal

to 162 statute acres)

1 Welsh 4320 (sometimes called " erw ")

1 Cornish 5760 (equivalent to about 1'19 statute

acre)
1 Leicestershire acre con tains 2308*75 ,, (equivalent to about 0*477 statute

acre)
1 Westmoreland 6760 (equivalent to about 1-397 statute

acre)
1 Cheshire ,, 10,240 (equivalent to about 2*115 statute

acres)
1 Lancashire 7810 ,, (equivalent to about 1 '61 3 statute

acre)

Planimeter. For the rapid measurement of numerous areas
with sinuous boundary-lines, Amsler's planimeter is of great
use to the surveyor. By means of this instrument, shown
in Fig. 156, the area of any given figure is measured in square
inches ; the area so obtained can be converted into square
chains by simple multiplication. Thus if the area measured is
6 sq. inches, and the scale of the plan is 1 chain to an inch,

1 The authority for most of these figures is the Century Dictionary, recently
published by the Times, London.

CONSTRUCTION OF PLANS.

273

the area is 6 sq. chains ; if the plan is on a 2-chain scale,
the area is four times as great, because each square inch
contains 4 sq. chains, therefore the 6 sq. inches represent 24
sq. chains ; if the scale of the plan is 3 chains, then each

FIG. 156. Amsler's planimeter.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

square inch contains 9 sq. chains, and the 6 sq. inches con-
tain 54 sq. chains : 10 sq. chains equal an acre ; therefore the
area, as measured in square chains, if divided by 10, gives the
area in acres and decimals of an acre.

Rule. Let X = area in square inches, Y = number of chains
per inch of scale, Z = area in square chains. Then Z = X X Y 2 .

EXAMPLE. Let the area measured in square inches (X) be 5 - 64 ; let the scale
of the plan be 3 chains to an inch, or Y = 3 ; then the area (Z) = 5-64 x 3 2
= 50-76; the acreage = 50*76 -f- 10 = 5-076. To write the decimal portion down
in roods and perches, we multiply by 4 for roods, giving 0*304 of a rood ; to turn
this decimal into perches, we multiply by 40, giving 12' 16 ; the area is therefore
5 acres roods 1216 perches.

The method of working the planimeter is to fix one arm with
a weight, and to move the pointer at the end of the other arm
round the boundary of the plot ; the number of square inches
is then shown on a scale marked on a revolving drum. The
accuracy of the work done with this planimeter is more than equal
to that of ordinary scaling, and the method is much quicker.

Stang Planimeter. An exceedingly simple instrument for
measuring areas is the Stang planimeter made by Knudsen, of
Copenhagen. This instrument is shown in Fig. 157. It will
be seen that it consists of a light metal rod supported on two
legs ; one leg ends in a fine point, the other ends in a narrow
edge about J inch wide like the edge of a small axe.

Goodman's Planimeter. The above instrument has been

274

MINE SURVEYING.

modified by Professor John Goodman, by engraving on the bar a
scale by which the area measured can be read without calculation.
This scale constitutes the difference between the Goodman and
the Stang planimeters.

The method of using the instrument is thus described by
Professor Goodman : " Choose a point A (see Fig. 158), as near
the centre of the -figure as can be judged by eye, and from it
draw a line AB to the boundary. Hold the tracing-leg of the

FIG. 157. Stang planimeter.

instrument in the right hand, placing the point at A and the
hatchet at X i.e. with the instrument roughly square with AB
and press the hatchet in order to make a slight dent in the paper
at X ; then, the finger having been removed from the hatchet,
the tracing-point of the instrument is caused to traverse the line
AB and the boundary in the direction indicated by the arrows,
returning to A via AB, when it will be found that the hatchet
has taken up a new position, and it must be again lightly pressed
in order to make a fresh dent in the paper at Y (Fig. 158). The
instrument being held in this position, revolve the paper on
which the figure is drawn through about 180 (by eye), using Jhe
point of the instrument as a centre, and taking care that neither
the point nor the hatchet shifts while the paper is being turned.
The line AB will again be roughly at right angles to the axis of
the instrument, but in a reversed position (see dotted figure,
Fig. 158). Now cause the tracing-point to traverse the boundary
as before, but in the opposite direction, as indicated by the

CONSTRUCTION OF PLANS.

275

dotted arrows. The hatchet will take up the new position X,,
which may or may not coincide with X ; then, the mean of XY
and XjY measured on the scale engraved on the instrument is the

> x

i i

fee

> X

I l-l

area of the figure ; this can be readily read off by pricking a
central point, as shown between X and Xj by eye. When it is
inconvenient to turn the paper round, the instrument itself may

2 7 6

MINE SURVEYING.

be turned round to form a dent, X 1( on the opposite side of the
figure, as shown on the right-hand side of Fig. 158. Then, by
following the boundary in the direction of the arrows, Y x is
obtained. The area is the mean of the lengths XY and X i y i

measured off on the scale as before, or the area = - .

" When the area is large, the instrument will move through a
large angle, and consequently, if approximately square with AB
at starting, it will be a long way out at the finish. In such a
case all that is necessary is to see that the mean position of the
instrument is square with AB."

Professor Goodman considers that his planimeter is quite
accurate ; in comparing it, however, with Amsler's planimeter,
he would liken his to an ordinary foot rule, and Amsler's to a
carefully made vernier reading-gauge.

Area-computing Scale. Mr. W. F. Stanley makes a useful
scale for computing areas. The scale and method of using it
can be explained on reference to Fig. 158A. The area to be

-b

^^^^^^^^^

.N\

^J^S^iRs^iS^SisS^

"" ' f

1 i

i i i i i

Jo o^H

FIG. 158A. Stanley's scale for computing areas.

measured is covered with a sheet of transparent paper on which
parallel lines are ruled, the distance between these lines being
equal to 1 chain on the scale of the plan ; thus, if the scale is
2 chains, the lines will be half an inch apart.

CONSTRUCTION OF PLANS.

277

The scale has a sliding frame, a, attached
to it, across which is stretched a fine wire, I,
and under the wire is a pointer, c.

The pointer is put at on the scale, and
the wire is then placed over the point A on
the figure to be scaled, and the slide moved
to B. The scale is then moved so that the
wire is over the point C and the slide moved
to D, and so on to the bottom of the figure.
The reading of the pointer on the scale gives
the acreage.

Slide Rule. In the calculation of areas
and of many other figures required by the
surveyor, the slide rule (shown in Fig. 159) is
of great use. By means of this instrument,
calculations can be rapidly accomplished
without any strain on the head, the detection
and elimination of errors being achieved by
repetition of the calculations by several per-
sons. For the method of using the slide
rule, the reader is referred to one of the
numerous treatises on the subject. 1

Professor Fuller's Calculating Slide Rule.
This form of calculating machine (shown
in Fig. 160), which is said to be the simplest
yet made, is found to facilitate very greatly
the numerous arithmetical calculations re-
quired in the office of the engineer, architect,
and actuary. 2

Its range is greater than most arithme-
tical machines, as, besides the operations of
multiplication and division which many in-
struments can only perform, results requiring
the reciprocals, powers, roots, or logarithms
of numbers can be quickly and easily obtained
by its use.

1 "The Slide Rule," by Charles N. Pickworth, Whit.
Sch., price 2s. ; " The Slide Rule, its Principles and Appli-
cations," by John W. Nasmith, price 3. 6d.

See pamphlet by Professor George Fuller, on the
Spiral Slide Rule, published by E. and F. Spon, London.

FIG. 159. Slide rule.

278

MINE SURVEYING.

The rule consists of a cylinder, d, that can be moved up and
down upon, and turned round, an axis,/, which is held by a
handle, e. Upon this cylinder is wound in a spiral a single
logarithmic scale. Fixed to the handle is an index, b. Two
other indices, c and a, whose distance apart is the axial length
of the complete spiral, are fixed to the cylinder g. This cylinder
slides in /like a telescope tube, and thus enables the operator
to place these indices in any required position relative to d.

FIG. J 60. Fuller's slide rule.

(Kindly lent ly Messrs. W. F. Stanley awl Co., Ltd.)

Two stops are so fixed that when they are brought in contact,
the index b points to the commencement of the scale, n and -ni
are two scales, the one on the movable index >/, the other on
the cylinder d.

The use of slide rules has been confined to roughly approxi-
mate calculations, as the length of scale hitherto made was
sufficient only for about 160 divisions. In the new rule above
shown the length of scale is 500 inches, and the number of
divisions 7250 ; consequently, the approximation obtained by
its use is sufficient for most of the calculations required by
engineers.

CHAPTER XIV.

MEASUREMENT OF MINERAL TONNAGES CALCULATION OF CONTENTS
OF PIT-HILLS CALCULATION OF EARTHWORK, ETC.

Calculation of Tonnages. To calculate the tonnage of coal
contained in any given acreage, it is necessary to know the
specific gravity of the coal and the average thickness of the
seam.

Specific Gravity. By " specific gravity " is meant the ratio
of the weight of any substance to that of a standard substance
(usually pure distilled water).

The specific gravity of any solid which is not soluble in
water may be found as follows :

Weigh the body in air, then in pure distilled water. Then

. ., weight in air

specific gravity = . , , . r- 5 r-r-r^

weight in air weight in water

If the substance is lighter than water, a known weight
is attached to it to cause it to sink, which is afterwards
deducted.

Knowing the weight of the standard (water), we can find the
weight of the substance if we know its specific gravity. Thus,
if the specific gravity of a certain coal is 1*3, the weight of a
cubic foot may be calculated. The specific gravity of water is
1, and the weight of a cubic foot is 62'5 Ibs. ; the calculation
will therefore be as follows :

1:1-3:: 62-5 : 81-25

Weight of a cubic foot of coal whose specific gravity is 1/3,
81-25 Ibs.

Table XV. shows the specific gravity of various coals and
other substances, and the authority :

280

MINE SURVEYING.

TABLE XV.

SPECIFIC GRAVITIES OF VARIOUS SUBSTANCES.

Substance.

Specific gravity.

Authority.

Substance.

Specific gravity.

Authority-

Coal-

Sandstone

Anthracite

. 1-53

Molesworth

Caithness

2-638

Molesworth

1-3 to 1-84

Trautwine Derby Grit

2-4

Molesworth

usually 1-5 Cheshire

Cannel ...

1-272 | Molesworth j Eed ...

2-15

Molesworth

Fire-clay ...

1 -8 Molesworth ! Slate

Granite

Anglesea

2-87

Molesworth

Aberdeen

2-62

Molesworth

Welsh ...

2-83

Molesworth

2*56 to 2-88 ! Trautwine

Basalt-

Limestone...

2-58

Molesworth

Scotch . . .

2-95

Molesworth

2-4 to 2-86 Trautwine

Sand-pit

Limestone

Coarse . .

1-61

Molesworth

Blue Lias

2-467

Molesworth

Fine

1-52

Molesworth

Portland

2-423

Molesworth Shingle . . .

1-42

Molesworth

Bath

1-978
2-1

Molesworth ,-, ,, (from
Trautwine Earth Uo

1-52 \
2-00 /

Molesworth

Sandstone

Gypsum . . .

2-286

Molesworth

Bramley

Shales ...

2-4 to 2-8

Trautwiue

Fall ...

2-5

Molesworth

The ordinary coal of this country weighs from 78 Ibs. to
82 Ibs. a cubic foot : 80 Ibs. may be taken as an approximate
average (or specific gravity = 1*28).

It is usual to calculate the weight of coal per foot thick per
acre ; thus an acre contains 4840 sq. yards, or 43,560 sq. feet.
At a foot thick, 1 acre contains 43,560 cub. feet, which, at 80 Ibs.
to the cubic foot, weigh 3,484,800 Ibs., or about 1555 tons.
Probably no coal in this country weighs less than 1500 tons per
foot thick per acre, and very few seams, except anthracite, reach
1600 tons per foot thick per acre ; 1550 tons may be taken as
an approximate average weight. Having fixed on the weight
per foot thick per acre, it is a simple matter to multiply this by
the average thickness of the seam in feet and decimals ; thus,
if the coal averages 4 feet 8 inches in thickness, the weight per
acre is say 1550 tons x 4*66, or 7233 tons.

Produce of Coal Seams. Owing to loss in working, the
tonnage of coal obtained per acre is, of course, less than the
actual tonnage existent ; a very usual figure taken to represent
the actual produce of coal is 110 tons per inch per acre. Thus,
if the thickness of the seam is 5 feet, the produce will be
110 x 60 = 6600 tons per acre. The actual weight of coal
existing per acre, supposing it to be of the average specific

MEASUREMENT OF MINERAL TONNAGES.

281

gravity, will be 1550 X 5 = 7750 ; thus the allowance for waste
in working in this case is just under 15 per cent.

Increase of Area or Thickness due to Inclination. When the
acreage of coal is measured off a plan, it is necessary, in order
that the correct tonnage may be found, that the thickness of
the coal should be measured on a line perpendicular to the
plan, that is to say, on a vertical line. If the seam is inclined,
the thickness measured on a vertical line will be greater than
the thickness -as measured at right angles from roof to floor.
If, therefore, the thickness of the seam as given is a measure-
ment at right angles to the dip, it will be necessary to increase
the thickness to that given by the measurement of a vertical
line through the coal. The proper increase in thickness can be
ascertained from a drawing on a large scale (see Fig. 161). A
horizontal line is shown,
and the seam is drawn
according to the angle
of inclination, say 25,
and is plotted to the
thickness measured, 4
I'eet ; a vertical line is
now drawn, and the
thickness of the coal on
this line can be scaled.

Instead of making
this drawing, the thick-
ness on the vertical line
can be more quickly and
accurately calculated. It will be" seen from the figure that if
the horizontal line is treated as the length of the radius of an
arc, the inclined line (of which the horizontal line is the plan)
is equal to the secant. In the same way, if the thickness of the
seam measured at right angles to the dip is treated as the
radius of an arc, the secant of that arc is equal to the thickness
of the seam measured on a vertical line.

Assuming the inclination of the seam to be 25, and radius
1, the secant is M033779, or say M0338; this, multiplied by
4, gives the thickness of the coal in a vertical line. The
tonnage of coal under any horizontally measured area is then
found by multiplying it by this increased thickness in inches,
and the tons weight per inch. The same result is arrived at if,

HORIZONTAL LINE

FIG. 161. Increased thickness pf coal measured
on a vertical line when seam is inclined.

282 MINE SURVEYING.

instead of increasing the thickness, that is taken as measured
at right angles to the dip, and the acreage is increased from
that measured on the plan to that which might be measured
on the slope ; the increase of measurement will be in the ratio
of the radius to the secant. Thus, if the acreage on the plan
was 100, the acreage of a seam of coal lying at an inclination of
25 will be found as follows :

1 : 110388 : : 100 : 110-838

Increased acreage 110 - 338.

The shape of the figure from which the acreage is scaled
is immaterial as long as the whole acreage is on the same
inclination.

Increase of Tonnage due to Inclination. In case the tonnage
has been calculated from the thickness of the seam as measured
at right angles to the dip and from the area on the plan, the
increase of tonnage due to the dip can be calculated by increasing
the tonnage in the same ratio as the secant of the angle of
inclination is greater than the radius : thus, if the tonnage
calculated is 1000, then, to allow for the increased tonnage due
to a dip of 25, we have the following sum :

1 : 1-10338 : : 1000 : 1103-38

Increased tonnage, 1103'38.

The calculation of tonnages extracted from veins or pockets
of ore or quarries and sandpits is much less simple, owing to
the irregular shape of the excavation, and a number of longi-
tudinal and transverse sections are often necessary for accurate
calculations.

Calculation of Contents of Cuttings and Embankments. The
contents of a cutting may be calculated from the average width,
depth, and length. The quantity is generally given in cubic
yards ; if the calculation is made in feet, the sum must be
divided by 27 to give the result in cubic yards.

Fig. 162, a, shows a cutting in section, from which it will be
seen that the average depth of the cutting is ascertained from
the measurement of the depth in six equidistant lengths of cross-
section, measuring respectively 8, 9, 12, 12, 9, 8, the sum of
which, divided by 6, gives the average depth as 8 feet. The
total width of the cutting is 60 feet, and the area of the cross-
section is therefore 60 x 8 = 480 sq. feet, and if the length is
100 feet, the cubical contents are 480 x 100 = 48,000 cub. feet.

CALCULATION OF CONTENTS OF PIT-HILLS.

283

In case the cutting varies in section, measurements must be
taken to ascertain the average area of the cross-section. Thus,
referring to Fig. 162, b, a cross-section is shown of which the
average width is 40 feet and the average depth 4'5 feet ; the area
of the cross-section is therefore 40 x 4'5 = 180 sq. feet. If the
distance between a and b is say 100 feet, and the change of section

6OFeet

FIG. 162. Calculation of earthwork.

is regular and gradual, the average width of the top of the
cutting will be 50 feet, and the average depth at the centre will
be 9 feet. The area of a cross-section midway between a and b
will thus be (20 X 9) + (15 x 9) = 315 sq. feet. The cubic
contents may then be found by the prismoidal formulae. 1

Prismoidal Formulae. Let A], A 2 , A 3 be the areas of three
sections at equal distances apart, then the volume of the portion

between A x and A 3 will be V =

where d is the

distance between A x and A 3 . In the case above taken

v _ 480 + (4 x 315) + 180 -

V 7i X

100 = 32,000 cub. feet

Where the cross-slope of the ground is considerable, and the
depths of the cutting differ widely, cross-sections must be taken
at each place, and the areas calculated independently ; and the
cubic contents should then be calculated by the prismoidal
formulae.

Central
*Sfope Port, *Slope*~

FIG. 163. Calculation of earthwork.

The following formulae may also be used in the measure-

1 If the central cross-section had been multiplied by the length, it would give
the contents as 31,500 cub. feet, or within 2 per cent, of the real quantity.

284

MINE SURVEYING.

ment of earthworks. 1 Keferring to Fig. 163, H and h are heights
of section in feet at each end of a length I in feet; V is the
sum of the areas of the two slopes at one end ; v is the sum of
the areas of the two slopes at the other end; and e is width
of base of cutting. The slopes are calculated as the frustum of
a pyramid, the centre as that of a wedge.

B = cubic contents of both slopes = J(V + \/Vv 4- v) x I
D = cubic contents of central part = 4(H 4- h)e X I
C = total cubic contents of length I in feet = B + D

If the transverse section is on a slope instead of horizontal,
as in Fig. 164, the two slopes must be calculated separately.

e e

FIG. 164. Calculation of sidelong ground.

A and A! are the areas of slopes at one end, and a, a^ at the
other.

Then B = }(A + ^/Ka + a)l + ,\(A, + \Mi rt i + a,)Z
D = i(H + h)e X I
C = as before (B + D)

Earthwork tables are published which are designed to make
the calculations shorter. 2 They are all based on similar formulte
to the above.

1 Royal Engineers 1 Aide Memoire Pocket-book.

2 "Handy General Earthwork Tables," by I. H. Watson Buck (Crosby Lock-
wood and Son, London). Price 3. 6d.

" Earthwork Tables," by Joseph Broadbent (Crosby Lockwood and Sou, London)
Price 5.

"Earthwork: A Method of calculating the Cubic Contents of Excavations and
Embankments by the aid of Diagrams," by J. C. Trautwiue, C.E. (E. and F. Spon,
London). Price 8s. Qd. net.

"Earthwork: Diagrams for the Graphic Calculation of Earthwork Quantities,"
by Alfred Henry Roberts, C.E. (E. and F. Spon, London). Price 10s. Gd. net.

" Earthwork Tables," by W. Mucgregor (E. and F. Spon, London). Price 6*.

"Earthwork Tables," by David Cunningham, C.E. (E. and F. Spon, London).
Price 10s. Qd.

" Tables showing the Contents of Excavations, Areas of Slopes, etc.," by George
P. Bidder (published by Vacher and Sons, Westminster). Price 2.

CALCULATION OF EARTHWORK.

285

The calculation of the contents of embankments is similar
to that of cuttings.

Restoration of Damaged Land. When a mine is abandoned, it
is often necessary to restore the land to an agricultural condi-
tion, and, if there are heaps of shale or other waste, they must
be levelled and covered with soil. The soil from under this heap
will probably have been removed before the heap was tipped,
and will now be available ; if not, it might be necessary to incur
the increased expense of removing the shale-heap in order to
excavate from beneath it the soil so buried. This, of course,
would be a very expensive process, in many cases more than
the value of the land. In levelling the heap, however, it will
cover a greatly increased area : if the soil from this increased
area is removed and respread over the levelled shale, it may be
made to cover the whole area.

tt~S5F"*l* w '~
,ig^--^-O

FIG. 165. Calculation of contents of shale-heap.

Calculation of Contents of Shale-heap. It is sometimes desired
to calculate the area that will be occupied by the shale-heap
when levelled, and to do this the cubical contents of the shale-
heap are measured. This may involve a great deal of calcula-
tion and measurement. Fig. 165 shows a plan and elevation

286 MINE SURVEYING.

of a shale-heap. In order to obtain the exact cubical contents
of this heap, it would be necessary to mark out, with the level,
contour lines, as shown on the plan, and then to survey the
position of the pegs. If these contour lines are at equidistant
altitudes of say 6 feet, the heap will be divided into a series of
horizontal sections, shown on the plan 1, 2, 3, 4, 5, 6, 7, 8.
The average area of each section will be the area enclosed by
the dotted lines half-way between the contour lines ; and the
cubical contents of each section can be calculated by multiply-
ing this area in square feet by the depth in feet, which, in this
case, is 6 feet.

Where there is no particular reason for desiring to know the
number of cubic yards in the heap, the area it will occupy when
levelled can be roughly ascertained with much less labour.
Thus, if it is decided that the slopes of the waste-heap, when
it is "levelled," shall be 1 in 10, it is only necessary to know
the profile of the shale-heap, and to draw a give-and-take line
of section at a slope of 1 in 10, equalizing cutting and bank, to
find approximately the distance to which the slope will extend.

It must be borne in mind, in drawing the give-and-take line,
that it represents one of an infinite number of equidistant radial
lines drawn from the centre of the hill to the circumference,
and that the width of the cutting between any two radial lines
is therefore less near the centre than near the circumference,
and for equal depths of cutting the amount of material on any
given line of section between any two radial lines varies directly
as the distance from the centre. If the hill is levelled down
from the centre in every direction all round, the average depth
of the cutting on the hill must be greater than the average
depth of the embankment formed, in proportion to the area of
the cutting on the hill and the area occupied by the ground
removed from the hill. Thus, referring to Fig. 165, the centre
of the hill is at a, the average radius of the cutting may roughly
be taken as ab, and the average radius of the ground to be
filled up may be roughly taken as ac. Suppose the length ab to
be 133 feet, and the length ac to be 400 feet, then the relative
areas of the circle and ring as described by those radii is as
133 2 : 400 2 133 2 : : average depth of bank : average depth of
cutting ; therefore the depth of the cutting at b will be 8 feet for
1 foot in depth of embankment at c. It must, however, be
borne in mind that the cutting at b will be more solid than the

CALCULATION OF EARTHWORK.

287

embankment at c, and, making some allowance for this, the
depth of the cutting at b may be say six times the depth of
the embankment at c. In order to arrive at this result, it may
be necessary to draw a few trial sections, and modify the radii
b and c.

In cases which very frequently happen in practice, no calcu-
lation is necessary (see Fig. 166). In this case the slope agreed

Longitiutuuil Section

FIG. 166. Approximate method of finding the area occupied by shale-heap
when levelled.

upon as suitable for restored I land, say 1 in 10, is first ruled off
as shown on the longitudinal section, giving approximately
equal bank and cutting. This reduces the height of the hill,
and this reduced height is shown on the transverse section by
a dotted line. A give-and-take line at a slope of 1 in 10 is then
drawn on the transverse section, and the height of the hill still
further reduced. The area occupied by the heap spread out can
be scaled off the plan made by projecting the give-and-take
section lines.

CHAPTER XV.

SUEVEYING BORE-HOLES.

IT frequently happens that bore-holes are deflected from their
vertical course. This has been noticed particularly with the
diamond boring tool, of which the grinding action is more easily
carried on in a crooked hole than boring by percussion. It
is not surprising that bore-holes should be crooked; the only
wonder is that they are so often straight, or nearly straight.
Take the case, for instance, of rope boring. The bore-hole is
made by a falling chisel at the bottom of a straight, stiff bar of
iron not more than 30 feet in length. Such a bar cannot, of
course, go round an angle, but it can go round a curve, just as
a railway waggon with a long wheel-base can go round a curve.
Suppose that there are enlargements on the rod intended to
nearly Qt the hole, these enlargements being 20 feet apart and
i inch less in diameter than the hole, then the rod may lie at
an inclination of 1 inch in 20 feet to the direction of the hole,
or 1 in 240. Considering, however, the rod as the chord of an
arc, and the 1-inch play as the versed sine, this corresponds to
an angle of about 58', and the radius of the circle will be found
as follows: The natural sine of 58' is 0'0169 feet; the actual
sine taken in the bore-hole is 10 feet ; then 0*0169 : 10 : : 1 :
radius of the circle. The bore-bole is thus started on a curve
with a radius of about 593 feet, and if it should continue on this
curve for a distance equal to the radius that is, 593 feet the
direction of the bore-hole may be changed to the extent of 60.
There is, however, a continual tendency on the part of the
falling weight to straighten the hole. If the length of the
straight, stiff bar between guides is less than 20 feet, the angle
of possible deflection will be greater than 58'.

In boring with rods there is the same liability to deflection,

SURVEYING BORE-HOLES. 289

and the angle of deflection does not depend on the length of the
boring-rods, but on the length of absolutely stiff rod below the
sliding-joint or free-fall arrangement. Although the boring-
rods, when taken individually, may seem very stiff, yet when
several hundred feet are screwed together, they make a very
flexible rod, that will easily go round a curve. As in the case
of rope-boring, the tendency of the cutting tool is to go straight,
and a crooked hole is the result of some deflecting cause, such
as a hard pebble or boulder, or the hard surface of some highly
inclined stratum.

In considering the action of a revolving or grinding borer
like the diamond rock-drill, somewhat similar considerations
prevail, but there is a greater tendency to deflection from a
straight line ; part of the weight of the rods necessarily rests
upon the boring head in order to give the requisite pressure to
grind away the ground. This weight would naturally tend to
bend the rods in case of any jar, tending temporarily to deflect
them from a perfectly straight line ; the stiffness of the rods,
and the length of the stiff part, and the tightness with which
they fit the bore-hole, have to be relied on to keep the hole
straight.

In the diamond borer the crown fits the hole, but the core-
tube, to permit the free passage of water and sand up the bore-
hole, is frequently a good deal smaller than the bore-hole, thus
permitting of a considerable deflection, the amount of which
can be calculated in the same manner as that given in the
example for rope boring.

If the bore-hole should be deflected by coming in contact
with a highly inclined smooth surface of rock, there is no reason'
why the deflection should not continue until some other surface
is met with, tending to cause a deviation in the other direction.
This accounts for the circumstance that bore-holes frequently
deviate greatly from the vertical, sometimes, it is said, to the
extent of 40 or 50, or even more ; and, indeed, there is no
absolute security that a bore-hole will continue to descend ; it
might gradually turn into a horizontal direction, or even into
an upward direction.

In order to ascertain the course that has been taken by a
bore-hole, and to prevent great and wasteful deviations from
the intended line, it is just as necessary to survey a bore-hole
as it is in tunnelling to survey the tunnel. There are, however,

290

MINE SURVEYING.

FIG.

great difficulties in surveying a hole which naturally suggest
themselves. These difficulties have been overcome by several
ingenious instruments. The first of which the writer has any
knowledge was designed by Mr. G. Nolten, Dortmund, Germany. 1
Nolten's Instrument. The object of this instrument is to
ascertain the inclination of the bore-hole and the direction of
the inclination that is to say, whether the inclination is
towards the north, south, east, west, or
some intermediate point of the compass.
One of the most important parts of the
instrument is shown in Fig. 167. This
is a glass cup, in which is a liquid, the
level of which is shown by the line ab ;
this liquid may be hydrofluoric acid,
which acid has the quality of dissolving
glass. If, therefore, it is allowed to stand
in a glass cup, the glass below the surface
of the liquid will be gradually dissolved.
167. Nolten's in- Suppose, then, that the glass is inclined
so that the level surface of the liquid is on
the line ab; if the liquid is allowed to rest
with the cup in this inclined position, it will eat away the glass
up to the line ab.

If, instead of pure hydrofluoric acid, a mixture of 1 part acid
and 4 parts water is used, half an hour will be sufficient time
to make a clear and permanent mark at the surface of the
liquid. If some of the liquid is now poured out of the glass,

and the vessel is allowed to stand in a
perfectly vertical position, the surface
of the liquid dc (see Fig. 168) will be
level, and if left stationary for half an
hour, this lower surface-line will be
etched upon the glass. It will be

ment, showing glass cup, readily seen that the angle the line ab
{ion'CteZnyLf lina " m ^ s with the line dc is equal to the
angle made by the sides of the glass

with the vertical line xy (Fig. 167) when it is held in an in-
clined position, or in other words, the angle aec (Fig. 168) is
equal to the angle bxy (Fig. 167).

1 N. Eng. Inst. M.E., vol. xxix. pt. 2: Paper by C. Ziethen Buuuing and .1.
Kenneth Guthrie.

FIG. 1G8. Nolten's instru-

SURVEYING BORE-HOLES. 291

Then, in order to ascertain the inclination of a bore-hole, it
is only necessary to lower such a glass, partly filled with this
acid liquid, rigidly fixed in a straight line with the sides of a
long tightly closed tube.

Let this tube, then, be lowered down the bore-hole to the
bottom, or to any other required depth. Whilst it is being
lowered, the acid will shake about and will leave no clear mark
upon the glass ; when it has reached the required depth, if it
is allowed to remain unmoved for half an hour, the level of the
liquid in the cup will be etched upon the glass, and will form
a permanent record of the angle of inclination of the glass, and
also of the tube in which it was fixed. The glass may now be
withdrawn and placed upon a perfectly horizontal table, and
the difference between the surface of the liquid and the mark
upon the glass will show the angle of inclination of the bore-
hole. If a little of the liquid is poured out of the glass, and it
is then placed on the horizontal table, and left stationary for
half an hour, a line corresponding with the horizontal line will
be permanently etched on the glass, and the angle of inclination
can afterwards be measured at leisure.

In order to record the direction in which the hole is pro-
ceeding, in case it is not perfectly vertical, another instrument
is combined with this one, and fixed in the same tube. This
instrument consists of a compass-needle free to revolve in a
horizontal plane on a vertical pivot, and of a watch which can
be set to operate a lever, so that the needle can be clamped at
the exact time to which the watch is set. Then, suppose the
instrument to be lowered down the bore-hole, the watch having
been set to operate in three quarters of an hour, one half-hour
is occupied in lowering the instrument to the required depth in
the bore- hole; one quarter of an hour remains for the needle
to steady. At the expiration of that time, by the action of the
watch, the needle is clamped in the magnetic meridian. Since
the compass-box is fixed in the same case as the glass contain-
ing the acid, the direction of the inclination of this glass can be
ascertained before they are disconnected one from the other.

The construction of the apparatus can be gathered by
reference to Figs. 169 and 170. The points to be noted are that
the recording apparatus must be placed in a water-tight case
made of brass or some other metal which has no attraction for
the needle ; this case must be not only water-tight at ordinary

292 MINE SURVEYING.

pressures, but at very high pressures, as it may be lowered to
the bottom of a hole (containing water) several thousand feet
in depth. It must also be remembered that, if the instrument
is put in a hole already cased with iron tubing, the compass-
reading will not be exact, although the average of a number of
readings may be approximately correct ; where, however, there
is no iron the reading of the needle will be correct, unless there
are magnetic minerals or rocks, the existence of which will
be discovered in boring.

As the sides of the hole are probably not perfectly straight,
the longer the tube in which the apparatus is put the more
likely will it be to show the correct inclination. The apparatus
has been constructed small enough to go into a 3-inch hole, and
doubtless, if necessary, one could be made to suit the smallest
size of bore-hole.

The following is a description of the figures, given by Messrs.
Bunning and Guthrie : *

" The cylindrical casing of the instrument is shown in
section in Fig. 1. The opening aa of the cylinder A, Fig. 1,
is shown in Fig. 3 in section, and in Fig. 4 in perspective. Into
the space dp (Fig. 1) is fixed, by means of a rod, the instrument
shown in Figs. 2 and 5, which consists of three plates, a, e,
and o (Fig. 2), shown by dotted lines in Fig. 1.

" These plates, or divisions, are placed at right angles to the
longitudinal axis of the instrument, and are connected together
by three vertical strips of brass, shown in Fig. 5.

" Fig. 4 shows the inner projecting flange of the cylindrical
casing, also seen in ad (Fig. 1). This flange is divided into six
equal parts, three of which are alternately cut out. Fig. 5 shows
how the three plates are similarly cut out, so that they can
slide through the projecting flange. After sliding the inner
instrument through the flange in Fig. 4, it is turned one-sixth
of its circumference towards the right, the catch z preventing
it from going further ; then the three outer projections of the
upper plate in Fig. 5 will stand under the three inner projecting
parts in Fig. 4.

" The cover oa (Fig. 1), is now placed over the rod, which, by
means of the nut m, can be tightly screwed down. The rounded
end-pieces in Fig. 1, held by nuts, are only used to round the

1 For convenience in reference, Figs. 169 and 170 are subdivided ipto separate
Figs. (1 to 17), and these latter arc the figures referred to in this description.

SURVEYING BORE-HOLES. 293

FIG. 1. FIG. 2. FIG. 3.

.'.' o

FIG. 6.

Fir,. 4.

FIG. 5.

FIG. 7.

FIG. 8.

FIG. 9.

FIG. 10.

Fia. 160. ^Tolten's instrument. Details of working parts.

294 MINE SURVEYING.

instrument. The glass containing the etching liquid is placed
in a brass ring, ktno (Figs. 9 and 10), which is fastened into the
lowest plate (Fig. 2).

" This glass is closed by a flat lid, the lower surface of which
is lined with gutta-percha, and which is kept in its place by the
cone gli (Fig. 2), and a screw above.

" The compass is placed upon the middle plate, the pin upon
which the needle swings being made high. Over the compass
is placed the watch with its stop arrangement, which is shown
in natural size in Fig. 11, and in Fig. 13 the lever arrangement
is seen twice its natural size. The watch is fastened on its
upper side to the plate c (Fig. 2), and on the lower side is
soldered the pin d, which keeps the watch in position by fitting
into the hole in the guide d, shown in Fig. 6.

" The winding axle, which is lengthened outwardly, and to
which is connected a small metal plate, m (Fig. 11), pushes the
lever arrangement by means of a pin towards the right ; this
pin is seen at d in the small anchor drf(Fig. 13). This anchor
is sketched as seen from above, and the rods under it are drawn
in elevation. The former is placed in a horizontal position
on the vertical rod abr, upon which a movable rod turns on
the axle g.

" Upon the top of this rod the catch /is fixed, which moves
in the slotting / of the anchor, while the pin r of the latter
fits into the hole r shown in the rod abr. In the lower catch p
the moving rod acts upon a brass spring, x.

" When this rod is moved towards the right, the spring is
released, and strikes the pin h in Fig. 11, which, on being
pressed down, fixes the magnetic needle. In Fig. 12 the movable
rod is shown in two positions, before and after being stopped.
The point d is kept out of reach of the plate m by the movable
rod, and retained in that position so that the watch is free to
work. The anchor and movable rod are held fast in the position
shown by the dotted lines. The stopping of the watch at any
required time is effected by the placing of the plate m in
Fig. 11.

" This plate, as shown in dotted lines in the figure, is placed
at the number 4, if the watch is required to fix the needle after
an interval of four-fourths of an hour ; and is placed at the
number 3 or 5, if it is desired to fix it at three-fourths or five-
fourths of an hour respectively.

SURVEYING BORE-HOLES.

295

FIG. 13.

FIG. 11

FIG. 14.

FIG 16.

FIG. ]5.
FIG. 170. Nolten's instrument. Details of working parts.

296 MINE SURVEYING.

" Should it take, for example, half an hour to lower the
instrument to the measured depth where it is to remain, the
stopping of the magnetic needle occurs when it is in perfect
rest, if the plate m is set on the number 3.

" That the stopping of the needle is occasioned through the
plate m, and not, perhaps, by the shaking loose of the spring
in lowering, and also that it takes place at the required time,
is proved by a small mark, made by a pencil fixed in the point
of the anchor, upon a piece of paper fixed upon m.

" The compass case (Fig. 11) is covered by a glass lid, kept
in its place by a pin placed above. The upper rim of this lid is
divided into a hundred parts visible from within and from
without, and stands concentric with the ring Jcmo (Figs. 9 and
10), in which the acid glass is placed, the under half of which,
mo is also divided into a hundred parts, so that in both vessels
the zero point and all other . divisions stand vertically under
each other.

" The upper half of this ring is turned down to half its
thickness, seen in Fig. 10. Over this part a brass ring is fitted,
which can be turned round, and is divided into 360.

" Suppose, for example, the north point of the needle in Fig. 2
is to the right. Also suppose the glass fixed into the ring
(Fig. 10) has the etched marks shown in Fig. 7. The dip of
the instrument will be towards the south, the dip being where
the water-level ab is lowest, therefore towards a, which stands
exactly opposite the north point if the marks are as shown.

"In Fig. 8, with the lower curve as representing the lowest
point, which is exactly in the middle of the back side of the
glass #, the dip will in this case be towards the west. If the
upper curve in Fig. 8 represents the lowest point of the etching
fluid at y, so will the dip be south-west.

" To find easily, and at the same time accurately, the direc-
tion of the dip of the instrument, the position of the north point
is compared with the before-described glass lid of the compass,
which is divided mto-aJiundred parts, and the number on the
compass-holder which happens to be opposite the north point
of the needle when stopped.

" Take, for example, this number to be 50. Then the movable
ring Jem (Fig. 9) is turned round until the zero point is over 50
on the bottom ring mo, which is concentric with, and similarly
marked to, the divisions on the compass case above mentioned.

SURVEYING BORE-HOLES. 297

Upon the movable ring, the zero point of which will be vertically
under the north point of the needle, the bearing is read of the
lowest point of the etched ring in the glass, which, in the
example given in Fig. 7, is 180, and in Fig. 8, 270 and 225
respectively.

" Finally, the Figs. 14, 15, and 17 represent the screw-
press, which is placed over the lid of the instrument ao
(Fig. 1). The key (Fig. 16) works in the space q of the part
(Fig. 17). On this press being placed over the lid, pressure is
brought to bear on the cover ao by means of the two screws
shown in Fig. 14, the pressure being followed up by the nut mo
turned by the key (Fig. 16) ; the whole of which is shown in
section in Fig. 15. After sufficient pressure has been brought
to bear, the nut h is loosened, and the parts 14, 15, and 17
taken off.

" This covering, together with the packing round the rod, has
been proved water-tight at a depth of 3280 feet. The manner
by which the middle rod is made water-tight is shown in Fig. 1,
where ad represents a sort of metal gland, round the top inner
edge of which packing is placed. ... As regards the imper-
meability to water of the instrument, the following experience
was gained : When hard or soft gutta-percha was used, it
proved ineffective at a depth of 1312 feet ; but when varnished
paper was used at a depth of 3280 feet, no water was found in
the instrument."

The writers of the paper found that when the instrument
was put into a wrought-iron tube, the reading of the compass
needle was sometimes 39 different from the true direction of
the tube, but an average of three readings made within a length
of 8 feet gave a bearing within 5 of the true direction. There-
fore, in ascertaining the direction of a hole lined with iron tubes,
it would be necessary to take at least three observations at a
distance of 2 or 3 feet one from the other.

Messrs. Bunning and Guthrie refer to the use of this
apparatus in ascertaining the inclination of some bore-holes.
Referring to the bore-hole Sirius, near Crefeld, on being tested
at the depths of 890, 1100, and 1230 feet, it was found that the
inclination from the perpendicular was 3, and the bearing
W.S.W. Another bore-hole at Tellus, by Uerdingen, at depths
of 750 and 796 feet, gave an inclination of 11. In the bore-hole

298 MINE SURVEYING.

at Berggeist, at a depth of 600 feet, the inclination was 4|.
These three bore-holes were put down by percussion boring.

In 1874 the bore-hole Gustav Adolph, near Dienslaken,
bored with a turning borer, 1 was stopped at a depth of 750 feet,
and was tubed all the way with the intention of proceeding
further at some future time. It was subsequently surveyed, with
the following results :

At a depth of 200 feet 2 inclination

BOO 3f

,, 430 8i

750 47

After this it was decided not to proceed with the boring.

Other experiments were made in a bore-hole to a depth of
3280 feet. The diameter of the instrument used in the above
experiments was 3 inches.

Macgeorge's Clinometer and Compass. This ingenious instru-
ment, designed by E. F. Macgeorge, of Victoria, Australia,
is described in Engineering of March 13 and April 3, 1885.
The principle upon which it is constructed is somewhat similar
to the one last described; but gelatine is substituted both for
the hydrofluoric acid and for the stop-watch. Ordinary gelatine
is easily melted if the vessel containing it is immersed in hot
water, whilst it solidifies at a temperature of about 70 F.
When once the jelly has been melted, it takes several hours
to stiffen, so that if a phial containing liquid gelatine is lowered
into the bore-hole, it will not stiffen till some time after it has
reached the bottom ; if, therefore, a plumb-bob is suspended in
the liquid gelatine in the phial, after the phial has been lowered
to the bottom of the hole, or to some less distance, the plumb-
line will hang in a vertical line ; if the phial is now left for some
hours, the jelly will stiffen round the plumb-bob. If the phial
is vertical, its axis will be parallel to the plumb-bob ; if, however,
the phial is not vertical, the plumb -bob will not be parallel with
its axis, and when it is withdrawn from the hole, the angle of
inclination can be measured by putting the phial in a vertical
position, and measuring the inclination from the vertical of the
plumb-bob, which remains firmly embedded in the stiffened

jelly.

If another phial is lowered down the hole in the same holder

1 Probably the diamond borer is meant.

SURVEYING BORE-HOLES.

299

as that which contains the plumb-bob, and in this phial is a
compass needle free to revolve in a horizontal plane upon a
vertical pivot, and this phial is also filled with liquid gelatine,
the needle will be free to swing into the magnetic meridian, and
will take that direction as soon as the phial becomes stationary
in the bore-hole. In the course of several hours the gelatine
will stiffen, and the needle will be fixed in the meridian. If
the hole is vertical, nothing
is to be learned from the
observation of this needle ;
but if the hole is inclined,
the direction of the inclina-
tion is recorded.

Fig. 171 is a sketch, not
of the instrument, but in-
tended to show the principle
upon which it acts, aa is
part of a bore -hole ; 1>1> is a
strong brass tube, water-
tight and capable of resist-
ing the external pressure of
water at the bottom of the
bore-hole ; c is a glass phial
filled with gelatine ; d is a
small plumb-bob suspended
in the phial ; e is another
glass phial filled with gela-
tine ; and / is a compass
needle on a vertical pivot ;
N is the north-seeking end,
S the south-seeking end of
this needle.

According to the above
sketch, the bore-hole is in-
clined towards the south, and the angle of inclination is about
22 J. On looking at the figure, it is evident that the observer is
on the east side of the needle, looking towards it, and the hole
slopes towards the left hand, and is therefore sloping southwards.
If it had happened that the hole was sloping towards the right
hand, the slope would have been northwards ; if the hole had
been sloping towards the observer, it would have an easterly

FIG. 171. Macgeorge's instrument. Dia-
grammatic sketch, showing principle.

300

MINE SURVEYING.

inclination, and if it had been sloping from the observer, a
westerly inclination ; and if the slope of the hole had been at
some intermediate inclination, the exact bearing could be read
off by careful observation.

Description of Macgeorge's Clinograph. Fig. 172 shows the
clinograph as made by Mr. Macgeorge. It is
sketched by the writer from the descriptions
given in Engineering. It shows a strong
brass cylinder or guide-tube, aa, about 6 feet
long, the diameter depending on the size of
the hole. This tube is closed at the top with
the solid plug b, the bottom of the tube is
also closed tight; the tube and the plugs
closing it must be strong and tight enough
to resist the water-pressure at the bottom of
the deepest bore-hole down which it may be
sent. The kind of washer or other means
required for making the plug water-tight are
not shown.

On the top of this guide-tube, and fastened
to the plug I), is fastened a hollow brass tube
c, with a bore in its upper part of not less
than half an inch ; where this tube joins the
plug it is thickened and the bore enlarged ;
there are six holes, ee. It is intended to
force cold water down this tube, which,
escaping at the holes ee, will fall down out-
side the guide-tube aa, and so keep it cool in
case the bore-hole should be warm. The
tube c is made of brass, in order that it
may not influence the magnetic needle ; the
top of the tube is jointed to a series of half-
inch iron tubes reaching to the surface.

f r the

showing guide-tube cooling water, but also for pushing the clino-
e g ra P h alon g the ^re-hole to the required
distance, the use of stiff tubes or rods being
necessary if the hole should be horizontal or not very steeply
inclined.

In the case of holes which are nearly vertical, or inclined at
an angle of not less than 45 from the horizontal, and which

SURVEYING BORE-HOLES.

301

are sufficiently cold for the jelly to congeal, these tubes are
unnecessary, and a cord may be substituted as shown in Fig.
171. The lower part of the cord should be made of brass wire
or vegetable fibre. Inside the strong guide-tube is a brass slide,
/; in this brass slide are fixed a series of clinostats, one above
the other, g, g. Mr. Macgeorge fixes five or six. The reason
for having this number is in order that any accidental inaccuracy
in the record given by one instrument may be checked by the
record from another. On the top of the slide is a spiral spring,
which keeps it tight and saves it from the shock of any
concussion. 1 This instrument serves the purpose of taking the
angle and direction of inclination of a bore-hole.

Inclination of Strata from Core. It can, however, be adapted
for the observation of the inclination of planes of stratification or
other joints in the strata. For the purpose
of this observation a core is left standing in
the bottom of the bore-hole (Fig. 173); a
core-holder is rigidly and securely attached
to the bottom of the 6-feet brass guide-tube
containing the clinostats. This core-holder
is a brass tube set eccentrically to the guide-
tube with a bell mouth, however, that guides
the core-holder over the core. Inside the
bell-mouthed tube is an inner split tube of
brass, smaller than the core, and also bell-
mouthed at the bottom. The apparatus is
forced down by the tubes from the surface,
and the bell mouth forced over the core ; the
inner tube is expanded as it is forced down
over the core, and holds it firmly at the
same time ; the centre of this tube not being
concentric with the core, great pressure is Sectvorvat/A
put upon the latter, and it is broken off by F IG . 173.]
the descending movement of the holder. instrument. Core-ex-

The instrument is now left unmoved for

several hours for the gelatine in the clinostats to stiffen, alter
which the whole apparatus is withdrawn, including the core,
which will have on the surface the same position in regard to

1 The writer presumes that there will be a similar spring at the bottom, and
thus the slide will be saved from severe concussion both when being lowered down
and when being drawn up.

yp5

302 MINE SURVEYING.

the compass needles and plummets of the clinostats as it had

in the bore-hole. 1

The clinostat is shown on a larger scale in Fig. 174/ 2 a is

a straight cylinder of glass, fitting accurately within the guide-tube
/(Fig. 172). The lower end of this glass cylinder
terminates in a short neck and a bulb, b ; the bulb is
filled with liquid gelatine; a small glass float, c,
carries a compass needle, d. 3 This lower bulb b is
closed with a cork, e, thus preventing the escape of
the needle and float. A small glass tube, /, passes
f\\a through this cork to the top of the glass barrel, and
out of the barrel through an air-tight cork and a
screw capsule, g. The upper part of the tube / is
enlarged into the bulb h ; this bulb is also filled
with liquid gelatine, in which is placed the plummet
i. This plummet consists of a thin glass rod, Jc,
terminating at the bottom in a plumb of solid glass ;

FIG. 174. and at the top in a hollow glass bulb, m ; this hollow

Srument 8 laSS bulb is a float - The size f this bulb is care -

Eniarged fully adjusted to the specific gravity of the gelatine,

nosTat! C so as J us t to carry the weight of the glass without

being so light as to press with appreciable force

against the top of the bulb h ; the weight I naturally seeks the

centre of gravity, and the glass rod k is in a vertical line, no

matter what is the angle at which the barrel a is held.

1 This method of taking the dip of the strata might be adapted to the hydrofluoric
acid apparatus. It must, however, be borne in mind that any indications of the dip
from a small bore-hole are apt to be misleading, as it is quite probable that the
inclination of the piece of ground from which the core was extracted might be in
the reverse direction of the general dip. If the inclination of a series of cores from
top to bottom of a deep bore-hole is taken, there is a greater probability of being
able to observe the general dip of the strata; but, in any case, the dip, as observed
in the bore-hole, is only the dip that the rocks happen to have under the very small
plot of ground through which the bore-hole passes.

2 Sketched by the writer from the description given in Engineering.

3 The description in Engineering refers to a pivot; it does not say what the
pivot is. Possibly there may be a point underneath the needle, partly supporting it,
but, if this is so, it is not plain, and it is not explained how the needle is kept from
being jerked off the point. The writer is, therefore, driven to the conclusion above
stated. If this is right, the only friction the magnetic force would have to overcome
in drawing the needle into the meridian line would be that due to the liquid
gelatine, and the friction of the upper part of the glass float pressing against the
surface of the bulb; this pressure, however, would be very slight. As the float will
have only just sufficient lifting power to carry the magnet clear of the bottom of the
bulb, the needle itself can never come in contact with the sides of the bulb.

SURVEYING BORE-HOLES.

303

Before lowering into the hole, the gelatine is melted by
warming ; the apparatus is then lowered into the hole, and left
stationary for say three hours, when it is withdrawn; the
plummet and the compass needle are thus fixed in the trans-
parent jelly in the relative positions they occupied at the bottom
of the hole.

As the needle, when it is freely suspended, always turns to
the magnetic north, it is only necessary to turn the phial till
the needle points to the magnetic north in order to place the
clinostat in the direction it had at the bottom of the hole ; and
since the plummet i, when freely suspended, always occupies a
vertical position, it is only necessary to incline the barrel a till
the plummet fixed in the jelly is in a vertical position, and then
the instrument will be at the same inclination that it had at the
bottom of the hole.

Macgeorge's Clinometer. In order to facilitate the exact
reading of the inclination and bearing of a bore-hole as
recorded by the ap-
paratus, before melting
the jelly for future use,
each clinostat that
is, the instrument
shown in Fig. 174 is
placed in a clinometer
specially designed for
this purpose. This
clinometer is shown in
Fig. 175. aa is a brass
tube in which the
clinostat is placed, and
which it exactly fits ;
the bulbs appearing at
either end, the plum-
met bulb at the top
end, the compass bulb
at the lower end. aa is fixed to a radial bar, bb, extending from
and fastened to the horizontal axis c. Attached to this same
radial bar are two microscopes, d and d' ; the horizontal axis
is attached by brackets to the horizontal tripod ee ; the micro-
scopes d, d' are so attached that they shall always be parallel
to the horizontal tripod stand ee. If, therefore, this stand is

FIG. 175. Macgeorge's instrument. Clinometer,
with clinostat in position.

304 MINE SURVEYING.

carefully levelled with a spirit-level, the plane of the microscopes
d, d' will also be level ; if the stand ee is inclined, the plane of
the microscopes d, d' will be parallel to it.

It is not important that ee should be level. "What is im-
portant is that the longitudinal axis of the microscopes should
always be in a plane parallel to the stand, which is assumed to
be a horizontal plane ; but the phial-holder aa, attached to the
radial arm bb, can be moved through an arc of 90 ; therefore,
as it is moved it is necessary that the microscopes should also
be moved. The right-hand microscope d will always have its
axis parallel to the base of the instrument ; but the other
microscope, d' } will require to be altered whenever the position
of the radial arm bb is altered. For this reason it is fitted with
a parallel motion, of which one rod is shown, marked//; the
action of this parallel motion keeps the longitudinal axis of d'
always parallel to the base.

The object-glass of each microscope has one or more vertical
lines drawn upon it. When the radial bar bb is moved, these
vertical lines on the object-glass of the microscope d' will retain
their vertical position, but those of the object-glass d will be
moved through an angle similar to that through which the
radial bar bb is moved; but, by means of the parallel motion
above mentioned, the object-glass of the microscope d is adjusted
to the movement of the radial bar, so that the vertical lines on
the glass remain vertical.

It must be borne in mind that these lines are vertical only
so long as the axis of the microscopes is horizontal ; what is
meant is that the lines are perpendicular to the plane of the
base of the instrument, which is assumed to be horizontal.

These two microscopes are at right angles to each other, and
with them the small plummet in the upper bulb of the clinostat
can be clearly observed. The phial having been put into the
holder, the observer looks through the microscope d', and if the
plummet is not parallel to the vertical lines, he turns the phial
round in the tube until the plummet is parallel to the vertical
lines. The observer then looks through the microscope d, and
if the plummet is not parallel to the vertical lines on the object-
glass, he moves the radial bar bb until the plummet becomes
vertical. (The reader will bear in mind that all this time the
jelly inside is congealed.) When the phial has been thus
adjusted, so that the plummet appears vertical through both

SURVEYING BORE-HOLES. 305

microscopes, the angle of inclination can be read by the pointer
on the figures of the graduated arc g, which is attached to the
base of the instrument.

The lower bulb is an inch or more above the centre of a
horizontal revolving circular mirror with five parallel lines
engraved across its face. Attached to the mirror is a graduated
circle, which can be turned round in the ring that carries it.
On the fixed ring is a pointer ; this pointer is in a line drawn
through the centre of the mirror at right angles to the hori-
zontal axis c, and parallel to the direction of the radial arm bb,
and opposite to the centre of the glass phial or clinostat. The
centre line of the five engraved on the glass is coincident with
the zero of the graduated circle ; the mirror is turned so that
the zero and centre line are coincident with the fixed pointer.

Reflected in the mirror will be seen the image of the needle
embedded in gelatine, which, as we know, pointed north before
it was fixed by congelation in the bore-hole. If, then, the
reflected image of the needle is parallel to the lines engraved on
the mirror, these engraved lines are in the magnetic meridian,
and it follows that the clinostat, as placed in the tube-holder, is
also in the magnetic meridian, and that the inclination of the
bore-hole is northerly or southerly, according as the notched or
north-seeking end of the needle, or the south-seeking end of the
needle is pointing towards the index finger of the horizontal
graduated circle.

If, however, the image of the needle is not parallel to the
engraved lines, the mirror must be revolved until it is parallel,
and until the zero of the graduated circle is opposite to the
north- seeking end of the needle. The number of degrees through
which the mirror has been moved will be the number of degrees
from the magnetic north that the clinostat is now pointing.
Thus, if the circle is moved through 20 to the right, it shows
that the clinostat has been fixed 20 to the left of the magnetic
meridian, that is, 20 north-west, and that is the direction of the
bore-hole. If, however, the graduated circle were moved to the
left 20, it would show that the direction of the clinostat, as held
in this clinometer, is 20 eastward of the magnetic meridian,
and that is the direction of the bore-hole. If the graduated
circle were moved 120 to the right, it would show that the
clinostat is 120 to the left of the magnetic meridian. As 180
would be south, 120 is 60 east of south. If the graduated

MINE SURVEYING.

Depth to top

of borehole 455 ft

circle had been moved 130 to the left, it would show that the
direction of the clinostat is 130 to the right of the magnetic
meridian ; and as 180 would be south, the direction of the hole
is 50 south-west. Each of the six clinostats is observed in turn,

and the mean of the observations
is taken to represent the angle of
inclination and direction of the
bore-hole.

The upper part of the clinostat
which Mr. Macgeorge recommends
for use with his core-extractor,
differs from the preceding ones in
having a minute compass floating
in the hollow glass head of the
plummet. 1

This instrument has been used
in surveying bore-holes in Aus-
tralia. In one case, at a depth of
370 feet it was found that the
bore-hole had deviated 37J feet in
a horizontal direction from the
position of the bore-hole at the
top.

Fig. 176 shows the survey of
the bore-hole. The positions in
which the clinostat was placed
are there shown in the vertical
section, the test being applied at
130 feet, 230 feet, 320 feet, and
that the deflection of the bore-hole is

Tested \

Testedi

Testedl

Testedj

75'J)etlectu>n,

FIG. 17G. Bore-hole surveyed with
Macgeorge's instrument.

367 feet. It will be seen

on a curve, which, if continued to a depth of 500 feet, would

give a horizontal deflection of 75 feet.

1 It is not stated in the description from which the writer takes his account
how the compass needle is fixed in the magnetic meridian before it is withdrawn
from the bore-hole. If the hollow head of the plummet were filled with gelatine,
the plummet would not float; it may bo that a portion only of the plummet bulb
has gelatine in it just enough to fix the position of the needle.

CHAPTER XVI.

MISCELLANEOUS.

Surveying by Photography. The photographic camera may often
be useful to the surveyor, especially when collecting information
in foreign countries, in helping to give a general idea of the con-
figuration of the country, the shape of cliffs, and the situation of
works ; interesting views may also be got of underground work-
ings by the aid of the magnesium, or the electric light. These
views are rather for the adornment of a report, for its verification,
and for the consideration of persons financially interested in
mines, than for the practical use of the engineer.

The photographic camera can, however, be used for actual
surveying, the process being known as " photogrammetry." l
It is said to have originated with Colonel Laussedat, in 1850,
and has since been largely developed in Germany, Austria, and
Italy, and is also frequently used in Canada, America, etc., both
for engineering and for military purposes.

The principle of the method is briefly thus : If a photograph
is taken from a point whose position is already known, the direc-
tion of the axis of the object-glass and the focal length of the
lens being also known, and the line of the horizon being marked
on the picture, then the picture can be laid down on a sheet of
paper on which it is desired to plot the survey, and will give
the direction from the point of observation to all the points in
the picture whose position is required. Two photographs of the
same objects, taken from different points, define completely the
position of each object, and also enable altitudes to be calcu-
lated or graphically determined.

The method is the same as that of the plane table, to be

1 " The Application of Photography to Surveying," by E. Mouet (Imt. C E.
Proceedings, vol. cxix. p. 414).

3 o8 MINE SURVEYING.

referred to later on, with the difference that most of the work
which, with the plane tahle, has to be done in the field, is, with
the photographic method, done in the office.

The camera used may be an adaptation of the ordinary
photographic camera, or may be specially designed for photo-
graphic work.

This method of surveying is described by Mr. H. M. Stanley,
in a paper read before the American Institute of Mining Engi-
neers ; l and there is no doubt that, by the careful use of
cameras, a map may be produced from which the relative dis-
tances and altitudes of objects may be scaled, though this
system would not be used where anything more than a rough
approximation to the actual distance was required.

Eeferring to Mr. Stanley's paper, the properties to be sur-
veyed comprised about six square miles of broken, mountainous
country.

Mr. Stanley used an 8 x 10 Eastman camera ; he used for
the negatives celluloid films, with a " matt " surface on the
back he also used celluloid films for the positives, as being less
likely to shrink than paper positives. Attached to the camera
were four cylindrical levels, by means of which the optical axis
could be set in a level line, and the base of the ground-glass
also made level. The centre of the ground-glass was marked,
and vertical and horizontal lines drawn through it. The posi-
tion of these centre-lines was photographed on the negative
by marks fixed on the carriers. The front board, carrying
the lens, was adjusted till the optical axis passed through the
centre of the ground-glass ; the position of the front board was
then noted, and a scale marked upon it, by which its movement
above or below the central position could be measured.

In taking the photograph, the height of the front board
above or below the centre-mark, and the height of the optical
axis above the ground, were measured.

Mr. Stanley's method was to use the camera as an adjunct
to a system of triangulation, the camera being fixed at a known
point, and the view including some other known point (see Fig.
177). Here the camera is fixed at X, and pointed in the direc-
tion A, and includes a known point, Y.

On examining the negative, or the print from it, the distance
of Y to the right of the centre-line XA can be measured with a

1 Glen Summit Meeting, October, 1891,

<4-l

3io MINE SURVEYING.

scale. This distance is the altitude of a right-angled triangle
whose base is the focal distance of the lens. In this case the
drawing was made to a scale of one-half inch to 150 feet, and
the focal distance of the lens used was 20*3 half-inches ; the
altitude of the right-angled triangle measuring 5 '53 half-inches.
The angle at the base of the right-angled triangle can there-
fore be calculated. Tangent of angle = - ^ n - ' r = ^[

= 0*27241, therefore angle = 15 15'.

The centre line of the picture, that is, the optical axis, may
now be drawn on the plan at an angle of 15 15' from the line
XY, and the length of the line is 20'3 units. A line perpen-
dicular to this, LAB, is the position of the picture.

In the same manner, the position EFN of the picture taken
from the station W may be plotted by means of the known
station V in the picture. A point, P, in both pictures is now
observed, and with a scale the horizontal distance of this point
to the left of the line XA is measured 3*8 units, from which
the angle 10 36' can be calculated. Similarly, the angle 6 36'
is obtained from the picture taken at W, and if these two
angles are then plotted on the plan, the point of intersection
gives the position of the point P. Instead of calculating the
angles, the point P could have been located graphically thus,
the distance AB, 3*8 as measured on the photo, may be plotted
on the plan, and the distance FE is also plotted on the picture
taken from W ; it is 2'35 units to the right of the vertical axis.
The lines WE and XB may then be produced to their point of
intersection at P, and thus the position P is marked on the plan.

The elevation of P may also be measured. In the picture
taken at X, P is 0*81 above the horizontal axis. To find the
altitude of P, draw BC at right angles to BX, and equal to
0'81 units; prolong XC to M ; let PM be at right angles to
PBX; measure the distance PM, which is equal to 222*8',
which is the height of P above X. In the same way the height
of P above W may be measured.

Instead of measuring the altitude, it may be calculated. In

OA -Q

the right-angled triangle X AB, the side XB = '' , = 20'6

COS J.U t5t)

units; in the right-angled triangle XBC the tangent of the

n.Q-i

angle at the base = ^^ = 0'03932, the angle of elevation =

MISCELLANEOUS. 311

2 15'. In the triangle XPM the side PM = 5668 (the length
from X to P) X tan 2 15' = 222*8 feet.

Mr. Stanley says the best results are obtained when the sun

OTO -THEODOLITE
L.CASELU LONDON.

FIG. 178. Bridges Lee photo-theodolite (outside elevatioii).

is low, the lens being shielded from the direct rays of the sun,
as there is a greater alternation of light and shade.

312

MINE SURVEYING.

Bridges Lee Photo-Theodolite. 1 This instrument, shown in
Figs. 178 and 178A, is an ingenious combination of photographic

Fio. 178A. Bridges Lee photo-theodolite, showing interior arrangements.

camera and theodolite, specially designed for accurate photo-
graphic surveying by J. Bridges Lee, M.A., F.G.S. It will be

1 Maker, L. Casella, 147, Holborn Bars, London, E.G.

MISCELLANEOUS. 313

seen that the instrument consists of a rectangular box of
aluminium, A, fitted with a rectilinear photographic lens, B,
with iris diaphragm. The camera is mounted on a vertical
axis, and can revolve round a horizontal graduated circle, C, a
vernier reading on to this circle heing fixed at the back of the
camera.

The instrument is carried on a tribach stage with locking-
plates and levelling-screws, D. On the top of the camera is
fixed a telescope, which is free to rotate in a vertical plane
when the instrument is accurately levelled ; and, by means of a
graduated arc, F, and vernier, vertical angles can be read to
minutes. A revolving bubble-tube, G, is let into a recess on
the top of the camera, which enables it to be levelled without
disturbing its position.

The camera is provided with the usual ground-glass shutter
H, and in the ground glass is a window of polished glass, h',
through which the inside arrangements of the camera may be
seen.

Inside the camera box is a strong rectangular frame, I,
which carries the compass-box M, and the vertical .and hori-
zontal hairs K and K' ; by means of a rack and pinions, J J, this
frame can be moved along the bottom of the box, and is of such
a size that when the dark slide is in position, and the shutter
is raised, the hairs K and K' can be brought into actual contact
with the sensitized plate; there are pointers attached to the
pinion which indicate the position of the frame.

The magnetic compass M is provided with a vertical trans-
parent scale, which passes quite close to the vertical hair K,
and by this means the magnetic bearing of the centre line of
the instrument is recorded on the photograph.

Attached to the frame which carries the hairs is a trans-
parent horizontal scale of angular distances, which is photo-
graphically prepared by the makers.

Other parts of the instrument are : S, clamp and tangent
screw for telescope ; Q, clamp and tangent screw for horizontal
graduated circle; R, clamp and tangent screw for camera; P,
adjustable microscope for reading vertical angles ; O, micro-
scope with universal joint, to permit of its being used either
for reading horizontal angles on the horizontal circle, or for
reading the compass-bearings through the window in the
ground-glass back ; LL are small transparent tablets, on which

MINE SURVEYING.

the place, date, time, etc., can be written, and so recorded on
the photograph.

The instrument is supplied with six double dark slides, to
carry a dozen 5x4 plates either horizontally or vertically.

Fig. 178s shows a photograph taken with this camera, on
which will be seen faint vertical and horizontal lines represent
ing the images of the vertical and horizontal hairs in the
camera.

FIG. 178b. Photograph taken with the Bridges Lee photo-theodolite.

The vertical hair intersects the compass scale at 37; thus
the magnetic bearing of the line joining the station where the
camera was fixed, and any point on the vertical line on the
picture is 37. By means of the scale of angular distances
the magnetic bearing of other points in the picture can now be
ascertained. Whilst using the instrument for photography, it
can also be used as a theodolite, and positions in the picture (or
out of it) fixed in the same way as in ordinary surveying.

If a tacheometer is used, the distances to points in the

MISCELLANEOUS. 315

picture can also be determined approximately, independently of
observations from other stations.

Pillars of Coal or other Mineral left to protect Buildings. As
it is well known that the excavation of coal or other minerals
leads to a subsidence of the surface, it is usual to leave a pillar
of mineral ungot, or only partially got, for the support of
buildings and works of a valuable kind. The conditions which
decide whether or no it is necessary to leave a pillar come rather
within the province of the engineer than the surveyor. When it
has been decided to leave a pillar, it is the surveyor's business
to set it out in the correct position, and to see that it remains
un worked.

Size of Pillar. The pillar is always larger than the building
to be supported, in the same way as the foundations of a house
or the pedestal of a column are larger than the house itself or
the column erected.

As, however, the base of the pillar is many times deeper
than the height of the building, ordinary architectural con-
siderations do not govern the size of the pillar ; this, indeed, is
usually governed by experience gained in the locality. There
is, however, a general consensus of opinion that the deeper the
bed of mineral below the surface the larger the pillar required,
if any pillar is left at all; thus, if a seam of coal 50 yards deep
and 5 feet thick is left to protect the building, a margin of 25
yards would be considered ample ; at a depth, however, of 150
yards a wider margin will be required, and at 300 yards a wider
margin still. For ample security 1 the margin should be about one-
third of the depth ; thus at a depth of 300 yards the pillar should
extend on every side a distance of 100 yards from the building ;
it is, however, only in the case of very important buildings
indeed that such a large margin is left. Eailway companies,
who have to buy pillars for the support of important viaducts
and tunnels, and frequently pay at a very heavy rate for the
mineral left, usually consider a much smaller margin sufficient,
and will probably in no case allow a margin of more than 40
yards, whilst in others the margin is very much less.

In a recent paper read before the Institution of Civil
Engineers, 2 the following rule is laid down by Mr. S. B. Kay,
Assoc. M.I.C.E., as to the size of pillar required under normal

1 Even this margin does not give perfect security.

2 Vol. cxxxv. Proceedings of the Tnst. C E., pp. 114, et seq.

316 MINE SURVEYING.

conditions. Let d denote the depth in yards ; t, the thickness
excavated in feet ; and r, radius of support in yards. Then

r =

0-8

For example, an arched bridge for a road or railway requires
support. The depth of the seam is, say, 400 yards ; the thickness
of the material excavated, say, 4 feet. Then

x 400 x y/4 _

0-8

= 68 yards

or a pillar extending 68 yards beyond the structure on each side,
will give the support necessary. The following table is taken
from Mr. Kay's paper :

TABLE XVI.

TABLE OF MINIMUM RADIUS OF PILLAR (IN YARDS) ACCORDING TO DEPTH OF SEAM
AND THICKNESS OF EXCAVATION, CALCULATED FROM THE FOREGOING FORMULA

x
O 7

Depth in

THICKNESS OF EXCAVATION.

yards.

, j

2 feet.

3feit. 4 feet. ; 5 feet.

6 feet.

7 feet. 8 feet.

9 feet.

19-3

22-1 24-3

26-2

27-8

29-3 30-6

31-8

100

27-3

31-2 i 34-4

37-0

39-3

41-4 4H-3

45-0

150

33-4

38-2 42-1

45-3

48-2

50-7 53-0

55-2

200

38-5

44-1 48-5

52-2

55-5

584 61-1

63-5

250

43-1

49-4 54-3

58-5

62-2

65-5 68-5 71-2

300

47-3

54-1 59-5

64-1

68-1

71-7 75-0 78-0

350

51-0

58-4 64-3

693

73-6

77-5 81-0 84-3

400

54-6

62-5 68-7

74-0

78-9

82-8 86-6

90-1

450

57-9

66-2 729

78-5

83-5

87-9 91-9

95-5

500 61-0

69-8 76'9

82-8

88-0 j 926 96-8

100-7

600 66-8

76-5 84-2 90-7

96-4 ; 101-5 106-1 j 110'3

700 72-2

82-6 90-9

98-0

104-1 1096 114-6

119-2

In each case the half-diameter of the piece of ground to be
supported must be added to the calculated radius, to give the
actual radius of the circle within which the coal is to be left.

Another rule sometimes recognized is that the pillar should
extend on all sides to a distance equal to -j 1 ^ of the depth of the
seams plus 20 yards. This rule would apply to horizontal
seams in which the thickness does not exceed 5 or 6 feet.

The shape of the plan of the coal-pillar left is generally an
enlargement of the plan of the plot of ground to be supported.

MISCELLANEOUS.

317

Pillars in Inclined Seams. In case the seam is level, the
pillar of coal, by universal consent, should extend equally on
each side of the building or ground to be protected ; but if the
seam is inclined, then all unanimity of opinion ceases. A
majority are of opinion that the pillar of coal should be moved
so that it extends further from the building on the rise side, and
does not extend so far on the dip side ; in other words, the pillar
of coal is moved uphill ; the total acreage of the coal left (as
measured on the plan) being the same as if the coal-seam was
horizontal. Some mining engineers have gone so far as to say
that the line of fracture of the strata (which occurs when the
ground subsides to fill up the place from which the coal has
been extracted) is at right angles to the dip, and that therefore
a pillar of coal should be placed not vertically under the build-
ing, but around a spot fixed by drawing a line from the building
at right angles to the dip of the
seam. It is, of course, evident
that this theory cannot be
carried very far, as, in the case
of highly inclined seams, it would
lead to an absurdity. Other
mining engineers deny that the
inclination of the seam has to
be considered, and would set out
the coal-pillar for inclined and
horizontal seams in the same
form. Each side has cases in
support of its theory. The
author of this treatise has never
taken either side, but would
state that it is an undoubted
fact that the line of fracture is
sometimes vertical, sometimes
inclined ; and would suggest
that a very little irregularity in
the fracture might cause the
subsidence to "pull" a Jong
way over the edge of the pillar.

On this subject Mr. Kay
makes the following remarks :

"It is often assumed that subsidence takes place at right

PLAN.

DISPLACEMENT OF PILLAR DUE TO DIP.

FIG. 179. Position of pillar of coal in
inclined seam.

MINE SURVEYING.

angles to the dip, as in horizontal mines ; and again, that it takes
place vertically as being directly due to gravitation. The author
(Mr. Kay), however, believes that a line midway between the two
gives the more general line of break that is to say, supposing
the angle of dip to be 0, then the angle that the line of break
makes with the horizon is 90 - J0, as shown in Fig. 179.

" In laying out upon a plan a pillar for the support of a
bridge, as in Fig. 179, to be left in inclined seams up to 30, the
size of pillar necessary may be calculated by the formula given.
Marking this upon the plan, round the bridge, the position of
the pillar is given supposing the measures to be horizontal.
Its lateral displacement to the high side due to the inclination,
at a depth d, is d tan J0 cos 0. This lateral displacement may
be graphically determined as shown in the vertical section on
the line of dip.

"Let A represent the bridge to be supported by a pillar to
be left in the coal DD at a depth of d yards. Calculate the
size of the pillar from the formula given, and mark it upon
the horizontal line at B and C drawn through the ground-level
at A. Draw BJ and CK, making an angle of 90 - J0 with
the horizon from B and C respectively. Then JE and KF

represent the lateral displace-
ment due to the dip in the coal,
and JE' and KF' the displace-
ment in plan. This is shown
in the plan, where the dotted
circle represents the position of
the pillar when the coal is hori-
zontal, and the circle in a fall
line its position corrected for
dip."

It is frequently necessary to
make roads through the pillar
for the purposes of haulage and
ventilation ; the size and num-
ber of these roads is a matter
of agreement, and they must be
carefully limited to the autho-
rized dimensions. Provision
should be made for these roads
by a corresponding enlargement of the pillar. In case it is

FIG. 1 80. Pillar of coal left in pillar-
and-stall workings.

MISCELLANEOUS. 319

decided that a solid pillar of coal is not required, then partial
support may be given, as shown in Figs. 180 and 181.

A pillar is set out in the following manner: An accurate
plan is made of the surface and of the underground workings,
surveyed in each case from the shaft. The pillar as agreed upon
is drawn on the plan as shown in Fig. 182. The surveyor gives
the underground steward the lengths that he may drive from
station A on the plan. When the road reaches the point B, the
surveyor hangs lines by which headings are driven round two

FIG. 181. Viaduct supported by a number of pillars
loft in the ordinary course of working.

sides of the pillar ; at C and D the surveyor again hangs lines,
by means of which the boundary heading is completed. The
steward now knows that the coal inside these headings is not to
be got, whilst the coal outside may be removed.

Setting out. In addition to preparing plans of mines as they
exist, the surveyor has to set out the works that are designed by
the engineer.

Setting out Surface Works. The engineer marks on the plan
the position of the shafts, engine-houses, offices, etc. ; the sur-
veyor, by means of pegs, trenches, etc., marks on the ground
the actual position, so that the contractor or other workmen
can proceed with the necessary excavations. When once the
place for the excavation of the shaft or foundations has been
marked out, it becomes rather the province of the engineer and
architect to set out with minute accuracy the actual lines of
masonry.

Fig. 183 shows a portion of an estate on which the engineer
has marked the position of a shaft which is to be sunk, and
some buildings to be erected. In this particular case it happens
that the exact position of the shaft to within a few inches, or

320

MINE SURVEYING.

even perhaps to within 2 or 3 feet, is not a matter of prime
importance ; it is, therefore, easily marked out in the following
manner: The surveyor draws on the plan lines similar to those

FIG. 182. Method of setting out a pillar of coal.

he would have set out in surveying the fences of the field in
which the shaft is situated ; he measures from the plan the total
length of each line, the position of the offsets and the length of
the offsets ; he then proceeds to the field, and measures from the
centre of the fence the length of the offsets, putting in pegs ; he
then ranges a line over these pegs and measures it, setting out

MISCELLANEOUS.

321

all the lines in a similar manner. As the lengths of the offsets
as measured will probably not give a line that is quite straight,
he will set out a straight line running past the pegs as put
down from the offset measured, but correcting the irregularities.
Having set out the four lines parallel with the four sides of the
field, he will then measure a diagonal, and if this does not agree

FIG. 183. Setting out surface works.

with the length on the plan, it will indicate a corresponding
error in the plan or in the setting out of the lines by means of
offsets. As measurements to and from the centre of a hedge
are necessarily very rough and cannot ordinarily be taken
nearer than a link, and in the case of a thick hedge to 2 or 3
links, the lines as first set out may be susceptible of little adjust-
ments, and the real position of the line can only be approxi-
mated by means of a great many offsets, the average length of

322 MINE SURVEYING.

which should agree pretty nearly with the average length as
measured from the plan. Having poled out these lines, the
surveyor can then take measurements from them with as much
accuracy as the case requires to fix the position of the shaft by
setting out lines which form sides of triangles, or lines measured
from a fixed point on one side of a triangle to a fixed point on
the side of another triangle, as shown in the figure.

In order that, when the work is pegged out, the labour
shall not be lost by the careless removal of the pegs, the surveyor
should cut holes or trenches along the sides of the excavation ;
and in order that the trench so cut may not be prematurely
lost in the subsequent operations, it should be understood that
the excavation for the foundations of the buildings is to be
inside the trench, say one foot. The pegs are put down at
corners of the excavation in the trench ; a circular trench may
be cut round the position of the shaft. As the peg representing
the centre of the shaft will be removed as soon as the work is
begun, four pegs should be put down equidistant from the centre
of the shaft, say 20 feet ; two 20-feet lines from the top of any
two of these pegs will then meet in the centre of the shaft. For
greater security, these four pegs may be duplicated, as shown in
the figure. If the two cross-lines over these four (or eight) pegs
are set out at right angles to each other, the winding-engine
house and other buildings may be squared from them.

Setting out Shaft with Extreme Accuracy. It sometimes
happens that a shaft has to be sunk at a given distance from
another existing shaft or precisely over some underground works
already made, and that it is important that the centre of this
new shaft should be set out with all the accuracy attainable by
the surveyor's art. In this case it may be necessary for the
surveyor to prepare an entirely new survey, both surface and
underground. However that may be, the survey, whether old or
new, must of course be exact, and the new shaft must be set out
by measurements taken from the main lines of survey as shown
in Fig. 184, and it is assumed in this figure that the stations on
these main lines can be found ; if not, the setting out of the
original survey-lines is tantamount to making a new survey.
In the case shown in Fig. 184 portions of three main survey -
lines are measured on the plan, triangles set out and measured,
so that six lines meet in the centre of the shaft ; the angles made
by the intersection of the lines are calculated, the cross-lines

MISCELLANEOUS.

323

being set out at the proper angle from the main survey-lines by
means of the theodolite. The accuracy of the original survey
as shown on the plan will be tested by the remeasurement of
the parts shown in the figure and cross-lines which form ties ;
then, assuming the necessary accuracy of the plan, the centre
of the shaft can be set out to the twentieth part of an inch.

Of course it will be necessary to erect permanent stations
round the shaft, from which cross -lines can be stretched as
shown in Fig. 183. These permanent stations must consist
either of strong posts of timber, say 12 inches square, securely

Li>rv& 5 of Mairv Survey

FIG. 184. Setting out position of shaft.

fixed into holes 6 feet deep and tightly rammed, or else they
must be masonry pillars, say 3 feet square. On the top of these
pillars must be a cap of stone or iron, on which a centre-line
can be chiselled, or, in the case of wooden posts, the centre-
line may be cut in the wood itself. These posts must each
be on lines connected with the main survey ; the exact centre
of the shaft can then at any time be found by stretching two
lines across the four posts ; the intersection of these lines will
be the centre of the shaft.

324

MINE SURVEYING.

Setting out Centre of Shaft by Meridian Line. It may be that
the position of the new shaft is to be set out entirely with
regard to an existing shaft at a given distance and bearing. If
the geographical meridian is shown on the surface by carefully
placed marks, it will be easy to set out the bearing from this
line. In case the meridian line is not so marked out, it may be
that the stations of some main survey-line are accessible, and
that the bearing of this line has been carefully ascertained and
checked against the bearings of the other main survey-lines.

FIG. 185. Setting out centre of shaft by meridian line.

Such a case is illustrated in Fig. 185. In this case the pro-
posed new pit is N. 39 45' W., 803 links from the centre of
No. 2 pit ; No. 1 line of main survey passes through the No. 2
pit; the bearing has been ascertained to be N. 10 E. It is
then ascertained by calculation that the No. 3 pit is 617'38 links
north (cos 39 45' x 803) and 513-47 links west (sin 39 45'
X 803) of No. 2 pit. If a line is drawn from the centre of the
No. 3 pit perpendicular to the meridian, it cuts the No. 1 line
at the station A, crossing the meridian at B. The line BA
is a tangent of the angle of 10 to the radius 617*38, and by

MISCELLANEOUS. 325

calculation is found to be 108-86 links long. The length from A
to the centre of No. 2 pit is the secant of the angle ACB, and by
calculation is found to be 626*91 links long. This length is then
measured on the No. 1 line, and the point A marked with a
peg. The angle ABC is a right angle, the angle ACB is 10,
therefore the angle BAC is 80; then with the theodolite a
straight line ABD is set out, making an angle of 80 with the
line AC. The distance of the No. 3 pit is 108-86 + 513'47
= 622-33 links.

In order to test the accuracy with which the position D is
set out, the theodolite may be set up over this peg ; the angle
BCD is 39 45', the angle DBC is 90; therefore the angle
BDC is 50 15', and this angle should be read by the theodolite
if the work has been correctly done; the distance DC is 803
links, and it should measure this length precisely. In case of
buildings existing on the line AC which make it impossible to
measure the line without deviation, the distance FC may be
set out by fixing up the theodolite at E, and measuring the angle
FEC and the distances EC and FE; the length FC can then
be calculated. This length can be checked by fixing the theo-
dolite again at G, measuring the angle FGC and the lengths
CG and FG, by which again the length FC can be ascertained.
In the same way, the length DC may be measured round any
building or other obstruction. No. 1 line of survey will, of
course, be poled out, if not for its whole length, at any rate for
a length of half a mile, so as to make sure that the real line
has been taken.

Setting out Underground. Fig. 186 shows a heading in a

FIG. 186. Setting out a heading underground.

mine proceeding N. 20 15' W. ; the direction of this heading
has to be changed to go N. 29 45' W. The surveyor proceeds
to the place with his dial, and puts a chalk mark or other mark
in the heading to guide the miners along the given bearing.
When the heading has been driven a sufficient distance for
permanent marks to be conveniently put in, the surveyor returns
to the place and makes three marks in the roof in the bearing

326

MINE SURVEYING.

as shown by his dial ; at these three marks holes are drilled,
and into the drill-holes wooden pegs are firmly driven. The
dial is now turned on to these pegs, and a pencil-mark carefully
made on each peg, so that these three marks shall all be in one
straight line, which has a bearing of 29 45'. Into the pegs
at these marks a small hole is bored, and into this small hole
is screwed a small screw with a little brass hook at the lower
end, care being taken that the centre of the hook corresponds
with the pencil-mark on the peg. From each of these hooks
a plumb-bob line is suspended. The line of pegs is generally
on one side of the heading, say 1 foot from the right-hand side.
The miner must now drive the heading so that a light held
at the face 1 foot from the right-hand side shall be in the line
of these three strings. The reason for having three strings
instead of two is to detect any variation in the position of the
pegs or hooks ; if there were only two, the position of one might

be changed without
being noticed. At
every fresh turn in
the heading the sur-
veyor must repeat
the operation.

Setting out Gra-
dient. It is not only
necessary to set out
the direction of a
heading, but to set
out also the gradient.
This may be done in
various ways. Sup-
pose the road is to
be driven level; a
straight - edge and
spirit-level must be
provided, and the
miner or officer in
F I charge must from

FIG. 187. Method of setting out gradients. time to time see that

the floor of the head-
ing is level (see a, Fig. 187). Suppose, however, it is intended
to drive at an inclination of 1 in 10, then the same straight-

10 ft

MISCELLANEOUS. 327

edge and spirit-level will do ; but underneath the straight-edge
should be fastened a piece of wood, the under side of which is
cut to the required slope; thus if the straight-edge were 10
feet long, the piece of wood on the under side would be 1 foot
deep at one end and taper away to nothing at the other (see b,
Fig. 187). For steeper inclinations a shorter straight-edge must
be used.

Instead of a spirit-level, a T-square and plumb-bob may
be used (see c, Fig. 187). The writer has designed a modifica-
tion of the T-square for setting out a gradient by the angle
instead of at the rate per cent, (see d, Fig. 187). In this case
a graduated arc is fixed to the T-square, with the degrees
marked on; a pin is fixed at a point corresponding with the
centre of the circle of which the arc is a part ; a small ring fits
over the pin, and from this is suspended, by a fine string, a
plumb-bob ; the plumb-bob is shaped like the weight in the
pendulum of a clock, and just hangs clear of the frame. If
the heading is driven at a gradient of 10, the string will hang
over the tenth degree on the graduated circle when the straight-
edge is laid on this slope.

A clinometer on a somewhat similar principle has been
designed and invented by Colonel G. P. Evelyn, in which he
uses a bubble of compressed air in a curved tube ; the tube is
curved to the sweep of a circle. Adjoining the curved tube is
a scale graduated in degrees. When the straight-edge is level,
the bubble is in the centre; when the straight-edge is inclined,
the bubble comes to rest opposite the degree on the graduated
circle that corresponds with the inclination of the straight-edge.

Where there is water, it is easy to drive a level ; if the water
flows from the face of the heading, it is evident that it is rising ;
if it flows towards the face, it is evident that the heading is
falling; if it is stagnant, it shows that the floor of the drift
is level.

It is obviously difficult to ascertain the precise inclination
of a road by means of a straight-edge laid upon the rough floor.
It may be more accurately done by raising the straight-edge
above the floor, either by building temporary supports or fixing
two side-posts, and then, looking along the edge, adjust it so as
to point to a light at the end of the heading, which is held at the
same height above the floor ; the angle of the straight-edge can
then be observed by means of a clinometer. A straight-edge

328

MINE SURVEYING.

may be permanently fixed to posts at the required angle, and
by looking along the top of the edge from time to time, the miner
or the official in charge can see if the inclination of the heading
is parallel to this fixed straight-edge.

Instead of a straight-edge, a metal tube, say ^-inch gaspipe,
may be suspended from the roof, and adjusted to the desired
inclination by means of suspending strings or wires. By look-
ing through the tube, a light can be fixed at the end of the
heading which will be in a line with the tube (see Fig. 188).

FIG. 188. Method of setting out gradients.

A tube is sometimes used in a similar manner for giving the
direction as well as the inclination.

Setting out Cuttings and Embankments on the Surface. In
addition to pegging out the position of surface-works, it is often
necessary to mark the depth of cuttings and the height of
embankments. This must be done by means of measurements
taken from the drawn section. Fig. 189 is a section showing

Ism&ankntent

FIG. 189. Setting out heights of embankments and depths of cuttings.

cutting and embankment. In order to show the height of the
embankment, poles are fixed in the ground ; if they are long,

MISCELLANEOUS. 329

they are stayed with diagonal struts. On to these poles are
nailed cross-bars, which indicate the height of the embankment ;
the poles are placed, say at chain-lengths, along the centre-
line of the embankment, and their correct position is measured
from the nearest fence or other fixed point shown on the plan.
In the absence of fences or other fixed points in the neighbour-
hood, the position of the line has to be set out by bearings or
angles from some base-line.

In the case of a cutting, the level and gradient of this is
fixed by sights taken from two or more cross-bars or poles fixed
in the ground near the commencement of the cutting. By
taking sights from these cross-bars the cutting can be made
at the required level and inclination.

In the case of an excavation on the top of a hill or in a flat,
and not on the side of a hill, two posts must be fixed, one on
each side of the excavation, and a cross-bar nailed to each at a
given elevation above the bottom of the intended excavation ;
the cross-bar is, say, 3 feet above the ground, and the excavation
is to be 20 feet below the ground ; then the cross-bar is marked
23 feet, that being the depth to which the excavation is to be
carried below that level. A string can be stretched from cross-
bar to cross-bar over the excavation, and the depth measured
from these strings by means of a pole. The posts carrying the
cross-bars must be ranged along each side of the excavation,
say at chain-lengths.

Tunnel Shafts. 1 In driving a tunnel, either for railway or
drainage purposes, it is frequently necessary to sink shafts
along the line of the tunnel, in order that the work may be
carried on simultaneously at a number of points. Taking the
case of a tunnel 2000 yards long, if the rate at which the heading
advances, having regard to the nature of the ground and the tools
used, is, say, 10 yards a week, and the tunnel is started at each
end simultaneously, the total rate will be 20 yards, and it will
take 100 weeks to get the heading through. If, however, two
intermediate shafts are sunk, each at a distance of 666 yards
from one end of the tunnel, two headings can be driven from
the bottom of each shaft, so that the total number of headings
in progress at one time will be six, and thus the tunnel may be

1 An interesting paper on this subject will be found in the Proceedings of Civil
Engineers, vol. xcii. p. 259, ' The Alignment of the Nepean Tunnel, New South
Wales," by Thomas William Keele, Assoc. M, Inst. C.E.

OF THE

UNIVERSITY J

330 MINE SURVEYING.

put through in about 33 weeks. It is, of course, of the utmost
importance that the intermediate lengths of tunnel should be in
the correct position both as regards situation, direction, and level.

As regards the position of the shafts, they can be set out
in the method already described (Figs. 183, 184), in case there
happens to be a sufficiency of marks on the surface and an
accurate plan from which the measurements can be taken.
If, however, as is frequently the case, the ground between
the ends of the tunnels contains but few land-marks, the posi-
tion of the intermediate shafts must be set out by lines specially
ranged between the two entrances of the tunnel, supposing
the tunnel to be in a straight line between the entrances ;
this straight line must be carefully poled out with the aid
of a theodolite, and at convenient places stations are built on
which the theodolite can be fixed. These stations may be of
masonry or of timber, and must be sufficiently firm, so that
the theodolite is not affected by wind or the movements of the
persons observing it. The distance of the shaft from the
entrance can then be set out by ordinary chaining, the errors
incidental to chaining not being of importance in this case.
The depth of the shaft is measured from the section on which
the height of some fixed mark near the top of the shaft is
shown. By means of the spirit-level, the level of this mark
is transferred to the walling of the shaft, and the depth to the
bottom of the tunnel can be set out either by chaining down
the side of the shaft or by a measured length of wire. The
direction of the headings is set out by means of plumb-lines
suspended down the shaft, and fixed on the surface in the
direction of the centre-line of the tunnel, or the line can be
transferred to the bottom of the shaft by means of the transit
telescope, as described in Chapter XL

It sometimes happens, however, that the shaft is sunk on
one side of the centre-line of the tunnel, which has to be reached
by a cross-drift (see Fig. 190). In this case the surveyor hangs
his lines down the shaft at right angles to the direction of the
tunnel, or, if he uses the transit instrument, sets out marks at
the bottom of the shaft by means of it at right angles to the
direction of the tunnel. He then fixes his theodolite in the drift
in the direction of these lines, and sets out an angle of 90,
which is, of course, the direction of the tunnel. Or, instead
of fixing the lines at right angles, he may fix them at any

MIS CELL A NEO US.

33i

other angle that the circumstances of the case make con-
venient. The inclination at which the head is driven can be
set out by any of the methods already described.

In driving large tunnels, it is often convenient to let the
men at the face be able to see their position in regard to the

Centreline'

_ Jt

FIG. 190. Setting out centre line of tunnel.

centre-line. In this case lamps may be suspended from cross-
bars in the line, and a man at the face, placing himself in a
line with two lamps, gets the centre approximately. Similarly,
candles fixed in triangular stirrups may be suspended in place
of lamps. For the exact setting out of the brickwork, stations
are fixed at intervals of say 50 feet along the tunnel, and at
these stations are fixed spikes with small eye-holes, placed
exactly in the line by means of the theodolite ; through these
eye-holes strings can be stretched, and from these the requisite
measurements can be taken.

Setting out Curves, No railway, canal, or culvert should ever
change its direction except by means of a curve. In ordinary
canals and culverts the exact ranging of the curve is sometimes
not of serious importance ; in railways the accuracy with which
the work is set out is of the very highest importance, as without
that accuracy it is impossible to run a train with safety. The
surveyor has therefore frequently to set out curves both on the
surface and in the mine.

Curves may be roughly set out by means of chain and poles

332

MINE SURVEYING.

in the manner shown in Fig, 191. In this case the straight
portions are shown by the pieces marked ab Bindpq. The line ab is
prolonged indefinitely, and at a distance of 1 chain from /> the
offset cd is marked off by swinging the chain in the direction
of the curve a distance equal to cd ; the line bd is now set out,
and at a distance of 1 chain from d the offset ef is marked off ;
the line df is now set out, and at a distance of 1 chain from /

fL 6

FIG. 191. Laying out railway curves by the chain only.

the offset gh is marked off; the line fh is now set out, and at a
distance of 1 chain the offset ij is marked off ; the line hj is now
produced, and the offset Jcl set out ; and so on to p, being the
commencement of the straight portion pq. The lengths of the
offsets cd, ef, gh, ij, kl, mn, and op may be calculated by well-
known rules (see following pages). But in case the surveyor
should have forgotten the rule, and fail to have at hand any
pocket-book or text-book to remind him, he can easily find the
offsets with approximate accuracy by measuring them from the
plan the accuracy, of course, of these measurements depending
on the scale of the plan and the care with which the drawing is
made and scaled.

MISCELLANEOUS.

333

There is a difficulty, however, in making the drawing to a
large scale when a large radius is required ; for instance, if the
radius of the curve were 80 chains, then to draw the curve with
that radius to a scale of 1 chain to an inch, would require the
arm of a compass 80 inches in length ; but the scale of 1 chain
to the inch would be too small to give the measurement with any
approach to accuracy, and even a compass arm of 80 inches and
the requisite table surface for setting out the curve might be
difficult to obtain, but by means of a box of curves which are cut
in cardboard, pearwood, or vulcanite, to radii varying from V 2
inches to 240 inches, a small portion of a curve may be set out
on a small piece of paper. If, however, the radius is not large,
say 10 chains, then the drawing may be made to a large scale,
especially with the aid of the wooden curves ; by taking a curve of
120 inches radius a scale of 12 inches to a chain might be used,
on which the offsets could be measured with considerable accuracy.

Setting out Curves by Offsets from Tangent. The required
offsets for a curve may, however, be measured with much less
liability to error from the tan-
gent to the curve, as shown in
Fig. 192. In this case the first
offset is similar to cd in Fig.
191 ; the second, third, and suc-
ceeding offsets are also measured
from the same tangent line. By
this method, any error made in
fixing the first stations d, f, //,
merely affects the accuracy of
those particular points, and the
long offset at j can be measured
with substantial accuracy from
the plan.

Assuming the case shown in
Fig. 192, here is a curve with a
radius of 80 chains (a radius
much greater than is to be ex-
pected on a branch railway to a
mine) ; this is drawn on paper
to a scale of 1 chain to an inch ; the tangent is drawn, and
chords, od, df t jh, hj, etc., each 1 chain in length, are marked
off along the curve from the point o, where it commences ; the

FIG. 192. Laying out railway curves
by offsets from the tangent to equi-
distant points on the curve.

334

MINE SURVEYING.

length of the offset to the tangent from each of these points
can be measured, and will be as shown in the following table :

RADIUS OF CURVE 80 CHAINS.

Distance measured

along curve in
chain-lengths.
1

Offset.
Inches.

(cd) 4-9

Deflection angle,
or angle at centre.

.. (oad)0 42' 58"

(ef) 19-8

.. (oa/)l 25' 57"

- (qh) 44-5

.. (oaA)2 8' 55"

(y) 79-2

(oa/)2 51' 53"

(kf) 123-6

(oaZ)3 34' 52"

178-0

4 17' 50"

242-3

5 0' 48"

316-5

5 43' 47"

400-5

6 26' 45"

494-4

7 9' 43"

At the tenth chain (which corresponds to an angle of 7 10'
nearly) the offset is 494*4", or 62*4 links, which is a length that
can be scaled off the drawing with approximate accuracy.

If, instead of 80 chains, the radius of the curve was 20
chains, and a curve of 80 inches is marked out on the paper, the
scale of the drawing would be four times as great, and the
measurements taken from the drawing would be more accurate
in a corresponding degree.

Before proceeding to set out the curve on the ground, the
surveyor should provide himself with a sketch-plan showing the
lengths of tangent, offset, and chord. An offset of greater
length than 50 links cannot be set out with accuracy by eye,
and unless a cross-staff, dial, or theodolite is employed, a new
tangent to the curve must be set out as a base from which to
continue further offsets. Suppose that after setting out the
offset Jcl (Fig. 192) a new tangent is required, the surveyor can
put a pole in at the point h, 2 chains back along the curve ;
then the tangent to the curve from the point h will have an off-
set to the curve at the point I of 19*8 inches ; and if this length
is set out from I in a direction perpendicular to the new tangent,
it will give the point through which the tangent can be drawn.

This method of setting out curves from the tangent can only
be practised in the pit when the length of the longest offset
does not exceed half the width of the road, and is, therefore,
only applicable to very short curves. On the surface the method
will do very well for ordinary ground where there are no cliffs,
rivers, or buildings to interrupt the measurement of the tangent
or of the offsets.

MISCELLANEOUS.

335

Setting out Curves by Angles. It is also possible for the
surveyor to set out the curve with his dial or theodolite, by
measuring the angle of each successive chord (see Fig. 193).
In this case a drawing is made showing the curve connecting
two straight portions of a railway, AB and XY. Chords of
1 chain are marked off on the curve with a scale, and drawn,
BD, DE, EH, etc. Taking the tangent AB as the meridian,
produce it to C ; the chord BD is also produced, and the

,Y'

\ Y <

FIG. 193. Laying out railway curves by angles.

angle CBD, which it makes with the meridian, is measured
by means of the protractor; the angle that the chord DE
makes with the meridian is also measured with the protractor,
and the angle of all the other chords. For instance, if the
protractor is laid on the line ABC so as to read 360, then the
bearing of the chord BD, as read off the protractor, would be,
in the case of a 25-chain curve, 1 8' 46". The bearing of the
chord DE would be 3 26' 18"; the bearing of the chord EH
would be 5 43' 50", and so on.

336 MINE SURVEYING.

To set the work out, the dial or theodolite is fixed at B, and
the sights clamped in the direction ABC, the vernier being
at 360. By means of the rack the sights are then turned
through the angle CBD and clamped with the vernier at 1 8' 46",
and a chain-length measured from B, and a peg put in at the
point D ; the instrument is now fixed at the point D in the
direction BD, the vernier reading as before 1 8' 46", and
the sights moved by the rack through the angle JDE, the
reading on the vernier being made to correspond with the bear-
ing of the chord DE as read by the protractor. The chord DE,
1 chain in length, is then set out in the direction as given by
the sights. The operation is repeated at the length of every
chain till the end of the curve is reached. It will be found
that if equal chords are taken on the curve, the angles JDE,
^'EH, /i'HI, etc., are all equal, and that they are twice the angle
CBD. It is very likely that the end of the curve will not
coincide with a chain-length. The exact length can be measured
off the drawing ; and if on setting out this last length at the
angle measured from the plan the point so marked out corre-
sponds with the point X, the beginning of the straight portion,
it shows that the work has been correctly done.

If great care is taken, the curve may be set out with approxi-
mate accuracy in this way. The sources of error will be, firstly,
the measurement of the lengths on the drawing ; secondly, the
measurement of the angles on the drawing ; thirdly, the fixing
of the instrument over the pegs. An error of \ inch at each
end of the chain-length would cause an error of 1 in 792. Of
course, there is no reason why there should be an error of this
amount in setting out, because three tripod stands may be used,
as in fast-needle dialling, and with the vernier the angle may be
set out with great accuracy, so that the errors in the work will
be chiefly those due to an incorrect drawing or inexact mea-
surements from the drawing.

Another method of setting out the curve by angles will be
found on referring to Fig. 194. Let AB be the straight
portion of the line, the curve beginning at B. C, D, E, F
are chain-lengths measured as chords of the curve; B' is an
extension of the tangent AB. The point C may be found by
fixing the theodolite or dial at B, clamping it in the direction
BA, and then turning the sights in the direction BC.

The angle CBD is the same as the angle CBB'; the

MISCELLANEOUS.

337

angle DBE is also the same as the angle CBD, and so is

EBF; so that the sights can be turned in succession upon

C, D, E, and F. To mark

out C, one end of the chain

is held at B, and the other

swung into the line of sight

of the theodolite or dial, and

the peg put down at the

chain-end at C. The chain

is now drawn on; the follower

holds one end at C, and the

other is swung into the line

of sight, and a peg put down

at D, and so on.

This method is, of course,
only suitable on the surface,
because the line of sight BF
would be obstructed by the
solid ground, if in a tunnel.
It will, therefore, be neces-
sary underground to be con-
stantly moving the instru-
ment forward along the line
of the curve, as previously

described. FIG 194 _ L ing out rai i way curves

Of course, if there hap- by angles,

pens to be room in the

tunnel, and the curve is of large radius, a number of points may
be set out from once fixing the instrument ; or, if the curve is
of small radius, it may be desirable to set out points nearer
together than 1 chain, possibly every 10 links, in which case
once fixing the instrument may be sufficient for setting out a
number of points on the curve.

It frequently happens that a curve does not end in a straight
line, but in another curve, either curving in the same direction
with a greater or less radius, or in a reverse direction, as shown
by the dotted lines XY', XY" (Fig. 193). In this case the point
X is simply the ending of the first curve and the beginning of a
new curve. The radius of the new curve must be struck from a
centre on a line drawn through X, which line, if produced, will
pass through the centre of the circle of which the first curve is

338 MINE SURVEYING.

an arc. This line is shown on Fig. 193, VW. In setting out
large curves, the wooden curves previously referred to are used
instead of compasses, and they must be held as if the centre
from which they were struck were on this line. The curves, if
properly laid down, will never cut each other, when produced so
as to form a circle, and will only touch at one point, X.

Calculation of Offsets, In order to avoid the errors likely to
result from scaling offsets off a plan, or measuring angles with
a protractor, the length of the offsets and also the angles are
generally obtained by calculation. Eeferring to Fig. 191, in
which the curve is divided up by equal chords, the length of the
offset cd may be calculated from the rule

chord 2
2E

where E is the radius of the curve. The length of the chord
may be 100 links, in which case the radius will be expressed in
links, and the offset will be in links.

The length of the offset ef is twice the length of the offset cd,
and can be calculated from the rule

chord 2

The length of the offsets gli, ij, etc., are equal to ef. The
offset cd is called the tangential offset, as it is measured from
the tangent ; the offset ef is measured from the extension of the
chord bd at e.

Eeferring to Fig. 192, the length of the offsets cd, ef, etc.,
may also be calculated as follows :

The chords od, df, fit, etc., are each equal to 1 chain in
length, and the radius of the curve being 80 chains, it will be
seen that the natural chord of the angle oad is equal to

chord od l , mO -

=n == =: STT == Ul^o
radius oa

On reference to the table of natural chords, this is found to
correspond with an angle of 42' 58". The required distance cd
is equal to ob, which is the versed sine of the angle oad. On again
referring to the tables the versed sine of 42' 58" is found to be
0*0000781 ; multiplying this by the radius in inches (80 X 792)
gives the length 4*9 inches for the first offset cd.

MISCELLANEOUS. 339

The other offsets are obtained in a similar manner, and a
rule might be stated as follows :

cd = E . versed sine oacl
ef = E . versed sine oaf
gli = E . versed sine oali, etc.

If the length on the tangent is required, it can be calculated ;
for instance

oc = E . sin oad

oe = E . sin oaf, etc.

As this calculation is a somewhat tedious one, tables are
published giving the lengths of the offsets for curves from radii
of 5 chains to 8 miles. 1

Calculation of Angles, The angles necessary for setting out
curves with the dial or theodolite can also be obtained by calcu-
lation. Eef erring to Fig. 193, the angle CBD, or tangential
angle (so called because it is the angle made by the chord with
the tangent), is equal to half the deflection angle, or angle sub-
tended at the centre of the circle by the chord BD, and can be
found by the following rule :

Tangential angle (minutes) = ,. x 1718'873

EXAMPLE. What is the tangential angle for a chord 1 chain in length of a
circle whose radius is 80 chains ?

Tangential angle in minutes = g^ x 1718-873

= 21-486 mins., or 21' 29"

The angle JDE (Fig. 193) is double the angle CBD, pro-
vided that the chord BD equals the chord DE. The angles
made by successive chords of equal length are also equal to
each other, and a rule might be expressed as follows :

Angle between equal chords (in minutes) = ^ x 3437*746

Eeferring now to Fig. 194, one of the fundamental properties
of the circle is that equal chords subtend equal angles at the
centre of a circle, and also at the circumference, if the angles
are contained in similar segments ; thus, having calculated the
tangential angle B'BC by the above rule, the succeeding angles

1 Kennedy and Hackwood's Tables for Setting out Curves. London, E. and F.
N. Spon.

340 MINE SURVEYING.

are all equal to it, and their sum might be found at once, as they
are all tangential angles.

It is sometimes convenient to calculate the radius of the
curve that will connect two straight portions of line. Eeferring
to Fig. 195, two straight portions of line, AB and XY, are

FIG. 195. To find the radius of a curve.

shown. What is the radius of the curve, commencing at B, that
will connect these straight parts ? This may be found geometri-
cally as follows : Produce AB and XY till they meet at O ; on
OX make OC = OB, and at B and C erect perpendiculars
cutting in D ; then D is the centre of a curve that will join
AB and XY, and the radius of this curve can be measured from
the drawing.

The radius can also be found by calculation, if the length
OB from the tangential point at which it is required to strike
the curve to the point of intersection of, and also the angle
AOX between, the two tangents, are known. 1

Thus, in Fig. 195 it will be seen that is the tangent of

the angle DOB (which is half the angle AOX).

Radius of curve = OB x tangent of angle DOB

Calculation of Average Dip or Inclination of Measures. It is
often desired to measure the angle and direction of dip, but " it
is not always possible to ascertain the true dip by one observa-
tion ; it often happens that it must be ascertained from two
observations, neither of which is on the line of greatest dip.

1 The length OB can be calculated, if the length of a straight line BC
perpendicular to OD is known, by the rule

OB =

natural chord of the angle AOX

MISCELLANEOUS. 341

Fig. 196 shows in plan two lines along which the dip has been
observed : CD, direction south-east 50, dip 1 in 10 ; EF, direction
north-east 30, dip 1 in 20. These two lines must be plotted
on paper to scale, showing their direction and position correctly,
and prolonged till they meet in G. On the line GD must then
be marked out a length of 10, GH (because the dip is 1 in 10) ;
and on the line GF a length of 20, G! (because the dip is 1 in

FIG. 196. Method of finding the true dip from two observations.

20) ; H and I must be connected by the line HI, and a perpen-
dicular to this line drawn from the apex G. GK is then the
direction of the greatest dip, and represents the amount of dip.
The length GK is 8J, and therefore the inclination is 1 in 8J.

" In a similar manner the true dip may be ascertained from
the depth of three pits, represented in Fig. 196 by the letters
G, D, and F. It is first necessary to reduce the actual depths to
their relative depths above or below the sea-level. Thus suppose
G is 150, D 220, and F 250 yards deep, all down to the same
coal ; if the top of G pit is 300 feet above the sea-level, D 360
feet, and F 390 feet, then 60 feet must be taken off D, and 90
off F, reducing the depth of D to 200 yards, and of F to 220
yards. Then, if the distance between GD and GF is known,
the rate of inclination on those lines can be calculated, and the
true dip set out in the manner given in the first instance.

" If the dip is ascertained by means of a clinometer, and is
recorded in degrees, the rate of inclination can be quickly ascer-
tained by bearing in mind that it is equal to the ratio of the
radius of the circle to the cotangent of the angle of inclination.
If, for instance, the radius is 1 and the cotangent of the angle 10,
the inclination would be 1 in 10 ; for an angle of 6 the (natural)
cotangent is 9*5, and the inclination is therefore 1 in 9*5." l

1 " Mining," by Arnold Lupton (Longmans, Green, and Co.).

342 MINE SURVEYING.

Levelling to ascertain Subsidence of Surface due to Under-
ground Workings, In order to ascertain the subsidence due to
underground workings, there are two methods which can be
adopted. The first is to observe the subsidence under a canal,
reservoir, railroad, high-road, wall, or building, the levels and
gradients of which are known ; then, if one portion has been
lowered by the underground workings, the amount can be
measured. Thus in a canal the water from lock to lock is
maintained at one level, and this level is, say, 1 foot below the
top of the towing-path ; if the towing-path is lowered by under-
ground workings till it becomes level with the top of the water,
the subsidence is 1 foot. The towing-path will, of course, be
raised, and it may again subside another foot; the amount
of subsidence is therefore known to those who have raised
the towing-path from time to time.

The subsidence, however, may have taken place under some
bridge crossing the canal, which is lowered by the extraction of
minerals from below. The crown of the arch of this bridge was,
say, 6 feet above the surface of the water. If after the extrac-
tion of the minerals it is found that the crown of the arch is
only 5 feet above the water, the crown has been lowered 1 foot ;
and until the bridge is rebuilt, the height of the arch above the
water will continue to give a measure of the total subsidence.

In a similar manner, in the case of a railway which is level
for a long length, or of which the gradient is known, if the
ground subsides there will be a hollow where the line was
previously level, and the amount of subsidence can be measured.
The plate-layers will, of course, raise the rails from time to time
as they fall ; the amount of subsidence is therefore known to
the plate-layers, who know the extent to which the rails have
been raised.

In a similar manner with a turnpike road which is well kept
at a uniform gradient, subsidence of the ground will cause a
hollow, the amount of which can be measured. Also in the case
of a long wall, the coping-stones of which have been laid on a
level or on a uniform slope, any subsidence of the ground
beneath would be shown by a breach in the regularity of the
surface-line of the coping-stone.

In the absence, however, of any such marks as those above
mentioned, the amount of subsidence cannot be determined
unless, previous to the working of the coal, the ground has been

MISCELLANEO US.

343

levelled and accurate cross-sections of the surface of lines which
are marked on the plan are made ; subsequent levellings will
show any variation in the surface. It is necessary, of course,
that the levels should start from some permanent mark which
is not altered by the subsidence. For very accurate observa-
tions of the subsidence, bench-marks should be made on gate-
posts, walls, trees, posts, and rails, or, in the absence of a
sufficiency of these, on posts specially fixed in the ground.

Candles and Lamps. In ordinary mine surveying no means
of illumination is more convenient than the candle, both for
reading the instrument and for sighting. There are many
places, however, where the candle cannot be used, on account
either of wind or gas. In these cases an oil-lamp
is generally used ; and for reading the dial a
small lamp made of copper, and provided with
a burnished reflector and side handle (similar to
a bicycle lamp), is very convenient. Where there
is gas, safety-lamps are used exclusively. For
reading the dial the lamp must be made exclu-
sively of brass or copper, or of aluminium ; the
latter is a great improvement, as the weight of
the lamp often becomes irksome. A swinging
handle, as shown in Fig. 197, is also useful,
because the lamp generally becomes too hot to
be held with comfort without the aid of a handle,
and it is impossible to hold it in the right place
by the suspending ring. The lamp shown in the figure can be
held by grasping the two sides of the handle, and so held the
lamp may be above the hand.

Coloured Lights. In order to avoid mistakes through multi-
plicity of lamps near the object sighted, some surveyors adopt
the plan of coloured lights, so as to distinguish the lamp at
the station from other lamps in the vicinity. This is a good
plan, especially where the theodolite is used, but where the dial
is used the coloured glass diminishes the light, and makes it
less easy to see at long distances. When coloured lamps are
not used, the surveyor waits till all the lamps but one are
hidden, and then takes that as the station lamp.

It is often difficult to read a finely graduated theodolite with,
the ordinary safety-lamp, and a lamp with a reflector and con-
densing lens would be a great advantage for this purpose.

FIG. 197. Sur-
veyor's safety-
lamp.

344

MINE SURVEYING.

For fast-needle and theodolite work care must be taken to
have a lamp to fit the lamp-cups on the tripod, and that the
wick-tube is exactly in the centre of the lamp ; unless the lamp-
flame is precisely over the centre of the tripod, it will lead to
inaccuracy.

Plane Table, The plane table shown in Fig. 198 is an
instrument much used in some countries for preparing maps.
It is considered specially useful for contouring. The instrument
consists of a drawing-board, mounted on a tripod stand ; there
are levelling screws, by which the board can be levelled, and it

FIG. 198. Plane table.
(Kindly lent by Messrs. W. F. Stanley and Co., Ltd.)

can be turned round on a brass ring, supported by the levelling
screws, and revolving on a centre pin, with coned or special
head. The surveyor is also provided with a rule (termed an
alidade) with sights placed at its ends (in Fig. 198 a telescope
is shown instead of sights), and carrying a trough compass.
A loose spirit-level is also provided with which to level the board.
The intention is to make a drawing or sketch upon this
board, showing the salient features of the landscape ; if it is on
a small scale, these will be mountains, hills, churches, towns,
clumps of trees, rivers, lakes, roads, etc. ; if it is on a large
scale, more detailed objects, such as corners of buildings, fences,
brooks, outcrops of minerals, position of shafts, etc., may be
sketched. In the first place, it might be considered that the
drawing on the plane table is a picture representing the land-
scape, such as would be seen from the top of a very tall towel-
infinitely high, so that all the objects in the landscape would

MISCELLANEOUS.

345

appear in their correct relative positions, and be so sketched
upon the plan.

In an ordinary landscape the near objects appear large, and
the distant objects small ; but this would not be the case if the
artist were at the top of a tower infinitely high, and were sketch-
ing a limited landscape. From this great height he would see
the buildings, hills, rivers, and lakes separated from each other
by an apparent distance, which would in each case be propor-
tional to the real distance.

Method of working the Plane Table. The surveyor, using the
plane table, stands on an elevation, so that his line of sight
passes over hedges, walls, and other obstructions. He sees two
villages, say 2 miles distant from him, and 2 miles ' distant
from each other ; he cannot tell what distance they are apart or
from himself, but having fixed a clean sheet of paper to the
table, he puts a mark (a) upon it, representing the place where
he is standing (see Fig, 199), which is, perhaps, near to a village

A B

FIG. 199. Method of working the plane table.

church, which he sketches on the paper, and puts 011 the name
of the village : this is station A. He then takes the ruler or
straight-edge, lays it on the paper with its edge on the point a,
and directs it towards the church spire in village B, and rules
a light line over the paper, or, to avoid too many lines, rules a
short line at the edge of the paper, writing on it A to B. He
then turns the ruler into the direction of the church at village
C, and rules a similar line, writing on the end of the line A to
C. He may proceed to rule any number of other lines in the
direction of buildings, hills, and other objects, which he desires
to place on the map.

346 MINE SURVEYING.

He then, leaving a flag to mark the station at A, proceeds
with his instrument to station B ; he measures the distance
from A to B as he walks by counting paces, or, as this is the
first line and may be the base of a system of triangulation,
by accurate chaining. It may be that he can take the distance
AB from some existing map with accuracy ; if the distance
AB is not accurately placed on the map, then any distances
calculated from that base will, of course, be inaccurate. This
measurement enables him to mark the point b on the line al>
previously ruled.

He now fixes the tripod with the point b on the paper over
the station B, and turns the plane table until the point a on the
paper is exactly in the direction of the station mark at A. He
now takes the ruler, and places it on the paper with its edge on
the point b, sights to C, and rules a line. The intersection of
this line be with the line ac gives the exact position of the
point C. If the base-line AB has been accurately measured, the
position C is accurately fixed, and the distances BC and AC
can be scaled off the plan which is so made.

From the position B the ruler may be directed towards all
the other stations previously sighted from A, and by the inter-
sections so given their positions are all fixed upon the plan, and
if the angles are not too acute, their positions are accurately
fixed, and in addition lines may now be ruled towards other
buildings, hills, etc., which were not seen from station A.

The surveyor then proceeds to C, fixing the mark c over the
station, and turning the plane table till b on the paper is in the
direction of station B ; and, of course, a on the paper is at the
same time in the direction A, if the work has been correctly done.
He now lays the ruler in the direction of the stations sighted
from B, and marks the intersections by which the position of
all these places is accurately fixed. The work may thus be
continued without fresh measurements from station to station.

This is a system of triangulation exactly similar to that
described in Chapter VII. for use with the theodolite ; but instead
of booking angles in a note-book, and subsequently plotting
them with a protractor, the angles are all drawn out by sight
upon the plan, and no booking is necessary. If the survey is
started with an accurately measured base-line, and sufficient
care is taken, the result will be an approximately accurate plan
suitable for a preliminary survey.

MISCELLANEOUS. 347

To get the table level, a small pocket-level is placed upon
it ; a fine pencil is used in ruling the lines.

Sketching in Contours, Roads, etc. When the instrument is
set up at the first station, only radial lines from the station A
can be drawn ; but when the instrument has been set up at B,
and intersections at C and other places marked on the plan,
details of the landscape may be sketched' in. The position C
having been accurately fixed on the plan, shading may be added
to show that it is a hill ; the position of a river running past A
and B may also be sketched with approximate accuracy ; and
a road or railway going from A to B may be sketched on the
plan in the same way.

When a telescope is used instead of plain sights, the plane
table becomes a much more precise instrument. The telescope
is fixed upon a ruler which has a broad base, so that it is
not easily upset. The plane table being fixed level, the vertical
axis] of the telescope is, of course, vertical. The telescope can
be moved through an arc, so as to measure elevations and
depressions. A spirit-level on the top of the telescope is a check
upon the levelling of the plane table.

By means of parallel hairs the telescope can be used for
tacheometry. By this means positions can be marked upon the
plan, when there are no intersections, by simply ruling a line
in the direction of the object, and measuring the distance by
the readings of a staff seen through the telescope.

Advantage of the Plane Table. The chief advantage of the
use of the plane table is the facility for sketching in the
contours of hills, and the course of streams and rivers from a
vantage-ground. With the main stations accurately fixed by
intersections and tacheometrical measurements, the details may
be sketched in with considerable accuracy in a short time ;
whereas to do this from measurements and angles recorded
in the note-book would require a great deal of measuring and
note-taking.

Plane Table and Trough Compass. The plane table is often
used with the trough compass. The compass is placed on the
table and turned until the needle is parallel to the centre-line of
the box. This direction may be ruled on the board, and at
every fresh station the board may be turned until this line so
marked comes into the meridian. If this is done, it obviates
the necessity for taking a back sight as a base-line for fresh

348 MINE SURVEYING.

intersections, as every line ruled upon the plan makes an angle
with the meridian. It is better, however, to use the needle as
a check upon the accuracy of the work done without it than as
a substitution for it.

In the United States it is the practice to make the field-map
twice the scale of the map to be published ; thus any errors
made in the original survey are much reduced.

In the topographical land survey of Wurtemberg the drawing
on the plane table was -Vo, or 25^ inches to the mile, and
the scale of the published plan was -oihro > thus 400 plane-table
sheets were required for one published map of the same size. 1

Plane-table work is most suitable for countries where a con-
tinuance of fine, dry weather can be expected.

For rapid work the plane table may be used strapped to the
arm, and in this case a magnetic compass is often fixed to the
table, so that it can always be held in the meridian, and
the bearings of the various points sketched, as the angles could
not be taken correctly from a fixed base without the use of a
tripod.

Simultaneous Use of Two Plane Tables. By the simultaneous
use of two plane tables the intersections of lines of sight can be
obtained with increased rapidity without the need of permanent
stations being fixed, or for refinding stations observed from the
first position of the table.

In some cases a flag may be carried by a horseman ; at
every place where he stops the line of his direction is marked
on the plan, and their intersections found by subsequent com-
parison of the two plans. 2 A surveyor using the plane table
has constant opportunities of correcting his drawing as he
changes his station, and ultimately arriving at a fairly correct
representation of the chief features which are important for his
purpose. Such a plan would be useful for many mining
purposes, especially in conjunction with photographs.

Portable Boards. Boards are sometimes made to roll up
with light folding tripods, so as to be easily carried by a
horseman.

1 J. Pierce, Junr., M.A., A.I.C.E., "Economic Use of the Plane Table," Inst.
C. JE 1 ., p. 187, vol. xcii.

2 Pierce, on the Use of the Plane Table.

CHAPTER XVII.

PROSPECTING FOR MINERALS BY MEANS OF THE MAGNETIC NEEDLE.

THE properties possessed by the magnetic needle have enabled
it to be used to advantage in searching for ore deposits. Instru-
ments for this purpose have reached a high state of perfection
in the country of Sweden, and Professor G. Nordenstrom, of the
Stockholm School of Mines, gives an account of these instru-
ments and the method of using them, in a valuable paper read
before the Iron and Steel Institute, at their Stockholm meeting. 1

Magnetic instruments have been employed in Sweden for
more than two hundred years in exploring for ore. This fact
can doubtless be ascribed to the interest for exploring for ore
among the mining engineers, and also among the inhabitants
of the mining districts in general, the Government encouraging
this interest by rewards to such as discover new deposits.

The ores occurring most frequently in the country are the
magnetite iron ores, which are strongly magnetic ; the next
commonest, the hematites, are also magnetic, but in a lesser
degree, since they are always more or less mixed with
magnetite.

Other ore deposits, such as copper, zinc, cobalt, and nickel,
have also been and may be found by the aid of the needle, since
these ores contain a greater or lesser proportion of magnetite or
magnetic pyrites.

The miner's dip compass was introduced in 1770, and by its
use all the Swedish iron ores have been explored. It was con-
structed as follows : In a round brass box a magnetic needle
is suspended in such a way that it can move freely on a
horizontal plane and on a vertical plane to an angle of about

1 Published in Engineering, September 30 and October 17, 1898, from which this
description and illustrations are taken, with the Editor's kind permission.

350 MINE SURVEYING.

70 from the horizon. It is compensated for the earth's
magnetism, so that it takes a horizontal position in districts
void of ore, or where there are no magnetic ores. As a rule,
miner's compasses without graduation are used ; the horizontal
plane of the needle is only indicated by a ring inside the
compass. The dip of the needle is estimated only by the eye,
and is not actually measured.

The miner's compass is still used, and with success, for
exploring for ores, but more particularly for the preliminary
exploring work in ore fields.

In later times, however, the demand for more accurate
results has grown, and during the past thirty years there have
been introduced magnetic instruments by means of which a still
more exact knowledge of the magnetic conditions of our iron-
ore fields can be obtained.

Thalen's Magnetometer. This instrument, constructed by
Professor Thalen, of the Upsala University, is a modification of
Lamont's theodolite.

It consists of a declination compass A (Fig. 200) of about
80 millimetres (3fV inches) in diameter/which is provided with a

FIG. 200. Plan and side elevation of Thalen's magnetometer.

scale graduated to degrees and half-degrees from to 90. At
right angles to the diameter, which passes through the zero
point of the scale, there is attached an arm B from 200 to 220
millimetres (7|- to 8f inches) long.

On this arm, which is graduated in millimetres, is placed the
bar magnet C for the deviation measurements, which can, at

PROSPECTING WITH MAGNETIC NEEDLE. 351

the will of the operator, be given a certain fixed distance from
the centre of the needle.

The instrument is rotated on a vertical axis, whose central
line passes through the centre of the magnetic needle. It is
provided with a spirit-level D, sights E and F, and levelling
screws, and is placed on a tripod.

This instrument, which has been in use for more than
twenty-five years, is now used principally for measuring hori-
zontal intensity. In so doing two methods may be used the
tangent method and the sine method.

In using the tangent method, the magnetic needle is first
placed at zero, after the instrument has been levelled, and the
bar magnet has been removed from its place. Then the bar
magnet is put in its proper place on the arm, and the angle of
deviation a is read.

In using the sine method, the bar magnet is put in place on
the arm. Then the magnetic needle is placed at zero, and, after
the bar magnet has then been removed, the angle of deviation a
is read. This latter method gives the more accurate results,
but in practice the tangent method is generally used, partly
because it is more convenient, and partly because it is every-
where applicable, which is not the case with the sine method in
certain points of the ore field north of the ore mass.

Method of using the Magnetometer, Before the measurements
are begun, the instrument is adjusted at a place where there are
no magnetic ores, and consequently no other magnetic force than
the earth's magnetism. The angle of deviation found here is noted
a , and is generally so arranged that it is equal to 25 or 30 . 1
Then begins the measurement of the ore field, which for this
purpose is divided into squares with sides 10 metres in length.

By the aid of the tangent method the angle of deviation a
is afterwards obtained in each corner of every square. These
a values are noted on a map (see ideal map, Fig. 201), and the
points for which equal angles have been obtained are joined.
This gives two systems of curves, which in a more or less
regular manner are grouped round their centres. One of these
is situated north of the ore, and where the a values are greatest,
and is therefore noted with a maximum ; the other is situated
either directly above the greatest mass of ore, or somewhat to the

1 The angle of deviation means the angle between the magnetic meridian and
the position of the compass needle, and the deviation is caused by the bar magnet .

352

MINE SURVEYING.

south of it, and represents the smallest a value, being therefore
noted with a minimum. Between these two sets of curves
there is a wavy line, whose angle of deviation is the same as
obtained where there is no ore, and it is noted with a ; this
curved line is called a neutral line.

The line which unites the maximum point and the minimum
point indicates the direction of the magnetic meridian of the

V=20

SOUTH

ISODYNAMIC LINES, obtained with Tfialerts Magnetometer
ISOCLINE LINES, obtained with Tib era's Snclinater.

Fm. 201. Ideal map, showing curves obtained with Thalen's magnetometer
and Tiberg's incliuator.

ore field. The centre of the greatest mass of ore is situated
either at the point of intersection of the magnetic meridian
and the neutral line, or else directly under the point marked a
minimum. In order to get correct results, the levelling of the
ore field which is being measured should be known.

Tiberg's Inclinator. This instrument has been in use since
1880, when it was invented by E. Tiberg. It consists of a dip
compass 80 millimetres in diameter, graduated from to 90,
and a magnetic needle so hung that it cannot move except in
the plane of the graduated circular scale. The instrument
furthermore differs from other dip compasses in that the centre
of gravity of the magnetic needle is a little below its horizontal

PROSPECTING WITH MAGNETIC NEEDLE.

353

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 or by a counterbalance of aluminium fixed to it.
For some years this instrument has been generally used in
combination with Thalen's magnetometer, and by means of this

FIG. 202. Combined instrument fitted with Tiberg's compass.

combination measurements according to both Thalen's and
Tiberg's methods may be quickly made. The combined instru-
ment is illustrated in Figs. 202 and 203. Fig. 202 shows the

FIG. 203. Combined instrument fitted with Thale'n's compass.

instrument furnished with Tiberg's compass, but in Fig. 203
Thalen's compass is substituted. In order to make it possible
to use first the one and then the other of these compasses,
they are provided with axle-pins fitting into the bearings

2 A

354 MINE SURVEYING.

in the standards a. The centre-lines of the axle-pins in the
Tiberg compass run through the zero points, but in the Thalen
compass through the 90 point. The instrument is furnished
with a spirit-level b, a transverse arm c, and sights d. The
arm c, secured on one of the standards, serves to receive the
bar magnet for the deviation measurements, when measurements
according to the Thalen method are to be made.

Tiberg' s Method, The instrument is first adjusted on per-
fectly neutral ground. After the ore field to be explored has
been divided into squares with sides 10 metres long at the most,
observations are made with the inclinator in each corner in
every square, in the following manner : The compass is placed
horizontally, and is turned on the horizontal plane till the
central line through the axle-pins of the compass is at right
angles to the direction of the needle, or, in other words, so that
the needle is placed at 90 ; then the compass is turned on its
axle-pins so that it has a vertical position. In this position the
needle is only affected by the vertical component of the attrac-
tion of the ore, and this causes a greater or lesser inclination of
the needle. If the magnetic force of the ore is P, and the angle
of inclination is V, then we have P = K tan V.

If we mark the value of V on a map, and the points for
which equal values are obtained are united, we get a system of
curves which are more or less regularly grouped round a certain
centre whose V value is greater than that of all the others.
Immediately under this centre, where Y = V max. (see Fig. 201),
the greatest mass of ore always occurs.

TJse of Instruments Underground. Besides for surveys at the

FIG. 204. Method of prospecting underground.

surface, both these instruments are used for surveys under-
ground. For this purpose the sine method is generally used.

PROSPECTING WITH MAGNETIC NEEDLE. 355

If H (Fig. 204) is the horizontal component of the earth's
magnetism, and F that of the ore, and R is the resultant of
both, we obtain for each point of observation R!, R 2 , R 3 , etc.,

according to the formula E = H -, where a Q is the angle

of deviation found when there is no magnetic ore present, and a
is the angle of deviation as read in the gallery of the mine. If
we give an arbitrary value to H, which is considered to be a
constant, we get the lengths R lf R 2 , R 3 , etc., and also their
direction. The length and direction of the component F is
then obtained by construction. The position of the centre of
the ore sought for, c, is indicated by the direction of F L , F 2 ,
F 3 , etc., all of which converge more or less to this centre.

Professor Nordenstrom concludes his valuable paper by
expressing his opinion as to the value of magnetic measure-
ments in all countries where magnetic ores are known to
occur.

CHAPTEE XVIII.

METHODS OF FINDING TRUE NORTH, OR GEOGRAPHICAL MERIDIAN.

IN connection with every important mining survey it is highly
desirable that a line in the direction of the geographical meri-
dian, that is to say, a north-and-south line, should be set
out and fixed by permanent marks for a considerable length,
say 10 chains. These marks should be on pillars of brick,
stone, iron, or oak, and the centre line indicated with great
accuracy. There are many ways in which the direction of the
north pole or of the south pole may be ascertained. The sun
is the best indicator of direction in the temperate regions. In
the northern hemisphere, north of the tropics, the sun is always
due south at noonday ; and in the southern hemisphere, south of
the tropics, the sun is always due north at noonday. On the
northernmost tropic the sun is vertically overhead at noonday
on June 21, and on the southernmost tropic the same is the
case on December 22, while at the equator the sun is in the
zenith at the equinoxes.

The following are some of the methods used by surveyors for
ascertaining the north-and-south line :

By Equal Shadows of the Sun. At apparent noon the sun, in
the northern hemisphere north of the tropics, is due south, and
the shadow thrown by a vertical pole 1 would represent the direc-
tion of a line joining the north and south poles ; that is to say,
the true meridian. At equal times before or after apparent noon,
the shadows thrown by the pole would be of equal length. This
method is applied in practice as follows : A vertical pole, shown
in plan at O (Fig. 205), is erected on the south side of a level
surface. A few hours before noon a mark is made at the end
of the shadow cast by the pole, and a circle is described having
its centre at the foot of the pole O, and with radius equal to

1 Where there is shelter from the wind, a plumb-line might be substituted for
the pole.

METHODS OF FINDING TRUE NORTH.

357

the shadow OA. At an equal interval of time after noon the
shadow will be again equal to OA, and the position of the end
of the shadow is marked
at the exact point, B,
where it touches the circle
already described. The
arc AB is then bisected
at the point C, and the
line OC represents the
direction of the true meri-
dian. This direction may
be produced and pegged
out on the surface. If
two or three circles are
drawn at different hours
before noon, and the two
points marked in which
each is touched by the
shadow of equal length in
the afternoon, a number
of arcs are obtained ;
these may all be bisected,
and a more accurate re-
sult obtained by taking
the average. This method is only perfectly correct at the time
of the solstices (June 21 and December 22). To get accurate
results the ground should be quite level and white, and the
circles of large diameter, so as to minimize the effect of any
error in fixing the exact position of the end of the shadow.

Meridian Dial. Mr. E. T. Newton of Camborne has utilized
the principle, and constructed a special instrument for obtaining
the true meridian. This consists (as shown in Fig. 206) of a
brass ring 10 inches outside diameter, and 2 inches wide, with
four arms and central boss ; this fits on to a dial from which
the sights have been unscrewed. The ring is provided with an
alidade working round a centre pin in the boss, with plain
sights at each end. A pillar 3^ inches high is screwed into a
hole exactly in the centre of the boss. This pillar may either
end in a needle-point, or may have a small plate fastened to the
end, in which a small hole is pierced. If the former, a shadow
is cast ; if the latter, a small bright spot.

FIG. 205. Finding north-and-south lines by
shadows of sun.

358

MINE SURVEYING.

As the position of the sun alters during the day, the shadow
or spot crosses different circles drawn on a white celluloid disc,
which is secured to the brass plate ; the circles are struck from
the centre of the boss. The points where the spot or end of the
needle shadow touch each circle are marked. The two points

FIG. 206. Meridian dial.

on each circle equidistant from the centre are joined by a
straight line, which is bisected in each case ; a line drawn from
the centre of the boss through these bisections (which, if correct,
will be in the same straight line) will be a north-and-south line.

The alidade can now be fixed in the direction of this line,
which may then be set out by means of the sights.

The decimation can be read off from the compass-needle of
the dial, which can be seen through the openings between the
arms connecting the ring with the centre boss.

Neither of the above methods provides for accuracy, and they
are unsuitable for important surveys.

By Equal Altitudes of the Sun, or a Star. If a theodolite be
substituted for the pole (or plumb-line), the altitude of the sun
(taking, say, the lower edge) may be observed very accurately
before noon (at, say, 10 a.m.), reading the azimuth circle
simultaneously. The observer then waits until the sun reaches
the same altitude after noon (at, say, 2 p.m.), and again
observes the azimuth. The mean of the two azimuth readings
would be the south point, very nearly. A small error will
arise from the sun's motion in declination during the interval

METHODS OF FINDING TRUE NORTH. 359

between the observations. But the amount of this error may be
very easily calculated. It would not, as a rule, amount to more
than four or five minutes of arc. If, instead of the sun, any
bright star be observed, this method admits of great accuracy.

In order to calculate the error due to the sun's motion in declination, the
following facts must be considered. From December 21 to June 21, the sun is
rising higher in the heavens at noonday in the northern hemisphere (north of the
Tropic of Cancer), and of course is falling in the southern hemisphere ; and from
June 21 to December 21, the sun is falling lower in the heavens at noonday in
the northern hemisphere, and of course is rising for the same period in the
southern hemisphere (south of the Tropic of Capricorn).

This rising and falling is due to the variation of the declination of the earth's
axis of rotation, towards or from the sun .

At the equinoxes, that is, about March 21 and September 23, there is no
declination (these dates are for 1902).

After March 20, the declination (see Nautical Almanack) is north, and
increases each day about 23 minutes or about 59 seconds per hour ; but the rate
of increase or variation gradually diminishes as midsummer approaches, until
the maximum northern declination of 23 27' is reached on June 21.

The rate of variation on June 1 is 21 seconds per hour. On June 20 it is
2 seconds per hour ; after June 21 the rate of variation gradually increases to
about 59 seconds per hour at the September equinox, after which the rate of
variation gradually decreases, until the maximum southern declination of nearly
23 27' is reached on December 22 (1902).

If, then, the observation is made on June 21 or December 22, no correction
for variation of declination is necessary.

If the observation is made on March 21 or September 21, a correction must
be made, due to a variation in declination of 59 seconds per hour between the
times of the first observation (say 10 a.m.) and the second observation (say 2
p.m.). Between the above dates a proportional correction must be made, the
exact variation per hour being obtained from the Nautical Almanack. At the
latitude of Greenwich on August 18, 1901, the variation of declination per hour
is 48 seconds, and the second observation at 2 p.m. will be 10 minutes too far
-r-* nn/i the line drawn halfway between the two observations would be 5

' *-n ro w rule. 1 Let

316 49* 38".

Sun's declination August 18, 13 21'.

Difference of declination = 48 seconds x 4 hours = 192 seconds.

Diff. dec. = - 192" log is 2*2833

Declination = 13 21' log cosine 9*9881

Azimuth = 43 20' log cosecant 0-1634

Altitude = 44 52' log secant 0*1495

Latitude = 51 28' log secant 0-2055

2-7898

1 Kule given by Mr. C. R. Davidson, Royal Observatory, Greenwich.

EKEATA.

Page 359, lines 34 and 35, for " west " read " east.

METHODS OF FINDING TRUE NORTH. 359

This rising and falling is due to the variation of the declination of the earth's
axis of rotation, towards or from the sun.

At the equinoxes, that is, about March 21 and September 23, there is no
declination (these dates are for 1902).

If, then, the observation is made on June 21 or December 22, no correction
for variation of declination is necessary.

If the observation is made on March 21 or September 21, a correction must
be made, due to a variation in declination of 59 seconds per hour between the
times of the first observation (say 10 a.m.) and the second observation (say 2
p.m.). Between the above dates a proportional correction must be made, the
exact variation per hour being obtained from the Nautical Almanack. At the
latitude of Greenwich on August 18, 1901, the variation of declination per hour
is 48 seconds, and the second observation at 2 p.m. will be 10 minutes too far
west, and the line drawn halfway between the two observations would be 5
minutes west of true south.

The second observed azimuth may be corrected by the following rule. 1 Let
A = second observed azimuth, and A x corrected second azimuth. A 1 = A +
difference of declination x cosine declination x cosecant azimuth x secant
latitude x secant altitude.

In the spring half of the year the + sign is used, and in the autumn of the
year the sign .

Example. At Greenwich (Lat. 51 28') on August 18, at 10 a.m., sun
is observed at altitude 44 52' 10". Azimuth 43 20' 40" (from south point).
In afternoon at 2 p.m., at an equal altitude, the azimuth is observed to be
316 49' 38".

Sun's declination August 18, 13 21'.

Difference of declination = 48 seconds x 4 hours = 192 seconds.

Diff. dec. = - 192" log is 2-2833

Declination = 13 21' log cosine 9-9881

Azimuth = 43 20' log cosecant 0-1634

Altitude = 44 52' log secant 0-1495

Latitude = 51 28' log secant 0*2055

2-7898

Rule given by Mr. C. R. Davidson, Royal Observatory, Greenwich.

360 MINE SURVEYING.

which is the log of -616" = -Iff 16".

Second azimuth = 316 49' 38"
Correction = - 10' 16"

316 39' 22"
First azimuth = 43 20' 40"

Mean 180 0' 1"

Observation of the Sun at Noon. Mr. S. A. Warburton of
Moira, near Ashby-de-la-Zouch, has sent the author the following
description of his method. The instruments he uses are a good
theodolite, and a good watch set to Greenwich mean time :

" The method which I employed was to ascertain, by obser-
vation, the actual passage of the sun's centre over the meridian
of the place of observation, which seems to me to be the best
method, only there are a number of calculations to be made, and
it is necessary to have a good watch set exactly to Greenwich
mean time ; this must be got by setting the watch exactly at
10 a.m., or other telegraphed hour, on the day of observation
by a time-ball.

" Now, Greenwich mean time is not apparent time, the latter
being solar time, such as would be given by a sun-dial, and Green-
wich mean time noon is not apparent noon, the difference being
about 16 minutes at one time of the year and varying to nothing ;
these differences are given for every day of the year in the
Nautical Almanack. Take, for instance, a certain day when
from the Nautical Almanack you find the solar time at Greenwich
to be 10 minutes 5 seconds earlier than Greenwich mean time ;
this would mean that a theodolite pointed to the centre of the
sun at Greenwich at 11 hours 49 minutes 55 seconds, would
give the true Greenwich meridian ; but as our place of observa-
tion is not likely to be at Greenwich, but some place east or
west of it, another factor is brought in, and a correction for
our longitude east or west of Greenwich must be made ; again,
we are unable to observe the sun's centre with accuracy, there-
fore his right or left limb is observed ; then adding his semi-
diameter (if we observe his left limb), we find his centre. The
sun's apparent diameter varies with his distance from the earth,
and his semi-diameter is given in the Nautical Almanack for
every day in the year at mean noon. First, then, we must know
our longitude east or west of Greenwich, and in order to do this
take an Ordnance sheet and draw a vertical line through the point

METHODS OF FINDING TRUE NORTH. 361

of observation, and the longitude east or west will be given on the
top and bottom of the sheet. Take the following example :

" Place of Observation. Hyde Park Corner, Leeds.

" Date, October 2, 1899.

" Take the 1" Ordnance sheet, 1 and drawing a vertical line through Hyde
Park Corner, we shall find that it is situated in long. 1 33' 40" W.

" Referring to the Nautical Almanack (or Brown's), we see that on October 2,
the equation of time is 10 minutes 38'3 seconds to be added to mean time ;
in other words, that 10 minutes 38'3 seconds must be added to Greenwich time
to find the apparent time at Greenwich.

Thus when it is mean noon at Greenwich by the clock, the real or apparent
hour by the sun is 12 hours 10 minutes 38 seconds, and the apparent noon is
12 hours less 10' 38'3" = 11 hours 49 minutes 21'7 seconds.

" We must next reduce our 1 33' 40" W. long, into time. Now, 15 longitude
= 1 hour of time ; therefore 1 = 4 minutes, and 1' = 4 seconds of time ; and
1 33' 40" = 6 minutes 15 seconds very nearly; and as it is west longitude, we
must add this to the time we know the true sun passed the meridian of Green-
wich, which we have already found to be 11 hours 49 minutes 21*7 seconds.

Hrs. Mins. Sees.

11 49 21-7 = true sun passes the meridian of Greenwich.

G 15-0 = time taken by sun to arrive at long. 1 33' 40" W.

11 55 36-7 = time (Greenwich mean time) of sun passing long. 1 33' 40" W.

" We can now set up our theodolite, fitted with coloured eye-piece for solar
observations, and we will observe the left limb of the sun, and, with the vernier
clamped at 360, follow the sun with the tangent screw carrying the whole
instrument (as the telescope will probably be an inverting one, we shall appear
to be observing the right limb, and the sun to be moving from right to left) ; say
we begin this at 11 hours 54 minutes by our correctly timed watch, then at
11 hours 55 minutes 36 seconds we stop, because at that moment the sun is on
our meridian.

" Referring to the Nautical Almanack, we find that the sun's semi-diameter
on October 2 is 16' 0*8" ; we advance our vernier to read 16' 0'8", and our
telescope is now in the true meridian for our place of observation. Had the
right limb of the sun been observed, we should have had to bring the vernier
back 16' 0-8".

" If we cannot obtain onr longitude east or west from an Ordnance map, we
must do it from an atlas, only, as this will not give it very accurately, we must
mind and use the same figure in any future observations at the same place in
order to avoid discrepancies, but of course the accuracy of the result will be
affected by any inaccuracy in ascertaining the longitude.

" To convert longitude into time, multiply the degrees by 4, and this will give
you minutes ; multiply the minutes by 4, and this will give seconds ; and multiply
the seconds by 4, and this will give sixtieths of a second.

" To reduce 6 10' 20" to time.

Mins. Sees.

6 x 4 = 24
10' x 4 = 40

20" x 4 = li

24 411

By Observation of the Pole Star. The pole star (Polaris a
Ursae Minoris) is 1 15' from the north pole of the heavens, and

1 The 6-inch Ordnance Map gives greater accuracy in fixing the longitude.

362 MINE SURVEYING.

moves in a circle round it ; twice in 24 hours (more precisely,
23 hours 56 minutes) it is in the true meridian. Another star
known as Alioth (e Ursse Majoris) comes
North Star ^ n * * ne meridian on its right ascension

c about half an hour before the pole star

* reaches the meridian on its lower transit.

Thus, if the pole star is sighted with the
vertical hair of the theodolite telescope,
and followed till the vertical line through
it cuts the star Alioth, then, if at the
moment when this happens the theodolite
* is clamped, we obtain a line approximately
t * in the meridian. If the observation is
* made when Alioth is below the pole the

line is 17 minutes east of north, and if

FIG. 207.-Finding north when AH th is ab V6 the P le the Hne ls

by pole star and others. 17 minutes west of north. The north star
is exactly in the meridian some 31 l minutes
after the above observation has been made, and if the telescope
is then directed to the north star, it will be exactly in line with
the true meridian. Fig. 207 shows the relation to each other of
Polaris and Alioth and some other stars of the Great Bear, and
shows the north star vertically over the pole and the star Alioth.
The " upper transit " that is to say, when the pole star is above
the pole is the most convenient, because at the lower transit
the star Alioth (e Ursae Majoris) is at its upper transit and too
high to be conveniently observed. 2

A second method is as follows :

On referring to Fig. 208 it will be seen that there are two
points, B and D, which represent the extreme easterly movement

1 This figure of 31 minutes is correct for the year 1901, but the time increases
at the rate of about 23 seconds a year, and in 1911 it will be about 35 minutes.
The correction for any year may be found on reference to the Nautical Almanack.

For the year 1901, the right ascension of Polaris is 1 hour 22 minutes 57 seconds,
and the R.A. of Alioth is 12 hours 49 minutes 41 seconds, the difference between
the upper transit of Polaris and the lower transit of Alioth being 33 minutes 17
seconds. Alioth and Polaris are in the same vertical line 2 minutes after the
transit of Alioth; deducting these 2 minutes leaves the interval of 31 minutes
above given.

2 In England, with the ordinary telescope of a theodolite, the upper transit (right
ascension) of Polaris may be observed at night in the months of September, October,
November, December, and the first twelve days of January, and the lower transit
may be observed between January 1 and May 12.

METHODS OF FINDING TRUE NORTH. 363

and the extreme westerly movement of the pole star. If
observations be taken of these two points with a theodolite, and
the angle bisected, then the bisecting line would pass exactly
through the pole, i.e. would repre-
sent the true meridian. Unfor-
tunately, one or other of these two
positions occurs usually in day-
light, when it will generally be ,**
invisible except with the aid of a /
very powerful telescope. /

Third method. In the months
of December and January it is x
possible to observe the pole star \
at equal distances from the upper \

and lower transit in the same
night. Thus the first observation
may be made early in the evening,

. J t . , J bJ FIG. 208. Finding north by pole

when the pole star would be near star only,

its upper transit. A mark should

then be fixed at a convenient distance in the direction given by
the star. The observation is then repeated after an interval of
11 hours 58 minutes, when the star would be near its lower
transit ; the theodolite being fixed at the same centre, and a
distant mark put as before. Thus, whatever might be the
deviation of the star from the meridian at the evening obser-
vation, there would be the same deviation in the opposite
direction in the morning observation ; and, accordingly, if we
took the middle point between the two distant marks, this point,
as seen from the instrument, would give the direction of the
meridian line near enough for all practical purposes.

By Observation of Various Stars. The north- and-south line
may be ascertained by reference to many other stars, the
apparent places of which are given in the Nautical Almanack
and other almanacks. Mr. A. L. Steavenson, in a paper read
before the Federated Institute of Mining Engineers, 1 describes a
method of ascertaining the north-and-south line as follows :

" The meridian of any place is represented by a line drawn through it from
the north to the south pole, and as the sun or stars cross this line, they reach
their greatest elevation, and are said to transit. The times of right ascension or
transit are given for the principal stars, and the sidereal time each day at noon

' Vol. x. p. 53 (August, 1895).

364 MINE SURVEYING.

in the Nautical Almanack and also inWhitaker's Almanack each year. Perhaps
the shortest and best way to describe the modus operandi is to take a case, and
suppose that the writer wishes to describe a meridian line at his own house.

" Referring to the Ordnance Survey map, and with a parallel ruler drawing
lines vertical and horizontal through the point in question, he finds that the
latitude is 54 43' 49" N., and the longitude 1 36' 41" W., and as there are 360
degrees of longitude which the revolution of the earth performs in 24 hours, he
finds that the allowance of time to be made for the position west of Greenwich is
6 minutes 26*7 seconds, that is to say, local time at Holywell is so much behind
Greenwich time.

" Now, with respect to the altitude of a star, the elevation is given as
' declination.' Declination is measured vertically above or below the equator,
and corresponds to latitude on the earth's surface ; and the height of the equator
corresponds with the co-latitude of a place, that is to say, its height on the
meridian is equal to our co-latitude ; thus

Degs. Mins. Sees.

Constant 90

Latitude of Holywell 54 43 49

Co-latitude or height of the equator on the meridian at Holywell 35 16 11

" Now we are in a position to find our star to-night, say, August 3. On
referring to Whitaker's Almanack, p. 42, we find that on August 3 the sidereal
time at mean noon is 8 hours 47 minutes 16 seconds, and as we want to do our
work as soon after dark as possible, we will take a star passing about 10 o'clock.
On p. 80 we find that the star Vega (a Lyrae) has a right ascension of 18 hours
33 minutes 23 seconds

Hrs. Mins. Sees.

18 33 23
From this deduct sidereal time of August 3 8 47 16

Difference , 9 46 7

From this we must deduct the difference which h'as occurred
between our mean time and sidereal time since noon, at the
rate of 9-85 or 10 seconds per hour 1 37

Due at Greenwich ... 9 44 30
And add to this the time allowance required by our longitude ... 6 27

The star Vega passes our meridian on August Sat ... . . 9 50 57
" But we must next find the elevation, thus

To our co-latitude 35 16 11

We add the declination of Vega ... ... 38 41 10

And we get the altitude ... 73 57 21

" If, however, this is too high to be seen in the theodolite, we might take the
star n Sagittarii, the declination being -21 5' 10"; in this case it must be
deducted from the co-latitude, being a minus, or south declination.

" Having, then, a good watch carefully set by Greenwich time say by the
gun at Shields we proceed about 9.30 p.m. to put the theodolite in position to
observe the star, which the instrument very soon indicates, for a few minutes
before the watch reaches the time of 9 hours" 50 minutes 57 seconds p.m., and at
the exact moment the instrument is pointing true south. Before making
permanent marks, it will be well to repeat the observation, both on other stars
and on other nights, and take the average or mean of them.

" In conclusion, it seems only desirable to point out, having once got this

METHODS OF FINDING TRUE NORTH. 365

base-line or meridian, how interesting and valuable a means it affords for after-
wards checking and regulating clocks and watches. To set a transit instrument
for a given star on a fine clear night, watch it appear in the field of observation,
exhibiting as it does the incomprehensible regularity of the heavenly bodies, is a
delightful recreation, which has served to amuse and occupy the writer for many
years, and induces him to encourage his hearers and readers to try it."

In the discussion Mr. Steavenson added the following note : "A slight
correction was required for latitude to find the elevation, but it was so very small
that it was not sufficient to carry the star outside the range of the instrument,
and it was an easy matter to raise or lower it to the position required."

One of the obvious objections to the method described by Mr.
Steavenson is the difficulty of having a watch set to the correct
time. The star (and the same observation applies to the sun)
is apparently moving at the rate of 1 minute of angle in
4 seconds of time ; therefore, if the watch is 4 seconds wrong,
there may be an error of 1 minute in the angle; for that
reason surveyors prefer the observation of a star like the pole
star, whose apparent movement is much slower, so that in the
case of the pole star an error of 1 minute in the watch of the
observer would only affect the accuracy of the observation to
the extent of half a minute of angle. The following is Mr.
Beanlands' description 1 of his methods of ascertaining the north -
and-south line :

"1. The pole star might be observed on the meridian either
at its upper or lower transit, the time being determined in the
manner explained by Mr. Steavenson. He (Mr. Beanlands)
thought it would be more convenient, however, to obtain the
time of transit from the data furnished by the Nautical Almanack.
If they referred to p. iii. in each month of that almanack, they
would find a column giving for each day the ' mean time of
transit of the First Point of Aries.' The time of transit of the
pole star would be found by adding to this the right ascension
of the star as given on p. 290. The lower transit would take
place about 12 hours, or more correctly 11 hours 58 minutes,-
after the upper transit.

"2. A meridian line might be determined by observing the
pole star, in conjunction with another star having the same, or
nearly the same, right ascension, or differing from it by 12
hours in right ascension. Perhaps the most convenient star for
the purpose was (zeta) in the constellation Ursa Major in
other words, the middle star in the tail of the Great Bear. The
time of transit 2 must first be ascertained approximately ; and

1 August, 1895. 2 Upper transit or right ascension of Polaris.

366 MINE SURVEYING.

the theodolite being previously adjusted, the telescope must be
pointed to the pole star, which must be bisected with the cross-
wires. The instrument being then clamped in azimuth, the
telescope must be lowered nearly to the horizon, when the star
Ursae Majoris would be seen at an 'altitude of about 5 . 1
Without altering the horizontal position of the instrument, the
star must then be watched until it appeared in the centre of
the field of view. The telescope should then be raised and
directed to the pole star, which should be again bisected, if
necessary, by means of the tangent-screw. In this way we
could obtain the direction of the pole star when the other star
2 Ursae Majoris was in the same vertical plane. This method
would give the meridian line with considerable precision. This
observation, however, could only be made in the autumn and
winter, 2 when the pole star would be visible at its upper transit
during the hours of darkness.

"There are two other stars, however, which might be con-
veniently observed in conjunction with the pole star at its lower
transit. These were S (delta) Cassiopeiae in the northern hemi-
sphere, and Spica, or a (alpha) in the southern constellation
Virgo. These stars would both be seen on the meridian almost
precisely at the same time as the pole star ; and by directing
the transit instrument so as to observe all the three stars in the
same vertical plane, a very good determination of the meridian
line might be obtained.

" The constellation Cassiopeia could be easily recognized, as
it was always visible in the northern hemisphere, being about

the same distance from the pole star as

Ursa Major in the opposite direction.

The principal stars were five in number,
*P arranged in a zigzag form (Fig. 209),

and the star in question was the fourth
^ in order, counting from east to west

a when the constellation was below the

FIG. 209. Finding north by -i
observation of 5 Cassiopeia}. P oie '

'' The star Spica would be at once
recognized towards the south, at an elevation of about 25.

1 Note by author. It appears to the author that this is a misprint, and should
be 20.

2 See footnote 2 to p. 362, as to months for this observation. When the observation
is made at the lower transit of C Ursae Majoris the deviation from true north is 2
minutes 14 seconds east ; at the upper transit the deviation is the same amount west.

METHODS OF FINDING TRUE NORTH. 367

There was no other very bright fixed star near it, but occa-
sionally one of the brighter planets Mars, Jupiter, or Saturn
would appear in this quarter of the heavens, and might possibly
be observed by mistake. These stars, Spica and 3 Cassiopeiae,
might be conveniently observed in conjunction with the pole
star, during the earlier months of the year, from about January
15 to May 10.

" 3. Another method was to observe the pole star six hours
before or after the upper transit, when at its greatest distance
east or west of the meridian. This observation might be made
with considerable precision, as the star would then be apparently
moving in a vertical direction. During the winter months it
would be most convenient to observe the star six hours after
the upper transit at its farthest distance to the west. The
instrument should be fixed and adjusted somewhat before the
time specified, and pointed to the star which would then appear,
with an inverting telescope, to be moving slowly upwards, and
diverging slightly to the right. The star should then be
followed by means of the tangent screw, until it has reached its
farthest point westward, and apparently to the right. If the
telescope was now lowered to the horizontal position, it would
point in a direction inclined at an angle of 2 10' west of the
true meridian, and accordingly it was simply necessary to move
the instrument in azimuth towards the east, through this small
angle as shown by the verniers. The correction, 2 10', was calcu-
lated for the present year (1895), and for the latitude 54 45'.
For places somewhat north of Newcastle it might be stated as
2 11'. Owing to the slow progressive increase in the star's
declination, this angle would be slightly reduced in future years,
the change being at the rate of about 1' in two years. It was
scarcely necessary to remark that if this star was observed in
this way six hours before its upper transit, as it might be
during the summer months, it would then be at its greatest
distance east of the meridian, and the correction of 2 10' would
have to be made towards the west.

" He (Mr. Beanlands) considered that each of the foregoing
methods was suitable for the purpose required, and might be
recommended for general adoption. They were all sufficiently
accurate, and, with one exception, they required no special
determination of the time. Moreover, they might be employed,
one or other of them, almost at any period of the year."

368 MINE SURVEYING.

By Observation of Stars in the Southern Hemisphere. In the
southern hemisphere, the stars a Crucis and /3 Hydri can be
used for setting out a north and south line. When they are
both in the same vertical line they are almost due south; if
/3 Hydri is above the pole, then the line is 2 minutes l west of
south, and when /3 Hydri is below, the line is 2 minutes east of
south ; the upper transit of j3 Hydri is 12 hours 32 seconds in
advance of the upper transit of a Crucis. This observation can
be made all the year except from about the middle of November
to the end of January (the period depending on the latitude).

The writer is indebted to Professor Liveing, of the Yorkshire
College, for the following statement :

"There are several methods of finding the true meridian.
One of the best for common purposes is to place the transit
instrument or transit theodolite carefully levelled approximately
in the meridian, and observe the meridian passage of some star
near the zenith (that is, one with a north declination about
equal to the latitude of the place). At the moment the star
passes the central wire, set a watch, carefully regulated to gain
4 minutes per day, to the right ascension in hours and minutes
of the star from the Nautical Almanack : your watch now shows
approximate sidereal time. Note the next upper transit or
meridian passage of the pole star, which should occur in the
present year (June, 1901) at 1 hour 23 minutes sidereal time,
or, for the lower transit, at 13 hours 23 minutes. If the passage
does not occur at this time, shift the azimuth of your instru-
ment to make it occur at this time, and the line of sight will be
in the meridian. Kepeat once or twice on different nights to
obtain an average.

"The most exact method, however, is to observe the time-
intervals between the upper and lower and lower and upper
transits of the pole star. If these intervals are equal, the line
of sight is in the meridian ; if not, the line of sight lies to the
side of the shorter interval. This method is employed for
astronomical purposes, but needs a telescope of sufficient aper-
ture to show Polaris in daylight. The clock employed need not
be regulated or show correct time, but only needs a uniform
rate."

1 The deviation given is correct for about latitude 50 south. If the latitude is
smaller the error is smaller; thus for latitude 40 it is 1-6', and for latitude 30 it
is 1-4'.

METHODS OF FINDING TRUE NORTH. 369

Setting out North Line from Ordnance Map. Where Ordnance
maps are obtainable, the north-and- south line can be set out
from them with sufficient accuracy for most purposes. It is
necessary to set out a line of considerable length, say one mile
or more (the longer the line the greater the accuracy). The
sides of the map are all north-and-south, and any line parallel
to the sides is also north-and-south, and such a parallel line
can be ruled on the map at some place convenient for staking
out a line and fixing permanent marks on some part of it ; the
position of the line on the map can then be measured from
the fences and buildings and other marks, and set out on the
ground by means of poles. If these are not all in an exactly
straight line, the average must be taken, and if this is carefully
done, great accuracy may be obtained.

Accurate tracings may be obtained from the Ordnance
Survey Department, and so the errors due to the shrinkage of
the paper on which the maps are usually printed is avoided.

Corelation of Various Plans. It is usual in mining districts
to make a separate survey of each particular leasehold or
ownership, and of each particular mine; and if a number of
these plans were put side by side, it might be impossible to
place them in their true relative positions unless the boundary
fences of neighbouring collieries happened to be included in each
survey.

If, however, each plan has its latitude and longitude marked
upon it, it can be transferred to an Ordnance map, and if all the
plans were so transferred, they could be seen in their true
relative positions to one another.

If the exact latitude and longitude of each mine shaft is
marked on its own plan, then the latitude and longitude of any
point underground or on the surface can be calculated, and the
distance of any point on that plan from any point on one of
the neighbouring plans can also be calculated, assuming that
the latitude and longitude of the mine shaft is given on the
neighbouring plan. In any country where there is a Govern-
ment Survey corresponding to our Ordnance Survey, the latitude
and longitude of any place on the map can be easily ascertained
with accuracy corresponding to that of the map.

In England the Ordnance Survey is published, for many
parts of the country, on three scales as follows : 1 inch to the
mile, 6 inches to the mile, and 25'344 inches to the mile. If

2 B

370 MINE SURVEYING.

the latter scale is used, the position of a mine shaft may be
marked upon it with great accuracy ; but this map does not
show the latitude and longitude, which must be ascertained by
reference to the 6-inch map of the same district. The 6-inch
quarter sheet covers an area which, on the scale of 25*344
inches, is covered by four maps. On the sides of the 6-inch
quarter sheet the latitude is given in degrees, minutes, and
half-minutes, and the longitude is given in degrees and minutes.
By measuring from the top or bottom of one of the 6-inch
maps, which corresponds with the top or bottom of a 25-inch
map, the position of the degrees, minutes, and half-minutes of
latitude can be transferred, by the use of a pair of dividers set
to the required scales, to the 25 -inch map ; and by measuring
from the side of the 6-inch map, which corresponds to the side
of the 25-inch map, the degrees and minutes of longitude can
be transferred to the 25 -inch map. As many points of latitude
and longitude as are on both the similar maps should be trans-
ferred to the 25-inch map, so that any inaccuracy in one
measurement can be corrected. One minute of latitude is equal
to approximately 6076 feet. A minute of longitude varies with
the latitude, from 6086 feet at the equator to nothing at the
poles, and, of course, covers a different length, going north or
south on every map (and it can easily be measured on the
map). The length covered by 1 minute of longitude varies
approximately with the cosine of the angle of latitude. Thus
at a latitude of one minute of longitude is 6086 feet, then the
length at a latitude of, say, 55 is equal (approximately) to
6086 X cosine 55 = 6086 x 0-5735764 = 3490*7 feet. On re-
ferring to the Smithsonian Geographical Tables (published by
the Smithsonian Institute, Washington), it will be found that
the length of 1 of longitude in latitude 55 is given as 39'766
miles, which makes 1 minute of longitude = 3499*4 feet.
In a similar manner the length of 1 minute of longitude can
be got approximately for any latitude.

On the 25-inch map it is quite possible to scale a distance
with an error not exceeding 2 feet, assuming the perfect accuracy
of the map. It would be therefore possible to ascertain the lati-
tude to say aoVo of a minute, or ^ of a second. With mining
maps thus referred, with care, to the latitude and longitude, it
would be possible to calculate, with considerable accuracy, the
distance from each other of places in different mines.

APPENDIX

EXAMINATION QUESTIONS VAKIOU'S.

1. How many tons of coal are there in an estate of 672 acres containing one
seam 3 feet 7 inches thick, assuming the specific gravity of the coal to be T27,
and the weight of a cubic foot of water 62-5 Ibs. ? (Colliery Managers, New-
castle, 1900.)

Answer. 3,716,893 tons.

2. In consulting old plans, what source of error must especially be guarded
against? (Colliery Managers, Newcastle, 1900.)

3. A road driven east in a seam rising 2 inches per yard cuts a trouble, an
upthrow of 6 fathoms with a vertical hade, beyond which the seam rises to the
east 3 inches to the yard. It is desired to connect the two portions of the seam,
one on each side of the trouble, by means of a stone drift rising 6 inches per
yard. At what distance from the trouble, measured in the seam on the west
side, must this drift be set away in order that it may cut the seam on the east
side at a distance of 40 yards from the trouble measured in the seam ? (Colliery
Managers, Newcastle, 1900.)

Answer. 79 yards (nearly).

4. What is the diameter of a circular shaft having the same area as an
oblong shaft 12 feet 6 inches long by 9 feet 6 inches wide ? (Colliery Managers,
North Staffordshire, 1900.)

Answer. 12' 3 feet.

5. Give the value of 3 acres 2 roods 17 perches of coal, 4 feet 5J inches in
thickness, at 25 per foot per acre. (Colliery Managers, North Staffordshire,
1900.)

Answer. 4001s.4%d.

6. How would you connect an underground and surface survey ? (Colliery
Managers, North Staffordshire, 1900.)

7. How would you survey a field without the aid of any instrument for
measuring angles? (Colliery Managers, Newcastle, 1899.)

8. Describe the vernier ; make a sketch of one, and describe what it is used
for. (Colliery Managers, Newcastle, 1899.)

9. Plot the following survey, and give the direction and distance of the last
set (No. 10) so as to tie into the starting-point :

Bord. 164.

Bord. 107.

Bord. 53.

N. 88 E.

372

APPENDIX.

(9)

Headways.

148.

S. 8 W.

Bord.

(8)
58.

N. 82 W.

Headways.

(7)
162. Headways.
8, 6 W.

Bord.

(6)
54.

N. 88 W.

(5)
Bord.

Headways.

154. Headways.

S. 3 W.

Bord.

(4)
200.

Bord.

144. Bord.

Bord.

93. Bord.

Back bord.

40. Back bord.

N. 87^ W.
in (2).
From 297.

(3)

going Bord.
Face of

339.

Headways.
Headways.

297.
140.
N. 3 W.

Headways.

(2)
152.

N. 2J E.

(1)
Second west 287 from engine plane.
Survey from mark in Mothergate bord.

(Colliery Managers, Newcastle, 1899.)

10. The debris from the sinking of two shafts, each 500 yards deep, 16 feet
diameter inside the brickwork of 9 inches thick, has to be deposited on an area
of 4 statute acres. What will be the average thickness ? (Colliery Managers,
Lancashire, 1898.)

Answer. 4" 14 feet (assuming that the debn* will occupy the same volume as when
in the solid).

11. A colliery reservoir is 100 feet long, and 60 feet wide at the bottom

APPENDIX. 373

10 feet in perpendicular height to the surface of the water when full ; the sides
are at an angle of 45. How many gallons of water will it contain when filled ?
(Colliery Managers, Lancashire, 1898.)
Answer. 483,112-5 gallons.

12. Describe a surveying compass, Gunter's chain, protractor, and drawing-
scales ; and state what they are used for. (Colliery Managers, Newcastle, 1898.)

13. What method would you adopt for ensuring that a drift below the ground
was driven in a given direction, and at a given gradient? (Colliery Managers,
Newcastle, 1898.)

14. Plot the following survey :

No. 1. ... N. 86fW. ... 474 links
2. ... N. 441 W. ... 163
3. ... N. 111 E. ... 322
,,4. ... N. 83|E. ... 291
5. ... S. 7i E. ... 515

6. ... S. 3i W. ... 171

7. ... S. 86E. ... 169
8. Give bearing and distance to tie the survey.

(Colliery Managers, Newcastle, 1898.)
Answer. N. 2 17' 27" E. ; length, 200' 15 link*.

15. Why do you need to make allowances in the measurements of lengths in
steep mines ? (Colliery Managers, Liverpool District, 1898.)

16. State briefly the requirements of the Coal Mines Regulation Acts, 1887
and 1896, with regard to plans. (Colliery Managers, Liverpool District, 1898.)

17. Describe and give sketch of how you would make a section of surface
between two points, A and B, 1000 yards apart, with undulating ground between.
(Colliery Managers, Liverpool District, 1898.)

18. What are the provisions of the Mines Regulation Act with regard to
plans of workings? (Colliery Managers, South- Western District, 1898.)

19. A level course of road extends 7 chains from the centre of a pit ; the
direction of the road is 64 20' east of north. At 575 links from the pit is a
branch which extends 850 links in the direction of 25 40' west of north. Plot
the two drives to a scale of 100 links to an inch. (Colliery Managers, South-
western District, 1898.)

20. On a plan drawn to a scale of 4 chains to an inch, how many perches
are represented by a circle of 1 inch diameter? (Colliery Managers, South-
western District, 1898.)

Answer. 201-06 perches (square measure).

21. How would you test the adjustment of a theodolite ? (Colliery Managers,
South-Western District, 1898.)

22. The workings of two collieries are separated by a barrier of coal 400 feet
wide. The barrier extends on the line of dip. It is necessary to drive on the
level course 200 feet into the barrier from each colliery, so that the drives shall
meet at the middle of the barrier, and shall be 50 feet vertically above the down-
cast pit-bottom of one of the collieries. How would you determine the correct
starting-points for both drives? (Colliery Managers, South-Western District, 1898.)

23. A seam of coal and ironstone lies at an angle of 45. The stone is 3 feet
thick, and the coal is 2 feet 8 inches thick, measured at right angles to the dip.
The royalty on the coal is 25 per acre per foot thick, measured vertically ; the

374 APPENDIX.

royalty on the ironstone is 6d. per ton, calcined. What is the royalty value of
one surface acre of coal ? and what is the value of one surface acre of stone,
supposing the yield to be 1800 calcined tons per acre per foot thick, measured
vertically ? (Colliery Managers, North Staffordshire District, 1898.)
Answer. Coal, 94 5s. per acre ; ironstone, 190 18s. per acre.

24. State briefly what precautions you would take in making (1) a loose-
needle survey where the conditions are favourable ; (2) a fast-needle survey with
outside vernier dial under favourable conditions ; (3) in taking a meridian on the
surface. (Colliery Managers, North Staffordshire District, 1898.)

25. The base-line ab, 1000 feet long, is measured along a straight bank of a
river ; c is an object on the opposite bank ; the angles bac and cba are observed
to be 65 37' and 53 4' respectively. What is the breadth of the river at c ?

Answer. 829'87feet.

26. a and b are two positions on opposite sides of a mountain ; c is a point
visible from a and b ; ac and be are 10 miles and 8 miles respectively ; and the
angle bca is 60. What is the distance between a and b ?

Answer. 9-165 miles.

27. The sides of a triangular field are 1250 feet, 790 feet, and 585 feet. What
is its area in acres, roods, and perches ?

Answer. 4 acres roods 8 perches.

28. Find the sixth root of 16,777,290. (City and Guilds of London Institute.
Mine Surveying, 1891.)

Answer. 16'OOOQl.

29. Find the cube of 649. (City and Guilds of London Institute, Mine
Surveying, 1891.)

Answer. 273,359,449.

30. Find the value of the seventh root of 78,125. (City and Guilds of London
Institute, Mine Surveying, 1891.)

Answer. 5.

31. Find the angle of which the logarithmic sine is 9-7382412. (City and
Guilds of London Institute, Mine Surveying, 1891.)

Answer. 33 11'.

32. Find the radius of an arc of which the angle is 28 26', and of which the
logarithm of the natural sine is 2-1122998. (City and Guilds of London Institute,
Mine Surveying, 1891.)

Anstoer. 272.

33. abc is a triangular plot of ground, of which the side ab measures 1200
links ; the angle at a equals 39 ; the angle at b equals 68. Find the area in
acres, roods, and perches. (City and Guilds of London Institute, Mine Surveying,
1891.)

Answer. 439,312 square feet, or 10 acres roods 13 -6 perches.

34. Under the plot of ground in Question 33 is a seam of coal dipping at an
angle of 15. The thickness of the seam, measured at right angles to the dip, is
7 feet 3 inches. A cubic foot of this coal weighs 80 Ibs. The royalty is 200
per acre of surface. Of the total area, 5 per cent, is occupied by faults. Of the
remaining coal, 10 per cent, is lost in working. Find the tonnage of coal to be
sent out of pit, and the royalty per ton in pence to two places of decimals. What
is the specific gravity of the coal ? (City and Guilds of London Institute, Mine
Surveying, 1891.)

Answer. Specific gravity, 1'28 ; 100,098 tons; 2017 royalty - 4'83d. per ton.

APPENDIX. 375

CITY AND GUILDS OF LONDON INSTITUTE.

THE City and Guilds of London Institute holds Annual Examinations in Mine
Surveying. There are two grades, Ordinary and Honours. There is also a
Preliminary Examination, which it is necessary to pass before becoming a candi-
date in the Ordinary Grade. Candidates for Honours also must have previously
passed in the Ordinary Grade.

The programme of Examinations contains information as to the subjects
included in the syllabus. 1 The fee for the Ordinary Grade Examination is Is. ;
and both the Preliminary and Ordinary Examinations are held about the 1st of
May of each year. The Honours Examination is a two-days' Examination, and
the fee is 10s. It is held at any centre at which a sufficient number of candidates
undertake to attend, and is of a practical nature, candidates having to make
actual surveys in the mine.

The Examination Papers in the Preliminary and Ordinary Examinations for
1900 and 1901 are given as a guide to intending candidates.

MINE SURVEYING-.

PRELIMINARY EXAMINATION.

MONDAY, APRIL SOin, 1900, 7 TO 10 P.M.

Drawing instruments and mathematical tables may be used.

Not more than seven questions to be answered.

1. The three sides of a triangle measure 370, 295, and 466 yards respectively.
Draw the triangle to a scale of 100 feet to the inch, and calculate its area in
acres, etc. (50 marks)

Answer. 11-27 acres.

2. An embankment is 30 chains long ; the top is 10 feet wide ; one side has
a slope of 55 and the other of 50 to the vertical ; the ground and top of the
embankment are level, and the embankment is 13 feet high at the centre.
Calculate its contents in cubic yards. (50)

Answer. 25767'8 cubic yards.

3. Draw a scale of -^ to show feet, and long enough to measure 20 feet. (30)

4. Plot the following traverse lines, all starting from one central point ; scale,
25 feet to the inch :

No. 1.

N. 77 E.

64 feet

N. 21 30' W.

1 chain 12 links

N. 15 15' E.

15 yards

S. 2920'W.

187 links

,. 5.

S. 5645'E.

14 fa thorns (30)

1 It can be obtained from Messrs. Whittaker & Co., Paternoster Square, price
Is. 4d. post free.

376 APPENDIX.

5. How fnany tons of coal per acre will there be in a searn 3 feet 9 inches
thick, dipping at an angle of 9, allowing 20 per cent, deduction for faults, etc. ?

(30)
Answer, (Coal taJcen as 80 Us. to the culicfoot) 47 25' 3 tons.

6. In an ordinary miner's dial the E mark is to the left of the N. Why is
this? (30)

7. Explain the terms " diurnal variation," " dip," " declination," and " secular
variation " of the magnetic needle. (30)

8. You have to measure the width of a deep river about 150 yards wide, and
your only measuring instrument is an ordinary chain. How would you proceed ?

(30)

9. A vertical shaft is 400 feet deep. Halfway down it an incline starts from
it, which meets a drift dipping towards the shaft-bottom at a grade of 2 inches
to the yard at a distance of 4 chains from the shaft, this distance being measured
along the floor of the drift. Find the length and inclination (in degrees and
minutes) of the incline. (50)

Answer. Length, 322 feet ; angle of inclination (from the vertical), 54 53'.

10. A theodolite is set up in line with two telegraph-poles, 150 feet from the
nearer pole, and 420 feet from the further pole. The top of the further pole
subtends an angle of 18, the line of sight passing through a hole exactly half-
way up the nearer pole, llequired the heights of the two poles, the theodolite
standing 5 feet above the ground. (50)

Answer. First pole, 107 -47 feet ; second pole, 141-4 feet.

11. A seam of mineral dipping 12 is thrown down 200 feet by a vertical
fault ; an inclined drift is started from the top of the downthrow, and cuts the
seam 400 feet horizontally from the fault. Required the length and dip of the
inclined drift, (40)

Answer, Length, 491-16 feet; angle of dip from vertical, 54 32'.

ORDINARY GRADE.
THURSDAY, MAY SRD, 1900, 7 TO 10 P.M.

INSTRUCTIONS.

A sheet of drawing-paper is supplied to each candidate.

Candidates may use protractor, parallel ruler, T-square, set-squares, scales,
compasses to span 16 inches, drawing instruments, tables of logarithms,
logarithmic and natural sines, tangents, etc.

[The working out of all answers must be shown.]

Question 1 must be attempted by all candidates, and not more than Jive
others in addition. The maximum number of marks obtainable is affixed to
each question.

1. Plot the following chain survey of a field to a scale of 2 inches = 1 chain.
All dimensions are in links ; all offsets are to the boundary :

399

Tie Line

going about N.W.

' *

506

442

401

385

348

297

261

221

199

175

Line 4

going about E.S.E.

277

261

227

* v

196

"--4&

X. " x

192

ii***"""*''^,,

^^ .

e '1'a ~~-

Lines

going about S.W.

348

298

268

192

106

Line 2

going about W.N.W.

<fc\

221

A*N

200

^ N s

151

-. *^v NN *

""~~""--..*(J\

"""m

Linel

going about N.N.E.

(60)

378 APPENDIX.

2. Calculate the area of the field (survey of which is given in Question 1) in
acres, etc. (45)

Answer. lacreO roods 36 perches.

3. Calculate the co-ordinates of the following traverse survey ; calculate the
length and bearing of the line GA, and plot by co-ordinates to a scale of 1 chain
to the inch :

Traverse survey of polygonal area made by double foresight method l
with a right-handed theodolite reading to 30 seconds ; the theodolite
was originally set in the true meridian, true north reading 360 00' 00".

Line. Observed angle. Length in links.

AB ... 14 48' 00" ... 245

BC ... 198 06' 30" ... 310

CD ... 284 01' 30" ... 480

DE ... 200 12' 30" ... 709

EF ... 271 33' 30" ... 430

FG ... 268 01' 30" ... 607
GA (GO)

Answer. Bearing of GA is N. 61 25' 43" W. ; length, 220'6 links.

4. Calculate the area of the above polygon in acres, etc., by the method of
co-ordinates. (60)

Answer. 4 acres 2 roods 18 perclies.

5. A bed of mineral dips 58 (to the horizontal), the direction of full dip
being S. 24 56' E. What will be the dip of a road running N. 80 20' W. ?

(45)
Answer. Angle of dip, 42 15' 42", or 1 in 1' 10047 3.

6. Two horizontal levels are driven in a vein dipping 77 towards N. 56 E.,
the levels being 200 feet apart vertically. A flat winze in the vein connecting
the levels is 446 feet long. What is its dip and bearing ? (45)

Answer. Bearing, S. 40 39' 5" E. ; angle of dip, 26 38' 34".

I. How would you proceed to level along an inclined drift about 3 feet
6 inches high, and inclined about 40? (30)

8. Draw a section of the telescope used in the ordinary dumpy level, showing
clearly the path of the rays of light through it. (30)

9. Under what circumstances must a correction for the earth's curvature be
applied in levelling ? State a formula for this correction. (30)

10. Sketch and explain the action of the tangent screw and clamp, as applied
to any part of a theodolite. (30)

II. Describe a. method of connecting underground and surface traverses
through a single shaft, the use of the magnetic needle being inadmissible. (30)

1 Note by author. By the " double fore sight method " is meant taking the
exterior angle between each sight and the next. Thus at A the theodolite is at a
place where there is no attraction, therefore the bearing of AB is N. 14 48' E. The
theodolite is then moved forward to B, and the angle between AB and BC is
observed to be 198 6' ^0".

To get the meridian bearings of BC and the following sights, the following rule
is used : " Add the observed theodolite reading to the last meridian bearing, and
subtract 180 from, or edd 180 to, the sum, nccording as the sum is greater or
less than 180."

APPENDIX.

379

PRELIMINARY EXAMINATION.

MONDAY, APRIL 29TH, 1901, 7 TO 10 P.M.

INSTRUCTIONS.

No certificates will be given to candidates on the results of this Preliminary
Examination, but their successes will be notified.

The number of the question must be placed before the answer in the worked
paper.

Drawing instruments and mathematical tables may be used.

Not more than seven questions to be answered.

Three hours allowed for this Examination.

The maximum number of marks obtainable is affixed to each question.

1. If a plan is drawn to the scale of 2 inches to the chain, what is the pro-
portion between the actual area in the field and the area as shown on the plan ?

(30)
Answer. As 156,816 \ 1.

2. Draw a scale of 1^ fathom to the inch, long enough to measure 1 chain,
and a corresponding scale of metres to read to decimetres. (30)

3. Draw the plan of the following field to a scale of 2 chains to the inch, and
calculate its area. The measurements are given in links :

2,165

815

1,787

1,463

336

719

1,100

217

1987

[654

508

415

F 219

(45)
Answer. 16 acres 1 rood 37 perches.

4. A right-angled triangle has a base 27 yards long, and the angle between
the base and the hypothenuse is 27 19'. Find its area in square feet. (40)

Ansiuer. 1694'4 square feet.

5. Determine the volume of a railway cutting 3 chains long, the end sections
being as given below, the ground sloping uniformly, and the slopes of the sides
of the cutting being 1 in 2 :

-< 30ft

(NOTE. The drawings are not to scale.)
Anstcer. 42,566 cubic feet.

(45)

380 APPENDIX.

6. How can you set out a right angle by means of a chain alone ? (30)

7. From two points, A and B, 1500 feet apart, the bearings of a point, C, are
found to be respectively N. 67 E. and N. 4 E. B bears S.E. exactly from
A. Required, the lengths AC and BC. (45)

Answer. AC = 1270-54 feet ; BC = 1560-90 feet.

8. A vein of mineral, of specific gravity 3'7, is 4 feet 8 inches thick, and dips
70 to the horizontal. A drift along the vein, the full width of the vein, is
6 feet 3 inches high vertically, and 110 yards long. How many tons of mineral
will it yield ? (40)

Answer. 1056 tons.

9. Write a brief description of the plain miner's dial. (30)

10. A drift rising 1 in 27 cuts a seam of coal dipping 49, the dip of the
seam and of the drift being in opposite directions. The width of the seam, as
measured along the floor of the drift, is 12 feet. What is the true width of the
seam ? (40)

Answer. 9-4 feet.

11. A shaft is su*ik 20 feet in diameter arid 200 yards deep; assuming the
rock to occupy a volume 30 per cent, greater after excavation, and that the
excavated material is piled in the form of a square pyramid, the sides of which
are inclined 40 to the horizontal, calculate the area of the base of the pyramid.

(45)
Answer. Area of base, 14,534-7 square feet.

ORDINARY GRADE.

TUESDAY, APRIL 30ra, 1901, 7 TO 10 P.M.

INSTRUCTIONS.

Candidates for the Ordinary Grade must have previously passed the Pre-
liminary Examination.

If the candidate has already passed in this subject in the first class of the
Ordinary Grade, he cannot be re-examined in the same grade.

The number of the question must be placed before the answer in the worked
paper.

A sheet of drawing-paper is supplied to each candidate.

Candidates may use protractor, parallel ruler, T-square, set-squares, scales,
compasses to span 16 inches, drawing instruments, tables of logarithms,
logarithmic and natural sines, tangents, etc.

Three hours allowed for this paper.

[The working out of all answers must be shown.]

Question 1 must be attempted by all candidates, and not more than four
others in addition. The maximum number of marks obtainable is affixed to
each question.

APPENDIX.

467

7 \

430

15 \

360

37 \

323

27 /

Line No. 9.

266

30 /

227

10 30|jo5

215

30 Jte

140

14 \

5 \

14*

FromE.

go about W.S.W. to F.

Line No. 8.

FromC.

482

462

378

250

172

go about N.W. to E.

382

APPENDIX.

Line No. 7. Tie Line.

817

FromF.

goaboutS.E.toC.

/12

423

/ 23

377

/ 38

345

/ 60

267

Line No. 6. \ 53

190

\ "

155

\ 23

\ 15

From B.

go about N.N W. to F.

737

Line No. 5. Tie Line.

From A.

go about N.E. to C.

APPENDIX.

383

Line No. 4.

FromD

725

678

642

610

506

408

350

315

268

186

175

133

112

go littles, of W. to A.

384

APPENDIX.

Line No. 3.

From C.

402

338

288

217

170

105

go about S.S.E.toD.

Line No. 2.

550
492
423
335
260
175

152
118

FromB.

go a little N. of E. to 0.

APPENDIX.

385

Line No. 1.

From A.

394

365

337

288

252

210

180

132

go due North to B-

1. Plot the preceding survey to a scale of 1 chain to the inch. All measure-
ments are in links. (100)

2. Calculate the area of the more southerly of the two fields in Question
No. 1. (40)

Answer. 2 acres 2 roods 1 perch.

3. Make out an imaginary page from a level-book, showing twelve readings
taken with four settings of the instrument over undulating ground. Work out
and plot the section. (50)

4. A mineral seam dips 70, outcropping in ground sloping 17 to the
horizon ; a shaft is to be started downhill from the outcrop so as to cut the seam
at a depth of 400 feet below the shaft collar. How far horizontally must the
shaft be from the outcrop ? (50)

Answer. 163'81 feet.

5. Three bore-holes, A, B, and C, intersect a seam of coal ; they are situated
at the angles of an equilateral triangle whose sides are 300 yards in length. B is
N. 17 20' E. of A, and C is to the westward of the line AB. A cuts the seam
at a depth of 175 feet, B at a depth of 342 feet, and C at a depth of 240 feet.
Determine the direction and amount of dip of the coal seam. (50)

Answer. Dip 1 in 5'3 (nearly) ; N. 24 20' E.

6. Describe in detail how you would set out underground a curve of 10 chains
radius to connect a main travelling road with a branch road, the directions of the

2 c

386 APPENDIX.

two roads making an angle of 60 with each other. Draw a plan to a scale of
50 links to the inch. (50)

7. Describe the German miner's compass, and the method of using it. (30)

8. What is a plane table, and how is it used ? (30)

9. Explain the principle of the vernier. (30)

SURVEYORS' INSTITUTION EXAMINATION PAPERS.

THE Surveyors 1 Institution, Westminster, holds Annual Preliminary and Pro-
fessional Examinations, which it is necessary to pass before being able to
subscribe one's self as a Fellow of the Surveyors' Institution (F.S.I.). The
Examinations include a great number of subjects, but the papers in Land
Surveying, and Levelling, and Mensuration only are given here.

SURVEYING AND LEVELLING.
MORNING PAPER.

Time allowed, three hours.

NOTE. All candidates are required to attempt Questions Nos. 1, 2, and 3.

Candidates other than Building candidates ivill receive full marks for any
10 questions correctly answered.

Building candidates will receive full marks for any 8 questions correctly
answered.

Candidates omitting to have figures by which results are arrived at ivill risk
a loss of marks in case of a wrong answer being given through accident.

Questions 1, 2, 3, 6, 7, and 9 carry higher marks than the remainder.

1. On the plan given (see p. 387) draw in pencil the lines it would be necessary
to run to enable you to make a complete survey with the chain only.

2. Compute the areas of the enclosures in the corner of the plan above
mentioned, giving the results in acres, roods, and perches. One of these
enclosures must be computed by means of the ordinary plotting scale, and the
other in any way the candidate may elect. (Enclosure No. 1, if well done and
a correct answer arrived at by the ordinary plotting scale, will carry full marks.)

Answer. Enclosure No. 1, 6 acre* 3 roods 7 perches; No. 2, 3 acres roods
16 perches.

3. From the field notes given lay down the survey lines, and plot a plan to a
scale of 2 chains to an inch.

4. Required to set out a circular space for a reservoir to contain 1 acre
1 rood and 20 perches. Give the radius in links.

Answer. 209-2 links.

APPENDIX.

337

388 APPENDIX.

5. Divide the triangle ABC into three equal portions by lines parallel to the
side AB. AB = 2500 links; AC = 2100 links; and BC = 1800 links. Give
the area of ABC, and the distances Aor, ab, and bC.

Answer. Arm ABC = 185-73 square chains ; Aa - 3~854 chains, al =
cHaim, be = 1&124 chains.

Figure referred to in Figure referred to in

Question 5. Question 6.

6. The points A and B are only both visible from one point, C. Lines
CD = 1260 links, and CE = 1040 links, were run, and the following angles
were taken, viz.: ADC = 67 30', ACD = 45 0', ACB = 70 20', BCE = 39 10',
and BEG = 81 50'. Find the length AB in links. |

Answer. 1418 links.

7. Plot the above figure to a scale of 1 chain to an inch, and give the distance
AB as it measures upon your plan.

8. A traverse round a wood is as follows :

A to B = 290 links, bearing 255 5' A . . B
B to C = 1000 . 194 10'
C to D = 680 77 12' D . . C
Give the calculated distance D to A.
Answer. 905'1 links.

9. Protract and plot the above to a scale of 1 chain to an inch.

10. Convert 17 acres 1 rood and 20 perches, statute measure, into square
yards.

Answer. 84,095 square yards.

11. How would you determine the latitude of any position (on land) ? and
what instrument would you require ?

12. Illustrate and describe in what way you would produce a survey line
obstructed by a large tree or building.

13. If a plan is plotted to a scale of 3 chains to an inch, what proportion
does the area of the plan bear to the ground ?

Answer. 1 : 5,645,376.

AFTERNOON PAPER.

Time allowed, two hours and a half.

NOTE. All candidates are required to attempt Questions Nos. 1 and 2.

Candidates other than Building candidates will receive full marks for arty
9 questions correctly answered.

Building candidates will receive full 'marks for any 1 questions correctly
answered.

Candidates omitting to leave figures by which results are arrived at will risk
a loss of marks in case of a wrong answer being given through accident.

Questions 1, 2, 8, 9, and 11 carry higher marks than the others.

APPENDIX.

389

1. Make up the following level-book :

LEVEL-BOOK FOU QUESTION No. 1.

Back sight

Inter-
mediate.

Fore sight. | Rise.

Fall.

Reduced

levels.

Distance.

Remarks.

Feet.

Chains.

6-GO

45-80

4-00

2-60

48-40

i-oo

570

1-70

46-70

2-00

0-80

12-20

6'50

40-20

3-00

6-90

6-10

34-10

4-00

11-20

4-30

29-80

5-00

0-24

13-12

1-92

27-88

6-00

4-80

] -

4-56

23-32

7-00

8-30

3-50

19-82

8-00

110

13-75

5-45

14-37

9-00

6-70

5-60

S-77

10-00

5-70

1-00

9-77

11-00

8-10

2-40

7-37

12-00

2-90

7-10
10-60

15-05 i

6-95
4-20
3-50

0-42
-3-78
-7-28

13-00
14-00
14-30

(1st side of pond
\ water-level

11-70

1-10

-8-38

15-00

13-75

10-80
7-10

0-90
370
6-85 | 0-25

-7-48
-3-78
-3-53

16-00
16-40
17-00

( 2nd side of pond
\ water-level

11-10

2-65

-0-88

18-00

8-60

2-50

1-62

19-00

2-30

6-30

7-92

20-00

0-85 . 1-45

9-37

21-00

25'39 61-82 21-35 57-78

25-39 21'35

36-43 36-43

(The figures in italics are those required in answering the question.')

2. Plot the following section to a horizontal scale of 2 chains to an inch, and
to a vertical scale of 20 feet to an inch :

-So

OOOi it^

** ;r m -u

sill

h5-2^ptH

3. In setting out the centre line for a new road or a railway, illustrate and
describe in what way you would proceed to connect two pieces of straight by a
curve of, say, 10 chains radius.

4. Before commencing to take a series of levels, briefly describe how you
would ascertain if your level was in adjustment.

5. The point A being inaccessible and at a considerable altitude above the
surrounding country, illustrate and describe in what way you would ascertain its
height above the point B (the nearest convenient point of observation), using a
theodolite for the purpose.

390 APPENDIX.

Distance. Height.
Chains. Feet.

6. Give the rates of inclination between the given
points of level .taken upon a line chained along the invert
of a water- course. 2'40 42-16

Answer, (i) 1 in 136'5 ; (2) 1 in 116-5 (nearly); (3) 1 in 3'00 42-50

7. What is the rate per chain (in feet and decimals) of a gradient rising
1 in 250 ?

Answer. 0' 264 feet per chain.

8. Give the levels of points B, C, and D on a continuous section, the level of
point A being 25 feet, and the horizontal distances and angles as follows :

A to B, 12 chains ; angle of elevation, 3 20'
B to C, 9 depression, 4 25'

C to D, 15 elevation, 2 15'

Answer. Level of B, 71 -128 feet ; level of C, 25' 249 feet ; level of D, 64-146 feet.

9. The telescope of a theodolite set 4*25 feet above the point A, having a
level value of 25 feet, is directed towards the bottom of a staff at B, and shows
an angle of elevation of 10 4' ; it is then directed to 10 feet on the staff, when
it shows an angle of elevation of 10 35'. Required the horizontal distance A to
B in feet, and also the level of point B.

Answer. A to B = 1073-31 feet ; level of B, 21979 feet.

10. Illustrate by diagram the difference between " true " and " apparent "
level, and give a rule for determining same.

11. Construct a triangle ABC, having its sides AB = 3 inches, BC = 2
inches, and AC = 1| inch. Suppose the points A, B, and C to be trigono-
metrical stations of a survey, and that from a point D of a traverse A bears 120,
B, 150, and C, 165. Find the point D by construction.

12. Explain and illustrate by diagram how you would obtain the distance to
an inaccessible point, using only chain and poles.

MENSURATION.
Time allowed, two hours.

1. How many rods of brickwork are there in a circular pier 4 feet in diameter
and 20 feet in height? (One rod of brickwork is equal to 306-2812 cubic feet.)

Answer. 0'82 rod.

2. A circular water-tank is 12 feet internal diameter, and is 10 feet deep. A
drawing of it was made to a scale of ^ inch to a foot. Some one carelessly scaled
it with a scale of inch to a foot. What error would be made in calculating
the number of gallons contained in the tank when full ?

Answer. 1549 cubic feet ; 9686 gallons.

3. A road rises with a gradient of 1 in 75 from its commencement to a point
distant l\ mile (on. a horizontal datum). It then falls with a gradient of 1 in
100 to its termination at a further distance of 140 chains (on a horizontal
datum). What is the difference of level between the beginning and the end of
the road?

Answer. The end of the road is 13 '2 feet above the beginning.

APPENDIX. 391

4. The air in a room 30 feet x 25 feet x 10 feet has to be changed three
times in an hour by air conveyed through a pipe 6 inches in diameter. At what
velocity must the air move in the pipe to do this ?

Answer. 114,591 feet per hour.

5. A shower of rain is registered to give 1^ inch. How many gallons would
have fallen on a field containing 100 acres ?

Answer. 2,552,343 gallons.

6. What is the sectional area of a cutting with slopes, as shown in the
sketch ? and how many cubic yards are there in 1 chain of this cutting ?

12ft.

Answer. Area 298 square feet; 728'4 cubic yards in 1 chain of cutting.
The sketch evidently shows that by % to 1 a rise of 1 in J horizontal is meant.

7. A railway bank is half a mile in length, and is 20 feet above the ground
at one end, and 30 feet above the ground at the other. The slopes are 2 to 1
throughout. How many acres of ground does it cover ?

THE LAW AND MINE SUEVEYING.

PROVISIONS OF THE COAL-MINES KEGULATION ACTS, 1887 AND 1896, IN
RECAIID TO PLANS AND SECTIONS OF MINES.

Coal-Mines Regulation Act, 1887.

34. (1) The owner, agent, or manager of every mine shall keep in the office
at the mine an accurate plan of the workings of the mine, showing the workings
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 may be not reasonably practicable, a statement of the depth of the
shaft, with a section of the seam.

(2) The owner, agent, or manager of the mine shall, on request at any time
of an inspector under this Act, produce to him, at the office at the mine, such
plan and section, and shall also, on the like request, mark on such plan and
section the then state of the workings of the mine ; and the inspector shall be
entitled to examine the plan and section, and, for official purposes only, to make
a copy of any part thereof respectively.

(3) If the owner, agent, or manager of any mine fails to keep, or wilfully
refuses to produce or allow to be examined, the plan and section aforesaid, or
wilfully withholds any portion thereof, or wilfully refuses, on request> to mark

392 APPENDIX.

thereon the state of the workings of the mine, or conceals any part of those
workings, or produces an imperfect or inaccurate plan or section, he shall (unless
he shows that he was ignorant of the concealment, imperfection, or inaccuracy)
be guilty of an offence against this Act ; and, further, the inspector may, by
notice in writing (whether a penalty for the offence has or has not been inflicted),
require the owner, agent, or manager to cause an accurate plan and section,
showing the particulars hereinbefore required, to be made within a reasonable
time, at the expense of the owner of the mine. Every such plan must be on a
scale of not less than that of the Ordnance Survey of 25 inches to the mile, or
on the same scale as the plan for the time being in use at the mine.

(4) If the owner, agent, or manager fails within twenty days after the requi-
sition of the inspector, or within such further time as may be allowed by a
Secretary of State, to cause such plan and section to be made as hereby required,
he shall be guilty of an offence against this Act.

38. (1) 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 abandon-
ment, 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 surfaces, 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 of not less than
that of the Ordnance Survey of 25 inches to the mile, or on the same scale as
the plan used at the mine at the time of its abandonment.

(2) The plan and section shall be preserved under the care of the Secretary
of State ; but no person, except an inspector under this Act, shall be entitled,
without the consent of the owner of the mine or seam, to see the plan when so
sent until after the expiration of 10 years from the time of the abandonment.

Coal-Mines Regulation Act, 1896.

3. Plan of mine in working. The plan required to be kept in pursuance of
section 34 of the principal Act shall show the position of the workings therein
mentioned with regard to the surface, and the position, extension, and direction
of every known fault or dislocation of the seam, with its vertical throw.

4. Plan of abandoned mine. (1) For sub-sections (1) and (2) of section 38
of the principal Act shall be substituted the following sub-sections :

" (1) Where any mine or seam is abandoned, the person who is 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

" (i.) An accurate plan of the mine or seam, being either the original working
plan or an accurate copy thereof made by a competent draughtsman, and
showing

" (a) The boundaries of the workings of the mine or seam, including not only
the working faces, but also all headings in advance thereof, up to the time of the
abandonment ;

" (b) The pillars of coal or other mineral remaining'unworked ;

APPENDIX. 393

" (c) The position, direction, and extent of every known fault or dislocation of
the seam, with its vertical throw ;

" (d) The position of the workings with regard to the surface boundary ;

" (e) The general direction and dip of the strata ; and

" (/) A statement of the depth of the shaft from the surface to the seam
abandoned ; and

" (ii.) A section of the strata sunk through ; or, if that is not reasonably prac-
ticable, a statement of the depth of the shaft, with a section of the seam.

" Every such plan must be on a scale of not less than that of the Ordnance
Survey of 25 inches to the mile, or on the same scale as the plan used at
the mine at the time of its abandonment; and its accuracy must be certified,
so far as is reasonably practicable, by a surveyor or other person approved in
that behalf by an inspector of mines.

" (2) The plan and section shall be preserved under the care of the Secretary
of State ; but no person, except an inspector under this Act, shall be entitled,
without the consent of the owner of the mine or seam, or the licence of a
Secretary of State, to see the plan when so sent until after the expiration of ten
years from the time of the abandonment. Provided that such licence shall not be
granted unless the Secretary of State is satisfied that the inspection of such plan
is necessary in the interests of safety."

(2) The High Court, or, in Scotland, the Court of Session, may, on applica-
tion by or on behalf of the Secretary of State, make an order requiring any
person who has for the time being the custody or possession of any plan or
section of an abandoned mine or seam, to produce it to the Secretary of State for
the purpose of inspection or copying.

ATTEACTION OF THE MAGNETIC NEEDLE BY IEON.

IT is well known that many substances attract the needle, especially magnetic
iron ore (called magnetite, or magnetic oxide of iron, Fe 3 4 ), whilst other more
or less magnetic substances include hematite iron ore, nickel, cobalt, manganese,
and some kinds of platinum.

The chief sources of attraction against which the surveyor must guard are
iron rails, girders, safety-lamps, or iron in. any form. It must be borne in mind
that the magnetic attraction is not interrupted by the presence of rocks, and
therefore the iron in one road might affect the compass needle in another
road.

Dialling lamps supposed to be non-magnetic can be obtained; but before
being relied upon they should be carefully tested, as the author has frequently
found that such lamps affect the needle to a certain extent.

394 APPENDIX.

The author has made a number of experiments to ascertain the effect of iron
rails, etc., upon the needle, some of which are given below :

Old iron rails, about 30 Ibs. to the yard, 5 yards long

At 5 feet 10 inches 1 pair of rails deflected the needle .
At 7 8 , 1 nil.

At ? i. 8 2 !.

At 7 8 3 1.

At 7 8 1 ,, 1J (when raised up

level with needle).

At 7 feet 8 inches three rails (not three pairs) on each side of the dial
deflected the needle If .

By altering one side, so that three rails on one side were 7 feet 8 inches away,
and on the other side 17 feet away, 1 J deflection was given.

With three rails on each side 17 feet distant, \ deflection.

At 18 feet away, disturbance only just perceptible, even with five rails on
each side of dial. The weight of each rail was 150 Ibs. (5 yards), so that in this
experiment there was over a quarter of a ton of metal on each side of the dial
at 18 feet distance.

At 21 feet away there was no disturbance.

When the rails were laid down again, without disturbing the dial, lj
deflection was caused ; but after disturbing the needle it would settle anywhere
with up to 3 deflection.

Substituting new steel rails, 22 Ibs. to the yard, 4-yard rails, the results were
as follows :

After setting the needle, 528 Ibs. of rails were gradually advanced towards
the dial in distances of 1 yard at a time, starting at 14 yards distance. No deflection
was noticed until a distance of 6 yards was reached, when there seemed to be a
very slight disturbance, hardly measurable, but probably ^.

At 5 yards the disturbance was clearly perceptible, and would be about ^g.

At 4 yards the deflection was J.

At 4 yards, but instead of the ends of the rails being towards the dial, they
were placed broadside on, the deflection was 1.

The disturbance of small articles which might be accidentally left near a dial
was noted.

A pocket-knife exerted no influence until brought within 12 inches of the
needle.

An iron locker 8 Ibs. in weight caused disturbance at 2 yards distant ; G Ibs.
of fish-plates, at 1^ yard.

A pick, an adze, and several ordinary iron safety-lamps caused no disturbance
when 1 yard away, even if brought level with the needle.

The conclusions the author has arrived at from these and similar experiments
are as follows :

1. That provided that the only iron to be guarded against is the rails, then
at 8 yards on either side of the dial it is absolutely safe.

2. That dialling " over the rails," under the impression that the a pull " on
one side will balance that on the other, is erroneous, and liable to serious
error.

3. That provided 8 yards of rail are taken up, it does not seem to matter

APPENDIX. 395

whether all the rails taken up go all on one side or one-half one way and one-half
another.

4. That small iron articles weighing not more than 2 or 3 Ibs., e.g. pick,
wedge, lamp, etc., will not disturb the needle if more than 1 yard away.

5. That no rule can be deduced based on weight of metal and distance,
because in one case a rail may be brought to within a few feet without causing
disturbance, whilst another rail will deflect the needle twice the distance
away, this being due, no doubt, to the rail having acquired some permanent
magnetism.

MATHEMATICAL TABLES.

396

APPENDIX.

LOGARITHMS.

0000

0043

0086

0294

0334

0374

I 2

3 4

6 7

8 9

0128

0170

0212

0253

12 17

25 29

33 37

14
15

0414
0792

1139

1461

1761

0453
0828

"73
1492
1790

0492 0531
08640899

I20C 1239
1523 1553

1818 1847

0569

0934
1271

1584
l8 75

060 7

1303
1614
1903

0645
1004
1335
1644

0682
1038
1367
1673
1959

0719
1072

1399
1703
1987

o/SS
1106

1430
1732
2014

4 8

II 15

10 14

10 11

9 12
8 ii

19
17

15
14

23 26

21 24
19 23

18 21

17 20

30 34
28 31
26 29
24 27

22 2 5

16
17
18

2041
2304

2553
2788
3010

2068
2330
2577
2810
3032

2O95 2122
2355 2380
2001 2625
28332856
3054 3075

2148

240 c

2648
2878
3096

2175
2430
26 72
2900
3 II8

22OI

2455
2695

2923
3139

2227
2480
2718

2945
3160

22532279

2504 2529
274^ 2765
296712989'
3181 3201

3 5
2 5
2 5
2 4

8 ii
7 10
7 9

I I

12
12
II
II

16 18

IS 17
14 16
13 16
13 1.5

21 24

20 22
19 21

18 20

I 7 I 9

21
22

23
24

3222

3424
3617
3802
3979

3243

3 1 4 1
3636

3820
3997

3263 3284
34643483

38383856
4014 4031

3304
3502
3692
3874
4048

3324
3522

37"
3892
4065

3345
3541
3729
3909
4082

3365
3S6o

3747
3927
4099

3385

35 ^
3766

3945
4116

3404 2 4
3598 ' 2 4
3784 2 4
3962 2 4
4i33 2 3

6 8
6 8
6 7
5 7
5 7

IO
10

9
9
9

12 14
12 14
II I 3
II 12
10 12

16 18
15 17
15 17
14 16

*4 *5

29
30

4150
4314
4472
4624
477i

4166
4330
4487
4639
4786

4183 4200
4346 4362
4502 4518
4654 4669
48004814

4216

4378

4533
4683
4829

4232
4393
4548
4698

4843

4249
4409
4564
4713
4857

4265
4425
4579
4728
4871

4281
4440
4594
4742
4886

4298

4456
4609

4757
4900

2 3
2 3
3
3
3

f j

5 6
4 6
4 6

8
8
8
7
7

IO II

9 "
9 I}
9 10
9 10

M to to to to
to to 4> 4* tn

CO CO CO CO CO

4914
5051
5185
5315
544i

4928
5065
5198
5328
5453

4942 4955
5079 5092
52" 5224
53405353
5465 5478

4969
5105
5237
5366
5490

4983

5250
5378
5502

4997
5132
5263

5514

5011

5145
5276
5403
5527

5024

5159
5289
54i6
5539

5038
5172

5302
5428
5551

3
3
3
3

4 6
4 5
4 5
4 5
4 5

7
7
6
6
6

8 10 II 12

8 911 12
8 9Jio 12
8 9)10 ii
7 9 10 ii

5563

5798
59"
6021

5575
5694
5809
5922
6031

5587
5705
5821

5933
6042

5599
5717
5832
5944
6053

56"

S3
gg

5623
5740
5855
5966
6075

5635

5866

5977
6085

5647

5877
5988
6096

5658
5775
5888

5999
6107

5670
5786

5899
6010
6117

2
2
2
2
2

4 5
3 5
3 5
3 4
3 4

6
6
6
5
5

7 8
7 8
7 8
7 8
6 8

10 II

9 10
9 10
9 10
9 10

43
44
45

6128
6232
6335
6435
6532

6138
6243
6345
6444

6542

6149 6160
62536263

6355 6365
6454 6464
6551 6561

6i 7 o
6274

6375
6474

6571

6180
6284
6385
6484
6580

6191
6294
6395
6493
6590

6201
6304
6405
6503
6599

6212
6314
6415
6513
6609

6222
6325
6425
6522
6618

2
2
2
2
2

3 4
3 4
3 4
3 4

3 4

5
5
5
5
5

6 7
6 7
6 7
6 7
6 7

8 9
8 9
8 9
8 9
8 9

47
48

49
50

6628
6721
6812
6902
6990

6637
6730
6821
6911
6998

6646

6739
6830
6920
7007

6656
6749
6839
6928
7016

666 5
6758
6848

6937
7024

6675
6767
6857
6946

7033

6684
6776
6866

6 955
7042

6693 6702
6785 6794
68756884
69646972
7050 7059

6712
6803

7067

2
2
2
2

3 4
3 4
3 4
3 4
3 3

5
5
4
4
4

6 7
5 6

S 6

5 6

7 8
7 8
7 8
7 8
7 8

51
52
53
54

7076
7160
7243
7324

7084 7093
716817177
72517259
73327340

7101
7185
7267
7348

7110
7193
7275
7356

7118
7202
7284
7364

7126
7210
7292
7372

7135 7143
721817226
7300,7308
73807388

7152
7235
73i6
7396

2
2
2
2

3 3

2 '*

2 ;

2 '.

4
4
4
4

5 6
5 6
5 6

5 6

7 8
7 7

These Tables enable the logarithm to be found of numbers i to 10000. Example : To find
the logarithm of 5779. Looking down the first column on p. 397. we find the figure 57, and in
the same line, under the figure 7, we find the figures 7612, which is the mantissa portion of

APPENDIX.

397

LOGARITHMS.

7404

1
7412

3 4

6 7

8 9

7419

7427

7435

7443

745i

7459

7466

7474

I 2

2 3

5 5

6 7

59
60

7482
7559
7634
7709
7782

7490
7566
7642
7716
7789

7497
7574
7649

7723
7796

7505
7582

7657
773i
7803

7513

7g9
7664

7738
7810

7520
7597
7672

7745
7818

7528
7604
7679
7752
7825

7536
7612
7686
7760
7832

7543
7619
7694
7767
7839

755i
7627
7701

7774
7846

2 3
2 3
2 3
2 3

2 3

4
4
4
4
4

5 5
5 5
4 5
4 5
4 5

6 7
6 7
6 7

6 7
6 6

61
62

?
64

7853
7924

7993
8062
8129

7860

7931
8000
8069
8136

7868
7938
8007
8075
5142

7875
7945
8014
8082
8149

7882
7952
8021
8089
8156

7889

7959
8028
8096
8162

7896
7966

8035
8102
8169

7903
7973
8041
8109
8176

7910
7980
8048
8116
8182

7917
7987
8055
8122
8189

2 3

2 3
2 3
2 3
2 3

4
3
3
3
3

4 5
4 5
4
4
4

6 6
6 6

5 S

5 6

66
67
68
69
70

8i95
8261

8325
8388

845i

8202
8267
8331
8395
8457

8209
8274
8338
8401
8463

8215
8280

8344
8407
8470

8222
8287

8351
8414
8476

8228
8293

8357
8420
8482

8235
8299

36 2
8426

8488

8241
8306
8370
8432
8494

8248
8312
8376

8439
8500

8254
8319
8382

8445
8506

2 3
2 3

2 3

2 2
2 2

3
3
3
3
3

4
4
4 4
4 4
4 4

5 6

5 S
5 6

5 6

74
75

8513
8573

! 33
8692

8751

8519
8579
8639
8698
8756

8525
8585
8645
8704
8762

8 S3 i
859i
8651
8710
8768

8537
8597
8657
8716
8774

8543
8603
8663
8722
8779

8549
8609
8669
8727
8785

8 S55
8615
8675
8733
8791

8561
8621
8681
8739
8797

8567
8627
8686

8745
8802

2 2
2 2
2 2
2 2
2 2

3
3
3
3
3

4 4
4 4
4 4
4 4
3 4

5 5
5 5
5 5
5 5
5 5

77
78

79
80

ssos
8865
8921
8976
9031

8814
8871

8927
8982
9036

8820
8876
8932
8987
9042

8825
8882
8938
8993
9047

8837
8887

8943
8998

9053

8837
8893
8949
9004
9058

8842
8899
8954
99
9063

8848
8904
8960

9015
9069

8854
8910
8965
9020
9074

8859
8915
8971
9025
9079

2 2
2 2
2 2
2 2
2 2

3
3
3
3
3

3 4
3 4
3 4
3 4
3 4

5 5
4 5
4 5
4 5
4 5

81
82

83
84
85

9085
9138
9191

9243
9294

9090

9143
9196
9248
9299

9096
9149
9201
9253
9304

9101

9154

9206
9258
9309

9106

9159
9212
9263
9315

9112
9165

9217
9269
9320

9117
9170
9222
9274
93 2 5

9122

9175
9227
9279
933

9128
9180
9232
9284

9335

9133
9186

9238
9289

9340

2 2
2 2
2 2
2 2
2 2

3
3
3
3
3

3 4
3 4
3 4
3 4
3 4

4 5
4 5
4 5
4 5
4 5

87
88
89
90

9345
9395
9445
9494
9542

9350
9400
9450
9499
9547

9355
9405
9455
9504
9552

9360
9410
9460
9509
9557

93 6 5
9415
9465
95*3
9562

937
9420
9469
95i8
9566

9375
9425
9474
9523
957i

9380
943
9479
9528

9576

9385

943^
9484

9533
958i

9390
9440

9489
953 8
9586

2 2

2
2
2
2

3 4
3 3
3 3
3 3
3 3

4 5
4 4
4 4
4 4
4 4

9i
92

9590
9638
9685
973i
9777

9595
9643
9689
9736
9782

9600
9647
9694

974i
9786

9605
9652
9699

9745
9791

9609
9657
973
975o
9795

9614
9661
9708

9754
9800

9619
9666

9713
9759
9805

9624
9671
9717

9763
9809

9628

9675
9722
9768
9814

9633
9680
9727

9773
9810

2
2
2

3 3
3 3
3 3
3 3
3 3

4 4
4 4
4 4
4 4
4 4

97
98

9823
9868
9912
9956

9827
9872
9917
9961

9832
9877
992i
9965

9836
9881
9926
9969

9841
9886
993
9974

9845
9890

9934
9978

9850
9894
9939
9983

9854
9899
9943
9987

9859
993
9948
9991

9863
9908
9952
9996

o
o

2
2
2
2

3 3
3 3

4 4
4 4
4 4
3 4

the logarithm of 5770. Still further along the same line are the difference columns, and under
the figure 9 we find the figure 7, which, added to 7612, gives 07619 as the mantissa portion
of the logarithm 5779.

398

APPENDIX.

ANTILOGARITHMS.

1 2

6 7

8 9

1000

1002

1005

1007

1009

IOI2

1014

1016

1019

1021

o o

I I

I 2

2 2

'OI

1023

IO26

1028

1030

<33

1035

1038

1040

1042

1045

I 2

2 2

'02
03

1047

1072

I050JI052
1074 1076

1054
1079

1057
108

1059
1084

1062 1064
1086 1089

106711069
1091 1094

o o

I
I

i
i

I 2
I 2

2 2
2 2

1096

IC99;iIO2

1104

1107

1 109

III2 1114

1117

IIT9

2 2

1122

1125

1127

1130

1132

H35

1138

1140

H43

1146

2 2

1148

II5I

"S3

1156

"59

116

1164

1167

1169

1172

2 2

"75

II 7 8

1180

1183

1186

1189

II9I

1194

1197

1199

2 2

1202

1205

1208

I2II

I2I v -

1216

1219

1222

1225

1227

2 2

2 3

I2 3

1233

1236

I2 39

1242

124

1247

1250

1253

1256

2 2

2 3

1259

1262

1265

1268

I2 7 I

1274

1276

1279

1282

1285

2 2

2 3

1288

1291

1294

1297

1300

J 33

1306

1309

1312

1315

2 2

2 3

'12

1318

I 3 2I

1324

1327

1330

1334

1337

1340

1343 1346

2 2

2 3

'IS

1349

1352

1355

J 358

1361

T36 5

1368

1371

1374 1377

2 2

3 3

1380

I3 8 4

1387

1390

1393

1396

1400

I 43

1406

1409

2 2

3 3

-I 5

1413

I 4 I6

1419

1422

1426

1429

HS 2

J 435

1439

1442

2 2

3 3

1445

I 449

1452

'455

M59

1462

1466

1469

1472

1476

2 2

3 3

1479

1483

1486

1489

1493

1496

I 5 00

i53

J 57

1510

2 2

3 3

1514

I5 r 7

1521

1524

1528

tS3

1535

1538

J S4 2

J545

2 2

3 3

1549

1552

1556

1560

1563

1567

1570

1574

1578

1581

2 3

3 3

1585

1589

1592

1596

1600

1603

1607

1611

1614

1618

2 ^

3 3

1622

1626

1629

1633

1637

1641

1644

1648

1652

1656

3 3

!66o

1663

1667

1671

i675

1679

l68 3

1687

1690

1694

2 ^

3 3

1698

1702

1706

1710

1714

1718

1722

1726

1730

1734

2 ;

3 4

1738

1742

1746

1750

1754

1758

1762

1766

1770

1774

2 ;

3 4

1778

1782

1786

1791

1795

1799

1803

1807

1811

1816

2 ;

3 4

1820

1824

1828

1832

i837

1841

18-45

18-19

J 854

1858

3 4

1862

1866

1871

1875

1879

1884

1888

1892

1897

1901

3 4

1905

1910

1914

1919

1923

1928

1932

1936

1941

1945

4 4

2 9

1950

1954

J 959

1963

1968

1972

I 977

1982

1986

1991

4 4

'30

1995

2COO

2004

2009

2014

2018

2023

2028

2032

2037

3 3

4 4

'SI

2042

2046

2051

2056

2061

2065

2070

2075

2080

2084

3 3

4 4

32
'33

2089
2138

2094
2143

2099
2148

2104

2153

2109

2158

211^

2163

2118

2168

21232128
2173 2178

2133
2183

o
o

2
2

3 3
3 3

4 4
4 4

'34

2188

2193

2198

2203

2208

221^

22l8 2223)2228

22 34

3 4

4 5

'35

2239

2244

2249

2254

2259

2265

2270

2275

2280

2286

3 4

4 5

2291

2296

2301

2307

2312

2317

2323

2328

2333

2339

3 4

4 5

'37

2344

2 350

2355

2360

2366

2 37I

2377

2382 2388

2393

3 4

4 5

2399

2404

2410

2415

2421

2427

2432

2438

2443

2449

3 4

4 5

'39

2455

2460

2466

2472

2477

2483

2 4 8 9

2495

2500

2506

3 4

5 5

2512

2518

2523

2529

2535

2541

2547

2553 2559

2564

4 4

5 5

'4i
42

2570
2630

2576
2636

2582
2642

2588
2649

2594
2655

2600
266l

25o6
2667

2612 2618
2673 2679

2624
2685

2
2

3
3

4 4
4 4

'43

2692

2698

2704

2710

2716

723

2729

2735 2742

2748

4 4

5 6

'44

2754

2761

2767

2773

2780

7 86

2793 2799 2805

28l2

4 4

5 f

'45

2818

2825

2831

2838

2844

851

2858

2864 2871

2877

4 5

5 6

'46

2884

2891

2897

2904

2911

9 I 7

2924

29312938

2944

2 3

4 5

5 6

'47

2951

2958

2965

2972

2979

985

992

2999 3006 3013

2 3

4 5

5 6

3020

3027

3034

34'

3048

062

3069 3076 3083

2 3

4 5

6 6

'49

3090

3097

3i5

3112

126

133

3141 3148 3155

2 3

4 5

6 6

These Tables enable the numbers to be found corresponding to logarithms "oooo to "9999-
Example : To find the number of which s'ogjS is the logarithm. Looking down the first
column on p. 398, we find the figures "09, and in the same line under the figure 7 we find

APPENDIX.

399

ANTILOGARITHMS.

6 7

8 9

*5o

3162

3170

3177

3184

3192

3199

3206

3214

3221

3228

i i

2 3

4 5

6 7

'Si

3236

3243

3251

3258

3266

3273

3281

3289 3296

3304

2 3

5 5

6 7

52
'53
'54
'55

33"
3388
3467
3548

3319
3396
3475
3556

3327
3404
3483
3565

3334
34i2
349i
3573

3342
3420
3499
358i

335
3428
3508
3589

3357
3436
35i6

3597

3365
3443
3524

3373
345i
3532
3614

338i
3459
3540
3622

2
2
2
2

2 3
2 3

2 3

4
4
4
4

5 5
5 6

5 S

5 6

6 7

6 7
6 7

7 7

3631

3 6 39

3648

3656

3664

3673

3681

3690

3 5 9 8

3707

3 3

5 6

7 8

3715
3802

3724
3811

3733
3819

374i
3828

3750
3837

3758
3846

3767
3855

3776 378413793
3864 3873i3882

2
2

3 3
3 4

4
4

5 6
5 6

7 8
7 8

'59

3890

3899

3908

3917 3926

3936

3945

3954 3963

3972

3 4

5 6

7 8

398i

3990

3999

4009

4018

4027

4036

4046

4055

4064

3 4

6 6

7 8

61
62

4074
4169

4083 4093
41784188

41024111
419814207

4121
4217

41304140
4227 4236

4i5o
4246

4159
4256

2
2

3 4
3 4

5
5

6 7
6 7

8 9
8 9

4266

4276 4285

4295 4305

4315

43 2 5 4335

4345

4355

3 4

6 7

8 9

64
65

4365
4467

4375 4385
4477 4487

4395
4498

4406
4508

4416
4519

4426
4529

4436
4539

4446
4550

4457
456o

2
2

3 4
3 4

5
5

6 7

8 9
8 9

457i

458i

4592

4603

4613

4624

4634

4645

4656 4667

3 4

6 7

9 10

4677

4 688; 4 6 99

47104721

4732

4742 4753

4764

4775

3 4

7 8

9 10

68
69
70

4786
4898
5012

4797
4909

5023

4808
4920
5035

4819
493 2
5047

4831
4943
5058

4842
4955
5070

4853 4864
4966 4977
50825093

4875
4989
5i5

4887
5000
5H7

2
2
2

3 4
3 5

4 5

6
6

7 8
7 8
7 8

9 10
9 10
9 u

5129

5 X 4Q

5152

5164

5176

5188

5200 5212 5224

5236

4 5

7 8

10 II

5248
5370

5260 5272
53835395

5284
5408

5297
5420

5309
5433

5445

5333:5346
5458J5470

5358
5483

4 5
4 5

6
6

7 9
8 9

10 II

5495

5508)5521

5534

5546

5572

55 8 5| 5 598

5610

4 5

8 9

10 12

5623

56365649

5662

5675

5689

5702

5715 5728

574i

4 5

8 9

10 12

5754

5768 5781

5794

5808

5821

5834

5848 5861

5875

4 5

8 9

II 12

77
78

5888
6026

5902 5916 5929
6039 6053 6067

5943
6081

5957
6095

5970
6109

5984 5998
6124 6138

6012
6152

3
3

4 5
4 6

7
7

8 10
8 10

II 12
II 13

6166

618061946209

6223

6237

6252

6266:6281

6295

9 10

II 13

6310

6324 6339

6353

5368

6383

6397

6412)6427

6442

9 10

12 13

81
82

6457
6607

6471 6486
66226637

6516
6668

6 53i

6683

6546 6561 6577
6699 6714 6730

6592
6745

2 3
2 3

5 6

8
8

9 ii
9 ii

12 14

I 3
'84

$**

6918

6776 6792
6934I6950

6808
(3965

6823
6982

6998

68556871(68876902
7015 7031 7047 7063

2 3
2 3

56
5 6

8
8

9 ii 13 14

10 II 13 it;

7079

709617112

7129 7145

7161

717871947211:7228

2 3

5 7

IO 12

13 IS

7244

726117278

7295:73"

7328

7345i73 6 273797396

2 3

5 7

10 12

13 '5

741-

7430 7447 7464 7482

7499

75167534 75517568

2 3

5 7

10 I2JI4 16

88
89
90

7586

7762

7943

7603
7780
7962

762117638
77987816
79807998

7656
7834
8017

7674
7852
8035

76911770977277745
7870,7889179077925
80541807280918110

2 4
2 4
2 4

5 7
5 7
6 7

9
9

ii J2 14 16
ii 12,14 16

II 1315 17

8128

8147

816681858204

8222

5241 8260 8279)8299

2 4

6 8

ii 13^5 17

8318

8337

8356

8375 8395

8414

8433 8453 8472

8492

2 4

6 8

2 I4JI5 17

'93

8511

8531

855i

8570 8590

8610

8690

2 4

6 8

2 1416 18

'94

8710

8730

8750

8770

8790

8810

8831 8851:8872

8892

2 4

6 8

2 I4 ! i6 18

*95

8913

8933

8954

8974

8995

9016

9036

9057

9078

9099

2 4

6 8

2 15 17 19

9120

9141

9162

9183

9204

9226

9247

926819290

93"

2 4

6 8

3 1517 19

'97 9333
"98 9550

9354
9572

9376
9594

9397l94i9
96i6j 9 6 3 8

9441
9661

9462,948419506
9683 9705 9727

9528 2 4
9750 2 4

7 9
7 9

II
II

3 15 17 20
3 16 18 20

'99

9772

9795

9817

98409863

9886

9908 9931

9954

9977 25 79

4 16 18 20

the figures 1250. Still further along the same line we get the difference for 8, (2),! which
added to 1250, gives 1252, the number required.

4oo

APPENDIX.

SQUARES OF NUMBERS FROM i TO 10000, CORRECT TO FOUR
SIGNIFICANT FIGURES.

1 2

.3 4

6 7

8 9

IOOO

IO20

104

1061

108

1124

"45

1166

1188

3 i

7 S

13 i5

17 19

1210

1232

1254

1277

1300

132

1346

1369

1392

1416

7 c

14 17

19 21

1440
1690

1464
I7 oo

148

174

1513
1769

153
179

156
182

1588
1850

1613
1877

1904

1664
1932

3 5|8 c
3 6| 9

15 18
17 19

20 23

22 25

I 9 60

I 9 88

2016

2045

2074

2IO

2132

2161

2190

2220

3 6

9 2

18 21

24 27

2250

2280

2310

2341

2372

2402

2434

2465

2496

2528

4 7

IO ^

19 22

25 28

2560

2592

2624

2657

2690

272

2756

2789

2822

2856

4 7

10 4

20 24

2 7 30

2890

2924

2958

2993

3028

3062

3098

3133

3168

3204

4 7

n t.

21 25

28 32

18
19

3240
3 6lO
4000

3276
3648
4040

3312
3686
4080

3349
3725
4121

3764
4162

3422
.202

3460
3842
4244

3497
3881
4285

3534
3920
4326

3572
3960
43 68

4 8
4 8
5 9

12 5

12 6

13 7

20
21

23 26
2 4 28
2 5 2 9

30 34
3 2 36
33 37

4410

4452

4494

4537

458o

4622

4666

4709

4752

4796

5 9

13 18

26 3 I

35 39

*j*j *J 7

4840

4884

4928

4973

5018

5062

5108

5*53

5244

5 914 18

2 3

27 32

36 41

5290

5336

5382

5429

5476

5522

557

5617

5664

5712

5 1015 19

27 33

38 43

5760

5856

5905

5954

6002

6052

6101

6150

62OO

5 1015 20

2 5

3 35

40 45

6250

6300

6 35o

6401

6452

6 5 02

6 554

6605

6656

6708

6 n

16 21

3i 36

4i 46

6 7 60

6812

6864

6917

6970

7022

7076

7129

7182

7236

6 n

16 22

2 7

32 38

43 48

7290

7344

7398

7453

7508

7562

7618

7673

7728

7784

6 n

17 22

33 39

44 50

28
29

7840
8 4 IO

7896
8468

7952
8526

$009
8585

5o66

8l22
8702

8180
8761

8237
8821

8294
8880

8352
8940

6 12
6 12

18 23

18 24

3540
3 6 4

4652
48 54

9000

9060

9120

9181

Q2 Af

3 02

93 6 4

9425

9486

9548

7 i -

19 25

37 4

49 55

V *T

9610

9672

9734

9797

9860

922

9986

005*

ion*

1018*

7 J 3

19 26

3 2

8 4

5 1 57

3 2

1024

1030

1037

1043

050

056

063

069

1076

1082

2 3

5 6

I08 9

1096

1 102

1109

115

122

129

136

1142

1149

2 2

6 6

HS6

1163

II 7

1176

183

100

197

204

I2II

1218

2 2

6 6

1225

1232

I2 39

1246

253

200

267

274

1282

1289

2 I

6 7

1296

1303

1310

1318

325

332

339

347

1354

1362

2 3

6 7

369

1376

1384

39 1

399

4 06

414

421

1429

I43 6

2 3

6 7

1444

1452

1459

467

474

4 82

490

498

1505

2 3

5 6

6 7

521

1529

1537

544

552

560

568

576

1584

1592

3 3

5 6

6 7

600

1608

1616

624

632

6 4

648

656

1665

1673

3 3

5 6

7 7

681

689

1697

706

714

722

730

739

1747

I75 6

3 3

5 6

7 8

764

772

1781

789

798

806

823

1832

1840

3 4

5 6

7 8

849

858

1866

875

883

8 9 2

901

910

1918

1927

3 4

5 6

7 3

93 I

945

954

962

971

9 80

989

998

2007

2016

3 4

5 6

7 8

025

2034

2043

052

061

070

079

088

2098

2107

3 4

6 7

7 8

116

125

2134

144

153

162

171

181

2190

2200

3 4

6 7

8 9

209

218

2228

237

247

256

266

275

2285

2294

3 4

6 7

8 9

304

314

2323

333

342

352

362

372

2381

2391

3 4

6 7

8 9

401

411

2421

430

440

460

470

2480

2490

3 4

6 7

8 9

500

5 10

2520

2540

570

2581

2591

3 4

6 7

8 9

5 1

601

621

632

2642

652

662

673

2683

2694

3 4

6 7

8 9

5 2

704

714

725

735

2746

756

767

777

2788

2798

3 4

6 8 i 9 10

809

820

830

841

2852

862

873

884

2894

2905

3 4

7 8 9 10

916

927

938

948

2 959

970

981

992

3003

3014

3 5

7 8 9 10

Squares from i to 3 contain i figure.
4 to 9 2 figures.
,, 10 to 31 3
321099 4

Squares from 100 to 316 contain 5 figures.
,, 317 to 999 6
> 1000 to 3163 ,, 7 ,,
> 3*63 to loooo ,, 8

The differences for squares from 3171 to 3199 are i, i, 2, 3, 3, 4, 5, 5, 6.

APPENDIX.

401

SQUAKES OF NUMBERS FROM i TO loooo, CORRECT TO FOUR
SIGNIFICANT FIGURES.

1 2

3 4

8 7

8 9

3025

303^

3047

3058

306

3080

3091

3102

3H4

3125

I 2

3 5

7 8

9 10

3136

3147

3158

3170

318

3192

3204

3215

3226 3238

4 5

7 8

9 10

3249

3260 3272 3283 3295

3306

3318,3329 334i 3352

245

7 8

9 ii

3364

3376 3387 3399 34i

3422

3434344634573469 245

7 8

IO II

3481

3493 355 35 z 6 3528

3540

3552|356435763588| 345

7 8

IO II

3600 3612 3624 3636 36.48

3660

367213684

3697 3709

345

7 9

10 II

61
62

372i|3733i3745
384438563869
3969 3982 3994
4096 4109 4122

3758 3770
3881 3894
40074020
41344147

3782
3906
4032
4160

37953807
39193931
40454058
417314186

38193832

39443956
4070 4083
41994212

3
3
3
3

4 5
4 5
4- ^

4 5

6
6
7
7

o 9
8 9

8 9
8 9

10 II
10 II
10 12
IO 12

422542384251

4264 4277

4290

4303

43i6

43304343

4 5

8 9Jii 12

67
68
69
70

4356 4369 4382 4396
4489450245164529
4624463846514665
476i4775!478948o2
4900 4914 4928 4942

4409
4543
4679
4816
4956

4422
4556
4692
4830
4970

4436
4570
4706
4844
4984

4449
4583
4720
4858
4998

4462 4476
4597j46io

47334747
48724886
50135027

1345
2340
2 3! 4 6

2 si 4 6
2346

7
7
7
7

8 Oil 12

8 io : n 12

8 10 II 12

8 10 ii 13
9 io|n 13

7 j

5 4i

555

50695084

5098

5112

51275141

51555^0

2 3

4 &

9 10 12 13

72
73
74
75

5184

5476
5625

519852135227
5344 5358 5373
549155065520
5640 5655 5670

5242
5388

5535
^68 ^

5256
5402
5550
5700

271

5417
5565
715

5285
5432
558o
5730

5300 5314
5446 5461
5595 5610
5746 5761

2 3
2 3
2 3
2 3

5 6
5 6
5 6
5 6

7
8
8
8

9 10
9 10
9 ii
9 n

12 13
12 13

12 14
12 14

5776

5791 5806

5822

5837

5852

868

5883

5898

59H

2 3' 5 6

9 ii

12 14

5929

5944 5960

5975

5991

006

6022 6037

6053 6068

2356

9 ii

6084

61006115

6131 6147

162

178

6194

62096225

2 3i 5 6

10 II

!3 14

6241

6257 6273

6288

630^

320

336

6352

63686384

2 3: 5 7

IO II

13 14

J400

6416 6432

6448

646^

480

4966512

6529

6545

2357

10 II

13 15

81
82

6561
6724

6577 6593
6740 6757

6610

6773

6626
6790

642
836

659,6675
823 6839

6691
6856

6708:
6872

2 3; 5 7

2357

8
8

10 12
IO 12

13 15
13 15

83
84

6889 6906 6922
705670737090

6939
7106

6956
7123

972
140

989 7006
I57J7I74

7022
7191

70392 3 | 5 7

7208 2 4; 5 7

9
9

10 12

IO 12

14 15

T 4 J 5

7225

7242 7259

7276

7293

310

3277344

7362

7379 2457

10 12

14 16

7396

74i3

743

7448

7465

482

5007517

7534

7552

2 4

5 7

I 12

14 16

7569

75867604

7621

7639

656

6747691

7709

7726

2 4

5 7

I 12

14 16

88
89

7744
792i

7762
7939

7779
7957

77977815
79747992

832
ioio

8 5 o! 7 868
0288046

7885
8064

7903
8082

2 4
2 4

5
6

9
9

I 13

14 16
14 16

8100

8118

8136

81548172

190

208 8226

8245

8263

2 4

I 13

15 16

OT
92

8281
8464

8299
8482

8317
8501

83368354
85198538

372

556

391 8409
575 8593

8427
8612

8446
8630

2 4
2 4

6 7
6 8

I 13

1 *3

IS *7

15 17

8649

8668

8686

8705 8724

742

7618780

8798

8817

2 4

6 8

1 *3

15 17

8836

8855

8874

8892

8911

930

9498968

8987

9006

2 4

6 8

1 J 3

15 17

9025

9044

9063

9082

9101

120

I399I5 8

9178

9197

2 4

6 8

12 I 4

15 17

9216

9235

9254

9274

9293

312

33i

935i

9370

9390

2 4

6 8

12 14

16 18

9409

9428

9448

9467

9487

S 06

526 9545

9565

9584

2 4

6 8

12 14

16 18

98 604

9624

9643

9663

9683

7O2

722 9742

9761

978i

2 4

6 8

12 14

16 18

99 98019821

9841

9860

9880

900

920

9940

99609980 2 4

6 8

12 14

16 18

Squares from i to 3 contain i figure.
,, ,, 4 to 9 ,, 2 figures.
., 10 to 31 3 ,,
32 to 99 4

Squares from 100 to 316 contain 5 figures.

317 to 999 6
,, looo to 3162 ,, 7
,, 3163 to loooo 8

The differences for squares from 3171 to 3199 are i, i, 2, 3, 3, 4, 5, 5, 6.

2 D

4 02

APPENDIX.

RECIPROCALS OF NUMBERS FROM i TO 10000.

9804

9*74

1 23 4

6 7

8 9

72 81

0100

9901

9709

9615

9524

9434

9346

9259

9 18 27 36

54 63

H H H H H

In 4^ CO 10 H

0091 9009 8928

8333 8264 8197
7692 7633 7576
7143 7092 7042

6667 6622 6579

8849 8772
81308064
75*9 7463
6993:6944
6536 6493

8696
8000
7407
6896
6452

8621
7936
7353
6849
6410

8547
787-1
7299
6803

6369

8474
7812
7246

6757
6329

8403
7752

7 IQ-i

6711
6289

8 1623 31
6 13 19 26
5 ii 16 22
5 9*4 19

38
32
27

2 3

46 53
38 45
32 58
28 33
25 29

61 68
5i 57

43 49
37 42
3438

17
18

625062116173

5882 5848 5814

5555 5529 5494
5263 5236 5208
500049754950

6135
578o
5464
5181
4926

6097
5747

5435

4902

6061
5714
5405
5128
4878

6024
5682
5376
5102
4854

5988

5347
5076

4831

5952
5618

53i9
55
4808

5917
5586
5291
5025
4785

4 I
3 6
3 6
3 5
2 5

II 15
10 13
8 ii
8 10
7 10

16
14
13

22 2630 33
19 23 26 29
17 2023 26
16 1821 23
14 17119 21

21
22
23
24
25

4762 4739 4717

4545 4525 4504
434843294310
416741494132
400039843968

4695
4484
4292
4"5
3952

4673
4464

4273
4098

3937

4651
4444
4255
4082
3921

4630
4425
4237
4065
3906

4608

4405
4219
4048
3891

4587
4386
(.202
4032
3876

4566

4367
4184

4016

3861

2 4
2 4
2 3

2 4

i 3

6 9
6 8

5 7
5 7
4 6

II
10

9
9

13 1517 '9
ii 1315 17

II 12 14 l6
10 12 14 15

9 10 12 13

29
30

3846 3831
3704^3600

357i;3559
34483436
3333 3322

3817
3676
3546
3424
33"

3802
3663
3533
3413
3300

3788
3650
352i
340i
3289

3773
3636
3509
339
3279

3759
3623
3496
3378
3268

3745
3610

3484
3367
3257

373i
3597
3472
335 6
3247

3717
3584

3460

3344
3237

I 2
I 2
2 3
I 3

i 3

4 5
4 5
4 5
4 5
4 5

7
6
6
6
6

8 9 ii 12
8 9Jio 12
8 910 ii
7 8 9 ii
7 8 9 10

31
32

33
34
35

322632153205
3125,31153105
3030302113012
2941,29322924
2857 2849 2841

3003

2915
2839

3185
3086

2994

2907
2825

3*75
3077
2985
2898
2817

3 l6 4
3067
2976

3 T 54
3058
2967
2882
2801

3145
3049
2958
2873

2793

3135
3039
2950
2865

2785

2 3

I 2
I 2
I
I 2

4 5
3 4
3 4
2 3
3 3

6
5
4
4
4

7 8
6 7
5 6

5 5
5 6

9 10

8 9
7 8
6 7
7 7

39
40

2778 2770 2762
270326952688
263126252618

256425572551
250024942487

2755
2681
2611

2544
2481

2747
2674
2604
2538
2475

2740
2667
2597
2532
2469

2732

2659
2591
2525
2463

2725
2652
2584
2519
2457

2717
2645
2577
2512

^45i

2710
2638

2 57i
2506

2445

I 2
I 2
I
I 2

3 3
3 3

2 2

2 3
2 2

4
4
3
4
3

5 6

5 5
4 4
4 5
4 4

6 7
6 7
5 6
6 6

5 5

42
43
44
45

243924332427
238123752370
232523202315
227322672262
222222172212

2421
2364
2309
2257
2207

2415
2358
2304
2252
2203

2410

2353
2299
2247

2! 9 8

2404

2347
2293
2242
2i 93

2398
2342
2288
2237
2188

2392
2336
2283
2232
2183

2387

2278

2227
2179

I \

I I
I
I I

2 3
2- 2
2 2
I 2
2 2

3
3
3

4 5
3 4
3 4
3 3
3 4

5 6
5 5
4 5
4 4
4 5

47
48

49
So

2174 2169 2164
212821232119
208320792075
20412037,2032
200019961992

2160
2114

2070
2028
1988

2155

2110
2066
2O24
1984

2150
2105
2062
2O2O
I 9 80

2146

2101
2058
2Ol6
1976

2141
2096
2053

2OI2
1972

2137
2092
2049
2008
1968

2132
2088
2045
2004
1965

O O
I

I I

O I
I

I I
I 2
2 2
I 2
I I

2
2
2
2
2

2 3
2 3
3 3
2 3
2 3

3 4
3 4
4 4
3 4
3 3

52
53
54

19611957
19231919
1887 1883
1852 1848

1953
1916
1880
1845

1949
1912
1876
1842

1945
I008
1873
l8 3 8

1942

1935
1869

1835

1938
1901

1866

J 934
1897
1862
1828

1930
1894

1859
1825

1890

1855
1821

I I
I I

O I

I I

I 2
I 2
I I

I 2

2
2
2

3 3
3 3

2 2
2 3

3 4
3 4
3 3
3 3

Reciprocals from 2 to 10 = o' Reciprocals from 101 to 1000 = o'oo

>? ,, iitqioo^o'o ,, loot to icooo = o ooo

Numbers in difference columns to be subtracted, not added.

The reciprocal of a number is obtained by dividing it into i. Example : To find the value
of ,| . Looking down the first column on p. 403, we find the figures 88, and in the same

APPENDIX.

RECIPROCALS OF NUMBERS FROM i TO IOODO.

403

il 1

6 7

8 9

Jlfll

51811

i8o

5i8o

180

1798

179

I 7 8c

i ]

[ i

3 3 3

178^

) 1782! I 77 c

)i 77 <

>i77

177

176;

176

i 7 6c

1757

2233

i754;i75 I : I 74^

5 174.

5i74

173

>i73

I 73 C

1727

2223

S 8 11724117211718

!i 7 i^

5171

170

I 7 0t

170

1698

I 2j 2 2

59 '1691

51692

>i68c

>i68<

)i68

1 68

1678

167

1672

1665

2 2j 3 3

1663

'i66,

165*

5165

165

i6 5 c

164

164.

1642

2 :

2, 2 3

l6 3^

> l6 3y

1634

^163]

162

162;

162

1618

1615

2 i

J 2 2

i6ir

i6ic

>i6o8

160-

,160

160

1597

159.

159'

1550

2222

1587 1581:

51582

i5&

>*57

157

1572

I57C

156;

1565

2 2 | 2 3

1562 i56c

>i55*

J 55f

155

1548

154

J 54C

I 54 I

I ]

2 2

I53S

J 534

i53i

152

IS 2

1524

1522

I 5 2C

1517

I I

2 i

2 2

! 5lq

J 5 J c

1510

1508

150

1501

1500

T497

H95

I I

2 2

1492

1490

1488

148^

148

1479

1477

147 c

1473

I I

I 2

I47C

1468

1466

146^

146

1458

1456

145;

1451

O I

2 2

1449

1447

1445

'443

144

14^

1437

J 435

143 1

2 2

1428

142

1424

1422

142

141

1416

1414

1412

1.410

I I

1408

140

1404

1402

1400

139

J 397

*395

I393

1391

I I

2 2

1389

138

1385

1383

138

137

1377

1375

T 37*

1372

o o

I I

1370

136

1366

1364

136

1359

T 35 C

o o

I I

134

1348:1346 134

J 339

T337

335

o o

I I

_/:

J 333

" 4

1330

1328

TOT T

132

T **r\

132

1323

1321

Torv*

I 1

I I

1299

1297

1295

1 O 11 | A O V 'V

1294 129

130
129

I 35
1289

I 34
1287

1302
285

1300
1284

o c

o o

I I

1282

1280

1279

1277(127

127

1272

1271

269

267

O I

I I

2 2

1266

1264

1263

1261

1259

125

1256

I2 55

2 53

251

I I

2 2

1250

1248

1247

1245

I2 44

1242

1241

1239

238

236

I I

234

I2 33

1231

1230

1228

1227

1225

224

222

221

I I

219

i2ii

1216

1215

121;

1212

I2II

1209

208

206

o o

I I

205

1203

1 202

1200

"99

1198

II 9 6

"95

193

I 9 2

I I

2 2

190

1189

1188

1186

"85

1183

1182

1181

179

I 7 8

o o

I I

176

"75

174

1172

1171

169

1168

1167

165

II6 4

I I

163

1161

160

"59

"57

156

155

"53

152

"5i

O I

I I

149

1148

147

"45

"44

141

[I 4

"39

11380 i

I I

88
89

136
123

"35

1122

134

121

Trw~i

"32

[120
IO7

1131

EZIJ

130

129
116

[I2 7

CII 5

1126
1113

1125 o o

III20

I I

I
I

I I
I I

099

-.Q

CIIO

IOC

096

r\Q A

[095
[083

" IOO

C0 94

093
08 r

104
092

O8O 1

[090

[089

[088

^ \~r

I I

92
93

087
075

ro86, iwu^ j
[074 1073 ]

[072

[071

069

o68|io67

[ 77
[066

[065

064

1:063 i

061 ]

[060

[O 59

5 8

0571*056

[ 55

[054

I I

053 ]

[0511

0501

049 :

[048

047

0461

045

044

I0 43

1 J

4 2]

0401

0391

038 ]

037

3 6

0351

034

033

032

0311

0301

0291

0283

027

026

024 1023

022

02 1

C I

I I

020]

0191

018 i

017 ]

016

015

014 1013

012

I I

OIQ]

0091

0081

007 i

006

005

0041003

002

001

I I

Reciprocals from 2 to 10 = o' Reciprocals from 101 to 1000 = o'oo

,, ,, iitoioo = o'o ,, ,, looi to loooo = o ooo

Numbers in difference columns to be subtracted, not added.

line under the figure 8 we find the figures 1126; the reciprocal required is therefore
0*001126,

404

APPENDIX.

NATURAL TANGENTS.

.30

.90

oooo

0017

0035

0052

0070

0087

0105

OI22

0140

oi57

0175

0192

0209

0227

0244

0262

0279

0297

03H

0332

0349

0367

0384

0402

0419

0437

0454

0472

0489

0507

0524

0542

0559

0577

0594

0612

0629

0647

0664

0682

0699

0717

0734

0752

0769

0787

0805

0822

0840

0857

0875

0892

0910

0928

0945

0963

0981

0998

1016

1033

1051

1069

1086

1104

1122

"39

1157

U75

1192

1210

1228

1246

1263

1281

1299

1317

1334

1352

1370

1388

1405

1423

1441

1459

1477

H95

1512

1530

1548

1566

1584

1602

1620

1638

1655

1673

1691

1709

1727

1745

1763

1781

1799

1817

1835

1853

1871

1890

1908

1926

1944

1962

1980

1998

2Ol6

2035

2053

2O7I

2089

2IO7

2126

2144

2162

2180

2199

2217

2235

2254

2272

2290

2309

2327

2345

2364

2382

2401

2419

243

2456

2475

2493

2512

2530

2549

2568

2586

2605

2623

2642

2661

2679

2698

2717

2736

2754

2773

2792

2811

2830

2849

2867

2886

2905

2924

2943

2962

2981

3000

3019

3038

3057

3076

3096

31*5

3134

3153

3172

3i9i

3211

3230

3249

3269

3288

3307

3327

3346

3365

3385

3404

3424

3443

3463

3482

3S02

3522

3541

3561

358i

3600

3620

3640

3659

3679

3699

3719

3739

3759

3779

3799

3819

3839

3859

3879

3899

3919

3939

3959

3979

4000

4020

4040

4061

4081

4101

4122

4142

4163

4183

4204

4224

4245

4265

4286

4307

4327

4348

4369

4390

4411

4431

4452

4473

4494

4515

4536

4557

4578

4599

4621

4642

4663

4684

4706

4727

4748

4770

479i

4813

4834

4856

4877

4899

4921

4942

4964

4986

5008

5029

5051

573

5095

5"7

5 ! 39

5161

5^4

5206

5228

5250

5272

5295

5317

5340

5^62

5384

5407

5430

5452

5475

5498

55 20

5543

5566

5589

5612

5635

5658

5681

5704

5727

5750

5774

5797

5820

5844

5867

5890

59U

5938

596i

5985

3 1

6009

6332

6056

6080

6l04

6128

6152

6176

6200

6224

6249

6273

6297

6322

6346

6371

6395

6420

6445

6469

6494

6 5i9

6544

6569

6594

6619

6644

6669

6694

6720

6745

6771

6796

6822

6847

6873

6899

6924

6950

6976

7002

7028

7054

7080

7107

7133

7159

7186

7212

7239

7265

7292

7319

7346

7373

7400

7427

7454

7481

7508

7536

7563

7590

7618

7646

7673

7701

7729

7757

7785

7813

7841

7869

7898

7926

7954

7983

8012

8040

8069

8098

8127

8156

8185

8214

8243

8273

8302

8332

8361

8391

8421

8451

8481

8511

8541

8571

8001

8032

8662

8693

8724

8754

8785

8816

8847

8878

8910

8941

8972

9004

9036

9067

9099

9I3 1

9163

9195

9228

9260

9293

9325

93 S8

9391

9424

9457

949

95 2 3

9556

9590

9623

9657

9691

9725

9759

9793

9827

9861

9896

9930

996S

From o to 45 the natural tangent increases from o to i.

APPENDIX.

405

NATURAL TANGENTS.

1
1

. 3 o

.50

.go

. 9 o

I -0000

0035

0070

0105

0141

0176

0212

0247

0283

0319

1*0355

0392

0428

0464

0501

0538

0575

0612

0649

0686

I -0724

0761

0799

0837

0875

0913

0951

0990

1028

1067

i -1106

"45

1184

1224

1263

1303

1343

1383

1423

1463

1-1504

1544

1585

1626

1667

1708

175

1792

1833

1875

1-1918

1960

2OO2

2045

2088

2131

2174

2218

2261

2305

i -2349

2393

2437

2482

2527

2572

26l7

2662

2708

2753

i -2799 i 2846

2892

2938

2985

3032

3079

3127

3175

3222

1*3270 33'9

3367

34i6

3465

35M

3564

3613

3663

3713

i -3764

3814

3865

3916

3968

4019

4071

4124

4176

4229

JT^

1-4281

4335

4388

4442

4496

4550

4605

4659

4715

4770

i -4826

4882"

4938

4994

55i

5108

5166

5224

5282

5340

i '5399

5458

5517

5577

5637

5697

5757

5818

5880

5941

i '6033

6066

6128

6191

6255

6319

6383

6447

6512

6577

1-6643
17321

6709
739i

6775
7461

6842
7532

6909
7603

6977
7675

7045
7747

7"3
7820

7182
7893

7251
7966

i '8040

8115

8190

8265

8341

8418

8495

8572

8650

8728

i -8807

8887

8907

9047

9128

9210

9292

9375

9458

9542

i -9626

9711

9797

9883

9970

0057

0145

0233

0323

0413

2-0503

0594

0686

0778

0872

0965

1060

"55

1251

1348

2-1445

1543

1642

1742

1842

1943

2045

2148

2251

2355

2-2460

2566

2673

2781

2889

2998

3109

3220

3332

3445

2*3559

3673

3789

3906

4023

4142

4262

4383

4504

4627

2-4751

4876

5002

5129

5257

5386

5517

5649

5782

59i6

2*6051

6187

6325

6464

6605

6746

6889

7034

7179

7326

2-7475

7625

7776

7929

8083

8239

8397

8556

8716

8878

2 '9042

9208

9375

9544

97 H

9887

0061

0237

0415

0595

3-0777

0961

1146

1334

1524

I7l6

1910

2106

2305

2506

3-2709

2914

3122

3332

3544

3759

3977

4197

4420

4646

3-4874

5105

5339

5576

5816

6059

6305

6554

6806

7062

37321

7583

7848

8118

8391

8667

8947

9232

9520

9812

4*0108

0408

0713

1022

1335

1653

1976

2303

2635

2972

4-33I5

3662

4015

4374

4737

5107

5483

5864

6252

6646

4-7046

7453

7867

8288

8716

9152

9594

0045

0504

0970

5-I446

1929

2422

2924

3435

3955

4486

5026

5578

6140

5'67i3

7297

7894

8502

9124

9758

0405

Io66

1742

2432

63138

3859

4596

5350

6122

6912

7920

8548

9395

0264

7'ii54

2066

3002

3962

4947

5958

6996

8062

9158

0285

8-1443

2636

3863

5126

6427

7769

9152

0579

2052

3572

9'5 I 44

9-677

9'845

10*02

10*20

10-39

10-58

10-78

10-99

11-20

n-43

i r66

11-91

I2'l6

12-43

12-71

13-00

13*30

13-62

i3'95

14-30

14-67

15-06

15'46

i5*89

16-35

16*83

17*34

17-89

18*46

19-08

1974

20-45

21*20

22*02

22-90

23*86

24-90

26-03

27-27

88 28-64

30-14

31-82

33-69

35-80

38-19

40-92

44-07

47*74

52-08

57-29

63-66

71*62

81*85

95*49

114*6

143*2

191-0

286-5

573*o

From 45 to 90 the natural tangent incteases from i to infinity. A dash over the number
indicates that the whole number part is increased by i.

406

APPENDIX.

NATURAL SINES.

. 3 o

.40

.go

9 e

0000

0017

0035

0052

oo/o

0087

0105

0122

0140

0157

0175

0192

0209

0227

0244

0262

0279

0297

0332

0349

0366

0384

0401

0419

0436

0454

0471

0488

0506

0523

054 1

055*

0576

0593

0610

0628

0645

0663 0680

0698

0715

0732

0750

0767

0785

0802

0819

0837 j 0854

0872

0889

0906

0924

0941

0958

0976

0993

ion

1028

1045

1063

1080

1097

i"5

1132

1149

Il67

1184

1201

1219

1236

I2 53

1271

1288

1305

1323 1340

1357

1374

1392

1409

1426

1444

1461

1478

H95 1513

1530

1547

1564

1582

1599

1616

1633

1650

1668

1685

1702

1719

1736

1754

1771

1788

1805

1822

1840

1857

1874

1^91

1908

1925

1942

1959

1977

1994

2OII

2028

2045

2C62

2079

2096

2113

2130

2147

2l6|

2181

2198

2215

2232

2250

2267

2284

2300

2317

2334

2351

2368

2385

2402

2419

2436

2453

2470

2487

2504

2521

2538

2554

2571

2588

2605

2622

2639

2656

2672

2689

2706

2723

2740

2756

2773

2790

2807

2823

2840

2857

2874

2890

2907

2924

2940

2 957

2974

2990

3007

3024

3040

3057

3074

3090

3107

3123

3HO

3156

3173

3190

3206

3223

3239

3256

3272

3289

3305

3322

3338

3355

3371

3387

3404

3420

3437

3453

3469

3486

3502

35i8

3535

355i

3567

3584

3600

3616

3 6 33

3 6 49

3665

3681

3697

37H

3730

3746

3762

3778

3795

3811

3827

3843

3859

3875

3891

3907

3923

3939

3955

397i

3987

4003

4019

4035

4051

4067

4083

4099

4"5 4!3i

4H7

4163

4179

4195

4210

4226

4242

4258

4274 4289

4305

432i

4337

4352

43 68

4384

4399

4415

443 * 4446

4462

4478

4493

4509

4524

4540

4555

457i

4586

4602

4617

4633

4648

4664

4679

4695

4710

4726

474i

4756

4772

4787

4802

4818

4833

2 9

4848

4863

4879

4894

4909

4924

4939

4955

4970

4985

5000

5i5

5030

5045

5060

575

5090

5i5

5120

5135

5150

5165

5180

5195

5210

5225

5240

5255

5270

5284

3 2

5299

53H

5329

5344

5358

5373

5388

5402

5417

5432

5446

546i

5476

5490

5505

55i9

5534

5548

5563

5577

5592

5606

5621

5635

5650

5664

5678

5693

5707

5721

5736

5750

5764

5779

5793

5807

5821

5835

5850

5864

5878

5892

5906

5920

5934

5948

5962

5976

5990

6004

6018

6032

6046

6060

6074

6088

6101

6115

6129

6i43

6157

6170

6184

6198

6211

6225

6239

6252

6266

6280

6293

6307

6320

6 334

6 347

6361

6374

6388

6401

6414

6428

6441

6 455

6468

6481

6494

6508

6521

6534

6547

6561

6574

6587

6600

6613

6626

6639

6652

6665

6678

42 6691

6704

6717

6730

6743

6756

6769

6782

6794

6807

6820

6833

6845

6858

6871

6884

6896

6909

6921

6934

6947

6959

6972

6984

6997

7009

7022

7034

7046

7059

APPENDIX.

407

NATURAL SINES.

1 -o j -i

.go

45 1 7o7i

7083

7096

7108

7120

7133

7H5

7157

7169

7181

7193

7206

7218

7230

7242

7254

7266

7278

7290

7302

73H

7325

7337

7349

7361

7373

7385

7396

7408

7420

743i

7443

7455

7466

7478

7490

7501

7513

75 2 4

7536

49
50

7660

755*
7672

7570
7683

758i
7694

7593
7705

7604
7716

76i5
7727

7627
7738

7638
7749

7649
7760

5 1

7771

7782

7793

7804

78i5

7826

7837

7848

7859

7869

5 2

7880

7891

7902

7912

7923

7934

7944

7955

7965

7976

7986

7997

8007

8018

8028

8039

8049

8059

8070

8080

8090

8100

8111

8121

8131

8141

8151

8161

8171

8181

8192

8202

8211

8221

8231

8241

8251

8261

8271

8281

8290

8300

83-10

8320

8329

8339

8348

8358

8368

8377

8387

8396

8406

8415

8425

8434

8443

8453

8462

8471

8480

8490

8499

8508

8517

8526

8536

8545

8554

8563

8572
8660

8581
8669

8590
8678

599
8686

8607
8695

8616
8704

8625
8712

8634
8721

8643
8729

8652
8738

8746

8755

8763

8771

8780

8788

8796

8805

8813

8821

8829

8838

8846

8854

8862

8870

8878

8886

8894

8902

8910

8918

8926

8934

8942

8949

8957

8965

8973

8980

8988

8996

9003

9011

9018

9026

9033

9041

9048

9056

9063

9070

9078

9085

9092

9100

9107

9114

9121

9128

9U5

9H3

9150

9157

9164

9171

9178

9184

9191

9198

9205

9212

9219

9225

9232

9239

9245

9252

9259

9265

9272

9278

9285

9291

9298

9304

93"

9317

9323

9333

9336

9342

9348

9354

9361

9367

9373

9379

9385

9391

9397

9403

9409

9415

9421

9426

9432

9438

9444

9449

9455

9461

9166

9472

9478

9483

9489

9494

9500

955

95"

9516

9521

9527

9532

9537

9542

9548

9553

9558

9563

9568

9573

9578

9583

9588

9593

9598

9603

9608

9613

9617

9622

9627

9632

9636

9641

9646

9650

9655

9659

9664

9668

9673

9677

9681

9686

9690

9694

9699

9703

9707

9711

9715

9720

9724

9728

9732

9736

9740

9744

9748

9751

9755

9759

9763

9767

9770

9774

9778

978i

9785

9789

9792

9796

9799

9803

9806

9810

9813

9816
9848

9820
9851

9823
9854

9826
9857

9829
9860

9833
9863

9836
9866

9839
9869

9842
9871

9845
9874

9877

9880

9882

9885

9888

9890

9893

9895

9898

9900

9903

9905

9907

9910

9912

9914

9917

9919

9921

9923

9925

9928

S93Q

9932

9934

9936

9938

9940

9942

9943

9945

9947

9949

9951

9952

9954

9956

9957

9959

9960

9962

9963

9965

9966

9968

9969

9971

9972

9973

9974

9976

9977

9978

9979

9980

9981

9982

9983

9984

9985

9986

9987

9988

9989

9990

9991

9992

9 93

9993

9994

9995

9996

9997

9997 9998

9998

9999

I '000

I OOO

I'OOO I'OOO

I '000

nearly.

nearly, nearly

nearly.

INDEX

Abney's level, 226

Acreage, measurement of, 268

Acres, various, 272

Acute angle, definition of, 97

Adjustment of level, 208

for focus, 212

for parallax, 212
Admiralty chart of declination, 46
Alioth, 362

Almanack, nautical, 359

, Whitaker's, 364
Amsler's planimeter, 272
Aneroid barometer, 236
Angle, definition of, 97

, cosecant of, 102
, cosine of, 102

, cotangent of, 102
, measurement of, 97

, secant of, 102

, sine of, 102

, tangent of, 102

of depression, 174

of elevation, 174
Arc, definition of, 96
Arrows, 10

Atmosphere, temperature of, 245
Atmospheric pressure, 231
Average dip, calculation of, 340

Babbage and Callet's tables of loga-
rithms, 169

Back sight, 205

Barometer, 232
, aneroid, 236
, compensated, 235
, fixed-scale, 237
, portable, 236

Ban and Stroud range-finder, 84

Base line, 113

, measurement of, 1 14

Beam compasses, 89
Beanlands, A., referred to, 365
Bench-mark, 210
Blue prints, 260
Boiling-point thermometer, 238

of water at various pressures, 239

Booking levels, 205

underground survey, 131

Borcher's vane rod, 217
Bore-holes, surveying, 288

, true dip from, 340

Box sextant, 72
Brass protractor, 91

, plotting with, 149

Bridges Lee photo-theodolite, 312
Bullock's levelling-joint, 61

Calculations, logarithmic, 104, 165
Cardboard protractor, 92

, plotting with, 151

Casartelli's dial, 57
Chain, Cornish mine, 6
, engineer's, 6

, Gunter's, 5

, testing, 9

Chaining, method of, 10

, underground, 13

Chaldron, 268

Chambers's tables of logarithms, 105

Characteristic of logarithms, 105

Chord, definition of, 96

( 'ircle, definition of, 96

, graduation of, miner's dial, 54
Clinometer, Abney's, 226

, Macgeorge's, 298

Clinograph, Macgeorge's, 300
Coal Mines Regulation Act, 86, 392

INDEX.

Coal pillars, 315

seams, produce of, 280

, specific gravity of, 280

domination, line of, 210
Colours, 95
Coloured lights, 343
Compass, hanging, 65

, magnetic, 43

, mariner's, 48

, prismatic, 49

, trough, 70

Compasses, 88

, beam, 89

, proportional, 263

Compensated barometer, 235
Connecting surface and underground

survey, 188

by Professor Liveing's method, 199

by suspended wires, 193

by transit instrument, 196

by two shafts, 189

Contents of cuttings and embankments,

282

Contouring, 227
Contour Hues, 227
Co-ordinates, plotting by, 155
Copying plans, 258

by glass table, 259

by photography, 260

Corelation of plans, 369
Cornish acre, 272

mine chain, 6

Cosecant of angle, 102
Cosine of angle, 102
Cotangent of angle, 102
Crown lands, 268
Curvature of the earth, 214
Curves, railway, 94

, setting out, 331

Cuttings, contents of, 282

and embankments, setting out, 328

Damaged land, restoration of, 285
Datum, Ordnance', 174
Declination, magnetic, 43

, Admiralty chart of, 46

Definition of acute angle, 97

of angle, 97

of arc, 96

of circle, 96

Definition of equilateral triangle, 97

of isosceles triangle, 97

of obtuse angle, 97

of parallel lines, 97

of rectangle, 97

of right angle, 97

of right-angled triangle, 97

of square, 97

of trapezium, 97

of triangle, 97

Departure, 157
Depression, angle of, 174
Diagonal eye-pieces, 196
Dial, Casartelli's, 57

, Halden's, 56

, Hedley, 55

, with telescope, 63

, inside vernier, 57

=, joint, 59

, legs, 62

, miner's, 53

, with eccentric telescope, 64

, with outside vernier, 58

Dialling, fast-needle, 133, 137

, loose-needle, 149

Dip, measurement of, 340

Distance measured by tacheometer, 75

by theodolite, 77

Distorted scale, 224
Drawing paper, sizes of, 95

pen, 94

table, 256

Duchy of Lancaster, 268
Dumpy level, 201

Earth's curvature, 214
Earthwork, calculation of, 282

, tables of, 281

Eccentric telescope, 64
Eidograph, 263
Elementary geometry, 98
Elevation, angle of, 174
Embankments, contents of, 282
Engineer's chain, 6
Enlargement of plans, 261
Equilateral triangle, definition of, 97
" Erw," 272

Estate, survey of, 18, 25
Euclid's elements, 96
Exploring for iron ore, 349

INDEX.

411

Fast-needle dialling, 133, 137
Faults, delineation of, 258
Fixed-scale barometer, 237
Focus, adjustment for, 212
Foot wall, 183
Fore sight, 205
French mining plans, 155
Fuller's slide rule, 277

Geographical meridian, 43

, method of finding, 356

Geometry, elementary, 98

, practical, 99

Gilbert, G. K., referred to, 243
Give-and-take lines, 268
Glass table for copying plans, 259
Goodman's planimeter, 273
Gradient, setting out, 326

, telemeter level, 219

Graduation of circle, miner's dial, 54
Gribble, Theodore G., referred to, 239
Gunter's chain, 5

Halden's dial, 56

Hanging dial, surveying with, 147

compass, 65

wall, 183

Heading, setting out underground, 325
Hedley dial, 55

with telescope, 63

Henderson's rapid traverser, 72

, plotting survey made with, 180

, surveying with, 144

Hoffman levelling-joint, 59

Illumination of cross-wires of theodolite,

Improved drawing-table, 256
Inclination of strata, 301
Inclination, measurement of, with dial,

55
Inclination, reduction of length due to,

126, 170
Inclined seams, tonnage in, 281

Inclined seams, pillar in, 317

shafts, measurement of, 252

Inside-vernier dial, 57

Instruments for plotting, 85

Intermediate sight, 205

Irish acre, 272

Iron rails, influence of, 394

Isogonals, 44

Isosceles triangle, 97

Jee's levelling-staff, 204
Joint, dial, 59

Kay's rule for size of pillar, 315

Lamp for theodolite, 71
Lamp-cups, 62
Lancashire acre, 272
Lancaster, Duchy of, 268
Latitude, 157, 359
Lease, term of, 266
Legs, dial, 62

, telescopic, 62

Leicestershire acre, 272
Length of off-sets, 24
Level, Abney's, 226

, adjustment of, 208, 210

, dumpy, 201

, gradient telemeter, 219

, Y, 202

Level-book, method of keeping, 205
Levelling by angles, 220
, barometric, with three barometers

242

by boiling-point thermometer, 238

with barometer, 231

with straight-edge and spirit-level

218

with theodolite, 227

with water-level, 218
Levelling-joint for dial, Bullock's, 61

, Hoffman's, 59

Levelling-screws, 202
Levelling-staff, 203

pit, 203

Life interest, 266

412

INDEX.

Lineal measure, 17

Line of colliination, 210

Lines of equal magnetic declination, 44

Link, 5

Liveing, Professor, referred to, 199, 368

Logarithmic sines, cosines, etc.. 103

Logarithms, 101

, Babbage and Callet's tables of, 169
, Chambers's tables of, 105
, characteristic of, 105

, mantissa of, 105

Longitude, 157, 359

Loose-needle surveying, 129

Macgeorge's instruments for surveying

bore-holes, 298, 300
Magnetic compass, 43

declination, 43

, variation of, 44

meridian, 43, 122, 356

needle, 53

in prospecting, 350

, remagnetization of, 54

Magnetometer, Thalen's, 350
Mantissa of logarithms, 105
Maps, Ordnance, 88
Mariner's compass, 48
Measurement of acreage, 268
of angle, 97

of base-line, 114 ^

of inclination with dial, 55

of true dip, 340

of vertical shafts, 251

with tacheometer, 75

with theodolite, 77

Measures, 17

Measuring heights by angles, 220

in steps, 12

past obstructions, 12

rough ground, 11

Measuring-pole, 7
Measuring-wheel, 8
Mercury, weight of, 231
Meridian, magnetic, 43, 122, 356

, geographical, 43, 357

Metalliferous mine surveying, 181
mine survey, method of plotting,

186

, plan and section, 185

Method of chaining, 10

Mine surveying, metalliferous, 181

Minerals, prospecting for, 349

Miner's dial, surveying on surface with ,

121
Models, 265

Natural scale, 224

sines, cosines, etc., 103

Nautical almanack, 359

Needle, various forms of magnetic, 53

, remagnetizatiou of magnetic, 54

Nolten's instrument for surveying bore-
holes, 290

Nordenstrom, Professor, referred to, 34 ( J
North, method of finding true, 356

Obtuse angle, definition of, 97
Offset scale, 86
Offsets, 22

, accuracy with which measured, 24

, length of, 24

, setting out curve by, 332

Ogle's protractor, 154
Opisometer, 265
Ordnance datum, 174

maps, 88

, north-and-south line from,

369

survey, 117

Outside- vernier dial, 58

Pace, length of, 8
Pacing, 8
Pantagraph, 262
Parallax, adjustment for, 212
Parallel lines, 97

plates, 59, 71

ruler, 89

Pegs, station, 16

Pen, drawing, 94

Pencil, 90

Percy's protractor, 93

Photographic surveying, 307

Pillars of coal, 316

in inclined seams, 317
Pit hills, contents of, 285

INDEX.

413

Pit levelliDg- staff, 203

Hane table, 344

Flanimeter, 272

Plans, copying, 258
, French mining, 155
, importance of accurate, 3

, notes on, 255

, reduction and enlargement of, 261

, uses of, 1

Plotting on squared paper, 163

section from contour lines, 231

survey made with Henderson's

traverser, 180

trigonometrically, 155

with drawing-board and T-square,
163

Pole, measuring, 7

star, 361

Poles, surveying, 14
Portable barometer, 236
Practical geometry, 99
Pricker, 90

Pricking through, 260
Prismatic compass, 49

stadia telescope, 80

, staff for use with, 82, 83
Prismoidal formula, 283
Produce of coal-seams, 280
Proportional compasses, 263
Prospecting for minerals with magnetic

needle, 349
Protractor, 91

, brass, 91
, cardboard, 92

, Ogle's, 154

, Percy's, 93
, vernier, 152

with folding arms, 92

Railway curves, 94

, setting out, 331

pillars, 315
Range-finder, 84
Ranging out survey lines, 14

with theodolite, 118

Rapid traverser, Henderson's, 72
Rectangle, 97
Reduced level, 207

Reduction of length due to inclination,
126, 170

Reduction of plan, 261

Refraction, 214

Right angle, definition of, 97

Right-angled triangle, 97

Rough ground, measuring, 11, 118

Royalty, 266

Riicker, Professor, referred to, 44

Scale, natural and distorted, 224

, offset, 86

Scales, 85

Scaling of coal worked, 271

Scotch acre, 272

Secant of angle, 102

Section plotted from levels, 223

Sectional paper, enlarging or reducing

by, 264

Set squares, 91
Setting out, 319

curves by angles, 335

- by offsets, 331

cuttings and embankments, 328

gradient, 326

tunnels, 329
Sextant, 72
Shaft, setting out, 332
Shafts, measurement of, 251
Shale-heap, contents of, 285
Short's gradient telemeter level, 219
Sine of angle, 102
Sizes of drawrng-paj.er, 95
Slide rules, 277
Solution of triangles, 20, 107
Specific gravity, 279

of various substances, 280

Square, definition of, 97

measure, 17

Staff, levelling, importance of correctly

holding, 213
Stang planimeter, 273
Stanley's theodolite, 69

area-computing scale, 276

Stars, observation of, 361

Station pegs, 16

Statute acre, 272

Steavenson, A. L., referred to, 363

Steel tape, 7

, accuracy of, 8

Straight-edge, 89
Subsidence, 342

INDEX.

Surface surveying with theodolite, 113
Surface works, setting out, 319
Survey book, 19, 25, 30

, trigonometrical survey, 176

, underground, 131

, booking a simple, 19

: , discovery of errors in a, 22

jine ranging out with theodolite,

118

lines, number of, 25

, ranging out, 14

, loose-needle, 129

, Ordnance, 117

, plotting a simple, 19

Surveying bore-holes, 288

, photographic, 307

, railway, 40

,town, 120

underground with theodolite, 142

with chain and poles, method of, 18

with hanging dial, 147

with Henderson's rapid traverser,

144

with plane table, 344

with prismatic compass, 144

with theodolite, 112
Surveying-poles, 14
Surveyor's measures, 17

Tacheometer, 75

, prismatic, 80

Tables, earthwork, 281

of logarithms, Chambers's, 105

, Babbage and Callet's, 169

, traverse, 169

Tangent, 102
Tape, 6

, steel, 7

Telescopic legs, 62
Thalen's magnetometer, 350
Theodolite, Bridges Lee photo, 312
lamp, 71

- legs, 62
, measurement of distances with, 77

, Stanley's, 69

, surface surveying with, 113

, surveying underground, 142

Theodolites, 68

, size of, 69, 112

, transit, 68

Theodolites, use of, 69

Thorpe, Professor, referred to, 44

Tiberg's inclinator, 352

Tonnage, calculation of, 279, 281

Town surveying, 120

Tracings, 95

Transferring plans, 259

Trapezium, 97

Traverser, Henderson's rapid, 72

Triangle, definition of, 97

, equilateral, 97

, isosceles, 97

, right-angled, 97

Triangles, measurement of acreage by,

268

Triangles, solution of, 20, 107
Triangulation, 113
Trigonometrical plotting, 155
Trigonometry, 96, 102
Trough compass, 70
True north, 356

dip, 340
Tunnel shafts, 329

Underground survey, plotting, 149

surveying, 129

with miner's dial, 129

with theodolite, 142

workings, delineation of, 258

Variation of magnetic declination, 43

needle, diurnal, 44

Vernier, explanation of, 66

, inside, 57

, outside, 58

-, protractor, 152

, use of, 57

Warburton, S. A., referred to, 360
Water-level, 218
Welsh acre, 272
Westmorland acre, 272
Whitaker's almanack, 364

Y-level, 202

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