MINE GASES AND VENTILATION
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MINE GASES AND VENTILATION
TEXTBOOK FOR STUDENTS OF MINING, MINING
ENGINEERS AND CANDIDATES PREPARING
FOR MINING EXAMINATIONS
Designed for Working Out the Various Problems That
Arise in the Practice of Coal Mining, as They Relate
to the Safe and Efficient Operation of Mines
BY
JAMES T. BEARD, C.E., E.M.
SENIOR ASSOCIATE KDITOB, COAL AGE; FORMERLY PRINCIPAL SCHOOL OF MINES, INTER-
NATIONAL CORRESPONDENCE SCHOOLS, AND ASSOCIATE EDITOR MINES AND MINER-
ALS, 8CRANTON, PA.; PROFESSOR OF CHEMISTRY, SCHOOL OF THE LACKAWANNA ;
SECRETARY STATE BOARD OF MINE EXAMINERS, IOWA; MEMBER AMERICAN INSTITUTE
MINING ENGINEERS; INSTITUTION OF MINING ENGINEERS, ENGLAND; MINE INSPEC-
TORS' INSTITUTE OF AMERICA; FELLOW AMERICAN ASSOCIATION FOR THE ADVANCE-
MENT OF SCIENCE.
SECON.O EDITION
REVISED* AND ENT,ARGFI>
McGRAW-HILL BOOK COMPANY, INC.
NEW YORK: 239 WEST 39TH STREET
LONDON: 6 & 8 BOUVERIE ST., E. C. 4
1920
T/V 3 0V
COPYRIGHT, 1916, 192J
BY
JAMES T. BEARD
TMK MAPLE PRESS YORK PA
PREFACE TO SECOND EDITION
Any one who has been closely associated with the practi-
cal operation of coal mines will realize quickly the need of
technical knowledge relating to the safe and economical
production of coal. In no department of the work is this
need more urgent than in the ventilation of the mine.
A knowledge of the properties and behavior of' the gases
found or generated in the mine, and the means for effecting
their safe removal or rendering them harmless are of chief
importance, requiring careful study combined with practical
experience in the operation of mines.
Experience, without a knowledge of the theory of mining, is
little better than is the possession of such knowledge by
one who has had no experience in the practical work. Ex-
perience and knowledge must go hand in hand.
The problems relating air, gases, ventilation, safety lamps,
breathing apparatus, rescue work, gas and dust explosions
in mines are treated in a thoroughly practical manner, while
at the same time showing their correct solution. Formulas
must always play an important part in mine ventilation and
their treatment is made as simple as possible.
No effort has been spared to make this volume a standard
of ventilating practice. With this end in view, the various
constants used have been carefully selected and are those
most generally adopted. Particularly is this true of the
tables of weight and measures and the conversion tables
relating to the common and metric systems given in the
Addenda. Their use is recommended.
The present volume, which replaces the little booklet issued
by Coal Age, some time previous, under the same title, will be
recognized as a second edition of that handbook, though greatly
enlarged by the addition of whole new sections on Safety
Lamps, Oils, Breathing Apparatus, Rescue Work and numer-
ous tables, making it a complete treatise on the subject. The
author desires to thank those who have generously lent their
vii
\ tr <i :
viii PREFACE
aid in the work, among whom he would particularly mention
James W. Paul, Mining Engineer, Federal Bureau of Mines,
and J. T. Ryan, Vice-president and General Manager, Mine
Safety Appliances Co., Pittsburgh, Pa.
JAMES T. BEARD.
NEW YORK CITY,
June, 1920.
PREFACE TO FIRST EDITION
In March, 1913, there was started in Coal Age a depart-
ment entitled " Study Course in Coal Mining," and each
week following that date there have appeared two pages of
matter in pocket-book form, which were intended to be later
compiled and published as "The Coal Age Pocket Book."
The publication of these weekly pages was not confined
to a consecutive order, which gave to that department of
Coal Age an increasing and widening interest among readers
and students of technical mining subjects. The matter
treated was in response to the requests of coal-mining men,
who were seeking to know the development of formulas, the
explanation of principles, and the most approved and gener-
ally adopted methods in the practice of coal mining. The
requests that have been received from publishers of similar
technical matter, asking for the privilege of reproducing many
of the pages already published in Coal Age, is sufficient evid-
ence of the technical value of the work.
Recently, so many letters have come from mining men
and from several mining classes who have been studying the
pages as they have appeared each week, asking that the
matter already prepared be published at once in suitable book
form, it has been decided to issue the following sections on
the atmosphere, gases and ventilation of mines. Although it
is not assumed that these sections are in their final form, they
contain much valuable matter that will be appreciated by
practical mining men and students of coal mining.
Coal Age particularly commends this work to mining
students, engineers, mine foremen, assistant foremen and
firebosses, superintendents and managers. The book con-
tains only original matter, prepared at great expense of time
and labor, involving much careful research and experiment.
The author does not hesitate to say that many of the practical
problems in the ventilation of mines, which cannot be solved
ix
x PREFACE
by the usual methods employed, are easily worked by the
potential methods explained fully in these pages. No mine
official or mine employee can afford to be without this edition
in his reference file or library.
JAMES T. BEARD.
NEW YORK CITY,
July, 1916.
CONTENTS
PAGE
CHAPTER I
Am -. 1
The atmosphere — The barometer — Physics of air and gases —
Matter — Measurement — Density and volume — Specific gravity
—Occlusion, emission, diffusion of gases.
CHAPTER II
HKAT 42
Sources and measurement of heat — Chemistry of gases —
Thermochemistry — Hygrometry — Steam.
CHAPTER III
MINE GASES 86
Geological conditions — Common mine gases — Hydrocarbon
gases — Properties and behavior of mine gases — Methane —
Firedamp — Carbon monoxide — Carbon dioxide — Blackdamp —
Afterdamp — Inflammable and explosive mine gases.
CHAPTER IV
EXPLOSIONS IN MINES 116
Definition, gas explosion, dust explosion — Inflammation of gas
— Nature and temperature of flame — Explosion of gas — Coal
dust, its inflammability and influence; effect of stone dust —
Mine explosion, development, causes, mixed lights, electric
mine lamps, prevention of mine explosions.
CHAPTER V
MINE RESCUE WORK AND APPLIANCES 131
Preliminary, entering a mine after explosion, first-aid sugges-
tions— Breathing apparatus, principle, action and requirements
in respiration, development, design and testing of breathing
apparatus — Types of breathing apparatus, Draeger, Fleuss
Proto, Gibbs, Paul — Bureau of Mines, permissible breathing
apparatus — Specifications by the Bureau of Mines — First-aid
work.
CHAPTER VI
THEORY OF VENTILATION 161
Mine ventilation — Problems — Flow of air in airways — Ventil-
ating pressure, how produced and measured, the water gage —
Velocity of air currents — Quantity of air, requirements — Work
or power on the air — Equivalents in measurement — Examples
xi
xii CONTENTS
for practice — -Mine airways — Symbols and formulas — Mine
potential methods — Measurement • of air currents — Examples
for practice — Tandem circulations — Splitting the air current —
Natural division of air — Examples in natural division — 'Pro-
portionate division of air, kinds of regulators — Secondary split-
ting—Theoretical considerations in splitting — Practical problem.
CHAPTER VII
PRACTICAL VENTILATION 248
Conducting air currents, air bridges — General plan of mine —
Distribution of air in the mine — Splitting air currents — Sys-
tems of ventilation — Systems of mine airways.
CHAPTER VIII
MINE LAMPS AND LIGHTING 26$
Principles of construction — Safety lamps, classification and
requirements — Characteristic types of lamps — Special types of
safety lamps — Permissible mine safety lamps — Use and care of
safety lamps — Testing for gas by indicators — The flame test —
Illuminants for safety lamps, oils, etc. — Miner's carbide lamps —
Electric mine lamps — Permissible portable electric mine lamps.
ADDENDA 328
Logarithms — Circular functions, sines and cosines, tangents
and cotangents — Squares, cubes, roots and reciprocals of num-
bers— Circumferences and areas — Denominate numbers —
Weights and meaures — United States and British systems —
Metric systems of weights and measures — Conversion tables
— Conversion of compound units.
INDEX . .415
MINE GASES AND VENTILATION
SECTION I
AIR
THE ATMOSPHERE — THE BAROMETER — PHYSICS OF AIR AND
GASES — MATTER — MEASUREMENT — DENSITY AND VOL-
UME— SPECIFIC GRAVITY — OCCLUSION, EMISSION, DIFFU-
SION OF GASES
Little was known of the aerial envelope that surrounds the
earth, until the researches of Cavendish and Priestley in Eng-
land and Lavoisier in France, in the latter part of the 18th
century showed that air was not an element, as had been
supposed, but a mechanical mixture of gases.
Up to this time, air and all combustible material was be-
lieved to contain a certain substance called "phlogiston,"
which escaped as flame when the substance was burned.
Both Cavendish and Priestley held this phlogistic theory even
after they discovered the complex nature of air. Hence, the
name " dephlogisticated air" was applied to oxygen; while
hydrogen was called "inflammable air" and carbon dioxide
" fixed air."
It remained for Lavoisier to expose this fallacy by showing
that no matter was lost, but the .weight of the products of a
combustion was equal to that of the combustibles burned.
A large number of carefully made analyses showed a prac-
tically constant proportion of the two chief gases of which
air is formed. This seemed to suggest that the oxygen and
nitrogen of the air were chemically united, although the pro-
portion of each gas did not correspond to its combining power
1
2 MINE GASES AND VENTILATION
as determined by the5 Analyses of well-known chemical com-
pounds. The character of air as a mechanical mixture thus
became definitely established.
Besides the two principal gases oxygen and nitrogen that
constitute- the air we breathe, there are other gases whose
presence in the atmosphere is of much vital importance,
although their proportion is small. Of these may be men-
tioned carbon dioxide, water vapor, ammonia, argon and
ozone.
Carbon dioxide is most important, because of its toxic effect
on the human system. This effect, it is stated on the highest
authority, increases with the barometric pressure. Thus, for
example, air containing but 1 per cent, carbon dioxide, at a
pressure of 4, 5 or 6 atmospheres produces the same effect on
the respiratory organs as air containing 4, 5 or 6 per cent, of
the gas at a pressure of 1 atmosphere. In other words, the
true gage of the effect of this gas in inspired air is the percentage
of the gas multiplied by the number of atmospheres.
Water vapor present in the atmosphere breathed has a
marked effect on the vital activities and the consequent de-
velopment of physical energy in the body. In what manner
the relative humidity of the inspired air operates to impair
the physical force has not been fully explained; but experience
has shown that a high degree of humidity in a warm atmos-
phere or climate has an extremely weakening effect on the
human system.
The association of high humidity and temperature marks a
comparatively large amount of water per unit volume of air
and, to that extent, it may be assumed impairs the respiratory
functions of the lungs. The result is to incapacitate men
exposed to such conditions and render them wholly or in part
unfit to perform the required manual or mental labor. These
effects are continually observed in the warm moist atmosphere
of deep mine workings and other similar places.
The Respiratory System. — Respiration is the prime means
of maintaining the vital action in animal organisms. Its
objects are twofold: 1. The oxidation of the organic matter
of the animal tissues with the resulting development of vital
AIR 3
energy. 2. The removal of the carbon dioxide produced in
the process of oxidation. Both of these processes are per-
formed through the medium of the blood.
The Circulation. — Under the action of the respiratory sys-
tem, the blood flows from the heart into and through the
arteries of the body, as water flows through a circulating
pipe system under the action of a pump. The pulsations of
the heart, corresponding to the strokes of the pump, force the
blood through a complex system of arteries and veins to every
portion of the body and limbs.
All the blood does not flow in a continuous circuit, but the
arteries branch, forming separate channels leading to different
parts of the body. The time required to complete a circuit and
return to the heart is obviously widely different, varying from
20 or 30 sec. to one-fourth as many minutes. This is of in-
terest in relation to the time required for poison entering the
blood to be disseminated throughout the system.
Respiratory Action. — The action known as " breathing"
originates, or, at least, is regulated by a nerve center at the
base of the brain from which impulses are transmitted through
the spinal column to the respiratory muscles. By this means
air enters the air cells of the lungs and oxygen, absorbed there-
from by the red corpuscles (haemoglobin) of the blood, is
carried by the circulation to the tissues of the body, where it is
consumed with the production of carbon dioxide. This gas
is absorbed by the blood and carried back through the-veins to
the heart and lungs, where it gives up a portion of its gas,
which enters the lungs and is expelled by each succeeding
exhalation.
While air expired by a healthy adult, at rest, contains from
2 to 3 per cent, carbon dioxide, careful determinations show a
constant production of 5.6 per cent, of this gas in the lungs
when the person is at rest.
Quantity of Oxygen Consumed in Breathing. — A man at rest
consumes 263 cm.3 of oxygen per min., or 263 X 0.06102 = 16
cu. in. per min. and exhales an equal volume of carbon dioxide.
Air exhaled from the lungs contains 2.6 per cent, carbon
dioxide, 18.3 per cent, oxygen, 79.1 per cent, nitrogen. In vio-
4 MINE GASES AND VENTILATION
lent exercise, a man consumes from eight to nine times the
amount of oxygen required when at rest; or, say 128 to 144
cu. in. per min. The exhaled breath may then contain 6.6 per
cent, carbon dioxide and only 14.3 per cent, oxygen.
Depletion of Oxygen in Air, Effect on Life. — Air containing
3 per cent, carbon dioxide can be breathed without discomfort,
even when the oxygen content has been reduced to 16 per
cent.; but 5 per cent, carbon dioxide causes headache, dizzi-
ness and nausea, after a short time. When no carbon dioxide
is present in the air the oxygen content may fall as low as
14 per cent, before much difficulty is experienced in breathing;
but air containing but 10 per cent, is no longer breathable;
but will cause death quickly by suffocation.
Composition of Air. — Normal air is composed chiefly of
oxygen and nitrogen, which are invariably mixed in the fol-
lowing proportions expressed as percentage by volume and
by weight of each of these gases :
TABLE SHOWING COMPOSITION OF NORMAL AIR
By Volume By Weight
Oxygen 20 . 9 per cent. 23 . 0 per cent.
Nitrogen 79 . 1 per cent. 77 . 0 per cent. '
100 . 0 per cent. 100 . 0 per cent.
Air also contains 0.04 per cent, of carbon dioxide (CO2),
together with smaller amounts of argon, ammonia and water
vapor. Atmospheric air, it may be said, is never absolutely
dry or free of moisture. The term "dry air" in respect to the
atmosphere is only a relative expression, meaning that such
air is comparatively dry.
Weight of Dry Air. — The weight of dry air, per unit volume,
varies directly with the pressure it supports, and inversely
as its absolute temperature. There are two formulas for
finding the weight of 1 cu. ft. of air, one being expressed in
terms of the barometer (B), in inches, and the other in terms
of the pressure (p) in pounds per square inch.
1.3273 B
By the barometer, w -
By the pressure, w
0.37 (460 + «)
AIR 5
Moisture in Air. — This subject is fully treated under
"Hygrometry," and it is sufficient here to say that the water
absorbed or held by the air is an invisible vapor that resem-
bles a gas in its behavior, until a sufficient amount is present
to fully saturate the space it occupies. This point of satura-
tion is called the "dew point," because at that point any excess
of vapor condenses and appears as a mist or cloud. The con-
densation is more rapid in contact with a cold surface.
Normal Air. — The term " normal air" in respect tb its com-
position refers to air containing a normal percentage of
oxygen (20.9 per cent.) as given above. When the percentage
of oxygen present is less than normal the air is said to be
" depleted" of its oxygen. This frequently occurs in poorly
ventilated places in mines. The depletion of oxygen is the
result of the various forms of combustion or oxidation that
are constantly taking place in mines, and is also caused by
the absorption of oxygen from the air by the coal.
Mine Air. — Except when diluted with other gases, the air
I'n a well-ventilated mine never shows any appreciable deple-
tion of its oxygen content. Even in poorly ventilated places
it is exceptional to find less than 20 per cent, of oxygen ex-
cept where other gases are being generated in considerable
volume whereby the air is diluted and the percentage of
oxygen correspondingly diminished. This fact has been well
established by innumerable tests of mine air made at different
mines and under varying conditions of ventilation.
THE ATMOSPHERE
The atmosphere is the aerial envelope surrounding the
earth. The term is also used to describe the air or gaseous
mixture filling any given space; as, for example, the mine
atmosphere is the air and gases filling the mine or any por-
tion of the workings.
Atmospheric Pressure. — The weight of the air surrounding
the earth causes a pressure, which decreases as the height
above the surface increases; and the density of the air de-
creases in like manner, with the elevation above sea level.
6 MINE GASES AND VENTILATION
Variation of Atmospheric Pressure. — Atmospheric pressure
at any given place varies irregularly with the condition in
respect to storms; the storm center being always an area of
lower pressure than that surrounding the storm. In this
country, a variation of 2 in. of mercury (say 1 Ib. per sq. in.)
in atmospheric pressure, in 48 hr., is not uncommon.
There is also a regular daily variation, the pressure at-
taining a maximum about 10 o'clock and a minimum at 4
o'clock, morning and evening. There is, likewise, a yearly
variation, the general pressure reaching a maximum, in the
northern hemisphere, in January and a minimum in July.
THE BAROMETER
The Mercurial Barometer. — The pressure of the atmosphere
is measured by the height of mercury column it will support
against a vacuum. The mercurial barometer is a glass tube,
about 36 in. long, closed at one end. This is first filled with
mercury and then inverted. The open end being immersed in
a basin of the same liquid, the mercury in the tube will fall to
a height above the surface .of that in the basin, such that
the pressure of the atmosphere acting on the surface of the
liquid in the basin will support the mercury column in the
tube.
Barometric Pressure. — The pressure of the atmosphere ex-
pressed in inches of mercury is called the barometric pres-
sure. For example, at sea level, the atmospheric pressure
will commonly support 30 in. of mercury column; or is equiva-
lent to a barometric pressure of 30 in.
Calculation of Barometric Pressure. — One cubic inch of
mercury (32°F.) weighs 0.49 Ib. A barometric pressure of
30 in., therefore, indicates an atmospheric pressure of
0.49 X 30 = 14.7 Ib. per sq. in.
which is the normal pressure at sea level.
Calculation of Water Column. — The height of water col-
umn, in feet, the atmospheric pressure will support is found
by multiplying the pressure (Ib. per sq. in.) by 2.3; or dividing
the same by 0.434. Or the barometric pressure, in inches,
AIR
multiplied by one and one-eighth will give the equivalent
water column, in feet. For example, at sea level,
14.7 X 2.3 = 33.8, say 34 ft.
30 X 1>6 = 33.75, say 34 ft.
Principle of the Barometer. — In the mercurial barometer
the pressure of the atmosphere supports the column of mercury
in the tube. The weight of the atmosphere counterbalances
the weight of the mercury
column, which rises as the
atmospheric pressure increases
and falls as it decreases. The
height of the mercury column
is therefore a true index of the
pressure of the atmosphere at
the surface of the earth, at the
moment of taking the
observation.
The principle of the balance
pressure between the air and
the mercury is clearly illus-
trated in Fig. 1, where a glass
tube) closed at one end, is
shown supported in a basin of
mercury. The surface of the
liquid in the basin is shown as
divided into imaginary squares, by lines one inch apart; and
the small arrow-heads represent the pressure of the atmosphere
exerted on each square inch of surface.
Suppose for a moment, that the column of mercury in
the tube is exactly one square inch in cross-section; it is evident,
in that case, that the mercury column takes the place of the
atmospheric pressure on one square inch of surface; and,
since there is perfect equilibrium, its weight is equal to the
pressure of the atmosphere per square inch.
Furthermore, whatever the sectional area of the mercury
column, it is clear that its weight will always equal the atmos-
pheric pressure for the same area of surface. Hence, the
area of mercury column is not important, but its height only.
FIG. l.
8 MINE GASES AND VENTILATION
If the weight of one cubic inch of mercury (0.4911 Ib.)
be multiplied by the observed height of the column of mercury
measured in inches, the product will be the pressure of the
atmosphere, in pounds per square inch, at the place where the
observation was taken. This assumes, that the barometric
reading has been reduced to a standard reading, at a tem-
perature of 32 deg. (Fahr.), which must be done when mak-
ing accurate determinations.
Standard Barometric Readings. — Owing to the fact that
the mercury in the tube expands and contracts more rapidly
than the glass of the tube, the reading of the barometer will
vary slightly for the same pressure, at different temperatures.
In comparing barometric readings taken at different times
and at varying temperatures, it is necessary to carefully
note the temperature when the reading was taken and reduce
the observed reading to a so-called standard reading at 32
deg. F.
Calling the standard reading H, the observed reading h and
the temperature t (Fahr.), the corrected reading is found by
the formula,
H = h(l - 0.0002 0
For example, the standard reading corresponding to 30 in.
of barometer, observed at a temperature of 60 deg. is
30 (1 - 0.0002 X 60) = 29.64 in.
It is even possible, owing to the more rapid expansion or
contraction of the mercury than of the glass, that an observed
fall of barometer may correspond to an actual rise in atmos-
pheric pressure, or vice versa, within about 0.4 in.
Description of the Instrument. — In the illustration, Fig. 2,
is shown the common form of the standard mercurial barom-
eter. The glass tube that contains the mercury column is
here inclosed in the metal case A, to the bottom of which is
attached a somewhat larger casing B. The latter holds a
glass cylinder G terminated at the bottom with a chamois-
skin bag, the whole forming the basin that holds the mercury.
The entire case AB is hung in a truly vertical position, sup-
ported on a substantial base; as shown in the figure. The top
AIR
of the mercury column is observed through the opening O,
in the upper end of the case. In this opening, is arranged a
sliding vernier V, which can be adjusted, by means of the
thumbscrew D, so that its lower edge exactly corresponds with
the top of the mercury column. The position of the vernier
is then read on the scale S marked on the sides of the opening
in the case. This scale is graduated in
inches, but only extends an inch or two
above and an equal distance below the
normal barometric reading. The normal
reading at sea level is about 30 in., and
the scale extends from 26 to 32 inches.
Before setting the vernier, however, it is
necessary to adjust the level of the mercury
in the basin so that it corresponds exactly
with what would be the zero of the ex-
tended scale. To enable this to be done
with precision, there is attached to the
scale a long rod that extends downward
inside the casing. The lower end of the
rod is drawn to a fine point that marks
the zero of the scale.
To adjust the level of the mercury in the
basin, the thumb-screw C is turned. This
screw bears against the bottom of the
chamois-skin bag and operates to raise or
lower the level of the surface of the mer-
cury in the glass cylinder. The adjustment
is complete when the. fine pointed end of
the rod is seen to just prick the surface of
the mercury. The point of the rod is observed through the
glass cylinder above the surface of the mercury.
A thermometer T is shown attached to the metal case. In
making accurate observations it is necessary to reduce all
readings to standard readings.
The Aneroid Barometer. — The aneroid barometer consists
of a metallic case, having a flexible vacuum box within, which
is sensitive to the slightest change in atmospheric pressure.
FlG 2.
10 MINP GASES AND VENTILATION
The corrugated diaphragm forming the back of the vacuum
box is supported against the pressure of the atmosphere by a
steel spring, and its movement under changes of pressure is
communicated to the index hand or needle that registers
the pressure on a dial calibrated to read inches of mercury
corresponding to the readings of the mercurial barometer
under the same pressures (Fig. 3).
FIG. 3.
The aneroid being portable is very useful in ascertaining
quickly differences in elevation of two or more points in
mines and on the surface. The dial of mining aneroids has
two concentric scales. The inner scale of the aneroid shown
in the accompanying figure is graduated to read inches of
mercury, while the outer scale reads feet of elevation. It
has always been the custom, in arranging the graduation of
these two scales, to make the altitude scale read
AIR
11
TABLE SHOWING ATMOSPHERIC PRESSURE AT DIFFERENT
ELEVATIONS AND CORRESPONDING DENSITY OF AIR
FOR DIFFERENT TEMPERATURES
"- eg
ii
•8|2
»ll
&**
c
*o .
II
&
e
go,
If
f
!?
n
Temperature (deg. F.)
-20
0
32
60
100
200
300
400
Weight of dry air (Ib. per cu. ft.)
25,000
11.343
5.571
0.0
0342
.0327
.0306
.0290
.0269
'.0228
.0198
.0175
20,000
13.874
6.814
8.0
0418
.0400
.0373
.0354
.0329
.0279
.0242
.0214
15,000
16.948
8.323
17.0
0511
.0489
.0457
.0433
.0402
.0341
.0296
0262
14,000
17.626
8.656
18.8
0532
.0509
.0475
.0450
.0418
.0354
.0308
.0272
13,000
18.328
9.000
20.7
0553
.0529
.0494
.0468
.0434
.0369
.0320
.0283
12,000
19 053
9.357
22.7
0575
.0550
.0514
.0486
.0452
.0383
.0333
.0294
11,000
19 805
9.726
24.8
0597
.0571
'.0534
.0505
.0469
.0398
.0346
.0306
10,000
20.582
0.107
27.0
0621
.0594
.0555
.0525
.0488
.0414
.0359
.0318
9,000
21 .392
0.505
29.4
0645
.0617
.0577
.0546
.0507
.0430
.0374
.0330
8,000
22 229
0.916
32.0
0670
.0641
.0600
.0567
.0527
.0447
.0388
.0343
7,000
23.088
11.339
34.8
.0696
.0666
.0623
.0589
.0547
.0464
.0403
.0356
6,000
23.975
11.774
37.8
.0723
.0692
.0647
.0612
.0568
.0482
.0419
.0370
5,000
24.890
12.224
41.0
.0751
.0718
.0671
.0635
.0590
.0500
.0435
.0384
4,500
25.360
12.455
42.7
.0765
.0732
.0684
.0647
.0601
.0510
.0443
.0391
4,000
25.837
12.689
44.4
.0779
.0745
.0697
.0659
.0612
.0520
.0451
.0399
3.500
26.322
12.927
46.2
.0794
.0759
.0710
.0672
.0624
.0529
.0460
.0406
3,000
26.813
13.169
48.0
.0809
.0774
.0723
.0684
.0635
.0539
.0468
.0414
2,500
27.315
13.415
49.9
.0824
.0788
.0737
.0697
.0647
0549
.0477
.0422
2,000
27.824
13.665
51.8
.0839
.0803
.0751
.0710
.0659
.0559
.0486
.0429
1,500
28.339
13.918
53.8
.0855
.0818
.0764
.0723
.0672
.0570
.0495
.0437
1,000
28.861
14.174
55.8
.0871
.0833
.0778
.0737
.0684
.0580
.0504
.0445
900
28.966
14.225
56.1
.0874
.0836
.0781
.0739
.0686
.0582
.0506
.0447
800
29.072
14.277
56.4
.0877
.0839
.0784
.0742
.0689
.0585
.0508
.0449
700
29.178
14.329
56.7
.0880
.0842
.0787
.0745
.0691
.0587
.0510
.0450
600
29.296
14.387
57.0
.0884
.0845
.0790
.0748
.0694
.0589
.0512
.0452
500
29.390
14.433
57.4
.0886
.0848
.0793
.0750
.0696
.0591
.0513
.0454
400
29 .496
14 .486
57.8
.0890
.0851
.0796
.0753
.0699
.0593
.0515
.0455
300
29 603
14.538
58.3
.0893
.0854
.0799
.0756
.0702
.0595
.0517
.0457
200
29.710
14.591
58.8
.0896
.0857
.0801
.0758
.0704
.0597
.0519
.0458
100
29.818
14.643
59.4
.0899
.0860
.0804
.0761
.0707
.0600
.0521
.0460
Seal
level/0
29.925
14.696
60.0
.0903
.0863
.0807
.0764
.0709
.0602
.0523
.0462
-500
30.469
14 .963
.0919
.0879
.0822
.0778
0722
.0613
.0532
.0470
- 1,000
31 .022
15.235
.0936
.0895
.0837
.0792
.0735
.0624
.0542
.0479
- 1,500
31.582
15.510
.0953
.0911
.0852
.0806
.0749
.0635
.0552
.0487
- 2,000
32.1-51
15.789
0970
.0928
.0867
.0821
.0762
.0647
.0561
.0496
- 2,500
32.727
16.072
.0987
.0944
.0883
.0835
.0776
.0658
.0572
.0505
-3,000
33.312
16.359
.1005
.0961
.0899
.0850
.0790
.0670
.0582
.0514
- 3,500
33 .903
16.650
.1023
.0978
.0915
.0865
.0804
.0682
.0592
.0523
- 4,000
34.504
16.945
.1041
.0996
.0931
.0881
.0818
.0694
.0603
.0533
-4,500
35.113
17.244
.1059
.1013
.0947
.0896
.0832
.0706
.0613
.0542
- 5,000
35 73C
17.547
.1078
.1031
.0964
.0912
.0847
.0719
.0624
.0551
12
MINE GASES AND VENTILATION
The table on the preceding page is deduced from the de-
terminations of atmospheric density and pressure, under nor-
mal conditions, at different elevations above and below sea
level, as established by the celebrated British astronomer
royal, Sir George Biddle Airy (1840), and the aeronautic ob-
servations of Herschel and Glaisher.
The atmospheric pressures in the third column of the table
are the mean of many direct observations taken at different
altitudes, under normal conditions, and constitute what are
generally known as "Airy's tables."
The temperatures in the fourth column correspond to the
mean observed temperatures, -at different altitudes and are
based on a sea-level temperature of 60 deg. F. They are sug-
gestive of the rate of cooling or fall of temperature with re-
spect to increase of altitude.
The following table shows the mean observed temperatures
of the atmosphere at different altitudes, the rate of fall (deg.
per 1000 ft.) and the estimated average temperature of air
column extending from sea level to each respective altitude
given :
TABLE SHOWING RELATION OF MEAN TEMPERATURE TO ALTITUDE,
IN THE ATMOSPHERE
Altitude or elevation
above sea level, ft.
1
Mean observed
temperature,
deg. F.
Rate of fall in
temperature,
deg. per 1000 ft.
Mean average
temperature of air
column, deg. F.
25,000
0
1.6
24
20,000
8
1.8
29
15,000
17
2.0
35
10,000
27
2.5
42
8,000
32
3.0
45
5,000
41
3.5
50
3,000
48
4.0
54
0
60
The mean average temperature of air column extending
from sea level to any altitude given in the above table makes
it possible to calculate the normal barometric pressure for
that altitude, by means of the following formula :
AIR 13
The application of this formula requires the use of a table of
seven-place logarithms or more. It serves to check the tem-
perature observations at these altitudes.
Bh = 29.926[l ± ^~m]k
in which
Bh = barometric pressure, at altitude h (in.) ;
T = average absolute temperature of air column, ex-
tending from sea level to altitude h (deg. F.);
h = altitude above sea level (ft.).
The sign ± , in the formula, relates to the altitude h, as
being above or below sea level. For altitudes above sea
level, the second term within the brackets is negative and the
minus ( — ) sign must be used. For altitudes below sea level,
this term is positive and the plus (+) sign is employed.
Relation of Drop in Temperature to Altitude. — Approxi-
mately, the fall in temperature (t), in the atmosphere, varies
as the 1.4 root of the height (h) above the sea level; thus,
Applying this principle and assuming a temperature drop
of 6 deg. at an altitude of 1000 ft. above sea level, disregard-
ing the effect of the radiation of heat from the earth, the
mean average temperature (/), for any altitude (h), expressed
in thousands of feet, can be calculated approximately thus :
This formula assumes a normal sea-level temperature of 60
deg. F., which is the first term in the second member of the
equation. The second term of this member accounts for the
fall of temperature corresponding to the increase of altitude;
while the third term expresses the effect of the radiation of
heat from the earth, which varies inversely as the square of
the altitude factor h — 2, probably owing to the influence of
clouds or vapor in the lower atmosphere.
Example. — Let it be required to find the temperature, at an elevation
of 8000 ft. above sea level, corresponding to a normal temperature of
60 deg. at sea level.
14 MINE GASES AND VENTILATION
Solution. — In this case, the altitude expressed in thousands of feet is
h = 8 ; which substituted in the formula gives :
t = 60 - 6 '^8 + (8-^2)2 = 33.4 deg. F.
The mean observed temperature for this altitude as given in the table is
32 deg. F.
Average Temperature of Air Column. — The average tem-
perature of the air column extending from sea level to any
altitude h, expressed in thousands of feet, can be calculated
with close approximation by the formula
1.28 / —
Average temp. = 60 — 3 \/h
The mean average air-column temperature, as calculated by
this formula, can be used to find the corresponding normal
atmospheric pressure by substituting its value, reduced to ab-
solute temperature (T), in the formula
The use of this formula will require a table of seven-place
logarithms or more. In the solution of the following example,
a ten-place logarithmic table was employed.
Example. — Find the mean average air-column temperature correspond-
ing to a sea-level temperature of 60 deg. F., for an elevation of 12,000 ft.
above the sea.
Solution. — In this case, h = 12, which gives for the mean average air-
column temperature
Average temp. = 60 - 3^/12 = 39 deg. F.
The absolute temperature is 460 + 39 = 499 deg.F., abs.
Example. — Calculate the normal atmospheric pressure for an altitude
of 12,000 ft., using the mean average air-column temperature found in
the last example, T = 499 deg. F. abs.
Solution. — Substituting the given values in the formula gives for the
normal atmospheric pressure at this altitude,
Pi2.ooo = 14.696 (l - 53 28^ 499) ^ '°° = 9-359 lb- Per scl- in-
The diagram shown on the following page compiles the
data relating to average observed temperatures at different
elevations, and the calculated heights of the corresponding
AIR
15
water and mercury columns, weight and pressure of air, of
interest to the student of atmospheric conditions.
^ Atmospheric Pressure^
1! l!
\.
£
.c
I
if
olumn(lnches>
11 it
11 |!
£j"> ££
0 ;J
Lb. per so.
Lb.persq.
Water Co,
Maximum L
Mercury C
25,000-
yJS
\
I
I
0"
0.0327
802.2
5.571
12.85
11.343
30,000-
'
1
\
\
P"
0.0393
9812
6.814
15.70
f 3.874
15,000-
(/)
17°
0.0472
1198.5
8.323
19.17
16.948
k,
] 0,000-
c
5
27"
0.0561
1455.4
10.107
23.30
20.582
5POO-
i
41°
0.0659
1760.3
12.224
28.'dO
24.890
1,000-
SeaLeveL
-1.
55'
60"
0.0744
0,0764
2041.1
2116.2
14.174
14.696
32.70
33.90
28JB61
29.925
The Differential Method. — The pressure of the atmosphere,
per unit area, at any altitude x is due to the weight of air
column above such point of observation. Air being com-
pressible, any increment of pressure (dp z), causes a corre-
sponding minus increment of height (—&x)', and, calling the
unit weight of air wx at the altitude x, we have
8px = —wx5x (1)
But the unit weight of air varies with the pressure it sup-
ports. Hence, calling this unit weight and pressure at sea
16 MINE GASES AND VENTILATION
level WQ and po, respectively, and that at any altitude x, wx,
and px, we have
Wx px W0
— = — ; and wx = ~px (2)
W0 Po Po
Substituting this value in equation 1 and dividing both mem-
bers of the equation by px, gives
&5--2U. (3)
Px Po
But, the differential of a quantity divided by the quantity is
equal to the differential of its Naperian logarithm.
Hence, 5 log p* = - — 5X; or 5X = -^° d log px (4)
PO ™o
Then integrating between the limits x = 0, and x = h, remem-
bering that when x = 0, px = p0; and when x = h, px = p^
and subtracting the lower integral from the higher,
fc-0=£(logp0-logpft) (5)
Wo
But the unit weight of dry air at sea level, normal atmos-
pheric pressure (Ib. per sq. ft.), is
(6)
which, substituted in equation 5, gives for the altitude corre-
sponding to any pressure, under normal conditions,
h = 53.28T7 (log po - log Ph) (7)
Or, expressed in common logarithms,
h = 122.6877(log po - log Ph) (8)
For normal atmospheric pressure, at sea level, po = 14.696 Ib.
per sq. in., and log 14.696 = 1.1672; hence
h = 122.68T (1.1672 - log ph)
Or, log ph = 1.1672 - (10)
AIR 17
PHYSICS OF AIR AND GASES
The volume of any given weight of air or gas depends on
two factors — the temperature of the gas and the pressure it
supports.
Effect of Temperature. — -For any given weight of air or gas,
its volume varies directly as its absolute temperature, as-
suming the pressure remains constant.
Effect of Pressure. — For any given weight of air or gas, its
volume varies inversely as the pressure it supports, assuming
the temperature remains constant.
Expansion and Contraction of Air or Gas. — Any change in
temperature or pressure causes a corresponding change in the
volume of the air or gas, as follows :
Increase of temperature causes expansion.
Decrease of temperature causes contraction.
Increase of pressure causes contraction.
Decrease of pressure causes expansion.
Coefficient of Expansion or Contraction. — The coefficient of
expansion is the same as that of contraction. This coefficient
relates to change in volume due to change in temperature and
is practically the same for all gases and air and independent
of the pressure.
The coefficient of expansion of air or gas is the ratio of
the increase in volume to the original volume, for an increase
of one degree in temperature. Since a degree of the Fahren-
heit scale is % of a degree of the centigrade scale, it is evident
that the Fahrenheit coefficient of expansion will be exactly
% of the centigrade coefficient. These coefficients are as
follows: Centigrade, 0.003663; Fahrenheit, 0.002035.
Illustration. — Let it be required to find the increase in volume in an air
current of 100,000 cu. ft. entering a mine at a temperature of 32 deg. F.
and discharged at a temperature of 68 deg. F.
Solution. — The rise in temperature is 68-32 = 36 deg. F. The
increase in volume, calculated by the Fahrenheit scale, is
100,000 X 0.002035 X 36 = 7326 cu. ft.
Or, since 68 and 32 deg. F. correspond to 20 and 0 deg. C., the rise
in temperature is 20 — 0 = 20 deg. C., and the increase in volume,
calculated by the centigrade scale, is
100,000 X 0.003663 X 20 = 7326 cu. ft.
18 MINE GASES AND VENTILATION
Note. — Instead of multiplying by these coefficients, it is
possible to divide by their reciprocals, which are
Fahrenheit, ^^ = 491.4, say 492
Centigrade, ± = 273
These numbers, being divisors, show that air or gas ex-
pands or contracts H?3 of its volume, for each degree rise or
fall in temperature (centigrade); or ^92 of the san.3 volume
for each degree rise or fall in temperature (Fahrenheit) . The
figures point to what has been called the "absolute zero" of
temperature scales as being 273 deg. below freezing ( — 273°C.)
or 492 deg. below freezing (-460°F.).
Absolute Zero. — The so-called "absolute zero" of tempera-
ture scales is based on the observed rate of expansion and
contraction of all gases and air. This rate is practically
M?3 of the volume, per degree centigrade; or 3^92 of the
volume, pier degree Fahrenheit. It is clear that if this rate
continued unchanged a fall in temperature of 273 deg. C., or
492 deg. F., below the freezing point of water, would reduce
the volume of the gas to zero, when all molecular vibrations
would cease, indicating a total absence of heat and pressure.
The absolute zero has therefore been fixed at 273 deg. below
the common zero of the centigrade scale ( — 273°C.), which
corresponds to 460 deg. below zero on the Fahrenheit scale.
The fixing of this point is purely arbitrary, its chiel value being
the facility it affords in the calculation of gaseous volumes
with respect to temperature.
Absolute Temperature. — Absolute temperatures differ from
common temperatures only in being estimated from the
absolute zero. Hence the absolute temperature is obtained
from the common temperature by adding 273 in the centi-
grade or 460 in the Fahrenheit scale; thus,
30 deg. C. = 273 + 30 = 303 deg., absolute.
60 deg. F. = 460 + 60 = 520 deg. absolute.
Relation of Volume and Absolute Temperature of Air and
Gas. — The law commonly known as Gay Lussac's or Charles'
AIR
10
law makes the volume of all gases and air, under constant
pressure, vary directly as the absolute temperature.
This relation is clearly illustrated in Fig. 4, which assumes
a volume of 460 cu. ft. of air or gas at 0 deg. F., corresponding
to the absolute temperature at that point. It will be ob-
served that this volume expands and contracts exactly as the
absolute temperature rises or falls,
except at the lowest temperatures £
approaching the liquefaction of the
air or gas* where the law naturally
fails, owing to the changing state
of the matter.
Relation of Volume and Pressure
of Air and Gas. — For a constant
temperature, the volume of air
and gases varies inversely as the
pressure supported. In this con-
nection, pressure is often estimated
as one, two, three, etc . , atmospheres,
meaning that the pressure sup-
ported by the air or gas is one,
two, three, etc., times the normal
atmospheric pressure at that place.
This is commonly known as Boyle's
or Mariotte's law of volume.
An " atmosphere" is sometimes
incorrectly taken to mean normal
sea-level pressure (14.7 Ib. per sq.
in.). ' Such a meaning of the term,
however, would manifestly limit
its application to sea level, or
furnish an arbitrary standard inconvenient for use.
The term "free air" relates to atmospheric air at any
elevation and for any condition. According to the above rule,
when free air is compressed to two, three or four atmospheres
its volume is reduced to J^, % or Y± of the original volume,
assuming the temperature remains constant. At the same
time, the pressure or tension of the air is increased to two,
60
0-460
AIR LIQUEFIES
\AB50LUTE ZERO
FIG. 4.
20 MINE GASES AND VENTILATION
three or four times the atmospheric or free-air pressure, what-
ever that may have been, assuming always a constant tem-
perature of the air.
The expansion of air, by the same law, is accompanied by
a fall of pressure, the volume ratio being equal to the inverse
pressure ratio, for the same temperature. The pressure re-
ferred to here is the absolute pressure, or the pressure above
a vacuum or zero.
Relation of Absolute Temperature and Pressure of Air and
Gas. — For a constant volume, the absolute temperature of air
and gases varies directly as the absolute pressure.
Volume, Temperature, Pressure of Air and Gas. — The rela-
tion of the volume (v), pressure (p) and absolute temperature
(T), for a given weight of air or gas is expressed simply by
the following formulas :
Constant pressure Constant temperature Constant volume
02 = T* Vz = pi p2 = Tz
vi Tl vi p2 pi ' Ti
The relations of volume, temperature and pressure of air
and gas depend on two main conditions: 1. The gas may or
may not be free to expand. 2. Heat may or may not be added
or taken from the gas.
Addition of Heat. — Two cases may arise, as follows :
(a) If the air is confined (constant volume) the rise in
temperature is more rapid, since all the heat is then trans-
formed into heat energy or internal work, and the pressure
rises accordingly.
(6) If the air is free to expand (constant pressure) the
rise in temperature, for the same addition of heat, is much
less rapid. In this case, the air in expanding performs ex-
ternal work against the pressure it supports. A part of the
heat added is thus absorbed in doing outside work while the re-
mainder, only, is available for internal work and manifest
as heat energy, thus causing a lesser rise of temperature.
Work of Expansion of Air. — When air is expanded by the
addition of heat the external work performed can be calculated
in two ways, as follows :
1. On a heat-unit basis, by subtracting the heat absorbed,
AIR 21
per pound of air, per degree rise in temperature, for constant
volume, from the heat, per pound, per degree, for constant
pressure; and multiplying this difference, which is the heat
converted into external work, by the foot-pounds per heat
unit; thus, since 1 B.t.u. = 778ft.-lb.,
Heat, per Ib.-deg. (sp. heat, const, pressure) ............ 0.2374 B.t.u.
Heat, per Ib.-deg. (sp. heat, const, volume) ............. 0. 1689 B.t.u.
Heat, per Ib.-deg., available for external work ......... 0.0685 B.t.u.
External work, per Ib.-deg ......... 0.0685 X 778 = 53.29 ft.-lb.
2. The external work performed in the expansion of air, per
pound, per degree, can be calculated, also, very simply by
multiplying the volume of 1 Ib. of dry air, at 1 deg. F., abso-
lute, and 1 Ib. per sq . in. .pressure (0.37 cu. ft.), by 144, the
number of square inches in 1 sq. ft. ; thus,
External work, per Ib.-deg. . . . 0.37 X 144 = 53.28 f t.-lb.
Adiabatic Expansion and Compression. — When there is no
addition of heat in the expansion, or no loss of heat in the com-
pression of air or gas, the relations of volume, temperature
and pressure follow other laws than those previously given.
Such expansion or compression is described as "adiabatic,"
meaning no passage (of heat) in or out of the gas.
In adiabatic expansion, there being no addition of heat,
the increase in volume is at the expense of the internal en-
ergy and a fall of temperature is the result, which is accom-
panied also by a fall of pressure.
In adiabatic compression, there being no loss of heat, the
internal energy is augmented by the heat of compression, and
the result is an increase of both temperature and pressure.
Adiabatic Formulas. — The following formulas express the
relation of volume (v)f pressure (p) and absolute tempera-
ture (T), for any given weight of air or gas, when expanded
or compressed without gain or loss of heat. In actual prac-
tice it is only possible to approximate adiabatic expansion
or compression:
7117 v* = /T\\ 2-469 p, = (T,\ 3-
vi \Tj Pl \Tj
2=yj .
Pi W
^ /tM
T, W
P?°'288
22 MINE GASES AND VENTILATION
It is important to observe that adiabatic expansion or
compression always involves a change in temperature. Where
the temperature is maintained constant, by adding heat in
expanding, or extracting heat (cooling) in compressing, the
change in volume is described as "isothermal" expansion
or compression. In practice, it is only possible to approximate
isothermal conditions in the expansion or compression of air
or gas.
The application of the above formulas necessitates the use
of logarithms.
MATTER
Definition. — Matter is the tangible substance occupying
space and endowed with properties that give to it form, motion
and other distinguishing characteristics, by virtue of an all-
pervading or impressed subtle force generally described as
electrical.
Divisions of Matter. — Until recently, the ultimate or small-
est conceivable division of matter was assumed to be the
atom (Dalton, 1808). Later researches of radio-active sub-
stances have developed the infinitely smaller particles which
have been termed "electrons" (Stoney, 1891) and "corpus-
cles" (Thomson, 1897). The electron is assumed to be a
minute particle of matter having a negative charge of elec-
tricity; and its mass is variously estimated at from H?oo to
/^ooo °f the mass of the atom of hydrogen.
The chemical divisions of matter are the familiar atoms
and molecules.
Properties of Matter. — The universal attribute of all matter
is that described as "mass," which may be simply defined as
amount of matter. By virtue of its assumed electrical state
or condition, all matter is endowed with certain tangible and
measurable qualities or properties, such as weight, inertia,
density, elasticity, cohesion, divisibility, impenetrability, ex-
pansion, contraction.
Matter undergoes many changes but is absolutely inde-
structible.
Law of Attraction. — The universal law of attraction is that
every particle of matter attracts every other particle of mat-
AIR 23
ter, the force of attraction varying inversely as the square of
the distance between the particles.
Terrestrial attraction is the attraction that the mass of
the earth exerts on the mass of a body. This is commonly
called "gravitation" and the attractive force, the "force of
gravity" or simply "gravity."
Form or State of Matter. — All matter exists in one of three
different forms, namely, solid, liquid, or gaseous. The same
matter may pass from one form or state to another owing to
a change in density.
Molecular State. — The molecular theory assumes that all
matter, solid, liquid or gaseous, in respect to its physical con-
dition, is composed of molecules, each complete in itself. It
is assumed that these molecules are subject to two opposite
or opposing forces known as the "molecular forces" of at-
traction and repulsion.
Molecular attraction, acting to bind the molecules of mat-
ter together, is in obedience to the common law of attraction
in all matter.
Molecular Repulsion, acting to drive the molecules of mat-
ter apart, is the result of a state of incessant molecular vibra-
tion, which produces the effect called "heat."
Solids. — Matter in the solid state is characterized by a
greater or less rigidity of its molecules. The force of molecu-
lar attraction is here stronger than that of repulsion, and the
molecules are held in a firmer grasp.
Liquids. — -In the liquid state, the forces of attraction and
repulsion are about evenly balanced, and the molecules move
freely among each other.
Gases. — In the gaseous state, the repulsive forces are in the
ascendency and the molecules are driven so far apart that the
density of the matter is reduced to that of a gas.
Liquids and gases are both fluids, which is a general term
applied to any form of matter other than a solid.
Illustration. — Ice, water and steam furnish a good illustra-
tion of how the same matter can pass successively from the
solid to the liquid and gaseous states. In the passage
from one state to another, there is no change in the matter
24 MINE GASES AND VENTILATION
itself, the difference being due to the heat condition of the
mass.
In the passage from solid to liquid, or from liquid to gas
or vapor, heat is given out; and, vice versa, heat is absorbed
when a gas or vapor becomes a liquid, or a liquid becomes a
solid. The change is thus a heat condition only.
Vapors and Gases.— The term vapor properly describes the
gaseous condition of most substances that, at ordinary tem-
peratures, exist as liquid or solid ; or a gas at or near its point
of liquefaction. The term thus has a suggestive meaning of
the possible liquid or solid state of the substance now in the
gaseous state.
The term gas, on the other hand, is a general term that re-
lates solely to the gaseous condition of matter; and is thus
more properly applied to those substances that, at ordinary
temperatures, exist as gas; although they may be liquefied or
solidified by a decrease of temperature and an increase of
pressure.
Thus, we speak of air, oxygen, hydrogen, nitrogen, carbon
dioxide, methane, etc., as " gases," in contrast to steam (water
vapor) and the vapors of such volatile liquids and solids as
naphtha, benzine, camphor and other similar substances.
Vaporization takes place at all temperatures; and in many
instances, a substance will pass directly from the solid to the
gaseous condition, without becoming liquid.
Mass, Volume, Density. — Since mass is amount of matter,
the mass (M) of a body is the quantity of matter it contains,
which is determined by the volume (V) of the body and
the density (D) of the matter. The relation of these ele-
ments is expressed by the formula
M = VD
Then, considering a unit volume (V = 1), it is evident that
the "unit of mass" is equal to the "unit of density." In other
words, whatever is taken as the accepted unit or standard of
density is also the unit and standard for the measurement of
mass, which is the ultimate unit.
AIR 25
MEASUREMENT
The valuation and comparison of the various forms and condi-
tions of matter and the estimation of physical phenomena are
made by reference to three general standards of measurement,
namely, distance, force and time. There are many modifica-
tions and combinations of these three elemental standards.
Distance. — This includes the measurement of length, sur-
face and volume, all of which are derived from the same
standard of measure.
Force. — -All measurement of force is based on the attractive
force exerted by the earth on an assumed unit of mass at the
surface (sea level), in any given latitude. Mass thus becomes
the true unit in this measurement; but being intangible, the
adopted unit is the pound, which represents a certain definite
mass, taken as the "unit of mass," for purposes of measure-
ment. A force is measured by the effect of its action on a
known mass. There are two conditions: 1. Static condition
(mass fixed, immovable), force applied to a body produces
pressure, weight. 2. Dynamic condition (mass free to move)
force produces motion, velocity.
Under these two conditions, there are, therefore, two units
of force. The unit of measure for static force is the pound,
while the unit of measure for dynamic forces is the force
that will produce a unit of velocity in a unit of mass, in a
unit of time. In other words, the force that will increase the
rate of motion of a unit mass, by a unit distance, in a unit time.
Application. — Applying these units of measure, the weight
(W) of a body, expressed in pounds, is the static force (F)
acting on the body, due to gravity.
Hence, in statics,
F = W (1)
In dynamics, the force (Fi) producing motion is measured
by the mass (M) of the body and the velocity (v) produced
per unit of time. Hence, in dynamics,
Fi = Mv . (2)
The velocity produced may be constant or accelerated.
Constant velocity is the distance passed over in a unit of
26 MINE CASES AND VENTILATION
time. Acceleration is the gain in velocity per unit of time.
A constant force, as gravity, acting on a body free to move
produces a uniform acceleration; that is to say the gain in
velocity, each unit of time, is constant.
Assuming a falling body, the force producing motion is
the weight (W) of the body, and the gain in velocity per
unit of time (acceleration due to gravity, g) is the velocity
produced in the mass (M). Hence, in falling bodies,
W = Mg (3)
and
M = Wg (4)
which enables the calculation of the mass of a body from its
weight.
Combining formulas (2) and (3),
Fi v
W = g
Hence a force acting to produce motion in a body bears the
same ratio to the weight of the body, as the acceleration due
to the force bears to the acceleration due to gravity. Or, ex-
pressed as a proportion,
FnWi-.v.g (6)
Time. — The element of time is important in the estimation
of velocity and power. For example, to traverse the same
distance in one-half the time will require twice the velocity.
Likewise, to perform the same work in one-half the time will
require twice the power.
Special Units. — There are numerous other units of limited
significance; such as units of capacity, pints, quarts, gallons,
barrels, etc.; units of currency, cents, dimes, dollars, etc.;
circular units, degrees, radians, etc.; electrical units, amperes,
volts, ohms, watts, etc.
Compound Units. — Many units of measure are composed of
two or more simple units. The following are examples:
Unit velocity — (distance) -f- (time) Ft. per sec., or ft. per min.
Unit work— (distance) X (force) Ft.-lb.
Unit power — (distance) X (force) -f- (time). . .Ft.-lb. per min.
AIR 27
The above are only given as samples of many similar com-
pound units; such as inch-pounds; miles per hour; gallons per
hour; cubic feet per minute; pounds per cubic foot; tons per
acre; foot-acres, etc.
All of these, it will appear, are derived from the simple units
of distance, force, time, or the special units to which reference
has been made.
Energy. — Energy, in physics, is capacity to perform work.
It is the vitalizing force that is manifested in matter by the
familiar agencies of heat, light, electricity, magnetism, molecu-
lar attraction, chemical affinity, etc., all of which are equally
convertible, one into the other, without loss.
The physical agencies or forms of energy just mentioned
are each and all convertible into mechanical motion, which,
again, can be reconverted into heat, light, electricity, and mag-
netism. This fact gives rise to what is called the "mechanical
equivalent" in reference to heat.
Forms of Energy. — Energy is of two kinds that differ from
each other only in the sense that one (kinetic) is actual and
present, while the other (potential) is possible only.
Kinetic energy (E) is the energy possessed by a body by
virtue of its motion. The force producing an acceleration (/)
in a mass (Af), or the " living force" in the body (momentum),
is Mf. The acceleration (/) being uniform or the velocity in-
creasing uniformly, the distance increase, per unit of time is
//2, and the work performed in producing this acceleration is
stored in the body as " kinetic energy," by virtue of which the
body would continue to move at the velocity imparted, till
opposed by some force. The energy stored per second is cal-
culated by the formula
Kinetic energy, E = Mf X | = J^M/2
Potential energy is the energy that is possessed by a body
by virtue of the position or state in which it is held or re-
strained so that motion cannot take place till the restraining
force is removed. Examples of bodies having potential energy
are, a suspended ball, a confined spring, etc.
28
MINE CASES AND VENTILATION
A common method of making physical measurements for
the estimation of weight, volume, heat, etc., is by reference
to some adopted standard. All such measurements are rela-
tive and are frequently termed " specific." Such, for example,
are specific gravity, specific volume, specific heat, etc. The
atomic weight of elements is often called specific weight.
The Elements. — An element is a substance that has not, as
yet, been resolved into parts of a different nature and is,
therefore, regarded as being composed wholly of one kind
of matter or simple, in contrast with a compound, which
is composed of two or more elements or kinds of matter.
The following table gives the more important elements,
together with their chemical symbols and specific or atomic
weights :
TABLE OF THE MORE IMPORTANT ELEMENTS
International Committee (1910)
Elements
Sym-
bols
Atomic
weights
Elements
Sym-
bols
Atomic
weights
H = l
0 = 16
H = l O = 16
Aluminum
Antimony
Al
Sb
A
As
Ba
Bi
B
Br
Cd
Cs
Ca
C
Ce
Cl
Cr
Co
Cb
Cu
F
Au
He
H
I
Ir
Fe
Pb
Li
Mg
26.9
119.3
39.6
'74.36
136.27
206.34
10 91
79.28
111.5
131 .75
39.77
11.9
139.13
35.18
51 .58
58.5
92.75
63.06
18.85
195.62
3.97
10
125.9
191.56
55.4
205.44
6.94
24.13
27.1
120.2
39 9
74.96
137.37
208 0
11 .0
79.92
112.4
132.81
40.09
12 0
140.25
35.46
52.0
58.97
93.5
63.57
19.0
197.2
4.0
1.008
126.92
193.1
55.85
207.1
7.0
24.32
Manganese
Mercury
Molybdenum
Mn
Hg
Mo
Ni
N
Os
0
Pd
P
Pt
K
Ra
Rh
Se
Si
Ag
Na
Sr
S
Te
Tl
Sn
: Ti
W
u
v
Zn
Zr
54.49
198.4
95 23
58.21
13 9
189.37
15.88
105.9
30.77
193.44
38.78
224.6
102.08
78.6
28.1
107.02
22.82
86.92
31.81
126.48
202 37
118.05
47 72
182.53
236.59
50.79
64.85
89.88
54.93
2CO 0
96.0
58.68
14.01
190.9
16 0
106.7
31.0
195.0
39.1
226.4
102.9
79.2
28.3
107.88
23.0
87.62
32 07
127.5
204.0
119.0
48.1
184.0
238.5
51.2
65.37
90.6
Arsenic
Barium
Bismuth
Boron
Nickel
Nitrogen
Osmium
Oxygen
Palladium
Phosphorus
Bromine
Cadmium
Calcium
Carbon
Cerium
Potassium
Radium
Rhodium
Selenium
Silicon
Silver
Chlorine
Chromium
Cobalt
Columbium
Copper
Fluorine
Gold
Sodium
Strontium
Sulphur
Tellurium
Thallium .
Tin
Titanium
Helium
Hydrogen
Iodine. .
Iridium. . . .
Tungsten
Uranium
Vanadium
Zinc
1 Zirconium 6
ylron
Lead
Lithium
Magnesium
AIR 29
The preceding table contains only 56 out of the 80 or more
elements that have been discovered, many of which are so
rare as to be of little practical importance. The values of
the atomic weights are given referred both to hydrogen as
unity and oxygen as 16. The heavy type indicates the values
commonly used in the study of mine gases.
DENSITY AND VOLUME
Density Defined. — The term " density " refers to the amount
of matter in a given volume or space. The commonly adopted
measure of density is the ratio of the weight of a body to its
volume or the space it occupies, as expressed by the formula :
~ ._, weight
Density = — r--
volume
In a general sense, the term density has thus come to
mean the weight per unit volume. For example, the density
of water is commonly understood to mean its weight per
cubic foot (62.4283 lb., max. dens., 4°C.).
Specific or Atomic Volume. — These terms have reference to
an assumed unit volume for all gases, which unit is the as-
sumed vo'.ume of a single gaseous atom.
Avogadro's Law of Gaseous Volume. — This law may be
stated briefly and clearly as follows :
At the same temperature and pressure all gaseous molecules
are assumed to be of the same size.
With a few unimportant exceptions, this law applies to all
gases, whether simple or compound. It holds true for all mine
gases and is important in the calculation of the relative volume
of gases concerned in chemical reactions.
Molecular Volume. — Chemical hypothesis assumes that the
molecules of simple substances each contain two atoms only,
while the molecules of a compound substance may contain any
number of atoms, but never less than two. Notwithstanding
this multiplicity of atoms, Avogadro's law makes all gases,
with a few unimportant exceptions, to contain the same num-
ber of molecules, per unit volume, when measured at the same
temperature and pressure. In other words, measured at the
30 MINE GASES AND VENTILATION
same temperature and pressure, all gaseous molecules are of
the same size.
Calculation of Density. — The elements form the basis of all
relative measurements with respect to volume, density and
weight. For example, the density of air, referred to hydrogen
as unity (H = 1), can be calculated from the relative weights
and volumes of oxygen and nitrogen, which are the chief
constituents of air. The composition of pure air, by volume,
is practically, oxygen (O), 20.9 per cent.; nitrogen (N), 79.1
per cent. Then, since the atomic weight of oxygen is 16 and
that of nitrogen 14, the relative weight of 100 volumes of air,
referred to hydrogen as unity, is found as follows:
Oxygen, 20.9 X 16 = 334.4
Nitrogen, 79.1 X 14 = 1107.4
Air, 100 vol's = 1441.8
Therefore, one volume of air is 1441.8 -r- 100 = 14.418 times
as heavy as the same volume of hydrogen; or, the density of
air referred to hydrogen is 14.418.
The percentage composition of pure air, by weight, is
readily calculated from the above figures; thus:
Oxygen, (334.4 X 100) -r- 1441.8 = say 23.2 per cent.
Nitrogen, (1107.4 X 100) -r- 1441.8 = say 76.8 per cent.
SPECIFIC GRAVITY
The specific gravity of a substance — solid, liquid, or gas —
is the ratio of the weight of that substance to the weight
of another substance taken as a standard, volume for volume;
„ wt. of unit vol. of substance
W/vj /IT* — T — - - -, •
wt. of unit vol. of standard
Comparison of Standards. — Hydrogen, air and water are
the three standards commonly used in the determination of
the specific gravity of gases, liquids and solids. The relative
densities of these standards are as follows :
Air (dry) is 14.418 times as heavy as hydrogen, at the same
temperature and pressure, volume for volume.
AIR 31
Water (max. density, 4°C.) is 773 times as heavy as dry
air at 32 deg. F., bar. 29.92 in.; and 815 times as heavy as dry
air at 60 deg. F., bar. 30 in., volume for volume.
Standard for Gases. — The standard adopted for gases is air
or hydrogen, of the same temperature and pressure as the gas.
Standard for Liquids and Solids. — The standard adopted for
liquids and solids is water at maximum density. Except
where great accuracy is desired, the weight of 1 cu. ft. of
water is taken as 62.5 Ib. Exactly, 1 cu. ft. of pure water, at
maximum density weighs 62.4283 Ib.; or 1 cu. in. weighs
252.89 grains = 0.03613 Ib.
Calculation of the Specific Gravity of Gases. — Since air is
14.4 times as heavy as hydrogen, at the same temperature
and pressure, the specific gravity of a gas, referred to air as
unity, can be calculated by dividing one-half of its molecular
weight by 14.4. For example, the molecular weight of carbon
dioxide is 44; therefore, 44 -f- 2 = 22, and 22 -r- 14.4 = 1.528.
The actual specific gravity is 1.529.
Finding Specific Gravity of Gases. — A glass globe, any con-
venient size, is first weighed empty (air exhausted), w; then
full of air, w\\ and, lastly, filled with the gas, w*: the tem-
perature and pressure remaining constant.
wz — w
Sp. gr. =
Finding Specific Gravity of Liquids. — A glass-stoppered bot-
tle is first weighed empty, w; then filled with water w\\ and,
lastly, filled with the liquid, w%. The specific gravity is then
calculated by the above formula for gases. Or, the specific
gravity is determined by a graduated float (hydrometer).
Finding Specific Gravity of Solids. — Weight of the solid in
air, wmj weight immersed in water w\. The weight of the
water displaced is then w — 10 1, which has the same volume
as that of the solid.
Sp. gr.
32 MINE GASES AND VENTILATION
SPECIFIC GRAVITIES AND UNIT WEIGHTS OF SOLIDS AND LIQUIDS
Substance
Average
specific gravity
(water = 1)
Average
weight (Ib.
per cu. ft.)
Alcohol pure
0 793
49 5
commercial
Aluminum
0.834
2 66
52.1
166 0
Asphalt (1 to 1.8)
1 4
87 0
Brass, east (7.8 to 8.4)
8.1
506 0
rolled
8 4
525 0
Brick, pressed
2 4
150 0
common, hard
2.0
125 0
Brickwork, masonry (1.8 to 2.3)
Bronze (8.7 to 8.9)
Clay (1.8 to 2.6)
8.8
2.2
110 to 140
550.0
137 5
Coal, anthracite (1.3 to 1.7)
bituminous (1.2 to 1.5)
cannel, gas coal (1.18 to 1.28) . . . .
lignite, brown coal
Coke, loose piled
1.5
1.3
1.23
1.1
93.75
81.25
76.88
68.75
20 to 25 0
Concrete
2.3
144.0
Copper, cast (8.6 to 8.8)
rolled (8.8 to 9)
8.7
8 9
543.0
556 0
Earth, dry, loose to well rammed
moist, loose to well rammed. . . .
wet, flowing mud
76 to 95 . 0
78 to 96.0
105 to 115
Granite (2 56 to 2 88)
2 72
170 0
Gold, cast (18.29 to 19.37)
18 83
1176 0
Gravel, loose
95 to 100
Gypsum, ground or calcined, loose
well shaken
Ice
0 92
56.0
64.0
57 5
Iron, cast (6.9 to 7.4)
rolled
wrought, sheet (7.6 to 7.9)
Lead (11.3 to 11.47)
Lime (quicklime)
ground, loose (66 Ib. per bus.) ....
Limestone
7.2
7.68
7.8
11.38
1.5
2.7
450.0
480.0
485.0
710.0
93.75
53.0
168.0
Marble (2.5 to 2.8)
Mercury (32 deg. F.)
(62deg. F.)..
2.65
13 . 593
13.555
165.0
850.0
847.0
AIR 33
Pitch 1.155 72.0
Platinum 21.6 1348.0
Rosin 1.1 68.67
Sand, dry 100.0
wet. 130.0
Sandstone (2.1 to 2.7) 2.4 150 . 0
Shale (2.4 to 2.8) 2.6 162.0
Silver 10.5 655.0
Slate (2.7 to 2.9) 2.8 175.0
Steel (7.8 to 7.9) 7.85 490.0
Sulphur 2.0 125.0
Tallow 0.94 58.7
Tar 1.0 62 . 5
Tin, cast (7.2 to 7.5) 7.35 459,0
Traprock 3.0 187.0
Water (max. density, 4°C.) 1.0 62.428
(pure, 62°F.) 0.999 62.366
(pure, 212°F.) 0 . 958 59 . 806
sea, average 1 • 028 64 . 176
WEIGHT OF WOODS (DKY, SEASONED)
Lb. per cu. ft.
Ash, white 38
Birch 41
Cedar, white 23
red 35
Cherry 42
Chestnut 41
Elm 35
Ebony 76
Hemlock 25
Hickory 53
Mahogany, Spanish 53
Honduras 35
Maple 49
Oak, live 59
white 48
black, jack, etc 35 to 45
Pine, white. 25
yellow, Northern 34
Southern 45
Poplar (cottonwood) 33
Spruce 25
Sycamore 37
Walnut 37
3
34 MINE GASES AND VENTILATION
SPECIFIC GRAVITIES AND WEIGHTS OF OILS
Sp. Gr.
Lb. per Gal.
Animal — lard
0.916
7.64
sperm (pure)
. 0 . 880
7.34
whale
0.925
7.72
Vegetable — cottonseed
.... 0.923
7.70
linseed (raw)
0 . 933
7.79
(boiled)
0.780
6.51
olive
0.917
7.65
rape (colza)
0.915
7.63
Mineral — petroleum (crude)
0 . 77-1 . 06
gasoline
.. 0.700
5.84
kerosene (coal oil)
... 0.800
6.68
naphtha
0.730
6,09
Use of Specific Gravity. — To find the weight of any volume
of a substance, multiply the unit weight of the standard, by
the specific gravity of the substance, and that product by the
given volume; or, expressed as a formula,
Wt. = unit weight of standard X sp. gr. X vol.
For example, taking the average specific gravity of anthra-
cite coal as 1.5 the weight of this coal underlying 1 acre
(43,560 sq. ft.) of land, for a thickness in the seam of 1 ft.;
or, as we say, per foot-acre, in long tons (2240 Ib.) is
62.5 X 1.5 X 43,560
00,n = 1823 long tons
ZZ^±(J
Or, taking the weight of 1 cu. ft. of air (60°F., bar. 30 in.)
as 0.0766 Ib., since the specific gravity of carb.on dioxide (CO2)
referred to air as unity is 1.529, the weight of 100 cu. ft. of
this gas, at the same temperature and pressure, is
0.0766 X 1.529 X 100 - 11.712+ Ib.
OCCLUSION, EMISSION, DIFFUSION OF GASES
Occlusion of Gases. — The occlusion of gases in coal or other
solid substances is the result of the absorptive power of the
substance for that particular gas. For example, platinum,
palladium, gold and other metals, as well as coal (carbon),
absorb varying quantities of hydrogen, nitrogen, oxygen,
the hydrocarbon and other gases.
AIR 35
The most common examples of occlusion are the absorp-
tion of hydrogen by platinum; and of methane, nitrogen, oxy-
gen and carbon dioxide by coal and coal dust. The law that
governs this absorption is unknown. The occluded gas is
often held very strongly by the substance with which, how-
ever, it is not combined.
The occluded gases of coal seams were probably produced
in the metamorphic processes that formed the coal; and their
absorption (occulsion) in the solid formation may have re-
sulted in the oxidation, to a limited extent, of the carbon-
aceous matter that was being transformed into coal. Such
reactions, if taking place in the measures, together with the
consolidation that accompanied the formation, would natur-
ally give rise to the observed pressures of occluded gases.
The pressure of occluded gases in coal formations is very
variable, depending not only on the conditions attending the
occlusion; but to an even greater extent on the impermea-
bility of the infolding strata, which has prevented the escape
of the gases from the measures where they are formed.
Transpiration, Emission of Gases from Coal. — The gases
occluded in coal exude from its exposed surface in the same
manner as perspiration exudes from the pores of the skin.
The term " transpiration" relates to the motion of a gas
through a capillary tube and thus describes the emission of
gas from coal.
The velocity of transpiration is according to a different
law from that governing the rate of the diffusion of gases.
For the same gas, the rate of transpiration varies directly
as its pressure or density, and inversely as the length of the
tubes through which it must pass. The velocity of trans-
piration is independent of the material that forms the tube,
but is affected by temperature, being less for a higher tem-
perature, and vice versa.
RELATIVE VELOCITY OF GASES (AIR = 1)
Gas Rel. Veloc. Gas Rel. Veloc.
Hydrogen 2 . 066 Carbon dioxide 1 . 237
Olefiant gas 1 . 788 Carbon monoxide 1 . 034
Methane '. 1 .639 Nitrogen 1 . 030
Hydrogen sulphide 1 .458 Oxygen 0.903
36 MINE GASES AND VENTILATION
The above table gives the relative rates or velocities with
which the common mine gases transpire, referred to the rate
for air as unity. The actual rate of emission of gas from
coal, however, will depend chiefly on the pressure of the gas
in the coal Any sudden fall in barometric pressure is always
accompanied with an increase in the emission of gas from
the coal, but the increase is almost inappreciable.
Diffusion of Air and Gases. — If the molecules of all matter
are assumed to be in a constant state of vibration, it nat-
urally follows that the vibratory movement or force will vary
with the density of the matter. In the case of fluids — air,
gas, or liquid — 'the molecules are free to move among them-
selves, which is not true of solids, whose molecules, normally,
hold fixed relations to each other.
If the densities of two fluids are equal, the vibratory force
is equal in each fluid; and, at the plane of contact of the two
fluid bodies, action and reaction are equal between the vi-
brating molecules and there is no tendency of these fluids to
mix. The laws governing the mixture of liquids is not as
simple as in the case of gases, owing chiefly to numerous
physical properties of liquids that modify and retard the
diffusive action. While the diffusion of gases into each other
and into air is extremely rapid, the diffusion of liquids is
often very slow and in some cases does not take place at all
because of the counteracting forces.
Gases of different densities diffuse into each other and
into air. The action is extremely rapid and conforms very
closely to certain well defined laws. The diffusion of mine
gases into the mine air and into the air current is an impor-
tant feature of mine ventilation.
Law of Diffusion of Air and Gases. — By a similar experi-
ment, showing the diffusion of hydrogen into oxygen, Graham
found that for every volume of oxygen that passed into the
hydrogen, four volumes of the hydrogen passed into the oxy-
gen, the ratio thus being 4:1, in this case. But, calling the
density of hydrogen unity or 1, that of oxygen is 16 and
A/16 = 4. This and other similar experiments, all confirming
the first; led Graham to propound the following law:
AIR 37
Graham's Law. — The velocity or rate of diffusion of air
and gases varies inversely as the square roots of their densi-
ties or specific gravities, density being referred to hydrogen
as unity, and specific gravity to air.
This law is simply expressed by the following formulas:
Rel. vel. of diffusion (hydrogen : gas) = — -=
V density of gas
Rel. vel. of diffusion (air : gas) = — -j=.
V sp. gr. of gas
Experiment. — The diffusion of air and gases has been shown
to take place through certain substances with practically the
same rapidity as when they are in direct contact. The dif-
fusion of hydrogen into air is well shown by the following
simple experiment. A glass tube, say 18 or 20 in. long, 1-in.
bore, is closed at one end with a plug of plaster. The tube is
first filled with the gas and the open end then immersed be-
neath the surface of a basin of mercury. At once the mercury
is observed to rise slowly in the tube to take the place of the
hydrogen that is passing out through the plug and escaping
into the air. Investigation shows, however, that while hydro-
gen has passed out of the tube, some air has passed into the
tube, as there remains in the tube a mixture of hydrogen and
air.
Illustration of Graham's Law. — The relative velocities or rates of
diffusion of different gases (hydrogen = 1) are calculated from their
respective densities referred to hydrogen as unity ; thus,
Methane (CH4); density, 8; Rel. vel. = —L = -±— = 0.354 (H = \]
•y/g Z.828
In like manner, the relative velocities or ratio of diffusion of different
gases (air = 1) are calculated from their respective specific gravities,
referred to air as unity; thus,
Carbon dioxide (CO2); sp. gr., 1.529; v = , = 0.808
*-529 (Air = l)
Methane (CH4); sp. gr., 0.559; v = -y== = 1.337
V 0.559
Experiment Showing Effect of Diffusion. — An interesting
experiment, showing the relative increase or decrease of the
volume of gas contained in a vessel owing to diffusion, is
38
MINE GASES AND VENTILATION
illustrated in Fig. 5. The velocity of diffusion of methane
being greater than that of carbon dioxide, when the latter
is contained in the inner jar and the former in the outer bell-
jar the bladder is expanded, because the methane passing
into the small jar is greater in volume than the carbon di-
oxide passing out. Again, the bladder is depressed when
the gases change places.
FIG. 5.
Composition of Gases. — Gas, like other material substances,
is composed of the elements of matter. A simple or element-
ary gas is composed wholly of one kind of matter; as hydro-
gen (H), oxygen (O), nitrogen (N), etc.
Many gases, like many solids and liquids, are compound.
The molecule of such a gas is formed by the chemical union
of two or more atoms of different elements; as methane
(CH4), carbon monoxide (CO), carbon dioxide (CO2), etc.
A gaseous mixture is a mechanical mixture of different
gases, simple or compound. These gases are mixed together
in any proportion, but are not chemically united.
Firedamp is a mechanical mixture of a combustible gas
or gases with air in such proportions as to render the mix-
ture inflammable or explosive. The term, however, is gener-
ally understood to mean an inflammable or explosive mixture
AIR 39
of methane (CH4) and air. In English and other foreign text-
books, the term "firedamp" is improperly applied to any mix-
ture of explosive gas and air, without regard to whether the
proportions are within the inflammable or explosive limits of
the gas. Such a mixture will not inflame or explode and is
not, properly speaking, a firedamp mixture.
Percentage Composition by Weight. — By the "percentage
composition" of a compound is generally meant the percent-
age, by weight, of each element composing the substance.
This is calculated from the ratio of the relative weight of
each constituent element to its molecular weight. The term
" percentage composition" may refer, however, to the per-
centage by volume of each constituent element.
For example, a molecule of methane (CH4) contains one
•atom of carbon and four atoms of hydrogen. Then, since the
atomic weight of carbon is 12 and that of hydrogen 1, the
molecular weight of methane is 12 -h (4 X 1) = 16, and the
percentage composition of this gas is calculated as follows:
Carbon(C); atomic weight, 12; relative weight ..... 12
Hydrogen (H4) ; atomic weight, 1 ; relative weight, 4X1= 4
Molecular weight of gas ... ....... 16
The percentage of each constituent element is then :
Carbon. ................. i%6 (100) = 75 per cent.
Hydrogen ................. £{6 (100) = 25 per cent.
100 per cent.
In like manner, a molecule of carbon dioxide (CO2) con-
tains one atom of carbon and two atoms of oxygen. The
atomic weight of carbon being 12 and that of oxygen 16, the
molecular weight of carbon dioxide is 12 + (2 X 16) = 44, and
the percentage composition of the gas is found as follows:
Carbon (C); atomic weight, 12; relative weight ..... 12
Oxygen (O2); atomic weight, 16; relative weight, 2 X 16 =32
Molecular weight of gas ........... 44
40 MINE GASES AND VENTILATION
The percentage composition is then :
Carbon i%4 (100) = 27.27 per cent.
Oxygen s%4 (100) = 72.73 per cent.
100.00 per cent.
Percentage by Volume. — When applied to a gaseous mix-
ture the term " percentage composition" is usually taken as
referring to the percentage by volume of the several gases
forming the mixture, unless otherwise stated. The method of
making this calculation is given on page 102.
Specific Gravity of Mixtures of Gases. — When different vol-
umes of gases of different densities are uniformly mixed the
density of the mixture is determined by dividing the combined
weight of the mixed gases by the total volume of the mixture,
which will give the unit weight or the weight per unit of
volume of the mixture.
The actual weights of the gases may not be known, but
only the volume of each gas and its density or specific gravity.
In that case, multiply the density of each gas by its volume,
add the products together and divide the sum by the total
volume of the mixture; the quotient obtained will be the
required density of the mixture.
Or, in like manner, multiply the specific gravity of each
gas by ts volume, and divide the sum of these products by
the total volume of the mixture, and the quotient obtained
will be the specific gravity of the mixture.
Calculation. — For illustration, let it be required to calculate the
specific gravity of flashdamp, which has a theoretical composition of
1658 volumes of methane (CH4) to each 1000 volumes of carbon dioxide
(CO-.). The process is as follows:
Volume Sq.gr.^I6^1-
Methane 1658 X 0.559 = 926.8
Carbon dioxide. . . 1000 X 1.529 = 1529.0
2658 2455.8
The specific gravity of the flashdamp is then calculated, in accordance
with the above rule, as follows:
relative wt. (air = 1) 2455.8 7
Sp. gr. = j—-. — y-r — =—* ~ 0-go = 0.924, nearly
v - relative total vol. 2658
AIR 41
Calculation Based on the Law of Diffusion of Gases. — If
two gases diffuse into each other, directly, without being di-
luted with air, the volumes of the gases are inversely propor-
tional to the square roots of their densities or specific gravities.
This law makes it possible to calculate the density or specific
gravity of such an undiluted mixture of two gases directly
from their densities or specific gravities, without reference
to their relative volumes. This is accomplished by means of
the formula
_ a Vfr + b\/g
Va + VT
in which D = density or specific gravity of the mixture; a and
6 = the corresponding densities or specific gravities of the
two gases, respectively.
Calculation. — For illustration, let it be required to calculate the
specific gravity of flashdamp (undiluted mixture of methane and carbon
dioxide) directly from the specific gravities of these gases; methane =0.559
and carbon dioxide = 1.529. The process is as follows:
Q.559VL529 + 1.529\/a559
Sp.gr. = 7 — — ; — - = 0.924
A/0.559 + Vl.529
SECTION II
HEAT
SOURCES AND MEASUREMENT OF HEAT — CHEMISTRY OF
GASES — THERMOCHEMISTRY — HYGROMETRY— STEAM
Definition. — Heat is DOW understood to be a form of motion.
All matter is assumed to be in a state of molecular vibra-
tion. The rapidity of the vibration depends on the degree of
heating of the mass. The theory assumes that the amplitude
of the vibrations or the swing of the molecules is greater as
the density of the mass is less. This would lead naturally
to the conclusion that pressure, which increases the density
of matter, will decrease the amplitude and increase the rapid-
ity of vibration.
Heat is thus assumed to be a form of energy, the ampli-
tude and rapidity of the vibrations being functions, respec-
tively, of pressure and velocity, the factors of energy, in
mechanics. The theory is well supported by observed facts,
as the blow of a hammer or the friction of rubbing surfaces
alike develop heat.
Heat in Bodies. — Assuming that heat is a form of molecu-
lar vibration, which varies in different kinds of matter, it
is clear that each kind of matter has its own peculiar ca-
pacity for heat. This is shown to be the case by the fact
that different bodies when exposed to the same source of
heat are heated differently. For example, when equal weights
of water and mercury are exposed, for the same time, to the
same heat it is found that the mercury becomes much hotter
than the water. When water and mercury at the same tem-
perature are allowed to cool in the atmosphere, the air ab-
sorbing the same heat from each, the mercury is found to
cool much quicker than the water. It is evident that the
water absorbs more heat and gives out more heat, per pound,
42
HEAT
43
than the mercury, for the same change in temperature. In
other words, water has a greater heat capacity.
Temperature. — The temperature of any body or mass of
matter is the degree of heat it can radiate or impart to other
bodies or matter with which it is in contact; or, in other
words, the degree of sensible heat of the body. It is not the
amount of heat in the body; as water contains 20 times the
quantity of heat contained in an
equal weight of mercury, at the
same temperature.
The temperature of a body de-
pends on the quantity of heat the
body contains, per unit weight, and
its heat capacity. A body or
matter having a large heat capacity
will have a comparatively low
temperature.
How Temperature is Measured.
Temperature is measured by the
thermometer, an instrument so
common as to need no description.
The principle involved is that the
expansion of the liquid contained
in the bulb of the thermometer
is much magnified in the capillary
stem. Any rise of temperature is
thus clearly indicated by a cor-
responding rise of the liquid in the
stem and a fall of temperature is
likewise accompanied by the con-
traction of the liquid, which drops
in the stein.
Two Scales. — There are two principal thermometer scales,
the Fahrenheit and the centigrade. These are each cali-
brated with reference to the melting of ice and boiling of water.
As shown in the illustration, Fig. 6, these points are marked
32 and 212 deg., respectively, in the Fahrenheit, and 0 and 100
deg., respectively, in the centigrade scale. Thus, 180 deg. of
FIG. 6.
44
MINE CASES AND VENTILATION
the former correspond to 100 deg. of the latter; or the ratio is
9:5.
TABLE SHOWING CORRESPONDING VALUES OF THE FAHRENHEIT SCALE
FOR EACH FIVE DEGREES OF THE CENTIGRADE SCALE
c.
' F.
C.
F.
C.
F.
C.
F.
C.
F.
-50
--58
200
392
450
842
700
1292
950
1742
-45
-49
205
401
455
851
705
1301
955
1751
-40
-40
210
410
460
860
710
1310
960
1760
-35
-31
215
419
465
869
715
1319
965
1769
-30
-22
220
428
470
878
720
1328
970
1778
-25
-13
225
437
475
887
725
1337
975
1787
-20
- 4
230
446
480
896
730
1346
980
1796
-15
+ 5
235
455
485
905
735
1355
985
1805
-10
14
240
464
490
914
740
1364
990
1814
- 5
23
245
473
495
923
745
1373
995
1823
0
32
250
482
500
932
750
1382
1000
1832
+5
41
255
491
505
941
755
1391
1005
1841
10
50
260
500
510
950
760
1400
1010
1850
15
59
265
509
515
959
765
1409
1015
1859
20
68
270
518
520
968
770
1418
1020
1868
25
77
275
527
525
977
775
1427
1025
1877
30
86
280
536
530
986
780
1436
1030
1886
35
95
285
545
535
995
785
1445
1035
1895
40
104
290
554 540
1004
790
1454
1040
1904
45
113
295
563
545
1013
795
1463
1045
1913
50
122
300
572
550
1022
800
1472
1050
1922
55
131
305
581
555
1031
805
1481
1055
1931
60
140
310
590
560
1040
810
1490
1060
1940
65
149
315
599
565
1049
815
1499
1065
1949
70
158
320
608
570
1058
820
1508
1070
1958
75
167
325
617
575
1067
825
1517
1075
1967
80
176
330
626
580
1076
830
1526
1080
1976
85
185
335
635
585
1085
835
1535
1085
1985
90
194
340
644
590
1094
840
1544
1090
1994
95
203
345
653
595
1103
845
1553
1095
2003
HEAT
45
c.
F.
C.
F.
c.
F.
C.
F.
C.
F.
100
212
350
662
600
1112
850
1562
1100
2012
105
221
355
671
605
1121
855
1571
1105
2021
110
230
360
680
610
1130
860
1580
1110
2030
115
239
365
689
615
1139
865
1589
1115
2039
120
248
370
698
620
1148
870
1598
1120
2048
125
257-
375
707
625
1157
875
1607
1125
2057
130
266
280
716
630
1166
880
1616
1130
2066
135
275
385
725
635
1175 ! 885
1625
1135
2075
140
284
390
734
640
1184
890
1634
1140
2084
145
293
395
743
645
1193
895
1643
1145
2093
150
302
400
752
650
1202
900
1652
1150
2102
155
311
405
761
655
1211
905
1661
1155
2111
160
320
410
770
660
1220
910
1670
1160
2120
165
329
415
779
665
1229
915
1679
1165
2129
170
338
420
788
670
1238
920
1688
1170
2138
175
347
425
797
675
1247
925
1697
1175
2147
180
356
430
806
780
1256
930
1706
1180
2156
185
365
435
815
685
1265
935
1715
1185
2165
190
374
440
824
690
1274
940
1724
1190
2174
195
383
445
833
695
1283
945
1733
1195
2183
To convert Fahrenheit (F.) readings into centigrade (C)
or vice versa, the following formulas are useful :
F = % C + 32
C = % (F - 32)
Example — (a) What are the readings of the Fahrenheit scale corre-
sponding to 40°, and — 10° centigrade?
Solution —
F = % X 40 + 32 = 104°F.
F = % ( - 10) + 32 = 14°F.
Example — Convert — 4 F. and 50 F. into centigrade readings.
Solution —
C = % (- 4 - 32) = - 20 C.
C = % (50 - 32) = 10 C.
Readings above zero are plus ( + ) and those helow zero minus ( — ).
46 MINE GASES AND VENTILATION
SOURCES AND MEASUREMENT OF HEAT
Sources of Heat. — In a sense the sun is the original source
of most of the heat of the solar system — in other words, the
sun is the power house of that system. It may be said that
much of the terrestrial life and activity emanates from the
sun. The source of the sun's heat is understood to be the
chemical and possibly electrical activities that are constantly
developed in its huge mass and radiating heat, light and elec-
trical energy.
The same chemical and possibly electrical activities are
taking place to a less degree in the mass of the earth, creating
internal heat. Both the radiated heat of the sun and the
internal heat of the earth are natural sources of heat.
Besides these natural or physical sources of heat, there
are the mechanical sources of heat, such as friction, impact
and pressure. These each develop heat as the result of force
applied mechanically.
Sensible Heat. — The heat that is accompanied by a change
of temperature when absorbed or given out by a body is called
"sensible heat," because it is manifest to the senses.
Latent Heat. — When matter passes from the solid to the
liquid state, or from the liquid to the gaseous state, the
change is always accompanied by the absorption of a con-
siderable amount of heat, although the temperature remains
constant. The heat thus absorbed is called "latent heat," it
being absorbed in performing the work of driving the mole-
cules of matter farther apart than they were in the previous
state. This heat is again given out when the matter passes
from a gas to a liquid, or from a liquid to a solid.
Chemical Heat. — Theory assumes that chemical heat is the
result of the chemical affinity of material atoms for each other,
by which they are drawn and held in more or less close con-
tact and union. This condition is in harmony with the notion
of "atomic heat," explained elsewhere, and suggests the esti-
mation of the heat of formation, or heat of combination, as
the result of chemical union.
In contrast with atomic heat, molecular heat is akin to
specific heat and representative of the heat capacity of a sub-
stance, or the quantity of heat a particular substance will
HEAT 47
absorb, per unit weight, per degree of rise in its temperature.
Theory assumes that all heat of any nature is a vibratory
state of atoms or molecules and, as such, is convertible into
or created by other forms of energy.
The molecular heat of a substance is found by multiplying
a gram-molecule (page 54) of the substance by its specific heat.
Combining Heat. — All matter is assumed to possess a cer-
tain definite heat energy peculiar to itself, which is expressed
in heat units, per unit weight of substance and called the
"combining heat" of the substance.
Heat of Formation. — In the combining of atoms to form
compound molecules, a neutralization of the energies of the
combining atoms causes either an evolution or an absorption
of heat, the molecule formed then possessing an amount of
heat called "heat of formation" or "heat of combination."
Heat Due to Friction, — Friction is caused by one body rub-
bing against another, whereby a molecular vibration is set up
in the two bodies, as manifested by the heat generated.
Heat Due to Impact. — The impact of one body against an-
other likewise sets up a molecular vibration in the bodies, which
is manifested by the heat generated.
Heat Due to Pressure. — Pressure applied to a body having
a degree of elasticity, or being compressible, forces the mole-
cules of matter closer together, which reduces the intermo-
lecular space and, as a result, there being no loss of molecular
energy, the speed of vibration is increased in proportion as the
space is diminished arid heat is developed.
Transformation of Heat Energy. — Heat energy of any na-
ture, whether chemical or physical, is convertible, without
loss, into mechanical energy measured in foot-pounds, which
is the "mechanical equivalent of heat."
At each change of state in matter heat is either absorbed
and becomes latent in the mass, or is given out and becomes
sensible, causing a rise of temperature in the surrounding
medium. Heat is absorbed when a solid becomes a liquid or
a liquid becomes a gas, the change being one in which the
density of the mass is made less. On the other hand, heat is
given out when a gas is condensed to a liquid or a liquid to a
solid, the density of the mass being then increased.
48 MINE GASES AND VENTILATION
Heat of Fusion. — The change from a solid to a fluid state
is described as "liquefaction" when solution takes place, or
"fusion" if the solid is melted. The heat absorbed in the
latter case is called "heat of fusion."
Liquefaction may take place as the result of the absorp-
tion of moisture from the air, the substance dissolving either
wholly or in part in the water absorbed. Such a substance
is said to be "deliquescent."
Solution takes place when a solid disappears in a liquid
in which it is immersed. The solid is "dissolved," in the
liquid, which is called the "solvent."
In any case of liquefaction or fusion heat is absorbed and
becomes latent in the liquid, causing a seeming loss or dis-
appearance of heat. When a solid is dissolved in a liquid the
liquid is cooled provided no chemical reaction takes place,
which might produce heat.
Heat of Vaporization. — The formation of vapor or the
change from a solid or liquid to a gaseous state is known as
"vaporization" and the heat absorbed and rendered latent in
the vapor is called "heat of vaporization" or frequently "heat
of evaporation," especially when the vapor is formed by boil-
ing the liquid.
Heat of Condensation. — When a gas or vapor is condensed
to a liquid or a liquid is frozen or condensed to a solid the
latent heat of the gas, vapor or liquid is given out and appears
as sensible heat, which causes a rise of temperature. The
heat given out is called "heat of condensation" and is exactly
equal to the heat of vaporization or the heat of fusion or
liquefaction, as the case may be.
Total Heat in a Body. — By this is meant the total heat
absorbed by a body in a given change of temperature or state.
For example, the total heat in 1 Ib. of water, in passing from
ice at 32 deg. F. to steam at 212 deg. F. is as follows:
Latent heat of fusion of ice, from and at 32°F 144 B.t.u.
Sensible heat absorbed by water, 32° to 212°F 180 B.t.u.
Latent heat of vaporization, from and at 212°F. . . 970.4 B.t.u.
Total heat absorbed. . . 1294.4 B.t.u.
HEAT 49
The total heat of steam at any temperature or pressure
is usually estimated from water at 32 deg. F.; thus the total
heat in steam (water vapor) at 212 deg. F. is 180 + 970.4 =
1150.4 B.t.u. This is the heat in steam at atmospheric pres-
sure at sea level (14.7 Ib. per sq. in.). When steam is gener-
ated in a boiler, its temperature increases with the pressure.
Effect of Pressure on Fusion. — Pressure acts to oppose
increase of volume. Some substances, as water, for example,
expand when passing from the liquid to the solid state and
an increase of pressure therefore lowers the freezing point
of such substances. The decrease of atmospheric pressure at
high altitudes facilitates the formation of ice, though to a
less degree than other more potent causes.
On the other hand, some substances, as wax, contract when
solidifying, and an increase of pressure then acts to raise the
freezing point or point of solidifying. In other words, an in-
crease of pressure acts to assist the melting of wax and similar
substances, while it retards that of ice.
Melting Points of Substances. — The melting point of sub-
stances depends largely on their purity and treatment. For
this reason different authorities often give different values
for the same substance. The table on the following page
gives the approximate melting points and the heat of
fusion, in British thermal units, per pound, for the
substances named.
Difference Between Melting and Freezing Points. — The
melting point of a substance does not always correspond ex-
actly with its freezing point, even at the same pressure. The
melting point of ice is more uniformly constant than the
freezing point of water, and for this reason is taken to indi-
cate the zero of the centigrade scale (32°F.).
The solidification of a liquid is generally accompanied with
crystallization, and the formation of the crystals is often
delayed in a quiet medium, so that the temperature of water
free of air may fall as low as 5 deg. F. when perfectly quiet
and not freeze. But if the water at this low temperature be
stirred or jarred the whole will instantly change to ice or
become solid.
50 MINE GASES AND VENTILATION
MELTING POINTS AND HEATS OF FUSION OF SUBSTANCES
Substance
Melting point,
deg. Fahr.
Heat of fusion,
B.t.u. per Ib.
Aluminum
Beeswax
Copper
Gold
1211
148
1980
1947
138.6
76.1
77.4
Ice ...
32
144 0
Iron, cast (white)
Iron, cast (gray)
2000
2400
41.4
59.4
Iron, wrought
Lead
Nickel
2820
620
2600
9.0
8 3
Platinum
Silver
Spermaceti
3100
1764
120
48.6
37.9
66 5
Steel
2462
36.0
Sulphur
Tallow
235
92
16.2
Tin
450
25 6
Zinc
786
50.4
To express heat of fusion in calories per kilogram:
B.t.u. per Ib. X % = cal. per kg.
. Effect of Pressure on Vaporization. — Pressure acts to re-
tard vaporization. An increase of pressure, therefore, raises
the boiling point of water and other liquids. For the same
reason a decrease of pressure lowers the boiling point of
liquids. At an elevation of 10,000 ft. above sea level, under
normal atmospheric conditions, pure water boils at 193 deg.
F., and at an elevation of 15,000 ft. the boiling point, for the
same normal atmospheric conditions, is reduced to 185 deg. F.
Vaporization, Evaporation, Betting. — Vaporization is a
general term relating to the formation of vapor, or the change
from a solid or liquid state to a vaporous or gaseous con-
dition, without regard to whether the change is slow or rapid.
The term "evaporation" relates to the slow vaporizing of
a solid or liquid that takes place at its surface when the
latter is exposed to an atmosphere that is not fully saturated.
HEAT 51
The evaporation of a liquid may also be caused by the applica-
tion of heat.
The term "boiling" refers to the violent ebullition that
takes place throughout the mass of a liquid, caused by the
formation of vapor in the liquid and its escape to the surface.
Boiling results from the application of heat to the liquid, or
may result from a sudden decrease of pressure.
Boiling Points of Liquids. — A liquid boils when raised to
such a temperature that the tension of its vapor is equal to
the pressure at its surface. At this point the liquid becomes
vapor. The term "boiling point," as commonly used, however,
refers to atmospheric pressure at sea level, unless otherwise
stated. The following table gives both the freezing and the
boiling points of a few liquids of interest in mining:
FREEZING AND BOILING POINTS OF LIQUIDS
T ioiljj Freezing Point, Boiling Point,
Deg. Fahr. Deg. Fahr.
Alcohol (ethyl) ..'. -202 172
Ammonia. . . .' —106 140
Linseed oil -18 597
Mercury —38 . 676
Nitroglycerine 45
Measurement of Heat. — Although heat, as already ex-
plained, is a condition of matter and not a tangible quantity, it
is possible to measure its intensity or degree through the effect
it produces, referred to certain established standards of meas-
urement. The most convenient standard is the heat energy
that will cause a rise of one degree in the temperature of a
unit weight of pure distilled water at its point of maximum
density. This is called a "heat unit" or "thermal unit" and
is a quantity capable of exact measurement.
Heat or Thermal Units.— There are several heat units in
common use, the principal ones being the British unit and
the French unit. A third unit that is largely used combines
these two units.
The British Thermal Unit.— The British thermal unit
(B.t.u.) is the quantity of heat required to raise the tempera-
52 MINE GASES AND VENTILATION
ture of 1 Ib. of pure distilled water at maximum density, 1
deg. of the Fahrenheit scale.
The French Thermal Unit or Calorie. — This is the quantity
of heat required to raise the temperature of 1 kg. of pure dis-
tilled water at maximum density, 1 deg. of the Centigrade
scale.
The Pound Calorie. — This is the quantity of heat required
to raise the temperature of 1 Ih. of pure distilled water, at
maximum density, 1 deg. of the Centigrade scale.
Conversion Formulas —
B.t.u. X 0.252 = Calories
B.t.u. X % = Pound-calories
Calories X 3.968 = B.t.u.
Calories X 2.2046 = Pound-calories
Pound-calories X % B.t.u.
Pound-calories X 0.4536 = Calories
Note. — Since 1 Ib. (avoirdupois) = 0.4536 kg.; and
1 deg. (Fahr.) = % deg. (Cent.),
1 B.t.u. = 0.4536 X % = 0.252 cal.
Again, since 1 kilogram = 2.2046 Ib. (avoir.); and
1 deg. (Cent.) = '% deg. (Fahr.),
* 1 cal. = 2.2046 X H = 3.968 B.t.u.
These simple calculations show the derivation of the constants used
in the above formulas.
Transmission of Heat. — The condition known as "heat" is
transmitted in any one of the three following ways: 1. By
radiation. 2. By conduction. 3. By convection.
Heat is radiated in straight lines in all directions from its
source and is then called "radiant heat." It is transmitted
through the vibrations of the ether that fills all space and the
radiated heat is imparted in varying degree to all matter in
its path. Heat so imparted to a body is said to be "absorbed "
by the body.
When heat travels through a body the process of transmis-
sion is known as "conduction." Heat thus spreads through-
out the mass as a solid.
The spread of heat in any fluid (liquid or gas) is through the
circulation caused by the unequal distribution of the heat.
This mode of transmission is known as "convection."
HEAT 53
Mechanical Equivalent of Heat. — Since heat is assumed to
be a form of energy, it must be capable of performing work,
which is expressed in foot-pounds. This has given rise to
what is properly called the " mechanical equivalent of heat."
It is the theoretical amount of work expressed in foot-pounds
or kilogram-meters per unit of heat absorbed.
The values of the several heat units are as follows:
Foot-pounds Kilogram-meters
1 British thermal unit 778 107 . 5
1 calorie 3087 426 . 8
1 pound-calorie 1400 193 . 5
The reverse of these values is as follows:
B.t.u. Calories Lb.-cal.
1000 foot-pounds 1 . 285 0 . 324 0 . 714
100 kilogram-meters 9 . 297 2 . 343 5 . 168
Atomic Heat. — -An important relation has been found to
exist between the atomic weights of the elements and their
specific heats. Dulong and Petit (1819) found that the spe-
cific heats (relative heat capacity) of most of the solid ele-
ments vary inversely as their atomic weights, so that the
product of these two factors is a constant quantity (6.4),
which has been properly called the "atomic heat." Thus, tak-
ing the specific heats of iron, lead and mercury, respectively,
as 0.1190, 0.0305 and 0.0333, gives the value for the atomic
heat in each case as follows :
Iron
At.
55.
wt.
40
44
40
X
X
X
Sp. ht.
0.1190
0.0305
0.0333
= .6.
- 6
= 6
59
.27
61
At. ht.
heat units,
heat units,
heat units.
Lead
Mercury. . .
. 205.
. 198.
The average value for the atomic heat of the elements may
be taken as 6.4, though it is sometimes given as low as 6.25
(Remsen). Atomic heat may be briefly defined as the heat
capacity of matter per unit-weight atom.
A gram-atom of any elementary substance is a weight of
that substance, in grams, equal to the atomic weight of the
54 MINE GASES AND VENTILATION
element. Thus, the atomic weight of iron being 55.4 (H = 1),
a gram-atom of iron is 55.4 grams of that substance; and its
heat capacity is the atomic heat value (6.4 heat units).
This average value of atomic heat often assists the deter-
mination of the specific heat from the atomic weight of an
elementary substance, or, vice versa, its atomic weight when
the specific heat is known. For example, since the heat ca-
pacity of 55.4 grm. of iron is 6.4 heat units, the average
specific heat of iron is 6.4 -r- 55.4 = 0.1155.
In like manner, a gram-molecule of any compound sub-
stance is a weight of that substance, in grams, equal to the
molecular weight of the substance.
Specific Heat. — Investigation has shown that the same
quantity of heat imparted to equal weights of different sub-
stances does not produce the same rise of temperature in each
substance. Also, equal weights of different substances when
cooling give out different quantities of heat for each degree
the temperature falls. These facts show that different
substances have different capacities for absorbing and holding
heat as sensible heat causing a rise of temperature.
The " specific heat" of any substance is its relative heat
capacity, or its heat capacity referred to that of an equal
weight of pure water. The unit of heat is the amount of heat
required to raise the temperature of a unit weight of water
one degree. Therefore, the specific heat of a substance
being referred to water expresses the heat units required to
raise the temperature of a unit weight of the substance one
degree.
The specific heat of a solid or liquid always refers to the
heat per unit weight. The specific heat of a gas may be re-
ferred to the unit weight or unit volume, as desired. The
specific heat of air and gases is different according as the air
or gas is confined (constant volume) or is allowed to expand
(constant pressure). The specific heat of a gas for "equal
volumes" is the heat capacity of the gas referred to that of
an equal volume of air at the same temperature and pressure.
The following table gives the specific heats of a few of
the common solids and liquids of interest in mining:
HEAT 55
SPECIFIC HEATS OF SOLIDS AND LIQUIDS
Substance
Temperature,
deg. Fahr.
Specific heat
Aluminum
60-1150
0.2145-0 3077
Copper.
32-1650
0.0933-0 1259
Iron
32-1100
0 1050-0 1989
Lead
60- 600
0.0299-0.0338
Lead (at melting point, 610°F.)
Mercury
610- 680
32- 500
0.0356-0.0410
0 0334-0 0320
Platinum
Silver
Tin
60- 210
32-1200
32- 210
0.0324
0.0559-0.0750
0 0545
Zinc
32- 700
0 0935-0 1220
The following table gives the specific heats of the common
mine gases, for equal weights at constant pressure and con-
stant volume, and for equal volumes under constant pressure:
SPECIFIC HEATS OF AIR, MINE GASES AND VAPORS
Equal
weights
Equal volumes
Const, pres.
Const, vol.
Const, pres.
Air
0 . 2374
0 . 1689
0.2374
Methane
0.5929
0.4219
0.3314
Olefiant gas
0.4040 .
0 2875
0 3951
Carbon monoxide
Carbon dioxide
Hydrogen sulphide
0.2450
0.2163
0 2432
0.1743
0.1539
0 1731
0 . 2369
0 . 3307
0 2897
Oxygen
0 2175
0 1548
0 2405
Nitrogen
Hydrogen. ...
0.2438
3 4090
0.1735
2 4260
0.2368
0 2361
Water vapor
Ammonia
0.4805
0 5080
0.3419
0 3615
0.2996
0 2992
When gas, air or vapor is free to expand (constant pres-
sure)- heat is absorbed and becomes latent. -For this reason
more heat is required to produce the same rise of tempera-
ture when expansion occurs than when the volume remains
56 MINE OASES AND VENTILATION
constant, and the specific heats in the first column are there-
fore higher than those in the second column of the table
given above.
The values given in the first column of this table have
been determined by experiment directly, while those in the
second column have been derived from the first by dividing
the latter by 1.405, the ratio of the specific heat of gases at
constant pressure to that at constant volume. Likewise, the
values given in the third column have been derived from
those in the first by multiplying the latter by the specific
gravity of the gas or vapor referred to air.
The specific heat of all substances varies more or less with
the temperature as appears in the above table. In the case of
gases, the increase per degree (Fahr.) above zero is roughly
estimated as follows : Air, nitrogen, carbon monoxide, 0.000012;
oxygen, 0.00001; carbon dioxide, 0.00006; hydrogen, 0.0002;
and water vapor, 0.0001; etc.
CHEMISTRY OF GASES
The chemistry of all matter treats of the interchange of
the atoms constituting molecules, by virtue of which inter-
change the character and nature of the matter is wholly
altered. In other words, the matter is transformed and a.
new substance created having properties that vary widely
from those of the original substance.
Chemical Reaction. — The change that takes place when
matter is thus transformed is a chemical change, and the
action is described as a " chemical reaction." It assumes an
intimate contact between two unlike substances, under con-
ditions that favor an interchange of atoms. The reaction that
takes place is the direct result of different affinities of the
atoms for each other.
Chemical Affinity. — The theory of chemical change supposes
that all atoms constituting matter have various affinities or
degrees of attraction for each other. By reason of this dif-
ference in the affinities of atoms, an interchange may or may
not occur when two unlike substances are brought into inti-
mate relation with each other, according as the atoms of the
HEAT 57
original substances possess a less or a greater affinity for
each other in their present state or grouping. If the atoms
of one of these substances possess a greater affinity for atoms
of the other substance an interchange of atoms will take
place and new substances will be formed that will be wholly
different from the original substances.
Influence of Heat to Produce Chemical Change. — 'The
theory of heat assumes a wider separation of the particles of
matter as the amount of heat in a substance is increased.
Thus, it naturally follows that a higher temperature invites a
more intimate mingling of two different gases in contact with
each other. This intermingling of the gaseous molecules
greatly assists a chemical reaction that otherwise would not
take place.
Examples of Chemical Change. — The most common and fa-
miliar examples of chemical change are those due to the strong
affinity of the oxygen of the air for most other matter. The
resulting reaction is described as oxidation. The more familiar
forms of oxidation are the rusting of iron and some other
metals in a damp atmosphere. The action results in the
" corrosion " or eating away of the metal and the formation
of an oxide, which is quite different in its character and
properties from the original metal.
Combustion. — In a general sense, any form of oxidation is
combustion, and the latter term does not relate alone to oxida-
tion, but describes generally any chemical reaction in which
one substance is consumed either slowly or rapidly by reason
of the presence of another substance whose atoms possess an
affinity for those of the first that invites reaction.
The substance consumed is termed the combustible and
the other the supporter of the combustion, while the sub-
stances produced are the products of the combustion. The
products of a combustion may be gaseous, vaporous or solid,
the last named being the ash of an active combustion.
Slow Combustion. — This term implies a slow but continuous
wasting away of the substance consumed, the conditions
being unfavorable or the affinities of the atoms being insuffi-
cient to support a more rapid reaction. Slow combustion is
58 MINE GASES AND VENTILATION
characterized by the generation of heat without the production
of flame.
Active or Rapid Combustion. — Active combustion is gen-
erally accompanied by the production of flame. The same
amount of heat is generated in less time, resulting in a higher
temperature, which in turn frequently modifies the products of
the combustion.
Spontaneous Combustion. — Under certain favorable condi-
tions, combustion may start in a mass of combustible ma-
terial without the application of flame or other exciting cause.
This is due to the natural generation of heat within the mass,
owing to chemical reaction taking place between the sub-
stances. The action is explained as being chiefly due to the
absorption of oxygen from the air by the substance, when the
ensuing oxidation generates sufficient heat to ignite both the
gas produced by the combustion and the material. The com-
bustion, which is at first slow, may, in time, develop actively
and inflame and consume the material.
Chemical Symbols. — A chemical symbol is a letter or letters
used to designate an element or simple substance. The sym-
bols of the more common elements together with their atomic
or specific weights have been given in a table, previously.
The symbol written alone expresses a single atom of the sub-
stance; but, since an atom is not conceived to exist alone, the
symbol of an element should always be written as a molecule.
Symbol of a Molecule. — A molecule is assumed to be the
smallest chemical division of matter that can exist in a free
state. A molecule of any simple or elementary substance is
assumed to contain two atoms only. Its symbol is expressed
by writing the symbol for that element with a subscript (2) to
indicate two atoms; thus for the molecule of carbon, write
C2; oxygen, O2; etc.
The molecule of a compound substance may contain any
number of atoms and is expressed by writing the symbols of
its elements each with a subscript figure indicating the num-
ber of atoms of that element in the molecule. A single atom
of an element is indicated by the symbol only, omitting the
subscript figure.
HEAT 59
The following examples will serve to illustrate the fact
that, while a molecule o.f any simple substance is taken to
contain two atoms only, the molecule of a compound may
contain any number of atoms :
Substance Composition Symbol
Carbon monoxide, carbon, 1 atom; oxygen, 1 atom =» 2 atoms; CO
Carbon dioxide, carbon, 1 atom; oxygen, 2 atoms = 3 atoms; COj
Ammonia, nitrogen, 1 atom; hydrogen, 3 atoms = 4 atoms; NHi
Methane, carbon, 1 atom; hydrogen, 4 atoms = 5 atoms; CH«
Olefiant gas, carbon, 2 atoms; hydrogen, 4 atoms = 6 atoms; C2H4
All these gaseous molecules are of equal size, though con-
taining different numbers of atoms.
Molecular Theory of Matter. — Chemical investigations have
led to the accepted conclusion that all matter is composed of
minute particles called molecules, the molecule being con-
sidered the smallest division of which the matter is capable
without destroying its identity.
Theory further assumes that the molecule is composed of
two or more atoms, like or unlike, but bound together by a
force of attraction for each other known as affinity. Each of
these combined atoms represents an element or a particular
kind of matter and their combination as molecules diversifies
matter and creates substances of various nature and kind.
Atomic Weight. — Atomic weight is simply relative. The
atom of each element has a weight peculiar to that element,
referred to the weight of the hydrogen atom as unity.
Molecular Weight. — The molecular weight of a substance is
equal to the sum of the atomic weights of the elements of
which it is composed. These elements combine in fixed pro-
portions, which are determined by the number of atoms that
saturate each other or the " valences" of the elements.
Valence or Valency. — The valence of an element is a term
used to express its combining power in relation to the number
of atoms of hydrogen (the assumed unit) or its equivalent
required to satisfy the affinity. For example, two atoms of
hydrogen are required to saturate a single atom of oxygen,
and the valence of hydrogen being one, the valence of oxygen
is two. The reaction is expressed by the chemical equation
2H2 + O2 = 2H2O.
60 MINE GASES AND VENTILATION
There are many elements, however, that do not unite with
hydrogen and to determine their valency it is necessary to
compare them with other elements that combine with them
and whose valence is known. For this purpose the elements
oxygen and chlorine are most convenient. The valence of
oxygen, as shown above is two. The valence of chlorine is
one, since one atom of hydrogen completely saturates one
atom of chlorine.
H2 + C12 = 2HC1.
The element calcium combines both with oxygen and with
chlorine but not with hydrogen -alone. Its valence is two
as shown by the following equations :
Ca2 + O2 = 2CaO
Ca2 + 2C12 = 2CaCl2.
The valence of most elements is not absolute but changes,
often by two and frequently by successive units. For example,
calcium has a valence of two and four; gold, one and three;
copper, one and two; iron, two, three, four and six; while
nitrogen forms the following series of oxides:
N20, N202, N203, N204, N205.
Classification of Elements by Valence. — Owing to the
change in valency exhibited by many elements it is not pos-
sible to make an unvarying classification in this respect. For
the sake of convenience, however, many of the elements are
designated as univalent, bivalent, trivalent, quadrivalent, etc.;
or as monads, dyads, triads, tetrads, pentads, hexads, etc.,
according as they exhibit valencies of one, two, three, four,
five, six, etc., in combining with other elements.
A Chemical Compound. — A chemical compound is a sub-
stance composed of molecules formed by the chemical union
of two or more unlike atoms. In a chemical compound the
elements are always combined in fixed proportions and the
substance has fixed properties that are always the same.
A Mechanical Mixture. — A mechanical mixture is composed
of unlike substances mixed together in any proportion and
not chemically combined. The properties of such a mixture
HEAT 61
vary with the kind and proportion of the substances of which
it is formed.
The atmosphere is a mechanical mixture of oxygen and
nitrogen. Although the proportion of these gases is practi-
cally always the same in pure air, the gases are only mixed
and do not combine with each other.
Acids, Bases and Salts. — Chemistry considers three general
classes or conditions of matter, which make the substance
either an acid, a base, or a salt.
Briefly and plainly stated, an acid is a substance that dis-
sociates in aqueous solution yielding hydrogen ions.
A base is a compound capable of reacting with an acid to
produce a salt. It is an alkaline metallic oxide.
A salt is a generally neutral compound formed by the
union of an acid and a base.
In general the nature of an acid is the direct opposite to
that of a base. In combination they neutralize each other,
forming a neutral salt and water. The distinguishing charac-
teristics of all acids are: 1. The sour taste. 2. The turning of
blue litmus red. 3. The evolution of hydrogen by contact
with a metal.
A number of acids are formed by the direct union of
hydrogen with another element; as hydrochloric acid (HC1);
hydrogen sulphide (H2S). Other acids are formed by the
union of two radicals — the hydrogen radical or hydroxyl
(HO) and an acid radical; or they may be considered as
the result of the addition of water (H20) to an anhydrous
acid (anhydride).
In the first instance, the formation is as follows:
Hydrogen radical (hydroxyl) 2(HO)
Acid radical . . SO,
Sulphuric acid H2SO4
Or, again, the formation may be regarded thus:
Water H2O
Sulphuric anhydride SO3
Sulphuric acid H2SO4
62 MINE GASES AND VENTILATION
Oxides. — Nearly all the elements unite with oxygen to form
oxides, but the affinity for oxygen is stronger in some cases
than in others. When the affinity of the elements for each
other is strong the compound formed is more stable than
when the affinity is weak.
A monoxide is formed when the molecule contains but one
atom of oxygen; as for example, carbon monoxide (CO).
A dioxide is formed when the molecule contains two atoms
of oxygen, as carbon dioxide (CO2).
A trioxide contains three atoms of oxygen.
Chemical Change, Reaction. — Any interchange of atoms
between two substances, or a combination of two unlike sub-
stances, by which one or more new substances are formed, is
a chemical change and the process is called a "chemical
reaction."
A Chemical Equation. — It is a natural law that no matter
is ever lost or destroyed. Matter is Indestructible. As a
result of chemical change both the form and nature of the
matter may be altered — a solid may become a liquid or gas,
or vice versa; but the weight of the resulting products is the
same as that of the original substances that are involved in
the reaction.
Since there is no change in the weight of matter before
and after chemical reaction takes place, it is possible to ex-
press the reaction by an equation showing the equality of
matter. This is called a chemical equation. It is formed by
writing in the first member the chemical symbols of all the
substances entering or involved in the reaction, connecting
these together with a plus (+) sign. Likewise, in the second
member of the equation, write the chemical symbols of the
several products of the reaction, connecting them together,
as before, with a plus (+) sign. Then complete the equation
by writing the sign ( = ) of equality between the two
members.
For reasons that will be better understood when discussing
molecular volume, when writing a chemical equation each
substance should be expressed by its molecular formula. This
means that any elementary or simple substance as carbon (C),
HEAT 63
hydrogen (H) nitrogen (N), etc., should be expressed as a
molecule; thus, C2, H2, N2, etc.
Illustration. — When carbon (C) is completely burned in a
plentiful supply of oxygen (O) there is produced carbon dioxide
(CO2). The reaction is expressed by the equation
C2 + 2O2 = 2CO2
The expression 2CO2 should be interpreted to mean two mole-
cules of CO2, each comprising one atom of carbon and two
atoms of oxygen.
Observe there are the same number of atoms of carbon and
the same number of oxygen on each side of the equation.
Not an atom is lost in the reaction, although these are grouped
differently. In this case the solid carbon unites with the
oxygen (gas) and carbon dioxide (gas) is produced. Also, the
weight of the carbon dioxide is equal to the sum of the weights
of the carbon burned and the oxygen consumed. There is
no loss in weight.
It is important to note that the atoms involved in any re-
action represent the weights of the substances they form,
while the molecules or molecular formulas of the several sub-
stances represent their respective volumes. Hence, when each
substance is expressed by its molecular formula the chemical
equation shows both the relative weights of all the substances
and the relative volumes of the gases.
In the reaction represented by the above equation each
atom of the carbon molecule (C2) takes up two atoms of
oxygen to form the molecule of carbon dioxide (CO2), the
valence of carbon being four and that of oxygen two. The
reaction in this case is complete, the affinity of the carbon for
oxygen being fully satisfied.
Use of Chemical Equations. — As previously stated, when
properly written a chemical equation shows both the relative
weights and relative gaseous volumes of each respective sub-
stance involved in a chemical reaction. The relative weights
are indicated oy the molecular weights of the substances as
shown by the completed equation.
In estimating relative gaseous volumes, the volume of a
64 MINE GASES AND VENTILATION
gaseous atom is taken as unity and since, as previously ex-
plained, an elementary molecule is assumed to contain two
atoms and all gaseous molecules at the same temperature and
pressure are of equal size regardless of the number of atoms
they contain, it follows that the relative* volume of all gaseous
molecules is two.
Application of the Law of Volumes. — The law of molecular
volume as just explained finds important application in cal-
culating the volumes of gases that are involved in a chemical
reaction. While there is never any change in the weight or
amount of matter due to chemical reaction, there frequently
results a change in the volume of the gases concerned in the
reaction.
To illustrate such change of gaseous volume, write the
chemical equation representing the dissociation of ammonia
gas (NH8) by electrolysis, forming free nitrogen (N) and
hydrogen (H) gases, placing below each molecular formula its
relative or molecular volume ; thus,
2NH3 = N2 + 3H2
Mol. vol 2 1 3
It is evident that two molecules of ammonia gas, in disso-
ciation, yield one molecule of nitrogen and three molecules of
hydrogen, making four volumes in all. In other words, two
volumes become four. The volume of the gases resulting
from the breaking up of the molecule of ammonia is, there-
fore, double that of the original gas.
There is no chemical change of volume when methane or
marsh gas (CH4) is exploded in a plentiful supply of normal
air, and the methane is completely burned, forming only car-
bon dioxide (CO2) and water (H2O). The nitrogen of the air
being unchanged it may be omitted in writing the equation
expressing this reaction, which is as follows:
CH4 + 2O2 = CO2 + 2H2O
Mol. vol 1 2 1 2
The equation shows that the complete combustion of
methane requires twice its volume of oxygen; and there is
HEAT 65
produced an equal volume of carbon dioxide and two volumes
of aqueous vapor.
On the other hand, when carbon monoxide (CO) is burned
in air, producing carbon dioxide (CO2), there results a reduc-
tion in volume, as shown by the following equation:
2CO + O2 + 4N2 - 2CO2 + 4N2 .
Mol. vol 2 1 4 2 4
Normal air consists of practically one-fifth oxygen and
four-fifths nitrogen. The equation shows that two volumes
of carbon monoxide, in burning, consume five volumes of air,
and there remain two volumes of carbon dioxide and four
volumes of unchanged nitrogen. The seven volumes of the
original gas and air are thus reduced to six volumes of burned
gases.
THERMOCHEMISTRY
Thermochemistry treats of the heat changes that accom-
pany all chemical reactions. A knowledge of such heat
changes is of the greatest importance in the study of ex-
plosive phenomena.
Heat Changes. — In. a chemical reaction, when combination
takes place, the heat energy of the compound or compounds
formed is the heat of formation or combination.
Chemical reaction may also be accompanied by dissocia-
tion or decomposition of a compound, its heat of formation
being then heat of decomposition, which neutralizes or is
neutralized by the heats of formation of the products of the
reaction. The heat of decomposition of a substance is always
equal to its heat of formation.
The heat of elements, in a reaction, is always zero, there
being no combination or dissociation in the element.
When the sum of the heats of formation of the products of
a reaction is greater than the total heat of decomposition heat
is liberated and the reaction is ' l exothermic ." . When the total
heat of decomposition is the greater, heat is absorbed and the
reaction is then "endothermic."
5
66
MINE CASE 8 AND VENTILATION
Heat of Combustion. — This term is generally applied to the
heat liberated in the oxidation of a combustible. The reaction
is exothermic; and, in general,
TT f 7 .• Heat of formation Heat of formation
Heat of combustion = f , ,
of products of combustible
The heat -of combustion of a substance, like combining
heat and heats of formation or decomposition, is expressed
in heat units, per unit weight of substance. The following
table gives the heats of combustion of some of the more
important combustibles in mining:
TABLE OF HEATS OF COMBUSTION
(Favre & Silbermann)
Combustible
Methane, to carbon dioxide and water at 32 deg. F. . . .
Olefiant gas, to carbon dioxide and water at 32 deg. F.
Carbon, to carbon dioxide
Carbon, to carbon monoxide
Carbon monoxide, to carbon dioxide
Hydrogen, to water at 32 deg. F
Hydrogen, to steam at 212 deg. F .-
Sulphur, to sulphur dioxide
Petroleum, heavy (sp. gr. 0.886)
Petroleum, light (sp. gr. 0.833)
Coal (average values)
Pennsylvania .
Pennsylvania
West Virginia
Illinois .
Ohio
Kentucky
Alabama
Indiana
Anthracite . .
Bituminous .
Bituminous .
Bituminous .
Bituminous .
Bituminous .
Bituminous.
Bituminous .
State
Fixed carbon,
per cent.
Heat of com-
bustion, B.t.u.
per Ib.
84.3
57.0
65.8
46.4
51.5
50.1
59.3
44.3
23,513
21,344
14,544
4,451
4,325
62,032
51,717
4,000
19,000
18,200
14,200
14,900
14,240
14,460
14,400
12,700
13,700
14,140
The above are average values for each entire state, as
taken from Government analyses and do not represent mining
districts.
HEAT 67
Heat Calculation. — The calculation of the heat of com-
bustion from the heats of combination of the combustible and
the several products, formed, will be best understood by a
practical illustration following the statement of a few funda-
mental principles that always govern the operation. Briefly
stated these are as follows :
1. No heat energy is lost, but the heat of an element, in
any reaction, is zero, there being neither combination nor
dissociation possible in the element as in a compound.
2. Total heat of formation of products is the positive (+)
heat developed in the reaction.
3. Heat of decomposition (same as heat of formation) of
the combustible is the negative ( — ) heat or the heat absorbed
in the reaction.
4. The heat of combustion is the net heat, or the difference
between the total heat in the products and the heat in the
combustible.
5. The reaction generates heat, or is exothermic, when
there is an excess of positive (+) heat.
6. The reaction absorbs heat, or is endothermic, when
there is an excess of negative ( — ) heat.
NOTE.— The chemical equation expressing a reaction shows
the equivalence of weight of matter before and after reaction,
but does not show the thermal effect.
A thermochemical equation is written by adding to the
chemical equation a positive or a negative term indicating the
heat generated or absorbed in the reaction. This heat may
be expressed as " gram-calories " " kilogram-calories " or
" pound-calories," according as the weight of the combustible
taken is a gram-molecule, a kilogram-molecule or a pound-
molecule. Or, the heat of the reaction may be given as
B.t.u. per pound, or other denomination. The weight-unit
is immaterial, since the heat of the reaction is always that
due to the molecular weight of the combustible expressed in
the same weight-unit.
The amount of heat corresponding to the molecular weight
of the combustible (expressed in any weight-unit) is fre-
quently called the "molecular heat" of the reaction.
68
MINE GASES AND VENTILATION
The molecular heat of a chemical reaction, divided by the
molecular weight of the substance consumed, gives the heat
of the reaction per unit weight of substance, which is the
heat of the combustion expressed in the same denomination as
the weight of the substance.
Illustration. — The heat of combustion of methane (CH4),
as determined by Favre and Silbermann (See Table), is 23,513
B.t.u. per lb.; or 23,513 X % = 13,063 Ib.-cal. per lb.; or
13,063 kg.-ca1. per kg. or grm.-cal. per grm of the gas.
The molecular heat of this reaction is therefore
16 X 23,513 = 376,208 B.t.u.
or 16 X 13,063 = 209,008 cal.
It is observed, thus, that the molecular heat, in the com-
bustion of methane, is the heat (B.t.u.) generated by 16 lb.
of the gas; or the heat (Ib.-cal.) generated by the 16 lb.; or
the heat (kg.-cal.) due to 16 kg.; or the heat (grm.-cal.) due
to 16 grm. of this gas. Different authorities have obtained
slightly varying heat values of the gases.
Heats of Formation of Substances.— The heats of formation
of a few substances that are of interest in mining are given
in the following table. The heats are given as molecular
heats for convenience of substitution in equations.
TABLE OF HEATS OF FORMATION OF SUBSTANCES
Substance
Symbol
Molecular heats of formation
B.t.u.
Cal.
Methane
Acetylene ....
CH4
C2H2
C2H4
C2H6
CO
CO2
H2S
S02
H2O
H2O
H20
H2O
39,060
98,550
-20,250
47,970
52,200
174,600
8,640
124,668
128,880
126,288
123,048
105,660
21,700
54,750
-11,250
26,650
29,000
97,000
4,800
69,260
71,600
70,160
68,360
58,700
Ethene (olefiant gas)
Ethane
Carbon monoxide
Carbon dioxide
Hydrogen sulphide
Sulphur dioxide
Ice (32°F.)
Water (32°F.)
Water (212°F )
Steam (212°F )
HEAT 69
For the most part, the heat values in the above table have
been determined by experiment, by means of the calorimeter.
The values of the heats of combustion, as calculated from
these molecular heats of formation, by substitution in the
chemical equation expressing the reaction, will not be found
to check the earlier determinations of Favre and Silbermann;
but the variation is slight.
For example, writing the thermochemical equation for the
combustion of methane, indicating the required heat of com-
bustion by x, we have
CH4 + 2 O2 = CO2 + 2 H2O - x
39,060 + 0 = 174,600 + 2(126,288) - x
x = 174,600 + 2(126,288) - 39,060 = 388,116 B.t.u.
Then, the molecular weight of methane being 16, the unit heat
of combustion is 388,116 -r- 16 = 24,257, instead of 23,513
B.t.u.
Writing a Thermochemical Equation. — The thermochemical
equation expressing the reaction that takes place and the
heat that is generated in the combustion of methane (CH4)
is written thus:
CH4 + 2O2 = CO2 + 2H2O - 388,116 B.t.u.
Or, in the French system,
CH4 + 202 = C02 + 2H2O - 215,620 col.
The reaction is exothermic, or generates heat, which is the
excess of the heats of formation of the products of the com-
bustion (carbon dioxide and water), over the heat of forma-
tion of the combustible (methane).
Likewise, for the combustion of carbon to carbon dioxide,
which generates 14,550 B.t.u. per lb., or 14,500 X % = 8083
cal., the molecular heat of the reaction is 12 X 14,550 =
174,600 B.t.u., or 12 X 8083 = say 97,000 cal. The thermo-
chemical equation expressing this combustion is
C + O2 = CO2 - 174,600 B.t.u.
or C + O2 = C02 - 97,000 cal.
In these equations, the heat of combustion is equal to the
heat of formation of the product (carbon dioxide), the heats
of the elements (carbon and oxygen) being zero.
70 MINE GASES AND VENTILATION
HYGROMETRY
Hygrometry is the measurement of the amount of vapor
in the air, at any given time. The capacity of the air for
holding moisture varies with the temperature. For example,
at 32 deg. F., a cubic* foot of air will hold or has a capacity
of only 2.13 grains of water; while at 60 deg. the capacity is
5.77 gr. per cu. ft.; at 100 deg., 19.84 gr. per cu. ft.; and at
212 deg. F., air fully saturated with moisture holds about
258 gr. per cu. ft.
Hygrometric State of Air. — Air absorbs moisture from
bodies in contact with it, and thus exerts a drying action,
which is of great importance in mining. The absorptive power
of the air varies with its degree of saturation. For example,
air at 60 deg. F., containing, say 2.9 gr. per cu. ft., is only
about half saturated and is then said to contain 50 per cent,
of moisture. In this condition, the air will readily absorb
more moisture. The degree of saturation of air is called its
"hygrometric state."
Air is said to be "dry" or "wet," according to the degree
of its saturation. It is important to observe that these terms
have no reference to the actual amount of vapor present in
a given volume of air; but only express how nearly the air is
saturated. For example, air fully saturated at 32 deg. F. con-
tains 2.13 gr. of moisture per cubic foot and is "wet" because
it is full of water vapor; but if the temperature now rises to,
say 60 deg., the vapor capacity of the air is thereby increased
to 5.77 gr. per cu. ft., and its degree of saturation or humidity"
is then 2.13/5.77 X 100 = 36.9 per cent. In other words, the
air at this temperature contains only 36.9 per cent, of its ca-
pacity, and is therefore comparatively speaking, "dry" air.
Owing to the rise of temperature, from 32 to 60 deg., the air
is capable of absorbing 5.77 — 2.13 = 3.64 gr. of moisture per
cubic foot.
Calculation of Weight of Moisture in Air. — In order to cal-
culate the weight (w), in pounds, of moisture contained in
one cubic foot of air, it is necessary to know the degree of
saturation of the air (c), its temperature (t), and the vapor
pressure (pv) corresponding to that temperature. This last
HEAT 71
must be taken from tables known as psychrometric tables.
Calling the absolute temperature T = 460 + t, the formula is
» = 0.8235^
The constant 0.6235 is the specific gravity of water vapor,
and the constant 0.37 is the reciprocal of the weight of one
cubic foot of dry air, at a temperature of 1 deg. F. (absolute)
and a pressure of 1 Ib. per sq. in.
Example. — Calculate the weight of water vapor carried in
an air current of 100,000 cu. ft. when the saturation is 80 per
cent, and the temperature 70 deg. F., if the vapor pressure at
the given temperature is tv = 0.3602 Ib. per sq. in. (see Table,
P. 77).
Solution. — The absolute temperature, in this case, is T- =
460 + 70 = 530; and the total weight of vapor is
100,000 X 0.6235 008g7Xx05336Q02 - 91.62/6.
How Humidity is Measured. — The humidity of the air is
commonly measured by an instrument called the " hygrome-
ter" or "psy chrome ter." This is the " wet-and-dry-bulb
hygrometer."
Other forms of hygrometer have been employed depending
on the absorption of the moisture from the air by certain hy-
groscopic substances, and dew-point hygrometers; but these
are less simple and not as portable as the wet-and-dry-bulb
hygrometer, which indicates the humidity by the difference
in the reading of the wet- and dry-bulb thermometers.
The Hygrometer or Psychrometer. — A neat and portable
form of the wet-and-dry-bulb hygrometer, designed by the
Davis Instrument Manufacturing Co., is shown in the Fig. 7.
Two delicate thermometers are mounted on springs on the in-
side of a light cylindrical folding metallic case, the dry bulb
on the door and the wet bulb in the case. To the latter bulb
is attached a fine silk or muslin sack, which forms a wick that
extends downward to the small vessel which holds the water
that keeps this bulb wet.
72
MINE GASES AND VENTILATION
Still another form of this instrument is that known as the
" Swing psychrometer," from the manner of its use. As
shown in Fig. 8, it consists of two thermometers mounted
on a metal support, which is firmly attached to a handle on
which it is arranged to swing. The left-hand thermometer
has a dry bulb and its reading indicates the actual tempera-
FIG. 7.
ture of the air; while the bulb of the right-hand glass is
covered with a sack that is wet with water when an observa-
tion is to be taken.
Holding the handle in a firm grasp, the operator swings
the instrument so that the metal support holding the two
thermometers rotates rapidly on the handle as an axis. The
swift movement accelerates the evaporation from the wet
sack and cools the bulb of that thermometer, whose reading
enables the calculation of the degree of saturation by differ-
ence with the dry-bulb reading.
HEAT
73
The swing psychrometer is a popular form of the wet- and
dry-bulb hygrometer, because of its portability and the
reliability of its indications, which are generally assumed to
be more representative of the actual state of the air, because
of its movement when an observation is being taken.
FIG. 8.
Principle of Hygrometer. — Unsaturated vapors, like gases,
obey Boyle's law; and, for any given temperature, the ratio of
the quantity or volume of vapoT is equal to the pressure ratio,
or the relative humidity (H), is expressed by the formula.
j, _ Actual vapor pressure
Saturated vapor pressure
74 MINE GASES AND VENTILATION .
The saturated vapor pressure (dry-bulb temp.) is given in
the tables. The actual vapor pressure, at the time of obser-
vation, is equal to the saturated vapor pressure of the tables,
for the dew-point temperature, which, if known, would make
the calculation easy by the use of the above formula. In the
use of the wet-and-dry-bulb hygrometer, however, the rela-
tive humidity is calculated by the formula
„ P" ' 30V 88
fl -
Pd
in which H = relative humidity; pw and pd the respective
saturated vapor pressures of the tables, for the corresponding
wet-and-dry-bulb temperatures tw and id', and B the barometric
pressure, in inches.
What the Wet-and-dry-bulb Hygrometer Indicates. — The
wet-and-dry-bulb hygrometer shows the difference between
the readings of the two thermometers. The dry-bulb ther-
mometer, of course, indicates the actual temperature of the
air. The reading of the wet-bulb thermometer is lowered by
the evaporation of the water from the little sack surrounding
this bulb, and which is kept moist by the water drawn up
through the wick from the vessel below.
The difference of temperature indicated by these two ther-
mometers depends on the rapidity of the evaporation of the
water from the wet bulb. The evaporation is more, rapid in
dry than in wet air; and the difference of reading is, thus, an
index or measure of the degree of saturation of the air. When
the ah* is fully saturated with moisture there is no evapora-
tion from the wet bulb and the readings of the two thermome-
ters are the same. The difference increases with the dryness
of the air.
Relative Humidity of Air. — -As previously explained the
relative humidity of air is expressed by the ratio of the actual
vapor pressure in the air at the time, to the saturated vapor
pressure. The following table gives the percentage of satu-
ration or the hygrometric state of air for various differences
of readings, at different temperatures.
HEAT
DIFFERENCE BETWEEN DRY AND WET BULBS
75
Reading of
dry-bulb
ther.,deg.F
65
-
N
CO
'-t
tQ
''-•
i-
00
0!
c
S
01
«
-r
IK
'-r
t*
'-.
N
co
•-
S:
OS
• 0
'?,
tfi
i
?i
Relative humidity
95
90
85
so
?.->
70
H(l
r>2
57
53
IS
11
10
:«;
:?2
2S
25
2:<
21
l<)
17
15
13
12
10
66
95
90
85
so
76
71
66
62
58
53
I!)
45
11
:57
33
2'.)
2(1
21
22
20
18
17
15
1H
11
67
95
90
85
so
7(1
71
87
62
5s
54
.-,()
1(1
12
MS
34
:«)
27
25
2:i
21
20
IS
1(1
15
13
68
95
90
85
81
7C,
71'
67
63
.v.»
.I,-)
51
17
}:•!
:•!«)
35
:>1
2S
2(1
2-1
2,'{
21
19
17
1(1
14
69
95
90
86
81
77
72
68
6-1
5<>
55
5]
17
11
10
36
32
29
27
25
21
22
20
19
17
!5
70
95
90
90
86
81
77
72
(is
(11
(10
r,(i
52
IS
11
10
:57
:n
:«)
28
2(1
25
23
21
20
IS
17
71
95
86
S2
77
7:i
(1<)
M
(10
r,d
53
10
15
11
:<s
:<l
:u
20
27
2(1
21
22
21
11>
IS
72
95
91
86
S2
7S
7:<
fl'.)
115
61
57
53
1'.)
Ml
12
:«»
:i5
:<2
:«>
2S
27
25
2:<
22
20
1!)
73
95
91*
86
S2
7S
T.\
(19
(i,-,
61
58
54
.',()
46
1:5
10
:{6
:w
31
29
2S
2(1
21
215
21
20
74
95
91
86
82
78
74
70
(1(1
(12
5s
54
51
17
11
40
37
:M
:{2
30
2<)
27
25
21
22
21
75
96
91
87
82
78
71
70
66
<;:•!
59
55
51
48
11
41
38
:M
:{:<
:n
:«»
2S
2(1
25
1W
22
76
96
91
87
83
7S
71
70
(17
63
59
55
:,2
•is
15
12
:{.s
:15
:i4
\V2
:<o
2!)
27
2(1
21
2)5
77
96
91
87
s:<
79
7f,
71
(17
6.S
60
56
r,2
IS)
id
12
:w
:«;
34
:u
31
••».)
2S
27
25
21
To use the table, find the observed temperature of the air,
in the left-hand column, and the difference of the observed
readings of the wet- and dry-bulb thermometers, at the top
of the table; the corresponding number in the table is the
percentage of saturation which expresses the degree of humid-
ity of the air. For example, if the dry-bulb temperature is
70 deg. and the wet-bulb 64 deg. F. the difference of readings
is 6 deg. and the corresponding humidity as taken from the
above table is 72 per cent.
Actual Vapor Pressure. — The pressures given in the table
below are the pressures the vapor exerts when the space it
occupies is fully saturated; they are called the " saturated
vapor pressures." When the weight of vapor in the air is not
sufficient for saturation the vapor pressure will be exactly pro-
portional to the degree of saturation. For example, if 50 per
cent, of moisture is present or the air only half saturated, at,
say 70°F., the " actual vapor pressure," as it is called, is one-
half of the saturated vapor pressure, in the table given later;
or Y^ X 0.3602 = 0.1801 Ib. per sq. in.
To calculate the actual vapor pressure from the difference
of the wet- and dry-bulb temperatures (t<* — tw) and the
76 MINE GASES AND VENTILATION
barometric pressure (B), in inches of mercury, first find the
saturated vapor pressure (pw), in inches of mercury, corre-
sponding to the wet-bulb temperature (£„,), from the table;
and substitute this and the given values in the formula
Actual vapor pressure at temperature td = pw — ™( docT^ )
oU \ oo /
Example. — Find the actual vapor pressure when the dry bulb reads
60° and the wet bulb 54°F., the barometric pressure being B = 30 in.,
and the saturated vapor pressure for the wet-bulb temperature (54°F.)
being 0.4178 in. of mercury.
Solution. —
Pv = 0.4178 - = 0.3497 in. of mercury
Since the saturated vapor pressure (see table) for the dry-bulb tem-
perature (60°F.) is 0.5183 in., the relative humidity in the above ex-
ample is
TT P* ^ inn 0.3497 X 100 __ .
H=pdXl™= -05183" = b7-4 *""•«**
The Dew Point.— What is called the "dew point," in hy-
grometry, is the temperature below which the moisture con-
tained in the air begins to be deposited. For example, the
weight of moisture, in grains per cubic foot, contained in the
air, in the above example is (1 Ib. = 7000 grs.)
7000 X 0.6235 - 3.9 „. per cu. ft.
The temperature at which this weight of moisture will
fully saturate a cubic foot of air is the dew point, because
the slightest fall of temperature below that point will cause
a deposition of moisture from the air.
The dew-point temperature is ascertained, in any given
case, by first calculating the actual vapor pressure of the
moisture in the air, as in the above example; and then, by
referring to the table of saturated vapor pressures, find the
temperature orresponding to that vapor pressure. This is
true, because, as previously stated, the actual vapor pressure,
at any given time, is equal to the saturated vapor pressure
for the dew-point temperature. Thus, the actual vapor pres-
sure for dry bulb 60° and wet bulb 54° was found to be 0.3497 in.,
which corresponds to a saturated vapor pressure or dew point
of about 49 deg. F.
HEAT
77
TABLE SHOWING SATURATED VAPOR PRESSURES FOR DIFFERENT
TEMPERATURES
Degrees,
Fahr
Barometric
pressure,
mercury
(32°F.) in.
Pressure,
pounds per
square inch
!
Degrees,
Fahr
Barometric
pressure,
mercury
(32°F.) in.
Pressure,
pounds per
square inch
-30 0.0099
0.0049
70
0.7335
0 . 3602
-20 0.0168
0.0082
71
0.7587
0.3726
-10 0.0276 0.0136
72
0.7848
0.3854
0 0.0439
0.0216
73
0.8116
0.3986
5 0.0551
0.0271
74
0.8393
0.4122
10 0.0691
0.0339
75
0.8678
0 . 4262
15 0.0865
0.0425
76
0.8972
0.4406
20 0.1074
0.0527
77
0.9275
0.4555
26
0.1397
0.0686
78
0.9587
0 . 4708
32
0.1815
0.0891
79
0.9906
0.4865
34
0.1961
0.0963
80
1.024
0.5027
36
0.2122
0.1042
81
1.058
0.5194
37
0.2205
0.1083
82
1.092
0.5365
38
0.2293
0.1126
83
1.128
0 . 5542
39
9. .2382
0.1170
84
1.165
0.5723
40
0*2476
0.1216
85
1.203
0.5910
41
0.2574
0.1264
86
1.243
0.6102
42
0.2674
0.1313
87
1.283
0.6299
43
0.2777
0.1364
88
1.324
0.6502
44
0.2885
0.1417
89
1.367
0.6711
45
0.2995
0.1471
90
1.410
0.6925
46
0.3111
0.1528
95
1.647
0.8090
47
0.3229
0.1586
100
1.918
0.9421
48
0.3352 .
0.1646
105
2.227
1.0938
49
0.3478
0.1708
110
2.578
1 . 2663
50
0.3610
0.1773
115
2.977
1.4618
51
0.3745
0.1839
120
3.427
1.6828
52
0.3885
0.1908
125
3.934
1.9318
53
0.4030
0.1979
130
4.504
2.2119
54
0.4178
0.2052
135
5.144
2.5261
55
0.4333
0.2128
140
5.859
2.8774
56
0.4492
0.2206
145
6.658
3.2696
57
0.4657
0.2287.
150
7.547
3.7063
58
0 . 4826
0 . 2370
155
8.535
4.1914
59
0.5001
0 . 2456
160
9.630
4.7292
60
0.5183
0.2545
165
10.841
5.324
61
0.5370
0 . 2637
170
12.179
5.981
62
0.5561
0.2731
175
13.651
6.704
63
0.5760
0.2829
180
15.272
7.500
64
0.5964
0.2929
185
17 . 050
8.373
65
0.6176
0.3033
190
18.954
9.330
66
0.6394
0.3140
195
21.130
10.377
67
0.6618
0.3250
200
23 . 457
11.520
68
0.6850
0.3364
205
25.993
12.765
69
0.7086
0.3481
212
29.925
14.696
78 MINE GASES AND VENTILATION
Caution. — It is absolutely necessary in the use of such
formulas as embrace terms or constants of a given denomi-
nation to use only values of that denomination. For ex-
ample, the formula for finding the weight of moisture that
will saturate a cubic foot of air at a temperature of t degrees, is
'
This is recognized as being derived from the formula previ-
ously given (p. 71) to find the weight of a cubic foot of dry
air at a pressure p and temperature /, by substituting for the
atmospheric pressure p (Ib. per sq. in.), the saturated vapor
pressure for pv (Ib. per sq. in.); and multiplying the formula
by the specific gravity of water vapor (0.6235) referred to air.
In these formulas, the pressure must always be expressed
in pounds per square inch, because the constant 0.37 is in
that denomination; and the temperature must be given in
Fahrenheit degrees, for a like reason. Also, the weight will
be found in pounds per cubic foot and, if desired in grains per
cubic foot, must be multiplied by 7000, as there are 7000 gr.
in a pound (avdp.).
On the other hand, the formulas given for Calculating the
relative humidity of the air, or the actual vapor pressure
contain the constant 88, which is based on barometric pres-
sure (in. of mercury) and Fahrenheit temperatures. The
constant 88 is used for all temperatures above 32 deg., and 96
for any temperature below 32 deg.
The table of saturated vapor pressures, on the preceding
page, gives the pressure or tension of water vapor for differ-
ent temperatures (Fahr. scale), from —30 deg. to 212 deg.
The pressures are given both in inches of mercury and pounds
per square inch.
Example. — Find the actual vapor pressure, the relative humidity,
dew point and weight of moisture present, in grains per cubic foot, when
the readings of the dry- and wet-bulb thermometers are 62 deg. and 54
deg. F., respectively, and the barometric pressure is 28.2 in.
Solution. — The actual vapor pressure, in this case, as calculated from
the saturated vapor pressure corresponding to the wet-bulb reading
(pM = 0.4178 in.), is
, = 0.4178 -
HEAT 79
The saturated vapor pressure for the given temperature
(see Table) is pQ2 = 0.5561 in. and the relative humidity,
The dew-point temperature corresponding to a saturated
vapor pressure of 0.3323 (see Table) is 47.7 deg. F.
The actual weight of vapor the saturated vapor pressure
corresponding to the dry-bulb temperature 62 deg. F. (see
Table) being 0.2731 Ib. per sq. in., is
7000 X 0.6235 - 3.6 gr. per cu. ft.
Dry and Wet Air Compared. — Strange as it may at first
appear, wet air is lighter than dry air, volume for volume.
This is because the water vapor in the air is much lighter
than the same volume of air which it displaces. The specific
gravity of water vapor referred to air as a standard or unity
is 0.6235.
The weights, per cubic foot, of water vapor and dry, partly-
saturated and fully-saturated air, respectively, are calculated
by the following formulas :
Water vapor, w = 0.6235 —^ (1)
Dry air, .w= „ (2)
Air partly saturated, w = — ' — — (3)
pa — .r
Air fully saturated, w = - -Q (4)
w = weight (Ib. per cu. ft.)
c = degree of saturation, expressed as a decimal
pa = atmospheric pressure (Ib. per sq. in.)
pv = saturated-vapor pressure (Ib. per sq. in.)
T = absolute temperature (deg. Fahr.)
It is readily seen, from Formulas 2, 3 and 4, that perfectly
dry air is always heavier than air containing water vapor,
and that the weight of air decreases as its degree of satura-
tion increases. The weight of moisture in air is usually
80 MINE GASES AND VENTILATION
estimated in grains instead of pounds, per cubic foot, and it
is necessary to multiply the results obtained from the above
formulas by 7000 (1 Ib. = 7000 gr.).
The same formulas expressing the atmospheric pressure
and the vapor pressure in inches of barometer B, instead of
pounds per square inch, are as follows :
Q.82757cpv
Water vapor, w -- —jr~ (5)
1.32735
Dry air, w = - —— (6)
1
Air partly saturated, w = ~ (B - 0.3765cp,) (7)
Air fully saturated, w = -r (B - 0.3765pv) (8)
It is evident that when air is fully saturated, c = 1, and
disappears from the formula. The values of pv are given
in a preceding table, in pounds per square inch and inches
of mercury.
Formula 3 is obtained by the addition of Formulas 1 and
2, making pa = pa — cpv; and Formula 5 is derived from
Formula 1, by reducing the pressure (Ib. per sq. in.) to
pressure (in. barom.), since 1 in. barom. = 0.4911 Ib. per sq.
in. and (0.6235 X 0.4911) ^ 0.37 = 0.82757. But the value
of pv, in Formulas 5, 7, 8, must be given in inches of
barometer, instead of pounds per square inch as in Formulas
1, 3, 4.
Important. — Properly speaking, a vapor does not saturate
the air, but the space it occupies; since, for any given tem-
perature, the same weight of vapor serves to fill a given
space whether that space is full or void of air. Commonly
speaking, vapor is said to be saturated or unsaturated ac-
cording as the space it occupies is saturated or otherwise.
Laws of Vapors. — The following laws express the chief
characteristics of vapors:
1. Vaporization takes place at the surface of all volatile
liquids, at all temperatures, till the space surrounding the
liquid is saturated or the critical temperature is reached.
HEAT
81
2. Vapor pressure (different for different vapors) depends
on the temperature and the degree of saturation.
3. For any given temperature, the weight and pressure
of a vapor saturating a given space is the same whether that
space is full or void of air or other gas.
4. Saturated vapor pressures increase with the tempera-
ture and when equal to the pressure above the liquid vaporiz-
ing, the ebullition of the liquid begins, which marks the boiling
point of the liquid for that pressure.
K>090 SO 70 60
20 25 30 35 40 45 50 55 60 65 70 75 60 .65 90 95 100 105
DRY-BULB TEMPERATURES ( DEG. FAHR.)
FIG. 9.
5. In a confined space, a further addition of heat to the
liquid causes a rise of both temperature and vapor pressure
till an equilibrium of densities of the liquid and vapor stops
further vaporization and marks the so-called "critical tem-
perature " for that liquid.
The diagram, Fig. 9, is useful in showing at a glance the
weight of water vapor that will saturate a cubic foot of
space at any temperature from 20 to 105 deg. F. and the
82 MINE GASES AND VENTILATION
degree of humidity for different dry- and wet-bulb readings
of the psychrometer.
STEAM
Steam is the vapor of water formed at any temperature
at or above the boiling point of the water. It is a certain
vaporized or gaseous state of water. Water vaporizing below
its boiling point forms vapor but not steam. Thus, while all
steam is vapor, correctly speaking, all vapor is not steam.
Steam in its natural state or when saturating a given space,
has a temperature corresponding to the pressure it supports.
This will be more clearly understood by taking an example of a
given volume of steam in contact with the water from which
it was formed. For instance, the steam in a steam boiler,
at a pressure of 65 Ib. gage (sea level) or, say 80 Ib. absolute,
has a temperature of 312 deg. F. But any increase of pressure
will be accompanied with a corresponding increase in its tem-
perature, so that, at a pressure of 155 Ib. absolute, the tempera-
ture of the steam will have increased to 361 deg. F.
Again, assuming a given volume of steam in contact with the
water from which it was formed, such steam can neither be
compressed nor expanded without a corresponding change
taking place in its temperature. For example, for the same
temperature, any increase of pressure would cause some of the
steam to condense, while a decrease of pressure would cause
more steam to form, as the water would vaporize under the
decreased pressure. Thus, the space above the water is
always saturated by a weight of steam corresponding to the
temperature, which is fixed for any given pressure.
Saturated Steam. — Saturated steam may be defined as
steam in contact with water. From the foregoing, it will be
understood that saturated steam is in its natural state, having
a temperature corresponding to its pressure. Saturated
steam may be either dry or wet, according as it does or does
not hold any entrained water. The density of dry saturated
steam is always the same for the same temperature.
Superheated Steam. — When steam is not in contact with
water, any addition of heat causes an increase in both
HEAT
83
temperature and pressure, the pressure increasing with the
absolute temperature. The steam is no longer saturated,
and is said to be " superheated." Superheated steam is
always dry.
Unlike saturated steam, superheated steam follows the laws
of a perfect gas. For a constant volume, its pressure increases
with the absolute temperature; and, for a constant tempera-
ture, the pressure increases inversely as its volume. Steam is
superheated, therefore, whenever its temperature exceeds that
of saturated steam, for any given pressure.
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Steam Pressure ( Gage, Sea Level )
FlG. 10.
Steam Tables. — The table, in the following pages, gives the
temperature, specific volume, heat of the liquid above 32 deg.
F., latent heat of evaporation, and the total heat in the steam,
for different absolute pressures, as taken from Marks & Davis
Steam Tables, which are the generally accepted values, today.
The diagram, Fig. 10, was compiled by J. T. Beard, Jr. from
the same source, and will be found convenient for use in
connection with the tables.
84
MINE CASES AND VENTILATION
PRESSURE TABLE FOR DRY SATURATED STEAM
(Condensed from Marks and Davis, by Permission)
Absolute
pressure,
Ib. per sq. in.
Temp.,
deg. F.
Sp. vol.,
cu. ft. per Ib.
Heat of
the liquid
B.t.u.
Latent heat
of evap.
B.t.u.
Total heat
of steam
B.t.u.
P
t
v or s
h or q
/ or r
h
1
101.83
333.0
69.8
1034 . 6
1104.4
2
126.15
173.5
94.0
1021.0
1115.0
3
141.52
118.5
109.4
1012.3 1121.6
4
153.01
90.5
120.9
1005.7
1126.5
5
162.28
73.33
130.1
1000.3
1130.5
6
170.06
61.89
137.9
995.8
1133.7
7
176.85
53.56
144.7
991.8 1136.5
8
182.86
47.27
150.8
988.2 1139.0
9
188.27
42.36
156.2
985.0 1141.1
10
193 . 22
38.38
161.1
982.0
1143.1
11
197.75
35.10
165.7
979.2 1144.9
12
201.96
32.36
169.9
976.6 1146.5
13
205 . 87
30.03
173.8
974.2 1148.0
14
209.55
28.02
177.5
971.9
1149.4
15
213.0
26.27
181.0
969.7
1150.7
16
216.3
24.79
184 . 4
967.6
1152.0
17
219.4
23.38
187.5
965.6
1153.1
18
222.4
22.16
190.5
963.7
1154.2
19
225.2
21.07
193.4
961.8
1155.2
20
228.0
20.08
196.1
960.0
1156.2
21
230.6
19.18
198.8
958.3
1157.1
22
233.1
18.37
201.3
956.7
1158.0
23
235.5
17.62
203.8
955.1
1158.8
24
237.8
16.93
206.1
953.5
1159.6
25
240.1
16.30
208.4
952.0
1160.4
26
242.2
15.72
210.6
950.6
1161.2
27
244.4
15.18
212.7
949.2
1161.9
28
246.4
14.67
214.8
947.8
1162.6
29
248.4
14.19
216.8
946.4
1163.2
30
250.3
13.74
218.8
945.1
1163.9
31
252.2
13.32
220.7
943.8
1164.5
32
254.1
12.93
222.6
942.5
1165.1
33
255.8
12.57
224.4
941.3
1165.7
34
257.6
12.22
226.2
940.1
1166.3
35
259.3
11.89
227.9
938.9
1166.8
36
261.0
11.58
229.6
937.7
1167.3
37
262.6
11.29
231.3
936.6
1167.8
38
264.2
11.01
232.9
935.5
1168.4
39
265.8
10.74
234.5
934.4
1168.9
40
267.3
10.49
236.1
933 . 3
1169.4
41
268.7
10.25
237.6
932.2
1169.8
42
270.2
10.02
239.1
931.2
1170.3
43
271.7
9.80
240.5
930 . 2
1170.7
44
273.1
9.59
242.0
929.2
1171.2
45
274.5
9.39
243.4
928.2
1171.6
46
275.8
9.20
244.8
927.2
1172.0
47
277.2
9.02
246.1
926.3
1172.4
48
278.5
8.84
247.5
925.3
1172.8
49
279.8
8.67
248.8
924.4
1173.2
50
281.0
8.51
250.1
923.5
1173.6
52
283.5
8.20
252.6
921.7
1174.3
54
285.9
7.91
255.1
919.9
1175.0
56
288.2
7.65
257.5
918.2
1175.7
58
290.5
7.40
259.8
916.5
1176.4
HEAT
85
PRESSURE TABLE FOR SATURATED STEAM — (Continued.)
Absolute
pressure,
Ib. per sq. in.
Temp.,
deg. F.
Sp. vol., Heat of
cu. ft. per Ib. the liquid
Latent heat
of evap.
Total heat
of steam
P t
v or s
h or q
I or r
h
60
292.7
7.17 262.1
914.9
1177.0
62
294.9
6.95 264.3
913.3
1177.6
64
297.0
6.75 266.4
911 .8
1178.2
66
299.0
6.56
268.5
910.2
1178.8
68
301.0
6.38
270.6
908.7
1179.3
70
302.9
6.20
272.6
907.2
1179.8
72
304.8
6.04
274.5
905.8
1180.4
74
306.7
5.89
276.5
904.4
1180.9
76
308.5
5.74
278.3
903.0
1181.4
78
310.3
5.60
280.2
901.7
1181.8
80
312.0
5.47
282.0
900.3
1182.3
82
313.8
5.34
283 . 8
899.0
1182.8
84
315.4
5.22
285.5
897.7
1183.2
86
317.1
5.10
287.2
896.4
1183.6
88
318.7
5 . 00
288.9
895.2
1184.0
90
320.3
4.89
290.5
893 . 9
1184.4
92
321.8
4.79
292.1
892.7
1184.8
94
323.4
4.69
293 . 7
891.5
1185.2
96
324 . 9
4.60
295.3
890.3
1185.6
98
326.4
4.51
296.8
889.2
1186.0
100
327.8
4.429
298.3
888.0
1186.3
105
331.4
4.230
302.0
885.2
1187.2
110
334.8
4.047
305.5
882.5
1188.0
115
338.1
3.880
309.0
879.8
1188.8
120
341.3
3.726
312.3
877.2
1189.6
125
344.4
3.583
315.5
874.7
1190.3
130
347.4
3.452
318.6
872.3
1191.0
135
350.3
3.331
321.7
869.9
1191.6
140
353.1
3.219
324.6
867.6
1192.2
145
355.8
3.112
327.4
865.4
1192.8
150
358.5
3.012
330.2
863.2
1193.4
160
363.6
2.834
335.6 858.8
1194.5
170
368.5
2.675
340.7
854.7
1195.4
180
373.1
2.533
345.6
850.8
1196.4
190
377.6
2.406
350.4
846.9
1197.3
200
381.9
2.290
354.9
843.2
1198.1
225
391.9
2.046
365.5
834.4
1199.9
250
401.1
1.850
375.2
826.3
1201.5
300
417.5
1.551
392.7
811.3
1204.1
350
431.9
1.334
408.2
797.8
1206.1
400
444.8
1.17
422.0
786.0
1208.0
450
456.5
1.04
435.0
774.0
1209.0
500
467.3
0.93
448.0
762.0
1210.0
550
477.3
0.83
459.0
751.0
1210.0
600
486.6
0.76
469.0
741.0
1210.0
SECTION III
MINE GASES
GEOLOGICAL CONDITIONS — COMMON MINE GASES — HYDRO-
CARBON GASES — PROPERTIES AND BEHAVIOR OF MINE
GASES — METHANE — FIREDAMP — CARBON MONOXIDE —
CARBON DIOXIDE — BLACKDAMP — AFTERDAMP — INFLAM-
MABLE AND EXPLOSIVE MINE GASES.
GEOLOGICAL CONDITIONS
Gas, Oil and Water. — The strata of the earth's crust form
a great natural reservoir for gas, oil and water. These collect
in the formations, in the order of their relative densities.
As illustrated in the Fig. 11, which represents an ideal geo-
FIG. 11.
logical section, the subterraneous water collects in the lower
permeable strata, the oil next above, while the gas is found
higher on the anticline.
This condition is only true, however, in a general way,
depending on the nature of the strata and their power to
absorb and hold these elements. Water, and oil to a less
extent, find their way by gravity to a " hard-pan" or stratum
impervious to them; while gas drains to the surface and
escapes, unless confined by an overlying stratum of clay or
cil, from the overlying rocks into the synclinal basins, creates
enormous pressures, which are exerted more or less equally
on the water, oil and gas.
86
MINE CASES 87
Water Level. — In every geological section, there is a more
or less defined " water level" or depth at which water is found
in quantity. Wells or boreholes sunk to this general level
strike a usually abundant supply of water. The same is
true, but to a less extent, of oil, in oil regions. The flow of
oil, in oil-bearing rocks, however, is not as free as that of
water, owing to its viscosity and limited supply.
The water level is not constant, but varies according to
the changing supply or surface drainage, being higher in
wet seasons and lower in seasons of drought. As the oil
floats on the water any change in water level is accompanied
by a similar change in the oil supply. It is due to this fact
that exhausted oil wells often become productive in a season
of flood, and producing wells frequently cease to flow in a
prolonged season of drought.
Natural Gas. — All gas formed and contained in the strata
is called " natural gas," in distinction from gas manufactured
in the industries. Natural gas commonly occurs in large
volume, in coal formations, where it accumulates in cavities
or pockets and in crevices in the strata. It is very largely com-
posed of what are commonly known as the "hydrocarbon" gases.
Effect of Faults. — Fault lines and other geological disturb-
ances of the strata have opened channels by which the gas
confined in certain strata escape to other strata or into the
mine workings or to the surface. For this reason, the near
approach of the working face to a fault line or a disturbed
condition of the strata is often accompanied by a marked
change in the gaseous condition of the mine air. The percent-
age of gas common to the mine may then either increase or
decrease depending on the location of the gas and the nature
of the fault.
Gas Feeders, Blowers. — Any continuous flow of gas from a
crack or crevice in the strata is called a "gas feeder," or
simply a "feeder." The gas flowing from the crevice is known
as "feeder gas."
When a gas feeder is under high pressure so that the gas
issues with considerable velocity, the feeder is called a "blower"
and the gas " blower gas."
88 MINE GASES AND VENTILATION
Occluded Gases. — The gases commonly occluded in the coal
formations .are methane, ethane, nitrogen, carbon dioxide and
oxygen. They are the result of the chemical changes that
took place in the formation of the coal; or are produced by
the action of acid waters on certain limestones or other car-
bonates. Occluded gases are held in the pores of the coal
and other strata, from which they drain into the mine open-
ings, or work upward through such pervious strata as shale
and sandstone. The process is called "emission" or "trans-
piration" of gases.
Pressure of Occluded Gas. — At times, the gas is confined in
the coal or other strata by an overlying stratum of clay or
impervious limerock that prevents its escape to the surface,
and the pressure of the gas is then often very great, varying
from 500 and 600 Ib. per sq. in. to four or five times that
amount. This pressure is manifested in different ways. As
the mine workings are extended the flow of gas into the mine
increases with the exposure of fresh faces of coal, except
where the conditions are such as to allow the gas to drain off
and reach the surface.
Effect of Gas Pressure in Mining. — The pressure of gas
confined in the coal is often sufficient to splinter the coal in
its effort to escape, the fine coal being thrown into the face
of the miner at work. At times, the gas escapes from the
coal with a peculiar hissing sound known as the "singing of
the coal." The pressure of gas in the roof frequently causes
heavy roof falls, and gas in the floor causes the bottom to
heave. In some instances, the gas pressure assists the ex-
traction of the coal and lessens the work of the miner by
helping to break down the coal.
Outbursts of Gas. — In the mining of gaseous seams, it is
not uncommon for gas to work in the strata as the coal is
extracted. As a result, the gas often accumulates in pockets
as shown in the ideal section, Fig. 12. The settlement of the
roof incident to the removal of the coal affords opportunity
for the gas to expand and work forward toward the opening.
The working of the gas in the strata is often accompanied by
severe "poundings" or "bumps," due to sudden displacement
MINE CASES
89
of the gas. Such sounds often continue for several days pre-
vious to a sudden outburst of the gas into the mine workings.
The continuance of these poundings are a sufficient warning to
experienced miners to vacate that part of the mine till the
strata have become
more quiet by the
gradual draining
off of some of the
gas.
In many cases,
where the gas
works down into
the coal, either at
7/^^
FlQ 12
the face or in the
"ribs, " as shown
in the figure above,
the pressure of the gas becomes distributed over a considerable
surface, and is sufficiently great to throw down the coal.
This is called an " outburst" of gas, since large volumes
of gas escape and often hundreds of tons of coal are thrown
violently into the opening.
THE COMMON MINE GASES
The gases of most importance in coal mining, together with
their chemical symbols, molecular weights, densities referred
to hydrogen and specific gravities referred to air of the same
temperature and pressure, are the following:
Gas
Symbol
Molecular
weight'
Density
H = 1
Spec. gravity
air = l
Methane (marsh gas)
Ethene , Ethylene ( olcfiant
gas)
CH4
C2H4
16
28
8
14
0.559
0 978
Ethane
Carbon monoxide
Carbon dioxide . . ...
C2H6
CO
CO2
30
28
44
15
14
22
1 . 0366
0.967
1 529
Hydrogen sulphide
H2S
34
17
1 1912
Oxygen
O2
32
10
1 . 1056
Nitrogen ....
N2
28
14
0 9713
Hydrogen
H2
2
1
0 06936
90
MINE GASES AND VENTILATION
Occurrence of Mine Gases. — Aside from the oxygen and
nitrogen of the air, the gases commonly occurring in coal
mines are methane, carbon dioxide, carbon, monoxide, and
less frequently or in less quantity, hydrogen sulphide and
olefiant gas. These gases are produced by the processes of
decomposition or combustion constantly going on in the mine,
or they emanate from the coal or other strata, where they
exist as natural gases.
Condition of Gas Confined in Coal. — The results of careful
experimental study of coal indicate (Chamberlin) that gas
may exist in coal in three different ways: 1. The gas is oc-
cluded, in a true sense, or absorbed (possibly condensed) by
the coal. 2. The gas is entrapped or held mechanically in
the cavities, cracks or pores of the coal. 3. The gas may
result from chemical changes going on in the coal.
Escape of Gas from Coal. — Experiments made by the Bu-
reau of Mines, by crushing weighed samples of different coals
in closed vessels of known capacity, show that coal con-
tinues to give Off gas for a long time after it is mined.
Coal exposed to the atmosphere loses much of its occluded
gas, but the gas is liberated more freely by crushing the coal,
which would indicate that much of the gas is held mechan-
ically within the mass. It is also shown that the coal con-
tinues to absorb oxygen from the air, during the same period.
The following table gives the percentages, by volume, of the
constituents of natural gases obtained from various coals, in
different localities.
TABLE SHOWING THE COMPOSITION OF GAS EVOLVED FROM COALS AT
212 DEG. F., IN VACUO
Locality
CH4
N2
C02
0-2
.C2H6
Remarks
South Wales
South Wales
South Wales
63.76
87 30
62.78
29.75
7.33
36.42
5.44
5.04
0.80
1.05
0.33
....
Bituminous
Bituminous
Steam coal
South Wales
93.13
4.25
2.62
Anthracite
Lancashire
Lancashire
80.69
77.19
8.12
5.96
6.44
9.05
4.75
7.80
Cannel
Cannel
Westphalia
89 91
7.50
2.59
Gas coal
Westphalia
34 85
58 48
2.56
4.11
Gas coal
MINE GASES
91
Composition of Feeder or Blower Gas. — A large number of
analyses of gas issuing from coal seams as "feeders" or
"blowers" have been made. Gas has also been obtained by
drilling holes several feet into the face of the coal. These
analyses show a wide variation in the composition of the
gas in different localities. Moreover, since the rate of emis-
sion of gases varies, the composition of feeder gas is only
suggestive of the contamination of the mine air.
The following table gives the composition, by volume, of
blower gas in different localities, which shows in a general
way a higher percentage of methane, in comparison with that
of nitrogen. This may be due, to a large extent, to the
higher rate of transpiration of the methane, as compared
with nitrogen, which tends to increase its percentage in blower
gas over what actually exists in the pores of the coal :
TABLE GIVING COMPOSITION OF BLOWER GAS IN DIFFERENT LOCALITIES
Locality
CH4
N,
C02
O2
CO
C2H4
Austria
88 9
10 8
1 0
0 3
Austria
99 1
0 7
0 2
Austria
90 0
9 2
0 2
0 6
Germany
87 2
11 7
1 l
Germany
77 7
18 5
3 7
0 1
South Wales
96 7
2 8
0 5
Wallsend, England
92 8
6 9
0 3
Jarrow, England
Oakwellgate, England
83.1
98 2
14.2
1 3
2.1
0 5
0.6
Wilkes-Barre, Penn
94.2
3:3
1.1
0.9
0.1
0.4
It is important to remember that the occluded gases of
coal are not chemically combined with the constituents of
the coal as shown by analysis, and do not form a part of the
coal itself, although adding much to its inflammability and
heat value.
HYDROCARBON GASES
General Formulas of Hydrocarbon Gases. — Carbon (C) and
hydrogen (H) unite in different ways to form groups of com-
pounds, having certain distinct characteristics. Such are
92 MINE GASES AND VENTILATION
the " paraffins," represented by the general f ormula CnH2n+2;
the "defines," CnH2n; the "acetylenes," CnH2n_2; and
other compounds of less importance in mining, as the " ben-
zenes," "naphthalines," etc.
Occurrence and Formation. — Methane or light carbureted
hydrogen (CH4) and ethane (C2H6), belong to the paraffin
or fatty group, while olefiant gas (C2H4) belongs to the olefine
or oily group. These are all products of the destructive distil-
lation of organic matter. Methane is often seen bubbling up
from the bottom of stagnant pools, in marshes, which fact
suggested the name "marsh gas." It is the result of the slow
decay of the vegetable matter (in the presence of water and
absence of air), at the bottom of the pool.
On the other hand, olefiant gas is the result of the dry
distillation of gas from organic matter, which takes place
less frequently in the strata, owing to the almost invariable
presence of moisture. The character of these hydrocarbon
gases, moreover, varies, also, with the kind of organic matter
that undergoes decomposition.
Of the hydrocarbon gases, the paraffins (methane and
ethane) are the ones chiefly occluded in the coal measures;
while olefiant gas, belonging to the olefine group is rarely
found even in minute quantity. Beside the hydrocarbon gases
occluded in coal, as has been stated, varying quantities of
nitrogen, oxygen and carbon dioxide have been absorbed.
The Heavy Hydrocarbon Gases.— The heavy hydrocarbons
occur in the coal measures as occluded gases, only to a limited
extent. Of these, there are but two that are worthy of
mention; they are
Olefiant gas, ethene or ethylene, (C2H4); sp. gr., 0.978;
Ethane, (C2H6); sp. gr., 1.0366.
Both of these gases are colorless and odorless; they occur
but to a limited extent in association with methane ; and their
chief importance lies in the fact that they each have a wider
explosive range and a lower temperature of ignition than pure
methane. The analyses of the gases exuded from coal rarely
show any appreciable quantity of olefiant gas (ethene); but
ethane (C2H6) occurs more frequently as an occluded gas.
MINE GASES 93
PROPERTIES AND BEHAVIOR OF MINE GASES
The symbols, molecular weights, densities and specific
gravities of the common mine gases have been given in an-
other place. The properties and behavior of these gases in
the mine will be treated here from a practical, rather than a
theoretical standpoint.
METHANE
This gas is commonly known as " marsh gas" or " light
carbureted hydrogen," it being the lightest of the hydro-
carbon gases. It is a colorless, odorless and tasteless gas. It
is combustible, burning with a pale-blue flame, in the air or
in oxygen. It contains no oxygen and is not, therefore, a
supporter of combustion, in the generally accepted meaning
of the term. A lamp flame is quickly extinguished by this
gas unmixed with air. Mixed with air in certain proportions,
the gas becomes explosive, the mixture being known as " fire-
damp. " Marsh gas is not poisonous, but when unmixed with
air suffocates by excluding oxygen from the lungs. The di-
luted gas can be breathed for a long time with no ill effects,
except a slight dizziness, which quickly passes away on re-
turn to fresh air.
Marsh gas is the most common of the occluded gases of
the coal formations. It seldom, if ever, occurs pure, but is
mixed in varying proportions with other hydrocarbons (olefi-"
ant gas and ethane) and often with nitrogen. These mixed
gases greatly modify the character and properties of the pure
gas.
Marsh gas issues from the strata into the mine workings
where it accumulates in quantity, unless removed by a copious
air current. The most gaseous seams are those that are over-
laid with a compact rock, slate, or shale that is impervious to
gas and not traversed by faults, which would allow the gas
to escape. Gas is generated most freely from a virgin seam
and from a freshly exposed face of coal. Hence, new work-
ings generate more gas than old workings; because, in the
old workings, the gas has mostly drained from the strata and
escaped.
94 MINE GASES AND VENTILATION
Marsh gas diffuses rapidly into the air and other gases,
the rate of diffusion depending on the relative densities of
the two mediums. The question is often asked, if the diffu-
sion of gas is so rapid how is it possible for a large body of gas
to accumulate in a void place in the mine. The reason is
that diffusion only takes place at the surface of contact, and
is therefore limited, and the gas is being generated faster
than it passes away.
Marsh gas being lighter than air tends to accumulate at
the roof and at the head of steep pitches and in rise workings.
It is found in such places where the air current is not suffi-
ciently strong to sweep away the gas and in other poorly
ventilated or abandoned places. Gas can generally be found
at the roof or .close to the face of the coal in chambers gen-
erating gas. It is detected by observing the flame of a safety
lamp. If gas is present in sufficient quantity in the air a
faint non luminous cap will appear surmounting the flame of
the lamp. The gas also lengthens and enlarges the flame.
FIREDAMP
All gases were formerly known to the miner as "damps,"
which is a word of Dutch or German origin meaning vapor or
fumes.. Later, as the characters of the different gases became
known, they were named according to their several charac-
teristics. The term " firedamp" was applied to any inflam-
mable or explosive mixture of gas and air.
The word firedamp, today, in this country, means any in-
flammable or explosive mixture of marsh gas and air, with
or without other gases. In England, the word is taken. to
mean any mixture of marsh gas and air without regard to
whether or not the mixture was inflammable or explosive,
which, however, is not its logical meaning.
When but a small amount of marsh gas is mixed with
pure air the gas is so diluted that the mixture is not inflam-
mable. In contact with flame, this small percentage of gas
in the air adds to the combustion and lengthens and enlarges
the flame; but the flame is not propagated throughout the
MINE GASES 95
mixture, as the absorption of the heat by the air is too great
to maintain the temperature necessary for combustion.
Lower Inflammable Limit. — As more gas is added to the air,
a point is soon reached where the combustion of the gas de-
velops sufficient heat to raise the temperature of the air to
that required to maintain the combustion. When this point
is reached the flame causing the ignition is extended or propa-
gated through the mixture. In other words, the mixture
becomes inflammable, because the combustion is supported in
the mixture independent of any other source. The theoretical
percentage of gas in the firedamp at this point, as calculated,
is slightly above 2 per cent., for dry air or saturated air.
The heat absorbed by the water of saturation is so slight in
comparison that it can be ignored without appreciable error.
There are heat losses, however, that cannot be calculated,
which fact raises the lower inflammable limit of pure marsh
gas to between 4 and 5 per cent.
Effect of Dust and Other Gases. — Owing to the fact that
marsh gas is rarely, if ever, found pure, but is generally
mixed with dust or other gases or both, it is never safe to work
with open lights, in air containing more than 1 per cent,
of gas, in bituminous mines; or 2J^ per cent, in anthracite
mines.
Gases are divided into two general classes, in respect to
the effect they produce on the inflammability of firedamp.
Gases having a lower ignition point than marsh gas, as for
example, carbon monoxide, hydrogen sulphide, ethane and
olefiant gas, lower the inflammable limit of firedamp, as given
above. Fine coal dust floating in the mine air has a similar
effect, in proportion as the dust is highly inflammable. On
the other hand, extinctive gases such as nitrogen and carbon
dioxide raise the limit given above.
In the working of bituminous mines, coal dust is a most
dangerous factor, especially when the coal is highly inflam-
mable. In many cases, the finely divided dust produces an
explosive atmosphere even when no gas is present. The pres-
ence of such dust in the mine air, acted on by the flame of a
blownout shot, is certain to cause trouble.
96 MINE CASES AND VENTILATION
To Calculate the Lower Inflammable Limit. — In order to
calculate the proportion of gas (methane) and air when the
firedamp mixture first becomes inflammable, it must be as-
sumed that all the heat generated by the combustion of the
gas is absorbed by the products of the combustion and thi?
remaining unburned air. Owing, however, to there being a
certain amount of heat lost by radiation or otherwise that
cannot be estimated or accounted for, the calculated inflam-
mable limit will only approach the actual, to the extent that
the conditions are fully realized in the calculation. The proc-
ess is as follows:
The weight of oxygen necessary to burn 1 Ib. of methane or
marsh gas (CH4) is shown by the relative weights of these
gases in the following reaction :
CH4 + 2O2 = CO2 + 2H2O
Molecular weights 16 64 44 36
Relative weights 1 4 2% 2>£
But oxygen forms 23 per cent., by weight, of the air, the
remaining 77 per cent, being practically all nitrogen. The
weight of nitrogen concerned in burning 1 Ib. of this gas in
air is then calculated as follows :
23 : 77 ::4 : N
and N = ^^ = 13.39 Ib.
£i€t
The table giving the heats of combustion of different sub-
stances (p. 66) shows that methane, burned in air or oxygen,
gives out 23,513 heat units (B.t.u.). The temperature of igni-
tion of this gas is 1200° F.
Now, since the specific heat of a substance is the heat
(B.t.u.) absorbed by 1 Ib. of that substance, during a rise of
1 deg. F. in its temperature, the heat absorbed by the prod-
ucts of combustion of 1 Ib. methane, for each degree rise in
temperature, is found by multiplying the specific heat of each
of the products, including the nitrogen of the air, by the rela-
tive weight of each product, respectively. The total heat is
then found by multiplying that result by the number of de-
MINE GASES 97
grees rise in temperature; and adding the latent heat in the
steam or water vapor, as follows:
The specific heats of the several products of combustion,
referred to water as unity (1), are carbon dioxide, 0.2163;
nitrogen, 0.2438; water vapor, 0.4805; and air, 0.2374. The
latent heat of the water vapor (steam) or the heat absorbed
when 1 Ib. ,water becomes steam at 212°F. is 970.4 B.t.u. The
heat absorbed by the products of combustion, for a rise of
1200 - 32 = 1168°F., is therefore
Carbon dioxide, 0.2163 X 2.75X1168= 694.7264
Nitrogen, 0.2438 X 13.39 X 1168= 3812.9360 4507.6624 B.t.u.
Water, 1.0000 X 2.25 X 180= 405.0000
Latent heal, 970.4000 X 2.25 =2183.4000
Water vapor, 0.4805 X 2.25 X 988 = 1068.1515 3656.5515 B.t.u.
Total heat absorbed by products .............. 8164.2139 B.t.u.
Having found the heat absorbed by the products, the next
step is to find the heat absorbed by the unburned air. Let x =
weight of air required to make 1 Ib. of the gas inflammable;
and, since 1 Ib. CH4 consumes 4 Ib. O + 13.39 Ib. N = 17.39 Ib.
air, the unburned air is x — 17.39 Ib. The original tempera-
ture of the air being 60°F., the rise is 1200 - 60 = 1140 deg.
and the heat absorbed is 0.2374(z - 17.39)1140 - 270.636z
- 4706.36 B.t.u., which makes the total heat absorbed
8164.2139+270.636z-4706.36 = 270.636z+3457.8539£.£.w.
Since the heat absorbed is assumed equal to the heat gen-
erated,
270.636z + 3457.8539 = 23,513 B.t.u.
23,513 - 3457.8539 _ . „ „ .
alld
270636
This is the total weight of air required to make 1 Ib. of
methane (CH4) inflammable. In other words, the weight
ratio of gas to air, at the lower inflammable limit, is 1 : 74.10.
But since the specific gravity of methane, referred to air as
unity, is 0.559, the volume ratio of gas to air, at this point, is
1 : 0.559 X 74.10; or 1 : 41.42. That is to say, a mixture of
7
98 MINE GASES AND VENTILATION
pure methane and air first becomes inflammable when 1 vol-
ume of this gas is mixed with 41.42 volumes of air.
The percentage of gas in this mixture is
fTlL42 X 10° " 4^f2 = 2'3 Per CmL
Lower Explosive Limit. — The continued addition of gas to
the air causes the firedamp mixture to become more and
more inflammable till a point is reached when the combustion
of the gas is so rapid that the mixture is explosive. As this
condition is approached, in practice, owing to the mixture of
the gas and air not being uniform, the ignited gas often snaps
and cracks in the combustion chamber of a safety lamp.
In the same manner, an accumulation of firedamp, in the
mine, when ignited, may burn with greater or less energy or
violence and small explosions may occur here and there, fol-
lowed perhaps by the general explosion of the entire body of
the firedamp. The explosion depends not alone on the propor-
tion of gas and air in the mixture, although that is important,
but on the intensity and volume of the igniting flame. Thus,
it happens that a firedamp mixture ignited in the narrow
confines of the mine workings may, after burning for a brief
period with more or less energy, suddenly develop a violent
explosion.
The lower explosive limit of pure methane has been de-
termined, by experiment, to occur when 1 volume of the gas
is mixed with 13 volumes of air; or the percentage of gas in
the mixture is
X 100 = -^ = 7-14 P^ cent.
This limit, however, is considerably modified by any condi-
tions that tend to increase or decrease the amount of heat
developed.
Maximum Explosive Point. — The maximum explosive force
of a combustible gas is developed when the proportion of gas
to air is just sufficient for complete combustion. If the gas in
the mixture is in excess of this proportion the full heat en-
ergy is not developed, owing to the incomplete combustion of
MINE GASES 99
the gas. On the other hand, if the air is in excess of what
is required for complete combustion, the unburned air ab-
sorbs a portion of the heat generated by the combustion,
which thus becomes latent.
The maximum explosive force of methane is developed
when the proportion of gas to air is 1 : 9.57. - It is calculated
in the following manner: Write, again, the chemical equation
expressing the reaction that takes place when this gas burns
in oxygen, forming carbon dioxide and water; thus,
CH4 + 2O2 = CO2 + 2H2O
Molecular volumes, 1212
It should be observed that when the symbol of each gas
is written as a molecule (oxygen = O2) the prefix or number
written before the symbol, indicating the number of mole-
cules of that gas taken, shows also the relative volume of the
gas concerned in the reaction; because the volume of all
gaseous molecules at the same temperature and pressure is
the same.
The above equation shows that two volumes of oxygen
(2O2) are required to completely burn one volume of methane
(CH4); and there are formed one volume of carbon dioxide
(CO2) and two volumes of water (2H2O).
But, oxygen forms 20.9 per cent., by volume, of the at-
mosphere. Therefore, when methane is burned in air, the
volume of air required to completely burn two volumes of the
gas is
2 volumes
~0209~ = 9>569' Say 9'57 voL
Hence the proportion of gas to air that will develop, in ex-
plosion, the maximum force is 1 : 9.57. The percentage of
gas in the mixture, at this point, is
Higher Explosive Limit. — The continued addition of gas
after the maximum explosive point is reached, causes the ex-
plosion of the firedamp mixture to be less and less violent,
till a point is finally reached where the proportion of air is so
100 MINE GASES AND VENTILATION
*
reduced that explosion ceases and the mixture becomes
simply inflammable.
The point at which explosion ceases is called the " higher
explosive limit," For pure methane, this point is practically
reached when the proportion of gas to air is 1 : 5, although the
position and character of the igniting flame, may vary this pro-
portion slightly. The percentage of gas in the firedamp, at
this point, is practically
; X 100 = ~ = 16.67 per cent.
1 -)- 5 D
Higher Inflammable Limit. — By the continued addition of
gas, the firedamp having ceased to be explosive, now becomes
less and less inflammable. The mixture not only ignites less
readily, but when ignited burns less regularly and quietly than
did the same firedamp mixture, in the lower inflammable stage
when less gas and more air were present.
The higher inflammable stage of the gas is more danger-
ous, in mining practice, than the lower inflammable stage of
the same gas, because the slightest addition of air, which is
liable to occur at any moment in the mine, causes the mix-
ture to approach the maximum explosive point. The addi-
tion of air to firedamp in the lower explosive or inflammable
stages makes the mixture less explosive or inflammable.
Another important distinction between the lower and
higher stages of firedamp mixtures is the relative ease with
which the flame cap may be detected in the two stages. While
the flame of a safety lamp burns steadily and yields a good
cap that is easily detected, in the lower inflammable stage;
the lamp flame is unsteady and the flame cap generally hard
to discern in the higher inflammable stage. The reason is
probably to be found in the uncertain and varying amount
of air in the mixture feeding the flame, which makes the gas
continually approach the explosive point The gas in this
(higher) stage is said to be " sharp."
The following table will make the several stages of fire-
damp more clear; but it must be remembered the proportions
of gas to air and percentages of gas given as marking the
MINE GASES
101
dividing line between the different stages or the inflammable
and explosive limits are only suggestive and vary with the
degree of purity of the gas; the volume, intensity and posi-
tion of the igniting flame, and the pressure and temperature
of the surrounding atmosphere.
FIREDAMP MIXTURES (METHANE AND AIR)
Lower
Explosive
stages Higher
inflammable
—
inflammable
stage
Lower stage
Maximum
point Higher stage
stage
Proportion of Gas to Air
1 :40
| 1 :13
1:9. 57
1 :5
1 :2.4
2.5%
7.14%
I
Percentage of Gas
9.46%
16.67%
29.5%
The continued addition of gas thus renders the firedamp
extinctive of its own flame and therefore noninflammable.
The proportions and percentages given in the table denote
more or less closely the limits of the several stages.
Flashdamp. — -This is a mixture composed almost wholly of
marsh gas (CH4) and carbon dioxide (CO2), mixed in the pro-
portion in which these gases diffuse into each. It is formed
under special conditions, in mines, where carbon dioxide from
the old workings of an abandoned seam becomes mixed with
the undiluted marsh gas generated in the strata. The mix-
ture is lighter than air and possesses the peculiar and mis-
leading property of extinguishing the lamp at the roof of
the .seam or the face of a steep pitch.
Calculation of Composition of Flashdamp. — According to
the law of diffusion, gases diffuse into each other in the in-
verse ratio of the square roots of their densities or specific
gravities. For example, the specific gravities of methane
and carbon dioxide are 0.559 and 1.529, respectively; and the
ratio of the velocities of diffusion of these two gases into
each other is then the inverse ratio of the square roots of
these numbers.
CH4 = VL529 L236 =
C02 ~ 0.747 =
102 MINE GASES AND VENTILATION
which can' be written 1.65 : 1 ; or 1650 : 1000. This ratio
shows that when these gases diffuse' into each other, directly,
before dilution with air takes place, the mixture will contain
1650 volumes of methane for each 1000 volumes of carbon di-
oxide. The same result is obtained by stating the law thus:
The ratio of diffusion is equal to the square root of the inverse
ratio of the densities or specific gravities of the gases; or, as
follows:
CH4 /1. 529 /
CO, ==V0559 =: V 2.735:
A slightly different, though theoretically more correct re-
sult is obtained when the calculation is based on the den-
sities of these gases, referred to hydrogen as unity (1). The
process is as follows:
Methane (CH4) :
Q = 1 X 12 = 12
H4 = 4 X 1 = 4
Molecular wt. ==16; density, 16 -r- 2 = 8
Carbon dioxide (CO2) :
C = 1 X 12 = 12
02 = 2 X 16 = 32
Molecular wt. = 44; density, 44 -f- 2 = 22
The ratio of diffusion is then equal to the square root of
the inverse ratio of these densities; or
~* = Jf = V2J5 = 1.658
^U2 \ O
Calculation of Percentage Composition, by Volume. — The
mixture is estimated to contain
Methane (CH4) ................. .............. ____ 1658 volumes;
Carbon dioxide (CO2) ......................... .... 1000 volumes;
Total . . ........................................ 2658 volumes.
Percentage, by volume,
Methane, 165^Q100 = 62.38 per cent.
1000 X 100
Carbon dioxide, -^r^ -- = 37.62 per cent.
100.00 per cent.
MINE GASES 103
CARBON MONOXIDE
This gas, formerly known in mining textbooks as "car-
bonic oxide/' or "whitedamp," is the product of the com-
bustion of carbon in a limited supply of pure air. Because
the supply of oxygen is limited the combustion of the carbon
is incomplete and the monoxide is formed instead of the
dioxide.
Carbon monoxide is a colorless gas. It is extremely
poisonous, owing to its being absorbed very rapidly by the
haemoglobin or red coloring matter of the blood, from which
it is separated slowly and with difficulty. The effect on the
system is therefore cumulative when exposed to the smallest
percentage of this gas in the atmosphere breathed. The
affinity of carbon monoxide for the haemoglobin is from 250
to 400 times as great as that of oxygen, so that the blood
corpuscles are quickly rendered inert and death is the sure
result. The gas is not displaced by the oxygen administered in
treatment, but is eliminated slowly by natural processes that
take place in the system, unless the latter is too weak or the
percentage of the gas absorbed is too great for such result
to take place.
The treatment for carbon-monoxide poisoning is the en-
forced inhalation of pure oxyge'n, by the use of the pulmotor.
This is a device that consists essentially of a small portable
tank containing compressed oxygen, which is pumped into
the lungs by a bellows, while another belows withdraws
the same from the lungs after use. The pressure of the gas
in the oxygen tank automatically operates the bellows at
a rate of 16 strokes per minute as in normal breathing. A
face mask completes the equipment. It is important to draw
the tongue forward with tongs provided for that purpose,
and to close the gullet leading to the stomach, by a gentle
pressure of the thumb on the throat, in order to avoid the
gas filling the stomach.
The presence of the smallest percentage of carbon mon-
oxide in the atmosphere breathed is dangerous to health and
life because of its cumulative tendency, its possible toxic
effect on the nervous system and the impairment of the vital
104 MINE GASES AND VENTILATION
organs of the body. The fatal percentage of this gas cannot
be definitely stated because of numerous other factors that
together determine a fatal effect. The more important of
these are the following: The depletion of the oxygen of the
air breathed; the length of the time of exposure to the poi-
sonous atmosphere; the energy expended in physical work
in such atmosphere ; the state of health and the normal physical
condition of the person.
Some persons are more sensitive to gas poisoning than
others, owing to a less vigorous constitution, a temporarily
weakened condition, a more nervous temperament, or pre-
vious exposure to gas poisoning, the baneful effects being hard
to eradicate from the system. For these reasons, what would
prove a fatal percentage in some instances of less purity of
atmosphere, longer exposure, more difficult work, or physical
ailment of any nature, would not necessarily produce fatal
results under better conditions and more robust health of the
individual exposed to the gas.
Relative Rate of Absorption by Blood. — The experiments
of Dr. J. S. Haldane and others have shown that 0.02 per
cent, of carbon monoxide in otherwise pure air produces
about 20 per cent, of saturation in a brief period of time
(20 min.?). Since pure air contains 20.9 per cent, of oxygen,
the ratio of carbon monoxide to oxygen, in the air breathed,
is 2:2090, or 1:1045. But the ratio of absorption, carbon
monoxide to oxygen, in this case, is 20 :80, or 1 :4, the blood
showing only 20 per cent, carbon monoxide and 80 per cent,
oxygen. Hence, the relative rate of absorption by the blood,
carbon monoxide to oxygen, is about 260:1, since 104,5^4 =
say 260. In other words, the blood in this experiment ab-
sorbed carbon monoxide about 260 times as rapidly as it ab-
sorbed oxygen, under the same conditions.
Another experiment showed 50 per cent, saturation in
the blood when the air breathed contained 0.08 per cent, of
carbon monoxide. In this case, the ratio of carbon monoxide
to oxygen in the air breathed is 8 : 2090, or 1 : 260. But the
corresponding ratio of absorption is 1:1, the blood showing
50 per cent, of saturation, or equal quantities of these two
MINE CrASES 105
gases. Hence, in this case also, the relative rate of absorp-
tion of carbon monoxide and oxygen is the same as before,
namely, 260:1.
Another experiment showed 50 per cent, saturation in the
blood when the air breathed contained 0.05 per cent, of
carbon monoxide. Here the ratio of carbon monoxide to
oxygen in the air breathed being 5 :2090, or 1 :418, and the
ratio of absorption, as before, 1:1, the relative rate of ab-
sorption is 418:1, showing that the blood absorbed carbon
monoxide, in this case, about 400 times as rapidly as it ab-
sorbed oxygen, under like conditions, in the two previous
experiments.
The experiments suggest not only the variation in the
rapidity of the absorption of carbon monoxide by the blood
of different individuals, with varying constitutions and de-
grees of health; but show clearly the great affinity of the
haemoglobin of the blood for carbon monoxide as compared
with oxygen. These facts demonstrate forcibly the danger
of working in a mine atmosphere containing the smallest
possible percentage of this gas even when the worker is in
robust health.
Production of Carbon Monoxide in Mines. — Carbon mon-
oxide does not occur naturally in mines, but may be and
often is produced in dangerous quantities under the prac-
tically unavoidable conditions and occurrences incident to
coal mining.
This gas is produced in considerable quantities by any
combustion, on a large scale, commonly occurring in the
limited confines of mine workings. Examples of this are
mine fires and explosions of gas or dust. This gas is also
produced by the explosion of powder in blasting. It is pro-
duced in dangerous quantities by the slow combustion of
fine coal and slack thrown in the waste, in poorly ventilated
places and abandoned areas void of circulation. Carbon
monoxide is the deadly component of afterdamp, which renders
the latter so quickly fatal to life, as shown by the fatal results
that follow many mine explosions.
106 MINE GASES AND VENTILATION
Detection of Carbon Monoxide in Mines. — There is no re-
liable flame test for the detection of carbon monoxide as it
occurs in mines. The lamp flame is, no doubt, lengthened
when fed with air containing the gas, but this effect is im-
perceptible in a percentage that would be fatal to life.
The lengthening of the flame is plainly noticeable when
the fine dust of an inflammable coal is suspended in consid-
erable quantity in the still air of a mine entry or chamber.
This is the result of the increased combustion owing to the
dust-laden air feeding the flame. It is possible that a barely
perceptible cap may be discerned at times under particularly
favorable conditions. This, however, would be a dust cap
and would not indicate the presence of the gas.
What is known as the "blood test" will reveal the pres-
ence of very small percentages (0.01 per cent., Haldane*) in
the air. The delicacy of this test, however, is greatly im-
paired by the difficulty of correctly judging of the change in
the color of the blood solution employed in making the test.
The difficulty is increased by the dim, artificial light of the
mine and the impaired eyesight and possible partial color-
blindness of the observer. The blood test also requires time
and care in its making, which together with the necessary
apparatus do not recommend its use in the mine.
The experiments of Dr. J. S. Haldanef to ascertain the
extent to which animal life is affected by the presence of
carbon monoxide in the atmosphere breathed into the lungs
led him, first, to suggest the use of small animals as a plainly
visible and thoroughly reliable index of the presence of gas
in quantity dangerous to human life. Dr. Haldane observed
that mice and small birds, preferably canaries, were pros-
trated by the gas in a much briefer period than is required
to produce the same effect on a man.
Exposed to an atmosphere containing 0.1 per cent, of
carbon monoxide, a mouse became giddy in 12 min., while a
man experienced a like effect only after breathing the same
atmosphere for a period of two hours. Again, three small
*Trans. I. M. E., Vol. 38, p. 275.
•jTrans. I. M. E., Vol. 38, pp. 267-280.
MINE GASES 107
mice and a canary were exposed to an atmosphere containing
0.6 per cent, of this gas. In 4 min. the canary fell from its
perch and died, and the mice became helpless, but recovered
quickly in fresh air. A man continued to breathe the same
atmosphere and, at the expiration of 10 min., was unaffected,
a test of his blood showing but one-fourth saturation.
Dr. Haldane's conclusions, based on his experiments, are
briefly as follows:
1 . Noticeable symptoms are never produced by less than
about 0.02 per cent, of carbon monoxide in otherwise pure
air.
2. The poisonous effect is decreased somewhat by a mod-
erate addition of carbon dioxide; but increased by depletion
of the oxygen of the air.
3. Small animals recover quickly and do not exhibit the
after effects of the poisoning so often fatal to man.
4. The analyses of the blood of victims of the afterdamp
of mine explosions usually show 80 per cent, saturation.
A series of experiments made at the Pittsburgh testing
station to determine the effect of repeated exposure of mice
and canaries corroborates the conclusion of Dr. Haldane in
respect to the complete rapid recovery of these small animals
from the effects of carbon-monoxide poisoning.
As previously explained, men who have been once over-
come by this gas are more sensitive to its effects again. This
is not the case, however, with mice and birds, which fact
makes them the more useful in mining- practice. A bird or
a mouse that has been exposed to the .gas and- overcome a
great number of times shows no more sensitiveness to its
poisonous effects than one never poisoned by the gas.
Following is the record of eight exposures of a canary to
an atmosphere containing 0.25 per cent, carbon monoxide, as
given on p. 8, Technical Paper 62, of the U. S. Bureau of
Mines, each exposure, except the last, being made immedi-
ately upon the recovery of the bird from the previous one.
The table shows the time, in minutes intervening between the
moment of exposure, first signs of distress, collapse of the
bird and recovery in fresh air.
108 MINE GASES AND VENTILATION
TABLE 1. — EFFECT OF REPEATED EXPOSURE ON CANARY
Time in minutes
M f
Distress
Collapse
Recovery
1
3
1
7
2
3
1
8
3
1
3
8
4
2
3
7
5
2
2
7
6
2
2
7
7
2
1
12
(a 2-min. interval)
1 I 1
The above record shows earlier signs of distress after the
first two exposures. This may naturally be attributed to the
alarm and expectancy of the bird arising from its previous
experience; but the total interval to collapse was uniform (4
min.), except in the fourth and the two last exposures, which
were 5, 3 and 2 min., respectively.
The following table shows the same data recorded in four
successive exposures of a mouse to a 0.3-per cent, mixture of
carbon monoxide and pure air:
TABLE 2. — EFFECT OF REPEATED EXPOSURE ON MOUSE
Time in minutes
No. of exposure
Distress
Collapse
Recovery
1
3
6
17
2
3
10
23
3
4
12
34
4
3
14
not given
A similar series of experiments, performed by exposing a
canary at irregular intervals and on different days to at-
mospheres containing from 0.18 to 0.24 per cent, of carbon
monoxide and numbering 14 exposures in all, extending over
a period of nine days, showed practically the same results.
MINE GASES 109
CARBON DIOXIDE
This gas, often called "carbonic acid gas" or "chokedamp"
is a colorless and odorless gas, having a distinctly acid taste.
It is not combustible and will not support combustion in any
ordinary form.
How Produced. — Carbon dioxide is the product of the com-
plete combustion of carbon or carbonaceous matter in a
plentiful supply of air or oxygen. It is produced, in mines,
by the breathing of men and animals; burning of lamps;
explosion of powder slow combustion of fine coal and slack
in the gob; and other forms of combustion taking place.
Effect on Flame. — Carbon dioxide has a similar effect on
flame to that caused by an exces of nitrogen; or, what is the
same thing, a dep etion of oxygen in the air. The presence of
carbon dioxide in the air tends to reduce the activity of com-
bustion. It dims the flame of a lamp and extinguishes it
when present in sufficient quantity.
The percentage of carbon dioxide that will extinguish
flame depends on both the nature of the flame and the amount
of oxygen in the air feeding the flame. A gas-fed flame, as the
hydrogen flame of the Clowes lamp, or the acetylene flame of
a carbide lamp, is less susceptible to extinction from this
cause than is an oil-fed flame.
The flame of a lamp burning sperm or cottonseed oil is
extinguished in an artificial atmosphere (which is the usual
condition in a mine) containing 14 per cent, of carbon dioxide.
But, in a residual atmosphere formed by allowing the lamp
to burn in a closed place till extinguished, only 3 per cent,
of carbon dioxide is required for extinction of the flame.
Effect on Life. — Carbon dioxide is not classed as one of the
poisonous mine gases, although it exerts a toxic effect on the
human system. It is irrespirable when unmixed with air and
if breathed produces death by suffocation. In smaller quan-
tities, it causes headache, nausea and pains in the back and
limbs.
According to Dr. Haldane, no appreciable effect is pro-
duced by breathing air containing carbon dioxide, until there
110 MINE GASES AND VENTILATION
is about 3 per cent, of this gas present. Breathing then
becomes slightly more difficult; 5 or 6 per cent, of the gas
causes deckled panting; and 18 per cent, suffocation and death.
The effect of the gas is much increased if the oxygen content
of the air is below the normal.
For example, with 18 per cent, carbon dioxide present,
there is 0.209 (100 - 18) = 17.14 per cent, oxygen and 0.791
(100 — 18) = 64.86 per cent, nitrogen, under normal con-
ditions. This is a fatal atmosphere.
But, if the oxygen of the air has been depleted so that
the ratio, oxygen : nitrogen, is less than 20.9 : 79.1; then a less
percentage of carbon dioxide than that named above (18%)
would be fatal to life.
Treatment when Overcome. — Remove promptly to fresh
air; apply alternately cold and lukewarm bandages to the
chest; rub the limbs and body briskly to start circulation; and,
if necessary, use artificial respiration. When consciousness
is restored put the patient to bed and keep him quiet for
several days.
BLACKDAMP
It is a common mistake, in mining practice, to regard car-
bon dioxide as another name for "blackdamp," which is found
in such quantities in many poorly ventilated mines. Carbon
dioxide is one constituent only of blackdamp.
The term blackdamp describes a variable mixture of air
deficient in oxygen, and carbon dioxide. It consists therefore
of carbon dioxide, nitrogen and oxygen, in varying quantities.
The percentage of oxygen in the mixture will determine its
respirable quality. The nitrogen is wholly inert and acts
only to dilute the mixture and thus reduce the percentage of
oxygen present. The carbon dioxide not only dilutes the mix-
ture but produces also a toxic effect on the human system,
although this effect is not of such a nature as to class carbon
dioxide as a poisonous gas.
The production of blackdamp in coal mines is due to two
chief causes: 1. The absorption of the oxygen of the air by the
coal. 2. The generation of carbon dioxide by the various
MINE GASES 111
forms of combustion or oxidation continually taking place
in the workings of the mine.
The absorption of oxygen from the mine air by the freshly
exposed surfaces of coal is more rapid than what is generally
supposed. Experiment has shown that a certain freshly
mined bituminous coal absorbed from one-eighth to one-
seventh of its volume of oxygen from the surrounding air, in
24 hr.; while only about one-tenth of this oxygen was con-
verted into carbon dioxide. It is suggested that the remain-
ing nine-tenths of the oxygen absorbed unites chemically with
certain un saturated hydrocarbons in the coal.
The effect of this rapid absorption of oxygen, in the still
air of badly ventilated places, in coal mines, as can be readily
imagined, is to deplete the oxygen content of the air. This is
especially the case where tons of coal are shot down at night
and left to be loaded out the following day and the ventila-
tion during the night is much diminished in the mine.
On the other hand, where the ventilation is adequate and
there is still blackdamp produced in quantity, it is the result
of the generation of carbon dioxide from some cause, gen-
erally a mine fire or the slow combustion of fine coal.
AFTERDAMP
The term " afterdamp," as the word implies, is used to 'de-
scribe the variable mixture of noxious gases that remains
after any explosion of gas, dust or powder in a mine.
Composition. — It is impossible to give the composition of
afterdamp, except in the most general way; because the
gases formed depend on so many varying conditions, in respect
to the- character of the gas or dust burned ; the relative vol-
ume of available oxygen; the size of the workings where the
explosion takes place, as determining the temperature and
pressure developed; and the condition of the mine with respect
to gas, dust and moisture.
Afterdamp may contain variable quantities of nitrogen,
carbon dioxide, carbon monoxide, water vapor and, at times,
lesser amounts of nitrous oxide gas and possibly some un-
112 MINE GASES AND VENTILATION
burned methane. The mixture is extremely dangerous, being
fatal to life and often highly explosive.
INFLAMMABLE AND EXPLOSIVE MINE GASES
The presence of combustible gases in the atmosphere of
a mine is always an element of danger for three principal
reasons. 1. The percentage of gas in the mine air may be
sufficient to form an explosive mixture known as firedamp.
2. The temperature of ignition of most of these gases is lower
than that of methane, which is usually the chief constituent
of firedamp, and the latter is rendered more readily ignitable
by reason of their presence. 3. The presence of the smallest
percentage of a combustible gas assists to that extent the
ignition of a dust-laden atmosphere, and increases the vio-
lence of its explosion when ignited.
The Inflammable Gases. — The inflammable or combustible
mine gases, in the order of their importance, are methane
(CH4), carbon monoxide (CO), ethane (C2H6), ethene or olefi-
ant gas (C2H4), hydrogen (H2) and hydrogen sulphide (H2S).
Each of these gases is not only combustible but forms an ex-
plosive mixture when mixed with air in certain proportions.
Inflammable Range of Gases. — The combustion of an in-
flammable gas, under mining conditions, requires the presence
of air or available oxygen. The relative proportion of air and
gas in the mixture determines the character and completeness
of the combustion and the range of inflammability of the gas.
The maintenance of flame throughout a gaseous mixture
requires that the heat of combination between the combusti-
ble and the atmosphere supporting the combustion shall be
equal to that lost by radiation, conduction and absorption by
the air and gaseous products formed. Two conditions are
possible.
1. The proportion of gas to air may be such as to give a
low rate of combination and a correspondingly small genera-
tion of heat, which is insufficient to raise the adjacent gas-
eous molecules to an equal temperature, resulting in a still
lower rate of combination and a lesser generation of heat
as the action proceeds through the mass till it finally ceases.
MINE GASES 113
2. Again, the proportion of air to gas may be such as to
cause an absorption of heat greater than that generated when
the condition will likewise be a falling one and there can
result no general extension of flame throughout the mass.
The first of these two conditions (excess of gas) deter-
mines the higher inflammable limit of the gas, while the
second condition mentioned (excess of air) marks the lower
inflammable limit. Beyond these two limits the gaseous
mixture is not inflammable. In mining practice, mixtures
above the higher limit are more dangerous than those below
the lower limit, as more air will make them explosive.
Explosive Range of Gases. — A combustible gas is always
inflammable in proportions of gas to air outside of the ex-
plosive range of the gas. In other words, the range of
inflammability is wider than and embraces the range of ex-
plosibility. The same principles, however, apply in respect
to each of these conditions.
The degree of explosiveness of a gaseous mixture is in-
creased as the rate of combination is more rapid and the loss
of heat less; or decreased as the rate of combining is slower
and the loss of heat greater.
Maximum Explosive Point. — It is quite generally assumed
that the maximum explosive force of a gas is developed
when the proportion of air or oxygen is just sufficient for
the complete combustion of the gas. While this is sufficiently
close for all practical purposes, it is stated (Emich) that the
explosibility is not necessarily greatest at this point.
Inflammable and Explosive Limits. — The following table
gives the lower and higher inflammable and explosive limits
and the maximum explosive point of the three most important
combustible mine gases, except only the higher inflammable
limit of carbon monoxide, which has not been determined, but
is probably about 80 per cent. The table shows the percent-
age of gas present in the mixture, at each of the five stages
given. The lower inflammable limit and the maximum
explosive point have been calculated for each of these gases,
while the other data are the results of experiment. A normal
condition of the air is assumed :
114
MINE GASES AND VENTILATION
TABLE GIVING THE INFLAMMABLE AND EXPLOSIVE LIMITS AND THE
MAXIMUM EXPLOSIVE POINT OF METHANE, HYDROGEN AND
CARBON MONOXIDE
Gas
Lower
inflam.
limit
Lower
explo.
limit
Maximum
explo.
point
Higher
explo.
limit
Higher
inflam.
limit
Methane ; 4.5 7.1 9.5 16.7 20.5
Carbon monoxide 8.4
16.5
29.5
75.0
Hydrogen 5 . 0
9.5
29.5
66.3
72.0
The same data, in reference to olefiant gas (ethene or ethy-
lene), C2H4, are: Lower explosive limit, 4.0 per cent.; maximum
explosive point, 6.5 per cent.; and higher explosive limit, 22
per cent. These, however, have only a relative importance
in respect to mining, because the percentage of this gas pres-
ent in mines is very small.
Peculiarities of Explosion. — A peculiarity in the explosion
of a mixture of methane and air is that, at the temperature of
ignition (1200°F.), about 10 sec. are required before the gas
will ignite (Mallard and Le Chatelier), while both hydrogen
and carbon monoxide ignite at once, upon contact with the
flame. The time required for the ignition of methane grows
rapidly less as the temperature is increased.
The same authorities also claim that mixtures of methane
and air in any proportion are explosive at high temperatures,
and the same effect has been observed at high pressures. In
other words, an increase of temperature or pressure has the
effect to widen the explosive range of a gas
A mixture of carbon monoxide and air will not explode in
the absence of moisture. The explosion, in this case, seems
to require two stages, the carbon monoxide taking the oxygen
from the water, which is replaced immediately by the oxygen
of the air, as represented by the following equations:
and
CO + H2O = CO2 + H2
2H2 + O2 = 2H2O
It has been argued that, since carbon monoxide, which is
distilled from coal dust floating in the mine air, is not ex-
MINE CASES
115
plosive in dry air, the safest condition is a dry mine atmos-
phere, which, however, is practically impossible.
Explosive Mine Gases. — The diagram, Fig. 13, given below
combines, in a compact form, most of the important reactions
and data, relating to the combustion and explosion of those
mine gases that form explosive mixtures with air. In the upper
left-hand corner is a graphic illustration of the relative extent
E3 Inflammable lont
2!?5 [xplosive lone .
;__ Maximum t*p!osi*t point
tuphwe Limh
inflammable Limih
-— Life Line (fatal Per Cent )
EQUAL W
CONSTANT
_
3.4090
©AS
EQUATION SNOWING COMBUSTION
•OF 6AS IN OXYGtN
HEAT 0> COMBUSTION
IN OXY6EN
6.TU P£R POUND
[THYLCNl
OLtFIANl 6A$
UK BON MONO/UN
C AH BO NIC OJTIOf
>S 14
0.967
HOUCOIM WE/6HT
JHLATIVf VOLUME I
REACTION 2CO 1 0, • 2CO,
KllATIVl VOLUMf
2 I
URMPTOCO,
4.32S '
VOCS3
HfDffOCEH SULPHID[
WLPHURCTtl) HYDKOMN
34 17 \ 1 .91? \OJ9t? iO.St>
Rt 'ACTION 2H,tO,' 2H.O
HOLECULAK WEIGHT 4 3Z 36
RELATIVE Wfl6HT 169
RELATIVE VOLUME 2 I ? _
REACTION Z^JCV,?.;^?^
MOIKUIAR WEIGHT 66 36 Of J6
KHATIVC MIGHT n » j? 9
RELAT/Vf VOLUME 2322
BUKNEDTOHtO
AT 32* f
62.03Z
H,OAT 32T
7.J19
FIG. 13.
of the explosive and inflammable zones of each of these gases
when mixed with air. The horizontal lines, in each gas col-
umn, mark, approximately, the maximum explosive point and
the lower and upper explosive and inflammable limits; also
the fatal percentage is indicated by the dotted lines. These
marks are explained by the legend in the upper right-hand
corner The specific heats are given for equal weights of
the gases, for constant volume and constant pressure, referred
to water as unity.
SECTION IV
EXPLOSIONS IN MINES
DEFINITION, GAS EXPLOSION, DUST EXPLOSION— INFLAMMA-
TION OF GAS — NATURE AND TEMPERATURE OF FLAME —
EXPLOSION OF GAS — COAL DUST, ITS INFLAMMABILITY
AND INFLUENCE, EFFECT OF STONE DUST — MINE EXPLO-
SION, DEVELOPMENT, CAUSES, MIXED LIGHTS, ELECTRIC
MINE LAMPS, PREVENTION OF MINE EXPLOSIONS.
Definition. — A mine explosion is understood to be a violent
disturbance of the atmosphere within a mine, as manifested
by a destructive blast or rush of air accompanied by more or
less flame, and is the result of the ignition and combustion
with explosive rapidity of gas and dust or either accumulated
in the mine.
Gas Explosion. — An explosion produced and maintained
chiefly by gas accumulated in the mine workings and passages
or mixed with the air current is described as a "gas explosion,"
although practically every mine explosion involves the com-
bustion of both gas and dust.
Dust Explosion. — An explosion in which the fine coal dust
accumulated in the mine or suspended in the air current
plays a prominent part is commonly called a "dust explosion,"
although it may have originated in a local explosion of gas,
which is true of most mine explosions.
Few if any mine explosions are wholly due to gas or dust,
but combine both of these elements in varying proportions
the character of the explosion as "gas" or "dust" being deter-
mined by the later evidences.
INFLAMMATION OF GAS
Theory of Inflammation. — The inflammation of a combus-
tible gas involves, at least, two main conditions that are
essential to the reactfon. They are as follows :
116
EXPLOSIONS IN MINES
117
1. The presence of another gas that will support the com-
bustion by reason of the different affinities of the elements
of the gases that invite dissociation and recombination to
form other compounds.
2. A rise of temperature, at the point of contact of the
two gases, sufficient to start the reaction.
The ignition of a combustible gas in some cases (carbon
monoxide) requires, besides the above, the presence of water
vapor.
Temperature of Ignition. — At the same pressure and under
the same conditions of ignition, the temperature at which a
given gas inflames or the temperature of ignition for that gas
is fixed. The following table gives the average temperatures
of ignition of the principal mine gases, as determined by
experiment:
AVERAGE TEMPERATURES OF IGNITION OF THE COMBUSTIBLE MINE
GASES IN NORMAL AIR
Gas
Symbol
Temperature
of ignition
(deg. F.)
Carbon monoxide . .
CO
1240
Methane .
CH4
1212
Ethane
C2H6
1140
Ethene (olefiant gas)
C2H4
1124
Hydrogen .
H2
1077
Acetylene
C2H2
970
NATURE AND TEMPERATURE OF FLAME
The Nature of Flame. — Flame, as here considered, is burn-
ing gas. It may be luminous or nonluminous, according to the
presence or absence of carbon either free or combined as
hydrocarbons. The incandescence of the carbon particles
when present renders the flame luminous. This is the case
with most oil-fed flames and flames burning in a dusty atmos-
phere. The flame of hydrogen burning in clear, pure air is
practically nonluminous. Methane produces an almost non-
118 . MINE GASES AND VENTILATION
luminous flame, but the flame of the heavy hydrocarbon gases
is always more or less luminous.
The Temperature of Flame. — The temperature of flame is
variable, owing to numerous conditions that affect the com-
bustion of the gas both as to its rapidity and completeness.
The temperature will vary in different parts of the same
flame, because of a variable supply of air that not only affects
the combustion of the gas but absorbs much of the heat de-
veloped and lowers the temperature of the flame.
Owing to these varying conditions it is clearly impossible
to calculate the actual flame temperature of a burning gas.
This is often roughly assumed to be about one-half of the
theoretical value as calculated from the heat of combustion
per pound of gas and the heat absorbed by the corresponding
products of combustion, for each degree rise in temperature.
It is important not to confuse the flame temperature of a
combustible gas with its temperature of ignition, as they
have no connection with each other.
Calculation of the Theoretical Flame Temperature. — The
theoretical temperature of the flame of a burning gas is the
highest possible temperature that results from its complete
combustion, assuming (what is never the case in an open-
burning flame) that only sufficient air is present for the com-
plete combustion of the gas.
There is always an excess of air in the outer envelope or
zone of a flame exposed to the air, and this excess of air beyond
what is required for the combustion absorbs heat and lowers
the temperature of the flame in the outer zone.
The temperature within or in the body of the flame more
nearly approaches the theoretical maximum, which can be
calculated. This maximum temperature is found by dividing
the total heat of combustion above 32 deg. F., per pound of
combustible, less the heat rendered latent in the water vapor
produced, by the heat required to raise the temperature of
the products of combustion one degree. The quotient ob-
tained gives the rise of temperature above 32 deg. F., which
must therefore be added in order to find the theoretical tem-
perature of the flame.
EXPLOSIONS IN MINES 110
Flame Temperature ot Methane Burning in Air. — The first
portion of the process is similar to that explained in the
calculation of the lower inflammable limit of methane and
need not be repeated here. It was found that for every
pound of methane burned there was produced carbon dioxide,
' 2% lb.; water vapor, 2K lb.; and nitrogen, 13.39 Ib. So far
the two operations are the same. (Page 96.)
As before, one pound of methane, burning to carbon dioxide
and water at 32 deg. F., develops 23,513 B.t.u. From this
must be subtracted the heat required to convert 2% lb. of
water at 32 deg. into steam at 212 deg., which is absorbed in
the formation of the water vapor; thus,
23,513 - 2>i (212 - 32 + 970.4) = 20,924.6 B.t.u.
The result obtained is the net heat available for raising the
temperature of the products of combustion, which constitute
the larger portion of the body of the flame.
It is necessary now to calculate the heat required to raise
the temperature of the respective weights of the products of
combustion one degree. The weight of each of these products,
as previously given, is multiplied by its specific heat for
constant pressure and the sum of these products is the total
heat required for each degree of rise in temperature; thus,
Sp. heat Weight B.t.u.
Carbon dioxide 0.2163 X 2.75 = 0.5948
Water vapor 0 . 4805 X 2 . 25 = 1 . 0811
Nitrogen 0.2438 X 13.39 = 3.2645
Heat absorbed, per degree rise ... 4 . 9404
Finally, the rise of temperature in the body of the flame
that is possible, in this case, assuming that all of the heat
developed is absorbed by the products of the combustion only,
is as follows:
Rise of temperature, 20,924.6 -5- 4.9404 = 4235 deg. F.
This rise of temperature, like the heat developed by the
combustion, is estimated from 32 deg. F. The theoretical
flame temperature is therefore 4235 + 32 = 4267 deg. F.
120 MINE GASES AND VENTILATION
Flame Temperature of Carbon Monoxide. — The first step
in calculating the flame temperature of this gas is to write
the chemical equation expressing the reaction that takes place
when carbon monoxide burns to carbon dioxide, ignoring for
the present the nitrogen in the air; thus,
2CO + O2 = 2CO2
Molecular weights, 56 32 = 88
Relative weights, 1 % l%
Since oxygen forms 23 per cent, of normal air, by weight,
and nitrogen 77 per cent., the ratio of nitrogen to oxygen is
77 : 23, and the relative weight of nitrogen involved here is
4 77 44
Hence, for every pound of carbon monoxide burned, there is
produced carbon dioxide, l% lb.; and nitrogen, 1.91 Ib.
The heat of combustion of carbon monoxide burning to
carbon dioxide, as taken from a table giving the heat of com-
bustion of various substances, is 4325 B.t.u. per lb. of gas
burned. There being no water vapor formed in this reaction,
the above is the actual heat available for raising the tempera-
ture of the products of the combustion, which form the body
of the flame, disregarding radiation and conduction losses.
Now, calculating, as before, the heat required to raise the
temperature of the respective weights of the products of this
combustion one degree, by multiplying the weight of each
product by its specific heat for constant pressure and finding
the sum of those products, we have
Sp. heat Weight B.t.u.
Carbon dioxide ................... 0.2163 X 11/7 = 0.3399
Nitrogen ...... . .................. 0.2438 X 1.91 = 0.4657
Heat absorbed, per degree rise .... 0 . 8056
The resulting rise of temperature above 32 deg. F., in the
body of the flame, which determines the theoretical flame tem-
perature, is then 4325 -r- 0.8056 = 5369 deg. F. and the corre-
sponding temperature, 5369 + 32 = say 5400 deg. F.
EXPLOSIONS IN MINES 121
Although the presence of moisture (water vapor, H2O) is
necessary to the ignition of carbon monoxide, it is not re-
quired to take this into account in making the above calcu-
lation, for the reason that the heat of dissociation is balanced
by the heat of recombination in the molecule of water and no
loss of heat is assumed to occur. It has been suggested that
the water only serves to start the reaction by effecting the
ionization of the elements.
The theoretical flame temperature as calculated above,
however, both for methane and carbon monoxide, is consid-
erably modified by the humidity of the air supporting the
combustion.
Volume of Flame. — It is frequently estimated roughly that
the volume of a flaming gas is proportional to its absolute
temperature. For example, assuming the original tempera-
ture of the gas as 0 deg. F., the theoretical flame volumes of
methane and carbon monoxide are, respectively,
Methane, 460 -f- 4267 -r- 460 = say, 10 volumes.
Carbon monoxide, 460 + 5400 -r- 460 = say, 12% volumes.
EXPLOSION OF GAS
Influence of Temperature on Explosion. — A rise of the
initial temperature of an explosive mixture slightly extends
the lower inflammable limit, but has no appreciable effect
on the higher limit, owing to the small relative value of the
increase as compared with the high temperature developed
in the explosion.
Influence of Pressure on Explosion. — Pressure exerted on
an explosive mixture increases its density and temperature
and renders it more readily igriitable. In other words, an
increase of pressure lowers the lower inflammable limit of
an explosive gaseous mixture. An increase of pressure, like-
wise increases the velocity of propagation of explosion in
the mixture, raises the temperature developed and extends
the higher inflammable limit. In other words, an increase
of pressure widens the explosive range of a combustible gas.
122 MINE GASES AND VENTILATION
Influence of Relative Humidity on Explosion. — While the
presence of moisture (water vapor) in a gaseous mixture is
often necessary to secure its explosion, as explained in ref-
erence to carbon monoxide, the water vapor absorbs much
of the heat and lowers the temperature developed, thereby
reducing the rate of combination and the force of the ex-
plosion, except where fine coal dust is suspended in the air,
when partial dissociation may take place in the water vapor
and result in increasing the energy of the reaction.
Influence of Catalysis to Cause Explosion. — Catalysis is
the effect produced by a foreign substance to assist chemical
reaction between two other substances, while the substance
itself undergoes no change — -first discovered by Berzelius.
Much difference of opinion exists as to the suggested catalytic
action of fine incombustible dust suspended in mine air, to
assist the explosion of combustible gases. Finely powdered
stone dust has been shown to retard the ignition of coal
dust by mixing with and diluting the latter. This effect,
however, is wholly physical and not related to the possible
catalytic action referred to by Sir Frederick Abel and others
who have studied the subject closely.
Influence of Character of Initial Impulse. — The manner in
which the gas is ignited or the character of the initial im-
pulse determines largely the explosion of gaseous mixtures. .
For example, a firedamp mixture ignited by a lamp flame
may not explode, while if fired by the flame of a blownout
or windy shot, the greater volume and intensity of the flame
may cause an explosion.
The volume of the flame is important, because it envelops
a larger portion of the gaseous mixture and ignition is thus
started generally throughout the mass, causing a greater
development of heat and reducing the percentage of loss by
radiation, convection and conduction.
The intensity of the initial impulse or the higher tem-
perature of the igniting flame will often cause the explosion
of a gaseous mixture that would burn quietly if ignited by
a less intense source of heat energy. The dissipation of heat
is so rapid and general in a burning gas that the transition
EXPLOSIONS IN MINES 123
from inflammation to explosion requires a conservation of
heat or greater local energy than can often be realized in
the large open workings of a well-ventilated mine.
COAL DUST
Influence of Coal Dust on Explosion. — The fine dust of an
inflammable coal when floating in the mine air may render
the air explosive in the entire absence of explosive gas. Under
such conditions, however, the ignition and explosion will
only take place when the floating dust is acted upon by a
flame of considerable volume and intensity.
When a small percentage of methane is present, insufficient
of itself to make the air explosive, the presence of the dust
floating in the air is more dangerous than when no gas is
present. The dust-laden air is more easily ignited and the
force of the resulting explosion is increased in proportion to
the inflammability of the mixture.
The purity, fineness, humidity and inflammability of the
dust are important factors in determining the character of
the explosion, since these with oxygen are the chief elements
that promote the rapidity of the combustion, which is the
necessary condition of any explosion.
The suspended dust feeds the flame of an explosion that
is started in a mine, and thus serves to propagate the blast
and extend what would otherwise have proved only a local
explosion. This action is cumulative in a dry and dusty
mine. The dust lying on the roads and clinging to the sides
and timbers of the passageways is blown into the air by the
force of the rushing wind that precedes the explosive wave,
producing what has well been called a "pioneering cloud"
of dust that is itself highly explosive.
The weight of fine bituminous coal dust required to render
normal air explosive has been variously estimated. Tests
made at the Pittsburgh Experiment Station- with dust from
a 200-mesh sieve showed explosion took place in a density of
32 grm. per cu. m. (0.032 oz. per cu. ft.) or, say 1 Ib. of dust
in 500 cu. ft. of air. The Taffanel experiments (Lievin) gave
explosion in 70 grm. per cu. m. (0.07 oz. per cu. ft.) or, say
124 MINE GASES AND VENTILATION
1 Ib. of dust in 230 cu. ft. of air. In one instance only, ex-
plosion occurred in 23 grm. per cu. m. (0.023 oz. per cu. ft.), or
1 Ib. of dust in about 700 cu. ft. of air.
It is quite evident, as experiments also show, that condi-
tions in respect to the purity, humidity and particularly the
inflammability of the dust are so variable that the question
of the density of the dust cloud has only an experimental
value. The size of the workings, as determining the con-
servation of heat and pressure, will also modify the results
in the mine.
Theoretically, since the atomic weights of carbon and
oxygen are 12 and 16, respectively, 1 Ib. of carbon will yield
12+16 28
— r~ — = — = 2>i Ib. carbon monoxide.
I - iZ
But, carbon monoxide measures 13.5 cu. ft. per Ib., at normal
temperature and pressure. Hence, 2^ Ib. of this gas pro-
duced by 1 Ib. of coal dust makes 2><j X 13.5 = 31.5 cu. ft.
Then, since the lower inflammable limit is reached when the
mixture of gas and air contains 8.4 per cent, of the gas, inflam-
mation might be expected wThen the dust present was 1 Ib. in
31.5-7- 0.084 = 375 cu. ft. of air. Also, the lower explosive
limit of the gas occurring when 1B.5 per cent, of gas is present,
explosion might be expected to take place when there was
1 Ib. of dust in 31.5 + 0.165 = 190 cu. ft. of air.
Inflammability of Coal Dust. — The inflammation of a dust
cloud in mine workings, under like conditions, depends largely
on the inflammable nature of the coal. The experiments at
different testing stations have demonstrated that the volatile
combustible matter contained in coal is a fair index of its
susceptibility to inflammation when held in suspension as
fine dust in the air.
Experiments performed with anthracite dust seem to indicate
that the fine dust of that coal is not capable of propagating
an explosion in a mine, under ordinary mining conditions.
This fact points significantly to the conclusion previously
stated that the volatile combustible matter in a coal is an
important index of its explosibility. It is not asserted or
EXPLOSIONS IN MINES 125
claimed that anthracite dust cannot be exploded under favor-
able conditions. However, the conditions that would cause
anthracite dust floating in the air to explode are not liable
to occur in ordinary mining practice.
Influence of Shale or Stone Dust. — Shale or other soft rock
of the coal formations have been ground to a fine powder
for use in mines and, in this form, have been sprinkled on the
roads in a manner to form stone -dust zones, or distributed
on shelves hung across and overhead in the entries to form
so-called stone-dust "barriers."
The purpose of these dust zones and barriers is to arrest
the progress of an explosion should one occur in the mine.
Their use, however, has not been attended with unvarying
success, which is due in part to the different conditions of
temperature, humidity, air space or volume of mine work-
ings available for expansion, inflammability of the gas- and
dust-laden air and the initial intensity of the explosion; also,
in part to the limited extent or adequacy of the dust zone or
barrier as compared with the strength developed by the
explosion.
Notwithstanding the apparent failure of these means for
preventing the spread of an explosion in a mine in many ob-
served instances, there is no question but that finely pow-
dered shale or stone dust blown into the path of an explosive
wave by the pioneering impulse, or suspended in the air with
the inflammable coal dust has a most decided effect and re-
duces explosive conditions.
The action of incombustible dust, suspended in an other-
wise explosive atmosphere, to allay the explosiveness of the
mixture or reduce the violence of the blast should ignition
and explosion occur, is wholly physical. The incombustible
particles disseminated through a dust-laden atmosphere sepa-
rate more widely the inflammable particles of coal dust and
dilute the air necessary for combustion. In other words, the
percentage of inflammable matter in the mixture is reduced
and the liability to inflame diminished in the same proportion.
Also, by its absorption of heat, the incombustible matter
lessens the heat available for ignition and decreases the heat
126 MINE GASES AND VENTILATION
energy developed when ignition has taken place. The action
is entirely similar to that of the inert nitrogen of air depleted
of its oxygen, or to the extinctive effect of carbon dioxide
when present in firedamp mixtures, both of which conditions
act to diminish the explosibility of gaseous mixtures.
MINE EXPLOSION
Development of a Mine Explosion. — Explosion does not nec-
essarily follow the ignition of gas in mine entries and work-
ings. The firedamp mixture must, of course, be within the
explosive range, as determined by the conditions in that
portion of the mine. But even then a mine explosion will
only take place when the conservation of heat is sufficient to
render the explosive action self-supporting. Otherwise, a
local explosion of gas or dust will expend its energy within
a limited area and the disturbance will not be propagated
throughout the mine.
The ignition of an inflammable mixture of gas or dust in
the mine air may produce a considerable body of flame that,
within the narrow confines of the mine, may gather force
and generate sufficient heat to cause an explosion. Experi-
ment has shown that an explosive mixture of gas and air
placed in a tube and ignited at one end will burn quietly at
first, then flutter or vibrate with increasing energy as the
combustion penetrates deeper in the tube, the contending
forces being the entering air and the escaping products of the
combustion. This action, however, quickly develops sufficient
energy to produce an explosion, which darts through the
entire length of the tube.
This experiment illustrates more or less closely the devel-
opment of an explosion in a mine entry or chamber. Inves-
tigation has shown that the explosion gathers force and
probably develops characteristic energy within a few yards
of its origin or the point where the ignition of the gas took
place. This may vary from 10 to 30 yd. or more, depending
on many conditions — chiefly the size or volume of air space
available for the expansion of the gases of the explosion, the
EXPLOSIONS IN MINES 127
intensity of the igniting flame and inflammability of the
mixture.
All of these factors determine severally the initiation as
well as the character of the explosion and its limitations in
the mine workings. .
Causes of Mine Explosions. — The causes of mine explosions
may be generally stated as the ignition of gas or dust by one
of the following causes:
1. By the use of open lights or defective safety lamps in
mines where the air current is charged with gas or dust, or
where gas has accumulated in void or abandoned places in
sufficient quantities to be dangerous.
2. By the use of mixed lights in mines generating gas.
3. By the inexperienced or careless use of a safety lamp,
or by fooling or tampering with the lamp, or exposing it to
gas too long or to a strong gas blower or strong current or
blast of air, or carrying too high a flame.
4. By the use of a dirty lamp or one that has been im-
properly assembled or injured by a fall or other accidental
cause.
5. By the explosion of powder in blasting or the accidental
explosion of a keg of powder, or the flame of a blownout shot
or a windy shot.
6. By the use of matches or other means of lighting.
7. By the sparking of electric wires, switches or brushes,
or the blowing out of an electric fuse, or the breaking of an
incandescent lamp.
8. By the spontaneous ignition of oily waste carelessly
thrown aside, or of fine coal or slack in the gob.
9. By the fall of certain hard roof rock striking sparks,
as claimed in the Bellevue mine explosion (1910), Alberta,
Canada.
10. By the possible generation of heat due to concussion of
the mine air in contracted workings in thin seams.
Mixed Lights in Mines. — By "mixed lights" is meant the
use of open lights in one or more sections of a mine in which
gas is generated in other portions of the mine in sufficient
quantity to require safety lamps being employed therein.
128 MINE GASES AND VENTILATION
The expression does not refer, however, to the use of
open lights by drivers, triprunners or motormen whose
duties are confined to the main intake haulage roads and
shaft or slope bottom of a mine worked on safety lamps,
provided there are lamp stations beyond which these men
may not pass.
The use of mixed lights is a dangerous practice. The
danger does not consist wholly in a man carrying an open
light into the safety-lamp section, or to a foreman or fire-
boss forgetting that he has an open light on his head while
carrying a " safety" at his side. These are possibilities that
can be prevented by properly safeguarding the entrances to
the gaseous section.
The real danger lies in a heavy fall of roof occurring in
the safety-lamp section and driving out the gas into other
parts of the mine where open lights are in use. Or, a squeeze
may develop in any part of the mine and permit the gas to
find its way without warning into an open-light section and
cause an explosion.
Electric Mine Lamps. — Any installation of electricity in a
mine worked on safety lamps is necessarily accompanied with
more or less danger. Whether the installation is for the pur-
posa of lighting, hauling, coal cutting or drilling, pumping or
ventilation, it should be made by a competent electrician.
The entire system of wiring should be closely inspected at
frequent intervals and tested to insure freedom from short-
circuiting or grounding of the current, which are not only
wasteful of power, but may start combustion and result in an
explosion of gas.
The use of incandescent lamps in mines has become so com-
mon that the Bureau of Mines has made a careful investiga-
tion to determine their safety. Their experiments show that
ignition of gas may follow the breaking of the glass bulb of
a lamp in an explosive mixture. The experiments also seem
to indicate that the liability of ignition increases with the
cross-section of the filament of the lamp. In the breaking of
an incandescent lamp two conditions may arise that materially
affect the possibility of the ignition of the gas. The same
EXTLOHIONS IN MINES 129
blow that breaks the bulb may or may not break the filament.
The result in either case may be briefly explained as follows :
1. If the filament is broken and its parts do not short-
circuit the current ignition of the gas is not likely to occur.
If the broken parts, however, fall across each other in such
manner as to again close the circuit their burning out in the
air will generally ignite any gas present.
2. If the filament remains intact when the bulb is broken
it will burn out more or less rapidly, according to the manner
of fracture and consequent inrush of air and gas. A small
hole due to the breaking of the tip may admit the air so slowly
that the gas is consumed without explosive violence. In
that case there may occur a slight explosion within the bulb,
which is not broken but only pierced. This feeble explosion,
however, may not be communicated to the outside gas.
Prevention of Mine Explosions. — No means has yet been
devised that will insure absolute freedom from mine explo-
sions. But the tendency to explosion and the frequency of
these occurrences can and has been greatly reduced by study-
ing their causes and adopting measures to remove them.
The following points are of chief importance:
1. Effective mine regulations and discipline.
2. Operation in accordance with the state mining law.
3. Enforcing by suitable penalties all mine regulations.
4. Thorough frequent inspection by competent men.
5. Education and training of all men employed in any
capacity in the mine, in respect to the proper performance of
their duties, the dangers to which they are exposed and the
mining law and mine regulations in force.
6. Eternal vigilance of mine officials and a regard for
safety greater than the desire for increasing the daily output
of the mine.
7. Cooperation of employers and employed in increasing
the safety of mine work.
8. Cooperation of all coal companies in respect to mining
requirements.
Aside from the above general outline there is the necessity
for each company to study carefully the conditions existing
130 MINE GASES AND VENTILATION
in its own mines, and to adopt a system of inspection and
methods of ventilating the mine and mining and hauling the
coal that will produce the best results and insure the greatest
freedom from accumulations of gas and dust on the roads and
in the workings. Immunity from explosion can only be se-
cured by removing the cause.
SECTION V
MINE RESCUE WORK AND APPLIANCES
PRELIMINARY, ENTERING A MINE AFTER EXPLOSION, FIRST-
AID SUGGESTIONS — BREATHING APPARATUS, PRINCIPLE,
ACTION AND REQUIREMENTS IN RESPIRATION, DEVELOP-
MENT, DESIGN AND TESTING OF BREATHING APPARATUS —
TYPES OF BREATHING APPARATUS, DRAEGER, FLEUSS
PROTO, GIBBS, PAUL — BUREAU OF MINES, PERMISSIBLE
BREATHING APPARATUS — SPECIFICATIONS BY THE BU-
REAU OF MINES — FIRST-AID WORK.
PRELIMINARY
Entering a Mine after an Explosion. — Prompt action and
intelligent and effective measures are necessary for the rescue
of any possible survivors of a mine explosion. The nature
of the work and the great risk incurred in its undertaking
demand that it shall be performed by the most experienced
of the volunteers, of whom there is never any lack.
Immediately after an explosion in a mine, the following
procedure is important:
1. Call for volunteers and from them choose those who
are more experienced and familiar with the mine and the
work to be performed.
2. At the same time, observe the mine entrances and judge
of the probable effect of "the explosion in the. mine; examine
the ventilating apparatus and have any necessary repairs
made at once.
3. Collect the necessary safety lamps, tools, timber, can-
vas, brattice boards, nails, etc. Caged canaries or mice should
also be provided, and two or more sets of breathing apparatus
should make up the equipment.
4. Divide the rescuers into three parties, as follows:
(a) Apparatus men to explore in advance;
131
132 MINE GASES AND VENTILATION
(b) Repair gang and rescuers;
(c) Supply gang to render every possible assistance.
Organize each party under a competent leader who shall
be in absolute control while underground.
5. Enter the mine at the earliest possible moment — the
apparatus men proceeding first and keeping from 100 to 200
yd. in the lead of the others, who must not advance ahead of
the air.
6. Each section of the mine should be explored by% the
apparatus men to discover any possible fire therein, before
restoring the circulation in that section.
As quickly as any survivors are found they must be promptly
removed to fresh air and the proper restoratives applied.
At the surface, physicians should be in attendance and am-
bulances provided for the prompt removal of those brought
out of the mine.
Suggestions on First-aid to Explosion Victims. — Those
trained in first-aid work are the ones who should assume
charge and have absolute control of the care of any survivors
as quickly as found, until the arrival of a physician. The
following brief suggestions are important:
1. Be calm and quiet; act promptly but not in a hurry;
keep cool and observe closely every symptom and condition.
2. Remove promptly but carefully to fresh air.
3. Do everything possible to stop bleeding.
4. Examine for broken bones before moving far.
5. Use aromatic spirits of ammonia if stimulant is needed.
6. If overcome by gas, give artificial respiration.
7. If unconscious, loosen clothing, warm and stimulate by
rubbing the limbs; give no stimulant if face is flushed and
pulse strong, but sprinkle cold water on face and chest. If
the body and limbs are cold, use warm applications; keep the
patient covered with blanket or other coverings; apply smell-
ing salts or spirits of ammonia cautiously to the nostrils.
BREATHING APPARATUS
Principle of Breathing Apparatus. — The principle of all
breathing apparatus is that the wearer breathes the same ah*
MINE RESCUE WORK AND APPLIANCES 133
over and over again, the carbon dioxide exhaled in the breath
being absorbed after each expiration while, at the same time,
the requisite amount of oxygen is restored, thus rendering the
expired air pure and fit to be again inhaled.
Action in Respiration. — In the act of inhalation, the air
enriched with oxygen passes from the breathing bag in the
bottom of the cooler, up through the latter and is drawn
through the inhalation valve and tube into the lungs.
In exhalations, the air, deprived of some of its oxygen and
containing from J^ to 4 per cent, of carbon dioxide, depending
on the amount of the exertion, is discharged through the ex-
halation tube and valve into the exhalation side of the cooler
where it meets the oxygen supply, as previously stated, and
passes into the regenerator where it is to give up its carbon
dioxide, by contact with the absorbent caustic soda.
Requirements in Respiration. — The average full capacity of
the lungs of an adult person is about 300 cu. in. This volume,
however, is never utilized in the act of breathing; that is to
say, all of the air contained in the lungs is never exhaled or the
lungs would collapse, which would be fatal. There is a certain
volume of residual air, about 100 cu. in., that remains in the
lungs after a deep expiration. In the ordinary act of breathing,
the average person expires only about 20 or 30 cu. in. of air at a
single breath. This has been called " tidal air." In the per-
formance of work or when undergoing any extra exertion, a
larger quantity of air is expelled from the lungs at each breath
and a corresponding quantity again inhaled.
The ordinary rate of respiration is 16 breaths per minute
when a person is at rest, making the volume inhaled, from 300
to 500 cu. in. per min. When making violent exertion in the
performance of work, breathing is more rapid and a much
larger volume of air is respired. This quantity will vary with
the person and the exertion made or the work performed.
When doing strenuous work a man may inhale 200 cu. in. of
air at a single breath.
Approximately, the volume of carbon dioxide exhaled is
equal to that of the oxygen breathed into the lungs, the ratio
of carbon dioxide to oxygen being slightly less when the person
134
MINE GASES AND VENTILATION
is at rest, than it is in the performance of work. However, for
the purposes of ordinary estimate, it may "be assumed that a
man, at rest, will inhale from 25 to 30 cu. in. of air at a single
breath and this may be increased to 150 or possibly 200 cu. in.
when making violent exertion. Practically, one-fifth of this
volume of air is oxygen ; but, in the act of breathing, only one-
third or one-half of this oxygen is consumed.
The standard supply of oxygen, in mine breathing apparatus,
has been fixed, therefore, at 2 liters per min. (122 cu. in.).
Compressed to 120 atmospheres, this rate of supply of oxygen,
for a 2-hr, period, will require a cylinder capacity of 2(122 X
60) -f- 120 = 122 cu. in. Again, assuming that the average
amount of carbon dioxide produced in breathing is equal to the
volume of oxygen consumed, it appears that the quantity of
the former gas required to be absorbed by the caustic soda in
the regenerator, in a 2-hr, period, is 2(2 X 60) = 240 liters,
or 8.47 cu. ft.
The following table gives carefully compiled data and the
results of actual tests regarding the oxygen consumed, carbon
dioxide produced, quantity of air breathed and number of
respirations per minute, under different conditions of rest and
exertion. These data were compiled by James M. Stewart,
Instructor at the Brazeau Rescue Station, Alberta, Canada.*
DATA REGARDING Am RESPIRED WHEN WALKING AND AT REST
Condition of subject
Oxygen
consumed
per minute
in liters
C02
expired
per minute
in liters
Air
breathed
per minute
in liters
Average
volume
of each
breath
Number
of breaths
per minute
At rest in bed . . .
0 237
0 197
7.7
0.457
16.8
At rest, standing
0.328
0.264
10.4
0.612
17.1
Walking, 2 mi. per hr.
0.780
0.662
18.6
1.270
14.7
Walking, 3 mi. per hr.
1.065
0.992
24.8
1.530
16.2
Walking, 4 mi. per hr.
1.595
1.395
37.3
2.060
18.2
Walking, 4*£ mi. per
hr
2 005
1.788
46.5
2 . 520
18.5
Walking, 5 mi. per hr.
2.543
2.386
60.9
3.140
19.5
* Bulletin, November, 1916, Rocky Mountain Branch of the Canadian
Mining Institute.
- MINE RESCUE WORK AND APPLIANCES 135
It is evident from the table that more than the standard
supply of oxygen allowed in the design of breathing apparatus
may be consumed by a person under great physical exertion.
Mr. Stewart suggests, therefore, that it is of the utmost im-
portance that the captain of a rescue team observe carefully
that his men do not overexert themselves while in the per-
formance of their duties in the mine. He also suggests that,
in the use of the nose-clip, greater comfort and security is
obtained by inserting a cotton-wool plug in each nostril,
before adjusting the clip.
Development of Breathing Apparatus. — The development
of breathing apparatus, during the past few years, since the
Government took up the work of improving mining conditions
(1907) has been rapid. In the earlier types of apparatus, a
helmet was employed to cover the head and oxygen was
supplied through rubber tubes that connected the helmet with
a gas cylinder or bag containing the gas. Owing to the dan-
ger of these connecting tubes being broken in the rough service
to which they are subjected in the mine, the first attempt to
improve the apparatus resulted in the adoption of a form that
was self-contained, so as to eliminate, as far as practicable,
the tube connections.
Mining practice quickly demonstrated that the substitution
of a simple mouthpiece, and noseclip to close the nostrils, gave
better service underground than the clumsy helmet, although
the latter afforded more comfort in breathing and enabled
the wearer to talk to his comrades with greater facility
than when the mouthpiece was used and a noseclip closed
the nostrils. However, these disadvantages were largely out-
weighed by the greater facility offered for work by this form
of apparatus.
Design of Breathing Apparatus. — Breathing apparatus is
designed to supply the wearer with a perfectly respirable air
independent of the atmosphere in which he may be placed.
The design of the apparatus is to enable the wearer to work in
an irrespirable atmosphere for a limited period of two hours.
The principal features of the device consist in maintaining a
sufficient supply of oxygen to replace that consumed by the
136 MINE GASES AND VENTILATION
wearer of the apparatus, and absorbing the carbon dioxide he
exhales.
Oxygen, compressed to 120 atmospheres, is contained in a
strong steel cylinder. The quantity is sufficient to afford a
supply of 2 liters of this gas (122 cu. in., normal temperature
and pressure) per minute. A pressure of 120 atmospheres,
at sea level, corresponds to about 1800 Ib. per sq. in. A re-
ducing valve is employed to control this pressure and reduce it
to the normal pressure of the atmosphere, for breathing. An
air-tight breathing bag filled with pure air and equipped with
a release valve, forms part of the apparatus and is connected
directly with the oxygen supply cylinder and the helmet or
mouthpiece.
Another important feature of breathing apparatus is the re-
generator, holding a supply of 4 or 5 Ib. of caustic soda or
caustic potash. This minimum weight of caustic soda (4 Ib.)
will absorb, if fully utilized, 532 liters of carbon dioxide and is
ample for all contingencies. By the absorption of the carbon
dioxide, the caustic soda is converted into sodium carbonate
and some water is produced according to the equation
2NaOH + CO2 = Na2CO3 + H2O
The molecular weight of the caustic soda or sodium hydrox-
ide is 2(23 + 16 + 1) = 80, while the molecular weight of the
carbon dioxide is 12 + 2 X 16 = 44. The ratio of the weight
of carbon dioxide absorbed to that of the caustic used is, there-
fore, 4^o = 1MoJ and the 4 Ib. of caustic soda, if completely
utilized, would absorb 4(1^0) = 2.2 Ib., or 18.78 cu. ft. of
carbon dioxide (532 liters), at normal temperature and pressure.
In the absorption of carbon dioxide, however, the caustic
soda becomes encrusted with the sodium carbonate formed,
which prevents or at least impedes the action of absorption.
The shaking of the regenerator helps to break up this crust
and restore the absorptive power of the caustic.
Testing Breathing Apparatus. — All breathing apparatus
should be regularly tested to insure its perfect condition.
Especially should this be done by the wearer before he enters
an irrespirable atmosphere. The apparatus may be defective
MINE RESCUE WORK AND APPLIANCES 137
from any one of a number of such causes as negative pressure ;
leaks in joints, tubes, breathing bag or other container; ob-
structed valves or tubes, imperfect regeneration, owing to
insufficient absorption of carbon dioxide or inadequate supply
of oxygen; etc
Before putting on the apparatus, the wearer should examine
and test its various parts to ascertain that it is tight, the valves
and tubes free from obstruction and the supply of oxygen and
caustic soda adequate. Each tube, the bag and the assembled
apparatus should be tested for leaks, by means of the pressure
gage and observing the constant water level in the U tube
kept for that purpose. The old habit of immersing apparatus
in water to show leakage is harmful.
TYPES OF BREATHING APPARATUS
The principal types of breathing apparatus now in use in
this country are the Draeger breathing apparatus, the Fleuss
Proto apparatus, the Paul type of apparatus and the more
recent and highly improved Gibbs apparatus, which combines
all of the best features of other types and many improvements.
Draeger Breathing Apparatus. — There are two general types
of this apparatus, one employing the helmet and the other the
noseclip and mouthpiece. These two types are shown in
Fig. 14 together with side and rear views of the apparatus as
worn by the rescuer. Owing to its bulkiness the helmet type
is not so well adapted to mine work as that equipped with the
noseclip and mouthpiece.
Since its introduction in 1903 the Draeger apparatus has
undergone various marked improvements and is at present
one of the standard types of rescue appliances in, use. The
canvas breathing bags, one for inhalation and the other for
exhalation, are rubber-lined. The oxygen cylinder is sup-
plied with a perfected high-pressure valve that enables the
wearer to shut off the pressure at any moment desired, by a
simple thumb pressure. These together with the safety
locked couplings securing- all tube connections, and the time
recorder and pressure gage, always ready for inspection by
the wearer, insure both safety and comfort.
138
MINE GASES AND VENTILATION
MINE RESCUE WORK AND APPLIANCES
139
Essential Parts. — The diagram, Fig. 15, shows the arrange-
ment of the several parts of the apparatus for the purpose of
making clear their relation and the circulation of the system.
The diagram shows the helmet H, the expiration valve V2,
the exhalation bagL2, that receives the exhaled air, the regen-
erator R, the cooler K, the aspiration pipe C, the inhalation
bag LI, holding the purified air and the inspiration valve V\.
The oxygen cylinder and pressure gage also appear, the former
has withstood an official test of 225 atmospheres and is com-
monly charged to a pressure of 120 atmospheres.
R
FIG. 15.
Capacity of the Apparatus. — This apparatus will purify
about 3000 liters (105 cu. ft.) of air per hour, besides supplying
120 liters (4.2 cu. ft.) of oxygen, and absorb 50 liters (1% cu.ft.)
of carbon dioxide. This is claimed to enable the wearer of the
apparatus to perform 260,000 ft.-lb. of work. While an un-
trained man will generally do less than this, the work done
in one instance amounted to 398,000 ft.-lb.
Fleuss Proto Apparatus. — This apparatus is designed to
supply the user with a perfectly respirable air, entirely inde-
pendent of any communication with the outside atmosphere
140
MINE GASES AND VENTILATION
for at least two hours at a time. It has been designed to with-
stand the severe conditions to which it must be subjected in
mining use and insure the safety of the wearer while engaged
in the dangerous work of rescuing men from mine workings
filled with poisonous or irrespirable gases.
FIG. 16.
Front and rear views of the apparatus are shown in the
Fig. 16, in the position in which it is worn, the large, double-
compartment breathing bag being in front and the oxygen
cylinder in the rear of the wearer. A diagrammatic view is
shown on the opposite page (Fig. 17) explaining the various
parts of the apparatus.
Essential Parts. — The principal features are the oxye-en
cylinder B; the reducing valve C; the breathing bag D with
MINE RESCUE WORK AND APPLIANCES.
141
inhaling and exhaling divisions; inspiratory and expiratory
valves T and 8; mouthpiece and noscclip R and Y.
The wearer exhales through valve *S, the air passing down
one side of the partition of the breathing bag and through the
caustic soda, which absorbs the carbon dioxide, and thence up
OXYGEN
CYLINDER
PRESSURE CAUCE
MAIN VALVE
EXHALING VALV
RELIEF VAL
SALIVA TRAP
END SECTION
SHEWING CAUSTIC
SODA SPACES
BREATHING BAC
WITH INHALING
AND EXHALING
COMPARTMENTS
REDUCING VALVE
BY- PASS
SKULL CAP
SMOKE COCCUS
NOSE CLIP
MOUTH PIECE
> JNHALINC VALVE
FIG. 17.
the other side of the partition to valve T to be again inhaled,
after mixing with fresh oxygen, which is being constantly de-
livered at the rate of two liters per minute from the oxygen
cylinder through the reducing valve C. Connected to a
flexible tube IF is a pressure gage P indicating the quantity
of oxygen in the cylinders and the duration of supply. An
142 MINE GASES AND VENTILATION
emergency by-pass 7 is for use in case the reducing valve fails ;
it enables the wearer to fill his breathing bag direct from the
oxygen cylinders. A saliva trap Z prevents the saliva from
entering the breathing bag.
The steel cylinder contains about 10 cu. ft. of oxygen, com-
pressed to 120 atmospheres, which gives a two-hours' supply
when the reducing valve is passing two liters per minute.
The cylinder can be charged to 150 atmospheres if desired,
which will give a 2^ hour-supply.
A reducing valve C is fitted to the bottle nipple and is so
adjusted as to pass a regular supply of from 2 to 2J<£ liters of
oxygen per minute, no matter what the pressure may be in the
cylinder. This valve can be readily adjusted to deliver any
flow from one to three liters per minute, as desired. The
valve is fitted with a by-pass, having a small wheel valve I
so that should it from any cause fail to act properly the
wearer of the apparatus can supply himself with what oxygen
he requires direct from the cylinder by turning the small
valve. Also, by the same means, the automatic supply of two
liters per minute can be increased at any time by the wearer if
desirable. When working in an excessively hot atmosphere
it is possible to cool the hot air by exhausting all the air from
the bag through the relief valve K, and then filling the bag
with pure, cool oxygen from the cylinder, by means of this
by-pass.
The reducing valve delivers the oxygen through the flexible
tube F to the breathing bag D, carried on the wearer's chest.
Another connection at V , made through a flexible high pres-
sure tube W with a pressure gage P, carried in a pocket of the
canvas cover, enables the wearer to ascertain the available
supply and duration of oxygen. Each division of the pressure
gage indicates 10 atmospheres of pressure, or 10 minutes of
time, assuming the valve to be passing two liters per minute.
The connection V is also fitted with a small valve, to enable
the wearer to shut off the oxygen should the gage or its flexible
tube become damaged.
The breathing bag D is of strong vulcanized India rubber
and contained in an outer strong canvas bag. The rubber
MINE RESCUE WORK AND APPLIANCES 143
bag has two compartments, connected, however, at the bottom
of the bag. The bag is fitted at the upper left-hand corner
with a saliva trap Z and relief valve K to allow the escape of
any excess oxygen that might be delivered by the reducing
valve. At the upper right-hand corner is a small connection
N for the oxygen supply from the cylinder. The mouth of the
bag is closed with metal clamps and wing nuts 0.
The mouthpiece is of soft vulcanized India rubber, fitted to
a German silver connection R and shaped to fit comfortably
between the lips and the gums. To the connecting piece R
are also fitted strong flexible corrugated tubes XX, sometimes
called " bellows tubes, " to the opposite ends of which are fitted
the exhaling and inhaling valves S and T, respectively. These
valves are of mica and extremely sensitive. They are screwed
into their respective connections L and M . The noseclip Y
is made to fit any nose comfortably. The skull cap has a
back apron to which the mouthpiece can be securely buckled,
which supports it comfortably.
One feature of the Fleuss Proto apparatus is the fact that
the caustic soda is held in a bag instead of a rigid container
and the movements of the wearer when walking or at work
automatically rubs off the carbonated surface of the soda, and
constantly exposes a fresh surface for the absorption of car-
bon dioxide. The bag is easily emptied after use, and a fresh
supply of soda added at once, thus making the apparatus ready
for use again in two or three minutes. The bag is so con-
structed that external pressure on it does not impede the
wearer's breathing. In fact, a man may lie flat upon the bag
and still be able to breathe freely.
Gibbs Breathing Apparatus. — This form of apparatus was
developed by W. E. Gibbs, of the Federal Bureau of Mines,
who sought to improve on the older types of English makes of
breathing apparatus in mining use.
The general requirements sought to be fulfilled in this de-
sign were: (1) Automatic control of oxygen supply in rest or
exertion. (2) Adequate absorption of carbon dioxide. (3)
Freedom of respiration under constant positive pressure.
(4) Avoiding collapse of breathing bag from any cause. (5)
144
MINE GASES AND VENTILATION
Efficient heat radiation and cooling to avoid high temperature.
(6) Simplicity, durability and strength and tight joints in
every part.
The position of the apparatus when in use is shown by the
side and rear views in the Fig. 18. For the better protection
of the parts from injury, in the mine, a cover is provided as a
FIG. 18.
shield. The general arrangement of the pai*ts is shown by the
Fig. 19 in which the several elements are numbered to cor-
respond to their description in the text.
Circulation in the Apparatus. — Oxygen from the bottle (1)
in which it is compressed to 135 atmospheres, passes through
the closing valve (2) to the reducing valve (3) ; thence, under
normal pressure, by rubber tube connection, it passes through
MTNE RESCUE WORK AND APPLIANCES
145
a metal tube surrounded by a cooler; through an admission
valve into another metal tube inclosed in cooler, being then
discharged into the exhalation side of the cooler where it meets
the exhaled air and passes downward with it into the regenera-
tor; then upward into the inhalation side of the cooler, where
FIG. 19.
it enters the breathing bag in the cooler. From the breathing
bag the air passes through an inhalation valve and enters the
lungs, from which it is discharged through the exhalation tube
into the exhalation side of the cooler.
Testing Gibbs Apparatus. — The following series of tests of
the Gibbs breathing apparatus are recommended by its
manufacturers :
10
146 MINE GASES AND VENTILATION
1. Oxygen bottle should be charged to 135 atmospheres. The
oxygen cylinder being tested under water for leaks, with main valve both
open and closed. The cylinder is first tested with valve closed, then cap
is placed on cylinder and tested with valve open. Connect oxygen bottle
to reducing valve, using wrench in order to make tight connections.
2. Examine seals of regenerators in order to see that they are not
broken. Connect regenerator to cooler, being sure that gaskets are in
place between the connections. Screw down screws by hand and tighten
with screw driver.
3. Lift breathing bag from bumper on admission valve, then turn
on main oxygen valve.
Observe mica inhalation valve — if admission valve leaks the mica
inhalation valve will raise and let oxygen escape.
Turn pressure tube valve on and observe the number of atmospheres
indicated by the pressure gage. Pressure gage valve should always
be left open. Squeeze bellows of reducing valve in order to open seat
over orifice; this approximately increases the pressure to five pounds in
rubber tube and metal tube. Safety valve will whistle at the above pres-
sure if working properly. Try all connections from oxygen bottle to
cooler for leaks by using brush and soap suds. Turn off main oxygen
valve.
4. Blow into exhalation valve and observe air returning by way of
inhalation valve, showing circulation of air through exhalation side of
cooler, regenerator, inhalation side of cooler, and breathing bag. Next,
close inhalation valve either by cupping hand over valve or by special
connection, then blow into exhalation valve until bag is fully inflated.
Exhalation valve seat and mica should make an air tight connection,
keeping bag fully inflated. Test all connections for leaks, using brush
and soap suds.
5. Connect mouthpiece to cooler, seeing that gaskets are in place.
Inflate breathing bag and test mouthpiece connections for leaks, using
brush and soap suds. Try release valve and saliva pumps for leaks.
6. After apparatus has been tested and adjusted to wearer, before
adjusting noseelip, it is essential that the wearer turn on main oxygen
valve, inhale from apparatus, exhale into open air several times before
readjusting the clip. In this way a high percentage of oxygen and a low
percentage of nitrogen will be contained in breathing apparatus. While
inhaling from the apparatus the wearer will observe whether the whole
apparatus is functioning properly. After noseelip is adjusted, the wearer
is ready for a preliminary test in room filled with fumes. After remain-
ing in room for five (5) minutes and no leaks being observed, the wearer
can feel assured that his apparatus is in good working condition for doing
work in poisonous gases and irrespirable air.
7. Under no. circumstances should grease or oil be used on apparatus
parts.
MINE RESCUE WORK AND APPLIANCES 147
The Paul Breathing Apparatus. — This type of apparatus
was designed by James W. Paul, long in charge of the mine-
rescue work, as engineer of the Federal Bureau of Mines, at
Pittsburgh, Penn. The apparatus is manufactured by the
old Draeger Company, now known as the American Atmos
Corporation, Mr. Paul having disposed of his right and title
in the apparatus to that company.
One of the highly essential improvements of the Paul
apparatus, which is modeled chiefly after the Gibbs, is the
combination of the self-adjusting oxygen-feed valve with a
low-pressure oxygen-control valve, at the intake of the cir-
culatory system. This device regulates the supply of oxygen
and proportions it to the rate of consumption, which varies
with the work performed by the wearer. Also, a pressure
slightly in excess of 1 cm. of water column is automatically
maintained in the system and minimizes the liability of
an outside poisonous atmosphere penetrating within the
apparatus.
BUREAU OF MINES
The Federal Bureau of Mines recommends that the circu-
lation in breathing apparatus be under positive pressure
throughout and that the apparatus be equipped with mouth-
piece and noseclip and provided with a by-pass valve. The
helmet, for mining use, is objectionable and dangerous, not
only because of the difficulty of obtaining a perfectly air-
tight joint around the face, but also because it is easily
dislodged and greatly cuts down the range of vision. Also,
the large dead-air space in the helmet permits an excessive
accumulation of carbon dioxide.
The injector used in some types of breathing apparatus is
complicated and liable to be out of order when needed. Any
slight particle is sufficient to choke the orifice and cut off the
supply of oxygen. The use of the injector also involves a
negative pressure, which would cause an inflow of the sur-
rounding atmosphere into the apparatus should there be any
leak in the joints or tube connections.
148 MINE GASES AND VENTILA TION
Permissible Breathing Apparatus. — Owing to the grave
importance of securing safe types of mining appliances manu-
factured in this country, an act of Congress (37 Stat., 681),
approved Feb. 25, 1913, authorized the director of the Bureau
of Mines to prescribe rules and regulations for testing such
appliances as may be submitted to the bureau for that purpose.
Acting under this authority the Federal Bureau of Mines
has prepared and published, Mar. 5, 1919, "Schedule 13,"
defining the requirements necessary to establish a list of so-
called " Permissible" self-contained, mine-rescue, breathing
apparatus. Following are the more important specifications
contained in that schedule.
Definition. — The Bureau of Mines considers a self-contained mine-
rescue breathing apparatus to be permissible for use in irrespirable and
poisonous gases if all the details of construction and materials are the
same in all respects as those of the self-contained mine-rescue breathing
apparatus that met the requirements and passed the tests for safety, prac-
ticability and efficiency made by the bureau and hereinafter described.
Conditions of Testing. — The conditions under which the Bureau of
Mines will examine and test self-contained mine-rescue breathing appa-
ratus to establish their permissibility are as follows:
1. The examination, inspection, and test shall be made at the experi-
ment station of the Bureau of Mines at Pittsburgh, Pa.
2. Applications for inspection, examination, and test shall be made
to the Director, Bureau of Mines, Washington, D. C., and shall be
accompanied by a complete written description of the self-contained
mine-rescue breathing apparatus including the regenerator, and a set
of drawings showing full details of construction of both the regenerator
and the apparatus.
3. The applicant submitting the self-contained mine-rescue breathing
apparatus for inspection, examination, and test will be required to furnish
the apparatus in duplicate, which shall be sent prepaid to the mine-
safety engineer, Bureau of Mines, 4800 Forbes Street, Pittsburgh, Penn.
In the event of the apparatus successfully passing all of the Bureau of
Mines tests and requirements hereinafter specified, one set will be re-
tained by the Bureau of Mines as a laboratory exhibit and the other set
will be returned to the owner. In the event that an apparatus does not
pass all of the bureau's tests or requirements, both sets will be returned
to the owner.
4. Each self-contained mine-rescue breathing apparatus shall have
marked on it in a distinct manner the name of the manufacturer and the
name, letter, or number by which the type is designated for trade pur-
MINE RESCUE WORK AND APPLIANCES 149
poses, and a written statement shall be made whether or not the appa-
ratus is ready to be marketed.
5. The applicant will supply the regenerators or regenerating material
for the test. For tests of self-contained mine-rescue, oxygen breathing
apparatus dependent on a supply of compressed gaseous oxygen, the
oxygen will be supplied by the Bureau of Mines and will be of the purity
specified by the bureau in contracts for the supply of its safety cars and
stations; namely, 98 or more per cent, oxygen and not more than 0.2 of
1 per cent, hydrogen; other impurity to consist of nitrogen only.
6. Upon receipt of the self-contained mine-rescue breathing apparatus
for which application has been made for examination, inspection, or
test, the mine-safety engineer in charge of breathing-apparatus testing
will advise the applicant whether additional spare parts are deemed
necessary to facilitate a proper test of the apparatus, and the applicant
will be required to furnish such parts as may be necessary.
7. No self-contained mine-rescue breathing apparatus will be tested
unless the type submitted is in the complete form in which it is to be
placed on the market.
8. Only the Bureau of Mines mine-safety engineer in charge of breath-
ing-apparatus testing, his assistants and one representative of the
applicant will be permitted to be present during the conduct of the
tests.
9. The conduct of the tests shall be entirely under the direction of
the bureau's mine-safety engineer in charge of the testing.
10. As soon as possible after the receipt of the formal application
for test, the applicant will be notified of the date on which the test of his
self-contained mine-rescue breathing apparatus will begin and the
amount and character of the additional material, if any, it will be neces-
sary for him to submit.
11. The tests will be made in the order of the receipt of the applica-
tions for test, provided the necessary apparatus and material are sub-
mitted at the proper time.
12. The details of the results of the tests shall be regarded as con-
fidential by all present at the tests, and shall not be made public in any
way prior to their official announcement by the Bureau of Mines.
13. The results of tests of the breathing apparatus that fail to pass
the requirements shall not be made public but shall be kept confidential,
except that the person submitting the apparatus will be informed with a
view to possible remedy of defects in future mine-rescue breathing appa-
ratus submitted, but such changes will not be permitted while testing is
in progress.
14. Tests will be made for manufacturers or accredited manufacturers'
agents and for inventors.
15. A list of permissible self-contained mine-rescue breathing appa-
ratus and the results of their tests will be made public, from time to time,
by the Bureau of Mines.
150 MINE GASES AND VENTILA TION
Character of Tests. — After the self-contained mine-rescue breathing
apparatus under test for permissibility has been thoroughly inspected
for mechanical principles, a series of fifteen (15) working tests, each of
two (2) hours' duration, will be made. At the beginning of the series of
tests, if an oxygen bottle is used on thte apparatus it shall be first charged
with oxygen to a pressure of 10 atmospheres and the oxygen permitted
to escape into the air. The bottle used in the tests shall be charged for
the tests at a pressure prescribed by the manufacturer of the apparatus
and shall be fully charged at the beginning of each test. At the be-
ginning of each test the breathing bag or bags shall be deflated to expel
any nitrogen contained within.
A single test must be continuous, without removal of the apparatus
from the wearer during, the test.
Samples of air will be obtained from the apparatus on the inhalation
side of the circulatory system and as near to the mouthpiece or the face
attachment as possible. The first sample will be taken from the oxygen
bottle to be used and just prior to the beginning of the test. The
second sample will be taken immediately after the apparatus has been
adjusted to the wearer and oxygen has been turned on. Samples will
be taken every half-hour thereafter during the test. The physiological
effects of the apparatus on the wearer will be noted in each test.
Not more than one test of 2 hours' duration will be made on any one
day. The tests will be completed within 60 days from date of beginning,
unless prevented by conditions arising which are beyond the control
of the mine-safety engineer in charge of the tests.
All tests of apparatus will be conducted in a specially equipped gallery
filled with an irrespirable atmosphere, at the Pittsburgh experiment
station of the Bureau of Mines.
Before beginning each test the apparatus shall be examined and
tested to insure that there is no air leakage under working conditions.
SPECIFICATIONS BY THE BUREAU OF MINES
In order to receive the approval of the Bureau of Mines, self-con-
tained mine-rescue breathing apparatus must pass satisfactorily each of
the 15 tests required by the bureau and meet the following requirements:
1. The amount of oxygen supplied by the apparatus must meet the
needs of the wearer at all times during the tests.
2. The regenerating material shall absorb, from the expired air, carbon
dioxide to the extent that not more than 2^ per cent, shall at any time
be present in the inspired air. The average shall not exceed 1 per cent,
for any of the two-hour periods of test. This average is to be deter-
mined by the analyses of air samples taken as near the point of inspira-
tion as practicable and at uniform intervals of time.
3. The apparatus shall be free from mechanical obstructions in order
that the wearer may breathe freely at all times.
MINE RESCUE WORK AND APPLIANCES 151
4. The temperature of the inspired air must not exceed a maximum
of 110 deg. F. when that of the external air does not exceed 85 deg. F.
A much lower temperature than 110 deg. F. for the inspired air is de-
sirable. Temperature readings will be taken at regular intervals.
5. The apparatus shall be sufficiently rugged in construction and all
vital parts so protected as to prevent material damage or wear to the
apparatus during the period of tests to which it will be subjected.
CONSTRUCTION
1. The apparatus shall be designed to meet the needs of the wearer
for not less than a period of two hours when worn in irrespirable air
without recharging. The apparatus shall be of a design using a mouth-
breathing device or other face attachment that when properly adjusted
to the face of the wearer, has a capacity of not more than 250 c.c. of
dead space inside the, face attachment or mouth-breathing device, ex-
clusive of tubes or connections thereto.
Preferably the apparatus shall not weigh more than 36 pounds com-
plete with headpiece and fully charged, and no apparatus weighing more
than 40 pounds, complete with headpiece and fully charged, will be
accepted for final test.
2. The mechanical construction of the apparatus shall be such that
every part can be tested, inspected and repaired by persons skilled in
such work, and all parts which require sterilizing shall be readily accessible
for this purpose.
3. All parts of the apparatus subject to or liable to be subjected to
pressures in excess of 5 pounds per square inch shall be of such construc-
tion or equipped with such safety devices as shall insure the safety of the
wearer, as determined by the 15 tests.
4. In apparatus equipped with breathing bag or bags, or their equiva-
lent, the inhalation and exhalation compartments shall have a com-
bined capacity of at least 8 liters. If a single breathing bag is used it
shall have a capacity of at least 5 liters.
5. The apparatus shall not have in its circulating system any zone of
constant negative pressure.
6. The apparatus shall be provided with a release valve, operated by
hand or automatically, placed at some point in the circulatory system
of the apparatus. The function of this valve shall be to permit the
escape to the outside air of a part of the air in the circulatory system
of the machine.
7. Where apparatus is equipped with high-pressure oxygen cylinders,
such cylinders shall be tested in accordance with the Interstate Commerce
Commission specifications No. 3- A. Such tests shall be made prior to
submitting the apparatus to the Bureau of Mines for test and the appli-
cant submitting the apparatus shall furnish the necessary certificate of
test as issued by the Interstate Commerce Commission or submit evi-
152 MINE GASES AND VENTILATION
dence satisfactory to the bureau's mine-safety engineer in charge of the'
testing of the apparatus, that such oxygen cylinders have been tested in
accordance with Interstate Commerce Commission specifications No. 3-^4.
8. Where apparatus is equipped with high-pressure oxygen cylinders
the safety cap attached to the closing valve shall, in addition to the
usual copper disk provided, be filled with a metal (such as Roses metal)
fusing at a temperature of approximately 94 deg. C. Such fusible metal
shall not extrude from the safety cap under a pressure of 150 atmospheres.
9. The closing valve of such oxygen cylinders shall be provided with
the necessary device to prevent the wearer of the apparatus from screw-
ing the stem entirely out of the valve. The closing valve shall also be
provided with such a device as will enable the wearer to lock the valve
stem when the valve has been opened to the desired point.
10. When apparatus is equipped with gages for recording time or
pressures of oxygen supply, such gages will be tested for accuracy of
calibration by the Bureau of Mines. A toleration of three atmospheres
will be allowed in comparison with the Bureau of Mines standard pres-
sure gage.
11. The apparatus shall be supplied with a valve that will cut off the
oxygen supply from the gage; this valve shall be so placed that it can
be readily manipulated by the wearer and at the same time not interfere
with the flow of oxygen from the oxygen container to the circulatory
system of the apparatus.
12. The gage shall be placed on the apparatus at such a point that it
can easily be read by the wearer.
13. Apparatus equipped with a reducing valve giving a constant flow
of oxygen shall be provided with a by-pass valve which will permit a
free flow of oxygen from the oxygen container to the circulatory system
of the apparatus independent of the reducing valve.
14. When the oxygen supply of the apparatus is controlled by auto-
matic devices, such devices shall readily adjust themselves to the needs
of the wearer.
15. When an apparatus is equipped with mouth-breathing device,
such apparatus shall be provided with an adequate saliva trap. The
adequacy of the saliva trap will be determined by the tests to which the
apparatus will be subjected.
16. When an apparatus is equipped with mouth-breathing attach-
ment, a suitable noseclip shall be provided and properly attached to the
apparatus. The suitability of the nose clip will be determined by the
tests to which the apparatus will be subjected.
The apparatus under test will be worn during each and all of the 2-
hour periods of the 15 tests by the Bureau of Mines safety engineer in
charge of the testing or by one or more of his assistants. Immediately
before participation in any or all of these tests the prospective wearer of
the apparatus under test shall pass, in a satisfactory manner, physical
examination by a qualified physician. If it is impossible to carry any
MINE RESCUE WORK AND APPLIANCES 153
one of these tests to completion solely on account of the physical condi-
tion of the wearer, where such condition has been brought about through
no fault of the apparatus under test, such test shall be disregarded and
the apparatus under test shall not be penalized or disqualified thereby.
At the conclusion of each test a note shall be made of the general
physical condition of the apparatus and the amount of oxygen, if any,
remaining in the container. The schedule of work to be performed by
the wearer of the apparatus in each one of the 15 working tests is as
follows:
Detail of Procedure in Tests. — Following is an outline of
the manner of proceeding in the making of each successive
test of breathing apparatus submitted to the bureau.
Test 1. — The wearer of the apparatus shall walk continuously, except
for time necessary to take air samples and temperature readings, over a
level measured course at the rate of 3^ miles per hour. At the end of
each 30-minute period, 2 minutes shall be allowed for taking air samples
and temperature readings.
Tests 2, 3, and 4 will be repetitions of Test 1.
Test 5. — In Test 5 the wearer of the apparatus shall —
(a) Walk over a level measured course at a rate of 3 miles per hour for
a period of 10 minutes.
(6) Carry a sack of bricks weighing 50 pounds over an overcast ten
times, making one complete trip in 2 minutes.
(c) Allow two minutes for taking of air samples and temperature
readings.
(d) Walk at the rate of 3 miles per hour over a level measured course
for a period of 10 minutes.
(e) Carry a 45-pound weight a distance of 1000 feet, consuming 5
minutes while doing this work.
(/) Raise a 45-pound weight through a vertical distance of 5 feet 75
times, consuming 5 minutes while doing this work.
(g) Saw wood for a period of 10 minutes.
(h) Allow two minutes for taking of air samples and temperature
readings.
(i) Carry a sack of bricks weighing 50 pounds over an overcast 10
times, making one complete trip in 2 minutes.
0') Walk at the rate of 3 miles per hour over a level measured course
until the end of the 2 hours allowed for this test, air and temperature
readings to be taken in 2-minute periods at 1^ and 2 hours after start
of test.
Tests 6, 7, and 8 will be repetitions of Test 5.
Test 9. — In Test 9 the wearer of the apparatus shall —
(a) Walk at the rate of 3 miles per hour over a level measured course
for a period of 10 minutes.
154 MINE GASES AND VENTILATION
(6) Crawl for a distance of 100 feet, consuming 5 minutes while doing
this work.
(c) Lie down on side for 5 minutes.
(d) Lie down on back for 5 minutes.
(e) Allow 2 minutes for taking of air samples and temperature readings.
(/) Walk at the rate of 3 miles per hour over a level measured course
for a period of 10 minutes.
(g) Run 600 feet at a rate of 6 to 8 miles per hour over a level mea-
sured course, consuming 2 minutes while doing this work.
(h) Walk 1000 feet over a level measured course at the rate of approxi-
mately 3 miles per hour, consuming 4 minutes while doing this work.
(i) Walk at the rate of 3 miles per hour over a level measured course
until end of the 2 hours allowed for this test. Air and temperature read-
ings to be taken in 2-minute periods at one hour, 1J£ hours and two
hours after the beginning of the test.
Tests 10 and 11 will be repetitions of Test 9.
Test 12. — In Test 12 the wearer of the apparatus shall—
(a) Walk 1000 feet at the rate of approximately 3 miles per hour
over a level measured course, consuming 4 minutes while doing this
work.
(6) Run 600 feet at a rate of 6 to 8 miles per hour over a level measured
course, consuming 2 minutes while doing this work.
(c) Walk 1000 feet at the rate of 3 miles per hour over a level mea-
sured course, consuming 4 minutes while doing this work.
(d) Raise a 45-pound weight 75 times through a vertical distance of
5 feet, consuming 5 minutes while doing this work.
(e) Carry a 45-pound weight over a level measured course 1000
feet, consuming 5 minutes while doing this work.
(/) Carry a sack of bricks weighing 50 pounds over an overcast 5
times, making one complete trip in 2 minutes.
(0) Allow 2 minutes for taking of air samples and temperature readings.
(h) Raise a 45-pound weight 75 times through a vertical distance of
5 feet, consuming 5 minutes while doing this work.
(1) Walk over a measured course at rate of 3 "miles per hour for a
period of 10 minutes.
(j) Carry a sack of bricks weighing 50 pounds over an overcast 10
times, making one complete trip in 1^ minutes.
(fc) Allow 2 minutes for taking of air samples and temperature readings.
(/) Walk 1000 feet at rate of approximately 3 miles per hour over a
level measured course, consuming 4 minutes while doing this work.
\m) Raise a 45-pound weight 75 times through a vertical distance of
5 feet consuming 5 minutes while doing this work.
(n) Walk at the rate of 3 miles per hour over a level measured course
until the end of the two hours allowed for this test. Air and temperature
readings are to be taken in 2-minute periods at 1^ and 2 hours after
the start of the test.
MINE RESCUE WORK AND APPLIANCES 155
Tests 13 and 14 will be repetitions of Test 12.
Test 15. — This test will be made to determine the maximum length
of time that the apparatus will supply the needs of the wearer when in a
quiescent state. The wearer will remain as far as possible in a sitting
posture throughout the test and perform no work. He will be allowed to
manipulate the devices controlling the oxygen supply with a view to
conserving such oxygen supply to the greatest advantage.
At the end of each 30-minute period, 2 minutes shall be allowed for
taking of air samples and temperature readings.
NOTE. — Self-contained mine-rescue breathing apparatus in
course of development may be submitted by manufacturers
and inventors for preliminary test or inspection with the view
of ascertaining defective construction or the misapplication of
safety principles. The nature of such tests or inspection will
be determined by the bureau's mine-safety engineer in charge
of the testing of such apparatus.
Approval of Apparatus. — The manufacturers of such types of self-
contained mine-rescue breathing apparatus as have passed the tests of
the bureau will be required to attach to each apparatus a plate containing
the following inscription:
Permissible Mine-Rescue Breathing Apparatus,
U. S. Bureau of Mines Approval No. _ .
The use of the plate will .not be required if the same inscription is
stamped or cast into the metal of the apparatus.
Manufacturers shall, before claiming the bureau's approval for any
modification of a permissible self-contained mine-rescue breathing appa-
ratus, submit to the Bureau drawings or parts that shall show the extent
and nature of such modifications, in order that the bureau may decide
whether test of the remodeled apparatus will be necessary for approval.
If it is decided by the, bureau that testing of the remodeled apparatus
is necessary, the word "permissible" shall not be used on the remodelled
apparatus until it has again passed the complete schedule of tests or such
part of these tests as the bureau's engineer in charge of the tests shall
deem necessary.
The bureau will, on application, make separate tests, identical with the
foregoing tests, of regenerators manufactured for use in connection
with any mine-rescue breathing apparatus that has been approved by the
bureau under the provisions of this schedule.
Regenerators that fulfill the requirements of the foregoing tests will
be approved for use only in connection with that particular type of
apparatus for which they are designed and which has previously re-
ceived the bureau's approval.
156 MINE GASES AND VENTILATION
The listing by the Bureau of Mines, as "permissible," any self-con-
tained mine-rescue breathing apparatus shall be construed as applying
only to apparatus of that specific type, class, form and rating, made by
the same manufacturer, which have the same construction in all details
directly or indirectly affecting the safety features of the apparatus.
The bureau reserves the right to rescind for cause, at any time, any
approval granted under the conditions herein set forth. Cause for
rescinding of approval shall be considered to be the use of the bureau's
issuance of approval in an unauthorized manner; that is, placing the
approval stamp on apparatus that has not been approved by the bureau,
or on apparatus certain parts of which have been altered in construction
or material without submittal to the bureau for test.
Notification to Manufacturer. — As soon as the mine-safety engineer of
the Bureau'of Mines is satisfied that a self-contained mine-rescue breath-
ing apparatus has passed all the tests herein set forth in a satisfactory
manner, the manufacturer or inventor shall be formally notified to that
effect.
When two or more applications for tests on different apparatus are
received within a period of 10 days, the announcement of approval for
each shall not exceed the interval of time between the receipt of the
applications.
When a manufacturer or inventor receives this formal notification he
shall be free to advertise this type of successfully tested self-contained
mine-rescue breathing apparatus as permissible according to the Bureau
of Mines standards and may attach approval plates to this type of
breathing apparatus.
Fees for Testing. — Careful investigation has been made regarding the
necessary expenses involevd in testing mine-rescue breathing apparatus,
at the Pittsburgh experiment station of the bureau. The following
schedule of fees to cover expenses to be charged on and after March 5,
1919 has been established and approved by the Secretary of the Interior,
in accordance with the provisions of the statute previously quoted,
Complete mine-rescue breathing apparatus test $100
Separate preliminary inspection and test $10
Separate regenerator test $5
Separate inspection and test of reducing valves $10
The fees specified above may be increased to cover the cost of testing
an unusually complicated type of mine-rescue breathing apparatus, and
are also subject to change upon the recommendation of the Director of
the Bureau of Mines and the approval of the Secretary of the Interior.
Application for Test of Apparatus. — 1. Application for tests should be
addressed to the director of the Bureau of Mines, Washington, D. C.
This application must be accompanied by check or draft made payable
to the Secretary of the Interior, and by a complete written description of
the mine-rescue breathing apparatus to be tested, and a set of the drawings
MINE RESCUE WORK AND APPLIANCES 157
as specified in the Conditions of Testing, page 148, and marked " Drawings
of Approved Mine-Rescue Breathing Apparatus to be Filed." Duplicate
copies of the application and drawings should be sent to the mine-safety
engineer, Bureau of Mines, Pittsburgh, Penn.
2. As soon as the application is received by the bureau's mine-safety
engineer, the applicant will be notified of the date the tests will begin.
3. After the applicant has received this notification, he should send the
material required to the mine -safety engineer, Bureau of Mines, Pitts-
burgh, Penn. This material should be delivered not less than one week in
advance of the date set for the beginning of the tests.
4. The tests will be begun on the date set and continued until the mine-
rescue breathing apparatus has been approved, rejected or withdrawn.
5. After the bureau's mine-safety engineer has considered the results
of the tests, a formal report of the approval of the self-contained mine-
rescue breathing apparatus will be made to the applicant, in writing, by
the director of the Bureau of Mines. No verbal report will be made, and
the details of the test will be regarded as confidential by all present.
Approved March 5, 1919.
.8. G. HOPKINS, VAN H. MANNING,
Assistant Secretary. Director.
FIRST-AID WORK
Practical Use of Breathing Apparatus. — It is of the greatest
importance that all breathing apparatus should be carefully
examined and tested before the wearer proceeds to enter an
irrespirable atmosphere. First, it is necessary to observe the
gage or meter to see that the proper supply of oxygen is con-
tained in the oxygen cylinder. Observe also that the required
quantity of oxygen (2 liters) is being delivered each minute, as
indicated by a registering meter. The breathing bag must be
carefully tested and all valves examined to see that they are in
good working condition and to ascertain that the breathing bag
contains no airleaks.
In use, always inflate the bag with pure air when ready to
put on the apparatus and before turning on the supply of oxy-
gen. It is well for the wearer, then, to take the precaution
of going into a smoke chamber, for a short period before enter-
ing the mine. This will enable him to ascertain that there are
no leaks in the apparatus and that breathing is normal.
Resuscitation. — To resuscitate is to revive, or to restore
animation in an unconscious person or one who is seemingly
158 MINE GASES AND VENTILA TION
dead. A person may be apparently lifeless as the result of any
one of several causes; (1) Fainting from overexertion. 2.
The result of a nervous shock. 3. An electric shock, received
by contact with a live wire. 4. Suffocation, by reason of in-
haling irrespirable gases, or the lungs being filled with water,
as in drowning. 5. A blow on the head. In fact, unconscious-
ness may result from any accidental occurrence affecting di-
rectly or indirectly the nervous system on which respiration
and animation depends.
In the work of resuscitation, due regard must always be had
to the cause of suspended animation. Where the lungs have
filled with water, as in drowning, or with gas inhaled in the
mine or elsewhere, immediate steps must be taken to drive the
water or gas from the lungs and permit the entry of fresh air
through artificial respiration applied vigorously and continued
till the person revives, or it is absolutely certain that life is
extinct. If the trouble arises from the inhalation of gas,
the victim must be removed promptly to fresh air before treat-
ment is administered, loosen the clothing about the neck and
chest and give artificial respiration, at the same time chafing
the limbs, rubbing them toward the body to assist the flow of
the venous blood back to the heart.
Smelling salts applied to the nostrils assist to quicken ani-
mation. As soon as the victim is able to swallow and on the
first signs of returning life, give a stimulant, hot coffee or tea,
or half a teaspoonful of aromatic spirits of ammonia in a
half-glass of water, administered in small doses at slight
intervals. Where shock has resulted from injury and loss of
blood, however, stimulants should not be given, as these will
assist the action of the heart and increase the flow of blood
from the wound. In all other cases, return of animation will
be assisted by any means that will assist the circulation of blood
and revive the respiratory system. Keep the patient warm
with blankets and give plenty of fresh air during treatment
for resuscitation.
•Artificial Respiration. — -There are two general methods of
applying artificial respiration. In the Sylvester method,
which is now little used, the patient is laid on his back, while
MINE RESCUE WORK AND APPLIANCES 159
the operator kneeling at his head grasps the wrists of both
arms and proceeds to alternately swing the arms, first forward
on the chest and then back to a position above the head, at
the normal rate of breathing or, say 16 times a minute. In
the forward movement, the arms are doubled at the elbow and
pressed down firmly against the sides of the chest so as to
compress the lungs and force out the gas therefrom. This is
followed by the backward movement, which has the effect
of expanding the lungs and inducing inhalation. These move-
ments are continued alternately, first compressing the lungs
and then expanding them in turn. While doing this, it is
m
important to secure the tongue and hold it forward in the
mouth so that it will not impede the access of air to the lungs.
A handkerchief covering the fingers will help to hold the ton-
gue forward, or a clip must be used for that purpose.
The common method of resuscitation now most generally
employed is that known as the "Schaefer method," or the
" prone method" of resuscitation. By this method, the pa-
tient is laid prone on his face, except that the head is turned
to one side to facilitate breathing. The operator, having made
sure that the tongue is drawn forward in the mouth so as to
give free access of air to the lungs, straddles the patient's
thigh, as shown in Fig. 20, and rests the -palms of his hands
160 MINE GASES AND VENTTLA TION
on the person's loins with the two thumbs together and the
fingers reaching well down on each side, in a manner to bring
pressure on the short ribs and across the small of the back.
In this position, the operator first swings forward so as to
throw his weight on the patient's body compressing the lungs
to drive out the gas or water they contain. Then, swinging
backward, he gives opportunity for the expansion of the lungs,
which induces the inhalation of fresh air. As in the Sylvester
method, this forward and backward movement must be
continued alternately, for a period of an hour or two, until
there are signs of returning life or it is absolutely necessary
that life is extinct. There are instances on record where the
victim has been revived after several hours of hard work.
It is often necessary for the operator to be relieved for a time
by another, but the process must be continued without cessa-
tion, until a doctor gives it as his opinion that life has fled.
In every case, send for a doctor while giving first-aid to the
patient.
SECTION VI
THEORY OF VENTILATION
MINE VENTILATION — PROBLEMS — FLOW OF Am IN AIRWAYS
— VENTILATING PRESSURE, How PRODUCED AND MEAS-
URED, THE WATER GAGE — VELOCITY OF AIR CURRENTS
— QUANTITY OF AIR, REQUIREMENTS — WORK OR POWER
ON THE AIR — EQUIVALENTS IN MEASUREMENT — EXAM-
PLES FOR PRACTICE — MINE AIRWAYS — SYMBOLS AND FOR-
MULAS— MINE POTENTIAL METHODS — MEASUREMENT OF
AIR CURRENTS — EXAMPLES FOR PRACTICE — TANDEM CIR-
CULATIONS— SPLITTING THE AIR CURRENT — NATURAL
DIVISION OF AIR — EXAMPLES IN NATURAL DIVISION-
PROPORTIONATE DIVISION OF AIR, REGULATORS — SECOND-
ARY SPLITTING — THEORETICAL CONSIDERATIONS IN
SPLITTING — PRACTICAL PROBLEM
MINE VENTILATION
The ventilation of a mine, as the term implies, involves
the supply and maintenance of a sufficient current of air
throughout the mine to render the same healthful and safe.
Requirements of Ventilation. — The quantity of air in circu-
lation must be sufficient to comply with the state mining law,
and to dilute, render harmless and sweep away the gases
that would otherwise accumulate in the mine. The air cur-
rent must be conducted so as to sweep the entire working
face and all void places with a moderate velocity sufficient
to remove the gas without danger from the lamps or inconven-
ience to the workmen.
The Circulating System. — In order to circulate a current of
air through a mine, it is necessary to provide two separate
openings, one for the air to enter, called the "intake opening,"
and the other for it to leave the mine, called the " return" or
" discharge opening.". Two distinct air passages or airways
are also required, leading from these openings into the mine,
in order to conduct the air current to and from the working
n 161
162
MINE GASES AND VENTILATION
face. These are called, respectively, the "intake" and "re-
turn " airways. These openings and airways form a part of the
circulating system in the mine, similar to the arteries and veins
of the human body.
Kinds of Ventilation. — There are three different kinds of
ventilation-, in mining practice, known as " natural ventila-
tion," "furnace ventilation" and mechanical or "fan ventila-
tion," according to the agency employed for its production.
Natural Ventilation. — Ventilation is natural when it is
produced by any natural agency, such as surface winds,
falling water or the natural heat of the mine. The accompany-
ing Fig. 21 illustrates the manner in. which the natural heat of
the mine produces a warm upcast air column, in either a drift
mine or a shaft mine.
Surface
FIG. 21.
In the drift mine shown on the left, the warmer air column
in the shaft only partly balances the cooler outside air. Above
the level of the top of the shaft the two air columns are of equal
temperature and equal weight, and, therefore, need not be
considered since they balance each other. The same is true
in the shaft mine shown on the right, whenever the two shafts
have the same elevation at the surface.
Natural Ventilation in Slope Mines and Dip Workings.—
A similar condition in respect to the natural heat of the mine
producing or modifying the circulation of the air, holds in
all slope mines and dip workings, the same as in shafts and
drifts. Whenever the mine temperature is much below or
above that of the outside atmosphere, the difference in tem-
perature makes the return air heavier or lighter than the
THEORY OF VENTILATION 163
intake air; and the difference in weight of these two air col-
umns destroys the equilibrium of the mine air and creates
a current in the airways throughout the mine.
A considerable difference of temperature is often observed
between the dip and rise air currents in particular sections
of a mine. It is this difference in the temperatures of the
intake and return currents that often makes dip workings
harder to ventilate in summer than in winter. For the same
reason, rise workings are frequently found to be more easily
ventilated in the summer season.
Air Columns. — The term "air column," like water column,
always refers to a vertical column. The air column, in ven-
tilation, is an imaginary vertical column of air, of unit sec-
tion (commonly, 1 sq. ft.) and of such height that its weight,
in pounds, is equal to the pressure it measures (Ib. per sq. ft.).
The density of the air (wt. per cu. ft.) is either stated or under-
stood, so that when the height of air column is given the
pressure it indicates is readily calculated.
In mining practice, it is common to express ventilating
pressure in feet of air column or, as we say, "head of air."
Calling the weight of 1 cu. ft. of air w (Ib.) and the head of
air column h (ft.), the pressure p (Ib. per sq. ft.) is calculated
by the formula
p = wh
Or the air column corresponding to any given pressure is
found by transposing this formula; thus,
w
Example. — What is the head of air column corresponding to a ventilat-
ing pressure of 10 Ib. per sq. ft., assuming a temperature of 60 deg. F.
and a barometric pressure of 30 in.?
Solution. — The weight of 1 cu. ft. of air, at the given temperature and
pressure is
1.3273J3 1.3273 X 30
460-+1 6
The required head of air is then
°-°766
~ = ?Ti^ = 130.5 /«.
w 0.0766
164 MINE GASES AND VENTILA TION
Example. — Find the ventilating pressure and water gage corresponding
to 80 ft. of air column, &t the same density.
Solution. —
p = Wh = 0.0766 X 80 = 6.128 Ib. per sq. ft.
w.g. = 6.128 -T- 5.2 = 1.18 in., nearly
Furnace Ventilation. — When the circulation of air through-
out a mine is created and maintained by means of a furnace
built in the mine the system is known as " Furnace
ventilation."
Principle of Furnace Ventilation. — The heat of the furnace
imparted to the air in the furnace shaft makes it lighter,
volume for volume, which causes it to rise in obedience to
the law of the equilibrium of fluids. The cooler and heavier
outside air, in obedience to the same law, flows into the mine by
way of another opening, to take the place of the air displaced.
The action is continuous as long as the furnace is in operation.
There is thus created and maintained a constant flow of air
into and through the mine.
Location of a Mine Furnace. — The furnace is built in the
main-return airway about 20 or 25 yd. back from the foot of
the upcast or furnace shaft, so as to reduce the danger of the
fire damaging or destroying the shaft.
Construction of Furnace. — The essential details to be con-
sidered in the construction of an efficient mine furnace are
the following:
1. Beginning, say 50 yd. back from the foot of the shaft,
the main-return airway should be gradually widened and its
height increased so that the unobstructed sectional area at
the furnace will not be less than 25 per cent, greater than
that of the original airway.
2. The roof of the enlarged airway should then be se-
cured by steel rails or I beams supported on posts or concrete
walls, as illustrated in Pig. 22, which represents a well built
mine furnace.
3. As shown in the figure, both the concrete walls and the
brick walls supporting the arch are started on a good firm
bottom below the floor line. The thickness of the concrete
walls will vary from 10 or 12 in. to 2 ft., depending on depth
THEORY OF VENTILATION
165
of cover and other roof conditions. The brick walls and arch
will vary in thickness from 8 to 12 in. A good quality of
vitrified brick should be used, except where the arch and
walls are exposed to the direct action of the flame they should
be lined with the best firebrick. All bricks should be first
soaked in water before being laid and only the best cement
mortar should be used.
4. The brick walls and arch should be started about 2 yd.
in front of the furnace proper and extended to the face of
the shaft. The clear width between the walls should equal
the width of the fire-grate, and should be such as to leave
a clear passageway between the brick and concrete walls.
CROSS- SECTION LONGITUDINAL SECTION ON CENTER LINE
THROU&H FURNACE OF ENTRY
FIG. 22.
The arch is semicircular and sprung at such a height above
the floor as to leave not less than 12 in. of space between the
crown of the arch and the rails that support the roof. The
purpose of this air space around the furnace is to isolate the
heat, which is thus more completely utilized in heating the
air current.
5. The area of the grate or the grate surface must be
sufficient to burn the weight of coal per hour required to heat
the volume of air passing the furnace in that time, to a tem-
perature that will create the air column, in a given depth
and condition of shaft, necessary to circulate such volume of
air against a specified mine potential.
The theoretical problem of determining the weight of coal
burned per hour, per volume of air circulated, is thus seen to
depend on many factors. In ordinary mining practice, how-
ever, a safe estimate is to assume that each pound of coal
burned per hour will cause a rise in temperature of from 10
166 MINE GASES AND VENTILATION
to 15 deg. F., per 1000 cu. ft. of air in circulation. Or, calling
the weight of coal burned W (Ib. per hr.); the volume of air
passing Qm (1000 cu. ft. per min.); the rise in temperature t
(deg. F.), and the temperature constant c = 10 to 15 deg. F.,
Example. — Find the weight of coal required per hour, to produce a
rise of temperature of 360 deg. F., in a furnace shaft when a current of
100,000 cu. ft. of air per minute is passing, under fair mining conditions.
Solution. — The weight of coal required is
Qmt 100 X 360
TV = ~— = ---- - 2 -- = 3000 Ib. per hr.
In very deep or wet shafts or a comparatively small mine
resistance, giving a larger air volume and greater loss of
heat, the constant 10 deg. should be used; while in dry shafts
of less depth, especially if the mine resistance is considerable,
a temperature constant of 15 or even 16 may be employed to
find the necessary weight of coal.
6. The grate area necessary to burn any required weight
of coal W (Ib. per hr.) varies with the hardness and the inflam-
mability of the coal. A mine furnace will commonly burn
from 15 to 20 Ib. of anthracite, or from 20 to 25 Ib. of bitumin-
ous coal, per square foot of grate, per hour. Hence the weight
of coal required, divided by such constant will give the neces-
sary area of grate surface, in square feet.
Example. — What grate area will be required to burn, say 3000 Ib. of a
very soft, inflammable coal per hour?
Solution. — In this case, the coal being a free-burning, inflammable
coal, the constant 25 should be used; and the required area is 3000 •*- 25
= 120 sq.ft.
Estimation of Air Columns in Practice. — In the ventila-
tion of shaft or slope mines or rise and dip workings in in-
clined seams, the weight of each respective downcast and
upcast column is sometimes calculated separately, by multi-
plying the weight of 1 cu. ft. of air, at a barometric pressure
B and a temperature t equal to the average temperature of
THEORY OF VENTILATION
167
the column, by the height or ojepth D of the same column, as
expressed by the formula
1.3273B
=
All air columns are of unit cross-section (1 sq. ft.) and the
calculated weight of the column, therefore, gives the corre-
sponding pressure in pounds per square foot.
Positive and Negative Air Columns. — An air column that
acts to assist the circulation in the mine or airway is called
a " positive" column; while one that acts to oppose the cir-
culation is termed a "negative" column. In fan ventilation,
a negative air column may exist in the downcast shaft by rea-
son of its temperature being greater than that of the upcast,
which frequently happens in the summer season.
Conditions. — The height or depth D of air column, in any
particular case, can only be determined by carefully consider-
ing the conditions. It is important to remember that, with
few exceptions, the temperature of a downcast-shaft column
will closely approximate that of the outer air with which this
shaft is constantly filled; while the temperature of the up-
cast column is practically determined by that of the mine or,
in furnace ventilation, by the furnace.
When two shafts, upcast and downcast, Fig. 23, (a), are sunk
from a level surface or, in other words, have the same surface
elevation it is evident that this level marks the upper limit
of both columns.
When, however, the two shafts are sunk on a hillside and
have different surface elevations, two cases may arise, as il-
lustrated in Fig. 22, (6) and (c), in which, for the sake of clear-
1G8 MINE GASES AND VENTILA TION
ness, the outside temperature is Assumed as 32 deg. F. and that
of the mine as 60 deg. F.
The two cases are as follows :
"l. When the shaft having the higher surface elevation is
made the upcast, as is usually done, that elevation marks the
upper limit of both shaft columns; because the downcast
shaft has practically the same temperature as the outer air.
2. When the shaft having the lower surface elevation is
made the upcast this elevation marks the upper limit of both
shaft columns; because the air in the other (downcast) shaft
above this level is balanced by the corresponding column of
outside air.
These two conditions, therefore, are simply expressed by
the statement that, in either case, the upper limit of both
shaft columns is the surface level of the upcast shaft.
In the same manner it can be shown that the lower limit
of both shaft columns is the bottom of the downcast shaft
when the seam has a general inclination. Hence, the length
(D) of both shaft columns is measured, in any case, from the
top of the upcast to the bottom of the downcast shaft. This
rule does not apply to slopes.
Ventilating Pressure and Shaft Columns. — Since the weight
of an air column, in pounds, expresses the corresponding
pressure, in pounds per square foot; and since ventilating
pressure (Ib. per sq. ft.) is the difference of pressure between
the intake and return; the unit pressure p, in any given
case, is found by subtracting the weight of the upcast-shaft
column from that of the downcast column; thus,
Downcast-shaft column, Wd = /„„ _, D
Upcast-shaft column, wu = .' ^D
Uait pressure, p = 1.3273
which can be written
1.3273B (T -- t) D
P " (460+ T} (460 + 0
THEORY OF VENTILATION 169
Calculation of Air Column. — The air column corresponding
to the above unit ventilating pressure can be expressed in
terms of either the downcast or upcast air. The air in the
downcast being heavier than that in the upcast, gives a
shorter air column for the same pressure.
To find the air column (hd) in terms of the downcast air,
divide the above expression for unit ventilating pressure by the
weight (wd) of 1 cu. ft. of downcast air (temp. = t), which gives
/, P_ =(T -t)D
Wd - 460 + T
To find the corresponding air column (hu) in terms of the
upcast air, divide the same expression for unit ventilating
pressure by the weight of 1 cu. ft. of upcast air (temp. = T),
which gives
p (T - t) D
wu 460 + t
Effective Depth of Air Column. — It has been shown that in
all shaft ventilation the effective "head of air column" D
is the difference in elevation of the top of the upcast and the
bottom of the downcast. This applies equally to all forms
of natural, furnace or fan ventilation, in shaft mines, where
a positive or negative air column may exist.
Likewise, in drift or slope mines, the same law will apply,
except where a long slope causes an appreciable rise in the
temperature of the downcast air; and in the furnace ventila-
tion of a slope mine. In either of these two cases, three tem-
peratures may be concerned: (1) average upcast temperature
in the shaft; (2) average downcast temperature in the slope;
(3) outside temperature.
In furnace ventilation, in inclined seams, also, three tem-
peratures must be considered: (1) average temperature of the
furnace (upcast) shaft; (2) mine temperature, rise or dip of
seam; (3) average downcast temperature. In a few cases, a
fourth (4) outside temperature may require consideration. In
all cases where more than two temperatures are concerned
it is necessary to calculate the column for each separate tem-
perature and corresponding depth and take their algebraic sum.
170 MINE GASES AND VENTILATION
In practice, the arrangement of the circulation in the mine
may be such that the rise or dip column is eliminated by a
balance of intake and return columns of equal temperature.
PROBLEMS
Example. — A shaft mine, in a level seam, is ventilated by a furnace.
The furnace shaft is 900 ft. deep and has an average temperature of
300 deg. F. ; the downcast shaft is 600 ft. deep. Calculate the air column
producing circulation in this mine and the corresponding ventilating
pressure and water gage when the temperature of the outside air is 20
deg. F. and the barometer 30 in.
Solution. — The effective head of air, in this case, is D = 900 ft. and,
assuming that the temperature of the downcast shaft is practically the
•same as that of the outside air, which is commonly true, the air column,
expressed in terms of the downcast air, is
(T - t)D = (300 - 20) 900 280 X 900
d 460 + T 460 + 300 760
Expressed in terms of the upcast air the air column, in this mine, is
_ (T - t)D _ (300 - 20) 900 _ 280 X 900
" '
460 +t ' 460 +20 480
The pressure is found by multiplying either of these air columns by the
corresponding weight of downcast or upcast air.
Thus (downcast), p = - ~i~ X 331.5 = 27.5 Ib. per sq. ft.
4oO "|" ^0
i
Or (upcast), p = + X 525 - 27.5 Ib. per sq. ft.
The corresponding water gage is, then,
w.g. = 27.5 -5- 5.2 = 5.3 in., nearly
Example. — A slope mine is ventilated by means of a blowing or force
fan located at the top of an air shaft 800 ft. deep. The slope is the main
return airway and the elevation at its mouth is 275 ft. below that of the
top of the air shaft. What natural air column exists, assuming the tem-
perature of the mine is 60 deg. and that of the outside air 10 deg. below
zero (•— 10°F.); and is this positive or negative?
Solution. — The effective head of air, in this case, is D = 800 — 275 =
525 ft.; because the downcast fan shaft has the same temperature as
the outside air column, which therefore balances 275 ft. of the shaft
column. The downcast air in the shaft being colder and heavier than
the upcast or return air in the slope, the resulting air column assists the
circulation produced by the fan and is, therefore, a positive air column.
It is
j, _ [60 -(-10)]X525 _ (60 + 10) 525 _ 70 X 525
hd ~ 460 + 60 520 520
THEOR Y OF YEN TIL A TION 171
This air column is in terms of the downcast air, which weighs, assum-
ing a barometric pressure B = 30 in.,
1.3273 X 30 39.819
Wd = 460 + (-10) = "450-
The natural pressure due to this air column is then
pn = 70.67 X 0.0885 = 6.25 Ib. per sq. ft.
Ques. — If the fan, in this example, were to be reversed so as to exhaust
air from the mine, thereby making the slope the intake and the fan shaft
the upcast, what air column would result, if the average slope tem-
perature is then 40° F.?
Arts. — In this case, three air columns exist, two assisting and one
opposing the circulation induced by the fan. They are as follows:
1.3273 X 30 .
Outside column (positive), w0 =
~~" JLU
1.3273 X 30 v
Slope column (positive), w, = „ ~ X 525
1 ^97*? V ^0
Shaft column (negative), wu = 46Q + ^0 X 800
The net air column, expressed in terms of, say the slope air, is now
found by dividing the algebraic sum of these positive (+) and negative
( — ) columns by the weight of 1 cu. ft. of the slope air, which gives after
simplifying,
, ,,AA , A. 275 525 800
A. = (460 +4
/275 . 525 800\
1450 + 500 ~ 520J
The weight of 1 cu. ft. of slope air is
1.3273 X 30 39.819
460+40 "SOOT :
The natural pressure assisting the circulation is then
pn = 61.3 X 0.0796 = 4.88 Ib. per sq. ft.
Example. — To show the effect of natural air columns in fan ventila-
tion, assume a shaft mine ventilated by means of a fan; the seam is
practically level ; the fan shaft is 800 ft. deep and the hoisting shaft 600
ft. deep.
(a) Assume the fan is exhausting and produces a circulation of 200,000
cu. ft. of air against a water gage of 2 in., in the winter when the outside
temperature is 30 deg. and that of the mine 60 deg. F., and calculate the
resulting water gage and the volume of air that the fan will circulate,
running at the same speed in the summer season when the outside tem-
perature is 70 deg.. and that of the mine, as before, 60 deg. F.
(6) Assume the same conditions in the mine and the same respective
temperatures and calculate the water gage and volume of air this fan will
172 MINE GASES AND VENTILATION
produce when running at the same speed and blowing instead of ex-
hausting the air, for the winter and summer seasons, respectively.
Solution. — (a) When the fan is exhausting, the fan shaft being the
upcast, the effective depth of air column is D = 800 ft. The natural
water gage due to this depth (barom., B. = 30 in.) is
1.3273 X 30(60 - 30)800
Winter, w.g.n - (460 + eo) (460 + 30)5.2 = °'72 in'
1.3273 X 30(70 - 60)800
Summer, w.g.n = (4qo + 70) (460 + 60)6.2 = °'22 m'
In the circulation of 200,000 cu. ft. of air, under a 2-in. water gage,
as stated in the question, therefore, the water gage due to the action of
the fan is 2 — 0.72 = 1.28 in., the natural water gage, in this case,
assisting circulation, being positive. In the summer season, the fan
exhausting at the same speed as before will create the same ventilating
pressure and water gage (1.28 in.) ; but, the natural air column now being
negative (0.22 in.), the effective water gage producing circulation is
1.28 — 0.22 = 1.06 in. Then, since the circulation in any given mine
or airway varies as the square root of the pressure or water gage, the
quantity ratio is equal to the square root of the water-gage ratio.
200,000
Summer (exhausting), x = 200,000 X 0.728 = 145,600 cu. ft. per min.
(b) When the fan is blowing the hoisting shaft is the upcast and the
effective depth of air column is then D = 600 ft. The natural water
gage is then 600/800 = ^ of the value previously found; or % X 0.72 =
0.54 in. (winter), and % X 0.22 = 0.165 in. (summer). As before, the
natural gage is positive in winter and negative in summer, which makes
the effective gage 1.28 + 0.54 = 1.82 in. (winter) and 1.28 — 0.165 =
1.115 in. (summer). The circulation is then
/I 00
Winter (blowing), x = 200,000-^^- = say 190,800 cu. ft. per min.
Summer (blowing), x = 200, 000 -y~ = say 149,400 cu. ft. per min.
FLOW OF AIR IN AIRWAYS
The flow of air in a conduit or airway is in obedience to
an excess of pressure at one end of the conduit over that at
the other end. Air always moves from a point of higher pres-
sure toward a point of lower pressure. The moving air is
called the air current.
THEORY OF VENTILATION 173
Velocity of Air Currents. — The rate of motion or the dis-
tance traveled per unit of time is called the velocity of the
air current. The velocity is commonly expressed in feet per
second or feet per minute, as most convenient.
Relation of Pressure and Velocity. — To double the velocity
of air in an airway or conduit requires four times the pres-
sure; and since 2 = \/4, the velocity v varies as the square
root of the pressure p\ thus
v varies as \/p
or, vice versa,
p varies as t>2
For example, if an airway in a mine is of such size and
length that the pressure per square foot at the intake is 3 Ib.
greater than that at the discharge opening, and this difference
of pressure produces a velocity of 5000 ft. per min.; it will
require a difference of pressure of 4 X 3 = 12 Ib. per sq. ft.
to produce a velocity of 1000 ft. per min. in the same airway.
Solution by Ratios. — -Expressed as ratios, the solution is
always simpler and shorter, because the method admits of
ready cancellation, thereby keeping the numbers small and
reducing the amount of necessary work. For example, when
quantities are proportional their ratios are equal. Or, in this
case, the velocity ratio is equal to the square root of the
pressure ratio. Calling the first velocity v\, second velocity
Vz', the first pressure p\ and the second pressure p2, we have
v* _ fpt
1)\
or, vice versa,
Example. — What difference of pressure per square foot will be required
to produce a velocity of 1200 ft. per min. in an airway where the air is
moving at the rate of 500 ft. per min., under a moving pressure of 3.5
Ib. per sq. ft.?
Solution. — Let x = the required difference of pressure; then
x /1200\2 /12\2 144
3^ = ( 5007 " V*7 = 25T = 5'76
x = 3.5 X 5.76 = 20.16 Ib. per sq. ft.
174 MINE GASES AND VENTILA TION
Example. — If a difference of pressure between the two ends of an air-
way, of 8 Ib. per sq. ft., produces a velocity of 600 ft. per min., what
will be the velocity in the same airway when the difference of pressure
is only 2 Ib per sq. ft.?
Solution. — In this case, calling the required velocity x,
JL _ J2 _ Ji _ 1
600 \8 \4 ~ 2
x = 600 X H =300 ft. per min.
VENTILATING PRESSURE
Pressure Producing Circulation. — In mine ventilation, the
term ''ventilating pressure" is the pressure exerted to move
the air. It is the difference between the intake pressure and
the discharge pressure. Since the pressure of the atmosphere
is equal at both ends of the airway it may be disregarded,
as far as the movement of the air is concerned.
The Blowing System of Ventilation. — To move the air or
cause it to circulate in an airway or a mine, an extra pres-
sure must be created at one end of the airway, so as to over-
come the resistance of the mine due to friction. This is
called the "blowing" system of ventilation, because the air
is blown through the airway by the pressure created.
The Exhaust System of Ventilation. — The same difference
of pressure may be caused by decreasing the atmospheric
pressure at one end of the airway, when the full pressure
of the atmosphere at the other end will cause the air to move
toward the point where the pressure is less. The principle
is that commonly called " suction;" but this system is known
HS the "exhaust" system of ventilation.
How Pressure is Produced. — Various means have been used
to cause a circulation of air in mine airways. The wind
cowl, waterfall and steam jet are useful under favorable
conditions and where a limited air supply only is needed. The
mine furnace, built in the mine near the bottom of the upcast
shaft, is often used in n on gaseous mines, especially in deep
shafts (see Furnace Ventilation). The most reliable means
of creating pressure in mine ventilation, however, is the mine
fan, which is generally erected at the surface, either at the
THEOR Y OF YEN TIL A TION 175
top of the downcast shaft, as a blower; or at the top of the
upcast, as an exhaust fan (see Fan Ventilation). The blow-
ing fan creates a pressure above that of the atmosphere, while
the exhaust fan reduces the atmospheric pressure.
How Pressure is Estimated. — In mine ventilation, the
pressure producing circulation is estimated in height of air
column, as in natural ventilation and often in furnace ven-
tilation. The more common method, however, is to state the
pressure in pounds per square foot or ounces per square inch.
Pressure is also stated in inches of water gage. These all refer
to the unit of ventilating pressure or simply "unit pressure."
Atmospheric pressure is given in pounds per square inch,
or, as barometric pressure (which is the same as atmospheric
pressure), in inches of mercury.
1 in. water gage = 5.2 Ib. per sq. ft.
1 in. mercury = 0.491 Ib. per sq. in.
1 oz. per sq. in. =9 Ib. per sq. ft.
1 in. mercury = 13.6 in. water gage
How Pressure is Measured. — In mine ventilation, the pres-
sure producing circulation is commonly measured by means
of the water gage; or, in case of high pressures a special form
of manometer is sometimes used. The manometer differs from
the water gage in having one end of the bent tube closed so
that the rise of the water level in that arm of the tube com-
presses the air above the water, which lessens the rise of
water level and gives a greater range of readings.
The Mine Water Gage. — This consists of a glass tube of
about %-in. bore, bent to the shape of the letter U and
mounted on a solid base. Three styles of water gage are
shown in Fig. 24. These differ only in the kind of scale. The
first two on the left have the zero at the center of the scale and
read up and down to the respective water levels. The first
of these scales is graduated to full-length inches, and to obtain
a correct reading it is necessary to add the two readings to-
gether, or double either of them, as they are equal. To avoid
this necessity the second scale is made of half-length inches, so
that either the upper or the lower reading gives the full gage
176
MINE GASES AND VENTILATION
required, which, in this case, is 3 inches. As shown in the
figure, the scale is adjustable by means of the screw rod on
which it is mounted.
When the zero of the scale is at the middle and the scale
reads up and down, it is evident that the scale must be adjusted
so that its zero will correspond with the two water levels, before
the pressure acts on the gage. When the pressure acts it
depresses the water level in one arm while that in the other
arm rises an equal amount. The difference between these
two levels is the actual water column supported by the differ-
Fio. 24.
ence in the pressures acting on the water in the two arms. As
will be explained later, one arm of the gage when in position
is open to the intake pressure and the other to the return.
The difference between these two pressures is the pressure that
circulates the air between these two points.
The scale shown on the right has its zero at the bottom and
reads upward. This scale must evidently be set, after the
gage is in position, so that the zero will correspond with the
lower water level, which is always that in the arm open
to the intake pressure, as that pressure is always greater than
the return pressure. The reading of the scale at the upper
level is then the required gage.
The reading of each of the three gages shown in the figure
is 3 in., which indicates a ventilating pressure of 3 X 5.2
= 15.6 Ib. per sq. ft.
THEORY OF VENTILATION
177
Reading the Water Gage. — In the common use of the water
gage, in mine practice, the scale is not read closer than % in.
On the left of Fig. 25, is shown a portion of a water column
and scale graduated to eighths of an inch. The scales
shown in Fig. 24 are decimal scales, being graduated to
tenths of an inch for greater accuracy. In all engineering
practice, therefore, and whenever accuracy is desired the
decimal scale shown in Fig. 24 is used and the reading taken
to tenths or hundredths of an inch.
There are several sources of possible error in reading the
mine gage. If the gage is not truly vertical the reading will
not be correct. Error often occurs from the cupping of the
surface of the water in the tube. As shown in Fig. 25, the
FIG. 25.
reading of the gage should be taken at the bottom of the con-
cave or bowl. This will give greater uniformity in the results
obtained.
In fan ventilation, especially when the reading is taken
in the fan drift, there is a constant oscillation of the water
level, which makes it difficult to decide on the true reading.
The oscillation is much reduced when the tube of the gage is
contracted at the bend. The best gages are provided with a
stop-cock in the bend by which the connection between the
two arms can be closed. The gage can then be carried to a
more convenient place to be read.
Unit of Ventilating Pressure. — In mine ventilation, the
unit of ventilating pressure, or the unit pressure producing the
circulation, is estimated in pounds per square foot This
12
1 78 MINE GASES AND V EN TIL A TION
is calculated from the reading of the water gage by multiply-
ing that reading, in inches, by 5.2.
On the right, in Fig. 25, is shown clearly how the constant
5.2 is derived. The weight of 1 cu. ft. of water is, practically,
62.5 Ib. The figure represents a cube that measures 12 in.
on each edge; the base of the cube being 1 sq. ft. Since the
weight of 12 in. of water, resting on this square foot, is 62.5
Ib., the weight of 1 in. of water covering the same area is 62.5
-7- 12 = 5.2 Ib., which represents the pressure, in pounds
per square foot, due to 1 in. of water column. The principle
involved is that the unit pressure on a given area of surface
depends only on the height of water column the pressure
supports.
The Water Gage in the Mine. — As used in the mine, the
reading of the water gage shows the difference of pressure
FIG. 26.
between the intake and return airways, at the point where
the reading is taken. The intake pressure is always greater
than the return pressure and this excess or difference of pres-
sure is what moves the air or creates the current.
The use of the instrument is clearly illustrated in Fig. 26
where two parallel airways are shown leading into the mine,
one of these being the intake and the other the return airway
of that section of the mine. It makes no difference on which
side of the brattice the instrument is placed; the water will
always be depressed in that arm of the gage which is open to
the intake, because the pressure on the intake is always greater
than that on the return airway.
What the Water Gage Shows. — The water-gage reading indi-
cates the ventilating pressure required to circulate the air,
THEORY OF VENTILATION 179
and is therefore equal to the resistance of the airways be-
tween the two points on the intake and the return; or, in
other words, the resistance inby from the point of observa-
tion. The nearer this reading is taken to the head of a pair
of entries, the closer it will approach zero, while at the next
to the last crosscut it would be practically zero.
The use of the water gage in mining practice is of great
importance. In connection with the observed velocity of the
air, it shows the " power on the air" or the power producing
the circulation. What is required in the practical ventilation
of a mine is the production of the necessary velocity and
volume of air, with the smallest expenditure of power. The
most economical circulation is obtained when the required
air volume is circulated by the least power, which means a
comparatively low water gage.
The circulation of a comparatively large quantity of air
under a low gage indicates ideal economic conditions, as far
as the circulation is concerned. On the other hand, a small
air volume and a comparatively high water gage shows a
needless waste of power. In practice, an unusual reduction
of the quantity of air passing in a mine or entry, accompanied
by a similarly uncommon rise of gage pressure would indi-
cate an obstruction of the airways.
VELOCITY OF AIR CURRENTS
The velocity of the air current is one of the most important
factors in the practice of mine ventilation. If the velocity of
the air current is too low the ventilation of the mine is ineffi-
cient, as the air will not sweep away the accumulating gases
from their lurking places in the mine. On the other hand, if
the air moves with too great a velocity, not only do the work-
men suffer inconvenience, but the high velocity of the current
is often dangerous.
Danger of High Velocity. — A rapid air current carries a
great quantity of dust, and, by supplying large quantities of
oxygen, maintains an unnecessarily active condition of the
mine atmosphere that favors the ignition of the gas and dust.
The high wind creates a draft that greatly intensifies the
180
MINE GASES AND VENTILATION
flame of lamps or of a blast of powder and increases the pos-
sibility of ignition.
How Velocity is Estimated. — In mine ventilation the ve-
locity of the ventilating current is commonly estimated in
feet per minute, or feet per second.
How Velocity is Measured. — A simple method of ascertain-
ing, with more or less accuracy, the average velocity of the
air current passing in an airway is to measure off a distance
of, say 300 ft. along a straight portion of the airway; and
FIG. 27.
note the exact time between the observed flash of powder at
one end and the smell of smoke at the other end of this dis-
tance. The distance (300 ft.) divided by the time will give
the velocity of the air in the center of the entry. The average
velocity of the current may then be taken as ££ of this observed
velocity. For example, if the observed time is 30 sec., the
center velocity is 300 -5- 30 = 10 ft. per sec.; and the average
velocity % x 10 = 8 ft. per sec. or 8 X 60 = 480 ft. per min.
The Anemometer. — The common method of measuring the
velocity of the air in airways is by the use of the anemometer,
one form of which is shown in Fig. 27. The dial hands record
THEORY OF VENTILATION 181
the number of revolutions of the vane. The instrument is so
calibrated that each revolution of the vane corresponds to
1 ft. of air travel. The reading of the dial, therefore, shows the
distance the air traveled during the time that the instrument
was exposed to the current. Hence, this reading divided by
the time of exposure, in minutes, will give the velocity of the
current in feet per minute. A single revolution of the large
hand corresponds to 100 revolutions of the vane. The small
dials register the total reading.
QUANTITY OF AIR
The term " quantity," in mine ventilation, refers to the
volume of air passing in an airway, estimated in cubic feet
per minute. This is often spoken of as the "circulation" of
the airway or mine.
How Quantity is Estimated. — As stated above, the quan-
tity of air circulated in an airway or mine, or the "circula-
tion," as it is called, is always estimated, in this country, in
cubic feet per minute.
How Quantity is Measured. — To measure the quantity, in
ventilation, it is necessary (1) to measure the sectional area
of the airway at the point of observation and (2) to care-
fully measure the average velocity of the air current at the
same point. From these measurements, the volume of air
passing or the circulation is calculated by means of the
formula,
Quantity = area X velocity
q — av
Example. — Calculate the circulation in an airway having a sectional
area of 50 sq. ft., the average velocity of the air current being 600 ft.
per min.
Solution. — Substituting the given values in the formula for quantity
in terms of velocity and area,
q = av = 50 X 600 = 30,000 CM. ft. per min.
Quantity of Air Required. — In determining the required cir-
culation of a mine, it is necessary to consider (1) the re-
quirements of the mining law of the state in which the mine
182 MINE GASES AND VENTILATION
is located and (2) the requirements of the mine as determined
by the natural conditions existing in the seam and the en-
folding strata.
Requirements of the Mining Law. — These vary somewhat
in different states. Owing to the numerous and changing
conditions, in mines, mining laws are of necessity arbitrary
standards, which must, however, be met, except in cases
where the law specially confers discretionary powers upon the
mine inspector or the mine foreman, thereby authorizing them
to decrease the circulation in any mine or section of the mine,
as conditions may require or their judgment dictate.
The mining law commonly specifies from 100 to 150 cu. ft.
per man, per min., for nongaseous, and 200 cu. ft. per min., for
gaseous mines. In addition, some of the laws require from
500 to 600 cu. ft. per min,, for each animal employed
underground.
Natural Requirements. — Gaseous mines naturally require
more air than nongaseous mines. The rise workings of seams
generating marsh gas or the dip workings of mines giving
off quantities of blackdamp are often difficult to ventilate and
require a circulation greater than what the law specifies, in
order to keep the workings free from gas and healthful and
safe for work. Slips and faults often give off much gas when
least expected and require, therefore, a larger circulation of
air than would otherwise be necessary in the same mine.
WORK OR " POWER ON THE AIR"
The terms "work" and "power" as used in mine ventila-
tion, are synonymous, because the work performed in moving
the air through the mine airways is based on a unit of time,
both the velocity and the quantity being rated per minute of
time.
Power on the Air. — The air current in an airway or mine
is moved by a pressure called the "ventilating pressure."
The ventilating pressure or the pressure producing the cir-
culation is the total pressure pa exerted on the entire sec-
tional area of the airway, as illustrated in Fig. 28. The small
THEOR Y OF V EN TIL A TIOK 1 83
arrowheads in the figure represent the unit pressure or the
pressure p on each square foot of cross-section. The large
arrow shown at A represents the total pressure P = pa.
It is a law of mechanics that when a force pa moves or is
exerted through a distance v the work performed is equal to
the product pav of the force and the distance. But in this
case, the force pa moves through the distance v in one
minute. The work (pav) is, therefore, performed in one
minute and is the " power on the air." The work performed
per minute or the power on the air is expressed in foot-pounds
FIG. 28.
per minute. Calling this work per minute or power on the air
u, the formula for power is
Power = unitpres. X area X vel.
u = pav
Again, since q = av, the formula for power on the air
may be written:
Power = quantity X unit pres.
u = qp
The formula for horsepower of the circulation is, there-
fore, since 1 hp. = 33,000 ft.-lb. per min.
qp
H
33,000
184 MINE GASES AND VENTILATION
The power formulas, in ventilation, make it possible to
calculate the power required to produce any given circula-
tion, against any given pressure or water gage when the
efficiency of the venilator is known or assumed.
EQUIVALENTS IN MEASUREMENT
Air Column and Water Gage. — Since water is practically
815 times as heavy as air at normal temperature and pres-
sure, 1 ft. of water column measures the same pressure as
815 ft. of ordinary air column; and 1 in. of water gage is there-
fore equal to 815 -f- 12 = say 68 ft. of air column, which
gives the following:
Rule. — -To reduce feet of air column to inches of water
gage, divide by 68.
To reduce inches of water gage to feet of air column, mul-
tiply by 68.
Air Column and Unit Ventilating Pressure.— Since air at
a normal temperature and pressure weighs, practically, 13
cu. ft. to the pound, every 13 ft. of air column represents, ap-
proximately, a ventilating pressure of 1 Ib. per sq. ft., which
gives the following:
Rule. — To reduce feet of air column to 'unit pressure, di-
vide by 13.
To reduce unit pressure (Ib. per sq. ft.) to feet of air col-
umn, multiply by 13.
Air Column and Barometric Pressure. — Since 1 cu. in. of
mercury weighs 0.491 Ib., each inch of mercury column indi-
cates a pressure of 0.491 Ib. per sq. in.; 0.491 X 144 = 70.7
Ib. per sq. ft.; and since each pound per square foot of pres-
sure corresponds to 13 ft. of air column, approximately, 1 in.
of barometer = 70.7 X 13 = say 920 ft. of air column, which
gives the following:
Rule (Approximate). — To reduce feet of air column to
inches of barometer, divide by 920.
To reduce barometric pressure (inches) to feet of air column,
multiply by 920.
Barometric and Unit Ventilating Pressure. — Barometric
pressure is always expressed in inches of mercury column.
THEORY OF VENTILATION
185
Unit ventilating pressure is expressed in pounds per square
foot, ounces per square inch, or inches of water gage.
Rule. — To reduce barometric pressure (inches) to ventilat-
ing pressure (Ib. per sq. ft.), multiply by 70.7; or to ventilat-
ing pressure (oz. per sq. in.), multiply by 0.491 X 16 = 7.856;
or to water gage (in.), multiply by 70.7 -f- 5.2 = 13.6, which
is the specific gravity of mercury referred to water as a
standard.
Since 13 ft. air column represents a pressure of 1 Ib. per
sq. ft., a pressure of 1 oz. per sq. in. corresponds to an air
column of (13 X 144) -s- 16 = 117 ft.
EQUIVALENTS IN PRESSURE
VOLUME OR QUANTITY or AIR IN CIRCULATION (cu rr PER HIM)
£ 60
$ so
£ 40
? M
5
f>
4*
--MO
r25.0"
= t
*"!
15.0 3
g
*.j
FIG. 29.
Air column (ft.)
Pressure (Ib. per sq. ft.)
Pressure (oz. per sq* in.)
Water gage (in.)
= 68
uo X water gage (in.);
13 X pressure (Ib. per sq. ft.);
117 X pressure (oz. per sq. in.) ;
920 X barometric pressure (in.);
5.2 X water gage (in.);
70.7. X barometric pressure (in.);
0.58 X water gage (in.);
7.86 X barometric pressure (in.);
13.6 X barometric pressure (in.).
Power- Volume -Pressure Diagram. — The diagram shown
in Fig. 29 is convenient as showing at a glance the power re-
186 MINE GASES AND VENTILATION
quired to circulate a given quantity of air against a certain
pressure, in pounds per square foot, ounces per square inch, cl-
inches of water gage. In order to find the power required to
pass any given volume of air against any given pressure or
water gage, follow the diagonal line corresponding to the given
water gage to its intersection with the vertical line corre-
sponding to the given volume and read this point of intersec-
tion on the power scale at the left of the diagram.
For example, it requires 50 hp. to pass 80,000 cu. ft. of air
per minute, under a 4-inch water gage or, reversing the order,
30 hp. will pass about 96,000 cu. ft. per minute under a 2-inch
gage. Since the power is proportional to the quantity and
pressure alike, in order to deal with higher values than those
given in the diagram, it is only necessary to treat these as
multiples of the values given in the diagram. Thus, 100 hp
would pass 160,000 cu. ft. under a 4-inch gage; or 320,000 cu.
ft. under a 2-inch gage. The horsepower in this diagram is
the power on the air, which is commonly, in fan practice, 60
per cent, of the horsepower of the engine or the indicated
horsepower.
EXAMPLES FOR PRACTICE
1. How many feet of air column is equivalent to a mine water gage
of three inches?
Solution. — Under ordinary or normal conditions water weighs 815
times as heavy as the same volume of air; hence,
1 ft. (12 in.) water column = 815 ft. air column
1 in. water gage = 815 -r- 12 = 68 ft. air column
3 in. water gage = 3 X 68 = 204 ft. air column
2. Express the pressure equivalent to 200 ft. of ordinary air column,
in pounds per square ft.; ounces per square inch; inches of barometer;
inches of water gage.
Solution. —
200 -=- 13 = 15.39 Ib. per sq. ft., nearly
200 -=-117= 1.71 02. per sq. in., nearly
200 -f- 920 = 0.22 in. of mercury, nearly
200 -5- 68 = 2.94 in. of water gage.
3. What is the pressure of the atmosphere, in pounds per square inch,
corresponding to a barometric pressure of 30 in.?
THEORY OF VENTILATION 187
Solution. —
30 X 7.86 = 235.8 oz. per sq. in.
235.8 -T- 16 = 14.74 Ib. per sq. in., nearly
4. Find the pressure in ounces per square inch corresponding to a
water gage of 2.5 in.
Solution. —
2.5 X 0.58 = 1.45 oz. per sq. in.
5. Find the barometric pressure in inches of mercury corresponding
to a water gage of 3.4 in.
Solution. —
3.4 + 13.6 = 0.25 in.
6. If an aneroid barometer gives a reading of 29.65 in. on the surface,
what should be the reading at the bottom of a downcast shaft 500 ft.
deep where the ventilating pressure caused by a blowing fan gives a
water gage of 2.85 in., assuming all readings are taken at about the same
time?
Solution. — The air column in this shaft will increase the barometric
pressure 500 -5- 920 = 0.54 in. The water gage due to the blower will
still further increase the barometric pressure, at the foot of the downcast
shaft, 2.85 -5- 13.6 = 0.21 in. The reading of the aneroid, therefore,
should be 29.65 + 0.54 + 0.21 = 30.4 in., approximately.
7. In a mine ventilated by an exhaust fan, giving a water gage of 2.33
in., if aneroid readings taken on the surface and at the bottom of the
upcast shaft show a difference of 0.77 in., what is the calculated depth of
the shaft?
Solution. — The action of the exhaust fan makes the aneroid reading
at the shaft bottom lower than it would be if the fan were not running,
and decreases the difference of the surface and underground readings
2.33 -T- 13.6 = 0.17 in. of mercury. The difference of reading due to
the depth of the shaft only is, therefore, 0.77 + 0.17 = 0.94 in. of
mercury. Reducing this barometric difference to air column gives for
the approximate depth of the shaft 920 X 0.94 = say 865 ft. under
ordinary conditions.
MINE AIRWAYS
Definition of Terms. — The term "airway," in mining, gen-
erally relates to a passageway for the circulation of the air
current, in distinction from a haulage road or travelingway,
although these entries may serve also as airways. The entry
by which the air current enters the mine is called the main
'•'intake," and that by which it is carried out, the main "re-
turn." In like manner, the two shaft or slope openings in
1 88 MINE GASES AND YEN TIL A TION
a mine are called, respectively, the "downcast" and the
"upcast."
The " perimeter "of an airway is the distance measured
around the circumference of its cross-section. The "area"
or " sectional area" of an airway is the area of its cross-
section.
The " rubbing surface" s of an airway is the entire inner
surface of the same; and is found by multiplying the perim-
eter o by the length /, of the airway; thus,
s = lo
Essential Features of Mine Airways. — Airways in mines
should be as straight as possible and avoid all sharp bends
and other obstructions that increase the resistance of the
airway to the flow of air. The shape of the airway is im-
portant as affecting the pressure required to pass a given
quantity of air.
Shape of Airways. — The cross-section of an airway may be
a circle, square, rectangle, ellipse, or any combination of these
that best meets the needs or conditions. For the purpose of
ventilation, that form of airway is best that has the shortest
length of perimeter, for the same area of section.
In this respect, the circular airway is first; the ellipsoidal
airway next, until the major axis exceeds 2.73 times the minor
axis when, for the same area, the perimeter is equal to that
of a square airway. The square airway is then third in the
series and the rectangular and trapezoidal forms last.
There are, however, other requirements than those of ven-
tilation. Haulage requires a level bottom for the roadway.
Roof conditions or economy of driving entries may put an
arched roof out of the question, making it necessary to adopt
the square, rectangular, or trapezoidal shape. Again, a weak
coal and heavy side pressure may demand an ellipsoidal shape
of section or a special type of timbering approaching the
same. It is not uncommon to arch the roof of airways for a
distance, using either a semicircle or a semiellipse to form
the arch, the latter being called a "flat arch."
THEORY OF VENTILATION 189
The closer the ellipse approaches the circle or the nearer a
rectangle comes to being a square, the less is the perimeter
of the airway, for the same area of section. For the same
length of airway, the perimeter is proportional to the rub-
bing surface of the airway.
Similar Airways. — Two airways are similar to each other
when their cross-sections are similar; the term "similar" has
no reference to the length of the airway.
The cross-sections of -airways are similar when their cor-
responding dimensions are proportional, each to each, and
their perimeters parallel throughout or can be so placed.
Illustration. — All circular or square airways are similar,
because they have but one dimension, the diameter of the
circle or the side of the square, and these dimensions are,
therefore, always proportional.
For example, one circular airway may have a diameter
twice or three times as great as that of another circular air-
way; or the side of a square airway may be two or three
times that of another square airway; and their perimeters
can always be placed so that their circumferences will be con-
centric or their sides parallel, each to each.
On the other hand, the rectangle, trapezoid and ellipse
each have two dimensions; and while one of these dimensions
may be two, three, etc., times as great as the corresponding
dimension of another airway of the same form, it does not
follow that the other dimensions of the two airways have the
same proportion; and unless they do the airways are not
similar. Thus, a 6 X 8-ft. airway and a 9 X 12-ft. airway are
similar, because their corresponding sides have the same
ratio, or are proportional and may be written
l = & or6:9::8:12
A 6 X 8-ft. airway and a 3 X 16-ft. airway, however, are not
similar airways, though they have equal sectional areas
6 X 8 = 48 sq. ft., and 3 X 16 = 48 sq. ft.); because the
second airway is twice as wide but only half as high as the
first.
190
MINE GASES AND VENTILATION
It is important to observe that in all similar airways, the
ratio of the sectional areas of the airways is equal to the square
of the ratio of the corresponding dimensions. For example,
in Figs. 30 and 31 showing two similar trapezoidal sections,
the top, bottom and sides of the larger airway are each twice
those of the smaller, and the area of the larger section is, there-
fore, 22 = 4 times that of the smaller.
Principle of Similar Airways. — Since corresponding dimen-
sions of similar airways have a fixed ratio, which is the same
, Perimeter- 2*5+6+12 '28 ft.
U-- ......... - ........... 24- ...................... ™
FIG. 31.
for each dimension (diameter, side, height or width) it is
possible to compare similar airways with respect to any of
these dimensions.
Application. — Assume, for example, the same pressure (p)
is applied to each of two similar circular airways, and it is
required to find how the quantity of air will vary in the two
airways. First write the formula for the quantity (q), in
terms of the pressure (p) and the dimensions, area (a), perim-
eter (o) and length (I) of the airway, and the coefficient of
friction (k)', thus,
T =
pa*
klo
Now, if the two airways have the same length, and are under
the same pressure, p, / and k are all constant and
vares as —
THEORY OF VENTILATION, 191
But, the area of a circle varies as the square of its diam-
eter (d2) and the perimeter varies as the diameter (d) ; hence,
a3 . d6
- vanes as -p or simply as d5
Hence,
q2 varies as d5
In the same manner, it can be shown in respect to all
similar airways of any form, that the square of the quantity
varies as the fifth power of any corresponding dimension (d),
whether diameter, side, height, or width.
Rule. — In comparing similar airways of equal length, for
the same unit pressure, the square of the quantity ratio is
equal to the fifth power of the dimension ratio; and, for the
same power on the air, the cube of the quantity ratio is equal
to the fifth power of the dimension ratio.
Example. — If 100,000 cu. ft. of air is passing per minute, in a 6 X 9-f t.
airway under a given pressure, what quantity of air will the same pres-
sure circulate in an airway 8 X 12 ft. of the same length? What quan-
tity will the same power circulate?
Solution. — These airways are similar because their corresponding
dimensions are proportional 6 : 8 : : 9 : 12. Therefore, calling the required
quantity x,
8V-/4V
~\3/
1024
243
4.214 = 2.0528
100,000
x = 100,000 X 2.0528 = 205,280 cu. ft. per min.
Assuming a constant power on the air:
x = 100,000 X 1.6152 = 161,520 cu. ft. per min.
Resistance of Airways. — ^The resistance that an airway
offers to the passage of air is of two kinds: frictional resist-
ance due to the rubbing of the air on the inner surface of
the airway, and the resistance due to the air striking against
obstructions such as timbers, roof falls, sharp bends, etc.
How Resistance Varies. — In mine ventilation, the entire re-
sistance of airways is estimated on a frictional basis, accord-
192 MINE GASES AND VENTILATION
ing to the extent of rubbing surface and the velocity of
the air. It is assumed that when the velocity of the air
current is doubled, each resisting particle in the airway is
struck twice as often and twice as hard, by the passing air,
which makes the resistance offered by each particle 2X2 = 4
times as great as before. If the velocity is increased three
times, the resistance of each particle is increased 3X3 = 9
times, etc. On this assumption, the resistance of an airway
varies as the extent of rubbing surface (s) and the square
of the velocity (v X v = v2), or as the expression sv* for
that airway.
Unit Resistance or Coefficient of Friction. — The amount of
resistance, per unit of rubbing surface (1 sq. ft.), for a unit
velocity (1 ft. per min.) is called the unit of resistance or
the coefficient of friction. The values most commonly
adopted for this unit are
k = 0.00000002 lb. (Atkinson, revised)
k = 0.00000001 lb. (Fairley)
Calculation of Resistance of Airways. — To find the resist-
ance of an airway for any given velocity, multiply the unit
resistance (k) by the rubbing surface in square feet (s), and
that product by the square of the velocity in feet per minute
(y2); the final product will be the total resistance (R), in
pounds, as expressed by the formula
R = ksv2
Example. — Find the resistance of an airway having 60,000 sq. ft.
of rubbing surface, when the velocity of the air current is 800 ft. per
min.
Solution. — The resistance, in this case, is
R = 0.00000002 X 60,000 X 8002 = 768 lb.
SYMBOLS AND FORMULAS
Most of the rules of mine ventilation are expressed by
means of formulas, which show at a glance the relation of
the several factors to each other, and make possible many
transformations and developments.
Symbols. — As far as practicable, the same symbols are used
throughout to designate the same factors; and these are, for
THEORY OF VENTILATION 193
the most part, those symbols commonly employed in ventila-
tion, as being the initial letter of the word for which they
stand. For example, p = pressure; v = velocity; # = quan-
tity, etc. The following table gives the more important sym-
bols used :
TABLE OF COMMON SYMBOLS, MINE VENTILATION
A = area of regulator, sq. ft.
a = area of airway, sq. ft.
B = height of barometer, in.
C = Centigrade reading, deg.
c — constanl,
D = depth of shaft, ft.
d = diam. or side of airway, ft.
F = Fahrenheit reading, deg.
g = gravity, ft. per sec.
H = horsepower, 33,000 ft.-lb. per min.
h = height of air column, ft.
K = Efficiency of fan, per cent.
k = coefficient of friction, 0.00000002
I = length of airway, ft.
n = number of revolutions, r.p.m.
o — perimeter of airway, ft.
P = total pressure, lb.
p — unit pressure, lb. per sq. ft.
Q = total circulation of air, cu. ft. per min.
q = single current, cu. ft. per min.
R = resistance of mine or airway, lb.
r = any ratio,
s = rubbing surface of airway, sq. ft.
T = absolute or higher temperature, deg.
t = actual or lower temperature, deg.
U = total power on air, , ft.-lb. per min.
u = power, single current, ft.-lb. per min.
v = velocity of air, ft. per sec. , or ft. per min.
V = volume of air or gas, cu. ft.
W = total weight of body, lb.
w = unit weight, lb. per cu. ft.
X = potential of mine or airway,
Xp = pressure potential,
Xu = power potential
x — the unknown quantity whose value is sought
w.g. — water gage reading, in.
Sp. gr. = specific gravity,
13
1 94 MINE GASES A ND YEN TIL A TION
Small subscript letters and figures are frequently written
immediately after any symbol to show its reference to a
particular kind or thing. For example, qi, q%, q3, etc., indi-
cate the quantities of air passing in three or more airways;
<?«> % Qc, etc., indicate the quantities passing in Splits A,
B, C, etc. In like manner, the potential values of different
airways and splits are indicated by Xi, Xz, X 3, etc.; or Xa, Xb,
Xc, etc., as the case may be.
In some cases, two or more subscript letters or figures are
used after a single symbol to indicate its reference; as for
example, the pressure potential for Split A is written Xpa
or the power potential Xua- The general potential, in a split
circulation, is written XQ; or Xp0 and XUQ to indicate the
general pressure and power potentials, respectively.
It is often necessary to indicate the summation of a num-
ber of items of the same kind, for which purpose the charac-
ter £ is written before the symbol indicating the kind. For
example, ^Xabc indicates the sum of the potential values for
the splits A, B and C, instead of writing Xa + Xb + Xc.
In a complex circulation, consisting of a main airway and
two or more splits, it is often necessary to indicate the gen-
eral split potentials by X0, Xao, Xbo, etc., and the mine potential
by X. (See Fig. 33, p. 236.)
Use of Formulas. — A comparatively few formulas form
the basis from which practically all the other formulas of
mine ventilation are derived. These few basal formulas
also show the true relation, one to the other, of the principal
factors of ventilation, such as pressure, velocity, quantity,
power, rubbing surface and the sectional area of mine airways.
The understanding of these formulas makes it unnecessary
to learn and remember a large number of rules of ventilation.
A formula is written as an algebraic equation in which each
factor is expressed by its proper symbol. The equation shows
the equality of certain factors grouped in the form of an
expression. For example, the formula
pa= ksv2
shows the equality of the total ventilating pressure pa and
THEORY OF VENTILATION 195
the resistance of the airway when the rubbing surface is s
and the velocity of the air current v.
How Factors Vary. — It is evident, from the inspection of
a formula, that :
1. Any factor in one member of the equation varies directly
as any like factor in the other member, provided the other
factors remain constant and none of the quantities expressed
in the formula are connected by the signs plus (+) or minus
(-)-
2. Any factor in either member varies inversely as any
like factor in the same member, with the provisions just stated
(1) above.
For example, the formula previously given shows that :
The total ventilating pressure (pa) for airways varies as
the resistance (ksv2) of the airway.
For any given airway, a, s and k being constant, the unit
pressure (p) varies directly as the square of the velocity (v2)
of the air current.
For the same total pressure (pa) , in an airway, k being
constant, the square of the velocity (v2) varies inversely as
the rubbing surface (s). Or, in other words, the velocity (v)
of the air current varies inversely as the square root of the
rubbing surface (\/s ) .
For the same velocity (v) of air and the same rubbing sur-
face (s) in an airway, k being constant, the unit pressure (p)
always varies inversely as the sectional area (a) of the airway.
3. Again, transposing the formula for total pressure, the
formula for unit pressure producing a given velocity in a
given airway or mine is
_ ksv2
An inspection of this formula shows that:
The other factors remaining constant and none of the
quantities being connected by the signs plus (+) or minus
( — ), any factor in the denominator of a fractional term form-
ing either member of the equation varies directly as any
factor in the numerator of that fraction; and likewise as any
similarly placed factor in the other member.
196 MINE GASES AND VENTILATION
Basal Formulas. — There are, in fact, but two truly basal
formulas, in mine ventilation; the one expressing the resist-
ance that an airway offers to the passage of an air current
having a certain velocity; the o'her expressing the power on
the air producing a certain velocity in an airway, against a
certain resistance. These formulas are as follows:
Resistance of airway, R = pa = ksv2
Power on the air, u = pav = ksv3
From these two simple formulas as a basis, with the aid
of a few other recognized formulas and principles for deter-
mining the quantity, horsepower, water gage, rubbing sur-
face, etc., all ventilation formulas are derived.
MINE POTENTIAL METHODS
An Important Principle. — One of the most important prin-
ciples of mine ventilation may be stated briefly as follows:
Every airway or mine possesses a certain definite resisting
power, which is determined by the ratio of its area of passage
to rubbing surface. For this reason, a given power will pro-
duce a certain velocity and develop a certain resistance, in a
given airway; the velocity of the air current varying in-
versely as the resistance. Ventilating pressure is caused by
and equal to the resistance developed. Power, then, creates
velocity, which in the airway develops resistance; and the
resistance produces pressure.
The conclusion is, therefore, evident that it is the resisting
power of a mine or airway that determines the velocity and
pressure a given power will produce in that airway. The
airway, it is clear only possesses this resisting power po-
tentially, its development requiring the passage, of an air
current. Hence, . it is proper to term such resisting power,
expressed in terms of the airway, the "potential of the airway"
or the "mine potential," in respect to a mine.
As has been explained, the equivalent of the mine potential,
expressed in terms of the power, quantity or pressure, is
properly called the "potential of the circulation."
THEORY OF VENTILATION 197
Illustration of Formulas. — To illustrate the use of formulas
in mine ventilation, and to make clear their application, the
following table is given, in which most of the formulas in
common use are classified under their proper heads. Many
of these formulas, as will be observed, are simple transposi-
tions of another formula or obtained by substitution. The
calculations, in the table, all refer to an airway 5 X 10 ft. in
cross-section and 4000 ft. long, passing an air current of, say
25,000 cu. ft. per min. against a pressure of 12 Ib. per sq. ft.
The Airway.—
Perimeter, o = 2(5 + 10) = 30 ft.
Length, I = 4000 ft.
Rubbing surface, (* = lo) s = 4000 X 30 = 120,000 sq. ft.
'Sectional area, o = 5 X 10 — 50 sq. ft.
Power potential of airway or mine,
a 50
Xu =: \/ks Xu =~~ ~ = 373'45
The Air Current.—
q 25,000 _„„ ,,
Velocity, v = - v = — ^— = 500 ft. per mm.
a
- fe? ., _ . / 12 X 50
).00000002 X 120,000
= 500 ft. per min.
300,000
).00000002 X 120,000
= 500 ft. per min.
300,000 K/m ft
V = 10 xx RA = 500/^ PCr mm'
Power potential of the circulation,
q 25,000
u= ^= =
The square of the pressure potential can always be used
instead of the cube of the power potential since these are
equal, as expressed by the formula
198 MINE GASES AND VENTILATION
Thus, Xp = Xu \/X~u = 373.45 \/373.45 = 7217, nearly
Pressure potential,
Xn =
q 25,000
Xp=Vp Xp= = 7217' nearly
Quantity, q = av q = 50 X 500 = 25,000 cu. ft. per mm-
12 X 50
).00000002 X 120,000
= 25,000 cu. ft. per win.
300,000"
).00000002 X 120,000
= 25,000 cu. ft. per min.
u 300,000
q = - q = — ~y = 25,000 cu, ft. per mm.
q = Xu\/u q = 373.45 \/300,000
= 25,000 cu.ft. per min.
q = Xp\/p q = 7217A/12 =25,000 cu.ft. per min
ksv2 0.00000002 X 120,000 X 5002
Pressure, p = — p = 5Q
= 12 lb. per sq. ft.
_ ksq2 _ 0.00000002 X 120,000 X 25,0002
p ~: T3~ p = 503
= 12 lb. per sq. ft.
u 300,000
p = 5.2 w.g. p = 5.2 X 2.307 = 12 lb. per sq.ft.
Resistance, R = pa R = 12 X 50 = 600 lb.
R = ksv2 R = 0.00000002 X 120,000 X 5002
= 600 lb.
»
500
THEORY OF VENTILATION 199
p 12
Water gage, w.g. = ^ w.g. = ^ = 2.307 + in.
Power on air, u = kw* u = 0.00000002 X 120,000 X 500*
= 300,000 ft.-lb. permin.
ksq* 0.00000002 X 120,000 X 25,000*
u = — f- u = - — r^ --
a3 503
= 300,000 ft.-lb. permin.
u = qp u= 25,000 X 12
= 300,000 ft.-lb. permin.
permin.
u = pav u = 12 X 50 X 500
= 300,000 ft.-lb. permin.
u 300,000
Horsepower, H = u = -- 9.09 hp.
MEASUREMENT OF AIR CURRENTS
The measurement of air currents, in mining practice, in-
volves the careful observation of the velocity and pressure
of the current and the accurate measurement of the sectional
area of the airway. From these data the volume and power
of the air current are determined.
Requirements. — The mining laws of the state, in most
cases, require a specified volume of air per man, per minute,
circulated throughout the mine. In order to meet this re-
quirement, it is necessary to estimate the power that will
produce such quantity in a given mine.
The Mine Potential. — Every airway and every mine has a
certain resisting power, in respect to the circulation of air.
For this reason, the same power will circulate different quan-
tities of air through airways that differ in respect to either
their size or length.
The formulas of mine ventilation show the following rela-
tion of the quantity of air circulated to the power producing
200 MINE GASES AND VENTILATION
the circulation, and the sectional area to the rubbing surface
of the airway.
Quantity sectional area
3/75-= '- varies as 3/ . . . ~ =j=
V Power v rubbing surface
Or, say: quantity (cu. ft. per min.) = q; power (ft. Ib. per
min.) = u] sectional area (sq. ft.) = a; and rubbing surface
(sq. ft.) = s; the unit resistance being k, we have
\/u \/ks
The first of these expressions, being given in terms of the
power and quantity of air circulated, may be called, prop-
erly, the " potential of the circulation;" while the second ex-
pression, being given in terms of the airway, is the " potential
of the airway," or the "mine potential." The significance of
the term "potential," in this connection, is apparent since it
describes the capacity of an airway or mine in respect to the
volume of air it will pass, per unit of power.
Values of the Potential. — Calling the potential factor X, its
value for any given mine or airway is calculated by the
formula
X =
The value of the potential for the circulation of any quan-
tity (q), by any power (u) or pressure (p), is found by the formula
A - ~3/=
\/u
The value of the potential lies in the fact that it gives
to every mine, or air split, a definite value that enables a
correct comparison to be made between them, and the
proper type of ventilator and system of ventilation to be
chosen.
Potential of Airway. — Calculate the potential of an airway
6 X 10 ft., in cross-section, and 2000 ft. long.
THEORY OF VENTILATION 201
Solution — The sectional area of this airway is 6 X 10 = *
60 sq. ft.; the rubbing surface is 2(6 + 10)2000 = 64,000 sq.
ft. The potential of the airway is, therefore,
v a 60
X = , ...__ = ,. = ooz.o
\/ks -\/ 0.00000002 X 64,000
Potential of Circulation. — What is the value of the poten-
tial factor in the circulation of 60,000 cu. ft. of air, by 10 hp.?
Solution. — The potential of this circulation is
a 60,000
X = 17= = -I/TTf^ ^^ = 868'2
•\u v 10 X 33,000
Find the potential value for the same volume of air when
circulated under a pressure of 8 Ib. per sq. ft.
Solution. — The potential value, in this case, is
Y .,* 3/60,0002
X"-^p--\^- = 766'3
Power, Pressure, Quantity. — By transposing the formulas
for potential, it is possible to calculate the power or pres-
sure required to circulate any given quantity of air against
any given mine potential; or to find the air volume a given
power or pressure will produce, for any given mine potential.
Example. — Find the (1) power, and (2) pressure required to circulate
24,000 cu. ft. of air through an airway 5 X 14 ft. in section and 3000
ft. long?
Solution. — The area and rubbing surface of the airway are: a =
5 X 14 = 70 sq. ft.; and * = 2(5 + 14)3000 = 114,000 sq. ft. The
potential factor of this airway is then
a_ 70 _
~ ^ks ~ -^0.00000002 X 114,000 ~
(1) Power, u = (-??) = ( K' 0 } = 91,900 ft.-lb. per min.
\A/ \5dl.8 /
(2) Pressure, p = J^ = r' = 3.83 Ib. per sq. ft.
p=JL = 9^900 =383J6 per
q 24,UUU
Example. — Find the volume of air circulated in the same mine, by
(1) 10 hp.; (2) a pressure of 7.8 Ib. per sq. ft.
202
MINE GASES AND VENTILATION
Solution. —
(1) By 10 hp.,
q = X v^T = 531.8 <y 10 X 33,000 = 36,750 cu. ft. per min.
(2) By 7.8 lb.,
q = X VlXp = 531.8 V 531.8 X 7.8 = 34,250 cu. ft. per min.
Potential Values of Different Airways. — In order to show
the resisting power of airways of different lengths, for those
sizes in more common use, the following table has been pre-
pared, showing the potential value of each airway, as calcu-
lated by the formula
Potential of airway, X =
Following this is another table giving the potential values
of different circulations, by which is meant the circulation of
different volumes of air under different pressures or water
gages. A comparison of the potential values in these two
tables will serve to show what circulation can be obtained in
airways of given size and length when properly arranged and
unobstructed.
TABLE. — POTENTIAL VALUES FOR DIFFERENT AIRWAYS
Length of Airway, Including Return (ft.)
Size of airway,
feet
1,000 2,000 3,000
5,000
8,000 | 10,000
Potential value of airway
4 X 10
485 . 3
385.0
336.5
283.8
242.6
225.2
4 X 12
557.0
441.9
386.2
325.7
278.5
258.5
4 X 14
624.8
495.7
433.2
365.4
312.4
290.0
5X8
497.4
394.6
344.9
290.9
248.7
230.9
5 X 10
592.8
470.3
411.0
346.7
296.4
275.2
6X8
582.3
462.0
403.8
340.6
291.2
270.3
6 X 10
696.2
552.4
482.7
407.2
348.1
323.2
7X8
664.0
526.7
460.4
388.3
332.0
308.2
7 X 10
796.0
631.5
552.0
465.5
398.0
369.5
8 X 10
892.6
708.1
618.9
522.0
446.3
414.3
Potential Values of Different Circulations. — The circulation
of a given quantity of air in a certain airway or mine requires
THEORY OF VENTILATION
203
a certain pressure or water gage, which determines the " poten-
tial of the circulation."
In the following table, the potential of the circulation is
calculated by the formula
3 Q2 3 I Q2
ion, X = \ — = Al- 0
\ p \5.2w.g.
Potential of circulation,
TABLE. — POTENTIAL VALUES FOR DIFFERENT CIRCULATIONS
Water
Siage
(in.)
Pressure
(lb. per
sq. ft.)
Volume of air circulated (cu. ft. per min.)
10,000
15,000 | 25,000
50,000
75,000
100,000
Potential value of circulation
0
31.2
147.4
193 . 2
271.6
431.1
564.9
684.4
5
26.0
156.7
205.3
288.6
458.1
600.3
727.2
4
20.8
168.8
221.2
310.9
493.5
646.7
783.4
3
15.6
185.8
243.4
342.2
543.2
711.8
862.2
2K
13.0
197.4
258.7
363.6
577.2
756.3
916.3
2
10.4
212.6
278.6
391.7
621.8
814.8
987.0
1M
7.8
234.0
306.7
431.1
684.3
896.8
1,086.4
1
5.2
267.9
351.1
493.5
783.4
1,026.5
1,243.6
X
2.6
337.6
442.3
621.8
987.0
1,293.4
1,566.8
Comparing this table with that on the preceding page
shows that to pass a current of 25,000 cu. ft. per min. through
an airway of 5 X 8 ft., 3000 ft. long, including the return will
require, practically, a 3-in. water gage. This is ascertained
by observing that the potential value of an airway 5 X 8 ft.,
3000 ft. long, as given in the first table, is, say 345. Then
find the water gage corresponding as nearly as possible to
this value, in the second table, in the vertical column for
25,000 cu. ft. per min. The potential of the circulation of this
air volume under a 3-in. gage is, say 342, showing that a
3-in. gage is a little in excess of what is required to circulate
25,000 cu. ft. of air per minute in a 5 X 8-ft. airway, 3000 ft.
long, including the return.
Effect of Splitting on Mine Potential. — As a mine is devel-
oped and its airways extended, it becomes impracticable to
carry the air in a single current throughout the entire length
of the airways, as the water gage then increases directly as
204 MINE GASES AND VENTILATION
the length or distance of air travel. To avoid this difficulty,
the air must be divided or " split" one or more times; so that
there will be two or more separate currents in the mine.
Each of these currents is called a " split of air," or simply
a "split" (see p. 219).
It should be observed that dividing the current does not
change the total rubbing surface (s) in the mine; but the
area of passage is increased in proportion to the number of
splits or currents. Calling the number of equal splits n, the
area of passage (p. 211), in splitting an air current is na,
and the formula for the potential can be written:
Split potential, X = ~TT=
V ks
Since the rubbing surface (s), the sectional area (a) and
the coefficient (k) are constant, the potential (X ) varies as n,
or as the number of equal splits or currents. Therefore, any
of the airway potentials of the first table can be multiplied 2,
3, 4, etc. tunes according to the number of splits or currents
employed.
For illustration, suppose the airways of a mine are 5 X 10
ft. and have a total length, including return, say 10,000 ft.;
and the required circulation is 100,000 cu. ft. per min. The
velocity of the ah- should not exceed, say 500 ft. per min.,
in the airways. This will require a total area of passage" of
100,000 -^ 500= 200 sq. ft. But the sectional area of these
airways is 5 X 10 = 50 sq. ft.; and there must, therefore, be
200 -s- 50 = 4 splits or currents to comply with the conditions
named. The potential value, as given in the table, for a single
current, is, say 275; and the mine potential for four splits is,
therefore, 4 X 275 = 1100. By referring, now, to the second
table giving the values of the potential of circulation, it is
found that a potential value of 1100, in the circulation of
100,000 cu. ft. per min. shows a water gage between 1 and 1J^
in. The true value may be found by interpolation, if desired,
and is 1.46 in.
The potential value of any desired circulation of air, as
compared with the potential value or "potential factor" of the
THEORY OF VENTILATION 205
proposed mine or airway is thus seen to have an important
practical value that commends it to all students of mining.
Example. — It is proposed to open a mine in a 6-ft. seam of coal and
provide for a capacity of 1000 tons a day* A general estimate is de-
sired of the requirements for the proper ventilation of the mine, under
working conditions. In other words, what volume of air will be re-
quired and what will be the approximate water gage and horsepower
necessary for the circulation of such quantity in this mine ?
Solution. — Assuming an average daily output of 2.5 tons of coal per
miner, the number of miners working will be 1000 -J- 2.5 = 400. Then
allowing for, say 150 loaders and 50 company men including bosses, the
total number of men in the mine will be 600, for whom the quantity of
air specified by law must be provided.
Assume that the mine generates considerable gas and to cover all
requirements, estimate on supplying 200 cu. ft. of air per man, per
minute, which gives a total required air volume of 200 X 600 = 120,000
cu ft. per min.
In order to estimate approximately what water gage will result in the
circulation of this quantity of air, it is necessary to decide on the size of
the entries; and make the sectional area such as will allow of a safe maxi-
mum velocity of the air current in the cross-headings and find the number
of splits required to meet these conditions.
In this case, suppose all entries to be 6 X 10 ft., giving a sectional
area of 60 sq. ft.; and the mine being gassy, say the velocity of the air
current on all cross-headings or splits must not exceed 360 ft. per min.
This condition will require a total area of passage or the sum of the
sectional areas of all the splits, 120,000 -;- 360 = 333 sq. ft. But the
area of the entries being each 60 sq. ft., the number of splits required to
give this area of passage and thus keep the velocity of the air currents
in the splits within the specified limit is 333 -f- 60 = 5.5, say 6 splits or
pairs of cross-headings.
The next step is to decide on the distance each pair of cross-headings
will be driven, from which the extent of rubbing surface can be approxi-
mately estimated. For example, assume the cross-headings to be driven,
say 2000 ft. on each side of the main heading, making 4000 ft. of entry,
including the return, in each split. The total length of entry for the six
splits is then 6 X 4000 = 24,000 ft. Assume the main headings are
driven four abreast, so as to provide two intake haulage roads affording
separate tracks for the empty and loaded trips; and two return airways.
If the cross-entries are turned to the right and left of the main
headings, every 500 ft., the length of these headings may be taken as
3 X 500 = 1500 ft., giving a total length for the four headings 4 X
1500 = say 6000 ft. The total length of all entries in the mine may
thus be assumed as 24,000 + 6000 = 30,000 ft.
206 MINE CASES AND VENTILATION
The estimated rubbing surface is then s = 2(6 + 10) X 30,000 =
900,000 sq. ft.; and the mine potential is
6a _6X60
-A — ,, — - — \ . — — 1 044
\/ks ^0.00000002 X 960,000
This is only an approximately correct value for this mine, because
the six splits do not start from the shaft bottom.
The water gage required is then calculated from the mine
potential and the air volume; thus,
Q2 120,0002
=
5.2 X 13443
It will be safe to assume, from the above calculation, that
the proposed mine can be properly ventilated by the circula-
tion of 120,000 cu. ft. of air per minute under a water gage of
say 1.5 in., providing for six main air splits as described, and
making due allowance for possible conditions.
The horsepower required to produce this circulation, assum-
ing a general efficiency of K = 60 per cent, is
„ 0(5.2 w.0.) 120,000 (5.2 X 1.5)
0.60 X 33,000
=47+, say 50^.
Example. — Find the unit pressure, water gage and horsepower re-
quired to circulate 80,000 cu. ft. of air per minute in a mine in two equal
splits. The airways are all 8 X 10 ft., and have a total length of 12,000
ft., including the return airways.
Solution. — The sectional area of the airways, in this case, is a = 8 X
10 = 80 sq. ft.; the perimeter is o = 2(8 + 10) = 36 ft. The potential
of the airway for two splits is then
na 2 X 80 = ?8()
\/klo -^0.00000002 X 12,000 X 36
The unit pressure is
Q* 80,000*
P = -£, =: 78Q3 = say 13.5 Ib. per sq. ft.
The corresponding water gage is 13.5 -s- 5.2 = say 2.6 in.
The horsepower on the air, as calculated from the above unit pressure,
Qp 80,000X13.5
B = 3^000 = 33,000"
THEORY OF VENTILATION 207
Or, the horsepower may be found directly from the mine potential,
as follows:
„
~
33,000
/#\3 __ i /8o,ooo\»
\X] ~ 33,000 V 780 )
Example. — Find the quantity of air in circulation in four equal splits
in a mine, when the size of the airways is 5 X 14 ft. and the total length
of airways in all the splits, including the returns in each case, is 40,000
ft. ; the water gage at the shaft bottom where the air is divided being 3 in.
Solution. — The rubbing surface, in this case, is s = 40,000 X 2(5 +
14) = 1,520,000 sq. ft., and the sectional area of each airway 5 X 14 =
70 sq. ft. The mine potential for four splits is then
X = — J^^= = 897
\/ks \/6. 00000002 X 1,520,000
The quantity of air in circulation under a 3-in. water gage is then
w.flO
=F 897 \/897 -T- 5.2 X 3 = say 106,000 cu. ft. per min.
Caution, — In the calculation of all problems in mine ven-
tilation, regard must be had to the conditions with respect
to the power and the pressure producing or resulting from
the circulation of the air in the mine.
Both the power and the pressure are commonly said to
produce the circulation; but, as a matter of fact, it is the
power that produces the circulation, while the pressure is
the result and measured by the resistance of the mine or
airway.
Unfortunately, these factors do not vary alike, but the
cube root of the power varies as the square root of the pres-
sure; or, more simply, the cube root of the power ratio, in any
mine or airway, is equal to the square root of the pressure
ratio, for the same circulation; thus,
El
p*
For example, in what proportion must the power be in-
creased in order to double the pressure (py/pi = 2)?
\/ 'power ratio = \/2 = 1.414
power ratio = 1.4143 = 2.828
208 MINE GASES AND VENTILATION
In other words, if 10 hp. on the air produces a given pres-
sure or water gage in a certain mine or airway, it will re-
quire 2.828 X 10 = 28.28 hp. to double that pressure or gage.
Use of Potential Factors. — Attention has been drawn to the
potentiality of an airway or mine, in respect to the resistance
it can offer to the passage of air, by virtue of its rubbing sur-
face (s) and its sectional area (a). The potential of an
airway or mine is the factor that determines the quantity of
air such airway or mine will pass, for any given power or
pressure. It is important, in the use of the potential, there-
fore, to consider whether the pressure or power is in question.
F.or every airway or mine, therefore, there is a power po-
tential (Xu) and a pressure potential (Xp). The cube of the
power potential is equal to the square of the pressure poten-
tial, for the same mine or airway, giving the equal values.
'x 3 - x ^ - t - £! - **_
u p- klo
An inspection of these equal values shows that :
1. The quantity of air a given power will circulate varies
as the power potential of the airway or mine.
2. The quantity of air a given pressure will circulate varies
as the pressure potential of the airway or mine.
Hence, in comparing the circulations in different airways
or mines, a constant power requires the use of the power po-
tential, and a constant pressure, the pressure potential.
Other Potential Formulas. — Transposing the values given
above makes it possible to calculate the power or pressure
required to circulate a given quantity of air in a certain air-
way or mine directly from its potential factor.
~ I Y ) : V 2
\-A u/ • -A p
It is, likewise, possible to calculate the quantity of air a
given power or pressure will circulate against any given po-
tential factor representing a certain airway or mine, by
simply multiplying the cube root of the power or the square
THEORY OF VENTILATION 209
root of the pressure by the corresponding potential of the air-
way or mine as expressed by the following formulas :
q = Xu\/u
q = Xp\/p
A few examples will serve to make the use of these for-
mulas clear and to show their practical application, in the
rapid estimation of what is required in the proposed develop-
ment of mines, in order to make suitable provision for their
proper ventilation.
EXAMPLES FOR PRACTICE
1. If 25 hp. produces a water gage of 1.5 in., in a certain mine, what
water gage will 40 hp. produce in the same mine?
Solution. — Since the square root of the pressure or water-gage ratio
is equal to the cube root of the power ratio, calling the required water
gage x,
= 1.172 = 1.37, nearly
l.o
x = 1.5 X 1.37 = 2.05 in.
2. It is proposed to provide for the circulation of 75,000 cu. ft. of air,
in two generally equal splits, the airways including the return in each
split being 6 X 10 ft. in section and about 8000 ft. long, (a) Find the
power potential for the entire mine ; and (6) calculate from that both the
power and the water gage of the circulation.
Solution. — (a) The sectional area of the airways, in this case, is a =
6 X 10 = 60 sq. ft.; the total rubbing surface in the mine, s = 2 X
2(6 + 10)8000 = 512,000 sq. ft. Substituting these values and that for
the coefficient of resistance fc = 0.00000002 in the formula for power
potential of mine,
v na 2 X 60 __OA
Xu = ,, = • . , = 552.6
\/ks y/0.00000002 X 512,000
The power on the air required to circulate 75,000 cu. ft. of air against
this potential is, then,
3= 2,500,000 ft.-lb. permin.
The water gage, as calculated directly from the power potential,
v = 552.6, is
q* 75,0002 aA1 .
W'g' = 5^X7 =5.2 X 552.63 = 6.41 in.
Or, the water gage may be found thus
w.g. = 2,500,000 4- (5.2 X 75,000) = 6.41 in.
14
210 MINE GASES AND VENTILATION
3. (a) Calculate the value of the pressure potential for the entire
mine mentioned in the preceding question, the airways being 6X10 ft.
in section and about 16,000 ft. long, including the return, assuming as
before two equal splits; and (6) calculate from this pressure potential the
power that will produce the desired circulation of air; namely 75,000 cu.
ft. per min. and the resulting water gage.
Solution. — (a) The total rubbing surface is s = 2(6 + 10) 16,000 =
512,000 sq. ft. For two equal splits, the area of passage in this mine is a
= 2(6 X 10) = 120 sq. ft. The mine pressure potential is then
X, - « V£ - 12° Vo.
2°
o.00000002X 512,000
(b) The power on the air, calculated from the pressure potential, is then,
u = -vT = = say 2,500,000 ft.-lb: per min.
The water gage, calculated in the same manner, is
2 2
4. What volume of air will 10 hp. circulate in an airway 6X8 ft., in
section, and 2500 ft. long?
. Solution. — The sectional area of this airway is a = 6 X 8 = 48 sq. ft. ;
the rubbing surface 2(6 -f 8) 2500 = 70,000sq. ft. The power potential
is therefore
a = 429.1, nearly.
-0.00000002 X 70,000
For 10 hp. on the air, the quantity of air in circulation in this airway is
q = Xu\/^ = 429.1-^10 X 33.000 = say 30,000 cu. /«,. per min.
5. (a) What quantity of air will be circulated, in the airway, in the last-
example, under a 3-in. water gage; and what power on the air will be
necessary to develop this quantity and gage? (6) What was the original
water gage when 10 hp. circulated 30,000 cu. ft. of air, in this mine?
Solution. — (a) Since the square of the pressure potential is equal to the
cube of the power potential
Xp = V~X*U = A/429. 13 = 8890, nearly
Then, q = Xp V7> = 8890 A/5.2 X 3 = say 35,000 cu. ft. per min.
The power required to produce a 3-in. water gage is
35,000 X 3 X 5.2
THEORY OF VENTILATION 211
(Jo) The previous water gage due to the circulation of 30,000 cu. ft.,
in this mine, under 10 hp. can be calculated in several ways; but most
simply, thus,
= 10 X 33,000 .
W'9' ~ 5.2 X 30,000
The calculation may also be made from the potential ; thus,
g2 30, OOP2
W'Q'~ 5.2X\ ~ 5.2 X429.P
Area of Passage. — It is important to notice that the poten-
tial value for any mine is determined by its area of passage
with respect to the resisting power of its rubbing surface.
For a single air current the area of passage is the sectional
area (a) of the airway. For 2, 3, etc., equal splits the area
of passage is 2a, 3a, etc.; for n equal splits the area of pas-
sage, for the mine, is na.
The unit of resistance being k, the resisting power of the
entire airway or mine is indicated by ks; and the potential
values of the mine with respect to power and pressure, respec-
tively, are thus expressed
Mine power potential, Xu —
Mine pressure potential, Xp = \/ j~~ = n<l \l
na
ks
It should be observed that the mine power potential varies
as the number of equal splits or currents, which is not true of
the pressure potential of a mine. This fact has an important
application, since, for the same mine, the rubbing surface
being constant, the number of splits (n) is equal to the power-
potential ratio. An example will serve to make this clear.
Example. — Suppose it is desired to ascertain quickly how many equal
splits would pass the same quantity of air (75,000 cu. ft. per min.), under
a 2-in. water gage, in Example 3, previously given where two splits of
air gave a water gage of 6.41 in., the power remaining constant.
Solution. — From the equat'ons expressing the potential values pre-
viously given (p. 208), it appears, for the same quantity of air in circula-
tion, the pressure or water gage varies inversely as the cube of the power
potential. But, since the power potential varies as the number of
splits in a mine, it follows that, for the same quantity of air in circula-
212 MINE GASES AND VENTILATION
tion, the power remaining constant, the pressure or water gage varies
inversely as the cube of the number of splits.
In other words, for the same quantity of air, and constant power,
the pressure or water-gage ratio is equal to the cube of the inverse
ratio of the number of splits. In this case, calling the required number
of splits n, the split ratio is n/2, and the corresponding water-gage ratio
2/6.41, and we write
3.205
2/ 2
n = 2v/3.205 = 2.95, say 3 splits.
The reference, thus far, has been to equal division of the
air current and the rules and formulas given above apply
strictly, only to mines in which the air current is divided at or
near the main entrance and passes through the mine in two
or more separate and equal splits.
Part Potential Value. — The part potential value is found
by omitting k in the calculation, and writing it outside the
parenthesis. The relative potential obtained by canceling
common factors cannot be used here. The relative potential,
so much used in the calculation of the splitting of air cur-
rents, can only be employed when the potential appears as a
ratio (see p. 221.)
General Potential of a Mine. — An important application of
the potential method, in mine ventilation, is the calculation
of the potential value for the entire mine when the airways
and shafts are of various dimensions.
Example. — Calculate the general mine power potential in the following
mine, shafts 1250ft. deep:
Area Rub. Sur.
Shafts, upcast and downcast, 8 X 10 ft., 2500 ft. 80 90,000
Main airway ("A" seam), 6 X 10 ft., 3750 ft. 60 120,000
Cross-headings (" A" seam), 6X 8 ft., 2500 ft. 48 70,000
Tunnel to "B" seam, 5X8 ft., 500 ft. 40 13,000
Return air course ("B" seam), 5 X 14 ft., 5500 ft. 70 209,000
Solution. — The total power producing a given circulation, is clearly
equal to the sum of the powers absorbed in the several sections of the
mine, as expressed by the following general formula:
kO3
H =
I 1 1 1 \
\YT3 + xT3 + !x73+ etcv
#33,000
It will be readily observed that this general formula, for a mine of
THEORY OF VENTILATION 213
various sections (K being the coefficient of efficiency of the ventilator),
is derived from the power formula
Q3 1
~ #33,000 \ Xj #33,000 Xu3
But, since l/Xuz = k s/a3 and k being constant, it is much simpler in
using the above general formula, to factor and write k outside of the
parenthesis, which makes each of the potential values within the paren-
thesis what may be called a ''part potential" whose value is, omitting k,
Part potential Xu = -£=; and _1_ = JL
Now, calculating the value of l/Xu3 = s/a3, for each separate section
of air passage in the mine given above,
Shafts,
Main airway ("A" seam),
Cross-headings ("A" seam),
Tunnel to "B" seam,
Return air course ("B" seam),
1
90,000
01 7^W
I1
80 X 80 X 80
120,000
.l/Oo
= 0.5555
n ft '-i '-in
1
60 X 60 X 60
70,000
I3
48 X 48 X 48
13,000
= 0.2031
- 0.6093
1
40 X 40 X 40
209,000
70 v 7n s/ 7n
Potential factor for entire mine v— - 2.1767
Ao"1
The part power potential for this mine is therefore
X0 = -. -.— = 0.7716
V 2. 1767
Example. — (a) From the part power potential calculated for the mine,
in the preceding example, find the horsepower required to circulate
30,000 cu. ft. of air per minute in a single current, assuming the ventilat-
ing fan to have a mechanical efficiency K = 60 per cent. (/>) What water
gage will be produced by the resistance in the mine, for this circulation?
Solution. — (a) The required horsepower of the ventilator is
kQ3 _1_ _ 0.00000002 X 30,000* 1 ,
" #33,000 *o3 " 0.60 X 33,000 X 0.77163
(b) The mine water gage due to this circulation is
kQ* 0.00000002 X 30,0002
w-°' = 6AX? = 5.2X0.77163
General Mine Potential, Equal Splits. — It is possible to calculate the
general mine potential when there are two or more airways of equal
dimensions, by simply multiplying the common sectional area by the
number of airways, as shown by the following example:
214 MINE GASES AND VENTILATION
Example. — A drift mine is opened on the triple-entry system. It is
proposed to drive the main intake 7X10 ft. in section, a distance of
3000 ft. to the boundary. The cross-entries are to be driven double,
5 X12 ft. in section and 1500 ft. to the side lines on each side of the main
road, making in all 6000 ft. of cross-entries, including the returns. The
main-return airways, on each side of the main intake are each 7X12 ft.
in section and 3000 ft. long. Calculate (a) the horsepower on the air;
and (6) the water gage produced, for a circulation of 50,000 cu. ft. of air
in this mine, in two equal parts.
Solution. — The first step is to calculate the value 1/XUZ = s/a3 for
each sectional division ; thus
Main intake, 7X10 ft., 3000 ft. long: a= 70 sq. ft.; s = 102,000 sq. ft.
Cross-entries 5X12 ft., 6000 ft. long : a = 120 sq. ft. ; s = 204,000 sq. ft.
Main returns, 7X12 ft., 3000 ft. long: a = 168 sq. ft.; s =228,000 sq. ft.
Substituting these values in the formula for finding the part
potential factor for each section,
Two splits,
Two main returns,
Xi3 70 X 70 X 70
1 204,000
= 0.1181
Xf 120 X 120 X 120
1 228,000
V 3 1 AQ \S 1 «C \s 1 no
VJ.VJtOV/
Potential factor for entire mine l/X03 0.4635
For the horsepower and water gage, we have
kQ* 1 0.00000002 X 50,0003 x
H = f = 33,000 - X
= kQ^ J_ = 0.00000002 X 50, OOP2
W'9' ~ 5.2 X03 ~ 5.2
TANDEM CIRCULATIONS
Summation of Potentials. — When an air current passes in
succession through two or more airways of different section,
the total unit pressure (Ib. per sq. ft.) due to the circulation is
equal to the sum of the unit pressures of the several sections.
The arrangement, in this case, may be described as "tandem."
Likewise, in a tandem circulation, the total power on the
air (ft.-lb. per min.) producing the circulation is equal to the
sum of the powers absorbed in the several sections through
which the current passes.
Indicating the potentials of the respective sections of the
THEORY OF VENTILATION 215
air-course in a tandem circulation by Xi, X2, X3, etc.; and the
corresponding unit pressures and powers on the air by pi, p2,
p3, etc.; and MI, M2, M3, etc., respectively, remembering that the
square of the pressure potential is equal to the cube of the
power potential, as expressed by the formula
we can write the following:
For tandem circulations, calling the general mine pressure
po and the total power on the air UQ.
Mine pressure, p(} = Q2 l^-r + -^- + etc
\A "i A 2
= Q2 (w~ + vT" + etc')
\A°tti A3u2 /
or 7>o
\tti u2
These formulas may be written more simply by indicating
the summation of the potential factors by the character £;
thus,
Mine pressure, pQ = Q~ £ (-«y)
\A i
In like manner, the total power on the air or power pro-
ducing tandem circulation in a mine is expressed by the
formula,
Power on the air, UQ = Q3 ( -^g~~ H~ ^T
\A ui A
or u0 = Q8 -- h
— h etc.)
2 '
These formulas may be expressed by indicating the sum-
mation of the potential factors by 2, as before; thus,
Power on the air u0 = Qs £
In a tandem circulation, if desired, the general mine po-
216 MINE GASES AND VENTILATION
tentials for power (Xu0) and for pressure (Xp0) can be calcu-
lated by the formulas
Xua = -T7 =; and Xvo =
"•*' 3 / _ -. / TT-rt \ * "
To illustrate the formulas that apply to a tandem circu-
lation where a single air current is carried continuously through
shafts and airways of different size or cross-section, assume
the following mine is passing 30,000 cu. ft. of air in a single
undivided current:
1. Downcast shaft ................ 8 X 12 ft., 600 ft. deep
2. Main road and return, each. ____ 6 X 10 ft., 1200 ft. long
3. Cross-tunnel and return, each. . . 6X8 ft., 200 ft. long
4. Upper seam and return, each. ... 5 X 14 ft., 2000 ft. long
5. Upcast shaft .................. 10 X 10 ft., 225'0 ft. deep
The sectional areas are 96, 60, 48, 70 and 100 sq. ft.; and
the rubbing surfaces, 24,000, 76,800, 11,200, 152,000 and
90,000 sq. ft., respectively.
Part potential factors, -!-, = -. -• -^T = " = °-0271
.AM a .A i yo
703
90,000
152,000 =
= 0.0900
oo8
Potential factors for entire mine, 2 (ip-J = 1-0170
Mine part % = ^ = = 0 9944
potentials, " \/S(l/^u3) " ^1.0170
Xpo = - — L = , l = 0.9916
vsa/Xp2) v i.oi7o
fcQ2 0.00000002 X 30,0002 1Q Q
Pressure, p- = ^3 - - - - = 18.3
u<jy± Ib. per sq.ft.
THEORY OF VENTILATION 217
Water gage, w.g. = p/5.2 = 18.3 -f- 5.2 = 3.5 in.
Power on _ fcQ3 _ 0.00000002 X 3Q,0003
the air, = X*uo~ 0.99443 fl
„ u 549,000 .
Horsepower, ff == - « - - 16.6 ftp.
Example. — A shaft mine has been opened on the triple-entry system.
The downcast and upcast shafts are each 600 ft. deep and 8 X 20 ft. in
section. The main headings have been driven a distance of 2000 ft.
from the shaft bottom. The center one of these headings is the intake
and is 7 X 14 ft. in section, while the two side headings are the return
airways for the respective sides of the mine and are each 6 X 12 ft. in
section. On each side of the main headings, cross-headings, 6 X 10 ft. in
section, have been driven 500 ft., including the return in each.
If the intake air divides at the face of the main heading and equal
currents ventilate the two sides of the mine, what power on the air will
be required to circulate a total of 60,000 cu. ft. per min. in this mine, and
what water gage will be produced in the fan drift?
Solution. — The first step is to calculate the potential values of the
two shafts, main intake, two cross-headings and two return airways, as
follows, remembering that these being equal splits, it is only necessary
to double the potentials of the cross-headings and return airways by tak-
ing twice the sectional area, in each case:
Shafts, 8X20 ft., 600ft.; a =160 sq.ft.; s= 67,200 sq. ft.
Main intake, 7 X 14 ft., 2000 ft.; a - 98' sq. ft.; s = 84,000 sq. ft.
Two cross-headings, 6 X 10 ft., 500 ft.; 2o = 120 sq. ft.; s == 32,000 sq. ft.
Two return airways, 6 X 12 ft., 2000 ft.; 2a = 144 sq. ft.; s = 144,000 sq. ft
The part potential factors are then as follows, omitting k
-
Main intake, ~ = -3 = ^||^ =0.0892
.A u CL aO
Two cross-headings, - ~ = -- = 0.0185
Two return airways, j^—s = . .3 = ""1443""
Sum of potential factors, 2 h^ ..... ....... 0.1723
The horsepower on the air in the fan drift, in this case, is found by sub-
stituting this general potential factor, in the formula for finding the power
in a tandem circulation; thus,
kQ3 ^/ 1 \ 0.00000002 X 60,0003 X 0.1723
H *" 3^000 SfeV = —33,000 = 22 55 hp'
218 MINE GASES AND VENTILATION
The water gage, in the fan drift, due to this circulation, can be calcu-
lated in like manner, independently, from the same general potential
factor, by substituting the same in the formula for finding the unit pres-
sure and water gage in a tandem circulation; thus,
0.00000002 X 60,0002 X 0.1723
-5±~ - - 2'38+ **•
The same result is obtained when the water gage is calcu-
lated from the power and the quantity of air in circulation.
u 22.55 X 33,000
~ ~~ H'
SPLITTING THE AIR CURRENT
Early Practice, Coursing the Air. — In the early practice
of mine ventilation, the method commonly adopted was that
known as " coursing the air." In this method the air was
conducted throughout the mine in one continuous current,
from the intake opening to the point where it was again
discharged into the atmosphere.
Single Current Not Adequate. — Experience has shown,
however, that a single air current is not adapted to the ven-
tilation of a large mine, for many reasons. As a mine is
developed and the workings extended, more men are employed
and greater quantities of air are required to ventilate the
mine and dilute and carry away the gases generated.
Need of Dividing the Air Current. — The division of the air
into two or more currents provides separate ventilation dis-
tricts in the mine and brings the ventilation under better
control, since the quantity of air can then be proportioned
to the requirements in each district
A larger volume of air can be circulated by the same power,
and the velocity of the current is kept low.
The smoke and gases generated in one section of the mine
are not carried by the current into another section, but pass
directly into the main return airway and are conducted out
of the mine.
A local explosion of gas or dust, in one portion of the mine,
is not as liable to extend throughout the mine.
THEORY OF VENTILATION 219
Method of Splitting the Air-current. — Whenever two or
more passages or airways are provided by which the air
current can travel in passing through the mine, the air will
always divide between them in proportion to their several
potential values. Hence, all that is required to split an air-
current is to provide two or more separate routes for its
pa'ssage. Each separate current is called an "air split" or
simply a " split."
Natural Splitting. — When all the airways are open to the
free passage of the air-current through them, the air divides
naturally between them, each airway or split taking a quan-
tity of air in proportion to its potential value. In other
words, the potential of the airway is an index of the quantity
of air that airway will pass, in natural splitting.
Proportionate Splitting. — When any other division of the
air is desired than the natural division, it is necessary to
introduce regulators in one or more of the airways so as to
obstruct the flow in those splits that naturally take more
than the desired proportion, and thereby increase the quantity
passing in the other airways till the desired proportion is
reached.
Primary and Secondary Splits. — -A branch or split off the
main air current is called a " primary split." If a primary
air split be again divided, the result is a " secondary split."
When the air current is equally divided between two or more
airways the splits are said to be "equal;" but when each
airway passes a different volume of air the splits are
"unequal."
Increase of Quantity Due to Splitting. — The quantity of air
in circulation is proportional to the general mine poten-
tial. In other words, the quantity ratio is always equal to the
mine-potential ratio; the power potential being used for a
constant power, and the pressure potential for a constant
pressure; always remembering, however, that the cube of
the power potential is equal to the square of the pressure
potential. Denoting the original quantity of air in cir-
culation, by Qi and the original mine potentials for power
and pressure by Xui and Xpi, respectively; and designating
220 MINE GASES AND VENTILATION
these factors after splitting, by Q2) Xu2 and Xp2, respectively,
we have the following formulas:
~ Xu2 ~ -3 \ /Xn$
Power constant, Q2 = Qi -^— ; or Q2 = Qi
3
Pressure constant,Q2 = Qi ^^; or Q2 = Qi
Api \ \^\ui/
An illustration of the use of these formulas is to be found
in the solution of the example given under Secondary Splitting.
In that example (p. 242), the power on the air remained
constant before and after splitting the current. The pressure
potential was used, which before splitting was Xpi = 0.6708,
and after splitting Xp2 = 0.8554:
Hence, Q2 = Qi^/(fj) ' = 120,000^ (gg) * = 141,100
cu. ft. per min.
NATURAL DIVISION OF AIR
In all splitting calculations, it is assumed that the unit
pressure (Ib. per sq. ft.) is the same at the mouth of each
split starting from the same point. Therefore, writing the for-
mula for unit pressure,
kloq2 , 9 p/a3\
P — — 11 and q = T (r-J
a3 k \lo I
Then, since p and k are both constant, qz varies as a3/lo
/•
and q varies as «A/T-
This expression, as previously explained is the pressure poten-
tial of the airway. It must be remembered that the square
of the pressure potential (Xp) is equal to the cube of the power
potential (Xu); thus,
It is the pressure potential that is always used in splitting
calculations; because, as stated above, the unit pressure is the
THEORY OF VENTILATION 221
same for all splits at one point. The calculation of the quan-
tity of air passing in any one of two or more splits starting from
the same point in a mine, is based on the following simple
rule :
Rule. — The ratio of the quantity of air passing in a single
split, to the total quantity for all the splits, is equal to the
ratio of the pressure potential of that split, to the sum of the
pressure potentials for all the splits.
Calling the quantities passing in the several splits, q\, qz,
q3, etc., and the corresponding split potentials Xi, X^ X3, etc.;
the total quantity of air in circulation in all the splits Q, and
indicating the sum of the split potentials by 2X;
Q = qi + q* + q-t + etc.
and
VX = Xi+ X2+ X3 + etc.
Then, according to the rule given above,
Q "
The work of calculation is much simplified and shortened
by using what may be called the " relative potential" values,
instead of finding the actual pressure potential for each split.
This is only possible in splitting calculations, where the
potentials are used as ratios, and the value of the ratio is
not changed by the cancellation of any like factors in all the
potentials.
Relative Potential Values. — Whenever the potential is
used as a ratio, as in splitting air currents, the relative values
should be used. These are calculated from the lowest relative
values for the areas, perimeters and lengths of the several
airways or splits. For example, if the areas are 48, 60 and
72 sq. ft., the lowest relative values, canceling the common
factor 12, are 4, 5 and 6, respectively Likewise, instead of
the perimeters, 28, 32, 34; use the lowest relative perimeters
14, 16, 17, canceling the common factor 2 from each.
The use of the ''relative potential'7 value, in all calculations
to determine the natural division of air between two or more
222 MINE GASES AND VENTILATION
airways, is one of the most important considerations in the
saving of time and labor and avoiding unnecessary mul-
tiplicity of figures, which increases the opportunities for
error and yields less accurate results. An example or two
will serve to make this fact plain.
Summation of Split Potentials. — The circulation of air in
two or more splits or currents, in a mine, differs from a tan-
dem circulation in the fact that the same unit pressure circu-
lates the air in each and all the splits, which are thus separate
currents moved by one pressure; while in a tandem circula-
tion one continuous current passes in succession through
different airways or sections of the mine.
While in a tandem circulation the mine pressure is equal
to the sum of the pressures for the several sections through
which the current passes; and, likewise, the total power for
the mine is equal to the sum of the powers absorbed in the
sections; in a split circulation, the total power for the mine
is equal to the sum of the powers absorbed in the splits, but
there is but one pressure, which is the same for all the
splits starting from the same point in the mine. As before,
indicate the several split pressure potentials by Xpi, Xp2,
Xp3, 'etc.; the corresponding powers on the air by MI, u2, u3,
etc.; and the total power on the air by MO, remembering that
it is necessary, in all splitting calculations, to use the pressure
potential, which has the value
The work is simplified by using the part potential value,
as previously stated, omitting k when finding the potential
values and multiplying the final result by that coefficient.
The following shows the development of the formulas for
the summation of the potentials in split circulations where
the splits all start from one point in the mine :
u0= MI+ u2 + etc. (1)
But, MI = JT-; u2 = -£-; etc. (2)
A pi A p2
THEORY OF VENTILATION 223
By the principle of splitting air currents,
Combining equations 2 and 3 and simplifying,
Finally, substituting these values (4) in equation 1, and
factoring,
From Equation 5 is obtained the formula for calculating
the horsepower on the air at the point of split, by the sum-
mation of the part pressure split potentials :
/cO3
Horsepower on the air, H = -
The formula for calculating the water gage, in like manner, is
kQ2
Water gage, _ „,.„.=___ (7)
Equal Splits. — When an air current is divided naturally be-
tween two or more equal splits, the calculation of the mine
potentials, velocity, pressure, power, etc., is the same as for
a single undivided current, except that the sectional area (a)
of the airways must be multiplied by the number of splits (n)
to obtain the total area of passage (no).
To illustrate the application of the formulas in this case,
assume an air current of 60,000 cu. ft. of air is circulated in
three equal splits, the size and total length of the airways,
including the returns being 5X8 ft. and 10,000 ft. long.
Q 60,000
Velocity, v = -'- = ' = 500 ft. per mm.
Hd o^O /\ oj
Mine part % = na _ 3(5 X 8) _
potentials, u ^/~g ^260,000
v /""* ion / l^u _ o K7Q
Z.^IUK/- = 120->26p>06-2-578
,.^ 0.00000002 X 60,0002
Pressure, p = -£- = -*****- ~ = 10-83
to. per sq. ft.
224 MINE GASES AND VENTILATION
Water gage, w.g. = p/5.2 = 10.83 -5- 5.2 = 2.08 in.
Power on
the air, _ kQ3 _ 0.00000002 X 60,0003
u — -^ — 3 — — — ^ 003 — — ooO,OOu
* ' ft.-lb. per min.
u 650,000
Horsepower, H -- ^^ -- -^^ -- 19.7 hp.
Unequal Splits. — To illustrate the formulas used in the cal-
culation of the natural division of an air current between
two or more airways and the pressure and power on the air,
assume a current of 75,000 cu. ft. per min. is passing in the
following three splits, starting from the same point of the
main airway or at or near the intake opening. The lengths
given for the several splits include the return, in each case;
and the pressure and power are for the circulation in the
splits only.
Split A, 6 X 10 ft. ; 2000 ft. long ; a = 60 sq. ft. ; o = 32 f t. ; Z = 2000 ft.
Split5, 6 X 8ft.; 1500ft, long; a = 48 sq.ft.; o = 28ft.; I = 1500ft,
Split C, 4 X 12 ft. ; 2500 ft. long; a = 48 sq. ft. ; o = 32 ft. ; I = 2500 ft.
The lowest relative values are as follows: Areas, 5, 4, 4; pe-
rimeters, 8, 7, 8; lengths, 4, 3, 5.
Relative split pressure potentials,
Sum of potentials, 2XP ........................... 4.987
Natural division of air current,
X 75'00° = 29'72° ™' fL
X 75,000 = 26,260 CM. ft.
= 19,020 cu. ft.
Total circulation, Q ................ 75,000 cw. ft.
THEORY OF VENTILATION 225
To calculate the pressure and power of the circulation, it
is necessary to employ the part-potential values, instead of the
relative values; thus,
Part potential values,
48
-^pc — 4oA /^^^^ . . «^. — 1.1/D
48
2500X32
General part potential for splits, SXP 4.636
kQ2 7 / Q \ 2
Pressure, p — -^ .2 = k ( „ j
p. = 0.00000002 (-^03°60) 2 = 5.2 Ib. per sq. ft.
Horsepower on the air,
feQ3 0.00000002 X 75,OOQ3
- oo ™«/ v, v N9. - 33^00 X 4.6362 P*
EXAMPLES IN NATURAL DIVISION
Example. — An air current of 100,000 cu. ft. per min. is divided at the
foot of the downcast shaft, between the following four air-courses or
splits, thereby providing two separate ventilation districts on each side of
the shaft :
Split A, 8 X 12 ft., 6000 ft. long
Split 5, 6 X 20 ft., 12,000 ft. long
Split C, 6 X 12 ft., 8000 ft. long
Split D, 4X6 ft., 1000 ft. long
All the splits are open to the free passage of the air, no regulators
being used, (a) Find the natural division of the main air current or the
quantity of air passing in each split. (6) What is the pressure due to this
circulation? (c) What is the horsepower on the air?
Solution. — (a) The first step is to calculate the relative pressure poten-
tial for each of the four air splits. The area, perimeter and length of
each airway are as follows:
Split A,
a
= 96
sq.
ft.;
0
= 40ft.;
I
= 6,000
Split B,
a
= 120
sq.
ft.;
o
= 52
ft.;
I
= 12,000
Split C,
a
= 72
sq.
ft.;
o
= 36
ft.;
I
= 8,000
Split D,
a
= 24
sq.
ft.;
0
= 20
ft.;
I
= 1,000
15
226 MINE GASES AND VENTILATION
Instead of using these full values as when finding the true potential
value of an airway, the lowest relative values for the areas, perimeters
and lengths are used. These relative values are obtained by canceling
the common factors in the areas, perimeters and lengths separately, which
gives the following :
Split A, a = 4; o = 10; / = 6
Split B, o = 5; o = 13; I = 12
Split C, a = 3; o = 9; I = 8
Split Z>, a = l; o=5; Z=l
Split
The relative split potentials are then found as follows :
4
Split D,
Sum of relative potentials ....................... 2 . 987
Since the quantity of air passing in each split, in natural division is
proportional to the corresponding potential, the quantity ratio is equal to
the potential ratio, which is true also for the sum of the quantities and
the sum of the potentials. Thus, the ratio 'of the quantity (q) passing
in any split, to the total quantity (Q) in circulation, is equal to the ratio
of the corresponding split pressure potential (Xp), to the sum of all the
split potentials
Therefore, substituting the relative potential values just found in this
formula gives the following :
1 0^*3
Split A, qa = ^ggy X 100,000 = 34,570 cu. ft. per min.
0 SQ^
Split B, qb = ^^ X 100,000 = 29,960 cu. ft. per min.
Split C, qe = 7 X 100,000 = 20,500 cu. ft. per min.
^.9o7
Split D, qd = ^^ X 100,000 = 14,970 cu. ft. per min.
Total quantity 100,000 cu. ft. per min.
THEORY OF VENTILATION 227
(6) Since the pressure is the same for all the splits, it can be calculated
from any one of the given splits, by substituting the values for that
split in the formula
= kloq2
a3
Thus, taking split A,
0.00000002 X 6000 X 40 X 34,5702
p = 96 X 96 X 96" = 6'48 ^ ^ Sq' fL
(c) The horsepower on the air in the main entry, or the horsepower
producing this circulation is, then,
Qp 100,000 X 6.48
H = 337)00 = 33,000 ' =
As an illustration of the usefulness of the summation of
potential values, we give below the calculation of the horse-
power on the air, unit pressure and water gage developed in
the circulation of 100,000 cu. ft. of air per minute, in four
splits, previously calculated by the usual method in the last
example, where it was necessary, first, to find the natural divi-
sion of the air.
Example. — An air current of 100,000 cu. ft. per ruin, is divided, at the
foot of the downcast shaft, between the following four splits:
Split A, 8 X 12 ft., 6,000 ft., long; a = 96 sq. ft.; s = 240,000 sq. ft.
Split B, 6 X 20ft., 12,000 ft., long; a = 120 sq. ft. ; s = 624,000 sq. ft.
Split C, 6 X 12 ft., 8,000 ft., long; a = 72 sq. f t. ; s = 288,000 sq. ft.
Split D, 4 X 6ft., 1,000 ft., long; a = 24 sq. f t. ; s = 20,000 sq. ft.
Calculate the horsepower on the air, unit pressure and water gage
concerned in producing this circulation, using the part potential values
and employing the method by summation of potentials; no regulators
being used in the mine, but the division of air being natural.
Solution. — The part potential values for the several splits are as follows:
XPI = a\l- = 96\/0^ ^ = 1.920
120
r~i2
Split U, Xp, - 12° \62p5a = L664
Split C, Xp3 = 72X^7^ =1-138
Split D, Xpt -
Sum of part pressure potentials (2ZP) 5.553
228 MINE GASES AND VENTILATION
Substituting this value for SZP, in the formulas for finding the horse-
power on the air and water gage, in natural splitting,
0.00000002 X 100,0003
Horsepower on air, H = 33>0oo x 5.5532 = 19-6 hp
0.00000002 X 100,0002
Unit pressure, p = - — - -P.»2 — - =6.48 Ib. per sq. ft.
0.00000002 X|100,0002
Water gage, w.g. = - 5.2 x 5.5532 = 1-24 in.
In natural splitting or when no regulators are employed
the general mine potential is always equal to the sum of the
several split potentials, which is true for either power or
pressure.
General Mine Potential. — The power potential for the
combined splits can be calculated from the total quantity of
air in circulation and the resulting pressure, using the
formula
02
X 3M = — ; or AM =
P
Example. — What is the general power potential for all the splits com-
bined, in the example given above, where 100,000 cu. ft. of air was circu-
lated under a pressure of 6.48 Ib. per sq. ft.?
Solution. — The general power potential for these combined splits is
3 |Q* 3 /100,0002
Mine power potential, AM =\— = \/ — TTTT; — = H55
\ p \ 6.48
Example. — An air current of 60,000 cu. ft. per min. is passing in an
airway 8 X 10 ft. in section, to a point 1500 ft. distant from the foot of
the downcast shaft, where it divides naturally between the following
four airways or splits:
Split A, 5 X 6 ft., 900 ft. long
Split B, 6X6 ft., 825 ft. long
Split C, 4 X 6 ft., 840 ft. long
Split D, 4X5 ft., 720 ft. long
What is the quantity of air passing in each split; and what will be the
water-gage reading for the entire mine and power on the air, at the foot
of the downcast shaft?-
Solution. — Since the water gage is required in this case, the relative
potential values cannot be used; but, instead, the part potential value
(omitting ft) is found for the main airway and for each split separately;
THEORY OF VENTILATION 229
thus, taking the length of the main airway including the return as
2X 1500 = 3000 ft.:
Main
Split
Split
Split
Split
airway,
A,
c,
A
a
a
a
a
a
o = 36; I =
3000;
900;
825;
840;
720;
Xl
xa
xb
xc
xd
= 80
J
80
= 2.177
= 1.168
Of).
\3000 X 36
J
30
— OU,
= 36;
= 24;
= 20;
n _ 04. / _
\900
X
22
J
36
U .£<*, £,
n 90-7
— 94
\825
X
24
0 Q07
J
24
o = 18; Z -
90
\840
X
20
= 0.786
J
20
\720
X
IS
The general split potential (XQ) is equal to the sum of the potentials
for the four splits; thus,
XQ = ZXabcd = 4.392
The quantity of air that will pass in each of these splits is proportional
to the corresponding split potential, assuming that no regulators are
employed but all the airways are free and unobstructed. The natural
division of the air between the four splits is therefore calculated in the
usual manner, as follows:
.1.168
Split
Split
Split
Split
A,
B,
c,
D,
9*
Qb
Qc
= 60,000^^ = 15,950 cu.
= 60,000^—^4= =20,920 cu.
= 60,000^000 =_12,390 cu.
60 000°*786 — 10 740 ni
ft.
ft.
ft.
ft.
per
per
per
per
min.
min.
min.
min.
- Ou,UUU. QOO '•"-" -'•U,<itU Git.
Total circulation 60,000 cu. ft. per min.
In order to find the water-gage reading at the foot of the
downcast shaft, for this circulation, it is necessary to cal-
culate the general mine potential Xp by combining, in tan-
dem, the main-airway potential (Xi) and the general split
potential (X0) previously found, using the formula (p. 215).
Mine water gage, w.g. = ^ s \X^*
Substituting the values of the potential factors previously found.
.Main airway, ^7- = ^ 1772 = 0-2109
Split section, -^- = T~oo2 = 0.0518
oqo2
Sum of values, S(1/AV) 0.2627
230 MINE GASES AND VENTILATION
Finally, substituting this value in the above formula for finding the
mine water gage,
0.00000002 X 60,0002 x 0.2627
w.g. = - 52 ~ = 3.64 in.
In like manner, the power on the air, at the foot, of the shaft is calcu-
lated by the formula
JcQ^_ ( 1 \ _ 0.00000002 X
~ 3,3,000 \XV-] ~ 33,000
PROPORTIONATE DIVISION OF AIR
Every large and well managed mine is, now, divided into
two or more separate ventilation districts. The natural divi-
sion of the air current between these several districts is not
generally in proportion to their respective needs.
The longer entries, working more men and requiring the
most air for their ventilation are the ones that have the
greater resisting power and, as a result, receive a lesser
proportion of the air, in natural division; while, on the other
hand, the shorter air-courses where fewer men are working
and less air is required, have a smaller resisting power and
naturally pass the larger quantity of air.
To Regulate the Air. — In order to overcome these natural
conditions, in mine ventilation, and divide the main air cur-
rent so as to give each district of the mine the required pro-
portion of air, it is necessary to employ some means that will
produce this result.
Two methods have been used to divide the air proportion-
ately; they are as follows:
1. The flow of air is obstructed in those airways that take
naturally more than the desired porportion.
2. The power on the air, at the mouth of each split, is
proportioned to the work to be performed in that split.
The former of these two methods has been in common use
for many years; the latter was suggested (Mine Ventilation,
Beard, 1894, p. 93) as an improvement and has been put in
use since in many mines where practical considerations would
permit.
THEORY OF VENTILATION
231
The Box Regulator. — This form of regulator is shown in
Fig. 32 (a), and consists of a brattice built in the return airway
or haulway. As shown in the figure, an opening is provided
in the brattice and a sliding shutter is used to regulate the
size of the opening so as to control the flow of air in that
airway or split. If more air is needed the shutter. is pushed
back so as to enlarge the opening ; or the shutter can be partially
closed to decrease the quantity of air passing in the split.
The Door Regulator. — Wherever the conditions will permit
this form of regulator to be employed it will be found an im-
provement over the common "box regulator," just described.
As shown in Fig. 32 (6) , the door regulator consists of a door
hung at the mouth of an entry or split and swung into the
FIG. 32.
wind. The door should be arranged so that it will fall natur-
ally against a set-stop, and when not in use will assume a posi-
tion whereby the air current will be divided in the desired
proportion, between the two airways or splits.
Effect of Regulator. — Any regulation of the air current in
a mine, to accomplish a distribution of air other than what
is natural, causes an increase of both the power producing
the circulation and the resulting pressure or water gage.
This is true in every case, whatever form of regulator is
employed, provided the total quantity of air in circulation is
not decreased. The reason *that an increase of power is
necessary in proportionate splitting, is that an increase in the
circulation in any split causes a corresponding increase in
pressure; and this pressure is the same for all splits starting
232 MINE GASES AND VENTILATION
from the same point in the mine. To circulate the same quan-
tity of air against this higher pressure requires a correspond-
ing increase of power.
Illustration. — Let it be required to find the horsepower and the pres-
sure per square foot, in the following distribution of the air current be-
tween the following four splits; the natural distribution of air, as previ-
ously calculated (p. 225), being repeated here, for sake of comparison:
Nat. div. Reqd. div.
(cu. ft. p. m.) (cu. ft. p. m.)
Split A, 8 X 12 ft., 6,000 ft. long, 34,570 20,000
Split B, 6 X 20 ft., 12,000 ft. long, 29,960 40,000
Split C, 6 X 12 ft., 8,000 ft. long, 20,500 30,000
Split D, 4 X 6 ft., 1,000 ft. long, 14,970 10,000
Total circulation, 100,000 100,000
Solution. — The first step is to calculate the natural pressure for each
split when passing the required quantity of air per minute, by substitut-
ing the following values for the area, perimeter and length of each split,
in the formula for finding the unit pressure:
Split A, a = 96 sq. ft. o = 40 ft.
Split B, a = 120 sq. ft. o = 52 ft.
Split C, a = 72 sq. ft. o = 36 ft.
Split D, a = 24 sq. ft. o = 20 ft.
I = 6,000ft.
I = 12,000 ft.
I = 8,000ft.
I = 1,000ft.
The natural pressure in each split is then calculated as follows :
0.00000002 X 6000 X 40 X 20,0002
Split A, p = - 96 x 96 x 96 = 2.17 Ib. per *q. ft.
0.00000002 X 12,000 X 52 X 40,0002
Spht B, p = - 12Q X 120 X 120 ~ = 1L55 lb' per «* *'
0.00000002 X 8000 X 36 X 30,0002
Split C, p = 72 X 72 X 72 = 3'89 l per sq' &'
0.00000002 X 1000 X 20 X 10,0002
Split D, p = 24 X 24 X 24 = 2<98 *' per sq' fi'
The highest natural pressure is developed in Split C, in the required
distribution of air, and that is, therefore, the "open" or "free" split,
regulators being necessary in each of the other splits, to raise the pres-
sure to the same amount.
The horsepower producing this circulation is then
100,000 X 13.89
33,000 42'09 hp'
Pressure Due to Box Regulator. — The primary effect of this
regulator is to increase the pressure on its intake side, by
THEORY OF VENTILATION 233
obstructing the flow of air in the airway or split that it con-
trols. This increase of ventilating pressure is necessary
to accomplish the desired increase of circulation in another
airway, which remains open or unobstructed and which, for
that reason, is called the "free split."
The increase of pressure is the pressure due to the reg-
ulator; and is equal to the difference between the natural
pressure of the free split and that of the split in which the
regulator is placed, calculated for the required distribution
of air. For example, in the illustration previously given, the
natural pressure required to circulate 30,000 cu. ft. of air in
Split C was 13.89 Ib. per sq. ft., while that, required to cir-
culate 20,000 cu. ft. in Split A was only 2.17 Ib. per sq. ft. The
pressure due to the regulator in Split A is, therefore,
13.89 - 2.17 = 11.72 Ib. per sq. ft.
Velocity of Air Passing Regulator. — The velocity of the air
flowing through the regulator is determined by the difference
of pressure on its two sides or the pressure due to the regulator.
This velocity is calculated from the well known formula
v = \/2gh
In the case of a regulator, the pressure head is equal to
the pressure (pr) due to the regulator, divided by the weight
of 1 cu. ft. of air (w = 0.0766 Ib.); and taking 2g - 2 X
32.16 = 64.32 ft. per sec., the theoretical velocity of the air
due to this pressure is
By this formula, the theoretical velocity corresponding to
the pressure due to the regulator in Split A is
v = 29-V/H.72 = 99.28 ft. per sec.
Quantity Passing Regulator. — Owing to the vena con-
tract a, at the opening in a box regulator, the effective area
of the opening is only 0.62 of the actual area A; and the
234 MINE GASES AND VENTILATION
quantity (Q), in cubic feet per minute, passing through the
opening, is
Q = 60(0.62At;) = 37.2Av
Or, substituting the value of v, as given above,
Q = 37.2 X
Or, since p = 5.2 w.g.
Q = 1078AV5.2ti>.0.= say
Area of Opening, Box Regulator.— The area of the opening
required to pass any given quantity of air, in splitting, is
found by solving the last formula given above, with respect
to A , as follows :
Q 0.0004Q
A. — • , ~ — — — ~
2460 \/w.g. \/w.g.
Example. — Calculate the size of opening in each of the regulators in
Splits A, B and Z), in the illustration previously given where the required
circulation was as follows:
Required circulation Natural pressure
Split A, 20,000 cu. ft.; 2.17 Ib. per sq. ft. Regulator
Split B, 40,000 cu. ft.; 11.55 Ib. per sq. ft. Regulator
Split C, 30,000 cu. ft.; 13.89 Ib. per sq. ft. Free split
Split D, 10,000 cu. ft.; 2.98 Ib. per sq. ft. Regulator
Solution.— The first step is to find the pressure due to the regulator
and reduce that to water gage, in each case. The pressure due to the
regulator is found by subtracting the natural pressure for the given
split from that of the free split, which is always the one having the
greatest natural pressure. Thus,
Pressure due to regulator Water gage
Split A, 13.89 - 2.17 = 11.72 Ib. per sq. ft.; 11.72 -*• 5.2 = 2.25 in.
Split B, 13.89 - 11.55 = 2.34 Ib. per sq. ft.; 2.34 -=- 5.2 = 0.45 in.
Split D, 13.89 - 2.98 = 10.91 Ib. per sq. ft.; 10.91 4- 5.2 = 2.10 in.
Substituting these values for the water gage due to regulator in the
formula for finding the area of opening,
Split A,
Split B,
Split D,
0.0004Q
0.0004 X 20,000
5.33 sq. ft.
23.85 sq. ft.
2.7G sq.ft.
Ai =
Ad =
0.0004 X 40,000
\/<X45
0.0004 X 10,000
V2710
THEORY OF VENTILATION 235
Use of the Door Regulator. — In the use of the door regu-
lator, the same general formulas apply, except that in esti-
mating the quantity of air that will pass the regulator, for
a given gage or pressure; or the area of opening necessary
to pass a given quantity under such gage, no allowance
should be made for vena contracta, which gives the following:
Quantity of air passing through an area of opening A, in a
door regulator under a water gage w.g.,
« =
Area of opening required to pass a quantity of air Q, in a
door regulator, under a water gage w.g.,
0.00025^
Area, A. = —7=
Vw.g.
Example. — What must be the width of opening of a regulator door
where the height of the entry is 5 ft. in the clear, in order to pass 40,000
cu. ft. per min., if the natural pressure for the required circulation pro-
duces a water gage of 1.25 in. for this split and 1.75 in. for the free split?
Solution. — The difference of pressure, in this case, is equivalent to a
water gage of 1.75 — 1.25 = 0.50 in.; hence,
0.00025 X 40,000
A =— — ; - = 14.14 sq.ft.
V0.50
Width of opening, 14.14 -r- 5 = 2.83 ft., or 2ft. 10 in.
SECONDARY SPLITTING
Secondary splitting involves the principles of both tan-
dem and split circulations. The tandem portion consists of
one airway of the primary split and the two airways branch-
ing from this and forming the secondary split section.
It is necessary to first find the general pressure potential
for the secondary split section. This is equal to the sum of
the pressure potentials of the airways forming that section.
This general potential for the secondary split is then com-
bined with the corresponding primary potential, according
to the method employed for a tandem circulation, which is
then regarded as one branch of the primary split.
236 MINE GASES AND VENTILATION
The diagram Fig. 33 shows clearly the method of naming
the splits and indicating them by symbols. The primary
splits, branching from the point where the air current is first
divided, are designated by the letters A, B, C, etc., and the
corresponding potentials by Xa, Xb, Xc, etc.
Secondary splits are designated AI, A2) etc., and BI, B%,
etc., depending on the primary split from which they branch;
and the corresponding split potentials by Xai, Xa2, Xbi, Xbt,
etc. The general potential for a primary split is designated
XQ, and for a secondary split Xao, Xb<>, etc.
In secondary splitting the operation is much simplified by
calculating the general potential for each consecutive point
or section, beginning always at the inby end of the system
and finding first the general potential for the secondary split;
Return
SPLIT C> 5000 FT.
FIG. 33.
then combining this in tandem with the corresponding pri-
mary potential; and using this result to find the general po-
tential for the primary split, in the same manner as for the
secondary split. Two formulas only are necessary; the one
expressing the summation of the potential values for a split
circulation, and the other a similar summation for a tandem
circulation. They as as follows:
General split potential,
General tandem potential (see p. 216),
In all splitting calculations it will generally be found more
convenient to use the pressure potential, for the reason that
the calculation of the distribution of the air is based on equal
pressures, for all splits starting from one point.
Illustration. — Primary splits are best indicated by the
large letters, as Splits A} B} C, etc. Secondary splits are
THEORY OF VENTILATION 237
named after the primaries in which they occur; thus AI, A2,
etc., or Bi, Bz, etc.
The corresponding split potentials are indicated thus:
i
Primary potentials, Xa, Xb, Xc, etc.
Secondary potentials, Xa\, Xaz; Xbi XL?; Xc\ Xci; etc.
General split potentials, Xao, Xio, Xco
General mine potentials, X0
To illustrate the calculation of the effect of making a sec-
ondary split in the circulation calculated under " Unequal
Splits" (p. 224), assume the air is again split in C, at a point
500 ft. inby from the main or primary split.
Splits A and B are the same as before, while Split C is now
500 ft. long; Split C}, 1200 ft. long; and Split C8, 800 ft. long.
The part potential values for the splits are, then,
Split A, Xp = eu/p Xa (as before) = 1.837
Split 5, Xb (as before) = 1.623
Split C, 'x.- 48^1-^ = 2.629
"48 "=1.697
Split Ci, Xei = 48 J
Split C2, XcZ = 48 J,
1200 X 32
= 2.078
800 X 32
General split potential, SXC = 1.697 + 2.078 = 3.775
Combining this general potential for Splits Ci and C2 with
the potential for Split C, in tandem, we have,
Part potential factors,
(Tandem circulation) X2C 2.6292
= °-0702
Tandem value, Xf0 = S (l/X2c) ..... 0.2149
General part potential,
(Primary split C) Xco = ^A^ = 2.157
Part potential, Split A, Xa = 1.837
Part potential, Split B, Xb = 1.623
Mine pressure potential, Xpo ..... 5.617
238 MINE GASES AND VENTILATION
Mine power potential, (After splitting)
= 3.160
Mine power potential, (Before splitting, p. 225)
Xul = \/4i6362 = 2.780
For a constant power, the quantity ratio is equal to the
power-potential ratio; thus,
Q* = X*_2. (
~'
Xul' 75,000 2.78'
n 75,000 X 3.16 Qr
62 = - -2~78~" = 85,240 CM. //. pe
Mine pressure, p = k($-} * = 0.00000002/|5^) 2 = 4.6 Ib.
VA^7 V5.617/ per sq.ft.
Power on the air, u = k (—-} * = 0.00000002 (^ |?) * = 1 1 .
\ A u/ \ o.lb /
The natural division of the main air current of 85,240 cu. ft.
between the three primary splits, A, B, C; and the two second-
ary splits Ci, C2, in the last example, is calculated first for
the primary division, and then for the secondary, as follows:
Primary splits,
Part pressure Natural Required
potentials (cu. ft. per min.)
Xa = 1.837; qa = X 85,240 = 27,880 20,240
O.
Xb = 1.623; qb = X 85,240 = 24,630 16,000
Xco = 2.157; qc = l~~ X 85,240 = 32,730 40,000
o .
2XP = 5.617 Q= ...... 85,240 85,240
Secondary splits,
Xel = 1.697; qel = \^ X 32,730 = 14.710 25,000
o . / «O
XcZ = 2.078; qc2 = = X 32,730 = 18.020 15,000
o . 775
SXP = 3 . 775 32,730 40,000
THEORY OF VENTILATION 239
The natural pressures are then calculated for the required
circulation of air in each split. The highest pressure of the
secondary splits determines the secondary pressure, which
must be added to the natural pressure of the tandem airway,
to obtain the effective primary pressure for Split C. Finally,
the highest primary pressure determines the primary pressure,
which is the pressure for the entire split circulation. The
process is as follows:
Secondary pressures,
<••-*(£)';
/OC f}(\0\ 2
Pd = 0.00000002 (p^) =4.341 Ib. per sq. ft.
pc. = 0.00000002 (^-^g) 2 = 1 -042 Ib. per sq. ft.
Tandem pc = 0.00000002 ' ' = 4 . 630 Ib. per sq. ft.
Primary pressures, pc0 = 2pc 8.971/6. per sq.ft.
/2Q 240\ 2
pa = 0.00000002 (y^) =5.067 Ib. per sq. ft.
pb = 0.00000002 (\-jJ23) 2 = 1-944 Ib. per sq. ft.
Qv
Horsepower, H = ^-^ ;
„ 85,240 X 8.971
-- =23-17/J-
The secondary pressure, as determined by the highest nat-
ural pressure in those splits, is that in Split Ci, which is 4.341
Ib. per sq. ft. Likewise the primary pressure (the highest of
those splits) is that of the tandem split Co, which is 8.971 Ib.
per sq. ft. These pressures are indicated above by the heavy
type.
Regulators. — The difference between the secondary pressure
and the natural pressure in any secondary split is the pres-
sure due to the regulator or the regulator pressure for that
split. The same is true for primary splits.
240 MINE GASES AND VENTILATION
The pressures due to the regulators required in Splits A,
B and C2, in order to accomplish the required distribution of
air are, therefore, as follows:
Split A, 8.971 - 5.067 = 3.904 Ib. per sq. ft. (0.751 in. w.g.)
Split B, 8.971 - 1.944 = 7.027 Ib. per sq. ft. (1.351 in. w.g.)
Split C2, 4.341 - 1.042 = 3.299 Ib. per sq. ft. (0.634 in. w.g.)
The necessary area of opening in a regulator to pass the
required quantity of air, under the given water gage is calcu-
lated as follows:
„ 0.0004?
Box regulator, A = — = ~ ;
Vw.g.
0.0004X 29,240 1Q _ .
Aa =— —7= - = 13.5 sq. ft.
\/0.751
0.0004 X 16,000 _ _• .
Ab = - , - = 5.5 sq.ft.
Vl.351
0.0004 X 15,000 _ r ,,
Ac2 = - —7= - = 7.5 sq.ft.
V0.634
If door regulators are used the openings have the following
areas :
0.00025?
Door regulator, A = j — — ;
Vw.g.
0.00025 X 29,240 ft
Aa = - . — - — = 8Asq.fi.
V0.751
0.00025 X 16,000
VI. 351
= .3 A sq.ft.
0.00025 X 15,000 . _ A
Ac2 = - —j=— - = 4.7 sq.ft.
V0.634
The results of making the secondary split in Primary C
may therefore be summarized as follows:
The above comparison shows: (1) The increase in the
quantity of air in circulation and the decrease in the unit
pressure and water gage, for the same power on the air,
caused by making a small secondary split, in one of the
original primaries. (2) The large increase of power on the
THEORY OF VENTILATION
241
air and pressure and water gage necessary to make the re-
quired distribution of air, in this case.
Distribution of air
Natural circulation
(No regulators)
Required
(Regulators)
Split A (cu. ft. per m.)
29,720
26,260
19,020
27,880
24,630
(32,730)
14,710
18,020
29,240
16,000
(40,000)
25,000
15,000
Split B
Split C
Split d
Split C2
Totals
75,000
5.2
1.0
11.9
85,240
4.6
0.88
11.9
85,240
8.97 '
1.72
23.17
Pressure (Ih. per sq. ft.)
Water gage (in )
Horsepower on air (hp.)
Example. — An air current of 120,000 cu. ft. per min. is passing in a
mine in two splits, as follows:
Split A, 5 X 10 ft., 20,000 ft. long; 40,000 cu. ft. per min.
Split B, 5 X 10 ft., 5,000 ft. long; 80,000 cu. ft. per min.
More air being required, a careful investigation shows that Split A
can be again divided at a point 2000 ft. inby from the foot of the down-
cast shaft, thereby forming two secondary air splits, each 5 X 10 ft.,
8000 ft. long, including the return. This would make Split A 4000 ft.
long including the return. With the same power on the air, what
quantity of air will be circulated in this mine after dividing Split A ?
Solution. — The first step is to calculate the potential values of the
different sections or splits, both before and after dividing Split A to form
the two secondary Splits- A i and Az. This being a comparison of two
circulations, it is possible to use the relative potentials, reducing the
areas, perimeters and lengths to their lowest relative values, which
gives the following:
Before dividing Split A :
Split A,
Split B,
= 50; o = 30; I = 20,000
= 50; o = 30; I = 5,000
(Relative values)
After dividing Split A :
Split A, a = 50; o = 30; I = 4,000
Split J5, a = 50; o = 30; I = 5,000
Split Ai, a = 50; o = 30; I = 8,000
Split A 2, a = 50; o = 30; I = 8,000
16
a = 1
0 = 1
I = 20
a = 1
0 = 1
I = 5
a = 1
0 = 1
I = 4
a = 1
0 = 1
I = 5
a = 1
0 = 1
I = 8
a = 1
a = 1
I = 8
242 MINE GASES AND VENTILATION
Relative potentials, before division :
T = —7= = 0.2236
^ 1 A/20
- 0.6708
5X1 h = °'4472 '
o X 1 A/5
Relative potentials, after division:
X. = «Ji = 1
Xi, = Same as before = 0.4472
T~ i
U'8_
Wslh ' T7« ' °-3838
= 0.707
Tandem summation (Xa and A'0o) :
= = 0.4082
+ 1/A200 Vl/0.52 + 1/6.707*
A 2 = A, + Xb = 0.4082 + 0.4472 = 0.8554
Since the power is the same, before and after division and calling these
respective general potentials Xit A2, we have
jOil = Q*. f , 120,0003 = _Q,»_
(Xi)2 A22' 0.67082 0.8554*
Q2 = 120,000^ (^|^)2 - 141,100 en. ft. per min.
THEORETICAL CONSIDERATIONS IN SPLITTING
Theory assumes that when an air current traveling in an
airway divides, at a certain point called the "point of split,"
into two separate currents or "splits," the unit pressure (p)
at the point of split is common to each split. In other words,
two splits starting from the same point in a mine have the
same unit pressure (p) and, for the same sectional area (a),
the resistance (R = pa) is the same for each split. The same
holds true for any number of splits (ri) of equal area.
Whether the unit pressure (p) or the unit work (pv) is the
factor common to each of two or more splits starting from the
same point will not be discussed here. The law of dynamic
THEORY OF VENTILATION 243
equilibrium of fluids points to the equality of unit work for
each split. The comparison of the relation of the quantity of
air (q), the rubbing surface (s) and the sectional area (a),
on these two bases of reasoning, is as follows:
Unit pressure Unit work
ksq2 u ksq*
a3 a a4
For constant unit pressure : For constant unit work :
q vanes as a •%/- q varies as
\s
Practical Conditions. — In considering the practical results
of splitting the air current in a mine, it may be assumed that
the power on the air ([/) at the mouth (intake) of the mine
remains constant. Assuming a number of splits (n), starting
from the same point in the mine, at or near the shaft bottom
or mine entrance, the total area of passage is na and the for-
mula for power is then
_.
" (na)3
which shows that, since in any case U, k, s and a are each
constant, Q3 varies as n3, or Q varies as n, which is the num-
ber of equal splits, each having an area a.
In other words, the quantity of air circulated in a given
mine, by a given power on the air (effective power), is pro-
portional to the number of splits, assuming the splits all start
from the mine entrance or so near to it that the resistance of
the main intake entry, slope or shaft may be ignored. Under
these conditions, splitting the air has no effect to alter the
velocity or the resistance in the mine.
When the point of split, however, is some distance inby
from the mouth of the mine or " daylight" the effect of split-
ting the air, in that case, is to cause a disproportion. The
quantity of air circulated by a. given power no longer varies
as the number of splits; but the ratio of increase in volume
is less, because the power on the air at the mouth of the splits
is decreased by splitting.
244 MINE GASES AND VENTILATION
Assuming, as before, a constant power on the air at the
mouth of the mine, since the quantity has been increased by
splitting, both the velocity and resistance have been increased
in the main airway, which absorbs more power thus decreas-
ing the power on the splits.
Effect of Splitting on Velocity. — In order to show the gen-
eral effect of splitting the air current, at any point in a mine,
on the velocity (VG) in the shaft or main airway and the velocity
(vi) in the splits, it is necessary to know the ratio (m) of the
rubbing surface (si) in the splits, to that of (s0) in the shaft
or main airway; also, the ratio (n) of the total area (Ai) of
the splits, to that of (Ao) in the shaft or main airway.
Then, si = raso; andAi = nA0; (1)
and, since for a given quantity the velocity varies inversely
as the area,
*-* , ~ ,2)
But, the power on the air (u) at the mouth of the mine is
equal to the power (MO) absorbed in the shaft or main airway,
or both, plus the power (MI) absorbed in the splits.
M = MO + MI (3)
or, expressed in terms of the mine, since M = ksv3,
u = k(s0v03 + s^i3) (4)
Substituting for Si and Vi3 the values given in Equations 1
and 2, gives after simplifying
o „ 0
u = fcWl + -3 = fcW—r- (5)
Equation 5 shows clearly that, for a constant power on the
air at the mouth of a mine, in splitting,
T?
#o varies as 3 (6)
V n3 + m
and, observing Equation 2,
vi varies as 3/ __ — =: ( 7)
\/n3 + m
THEORY OF VENTILATION 245
It appears from the last two equations that as the ratio
of the split area to the shaft or main-intake area, represented
by n, is increased the main-intake velocity (VQ) is increased,
while the split velocity (vi) is decreased, the increase and de-
crease of velocity, however, being less rapid than the change
in the area ratio.
Effect of Splitting on Quantity. — The quantity of air in
circulation varies directly as the intake velocity v0; or, for a
constant power (u) on the air,
Q varies as 3/—= (8)
V ft3 + ra
Effect of Splitting on the Mine Resistance. — The total mine
resistance is the sum of the main-intake and split resistances.
Thus, R = /c(W + sit i2) (9)
and R
Finally, from Equations 6 and 10 is derived
n2 + m, /11X
R varies as 3/ = (11)
PRACTICAL PROBLEM
Example. — A current of 25,000 cu. ft. per min. is passing in a shaft
mine. The shafts are 8 X 12 ft. in section and 250 ft. deep. The air-
ways are 6 X 10 ft. and 15,000 ft. long, including the return, (a) What
is the water gage due to this circulation? (6) Assuming the power
applied to the fan shaft remains unchanged and the current is divided
into two equal splits, at a point 1500 ft. inby from the foot of the shaft,
what volume of air may be expected to be passing? (c) What will be
the water-gage reading on the fan drift and at the bottom of the shaft,
after splitting?
Solution. — The rubbing surface and sectional area of the shafts and
airways are, respectively, as follows:
Shafts — Sq. Ft.
Rubbing surface 2(8 + 12)2 X 250 = 20,000
Sectional area 8 X 12 = 96
Airways (total) —
Rubbing surface 2(6 + 10)15,000 = 480,000
Sectional area.. . 6 X 10 = 60
246 MINE GASES AND VENTILATION
Main airway —
Rubbing surface 2(6 + 10)2 X 1500 = 96,000
Sectional area 6X10= 60
Two equal splits —
Rubbing surface 2(6 + 10)12,000 = 384,000
Sectional area 2(6 X 10) = 120
The relative part potential factors are then :
Before splitting —
Shaft, . ..(±. or 1 \ - A - ^°™ = 0.0226
Airwas (total) ............................... = = 2.2223
General relative mine potential factor ( S -==-5! ................ 2 .
2449
After splitting —
Shafts (as before) ............ '. .......................... 0. 0226
1 s 96,000
6Q3
,
Main airway ......................... - = — = 3 = 0.4444
spats
General relative mine potential factor ( S p-^1 ................ 0.6892
(a) Water gage (before splitting) —
1 \ 0.00000002 X 25,0002 X 2.2449
(6) For a constant power on the air, the quantity varies directly as
the mine power potential; but, for a constant power applied to the fan
shaft, owing to the efficiency of the fan varying inversely as the 3/5
power of the potential Xu the quantity varies as the 4/5 power of that
potential.
The mine potentials, in this case, are,
Before splitting— Since l/X3«i = 2.2449; Xui = . 1 = 0.7637
After splitting— Since 1/X3«2 = 0.6892; Xut = .x = 1.1321
^0.6892
Then, for a constant power applied to the fan shaft, the quantity of
air in circulation varies as the 4/5 power of the power potential, which
gives for the circulation after splitting
* = 25,000 = 34,250 cu. ft. per min.
(c) Water gage (after splitting). — In the fan drift the gage is
0.00000002 X 34,2502 X 0.6892
w.g, = -- — — - = 3.1 in.
THEORY OF VENTILATION 247
To find the gage at tho shaft bottom it is necessary to deduct the
potential factor for the two%shafts from the total potential factor for the
mine after splitting; thus
J- - _L = 0.6892 - 0.0226 = 0.6666
Ap* \pol
Then, since the gage is proportional to this potential factor, the gage at
the bottom of the shaft is
. 0.6666
'"•"•=3-1X 06892
Relative Variation of Factors. — The following relation of some of the
more important factors in the ventilation of mines by means of centrifugal
fans is based on the results of many experiments:
Power on Air Constant (KU = u) —
Unit pressure, p varies inversely as Q
1 J/~s
p varies as
Xu
Quantity, Q varies as X
Power Applied to Fan Shaft Constant (U)—
Efficiency, 1/K* varies as Xu3 = Xp2 = az
Effective power, u varies as K
Quantity, Q& varies as AV
Mine Potential Constant (Xu3 = Xp2 = a3/s) —
Effective power, u varies as Q3
Quantity, Q6 varies as n4
Water eage, (w.g.)& varies as n8
SECTION VII
PRACTICAL VENTILATION
CONDUCTING AIR CURRENTS, AIR BRIDGES — GENERAL PLAN
OF MINE — DISTRIBUTION OF AIR IN THE MINE — SPLIT-
TING AIR CURRENTS — SYSTEMS OF VENTILATION — SYSTEMS
OF MINE AIRWAYS.
The first step, in the practical ventilation of a mine, is
to determine the volume of air that will be required in order
to maintain a pure and wholesome atmosphere in the mine
workings. This will depend on conditions, such as the size
and depth of the mine; thickness and inclination of the
seam; character and quality of the coal; kind and quantity
of gas generated; methods of working the seam and mining
the coal. Aside from these conditions the volume of air
must always be sufficient to meet the requirements of the
mine law.
The second question to be determined is the general ventila-
ting pressure or water gage, under which the mine is to be
ventilated. This will depend on the possible extent and
size of the workings and the power available. The water
gage, in mining practice, varies from a fraction of an inch to 3
or 4 in., in this country; and higher gages are in use in the
deep mines of Belgium and other countries. The best practice,
however, employs such a system of mining that the required
volume of air can be circulated under, say 1 or 2 in. of water
gage. This can only be accomplished by so planning the mine,
in the start, that it can be divided into separate ventilation
districts. The number of ventilation districts should increase
with the development of the mine. Each district is thus
ventilated by a separate air split or current, which insures
good air, besides reducing the water gage necessary for the
ventilation of the mine.
248
PRACTICAL VENTILATION 249
Power Required to Produce a Given Circulation. — having
decided on the volume of air required and the water gage,
these factors determine the power that will be necessary to
produce the circulation. The power on the air may, gen-
erally, be safely taken as 60 per cent, of the indicated horse-
power of the engine driving the ventilating fan. For
example, the circulation of 75,000 cu. ft. of air against a water
gage of 2 in. will require, with a safe margin, an engine
capable of developing
75,000 X 2 X 5.2
0.60 X 33,000
= 39.4, say 40 hp.
The above calculation assumes a properly designed ven-
tilating fan, since a poorly designed fan, or a fan working
under conditions for which it is not adapted, may give an
efficiency of only 40 or 50 per cent.; or at times this may not
exceed 25 per cent., under particularly adverse conditions.
An unsuspected negative air column existing in some portion
of the mine may be the hidden cause of the low efficiency
of a ventilating fan.
CONDUCTING AIR CURRENTS
Conducting Air Currents in Mines. — To conduct the air on
its course through the mine, doors, stoppings, brattices, air-
crossings, or bridges — either overcasts or undercasts — are
employed to deflect the air current. When the air is divided
and made to travel in two or more splits regulators are used to
proportion the quantity of air to the requirements in each
split.
In Fig. 34 are shown two forms of self-closing doors used in
mines. There are many different methods in use to prevent
a mine door standing open, but these are as practical as any.
The door on the left is shown with canvas flaps to stop the
leakage of air. Both doors swing either way, being heavy
enough to overcome . the pressure of the ventilating current.
Stoppings, in mine ventilation, are built in entries or in
crosscuts for the purpose of closing the passage. When built
250
MINE GASES AND VENTILATION
in crosscuts they serve to carry the air current forward to the
head of the entry. A common form of stopping consists of
two walls of slate or rock built 10 or 12 in. apart and the space
between them filled tight with road dirt or sand. More sub-
stantial stoppings are built of brick laid in cement, or of
concrete.
In Fig. 34 is also shown the right and the wrong way of
erecting a line of brattice in a pair of headings. As shown in
FIG. 34.
each of the figures, a row of posts is set, one at a time, and
canvas or brattice boards nailed to them on the intake side.
The posts are stood 18 in. or 2 ft. from the right rib if the
intake is on the right, or the left rib if on the left. The
same order is followed on the return airway or heading. The
work of nailing the canvas or boards to the post is done on
the fresh-air side and the brattice extended as the current
sweeps away the gas accumulated in these headings. The
PRACTICAL VENTILATION 251
arrows show the course of the air as it circulates around the
brattice in each heading.
Air Bridges. — In Fig. 34 are also shown different methods of
constructing air bridges in mines, for the purpose of conducting
one air current across another. First is shown a standard
type of overcast built of reinforced concrete. Immediately
below this is shown two common types of air bridges, an over-
cast and an undercast. In the "undercast" shown on the
right, the cross-current of air is conducted under the main road
or heading, the bridge in that case forming the floor of the
roadway. A safer and more serviceable form of air bridge,
however, is the "overcast" shown on the left, by which the
cross-current is carried over the haulage road. The under-
cast possesses the disadvantage that it cannot be drained and
may become flooded and cut off the air current completely.
Natural Overcast. — Owing to the difficulty of keeping air
bridges air-tight, and for the further reason that the possible
destruction of an air bridge by an explosion would cut off
the circulation of air in the district fed by that means, a
natural overcast is frequently referred.
In the lower right-hand corner of Fig. 34 is shown a natural
overcast as driven in the upper portion of a thick coal seam,
although the same form of overcast is often driven in the rock
strata overlying a thinner seam. Such a natural overcast
is formed by starting an uprise in the roof of the cross-entry,
a short distance on either side of the main heading, and then
driving a crosscut in the solid formation above and across the
main roadway, thereby forming a wholly separate air passage
for the intake and return air currents.
Regulators. — As described previously and illustrated in Fig.
32, regulators are used to divide an air current in any desired
proportion between two entries or splits. The "box" regu-
lator is commonly placed on the return airway, where it offers
no obstruction to haulage, while the "door" regulator is al-
ways placed on the intake. The use and effect of these two
forms of regulators are fully treated under "Proportionate
Division of Air," page 231, in the section "Theory of
Ventilation."
252 MINE GASES AND VENTILATION
GENERAL PLAN OF MINE
Requirements. — In the planning or laying cut of a mine the
most careful consideration must be given to the questions of
ventilation, drainage and haulage, as these arrangements, to
a great degree, determine the successful operation of the
mine.
In order to insure the safe and economic extraction of the
coal, the same careful consideration must be given to ascer-
taining the extent and character of the seam, its depth below
the surface, inclination and thickness, the character of the
roof and floor and the hardness of the coal; its cleavages and
faults, impurities, etc.
The information thus gained will be of the first import-
ance in deciding on the most suitable method of mining to
adopt, in order to secure the largest returns on the invest-
ment, the most complete extraction of the coal and the great-
est safety in mining the same.
Economy and Efficiency. — The economic ventilation of a
mine premises the circulation of the required air volume,
with the least expenditure of power. Efficient ventilation re-
quires the circulation and proportionate distribution in the
mine workings, of such a volume of air as will not only meet
the requirements of the law, but, likewise, produce the neces-
sary velocity in all roads and passageways and at the working
faces of all headings and chambers, so as to sweep away the
smoke and gases that would otherwise accumulate therein;
and to so ventilate all waste, void and abandoned places as to
prevent them from becoming a menace to the safety of the
mine as reservoirs for the accumulation of gas.
Drainage. — Economic mine drainage requires such a dis-
position of the openings driven in the seam for the extrac-
tion of the coal, including all passageways, headings and
chambers, that the water coming from the strata will flow
by gravity, either to the main sump at the shaft or slope
bottom, or to certain gathering centers from which it can
be readily siphoned to the main sump or pumped directly
to the surface.
PRACTICAL VENTILATION 253
In practically level seams or seams having slight inclina-
tion, the question of drainage does not materially affect
the general mine plan. In this case, good roadside ditches
afford the necessary waterways by which the underground
water flows to the sumps provided to receive it Such sumps
or catch basins are located at one or more convenient low
places or " swamps," in the mine, where it is possible to
install a pump of sufficient size to handle the water of that
section at all times.
The rooms or chambers, in practically level seams, are
turned off both entries of a pair, which greatly reduces the
expense of entry driving and necessary maintenance of road-
ways and air-courses.
In inclined seams the direction and amount of pitch are
controlling factors in determining the general plan of the
mine, in respect to the course of main roads, cross-headings
and rooms or chambers. In respect to drainage, it is im-
portant to drive all such openings to the rise, in order to
avoid the annoyance and expense of providing artificial
means of draining the working faces.
Haulage. — Economic mine haulage requires that the coal,
like water must gravitate, as far as practicable, from the
coal face where it is mined, to the foot of the shaft or slope
opening from whence it is hoisted to the surface.
In level seams, the question of haulage does not affect
the plan of mine; but, in seams of more or less inclination,
it becomes a matter of first consideration.
In inclined seams, it is always possible to drive the main
haulage roads in such a direction that the grade of the road
will not only favor the movement of the loaded cars,
but will be such that the power required to haul the loaded
trip out of the mine will be equal to that necessary for hauling
the empty trip back into the mine. This- is called the " eco-
nomical grade."
The grade of any road, or the road grade, in an inclined
searn, may be calculated when the angle of inclination of
the seam and the angle the road makes with the strike of
the seam are known, by the following rule:
254
MINE GASES AND VENTILATION
Rule. — -The tangent of the grade angle is equal to the
tangent of the angle of inclination of the seam, multiplied
by the sine of the angle the road makes with the strike of
the seam.
Or, calling the angle between the road and the strike of
the seam, the "road angle," this angle is calculated by the
use of the formula
sin road angle =
tan grade angle
tan inclination
There is shown clearly in Fig. 35, a perspective plan of a,
pair of entries with rooms turned off the haulage road. The
FIG. 35.
left-hand entry is the return air-course, while the haulage
road is the intake. • A canvas or curtain hung on the entry
just inside of the mouth of the first room deflects the intake
air mostly into the rooms, where it passes through the break-
throughs from room to room. Better results are generally
obtained when the breakthroughs are staggered Or not driven
directly opposite each other, as shown in the figure. The
PRACTICAL VENTILATION
2.55
FIG. 36.
FIG. 37.
256 MINE GASES AND VENTILATION
crosseuts on the entries are closed by substantial stoppings,
except the last crosscut where the intake air passes into the
return, as shown by the arrows.
General Plan, Level Seam. — In Fig. 36 is illustrated the
general plan of a mine shaft bottom in a level seam. At
times, it may be necessary to drive the shaft bottom at an
angle with the main and cross-entries, as shown in Fig. 37,
in order to square the hoisting shaft with the loading tracks
FIG. 38.
on the surface. In each of these figures the intake current is
divided, forming two main splits of air near the foot of the
downcast or air shaft and these main splits are again divided
two or more times to ventilate different sections of the mine,
as indicated by the arrows.
Ventilation of Longwall Workings.— Figs. 38 and 39 are
two general plans of longwall workings, showing the main
air current carried, in two or more splits, from the bottom
PRACTICAL VENTILATION
257
of the downcast shaft directly to the working face, where it
is again divided and made to sweep the entire face, returning
by the numerous roads to the main-return airways, by which
it is conducted to the foot of the upcast shaft. Fig. 39 shows
Overcasts shown thus: X Curtains shown thus:
FIG. 39.
a more extended development of the mine, on a slightly dif-
ferent plan from that given in the preceding figure.
DISTRIBUTION OF AIR
Ventilating a Mine. — Small mines are generally or often
ventilated by a single current of air passing in one continu-
17
258 MINE GASES AND VENTILATION
ous circuit around the mine. In larger mines the main
current entering the mine is divided into two or more currents
or " air splits," as they are called.
The current flowing into a mine or section of a mine is
called the "intake current" and that passing out from the mine
the "return." Likewise, these airways are termed the "in-
take" and the "return" airways respectively.
The figures previously given show clearly the general ar-
rangement of the circulation in a mine, as indicated by the
arrows. In a gassy mine, the hoisting shaft is made the down-
cast and the main-haulage road is then the intake airway.
The mine is ventilated by an exhaust fan located at the upcast
shaft, because it is impracticable to use a blower fan whenever
the main-haulage road is made the intake. A blower fan
would require doors placed on the haulage road, at the shaft
bottom, to prevent the air short-circuiting and passing out
through the hoisting shaft. All crosscuts, except those
through which the air must pass, are closed by stoppings or
doors. By this means, the air current is forced to travel cer-
tain airways from the downcast to the upcast shaft.
In Figs. 36 and 37, the hoisting shaft is the upcast and the
haulage road the return. The air is first split near the foot
of the downcast shaft. One current or split travels north to
ventilate that side of the mine, while the other current travels
in the opposite direction to ventilate the south side of the mine.
Each of these currents is shown returning to the upcast shaft
by the main return air-course. Double doors are used in the
crosscut at the shaft bottom to prevent the air current from
being broken or staggered, when it is necessary to pass through
this crosscut. Only one of these doors is open at a time, and
the air is thus prevented from short-circuiting at this point.
On the main south (Fig. 37), the air is divided into three
separate splits or currents, which ventilate respectively the
main south headings, the first and second east and the first
and second west. In order to do this, two overcasts are re-
quired, one to conduct the main-south intake current over the
first-west haulage road, and the other to carry the second-east
intake current over the main-south haulway. It should be
PRACTICAL VENTILATION
259
observed that the stables, in both Fig. 36 and 37, are venti-
lated by a separate scale of air, which is then carried directly
into the main return and passes out of the mine as indicated
by the arrows.
Ventilation of Cross-entries. — In the illustration (Fig. 40)
are shown two ways of ventilating a pair of cross-entries
turned off the main headings. As shown on the left, the
main-intake current is deflected into the cross-entries by
placing a door on the main heading. The total current is thus
made to pass down the first cross-entry and, returning through
the second by a crosscut at the face, continues on its way up
the main heading, thus forming one continuous current.
FIG. 40.
In the plan shown on the right in the same figure, the main-
intake current is divided at the mouth of the first cross-entry.
Part of the air enters the first cross-entry and returning by
the second passes over the air bridge at its mouth and through
the crosscut into the main-return air-course. The remainder
of the main intake current continues up the main heading,
passing under the air bridge on its way. This method fur-
nishes a separate current for each district of the mine and
leaves the main haulage road unobstructed by any doors. As
shown in the figure, an inclined crosscut, called a " crossover,"
connects the two cross-entries near their mouth, which permits
the coal from the back entry to reach the main haulage road
by passing through the door on the crossover. This door
divides the intake from the return on these entries.
260
MINE GASES AND VENTILATION
Ventilation of the Mine Stable. — The mine stable, as pre-
viously stated, should be ventilated by a small split commonly
caled a "scale" of air, taken from the main intake current.
This current, after ventilating the stables, passes directly to
the upcast shaft, without contaminating the air of the mine.
It is important to locate underground stables so that they can
be ventilated (Figs. 36, 37) with a small scale of air that is
conducted at once into the main return air-course. To make
possible the rescue of the animals in case of accident, and to
FIG. 41.
facilitate the handling of feed and refuse to and from the sur-
face, the stables should be located near the bottom of the
hoisting shaft or other opening.
SPLITTING AIR CURRENTS
Illustration of Air Splitting. — Fig. 41 gives a diagrammatic
perspective of a mine ventilated by two primary air splits,
A and B, and two secondary splits, C and D. In this case
either the downcast or the upcast may be made the hoisting
PRACTICAL VENTILATION
261
shaft, as desired. In gassy mines where haulage is performed
on the intake air, the downcast becomes the hoisting shaft,
which avoids the use of doors on the shaft bottom. In that
case, the air bridges are constructed to conduct the return
air over the intake current, thus leaving the haulage road
unobstructed.
SYSTEMS OF VENTILATION
Exhaust vs. Blowing System oi Ve: Dilation. — The natural
or physical conditions that exist in a mine will generally
determine whether it should be
ventilated on the exhaust or the j
blowing system. A mine
generating gas in sufficient
quantity to make the main-
return airway unsafe for haulage
will require the exhaust system,
in order to leave the hoisting
shaft, which would then be the
downcast, and the shaft bottom unobstructed by doors.
The exhaust system of ventilation is illustrated in Fig. 42,
which shows the circulation in a section or district where
FIG. 42.
FIG. 43.
the future development of a pair of cross-entries warrants
the building of an overcast on the main headings, and haulage
must be performed on the intake air.
As indicated by the arrows in the figure, a curtain hung
on the first cross-entry, just inby from the mouth of the first
262
MINE GASES AND VENTILATION
room working, deflects the air into the rooms so that the
major portion of the current sweeps the face of each room.
It is necessary also to hang canvas at the mouth of each room
except the last to keep the air at the working face.
The blowing system of ventilation is illustrated in Fig. 43
which shows the general arrangement under conditions similar
to those just described, except that here the haulage is per-
formed on the return air, the hoisting shaft being the upcast.
As indicated by the arrows, the air is carried directly to the
head of the cross-entries and returned through the crosscuts
in the rooms.
SYSTEMS OF MINE AIRWAYS
The Main Airways. — While two airways, an intake and a
return airway of sufficient size, furnish the necessary means
FIG. 44.
for conducting the air current to and from the working faces
of the mine, there are other considerations of economy and
PR A CTICAL YEN TIL A TION
203
safety of operation that frequently demand a larger number of
main airways.
Single-entry System. — In the early days of mining and in
some small mines, today, supplying local trade, the plan is
adopted of driving a single entry, which serves the double
purpose of haulage
road and air-
course, the air
being returned
through the rooms.
T h e single-entry
system is unsafe
and no longer used
in scientific mining.
Double-entry
System. — In this
system, all entries
are driven in pairs,
one entry being
made the intake
and the other the
return, in each pair.
This system is com-
monly employed in
a large majority of
coal mines and is
shown on the cross-
entries in Fig. 44.
Triple-entry
System. — In this
system, three parallel entries are driven abreast, as for example
the main entries in Fig. 44, and the same in Fig. 45, which
illustrates the workings in a slope mine. The main slope
haulage road being the intake for the entire mine, and the
air-course on either side being the return for that respective
side of the mine. In the use of the triple-entry system, the
center entry is generally made the intake and haulage road,
while the two side entries are the return air-courses for each
respective side of the mine.
FIG. 45.
264
MINE GASES AND VENTILATION
In the slope mine illustrated in Fig. 45, the rooms are driven
to the rise of each pair of gangway headings. The mine is
equipped with two ventilating fans operating on the exhaust
FIG. 46.
system. The air is split and overcast at each pair of headings
on the right of the slope, except the last; while there are but
two air splits ventilating the levels on the left of the slope
PRACTICAL VENTILATION 265
headings. Unfortunately for purposes of rescue and handling
feed and refuse, the mine stable is located far in the workings,
probably to av.oid the necessity of driving the mules to and
from the working face.
Multiple-entries. — In Fig. 46 is shown a mine opened on the
five-entry system for the main headings, thus providing three
intake airways and two separate return airways, one for each
side of the mine.
The number of main airways required, in any case, is de-
termined by their size and the necessary volume of air that
must pass through them. The limiting factor in this calcu-
lation is the safe and economic velocity of the air current
traveling the main airways.
While too low a velocity of the air is dangerous because
of its failure to remove the accumulating gases, too high a
velocity, on the other hand, is dangerous by reason of its
increasing explosive conditions in the mine air, by raising
and carrying in suspension fine dust, and by furnishing an
excessive supply of oxygen that invites active and explosive
combustion.
The velocity of main air currents in mines can safely vary
between 250 and 1200 ft. per min. : and for short distances a
velocity of 2000 ft. per min. may be permitted, although high
velocities rapidly increase the power producing the circulation.
Where the main intake airways are used for haulage roads,
it will not be possible or advisable to employ a velocity much
exceeding 400 or 500 ft. per min., owing to the annoyance
and danger of drivers losing their lights.
Economy of Multiple Main Airways. — The economy of
driving a multiple system of main airways will not be ques-
tioned in the planning of large operations. The same plan
should be applied to the opening of mines on a smaller scale,
the objective point being to keep the velocity of the main air
current so that it will not exceed 1200 ft. per min., for any
considerable distance.
The saving in power (fuel consumption, equipment and at-
tendance) will pay for the increased expense of upkeep of
entries; and the system affords a large increase in safety
200 MINE GASES AND VENTILATION
by reducing explosive conditions and providing additional
avenues of escape in case of accident. There is afforded,
besides, room for a double-track haulage system, which will
prove a great advantage in the operation of the mine.
Assuming that one-half the power on the air is consumed
in the main airways, which more or less closely approxi-
mates the fact, and taking the general efficiency of the fan
and engine as 60 per cent., a double-entry system, for the
main intake and return airways, would effect a saving in fuel
of 11.25 per cent.; a triple-entry system, 13.32 per cent., and
a4-entry system, 14.10 per cent.
Illustration. — -In the planning of a mine for an output of,
say 2000 tons of coal per working day, in a 6-ft. seam of more
or less inflammable bituminous coal (shaft, slope or drift
openings), the following data may be assumed as approxi-
mating possible conditions, but must be modified to suit known
facts that have been determined, in special cases:
Output per man per day (average) 2U tons
Number of miners employed (2000 -7-2.5) 800
Number of loaders or helpers • 400
Number of drivers, trackmen, timbermen, etc . 60
Foreman, assistant foremen and firebosses . 20
Total number of men and boys 1280
Number of mules 25
Assuming a gaseous mine requiring, by law, say 150 cu. ft.
of air per man, and 600 cu. ft. per mule, per minute, the neces-
sary circulation based on these data would be (1280 X 150) +
(25 X 600) = 207,000 cu. ft. per min.; or, to allow for .certain
leakage, say the necessary air volume is, in this case, 225,000
cu. ft. per min.
Driving 10-ft. openings in a 6-ft. seam and allowing for
necessary timbering would leave an unobstructed effective
area of, say 50 sq. ft. In this case adopting a 4-entry system
for the intake and the same for the return, would give for
the total effective intake and return areas, each 4 X 50 =
200 sq. ft., which would make the velocity of the intake air
PRACTICAL VENTILATION 267
current 225,000 4- 200 = 1125ft. per min., which is a safe
and economical velocity, provided these airways are not used
as haulage roads.
To provide for the expansion of the return air, owing to
rise of temperature and addition of mine gases, which may
altogether amount to 6 or 8 per cent., the return airways
should be driven, say 8 or 10 in. wider than the intake air-
ways.
SECTION VIII
MINE LAMPS AND LIGHTING
PRINCIPLES OF CONSTRUCTION, CLASSIFICATION OF SAFETY
LAMPS, REQUIREMENTS — CHARACTERISTIC TYPES OF LAMPS
— SPECIAL TYPES OF SAFETY LAMPS — PERMISSIBLE MINE
SAFETY LAMPS — USE AND CARE OF SAFETY LAMPS — TESTING
FOR GAS BY INDICATORS — THE FLAME TEST — ILLUMINANTS
FOR SAFETY LAMPS, OILS, ETC. — MINERS' CARBIDE LAMPS —
ELECTRIC MINE LAMPS— PERMISSIBLE PORTABLE ELECTRIC
MINE LAMPS.
A volume could be written on the development of the so-
called "safety lamp." It is not proposed to give, here, the
history of that development further than to say that it began
with the discovery of the two most important and essential
principles of all mine safety lamps. Strange to say, these
two principles were discovered at practically the same time
and by two men of different education and calling.
PRINCIPLES OF CONSTRUCTION
Principle of Protecting Shield. — George Stephenson was a
practical miner of considerable mechanical ability, which led
him into the practice of cleaning and repairing watches and
clocks, running engines and performing other similar services.
It was at the Killingworth colliery, Oct. 21, 1815, that he
made the first trial of a lamp he had devised for use in mines
generating gas.
The principle of the Stephenson lamp consisted in confining
the burnt air and products of combustion in the upper portion
of the lamp chimney or bonnet, the idea being that this would
furnish an extinctive atmosphere at the top of the lamp and
prevent the flame of the burning gases passing" out of the
chimney and igniting the gas-charged air surrounding the
lamp. This, today, is one of the important principles of all
268
MINE LAMPS AND LIGHTING
269
mine safety lamps, though the method of its application differs
from that employed by Stephenson.
Principle of Wire Gauze. — The principle of the isolation of
a lamp flame, by means of a wire gauze envelope or chimney,
was discovered by Sir Humphry Davy, an eminent chemist.
As the result of a series of experiments, Davy was able, Dec.
15, 1815, to announce to the world the fact, that an ordinary
lamp flame will not pass through the mesh of cool wire gauze.
The idea was suggested to the mind of Davy by observing
that a flame, as shown in Fig. 47, never comes in direct
contact with cool metal. The reason is that the
temperature of the burning gas is reduced, in
close proximity to the metal, below the point of
ignition. He showed that the burning gas, on
passing through the mesh of a wire gauze, is
broken up into tiny streamlets, which are so
cooled by contact with the metal of the gauze
that the flame is extinguished. As the gauze
becomes heated by the close proximity of the
flame, however, it loses its cooling effect and the
flame then passes through the mesh.
The effect of cool wire gauze to prevent the
passage of flame through its mesh is shown in
the lower half of Fig. 48. In the upper half,
appears the later passage ot the flame through
the mesh of the gauze when the wire has become
heated so that it is unable to absorb sufficient heat from the
burning gas to extinguish the flame. This isolation of the
flame of a safety lamp by means of a wire gauze chimney
found its earliest application in the Davy lamp. A careful
study of the problem and the experiments performed showed
that the greatest safety was secured by the adoption of a
standard mesh formed by 28 steel wires, No. 28 B.w.g.,
making 784 openings per square inch. This standard mesh is
still used in England and in this country, today. It was also
found that the volume of the chimney, including the combus-
tion chamber of the lamp, should bear a certain relation to
the surface of the gauze in order to produce the best results
FIG. 47.
270
MINE GASES AND VENTILATION
and insure the greatest security of the lamp when burning
in the presence of gas. There is, however, no fixed value
for this ratio, which controls the circulation of the air and gas
passing in and out of the lamp and varies with the type of
construction.
Classification of Safety Lamps. — Mine safety lamps are
divided into two general classes, according to their use in the
mine, as follows: (a) Lamps for testing for gas. (6) Lamps
for general use at the
working face. A
good working lamp
does not make a good
lamp for testing for
gas, neither does a
good testing lamp
answer for work at
the face. Each of
these lamps is design-
ed for the particular
service or work to
- be performed and the
requirements of each
Coo) Wire Gauze
FIG. 48.
are widely different.
Requirements of a
Good Testing Lamp.
— A good lamp for
testing for gas must
be sensitive to small
percentages of gas
present in the mine air and must possess, as nearly as practi-
cable, the same conditions with respect to gas in the combustion
chamber as exist in the air surrounding the lamp. Otherwise,
the test for gas observed within the lamp will not correctly
represent the gaseous condition of the outer air.
The sensitiveness of a lamp to gas depends on both the
character of the oil burned and the freedom of circulation
within the combustion chamber. A lamp burning hydrogen
gas (Clowes' hydrogen lamp) is more sensitive than a lamp
MINE LAMPS AND LIGHTING 271
burning oil, which is true in general of a gas-fed flame. The
Clowes lamp is the only safety lamp burning gas, however,
and has but a limited use in testing for gas in mines. There are
two general types of oil-burning lamps, according as the
illuminant is a non- volatile or a volatile oil, the former being
derived from animal or vegetable sources, while the latter
are chiefly derivatives of mineral oil or petroleum distilled
below 300 deg. F., such as naphtha, benzine, etc. Coal oil
(kerosene) is a distillate of petroleum between 300 and 500 deg.
F., and is not classed as a volatile oil. It is frequently mixed
with twice its volume or more of a vegetable oil to improve
the illuminating power of the latter.
The volatile oils, while more sensitive to the presence of gas,
possess the disadvantage of giving a more pronounced oil
or fuel cap that is frequently mistaken for a gas cap. More-
over, the height of the flame cap, for any given percentage of
gas, is always greater in a lamp burning a volatile oil and
allowance must be made for this fact, in estimating the per-
centage of gas present when making the test with such a lamp.
In order that a lamp shall present the same condition with
respect to gas, within as exists without the lamp, two con-
ditions must be fulfilled: (1) The air must enter the combus-
tion chamber at a point below the flame. (2) There must be a
free circulation within the lamp and it must always be ascen-
sional so as to avoid the contamination of the atmosphere in
the combustion chamber with the products of combustion
in the chimney, which are apt to descend from the upper portion
of the lamp if the chimney is too closely bonneted and the
circulation in the lamp is not wholly ascensional.
Other requirements of a good testing lamp are some means
of accurately measuring the height of the flame cap formed
in the lamp and, if possible, making the cap more plainly dis-
cernible by means of a good background and the absence of a
reflection that would interfere with the observation. A good
testing lamp should also be provided with a shield or suitable
bonnet to protect the lamp against strong air currents and as
an added protection against slight explosions that may occur
within the lamp, owing to a body of strong gas.
272 MINE GASES AND VENTILATION
Requirements of a Good Working Lamp. — -Unlike the test-
ing lamp, a lamp designed for general work in the mine must
not be too sensitive to gas. Its chief requirements are the
following :
1. The lamp must give a good light that will enable the
miner to perform his work readily and discover any dangers
that may exist in the roof or about him.
2. The lamp should be simple in construction, portable and
light and, at the same time, capable of resisting rough usage
that is liable to break the glass, injure the gauze or otherwise
damage the lamp. There should be as few parts as practi-
cable, and these should be assembled in such a manner that
no single part 'can be accidentally omitted when putting the
lamp together in the lamproom.
3. A good working lamp must be secure against strong air
currents. It should be suitably protected by a shield or bon-
net of such construction as will not unduly obstruct the circula-
tion within the lamp. The best type of lamp admits the
air to the combustion chamber, at a point below the flame, and
allows the products of combustion to pass out through tan-
gential openings in the bonnet. A shield protects the top
of the bonnet from dust and falling fragments of the roof.
4. It is important that every working lamp should be
provided with a lock fastening that will betray any attempt
on the part of the miner to tamper with the lock. Magnetic
locks, it is claimed can only be opened by means of a strong
magnet in the lamproom, but the claim has been questioned in
numerous instances, especially where a mine is equipped with
electrical installation. The fastening that has given, perhaps,
the greatest amount of satisfaction because of its simplicity
and security is the old lead lock that is fastened in the lamp-
room with a steel die of special design.
Working lamps are supplied with both round and flat
burners, as desired. When a flat burner is used the illumina-
tion is much improved by the simple device illustrated in Fig.
49, consisting of a semi-circular cut made in the center of
the top of the burner. This simple artifice has the effect of
producing a rounder and less smoky flame, besides giving a
hotter flame when the latter is reduced, in testing for gas.
MINE LAMPS AND LIGHTING 273
The illuminating power of a safety lamp is greatly influenced
by the way in which the air supply is brought into contact with
the flame and the volume of air supplied to the combustion
chamber of the lamp. The light-giving power of the flame is
also increased by the use of duplex flat-wick tubes, or triplex
round-wick tubes. Tin or aluminum tubes produce a better
light than either brass or copper, and porcelain is far better
than any metal, in this respect.
Increased light does not mean an increased cost in oil.
Petroleum having a high flashing point, such as mineral
colza oil, is probably best adapted for use in high-powered
lamps. The illuminating power of vegetable oils is greatly
increased by the admixture of one-third part of pretroleum
(coal oil) having a flashing point of 80 deg. F., although the
lamp flame will then have a greater tendency
to smoke and will require a better circulation
of air in the lamp.
The safety of gauze-protected lamps is much
increased by a suitable restriction of both the
inlet and the outlet openings, which is a promi-
nent feature of many lamps of high illuminat-
ing power. Another important feature of these
lamps and one that affords increased protection
at the top of the chimney is the inner metal bonnet sur-
mounted by a truncated cone. Still another feature that adds
to the protection of the lamp and increases its illuminating
power, by the concentration of the heat in the combustion
chamber, is the conical glass. All of these features originated
in the Ashworth-Gray lamp, a type of which was later styled
the Ashworth-Hepplewhite-Gray lamp.
A working lamp must be of a design that will make it most
convenient for the use of the miner. The base of the lamp
should be sufficiently broad to enable the lamp to be set on the
mine bottom, in a position to throw a good light where the
coal is being undercut or mined. It is often necessary for the
miner to hang his lamp on a timber or post. For that reason,
some lamps are furnished with a short hook instead of the
usual ring forming the handle. The hook is not commonly
18
274 MINE OASES AND VENTILATION
used in this country, the miner preferring to hang his lamp on
a nail driven in the timber.
Aji important feature of a working lamp is a good pricker,
which will enable the miner to remove the crust that forms on
the top of the wick of an oil-burning lamp. The pricker must
be of such a form that the wick can be cleaned without danger
of extinguishing the light.
A lamp burning a volatile oil, the most common form being
those of the Wolf type, requires some kind of igniter, in the
combustion chamber, to enable the lamp to be relit when acci-
dentally extinguished. Lamps burning a volatile oil are more
subject to extinction, either from a sudden jar or from gas,
than those burning a non-volatile oil. The chief objection to
lamp igniters is the opportunity that they afford the curious
miner of fooling with his lamp.
The old form of igniter consisted of a narrow ribbon of
waxed paper containing little nubs of fulminate, which were
ignited by a rod-scraper that extended up through the oil
vessel of the lamp. This form of igniter has now largely given
place to one in which ignition is caused by the sparks from a
cerium compound. The objection to the wax-taper igniter
is the flame of the burning taper and the charred remains that
often proves an annoyance in the lamp, especially when one
or more of the nubs fail to ignite, which is frequently the
case.
Specifications by the Bureau of Mines. — -In January, 1915,
the Federal Bureau of Mines, acting under the authorization
of an act of Congress (37 Stat., 681), approved Feb. 25, 1913,
issued " Schedule 7, entitled " Procedure for Establishing a
List of Permissible Miners' Safety Lamps." Following are
the more important announcements and specifications con-
tained in that schedule, which is still in force in relation to so-
called " Permissible "% safety lamps for mining use.
The Bureau of Mines is prepared, at its Pittsburgh experi-
ment station, to conduct tests of miners' flame safety lamps
for the purpose of establishing a list of permissible safety lamps
for use in mines in which explosive gas is liberated. This
schedule of tests is submitted for the information of those
MINE LAMPS AND LIGHTING 275
who may desire to submit a type of lamp for test, which must
fulfill the following general requirements. (See also, p. 288.)
1. The lamp must be provided with double gauzes or with some
other adequate arrangement serving the same purpose. Every gauze
must be of steel or best charcoal-annealed iron wire, not larger than 27
Brown & Sharpe gage (0.014 in. in diameter), with 28 meshes to the
lineal inch (784 to the square inch), nor less than 29 Brown & Sharpe
gage (0.01125 in. in diameter) with 29 meshes to the lineal inch (841
to the square inch).
2. If lamp standards are used, the standards must be so arranged
that a straight line touching the exterior part of any two consecutive
standards will not touch the glass.
3. The lamp must be so constructed that it will not be possible with-
out easy detection to assemble the component parts of the lamp without
the gauze.
4. The lamp must be provided with an efficient locking device to
prevent the fuel vessel, glass, or bonnet from being removed by un-
authorized persons, or being loosened to such an extent that the safety
of the lamp is impaired. Provision shall also be made for taking up the
play due to wear of the screw threads.
5. The glass globes shall have their two ends as nearly parallel as it
is practicable to make them.
6. The lamp will be examined in respect to its general design, strength,
and general character of construction.
CHARACTERISTIC TYPES OF LAMPS
The purpose, in this volume, is to show the general develop-
ment of the safety lamp, by explaining those characteristic
features that form the most essential elements of all safety
lamps. It would be useless to attempt to describe in detail
the construction of the many different lamps now on the mar-
ket, as such a description would not be instructive in the way of
demonstrating what features are essential in securing the high-
est efficiency and a maximum degree of security in the lamp.
While the number of different safety lamps in use are legion,
there are a comparatively few that are characteristic of the
essential features that promote safety in the use of the lamp.
The Davy Lamp. — This is one of the early types of safety
lamps that still survives. The common, unbonneted Davy
is shown in the illustration, Fig. 50 and consists of a brass
276
MINE GASES AND VENTILATION
or aluminum oil vessel surmounted by a wire-gauze chimney
of standard mesh. Three round iron or brass rods, called the
" standards" of the lamp, are attached to the oil vessel and
carry a brass ring that furnishes the upper support of the
gauze chimney. Above the ring is a cap or shield of brass to
which is attached the handle for holding the lamp.
There are several forms of the Davy lamp known, respec-
tively, as the "fireboss Davy," " pocket Davy," etc. The
common Davy has a single, gauze
chimney, in the form of a straight
cylinder I^{Q in. in diameter and
varying fro'm 4% to '6 in. in height.
The type known as the ' ' pocket Davy "
is somewhat smaller and the height
of its gauze is reduced to 4 in. One
form of the Davy lamp that was
much used in England had a glass
cylinder surrounding the lower portion
of the gauze chimney, while a steel
bonnet enclosed the top of the chim-
ney. Openings were provided in the
top of the bonnet for the escape of the
gases and burnt air formed in the
lamp. Other forms used in England
were the " tin-can Davy," having a
metal shield covering the entire gauze
chimney. This shield was provided
with openings for the circulation of
the air and a glass window for observ-
ing the indications of the lamp. In the "Davy with glass
shield" the metal shield was replaced with a glass cylinder
that extended the full height of the gauze chimney. The
"jack Davy" was a small sized lamp corresponding to the
pocket Davy used in this country.
The Davy lamp is designed to burn sperm, cottonseed,
or lard oil. Owing to the free circulation of air passing in and
out of the lamp, the unbonneted Davy is a favorite among
firebosses in this country. It is extremely sensitive to gas,
FIG. 50.
MINE LAMPS AND LIGHTING
277
and, on this account, flames readily when exposed to a con-
siderable body of gas. Owing to its sensitiveness to gas and
the dim light afforded, the Davy is not a safe or suitable
working lamp. Its use for that purpose is prohibited by the
mining laws of some states. The unbonneted Davy lamp is
unsafe in a current having a velocity exceeding 6ft. per second.
The Clanny Lamp.— The illustration, Fig. 51, shows the
common form of Clanny lamp, unbonneted and bonneted.
FIG. 51.
In this lamp the brass oil vessel is surmounted by a glass
cylinder above which is the wire-gauze chimney. The glass
of the Clanny lamp enables it to give a better light than the
Davy. The lamp is less sensitive to gas and more or less
liable to smoke, however, because the air must enter the lamp
above the glass, through the lower portion of the gauze
chimney and descend to the flame, which causes a conflict
of the descending and ascending currents of air, in the com-
bustion chamber of the lamp.
278
MINE GASES AND VENTILATION
Owing to the simplicity of its construction, the bonneted
Clanny lamp is largely used as a working lamp, in many mining
districts. Improved types of the Clanny lamp have been
introduced, from time to time, by different manufacturers.
Some of these have adopted the principle of the early Eloin
lamp, by which the air entered the combustion chamber of
the lamp at a point below the flame. This construction is
known as the "Eloin principle" of safety lamps. By this
means, the tendency of the lamp to
smoke is reduced to a minimum.
The Clanny lamp is designed to burn
sperm, cottonseed, or lard oil. It is
equipped either with the round or the
flatwick burner and the usual pricker for
cleaning and raising or lowering the wick
in the wick tube. The illuminating
power of different types of Clanny lamps
varies from 0.25 to 0.50 cp. While the
unbonneted Clanny lamp becomes unsafe
in a current velocity exceeding 8 ft. per
sec., different types of this lamp when
bonneted have been able to withstand
current velocities varying from 1200 to
1500 ft. per min., and, in a few cases,
certain lamps of this type have not failed
when the velocity has been increased to
2000 ft. per min., but this must be re-
garded as exceptional.
The Marsaut Lamp. — This lamp differs in no respect from
the Clanny lamp just described, with the one exception
that the single-gauze chimney of the Clanny lamp is here
replaced by two or three concentric conical gauzes forming the
chimney of the lamp. This feature is clearly seen in the illus-
tration, Fig. 52, which shows an unbonneted Marsaut lamp
having a conical gauze within the cylindrical gauze forming
the chimney of the lamp. The double-gauze chimney is the
characteristic feature of the Marsaut type.
The multiple gauzes give protection to the upper portion of
FIG. 52.
MINE LAMPS AND LIGHTING 279
the lamp. The top of a lamp chimney, where the heat is
concentrated, always presents the greatest danger of the trans-
mission of the flame through the gauze. This fact is recog-
nized in the construction of both the Davy and Clanny lamps
by providing a gauze cap, which serves as a means for the
better protection of that point.
The lamp shown here is a modified type of Marsaut, de-
signed on the "Eloin" principle of admitting the air below the
glass, which improves the circulation and the illuminating
power of the lamp. This type is known as the " Beard
Deputy7' and contains the Beard-Mackie Sight Indicator,
described later (see p. 297).
The Marsaut principle of multiple wire-gauze chimneys
has been found particularly applicable to lamps designed
on the Eloin principle, where the air is admitted to the com-
bustion chamber of the lamp at a point below the flame, which
increases the air column or the upward draft in the lamp.
One type of double-gauze Marsaut lamp, bonneted, when
tested, was found to be safe in an explosive mixture having a
velocity of 2600 ft. per min., while a triple-gauze lamp of
this type withstood a current velocity of 3100 ft. per min.
The illuminating power of the double-gauze lamp, burning
sperm oil, was found to be 0.70 cp.; but, in the triple-gauze
Marsaut, this was reduced to 0.50 cp.
The Mueseler Lamp. — The special feature of this lamp that
is characteristic is the central conical sheet-iron chimney,
supported with its mouth a short distance above the tip of the
flame of the lamp and concentric within the wire-gauze
chimney, as shown in the illustration, Fig. 53. The other
features of the Mueseler lamp are similar to those of the
Clanny lamp, except that the height of the glass cylinder
is somewhat reduced and the lamp is provided with a deflector
surrounding and supporting the metal chimney and directing
the air as it enters the lower portion of the wire-gauze chimney.
The chief effect of the metal chimney of the Mueseler lamp
is the increased protection afforded against explosion within
the lamp, by separating the descending and ascending air
currents. Although the inner chimney improves the circula-
tion, the illuminating power of the lamp is decreased.
280
MINE GASES AND VENTILATION
The Mueseler principle, however, presents the advantage of
increasing the security of the lamp against internal explosions.
The shape of the central chimney is conical, corresponding to
that of the gauze chimney above it. When the lamp is
exposed to a body of sharp gas, and slight explosions occur in
the combustion chamber of the lamp, the force of these ex-
plosions is broken by the solid metal chimney, and the danger
of flame being transmitted through the wire gauze is much less
than where the gauze 'chimney must withstand the full force of
the explosion within the lamp. This has always been con-
FIG. 53.
sidered as an important principle in safety lamp construction.
For some reason, however, the Mueseler principle has not
been generally adopted in the manufacture of safety lamps
in this country;
There are two types of the Mueseler lamp, known as the
English Mueseler, shown on the right in Fig. 53, and the
Belgian Mueseler, shown on the left. These types differ
only in the dimensions of. the central sheet-iron chimney.
The Belgian chimney is taller and narrower than that of the
English type. The tests of these two types of Mueseler have
MINE LAMPS AND LIGHTING 281
shown that the Belgian lamp is superior to the English type.
The former successfully withstood a current velocity of over
2800 ft. per min., while the English lamp failed at a velocity
of 1000 ft per min., the explosive condition of the current
being the same in each case.
The original Mueseler type of safety lamp has a horizontal
wire-gauze diaphragm, at the base of the gauze chimney.
This diaphragm separates the air in the combustion chamber
from that within the gauze chimney above, except for the
opening provided through the central metal chimney. The
failure of the English Mueseler at a comparatively low velocity
was probably due to the short and broad metal chimney
of that lamp, which provided an ample passage between the
combustion chamber and the gauze chimney above. The effect
of this was to counterbalance the protection afforded by the
gauze diaphragm separating these two compartments of the
lamp.
The Mueseler chimney, -as stated, in spite of its advantage
in increasing the security of the lamp, possesses the disadvan-
tage of decreasing its illuminating power, which is only from
0.20 to 0.40 cp. This type of lamp also possesses the dis-
advantage that it must be held in an erect position, as only a
slight deviation from the vertical interferes so seriously with
the circulation through the central chimney as to give op-
portunity for gas that accumulates between the gauze chimney
and the central tube, to enter the combustion chamber.
From this cause, explosions have resulted within the lamp and
caused its failure. Owing to the same conditions requiring
the lamp to be held in a vertical position, its flame is easily
extinguished by the burnt air and gases drawn into the combus-
tion chamber from the gauze-chimney above.
SPECIAL TYPES OF SAFETY LAMPS
Under the head of Special Lamps . may be classed those
designed for a special purpose only, such as testing for gas
for example, the Pieler, the Chesneau, the Ashworth, Stokes,
and the Clowes hydrogen lamps, besides lamps of the Wolf
282
MINE GASES AND VENTILATION
type designed to burn a volatile oil and the Beard-Deputy,
with the B-M sight indicator attachment for measuring small
percentages of gas with accuracy. These lamps will be
treated briefly, being modifications of the original types of
safety lamp described previously.
The Pieler Lamp. — This is a special Davy lamp designed to
burn alcohol and used for the purpose of testing for gas. The
alcohol flame, as is well known, is sensitive to gas to a high
degree The presence of Y± of 1
per cent, of gas in the air entering
the lamp elongates the alcohol flame
to a height of 3.2 in., while 1 J^> per
cent, of gas lengthens the flame hi
the Pieler lamp to a height close
to 7 in. Larger percentages of gas
than this cause the lamp to flame
and makes its use very dangerous
in coal-mining practice. In making
a test for gas with this lamp the
flame is first adjusted so that its tip
reaches the top of the conical shield
that surrounds the flame. The
height of this flame is 2 in.
Owing to the free circulation of
air in the Pieler lamp, as in the
original Davy, and the lengthening
of the alcohol flame, the gauze-
chimney of the Pieler lamp, as
shown in the illustration, Fig. 54, is increased to a height of
7.5 in. and made slightly conical. The lamp has four stand-
ards and is provided with a screen having horizontal slots
through which the height of the flame cap is observed and
measured. This screen is attached to two of the standards
of the lamp in a fixed position.
A slightly conical metal hood surrounds the flame of the
lamp and is of such height that the tip of the ordinary alcohol
flame just reaches the top of this hood. At times, the Pieler
lamp is bonneted, in which case a glass window is provided
FIG. 54.
MINE LAMPS AND LIGHTING
283
extending the full height of the bonnet and marked with a
scale for measuring the observed height of the flame in gas.
The Chesneau Lamp. — This lamp is very similar to the
Pieler lamp just described, except in a few details of construc-
tion. The lamp is bonneted and the air enters the lamp
through double-gauze openings at the bottom of the chimney.
A hollow sheet-metal cylinder surrounds the flame and sup-
ports the small gauze chimney, its purpose being similar to
that of the metal one in the Pieler lamp.
Like the Pieler, the Chesneau lamp is
designed to burn alcohol. In both of
these lamps cotton is inserted in the oil
vessel for the purpose of absorbing the
alcohol and preventing leakage in case
the lamp is overturned. However, the
absorptive power of the cotton is suf-
ficiently strong to modify the height of
the flame and affect the accuracy of the
determination of percentage.
Ashworth-Hepplewhite-Gray Lamp. —
This is a special form of lamp designed
to be used both as a working and a test-
ing lamp and which, at one time, attained
a considerable popularity in this country.
It is designed after the Gray lamp, so
widely used in England. As appears in
the illustration, Fig. 55, its principal
features are: The hollow brass tubes that
serve as standards for the support of the
cylindrical brass bonnet surrounding the gauze chimney.
These standards are arranged to draw the air from the top
of the lamp when testing for a thin stratum of air at the roof
of a mine airway or room. There are openings at the bottom
of these hollow standards that can be closed by sliding muffs
when it is desired to test for gas Otherwise, these openings
are exposed to the free admission of the air to the bottom of
the lamp. At thet op of the lamp, the standards are affixed
to a brass plate to which the bale or handle of the lamp is
FIG. 55.
284
MINE GASES AND VENTILATION
ALCOHOL
VESSEL
attached. Another sliding plate fits closely over the first and
is arranged to close the open ends of the standards when the
lamp is used as a working lamp.
The A.-H.-G. lamp is designed to burn ordinary sperm,
cottonseed or lard oil. The conical glass chimney has the
advantage of throwing the light upward on the roof. The
illuminating power of the lamp is 0.79 cp. When tested,
this lamp has withstood a current velocity of 6000 ft. per min.,
which is one of the features that
strongly recommended its use in this
country.
Stokes Alcohol Lamp. — This lamp
is designed by an English mine in-
spector, whose purpose was to supply
an alcohol flame in an oil burning lamp,
the oil flame to be used when the miner
was working at the face, and the
alcohol flame to be used for testing
for gas. The lamp is an Ashworth-
Hepplewhite-Gray lamp having n
small vessel for holding the alcohol
when the lamp is to be used for test-
ing for gas. As shown in the illustra-
tion, Fig. 56, this alcohol vessel is
screwed into the bottom of the reg-
ular oil vessel of the lamp, its long
slim wick tube passing up through a
hollow tube fixed in the oil vessel of
the lamp. In no other respect does
the lamp differ from an A.-H.-G. lamp. When the Stokes,
lamp is to be used for testing for gas, the alcohol vessel is
screwed in place beneath the oil vessel. The oil flame is drawn
down and the lamp tilted slightly to ignite the wick of the
alcohol lamp, after which the oil flame is extinguished. The
lamp is then ready for testing for gas.
The Clowes Hydrogen Lamp. — -This lamp is also a modified
Ash worth-Hepple white-Gray lamp. Like the Stokes lamp, it
is provided with an oil vessel and burner and a second burner
OIL VESSEL with
ALCOHOL VESSEL
inserted -from below
FIG. 56.
•MINE LAMPS AND LIGHTING
285
to which hydrogen gas is supplied from the strong brass
cylinder shown in the illustra-
tion, Fig. 57, and which can be
attached to or detached from
the lamp, as desired. There are
but few of this type of lamp in
the country where it has seldom
been used, as it is heavy and
cumbersome. The hydrogen
flame, though extremely sensi-
tive to gas, is easily extinguished
when testing and the use of the
lamp for that purpose requires
extreme care and caution. A
small scale with crossbars is at-
tached
to the
oil V6S- FIG. 57. — Oil Vessel and Hydrogen
| .for Cylinder Removed from Lamp.
the purpose of observing and estimat-
ing more accurately the height of the
flame in testing.
Hydrogen gas is compressed to 120
atmospheres or a pressure of 1800 Ib.
per sq. in. at sea level. This furnishes
an ample supply for making a large
number of tests in the mine. The gas
cylinder is attached to the side of the
oil vessel by a screw joint or union.
A valve controls the flow of gas into
the lamp when it is desired to make a
test in the mine. The oil flame is then
drawn down and extinguished after
the hydrogen has been turned on and
5g ignited in the lamp.
The Wolf Lamp. — The original
Wolf lamp shown in the illustration, Fig. 58, is a German
product that was widely introduced into this country and
280
MINE GASES AND VENTILATION
FIG. 59.
MINE LAMPS AND LIGHTING
287
PAKT OF HISTORICAL COLLECTION
howrny fAKLY TYPES OF SAFETY LAMPS
FIG. 60.
288 MINE GASES AND VENTILATION
became very popular as a working lamp. At the present
time, there are a number of lamps of this type in use and
manufactured in this country, among which may be mentioned
the Koehler, the American deputy, the Hughes acetylene lamp,
and many others . All of these, like the Wolf lamp, are designed
to burn a volatile oil contained in a strong oil vessel of pressed
steel, in which absorbent cotton is placed to retain the oil and
minimize the danger of leaking should the lamp be overturned.
The volatile oil flame is particularly sensitive to gas, which
enables this lamp to show gas when less than 1 per cent, is
present in the mine air. A volatile oil, however, cannot be
recommended for the purpose of testing for gas, owing to the
fuel cap that is often mistaken for a gas cap when no gas is
present. Owing to the ease with which a volatile oil flame is
extinguished in the mine, all such lamps are provided with
igniters. The original Wolf lamp is claimed to have an il-
luminating power of 1.45 cp., while the average of this type
of lamp will but slightly exceed a single candlepower.
On the two pages preceding will be found most of the impor-
tant types of mine safety lamps grouped in a historical setting
that cannot fail to be of interest in connection with the
subject. These appear as Figs. 59 and 60.
PERMISSIBLE MINE SAFETY LAMPS
In " Schedule 7, issued by the Federal Bureau of Mines, the
engineers of the bureau have defined what is to be understood
as a " permissible " miners' safety lamp in the following words:
Definition. — The Bureau of Mines considers a miners' safety lamp to
be permissible for use in gaseous mines if the details of the construction of
the lamp are the same as those of the type of lamp that has passed the
tests made by the bureau and hereinafter described.
Conditions of Testing. — The conditions under which the Bureau of
Mines will examine, inspect, and conduct tests on miners' safety lamps
are as follows:
1. The examination, inspection and tests will be made at the experi-
ment station of the Bureau of Mines, at Pittsburgh, Pa.
2. Applications, for inspection, examination and test shall be made to
the Director, Bureau of Mines, Washington, D. C., and shall be accom-
panied by a complete description of the lamp and a set of drawings
showing all the details of the lamp's construction.
MINE LAMPS AND LIGHTING 289
3. The applicant for the inspection, examination and test will be
required to furnish two lamps of each type, which shall be sent prepaid
to the Engineer in Charge of Lamp Testing, Bureau of Mines, Fortieth
and Butler Streets, Pittsburgh, Pa., and will be retained by the bureau
as a laboratory exhibit.
Each lamp shall have marked on it in a distinct manner the name
of the manufacturer and the name, letter or number by which the
type is designated for trade purposes, and a statement shall be made
whether or not the lamp is ready to be marketed; also a statement
describing the fuel used, its trade name and properties. The appli-
cant may supply t he fuel for the test if he so desires.
4. Upon the receipt of a lamp for which application has been made
for examination, inspection or test, the engineer in charge of lamp
testing will advise the applicant whether additional spare parts are
deemed necessary to facilitate a proper test of the lamp, and the appli-
cant will be required to furnish such parts as may be requested.
5. No lamp will be tested unless the type submitted is in the com-
pleted form in which it is to be placed on the market.
6. Only the engineer in charge of lamp testing, his assistants and
one representative of the applicant will be permitted to be present during
the conduct* of the tests.
7. The conduct of the tests shall be entirely under the direction of
the bureau's engineer in charge of the investigation. The tests will
be made in accordance with a predetermined schedule, which is outlined
herein.
8. As soon as possible after the receipt of the formal application
for test, the applicant will be notified of the date on which his lamp
will be tested and the amount and character of additional material it
will be necessary for him to submit.
9. The tests will be made in the order of the receipt of applications
for test, provided the necessary lamps and material are submitted
at the proper time.
10. The details of the results of the tests shall be regarded as confiden-
tial by all present at the tests and shall not be made public in any way
prior to their official announcement by the Bureau of Mines.
11. The results of tests made on lamps that fail to pass the require-
ments shall not be made public but shall be kept confidential, except
that the person submitting the lamp will be informed with a view of
possible remedy of defects in future lamps submitted; but such changes
other than changing the glass globe or chimney, will not be permitted
while the testing is in progress.
12. Tests will be made for manufacturers, manufacturers' agents,
state mine inspectors and mine operators.
13. A list of permissible lamps and the results of their tests will
be made public, from time to time, by the Bureau of Mines.
14. The glass globe or chimney shall be marked in a distinct manner
by a name or design by which its type is designated for trade purposes.
290 MINE GASES AND VENTILATION
Mechanical Tests. — The following mechanical tests will be
applied to every lamp submitted to the bureau to ascertain its
strength and resistance under the rough usage common to
mining work.
1. The lamp is dropped, by means of a mechanical arrangement,
onto a wooden floor, from a height of 6 ft. measured from the floor to the
bottom of the lamp, which has been fitted together complete with the
glass, a component, part of the lamp.
Five successive trials are made, the lamp being fitted with a dif-
ferent glass each time. The lamp passes the test if the glass is broken
in not more than one of the five trials. Should the glass be broken
in two but not more than two of the five trials, the lamp is submitted
to five more trials with fresh glasses and if the glass breaks in two of them
the lamp will be considered as having failed to pass the test.
2. A weight of 5 Ib. is dropped, from a height of 6 ft., onto the lamp
standing vertically on a wooden platform beneath the weight,.
The height of 6 ft. is measured between the bottom of the weight and
the top of the lamp. The weight is a lead disk 3 in. in diameter and 1%
in. thick and is dropped mechanically.
Should the glass of the lamp break, two more trials are made, each
with a different glass, and if the glass breaks in either the second or
third trial the lamp will be considered as having failed to pass the test.
3. A weight of 10 Ib., attached to a cord the other end of which is
secured to the bottom of the lamp, is dropped a distance of 6 ft., the lamp
being suspended at a height of 7 ft., from the ground.
The lamp is gripped by means of claws, or slung by means of straps
fastened around its upper part, above the standards protecting the
glass. A plate is fastened to the bottom of the lamp and the cord is
attached to the center of this plate. The weight is a lead disk 4%
in. in diameter and l^ in. thick. It is dropped mechanically.
This test is repeated three times. If, as the result of any one of
these three trials, the security of the lamp is found to be defective in
any way the lamp will be considered as having failed to pass the test.
Tests 1, 2, and 3 are to be made in succession on one lamp. Crack-
ing of the glass will be regarded as a breakage.
Photometric Test. — The lamp is required to give a minimum candle-
power of 0.30, as compared with a pentane standard, during a period of
10 hours.
Explosion Test. — After a lamp has passed the mechanical tests, it will
be tested by placing the lighted lamp in an explosive mixture of gas and
air, as follows:
1. In currents of air and gas containing 8% per cent, of natural gas
drawn from the Pittsburgh gas mains. In a gallery (lamp gallery
No. 1) a lamp which has passed the mechanical tests is tested, with a
MINE LAMPS AND LIGHTING 291
fresh glass if necessary, in horizontal, inclined and vertical currents
of the explosive mixture of gas and air:
a. In a horizontal current, velocity 600 to 2500 ft. per min.
b. In a 45 deg. descending current, velocity 600 to 2500 ft. per min.
c. In a 45 deg. ascending current, velocity 600 to 2500 ffc. per min.
d. In a vertical descending current, velocity 600 to 2500 ft. per min.
e. In a vertical ascending current, velocity 600 to 2500 ft. per min.
Trials will be made at velocities of 600, 800, 1000, 1200, 1500, 2000,
and 2500 ft. per min. Into the horizontal current moving at 1500 ft.
per min., the lamp will be suddenly thrust from below.
The duration of each trial is two minutes and each trial is repeated
three times. An ignition exterior to the lamp will cause the lamp
to be rejected.
2. In a still atmosphere (lamp gallery No. 3) containing 8>£ per cent,
of natural gas. The lamp is placed, with a fresh glass if necessary,
in this inflammable atmosphere for three minutes. Five separate
determinations will be made. An ignition exterior to the lamp will
cause the lamp to be rejected.
Tests of Glasses. — 1. A weight of 1 ,lb. is dropped by means of a
mechanical arrangement, from a height of 4 ft., upon the glass placed in a
vertical position on a wooden floor. The weight is a lead disk 2^ in. in
diameter ^ in. thick. Twenty glasses of any one kind will be tested.
Two failures in the twenty will cause the glasses to be rejected.
2. Ten glasses are heated in an air balh to a temperature of 212 deg. F.
and when at that temperature are removed from the bath and plunged
into water at a temperature of 60 deg. to 65 deg. F. One failure in
ten will cause the glasses to be. rejected.
If the lamp has two glasses the outer glass will be tested by mechan-
ical means only and the inner glass by heating onlv.
Igniter Tests. — Lamps having internal igniters will be tested to deter-
mine the safety and permissibility of the ignifcer device: The permissi-
bility of the lamp will be dependent in part on the result of the teste of the
igniter device.
These tests will be made to determine the liability of external ignition
when the igniter device is operated in the presence of inflammable mix-
tures of gas and air under such conditions as may be determined by the
engineer in charge of lamp testing, for each type of igniting device.
Tests will be made to determine :
1. If external ignition is possible when the igniter is operated in
still and moving currents of gas and air mixtures.
2. To determine if the residue left in the lamp after working the
igniter device is a source of danger in subsequent use of the lamp in
inflammable mixtures of gas and air.
3. To determine the nature of the material used in -the igniter device.
The igniter will have passed the tests if no external ignition is caused
by manipulating the igniter when in position within a double-gauze
292 MINE GASES AND VENTILATION
safety lamp, or if no external ignition is caused by the use of the lamp
in inflammable mixtures of gas and air after the igniter has been in
service.
Applicants for tests will be required to furnish two complete igniter
devices and 5 dozen igniter refills, which shall be shipped in sealed
boxes or packages with the trade name written on the outside and
addressed to the Engineer in Charge of Lamp Testing, Bureau of Mines,
Pittsburgh, Pa. When known by the applicant, the proximate chemical
composition of the igniter tape or point should be furnished and the
place of its manufacture.
Note. — The inflammable gas used in these series of tests will be the
natural gas supplied to the city of Pittsburgh The composition of this
gas is approximately: Methane, 83.1 per cent. ; ethane, 16 per cent. ; nitro-
gen, 0.9 per cent. ; carbon dioxide, a trace.
Lamps in the course of development may be submitted by manu-
facturers for inspection and preliminary tests, with a view to ascer-
taining defective construction or the misapplication of safety principles.
The nature of such inspection and tests will be determined by the
engineer in charge of lamp testing.
Approval of Safety Lamps. — The manufacturers of such types of lamps
as have passed the tests of the bureau may attach a plate containing, or
stamp into the metal of the lamp, the following inscription:
PERMISSIBLE MINERS* SAFETY LAMP.
U. S. BUREAU OF MINES APPROVAL NO. .
Before claiming the bureau's approval of any modification of any
approved type of lamp, the manufacturer shall submit to the bureau
drawings that show the extent and nature of such modifications. Each
approval of a permissible lamp will be given a serial number, and ap-
provals of modified types will bear the same serial number as the original,
with the addition of the letters a, b, c, etc.
The bureau will, on application, make separate tests of glasses manu-
factured for use in connection with any lamp that has been approved
by the bureau under the provisions of this schedule. Glass globes that
fulfill the requirements of the tests will be approved for types manu-
factured in every particular like those submitted that passed the test.
The bureau will, on application, make separate tests of internal
igniter devices for use with any type of lamp that has been approved
by the bureau under the provisions of this schedule. Igniters that
fulfill the requirements of the tests will be approved for types manu-
factured in every particular like those submitted that passed the tesl .
The bureau's approval of any lamp shall be construed as applying
to all lamps of the same type as tested, made by the same manufacturer
and having the same construction in detail, but to no other lamp. The
MINE LAMP 8 AND LIGHTING 293
bureau reserves the right to rescind, for cause, at any time, any ap-
proval granted under the conditions herein set forth.
Notification to Manufacturer. — As soon as the bureau's engineers are
satisfied that a lamp is permissible the manufacturer, agent or applicant
and the mine inspection departments of the several states shall be notified
to that effect. As soon as a manufacturer receives formal notification
that his lamp has passed the tests prescribed by the Bureau of Mines, he
shall be free to advertise such lamp as permissible.
Fees for Testing. — Careful investigation has been made regarding the
necessary expenses involved in testing miners' safety lamps at the Pitts-
burgh experiment station, and the following schedule of feesto be charged
on and after February 15, 1915, has been established and approved by
the Secretary of the Interior, in accordance with the provisions of the
statute previously quoted:
Preliminary inspection and test $10. 00
Complete lamp test 50 . 00
Candlepower test 5 . 00
Separate glass globe tests 5 . 00
' Separate igniter tests 10 . 00
The fees specified above may be increased to cover the cost of test-
ing an unusually complicated type of lamp, .and are also subject to
change upon the recommendation of the Director of the Bureau of
Mines and the approval of the Secretary of the Interior.
USE AND CARE OF SAFETY LAMPS
No safety lamp, however perfect, is safe when improperly
used; nor has the safety lamp yet been devised that is fool-
proof. For these reasons, a safety lamp should never be en-
trusted to an incompetent or an unreliable person. With the
single exception of the lamps used by the mine examiners or
firebosses, all lamps used in a mine should be the property and
care of the operator.
The Lamphouse or Station. — A lamphouse or lampstation
should be established convenient to the mine entrance, where
the miners can secure their lamps when entering the mine
and return the same on coming to the surface. Each lamp
should be stamped with a number and, as far as practicable,
the same lamp should be given to the same man, each day, and
he be made responsible for its use and condition.
The lamphouse should be in charge of a competent man and
one or more assistants, whose duties would be to receive and
204 MINE GASES AND VENTILATION
deliver all lamps in return for checks bearing the lamp number.
No lamp must be given out, except in return for this check,
which should be placed in the pigeonhole from which the
lamp is taken or hung on its hook ready to be given back to the
man when his lamp is returned at the close of the shift.
A properly organized and arranged lamphouse will have one
or more lampracks with holes or .hooks for the lamps. Each
hole or hook has a number corresponding to that on the lamp.
Tables are provided where the lamps can be taken apart,
cleaned, filled and trimmed, after which they are carefully
assembled, inspected and returned to their respective places
in the rack.
The oil for filling the lamps should be drawn from a tank or
reservoir outside of the building. No oil container other than
the lamp vessels should be permitted in the lamphouse or sta-
tion, which should be of fireproof construction and kept free
from all accumulations of oily waste or other material liable
to spontaneous combustion. The presence of a man's lamp or
check on the lamprack will indicate whether he has come out or
is still in the mine and will thus serve the same purpose as a
checking board, in that respect.
No one must be permitted in the lamphouse other than those
in charge. All lamps should be delivered through one or more
windows opening on a passageway. The work of delivering
and receiving lamps, where a large number of men are em-
ployed, will be greatly expedited if there are several windows,
each corresponding to a division in the numbering of the lamps.
A further advantage in such an arrangement is that each divi-
sion can be in charge of a man who is responsible for the lamps
in that division.
Handling of Safety Lamps. — A safety lamp must never be
given to a man who has not been instructed and drilled in re-
spect to its use. Before being entrusted with a safety lamp,
a man must show his ability to determine the presence of gas,
by observing the flame cap formed in his lamp. He should be
taught how to proceed when he has observed a cap in his lamp,
and cautioned to carefully lower his lamp and withdraw quietly
but promptly from the place.
MINE LAMPS AND LIGHTING 295
•
The man should be shown how his lamp may flame should
a larger proportion of gas be present in the air. He should be
instructed, in that case, as to the necessity of maintaining his
presence of mind and making no quick movement with the
lamp, which must be withdrawn promptly but cautiously from
the gas, by lowering the lamp toward the floor. The man
should be further cautioned in regard to the danger of dis-
turbing a body of gas, which may then surround him and make
it difficult for him to escape with safety.
A safety lamp must always be held in an upright position
and protected against a rush of air such as follows a blast in
the mine. It is necessary to protect the lamp when walking
against a strong air current. A lamp should never be swung,
but should be held quietly at one's side when going from place
to place in the mine. Care must be taken not to drop the
lamp or permit it to fall. Under no circumstances must a man
tamper with his lamp or attempt any experiment. If the
lamp is accidentally extinguished, the man's duty is to proceed
at once to the nearest relighting station, which should be pro-
vided at a convenient point in the mine.
TESTING FOR GAS BY INDICATORS
The work of testing for gas is the most important work to
be performed in the operation of a gaseous mine and can only
be safely entrusted to a mine examiner, fireboss or deputy who
has had experience both in the testing and the handling of gas.
The examination of a mjne for gas and other dangers must be
performed conscientiously and faithfully. The work will not
permit of the taking of chances, as the life of every worker in
the mine depends on the thoroughness and capability of the
examiner.
From time to time, different means have been employed in
making the test for gas in mine workings. These consist in
various forms of indicators and detectors especially designed
to reveal the presence of gas in mine air and ascertain its per-
centage. Besides these appliances, a few of which will be
described briefly, there is the old-established flame test, made
by the use of the Davy or other safety lamp, and which is
296 MINE GASES AND VENTILATION
•
still the most largely employed by mine examiners and fire-
bosses.
Numerous Gas Indicators.— Perhaps the earliest attempt to
devise a means of indicating the percentage of gas present in
air consisted of a glass tube into which had been fused a
platinum wire that could be rendered incandescent by an
electric current. A sample of the air to be tested was drawn
into the tube where the gas contained in the air was consumed
by the incandescent wire. The volume of the remaining gases
was then measured. Comparing this with the original volume
of gas and air gave the percentage of gas present in the air.
Devices of this nature, however, were never of practical value,
until the recent design of such a gas detector by George A.
Burrell, of the Federal Bureau of Mines, which will be described
later (see p. 299).
Another device depended on the increase of pressure in an
air container that was separated from a similar container of
gas and air by a porous partition through which diffusion of
the gas into the air took place. The resulting increase of
pressure in the first container was an index of the percentage
of gas present in the sample tested, but the device had no
practical value for use in mines. Still another device depended
on the rise in temperature caused by the absorption of gas by
platinum black, which coated the bulb of one of two ther-
mometers. The rise in temperature thus indicated furnished
the means of determining approximately the percentage of
gas present. Again, another device depended on the com-
pression of a sample of gas-charged air contained in a strong
glass tube into which was fitted a piston. The rapid compres-
sion of the air in the tube would ignite the gas and cause a
flash when not less than 5 per cent, of gas was present.
The Liveing indicator was a more accurate means of deter-
mining percentages of gas, but this also never came largely
into use. Two platinum wires of equal resistance were ren-
dered incandescent by an electric current. One of these wires
was inclosed in a tube containing a sample of the air to be
tested, while the other wire was in pure air. An ingenious
sliding arrangement of the two tubes containing the wires
MINE LAMPS AND LIGHTING 297
provided a means of comparing their relative brilliancy, which
furnished a suggestion of the percentage of gas present in the
air tested. None of these devices, however, can be considered
of any. practical importance in coal mining.
The Shaw Gas Machine. — This machine, though not of
portable form, on which account it could not be tak^n into
the mine but samples of air to be tested must be brought to the
surface, furnished a means of correctly determining the ex-
plosibility of samples of air collected in the mine workings.
For this purpose, it was formerly used at many large collieries.
The disadvantage in its use lay in the fact that a test could
not be made on the spot and time must elapse between the
taking of the sample of air and knowing the results of the test.
In that time, conditions in the mine might materially change,
which rendered the test valueless for the purpose intended.
The Shaw machine consists of two cylinders whose volume
ratio is known. Both cylinders are fitted with air-tight pis-
tons operated by a single lever arm. By this means exact
proportions of gas and air can be pumped into a combustion
chamber where they are ignited when the mixture becomes
explosive. A graduated scale indicates the volume percentage
of air and gas present when explosion occurs.
In the operation of this machine, it is first necessary to
standardize an artificial gas supply to ascertain the lower ex-
plosive limit of the gas. To do this the machine was arranged
so that the larger cylinder would pump pure air while the
smaller one pumped gas, and the point noted when explosion
occurred. This having been done, the tube that formerly
supplied pure air to the larger cylinder is now connected with
the bag containing the sample of mine air to be tested, while
the smaller cylinder continues to pump its proportion of the
standard gas. Evidently, a less ratio of the supply from the
two cylinders will now be required to produce an explosion,
should the air pumped by the larger cylinder contairi some gas.
The difference shown on the graduated scale gives the percen-
tage of gas present in the air tested.
The Beard-Mackie Sight Indicator. — This is a simple and
extremely practical device designed to be attached to the
298
MINE GASES AND VENTILATION
burner of a safety lamp burning sperm, cottonseed or lard oil
but* not a voltaile oil. As shown on the right, in the illus-
tration, Fig. 61, the device consists of a U-shaped support
mounted on a small brass disk that fits over the burner and
is held in place by the screw nipple of the lamp. On this sup-
port are arranged fine platinum wires at fixed heights above the
lamp flame.
The lower straight standard wire is for the purpose of stand-
ardizing the flame, which
is raised to a height just
sufficient to incandesce
that wire. This must
be done in pure air, al-
though a slight altera-
tion in the height of the
flame produces no prac-
tical effect in determin-
ing the percentage of gas
by the incandescence of
the successive percent-
age wires when the lamp
is taken into the mine.
Indeed, the standardiz-
ing of the flame is gener-
ally done after entering
the mine when the ex-
aminer has once become
FlG 61 acquainted with the use
of this indicator.
The percentage wires are each looped at the center, the
purpose being to make their incandescence more perceptible
when observed through the gauze of the Davy lamp, as shown
on the left of the figure. The incandescence mounts higher
in the percentage wires as the proportion of gas in the mine air
increases and the uppermost wire incandesced determines the
percentage of explosibility of the mine air.
The use of the sight indicator furnishes the means of deter-
mining with considerable ~ accuracy the explosibility of mine
DAVY LAMP
WITH
SIGHT INDICATOR
BEARD-MACKIE
S/GHT INDICATOR
FOR DETECT/NQ GAS
MINE LAMPS AND LIGHTING
299
air, at the point and at the moment the test is made. Its
use eliminates the necessity of the fireboss guessing the per-
centage from the height of the flame cap observed in his lamp.
It enables a just comparison to be made between the reports of
different firebosses whose judgment may differ, or who may
not be equally capable of discerning the caps formed in their
lamps.
With proper care, the sight indicator can be used, for a year
or more, by a fireboss when making
his morning examination of the mine.
Its construction is naturally some-
what delicate, which requires it to be
carefully handled when being inserted
or taken out of the lamp. A careless
fireboss will often permit his lamp to
smoke and carbonize the wires, which
interferes with their delicacy. The
same effect is caused by burning a
poor quality of oil or oil mixed with
kerosene, which increases the smoki-
ness of the flame.
The advantages derived by the use
of the indicator are that it standard-
izes all tests for gas, making them
comparable. It eliminates the guess-
ing of the height of a flame cap and
the percentage of gas indicated there-
by. It indicates the presence of gas
as low as one-half of 1 per cent. The
indications are plainly visible by the incandescence of the
looped wires. The presence of an indicator in a lamp has
often avoided the extinction of the lamp in gas and reduces
the tendency to internal explosion in the lamp. Finally, all
indications are made with a normal flame, which not only
saves time but avoids the necessity of lowering the flame and
possibly extinguishing it when making a test.
The Burrell Gas Detector. — This -device, which is shown in
section in the illustration, Fig. 62, consists of a brass tube A
FIG. 02.
300 MINE GASES AND VENTILATION
surmounted by a screw cap P equipped with a valve V, a
little cup K and two binding posts M and N. Connected
with and supported by the latter is a fine platinum-wire bridge
F, which can be rendered incandescent by the current from an
electric battery. A stout gage-glass C is surmounted by a
brass reservoir or cap H to which a rubber tube R is attached.
Both the gage-glass C and the brass tube A are set into an
aluminum base X, by which they are connected, forming a
U-tube after the manner of a water gage. A graduated scale
0 provides the means of measuring the height of water column
in the gage-glass.
In the use of this instrument for the detection of mine gas in
the workings, the brass cap P is unscrewed and water poured
into A, until it rises in the gage-glass to a level indicated by the
zero of the scale at S. This level corresponds to the level Q
in the brass tube A, just below the platinum wire F.
When a test is to be made in the mine the valve V is first
opened and the operator blows gently into the rubber tube R,
depressing the water level in the gage-glass and causing it to
rise in the brass tube, until it appears in the little cup K,
or until a slight click of the valve V tells that the water has
completely filled the combustion space Y, in the top of the
brass tube. The rubber tube attached at R is now pinched
with the fingers and the instrument raised to the roof or into
the cavity where it is desired to test the air for gas. In that
position, the rubber tube is released and the water level at
once falls in A and rises iri C to where it originally stood
at zero of the scale. By this action, the air to be tested is
drawn in through the open valve V and fills the combustion
space Y above the water level Q.
When equilibrium is established, the valve V is closed and
the battery current switched on, causing the incandescence of
the wire bridge F, which is plainly observed through the
small glass window E. About 1 J^ min. is required to consume
all the gas present in the air contained in the combustion space
above the water. The current is now turned off and the in-
strument shaken, for the purpose of cooling the air and gaseous
products of the combustion, and permit of their volume being
MINE LAMPS AND LIGHTING 301
measured at the original temperature. As cooling takes place,
the water rises in A arid falls in the gage-glass, until it becomes
stationary at a certain level. The graduation at that point
will show the percentage of gas that was present in the air
tested. The aluminum scale 0 is easily removable and is
graduated for the detection of any combustible gas or vapor.
The two scales that appear in the figure are for hydrogen (H)
and carbon monoxide (CO).
This instrument has proved quite effective for the purpose
intended in its design. There is no doubt but that some of the
carbon dioxide produced by the combustion of the gas is
absorbed in the water when the instrument is shaken; but this
is probably largely compensated by the slightly higher water
level in A above that in the gage-glass C, at the time the mea-
surement is taken. This difference of level is, moreover, ren-
dered extremely slight by reason of the relatively larger diameter
of the tube A, as compared with the bore of the gage-glass C.
Actual tests of the results obtained in the mine, by comparison
with the analysis of the same air, in the laboratory, show the
following percentages which are not exceptional.
By detector
By analysis
0.4
0.45
0.7
0.57
0.9
1.11
1.6
1.61
1.9
1.23
1.5
1.93
2.5
2.52
2.0
1.46
2.2
2.54
For all practical purposes, the slight differences shown by
these figures between the tests made in the mine and the
analyses made in the laboratory are immaterial.
THE FLAME TEST
From the earliest time, the most universal method of testing
for gas in mines has been that of observing the effect of the
gas on the flame of a safety lamp. As is well known, in every
candle, or lamp flame burning oil, there are three zones as
indicated in the illustration, Fig. 63. The inner zone A is
dark, being filled with the hydrocarbon vapors formed by the"
vaporization of the oil. There is no combustion taking place
in this zone. The heat of the flame dissociates the hydrogen
and carbon of these vapors, and the second zone B is rendered
302 MINE GASES AND VENTILATION
luminous by the incandescent carbon particles, which there
undergo combustion. The remaining hydrogen and the car-
bon monoxide resulting from this combustion pass into the
outer zone C where they burn with a non-luminous flame,
supported by the surrounding air which here has free
access to the flame. Owing to the brightness of the second
zone B, caused by the incandescence of the carbon par-
ticles, it is difficult to discern the non-luminous envelope
surrounding it and forming the third zone C.
Flame Caps. — 'When a lamp flame is lowered, almost to its
point of extinction, the surrounding air so closely approaches
the wick that the hydrocarbon vapors are consumed without
the incandescence of the carbon. The dark zone is here
greatly reduced, while the
second luminous zone is
practically eliminated, lea-
ving a small non-luminous
flame covering the wick, as
shown in the lower right-
hand corner of the figure.
Just above, in the upper
right-hand corner, the
flame is shown as slightly
FIG 63 increased in size by raising
the wick a trifle. There
now appears a small luminous zone surmounted by a non-
luminous cap, which can be readily discerned. This cap is
known as a "fuel cap," being due solely to the combustion of
the vaporized oil. This fuel cap is often mistaken for a gas
cap when testing for gas with a reduced flame.
The description given thus far refers to a flame burning in
pure air. Now, when a lamp flame is burning in air charged
with a small percentage of a combustible gas, as methane
for example, the gas in contact with the flame is consumed.
At the same time, the outer zone of the flame is lengthened and
rendered more luminous than before because of its increased
size, and there now appears what is known as the "gas cap"
or more commonly "flame cap."
MINE LAMPS AND LIGHTING
303
The height of the flame cap varies with the percentage of
gas present in the air, the kind of lamp employed and the oil
or luminant burned therein. The visibility of the cap is
greatly assisted by the free access of air to the combustion
chamber of the lamp. The air should enter the lamp at a point
below the flame; in other words, the ventilation in the com-
bustion chamber should be ascensional. Any other arrange-
ment interferes decidedly with the clear observance of the cap.
DIAGRAM OF LAMP
FLAMES
Top of Pieler Gauze
TABLE GIVING HEIGHT OF FLAME CAP OR ELONGATION OF FLAME FOR DIFFERENT
LAMPS ILLUMINANTS AND PERCENTAGES OF METHANE IN AIR
LAMP
ILLUMINANT
PERCENTAGE OF GAS
>4
k
1 I |!» I 2 I 2'4l 3 1 4 | 5
b
HEI6HT OF CAP OR FLA
ME. (INCHES
UN80NNETED
DAVY
SPERM. LARD
022
0.43
0.75
1.75
3.5*
MNNETED
DAVY
SEED OIL
0.?2
058
0.88
1.8
3.0*
WOLF
NAPHTHA
035
0.40
0.52
072
1.16
2.76
CLOWES
HYDROGEN
0.90
1.10
1.20
1.40
1.75
2.30
PIELER
ALCOHOL
1.2
2.00
3.00
4DO
5.00*
lamp flames beyond this poini-
^r^$i^$f^$$:$f:^$^K^^'^&»
^ Lamp flames and(
confinest>urnfgas
PERCENTAGE OF METHANE IN AIR
FIG. 64.
A dark background in the lamp also renders a cap more plainly
visible.
The effect of the form of the lamp and the illuminant burned,
to produce a given height of cap, for a given percentage of gas,
is clearly shown in the lamp diagram, Fig. 64. The tall gauze
chimney, free access of air and the alcohol burned in the Pieler
lamp very greatly increase the height of the flame, in the use
of that lamp, for the same percentage of gas present. On the
other hand, the bonnet of the Clowes lamp burning hydrogen,
or the Wolf lamp burning naphtha, materially reduce the
304 MINE GASE& AND VENTILATION
height of flame cap formed in these lamps, notwithstanding
the volatile nature of the illuminants burned. The effect of
the bonnet in the Davy lamp burning sperm, lard or cotton-
seed oil is clearly shown to reduce the height of the cap, for
the same percentage of gas, as compared with that obtained
in the unbonneted Davy.
The preceding diagram is of interest in connection with the
use of different types of safety lamps burning hydrogen,
alcohol, naphtha, or a non-volatile oil, as sperm, lard or cotton-
seed oil, in testing for gas. The height of flame cap, or the
elongation of the flame, produced by different percentages
of gas, in the use of different lamps is tabulated, in the upper
right-hand corner of the diagram.
The heights of flame cap given in the diagram, for the Davy
and Wolf lamps, are the minimum caps produced by drawing
down the flame to its lowest point. The heights given for
the Clowes (hydrogen) lamp and the Pieler (alcohol) lamp
are for the elongation of the flame due to the gas. The original
flame of the Clowes lamp is 0.3 in., while the flame of the
Pieler lamp is adjusted so that its tip just reaches the top
of the shield, at a height of 2 in., as shown in Fig. 64. (See
description of Pieler lamp, p. 282.)
The presence of other gases or dust will, of course, modify
the results shown in this diagram. The effect of carbon
dioxide is to diminish the length of the flame and obstruct
the formation of the cap. On the other hand, carbon monoxide
and dust when present in the air lengthen the flame and assist
the formation of a cap.
Calculation of Height of Flame Cap. — For a Davy lamp,
burning sperm or cottonseed oil of good quality, in an atmos-
phere charged with pure methane or marsh gas, experiments
have shown that the height of flame cap varies as the cube of
the percentage of gas present. Using a bonneted Davy
burning colza oil, William Galloway has estimated the height
of flame cap to be J'fo of the cube of the percentage of gas
present in the air surrounding the lamp
In a long series of experiments under favorable conditions,
the author found when using an unbonneted Davy lamp
MINE LAMPS AND LIGHTING
305
burning sperm oil the height of flame cap was J^g of the cube
of the percentage of gas present in the feed air entering the
lamp. The height of cap was accurately measured by a scale
in the lamp, and the percentage of gas in the air was obtained
by the use of a Shaw gas machine, which drew the air from
the testing chamber in which the lamp was placed and which
was ventilated by a continuous current of air charged with
the gas. The arrangement eliminated the effects that would
otherwise have been produced by accumulation of the products
of combustion in the lamp chamber.
I'-1
4)
42
s: —
Standard':
Reduced Flame
Percentage
FIG.
3
of
4
G a s in
Air
The results are expressed by the following formulas, giving
the height of flame cap h for any percentage of gas J:
J3
Unbonneted Davy, sperm oil (Beard), h = ^
ou
J3
Bonneted Davy, colza oil (Galloway), h = ^
The appearance of the flame and the height of cap, for dif-
ferent percentages of gas, as derived from the author's experi-
ments, are shown in the illustration, Fig. 65. These tests
were made with the flame reduced to a height of %6 m- It
will be observed that, as the height of the flame increases,
its volume is enlarged. At about 3.5 per cent, of gas, the flame
20
306 MINE GASES AND VENTILATION ,
became unsteady and, as the percentage of gas was increased
above that point, the flame became more voluminous, rotating
in a wierd manner about the gauze, then expanding at the top
into a fan-shape and finally filling the gauze chimney with
flame.
Beyond this point, the flame has been frequently seen to
leave the lampwick, while the gas continued to burn in the
upper portion of the chimney. When this occurred with a
sight indicator in the lamp, the flame would relight the wick
as the percentage of gas was reduced, all of the percentage wires
of the indicator being then brightly incandescent. The
same action has been observed by the author when holding
an unbonneted Davy, equipped with sight indicator, exposed
to a strong gas feeder. At that time, slight explosions occurred
within the gauze, but the lamp was not extinguished when
carefully withdrawn from the gas.
Making a Test for Gas in the Mine. — When approaching
a place where gas is suspected, one must move quietly so as
not to unnecessarily disturb the gas from its lodgment at the
roof or in a cavity. Having lowered the flame, the lamp is
cautiously raised into the gas and watched for the first ap-
pearance of a cap or the lengthening of. the flame. As quickly
as this is observed the lamp should be promptly but cautiously
withdrawn from the gas.
On finding a body of sharp gas that has caused the lamp to
flame, danger occurs when, in withdrawing the lamp, fresh
air enters the combustion chamber, creating a highly explosive
mixture within the lamp. For this reason, the lamp must be
withdrawn from such a mixture slowly and with great caution,
which often requires much presence of mind. One should never
trifle with gas he has found in a cavity of the roof or on the
falls.
Gas issuing from the coal, at the face of a chamber, will
often pass out in a thin film or layer at the roof, and may be
unobserved by a fireboss until he is well within the chamber.
His movement beneath the layer of gas may cause it to de-
scend as he passes and he finds, too late, that he is enveloped in
gas from which he is able to escape with difficulty. Under
MINE LAMPS AND LIGHTING 307
such circumstances, a fireboss will frequently smother his
lamp beneath his coat, while he retraces his steps cautiously.
A thin layer of gas at the roof of a chamber can often be
detected by holding the lamp erect toward the roof and blowing
a slight puff against the roof, so as to cause the gas to descend
on the lamp. This is a practice followed by many experienced
firebosses. Without doing so, it is possible for a fireboss to
miss the gas and report the place safe for work when it is quite
unsafe.
ILLUMINANTS FOR SAFETY LAMPS
The principal illuminants used in safety lamps are the various
kinds of vegetable, animal and mineral oils. Hydrogen gas
is used in the Clowes hydrogen lamp, but this is the only lamp
burning gas. For practical purposes, the oils burned in mine
safety lamps can be designated as volatile and non-volatile
oils. A few testing lamps are designed to burn alcohol (spirits
of wine), which is also a highly volatile illuminant.
Non-volatile Oils Used in Safety Lamps. — These are mostly
derived from the vegetable and animal kingdom. Among the
vegetable oils largely used in mining practice may be men-
tioned cottonseed and colza or rapeseed oil. The principal
animal oils, which are also non-volatile, are the sperm, lard,
seal and whale oils. Of these, sperm and lard oils are most
commonly used in safety lamps today.
Both vegetable and animal oils possess less illuminating
power than mineral oils, and have a greater tendency to in-
crust the wick of the lamp. They are more stable, however,
and the flame is not as readily extinguished in the mine as
when mineral oil is burned in the lamp. The addition of about
one-half of their volume of coal oil (kerosene) greatly improves
the illuminating power of these oils but increases their ten-
dency to smoke. The rate of burning is slightly increased and
the mixture does not incrust the wick as rapidly as when a
pure vegetable or animal oil is burned.
Mineral Oils. — -All mineral oils are classed under the general
term, "petroleum," which is derived in a crude state from the
oil-bearing strata. When the crude petroleum or "rock oil,"
308 MINE GASES AND VENTILATION
as it is sometimes called, is distilled, the more readily vaporized
hydrocarbon vapors condense on cooling to what are termed light
or volatile oils. These are distilled at temperatures below
300 deg. F. Coal oil, or kerosene, is the product distilled be-
tween 300 and 570 deg. F., while the heavy lubricating oils
are distilled at still higher temperatures. These last products
contain paraffin, which is separated from the heavy oils by
its solidifying at 130 deg. F., in cooling. Of the light oils,
gasoline is distilled below 140 deg., naphtha, below 230 deg.,
and benzine, below 300 deg. F.
Light, Volatile Oils. — The danger in the use of light volatile
oils, as illuminants in safety lamps, arises from their low flash-
ing points. The ready vaporization of the oil, as the lamp
heats in gas, renders the test for gas unreliable in the use of a
lamp burning such an oil. The storing of a highly volatile oil
at a mine and the filling of the lamps in the lamphouse requires
extra precautions to be taken to avoid accident. In order to
reduce the danger of its use in the lamp, the oil vessel is
filled with absorbent or filling cotton. A light volatile oil is
not as stable as a vegetable or animal oil, and its flame is
more easily extinguished when such an oil is used in the mine.
A volatile oil flame, however, is more sensitive to gas and has
a higher illuminating power than other oils, which has favored
its use in many mining districts.
MINERS' CARBIDE LAMPS
The acetylene or carbide lamp that has come into such ex-
tensive use in coal mining, within the past few years, is an
open-flame lamp constructed to burn acetylene gas, generated
within the lamp, by the slow feeding of water onto the carbide.
The water and the carbide are contained in two separate com-
partments of the lamp.
The supply of water to the carbide is regulated by a valve
having a screw adjustment at the top of the lamp. The water
is contained in the upper half of the lamp and the carbide in
the compartment below. The latter should not be more than
half filled with the carbide, which swells when moistened with
MINE LAMPS AND LIGHTING
309
the water. A charge of 2J£ oz. of carbide will supply gas suffi-
cient to maintain a flame 1J^ in. in length during a half -shift
or more but then it will be necessary to recharge the lamp.
Owing to the brightness of the acetylene flame, the carbide
lamp has very largely replaced the old open-flame torch so
commonly used in mines generating no gas. The general form
of carbide lamp in common use is shown in Fig. 66, although
there are different styles of this lamp manufactured, some hav-
ing no reflectors behind the flame and differing in other
details. The lamp shown in the figure is a type very largely
used in the anthracite district.
Most of these lamps in use differ
only in slight details.
Generation of Acetylene Gas.—
Carbide (CaC2) is a product of the
action of coke on quicklime, calcium
oxide (CaO). The lime and coke
are finely ground, thoroughly mixed
and heated to a white heat in an
electric furnace. Under the high
heat of this furnace a portion of
the carbon unites with the calcium
to form calcium carbide (CaC2), the
remainder of the carbon taking up the oxygen and passing off
as carbon dioxide (CO*), according to- the reaction,
4CaO + 5C2 = 4CaC2 + 2CO2
When water comes in contact with calcium carbide, calcium
hydroxide, Ca(OH)2, is formed and acetylene gas (C2H2) is
set free according to the equation.
CaC2 + 2H2O = Ca(OH)2 + O2H2
The acetylene gas is highly inflammable and when ignited
in the air burns, producing carbon dioxide and water vapor.
Ignoring the inert nitrogen of the air, this reaction is expressed
by the following equation :
FIG. 68.
2C2H2 + 5O2 = 4CO2 + 2H2O
310 MINE GASES AND VENTILATION
One ounce of pure crystallized calcium carbide will generate
622 cu. in. of acetylene gas, measured at a normal temperature
of 60 deg. F., barometer 30 in. Commercial carbide, however,
will commonly yield only from 400 to 500 cu. in. per ounce of
carbide used, depending on the completeness of its consump-
tion in the lamp.
Burning Acetylene Gas. — For the purpose of estimate, it
may be assumed that an average miner's carbide lamp con-
sumes H °z- °f carbide per hour and generates 250 cu. in.
of acetylene gas. Then, since one volume of this gas, in
burning, consumes 2J^ volumes of oxygen or, say 12^ volumes
of air and produces 2 volumes of carbon dioxide and 1 volume
water vapor, the burning of a carbide lamp may be estimated
as producing 500 cu. in. of carbon dioxide and half that volume
of water vapor, per hour. In the same time, the lamp takes
from the air 625 cu. in. of oxygen, leaving practically 2500 cu.
in. of excess nitrogen.
The effect of the burning of a carbide lamp to vitiate the
mine air is thus seen to be inappreciable and far less than the
breathing of a man, who consumes little short of 1000 cu. in.
of oxygen, per hour, when at rest, and over 8000 cu. in. per
hr., in violent exercise, and exhales an equal volume of air
containing from 2J^ to 6^ per cent, of carbon dioxide.
Calculation. — The molecular weight of calcium carbide
(CaC2) being 40 + 2(12) = 64; and that of acetylene (C2H2),
2(12 -}- 1) = 26; and the specific gravity of this gas referred
to air being 0.92, we have the following:
Weight of 1 cu. ft. air (60 deg. F., bar. 30 in.) . . 0.0766 lb.
Weight of 1 cu. ft. acetylene, 0.92(0.0766) 0.07047 lb.
Volume of 1 lb. acetylene
(60 deg. F., bar. 30 in.) M.07047- • • -14.19 cu.fi.
14 19 X 1728
Volume of 1 oz. acetylene - ^ — . . . . 1532.5 cu. in.
Then, since 64 parts, by weight, of calcium carbide yield
26 parts, by weight, of acetylene gas, one ounce of the pure
crystallized carbide will generate
f)(*
^ (1532.2) = 622 + cu. in. acetylene,
measured at 60 deg. F., bar. 30 in.
MINE LAMPS AND LIGHTING 311
Properties of Acetylene Gas. — The gas is colorless and has a
strong pungent odor, due to the presence of some sulphureted
and phosphureted hydrogen, as generated in the carbide lamp,
by the action of water on the carbide. It has a specific
gravity of 0.92, referred to air at the same temperature and
pressure. Under atmospheric pressure, the gas liquefies
at — 115 deg. F., the volume of the liquid being Hoo of that
of the original gas.
Acetylene gas is combustible, igniting, in contact with air,
at a temperature of 900 deg. F. When the gas is largely in
excess and the supply of air limited the acetylene is smoky
and deposits soot, but when a fine stream of the gas is spurted
into the air, as in the carbide lamp, a flame of exceeding bril-
liancy is the result. Owing to its low temperature of ignition,
the gas can be ignited by a lighted cigar.
Mixed with air the gas becomes highly explosive its explo-
sive range being wider than that of any other gas. While
the inflammable range of hydrogen extends from 5 to 72 per
cent., that of acetylene ranges from 3 to 82 per cent., as de-
termined by Clowes. This high value for the upper explosive
limit has not been obtained by other investigators, whose
results vary from 50 per cent. (Federal Bureau of Mines)
to 65 per cent. (LeChatelier).
The Carbide Lamp in Blackdamp. — What is known as
"blackdamp" in mining is a variable mixture of carbon
dioxide and air deficient in oxygen; in other words, an
atmosphere of blackdamp consists of nitrogen, oxygen and
carbon dioxide in varying proportions. When carbon dioxide
is generated in a mine ventilated by an ample air current
containing a normal percentage (20.9%) of oxygen the addi-
tion of any considerable amount of carbon dioxide to this
normal air reduces the oxygen content by the dilution of the
air with the gas. The air is then said to be "deficient in
oxygen," which is due solely to its dilution with the carbon
dioxide.
On the other hand a much greater reduction of the oxygen
content often occurs when a portion of the oxygen has been
consumed by the various forms of combustion that are con-
312 MINE GASE8 AND VENTILATION
stantly taking place in the mine. It -is this reduction of the
oxygen content, or the " depletion of oxygen" in the mine
air that is most harmful to life and affects the burning of
the lamps.
It is a well known fact that the carbide lamp will continue
to burn in air deficient in oxygen when oil-fed flames and
the hydrogen flame are quickly extinguished. The acetylene
gas burned in the carbide lamp is generated, in the lamp, by
the action of water on the carbide of calcium, the calcium
taking the oxygen and some of the hydrogen, while the
carbon takes the remaining portion of the hydrogen.
We cannot say but that, in the dissociation of the hydro-
gen and oxygen of the water (H^O) , some oxygen may go to
support the combustion of the acetylene gas (C^Hy, instead
of the flame being wholly dependent on the oxygen of the
air for support. However, it is safe to say that an atmos-
phere in which a carbide continues to burn may be danger-
ous to life and therefore unsafe for work.
In an atmosphere containing no carbon dioxide, the oxygen
content may fall as low as 14 per cent, before much difficulty
is experienced in breathing; but air containing but 10 per
cent, is no longer breathable and will cause death quickly by
suffocation."
The toxic effect of carbon dioxide is clearly shown by the
fact that the depletion of the oxygen content of air, by the
addition of carbon dioxide, produces a fatal atmosphere when
the oxygen is reduced to but 17 per cent.; while, if no car-
bon dioxide is present, a fatal atmosphere is produced only
when the depletion of the oxygen reaches 10 per cent.
In the former of these two cases, there is but 83 per cent,
of noxious gases present — carbon dioxide, 18 per cent, and
nitrogen, 65 per cent.; while, in the latter case, there is 90
per cent, of nitrogen present. In the former case a depletion
of oxygen to 17 per cent, marks a fatal atmosphere; while
in the latter case, a depletion of oxygen to 10 per cent, is
necessary to produce the same result.
It is quite doubtful if a carbide lamp is extinguished when
the oxygen of the atmosphere is reduced to 14 per cent., as
is frequently assumed.
MINE LAMPS AND LIGHTING 313
Precautions to be Taken. — In the use of carbide lamps in
mines, suitable rules and regulations should be made and
enforced limiting the supply of carbide that a miner may carry
into the mine to what is ample for his purpose in a single
shift and prohibiting its careless use. A supply of carbide
should never be permitted to be stored in a miner's box or
elsewhere in a mine. With proper care and precautions there
need be little fear of trouble. The carbide light being an open-
flame lamp should not be used in a mine generating gas.
ELECTRIC MINE LAMPS
The electric mine lamp is now almost universally used in
all up-to-date mines in the states and Canada, there being at
present 150,000 of these lamps installed by the Edison Storage
Battery Co. alone. Of this number, 80,000 of the lamps are
in daily use in the mines of Western Pennsylvania.
Selecting a Suitable Battery .-^In the endeavor to provide a
portable electric mine lamp that would meet the require-
ments of mine service, the chief difficulty was to find a bat-
tery that would be sufficiently light and have the necessary
watt-hour capacity to furnish a good light a full 8-hr, shift.
All forms of primary batteries that depend on the chemical
reaction set up between certain elements immersed in a solu-
tion, as well as the lead-sulphuric acid storage battery, proved
unsuited to service in the mine. The lead-lead battery was
too heavy, besides failing in other ways to meet the requirements
of mining use. Even the substitution of a gelatinous elec-
trolyte proved ineffectual, owing to the hardened jelly not
absorbing the water when once dried and the crack becoming
filled with sediment short-circuiting the cells and weakening
the battery.
The Edison Storage Battery.— The difficulties just men-
tioned have been practically overcome in the Edison storage
battery designed for mine use. This battery employs as
elements nickel hydroxide and iron oxide immersed in a potash
solution. The battery cells are incased in a strong nickel-
plated steel container, which is tightly sealed except for one
314
MINE GASES AND VENTILATION
small vent being left for the escape of the harmless gases that
result in the charging of the battery.
The illustration, Fig. 67, shows the two cells of the Edison
mine-lamp battery removed from the iiickeled-steel case.
The steel container of one cell is cut away to show the interior
arrangement. The positive plates (steel tubes of nickel
hydrate) and the negative plates (steel pockets of iron oxide)
are assembled on steel poles and intermeshed, which gives an
exceptionally strong and compact construction entirely of
steel, there being no acid to cause corrosion.
The construction of this
battery is such that it is
practically impossible for
the solution to find its way
out, even should the battery
be turned upsidedown ; and
no injury can result from a
possible- overcharging, or
from leaving the cell in a
charged, semi-charged or
discharged condition, for
an indefinite period . While
the cell must be charged in
the right direction to be fit
for service, no injury can
result from accidentally
reversing this direction.
The steel container is proof against rough usage, and no in-
sulation troubles can occur. Specific gravity tests are not re-
quired as the potash solution is renewed after 9 or 10 months
of use in continuous daily service.
Cap Lamp and Connecting Cable. — The illustration, Fig.
68, shows the electric cap lamp and the nickeled-steel carrying
case holding two cells. The cover of the case is removed to
show the steel contact plates affixed to but insulated from the
cover. These plates connect with the contact springs shown
mounted on the two terminals of the battery. The cover is
secured to the case by a strong hasp and padlock. To this
FIG. 67.
MINE LAMPS AND LIGHTING
315
cover is attached a twin-conductor, rubber-covered cable,
armored at both ends to prevent injury where sharp bending
is liable to occur. If injured the cable is easily replaced.
The supporting base of the lamp is a nickel-plated reflector
having a highly finished surface and provided with a hook to
fit into the regulation miner's cap. The angle of distribution
is considerably greater than the 130 deg. specified by the
government, (see p. 322). A tungsten lamp is forced into
a spring socket by means of a clip at its tip in such a way
that if the lamp should be broken the base is immediately
disconnected and the lamp extinguished. This safety feature
has been thoroughly tested by the Bureau of Mines and un-
FIG. 68.
qualifiedly approved under Schedule 6A. In place of a lens
is a plain glass that is easily replaced if broken. The entire
design is. such as to afford the greatest possible headroom
clearance.
Charging Miners' Lamp Batteries. — The recharging of a
large number of lamp batteries, between shifts, calls for a
special design of equipment that will provide at once for the
charging of the batteries and enumerating them so that any
individual battery can be found without delay.
A convenient form of charging rack that meets these require-
ments is one built up on the unit system, corresponding to the
sectional bookcase idea. The illustration, Fig. 69, is a view
of such a rack, designed and built by the Cutler-Hammer Mfg.
316
MINE GASES AND VENTILATION
Co., Milwaukee, Wis. The figure shows four units, but the
system can plainly be extended indefinitely to accommodate
an increasing number of lamps as the development of the mine
proceeds. The recharging room must be well ventilated and
open lights should not be permitted.
FIG. 70.
On the right of the figure are shown two rheostat panels and
a meter panel above. These panels are shown in greater de-
tail in the Fig. 70, together with front and top views of a
single unit capable of holding ten lamp batteries for charging.
MINE LAMPS AND LIGHTING 317
The contact parts supported by the upper slab are pressed
down in contact with the battery by the coil springs above the
slab. The batteries are charged in series and provision is
made for interpolating resistances to take the place of one or
more absent batteries.
Pipe columns to which are clamped supporting brackets,
as shown in this figure, form the framework of the rack on
which are hung the several battery units and panels by means
of the strong hooks shown attached to each.
Each rheostat panel is designed to control the current in
the corresponding line of units, and is equipped with a sliding
arm for adjusting the charging rate to any desired value.
The double-pole knife switch shown on this panel is so arranged
that when partly closed the ammeter on the meter panel is
thrown into circuit; but when closed completely the ammeter
is cut out and the current passed through the charging racks.
The meter panel not only holds the ammeter for measuring
the strength of the current and regulating it in accordance with
the number of units to be charged ; but is also provided with a
magnetic switch and compound relay, which prevents a rever-
sal of current from the partially charged batteries taking place
should the charging current be interrupted for a time. This
device automatically opens and closes the circuit as the cur-
rent is broken and again restored. The breaking of the current
is immediately announced by the signal bell on each rheostat
panel.
Edison mine-lamp batteries require a pressure of 40 volts,
which makes it possible to charge six 10-battery units, on a
250-volt circuit. However, it is generally advisable to install
but five such units on this circuit, which would allow the pres-
sure to drop to 200 volts without interrupting the charging.
Use of the Electric Cap Lamp. — The need of a reliable source
of illumination in mining work has long been sought but with
limited success. Open-flame lamps or torches are necessarily
restricted to non-gaseous mines, or where the conditions are
such as not to require the exclusive use of safety lamps. On
the other hand, the relatively dim light of a safety lamp and
its lack of adaptation to the requirements of mining work make
318 MINE GASES AND VENTILATION
it always desirable to find a suitable substitute that will be
both convenient and safe for general work.
The electric cap lamp with storage battery equipment simi-
lar to that shown in the illustration, Fig. 71, has apparently
solved the problem, and furnished the miner with a good light
that is convenient and safe. The principal objections that
have been urged against the miners' electric lamp are the
slightly increased cost of the equipment, and the fact that an
FIG. 71.
electric lamp affords no indication of the presence of gas,
either methane or blackdamp, and gives the miner no warning
of danger in that respect.
Notwithstanding these disadvantages, the electric lamp has
steadily grown in favor among miners, as shown by its general
adoption and successful use. In daily practice, the miner
straps the battery case to his back, by his ordinary belt. The
lamp is attached to the leather support in his cap, leaving his
MINE LAMPS AND LIGHTING 319
arms entirely free of lamp, cord and battery case. When the
case is locked and the equipment handed to the miner charged
and ready for use there can be no safer or surer means of
illumination.
PERMISSIBLE PORTABLE ELECTRIC MINE LAMPS
Schedule 6A, issued by the Federal Bureau of Mines, defines
what is to be understood as included under the appellation
"Permissible," in reference to portable electric mine lamps, in
the following words:
The Bureau of Mines considers a portable electric lamp to be per-
missible for use in mines if all the details of the lamp's construction
are the same, in all respects, as those of the lamp that passed the in-
spection and the tests for safety, practicability, and efficiency made
by the bureau and hereinafter described.
Conditions of Testing. — The conditions under which the Bureau of
Mines will examine and test portable electric lamps to establish their
permissibility are as follows:
1. The tests will be made at the experiment station of the Bureau of
Mines at Pittsburgh, Pa.
2. Applications for tests shall be addressed to the Director, Bureau
of Mines, Washington, D. C., and shall be accompanied by a com-
plete description of the lamp to be tested and a full set 'of the draw-
ings mentioned below.
A drawing or drawings clearly showing the size and general appear-
ance of the lamp mounting.
A drawing or drawings clearly showing the character, size and relative
arrangement of the parts of the lamp mounting and the principle of
operation of the safety devices.
Any other drawings that may be necessary to identify the safety
devices or to explain how they accomplish their purpose.
A copy of the description, a duplicate of the drawings and one complete
lamp shall be sent to the Electrical Engineer, Bureau of Mines, Fortieth
and Butler Streets, Pittsburgh, Pa.
3. As soon as possible, after the receipt of his application for test,
the lamp manufacturer will be notified of the date on which his lamps
will be tested and the amount of material that it will be necessary for
him to submit.
4. All material for test shall be delivered by the manufacturer to
the Electrical Engineer, Bureau of Mines, Fortieth and Butler Streets,
Pittsburgh, Pa., not less than one week prior to the date set for the
test.
320 MINE GASES AND VENTILATION
5. No lamp equipment will be tested, unless it is in the completed
form in which it is to be put on the market.
6. Lamps so constructed that they can be used both as cap lamps
and as hand lamps must pass the tests for both cap lamps and hand
lamps or they will not be approved for either class of service.
7.t No one is to be present at these tests, except the necessary govern-
ment officers, their assistants, and one representative of the manufacturer
of the lamp to be tested, who shall be present in the capacity of an ob-
server only.
The conduct of the tests shall be entirely in the hands of the bureau's
engineer in charge of the investigation. While the tests are in progress
the manufacturer's representative shall not make unsolicited suggestions
or criticismsof the method of conducting the test.
8. The tests will be made in the order of the receipt of application
for test, provided that the necessary lamp equipment is submitted
at ohe proper time.
9. The details of the results of the tests shall be regarded as con-
fidential by all present at the tests, and shall not be made public, in
any way, prior to their official publication by the Bureau of Mines.
Requirements for Approval. — The requirements that a portable electric-
lamp equipment must have, to pass successfully the inspection and tests
required by the bureau, are stated below :
1. The lamp equipment must comply with the following require-
ments for mechanical and electrical construction :
The construction of permissible portable electric-lamp equipment
shall be especially durable. All parts shall be constructed of suitable
material of the best quality and shall be assembled in a thorough. work-
manlike manner. Current-carrying parts shall be well insulated from
parts of opposite polarity and from parts not intended to carry current.
The battery shall be inclosed in a locked or sealed box so constructed
as to preclude the possibility . of anyone meddling with the electrical
contacts or making an electrical connection with them while the box cover
is closed.
The leads connecting the battery with the headpiece shall be made
up in a single cable efficiently insulated and provided, where it leaves
the battery casing and enters the headpiece, with a reinforcement of
flexible metallic tubing. The flexible metallic tubing will not be re-
quired if other equally durable means of reinforcement are provided.
It is recommended, but not required, that the headpiece be so de-
signed that it can be sealed or locked. The battery terminals and
leads connecting thereto, and the gas vent of the battery shall be so
designed and constructed as to prevent corrosion of the battery ter-
minals or of the essential metallic parts mounted in the cover of the
battery casing.
The following qualities will be considered in determining the excel-
MINE LAMPS AND LIGHTING 321
lence of the mechanical and electrical construction of lamps covered
by these specifications:
Simplicity of design; mechanical strength of parts and fastenings;
suitability of material used; design of moving and removable parts;
design and construction of terminals and contacts, for permanence
and electrical efficiency ; and ease of repair.
2. The lamp equipment must be provided with a safety device or
devices as follows:
Permissible portable electric lamps shall be so designed and constructed
that whenever the bulb of a completely assembled lamp equipment
is broken the lamp filament shall, at once and under all circumstances,
cease to glow at a temperature that will ignite explosive mixtures of mine
gas and air.
The mounting of the bulb may be designed so that a blow sufficient
to break the bulb will short-circuit it, open the electric circuit of the
lamp or otherwise insure that the filament will be wholly or practically
extinguished. All safety devices with which the lamps are provided
shall be so completely protected from injury or disturbance as to insure
that the devices will always be in condition to perform their functions.
The design of the safety features shall be such that their action can
not readily be hindered or prevented. The design of the safety devices
shall be such that they will not act to extinguish the lamp unnecessarily.
3. The lamp equipment must be provided with a battery having a
short-circuit current not in excess of the values here specified.
The bureau's engineers have made tests (reported in Technical Paper
47 of the bureau), which have satisfied them that mine gas can not be
ignited by the sparks from portable electric-lamp equipments if the
batteries used with such equipments are made so that their maximum
short-circuit current can not exceed the following values : For batteries
giving 2.5 volts or less, 125 amperes; for batteries giving more than
2.5 volts but not more than 4 volts, 85 amperes; for batteries giving
more than 4 volts but not more than 5 volts, 65 amperes; for batteries
giving more than 5 volts but not more than 6 volts, 45 amperes. There-
fore, lamps whose short-circuit current does not exceed these values will
be considered satisfactory in that respect.
4. The lamp equipment must meet the following requirements for
time of burning, flux of light, intensity of light and distribution of light:
All portable electric lamps offered for test under the provisions of
this schedule shall produce, for 12 consecutive hours, on one charge of
battery, a light stream having an averge intensity of light not less than
four-tenths of a candlepower. The to'al flux of light produced by
cap lamps shall not fall below IK lumens during the 12 hours, and the
total flux of light produced by hand lamps shall not fall below 3 lumens
during the 12 hours.
The distribution of light, by lamps that use reflectors, shall be deter-
mined both by observation and by photometric measurement. The
21
322 MINE OASES AND VENTILATION
lamps shall be placed so that the filaments are 20 in. away from a plane
surface that is perpendicular to the axis of the light stream of the lamp.
When so placed the lamp shall illuminate a circular area not less than
7 ft. in diameter.* All observations and measurements of distribution
shall be referred to this 7-ft. circle regardless of how large an area the
lamp may illuminate. As observed with the eye, there shall be no
"black spots" within the 7-ft. circle, nor any sharply contrasting areas
of bright and faint illumination anywhere. As measured with a photo-
meter, the distribution of light diametrically across the circle shall fulfill
the following requirements:
The curve of light distribution along the diameter of the circle shall
be obtained by rotating the lamp and thus obtaining the average distri-
bution curve.
The average illumination in foot-candles, on the best illuminated
one-tenth of the diameter, shall be not more than three times the average
illumination throughout the diameter; and, for at least 40 per cent,
of the diameter, the illumination shall be not less than the average.
5. The lamp equipment must be provided with lamp bulbs that
meet the following requirements, for variation in current consump-
tion, variation in candlepower and length of life :
The bulbs submitted for test shall be identified by the name of the
manufacturer and by a number or symbol with reference to which
approval will be granted.
The current consumption of at least 95 per cent, of the bulbs tested
shall not exceed, by more than 6 per cent., the average current con-
sumption of all the bulbs examined.
The candlepower of at least 90 per cent, of the bulbs tested shall
not fall short of the average candlepower, by more than 30 per cent.
The life of a lamp bulb will be considered as the number of hours that
the bulb can be burned, under normal conditions of voltage, before it
becomes so depreciated that when used with an average, standard,
freshly charged equipment it fails bo produce, for 12 consecutive hours,
the flux and intensity of light specified in paragraph 4.
The average life of lamp bulbs shall be not less than 300 hours, for
acid storage batteries, and not less than 200 hours, for primary batteries
and for alkaline storage batteries. Not more than 5 per cent, of the
bulbs examined shall give less than 250 hours' life, with acid batteries,
nor less than 150 hours' life, with primary batteries and alkaline batteries.
6. The lamp equipment must comply with the following requirements
as to leakage of electrolyte :
Lamps shall be so designed and constructed that they will not spill
nor leak electrolyte throughout an 8-hour test, during which they will be
placed in any position or sequence of positions that, in the opinion of the
bureau's engineers, will be most likely to prove whether or not the elec-
trolyte can be spilled.
0 This requirement will be met by lamps that have an angle of light
stream of 130° or more.
MINE LAMPS AND LIGHTING 323
Tests of Design and Construction. — The excellence of the mechanical
and electrical features of the design and construction of the lamps will
be carefully determined.
The following tests will also be made: Hand lamps and the head-
pieces of cap lamps will be dropped 10 times, upon a concrete floor
from a point 6 ft. above it. As the result of these dropping tests, there
must be no breakage of the battery jar or material distortion of the
casing of the battery or of the shell of the headpiece. The engineers
in charge of the investigation shall be the sole judges of whether or
not material distortion occurs. The dropping tests of the headpiece
must demonstrate that the safety devices will not operate unnecessarily.
Cap lamps will be dropped 10 times, upon a wooden floor, from a
point 3 ft. above it. There must be no breakage of the battery jar
or material distortion of the casing.
Tests of Safety Devices. — In making tests of the safety devices, it
will be assumed that if the short-circuit current of the battery does not
exceed a certain value, stated previously, the glowing filament of the
lamp is the only source of danger.
It will also be assumed (based on tests reported in Technical Paper
23) that the glowing filament presents an element of danger, in the
presence of mine gas, if the bulb of the lamp can be broken without
causing the filament to become wholly or practically extinguished as
the result of the action of the safety devices with which the lamp is
provided.
The tests will therefore be made with a view to determining whether
or not the lamp bulb may be broken without causing the safety device
of the lamp to extinguish the lamp or cause the filament to glow at a
temperature that is not high enough to ignite explosive mixtures of mine
gas and air.
If the safety devices are designed to extinguish the lamp before
the bulb is broken it will not be necessary to make the tests in gas,
unless the safety devices do not completely extinguish the lamp. It
will then be necessary to determine whether or not the filament is glow-
ing at a temperature sufficient to ignite gas.
If t-he safety devices are designed to extinguish the lamp at the same
time that the bulb is broken it will be desirable to make the tests in
explosive mixtures of gas and air.
Gas, if used, will be the natural gas supplied to the city of Pitts-
burgh. The composition of this gas, as determined from recent analyses,
is approximately 83.1 per cent, methane, 16 per cent, ethane, 0.9 per
cent, nitrogen and a trace of carbon dioxide.
The details of conducting the tests will, manifestly, not be the same
for all lamps submitted, because different lamps will no doubt have
safety devices differing in design, construction and basic principles.
The bureau proposes to determine, for each lamp separately, a schedule
of tests that, after due examination of the lamp and its safety devices,
324 MINE GASES AND VENTILATION
seem best adapted to ascertaining the merits of the equipment sub-
mitted. This schedule may be examined and discussed by the manu-
facturer's representative before the tests are begun.
In general, the tests will consist of striking the mounting or holder
of the lamp bulb, in an attempt to break the bulb without extinguish-
ing the lamp.
If the safety devices are designed to extinguish the lamp (as, by
disconnecting the bulb from circuit, or by opening the circuit at some
other point) the devices will be considered to have acted:
1. If, after the blow has been delivered, the lamp bulb, whether
broken or not, is clearly disconnected from circuit.
2. If, after the blow has been delivered:
(a) When the lamp filament is not broken by the blow and does not
glow;
(6) When the lamp filament is broken by the blow a sound filament,
replacing the broken filament, does not glow.
If the safety devices are designed to decrease the temperature of
the filament (by short-circuiting the filament or by other means),
the devices will be considered to have acted if, after the blow has been
delivered:
(a) When the lamp filament is not broken by the blow it does not
glow at a temperature sufficient to ignite gas;
(b) When the lamp filament is broken by the blow a sound fila-
ment, replacing the broken filament, does not glow at a temperature
sufficient to ignite gas.
If there is any question as to whether or not a filament is glowing
at a dangerous temperature the point will be settled by surrounding
the filament with an explosive mixture of gas and air.
If, after the blow has been delivered, the bulb has not been broken
and the safety devices have not acted the test will be repeated with
the same equipment, or with a different equipment, at the discretion
of the bureau's engineers.
The bureau believes that approximately 50 tests will be necessary
to determine whether or not the safety devices of a lamp are permis-
sible for use in gaseous mines; but more or fewer tests may be made
at the discretion of the engineer in charge of the tests.
To Determine Maximum Short-circuit Current. — The short-circuit
current of the battery will be measured under conditions that will give
the same current that would flow through a short-circuit between the
conductors of the flexible cord, at the point in the cord nearest to the
battery casing.
Tests of Lighting. — The tests to determine the time of burning, flux,
intensity and distribution of light will be made, for not less than 20
batteries, 6 reflectors or lamp mountings, and 100 lamp bulbs.
The average performance of the various equipments will be taken
as the average performance of the lamp. The measurements of flux
MINE LAMPS AND LIGHTING 325
and intensity of light will be made after the bulbs have been burned
for about 10 hours in order to season them somewhat.
Tests of Current Consumption, Candlepower, Life of Bulb. — Mea-
surements of current consumption and candlepower will be made with
bulbs that have been burned about 10 hours.
Measurements of current consumption will be made at approxi-
mately'the average potential given by the lamp battery, after having
been used for one hour.
Measurements of bulb candlepower will be made in one direction
only. Usually the direction that gives the largest exposure of filament
will be selected.
Determination of bulb-life will be made with batteries that have
the same voltage characteristics as those used with the lamp. Tests
will be made with the bulbs in a fixed position.
Although, as stated in Technical Paper 75, Bureau of Mines, the
bureau considers that the batteries of portable electric mine lamps
should give 3600 hours of service (300 12-hour shifts) without requiring
repairs or replacements of any part, it is manifestly impracticable for
the bureau to carry out the 3600-hour test upon each battery submitted
for approval. Therefore, the requirements of the bureau, with respect
to the durability of batteries, will be considered as satisfied if the batteries
shall perform their functions without repair while being used by the
bureau, in accordance with the written instructions of the lamp manu-
facturer, to conduct the bulb-life tests; and, at the completion of these
tests, the condition of the batteries shall give no evidence of weakness
that indicates the early failure of any part of the battery.
Test of Leakage of Electrolyte. — The lamps will be tested for leakage
and spilling of electrolyte, by placing the batteries for various lengths of
time, totaling eight hours, in various positions that seem most likely to
cause the cells to leak or spill. If a battery does not leak or spill more
than one full drop of electrolyte during the eight-hour test the battery
casing will be regarded as non-spilling.
Approval of Electric Mine Lamps. — The manufacturers will bo re-
quired to attach to the battery casing of each permissible lamp equip-
ment a plate bearing the seal of the Bureau of Mines and inscribed as
follows:
PERMISSIBLE PORTABLE ELECTRIC MINE LAMP. APPROVAL No. — .
Issued for safety and for practicability and efficiency in general
service to the Co.
The use of the plate will not be required if the same inscription is
stamped or cast into the casing of the battery.
Manufacturers shall, before claiming the bureau's approval for any
modification of any approved lamp, submit to the bureau drawings
326 MINE GASES AND VENTILATION
that shall show the extent and nature of such modifications, in order
that the bureau may decide whether or not it should test the remodeled
lamp before approving it. Each approval of a permissible lamp will
be given a serial number. Approvals of modified forms of a previously
approved lamp will bear the same number as the original approval
with the addition of the letters a, 6, c, etc.
The bureau will, upon request, make tests of lamp bulbs to deter-
mine whether or not they will comply with the bureau's requirements
when used in connection with any lamp that has been approved by
the bureau under the provisions of this schedule. Lamp bulbs that fulfill
the requirements will be specifically approved for use with stated lamps.
Applications for tests of bulbs should be made in a manner similar to
application for tests of lamps.
The bureau's approval of any lamp shall be construed as applying
to all lamps made by the same manufacturer that have the same con-
struction in the details considered by the bureau, but to no other lamps.
The bureau reserves the right to rescind, for cause, at any time, any
approval granted under the conditions herein set forth.
Notification of Manufacturer. — As soon as the bureau's engineers are
satisfied that a lamp is permissible, the manufacturer of the lamp and
the mine-inspection departments of the several states shall be notified
to that effect. As soon as a manufacturer receives formal notification
that his lamp has passed the tests prescribed by the bureau, he shall be
free to advertise such lamp as permissible. <•
Fees for Testing. — The necessary expenses involved in testing portable
electric mine lamps have been determined, and the following schedule
of fees to be charged, on and after the date of issue of this schedule, has
been established and approved by the Secretary of the Interior :
1. For a complete official investigation leading to the formal ap-
proval of a portable electric mine lamp, the investigation to
include tests of the safety devices and the determination of
the time of burning, flux of light, intensity of light, distri-
bution of light, bulb characteristics, leakage of electrolyte,
and durability $150.00
2. For tests of the safety devices only $30 . 00
For additional necessary tests, under the same investigation
(for each five tests or fraction thereof) $2 . 50
3. For tests to determine only the time of burning, flux of light,
intensity of light, distribution of light, bulb characteristics,
and leakage of electrolyte $120. 00
4. For tests to determine only bulb life, variation in bulb candle-
power and variation in bulb current consumption:
If such tests involve making discharge-voltage determin-
ations $75.00
If such tests do not involve making discharge-voltage
determinations — $50.00
MINE LAMPS AND LIGHTING 327
5. The following charges will be made for individual tests
included under item 3:
Discharge-voltage tests $25 . 00
Reflector tests $20 . 00
Time-of-burning tests $10. 00
Light-distribution tests $5 . 00
Electrolyte-spilling tests $3 . 00
Short-circuit tests of battery $1 . 00
Mechanical tests of cord $6 . 00
Bulb-life tests $35 . 00
Bulb-uniformity tests $15 . 00
0. Special tests that circumstances shall render necessary, during the
course of the investigation, will be made at the request of the lamp
manufacturer and will be charged for in accordance with the amount
of work involved.
ADDENDA
LOGARITHMS — CIRCULAR FUNCTIONS, SINES AND COSINES,
TANGENTS AND COTANGENTS: — SQUARES, CUBES, ROOTS AND
RECIPROCALS OF NUMBERS — CIRCUMFERENCES AND AREAS —
DENOMINATE NUMBERS — WEIGHTS AND MEASURES —
UNITED STATES AND BRITISH SYSTEMS — METRIC SYSTEMS
OF WEIGHTS AND MEASURES — CONVERSION TABLES — CON-
VERSION OF COMPOUND UNITS.
LOGARITHMS
The treatment of logarithms here will be simple and practical and such
as to enable their use to be clearly understood. Much time and labor
are saved when multiplying and dividing, or when extracting the roots
of numbers, or raising a number to a given power by the use of loga-
rithms.
Definition. — The logarithm of a number is the exponent of the power
to which it is necessary to raise a fixed number called the "base" to
produce the given number.
Systems of Logarithms. — There are two systems of logarithms in use:
1. The Briggs or common system employs 10 as a base. 2. The Na-
perian or hyperbolic or natural system is derived from 2.71828+ as a
base. The common logarithms (log) are those generally used, while the
natural logarithms (nat. log) are often employed in theoretical analyses.
The Naperian or natural logarithm of a number can always be found
by multiplying the common logarithm of the number by 2.302585, which
is expressed thus:
Nat. log. = 2.302585 com. log.
In any system of logarithms, the logarithm of 1 is zero, and the loga-
rithm of the base of the system is always 1.
The Logarithm. — Every logarithm is composed of two distinct parts
separated by a decimal point The number preceding the decimal
point, or the integer of the logarithm is called the characteristic," while
the decimal portion of the logarithm is the "mantissa." These two parts
of a logarithm must be regarded separately. The mantissa is always posi-
tive, but the characteristic may be either positive or negative, according
as the given number is greater or less than 1, in a system whose base is
greater than 1.
The characteristic is always 1 less than the number of figures in the
integral portion of the given number; or 1 greater than the number of
ciphers following the decimal point when the given number is wholly
328
ADDENDA 329
decimal. In the former case the characteristic is positive; in the latter
case it is negative. The following examples will make this clear :
log 325.00 = 2.51188 log 0.325 = 1.51188
log 32.50 = 1.51188 log 0.0325 =2.51188
log 3.25 = 0.51188 log 0.00325 = 3.51188
The mantissa, as is readily observed from the above examples, is
determined by the sensible figures of a number, without regard to the
decimal point. Also, the mantissa of the logarithm of a number is
unchanged when the number is multiplied or divided by 10, 100, 1,000,
etc. For example, the mantissa of the logarithm of 3, which is 0.47712,
is the same for 30, 300, 3,000 or for 0.3, 0.03, 0.003, etc.
A table of the common logarithms of numbers from Oto 10, 000 follows
and will be found useful. In this table the mantissas only are given and,
to avoid unnecessary repetition, the first two figures are not repeated.
An asterisk * appearing before the remaining three figures of the mantissa
indicates that the first two figures must be taken from the line below.
Bars are employed to mark the division by tens, which facilitates the
finding of the mantissa of any desired number given in the left-hand
column. In this table, the differences are given as proportion parts and
placed in the right-hand column marked " P. P.," which avoids the
necessity of multiplying by the decimal as will be explained.
To Find the Logarithm of a Number. — From the table of logarithms,
find the mantissa corresponding to the given number, ignoring the decimal
point. To do this, the first three figures on the left of the given number
are found in the left-hand column of the table, and the fourth figure in
the line at the top. The required mantissa is then taken from the line
and column thus indicated.
But if the given number contains five or more figures, write the excess
figures as a decimal and multiply the difference between the mantissa
found and the one next following by this decimal; point off and add the
integral portion of the result to the mantissa already found. If desired
this logarithm can be extended by annexing the decimal portion of the
same result, but this is not commonly necessary. When there is but one
excess figure, as when finding the mantissa of a number having five
figures, the difference to be added to complete the mantissa is taken
from the corresponding proportional part, in the right-hand column with-
out multiplying.
Having found the mantissa, prefix a decimal point preceded by a
characteristic one less than the number of integral figures in the given
number. If there is but one integral figure the characteristic of the
logarithm will be zero.
If the given number is a decimal, having no integral figures, the
characteristic will be negative and numerically one greater than the
number of ciphers that follow the decimal point.
330 MINE GASES AND VENTILATION
Illustrations. — The following examples will illustrate the method
of finding the logarithms of numbers under different conditions and make
clear the use of the table.
1. Suppose it is required to find the logarithm of the number 4,657.
Opposite 465, in the column under 7, is found 811, and this annexed to
66 found at the left gives for the mantissa of this number the decimal
0.66811. The characteristic, in this case, is 3, since there are four
integral figures in the given number. Hence, log 4,657 = 3.66811.
2. To find the logarithm of 32.567, ignoring the decimal point, opposite
325 in the column under 6, is found the mantissa, 0.51268; but there is
still another figure 7 in the given number. Therefore, to complete this
mantissa subtract it from the one following, giving the difference 14
found in the right-hand column. The proportional part of this difference
corresponding to the fifth figure 7 is 9.8 or, say 10. Then 51,268 + 10 =
51,278 and the complete mantissa is therefore 0.51278. In this case,
the given number contains but two integral figures, which makes the
characteristic 1; hence, log 32.567 = 1.51278.
3. To find the logarithm of 0.509065, ignoring the decimal point,
opposite 509, in the column under 0, is found the mantissa 0.70672.
To complete this mantissa subtract it from the one next following,
thus, 680 — 672 = 8, and multiply the remaining figures of the given
number written as a decimal, by the difference 8 and add the integral
of the result to the mantissa already found.
Thus, 70,672 + 0.65 X 8 = 70,672 + 5 = 70,677.
Now, since the given number is a decimal, the characteristic of its
logarithm is negative; and its numerical value is 1, as there are no ciphers
immediately following the decimal point. The complete logarithm is,
therefore, log 0.509065 = 1.70677, the minus sign being written over
the characteristic, since the characteristic only is negative.
Use of Logarithms. — By the use of logarithms the processes of multi-
plication, division, involution and evolution are greatly shortened and
simplified. The two latter processes are in fact a repetition of the two
former; while division and evolution are the reverse operations of multi-
plication and involution, respectively.
It is important to observe that the use of logarithms enables the finding
of decimal powers and decimal roots of numbers, which is impossible
by other means. When the index of a power or root of a number
can be expressed as a fraction the numerator and denominator of such
fraction express, respectively, the indices of the power and root or the root
and power, as the case may be. A decimal index, therefore, expresses
in one operation the extraction of any given root of any given power of a
number, which will be better understood later.
The application of this principle is shown in numerous instances
where quantities vary in their relation to each other according to different
powers. For example, in fan ventilation, the fourth power of the speed
ADDENDA 331
(n4) of the fan varies as the fifth power of the quantity (qr°) of air in circula-
tion ; which is expressed as follows :
n -4 varies as q5
or n varies as q*; or r/'-25
and q varies as n5; or n0-8
The expression n« or the fourth-fifths power of n is identical with
V/rt4 or the fifth root of the fourth power of n. Hence, to extract the
root of a power, divide the exponent of the power by the index of the
desired root and the quotient will be the new exponent, which combines
the two operations in a single transaction.
Rules for the Use of Logarithms. — The following four simple rules cover
all the operations of logarithms:
1. Multiplication : To find the product of two or more numbers, add
their logarithms; the number corresponding to this logarithmic sum is the
desired product.
In other words, the logarithm of the product of two or more numbers is
equal to the sum of the logarithms of the numbers.
2. Division : To divide one number by another, subtract the logarithm
of the divisor from that of the dividend; the number corresponding to
this logarithmic remainder is the required quotient.
In other words, the logarithm of the quotient is equal to the logarithm
of the dividend minus that of the divisor.
3. Involution: To find any given power of a number, multiply the
logarithm of the number by the exponent of the power; the number corre-
sponding to the resulting logarithm is the required power of the given
number.
4. Evolution : To find any given root of a number, divide the logarithm
of the number by the index of the root; the number corresponding to the
resulting logarithm is the required root of the given number.
Arithmetical Complement. — The arithmetical complement of a loga-
rithm is the remainder found by subtracting the log from 10; the logarithm
of 3 is 0.47712, and its arithmetical complement is, therefore, 10 -
0.47712 = 9.52288. Its use involves subtracting from the final result
as many tens as have thus entered the solution. The antilog is more con-
venient for use.
The Antilog. — The solution of problems frequently involves the
multiplication and division of many quantities. In the use of logarithms,
the sum of the logs of the divisors would be subtracted from the sum of
the logs of the multipliers, to obtain the log of the final result. By the use
of what is called the "antilog" of each divisor, it is possible to complete
such a solution in a single operation, by adding together the logs of the
multipliers and the antilogs of the divisors.
The antilog of a number is obtained as follows: Subtract the mantissa
of its log from 1, for the mantissa of the antilog. Then, add 1 to the
characteristic of the log and change its sign, the addition being always
algebraic. The following examples will make the process understood:
332 MINE GASES AND VENTILATION
1. To find the antilog of 800: Log 800 = 2.90309
Mantissa of antilog, 1 - 0.90309 = 0.09691
Characteristic of antilog, 2 + 1 =3; and changing sign = — 3
Hence Antilog 800 = 3 . 09691
2. To find the antilog of 2: log 2 = 0.30103
Mantissa of antilog, • 1 - 0 . 30103 = 0 . 69897
Characteristic of antilog, 0 + 1 = 1 ; giving - 1
Hence Antilog 2 = T. 69897
3. To find the antilog of 0.4: Log 0.4 = T . 60206
Mantissa of antilog, 1 — 0 . 60206 = 0 . 39794
Characteristic of antilog, —1+1=0 (zero has no sign)
Hence Antilog 0.4 = 0.39794
4. To find the antilog of 0.00125: Log 0.00125 = 3.09691
Mantissa of antilog, 1 - 0.09691 = 0.90309
Characteristic of antilog, —3 + 1 = — 2; giving + 2
Hence Antilog 0.00125 =2.90309
Note. — The use of the antilog accomplishes the same purpose as the
arithmetical complement and requires no correction of the final result as
explained in reference to the latter. It should be observed that the
antilog of a number is always the log of the reciprocal of that number.
Thus, Log 800 = antilog 1/800 or 0.00125
As shown above, log 800 = 2.90309; antilog 0.00125 = 2.90309.
Example. — Solve the following by the use of logarithms:
_ ksq2 _ 0.00000002 X 40,000 X 50,0002
a3 ~ 503
Solution.— log 0.00000002 , 8.30103
log 40,000 4 . 60206
log 50,0002 (4.69897 X 2) 9.39794
antilog 503, (log 503 = 1.69897 X 3 = 5.09691) 6.90309
Log p 1.20412
Hence p = 16 Ib. per sq. ft.
LOGARITHMIC TABLES
COMMON LOGARITHMS OF NUMBERS
No.
Log.
No.
Log.
NO.
Log.
No.
Log.
NO.
Log.
0
— 00
20
30 103
40
60206
60
77 815
80
90 309-
l
00 000
21
32222
41
61 278
61
78 533
81
90849
2
30 103
22
34 242
42
62 325
62
79 239
82
91 381
8
47712
23
36 173
43
63 347
63
79 934
83
91 908
4
60 206
24
38 021
44
64 345
64
80 618
84
92428
5
69897
2-5
39 794
45
65 321
65
81 291
85
92 942
6
77 815
26
41 497
4fi
66 276
66
81 954
86
93 450
7
84 510
27
43 136
47
67 210
67
82 607
87
93952
8
90 309
28
44 716
48
68 124
68
83 251
88
94 448
9
95 424
29
46 240
49
69020
69
83 885
89
94 939
10
00000
30
47712
50
69 897 •
70
84.510
90
95 424
11
04 139
31
49 136
51
70 757
71
85 126
91
95904
12
07 918
32
50 515
5?,
71 600
72
85 733
92
% 379
13
11 394
33
51 851
53
72 428
73
86 332
93
96848
14
14 613
34
53 148
54
73 239
74
86 923
94
97 313
15
17 609
35
54 407
55
74 036
75
87506
95
97 772
16
20412
36
55 630
56
74 819
76
88081
96
98 227
17
23 045
37
56820
57
75 587
77
88 649
97
98 677
18
,25 527
38
57 978
58
76 343
78
89 209
98
99 123
19
27 875
39
59106
59
77 085
79
89 763
99
99 564
20
30103
40
60206
60
77815
80
90309
100
00000
333
334
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
too
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
ISO
00000
043
087
130
173
604
*030
452
870
284
694
*100
503
902
217
647
*072
494
912
325
735
*141
543
941
260
689
*115
536
953
366
776
*181
583
981
376
303
732
*157
578
995
407
816
*222
623
*021
415
346
775
*199
620
*036
449
857
*262
663
*060
454
389
c
7
8
1
1
2
3
4
5
G
7
8
y
i
•i
3
4
5
6
7
8
g
a
a
4
5
0
7
8
9
44
4.4
8.8
13.2
17.6
22.0
26.4
30.8
35.2
39.6
41
4.1
8.2
12.3
16.4
20.5
24.6
28.7
32.8
36.9
38
8.8
7.G
11.4
15.2
19.0
22.8
26.6
30.4
34.2
35
8.5
7.0
10.5
14.0
17.5
21.0
24.5
28.0
31.5
32
3.2
6.4
9.6
12.8
16.0
192
22.4
25.6
28.8
43
4.3
8.6
12.9
17.2
21.5
25.8
30.1
34.4
38.7
40
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
36.0
37
8.7
7.4
11.1
14.8
18.5
22.2
25.9
296
33.3
34
3.4
6.8
10.2
13.6
17.0
20.4
23.8
27.2
30.6
31
3.1
6.2
9.3
12.4
15.5
18.6
21.7
24.8
27.9
42
4.2
8.4
12.6
16.8
21.0
25.2
29.4
33.6
37.8
39
3.9
7.8
11.7
15.6
19.5
23.4
27.3
31.2
33.1
33
3.6
7.2
10.8
14.4
18.0
21.6
25.2
28.8
32.4
33
3.3
6.6
9.9
13.2
16.5
19.8
23.1
26.4
29.7
'30
3.0
6.0
9.0
12.0
15.0
18.0
21.0
24.0
27.0
432
860
01 284
703
02 119
531
938
03 342
743
04 139
475
903
326
745
160
572
979
383
782
518
945
368
787
202
612
*019
423
822
561
988
410
828
243
653
*060
463
862
817
*242
662
*078
490
898
*302
703
*100
179
571
961
346
729
108
483
856
225
591
218
258
650
*038
423
805
183
558
930
298
664
297
336
493
532
922
05 308
690
06 070
446
819
07 188
555
610
999
385
767
145
521
893
262
628
689
*077
461
843
221
595
967
335
700
*063
727
*115
500
881
258
633
*004
372
737
*099
458
814
*167
517
864
209
551
890
227
5G1
766
*154
538
918
296
670
*041
408
773
*135
805
*192
576
956
333
707
*078
445
809
844
*231
614
994
371
744
*115
482
846
*207
883
*2G9
652
*032
408
781
*151
518
882
*243
918
954
990
*027
386
743
*096
447
795
140
483
823
160
*171
08279
636
991
09 342
691
10037
380
721
11 059
314
672
*026
377
726
072
415
755
093
350
707
*061
412
760
106
449
789
126
422
778
*132
482
830
175
517
857
193
528
493
849
*202
552
899
243
585
924
261
594
529
884
*237
587
934
278
619
958
294
565
920
*272
621
968
312
653
992
327
600
955
*307
656
*003
346
687
*025
361
694
394
428
461
494
628
661
727
12 057
385
710
13 033
354
672
988
14 301
760
090
418
743
066
386
704
*019
333
644
793
123
450
775
098
418
735
*051
364
826
156
483
808
130
450
767
*082
395
860
189
516
840
162
481
799
*114
426
893
222
548
872
194
513
830
*145
457
768
926
254
581
905
226
545
862
*176
489
959
287
613
937
258
577
893
*208
520
992
320
646
9G9
290
609
925
*239
551
*024
352
678
*001
322
640
956
*270
582
613
675
706
*014
320
625
927
227
524
820
114
406
737
799
*106
412
715
*017
316
613
909
202
493
829
*137
412
746
*047
346
643
938
231
522
860
891
922
15229
534
836
16 137
435
732
17 026
319
953
259
564
866
167
465
761
056
348
983
290
594
897
197
495
791
085
377
*045
351
655
957
256
554
850
143
435
*076
381
685
987
286
584
879
173
464
*168
473
776
*077
376
673
967
260
551
*198
503
806
*107
406
702
997
289
580
1
•1
9
609
638
1
667
696
725
754
782
811
840
869
N.
L.O
2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
335
N.
L.O
1
2
3
4
5
6
7
8
9
P.]
>
150
17 609
638
667
696
725
754
782
811
840
869
151
152
153
154
155
156
157
158
159
898
18 184
469
752
19 033
312
590
866
20 140
926
213
498
780
061
340
618
893
167
955
241
526
808
089
368
645
921
194
984
270
554
837
117
396
673
948
222
*013
298
583
865
145
424
700
976
249
*041
327
611
893
173
451
728
*003
276
*070
355
639
921
201
479
756
*030
303
*099
384
667
949
229
507
783
*058
330
*127
412
696
977
257
535
811
*085
358
*156
441
724
*005
285
562
838
*112
385
8
9
29
2.9
5.8
8.7
11.6
14.5
1T.4
20.3
23.2
2G.1
28
2.8
5.6
8.4
11.2
14.0
16.8
19.6
22.4
25.2
160
412
439
466
493
520
548
575
602
629
656
161
162
163
164
165
166
167
168
169
683
952
21 219
484
7-18
22011
272
331
- 789
710
978
245
511
775
037
298
557
814
737
*005
272
537
801
063
324
583
840
763
*032
299
564
827
089
350
608
866
790
*059
325
590
854
115
376
634
891
817
*085
352
617
880
141
401
660
917
844
*112
378
643
906
167
427
686
913
871
*139
405
669
932
194
453
712
968
898
*165
431
696
958
220
479
737
994
925
*192
458
722
985
246
505
763
*019
9
27
2.7
5.4
8.1
10.8
13.5
16.2
18.9
21.6
24.3
26
2.6
5.2
7.8
10.4
13.0
15.6
18.2
20.8
23.4
170
23 045
070
096
121
147
172
198
223
249
274
- 171
172
173
174
175
176
177
178
179
300
553
805
24 055
304
551
797
25 042
285
325
578
830
080
329
576
822
066
310
350
603
855
105
353
601
846
091
334
376
629
880
130
378
625
871
115
358
401
654
905
155
403
650
895
139
382
426
679
930
180
428
674
920
164
406
452
704
955
204
452
699
944
188
431
477
729
980
229
477
724
969
212
455
502
754
*005
254
502
748
993
237
479
528
779
*030
279
527
773
*018
261
503
2
1 2
2 £
3 1
4 If
5 15
7 r
8 2f
9 21
5
.5
.0
.5
.0
.5
.0
.5
.0
.5
180
527
551
575
600
624
648
672
696
720
744
181
182
183
184
185
186
187
188
189
768
26 007
245
482
717
951
27 184
416
646
792
031
269
505
741
975
207
439
669
816
055
293
529
764
998
231
462
692
840
079
316
553
788
*021
254
485
715
864
102
340
576
811
*045
277
508
738
888
126
364
600
834
*068
300
531
761
912
150
387
623
858
*091
323
554
784
935
174
411
647
881
*114
346
577
807
959
198
435
670
905
*138
370
600
830
983
221
458
694
928
*1G1
393
623
852
1
2
3
4
5
6
7
8
9
24
2.4
4.8
7.2
9.6
12.0
14.4
16.8
19.2
21.6
23
2.3
4.6
6.9
9.2
11.5
13.8
16.1
18.4
20.7
190
875
898
921
944
967
989
*012
*035
*058
*081
191
192
193
194
195
196
197
198
199
28 103
330
556
780
29 003
226
447
667
885
126
353
578
803
026
248
469
688
907
149
375
601
825
048
270
491
710
929
171
308
623
847
070
292
513
732
951
194
421
646
870
092
314
535
754
973
217
443
668
892
115
336
557
776
994
240
466
691
914
137
358
579
798
*016
262
488
713
937
159
380
601
820
*038
285
511
735
959
181
403
623
842
*060
307
533
758
981
203
425
645
863
*081
1
2
3
4
5
6
7
8
9
22
2.2
4.4
6.6
8.8
11.0
13.2
15.4
17.6
19.8
21
2.1
4.2
6.3
8.4
10.5
12.6
14.7
16.8
18.9
200
30 103
125
146
168
190
211
233
255
276
298
N.
L.O
1
2
3
4
5
G
7
8
9
P.I
>
336
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
G
7
8
9
p
.1
:>
200
30 103
125
146
168
190
211
233
255
276
298
201
202
203
204
205
206
207
208
209
320
535
750
963
31 175
387
597
806
32 015
341
557
771
984
197
408
618
827
035
363
578
792
*006
218
429
639
848
056
384
600
814
*027
239
450
660
8G9
077
406
621
835
*048
260
471
681
890
098
428
643
856
*069
281
492
702
911
118
449
664
878
*091
302
513
723
931
139
471
685
899
*112
323
534
744
952
160
492
707
920
*133
345
555
765
973
181
514
728
942
*154
366
576
785
994
201
2
2
4
6
8
11
13
15
8 17
9 19
2
2
4
8
&
0
2
4
8
8
21
2.1
4.2
6.3
8.4
10.5
12.6
14.7
16.8
18.9
210
222
243
263
284
305
325
346
366
387
408
211
212
213
214
215
216
217
218
219
428
634
838
33 041
244
445
646
846
34 044
449
654
858
062
264
465
666
866
064
469
675
879
082
284
486
686
885
084
490
695
899
102
304
506
706
905
104
510
715
919
122
325
526
726
925
124
531
736
940
143
345
546
746
945
143
552
756
960
163
365
566
766
965
163
572
777
980
183
385
586
786
985
183
593
797
*001
203
405
606
806
*005
203
613
818
*021
224
425
626
826
*025
223
9
J
.1
.
(
1
1
1
1
1
1
!0
.0
.0
..0
.0
).0
.0
t.o
>.o
$.0
220
242
262
282
301
321
341
361
380
400
420
221
222
223
224
225
226
227
228
229
439
635
830
35 025
218
411
603
793
984
459
655
850
044
238
430
622
813
*003
479
674
869
064
257
449
641
832
*021
498
694
889
083
276
468
660
851
*040
518
713
908
102
295
488
679
870
*059
537
733
928
122
315
507
698
889
*078
557
753
947
141
334
526
717
908
*097
577
772
967
160
353
545
736
927
*116
596
792
986
180
372
564
755
946
*135
616
811
*005
199
392
583
774
965
*154
1
2
3
9
'
'
1
1
1
1
1
19
.9
3
;.6
}.5
.4
5.3
).2
1.1
230
36 173
192
211
229
248
267
286
305
324
342
231
232
233
234
235
236
237
238
239
361
549
736
922
37 107
291
475
658
840
380
568
754
940
125
310
493
676
858
399
586
773
959
144
328
511
694
876
418
605
791
977
162
346
530
712
894
436
624
810
996
181
365
548
731
912
455
642
829
*014
199
383
566
749
931
474
661
847
*033
218
401
585
767
949
493
680
866
*051
236
420
603
785
967
511
698
884
*070
254
438
621
803
985
530
717
903
*088
273
457
639
822
*003
9
1
1
]
1
n
.8
14
5.4
r.2
).0
).8
2.6
i.4
5.2
240
38 021
039
057
075
093
112
130
148
166
184
241
242
243
244
245
246
247
248
249
202
382
561
739
917
39 094
270
445
620
220
399
578
757
934
111
287
463
637
238
417
596
775
952
129
305
480
655
256
435
614
792
970
146
322
498
672
274
453
632
810
987
164
340
515
690
292
471
650
828
*005
182
358
533
707
310
489
668
846
*023
199
375
550
724
328
507
686
863
*041
217
393
568
742
346
525
703
881
*058
235
410
585
759
364
543
721
899
*076
252
428
602
777
1
2
3
4
5
6
7
8
9
1
1
1
I
1
(7
1.7
J4
>.l
5.8
5.5
).2
.9
J.6
>.3
250
794
811
829
846
863
881
898
915
933
950
N.
L.O
1
2
3
4
5
G
7
8
0
P
]
>
LOGARITHMIC TABLES
337
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
-271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
39794
811
829
846
863
881
898
915
933
950
8
9
1
8
9
1
2
3
4
5
6
7
8
9
18
1.8
8.6
5.4
7.2
9.0
10.8
12.6
14.4
16.2
17
1.7
3.4
5.1
6.8
8.5
10.2
11.9
13.6
15.S
16
1.6
3.2
4.8
6.4
8.0
9.6
11.2
12.8
14.4
IS
1.5
3.0
4.5
6.0
7.5
9.0
10.5
12.0
13.5
14
1.4
28
4.2
5.6
7.0
8.4
9.8
11.2
12.6
967
40 140
312
483
654
824
993
41 162
330
985
157
329
500
671
841
*010
179
347
*002
175
346
518
688
858
*027
196
363
*019
192
364
535
705
875
*044
212
380
*037
209
381
552
722
892
*061
229
397
*054
226
398
569
739
909
*078
246
414
*071
243
415
586
756
926
*095
263
430
*088
261
432
603
773
943
*111
280
447
*106
278
449
620
790
960
*128
296
464
*123
295
466
637
807
976
*145
313
481
497
514
531
547
564
581
597
614
631
647
664
830
996
42 160
325
488
651
813
975
681
847
*012
177
341
504
667
830
991
697
863
*029
193
357
521
684
846
*008
714
880
*045
210
374
537
700
862
*024
731
896
*062
226
390
553
716
878
*040
747
913
*078
243
406
570
732
894
*056
217
377
537
696
854
*012
170
326
483
638
764
929
*095
259
423
586
749
911
*072
780
946
*111
275
439
602
765
927
*088
797
963
*127
292
455
619
781
943
*104
814
979
*144
308
472
635
797
959
*120
43 136
152
169
185
201
361
521
680
838
996
154
311
467
623
233
393
553
712
870
*028
185
342
498
654
249
409
569
727
886
*044
201
358
514
669
265
425
584
743
902
*059
217
373
529
685
281
441
600
759
917
*075
232
389
545
700
297
457
616
775
933
44 091
248
404
560
313
473
632
791
949
107
264
420
576
329
489
648
807
965
122
279
436
592
345
505
664
823
981
138
295
451
607
716
731
747
762
778
793
809
824
840
855
871
45 025
179
332
484
637
788
939
46090
88.6
040
194
347
500
652
803
954
105
902
056
209
362
515
667
818
969
120
917
071
225
378
530
682
834
984
135
932
086
240
393
545
697
849
*000
150
948
102
255
408
561
712
864
*015
165
963
117
271
423
576
728
879
*030
180
979
133
286
439
591
743
894
*045
195
994
148
301
454
606
758
909
*060
210
*010
163
317
469
621
773
924
*075
225
240
255
270
285
434
583
731
879
*026
173
319
465
611
300
315
330
345
494
642
790
938
*085
232
378
524
669
359
374
389
538
687
835
982
47 129
276
422
567
404
553
702
850
997
144
290
436
582
419
568
716
864
*012
159
305
451
596
449
598
746
894
*041
188
334
480
625
464
613
761
909
*056
202
349
494
640
479
627
776
923
*070
217
363
509
654
509
657
805
953
*100
246
392
538
683
523
672
820
967
*114
261
407
553
698
712
727
741
756
770
784
799
813
828
842
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
338
MINE GASES AND VENTILATION
N.
L.O
1
2
3
756
900
044
187
330
473
615
756
897
*038
4
5
6
799
943
087
230
373
515
657
799
940
*080
7
813
958
101
244
387
530
671
813
954
*094
8
9
P.P.
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
47 712
727
871
015
159
302
444
586
728
869
*010
741
885
029
173
316
458
601
742
883
*024
770
784
828
842
986
130
273
416
558
700
841
982
*122
262
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
15
1.5
3.0
4.5
6.0
7.5
9.0
10.5
12.0
13.5
14
1.4
2.8
4.2
5.8
7.0
8.4
9.8
11.2
12.6
13
1.3
2.6
3.9
52
6.5
7.8
9.1
10.4
11.7
it
1.2
2.4
3.6
4.8
6.0
7.2
8.4
9.6
10.8
857
48 001
144
287
430
572
714
855
996
914
058
202
344
487
629
770
911
*052
929
073
216
359
501
643
785
926
*066
972
116
259
401
544
686
827
968
*108
49 136
150
290
429
568
707
845
982
120
256
393
164
178
192
332
471
610
748
886
*024
161
297
433
206
346
485
624
762
900
*037
174
311
447
220
234
248
276
415
554
693
831
969
50 106
243
379
304
443
582
721
859
996
133
270
406
318
457
596
734
872
*010
147
284
420
360
499
638
776
914
*051
188
325
461
374
513
651
790
927
*065
202
338
474
388
527
665
803
941
*079
215
352
488
402
541
679
817
955
*092
229
365
501
515
529
542
556
691
826
961
095
228
362
495
627
759
891
569
583
596
610
745
880
*014
148
282
415
548
680
812
623
759
893
*028
162
295
428
561
693
825
637
651
. 786
920
ol 055
188
322
455
587
720
664
799
934
068
202
335
468
601
733
678
813
947
081
215
348
481
614
746
705
840
974
108
242
375
508
640
772
718
853
987
121
255
388
521
654
786
732
866
*001
135
268
402
534
667
799
772
907
*041
175
308
441
574
70G
838
970
*101
231
362
492
621
750
879
*007
135
851
865
996
127
257
388
517
647
776
905
033
161
878
904
917
930
*061
192
323
453
582
711
840
969
097
224
943
*075
205
336
466
595
724
853
982
110
957
983
o2 114
244
375
504
634
763
892
53 020
*009
140
270
401
530
660
789
917
046
173
*022
153
284
414
543
673
802
930
058
186
*035
166
297
427
556
686
815
943
071
199
*048
179
310
440
569
699
827
956
084
212
*088
218
349
479
608
737
866
994
122
148
237
250
263
341
342
343
344
345
346
347
348
349
350
275
403
529
656
782
908
54033
158
283
288
415
542
668
794
920
045
170
295
301
428
555
681
807
933
058
183
307
314
441
567
694
820
945
070
195
320
326
453
580
706
832
958
083
208
332
339
466
593
719
845
970
095
220
345
352
479
605
732
857
983
108
233
357
481
364
491
618
744
870
995
120
245
370
377
504
631
757
882
*008
133
258
382
390
517
643
769
895
*020
145
270
394
407
419
432
444
456
469
494
506
8
518
N.
L.O
1
2
3
4
5
6
7
9
P.P.
LOGARITHMIC TABLES
339
N.
L.O
1
2
3
4
456
580
704
827
949
072
194
315
437
558
5
6
7
8
9
P.P.
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
54 407
419
432
444
469
481
494
506
518
6
7
8
9
1
2
3
4
5
6
7
8
9
8
9
1
8
9
13
1.3
2.6
3.9
5.2
6.5
7.8
9.1
10.4
11,7
12
1.2
2.4
3.6
4.8
6.0
7.2
8.4
9.6
10.8
II
1.1
2.2
3.3
4.4
5.5
6.6
7.7
8.8
9.9
10
1.0
2,0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
531
654
777
900
55 023
145
267
388
509
543
667
790
913
035
157
279
400
522
555
679
802
925
047
169
291
413
534
654
568
691
814
937
060
182
303
425
546
593
716
839
962
084
206
328
449
570
605
728
851
974
096
218
340
461
582
703
823
943
*062
182
301
419
538
656
773
617
741
864
986
108
230
352
473
594
630
753
876
998
121
242
364
485
606
727
847
967
*086
205
324
443
561
679
797
642
765
888
*011
133
255
376
497
618
630
642
666
678
691
715
835
955
*074
194
312
431
549
667
785
739
859
979
*098
217
336
455
573
691
808
751
871
991
56 110
229
348
467
585
703
763
883
*003
122
241
360
478
597
714
775
895
*015
134
253
372
490
608
726
787
907
*027
146
265
384
502
620
738
799
919
*038
158
277
396
514
632
750
811
931
*050
170
289
407
526
644
761
820
832
844
855
867
879
891
902
914
926
937
57 054
171
287
403
519
634
749
864
949
066
183
299
415
530
646
761
875
961
078
194
310
426
542
657
772
887
972
089
206
322
438
553
669
784
898
*013
984
101
217.
334
449
565
680
795
910
996
113
229
345
461
576
692
807
921
*008
124
241
357
473
588
703
818
933
*019
136
252
368
484
600
715
830
944
*058
*031
148
264
380
496
611
726
841
955
*043
159
276
392
507
623
738
852
967
978
990
*001
*024
*035
149
263
377
490
602
715
827
939
*051_
162
*047
*070
*081
58092
206
320
433
546
659
771
883
995
104
218
331
444
557
670
782
894
*006
115
229
343
456
569
681
794
906
*017
127
240
354
467
580
692
805
917
*028
138
252
365
478
591
704
816
928
*040
161
274
388
501
614
726
838
950
*062
173
172
286
399
512
625
737
850
961
*073
184
297
410
524
636
749
861
973
*084
195
309
422
535
647
760
872
984
*095
59 106
218
329
439
550
660
770
879
988
60 097
118
129
140
151
184
195
207
229
340
450
561
671
780
890
999
108
240
351
461
572
682
791
901
*010
119
251
362
472
583
693
802
912
*021
130
262
373
483
594
704
813
923
*032
141
273
384
494
605
715
824
934
*043
152
284
395
506
616
726
835
945
*054
163
271
295
406
517
627
737
846
956
*065
173
306
417
528
638
748
857
966
*076
184
318
428
539
649
759
868
977
*086
195
304
206
217
228
239
249
260
282
293
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
340
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
7
Q
9
P.P.
400
60 206
217
228
239
249
260
271
282
293
304
401
402
403
404
405
406
407
408
409
314
423
531
638
746
853
959
61 066
172
325
433
541
643
756
863
970
077
183
336
444
552
660
767
874
981
087
194
347
455
563
670
778
885
991
098
204
358
466
574
681
788
895
*002
109
215
369
477
584
692
799
906
*013
119
225
379
487
595
703
810
917
*023
130
236
390
498
606
713
821
927
*034
140
247
401
509
617
724
831
938
*045
151
257
412
520
627
735
842
949
*055
162
268
II
l.l
2.2
410
278
289
300
310
321
331
342
352
363
374
i *•*
411
412
413
414
415
416
417
418
419
384
490
595
700
805
909
62 014
118
221
395
500
606
711
81''
920
024
128
232
405
511
616
'.21
826
930
034
138
242
416
521
627
731
836
941
045
149
252
426
532
637
742
847
951
055
159
263
437
542
648
752
857
962
066
170
273
448
553
658
763
868
972
076
180
284
458
563
669
773
878
982
086
190
294
469
574
679
784
888
993
097
201
304
479
584
690
794
899
*003
107
211
315
1 6.6
7 7.7
8 8.8
9 9.9
420
325
335
346
356
366
377
387
397
408
418
421
422
423
424
425
426
427
428
429
428
531
634
737
839
941
63 043
144
246
439
542
644
747
849
951
053
155
256
449
552
655
757
859
961
063
165
266
459
562
665
767
870
972
073
175
276
469
572
675
778
880
982
083
185
286
480
583
685
788
890
992
094
195
296
490
593
696
798
900
*002
104
205
306
500
603
706
808
910
*012
114
215
317
511
613
716
818
921
*022
124
225
327
521
624
.726
829
931
*033
134
236
337
1 1.1.0
2 2.0
3 3.0
4 4.0
5 5.0
6 6.0
7 7.0
8 8.0
9 . 9.0
430
347
357
367
377
387
397
407
417
428
438
431
432
433
434
435
436
437
438
439
448
548
649
749
849
949
64048
147
246
458
558
659
759
859
959
058
157
256
468
568
669
769
869
969
068
167
266
478
579
679
779
879
979
078
177
276
488
589
689
789
889
988
088
187
286
498
599
699
799
899
998
098
197
296
508
609
709
809
909
*008
108
207
306
518
619
719
819
919
*018
118
217
316
528
629
729
829
929
*028
128
227
326
538
639
739
839
939
*038
137
237
335
9
1 0.9
2 1.8
3 2.7
440
345
355
365
375
385
395
404
414
424
434
5 4.5
441
442
443
444
445
446
447
448
449
444
542
640
738
836
933
65 031
' 128
225
454
552
650
748
846
943
040
137
234
464
562
660
758
856
953
050
147
244
473
572
670
768
865
963
060
157
254
483
582
680
777
875
972,
070
167
263
493
591
689
787
885
982
079
176
273
503
601
699
797
895
992
089
186
283
513
611
709
807
904
*002
099
196
292
523
621
719
816
914
*011
108
205
302
532
631
729
826
924
*021
118
215
312
7 6.3
8 ' 7.2
9 , 8.1
450
321
331
341
350
360
369
379
389
398
408
N.
L.O
1
2
3
4
5
6
7
8
9
P. P.
LOG A Rl TUMI C TA BLES
341
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
4%
497
498
499
500
65 321
331
841
350
447
543
639
734
830
925
*020
115
210
360
456
552
648
744
839
935
*030
124
219
369
466
562
658
753
849
944
*039
134
229
379
475
571
667
763
858
954
*049
143
238
389
485
581
677
772
868
963
*G58
153
247
398
495
591
686
782
877
973
*068
162
257
351
445
539
633
727
820
913
*006
099
191
408
504
600
696
792
887
982
*077
172
266
861
10
1 1.0
2 2.0
3 3.0
4 4.0
• 5 5.0
6 6.0
7 I T.O
8 8.0
9 9.0
9
0.9
1.8
2.7
3.6
4.5
5.4
6.3
8 7.2
9 | 8.1
8
0.8
1.6
2.4
3.2
4.0
I 4.8
5.6
8 6.4
9 7.2
418
514
610
706
801
896
992
66 087
181
427
523
619
715
811
906
*001
096
191
285
437
533
629
725
820
916
*011
106
200
276
295
304
398
492
586
680
773
867
960
052
145
314
408
602
596
689
783
876
969
062
154
323
417
511
605
699
792
885
•978
071
164
332
427
521
614
708
801
894
987
080
173
342
370
464
558
652
745
839
932
67025
117
380
474
567
661
755
848
941
034
127
389
483
577
671
764
857
950
043
136
436
530
624
717
811
904
997
089
182
455
549
642
736
829
922
*015
108
201
210
219
228
237
247
256
265
274
284
376
468
560
651
742
834
925
*015
106
293
385
477
569
660
752
843
934
*024
115
302
394
486
578
669
761
852
943
68 034
311
403
495
587
679
770
861
952
043
321
413
504
596
688
779
870
961
052
330
422
514
605
697
788
879
970
061
339
431
523
614
706
797
888
979
070
348
440
532
624
715
806
897
988
079
169
357
449
541
633
724
815
906
997
088
367
459
550
642
733
825
916
*006
097
124
133
224
314
404
494
583
673
762
851
940
142
233
323
413
502
592
681
771
860
949
151
242
332
422
511
601
690
780
869
958
160
178
187
278
368
458
547
637
726
815
904
993
196
287
377
467
556
646
735
824
913
*002
205
215
305
395
485
574
664
753
842
931
251
341
431
520
610
699
789
878
966
260
350
440
529
619
708
797
886
975
269
359
449
538
628
717
806
895
984
296
386
476
565
655
744
833
922
*011
69020
028
037
046
055
064
073
082
090
099
108
197
285
373
461
548
636
723
810
117
205
294
381
469
557
644
732
819
126
214
302
390
478
566
653
740
827
135
223
311
399
487
574
662
749
836
144
232
320
408
496
583
671
758
845
152
241
329
417
504
592
679
767
854
161
249
338
425
513
601
688
775
862
170
258
346
434
522
609
697
784
871
179
267
355
443
531
618
705
793
880
188
276
364
452
539
627
714
801
888
975
897
906
914
923
932
940
949
958
966
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
342
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
69 897
906
992
079
165
252
338
424
509
595
680
914
923
*010
096
183
269
355
441
526
612
697
783
932
940
949
*036
122
209
295
381
467
552
638
723
958
*044
131
217
303
389
475
561
646
731
966
*053
140
226
312
398
484
569
655
740
975
*062
148
234
321
406
492
578
663
749
9
0.9
1.8
2.7
3.6
4.5
5.4
6.3
7.2
8.1
8
0.8
1.6
2.4
3.2
4.0
4.8
5.6
6.4
7.3
7
1 I 0.7
2 1.4
8 2.1
4 2.8
5 3.5
6 4.2
7 4.9
8 56
9 6.3
984
70 070
157
243
329
415
501
586
672
*001
088
174
260
346
432
518
603
689
774
*018
105
191
278
364
449
535
621
706
791
*027
114
200
286
372
458
544
629
714
757
766
800
808
817
825
834
842
927
71 012
096
181
265
349
433
517
600
851
935
020
105
189
273
357
441
525
609
859
944
029
113
198
282
366
450
533
617
868
952
037
122
206
290
374
458
542
625
876
961
046
130
214
299
383
466
550
634
885
969
054
139
223
307
391
475
559
642
893
978
063
147
231
315
399
483
567
650
902
986
071
155
240
324
408
492
575
910
995
079
164
248
332
416
500
584
667
919
*003
088
172
257
341
425
508
592
659
675
759
842
925
*008
090
173
255
337
419
501
684
767
850
933
72 016
099
181
263
346
692
775
858
941
024
107
189
272
354
700
784
867
950
032
115
198
280
362
709
792
875
958
041
123
206
288
370
717
800
883
966
049
132
214
296
378
725
809
892
975
057
'140
222
304
387
734
817
900
983
066
148
230
313
395
742
825
908
991
074
156
239
321
403
750
834
917
999
082
165
247
329
411
493
428
436
444
452
460
469
477
485
509
591
673
754
835
916
997
73 078
159
518
599
681
762
843
925
*006
086
167
247
526
607
689
770
852
933
*014
094
175
255
534
616
697
779
860
941
*022
102
183
542
624
705
787
868
949
*030
111
191
550
632
713
795
876
957
*038
119
199
558
640
722
803
884
965
*046
127
207
567
648
730
811
892
973
*054
135
215
296
575
656
738
819
900
981
*062
143
223
304
583
665
746
827
908
989
*070
151
231
312
392
472
552
632
711
791
870
949
*028
239
263
272
280
360
440
520
600
679
759
838
918
997
288
320
400
480
560
640
719
799
878
957
328
408
488
568
648
727
807
886
965
336
416
496
576
«56
735
815
894
973
344
424
504
584
664
743
823
902
981
352
432
512
592
672
751
830
910
989
368
448
528
608
687
767
846
926
*005
376
456
536
616
695
775
854
933
*013
092
384
464
544
624
703
783
862
941
*020
74036
044
052
060
068
076
084
099
107
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
343
N.
L.O
1
2
3
4
5
G
7
8
9
P.P.
550
74 036
044
052
060
068
076
084
092
099
107
651
552
553
554
555
556
557
558
559
115
194
273
351
429
507
586
663
741
123
202
280
359
437
515
593
671
749
131
210
288
367
445
523
601
679
7'57
139
218
296
374
453
531
609
687
764
147
225
304
382
461
539
617
695
772
155
233
312
390
468
547
624
702
780
162
241
320
398
476
554
632
710
788
170
249
327
406
484
562
640
718
796
178
257
335
414
492
570
648
726
803
186
265
343
421
500
578
656
733
811
560
819
827
834
842
850
858
865
873
881
889
g
561
562
563
564
565
566
567
568
569
896
974
75 051
128
205
282
358
435
511
904
981
059
136
213
289
366
442
519
912
989
066
143
220
297
374
450
526
920
997
074
151
228
305
381
458
534
927
*005
082
159
236
312
389
465
542
935
*012
089
166
243
320
397
473
549
943
*020
097
174
251
328
404
481
557
950
*028
105
182
259
335
412
488
565
958
*035
113
189
266
343
420
496
572
966
*043
120
197
274
351
427
504
580
0.8
1.6
2.4
3.2
4.0
4.8
5.6
8 6.4
9 7.2
570
587
595
603
610
618
626
633
641
648
656
571
572
573
574
575
576
577
578
579
664
740
815
891
967
76 042
118
193
268
671
747
823
899
974
050
125
200
275
679
755
831
906
982
057
133
208
283
686
762
838
914
989
065
140
215
290
694
770
846
921
997
072
148
223
298
702
778
853
929
*005
080
155
230
305
709
785
861
937
*012
087
163
238
313
717
793
868
944
*020
095
170
245
320
724
800
876
952
*027
103
178
253
328
732
808
884
959
*035
110
185
260
335
580
343
350
358
365
373
380
388
395
403
410
7
581
582
583
584
585
586
587
588
589
418
492
567
641
716
790
864
938
77 012
425
500
574
649
723
797
871
945
019
433
507
582
656
730
805
879
953
026
440
515
589
664
738
812
886
960
034
448
522
597
671
745
819
893
967
041
455
530
604
678
753
827
901
975
048
462
537
612
686
760
834
908
982
056
470
545
619
693
768
842
916
989
063
477
552
626
701
775
849
923
997
070
485
559
634
708
782
856
930
*004
078
1 0.7
2 1.4
3 2.1
4 2.8
5 3.5
6 4.2
7 4.9
8 5.6
9 6.S
590
085
093
100
107
115
122
129
137
144
151
591
592
593
594
595
596
597
598
599
159
232
305
379
452
525
597
670
743
166
240
313
386
459
532
605
677
750
173
247
320
393
466
539
612
685
757
181
254
327
401
474
546
619
692
764
188
262
335
408
481
554
627
699
772
195
269
342
415
488
561
634
706
779
203
276
349
422
495
568
641
714
786
210
283
357
430
503
576
648
721
793
217
291
364
437
510
583
656
728
801
225
298
371
444
517
590
663
735
808
600
815
822
830
837
844
851
859
866
873
880
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
344
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
600
77 815
822
830
837
844
851
859
866
873
880
601
602
603
604
605
606
607
608
609
887
960
78 032
104
176
247
319
390
462
895
967
039
111
183
254
326
398
469
902
974
046
118
190
262
333
405
476
909
981
053
125
197
269
340
412
483
916
988
061
132
204
276
347
419
490
924
996
068
140
211
283
355
426
497
931
*003
075
147
219
290
362
433
504
938
*010
082
154
226
297
369
440
512
945
*017
089
161
233
305
376
447
519
952
*025
097
168
240
312
383
455
526
8
1 0.8
2 1.6
610
533
540
547
554
561
569
576
583
590
597
4 8.2
611
612
613
614
615
616
617
618
619
604
675
746
817
888
958
79 029
099
169
611
682
753
824
895
965
036
106
176
618
689
760
831
902
972
043
113
183
625
696
767
838
909
979
050
120
190
633
704
774
845
916
986
057
127
197
640
711
781
852
923
993
064
134
204
647
718
789
859
930
*000
071
141
211
654
725
796
866
937
*007
078
148
218
661
732
803
873
944
*014
085
155
225
668
739
810
880
951
*021
092
162
232
6 4.8
7 5.6
8 6.4
9 j 7.2
620
239
246
253
260
267
274
281
288
295
302
621
622
623
624
625
626
627
628
629
309
379
449
518
588
657
727
796
865
316
386
456
525
595
664
734
803
872
323
393
463
532
602
671
741
810
879
330
400
470
539
609
678
748
817
886
337
407
477
546
616
685
754
824
893
344
414
484
553
623
692
761
831
900
351
421
491
560
630
699
768
837
906
358
428
498
567
637
706
775
844
913
365
435
505
574
644
713
782
851
920
372
442
511
581
650
720
789
858
927
1 0.7
2 1 1.4
3 2.1
4 2.S
5 3.5
6 4.2
7 4.9
8 5.6
9 6.3
630
934
941
948
955
962
969
975
982
989
9%
631
632
633
634
635
636
637
638
639
80003
072
140
209
277
346
414
482
550
010
079
147
216
284
353
421
489
557
017
085
154
223
291
359
428
496
564
024
092
161
229
298
366
434
502
570
030
099
168
236
305
373
441
509
577
037
106
175
243
312
380
448
516
584
044
113
182
250
318
387
455
523
591
051
120
188
257
325
393
462
530
598
058
127
195
264
332
400
468
536
604
065
134
202
271
339
407
475
543
611
6
1 0.6
1.1
1.8
640
618
625
632
638
645
652
659
665
672
679
, 3.0
641
642
643
644
645
646
647
648
649
686
754
821
889
956
81 023
090
158
224
693
760
828
895
963
030
097
164
231
699
767
835
902
969
037
104
171
238
706
774
841
909
976
043
111
178
245
713
781
848
916
983
050
117
184
251
720
787
855
922
990
057
124
191
258
726
794
862
929
996
064
131
198
265
733
801
868
936
*003
070
137
204
271
740
808
875
943
*010
077
144
211
278
747
814
882
949
*017
084
151
218
285
7 j 4.2
8 4.8
9 5.4
650
291
298
305
311
318
325
331
338
345
351
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
345
N.
L.O
1
298
2
305
3
311
4
5
6
331
7
338
8
345
9
351
P.P.
650
651
652
653
654
655
656
657
658
659
660
6fil
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
81 291
318
325
7
1 O.T
2 1.4
3 2.1
4 2.8
5 3.5
6 4.2
7 4.9
8 5.6
9 6.3
6
1 0.6
2 1.2
1.8
' 2.4
3.0
3.6
4.2
4.8
5.4
358
425
491
558
624
690
757
823
889
365
431
498
564
631
697
763
829
895
371
438
505
571
637
704
770
836
902
378
445
511
578
644
710
776
842
908
385
451
518
584
651
717
783
849
915
391
458
525
591
657
723
790
856
921
398
465
531
598
664
730
796
862
928
405
471
538
604
671
737
803
869
935
411
478
544
611
677
743
809
875
941
418
485
551
617
684
750
816
882
948
954
961
968
_974
040
105
171
236
302
367
432
497
562
981
046
112
178
243
308
373
439
504
569
633
987
994
*000
*007
*014
079
145
210
276
341
406
471
636
601
82 020
086
151
217
282
347
413
478
543
027
092
158
223
289
354
419
484
549
033
099
164
230
295
360
426
491
556
053
119
184
249
315
380
445
510
575
640
060
125
191
256
321
387
452
517
582
066
132
197
263
328
393
458
523
588
653
073
138
204
269
334
400
465
530
595
659
607
614
620
627
646
666
672
737
802
866
930
995
83 059
123
187
679
743
808
872
937
*001
065
129
193_
257
685
750
814
879
943
*008
072
136
200
692
756
821
885
950
*014
078
142
206
698
763
827
892
956
*020
085
149
213
705
769
834
898
963
*027
091
155
219
711
776
840
905
969
*033
097
161
225
718
782
847
911
975
*040
104
168
232
724
789
853
918
982
*046
110
174
238
730
795
860
924
988
*052
117
181
245
251
264
270
334
398
461
525
588
651
715
JZ
904
276
283
289
296
359
423
487
550
613
677
740
803
866
302
366
429
493
556
620
683
746
809
872
308
315
378
442
506
569
632
696
759
822
321
385
448
512
575
639
702
765
828
891
327
391
455
518
582
645
708
771
835
340
404
467
531
594
658
721
784
847
910
347
410
474
537
601
664
727
790
853
916
353
417
480
544
607
670
734
797
860
923
372
436
499
563
626
689
753
816
879
885
897
929
992
055
117
180
242
305
367
429
491
553
935
942
948
84 Oil
073
136
198
261
323
386
448
954
017
080
142
205
267
330
392
454
960
023
086
148
211
273
336
398
460
967
029
092
155
217
280
342
404
466
528
973
036
098
161
223
286
348
410
473
979
042
105
167
230
292
354
417
479
985
048
111
173
236
298
361
423
485
547
998
061
123
186
248
311
373
435
497
*004
067
130
192
255
317
379
442
504
510
516
522
535
&41
559
566
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
346
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
7
8
9
————————
P.P.
700
84 510
516
522
528
535
541
547
553
559
566
701
702
703
704
. 705
706
707
708
709
572
634
696
757
819
880
942
85 003
065
578
640
702
763
825
887
948
009
071
584
646
708
770
831
893
954
016
077
590
652
714
776
837
899
960
022
083
597
658
720
782
844
905
967
028
089
603
665
726
788
850
911
973
034
095
609
671
733
794
856
917
979
040
101
615
677
739
800
862
924
985
046
107
621
683
745
807
868
930
991
052
114
628
689
751
813
874
936
997
058
120
7
1 0.7
2 1.4
710
126
132
138
144
150
156
163
169
175
181
3 2.1
4 2.8
711
712
713
714
715
716
717
718
719
187
248
309
370
431
491
552
612
673
193
254
315
376
437
497
558
618
679
199
260
321
382
443
503
564
625
685
205
266
327
388
449
509
570
631
691
211
272
333
394
455
516
576
637
697
217
278
339
400
461
522
582
643
703
224
285
345
406-
467
528
588
649
709
230
291
352
412
473
534
594
655
715
236
297
358
418
479
540
600
661
721
242
303
364
425
485
546
606
667
727
5 3.5
6 4.2
T 4.9
8 5.6
9 6.3
720
733
739
745
751
757
763
769
775
781
788
721
722
723
724
725
726
727
728
729
794
854
914
974
86 034
094
153
213
273
800
860
920
980
040
100
159
219
279
806
866
926
986
046
106
165
225
285
812
872
932
992
052
112
171
231
291
818
878
938
998
058
118
177
237
297
824
884
944
*004
064
124
183
243
303
830
890
950
*010
070
130
189
219
308
836
896
956
*016
076
136
195
255
314
842
902
962
*022
082
141
201
261
320
848
908
968
*028
088
147
207
267
326
6
1 n.f?
2 1.2
3 1.8
4 2.4
5 3.0
6 3.6
7 4.2
8 4.8
9 5.4
730
332
338
344
350
356
362
368
374
380
386
731
732
733
734
735
736
737
738
739
392
451
510
570
629
688
747
806
864
398
457
516
576
635
694
753
812
870
404
463
522
581
641
700
759
817
876
410
469
528
587
646
705
764
823
882
415
475
534
593
652
711
770
829
888
421
481
540
599
658
717
776
835
894
427
487
546
605
664
723
782
841
900
433
493
552
611
670
729
788
847
906
439
499
558
617
676
735
794
853
911
445
504
564
623
682
741
800
859
917
5
0.5
1.0
1.5
740
923
929
935
941
947
953
958
964
970
976
2.5
741
742
743
744
745
746
747
748
749
982
87 040
099
157
216
274
332
390
448
988
046
105
163
221
280
338
396
454
994
052
111
169
227
286
344
402
460
999
058
116
175
233
291
349
408
466
*005
064
122
181
239
297
355
413
471
*011
070
128
186
245
303
361
419
477
*017
075
134
192
251
309
367
425
483
*023
081
140
198
256
315
373
431
489
*029
087
146
204
262
320
379
437
495
*035
093
151
210
268
326
384
442
.500
8.5
4.0
46
750
506
512
518
523
529
535
541
547
552
558
N.
L.O
1
•2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
347
N.
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
L.O
87 506
1
512
570
628
685
743
800
858
915
973
030
2
518
576
633
691
749
806
864
921
978
036
3
523
581
639
697
754
812
869
927
984
041
4
529
587
645
703
760
818
875
933
990
047
5
535
6
7
8
9
P.P.
541
547
552
558
6
1 0.6
2 1.2
3 1.8
4 2.4
5 3.0
6 3.6
7 4.2
8 4.8
9 5.4
5
1 0.5
2 1.0
3 1.5
4 2.0
5 2.5
6 3.0
7 3.5
8 4.0
9 4.5
564
622
679
737
795
852
910
967
88 024
593
651
708
766
823
881
938
996
053
599
656
714
772
829
887
944
*001
058
604
662
720
777
835
892
950
*007
064
610
668
726
783
841
898
955
*013
070
616
674
731
789
846
904
961
*018
076
133
081
087
093
098
104
110
116
121
127
138
195
252
309
366
423
480
536
593
144
201
258
315
372
429
485
542
598
655
150
207
264
321
377
434
491
647
604
156
213
270
326
383
440
497
553
610
666
161
218
275
332
389
446
502
559
615
672
167
224
281
338
395
451
508
564
621
677
173
230
2S7
343
400
457
513
570
627
178
235
292
349
406
463
519
576
632
184
241
298
355
412
468
525
581
638
190
247
304
360
417
474
530
587
643
700
649
660
683
689
694
705
762
818
874
930
986
89042
098
154
711
767
824
880
936
992
048
104
159
717
773
829
885
941
997
053
109
165
722
779
835
891
947
*003
059
115
170
728
784
840
897
953
*009
064.
120
176
734
790
846
902
958
*014
070
126
182
739
795
852
908
964
*020
076
131
187
745
801
857
913
969
*025
081
137
193
750
807
863
919
975
*031
087
143
198
756
812
868
925
981
*037
092
148
204
209
215
221
226
232
237
243
248
254
260
315
371
426
481
537
592
647
702
757
265
321
376
432
487
542
597
653
708
271
326
382
437
492
548
603
658
713
276
332
387
443
498
553
609
664
719
774
282
337
393
448
504
559
614
669
724
779
287
343
398
454
509
564
620
675
730
293
348
404
459
515
570
625
680
735
298
354
409
465
520
575
631
686
741
796
304
360
415
470
526
581
636
691
746
310
3G5
421
476
531
586
642
697
752
763
768
785
790
801
856
911
966
*020
075
129
184
238
293
347
8071
812
867
922
977
*031
086
140
195
249
304
818
873
927
982
90 037
091
146
200
255
823
878
933
988
042
097
151
206
260
829
883
938
993
048
102
157
211
266
834
889
944
998
053
108
162
217
271
840
894
949
*004
059
113
168
222
276
845
900
955
*009
064
119
173
227
282
851
905
960
*015
069
124
179
233
287
862
916
971
*026
080
135
189
244
298
309
314
320
325
331
336
342
352
358,
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
348
MINE GASES AND VENTILATION
N.
L.O
1
. 2
3
4
5
6
7
8
9
P.P.
800
90309
314
320
325
331
336
342
347
352
358
801
802
803
804
805
806
807
808
809
363
417
472
526
580
634
687
741
795
369
423
477
531
585
639
693
747
800
374
428
482
536
590
644
698
752
806
380
434
488
542
596
650
703
757
811
385
439
493
547
601
655
709
763
816
390
445
499
553
607
660
714
768
822
396
450
504
558
612
666
720
773
827
401
455
509
563
617
671
725
779
832
407
461
515
569
623
677
730
784
838
412
466
520
574
628
682
736
789
843
810
849
854
859
865
870
•875
881
886
891
897
811
812
813
814
815
816
817
818
819
902
956
91 009
. 062
116
169
222
275
328
907
961
014
068
121
174
228
281
334
913
966
020
073
126
180
233
286
339
918
972
025
078
132
185
238
291
344
924
977
030
084
137
190
243
297
350
929
982
036
089
142
196
249
302
355
934
988
041
094
148
201
254
307
360
940
993
046
100
153
206
259
312
365
945
998
052
105
158
212
265
318
371
950
*004
057
110
164
217
270
323
376
1 1 0.6
2 1.2
3 i 1.8
4 ; 2.4
5 3.0
6 3.6
7 : 4.2
8 ! 4.8
9 | 5.4
820
381
387
392
397
403
408
413
418
424
429
821
822
823
824
825
826
827
828
829
434
487
540
593
645
698
751
803
855
440
492
545
598
651
703
756
808
861
445
498
551
603
656
709
761
814
866
450
503
556
609
661
714
766
819
871
455
508
561
614
666
719
772
824
876
461
514
566
'619
672
724
777
829
882
466
519
572
624
677
730
782
834
887
471
524
577
630
682
735
787
840
892
477
529
582
635
687
740
793
845
897
482
535
587
640
693
745
798
850
903
830
908
913
918
924
929
934
939
944
950
955
5
831
832
833
834
835
836
837
838
839
960
92 012
065
117
169
221
273
324
376
965
018
070
122
174
226
278
330
381
971
023
075
127
179
231
283
335
387
976
028
080
132
184
236
288
340
392
981
033
085
137
189
241
293
345
397
986
038
091
143
195
247
298
350
402
991
044
096
148
200
252
304
355
407
997
049
101
153
205
257
309
361
412
*002
054
106
158
210
262
314
366
418
*007
059
111
163
215
267
319
371
423
|
0.5
: i.o
1.5
: 2.0
2.5
3.0
' 8.5
8 4.0
9 4.5
840
428
433
438
443
449
454
459
464
469
474
841
842
843
844
845
846
847
848
849
480
531
583
634
686
737
788
840
891
485
536
588
639
691
742
793
845
8%
490
542
593
645
696
747
799
850
901
495
547
598
650
701
752
804
855
906
500
552
603
655
706
758
809
860
911
505
557
609
660
711
763
814
865
916
511
562
614
665
716
768
819
870
921
516
567
619
670
722
773
824
875
927
521
572
624
675
727
778
829
881
932
526
578
629
681
732
783
834
886
937
850
942
947
952
957
962
967
973
978
983
988
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
349
N.
L.O
1
2
3
4
5
6
7
8
9
I
'.P.
850
92 942
947
952
957
962
967
973
978
983
988
851
852
853
854
855
856
857
858
859
993
93 044
095
146
197
24V
298
349
399
998
049
100
151
202
252
303
354
404
*003
054
105
156
207
258
308
359
409
*008
059
110
161
212
263
313
364
414
*013
064
115
166
217
268
318
369
420
*018
069
120
171
222
273
323
374
425
*024
075
125
176
227
278
328
379
430
*029
080
131
181
232
283
334
384
435
*034
085
136
186
237
288
a39
389
440
*039
090
141
192
242
293
344
394
445
1
2
6
O.ft
1.2
860
450
455
460
465
470
475
480
485
490
495
4
2.4
861
862
863
864'
865
866
867
868
869
500
551
601
651
702
752
802
852
902
505
556
606
656
707
757
807
857
907
510
561
611
661
712
762
812
862
912
515
566
616
666
717
767
817
867
917
520
571
621
671
722
772
822
872
922
526
576
626
676
727
777
827
877
927
531
581
631
682
732
782
832
882
932
536
586
636
687
737
787
837
887
937
541
591
641
692
742
792
842
892
942
546
596
'646
697
747
797
847
897
947
6
7
8
9
S.6
4.2
4.8
5.4
870
952
957
962
967
972
977
982
987
992
997
871
872
873
874
875
876
877
878
879
94 002
052
101
151
201
250
300
349
399
007
057
106
156
206
255
305
354
404
012
062
111
161
211
260
310
359
409
017
067
116
166
216
265
315
364
414
022
072
121
171
221
270
320
369
419
027
077
126
176
226
275
325
374
424
032
082
131
181
231
280
330
379
429
037
086
136
186
236
285
335
384
433
042
091
141
191
240
290
340
389
438
047
096
146
196
245
295
345
394
443
0.5
1.0
1.6
2.0
2.5
3.0
3.5
4.0
4.6
880
448
453
458
463
468
473
478
483
488
493
881
882
883
884
885
886
887
888
889
498
547
596
645
694
743
792
841
890
503
552
601
650
699
748
797
846
895
507
557
606
655
704
753
802
851
900
512
562
611
660
709
758
807
856
905
517
567
616
665
714
763
812
861
910
522
571
621
670
719
768
817
866
915
527
576
626
675
724
773
822
871
919
532
581
630
CSO
729
778
827
876
924
537
586
635
685
734
783
832
880
929
542
591
640
689
738
787
836
885
934
1
2
3
4
0.4
0.8
1.2
890
939
944
949
954
959
963
968
973
978
983
4
5
1.6
2.0
891
892
893
894
895
896
897
898
899
988
95 036
085
134
182
231
279
328
376
993
041
090
139
187
236
284
332
381
998
046
095
143
192
240
289
337
386
*002
051
100
148
197
245
294
342
390
*007
056
105
153
202
250
299
347
395
*012
061
109
158
207
255
303
352
400
*017
066
114
163
211
260
308
357
405
*022
071
119
168
216
265
313
361
410
*027
075
124
173
221
270
318
366
415
*032
080
129
177
226
274
323
371
419
6
7
8
9
2.4
2.8
3.2
S.ft
900
424
429
434
439
444
448
453
458
463
468
N.
L.O
1
2
3
4
5
6
7
8
9
P.
P.
350
MINE GASES AND VENTILATION
N.
L.O
1
2
3
4
5
6
•7
8
9
P.P.
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
95 424
429
434
439
444
448
453
458
463
468
5
0.5
1.0
1.5
2.0
2.5
3.0
3.5
8 4.0
»j 4.5
4
0.4
0.8
1.2
1.6
2.0
2.4
2.8
8 3.2
9 3.6
472
521
569
617
665
713
761
809
856
477
525
574
622
670
718
766
813
861
482
530
578
626
674
722
770
818
866
914
487
535
583
631
679
727
775
823
871
918
492
540
588
636
684
732
780
828
875
497
545
693
641
689
737
785
832
880
501
550
598
646
694
742
789
837
885
506
554
602
650
698
746
794
842
890
938
511
559
607
655
703
751
799
847
895
516
564
612
660
708
756
804
852
899
947
904
909
957
*004
052
099
147
194
242
289
336
384
923
971
*019
066
114
161
209
256
303
350
928
976
*023
071
118
166
213
261
308
355
933
942
952
999
96 047
095
142
190
237
284
332
961
*009
057
104
152
199
246
294
341
388
966
*014
061
109
156
204
251
298
346
980
*028
076
123
171
218
265
313
360
407
985
*033
080
128
175
223
270
317
365
412
990
*038
085
133
180
227
275
322
369
995
*042
090
137
185
232
280
327
374
421
379
393
398
402
417
426
473
520
567
" 614
661
708
755
802
431
478
525
572
619
666
713
759
806
853
435
483
530
577
624
670
717
764
811
858
440
487
534
581
628
675
722
769
816
445
492
539
586
633
680
727
774
820
867
450
497
544
591
638
685
731
778
825
454
501
648
595
642
689
736
783
830
459
506
553
600
647
694
741
788
834
881
464
511
558
605
652
699
745
792
839
468
515
562
609
656
703
750
797
844
848
862
872
876
886
890
895
942
988
97 035
081
128
174
220
267
900
946
993
039
086
132
179
225
271
904
951
997
044
090
137
183
230
276
909
956
*002
049
095
142
188
234
280
914
960
*007
053
100
146
192
239
285
918
965
*011
058
104
151
197
243
290
923
970
*016
063
109
155
202
248
294
928
974
*021
067
114
160
206
253
299
932
979
*025
072
118
165
211
257
304
937
984
*030
077
123
169
216
262
308
313
317
364
410
456
502
548
594
640
685
731
322
327
373
419
465
511
557
603
649
695
740
331
336
382
428
474
520
566
612
658
704
749
340
345
391
437
483
529
575
621
667
713
759
350
3%
442
488
534
580
626
672
717
763
354
359
405
451
497
543
589
635
681
727
368
414
460
606
552
598
644
690
736
377
424
470
516
562
607
653
699
745
387
433
479
525
571
617
663
708
754
400
447
493
539
585
630
676
722
768
772
777
782
786
791
795
800
804
809
813
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
LOGARITHMIC TABLES
351
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
950
97 772
777
782
786
791
795
800
804
809
813
951
952
953
954
955
956
957
958
959
818
864
909
955
98 000
046
091
137
182
823
868
914
959
005
050
096
141
186
827
873
918
964
009
055
100
146
191
832
877
923
968
014
059
105
150
195
836
882
928
973
019
064
109
155
200
841
886
932
978
023
068
114
159
204
845
891
937
982
028
073
118
164
209
850
896
941
987
032
078
123
168
214
855
900
946
991
037
082
127
173
218
859
905
950
996
041
087
132
177
223
960
227
232
236
241
245
250
254
259
263
268
5
961
962
963
964
965
966
967
968
969
272
318
363
408
453
498
543
588
632
277
322
367
412
457
502
547
592
637
281
327
372
417
462
507
552
597
641
286
331
376
421
466
511
556
601
646
290
336
381
426
471
516
561
605
650
295
340
385
430
475
520
565
610
655
299
345
390
435
480
525
570
614
659
304
349
394
439
484
529
574
619
664
308
354
399
444
489
534
579
623
668
313
358
403
448
493
538
583
628
673
1 0.5
2 1.0
3 1.5
4 2.0
5 2.5
6 S.O
7 3.5
8 4.0
9 4.5
970
677
682
686
691
695
700
704
709
713
717
971
972
973
974
975
976
977
978
979
722
767
811
856
900
945
989
99 034
078
726
771
816
860
905
949
994
038
083
731
776
820
865
909
954
998
043
087
735
780
825
869
914
958
*003
047
092
740
784
829
874
918
963
*007
052
096
744
789
834
878
923
967
*012
056
100
749
793
838
883
927
972
*016
061
105
753
798
843
887
932
976
*021
065
109
758
802
847
892
936
981
*025
069
114
762
807
851
896
941
985
*029
074
118
980
123
127
131
136
140
145
149
154
158
162
A
981
982
983
984
985
986
987
988
989
167
211
255
300
344
388
432
476
520
171
216
260
304
348
392
436
480
524
176
220
264
308
352
396
441
484
528
180
224
269
313
357
401
445
489
533
185
229
273
317
361
405
449
493
537
189
233
277
322
366
410
454
498
542
193
238
282
326
370
414
458
502
546
198
242
286
330
374
419
463
506
550
202
247
291
335
379
423
467
511
555
207
251
295
339
383
427
471
515
559
1 0.4
2 0.8
3 1.2
• 4 1.6
5 2.0
6 2.4
7 2.8
8 8.2
9 3.6
990
564
568
572
577
581
585
590
594
599
603
991
992
993
994
995
996
997
998
999
607
651
695
739
782
826
870
913
957
612
656
699
743
787
830
874
917
961
616
660
704
747
791
835
878
922
965
621
664
708
752
795
839
883
926
970
625
669
712
756
800
843
887
930
974
629
673
717
760
804
848
891
935
978
634
677
721
765
808
852
896
939
983
638
682
726
769
813
856
900
944
987
642
686
730
774
817
861
904
948
991
647
691
734
778
822
865
909
952
996
1000
00000
004
009
013
017
022
026
030
035
039
N.
L.O
1
2
3
4
5
6
7
8
9
P.P.
CIRCULAR FUNCTIONS
SINES AND COSINES
353
354
MINE GASES AND VENTILATION
© o°
.00000
.00029
.00058
.00087
.00116
.00145
.00175
.00204
.00233
.00262
.00291
.00320
.00349
.00378
.00407
.00436
.00465
.00495
.00524
.00553
.00582
.00611
.00640
.00669
.00698
.00727
.00756
.00785
.00814
.00844
.00873
.00902
.00931
.00960
.00989
.01018
.01047
.01076
.01105
.01134
.01164
.01193
.01222
.01251
.01280
.01309
.01338
.01367
.01396
.01425
.01454
.01483
.01513
.01542
.01571
.01600
.01629
.01658
.01687
.01716
.01745
.99997
.99997
.99997
.99996
.99995
.99995
!99995
.99994
.99994
.99994
.99987
.99985
.01745
.01774
.01803
.01832
.01862
.01891
.01920
.01949
.01978
.02007
.02036
.02065
.02094
.02W3
.02152
.02181
.02211
.02240
.02269
.02298
.02327
.02356
.02385
.02414
.02443
.02472
.02501
.02530
.02560
.02647
.02676
.02705
.02734
.02763
.02792
.02821
.02850
.02879
.02938
.02967
.02996
.03025
.03112
.03141
.03170
.03199
.03228
.03257
.03286
.03316
.03345
.03374
.03403
.03432
.03461
.03490
.03490
.03519
.03548
.03577
.03635
.03664
.03693
.03723
.03752
.03781
.03897
.03926
.03955
.03984
.04013
.04042
.04071
.04100
.04129
.04159
.04188
.04217
.04246
.04275
.04304
.04333
.04362
.04391
.04420
.04449
.04478
.04507
.04536
.04565
.04594
.04623
.04653
.04682
.04711
.04740
.04769
.04798
.04827
.04856
.04885
.04914
.04943
.04972
.05001
.05030
.05059
.05117
.05146
.05175
.05205
.05234
Cosine
Cosine Sine
87°
8°
Sine
.05234
.05263
.05292
.05321
.05350
.05379
.05408
.05437
.05466
.05495
.05524
.05553
.05582
.05611
.05640
.05727
.05756
.05785
.05814
.05844
.05873
.05902
.06018
.06047
.06076
.06105
.06134
.06163
.06192
.06221
.06250
.06279
.06308
.06337
.06395
.06424
.06453
.06482
.06511
.06540
.06569
.06598
.06627
.06656
.06685
.06714
.06743
.06773
.06918
.06947
.06976
4°
.07005
.07034
.07063
.07092
.07121
.07150
.07179
.07208
.07237
.07266
.07295
.07324
.07353
.07382
.07411
.07440
.07469
.07493
.07527
.07556
.07585
.07614
.07643
.07672
.07701
.07730
.07759
.07788
.07817
.07846
.07875
.07904
.07933
.07962
.07991
.08020
.08049
.08078
.08107
.08165
.08194
.08223
.08252
.08281
.08310
.08426
.08455
.08484
.08513
.08542
.08571
.08600
.08629
.08658
.08687
.08716
.99750
.99748
.99746
.99744
.99742
.99740
.99738
.99736
.99734
.99731
.99729
.99727
.99725
.99723
.99721
.99719
.99716
.99666
.99664
.99659
.99657
.99649
.99647
.99642
.99627
.99625
.99619
85°
SINES AND COSINES
355
/
j
>°
(
>°
0
{
IP
9
0
/
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
.08716
.99619
.10453
.99452
.12187
.99255
.13917
.99027
.15643
.98769
60
.08745
.99617
.10482
.99449
.12216
.99251
.13946
.99023
.15672
.98764
59
.08774
.99614
.10511
.99446
.12245
.99248
.13975
.99019
.15701
.98760
58
.08803
.99612
.10540
.99443
.12274
.99244
.14004
.99015
.157SO
.98755
67
.08831
.99609
.10569
.99440
.12302
.99240
.14033
.99011
.15758
.98751
56
.08860
.99607
.10597
.99437
.12331
.99237
.14061
.99006
.15787
.98746
65
.08889
.99604
.10626
.99434
.12360
.99233
.14090
.99002
.15816
.98741
54
.08918
.99602
.10655
.99431
.12389
.99230
.14119
.98998
.15845
.98737
53
a
.08947
.99599
.10684
.99428
.12418
.99226
.14148
.98994
.15873
.98732
52
9
.08976
.99596
.10T13
.99424
.12447
.99222
.14177
.98990
.15902
.98728
51
10
.09005
.99594
.10742
.99421
.12476
.99219
.14205
.98986
.15931
.98723
50
11
.09034
.99591
.10771
.99418
.12504
.99215
.14234
.98982
.15959
.98718
49
12
.09063
.99588
.10800
.99415
.12533
.99211
.142G3
.98978
.15988
.98714
48
13
.09092
.99586
.10829
.99412
.12562
.99208
.14292
.98973
.16017
.98700
47
14
.09121
.99583
.10858
.99409
.12591
.99204
.14320
.989C9
.16046
.93704
46
15
.09150
.99580
.10887
.99406
.12620
. .09200
.14349
.98965
.16074
.98700
45
16
.09179
.99578
.10916
.99402
.12649
.99197
.14378
.98961
J6103
.98695
41
17
.09208
.99575
.10945
.99399
.12678
.99193
.14407
.98957
.16132
.98690
43
18
.09237
.99572
.10973
.99396
.12706
.99189
.14436
.98953
.16160
.08686
42
19
.09266
.99570
.11002
.99393
.12735
.99186
.14464
.98948
.16189
.98681
41
20
.09295
.99567
.11031
.99390
.12764
99182
.14493
.98944
.16218
.98676
40
21
.09324
.99564
.11060
.99386
.12793
.99178
.14522
.98940
.16246
.98671
39
22
.09353
.99562
.11089
.99383
.12822
.99175
.14551
.98936
.16275
.98667
38
23
.09382
.99559
.11118
.99380
.12851
.99171
.14580
.98931
.16304
.98662
37
24
.09411
.99556
.11147
.99377
.12880
.99167
.14608
.98927
.16333
.98657
30
25
.09440
.99553
.11176
.99374
.12908
.99163
.14637
.98923
.16361
.98652
35
26
.09469
.99551
.11205
.99370
.12937
.99100
.14666
.98919
.16390
.98648
34
27
.09498
.99548
.11234
.99367
.12966
.99156
.14695
.98914
.16419
.98643
33
28
.09527
.99545
.11263
.99364
.12995
.99152
.14723
.98910
.16447
.98638
32
29
.09556
.99542
.11291
.99360
.13024
.99148
.14752
.98906
.16476
.98633
31
30
.09585
.99540
.11320
.99357
.13053
.99144
.14781
.98902
.16505
.98629
30
31
.09614
.99537
.11849
.99354
.13081
.99141
.14810
.98897
.16533
.98624
29
32
.09642
.99534
.11378
.99351
.13110
.99137
.14838
.98893
.16562
.98619
S3
33
.09671
.99531
.11407
.99347
.13139
.99133
.14867
.98889
.16591
.98614
27
34
.09700
.99528
.11436
.99344
.13168
.99129
.14896
.98884
.16620
.98609
26
85
.09729
.99526
.11465
.99341
.13197
.99125
.14925
.98880
.16648
.98604
25
36
.09758
.99523
.11494
.99337
.13226
.99122
.14954
.98876
.16677
.98600
24
37
.09787
.99520
.11523
.99334
.13254
.99118
.14982
.98871
.16706
.98595
23
38
.09816
.99517
.11552
.99331
.13283
.99114
.15011
.98867
.16734
.98590
22
39
.09845
.99514
.11580
.99327
.13312
.99110
.15040
.98863
.16763
.98585
21
40
.09874
.99511
.11609
.99324
.13341
.99106
.15069
.98858
.16792
.98580
20
41
.09903
.99508
.11638
.99320
.13370
.99102
.15097
.98854
.16820
.98575
19
42
.09932
.99506
.11667
.99317
.18399
.99098
.15126
.98849
.16849
.98570
13
43
.09961
.99503
.11696
.99314
.13427
.99094
.15155
.98845
.16878
.98565
17
44
.09990
.99500
.11725
.99310
.13456
.99091
.15184
.98841
.16906
.98561
16
15
.10019
.99497
.11754
.99307
.13485
.99087
.15212
.98836
.16935
.98556
15
46
.10048
.99494
.11783
.99303
.13514
.99083
.15241
.98832
.16964
.98551
14
47
.10077
.99491
.11812
.99300
.13543
.99079
.15270
.98827
.16992
.98546
13
48
.10106
.99488
.11840
.99297
.13572
.99075
.15299
.98823
.17021
.98541
12
49
.10135
.99485
.11869
.99293
.13600
.99071
.15327
.98818
.17050
.98536
11
50
.10164
.99482
.11898
.99290
.13629
.99067
.15356
.98814
.17078
.98531
10
51
.10192
.99479
.11927
.99286
.13658
.99063
.15885
.98809
.17107
.98526
62
.10221
.99476
.11956
.99283
.13687
.99059
.15414
.98805
.17136
.98521
69
.10250
.99473
.11985
.99279
.13716
.99055
.15442
.98800
.17164
.98516
ft*
.10279
.99470
.12014
.99276
.13744
.99051
.15471
.98796
.17193
.98511
55
.10308
.99467
.12043
.99272
.13773
.99047
.15500
.98791
.17222
.98506
56
.10337
.99464
.12071
.99269
.13802
99043
.15529
.98787
.17250
.98501
57
.10366
.99461
.12100
.99265
.13831
99039
.15557
.98782
.17279
.984%
58
.10395
.99458
.12129
.99262
.13860
99035
.15586
.98778
.17308
98491
59
.10424
.99455
.12158
.99258
.13889
99031
.15615
.98773
.17336
98486
60
.10453
.99452
.12187
.99255
.13917
99027
.15643
.98769
.17365
98481
Cosine
Sine
Cosine
Bine
Cosine
Sine
Cosine
Sine
Cosine
Sine
f
8-1
o
82
°
82
o
81
O
80
»
350
MIN'E GASES AND VENTILATION
' 1
]
0°
1
1°
]
2°
1
3°
]
4°
Sine
Cosine
Sine
Cosin
Sine
Cosin
Sine
Cosin
Sine
Cosine
0
.17365
.98481
.19081
.98163
.20791
.97815
.22495
.97437
.24192
.97030
60
.17393
.98476
.19109
.98157
.20820
.97809
.22523
.97430
.24220
.97023
59
.17422
.98471
.19138
.98152
.20848
.97803
.22552
.97424
.24249
.97015
58
.17451
.98466
.19167
.98146
.20877
.97797
.22580
.97417
.24277
.97008
57
.17479
.98461
.19195
.98140
.20905
.97791
.22608
.97411
.24305
.97001
56
.17508
.98455
.19224
.98135
.20933
.97784
.22637
.97404
.24333
.96994
55
.17537
.98450
.19252
.98129
.20962
.97778
.22665
.97398
.24362
.96987
54
.17565
.98445
.19281
.98124
.20990
.97772
.22693
.97391
.24390
.96980
53
8
.17594
.98440
.19309
.98118
.21019
.97766
.22722
.97384
.24418
.96973
52
9
.17623
.98435
.19338
.98112
.21047
.97760
.22750
.97378
.24446
.96966
51
10
.17651
.98430
'.19366
.98107
.21076
.97754
.22778
.97371
.24474
.96959
50
11
.17680
.98425
.19395
.98101
.21104
.97748
.22807
.97365
.24503
.96952
49
12
.17708
.98420
.19423
.98096
.21132
.97742
.22835
.97358
.24531
.96945
48
13
.17737
.98414
.19452
.98090
.21161
.97735
.22863
.97351
.24559
.96937
47
.H
.17766
.98409
.19481
.98084
.21189
.97729
.22892
.97345
.24587
.96930
46
15
.17794
.98404
.19509
.98079
.21218
.97723
.22920
.97338
.24615
.96923
45
16
.17823
.98399
.19538
.98073
.21246
.97717
.22948
.97331
.24644
.96916
44
17
.17852
.98394
.19566
.98067
.21275
.977U
.22977
.97325
.24672
.96909
43
18
.17880
.98389
.19595
.98061
.21303
.97 WS
.23005
.97318
.24700
.96902
42
19
.17909
.98383
.19623
.98056
.21331
.97698
.23033
.97311
.24728
.96894
41
20
.17937
.98378
.19652
.98050
.21360
.97692
.23062
.97304
.24756
.96887
40
21
.17966
.98373
.19680
.98044
.21388
.97686
.23090
.97298
.24-784
.96880
39
22
.17995
.98368
.19709
.98039
.21417
.97680
.23118
.97291
.24813
.96873
38
23
.18023
.98362
.19737
.98033
.21445
.97673
.23146
.97284
.24841
37
24
.18052
.98357
.19766
.98027
.21474
.97667
.23175
.97278
.24869
!96858
36
25
.18081
.98352
.19794
.98021
.21502
.97661
.23203
.97271
.24897
.96851
35
26
.18109
.98347
.19823
.98016
.21530
.97655
.23231
.97264
.24925
.96844
34
27
.18138
.98341
.19851
.98010
.21559
.97648
.23260
.97257
.24954
.96837
33
28
.18166
.98336
.19880
.98004
.21587'
.97642
.23288
.97251
.24982
.96829
82
29
.18195
.98331
.19908
.97998
.21616
.97636
.23316
.97244
.25010
.96822
31
30
.18224
.98325
.19937
.97992
.21644
.97630
.23345
.97237
.25038
.96815
30
31
.18252
.98320
.19965
.97987
.21672
.97623
.23373
.97230
.25066
.96807
29
32
.18281
.98315
.19994
.97981
.21701
.97617
.23401
.97223
.25094
.96800
28
33
.18309
.98310
.20022
.97975
.21729
.97611
.23429
.97217
.25122
.96793
27
34
.18338
.98304
.20051
.97969
.21758
.97604
.23458
.97210
.25151
.96786
26
35
.18367
.98299
.20079
.97963
.21786
.97598
.23486
.97203
.25179
.96778
25
36
.18395
.98294
.20108
.97958
.21814
.97592
.23514
.97196
.25207
.96771
24
37
.18424
.98288
.20136
.97952
.21843
.97585
.23542
.97189
.25235
.96764
23
38
.18452
.98283
.20165
.97946
.21871
.97579
.23571
.97182
.25263
.96756
22
39
.18481
.98277
.20193
.97940
.21899
.97573
.23599
.97176
.25291
.96749
21
40
.18509
.98272
.20222
.97934
.21928
.97566
.23627
.97169
.25320
.96742
20
41
.18538
.98267
.20250
.97928
.21956
.97560
.23656
.97162
.20348
.96784
19
42
.18567
.98261
.20279
.97922
.21985
.97553
.23684
.97155
.25376
.96727
18
43
.18595
.98256
.20307
.97916
.22013
.97547
.23712
.97148
.25404
.96719
17
44
.18624
.98250
.20336
.97910
.22041
.97541
.23740
.97141
.25432
.96712
16
45
.18652
98245
.20364
.97905
.22070
.97534
.23769
.97134
.25460
.96705
15
46
.18681
.98240
.20393
.97899
.22098
.97528
.23797
.97127
.25488
.96697
14
47
.18710
.98234
.20421
.97893
.22126
.97521
.23825
.97120
.25516
.96690
13
48
.18738
.98229
.20450
.97887
.22155
.97515
.23853
.97113
.25545
96682
12
49
.18767
.98223
.20478
.97881
.22183
.97508
.23882
.97106
.25573
96675
11
60
.18795
.98218
.20507
.97875
.22212
.97502
.23910'
.97100
.25601
96667
10
51
.18824
.98212
.20535
.97869
.22240
.97496
.23938
.97093
.25629
96660
9
62
.18852
.98207
.20563
.97863
.22268
.97489
.23966
.97086
.25657
96653
8
63
.18881
.98201
.20592
.97857
.22297
.97483
.23995
.97079
.25685
96645
7
64
.18910
.98196
.20620
.97851
.22325
.97476
.24023
.97072
.25713
96638
6
55
.18938
.98190
.20649
.97845
.22353
.97470
.24051
.97065
.25741
96630
6
66
.18967
.98185
.20677
.97839
.22382
.97463
.24079
.97058
.25769
96623
4
67
.18995
.98179
.20706
.97833
.22410
.97457
.24108
.97051
.25798
96615
3
68
.19024
.98174
.20734
.97827
.22438
.97450
.24136
.97044
.25826
96608
2
69
.19052
.98168
.20763
.97821
.22467
.97444
.24164
.97037
.25854
96600
1
00
.19081
.98163
.20791
.97815
22495
.97437
.24192
.97030
25882
96593
0
OMift*
fiiac
Coaina
Sine
Cosine
Sine
Cosine
Sine
Coein*
Sine
79
»
7S
9 '
77
5
76<
>
75C
•
SINES AND COSINES
357
/
1
5°
1
5°
1
7°
1
}°
1<
)°
/
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
0
.25882
.96593
.27564
.96126
.29237
.95630
.30902
.95106
.32557
.94552
60
.25910
.96585
.27592
.96118
.29265
.95622
.30929
.95097
.32584
.94542
69
.25938
.96578
.27620
.96110
.29293
.95613
.30957
.95088
.32612
.94533
68
.25966
.96570
.27648
.96102
.29321
.95605
.30985
.95079
.32639
.94523
57
.25994
.96562
.27676
.96094
.29348
.95596
.31012
.95070
.32667
.94514
56
.26022
.96555
.27704
.96086
.29376
.95588
.31040
.95061
.32694
.94604
55
.26050
.96547
.27731
.96078
.29404
.95579
.31068
.95052
.32722
.94495
64
.26079
.96540
.27759
.96070
.29432
.95571
.81095
.95043
.32749
.94485
53
.26107
.96532
.27787
.96062
.29460
.95562
.31123
.95033
.32777
.94476
52
.26135
.96524
.27815
.96054
.29487
.95554
.31151
.95024
.32804
.94466
51
10
.26163
.96517
.27843
.96046
.29515
.95545
.31178
.95015
.32832
.94467
50
11
.26191
.96509
.27871
.96037
.29543
.95536
.31206
.95006
.32859
.94447
49
12
.26219
.96502
.27899
.96029
.29571
.95528
.31233
.94997
.32887
.94438
48
13
.26247
.96494
.27927
.96021
.29599
.95519
.31261
.94988
.32914
.94428
47
14
.26275
.96486
.27955
.96013
.29626
.95511
.31289
.94979
.32942
.94418
46
15
.26303
.96479
.27983
.96005
.29654
.95502
.81316
.94970
.32969
.94409
45
16
.26331
.96471
.28011
.95997
.29682
.95493
.31344
.94961
.32997
.94399
44
17
.26359
.96463
.28039
.95989
.29710
.95485
.31372
.94952
.83024
.94390
43
18
.26387
.96456
.28067
.95981
.29737
.95476
.31399
.94943
.33051
.94380
42
19
.26415
.96448
.28095
.95972
.29765
.95467
.31427
.94933
.33079
.94370
41
20
.26443
.96440
.28123
.95964
.29793
.95459
.31454
.94924
.83106
.94361
40
21
.26471
.96433
.28150
.95956
.29821
.95450
.31482
.94915
.33134
.94351
39
22
.26500
.96425
.28178
.95948
.29849
.95441
.81510
.94906
.33161
.94342
88
23
.26528
.96417
.28206
.95940
.29876
.95433
.31537
.94897
.33189
.94332
37
24
.26556
.96410
.28234
.95931
.29904
.95424
.31565
.94888
.33216
.94322
36
25
.26584
.96402
.28262
.95923
.29932
.95415
.31593
.94878
.33244
.94313
35
26
.26612
.96394
.28290
.95915
.29960
.95407
.31620
.94869
.33271
.94303
34
27
.26640
.96386
.28318
.95907
.29987
.95398
.31648
.94860
.33298
.94293
33
28
.26668
.96379
.28346
.95898
.30015
.95389
.31675
.94851
.33326
.94284
32
29
.26696
.96371
.28374
.95890
.30043
.95380
.31703
.94842
.83353
.94274
31
80
.26724
.96363
.28402
.95882
.30071
.95372
.31730
.94832
.33381
.94264
30
31
.26752
.96355
.28429
.95874
.30098
.95363
.31758
.94823
.33408
.94254
29
32
.26780
.96347
.28457
.95865
.30126
.95354
.31786
.94814
.33436
.94245
28
33
.26808
.96340
.28485
.95857
.30154
.95345
.31813
.94805
.33463
.94235
27
34
.26836
.96332
.28513
.95849
.30182
.95337
.31841
.94795
.33490
.94225
26
35
.26864
.96324
.28541
.95841
.30209
.95328
.31868
.94786
.33518
.94215
25
36
.26892
.96316
.28569
.95832
.30237
.95319
.31896
.94777
.33545
.94206
24
3T
.26920
.96308
.28597
.95824
.30265
.95310
.31923
.94768
.33573
.94196
23
38
.26948
.96301
.28625
.95816
.30292
.95301
.81951
.94758
.33600
.94186
22
39
.26976
.96293
.28652
.95807
.30320
.95293
.31979
.94749
.33627
.94176
21
40
.27004
.96285
.28680
.95799
.30348
.95284
.32006
.94740
.33655
.94167
20
41
.27032
.96277
.28708
.95791
.30376
.95275
.82034
.94730
.33682
.94157
19
42
.27060
.96269
.28736
.95782
.30403
.95266
.82061
.94721
.33710
.94147
18
43
.27088
.96261
.28764
.95774
.30431
.95257
.32089
.94712
.83737
.94137
17
44
.27116
.96253
.28792
.95766
.30459
.95248
.32116
.94702
.33764
.94127
16
45
.27144
.96246
.28820
.95757
.80486
.95240
.32144
.94693
.83792
.94118
15
46
.27172
.96238
.28847
.95749
.30514
.95231
.32171
.94684
.33819
.94108
14
47
.27200
.96230
.28875
.95740
.30542
.95222
.82199
.94674
.33846
.94098
13
48
.27228
.96222
.28903
.95732
.30570
.95213
.32227
.94665
.33874
.94088
12
49
.27256
.96214
.28931
.95724
.30597
.96204
.32254
.94656
.83901
.94078
11
60
.27284
.96206
.28959
.95715
.30625
.95195
.82282
.94646
.33929
.94068
10
51
.27312
.96198
.28987
.95707
.30653
.95186
.32309
.94637
.33956
.94058
9
52
.27340
.96190
.29015
.95698
.30680
.95177
.32337
.94627
.83983
.94049
8
53
.27368
.96182
.29042
.95690
.30708
.95168
.32364
.94618
.34011
.94039
7
54
.27396
.96174
.29070
.95681
.30736
.95159
.82392
.94609
.34038
.94029
55
.27424
.96166
.29098
.95673
.30763
.95150
.32419
.94599
.34065
.94019
56
.27452
.96158
.29126
.95664
.30791
.95142
.32447
.94590
.34093
.94009
57
.27480
.96150
.29154
.95656
.30819
.95133
.82474
.94580
.34120
.93999
58
.27508
.96142
.29182
.95647
.30846
.95124
.32502
.94571
.34147
.93989
59
.27536
.96134
.29209
.95639
.30874
.95115
.82529
.94561
.34175
.93979
60
.27564
.96126
.29237
.95630
.30902
.95106
.32557
.94552
.34202
.93969
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
7
1°
?!
5°
75
>°
71
0
70
0
358
MINE GASES AND VENTILATION
2
0°
2
1°
2
2°
2
>o
Z
1°
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
0
.34202
.93969
.35837
.93358
.37461
.92718
.39073
.92050
.40674
.91355
60
1
.34229
.93959
.35864
.93348
.37488
.92707
.39100
.92039
.40700
.91S43
69
2
.34257
.93949
.35891
.93337
.37515
.92697
.39127
.92028
.40727
.91331
58
3
.34284
.93939
.35918
.93327
.37542
.92686
.39153
.92016
.40753
.91319
57
4
.34311
.93929
.35945
.93316
.37569
.92675
.39180
.92005
.40780
.91307
56
6
.34339
.93919
.35973
.93306
.37595
.92664
.39207
.91994
.40806
.91295
55
6
.34366
.93909
.36000
.93295
.37622
.92653
.39234
.91982
.40833
.91283
54
7
.34393
.93899
.36027
.93285
.37649
.92642
.39260
.91971
.40860
.91272
53
8
.34421
.93889
.36054
.93274
.37676
.92631
.39287
.91959
.40886
.91260
52
9
.34448
.93879
.36081
.93264
.37703
.92620
.39314
.91948
.40913
.91248
61
10
.34475
.93869
.36108
.93253
.37730
.92609
.39341
.91936
.40939
.91236
50
11
.34503
.93859
.36135
.93243
.37757
.92598
.39367
.91925
.40966
.91224
49
12
.34530
.93849
.36162
.93232
.37784
.92587
.39394
.91914
.40992
.91212
48
13
.84557
.93839
.36190
.93222
.37811
.92576
.39421
.91902
.41019
.91200
47
14
.34584
.93829
.36217
.93211
.37838
.92565
.39448
.91891
.41045
.91188
46
15
.34612
.93819
.36244
.93201
.37865
.92554
.39474
.91879
.41072
.91176
45
16
.34639
.93809
.36271
.93190
.37892
.92543
.39501
.91868
.41098
.91164
44
17
.34666
.93799
.36298
.93180
.37919
.92532
.39528
.91856
.41125
.91152
43
18
.34694
.93789
.36325
.93169
.37946
.92521
.39555
.91845
.41151
.91140
42
19
.34721
.93779
.36352
.93159
.37973
.92510
.39581
.91833
.41178
.91128
41
20
.34748
.93769
.36379
.93148
.37999
.92499
.39608
.91822
.41204
.91116
40
21
.34775
.93759
.36406
.93137
.38026
.92488
.39635
.91810
.41231
.91104
39
22
.34803
.93748
.36434
.93127
.38053
.92477
.39661
.91799
.41257
.91092
38
23
.34830
.93738
.36461
.93116
.38080
.92466
.39688
.91787
.41284
.91080
37
24'
.34857
.93728
.36488
.93106
.38107
.92455
.39715
.91775
.41310
.91068
86
25
.34884
.93718
.36515
.93095
.38134
.92444
.39741
.91764
.41337
.91056
35
26
.34912
.93708
.36542
.93084
.38161
.92432
.39768
.91752
.41363
.91044
34
27
.34939
.93698
.36569
.93074
.38188
.92421
.39795
.91741
.41390
.91032
33
28
.34966
.93688
.36596
.93063
.38215
.92410
.39822
.91729
.41416
.91020
82
29
.34993
.93677
.36623
.93052
.38241
.92399
.39848
.91718
.41443
.91008
31
30
.35021
.93667
.36650
.93042
.38268
.92388
.39875
.91706
.41469
.90996
30
81
.35048
.93657
.36677
.93031
.38295
.92377
.39902
.91694
.414%
.90984
29
32
.35075
.93647
.36704
.93020
.38322
.92366
.39928
.91683
.41522
.90972
28
33
.35102
.93637
.36731
.93010
.38349
.92355
.39955
.91671
.41549
.90960
27
34
.35130
.93626
.36758
.92999
.38376
.92343
.39982
.91660
.41575
.90948
26
35
.35157
.93616
.36785
.92988
.38403
.92332
.40008
.91648
.41602
.90936
25
36
.35184
.93606
.36812
.92978
.38430
.92321
.40035
.91636
.41628
.90924
24
37
.35211
.93596
.36839
.92967
.38456
.92310
.40062
.91625
.41655
.90911
23
38
.35239
.93585
.36867
.92956
.38483
.92299
.40088
.91613
.41681
.90899
22
39
.35266
.93575
.36894
.92945
.38510
.92287
.40115
.91601
.41707
.90887
21
40
.35293
.93565
.36921
.92935
.38537
.92276
.40141
.91590
.41734
.90875
20
41
.35320
.93555
.86948
.92924
.38564
.92265
.40168
.91578
.41760
.90863
19
42
.35347
.93544
.36975
.92913
.38581
.92254
.40195
.91566
.41787
.90851
18
43
.35375
.93534
.37002
.92902
.38617
.92243
.40221
.91555
.41813
.90839
17
44
.35402
.93524
.37029
.92892
.38644
.92231
.40248
.91543
.41840
.90826
16
45
.35429
.93514
.37056
.92881
.38671
.92220
.40275
.91531
.41866
.90814
15
46
.35456
.93502
.37083
.92870
.38698
.92209
.40301
.91519
.41892
.90802
14
47
.35484
.93493
.37110
.92859
.38725
.92198
.40328
.91508
.41919
.90790
13
48
.35511
.93483
.37137
.92849
.38752
.92186
.40355
.91496
.41945
.90778
12
49
.35538
.93472
.37164
.92838
.38778
.92175
.40381
.91484
.41972
.90766
11
50
.35565
.93462
.37191
.92827
.38805
.92164
.40408
.91472
.41998
.90753.
10
51
.35592
.93452
.87218
.92816
.88832
.92152
.40434
.91461
.42024
.90741
9
52
.35619
.93441
.37245
.92805
.38859
.92141
.40461
.91449
.42051
.90729
8
53
.35647
.93431
.37272
.92794
.38886
.92130
.40488
.91437
.42077
.90717
54
.35674
.93420
.37299
.92784
.38912
.92119
.40514
.91425
.42104
.90704
65
.35701
.93410
.37326
.92773
.38939
.92107
.40541
.91414
.42130
.90692
56
.35728
.93400
.37353
.92762
.38966
.920%
.40567
.91402
.42156
.90680
57
.35755
.93389
.37380
.92751
.38993
.92085
.40594
.91390
.42183
.90668
58
.35782
.93379
.37407
.92740
.39020
.92073
.40621
.91378
.42209
.90655
59
.35810
.93368
.37434
.92729
.39046
.92062
.40647
.91366
.42235
.90643
60
.35837
.93358
.37461
.92718
.39073
.92050
.40674
.91355
.42262
.90631
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
t
6<
>°
6J
o
61
0
66
0
65
0
/
SINES AND COSINES
359
25°
.42262
.42288
.42315
.42341
.42367
.42394
.42420
.42446
.42473
.42499
.42525
.42552
.42578
.42604
.42631
.42657
.42683
.42709
.42736
.42762
.42788
.42815
.42841
.42867
.42894
.42920
.42946
.42972
.42999
.43025
.43051
.43077
.43104
.43130
.43156
.43182
.43209
.43235,
.43261
.43287
.43313
.43340
.43366
.43392
.43418
.43497
.43523
.43549
.43575
.43602
.43628
.43654
.43680
.43706
.43733
.43759
.43785
.43811
.43837
.90631
.90618
.90606
.90594
.90557
.90545
.90532
.90520
.90507
.90495
.90483
.90470
.90458
.90446
.90433
.90421
.90371
.90358
.90346
.90334
.90321
.90309
.90296
.90284
.90271
.90259
.90246
.90233
.90221
.90208
.90196
.90183
.90171
.90158
.90146
.90133
.90120
.90108
.90095
.90082
.90070
.90057
.90045
.90032
.90019
.90007
.89956
.89943
.89930
.89918
.89905
.89892
Coilne Sine
64°
.43837
.43863
.43889
.43916
.43942
.43968
.43994
.44020
.44046
.44072
.44124
.44151
.44177
.44203
.44229
.44255
.44281
.44307
.44333
.44359
.44385
.44411
.44437
.44464
.44490
.44516
.44542
.44568
.44594
.44620
.44646
.44672
.44698
.44724
.44750
.44776
.44802
.44828
.44854
.44880
.44906
.44932
.44958
.44984
.45010
.45036
.45062
.45088
.45114
.45140
.45166
.45192
.45218
.45243
.45269
.45295
.45321
.45347
.45373
.45399
.89879
.89867
.89854
.89841
.89828
.89816
.89803
.89790
.89777
.89764
.89752
.89739
.89726
.89713
.89700
.89610
.89597
.89584
.89571
.89558
.89545
.89532
.89519
.89506
.89493
.89467
.89454
.89441
.89285
.89272
.89219
.89206
.89193
.89127
.89114
.89101
Cosine Sine
63°
27°
.45399
.45425
.45451
.45477
.45503
.45529
.45554
.45580
.45606
.45632
.45658
.45684
.45710
.45736
.45762
.45787
.45813
.45839
.45865
.45891
.45917
.45942
.45968
.45994
.46020
.46046
.46072
.46097
.46123
.40149
.46175
.46201
.46226
.46252
.46278
.46304
.46330
.46355
.46381
.46407
.46433
.46458
.46484
.46510
.46536
.46561
.46587
.46613
.46639
.46664
.46716
.46742
.46767
.46793
.46819
.46844
.46870
.46896
.46921
.46947
Cosine Sine
G2°
Sine Cosine
.46947
.46973
.46999
.47024
.47050
.47076
.47101
.47127
.47153
.47178
.47204
.47229
.47255
.47281
.47306
.47332
.47358
.47383
.47409
.47434
.47460
.47486
.47511
.47537
.47562
.47588
.47614
.47639
.47665
.47690
.47716
.47741
.47767
.47793
.47818
.47844
.47895
.47920
.47946
.47971
.47997
.48022
.48048
.48073
.48099
.48124
.48150
.48175
.48201
.48252
.48277
.48303
.48328
.48354
.48379
.48405
.48430
.48456
.48481
.88254
.88240
.88199
.88185
.88172
.88158
.88144
.88006
.87993
.87979
.87965
.87951
.87937
.87923
.87854
.87840
.87826
.87812
.87798
.87784
.87770
.87756
.87743
.87729
.87715
.87701
.87687
.87673
.87659
.87645
.87631
.87617
.87603
.87575
.87561
.87546
.87532
.87518
.87504
.87490
.87476
.87462
Cosine Sine
61°
29°
Sine Conine
.48481
.48506
.48532
.48557
.48684
.48710
.48735
.48761
.48786
.48811
.48837
.48862
.48888
.48913
.48938
.48964
.49014
.49040
.49065
.49090
.49116
.49141
.49160
.49192
.49217
.4C242
.49293
.49318
.49344
.49369
.49394
.49419
.49445
.49470
.49495
.49521
.49546
.49571
.49596
.49622
.49647
.49672
.49697
.49723
.49748
.49773
.49798
.49824
.49849
.49874
.49899
.49924
.49950
.49975
.50000
.87462
.87448
.87434
.87420
.87406
.87391
.87377
.87363
.87292
.87278
.87264
.87250
.87235
.87221
.87164
.87150
.87121
.87107
.87050
.87036
.87021
.87007
.86791
.86777
.86762
.86719
.86704
.86661
.86646
.86632
.86617
.86603
Cosine Si
60°
3(30
MINE GASES AND VENTILATION
3<
J°
3
P
3'
20
3
5°
34
0
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
.50000
.86603
.51504
.85717
.52992
.84805
.54464
.83867
.55919
.82904
60
.50025
.86588
.51529
.85702
.53017
.84789
.54488
.83851
.55943
.82887
59
.50050
.86573
.51554
.85687
.53041
.84774
.54513
.83835
.55968
.82871
68
.50076
.86559
.51579
.85672
.53066
.84759
.54537
.83819
.55992
.82855
67
.50101
.86544
.51604
.85657
.53091
.84743
.54561
.83804
.56016
.82839
66
.50126
.86530
.51628
.85642
.53115
.84728
.54586
.83788
.56040
.82822
65
.50151
.86515
.51653
.85627
.53140
.84712
.54610
.83772
.56064
.82806
54
.50176
.86501
.51678
.85612
.53164
.84697
.54635
.83756
.56088
.82790
63
8
.50201
.86486
.51703
.85597
.53189
.84681
.54659
.83740
.56112
.82773
62
9
.50227
.86471
.51728
.85582
.53214
.84666
.54683
.83724
.56136
.82757
61
10
.50252
.86457
.51753
.85567
.53238
.84650
.54708
.83708
.56160
.82741
50
11
.50277
.86442
.51778
.85551
.53263
.84635
.54732
.83692
.56184
.82724
49
12
.50302
.86427
.51803
.85536
.53288
.84619
.54756
.83676
.56208
.82708
48
13
.50327
.86413
.51828
.85521
.53312
.84604
.54781
.83660
.56232
.82692
47
14
.50352
.86398
.51852
.85506
.53337
.84588
.54805
.83645
.56256
.82675
46
15
.50377
.86384
.51877
.85491
.53361
.84573
.54829
.83629
.66280
.82659
45
16
.50403
.86369
.51902
.85476
.53386
.84557
.64854
.83613
.56305
.82643
44
17
.50428
.86354
.51927
.85461
.53411
.84542
.54878
.83597
.56329
.82626
43
18
.50453
.86340
.51952
.85446
.53435
.84526
.54902
.83581
.56353
.82610
42
19
.50478
.86325
.51977
.85431
.53460
.84511
.54927
.83565
.56377
.82593
41
20
.50503
.86310
.52002
.85416
.53484
.84495
.54951
.83549
.56401
.82577
40
21
.50528
.86295
.52026
.85401
.53509
.84480
.54975
.83533
.56425
.82561
39
22
.50553
.86281
.52051
.85385
.53534
.84464
.54999
.83517
.66449
.82544
38
23
.50578
.86266
.52076
.85370
.53558
.84448
.55024
.83501
.66473
.82528
37
24
.50603
.86251
.52101
.85355
.53583
.84433
.55048
.83485
.56497
.82511
36
25
.50628
.86237
.52126
.85340
.53607
.84417
.55072
.83469
.56521
.82495
35
26
.50654
.86222
.52151
.85325
.53632
.84402
.55097
.83453
.56545
.82478
34
27
.50679
.86207
.52175
.85310
.53656
.84386
.55121
.83437
. .56569
.82462
33
28
.50704
.86192
.52200
.85294
.53681
.84370
.55145
.83421
.56593
.82446
82
29
.50729
.86178
.52225
.85279
.53705
.84355
.55169
.83405
.56617
.82429
81
30
.50754
.86163
.52250
.85264
.53730
.84339
.65194
.83389
.56641
.82413
80
31
.50779
.86148
.52275
.85249
.53754
.84324
.65218
.83373
.56665
.82396
29
32
.50804
.86133
.52299
.85234
.53779
.84308
.65242
.83356
.56689
.82380
28
33
.50829
.86119
.52324
.85218
.53804
.84292
.55266
.83340
.56713
.82363
27
34
.50854
.86104
.52349
.85203
.53828
.84277
.65291
.83324
.56736
.82347
26
35
.50879
.86089
.52374
.85188
.53853
.84261
.55315
.83308
.56760
.82330
25
36
.50904
.86074
.52399
.85173
.53877
.84245
.65339
.83292
.56784
.82314
24
37
.50929
.86059
.52423
.85157
.53902
.84230
.55363
.83276
.56808
.82297
23
88
.50954
.86045
.52448
.85142
.53926
.84214
.55388
.83260
.56832
.82281
22
39
.50979
.86030
.52473
.85127
.53951
.84198
.55412
.83244
.66856
.82264
21
40
.51004
.86015
.52498
.85112 .
.53975
.84182
.65436
.83228
.56880
.82248
20
41
.51029
.86000
.52522
.85096
.54000
.84167
.55460
.83212
.56904
.82281
19
42
.51054
.85985
.52547
.85081
.54024
.84151
.55484
.83195
.56928
.82214
18
43
.51079
.85970
.52572
.85066
.54049
.84135
.55509
.83179
.56952
.82198
17
44
.51104
.85956
.52597
.85051
.54073
.84120
.55533
.83163
.56976
.82181
16
45
.51129
.85941
.52621
.85035
.54097
.84104
.55557
.83147
.57000
.82165
15
46
.51154
.85926
.52646
.85020
.54122
.84088
.55581
.83131
.57024
.82148
14
47
.51179
.85911
.52671
.85005
.54146
.84072
.55605
.83115
.57047
.82132
13
48
.51204
.85896
.52696
.84989
.54171
.84057
.55630
.83098
.57071
.82115
12
49
.51229
.85881
.52720
.84974
.54195
.84041
.55654
.83082
.57095
.82098
11
50
.51254
.85866'
.52745
.84959
.54220
.84025
.55678
.83066
.57119
.82082
10
51
.51279
.85851
.52770
.84943
.54244
.84009
.55702
.83050
.57143
.82065
9
52
.51304
.85836
.52794
.84928
.54269
.83994
.55726
.83034
.57167
.82048
8
53
.51329
.85821
.52819
.84913
.54293
.83978
.55750
.83017
.57191
.82032
54
.51354
.85806
.52844
.84897
.54317
.83962
.55775
.83001
.57215
.82015
55
.51379
.85792
.52869
.84882
.54342
.83946
.55799
.82985
.57238
.81999
56
.51404
.85777
.52896
.84866
.54366
.83930
.55823
.82969
.57262
.81982
57
.51429
.85762
.52918
.84851
.54391
.83915
.65847
.82953
.57286
.81965
58
.51454
.85747
.62943
.84836
.54415
.83899
.55871
.82936
.57310
.81949
59
.51479
.85732
.52967
.84820
.64440
.83883
.55895
.82920
.57334
.81938
60
.51504
.85717
.52992
.84805
.64464
.83867
.55919
.82904
.57358
181915
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
f
Bf
>°
a
5°
5'
JO '
5(
5°
K
o
/
SINES AND COSINES
361
36°
36°
37°
38°
39°
/
S, ie
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
0
.67358
.81915
.68779
.80902
.60182
.79864
.61566
.78801
.62932
.77715
60
.67381
.81899
.68802
.80885
.60205
.79846
.61589
.78783
.62956
.77696
69
2
.67405
.81882
.58826
.80867
.60228
.79829
.61612
.78765
.62977
.77678
58
8
.67429
.81865
.58849
.80850
.60251
.79811
.61635
.78747
.63000
.77660
57
4
.57453
.81848
.68873
.80833
.60274
.79793
.61658
.78729
.63022
.77641
66
fi
.67477
.81832
.68896
.80816
.60298
.79776
.61681
.78711
.63045
.77623
66
6
.67501
.81815
.58920
.80799
.60321
.79758
.61704
.78694
.63068
.77605
54
7
.67524
.81798
.68943
.80782
.60344
.79741
.61726
.78676
.63090
.77586
53
8
.67548
.81782
.68967
.80765
.60367
.79723
.61749
.78658
.63113
.77568
52
9
.67572
.81765
.68990
.80748
.60390
.79706
.61772
.78640
.63135
.77550
51
10
.57596
.81748
.59014
.80730
.60414
.79688
.61795
.78622
.63158
.77531
50
11
.67619
.81731
.69037
.80718
.60437
.79671
.61818
.78604
.63180
.77518
49
12
.67643
.81714
.69061
.80696
.60460
.79653
.61841
.78586
.63203
.77494
48
13
.67667
.81698
.69084
.80679
.60483
.79635
.61864
.78568
.63225
.77476
47
14
.67691
.81681
.69108
.80662
.60506
.79618
.61887
.78550
.63248
.77458
46
15
.57715
.81664
.59131
.80644
.60529
.79600
.61909
.78532
.63271
.77439
45
16
.67738
.81647
.59154
.80627
.60553
.79583
.61932
.78514
.63293
.77421
44
17
.57762
.81631
.69178
.80610
.60576
.79565
.61955
.78496
.63316
.77402
43
18
.57786
.81614
.59201
.80593
.60599
.79547
.61978
.78478
.63338
.77384
42
19
.57810
.81597
.59225
.80576
.60622
.79530
.62001
.78460
.63361
.77366
41
20
.57833
.81580
.59248
.80558
.60645
.79512
.62024
.78442
.63383
.77347
40
21
.57857
.81563
.69272
.80541
.60668
.79494
.62046
.78424
.63406
.77329
39
22
.57881
.81546
.69295
.80524
.60691
.79477
.62069
.78405
.63428
.77310
38
23
.57904
.81530
.59318
.80507
.60714
.79459
.62092
.78387
.63451
.77292
37
24
.57928
.81513
.59342
.80489
.60738
.79441
.62115
.78369
.63473
.77273
36
25
.57952
.81496
.59365
.80472
.60761
.79424
.62138
.78351
.63496
.77255
35
26
.57976
.81479
.59389
.80455
.60784
.79406
.62160
.78333
.63518
.77236
34
27
.57999
.81462
.69412
.80438
.60807
.79388
.62183
.78315
.63540
.77218
33
28
.68023
.81445
.59436
.80420
.60830
.79371
.62206
.78297
.63563
.77199
32
29
.58047
.81428
.59459
.80403
.60853
.79353
.62229
.78279
.63585
.77181
31
SO
.58070
.81412
.59482
.80386
.60876
.79335
.62251
.78261
.63608
.77162
30
81
.58094
.81395
.59506
.80368
.60899
.79318
.62274
.78243
.63630
.77144
29
82
.58118
.81378
.69529
.80351
.60922
.79300
.62297
.78225
.63653
.77125
28
83
.58141
.81361
.59552
.80334
.60945
.79282
.62320
.78206
.63675
.77107
27
34
.58165
.81344
.59576
.80316
.60968
.79264
.62342
.78188
.63698
.77088
26
35
.58189
.81327
.59599
.80299
.60991
.79247
.62365
.78170
.63720
.77070
25
36
.58212
.81310
.59622
.80282
.61015
.79229
.62388
.78152
.63742
.77061
24
37
.58236
.81293
.59646
.80264
.61038
.79211
.62411
.78134
.63765
.77033
23
38
.58260
.81276
.59669
.80247
.61061
.79193
.62433
.781 10
.63787
.77014
22
39
.58283
.81259
.59693
.80230
.61084
.79176
.62456
.78098
.63810
.76996
21
40
.68307
.81242
.59716
.80212
.61107
.79158
.62479
.78079
.63832
.76977
20
41
.58330
.81225
.59739
.80195
.61130
.79140
.62502
.78061
.63854
.76959
19
42
.68354
.81208
.59763
.80178
.61153
.79122
.62524
.78043
.63877
.76940
18
43
.68378
.81191
.69786
.80160
.61176
.79105
.62547
.78025
.63899
.76921
17
44
.58401
.81174
.59809
.80143
.61199
.79087
.62570
.78007
.63922
.76903
16
45
.58425
.81157
.59832
.80125
.61222
.79069
.62592
.77988
.63944
.76884
15
46
.58449
.81140
.59856
.80108
.61245
.79051
.62615
.77970
.63966
.76866
14
47
.68472
.81123
.59879
.80091
.61268
.79033
.62638
.77952
.63989
.76847
13
48
.58496
.81106
.59902
.80073
.61291
.79016
.62660
.77934
.64011
.76828
12
49
.58519
.81089
.69926
.80056
.61314
.78998
.62683
.77916
.64033
.76810
11
50
.68543
.81072
.59949
.80038
.61337
.78980
.62706
.77897
.64056
.76791
10
51
.58567
.81055
.59972
.80021
.61360
.78962
.62728
.77879
.64078
.76772
9
52
.68590
.81038
.59995
.80003
.61383
.78944
.62751
.77861
.64100
.76754
8
53
.58614
.81021
.60019
.79986
.61406
.78926
.62774
.77843
.64123
.76735
7
64
.58637
.81004
.60042
.79968
.61429
.78908
.62796
.77824
.64145
.76717
6
55
.58661
.80987
.60065
.79951
.61451
.78891
.62819
.77806
.64167
.76698
5
56
.58684
.80970
.60089
.79934
.61474
.78873
.62842
.77788
.64190
.76679
4
67
.58708
.80953
.60112
.79916
.61497
.78855
.62864
.77769
.64212
.76661
8
58
.58731
.80936
.60135
.79899
.61520
.78837
.62887
.77751
.64234
.76642
2
59
.58755
.80919
.60158
.79881
.61548
.78819
.62909
.77733
.64256
.76623
1
60
.68779
.80902
.60182
.79864
.61566
.78801
.62932
.77715
.64279
.76604
0
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
54°
53°
52°
51°
50°
/
362
MINE GASES AND VENTILATION
4
v>
4
L°
45
J°
4,
J°
44
0
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
0
.64279
.76604
.65606
.75471
.66913
.74314
.68200
.73135
.69466
.71934
60
1
.64301
.76586
.65628
.75452
.66935
.74295
.68221
.73116
.69487
.71914
59
2
.64323
.76567
.65650
.75433
.66956
.74276
.68242
.73096
.69508
.71894
58
3
.64346
.76548
.65672
.75414
.66978
.74256
.68264
.73076
.69529
.71873
57
4
.64368
.76530
.65694
.75395
.66999
.74237
.68285
.73056
.69549
.71853
56
5
.64390
.76511
.65716
.75375
.67021
.74217
.68306
.73036
.69570
.71833
55
6
.64412
.76492
.65738
.75356
.67043
.74198
.68327
.73016
.69591
.71813
54
7
.64435
.76473
.65759
.75337
.67064
.74178
.68349
.72996
.69612
.71792
53
8
.64457
.76455
.65781
.75318
.67086
.74159
.68370
.72976
.69633
.71772
52
9
.64479
.76436
.65803
.75299
.67107
.74139
.68391
.72957
.69654
.71752
51
10
.64501
.76417
.65825
.75280
.67129
.74120
.68412
.72937
.69675
.71732
50
11
.64524
.76398
.65847
.75261
.67151
.74100
.68434
.72917
.69696
.71711
49
12
.64546
.76380
.65869
.75241
.67172
.74080
.68455
.72897
.69717
.71691
48
13
.64568
.76361
.65891
.75222
.67194
.74061
.68476
.72877
.69737
.71671
47
14
.64590
.76342
.65913
.75203
.67215
.74041
.68497
.72857
.69758
.71650
46
15
.64612
.76323
.65935
.75184
.67237
.74022
.68518
.72837
.69779
.71630
45
16
.64635
.76304
.65956
.75165
.67258
.74002
.68539
.72817
.69800
.71610
44
17
.64657
.76286
.65978
.75146
.67280
.73983
.68561
.72797
.69821
.71590
43
18
.64679
.76267
.66000
.75126
.67301
.73963
.68582
.72777
.69842
.71569
42
19
.64701
.76248
.66022
.75107
.67323
.73944
.68603
.72757
.69862
.71549
41
20
.64723
.76229
.66044
.75088
.67344
.73924
.68624
.72737
.69883
.71529
40
21
.64746
.76210
.66066
.75069
.67366
.73904
.68645
.72717
.69904
.71508
39
22
.64768
.76192
.66088
.75050
.67387
.73885
.68666
.72697
.69925
.71488
38
23
.64790
.76173
.66109
.75030
.67409
.73865
.68688
.72677
.69946
.71468
37
24
.64812
.76154
.66131
.75011
.67430
.73846
.68709
.72657
.69966
.71447
36
35
.64834
.76135
.66153
.74992
.67452
.73826
.68730
.72637
.69987
.71427
35
26
.64856
.76116
.66175
.74973
.67473
.73806
.68751
.72617
.70008
.71407
34
27
.64878
.76097
.66197
.74953
.67495
.73787
.68772
.72597
.70029
.71386
33
26
.64901
.76078
.66218
.74934
.67516
.73767
.68793
.72577
.70049
.71366
32
29
.64923
.76059
.66240
.74915
.67538
.73747
.68814
.72557
.70070
.71345
31
30
.64945
.76041
.66262
.74896
.67559
.73728
.68835
.72537
.70091
.71325
30
31
.64967
.76022
.66284
.74876
.67580
.73708
.68857
.72517
.70112
.71305
29
82
.64989
.76003
.66306
.74857
.67602
.73688
.68878
.72497
.70132
.71284
28
33
.65011
.75984
.66327
.74838
.67623
.73669
.68899
.72477
,70153
.71264
27
34
.65033
.75965
.66349
.74818
.67645
.73649
.68920
.72457
.70174
.71243
26
35
.65055
.75946
.66371
.74799
.67666
.73629
.68941
.72437
.70195
.71223
25
36
.65077
.75927
.66393
.74780
.67688
.73610
.68962
.72417
.70215
.71203
24
87
.65100
.75908
.66414
.74760
.67709
.73590
.68983
.72397
.70236
.71182
29
38
.65122
.75889
,66436
.74741
.67730
.73570
.69004
.72377
.70257
.71162
2>
89
.65144
.75870
.66458
.74722
.67752
.73551
.69025
.72357
.70277
.71141
21
40
.65166
.75851
.66480
.74703
.67773
.73531
.69046
.72337
.70298
.71121
20
41
.65188
.75832
.66501
.74683
.67795
.73511
.69067
.72317
.70319
.71100
19
42
.65210
.75813
.66523
.74664
.67816
.73491
.69088
.72297
.70339
.71080
18
43
.65232
.75794
.66545
.74644
.67837
.73472
.69109
.72277
.70360
.71059
11
44
.65254
.75775
.66566
.74625
.67859
.73452
.69130
.72257
.70381
.71039
1C
45
.65276
.75756
.66588
.74606
.67880
.73432
.69151
.72236
.70401
.71019
15
46
.65298
.75738
.66610
.74586
.67901
.73413
.69172
.72216
.70422
.70998
14
47
.65320
.75719
.66632
.74567
.67923
.73393
.69193
.72196
.70443
.70978
1*
48
.65342
.75700
.66653
.74548
.67944
.73373
.69214
.72176
.70463
.70957
11
49
.65364
.75680
*66675
.74528
.67965
.73353
.69235
.72156
.70484
.70937
11
50
.65386
.75661
.66697
.74509
.67987
.73333
.69256
.72136
.70505
.70916
10
51
.65408
.75642
.66718
.74489
.68008
.73314
.69277
.72116
.70525
.70896
52
.65430
.75623
.66740
.74470
.68029
.73294
.69298
.72095
.70546
.70875
53
.65452
.75604
.66762
.74451
.68051
.73274
.69319
.72075
.70567
.70856
54
.65474
.75585
.66783
.74431
.68072
.73254
.69340
.72055
.70587
.70834
55
.65496
.75566
.66805
.74412
.68093
.73234
.69361
.72035
.70608
.70813
56
.65518
.75547
.66827
.74392
.68115
.73215
.69382
.72015
.70628
.70793
57
.65540
.75528
.66848
.74373
.68136
.73195
.69403
.71995
.70649
.70772
58
.65562
.75509
.66870
.74353
.68157
.73175
.69424
.71974
.70670
.70752
59
.65584
.75490
.66891
.74334
.68179
.73155
.69445
.71954
.70690
.70781
60
.65606
.75471
.66913
.74314
.68200
.73135
.69466
.71934
.70711
.70711
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
4
9°
4J
S°
4'
?o
4
i°
4£
0
r
TANGENTS AND COTANGENTS
304
MINE GASES AND VENTILATION
f
Of
»
1
3
2*
j
3
9
4
»
Twig
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
0
.00000
Infill.
.01746
57.2900
.03492
28.6363
.05241
19.0811
.06993
14.3007
60
.00029
3437.75
.01775
56.3506
.03521
28.3994
.05270
18.9755
.07022
14.2411
59
.00058
1718.87
.01804
55.4415
.03550
28.1664
.05299
18.8711
.07051
14.1821
58
.00087
1145.92
.01833
54.5613
.03579
27.9372
.05328
18.7678
.07080
14.1235
57
.00116
859.436
.01862
53.7086
.03609
27.7117
.05357
18.6656
.07110
14.0655
56
.00145
687.549
.01891
52.8821
.03638
27.4899
.05387
18.5645
.07139
14.0079
55
.00175
572.957
.01920
52.0807
.03667
27.2715
.05416
18.4645
.07168
13.9507
54
.00204
491.106
.01949
51.3032
.03696
27.0566
.05445
18.3655
.07197
13.8940
53
8
.00233
429.718
.01978
50.5485
.03725
26.8450
.05474
18.2677
.07227
13.8378
52
9
.00232
381.971
.02007
49.8157
.03754
26.6367
.05503
18.1708
.07256
13.7821
51
10
.00291
343.774
.02036
49.1039
.03783
26.4316
.05533
18.0750
.07285
13.7267
50
11
.00320
312.521
.02066
48.4121
.03812
26.2296
.05562
17.9802
.07314
13.6719
49
12
.00349
286.478
.02095
47.7395
.03842
26.0307
.05591
17.8863
.07344
13.6174
48
13
.00378
264.441
.02124
47.0853
.03871
25.8348
.05620
17.7934
.07373
13.5634
47
14
.00407
245.552
.02153
46.4489
.03900
25.6418
.05649
17.7015
.07402
13.5098
46
15
.00436
229.182
.02182
45.8294
.03929
25.4517
.05678
17.6106
.07431
13.4566
45
16
.00465
214.858
.02211
45.2261
.03958
25.2644
.05708
17.5205
.07461
13.4039
44
17
.00495
202.219
.02240
44.6386
.03987
25.0798
.05737
17.4314
.07490
13.3515
43
18
.00524
190.984
.02269
44.0661
.04016
24.8978
.05766
17.3432
.07519
13.2996
42
19
.00553
180.932
.02298
43.5081
.04046
24.7185
.05795
17.2558
.07548
13.2480
41
20
.00582
171.885
.02328
42.9641
.04075
24.5418
.05824
17.1693
.07578
13.1969
40
21
.00611
163.700
.02357
42.4335
.04104
24.3675
.05854
17.0837
.07607
13.1461
39
22
.00640
156.259
.02386
41.9158
.04133
24.1957
.05883
16.9990
.07636
13.0958
38
23
.00669
149.465
.02415
41.4106
.04162
24.0263
.05912
16.9150
.07665
13.0458
37
24
.00698
143.237
.02444
40.9174
.04191
23.8593
.05941
16.8319
.07695
12.S962
36
25
.00727
137.507
.02473
40.4358
.04220
23.6945
.05970
16.7496
.07724
12.9469
35
20
.00756
132.219
.02502
39.9655
.04250
23.5321
.05999
16.6681
.07753
12.8981
34
27
.00785
127.321
.02531
39.5059
.04279
23.3718
.06029
16.5874
.07782
12.8496
33
28
.00815
122.774
.02560
39.0568
.04308
23.2137
.06058
16.5075
.07812
12.8014
32
29
.00844
118.540
.02589
38.6177
.04337
23.0577
.06087
16.4283
.07841
12.7536
31
30
.00873
114.589
.02619
38.1885
.04366
22.9038
.06116
16.3499
.07870
12.7062
30
31
.00902
110.892
.0?,648
97.7686
.04395
22.7519
.06145
16.2722
.07899
12.6591
29
32
.00931
107.426
.02677
37.3579
.04424
22.6020
.06175
16.1952
.07929
12.6124
28
33
.00960
104.171
.02706
36.9560
.04454
22.4541
.06204
16.1190
.07958
12.5660
27
34
.00989
101.107
.02735
36.5627
.04483
22.3081
.06233
16.0435
.OT987
12.5199
26
35
.01018
98.2179
.02764
36.1776
.04512
22.1640
.06262
15.9687
.08017
12.4742
25
36
.01047
95.4895
.02793
35.8006
.04541
22.0217
.06291
15.8945
.08046
12.4288
24
37
.01076
92.9085
.02822
35.4313
.04570
21.8813
.06321
15.8211
.08075
12.3838
23
38
.01105
90.4633
.02851
35.0695
.04599
21.7426
.06350
15.7483
.08104
12.3390
22
39
.01135
88.1436
.02881
34.7151
.04628
21.6056
.06379
15.6762
.08134
12.2946
21
40
.01164
85.9398
.02910
34.3678
.04658
21.4704
.06408
15.6048
.08163
12-.2505
20
41
.01193
83.8435
.02939
34.0273
.04687
21.8369
.06437
15.5340
.08192
12.2067
19
42
.01222
81.8470
.02968
33.6935
.04716
21.2049
.06467
15.4638
.08221
12.1632
18
43
.01251
79.9434
.02997
33.3662
.04745
21.0747
.06496
15.3943
.08251
12.1201
17
44
.01280
78.1263
.03026
33.0452
.04774
20.9460
.06525
15.3254
.08280
12.0772
16
45
.01309
76.3900
.03055
32.7303
.04803
20.8188
.06554
15.2571
.08309
12.0346
15
46
.01338
74.7292
.03084
32.4213
.04833
20.6932
.06584
15.1893
.08339
11.9923
14
47
.01367
73.1390
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32.1181
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20.5691
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15.1222
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11.9504
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71.6151
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31.8205
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20.4465
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15.0557
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11.9087
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70.1533
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31.5284
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20.3253
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14.9898
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11.8673
11
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68.7501
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31.2416
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20.2056
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14.9244
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11.8262
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67.4019
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30.9599
.04978
20.0872
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14.8596
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11.7853
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66.1055
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30.6833
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19.9702
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14.7954
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11.7448
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64.8580
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30.4116
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19.8546
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14.7317
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11.7045
54
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63.6567
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30.1446
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19.7403
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14.6685
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11.6645
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62.4992
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29.8823
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19.6273
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14.6059
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11.6248
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29.6245
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19.5156
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14.5438
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11.5853
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60.3058
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29.3711
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19.4051
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14.4823
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11.5461
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29.1220
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19.2959
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14.4212
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11.5072
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28.8771
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19.1879
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14.3607
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11.4685
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57.2900
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28.6363
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19.0811
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14.3007
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11.4301
Cotang
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Cotang
Tang
Cotang
Tang
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8
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TANGENTS AND COTANGENTS
365
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6.31375
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11.3919
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7.10038
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6.30189
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7.07059
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6.27829
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7.05579
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6.26655
56
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11.2417
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9.38307
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8.04756
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6.25486
55
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11.2048
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9.35724
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8.02848
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7.02637
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6.24321
54
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11.1681
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9.33155
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7.01174
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6.23160
53
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11.1316
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9.30599
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6.22003
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11.0954
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9.28058
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7.97176
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6.98268
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6.20851
51
10
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11.0594
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9.25530
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7.95302
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6.96823
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6.19703
50
11
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11.0237
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9.23016
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6.18559
49
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10.9882
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6.93952
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6.17419
48
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10.9529
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9.18028
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6.92525
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6.16283
47
14
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10.9178
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6.91104
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6.15151
46
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10.8829
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9.13093
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7.86064
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6.89688
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6.14023
45
16
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10.8483
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9.10646
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7.84242
.14529
6.88278
.16316
6.12899
44
17
.09247
10.8139
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9.08211
.12781
7.82428
.14559
6.86874
.16346
6.11779
43
18
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10.7797
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9.05789
.12810
7.80622
.14588
6.85475
.16376
6.10664
42
19
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10.7457
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9.03379
.12840
7.78825
.14618
6.84082
.16405
6.09552
41
20
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10.7119
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9.00983
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7.77035
.14648
6.82694
.16435
6.08444
40
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10.6783
.11128
8.98598
.12899
7.75254
.14678
6.81312
.16465
6.07340
39
22
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10.6450
.11158
8.96227
.12929
7.73480
.14707
6.79936
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6.06240
38
23
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10.6118
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8.93867
.12958
7.71715
.14737
6.78564
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6.05143
37
24
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10.5789
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8.91520
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7.69957
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6.77199
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6.04051
36
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10.5462
.11246
8.89185
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7.68208
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6.75838
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6.02962
35
26
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10.5136
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8.86862
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7.66466
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6.74483
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34
27
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10.4813
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8.84551
.13076
7.64732
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6.73133
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6.00797
33
28
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10.4491
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8.82252
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7.63005
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6.71789
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5.99720
32
29
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10.4172
.11364
8.79964
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7.61287
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6.70450
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5.98646
31
30
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10.3854
.11394
8.77689
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7.59575
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6.69116
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5.97576
30
31
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10.3538
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8.75425
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7.57872
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6.67787
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5.96510
29
32
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10.3224
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8.73172
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28
33
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10.2913
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8.70931
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6.65144
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5.94390
27
34
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10.2602
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8.68701
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6.63831
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5.93335
26
35
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10.2294
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8.66482
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6.62523
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5.92283
25
36
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10.1988
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5.91236
24
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10.1683
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6.59921
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5.90191
23
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6.58627
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6.57339
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5.88114
21
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6.56055
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6.54777
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5.86051
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6.53503
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5.85024
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9.98931
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8.49128
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7.37999
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6.52234
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5.84001
17
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9.96007
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7.36389
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6.50970
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5.82982
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7.34786
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6.49710
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5.81966
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9.90211
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8.42795
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7.33190
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6.48456
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8.40705
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7.31600
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6.47206
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5.79944
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8.38625
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7.30018
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6.45961
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8.36555
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7.28442
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9.78817
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8.34496
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7.26873
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8,32446
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7.25310
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6.42253
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9.73217
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8.30406
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7.23754
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6.41026
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9.70441
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8.28376
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7.22204
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6.39804
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7
54
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9.67680
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8.26355
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7.20661
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9.64935
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8.24345
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7.19125
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5.71992
56
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9.62205
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8.22344
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7.17594
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6.36165
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5.71013
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9.59490
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8.20352
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7.16071
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9.56791
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8.18370
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7.14553
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6.33761
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5.69064
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9.54106
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8.16398
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7.13042
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6.32566
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5.68094
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.10510
9.51436
.12278
8.14435
.14054
7.11537
.15838
6.31375
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5.67128
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
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8-
1°
85
*°
8
2°
«•
L°
8
0°
t
366
MINE GASES AND VENTILATION
1(
IP
1
1°
1
2°
1
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]
40
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
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Cotang
.17633
5.67128
.19438
5.14455
.21256
4.70463
.23087
4.33148
.24933
4.01078
60
.17663
5.66165
.19468
5.13658
.21286
4.69791
.23117
4.32573
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4.00582
59
.17693
5.65205
.19498
5.12862
.21316
4.69121
.23148
4.32001
.24995
4.00086
58
.17723
5.64248
.19529
5.12069
.21347
4.68452
.23179
4.31430
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3.99592
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5.63295
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5.11279
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4.67786
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4.308CO
.25056
3.99099
56
.17783
5.62344
.19589
5.10490
.21408
4.67121
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4.30291
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3.98607
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5.61397
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5.09704
.21438
4.66458
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4.29724
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3.98117
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5.60452
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5.08921
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4.G5797
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4.29159
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3.97627
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5.59511
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5.08139
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4.65138
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4.28595
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3.97139
52
.17903
5.58573
.19710
5.07360
.21529
4.64480
.23363
4.28032
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3.96651
51
10
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5.57638
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5.06584
.21560
4.63825
.23393
4.27471
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3.96165
50
11
.17963
5.56706
.19770
5.05809
.21590
4.63171
.23424
4.26911
.25273
3.95680
49
12
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5.55777
.19801
5.05037
.21621
4.62518
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4.26352
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3.95196
48
13
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5.54851
.19831
5.04267
.21651
4.61868
.23485
4.25795
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3.94713
47
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5.53927
.19861
5.03499
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4.61219
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4.25239
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3.94232
46
15
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5.53007
.19891
5.02734
.21712
4.60572
.23547
4.24685
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3.93751
45
16
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5.52090
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5.01971
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4.59927
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4.24132
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3.93271
44
17
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5.51176
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5.01210
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4.59283
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4.2C530
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3.92793
43
18
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5.50264
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5.00451
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4.58641
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4.23030
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3.92316
42
19
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5.49356
.20012
4.99695
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4.58001
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4.22481
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3.91839
41
20
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5.48451
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4.98940
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4.57363
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4.21933
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3.91364
40
21
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5.47548
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4.98188
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4.56726
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4.21387
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3.90890
39
22
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5.46648
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4.97438
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4.56091
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4.20842
.25614
3.90417
38
23
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5.45751
.20133
4.96690
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4.55458
.23793
4.20298
.25645
3.89945
37
24
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5.44857
.20164
4.95945
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4.54826
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4.19756
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3.89474
36
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5.43966
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4.95201
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4.54196
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4.19215
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3.89004
35
26
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5.43077
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4.94460
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4.53568
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4.18675
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3.88536
34
27
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5.42192
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4.93721
.22078
4.52941
.23916
4.18137
.25769
3.88068
33
28
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5.41309
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4.92984
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4.52316
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4.17600
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3.87601
32
29
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5.40429
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4.92249
.22139
4.51693
.23977
4.17064
.25831
3.87136
31
30
.18534
5.39552
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4.91516
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4.51071
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4.16530
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3.86671
30
31
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5.38677
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4.90785
.22200
4.50451
.24039
4.15997
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3.86208
29
82
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5.37805
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4.90056
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4.49832
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4.15465
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3.85745
28
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5.36936
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4.89330
.22261
4.49215
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4.14934
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3.85284
27
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5.36070
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4.88605
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4.48600
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4.14405
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3.84824
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5.35206
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4.87882
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4.47986
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4.13877
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3.84364
25
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5.34345
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4.87162
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4.47374
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4.13350
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3.83906
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5.33487
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4.86444
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4.46764
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4.12825
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3.83449
23
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5.32631
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4.85727
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4.46155
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4.12301
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3.82992
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5.31778
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4.85013
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4.45548
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4.11778
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3.82537
21
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5.30928
.20648
4.84300
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4.44942
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4.11256
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3.82083
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5.30080
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4.83590
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4'.44338
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4.10736
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3.81630
19
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5.29235
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4.82882
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4.43735
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4.10216
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3.81177
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5.28393
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4.82175
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4.43134
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4.09699
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3.80726
17
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5.27553
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4.81471
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4.42534
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4.09182
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3.80276
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5.26715
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4.80769
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4.41936
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4.08666
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3.79827
15
46
.19016
5.25880
.20830
4.80068
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4.41340
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4.08152
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3.79378
14
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.19046
5.25048
.20861
4.79370
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4.40745
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4.07639
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3.78931
13
48
.19076
5.24218
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4.78673
.22719
4.40152
.24562
4.07127
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3.78485
12
49
.19106
5.23391
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4.77978
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4.39560
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4.06616
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11
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.19136
5.22566
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4.77286
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4.38969
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4.06107
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3.77595
10
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5.21744
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4.76595
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4.38381
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4.05599
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3.77152
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5.20925
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4.75906
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4.37793
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4.05092
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3.76709
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5.20107
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4.75219
.22872
4.37207
.24717
4.04586
.26577
3.76268
64
.19257
5.19293
.21073
4.74534
.22903
4.36623
.24747
4.04081
.26608
3.75828
55
.19287
5.18480
.21104
4.73851
.22934
4.36040
.24778
4.03578
.26639
3.75388
66
.19317
5.17671
.21134
4.73170
.22964
4.35459
.24809
4.03076
.26670
3.74950
67
.19347
5.16863
.21164
4.72490
.22995
4.34879
.24840
4.02574
.26701
3.74512
58
.19378
5.16058
.21195
4.71813
.23026
4.34300
.24871
4.02074
.26733
3.74075
68
.19408
5.15256
.21225
4.71137
.23056
4.33723
.24902
4.01576
.26764
3.73640
60
.19438
5.14455
.21256
4.70463
.23087
4.33148
.24933
4.01078
.26795
3.73205
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
/
7*
1°
' 71
5°
T,
o
7<
o
7
5°
/
TANGENTS AND COTANGENTS
307
/
1
3°
1
5°
1
7°
1*
*°
1
9°
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
.16795
3.73205
.28675
3.48741
.30573
8.27085
.32492
3.07768
.34438
J. 90421
60
.26826
3.72771
.28706
3.48359
.30605
8.26745
.32524
3.07464
.34465
2.90147
69
26857
3.72338
.28738
3.47977
.30637
3.26406
.32556
3.07160
.34498
2.89873
68
.26888
3.71907
.28769
3.47596
.30669
3.26067
.32588
3.06857
.34530
2.89600
67
.26920
3.71476
.28800
3.47216
.30700
3.25729
.32621
3.06554
.34563
2.89327
66
.26951
3.71046
' .28832
3.46837
.30732
3.25392
.32653
3.06252
.34596
2.89055
65
.26982
3.70616
.28864
3.46458
.30764
3.25055
.32685
3.05950
.34628
2.88783
64
.27013
3.70188
.28895
3.46080
.30796
3.24719
.32717
3.05649
.34661
2.88511
63
.27044
3.69761
.28927
3.45703
.30828
8.24383
.32749
3.05349
.34693
2.88240
62
.27076
3.69335
.28958
3.45327
.80860
8.24049
.32782
3.05049
.34728
2.87970
61
10
.27107
3.68909
.28990
3.44951
.30891
8.23714
.32814
3.04749
.34758
2.87700
60
11
.27138
3.68485
.29021
3.44576
.80923
8.23381
.32846
3.04450
.34791
2.87430
49
12
.27169
3.68061
.29053
3.44202
.30955
8.23048
.82878
3.04152
.34824
2.87161
48
13
.27201
3.67638
.29084
3.43829
.30987
3.22715
.32911
3.03854
.34856
2.86892
47
14
.27232
3.67217
.29116
3.43456
.31019
3.22384
.32943
3.03556
.34889
2.86624
46
15
.27263
3.66796
.29147
3.43084
.31051
3.22053
.32975
3.03260
.34922
2.86356
45
16
.27294
3.66376
.29179
3.42713
.81083
3.21722
.33007
3.02963
.34954
2.86089
44
17
.27326
3.65957
.29210
3.42343
.31115
3.21392
.33040
3.02667
.34987
2.85822
43
18
.27357
3.65538
.29242
3.41973
.31147
3.21063
.33072
3.02372
.35020
2.85555
42
19
.27388
3.65121
.29274
3.41604
.31178
3.20734
.33104
3.02077
.35052
2.85289
41
20
.27419
3.64705
.29305
3.41236
.31210
3.20406
.33136
3.01783
.35085
2.85023
40
21
.27451
3.64289
.29337
3.40869
.31242
3.20079
.33169
3.01489
.35118
2.84758
39
22
.27482
3.63874
.29368
3.40502
.31274
3.19752
.33201
3.01196
.35150
2.84494
38
23
.27513
3.63461
.29400
3.40136
.31306
3.19426
.33233
3.00903
.35183
2.84229
37
24
.27545
3.63048
.29432
3.39771
.31338
3.19100
.33266
3.00611
.35216
2.83965
36
25
.27576
3.62636
.29463
3.39406
.31370
3.18775
.33298
3.00319
.35248
2.83702
35
26
.27607
3.62224
.29495
3.39042
.31402
8.18451
.33330
3.00028
.35281
2.83439
34
27
.27638
3.61814
.29526
3.38679
.31434
3.18127
.33363
2.99738
.35314
2.83176
33
28
.27670
3.61405
.29558
3.38317
.31466
3.17804
.33395
2.99447
.35346
2.82914
32
29
.27701
3.60996
.29590
8.37955
.31498
3.17481
.33427
2.99158
.35379
2.82653
3t
30
.27732
3.60588
.29621
3.37594
.31530
3.17159
.33460
2.98868
.35412
2.82391
30
31
.27764
3.60181
.29653
3.37234
.31562
3.16838
.33492
2.98580
.35445
2.82130
29
32
.27795
3.59775
.29685
3.36875
.31594
3.16517
.33524
2.98292
.35477
2.81870
28
83
.27826
3.59370
.29716
3.36516
.31626
3.16197
.33557
2.98004
.35510
2.81610
27
34
.27858
3.58966
,29748
3.36158
.31658
3.15877
.33589
2.97717
.35543
2.81350
26
35
.27889
3.58562
.29780
3.35800
.31690
3.15558
.33621
2.97430
.35576
2.81091
25
36
.27921
3.58160
.29811
3.35443
.31722
3.15240
.33654
2.97144
.35608
2.80833
24
37
.27952
3.57758
.29843
8.35087
.31754
3.14922
.33686
2.96858
.35641
2.80574
23
38
.27983
3.57357
.29875
3.34732
.31786
3.14605
.33718
2.96573
.35674
2.80316
22
39
.28015
3.56957
.29906
3.34377
.31818
3.14288
.33751
2.96288
.35707
2.80059
21
40
.28046
3.56557
.29938
3.34023
.31850
3.13972
.33783
2.96004
.35740
2.79802
20
41
.28077
3.56159
.29970
3.33670
.31882
3.13656
.33816
2.95721
.35772
2.79545
19
42
.28109
3.55761
.30001
3.33317
.31914
3.13341
.33848
2.95437
.35805
2.70289
18
43
.28140
3.55364
.30033
3.32965
.31946
3.13027
.33881
2.95155
.35838
2.79033
n
44
.28172
3.54968
.30065
3.32614
.31978
3.12713
.33913
2.94872
.35871
2.78778
16
45
.28203
3.54573
.30097
3.32264
.32010
8.12400
.33945
2.94591
.35904
2.78523
15
46
.28234
3.54179
.30128
3.31914
.32042
3.12087
.33978
2.94309
.35937
2.78269
14
47
.28266
3.53785
.30160
3.31565
.32074
3.11775
.34010
2.94028
.35969
2.78014
13
48
.28297
3.53393
.30192
3.31216
.32106
8.11464
.34043
2.93748
.36002
2.77761
12
49
.28329
3.53001
.30224
3.30868
.32139
3.11153
.34075
2.93468
.36035
2.77507
11
60
.28360
3.52609
.30255
3.30521
.32171
3.10842
.34108
2.93189
.36068
2.77254
10
51
.28391
3.52219
.30287
3.30174
.32203
3.10532
.34140
2.92910
.36101
2.77002
52
.28423
3.51829
.30319
3.29829
.32235
3.10223
.34173
2.92632
.36134
2.76750
53
.28454
3.51441
.30351
3.29483
.32267
3.09914
.34205
2.92354
.36167
2.76498
54
.28486
3.51053
.30382
3.29139
.32299
3.09606
.34238
2.92076
.36199
2.76247
55
.28517
3.50666
.30414
3.28795
.32331
3.09298
.34270
2.91799
.36232
2.75996
56
.28549
3.50279
.30446
8.28452
.32363
3.08991
.34303
2.91523
.36265
2.75746
57
.28580
3.49894
.30478
3.28109
.32386
3.08685
.34335
2.91246
.36298
2.75496
58
.28612
3.49509
.30509
3.27767
.32428
3.08379
.34368
2.90971
.36331
2.75246
59
.28643
3.49125
.30541
3.27426
.32460
3.08073
.34400
2.90696
.36364
2.74997
60
.28675
3.48741
.30573
3.27085
.32492
3.07768
.34433
2.90421
.36397
2.74748
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
f
7
1°
7
3°
7
2°
7:
L°
7(
)°
f
368
MINE GASES AND VENTILATION
1
21
IP
2
L°
2
2°
2
J°
a
4°
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
.36397
2.74748
.38386
2.60509
.40403
2.47509
.42447
2.35585
.44523
2.24604
60
.36430
2.74499
.38420
2.60283
.40436
2.47302
.42482
2.35395
.44558
2.24428
59
.36463
2.74251
.38453
2.60057
.40470
2.47095
.42516
2.35205
.44593
2.24252
58
.36496
2.74004
.38487
2.59831
.40504
2.46888
.42551
2.35015
.44627
2.24077
57
.36529
2.73756
.38520
2.59606
.40538
2.46682
.42585
2.34825
.44662
2.23902
56
.36562
2.73509
.38553
2.59381
.40572
2.46476
.42619
2.84636
.44697
2.23727
55
.36595
2.73263
.38587
2.59156
.40606
2.46270
.42654
2.34447
.44732
2.23553
54
.36628
2.73017
.38620
2.58932
.40640
2.46065
.42688
2.34258
.44767
2.23378
53
.36661
2.72771
.38654
2.58708
.40674
2.45860
.42722
2.34069
.44802
2.23204
52
.36694
2.72526
.38687
2.58484
.40707
2.45655
.42757
2.33881
.44837
2.23030
51
10
.36727
2.72281
.38721
2.58261
.40741
2.45451
.42791
2.33693
.44872
2.22857
50
11
.36760
2.72036
.38754
2.58038
.40775
2.45246
.42826
2.33505
.44907
2.22683
49
12
.86793
2.71792
.38787
2.57815
.40809
2.45043
.42860
2.33317
.44942
2.22510
48
13
.36826
2.71548
.38821
2.57593
.40843
2.44839
.42894
2.33130
.44977
2.22337
47
H
.36859
2.71305
.38854
2.57371
.40877
2.44636
.42929
2.32943
.45012
2.22164
46
15
.36892
2.71062
.38888
2.57150
.40911
2.44433
.42963
2.32756
.45047
2.21992
45
16
.36925
2.70819
.38921
2.56928
.40945
2.44230
.42998
2.32570
.45082
2.21819
44
17
.36958
2.70577
.38955
2.56707
.40979
2.44027
.43032
2.32383
.45117
2.21647
43
18
.36991
2.70335
.38988
2.56487
.41013
2.43825
.43067
2.32197
.45152
2.21475
42
19
.37024
2.70094
.39022
2.56266
.41047
2.43623
,43101
2.32012
.45187
2.21304
41
20
.37057
2.69853
.39055
2.56046
.41081
2.43422
.43136
2.31826
.45222
2.21132
40
21
.37090
2.69612
.39089
2.55827
.41115
2.43220
.43170
2.31641
.45257
2.20961
89
23
.87123
2.69371
.39122
2.55608
.41149
2.43019
43205
2.31456
.45292
2.20790
88
25
.37157
2.69131
.39156
2.55389
.41183
2.42819
.43239
2.31271
.45327
2.20619
87
24
.37190
2.68892
.39190
2.55170
.41217
2.42618
.43274
2.31086
.45362
2.20449
36
25
.37223
2.68653
.39223
2.54952
.41251
2.42418
.43308
2.30902
.45397
2.20278
35
26
.37256
2.68414
.39257
2.54734
.41285
2.42218
.43343
2.30718
.45432
2.20108
34
V
.37289
2.68175
.39290
2.54516
.41319
2.42019
.43378
2.30534
.45467
2.19938
33
28
.37322
2.67937
.39324
2.54299
.41353
2.41819
.43412
2.30351
.45502
2.19769
32
29
.37355
2.67700
.39357
2.54082
.41387
2.41G20
.43447
2.30167
.45538
2.19599
31
30
.37388
2.67462
.39391
2.53865
.41421
2.41421
.43481
2.29984
.45573
2.19430
30
81
.37422
2.67225
.39425
2.53648
.41455
2.41223
.43516
2.29801
.45608
2.19261
29
32
.37455
2.66989
.39458
2.53432
.41490
2.41025
.43550
2.29619
.45643
2.19092
28
33
.37488
2. '66752
.39492
2.53217
.41524
2.40827
.43585
2.29437
.45678
2.18923
27
34
.37521
2.66516
.39526
2.53001
.41558
2.40629
.43620
2.29254
.45713
2.18755
26
35
.37554
2.66281
.39559
2.52786
.41592
2.40432
.43654
2.29073
.45748
2.18587
25
36
.37588
2.66046
.39593
2.52571
.41626
2.40235
.43689
2.28891
.45784
2.18419
24
37
.37621
2.65811
.39626
2.52357
.41660
2.40038
.43724
2.28710
.45819
2.18251
23
38
.37654
2.65576
.39660
2.52142
.41694
2.39841
.43758
2.28528
.45854
2.18084
22
39
.37687
2.65342
.39694
2.51929
.41728
2.39645
.43793
2.28348
.45889
2.17916
21
40
.37720
2.65109
.39727
2.51715
.41763
2.39449
.43828
2.28167
.45924
2.17749
20
41
.37754
2.64875
.39761
2.51502
.41797
2.39253
.43862
2.27987
.45960
2.17582
19
42
.37787
2.64642
.39*95
2.51289
.41831
2.39058
.43897
2.27806
.45995
2.17416
18
48
.37820
2.64410
.39829
2.51076
.41865
2.38863
.43932
2.27626
.46030
2.17249
17
44
.37853
2.64177
.39862
2.50864
.41899
2.38668
.43966
2.27447
.46065
2.17083
16
45
.37887
2.63945
.39896
2.50652
.41933
2.38473
.44001
2.27267
.46101
2.16917
15
46
.37920
2.63714
.39930
2.50440
.41968
2.38279
.44036
2.27088
.46136
2.16751
14
47
.37953
2.63483
.39963
2.50229
.42002
2.38084
.44071
2.26909
.46171
2.16585
13
48
.37986
2.63252
.39997
2.50018
.42036
2.37891
.44105
2.26730
.46206
2.16420
12
49
.38020
2.63021
.40031
2.49807
.42070
2.37697
.44140
2.26552
.46242
2.16255
11
50
.38053
2.62791
.40065
2.49597
.42105
2.37504
.44175
2.26374
.46277
2.16090
10
51
.38086
2.62561
.40098
2.49386
.42139
2.37311
.44210
2.26196
.46312
2.15925
52
.38120
2.62332
.40132
2.49177
.42173
2.37118
,44244
2.26018
.46348
2.15760
53
.38153
2.62103
.40166
2.48967
.42207
2.36925
.44279
2.25840
.46383
2.15596
54
.38186
2.61874
.40200
2.48758
.42242
2.36733
.44314
2.25663
.46418
2.15432
55
.38220
2.61646
.40234
2.48549
.42276
2.36541
.44349
2.25486
.46454
2.15268
56
.38253
2.61418
.40267
2.48340
.42310
2.36349
.44384
2.25309
.46489
2.15104
57
.38286
2.61190
.40301
2.48132
.42345
2.36158
.44418
2.25132
.46525
2.14940
58
.38320
2.60963
.40335
2.47924
.42379
2.35967
.44453
2.24956
.46560
2.14777
59
.38353
2.60736
.40369
2.47716
.42413
2.35776
.44488
2.24780
.46595
2.14614
60
.38386
2.60509
.40403
2.47509
.42447
2.35585
.44523
2.24604
.46631
2.14451
Cotang
Tang
Cotang
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TANGENTS AND COTANGENTS
369
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2t
0
X
o
2£
o
2
J°
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang.
Tang
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.46631
2.14451
.48773
2.05030
.50953
1.96261
.53171
1.88073
.55431
1.80405
60
.46666
2.14288
.48809
2.04879
.50989
1.96120
.53208
1.87941
.55469
1.80281
59
.46702
2.14125
.48845
2.04728
.51026
1.95979
.53246
1.87809
.65507
1.80158
68
.46737
2.13963
.48881
2.04577
.51063
1.95838
.53283
1.87677
.55545
1.80034
57
.46772
2.13801
.48917
2.04426
.51099
1.95698
.53320
1.87546
.55583
1.79911
56
.46808
2.13639
.48953
2.04276
.51136
1.95557
.53358
1.87415
.55621
1.79788
55
.46843
2.13477
.48989
2.04125
.51173
1.95417
.53395
1.87283
.65659
1.79665
54
.46879
2.13316
.49026
2.03975
.51209
1.95277
.53432
1.87152
.55697
1.79542
53
.46914
2.13154
.49062
2.03825
.51246
1.95137
.53470
1.87021
.55736
1.79419
52
.46950
2.12993
.49098
2.03675
.51283
1 .94997
.53507
1.86891
.55774
1.79296
51
10
.46985
2.12832
.49134
2.03526
.51319
1.94858
.53545
1.86760
.55812
1.79174
60
11
.47021
2.12671
.49170
2.03376
.51356
1.94718
.63582
1.86630
.55850
1.79051
49
12
.47056
2.12511
.49206
2.03227
.51393
1.94579
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1.86499
.55888
1.78929
48
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.47092
2.12350
.49242
2.03078
.51430
1.94440
.53657
1.86369
.55926
1.78807
47
14
.47128
2.12190
.49278
2.02929
.51467
1.94301
.53694
1.86239
.55964
1.78685
46
15
.47163
2.12030
.49315
2.02780
.51503
1.94162
.53732
1.86109
.56003
1.78563
45
16
.47199
2.11871
.49351
2.02631
.51540
1.94023
.53769
1.85979
.56041
1.78441
44
17
.47234
2.11711
.49387
2.02483
.51577
1.93885
.53807
1.85850
.56079
1.78319
43
18
.47270
2.11552
.49423
2.02335
.51614
1.93746
.53844
1.85720
.56117
1.78198
42
19
.47305
2.11392
.49459
2.02187
.51651
1.93608
.53882
1.85591
.56156
1.78077
41
20
.47341
2.11233
.49495
2.02039
.51688
1.93470
.53920
1.85462
.56194
1.77955
40
21
.47377
2.11075
.49532
2.01891
.51724
1.93332
.53957
1.85333
.56232
1.77834
39
22
.47412
2.10916
.49568
2.01743
.51761
1.93195
.53995
1.85204
.56270
1.77713
38
23
.47448
2.10758
.49604
2.01596
.51798
1.93057
.54032
1.85075
.56309
1.77592
37
24
.47483
2.10600
.49640
2.01449
.51835
1.92920
.54070
1.84946
.56347
1.77471
36
25
.47519
2.10442
.49677
2.01302
.51872
1.92782
.54107
1.84818
.56385
1.77351
35
26
.47555
2.10284
.49713
2.01155
.51909
1.92645
.54145
1.84689
.56424
1.77230
34
27
.47590
2.10126
.49749
2.01008
.51946
1.92508
.54183
1.84561
.56462
1.77110
33
28
.47626
2.09969
.49786
2.00862
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1.92371
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1.84433
.56501
1.76990
32
29
.47662
2.09811
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2.00715
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1.92235
.54258
1.84305
.56539
1.76869
31
30
.47698
2.09654
.49858
2.00569
.52057
1.92098
.54296
1.84177
.56577
1.76749
30
31
.47733
2.09498
.49894
2.00423
.52094
1.91962
.54333
1.84049
.56616
1.76629
29
32
.47769
2.09341
.49931
2.00277
.52131
1.91826
.54071
1.83922
.56654
1.76510
28
33
.47805
2.09184
.49967
2.00131
.52168
1.91C90
.54409
1.83794
.56693
1.76390
27
34
.47840
2.09028
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1.99986
.52205
1.91554
.54446
1.83667
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1.76271
26
35
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2.08872
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1.99841
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1.91418
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1.83540
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1.76151
25
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2.08716
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1.99695
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1.91282
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1.83413
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1.76032
24
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2.08560
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1.99550
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1.91147
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1.83286
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1.75913
23
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2.08405
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1.99406
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1.91012
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1.83159
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1.75794
22
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2.08250
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1.99261
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1.90876
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1.83033
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1.75675
21
40
.48055
2.08094
.50222
1.99116
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1.90741
.54673
1.82906
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1.75556
20
41
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2.07939
.50258
1.98972
.52464
1.90607
.54711
1.82780
.57000
1.75437
19
42
.48127
2.07785
.50295
1.98828
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1.90472
.54748
1.82654
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1.75319
18
43
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2. 7630
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1.98684
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1.90337
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1.82528
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1.75200
17
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2.07476
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1.98540
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1.90203
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1.82402
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1.75082
16
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2 07321
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1.98396
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1.90069
.54862
1.82276
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1.74964
15
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2.07167
.50441
1.98253
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1.89935
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1.82150
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1.74846
14
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2.07014
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1.98110
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1.89801
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1.82025
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1.74728
13
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2.06860
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1.97966
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1.89667
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1.81899
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1.74610
12
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2.06706
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1.97823
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1.89533
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1.81774
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1.74492
11
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2.06553
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1.97681
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1.89400
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1.81649
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1.74375
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2.06400
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1.97538
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1.89266
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1.81524
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1.74257
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2.06247
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1.97395
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1.89133
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1.81399
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1.74140
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2.06094
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1.97253
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1.89000
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1.81274
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1.74022
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2.05942
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1.97111
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1.88867
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1.81150
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1.96969
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1.96827
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1.88602
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1.96685
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1.88469
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1.80777
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1.73565
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2.05333
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1.96544
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1.88337
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1.80653
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1.73438
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2.05182
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1.96402
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1.88205
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1.80529
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1.73321
60
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2.05030
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1.96261
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1.88073
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1.80406
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1.73205
Cotang
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Tang
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1.73205
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1.66428
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1.60033
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1.53986
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1.48256
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1.73089
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1.66318
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1.59930
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1.53888
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1.48163
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1.72973
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1.66209
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1.59826
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1.53791
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1.48070
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1.72857
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1.66099
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1.59723
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1.53693
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1.47977
57
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1.72741
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1.65990
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1.59620
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1.53595
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1.47885
56
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1.72625
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1.65881
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1.59517
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1.53497
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1.47792
55
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1.72509
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1.65772
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1.59414
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1.53400
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1.47699
54
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1.72393
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1.65663
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1.59311
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1.53302
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1.47607
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1.72278
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1.65554
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1.59208
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1.53205
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1.47514
52
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1.72163
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1.65445
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1.59105
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1.53107
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1.47422
51
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1.72047
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1.65337
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1.59002
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1.53010
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1.47330
50
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1.71932
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1.65228
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1.58900
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1.52913
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1.47238
49
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1.71817
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1.65120
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1.58797
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1.52816
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1.47146
48
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1.71702
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1.65011
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1.58695
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1.52719
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1.47053
47
14
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1.71588
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1.64903
.63055
1.58593
.65521
1.52622
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1.46962
46
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1.71473
.60681
1.64795
.63095
1.58490
.65563
1.52525
.68088
1.46870
45
16
.58357
1.71358
.60721
1.64687
.63136
1.58388
.65604
1.52429
.68130
1.46778
44
17
.58396
1.71244
.60761
1.64579
.63177
1.58286
.65646
1.52332
.68173
1 .46686
43
18
.58435
1.71129
.60801
1.64471
.63217
1.58184
.65688
1.52235
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1.46595
42
19
.58474
1.710,15
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1.64363
.63258
1.58083
.65729
1.52139
.68258
1.46503
41
20
.58513
1.70901
.60881
1.64256
.63299
1.57981
.65771
1.52043
.68301
1.46411
40
21
.58552
1.70787
.60921
1.64148
.63340
1.57879
.65813
1.51946
.68343
1.46320
39
22
.58591
1.70673
.60960
1.64041
.63380
1.57778
.65854
1.51850
.68386
1.46229
38
23
.58631
1.70560
.61000
1.63934
.63421
1.57676
.65896
1.51754
.68429
1.46137
37
24
.58670
1.70446
.61040
1.63826
.63462
1.57575
.65938
1.51658
.68471
1.46046
36
25
.58709
1.70332
.61080
1.63719
.63503
1.57474
.65980
1.51562
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1.45955
35
26
.58748
1.70219
.61120
1.63612
.63544
1.57372
.66021
1.51466
.68557
1.45864
34
27
.58787
1.70106
.61160
1.63505
.63584
1.57271
.66063
1.51370
.68600
1.45773
33
28
.58826
1.69992
.61200
1.63398
.63625
1.57170
.66105
1.51275
.68642
1.45682
32
29
.58865
1.69879
.61240
1.63292
.63666
1.570G9
.66147
1.51179
.68685
1.45592
31
80
.58905
1.69766
.61280
1.63185
.63707
1.56969
.66189
1.51084
.68728
1.45501
30
31
.58944
1.69653
.61320
1.63079
.63748
1.56868
.66230
1.50988
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1.45410
29
32
.58983
1.69541
.61860
1.62972
.63789
1.56767
.66272
1.50893
.68814
1.45320
28
33
.59022
1.69428
.61400
1.62866
.63830
1.56667
.66314
1.50797
.68857
1.45229
27
34
.59061
1.69316
.61440
1.62760
.63871
1.56566
.66356
1.50702
.68900
1.45139
26
35
.59101
1.69203
.61480
1.62654
.63912
1.56466
.66398
1.50607
.68942
1.45049
25
36
.59140
1.69091
.61520
1.62548
.63953
1.56366
.66440
1.50512
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1.44958
24
37
.59179
1.68979
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1.62442
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1.56265
.66482
1.50417
.69028
1.44868
23
38
.59218
1.68866
.61601
1.62336
.64035
1.56165
.66524
1.50322
.69071
1.44778
22
39
.59258
1.68754
.61641
1.62230
.64076
1.56065
.66566
1.50228
.69114
1.44688
21
40
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1.68643
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1.62125
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1.55966
.66608
1.50133
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1.44598
20
41
.59336
1.68531
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1.62019
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1.55866
.66650
1.50038
.69200
1.44508
19
42
.59376
1.68419
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1.61914
.64199
1.55766
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1.49944
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1.44418
18
43
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1.68308
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1.61808
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1.55666
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1.49849
.69286
1.44329
17
44
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1.68196
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1.61703
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1.55567
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1.49755
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1.44239
16
45
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1.68085
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1.61598
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1.55467
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1.49661
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1.44149
15
46
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1.67974
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1.61493
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1.55368
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1.49566
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1.44060
14
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1.67863
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1.61388
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1.55269
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1.49472
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1.43970
13
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1.67752
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1.61283
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1.55170
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1.49378
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1.43881
12
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1.67641
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1.61179
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1.55071
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1.49284
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1.43792
11
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1.67530
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1.61074
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1.54972
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1.49190
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1.43703
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1.67419
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1.60970
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1.54873
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1.49097
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1.43614
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1.67309
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1.60865
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1.54774
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1.49003
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1.43525
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1.67198
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1.60761
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1.54675
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1.48909
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1.43436
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1.67088
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1.60657
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1.54576
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1.48816
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1.66978
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1.60553
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1.54478
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1.48722
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1.43258
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1.66867
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1.60449
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1.54379
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1.48629
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1.43169
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1.60345
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1.54281
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1.48536
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1.43080
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1.66647
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1.60241
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1.54183
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1.48442
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1.42992
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1.66538
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1.60137
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1.54085
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1 .48349
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1.42903
1
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1.66426
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1.60033
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1.63986
.67451
1.48256
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1.42815
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Ootang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
I
£
9°
51
*°
5
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5
5°
5
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TANGENTS AND COTANGENTS
371
/
3i
>°
3C
°
O'
0
38
0
3
9°
f
Tang
Cotang
Tang
Cotanc
Tans
Cotang
Tang
Cotang
Tang
Cotang
.70021
1.42815
.72654
1.37638
.75355
1.32704
.78129
1.27994
.80978
1.23490
60
.700«4
1.42726
.72699
1.37554
.75401
1.32624
.78175
1.27917
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1.23416
59
.70107
1.42638
.72743
1.37470
.75447
1.32544
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1.27841
.81075
1.23343
58
.70151
1.42550
.72788
1.37386
.75492
1.32464
.78269
1.27764
.81123
1.23270
57
.70194
1.42462
.72832
1.37302
.75538
1.32384
.78316
1.27688
.81171
1.23196
56
.70238
1 42374
.72877
1.37218
.75584
1 .32304
.78363
1.27611
.81220
1.23123
55
.70281
1.42286
.72921
1.37134
.75029
1.32224
.78410
1.27535
.81268
1 .23050
54
.70325
1.42198
.72966
1.37050
.75675
1.82144
.78457
1.27458
.81316
1.22977
53
8
.70368
1.42110
.73010
1 .36967
.75721
1.32064
.78504
1.27382
.81364
1.22904
52
9
.70412
1.42022
.73055
1.36883
.75707
1.31984
.78551
1.27306
.81413
1.22831
51
10
.70455
1.41934
.73100
1.36800
.75812
1.31904,
.78598
1.27230
.81461
1.22758
50
11
.70499
1.41847
.73144
1.36716
.75858
1.31825
.78645
1.27153
.81510
1.22685
49
12
.70542
1.41759
.73189
1.30033
.75904
1.81745
.78092
1.27077
.81558
1.22612
48
13
.70586
1.41072
.73234
1.36519
.75950
1.31666
.78739
1.27001
.81006
1 .22539
47
14
.70C29
.41584
.73278
1.36406
.75996
1.31586
.78786
1 .26825
.81655
1.22467
46
15
.70673
.41497
.73323
1.36383
.76042
1.31507
.78834
1.2C849
.81703
1.22394
45
16
.70717
.41409
.73368
1.3631)0
.70088
1.31427
.78881
1.26774
.81752
1.22321
44
17
.70760
.-11322
.73413
1.36217
.76134
1.81348
.78928
1 .26(>!i8
.81800
1.22249
43
18
.70804
.41235
.73457
1.36134
.76180
1.31209
.78975
1.26022
.81849
1.22176
42
19
.70848
.41148
.73502
1.36051
.76226
1.31190
.79022
1.26546
.81898
1.22104
41
20
.70891
.41061
.73547
1 35968
.76272
1.31110
.79070
1.26471
.81946
1.22031
40
21
.70935
1.40974
.73592
1.35885
.76318
1.31031
.79117
1.26395
.81995
1.21959
89
22
.70979
1.40887
.73637
1.35802
.76364
1.80952
.79104
1 .26319
.82044
1.21886
38
23
.71023
1.40800
.73681
1.35719
.76410
1.30873
.79212
1.26244
.82092
1.21814
37
21
.71066
1.40714
.73726
1.35637
.76456
1 .30795
.79259
1 .20109
.82141
1.21742
36
25
.71110
1.40C27
.73771
1.35554
.76502
1.30716
.79306
1 .26093
.82190
1.21670
35
2i>
.71154
1.40540
.73816
1.35472
.76548
1.30637
.79354
1.26018
.82238
1.21598
34
27
.71108
1.40454
.73861
1.353S9
.76594
1 .305f8
.79401
1.25943
.82287
1.21526
33
28
.71242
1 .403G7
.73906
1.35307
.76640
1.30480
.79449
1.25867
.82336
1.21454
32
2'J
.71285
1.40281
.73951
1 .35224
.76686
1.30401
.79496
1 .25792
.82385
1.21382
81
30
.71329
1.40195
.73996
1.35142
.76733
1.30323
.79544
1.25717
.82434
1.21310
SO
SI
.71373
1 .40109
.74041
1.35060
.76779
1.30244
.79591
1.25642
.82483
1.21238
29
82
.71417
1.40022
.74086
1.34978
.76825
1 .30106
.79639
1.25567
.82531
l.«1166
28
33
.71461
1.39936
.74131
1.34896
.76871
1 .30087
.79686
1.25492
.82580
1.2lt>94
27
34
.71505
1.39850
.74176
1.34814
.76918
1 .30009
.79734
1.25417
.82629
1.21023
26
85
.71549
1.39764
.74221
1 .34732
.76904
1.29931
.79781
1.25343
.82678
1.20951
25
36
.71593
1.39679
.74267
1.34650
.77010
1.29853
.79829
1.25208
.82727
1.20879
24
87
.71637
1.39593
.74312
1.34568
.77057
1.29775
.79877
1.25193
.82776
1.20808
23
88
.71681
1.39507
.74357
1.34487
.77103
1.29096
.79924
1.25118
.82825
1 .20736
22
89
.71725
1.39421
.74102
1 .34405
.77149
1.29618
.79972
1.25044
.82874
1.20665
21
40
.71769
1.39336
.74447
1.34323
.77196
1.29541
.80020
1.24969
.82923
1.20C93
20
41
.71813
1.39250
.74492
1.34242
.77242
1.29463
.80067
1.24895
.82972
1.20522
19
42
.71857
1.39165
1.34100
.77289
1 .29385
.80115
1.24820
.83022
1.20451
18
43
.71901
1.39079
!74583
1.34079
.77335
1.29307
.80103
1.24746
.83071
1.20379
17
44
.71946
1.38994
.74628
1.33998
.77382
1.29229
.80211
1.24672
.83120
1.20308
16
45
.71990
1.38909
.74674
1.33916
.77428
1.29152
.80258
1.24597
.83169
1.20237
15
46
.72034
1 .38824
.74719
1.33835
.77475
1.29074
.80306
1.24523
.83218
1.20166
14
47
.72078
1.38738
.74764
1 .33754
.77521
1.28997
.80354
1.24449
.83268
1.20095
13
48
.72122
1.38653
.74810
1.33673
.77568
1.28919
.80402
1.24375
.83317
1.20024
12
49
.72167
1.885C8
.74855
1.33592
.77615
1.28842
.80450
1.24301
.83366
1.19953
11
50
.72211
1.38484
.74900
1.33511
.77661
1.28764
.80498
1.24227
.83415
1.19882
10
51
.72255
1.38399
.74946
1.83430
.77708
1.28687
.80546
1.24153
.83485
1.19811
9
52
.72299
1.38314
.74991
1.33349
.77754
1. 28C10
.80594
1.24079
.-835H
1.19740
8
53
.72344
1 .38229
.75037
1.33208
.77801
1.28533
.80642
1.24005
.83564
1.19669
54
.72388
1.38145
.75082
1.33187
.77848
1.28456
.80690
1.23931
.83613
1.19599
55
.72432
1.38060
.75128
1.33107
.77895
1.28379
.80738
1.23858
.83662
1.19528
56
.72477
1.37976
.75178
1.33026
.77941
1.28302
.80786
1.23784
.83712
1.19457
57
.72521
1.37891
.75219
1.32946
.77988
1.28225
.80834
1.23710
.83761
1.19387
58
.72565
1.37807
.75264
1.328G5
.78035
1.28148
.80882
1.23637
.83811
1.19316
59
.72610
1.37722
.75310
1.32785
.78082
1.28071
.80930
1 .23563
.83860
1.19246
60
.72654
1.37638
.75355
1.32704
.78129
1.27994
.80978
1.23490
.83910
1.19175
Cotang
Tang
Cotang
Tang
Ootang
Tang
Cotang
Tang
Cotang
Tang
/
&
t°
&
J°
o
51
O
a
)°
/
372
MINE GASES AND VENTILATION
/
4(
>°
4]
o
At
)O
41
1°
4
1°
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
0
.83910
1.19175
.86929
1.15037
.90040
1.11061
.93252
1.07237
.96569
1.03553
60
.83960
1.19105
.86980
1.14969
.90093
1.10996
.93306
1.07174
.9ti625
1.03493
59
.84009
1.19035
.87031
1.14902
.90146
1.10931
.93360
1.07112
.96681
1.03433
58
.84059
1.18964
.87082
1.14834
.90199
1.10867
.93415
1.07049
.96738
1.03372
57
.84108
1.18894
.87133
1.14767
.90251
1.10802
.93469
1.06987
.96794
1.03312
56
.84158
1.18824
.8718$
1.14699
.90304
1.10737
.93524
1.06925
.96850
1.03252
65
.84208
1.18754
.87236
1.14632
.90357
1.10672
.93578
1.068G2
.96907
1.03192
54
7
.84258
1.18684
.87287
1.14565
.90410
1.10607
.93633
1.06800
.96963
1.03132
53
8
.84307
1.18614
.87338
1.14498
.90463
1.10543
.93688
1.06738
.97020
1.03072
52
9
.84357
1.18544
.87389
1.14430
.90516
1.10478
.93742
1.06676
.97076
1.03012
51
10
.84407
1.18474
.87441
1.14363
.90569
1.10414
.93797
1.06613
.97133
1.02952
50
11
.84457
1.18404
.87492
1.14Z96
.90621
1.10349
.93852
1.06551
.97189
1.02892
49
12
.84507
1.18334
.87543
1.14229
.90674
1.10285
.93906
1.06489
.97246
1.02832
48
13
.84556
1.18264
.87595
1.14162
.90727
1.10220
.93961
1.06427
.97302
1.02772
47
14
.84606
1.18194
.87646
1.14095
.90781
1.10156
.94016
1.06365
.97359
1.02713
46
15
.84656
1.18125
.87698
1.14028
.90834
1.10091
.94071
1.06303
.97416
1.02653
45
16
.84706
1.18055
.87749
1.13961
.90887
1.10027
.94125
1.06241
.97472
1.02593
44
17
.84756
1.17986
.87801
1.13894
.90940
1.099G3
.94180
1.06179
.07529
1.02533
43
18
.84806
1.17916
.87852
1.13828
.90993
1.09899
.94235
1.06117
.97586
1.02474
42
19
.84856
1.17846
.87904
1.13761
.91046
1.09834
.94290
1.06056
.97643
1.02414
41
20
.84906
1.17777
.87955
1.13694
.91099
1.09770
.94345
1.05994
.97700
1.02355
40
21
.84956
1.17708
.88007
1.13627
.91153
1.09706
.94400
1.05932
.97756
1.02295
39
22
.85006
1.17638
.88059
1.13561
.91206
1.09642
.94455
1.05870
.97813
1.02236
38
23
.85057
1.17569
.88110
1.13494
.91259
1.09578
.94510
1.05809
.97870
1.02176
37
24
.85107
1.17500
.88162
1.13428
.91313
1.09514
.94565
1.05747
.97927
1.02117
36
25
.85157
1.17430
.88214
1.13361
.913G6
1.09450
.94620
1.05685
.97984
1.02057
35
26
.85207
1.17361
.882G5
1.13295
.91419
1.09336
.94676
1.05624
.98041
1.01998
34
27
.85257
1.17292
.88317
1.13228
.91473
1.09322
.94731
1.05562
.98098
1.01939
83
28
.85308
1.17223
.88369
1.13162
.91526
1.09258
.94786
1.05501
.98155
1.01879
32
29
.85358
1.17154
.88421
1.13096
.91580
1.09195
.94841
1.05439
.98213
1.01820
31
30
.85408
1.17085
.88473
1.13029
.91633
1.09131
.94896
1.05378
.98270
1.01761
30
31
.85458
1.17016
.88524
1.12963
.91687
1.09067
.94952
1.0531?
.98327
1.01702
29
32
.85509
1.16947
.88576
1.12897
.91740
1.09003
.95007
1.05255
.98384
1.01642
28
33
.85559
1.16878
.88628
1.12831
.91794
1.08940
.95062
1.05194
.98441
1.01583
27
34
.85609
1.16809
.88680
1.12765
.91847
1.08876
.95118
1.05133
.98499
1.01524
26
35
.85660
1.16741
.88732
1.12699
.91901
1.08813
.95173
1.05072
.98556
1.01465
25
36
.85710
1.16672
.88784
1.12633
.91955
1.08749
.95229
1.05010
.98613
1.01406
24
37
.85761
1.16603
.88836
1.12567
.92008
1.08686
.95284
1.04949
.98671
1.01347
23
38
.85811
1.16535
1.12501
.92062
1.08622
.95340
1.04888
.98728
1.01288
22
39
.85862
1.16466
!88940
1.12435
.92116
1.08559
.95395
1.04827
.98786
1.01229
21
40
.85912
1.16398
.88992
1.12369
.92170
1.08496
.95451
1.04766
.98843
1.01170
20
41
.85963
1.16329
.89045
1.12303
.92224
1.08432
.95506
1.04705
.98901
1.01112
19
42
.86014
1.16261
.89097
.12238
.92277
1.08369
.95562
1.04644
.98958
1.01053
18
43
.86064
1.16192
.89149
.12172
.92331
1.08306
.95618
1.04583
.99016
1.00994
17
44
.86115
1.16124
.89201
.12106
.92385
1.08243
.95673
1.04522
.9C073
1.00935
16
45
.86166
1.16056
.89253
.12041
.92439
1.08179
.95729
1.04461
.901 31
1.00876
15
46
.8621 6
1.15987
.11975
.924'J3
1.08116
.95785
1.04401
.99189
1.00818
14
47
.86267
1.15919
!89358
.11909
.92547
1.08053
.95841
1.04340
.99247
1 .00759
13
48
.86318
1.15851
.89410
.11844
.92601
1.07990
.95897
1.04279
.99304
1.00701
12
49
.86368
1.15783
.89463
.11778
.92655
1.07927
.95952
1.04218
.99362
1.00642
11
50
.86419
1.15715
.89515
1.11713
.92709
1.07864
.96008
1.04158
.99420
1.00583
10
51
.86470
1.15647
.89567
.11648
.92763
1.07801
.96064
1.04097
.99478
1.00525
C2
.86521
1.15579
.89620
1.11532
.92817
1.07738
.96120
1.04036
.99536
1.00467
53
-86572
1.15511
.89672
1.11517
.92872
1.07676
.96176
1.03976
.99594
1.00408
54
-86623
1.15413
.89725
1.11452
.92926
1.07613
.96232
1.03915
.!i9f>52
1.00350
55
86674
1.15375
.89777
.92980
1.07550
.96288
1.03855
.99710
1 .00291
56
86725
1.15308
.89830
l!l!321
.93034
1.07487
.96344
1.03794
.99768
1.00233
57
.86776
1.15240
.89883
1.11256
.93088
1.07425
.96400
1.03734
.99826
1.00175
58
.86827
1.15172
.89935
1.11191
.93143
1.07362
.96457
1.03674
.99884
1.00116
59
.86878
1.15104
1.11126
.93197
1.07299
.96513
1.03613
.99942
1.00058
60
.86929
1.15037
190040
1.11061
.93252
1.07237
.96569
1.03553
1.00000
1.00000
0
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
Cotang
Tang
7
4
J°
45
S°
4
1°
4(
)°
4
5°
SQUARES, CUBES, ROOTS AND RECIPROCALS
OF NUMBERS, CIRCUMFERENCES AND
AREAS OF CIRCLES
373
374
MINE GASES AND VENTILATION
SQUARES, CUBES, SQUARE AND CUBE ROOTS,
CIRCUMFERENCES, AND AREAS
No.
Squure
Cube
Sq. Root
Cu.Root
Eeciprocdl
Circum.
Area
1
1
1
1.0000
1.0000
1.000000000
3.1416
0.7854
2
4
8
1.4142
1.2599
.500000000
6.2832
3.1416
3
9
27
1.7321
1.4422
.333333333
9.4248
7.0686
4
16
64
2.0000
1.5874
.250000000
12.5GG1
12.5664
5
25
125
2.2361
1.7100
.200000000
15.7080
19.635
6
36
216
2.4495
1.8171
.1G6666G67
18.850
28.274
7
49
343
2.6458
1.9129
.1-12857143
21.991
38.485
8
64
512
2.8284
2.0000
.125000000
25.133
50.266
9
81
729
3.0000
2.0801
.111111111
28.274
63.617
10
100
1,000
3.1623
2.1544
.100000000
31.416
78.540
11
121
1,331
3.3166
2.2240
.090909091
34.558
95.033
12
144
1,728
3.4641
2.2894
.083333333
37.699
113.10
13
169
2,197
3.6056
2.3513
.076923077
40.841
132.73
14
196
2,744
3.7417
2.4101
.071428571
43.982
153.94
15
225
3,375
3.8730
2.4662
.066666667
47.124
176.71
16
256
4,096
4.0000
2.5198
.062500000
50.265
201.06
17
289
4,913
4.1231
2.5713
.058823529
53.407
226.98
18
324
5,832
4.2426
2.6207
.055555556
56.549
254.47
19
361
6,859
4.3589
2.C684
.052631579
59.690
283.53
20
400
8,000
4.4721
2.7144
.050000000
62.832
314.16
21
441
9,261
4.5826
2.7589
.047619048
65.973
346.36
22
484
10,648
4.6904
2.8020
.045454545
69.115
380.13
23
529
12,167
4.7958
2.8439
.043478261
72.257
415.48
24
" 576
13,824
4.8990
2.8845
.041666667
75.398
452.39
25
625
15,625
5.0000
2.9240
.040000000
78.540
490.87
26
676
17,576
5.0990
2.9625
.038461538
81.C81
530.93
27
729
19,683
5.1962
3.0000
.037037037
84.823
572.56
28
784
21,952
5.2915
3.0366
.035714286
87.965
615.75
29
841
24,389
5.3852
3.0723
.034482759
91.106
660.52
30
900
27,000
5.4772
3.1072
.033333333
94.248
706.86
31
961
29,791
5.5678
3.1414
.0322,58065
97.389
754.77
32
1,024
32,768
5.65G9
3.1748
.031250000
100.53
804.25
33
1,089
35,937
5.7446
3.2075
.030303030
103.67
855.30
34
1,156
39,304
5.8310
3.2396
.029411765
106.81
907.92
35
1,225
42,875
5.9161
3.2717
.028571429
109.96
962.11
36
1,296
46,656
• 6.0000
3.3019
.027777778
113.10
1,017.88
37
1,369
50,653
6.0828
3.3322
.027027027
116.24
1,075.21
38
1,444
54,872
6.1644
3.3620
.026315789
119.38
1,134.11
39
1,521
59,319
6.2450
3.3912
.025641026
122.52
1,194.59
40
1,600
64,000
6.3246
3.4200
.025000000
125.66
1,256.64
41
1,681
68,921
6.4031
3.4482
.024390244
128.81
1,320.25
42
1,764
74,088
6.4807
3.4760
.023809524
131.95
1,385.44
43
1,849
79,507
6.5574
35034
.023255814
135.09
1,452.20
44
1,936
85,184
6.6332
3 5303
.022727273
138.23
1,520.53
45
2,025
91,125
6.7082
3.55G9
.022222222
141.37
1,590.43
46
2,116
97,336
67823
35830
.021739130
144.51
1,061.90
47
2,209
103,823
68557
36088
.021276600
147.65
1,734.94
48
2,304
110,592
6.9282
3.6342
.020833333
150.80
1,809.56
49
2,401
117,6-19
7.0000
36593
.020408163
153.94
1,885.74
50
2,500
125,000
7.0711
3.6S40
.020000000
157.08
1,963.50
51
2,601
132,651
7.1414
3.7084
.019607843
160.22
2,042.82
52
2,704
140,608
7.2111
3.7325
.019230769
63.36
2.123.72
53
2,809
148,877
7.2801
3.7563
.018867925
66.50
2,206.18
54
2,916
157,464
7.3485
3.7798
.018518519
69.65
2,290.22
65
3,025
166,375
7.4162
3.8030
.018181818
72.79
2,375.83
SQUARES, CTrBES, ROOTS, ETC.
375
No.
Square
Cube
Sq. Root
Cu. Boot
Reciprocal
Circum
Area
56
3,136
175,616
7.4833
3.8259
.017857143
175.93
2,463.01
57
3,249
185,193
7.5498
3.8485
.017543860
179.07
2,551.76
58
3,364
195,112
7.6158
3.8709
.017241379
182.21
2,642.08
59
3,481
205,379
7.6811
3.8930
.016949153
185.35
2,733.97
60
3,600
216,000
7.7460
3.9149
.016666667
188.50
2,827.43
61
8,721
226,981
7.8102
3.9365
.016393443
191.64
2,922.47
62
3,844
238,328
7.8740
3.9579
.016129032
194.78
3,019.07
63
8,969
250,047
7.9373
3.9791
.015873016
197.92
3,117.25
64
4,096
262,144
8.0000
4.0000
.015625000
201.06
3,216.99
65
4,225
274,625
8.0623
4.0207
.015384615
204.20
8,318.31
66
4,356
287,496
8.1240
4.0412
.015151515
207.34
3,421.19
67
4,489
300,763
8.1854
4.0615
.014925373
210.49
3,525.65
68
4,624
314,432
8.2462
4.0817
.014705882
213.63
3,631.68
69
4,761
328,509
8.3066
4.1016
.014492754
216.77
3,739.28
70
4,900
343,000
8.36G6
4.1213
.014285714
219.91
3,848.45
71
5,041
357,911
8.4261
4.1408
.014084517
223.05
3,959.19
72
5,184
373,248
8.4853
4.1602
.013888889
226.19
4,071.50
73
5,329
389,017
8.5440
4.1793
.013698630
229.34
4,185.39
74
6,476
405,224
8.6023
4.1983
.013513514
232.48
4,300.84
75
5,625
421,875
8.6603
4.2172
.013333333
235.62
4,417.86
76
5,776
438,976
8.7178
4.2358
.013157895
238.76
4,536.46
77
5,929
456,533
8.7750
4.2543
.012987013
241.90
4,656.63
78
6,084
474,552
8.8318
4.2727
.012820513
245.04
4,778.36
79
6,241
493,039
8.8882
4.2908
.012658228
248.19
4,901.67
80
6,400
512,000
8.9413
4.3089
.012500000
251.33
5,026.55
81
6,561
531,441
9.0000
4.3267
.012345679
254.47
5,153.00
82
6,724
551,368
9.0554
4.3445
.012195122
257.61
5,281.02
83
6,889
571,787
9.1104
4.3621
.012048193
260.75
5,410.61
84
7,056
592,704
9.1652
4.3795
.011904762
263.89
5,541.77
85
7,225
614,125
9.2195
4.3968
.011764706
267.04
5,674.50
86
7,396
636,056
9.2736
4.4140
.011627907
270.18
5,808.80
87
7,569
658,503
9.3274
4.4310
.011494253
273.32
5,944.68
88
7,744
681,472
9.3808
4.4480
.011363G36
276.46
6,082.12
89
7,921
704,969
9.4340
4.4647
.011235955
279.60
6,221.14
90
8,100
729,000
9.4868
4.4814
.011111111
282.74
6,361.73
91
8,281
753,571
9.5394
4.4979
.010989011
285.88
6,503.88
92
8,464
778,688
9.5917
4.5144
.010869565
289.03
6,647.61
93
8,649
804,357
9.6437
4.5307
.010752688
292.17
6,792.91
94
8,836
830,584
9.6954
4.5468
.010638298
295.31
6,939.78
95
9,025
857,375
9.7468
4.5629
.010526316
298.45
7,088.22
96
9,216
884,736
9.7980
4.5789
.010416667
301.59
7,238.23
97
9,409
912,673
9.8489
4.5947
.010309278
304.73
7,389.81
98
9,604
941,192
9.8995
4.6104
.010204082
307.88
7,542.96
99
9,801
970,299
9.9499
4.6261
.010101010
311.02
7,697.69
100
10,000
1,000,000
10.0000
4.6416
.010000000
314.16
7,853.98
101
10,201
1,030,301
10.0499
4.6570
.009900990
317.30
8,011.85
102
10,404
1,061,208
10.0995
4.6723
.009803922
320.44
8,171.28
103
10,609
1,092,727
10.1489
4.6875
.009708738
323.58
8,332.29
104
10,816
1,124,864
10.1980
4.7027
.009615385
326.73
8,494.87
105
11,025
1,157,625
10.2470
4.7177
.009523810
329.87
8,659.01
106
11,236
1,191,016
10.2956
4.7326
.009433962
333.01
8,824.73
107
11,449
1,225,043
10.3441
4.7475
.009345794-
336.15
8,992.02
108
11,664
1,259,712
10.3923
4.7622
.009259259
339.29
9,160.88
109
11,881
1,295,029
10.4403
4.7769
.009174312
342.43
9,331.32
110
12,100
1,331,000
10.4881
4.7914
.009090909
345.58
9,503.32
111
12,321
1,367,631
10.5357
4.8059
.009009009
348.72
9,676.89
112
12,544
1,404,928
10.5830
4.8203
.008928571
351.86
9,852.03
113
12,769
1,442,897
10.6301
4.8346
.008849558
355.00
10,028.75
114
12,996
1,481,544
10.6771
4.8-188
.008771930
358.14
10,207.03
115
13,225
1,520,875
10.7238
4.8629
.008695652
361.28
10,386.89
116
13,456
1,560,896
10.7703
4.8770
.008020690
364.42
10,568.32
117
13,689
1,601,613
10.8167
4.8910
,00arv47009
367.57
10,751.32
118
13,924
1,643,032
10.8628
4.9049
.008474576
370.71
10,935.88
376
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Hoot
Cu. Root
Reciprocal
Circum.
AIM
119
14,161
1,685,159
10.9087
4.9187
.008403361
373.85
11,122.02
120
14,400
1,728,000
10.9545
4.9324
.008333333
376.99
11,309.73
121
14,641
1,771,561
11.0000
4.9461
.008264463
380.13
11,499.01
122
14,834
1,815,848
11.0454
4.9597
.008196721
383.27
11,689.87
123
15,129
1,860,867
11.0905
4.9732
.008130081
386.42
11,882.29
124
15,376
1,906,624
11.1355
4.9866
.008064516
389.56
12,076.28
125
15,625
1,953,125
11.1803
5.0000
.008000000
392.70
12,271.85
126
15,876
2,000,376
11.2250
5.0133
.007936508
395.84
12,468.98
127
16,129
2,048,383
11.2694
5.0265
.007874016
398.98
12,667.69
128
16,384
2,097,152
11.3137
5.0397
.007812500
402.12
12,867.96
129
16,641
2,146,689
11.3578
5.0528
.007751938
405.27
13,069.81
130
16,900
2,197,000
11.4018
5.0658
.007692308
408.41
13,273.23
131
17,161
2,248,091
11.4455
5.0788
.007633588
411.55
13,478.22
132
17,424
2,299,968
11.4891
5.0916
.007575758
414.69
13,684.78
133
17,689
2,352,637
11.5326
5.1045
.007518797
417.83
13,892.91
134
17,956
2,406,104
11.5758
5.1172
.007402687
420.97
14,102.61
135
18,225
2,460,375
11.6190
5.1299
.007407407
424.12
14,313.88
136
18,496
2,515,456
11.6619
5.1426
.007352941
427.26
14,526.72
137
18,769
2,571,353
11.7047
5.1551
.007299270
430.40
14,741.14
138
19,044
2,628,072
11.7473
5.1676
.00724G377
433.54
14,957.12
139
19,321
2,685,619
11.7898
5.1801
.007194245
436.68
15,174.68
140
19,600
2,744,000
11.8322
5.1925
.007142857
439.82
15,393.80
111
19,881
2,803,221
11.8743
5.2048
.007092199
442.96
15,614.50
112
20,164
2,863,288
11.9164
5.2171
.007042254
446.11
15,836.77
113
20,449
2,924,207
11.9583
5.2293
.006993007
449.25
16,060.61
114
20,736
2,985,984
12.0000
5.2415
.006944444
452.39
16,286.02
115
21,025
3,048,625
12.0416
5.2536
.006896552
455.53
16,513.00
146
21,316
3,112,136
12.0830
5.2656
.006849315
458.67
16,741.55
147
21,609
3,176,523
12.1244
5.2776
.006802721
461.81
16,971.67
148
21,904
3,241,792
12.1655
5.2896
.006756757
464.96
17,203.36
149
22,201
3,307,949
12.2066
5.3015
.006711409
468.10
17,436.62
150
22,500
3,375,000
12.2474
5.3133
.006666667
471.24
17,671.46
151
22,801
3,442,951
12.2882
5.3251
.006622517
474.38
17,907.86
152
23,104
3,511,008
12.3288
5.3368
.006578947
477.52
18,145.84
153
23,409
3,581,577
12.3693
5.3485
.00653.5948
480.66
18,385.39
1.54
23,716
3,652,264
12.4097
5.3601
.006493506
483.81
18,626.50
155
24,025
3,723,875
12.4499
5.3717
.006451613
486.95
18,869.19
156
24,336
3,796,416
12.4900
5.3832
.006410256
490.09
19.113.45
157
24,649
3,869,893
12.5300
5.3947
.006369427
493.23
19,359.28
158
24,964
3,944,312
12.5698
5.4061
.006329114
496.37
19,606.68
159
25,281
4,019,679
12.6095
5.4175
.006289308
499.51
19,855.65
160
25,600
4,096,000
12.6491
5.4288
.006250000
502.65
20,106.19
161
25,921
4,173,281
12.6886
5.4401
.006211180
505.80
20,358.31
162
26,244
4,251,528
12.7279
5.4514
.006172840
508.94
20,611.99
1G3
26,569
4,330,747
12.7671
5.4626
.006134969
512.08
20,867.24
164
26,896
4,410,944
12.8062
5.4737
.006097561
515.22
21,124.07
165
27,225
4,492,125
12.8452
5.4848
.006060606
518.36
21,382.46
166
27,556
4,574,296
12.8841
5.4959
.006024096
521.50
21,642.43
167
27,889
4,657,463
12.9228
5.5069
.005988024
524.65
21,903.97
168
28,224
4,741,632
12.9615
5.5178
.005952381
527.79
22,167.08
169
28,561
4,826,809
13.0000
5.5288
.005917160
530.93
22,431.76
170
28,900
4,913,000
13.9384
5.5397
.005882353
534.07
22,698.01
171
29,241
5,000,211
13.0767
5.5505
.005847953
537.21
22,965.83
172
29,584
5,088,448
13.1149
5.5613
.005813953
540.35
23,235.22
173
29,929
5,177,717
13.1529
5.5721
.005780347
543.50
23,506.18
174
30,276
5,268,024
13.1909
5.5828
.005747126
546.64
23,778.71
175
30,625
5,359,375
13.2288
5.5934
.005714286
549.78
24,052.82
176
30,976
5,451,776
13.2665
5.6041
.005681818
552.92
24,?28.49
177
31,329
5,545,233
13.3041
5.6147
.005649718
556.06
24,605.74
178
31,684
5,639,752
13.3417
5.6252
.005617978
559.20
24,884.56
179
32,041
5,735,339
13.3791
5.6357
.005586592
562.35
25,164.94
180
32,400
5,832,000
13.4164
5.6462
.005555556
565.49
25,446.90
181
32,761
5,929,741
13.4536
5.6567
.005524862
568.63
25,730.43
SQUARES, CUBES, ROOTS, ETC
377
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Ciroum*
Area
182
33,124
6,028,568
13.4907
5.6671
.005494505
571.77
26,015.53
183
33,489
6,128,487
13.5277
5.6774
.005464481
574.91
26,302.20
184
33,856
6,229,504
13.5647
5.6877
.005434783
578.05
26,590.44
185
84,225
6,331,625
13.6015
5.6980
.005405405
581.19
26,880.25
186
34,596
6,434,856
13.6382
5.7083
.005376344
684.34
27,171.63
187
34,969
6,539,203
13.6748
5.7185
.005347594
587.48
27,464.59
188
35,344
6,644,672
13.7113
5.7287
.005319149
590.62
27,759.11
189
35,721
6,751,269
13.7477
5.7388
.005291005
593.76
28,055.21
190
36,100
6,859,000
13.7840
5.7489
.005263158
596.90
28,352.87
191
36,481
£,967,871
13.8203
5.7590
.005235602
600.04
28,652.11
192
36,864
7,077,888
13.85G4
5.7G90
.005208333
603.19
28,952.92
193
37,249
7,189,017
13.8924
5.7790
.005181347
606.33
29,255.30
194
37,636
7,301,384
13.9284
5.7890
.005154639
609.47
29,559.25
195
38,025
7,414,875
13.9642
5.7989
.005128205
612.61
29,864.77
196
38,416
7,529,536
14.0000
5.8088
.005102041
615.75
30,171.86
197
38,809
7,645,373
14.0357
5.8186
.005076142
618.89
30,480.52
198
. 39,204
7,762,392
11.0712
5.i>285
.005050505
622.04
30,790.75
199
39,601
7,880,599
14.1067
5.8383
.005025126
625.18
31,102.55
200
40,000
8,000,000
14.1421
5.8480
.005000000
628.32
31,415.93
201
40,401
8,120,601
14.1774
5.8578
.004975124
631.46
31,730.87
202
40,804
8,242,408
14.2127
5.8675
.004950495
634.60
32,047.39
203
41,209
8,365,427
14.2478
5.8771
.004926108
637.74
32,365.47
204
41,616
8,489,664
14.2829
5.8868
.004901961
640.88
32,685.13
205
42,025
8,615,125
14.3178
5.8964
.004878049
644.03
33,006.36
206
42,436
8,741,816
14.3527
5.9059
.004854369
647.17
33,329.16
207
42,849
8,869,743
14.3875
5.9155
.004830918
650.31
33,653.53
208
43,264
8,998,912
14.4222
5.9250
.004807692
653.45
33,979.47
209
43,681
9,129,329
14.4568
5.9345
.004784689
656.59
34,306.98
210
44,100
9,261,000
14.4914
5.9439
.004761905
659.73
34,636.06
211
44,521
9,393,931
14.5258
5.9533
.004739336
662.88
34,966.71
212
44,944
9,528.128
14.5602
5.9627
.004716981
666.02
35,298.94
213
45,369
9,663,597
14.5945
5.9721
.004694836
669.16
35,632.73
214
45,796
9,800,344
14.6287
5.9814
.004672897
672.30
35,968.09
215
46,225
9,938,375
14.6629
5.9907
.004651163
675.44
36,305.03
216
46,656
10,077,696
14.6969
6.0000
.004629630
678.58
36,643.54
217
47,089
10,218,313
14.7309
6.0092
.004608295
681.73
36,983.61
218
47,524
10,360,232
14.7648
6.0185
.004587156
684.87
37,325.26
219
47,961
10,503,459
14.7986
C.0277
.004566210
688.01
37,668.48
220
48,400
10,648,000
14.8324
6.0368
.004545455
691.15
38,013.27
221
48,841
10,793,861
14.8661
6.0459
.004524887
694.29
38,359.63
222
49,284
10,941,048
14.8997
6.0550
.004504505
697.43
38,707.56
223
49,729
11,089,567
14.9332
6.0641
.004484305
700.58
39,057.07
224
50,176
11,239,424
14.9666
6.0732
.004464286
703.72
39,408.14
225
50,625
11,390,625
15.0000
6.0822
.004444444
706.86
39,760.78
226
51,076
11,543,176
15.0333
6.0912
.004424779
710.00
40,115.00
227
51,529
11,697,083
15.0665
6.1002
.004405286
713.14
40,470.78
228
51,984
11,852,352
15.0997
6.1091
.004385965
716.28
40,828.14
229
52,441
12,008,989
15.1327
6.1180
.004366812
719.42
41,187.07
230
52,900
12,167,000
15.1658
6.1269
.004347826
722.57
41,547.56
231
53,361
12,326,391
15.1987
6.1358
.004329004
725.71
41,909.63
232
53,824
12,487,168
15.2315
6.1446
.004310345
728.85
42,273.27
233
54,289
12,649,337
15.2643
6.1534
.004291845
731.99
42,638.48
234
54,756
12,812,904
15.2971
6.1622
.004273504
735.13
43,005.26
235
55,225
12,977,875
15.3297
6.1710
.004255319
738.27
43,373.61
236
55,696
13,144,256
15.3623
6.1797
.004237288
741.42
43,743.54
237
56,169
13,312,053
15.3948
6.1885
.004219409
744.56
44,115.03
238
56,644
13,481,272
15.4272
6.1972
.004201681
747.70
44,488.09
239
57,121
13,651,919
15.4596
6.2058
.004184100
750.84
44,862.73
240
57,600
13,824,000
15.4919
6.2145
.004166667
753.98
45,238.93
241
58,081
13,997,521
15.5242
6.2231
.004149378
757.12
45,616.71
242
58,564
14,172,488
15.5563
6.2317
.004132231
760.27
45,996.06
243
59,049
14,348,907
15.5885
6.2403
.004115226
763.41
46,376.98
244
59,536
14,526,784
15.6205
6.2488
.004098361
766.55
46,759.47
378
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Ciroum.
- Area
245
60,025
14,706,125
15.6525
6.2573
.004081633
769.69
47,143.52
246
60,516
14,886,936
15.6844
6.2658
.004065041
772.83
47,529.16
247
61,009
15,069,223
15.7162
6.2743
.004048583
775.97
47,916.36
248
61,504
15,252,992
15.7480
6.2828
.004032258
779.11
48,305.13
249
62,001
15,438,249
15.7797
6.2912
.004016064
782.26
48,695.47
250
62,500
15,625,000
15.8114
6.2996
.004000000
785.40
49,087.39
251
63,001
15,813,251
15.8430
6.3080
.003984064
• 788.54
49,480.87
252
63,504
16,003,008
15.8745
6.3164
.0039G8254
791.68
49,875.92
253
64,009
16,194,277
15.9060
6.3247
.003952569
794.82
50,272.55
254
64,516
16,387,064
15.9374
6.3330
.003937008
797.96
50,670.75
255
65,025
16,581,375
15.9687
6.3413
.003921569
801.11
51,070.52
256
65,536
16,777,216
16.0000
6.3496
.003906250
804.25
51,471.85
257
66.049
16,974,593
16.0312
6.3579
.003891051
807.39
51,874.76
258
66,564
17,173,512
16.0624
6.3661
.003875969
810.53
52,279.24
259
67,081
17,373,979
16.0935
6.3743
.003861004
813.67
52,685.29
260
67,600
17,576,000
16.1245
6.3825
.003846154
816.81
53,092.92
261
68,121
17,779,581
16.1555
6.3907
.003831418
819.96
53,502.11
262
68,644
17,984,728
16.1864
6.3988
.003816794
823.10
53,'912.87
263
69,169
18,191,447
16.2173
6.4070
.003802281
826.24
54,325.21
264
69,696
18,399,744
16.2481
6.4151
.003787879
829.38
54,739.11
265
70,225
18,609,625
16.2788
6.4232
.003773585
832.52
55,154.59
266
70,756
18,821,096
16.3095
6.4312
.003759398
835.66
55,571.63
267
71,289
19,034,163
16.3401
6.4393
.003745318
838.81
55,990.25
268
71,824
19,248,832
16.3707
6.4473
.003731343
841.95
56,410.44
269
72,361
19,465,109
16.4012
6.4553
.003717472
845.09
56,832.20
270
72,900
19,683,000
16.4317
6.4633
.003703704
848.23
57,255.53
271
73,441
19,902,511
16.4621
6.4713
.003690037
851.37
57,680.43
272
73,984
20,123,613
16.4924
6.4792
.003676471
854.51
58,106.90
273
74,529
20,346,417
16.5227
6.4872
.003663004
857.65
58,534.94
274
75,076
20,570,824
16.5529
6.4951
.003649635
860.80
58,9&4.55
275
75,625
20,796,875
16.5831
6.5030
.003636364
8G3.94
59,395.74
276
76,176
21,024,576
16.6132
6.5108
.003623188
867.08
59,828.49
277
76,729
21,253,933
16.6433
6.5187
.003610108
870.22
60,262.82
278
77,284
21,484,952
16.6783
6.5265
.003597122
873.36
60,698.71
279
77,841
> 21,717,639
16.7033
6.5343
.003584229
876.50
61,136.18
280
78,400
21,952,000
16.7332
6.5421
.003571429
879.65
61,575.22
281
78,961
22,188,041
16.7631
G.5499
.003558719
882.79
62,015.82
282
79,524
22,425,768
16.7929
6.5577
.003546099
885.93
62,458.00
283
80,089
22,665,187
16.8226
6.5654
.003533569
889.07
62,901.75
284
80,656
22,906,304
16.8523
6.5731
.003522127
892.21
63,347.07
285
81,225
23,149,125
16.8819
6.5808
.003508772
895.35
63,793.97
286
81,796
23,393,656
16.9115
6.5885
.003496503
898.50
64,242.43
287
82,369
23,639,903
16.9411
6.5962
.003484321
901.64
64,692.46
288
82,944
23,887,872
16.9706
6.6039
.003472222
904.78
65,144.07
289
83,521
24,137,569
17.0000
6.6115
.003460208
907.92
65,597.24
290
84,100
24,389,000
17.0294
6.6191
.003448276
911.06
66,051.99
291
84,681
24,642,171
17.0587
6.6267
.003436428
914.20
66,508.30
292
85,264
24,897,088
17.0880
6.6343
.003424658
917.35
66,966.19
293
85,849
25,153,757
17.1172
6.6419
.003412969
920.49
67,425.65
294
86,436
25,412,184
17.1464
6.6494
.003401361
923.63
67,886.68
295
87,025
25,672,375
17.1756
6.6569
.003389831
926.77
68.349.28
296
87,616
25,934,836
17.2047
6.6644
.003378378
929.91
68,813.45
297
88,209
26,198,073
17.2337
6.6719
.003367003
933.05
69,279.19
298
88,804
26,463,592
17.2627
6.6794
.003355705
936.19
69,746.50
299
89,401
26,730,899
17.2916
6.6869
.003344482
939.34
70,215.38
300
90,000
27,000,000
17.3205
6.6943
.003333333
942.48
70,685.83
301
90,601
27,270,901
17.3494
6.7018
.003322259
945.62
71,157.86
302
91,204
27,543,608
17.3781
6.7092
.003311258
948.76
71,631.45
303
91,809
27,818,127
17.4069
6.7166
.003301330
951.90
72,106.62
304
92,416
28,094,464
17.4356
6.7240
.003289474
955.04
72,583.36
305
93,025
28,372,625
17.4642
6.7313
.003278689
958.19
73,061.66
306
93,636
28,652,616
17.4929
6.7387
.003267974
961.33
73,541.54
307
94,249
28,934,443
17.5214
6.7460
.003257329
964.47
74,022.99
SQUARES, CUBES, ROOTS, ETC.
379
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Circnm.
Area
308
94,864
29,218,112
17.5499
6.7533
.003246753
967.61
74,506.01
309
95,481
29,503,629
17.5784
6.7606
.003236246
970.75
74,990.60
310
96,100
29,791,000
17.6068
6.7679
.003225806
973.89
75,476.76
311
96,721
30,080,231
17.6352
6.7752
.003215434
977.04
75,964.50
312
97,344
30,371,328
17.6635
6.7824
.003205128
980.18
76,453.80
313
97,969
30,664,297
17.6918
6.7897
.003194888
983.32
76,944.67
314
98,596
30,959,144
17.7200
6.7969
.003184713
986.46
77,437.12
315
99,225
31,255,875
17.7482
6.8041
.003174603
989.60
77,931.13
316
99,856
31,554,496
17.7764
6.8113
.003164557
992.74
78,426.72
317
100,489
31,855,013
17.8045
6.8185
.003154574
995.88
78,923.88
318
101,124
32,157,432
17.8326
6.8256
.003144654
999.03
79,422.60
319
101,761
32,461,759
17.8606
6.8328
.003134796
1,002.17
79,922.90
320
102,400
32,768,000
17.8885
6.8399
.003125000
1,005.31
80,424.77
321
103,041
33,076,161
17.9165
6.8470
.003115265
1,008.45
80,928.21
322
103,684
33,386,248
17.9444
6.8541
.003105590
1,011.59
81,433.22
323
104,329
33,698,267
17.9722
6.8612
.003095975
1,014.73
81,939.80
324
104,976
34,012,224
18.0000
6.8683
.003086420
1,017.88
82,447.96
325
105,625
34,328,125
18.0278
6.8753
.003076923
1,021.02
82,957.68
326
106,276
34,645,976
18.0555
6.8824
.003067485
1,024.16
83,468.98
327
106,929
34,965,783
18.0831
6.8894
.003058104
1,027.30
83,981.84
328
107,584
35,287,552
18.1108
6.8964
.003048780
1,030.44
84,496.28
329
108,241
35,611,289
18.1384
6.9034
.003039514
1,033.58
85,012.28
330
108,900
35,937,000
18.1659
6.9104
.003030303
1,036.73
85,529.86
331
109,561
36,264,691
18.1934
6.9174
.003021148
1,039.87
86,049.01
332
110,224
36,594,368
18.2209
6.9244
.003012048
1,043.01
86,569.73
333
110,889
36,926,037
18.2483
6.9313
.003003003
1,046.15
87,092.02
334
111,556
37,259,704
18.2757
6.9382
.002994012
1,049.29
87,615.88
335
112,225
37.595,375
18.3030
6.9451
.002985075
1,052.43
88,141.31
336
112,896
37,933,056
18.3303
6.9521
.002976190
1,055.58
88,668.31
337
113,569
38.272,753
18.3576
6.9589
.002967359
1,058.72
89,196.88
338
114,244
38,614,472
18.3818
6.9658
.002958580
1,061.86
89,727.03
339
114,921
38,958,219
18.4120
6.9727
.002949853
1,065.00
90,258.74
340
115,600
39,304,000
18.4391
6.9795
.002941176
1,068.14
90,792.03
341
116,281
39,651,821
18.4662
6.9864
.002932551
1,071.28
91,326.88
342
116,964
40,001,688
18.4932
6.9932
.002923977
1,074.42
91,863.31
343
117,649
40,353,607
18.5203
7.0000
.002915452
1,077.57
92,401.31
344
118,336
40,707,584
18.5472
7.0068
.002906977
1,080.71
92,940.88
345
119,025
41,063,625
18.5742
7.0136
.002898551
1,083.85
93,482.02
346
119,716
41,421,736
18.6011
7.0203
.002890173
1,086.99
94,024.73
347
120,409
41,781,923
18.6279
7.0271
.002881844
1,090.13
94,569.01
348
121,104
42,144,192
18.6548
7.0338
.002873563
1,093.27
95,114.86
349
121,801
42,508,549
18.6815
7.0406
.002865330
1,096.42
95,662.28
350
122,500
42,875,000
18.7083
7.0473
.002857143
1,099.56
96,211.28
351
123,201
43,243,551
18.7350
7.0540
.002849003
1,102.70
96,761.84
352
123,904
43,614,208
18.7617
7.0607
.002840909
1,105.84
97,313.97
353
124,609
43,986,977
18.7883
7.0674
.002832861
1,108.98
97,867.68
354
125,316
44,361,864
18.8149
7.0740
.002824859
1,112.12
98,422.96
355
126,025
44,738,875
18.8414
7.0807
.002816901
1,115.27
98,979.80
356
126,736
45,118,016
18.8680
7.0873
.002808989
1,118.41
99,538.22
357
127,449
45,499,293
18.8944
7.0940
.002801120
1,121.55
100,098.21
358
128,164
45,882,712
18.9209
7.1006
.002793296
1,124.69
100,659.77
359
128,881
46,268,279
18.9473
7.1072
.002785515
1,127.83
101,222.90
360
129,600
46,656,000
18.9737
7.1138
.002777778
1,130.97
101,787.60
361
130,321
47,045,881
19.0000
7.1204
.002770083
1,134.11
102,353.87
362
131,044
47,437,928
19.0263
7.1269
.002762431
1,137.26
102,921.72
363
131,769
47,832,147
19.0526
7.1335
.002754821
1,140.40
103,491.13
364
132,496
48,228,544
19.0788
7.1400
.002747253
1,143.54
104,062.12
365
133,225
48,627,125
19.1050
7.1466
.002739726
1,146.68
104,634.67
366
133,956
49,027,896
19.1311
7.1531
.002732240
1,149.82
105,208.80
367
134,689
49,430,863
19.1572
7.1596
.002724796
1,152.96
105,784.49
368
135,424
49,836,032
19.1833
7.1661
.002717391
1,156.11
106,361.76
369
136,161
50,243,409
19.2094
7.1726
.002710027
1,159.25
106,940.60
370
136,900
50,653,000
19.2354
7.1791
.002702703
1,162.39
107,521.01
380
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Circum
Area
371
137,641
51,064,811
19.2614
7.1855
.002695418
1,165.53
108,102.99
372
138,384
51,478,848
19.2873
7.1920
.002688172
1,168.67
108,686.54
373
139,129
51,895,117
19.3132
7.1984
.002680965
1,171.81
109,271.66
374
139,876
52,313,624
19.3391
7.2048
.002673797
1,174.96
109,858.35
375
140,625
52,734,375
19.3649
7.2112
.002666667
1,178.10
110,446.62
376
141,376
53,157,376
19.3907
7.2177
.002659574
1,181.24
111,036.45
377
142,129
53,582,633
19.4165
7.2240
.002652520
1,184.38
111,627.86
378
142,884
64,010,152
19.4422
7.2304
.002645503
1,187.52
112,220.83
379
143,641
54,439,939
19.4679
7.2368
.002638521
1,190.66
112,815.38
380
144,400
54,872,000
19.4936
7.2432
.002631579
1,193.81
113,411.49
381
145,161
55,306,341
19.5192
7.2495
.002624672
1,196.95
114,009.18
382
145,924
55,742,968
19.54-18
7.2558
.002617801
1,200.09
114,608.44
383
146,689
56,181,887
19.5704
7.2022
.002610966
1,203.23
115,209.27
384
147,456
56,623.104
19.5959
7.2G85
.002604167
1,200.37
115,811.67
385
148,225
57,066,625
19.6214
7.2748
.002597403
1,209.51
116,415.64
386
148,996
57,512,456
19.64G9
7.2811
.002590674
1,212.65
117,021.18
387
149,769
57,960,603
19.6723
7.2874
.002583979
1,215.80
117,628.30
388
150,544
58,411,072
19.6977
7.2936
.002577320
1,218.94
118,236.98
389
151,321
58,863,869
19.7231
7.2999
.002570694
1,222.08
118,847.24
390
152,100
59,819,000
19.7484
7.3061
.002564103
1,225.22
119,459.06
391
152,881
59,776,471
19.7737
7.3124
.002557545
1,228.36
120,072.46
392
153,664
60,236,288
19.7990
7.3186
.002551020
1,231.50
120,687.42
393
154,449
60,698,457
19.8242
7.3248
.002544529
1,234.65
121,303.96
394
155,236
61,162,984
19.8494
7.3310
.002538071
1,237.79
121,922.07
395
156,025
61,629,875
19.8746
7.3372
.002531646
1,240.93
122,541.75
396
156,816
62,099,136
19.8997
7.3434
.002525253
1,244.07
123,163.00
397
157,609
62,570,773
19.9249
7.3496
.002518892
1,247.21
123,785.82
398
158,404
63,044,792
19.9499
7.3558
.002512563
1,250.35
124,410.21
399
159,201
63,521,199
19.9750
7.3619
.002506266
1,253.50
125,036.17
400
160,000
64,000,000
20.0000
7.3681
.002500000
1,256.64
125,663.71
401
160,801
64,481,201
20.0250
7.3742
.002493766
1,259.78
126,292.81
402
161,604
64,964,808
20.0499
7.3803
.002487562
1,262.92
126,923.48
403
162,409
65,450,827
20.0749
7.3864
.002481390
1,266.06
127,555.73
404
163,216
65,939,264
20.0998
7.3925
.002475248
1,269.20
128,189.55
405
164,025
66,430,125
20.1246
7.3986
.002469136
1.272.35
128,824.93
406
164,836
66,923,416
20.1494
7.4047
.002463054
1,275.49
129,461.89
407
165,649
67,419,143
20.1742
7.4108
.002457002
1,278.63
130,100.42
408
166,464
67,917,312
20.1990
7.4169
.002450980
1,281.77
130,740.52
409
167,281
68,417,929
20.2237
7.4229
.002444988
1,284.91
131,382.19
410
168,100
68,921,000
20.2485
7.4290
.002439024
1,288.05
132,025.43
411
168,921
69,426,531
20.2731
7.4350
.002433090
1,291.19
132,670.24
412
169,744
69,934,528
20.2978
7.4410
.002427184
1,294.34
133,316.63
413
170,569
70,444,997
20.3224
7.4470
.002421308
1,297.48
133,964.58
414
171,396
70,957,944
20.3470
7.4530
.002415459
1,300.62
134,614.10
415
172,225
71,473,375
20.3715
7.4590
.002409639
1,303.76
135,265.20
416
173,056
71,991,296
20.3961
7.4650
.002406846
,306.90
135,917.86
417
173,889
72,511,713
20.4206
7.4710
.002398082
,310.04
136,572.10
418
174,724
73,034,632
20.4450
7.4770
.002392344
,313.19
137,227.91
419
175,561
73,560,059
20.4G95
7.4829
.002386635
,316.33
137,885.29
420
176,400
74,088,000
20.4939
7.4889
.002380952
,319.47
38,544.24
421
177,241
74,618,461
20.5183
7.4948
.002375297
,322.61
39,204.76
422
178,084
75,151,448
20.5426
7.5007
.002369668
,325.75
39,866.85
423
178,929
75,686,967
20.5670
7.5067
.002364066
,328.89
40,530.51
424
179,776
76,225,024
20.5913
7.5126
.002358491
,332.04
41,195.74
425
180,625
76,765,625
20.6155
7.5185
.002352941
,335.18
41,862.54
426
181,476
77,308,776
20.6398
7.5244
.002347418
,338.32
42,530.92
427
182,329
77,a54,483
20.6640
7.5302
.002341920
,341.46
43,200.86
428
183,184
78,402,752
20.6882
7.5361
.002336449
,344.60
43,872.38
429
184,041
78,953,589
20.7123
7.5420
.002331002
,347.74
44,545.46
430
184,900
79,507,000
20.7364
7.5478
.002325581
,350.88
45,220.12
431
185,761
80,062,991
20.7605
7.5537
.002320186
,354.03
45.896.35
432
186,624
80,621,568
20.7846
7.5595
.002314815
,357.17
46,574.15
433
187,489
81,182,737
20.8087
7.5654
.002309469
,360.31
47,253.52
SQUARES, CUBES, ROOTS, ETC.
381
No.
Square
Cube
Sq. Boot
Cu. Root
Reciprocal
Circum.
Area
434
188,356
81,746,504
20.8327
7.5712
.002304147
1,363.45
147,934.46
435
189,225
82,312,875
20.8567
7.5770
.002298851
1,366.59
148,616.97
436
190,0%
82,881,856
20.8806
7.5828
.002293578
1,369.73
149,301.05
437
190,969
83,453,453
20.9045
7.5886
.002288330
1,372.88
149,986.70
466
191,844
84,027,672
U0.92S1
7.5944
.002283105
1,376.02
150,673.93
439
192,721
84,604,519
20.9523
7.6001
.002277904
1,379.16
151,362.72
440
193,600
85,184,000
20.9762
7.6059
.002272727
1,382.30
152,053,08
441
194,481
85,766,121
UUKXJO
7.6117
.002267574
1,385.44
152,745.02
442
195,364
86,350,888
21.0238
7.6174
.002262443
1,388.58
153,438.53
443
196,249
86,938,307
21.0476
7.6232
.002257336
1,391.73
154,133.60
444
197,136
87,528,384
21.0713
7.6289
.002252252
1,394.87
154,830.25
445
198,025
88,121,125
21.0950
7.6346
.002247191
1,398.01
155,528.47
446
198,916
88,716,536
21.1187
7.6403
.002242152
1,401.15
156,228.26
447
199,809
89,314,623
21.1424
7.6460
.002237136
1,404.29
156,929.62
448
200,704
89,915,392
21.1660
7.6517
.002232143
1,407.43
157,632.55
449
201,601
90,518,849
21.1896
7.6574
.002227171
1,410.58
158,337.06
450
202,500
91,125,000
21.2132
7.6631
.002222222
1,413.72
159,043.13
451
203,401
91,733,851
21.2368
7.6688
.002217295
1,416.86
159,750.77
452
204,304
92,345,408
21.2603
7.6744
.002212389
1,420.00
160,459.99
453
205,209
92,959,677
21.2838
7.6801
.002207506
1,423.14
161,170.77
454
206,116
93,576,664
21.3073
7.6857
.002202643
1,426.28
161,883.13
455
207,025
94,196,375
21.3307
7.6914
.002197802
1,429.42
162,597.05
456
207,936
94,818,816
21.3542
7.6970
.002192982
1,432.57
163,312.55
457
208,849
95,443,993
21.3776
7.7026
.002188184
1,435.71
164,029.62
458
209,764
96,071,912
21.4009
7.7082
.002183406
1,438.85
164,748.26
459
210,681
96,702,579
21.4213
7.7188
.002178649
1,441.99
165,468.47
460
211,600
97,336,000
21.4476
7.7194
.002173913
1,445.13
166,190.25
461
212,521
97,972,181
21.4709
7.7250
.002169197
1,448.27
166,913.60
462
213,444
98,611,128
21.4942
7.7306
.002164502
1,451.42
167,638.53
463
214,369
99;252,847
21.5174
7.7362
.002159827
1,454.56
168,365.02
464
215,296
99,897,344
21.5407
7.7418
.002155172
1,457.70
169,093.08
465
216,225
100,544,625
21.5639
7.7473
.002150538
1,460.84
169,822.72
466
217,156
101,194,696
21.5870
7.7529
.002145923
1,463.98
170,553.92
467
218,089
101,847,563
21.6102
7.7584
.002141328
1,467.12
171,286.70
468
219,024
102,503,232
21.6333
7.7639
.002136752
1,470.27
172,021.05
469
219,961
103,161,709
21.6564
7.7695
.002132196
1,473.41
172,756.97
470
220,900
103,823,000
21.6795
7.7750
.002127660
1,476.55
173,494.45
471
221,841
104,487,111
21.7025
7.7805
.002123142
1,479.69
174,233.51
472
222,784
105,154,048
21.7256
7.7860
.002118644
1,482.83
174,974.14
473
223,729
105,823,817
21.7486
7.7915
.002114165
1,485.97
175,716.35
474
224,676
106,496,424
21.7715
7.7970
.002109705
1,489.11
176,460.12
475
225,625
107,171,875
21.7945
7.8025
.002105263
1,492.26
177,205.46
476
226,576
107,850,176
21.8174
7.8079
.002100840
1,495.40
177,952.37
477
227,529
108,531,333
21.8403
7.8134
.002096486
1,498.54
178,700.86
478
228,484
109,215,352
21.8632
7.8188
.002092050
1,501.68
179,450.91
479
229,441
109,902,239
21.8861
7.8243
.002087683
1,504.82
180,202.54
480
230,400
110,592,000
21.9089
7.8297
.002083333
1,507.96
180,955.74
481
231,361
111,284,641
21.9317
7.8352
.002079002
1,511.11
181,710.50
482
232,324
111,980,168
21.9545
7.8406
.002074689
1,514.25
182,466.84
483
233,289
112,678,587
21.9775
7.8460
.002070393
1.517.39
183,224.75
484
234,256
113,379,904
22.0000
7.8514
.002066116
1,520.53
183,984.23
485
235,225
114,084,125
22.0227
7.8568
.002061856
1,523.67
184,745.28
486
236,196
114,791,256
22.0454
7.8622
.002057613
1,526.81
185,507.90
487
237,169
115,501,303
22.0681
7.8676
.002053388
1,529.96
186,272.10
488
238,144
116,214,272
22.0907
7.8730
.002049180
1,533.10
187,037.86
489
239,121
116,930,169
22.1133
7.8784
.002044990
1,536.24
187,805.19
490
240,100
117,649,000
22.1359
7.8837
.002040816
1,539.38
188,574.10
491
241,081
118,370,771
22.1585
7.8891
.002036660
1,542.52
189,344.57
492
242,064
119,095,488
22.1811
7.8944
.002032520
1,545.66
190,116.62
493
243.049
119,823,157
22.2036
7.8998
.002028398
1,548.81
190,890.24
494
244,036
120,553,784
22.2261
7.9051
.002024291
1,551.95
191,665.43
495
245,025
121,287,375
22.2486
7.9105
.002020292
1,555.09
192,442.18
496
246,016
122,023,936
22.2711
7.9158
.002016129
1,558.23
193,220.51
382
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Root
Cu. Boot
Reciprocal
Circom.
Area
497
247,009
122,763,473
22.2935
7.9211
.002012072
1,561.37
194,000.41
498
248,004
123,505,992
22.3159
7.9264
.002008032
1,564.51
194,781.89
499
249,001
124,251,499
22.3383
7.9317
.002004008
1,567.65
195,564.93
500
250,000
125,000,000
22.3607
7.9370
.002000000
1,570.80
196,349.54
501
251,001
125,751,501
22.3830
7.9423
.001996008
1,573.94
197,135.72
502
252,004
126,506,008
22,4054
7.9476
.001992032
1,577.08
197,923.48
503
253,009
127,263,527
22.4277
7.9528
.001988072
1,580.22
198,712.80
504
254,016
128,024,064
22.4499
7.9581
.001984127
1,583.36
199,503.70
505
255,025
128,787,625
22.4722
7.9634
.001980198
1,586.50
200,296.17
506
256,036
129,554,216
22.4944
7.9686
.001976285
1,589.65
201,090.20
507
257,049
130,323,843
22.5167
7.9739
.001972387
1,592.79
201,885.81
508
258,064
131,096,512
22.5389
7.9791
.001968504
1,595.93
202,682.99
509
259,081
131,872,229
22.5610
7.9843
.001964637
1,599.07
203,481.74
510
260,100
132,651,000
22.5832
7.9895
.001960785
1,602.21
204,282.06
511
261,121
133,432,831
22.6053
7.9948
.001956947
1,605.35
205,083.95
512
262,144
134,217,728
22.6274
8.0000
.001953125
1,608.50
205,887.42
513
263,169
135,005,697
22.6495
8.0052
.001949318
1,611.64
206,692.45
514
264,196
135,796,744
22.6716
8.0104
.001945525
1,614.78
207,499.05
515
265,225
136,590,875
22.6936
8.0156
.001941748
1,617.92
208,307.23
516
266,256
137,388,096
22.7156
8.0208
.001937984
1,621.06
209,116.97
517
267,289
138,188,413
22.7376
8.0260
.001934236
1,624.20
209,928.29
518
268,324
138,991,832
22.7596
8.0311
.001930502
1,627.34
210,741.18
519
269,361
139,798,359
22.7816
8.0363
.001926782
1,630.49
211,555.63
520
270,400
140,608,000
22.8035
8.0415
.001923077
1,633.63
212,371.66
521
271,411
141,420,761
22.8254
8.0466
.001919386
1,636.77
213,189.26
522
272,484
142,236,648
22.8473
8.0517
.001915709
1,639.91
214,008.43
523
273,529
143,055,667
22.8692
8.0569
.001912046
1,643.05
214,829.17
524
274,576
143,877,824
22.8910
8.0620
.001908397
1,646.19
215,651.49
525
275,625
144,703,125
22.9129
8.0671
.001904762
1,649.34
216,475.37
526
276,676
145,531,576
22.9347
8.0723
.001901141
1,652.48
217,300.82
527
277,729
146,363,183
22.9565
8.0774
.001897533
1,655.62
218,127.85
528
278,784
147,197,952
22.9783
8.0825
.001893939
1,658.76
218,956.44
529
279,841
148,035,889
23.0000
8.0876
.001890359
1,661.90
219,786.61
530
280,900
148,877,001
23.0217
8.0927
.001886792
1,665.04
220,618.34
531
281,961
149,721,291
23.0434
8.0978
.001883239
1,668.19
221,451.65
532
283,024
150,568,768
23.0651
8.1028
.001879699
1,671.33
222,286.53
533
284,089
151,419,437
23.0868
8.1079
.001876173
1,674.47
223,122.98
534
285,156
152,273,304
23.1084
8.1130
.001872659
1,677.61
223,961.00
535
286,225
153,130,375
23.1301
8.1180
.001869159
1,680.75
224,800.59
536
287,296
153,990,656
23.1517
8.1231
.001865672
1,683.89
225,641.75
537
288,369
154,854,153
23.1733
8.1281
.001862197
1,687.04
226,484.48
538
289,444
155,720,872
23.1948
8.1332
.001858736
1,690.18
227,328.79
539
290,521
156,590,819
23.2164
8.1382
.001855288
1,693.32
228,174.66
540
291,600
157,464,000
23.2379
8.1433
.001851852
1,696.46
229,022.10
541
292,681
158,340,421
23.2594
8.1483
.001848429
1,699.60
229,871.12
542
293,764
159,220,088
23.2809
8.1533
.001845018
1,702.74
230,721.71
543
294,849
160,103,007
23.3024
8.1583
.001841621
1,705.88
231,573.86
544
295,936
160,989,184
23.3238
8.1633
.001838235
1,709.03
232,427.59
545
297,025
161,878,625
23.3452
8.1683
.001834862
1,712.17
233.2S2.89
546
298,116
162,771,336
23.3666
8.1733
.001831502
1,715.31
234,139.76
547
299,209
163,667,323
23.3880
8.1783
.001828154
1,718.45
234,998.20
548
300,304
164,566,592
23.4094
8.1833
.001824818
1,721.59
235,858.21
549
301,401
165,469,149
23.4307
8.1882
.001821494
1,724.73
236,719.79
550
302,500
166,375,000
23.4521
8.1932
.001818182
1,727.88
237,582.94
551
303,601
167,284,151
23.4734
8.1982
.001814882
1,731.02
238,447.67
552
304,704
168,196,608
23.4947
8.2031
.001811594
1,734.16
239,313.96
553
305,809
169,112,377
23.5160
8.2081
.001808318
1,737.30
240,181.83
554
306,916
170,031,464
23.5372
8.2130
.001805054
1,740.44
241,051.26
555
308,025
170,953,875
23.5584
8.2180
.001801802
1,743.58
241,922.27
556
309,136
171,879,616
23.5797
8.2229
.001798561
1,746.73
242,794.85
557
310,249
172,808,693
23.6008
8.2278
.001795332
1,749.87
243,668.99
558
311,364
173,741,112
23.6220
8.2327
.001792115
1,753.01
244,544.71
559
312,481
174,676,879
23.6432
8.2377
.001788909
1,756.15
245,422.00
SQUARES, CUBES, ROOTS, ETC.
383
No
Square
Cube
Sq. Roo
Cu. Roo
Reciprocal
Circum
Area
560
313,600
175,616,000
23.664
8.2426
.001785714
1,759.2
246,300.86
561
314,721
176,558,481
23.6854
8.2475
.001782531
1,762.4
247,181.30
562
315,844
177,504,328
23.706
8.2524
.001779359
1,765.5
248,063.30
563
316,969
178,453,547
23.7276
8.2573
.001776199
1,768.7
248,946.87
564
318,096
179,406,144
23.7487
8.2621
.001773050
1,771.8
249,832.01
565
319,225
180,362,125
23.7697
8.2670
.001769912
1,775.0
250,718.73
566
32o!:!f>6
181,321,496
23.7908
8.2719
.001766784
1,778.14
251,607.01
567
321,489
182,284,263
23.8118
8.2768
.001763668
1,781.28
252,496.87
568
322,624
183,250,432
23.8328
8.2816
.001760563
1,784.42
253,388.30
569
323,761
184,220,009
23.8537
8.2865
.001757469
1,787.57
254,281.29
570
324,900
185,193,000
23.8747
8.2913
.001754386
1,790.71
255,175.86
571
326,041
186,169,411
23.8956
8.2962
.001751313
1,793.85
256,072.00
572
327,184
187,149,248
23.9165
8.3010
.001748252
1,796.99
256,969.71
573
328,329
188,132,517
23.9374
8.3059
.001745201
1,800.13
257,868.99
574
:wy,476
189,119,224
23.9583
8.3107
.001742164
1,803.27
258,769.85
575
330,625
190,109,375
23.9792
8.3155
.001739130
1,806.42
259,672.27
576
331,776
191,102,976
24.0000
8.3203
.001736111
1,809.56
260,576.26
577
332,929
192,100,033
24.0208
8.3251
.001733102
1,812.70
261,481.83
578
334,084
193,100,552
24.0416
8.3300
.001730104
,815.84
262,388.96
579
335,241
194,104,539
24.0624
8.3348
.001727116
,818.98
63,297.67
580
336,400
195,112,000
24.0832
8.3396
.001724138
,822.12
64,207.94
581
337,561
196,122,941
24.1039
8.3443
.001721170
,825.27
65,119.79
582
338,724
197,137,368
24.1247
8.3491
.001718213
,828.41
66,033.21
583
339,889
198,155,287
24.1454
8.3539
.001715266
,831.55
66,948.20
584
341,056
199,176,704
24.1661
8.3587
.001712329
,834.69
67,864.76
585
342,225
200,201,625
24.1868
8.3634
.001709402
,837.83
68,782.89
586
343,396
201,230,056
24.2074
8.3682
.001706485
840.97
69,702.59
587
344,569
202,262,003
24,2281
8.3730
.001703578
844.11
70,623.86
588
345,744
203,297,472
24.2487
8.3777
.001700680
847.26
71,546.70
589
346,921
204,336,469
24.2693
8.3825
.001697793
850.40
72,471.12
590
348,100
205,379,000
24.2899
8.3872
.001694915
853.54
73,397.10
591
349,281
206,425,071
24.3105
8.3919
001692047
856.68
74,324.66
592
350,464
207,474,688
24.3311
8.3967
001689189
859.82
75,253.78
593
351,649
208,527,857
24.3516
8.4014
001686341
862.96
76,184.48
594
352,836
209,584,584
24.3721
8.4061
001683502
866.11
77,116.75
595
354,025
210,644,875
24.3926
8.4108
001680672
869.25
78,050.58
596
355,216
211,708,736
24.4131
8.4155
001677852
872.39
78,985.99
597
356,409
212,776,173
24.4336
8.4202
001675042
875.53
279,922.97
598
357,604
213,847,192
24.4540
8.4249
001672241
878.67
280,861.52
599
358,801
214,921,799
24.4745
8.4296
001669449
881.81
281,801.65
600
360,000
216,000,000
24.4949
8.4343
001C66667
884.96
82,743.34
601
361,201
217,081,801
24.5153
8.4390
001663894
888.10
283,686.60
602
362,404
218,167,208
4.5357
8.4437
001661130
891.24
284,631.44
603
363,609
219,256,227
4.5561
8.4484
001658375
894.38
-85,577.84
604
364,816
220,348,864
24.5764
8.4530
001655629
897.52
-86,525.82
605
366,025
221,445,125
4.5968
8.4577
001652893
900.66
-87,475.36
606
367,236
222,545,016
24.6171
8.4623
001650165
903.81
-88,426.48
607
368,449
223,648,543
4.6374
8.4670
001647446
906.95
-89,379.17
608
369,664
224,755,712
24.6577
8.4716
001644737
910.09
>90,333.43
609
370,881
225,866,529
4.6779
8.4763
001642036
913.23
1,289.26
610
372,100
226,981,000
24.6982
8.4809
001639344
916.37
2,246.66
611
373,321
228,099,131
4.7184
8.4856
001G36661
919.51
3,205.63
612
374,544
229,220,928
4.7386
8.4902
001633987
922.65
94,166.17
613
375,769
230,346,397
24.7588
8.4948
001631321
925.80
5,128.28
614
376,996
231,475,544
4.7790
8.4994
001628664
928.94
6,091.97
615
378,225
232,608,375
4.7992
8.5040
001626016
932.08
7,057.22
616
379.456
233,744,896
4.8193
8.5086
001623377
935.22
8,024.05
617
380,689
234,885,113
24.8395
8.5132
001620746
938.36
8,992.44
618
381,924
236,029,032
4.8596
8.5178
001618123
941.50
9,962.41
619
383,161
237,176,659
24.8797
8.5224
001615509
944.65
00,933.95
620
384,400
238,325,000
4.8998
8.5270
001612903
947.79
1,907.05
621
385,641
239,483,061
24.9199
8.5316
001610306
950.93
2,881.73
622
386S884
240,641,848
24.9399
8.5362
001607717
954.07
3,857.98
384
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Boot
Cu.Root
Reciprocal
Circum
Area
623
388,129
241,804,367
24.9600
8.5408
.001605136
1,957.21
304,835.80
624
389,376
242,970,624
24.9800
8.5453
.001602564
1,960.35
305,815.20
625
390,625
244,140,625
25.0000
8.5499
.001600000
1,963.50
306,796.16
626
391,876
245,314,376
25.0200
8.5544
.001597444
1,966.64
307,778.69
627
393,129
246,491,883
25.0400
8.5589
.001594896
1,969.78
308,762.79
628
394,384
247,673,152
25.0599
8.5635
.001592357
1,972.92
309,748.47
629
395,641
248,858,189
25.0799
8.5681
.001589825
l,976.0f
310,735.71
630
396,900
250,047,000
25.0998
8.5726
.001587302
1,979.20
311,724.53
631
398,161
251,239,591
25.1197
8.5772
.001584786
1,982.35
312,714.92
632
399,424
252,435,968
25.1396
8.5817
.001582278
1,985.49
313,706.88
633
400,689
233,636,137
25.1595
8.5862
.001579779
1,988.63
314,700.40
634
401,956
254,840,104
25.1794
8.5907
.001577287
1,991.77
315,695.50
635
403,225
256,047,875
25.1992
8.5952
.001574803
1,994.91
316,692.17
636
404,496
257,259,456
25.2190
8.5997
.001572327
1,998.05
317,690.42
637
405,769
258,474,853
25.2389
8.6043
.001569859
2,001.19
318,690.23
638
407,044
259,694,072
25.2587
8.G088
.001567398
2,004.34
319,691.61
639
408,321
260,917,119
25.2784
8.G132
.001564945
2,007.48
320,694.56
640
409,600
262,144,000
25.2982
8.6177
.001562500
2,010.62
321,699.09
641
410,881
263,374,721
25.3180
8.6222
.0015GOOG2
2,013.76
322.705.18
642
412,164
264,609,288
25.3377
8.6267
.001557632
2,016.90
323,712.85
643
413,449
265,847,707
25.3574
8.G312
.001555210
2,020.04
324,722.09
644
414,736
267,089,984
25.3772
8.6357
.001552795
2,023.19
325,732.89
645
416,125
268,336,125
25.3969
8.6401
.001550388
2,026.33
326,745.27
646
417,316
269,585,136
25.4165
8.6446
.001547988
2,029.47
327,759.22
647
418,609
270,840,023
25.4362
8.G490
.001545595
2,032.61
328,774.74
648
419,904
272,097,792
25.4558
8.G535
.001543210
2,035.75
329,791.83
649
421,201
273,359,449
25.4755
8.6579
.001540832
2,038.89
330,810.49
650
422,500
274,625,000
25.4951
8.6624
.0015384G2
2,042.04
331,830.72
651
423,801
275,894,451
25.5147
8.6668
.001536098
2,045.18
332,852.53
652
425,104
277,167,808
25.5343
8.6713
.001533742
2,048.32
333",875.90
653
426,409
278,445,077
25.5539
8.6757
.001531394
2,051.46
334,900.85
654
427,716
279,726,264
25.5734
8.6801
.001529052
2,054.60
335,927.36
655
429,025
281,011,375
25.5930
8.6845
.001526718
2,057.74
336,955.45
656
430,336
282,300,416
25.6125
8.6890
.00152-1390
2,060.88
337,985.10
657
431,639
283,593,393
25.6320
8.6934
.001522070
2,064.03
339,016.33
658
432,964
284,890,312
25.6515
8.6978
.001519751
2,OG7.17
340,049.13
659
434,281
286,191,179
25.6710
8.7022
.001517451
2,070.31
341,083.50
660
435,600
287,496,000
25.C905
8.7066
.001515152
2,073.45
42,119.44
661
436,921
288,804,781
25.7099
8.7110
.001512859
2,076.59
343,156.95
662
438,244
290,117,528
25.7294
8.7154
.001510574
2,079.73
344,196.03
663
439,569
291,434,247
25.7488
8.7198
.001508296
,082.88
45,236.69
664
440,896
292,754,944
25.7682
8.7241
.001506024
,086.02
46,278.91
665
442,225
294,079,625
25.7876
8.7285
.001503759
,089.16
47,322.70
666
443,556
295,408,296
25.8070
8.7329
.001501502
,092.30
48,368.07
667
444,899
296,740,963
25.8263
8.7373
.001499250
,095.44
349,415.00
668
446,224
298,077,632
25.8457
8.7416
.001497006
,098.58
50,463.51
669
447,561
299,418,309
25.8650
8.7460
.001494768
,101.73
51,513.59
670
448,900
300,763,000
25.8844
8.7503
.001492537
,104.87
52,565.24
671
450,241
302,111,711
25.9037
8.7547
.001490313
,108.01
53,618.45
672
451,584
303,464,448
25.9230
8.7590
.001488095
,111.15
54,673.21
673
452,929
304,821,217
25.9422
8.7634
.001485884
,114.29
55,729.60
674
454,276
306,182,024
25.9615
8.7677
.001483680
,117.43
56,787.54
675
455,625
307,546,875
25.9808
8.7721
.001481481
,120.58
57,847.04
676
456,976
308,915,776
26.0000
8.7764
.001479290
,123.72
58,908.11
677
458,329
310,288,733
26.0192
8.7807
.001477105
,126.86
59,970.75
678
459,684
311,665,752
26.0384
8.7850
.001474926
,130.00
61,034.97
679
461,041
313,046,839
26.0576
8.7893
.001472754
,133.14
62,100.75
680
462,400
314,432,000
26.0768
8.7937
.001470588
,136.28
63,168.11
681
463,761
315,821,241
26.0960
8.7980
.001468429
,139.42
64,237.04
682
465,124
317,214,568
26.1151
8.8023
.001466276
,142.57
65,307.54
683
466,489
318,611,987
26.1343
8.8066
.001464129
,145.71
66,379.60
684
467,856
320,013,504
26.1534
8.8109
.001461988
148.85
67,453.24
685
469,225
321,419,125
26.1725
8.8152
.001459854
151.99
68,528.45
SQUARES, CUBES, ROOTS, ETC,
385
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Circum.
Are*
686
470,596
322,828,856
26.1916
8.8194
.001457726
2,155.13
369,605.23
687
471,969
324,242,703
26.2107
8.8237
.001455604
2,158.27
370,683.59
688
473,344
325,660,672
26.2298
8.8280
.001453488
2,161.42
371,763.51
689
474,721
327,082,769
26.2488
8.8323
.001451379
2,164.56
372,845.00
690
476,100
328,509,000
26.2679
8.8366
.001449275
2,167.70
373,928.07
691
477,481
329,939,371
26.2869
8.8408
.001447178
2,170.84
375,012.70
692
47,s!sW
331,373,888
26.3059
8.8451
.001445087
2,173.98
376,098.91
693
480,249
332,812,557
2G.3249
8.8493
.001443001
2,177.12
377,186.68
694
481,636
334,255,384
26.3439
8.8536
.001440922
2,180.27
378,276.03
G95
483,025
335,702,375
26.3629
8.8578
.001438849
2,183.41
379,366.95
696
484,416
337,153,536
26.3818
8.8621
.001436782
2,186.55
380,459.44
697
485,809
338,608,873
20.4008
8.8663
.001434720
2,189.69
381,553.50
G98
487,204
340,068,392
26.4197
8.8706
.001432665
2,192.83
382,649.13
699
488,601
341,532,099
26.4386
8.8748
.001430615
2,195.97
383,746.33
700
490,000
343,000,000
26.4575
8.8790
.001428571
2,199.11
384,845.10
701
491,401
344,472,101
26.4764
8.8833
.001426534
2,202.26
385,945.44
702
492,804
345,948,408
26.4953
8.8875
.001424501
2,205.40
387,047.36
703
494,209
347,428,927
26.5141
8.8917
.001422475
2,208.54
388,150.84
704
495,616
348,913,664
26.5330
8.8959
.001420455
2,211.68
389,255.90
705
497,025
350,402,625
2G.5518
8.9001
.001418440
2,214.82
390,362.52
706
498,436
351,895,816
26.5707
8.9043
.001416431
2,217.96
391,470.72
707
499,849
353,393,243
26.5895
8.9085
.001414427
2,221.11
392,580.49
708
501,264
354,894,912
26.6083
8.9127
.001412429
2,224.25
393,691.82
709
502,681
356,400,829
26.6271
8.9169
.001410437
2,227.39
394,804.73
710
504,100
357,911,000
26.6458
8.9211
.001408451
2,230.53
395,919.21
711
505,521
359,425,431
26.6646
8.9253
.001406470
2,233.67
397,035.26
712
506,944
360,944,128
26.6833
8.9295
.001404494
2,236.81
398,152.89
713
508,369
362,467,097
2G.7021
8.9337
.001402525
2,239.96
399,272.08
714
509,796
363,994,344
26.7208
8.9378
.001400560
2,243.10
400,392.84
715
511,225
365,525,875
26.7395
8.9420
.001398601
2,246.24
401,515.18
716
512,656
367,061,696
26.7582
8.9462
.001396648
2,249.38
402,639.08
717
514,089
368,601,813
26.7769
8.9503
.001394700
2,252.52
403,764.56
718
515,524
370,146,232
26.7955
8.9545
.001392758
2,255.66
404,891.60
719
516,961
371,694,959
26.8142
8.9587
.001390821
2,258.81
406,020.22
720
518,400
373,248,000
26.8328
8.9628
.001388889
2,261.95
407,150.41
721
519,841
374,805,361
26.8514
8.9670
.001386963
2,265.09
408,282.17
722
521,284
376,367,048
26.8701
8.9711
.001385042
2,268.23
409,415.50
723
522,729
377,933,067
26.8887
8.9752
.001383126
2,271.37
410,550.40
724
524,176
379,503,424
26.9072
8.9794
.001381215
2,274.51
411,686.87
725
525,625
381,078,125
26.9258
8.9835
.001379310
2,277.65
412,824.91
726
527,076
382,657,176
26.9444
8.9876
.001377410
2,280.80
413,964.52
727
528,529
384,240,583
26.9629
8.9918
.001375516
2,283.94
415,105.71
728
529,984
385,828,352
26.9815
8.9959
.001373626 .
2,287.08
416,248.46
729
531,441
387,420,489
27.0000
9.0000
.001371742
2,290.22
417,392.79
730
532,900
389,017,000
27.0185
9.0041
.001369863
2,293.36
418,538.68
731
534,361
390,617,891
27.0370
9.0082
.001367989
2,296.50
419,686.15
732
535,824
392,223,168
27.0555
9.0123
.001366120
2,299.65
420,835.19
733
537,289
393,832,837
27.0740
9.0164
.001364256
2,302.79
421,985.79
734
538,756
395,446,904
27.0924
9.0205
.001362398
2,305.93
423,137.97
735
540,225
397,065,375
27.1109
9.0246
.001360544
2,309.07
424,291.72
736
54 J, 696
398,688,256
27.1293
9.0287
.001358696
2,312.21
425,447.04
737
543,169
400,315,553
27.1477
9.0328
.001356852
2,315.35
426,603.94
738
544,644
401,947,272
27.1662
9.03G9
.001355014
2,318.50
427,762.40
739
546,121
403,583,419
27.1846
9.0410
.001353180
2,321.64
428,922.43
740
547,600
405,224,000
27.2029
9.0450
.001351351
2,324.78
430,084.03
741
549,801
406,869,021
27.2213
9.0491
.001349528
2,327.92
431,247.21
742
550,564
408,518,488
27.2397
9.0532
.001347709
2,331.06
432,411.95
743
552,049
410,172,407
27.2580
9.0572
.001345895
2,334.20
433,578.27
744
553,536
411,830,784
27.2764
9.0613
.001344086
2,337.34
434,746.16
745
555,025
413,493,625
27.2947
9.0654
.001342282
2,340.49
435,915.62
746
556,516
415,160,936
27.3130
9.0694
.001340483
2,343.63
437,086.64
747
558,009
416,832,723
27.3313
9.0735
.001338688
2,346.77
438,259.24
748
559,504
418,508,992
27.3496
9.0775
.001336898
2,349.91
439,433.41
2fi
386
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Circfum.
Area
749
561,001
420,189,749
27.3679
9.0816
.001335113
2,353.05
440,609.16
750
562,500
421,875,000
27.3861
9.0856
.001333333
2,356.19
441,786.47
751
564,001
423,564,751
27.4044
9.0896
.001331558
2,359.34
442,965.35
752
565,504
425,259,008
27.4226
9.0937
.001329787
2,362.48
444,145.80
753
567,009
426,957,777
27.4408
9.0977
.001328021
2,365.62
445,327.83
754
568,516
428,661,064
27.4591
9.1017
.001326260
2,368.76
446,511.42
755
570,025
430,368,875
27.4773
9.1057
.001324503
2,371.90
447,696.59
756
571,536
432,081,216
27.4955
9.1098
.001322751
2,375.04
448,883.32
757
573,049
433,798,093
27.5136
9.1138
.001321004
2,378.19
450,071.63
758
574,564
435,519,512
27.5318
9.1178
.001319261
2,381.33
451,261.51
759
576,081
437,245,479
27.5500
9.1218
.001317523
2,384.47
452,452.96
760
577,600
438,976,000
27.5681
9.1258
.001315789
2,387.61
453,645.98
761
579,121
410,711,081
27.5862
9.1298
.001314060
2,390.75
454,840.57
762
580,644
442,450,728
27.6043
9.1338
.001312336
2,393.89
456,036.73
763
582,169
444,194,917
27.6225
9.1378
.001310616
2,397.04
457,234.46
764
583,696
445,943,744
27.6405
9.1418
.001308901
2,400.18
458,433.77
765
585,225
447,697,125
27.6586
9.1458
.001307190
2,403.32
459,634.64
766
586,756
449,455,096
27.6767
9.1498
.001305483
2,406.46
460,837.08
767
768
588,289
589,824
451,217,663
452,984,832
27.6948
27.7128
9.1537
9.1577
.001303781
.001302083
2,409.60
2,412.74
462,041.10
463,246.69
769
591,361
454,756,609
27.7308
9.1617
.001300390
2,415.88
464,453.84
770
-592,900
456,533,000
27.7489
9.1657
.001298701
2,419.03
465,662.57
771
594,441
458,314,011
27.7609
9.1696
.001297017
2,422.17
466,872.87
772
595,984
460,099,648
27.7849
9.1736
.001295337
2,425.31
468,084.74
773
597,529
461,889,917
27.8029
9.1775
.001293661
2,428.45
469,298.18
774
599,076
463,684,824
27.8209
9.1815
.001291990
2,431.59
470,513.19
775
600,625
465,484,375
27.8388
9.185*5
.001290323
2,434.73
471,729.77
776
602,176
467,288,576
27.8568
9.1894
.001288660
2,437.88
472,947.92
777
603,729
469,097,433
27.8747
9.1933
.001287001
2,441.02
474,167.65
778
605,284
470,910,952
27.8827
9.1973
.001285347
2,444.16
475,388.94
779
606,841
472,729,139
27.9106
9.2012
.001283697
2,447.30
476,611.81
780
608,400
474,552,000
27.9285
9.2052
.001282051
2,450.44
477,836.24
781
609,961
476,379,541
27.9464
9.2091
.001280410
2,453.58
479,062.25
782
611,524
478,211,768
27.9643
9.2130
.001278772
2,456.73
480,280.83
783
613,089
480,048,687
27 9821
9.2170
.001277139
2,459.87
481,518.97
784
614,656
481,890,304
28.0000
9.2209
.001275510
2,463.01
482,749.69
785
616,225
483,736,625
28.0179
9.2248
.001273885
2,466.15
483,081.98
786
617,796
485,587,656
28.0357
9.2287
.001272265
2,469.29
485,215.84
787
619,369
487,443,403
28.0535
9.2326
.001270648
2,472.43
486,451.28
788
620,944
489,303,872
28.0713
9.2365
.001269036
2,475.58
487,688.28
789
622,521
491,169,069
28.0891
9.2404
.001267427
2,478.72
488,926.85
790
624,100
493,039,000
28.1069
9.2443
.001265823
2,481.86
490,166.99
791
625,681
494,913,671
28.1247
9.2482
.001264223
2,485.00
491,408.71
792
627,264
496,793,088
28.1425
9.2521
.001262626
2,488.14
492,651.99
793
628,849
498,677,257
28.1603
9.2560
.001261034
2,491.28
493,896.85
794
630,436
500,566,184
28.1780
9.2599
.001259446
2,494.42
495,143.28
795
632,025
502,459,875
28.1957
9.2638
.001257862
2,497.57
496,391.27
796
633,616
504,358,336
28.2135
9.2677
.001256281
2,500.71
497,640.84
797
635,209
506,261,573
28.2312
9.2716
.001254705
2,503.85
498,891.98
798
636,804
508,169,592
28.2489
9.2754
.001253133
2,506.99
500,144.69
799
638,401
510,082,399
28.2666
9.2793
.001251364
2,510.13
501,398.97
800
640,000
512,000,000
28.2843
9.2832
.001250000
2,513.27
502,654.82
801
641,601
513,922,401
28.3019
9.2870
.001248439
2,516.42
503,912.25
802
643,204
515,849,608
28.3196
9.2909
.001246883
2,519.56
505,171.24
803
644,809
517,781,627
28.3373
9.2948
.001245330
2,522.70
506,431.80
804
646,416
519,718,464
28.3549
9.2986
.001243781
2,525.84
507,693.94
805
648,025
521,660,125
28.3725
9.3025
.001242236
2,528.98
508,957.64
806
649,636
523,606,616
28.3901
9.3063
.001240695
2,532.12
510,222.92
807
651,249
525,557,943
28.4077
9.3102
.001239157
2,535.27
511,489.77
808
652,864
527,514,112
28.4253
9.3140
.001237624
2,538.41
512,758.19
809
654,481
529,475,129
28.4429
9.3179
.001236094
2,541.55
514,028.18
810
656,100
531,441,000
28.4605
9.3217
.001234568
2,544.69
515,299.74
811
657,721
533,411,731
28.4781
9.3255
.001233046
2,547.83
516,572.87
SQUARES, CUBES, ROOTS, ETC.
387
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Clrcum.
Area
812
659,344
535,387,328
28.4956
9.3294
.001231527
2,550.97
517,847.57
813
660,969
537,367,797
28.5132
9.3332
.001230012
2,554.11
519,123.84
814
662,596
539,353,144
28.5307
9.3370
.001228501
2,557.26
520,401.68
815
r,t;i,225
541,343,375
28.5482
9.3408
.001226994
2,560.40
521,681.10
816
665,856
543,338,496
28.5657
9.3447
.001225490
2,563.54
522,962.08
817
667,489
545,338,513
28.5832
9.3485
.001223990
2,566.68
524,244.63
818
669,124
547,343,432
28.6007
9.3523
.001222494
2,569.82
525,528.76
819
670,761
549,353,259
28.6182
9.3561
.001221001
2,572.96
526,814.46
820
672,400
551,368,000
28.6356
9.3599
.001219512
2,576.11
528,101.73
821
674,041
553,387,661
28.6531
9.3637
.001218027
2,579.25
529,390.56
822
675,584
555,412,248
28.6705
9.3675
.001216545
2,582.39
530,680.97
823
677,329
557,441,767
28.6880
9.3713
.001215067
2,585.53
531,972.95
824
678,976
559,476,224
28.7054
9.3751
.001213592
2,588.67
533,266.50
825
680,625
561,515,625
28.7228
9.3789
.001212121
2,591.81
534,561.62
826
682! 276
563,559,976
28.7402
9.3827
.001210654
2,594.96
535,858.32
827
683,929
565,609,283
28.7576
9.3865
.001209190
2,598.10
537,156.58
828
685,584
567,663,552
28.7750
93902
.001207729
2,601.24
538,456.41
829
687,241
569,722,789
28.7924
9.3940
.001206273
2,604.38
539,757.82
830
688,900
571,787,000
28.8097
9.3978
.001204819
2,607.52
541,060.79
831
690,561
573,856,191
28.8271
9.4016
.001203369
2,610.66
542,365.34
832
692,224
575,930,368
28.8444
9.4053
.001201923
2,613.81
543,671.46
833
693,889
578,009,537
28.8617
9.4091
.001200480
2,616.95
544,979.15
834
695,556
580,093,704
28.8791
9.4129
.001199041
2,620.09
546,288.40
835
697,225
582,182,875
28.8964
9.4166
.001197605
2,623.23
547,599.23
836
698,896
584,277,056
28.9137
9.4204
.001196172
2,626.37
548,911.63
837
700,569
586,376,253
28.9310
9.4241
.001194743
2,629.51
550,225.61
838
702,244
588,480,472
28.9482
9.4279
.001193317
2,632.65
551,541.15
839
703,921
590,589,719
28.9655
9.4316
.001191895
2,635.80
552,858.26
840
705,600
592,704,000
28.9828
9.4354
.001190476
2,638.94
554,176.94
841
707,281
594,823,321
29.0000
9.4391
.001189061
2,642.08
555,497.20
842
708,964
596,947,688
29.0172
9.4429
.001187648
2,645.22
556,819.02
843
710,649
599,077,107
29.0345
9.4466
.001186240
2,648.36
558,142.42
344
712,336
601,211,584
29.0517
9.4503
.001184834
2,651.50
559,467.39
845
714,025
603,351,125
29.0689
9.4541
.001183432
2,654.65
560,793.92
846
715,716
605,495,736
29.0861
9.4578
.001182033
2,657.79
562,122.03
847
717,409
607,645,423
29.1033
9.4615
.001180638
2,660.93
563,451.71
848
719,104
609,800,192
29.1204
9.4652
.001179245
2,664.07
564,782.96
849
720,801
611,960,049
29.1376
9.4690
.001177856
2,667.21
566,115.78
850
722,500
614,125,000
29.1548
9.4727
.001176471
2,670.35
507,450.17
851
724,201
616,295,051
29.1719
9.4764
.001175088
2,673.50
508,786.14
852
725,904
618,470,208
29.1890
9.4801
.001173709
2,676.64
570,123.67
853
727,609
620,650,477
29.2062
9.4838
.001172333
2,679.78
571,462.77
854
729,316
622,835,864
29.2233
9.4875
.001170960
2,682.92
572,803.45
855
731,025
625,026,375
29.2404
9.4912
.001169591
2,686.06
574,145.69
856
732,736
627,222,016
29.2575
9.4949
.001168224
2,689.20
575,489.51
857
734,449
629,422,793
29.2746
9.4986
.001166861
2,692.34
576,834.90
858
736,164
631,628,712
29.2916
9.5023
.001165501
2,695.49
578,181.85
859
737,881
633,839,779
29.3087
9.5060
.001164144
2,698.63
579,530.38
860
739,600
636,056,000
29.3258
9.5097
.001162791
2,701.77
580,880.48
861
741,321
638,277,381
29.3428
9.5135
.001161440
2,704.91
582,232.15
862
743,044
640,503,928
29.3598
9.5171
.001160093
2,708.05
583,585.39
863
744,769
642,735,647
29.3769
9.5207
.001158749
2,711.19
584,940.20
864
746,496
644,972,544
29.3939
9.5244
.001157407
2,714.34
586,296.59
865
748,225
647,214,625
29.4109
9.5281
.001156069
2,717.48
587,654.54
866
749,956
649,461,896
29.4279
9.5317
.001154734
2,720.62
589,014.07
867
751,689
651,714,363
29.4449
9.5354
.001153403
2,723.76
590,375.16
868
753,424
653,972,032
29.4C18
9.5391
.001152074
2,726.90
591,737.83
869
755,161
656.234,909
29.4788
9.5427
.001150748
2,730.04
593,102.06
870
756,900
658,503,000
29.4958
9.5464
.001149425
2,733.19
594,467.87
871
758,641
660,776,311
29.5127
9.5501
.001148106
2,736.33
595,835.25
872
760,384
663,054,848
29.5296
9.5537
.001146789
2,739.47
597,204.20
873
762,129
665,338,617
29.5466
9.5574
.001145475
2,742.61
598,574.72
874
763,876
667,627,624
29.5635
9.5610
.001144165
2,745.75
599,946.81
388
MINE GASES AND VENTILATION
No.
Square
Cube
Sq. Boot
Cu. Boot
Reciprocal
_
Area
875
765,625
'669,921,875
29.5804
9.5647
.001142857
2,748.89
601,320.47
876
767,376
672,221,376
29.5973
9.5683
.001141553
2,752.04
602,695.70
877
769,129
674,526,133
29.6142
9.5719
.001140251
2,755.18
604,072.50
878
770,884
676,836,152
29.6311
9.5756
.001138952
2,758.32
605,450.88
879
772,641
679,151,439
29.6479
9.5792
.001137656
2,761.46
606,830.82
880
774,400
681,472,000
29.6648
9.5828
.001136364
2,764.60
608,212.34
881
776,161
683,797.841
29.6816
9.5865
.001135074
2,767.74
609,595.42
882
777,924
686,128,968
29.6985
9.5901
.001133787
2,770.88
610,980.08
883
779,689
688,465,387
29.7153
9.5937
.001132503
2,774.03
612,366.31
884
781,456
690,807,104
29.7321
9.5973
.001131222
2,777.17
613,754.11
885
783,225
693,154,125
29.7489
9.6010
.001129944
2,780.31
615,143.48
886
784,996
695,506,456
29.7658
9.6046
.001128668
2,783.45
616,534.42
887
786,769
697,864,103
29.7825
9.6082
.001127396
2,786.59
617,926.93
888
788,544
700,227,072
29.7993
9.6118
.001126126
2,789.73
619,321.01
889
790,321
702,595,369
29.8161
9.6154
.001124859
2,792.88
620,716.66
890
792,100
704,969,000
29.8329
9.6190
.001123596
2,796.02
622,113.89
891
793,881
707,347,971
29.8496
9.6226
.001122334
2,799.16
623,512.68
892
795,664
707,932,288
29.8664
9.6262
.001121076
2,802.30
624,913.04
893
797,449
712,121,957
29.8831
9.6298
.001119821
2,805.44
626,314.98
894
799,236
714,516,984
29.8998
9.6334
.001118568
2,808.58
627,718.49
895
801,025
716,917,375
29.9166
9.6370
.001117818
2,811.73
629,123.56
896
802,816
719,323,136
29.9333
9.6406
.001116071
2,814.87
630,530.21
897
804,609
721,734,273
29.9500
9.6442
.001114827
2,818.01
631,938.43
898
806,404
724,150,792
29.9666
9.6477
.001113586
2,821.15
633,348.22
899
808,201
726,572,699
29.9833
9.6513
.001112347
2,824.29
634,759.58
900
810,000
729,000,000
30.0000
9.6549
.001111111
2,827.43
636,172.51
901
811,801
731,432,701
30.0167
9.6585
.001109878
2,830.58
637,587.01
902
813,604
733,870,808
30.0333
9.6620
.001108647
2,833.72
639,003.09
903
815,409
736,314,327
30.0500
9.6656
.001107420
2,836.86
640,420.73
904
817,216
738,763,264
30.0666
9.6692
.001106195
2,840.00
641,839.95
905
819,025
741,217,625
30.0832
9.6727
.001104972
2,843.14
643,260.73
906
820,836
743,677,416
30.0998
9.6763
.001103753
2,846.28
644,683.09
907
822,649
746,142,643
30.1164
9.6799
.001102536
2,849.42
646,107.01
908
824,464
748,613,312
30.1330
9.6834
.001101322
2,852.57
647,532.51
909
826,281
751,089,429
30.1496
9.6870
.001100110
2,855.71
648,959.58
910
828,100
753,571,000
30.1662
9.6905
.001098901
2,858.85
650,388.22
911
829,921
756,058,031
30.1828
9.6941
.001091695
2,861.99
651,818.43
912
831,744
758,550,825
30.1993
9.6976
.001096491
2,865.13
653,250.21
913
833,569
761,048,497
30.2159
9.7012
.001095290
2,868.27
654,683.56
914
835,396
763,551,944
30.2324
9.7047
.001094092
2,871.42
656,118.48
915
837,225
766,060,875
80.2490
9.7082
.001092896
2,874.56
657,554.98
916
839,056
768,575,296
30.2655
9.7118
.001091703
2,877.70
658,993.04
917
840,889
771,095,213
30.2820
9.7153
.001090513
2,880.84
660,432.68
918
842,724
773,620,632
30.2985
9.7188
.001089325
2,883.98
661,873.88
919
844,561
776,151,559
30.3150
9.7224
.001088139
2.887.12
663,316.66
920
846,400
778,688,000
30.3315
9.7259
.001086957
2,890.27
664,761.01
921
848,241
781,229,961
30.3480
9.7294
.001085776
2,893.41
666,206.92
922
850,084
783,777,448
30.3645
9.7329
.001084599
2,896.55
667,654.41
923
851,929
786,330,467
30.3809
9.7364
.001083423
2,899.69
669,103.47
924
853,776
788,889,024
30.3974
9.7400
.001082251
2,902.83
670,554.10
925
855,625
791,453,125
30.4138
9.7435
.001081081
2,905.97
672,006.30
926
857,476
794,022,776
30.4302
9.7470
.001079914
2,909.11
673,460.08
927
859,329
796,597,983
30.4467
9.7505
.001078749
2,912.26
674,915.42
928
861,184
799,178,752
30.4631
9.7540
.001077586
2,915.40
676,372.33
929
863,041
801,765,089
30.4795
9.7575
.001076426
2,918.54
677,830.82
930
864,900
804,357,000
30.4959
9.7610
.001075269
2,921.68
679,290.87
931
866,761
806,954,491
30.5123
9.7645
.001074114
2,924.82
680,752.50
932
868,624
809,557,568
30.5287
9.7680
.001072961
2,927.96
682,215.69
933
870,489
812,166,237
30.5450
9.7715
.001071811
2,931.11
683,680.46
934
872,356
814,780,504
30.5614
9.7750
.001070664
2,934.25
685,146.80
935
874,225
817,400,375
30.5778
9.7785
.001069519
2,937.39
686,614.71
936
876,096
820,025,856
30.5941
9.7829
.001068376
2,940.53
688,084.19
937
877,969
822,656,953
30.6105
9.7854
.001067236
2,943.67
689,555.24
SQUARES, CUBES, ROOTS, ETC.
389
No.
Square
Cube
Sq. Root
Cu. Root
Reciprocal
Clrcom.
Area
938
879,844
825,293,672
30.6268
9.7889
.001066098
2,946.81
691,027.86
939
881,721
827,936,019
30.6431
9.7924
.001064963
2,949.96
692,502.05
940
883,600
830,584,000
30.6594
9.7959
.001063830
2,953.10
693,977.82
941
885,481
833,237,621
30.6757
9.7993
.001062699
2,956.24
695,455.15
942
887,364
835,896,888
30.6920
9.8028
.001061571
2,959.38
696,934.06
943
889,249
838,561,807
30.7083
9.8063
.001060445
2,962.52
698,414.53
944
891,136
841,232,384
30.7246
9.8097
.001059322
2,965.66
699,896.58
945
893,025
843,908,625
30.7409
9.8132
.001058201
2,968.81
701,380.19
946
894,916
846,590,536
30.7571
9.8167
.001057082
2,971.95
702,865.38
947
896,808
849,278,128
30.7734
9.8201
.001055966
2,975.09
704,352.14
948
8US.704
851,971,392
30.7896
9.8236
.001054852
2,978.23
705,840.47
949
900,601
854,670,349
30.8058
9.8270
.001053741
2,981.37
707,330.37
950
902,500
857,375,000
30.8221
9.8305
.001052632
2,984.51
708,821.84
951
904,401
860,085,351
:;o.s:;s;;
9.8339
.001051525
2,987.65
710,314.88
952
906,304
862,801,408
30.8545
9.8374
.001050420
2,990.80
711,809.50
953
908,209
865,523,177
30.8707
9.8408
.001049318
2,993.94
713,305.68
954
910,116
868,250,664
30.8869
9.8443
.001048218
2,997.08
714,803.43
955
912,025
870,983,875
30.9031
9.8477
.001047120
3,000.22
716,302.76
956
913,936
873,722,816
30.9192
9.8511
.001046025
3,003.36
717,803.66
957
915,849
876,467,493
30.9354
9.8546
.001044932
3,006.50
719,306.12
958
917,764
879,217,912
30.9516
9.8580
.001043841
3,009.65
720,810.16
959
919,681
881,974,079
30.9677
9.8614
.001042753
3,012.79
722,315.77
960
921,600
884,736,000
30.9839
9.8648
.001041667
3,015.93
723,822.95
961
923,521
887,503,681
31.0000
9.8683
.001040583
3,019.07
725,331.70
962
925,444
890,277,128
31.0161
9.8717
.001039501
3,022.21
726,842.02
963
927,369
893,056,347
31.0322
9.8751
.001038422
3,025.35
728,353.91
964
929,296
895,841,344
31.0483
9.8785
.001037344
3,028.50
729,867.37
965
931,225
898,632,125
31.0644
9.8819
.001036269
3,031.64
731,382.40
966
933,156
901,428,696
31.0805
9.8854
.001035197
3,034.78
732,899.01
967
935,089
904,231,063
31.0966
9.8888
.001034126
3,037.92
734,417.18
968
937,024
907,039,232
31.1127
9.8922
.001033058
3,041.06
735,936.93
969
938,961
909,853,209
31.1288
9.8956
.001031992
3,044.20
737,458.24
970
940,900
912,673,000
31.1448
9.8990
.001030928
3,047.34
738,981.13
971
942,841
915,498,611
31.1609
9.9024
.001029866
3,050.49
740,505.59
972
944,784
918,330,048
31.1769
9.9058
.001028807
3,053.63
742,031.62
973
946,729
921,167,317
31.1929
9.9092
.001027749
3,056.77
743,559.22
974
948,676
924,010,424
31.2090
9.9126
.001026694
3,059.91
745,088.39
975
950,625
926,859,375
31.2250
9.9160
.001025641
3,063.05
746,619.13
976
952,576
929,714,176
31.2410
9.9194
.001024590
3,066.19
748,151.44
977
954,529
932,574,833
31.2570
9.9228
.001023541
3,069.34
749,685.32
978
956,484
935,441,352
31.2730
9.9261
.001022495
3,072.48
751,220.78
979
958,441
938,313,739
31.2890
9.9295
.001021450
3,075.62
752,757.80
980
960,400
941,192,000
31.3050
9.9329
.001020408
3,078.76
754,296.40
981
962,361
944,076,141
31.3209
9.9363
.001019168
3,081.90
755,836.56
982
964,324
946,966,168
31.3369
9.9396
.001018330
3,085.04
757,378.30
983
966,289
949.862,087
31.3528
9.9430
.001017294
3,088.19
758,921.61
984
968,256
952,763,904
31.3698
9.9464
.001016260
3,091.33
760,466.48
985
970,225
955,671,625
31.3847
9.9497
.001015228
3,094.47
762,012.93
986
972,196
958,585,256
31.4006
9.9531
.001014199
3,097.61
763,560.95
987
974,169
961,504,803
31.4166
9.9565
.001013171
3,100.75
765,110.54
988
976,144
964,430,272
31.4325
9.9598
.001012146
3,103.89
766,661.70
989
978,121
967,361,669
31.4484
9.9632
.001011122
3,107.04
768,214.44
990
980,100
970,299,000
31.4643
9.9666
.001010101
3,110.18
769,768.74
991
982,081
973,242,271
31.4802
9.9699
.001009082
3,113.32
771,324.61
992
984,064
976,191,488
31.4960
9.9733
.001008065
3,116.46
772,882.06
993
986,049
979,146,657
31.5119
9.9766
.001007049
3,119.60
774,441.07
994
988,036
982,107,784
31.5278
9.9800
.001006036
3,122.74
776,001.66
995
990,025
985,074,875
31.5436
9.9833
.001005025
3,125.88
777,563.82
996
992,016
988,047,936
31.5595
9.9866
.001004016
3,129.03
779,127.54
997
994,009
991,026,973
31.5753
9.9900
.001003009
3,132.17
780,692.84
998
996,004
994,011,992
31.5911
9.9933
.001002004
3,135.31
782,259.71
999
998,001
997,002,999
31.6070
9.9967
.001001001
3,138.45
783,828.15
1000
1,000,000
1,000,000,000
31.6228
10.0000
.001000000
3,141.59
785,398.16
CIRCUMFERENCES AND AREAS OF CIRCLES
391
392
MINE GASES AND VENTILATION
CIRCUMFERENCES AND AREAS OF CIRCLES FROM 1-64 to 100
Diam.
Circum.
Area
Diam.
Circum.
Area
Diam.
Circum.
Area
A
.0491
.0002
6
18.8496
28.2744
13}
41.2335
135.297
JL
.0982
.0008
6}
19.2423
29.4648
13}
41.6262
137.887
A
.1963
.0031
4
19.6350
30.6797
181
42.0189
140.501
i
.3927
.0123
6f
20.0277
31.9191
m
42.4116
143.139
JL
.5890
.0276
6*
20.4204
33.1831
13£
42.8043
145.802
1
.7854
.0491
6|
20.8131
31.4717
13}
43.1970
148.490
JL
.9817
.0767
6*
21.2058
35.7848
13|
43.5897
151.202
i
1.1781
.1104
61
21.5985
37.1224
14
43.9824
153.938
™
1.3744
.1503
7
21.9912
38.4846
14}
44.3751
156.700
i
1.5708
.1963
7}
22.3839
39.8713
14}
44.7678
159.485
A
1.7671
.2485
7}
22.7766
41.2826
14f
45.1605
162.296
i
1.9635
.3068
7i
23.1693
42.7184
14|
45.5532
165.130
A
2.1598
.3712
74
23.5620
44.1787
14|
45.9459
167.990
2.3562
.4418
71
23.9547
45.6636
14|
46.3386
170.874
ii
2.5525
.5185
7*
24.3474
47.1731
141
46.7313
173.782
i
2.7489
.6013
7|
24.7401
48.7071
15
47.1240
176.715
16
2.9452
.6903
8
25.1328
50.2656
15}
47.5167
179.673
1
3.1416
.7854
8*
25.5255
51.8487
15j
47.9094
182.655
If
3.5343
.9940
3
25.9182
53.4563
• 15|
48.3021
185.661
1}
3.9270
1.2272
8*
26,3109
55.0884
15*
48.C948
188.692
if
4.3197
1.4849
8*
26.7036
56.7451
15|
49.0875
•191.748
l{
4.7124
1.7671
81
27.0963
58.4264
15}
49.4802
194.828
1*
5.1051
2.0739
82
27.4890
60.1322
151
49.8729
197.933
1}
5.4978
2.4053
81
27.8817
61.8625
16
50.2056
201.062
1*
5.8905
2.7612
9
28.2744
63.6174
16}
50.6583
204.216
2
6.2832
3.1416
9j
28.6671
65.3968
16}
51.0510
207.395
2|
6.6759
3.5466
9?
29.0598
67.2008
16f
51.4437
210.598
2}
7.0686
3.9761
9i
29.4525
69.0293
16£
51.8364
213.825
2*
7.4613
4.4301
9i
29.8452
70.8823
16|
52.2291
217.077
3
7.8540
4.9087
91
30.2379
72.7599
16}
52.6218
220.354
2*
8.2467
5.4119
9i
30.6306
74.6621
161
53.0145
223.655
2*
8.6394
5.9396
9*
31.0233
76.589
17
53.4072
226.981
2*
9.0321
6.4918
10
31.4160
78.540
17*
53.7999
230.331
3
9.4248
7.0686
10*
31.8087
80.516
17}
54.1926
233.706
1
3|
9.8175
10.2102
10.6029
7.6699
8.2058
8.9462
10}.
a
32.2014
32.5941
32.9868
82.516
84.541
86.590
1
54.5853
54.9780
55.3707
237.105
240.529
243.977
9
10.9956
9.6211
10|
33.3795
88.664
17}
55.7634
247.450
3|
11.3883
10.3206
101
33.7722
90.763
171
56.1561
250.948
3*
11.7810
11.0447
loj
34.1649
92.886
18
56.5488
254.470
3*
12.1737
11.7933
11
34.5576
95.033
18*
56.9415
258.016
4
12.5664
12.5664
1H
34.9503
97.205
18}
57.3342
261.587
4«
12.9591
13.3641
111
35.3430
99.402
18|
57.7269
265.183
4^
13.3518
14.1863
Hf
35.7357
101.623
18*
58.1196
268.803
4*
13.7445
15.0330
11*
36.1284
103.869
181
58.5123
272.448
4
14.1372
15.9043
HI
36.5211
106.139
18}
58.9050
276.117
4|
14.5299
16.8002
11}
36.9138
108.434
181
59.2977
279.811
4|
14.9226
17.7206
111
37.3065
110.754
19
59.6904
283.529
4f
15.3153
18.6555
12
37.6992
113.098
19}
60.0831
287.272
5
15.7080
19.6350
12*
38.0919
115.466
19}
60.4758
291.040
5r
16.1007
20.6290
12!
38.4846
117.859
19£
60.8685
294.832
5}
16.4934
21.6476
12f
38.8773
120.277
19>-
61.2612
298-648
5
16.8861
22.6907
12*
39.2700
122.719
19|
61.6539
302.489
b,
17.2788
23.7583
12f
39.6627
125.185
19}
62.0466
306.355
5i
17.6715
24.8505
40.0554
127.677
191
62.4393
310.245
5;
18.0642
25.9673
12-
40.4481
130.192
20
62.8320
314.160
5*
18.4569
27.1086
13
40.8408
132.733
20}
63.2247
318.099
CIRCUMFERENCES AND AREAS OF CIRCLES 393
Diam.
Circum.
Area
Diam.
Circum.
Area
Diam.
Circum.
Area
20}
63.6174
322.063
28*
88.3575
621.264
36
113.098
1,017.878
201
64.0101
326.051
28;
88.7502
626.798
3Q1
113.490
1,024.960
20*
64.4028
330.064
28j
89.1429
632.357
36-
113.883
1,032.065
20|
64.7955
334.102
28j-
89.5356
637.941
361
114.276
1,039.195
20*
65.1882
338.164
28 J
89.9283
013.549
36*
114.668
1,046.349
20*
65.5809
342.250
28*
90.3210
649.182
36|
115.061
1,053.528
21
65.9736
346.361
28*
90.7137
654.840
36*
115.454
1,060.732
66.3663
350.497
29
91.1064
660.521
36*
115.846
1,067.960
21-
66.7590
354.657
29}
91.4991
6G6.228
37
116.239
1,075.213
21 1
67.1517
358.842
29!
91.8918
671.959
37}
116.632
1,082.490
21*
67.5444
363.051
291
92.2845
677.714
37!
117.025
1,089.792
67.9371
367.285
29*
92.6772
683.494
37f
117.417
1,097.118
21*
68.3298
371.543
29|
93.0699
689.299
37*
117.810
1,104.469
21*
68.7225
375.826
29*
93.4626
695.128
118.203
1,111.844
22
69.1152
380.134
29*
93.8553
700.982
37|
118.595
1,119.244
T>\
69.5079
384.4G6
30
94.2480
706.860
37*
118.988
1,126.669
22|
69.9006
388.822
30}
94.6407
712.763
38
119.381
1,134.118
22|
70.2933
393.203
30}
95.0334
718.690
38i
119.773
1,141.591
70.68GO
397.609
30|
95.4261
724.642
38!
120.1G6
1,149.089
22 1
71.0787
402.038
30*
95.8188
730.618
381
120.559
1,156.612
22*
71.4714
406.494
30|
96.2115
736.619
38*
120.952
1,164.159
22*
71.8641
410.973
30*
96.6042
742.645
38|
121.344
1,171.731
23
72.2568
415.477
30*
96.9969
748.695
38*
121.737
1,179.327
23}
72.6495
•420.004
31
97.3896
754.769
38*
122.130
1,186.948
23!
73.0422
424.558
31}
97.7823
760.869
39
122.522
1,194.593
23|
73.4349
429.135
31}
98.1750
766.992
39}
122.915
1,202.263
23*
73.8276
433.737
311
98.5677
773.140
39!
123.308
1,209.958
23|
74.2203
438.364
31*
98.9604
779.313
391
123.700
1,217.677
23*
74.6130
443.015
31 1
99.3531
785.510
39*
124.093
1,225.420
23*
75.0057
447.690
31*
99.7458
791.732
89*
124.486
1,233.188
24
75.3984
452.390
31*
100.1385
797.979
39*
124.879
1,240.981
241
75.7911
457.115
32
100.5312
804.250
39*
125.271
1,248.798
76.1838
461.864
32}
100.9239
810.545
40
125.664
1,256.640
24|
24*
76.5765
76.9692
466.638
471.436
32}
32|
101.3166
101.7093
816.865
823.210
40i
40}
126.057
126.449
1,264.510
1,272.400
24f
77.3619
476.259
32*
102.1020
829.579
401
126.842
1,280.310
24*
77.7546
481.107
32|
102.4947
835.972
40*
127.235
1,288.250
24*
78.1473
485.979
32*
102.8874
842.391
40|
127.627
1,296.220
25
78.5400
490.875
32*
103.280
848.833
40*
128.020
1,304.210
25}
78.9327
495.796
33
103.673
855.301
40*
128.413
1,312.220
25|
79.3254
500.742
33}
104.065
861.792
41
128.806
1,320.260
25|
79.7181
505.712
33}
104.458
8G8.309
41*
129.198
1,328.320
25*
80.1108
510.706
33|
104.851
874.850
41-1
129.591
1,336.410
25|
80.5035
515.726
33*
105.244
881.415
41 *
129.984
1,344.520
25*
80.8962
520.769
331
105.636
888.005
41*
130.376
1,352.660
25*
81.2889
525.838
33*
106.029
894.620
41*
130.769
1,360.820
26
81.6816
530.930
33*
106.422
901.259
41*
131.162
1,369.000
2Gi
82.0743
536.048
34
106.814
907.922
41*
131.554
1,377.210
26}
82.4670
541.190
34}
107.207
914.611
42
131.947
1J385.450
2C|
82.8597
546.356
34}
107.600
921.323
42}
132.340
1,393.700
26*
83.2524
551.547
3-1*
107.992
928.061
42!
132.733
1,401.990
26|
83.6451
556.763
34*
108.385
934.822
421
133.125
1,410.300
26*
84.0378
5G2.003
34|
108.778
941.609
42*
133.518
1,418.630
26*
84.4305
567.2G7
34*
109.171
948.420
42*
133.911
1,426.990
27
84.8232
572.557
34*
109.563
955.255
42*
134.303
1,435.370
27i
85.2159
577.870
35
109.956
962.115
42*
134.696
1,443.770
27}
85.6086
583.209
35|
110.349
969.000
43
135.089
1,452.200
27f
86.0013
588.571
110.741
975.909
431
135.481
1,460.660
27*
86.3940
593.959
35|
111.134
982.842
135.874
1,469.140
27f
86.7867
599.371
35*
111.527
989.800
431
136.267
1,477.640
27*
87.1794
604.807
35*
111.919
996.783
43*
136.660
1,486.170
27*
87.5721
610.208
35*
112.312
1,003.790
43*
137.052
1,494.730
28
87.9648
615.754
35*
112.705
1,010.822
43*
137.445
1,503.300
394
MINE GASES AND VENTILATION
Diam.
Circum
Area
Diam
Circum
Area
Diam
Circum
Area
43}
137.838
1,511.910
511
162.578
2,103.35
59f
187.318
2,792.21
44
138.230
1,520.530
51}
162.970
2,113.52
59?
187.711
2,803.93
44i
138.623
1,529.190
52
163.363
2,123.72
591
188.103
2,815.67
44}
139.016
1,537.860
52}
163.756
2,133.94
60
188.496
2,827.44
44f
139.408
1,546.56
52}
164.149
2,144.19
60}
188.889
2,839.23
44}
139.801
1,555.29
52|
164.541
2,154.46
60}
189.281
2,851.05
44|
140.194
1,564.04
52i
164.934
2,164.76
60|
189.674
2,862.89
44?
140.587
1,572.81
52*
165.327
2,175.08
60}
190.067
2,874.76
44}
140.979
1,581.61
52?
165.719
2,185.42
60|
190.459
2,886.65
45
141.372
1,590.43
521
166.112
2,195.79
60?
190.852
2,898.57
45i
141.7G5
1,599.28
53
166.505
2,206.19
601
191.245
2,910.51
45|
142.157
1,608.16
53}
166.897
2,216.61
61
191.638
2,922.47
45|
142.550
1,617.05
53*
167.290
2,227.05
61}
192.030
2,934.46
45}
142.943
1,625.97
53f
167.683
2,237.52
6l|
192.423
2,946.48
45|
143.335
1,634.92
53}
168.076
2,248.01
61J
192.816
2,958.52
45|
143.728
1,643.89
168.468
2,258.53
61}
193.208
2,970.58
45}
144.121
1,652.89
53?
168.861
2,269.07
61|
193.601
2,982.67
46
144.514
1,661.91
53}
169.254
2,279.64
61?
193.994
2,994.78
46}
144.906
1,670.95
54
169.646
2,290.23
611
194.386
3,006.92
46}
145.299
1,680.02
54}
170.039
2,300.84
62
194.779
3,019.08
46f
145.692
1,689.11
54}
170.432
2,311.48
62}
195.172
8,031.26
46}
146.084
1,698.23
54|
170.824
2,322.15
62}
195.565
3,043.47
46|
146.477
1,707.37
54}
171.217
2,332.83
62f
195.957
3,055.71
46|
146.870
1,716.54
54|
171.610
2,343.55
62}
196.350
3,067.97
46}
147.262
1,725.73
54?
172.003
2,354.29
62|
196.743
3,080.25
47
147.655
1,734.95
54}
172.395
2,365.05
62?
197.135
3,092.56
47}
148.048
1,744.19
55
172.788
2,375.83
621
197.528
3,104.89
47J
148.441
1,753.45
55}
173.181
2,386.65
63
197.921
3,117.25
47f
148.833
1,762.74
55}
173.573
2,397.48
63}
198.313
3,129.64
47|
149.226
1,772.06
55f
173.966
2,408.34
63}
198.706
3,142.04
47|
149.619
1,781.40
55}
174.359
2,419.23
63f
199.099
3.154.47
47?
150.011
1,790.70
55|
174.751
2,430.14
63}
199.492
3,166.93
47i
150.404
1,800.15
55?
175.144
2,441.07
63|
199.884
3,179.41
48
150.797
1,8C9.56
55^
175.537
2,452.03
63?
200.277
3.191.91
48}
151.189
1,819.00
56
175.930
2,463.01
63}
200.670
3,204.44
48}
151.582
1,828.46
56}
176.322
2,474.02
64
201.062
3,217.00
48f
151.975
1,837.95
56}
176.715
2,485.05
64}
201.455
3,229.58
48}
152.368
1,847.46
56f
177.108
2,496.11
64*
201.848
3,242.18
48|
152.760
1,856.99
56}
177.500
2,507.19
64|
202.240
3,254.81
481
153.153
1,866.55
177.893
2,518.30
64|
202.633
3,267.46
48|
153.546
1,876.14
56?
178.286
2,529.43
64|
203.026
3,280.14
49
153.938
1,885.75
561
178.678
2,540.58
64?
203.419
3,292.84
49}
154.331
1,895.38
57
179.071
2,551.76
64}
203.811
3,305.56
49|
154.724
1,905.04
.57}
179.464
2,562.97
65
204.204
3,318.31
49f
155.116
1,914.72
57}
179.857
2,574.20
65^
204.597
3,331.09
49}
155.509
1,924.43
57|
180.249
2,585.45
65J
204.989
3,343.89
49|
155.902
1,934.16
57}
180.642
2,596.73
65f
205.382
3,356.71
49?
156.295
1,943.91
57$
181.035
2,608.03
65}
205.775
3.369.56
49i
156.687
1,953.69
57*
181.427
2,619.36
65|
206.167
3;382.44
50
157.080
1,963.50
571
181.820
"630.71
65?
206.560
3,395.33
50}
157.473
1,973.33
58
182.213
2,63.09
65}
206 953
3,408.26
50|
157.865
1,983.18
58-
182.605
2,653.49
66
207.346
3,421.20
50|
158.258
1,993.06
58*
182.998
2,664.91
66^
207.738
3,434.17
50}
158.651
2,002.97
58|
183.391
2,676.36
66|
208.131
3,447.17
50|
159.043
2,012.89
58j
183.784
2,687.84
66|
208.524
3,460.19
50|
159.436
2,022.85
58|
184.176
2,699.33
66}
208.916
3,473.24
50}
159.829
2,032.82
58?
184.569
2,710.86
66f
209.309
3,486.30
51
160.222
2,042.83
581
184.962
2,722.41
66?
209.702
3,499.40
61*
160.614
2,052.85
59
185.354
2,733.98
66}
210.094
3,512.52
5l|
161.007
2,062.90
59}
185.747
2,745.57
67
210.487
3,525.66
51f
161.400
2,072.98
59|
186.140
2,757.20
67}
210.880
3,538.83
51}
161.792
2,083.08
59J
186.532
2,768.84
67}
211.273
3,552.02
51*
162.185
2,093.20
59}
186.925
2,780.51
671
211.665
3,565.24
CIRCUMFERENCES AND AREAS OF CIRCLES 395
Diam.
Circum.
Area
Diam.
Circum.
Area
Diam.
Circum.
Area
67*
212.058
3,578.48
75|
236.798
4,462.16
83}
261.538
5,443.26
67J
212.451
3,591.74
237.191
4,476.98
83}
261.931
5,459.62
67*
212.843
3,605.04
75|
237.583
4,491.81
83L
262.324
6,476.01
67}
213.236
3,618.35
75*
237.976
4,506.67
83*
262i716
5,492.41
68
213.629
3,631.69
75}
238.369
4,521.56
83*
263.109
5,508.84
68i
214.021
3,645.05
76
238.762
4,536.47
83}
263.502
6,525.30
68i
214.414
3,658.44
76i
239.154
4,551.41
84
263894
5,541.78
68*
214.807
3,671.86
76}
239.547
4,566.36
84}
264.287
5,558.29
215.200
3,685.29
76f
239.940
4,581.35
84}
264.680
6,574.82
68|
215.592
3,698.76
76*
240.332
4,596.36
84|
265.072
5,591.37
68*
215.985
3,712.24
76 J
240.725
4,611.39
84*
265.465
5,607.95
68}
216.378
3,725.75
76*
241.118
4,626.45
84*
265.858
5,624.56
89
216.770
3,739.29
76}
241.510
4,641.53
84*
266.251
5,641.18
217.163
3,752.85
77
241.903
4,656.64
84}
266.643
5,657.84
69f
217.556
3,766.43
77}
242.296
4,671.77
8?
267.036
5,674.51
69*
217.948
3,780.04
77}
242.689
4,686.92
267.429
5,691.22
69*
218.341
3,793.68
771
243.081
4,702.10
1}
267.821
5,707.94
69|
218.734
3,807.34
77*
2-13.474
4,717.31
85|
268.214
5,724.69
69*
219.127
3,821.02
77|
243.867
4,732.54
85*
268.607
5,741.47
69}
219.519
3,834.73
77|
244.259
4,747.79
85*
268.999
6,758.27
70
219.912
3,848.46
77}
244.652
4,763.07
85*
269.392
5,775.10
70i
220.305
3,862.22
78
245.045
4,778.37
85}
269.785
5,791.94
70*
220.697
3,876.00
7ft t
245.437
4,793.70
86
270.178
5,808.82
70|
221.090
3,889.80
78}
245.830
4,809.05
863
270.570
5,825.72
70*
221.483
3.903.C3
78J
246.223
4,824.43
86;
270.963
5,842.64
70 1
221.875
3,917.49
246.616
4,839.83
86
271.356
5,859.59
70*
222.268
3,931.37
78>-
247.008
4,855.26
86,
271.748
5,876.56
70}
222.661
3,945.27
78*
247.401
4,870.71
86
272.141
5,893.55
71
223.054
3,959.20
78}
247.794
4,886.18
86.
272.534
5,910.58
71}
223.416
3,973.15
79
248.186
4,901.68
86}
272.926
5,927.62
71}
223.839
3,987.13
79}
248.579
4,917.21
87
273.319
5,944.69
71 1
224.232
4,001.13
79}
248.972
4,932.75
273.712
5,961.79
71*
224.624
4,015.16
79J
249.364
4,948.33
87}
274.105
5,978.91
71*
225.017
4,029.21
79*
249.757
4,963.92
87|
274.497
5,996.05
71*
225.410
4,043.29
79|
250.150
4,979.55
274.890
6,013.22
71}
225.802
4,057.39
79*
250.543
4,995.19
87|
275.283
6,030.41
72
226.195
4,071.51
79}
250.935
6,010.86
87*
275.675
6,047.63
72}
226.588
4,085.66
80
251.328
5,026.56
87}
276.068
6,064.87
72^-
226.981
4,099.84
80}
251.721
5,042.28
88
276.461
6,082.14
1!
227.373
227.766
4,114.04
4,128.26
80|
252.113
252.506
5,058.03
5,073.79
881
88i
276.853
277.246
6,099.43
6,116.74
72*
228.159
4,142.51
80*
252.899
5,089.59
88
277.629
6,134.08
72*
228.551
4,156.78
80|
253.291
5,105.41
88,
278.032
6,151.45
72}
228.944
4,171.08
80*
253.684
5,121.25
88
278.424
6,168.84
73
229.337
4,185.40
80}
254.077
5,137.12
88:
278.817
6,186.25
a
229.729
230.122
4,199.74
4,214.11
81
81}
254.470
254.862
5,153.01
6,168.93
88}
89
279.210
279.602
6,203.69
6,221.15
73 1
230.515
4,228.51
81-
255.255
5,184.87
89^
279.995
6,238.64
73*
230.908
4,242.93
fflf
255.648
5,200.83
89;
280.388
6,256.15
73|
231.300
4,257.37
81*
256.040
5,216.82
89
280.780
6,273.69
73*
231.693
4,271.84
81*
256.433
5,232.84
89;
281.173
6,291.25
73}
232.086
4,286.33
81*
256.826
5,248.88
89
281.566
6,308.84
74
232.478
4,300.85
81}
257.218
5,264.94
893
281.959
6,326.45
74}
232.871
4,315.39
82
257.611
6,281.03
89}
282.351
6,344.08
74r
233.264
4,329.96
82?i
258.004
5,297.14
90
282.744
6.361.74
74|
233.656
4,344.55
82}
258.397
6,313.28
90}
283.137
6,379.42
74*
234.049
4,359.17
82f
258.789
5,329.44
90}
283.529
6,397.13
741
234.442
4,373.81
259.182
5,345.63
90|
283.922
6,414.86
234.835
4,388.47
82|
259.575
5,361.84
90*
284.315
6,432.62
74}
235.227
4,403.16
82*
259.967
5,378.08
90*
284.707
6,450.40
75
235.620
4,417.87
82}
260.360
5,394.34
90*
285.100
6,468.21
75}
236.013
4,432.61
83
250.753
6,410.62
90}
285.493
6,486.04
75}
236.405
4,447.38
83}
261.145
5,426.93
91
285.886
6,503.90
396
MINE GASES AND VENTILATION
Diam.
Circum.
Area
Diam.
Circum.
Area
Diam.
Circum.
Area
91}
286.278
6,521.78
94
295.703
6,958.26
97
305.128
7,408.89
91*
286.671
6,539.68
296.096
6,976.76
97
305.521
7,427.97
9H
287.064
6,557.61
94
296.488
6,995.28
97
305.913
7,447.08
91}
287.456
6,575.56
94
296.881
7,013.82
97
306.306
7,466.21
91}
287.849
6,593.54
94
297.274
7,032.39
97
306.699
7,485.37
911
288.242
6,611.55
94
297.667
7,050.98
97
307.091
7,504.55
91}
288.634
6,629.57
94t
•
298.059
7,069.59
97
307.484
7,523.75
92
289.027
6,647.63
95
298.452
7,088.24
98
307.877
7,542,98
289.420
6,665.70
95
298.845
7,106.90
98
308.270
7,562.24
92*
289.813
6,683.80
95;
299.237
7,125.59
98
308.662
7,581.52
92}
290.205
6,701.93
95
299.630
7,144.31
98
309.055
7.600.82
92}
290.598
6,720.08
95
300.023
7,163.04
98
309.148
7,620.15
92}
290.991
6,738.25
95
300.415
7,181.81
98
309.840
7,639.50
92J
291.383
6,756.45
95
300.808
7,200.60
98
310.233
7,658.88
92}
291.776
6,774.68
95
301.201
7,219.41
98
-
310.626
7,678.28
93i
292.169
6,792.92
96
301.594
7,238.25
99
311.018
7,697.71
292.562
6,811.20
96
301.986
7,257.11
99i
311.411
7,717.16
93*
292.954
6,829.49
96;
302.379
7,275.99
99!
311.804
7,736.63
93}
293.347
6,847.82
96
302.772
7,294.91
99}
312.1%
7,756.13
93}
293.740
6,866.16
96
303.164
7,313.84
99}
312.589
7,775.66
93}
294.132
6,884.53
96
303.557
7,332.80
99}
312.982
7,795.21
93}
294.525
6,902.93
96
303.950
7,351.79
99}
313.375
7,814.78
93}
294.918
6,921.35
96}
304.342
7,370.79
99}
313.767
7,834.38
94
295.310
6,939.79
97
304.735
7,389.83
100
314.160
7,854.00
DENOMINATE NUMBERS
A denominate number is one expressed in units of a certain kind; as, for
example, 5 days, 8 men, etc.
A compound denominate number is one expressed in two or more
units; as 3 hr. 20 min., 8-ton mi., 4-acre-ft., etc. The terms ft. per sec.,
mi. per hr., rev. per min., etc., are all compound units.
An abstract number is any number not expressed in units of a kind;
as 3, 5, 8, etc.
Kinds of Units. — The principal kinds of units may be classed as follows :
1. Units of weight; as tons, pounds, ounces, grains, etc.
2. Units of length or distance; as miles, feet, inches, etc.
3. Units of volume ; as cubic yards, cubic feet, etc.
4. Units of capacity ; as gallons, quarts, pints, etc.
5. Units of surface or area; as square miles, square feet, etc.
6. Units of time ; as years, months, days, hours, etc.
7. Units of circular measure ; as degrees, minutes, etc.
8. Units of currency ; as dollars, dimes, cents, etc.
WEIGHTS AND MEASURES
Systems in Use. — There are two systems of weights and measures in
general use, known as the "English, United States or British," and the
" French or metric" systems.
The basis of comf arison of the English and French systems is
expressed by- the following established values:
Weight. — The pound (7,000 grs.) is the same in the United States and
Great Britain. The pound avoirdupois is equal to 453.5924277 grams in
the French system.
Length. — (United States) The length of the meter, by act of Congress,
is 39.37 in. (Great Britain) The length of the meter, by act of Parlia-
ment, is 39.37079 in.
The slight difference in the length of the meter, as established by law
in the United States and in Great Britain, makes the English inch and
yard proportionally shorter than the same units in the United States.
Capacity. — The gallon and liter are the accepted units of comparison
in the English and French systems, respectively. The United States or
"Winchester gallon," however, is quite different from the "Imperial
gallon" of Great Britain, which was made the volume of 10 Ib. of distilled
water, at maximum density (4 deg. C.), weighed with brass weights in
air at 62 deg. F., barometer 30 in.
Since 1 cu. in. pure water, under the same conditions, weighs 252.458
397
398 MINE GASES AND VENTILATION
grs. and 1 Ib. = 7,000 grs., the volume of the imperial gallon of Great
Britain is
10 X 7000
The volume of the Winchester gal) on of the United States is 231 cu. in.
The French liter is the volume of 1 kg. of distilled water, at 4 deg. C.,
weighed in a vacuum, or 1,000 c.c., which gives
Winchester gallon (United States), 231 cu. in. = 3.78543 liters.
Imperial gallon (Great Britain), 277.274 cu. in. =• 4.54346 liters.
UNITED STATES AND BRITISH SYSTEMS
Following are the more useful of the tables of weights and measures in
the English system :
AVOIRDUPOIS WEIGHT
( United States)
16 drams = 1 ounce .................... 437 . 5 pounds
16 ounces = 1 pound .................... 7,000 grains
25 pounds = 1 quarter ................... 400 ounces
4 quarters = 1 hundredweight ........... . 100 pounds
20 hundredweight = 1 short ton ................ ... 2,000 pounds
(Greet Britian)
28 pounds = 1 quarter ................... 448 ounces
4 quarters = 1 hundredweight ............. 112 pounds
20 hundredweight = 1 long ton .................. 2,240 pounds
The short ton (2,000 Ib.) is more generally used in the United States,
although the long ton (2240 Ib.) is used at times.
TROY WEIGHT
24 grains = 1 pennyweight
20 pennyweights = 1 ounce ............................ 480 grains
12 ounces = 1 pound ............................ 5,760 grains
APOTHECARIES WEIGHT
20 grains = 1 scruple ......................
3 scruples = 1 dram ........................ 60 grains
8 drams = 1 ounce ....................... 480 grains
12 ounces = 1 pound ....................... 5,760 grains
The grain (troy) is the same as the grain (apothecaries) and is the basis
of comparison of these and avoirdupois weights. Thus,
1 Ib. avoirdupois = 7,000/5,760 = 1.21528 Ib. troy.
1 Ib. troy = 5,760/7,000 = 0.822857 Ib. avoirdupois.
1 oz. avoirdupois = 437.5/480 = 0.911458 oz. troy.
1 oz. troy = 480/437.5 = 1.097143 oz. avoirdupois.
DENOMINATE NUMBERS 399
LONG MEASURE
12 inches = 1 foot
3 feet = 1 yard 36 inches
5>^ yards = 1 rod, perch, or pole 16^ feet
40 rods = 1 furlong 660 feet
8 furlongs = 1 mile 5,280 feet
3 miles = 1 league
The old surveyor's chain of 100 links (1 link = 7.92 in.) was 66 ft.
long, making 80 chains = 1 rni. Chains now in common use are 50,100
and 300 ft. long, made up of 1-ft. links.
A fathom is 6 ft. or 2 yd., used in estimating depth.
SQUARE MEASURE
144 sq. inches = 1 square foot
9. square feet = 1 square yard 1296 square inches
30K square yards = 1 square rod 272 Y± square feet
40 square rods = 1 rood 10,890 square feet
4 roods = 1 acre 43,560 square feet
640 acres = 1 square mile 102,400 square rods
An acre contains 43,560 sq. ft. and measures 208.7 ft. on each side;
\/437560 = 208.7 ft.
CUBIC MEASURE
1728 cubic inches = 1 cubic foot
27 cubic feet = 1 cubic yard 46,656 cubic inches
16 cubic feet = 1 cord foot 27,648 cubic inches
8 cord feet = 1 cord 128 cubic feet
A cord of wood is a pile 8 ft. long, 4 ft. wide and 4 ft. high, and contains
8 X 4 X 4 = 128 cu. ft.
A cord foot is one foot of the length of the pile that makes a cord,
and contains 1 X 4 X 4 = 16 cu. ft.
A ton of round timber (green) is taken as 50 cu. ft.
A ton of squared timber (green) is 40 cu. ft., it being assumed that
hewed or squared timber has lost one-fifth of its original volume in
squaring.
A long ton (2,240 Ib.) of anthracite or a short ton (2,000 Ib.) of bitumi-
nous coal broken (mine-run) occupies about 40 cu. ft.
There are two measures of capacity, known as "Liquid" and "Dry"
measures, having like denominations but of different values. The old
English wine gallon (231 cu. in.) was replaced in England, in 1824, by the
imperial gallon (277.274 cu. in.), but is still the standard "Winchester"
gallon in the United States. The "Dry " gallon, now practically obsolete,
contained 268.8 cu. in.
400 MINE GASES AND VENTILATION
LIQUID MEASURE (U. S.)
4 gills = 1 pint
28 875 cubic inches
2 pints = 1 quart
. . . . 57 75 cubic inches
4 quarts = 1 gallon
231 cubic inches
1^ gallons = 1 barrel
4 21 cubic feet
2 barrels = 1 hogshead
2 hogsheads = 1 pipe
63 gallons
126 gallons
2 nioes = 1 tun . .
8 barrels
DRY MEASURE (U. S.)
2 pints = 1 quart 67. 2 cubic inches
8 quarts = 1 peck 537. 6 cubic inches
4 pecks = 1 bushel 2150. 4 cubic inches
36 bushels = 1 chaldron 44 . 8 cubic feet
Or, 4 quarts = 1 gallon 268 . 8 cubic inches
8 gallons = 1 bushel 2150. 4 cubic inches
The standard bushel, in the United States, is the old Winchester
bushel, which is a circular measure 18^ in. in diameter and 8 in. deep,
containing 8 (0.7854 X 18.52) = 2150.4 cu. in. This was replaced in
England, in 1826, by the imperial bushel (2218.192 cu. in.), which was
then made the legal bushel.
LIQUID AND DRY MEASURE (GREAT BRITAIN)
4 gills = 1 pint 34 . 659 cubic inches
2 pints = 1 quart 69.318 cubic inches
4 quarts = 1 gallon 277 . 274 cubic inches
2 gallons = 1 peck 554 . 548 cubic inches
4 pecks = 1 bushel 2218. 192 cubic inches
There is no separate standard for liquid and dry measures in Great
Britain, both being referred to the same unit or standard, which is the
imperial gallon (277.274 cu. in.).
MEASURE OF TIME
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
365 days = 1 common year
366 days = 1 leap year
12 calendar months = 1 calendar year
100 years = 1 century
Commonly speaking, a day is marked by one complete revolution
of the earth on its axis, and a year by one revolution of the earth in its
orbit about the sun. Unfortunately, however, the earth does not make
an even number of turns on its axis, while making one complete revo-
DENOMINATE NUMBERS 401
lution in its orbit. There are approximately 365^ revolutions on the
axis to a single revolution in the orbit.
In order to compensate for this eccentricity and make the calendar
year conform as closely as possible to the solar year, so as to preserve
uniformity in the return of the seasons, it was necessary to add one day
to the calendar every fourth year, except the closing year of the century.
Thus, the common year of 365 days was supplemented by a leap year
containing 366 days.
The "Gregorian" calendar, established by Pope Gregory XIII (1582)
and generally adopted in Great Britain and elsewhere (1752), replaced the
"Julian" calendar and, in dropping 10 days by making Oct. 5, Oct. 15,
1582, restored the equinoxes to their proper date. To obtain closer
correspondence of the calendar and solar years, the closing year of each
century, 1600, 1700, etc., was made a common year, although these
would be leap years in the regular course.
The Day. — A day is the interval of time marked by two successive
transits of a heavenly body across a given meridian, caused by the revolu-
tion of the earth on its axis.
The solar day (24 hr., 0 min.) is the time interval marked by two suc-
cessive transits of the sun across the meridian.
The sidereal day (23 hr., 56 min.) is the time interval marked by two
successive transits of a fixed star across a given meridian.
The Month. — The calendar year has been arbitrarily divided into 12
months, in correspondence to the "number of moons" or the revolutions
of the moon about the earth in a solar year. But, since 365 days are not
equally divisible by 12, it was necessary to make an unequal division, as
follows:
January 31 days May 31 days September 30 days
February 28 days June 30 days October 31 days
March 31 days July 31 days November 30 days
April 30 days August 31 days December 31 days
The extra day required in a leap year is added to the month of Feb-
ruary, making 29 days in that month every leap year, instead of 28 as in
the common year.
The Year. — A year is the period of time in which the earth completes
one revolution in its orbit.
The solar year (365 d., 5 hr., 48 min., 45.51 sec.) marks a complete
revolution about the sun.
The sidereal year (365 d., 6 hr., 9 min., 8.97 sec.) marks a complete
revolution with respect to a fixed star.
CIRCULAR MEASUBH
60 seconds = 1 minute
60 minutes = 1 degree 3,600 seconds
15 degrees = 1 hour angle 900 minutes
30 degrees = 1 sign 1,800 minutes
12 signs = 1 great circle or circumference 360 degrees
26
402 MINE GASES AND VENTILATION
The "sign" is one of the twelve divisions of the zodiac, which corre-
spond to the twelve calendar months of the year. The sign has no
practical value technically.
It is often convenient to express the length of an arc, or the angle it
subtends, in terms of the radius of the circle. In that case, the unit of
length is called a "radian." A radian is a length of arc equal to the
describing radius. Its value expressed in degrees is 180° -f- TT =
180/3.14159 = 57.2958 deg., or 57° 17' 44.88". Since the length of the
circumference of a circle is 2irr, there arc 2-n- radians in a circumference or
360 deg.
Circular measure is used in the measurement of angles and in the esti-
mation of latitude, longitude and solar or sun time, which varies from
standard time according to the location of the observer.
Measurement of Time. — The passing of time is measured 1 y the
revolution of the earth on its axis, as determined by the observation of
the sun or one of the fixed stars when crossing the meridian of a place.
A single revolution of the earth marks a period of 24 hr. or one day.
Sun Time. — Owing to the inclination of the earth's axis to the plane
of its orbit and the eccentricity of the orbit, the sun's apparent motion
in the celestial sphere is not wholly uniform, on which account solar time
is referred to a " mean sun" having an assumed uniform motion.
Equation of Time. — The difference between the mean sun and the true
or observed sun, expressed in hours, minutes and seconds, is called
the " equation of time." This is found for any date in the "Ephemeris"
or Nautical Almanac.
Sidereal Time. — The apparent movement of the fixed stars, unlike
that of the sun, is uniform, which makes the sidereal day correspond
precisely with one complete revolution of the earth on its axis. About
Mar. 21, or at the vernal equinox, sidereal time agrees with mean sun or
solar time.
Local Time. — When the 24-hr, cycle is referred to the local meridian as
zero (noon or midnight) the indicated hour is the local time, or the time
for that place only. Since there are 360 deg. in a circle, which marks
1 day or 24 hr. of the celestial equator, 1 hr. corresponds to 360 -r- 24 =
15 deg. Hence, a difference of 15 deg. marks a difference of 1 hr. in local
time.
Longitude, Latitude. — Longitude is the distance either east or west of
the meridian of Greenwich, which is marked by the Royal Observatory,
and measured in degrees, minutes and seconds, on the equator. There
are thus 180 deg. of east longitude and 180 deg. of west longitude.
Latitude is likewise distance north or south of the equator, measured
in degrees, minutes and seconds, on any meridian or great circle passing
through the poles. There are thus 90 deg. of north latitude and 90 deg.
of south latitude.
Standard Time. — To obviate the confusion caused by the difference
in local time, a system of "standard time" has been adopted. Starting
DENOMINATE NUMBERS 403
from the meridian of Greenwich, standard time is 1 hr. later for each
15 deg. of east longitude, and 1 hr. earlier for each 15 deg. of west longi-
tude. Calling the equatorial circumference of the earth 25,000 mi., a
degree of longitude represents a distance on the equator of 25,000 -=-
360 = 69.4 mi. One hour (15 deg.) corresponds to a distance of
practically 1,000 mi. at the equator.
In the United States and Canada, there are four divisions of standard
time, known as Eastern, Central, Mountain and Pacific time, which are
exactly 1 hr. apart. These are all referred to the observatory at Green-
wich, which marks the zero of longitude.
Eastern time is the solar time of the meridian 75 deg. west longitude,
and is the standard time for all places within 7}$ deg. on either side of that
meridian. Eastern time is therefore 75 -5- 15 = 5 hr. earlier than Green-
wich 'time.
Central time is solar time for the meridian 90 deg. west longitude, and
is likewise standard for all places within 7% deg. east or west of that
meridian. Central time is 1 hr. earlier than Eastern time.
Mountain time is solar time for the meridian 105 deg. west longitude
and standard for all places within 7 3^ deg. east or west of that meridian.
Mountain time is 1 hr. earlier than Central time.
Pacific time is solar time for the meridian 120 deg. west longitude and
standard for all places within 7% deg. east or west of that meridian.
Pacific time is 1 hr. earlier than Mountain time.
When it is noon at the observatory at Greenwich it is 7 a.m. at New
York, 6 a.m. at Chicago, 5. a.m. at Denver and 4 a.m. at San Francisco.
At the same time it is 1 p.m. at Berlin and Rome, 2 p.m. at Petrograd
and 8 p.m. in the Philippines.
Civil Time. — The day, for all common purposes of reckoning, begins
and ends at midnight. The 24 hr. are divided into two periods of 12 hr.
each. The hours from midnight to noon are designated by the letters
a.m. (ante meridian), and those from noon to midnight by the letters
p.m. (post meridian).
Astronomical Time. — The astronomical day is reckoned from noon to
noon, the hours being counted from 1 to 24. The astronomical day begins
12 hr. later than the civil day, as the following comparisons will show:
Civil time, Nov. 6, 3 a.m.; Nov. 6, 3 p.m.; Nov. 7, 3 a.m.
Astronomical time, Nov. 5, 15 hr.; Nov. 6, 3 hr.; Nov. 6, 15 hr
METRIC SYSTEM OF WEIGHTS AND MEASURES
The units of the metric system are the gram, meter and liter. The
system, unlike that of the United States and Great Britain is wholly
a decimal system and, for that reason, is more convenient for use.
Denominations. — The higher denominations of weight, length and
capacity are obtained by multiplying each respective urflt by 10, 100,
404 MINE GASES AND VENTILATION
1000, etc., while lower denominations than the unit are likewise obtained
by dividing the same by 10, 100 or 1000.
The denominations of the metric system are expressed by the Latin
and Greek prefixes, the former being used to indicate divisions of the
unit, while the latter are employed to express multiples of the same
unit. These prefixes and their respective values are as follows:
Milli, 1/1000 1 milligram (mg.) = 0. 001 gram
Centi, 1/100 1 centigram (eg.) =0.01 gram
Deci, 1/10 1 decigram (dg.) =0.1 gram
Unit of Weight 1 gram
Deca, 10 1 decagram = 10 grams
Hecto, 100 1 hectogram = 100 grams
Kilo, 1000 1 kilogram (kg.) =1000 grams
Myria, 10,000 1 myriagram = 10,000 grams
The same prefixes are used to express similar divisions and multiples
of the units of length and capacity. Area and volume are expressed by
the words square and cubic preceding the same denominations of length.
Following are the tables of the metric system and equivalents :
METRIC WEIGHT
10 milligrams = 1 centigram 0. 15432356 gr. (troy)
10 centigrams = 1 decigram 1 . 54323564 gr.
10 decigrams = 1 gram 15 . 43235639 gr.
0.03527396 oz. (avdp.)
10 grams = 1 decagram 0. 35273957 oz.
10 decagrams = 1 hectogram 3.52739575 oz.
10 hectograms = 1 kilogram 35.27395746 oz.
2.20462234 Ib.
10 kilograms = 1 myriagram 22 . 04622341 Ib.
0.22046223 cwt.
10 myriagrams = 1 quintal 2 . 20462234 cwt.
10 quintals = 1 tonne 1 . 10231117 tons
The French tonne (2204.6 Ib.) differs but slightly from the British long
ton (2240 Ib.)
METRIC LENGTH
10 millimeters = 1 centimeter 0.3937 inches
10 centimeters = 1 decimeter 3.937 inches
10 decimeters = 1 meter 39 . 37 inches
3.2808 feet
10 meters = 1 decameter 32 . 8083 feet
10 decameters = 1 hectometer 328 . 0833 feet
0.0621 miles
10 hectometers = 1 kilometer 0. 6214 miles
The Austrian, Prussian, Danish and Norwegian mile is equal to about
4.7 American miles; the Swedish, to about 6% American miles; while the
Russian "verst" is 3500 ft.
DENOMINATE NUMBERS 405
METRIC AREA
100 sq. millimeters = 1 sq. centimeter 0. 155 sq. in.
100 sq. centimeters = 1 sq. decimeter 15.500 sq. in.
100 sq. decimeters = 1 sq. meter (centare) 1549 . 997 sq. in.
10.764 sq. ft.
100 centares = 1 sq. decameter (are) 1076. 387 sq. ft.
0.025 acres
100 ares = 1 sq. hectometer (hectare). . . 2.471 acres
100 hectares = 1 sq. kilometer 247. 104 acres
0.386 sq. mi.
100 sq. kilometers = 1 sq. myriameter 38.610 sq. mi.
The unit of area is the square meter or centare.
METRIC VOLUME
1000 cu. millimeters = 1 cu. centimeter 0.061 cu. in.
1000 cu. centimeters = 1 cu. decimeter 61 . 023 cu. in.
1000 cu. decimeters = 1 cu. meter 35 . 314 cu. ft.
1 . 308 cu. yd.
The weight of 1 cu. centimeter of distilled water at maximum density
(4°C.), weighed in a vacuum, is 1 gram; or 1 cu. decimeter of same under
like conditions is 1 kilogram.
METRIC CAPACITY
10 milliliters = 1 centiliter 0. 610 cu. in.
10 centiliters = 1 deciliter 6 . 102 cu. in.
10 deciliters = 1 liter. 61 .023 cu. in.
0.035 cu. ft.
10 liters = 1 decaliter (centistere) 0 . 353 cu. ft.
10 centisteres = 1 hectoliter (decistere) 3.531 cu. ft.
10 decisteres = 1 kiloliter (stere) 35. 314 cu. ft.
10 steres = 1 myrialiter (decastere) . . 353. 145 cu. ft.
The liter is the unit of capacity in the metric system. Its volume is
1000 cu. centimeters or 1 cu. decimeter. It contains 61.02338189 cu. in.,
or 0.26417 gal. (Winchester). Or a single Winchester gallon contains
3.785434 liters.
The Fluid Ounce. — What is known as the "fluid ounce" is a quantity
of any liquid equal to that of pure water at maximum density (4°C.)
and weighing exactly 1 oz. avoirdupois. The volume of the fluid ounce
is calculated as follows:
1 cubic centimeter of water (4°C.) = 1 gram.
1 ounce avoirdupois = 437.5 grains.
1 gram = 15.43236 grains.
Hence, since the volume of 1 gram (water) is 1 c.c. and the fluid ounce
406 MINE GASES AND VENTILATION
has a volume based similarly on the avoirdupois ounce, the value of the
fluid ounce is
437 ^
Fluid ounce (fl. oz.), = 28.3495 c.c.
The minim (a drop), the smallest liquid measure, is Ko of a fluid dram
or the equivalent in volume of 1 grain, which is 1 -5- 15 . 43236 = 0.0648 c.c. ;
or 28.3495 -f- 437.5 = 0.0648 c.c.
Metric Abbreviations. — The following are the common abbreviations
used in the metric system:
Milligram, mg.; millimeter, mm.jmilliliter, ml.
Centigram, eg. ; centimeter, cm.; centiliter, cl.
Decigram, dg.; decimeter, dm.; deciliter, dl.
Gram, g. ; meter, m.; liter, 1.
Kilogram, kg. ; kilometer, km. ; kiloliter, kl.
Square millimeter, mm2; cubic millimeter, mm3.
Square centimeter, cm2; cubic centimeter, cm3.
Square decimeter, dm2; cubic decimeter, dm3.
Square meter, m2; cubic meter, m3.
Square kilometer, km2.
Compound Units. — It is often convenient to express values involving
two or more denominations in terms of a single compound unit. The
following are examples of such compound units:
Work is expressed as a force (pounds) exerted through a distance
(feet) and its unit, therefore, combines both of these denominations,
giving foot-pounds (ft.-lb.), or inch-pounds (in.-lb.), as the case may be.
Power is expressed as work performed per unit of time, as foot-pounds
per minute (ft.-lb. p.m.), or per second (ft.-lb. p.s.).
In like manner, the speed of rotatien is given in revolutions per minute
(r.p.m.); or the speed of a train as miles per hour (mi. p. hr.); or the
velocity of an air current as cubic feet per minute (cu. ft. p. m.).
It is common to estimate the value of coal lands in tons per acre, or
acre-tons; or to express the amount of underlying coal in acre-feet,
which combines in a single unit both the acreage of the seam and the
average thickness of the coal in feet.
CONVERSION TABLES
Numerous forms of tables are in use for converting denominations of
the United States system into the corresponding denominations of the
metric system and vice versa, but the following are believed to best
serve the purpose. For the sake of more ready reference, the denomina-
tions of weight, length, area, volume and capacity are here given in
separate tables, and the values given in the tables are simple multipliers:
DENOMINATE NUMBERS
407
AVOIRDUPOIS (METRIC TO U. S:)
1
1
1
1
1
I
1
I
1
1
milligram
centigram
decigram
gram
decagram
hectogram
kilogram
myriagram
quintal
tonne
Drams (
= 0.00056
= 0.0056
= , 0.0564
= 0.564 0
= 5.644 0
=56.438 3.
= 564.38 35.
)unce
035
353
527
274
Pounds
0.0022
0.022
0.220
2.205
22 . 046
220.46
Tons
0.0011
0.0110
0.1102
2204.62 1.1023
When closer determinations are desired the values given in the metric
tables should be employed.
AVOIRDUPOIS (U. S. TO METRIC)
Grams
1.77
28.35
453 . 59
Kilograms
1 dram =
1 ounce =
1 pound =
1 ton =
Milligrams
1771.8
0.02835
0.4536
907.184
TROY ( METRIC TO U. S.)
Penny
Tonne
0.90718
Grains
weights
Ounces
Pounds
1 milligram
=
0
0154
1 centigram
=
0
154
0
006
1 decigram
=
1
54
0.
064
0.
0032
1 gram
=
15.
43
0.
643
0.
032
1 decagram
=
6.
430
0
322
0
,0268
1 hectogram
BS
64.
302
3
215
0
.2679
1 kilogram
=
32
151
2
.679
1 myriagram
«
26
.79
grain
pennyweight
1 ounce
1 pound
1 milligram =
1 centigram =
1 decigram =
1 gram =
1 decagram =
1 hectogram =
1 kilogram =
TROY (U. S. TO METRIC)
Milligrams- Grams
= 64.8 0.065
1.555
31.103
APOTHECARIES (METRIC TO U.
Grains Scruples Drams
0.0154
0.154 0.0077
1.54 0.077 0.026
15.43 0.772 0.257
7.72 2.57
S.)
Ounces
0.032
0.322
3.215
32.15
Kilograms
0.031
0.373
Pounds
0.268
2.679
408
MINE GASES AND VENTILATION
1 grain =
1 scruple =
1 dram =
1 ounce =
1 pound =
1 millimeter
1 centimeter
1 decimeter
1 meter
1 decameter
1 hectometer
1 kilometer
APOTHECARIES (U. S. TO METRHC)
Milligrams Grams
64.8 0.065
1.296
3.888
31.103
LINEAR (METRIC TO U. S.)
Kilograms
0.031
0.373
1 myriameter
Inches
Feet
Yards
Rods
Miles
0.039
0.39
0.033
3.94
0.33
39.37
3.28
1.094
0.199
32.81
10.936
1.988
0.0062
109.36
19.884
0.0621
0.6214
6.2137
The old surveyor's chain (66 ft.) contains 20.1168 meters, and one
kilometer (3280.83 ft.) is 49.71 of such chains.
LINEAR (U. S. TO METRIC)
1 inch
1 foot
1 yard
1 rod
1 furlong
1 mile
Millimeters
25.400
304.800
Centimeters
2.540
30.480
91.440
Meters
0.0254
0.3048
0.914
5.029
201 . 168
1609.347
Kilometers
0.005
0.201
1.609
SQUARE (METRIC TO U. S.)
Sq
. in. Sq. ft.
1 sq. millimeter
= 0.
0015
1 sq. centimeter
= 0.
155
1 sq. decimeter
= 15.
500 0.
108
1 sq. meter
=
10.
764
(centare)
1 sq. decameter
=
1076
.387
(are)
1 sq. hectometer
=
,
(hectare)
1 sq. kilometer
=
1 sq. myriameter
=
Sq. rods Acres Sq. mi.
0.040
3.954 0.025
395.367 2.471
247.104 0.386
38.61
DENOMINATE NUMBERS 409
SQUARE (U. S. TO METRIC)
Sq. mm. Sq. cm. Centares Ares Hectares
sq. inch = 645.16 6.45
sq. foot = 929 .03 0 . 093
sq. yard = 0 . 836
sq. rod = 25.293 0.253
acre 40.469 0.405
sq. mile = 259.
CUBIC (METRIC TO U. S.)
Cu. inches Cu. feet Cu. yards
1 cu. millimeter = 0 . 00006
1 cu. centimeter = 0.06102
1 cu. decimeter = 61.0235 0.0353 0.0013
1 cu. meter 35.3145 1.308
CUBIC (U. S. TO METRIC)
Cu. mm. Cu. cm. Cu. dm. Cu. m.
1 cu. inch = 16,387 16.387 0.016
1 cu. foot = 28,316.84 28.317 0.028
1 cu. yard = 764.555 0.765
CAPACITY- (METRIC TO U. S., LIQUID)
Gills Pints Quarts Gallons Barrels Hhd.
milliliter = 0.008
centiliter = 0.085 0.021
deciliter =0.845 0.211 0.106
liter = 8.453 2.113 1.057 0.264
decaliter = 10.567 2.642 0.084
hectoliter = 26.417 0.839 0.419
1 kiloliter = 264.170 8.386 4.193
1 myrialiter = 83.864 41.932
One myrialiter contains 10.48295 tuns.
CAPACITY (METRIC TO U. S., DRY)
1
Pints
centiliter = 0.018
Quarts
Gallons
Pecks
Bushels
1
deciliter = 0.182
0.
091
1
liter = 1.816
0
.908
0.
227
0
,114
0
.028
1
centistere =
9,
081
2.
270
1
.135
0
,284
1
decistere =
.'
22.
702
11
351
2.838
1
stere =
28
.378
1
decastere =
283.
777
The decastere is equal to 7.88269 chaldrons.
410 MINE GASES AND VENTILATION
CAPACITY (U. S. TO METRIC)
(Liquid) Ml.
Cl. Dl.
L.
Kl.
gill = 118.29
11.829 1.183
0.118
pint
47.318 4.732
0.473
quart =
9.464
0.946
gallon =
37.854
3.785
barrel =
119.241
0.119
hogshead =
238 . 482
0.238
pipe
476.965
0.477
tun
953.929
0.954
(Dry)
pint = 550.61
55.061 5.506
0.551
quart =
110.122 11.012
1.101
gallon =
44.049
4.405
peck
88.097
8.810
L bushel =
35.239
0.035
1 chaldron =
1.269
CAPACITY (METRIC TO BRITISH)
(Wet and dry) Gills Pints Quarts Gallons Pecks Bushels
1
1
milliliter = 0.007
centiliter = 0.070
0.018
1
deciliter = 0.704
0.176 0.088
0
.022
1
liter = 7.043
1.761 0.880
0
.220
0
.110
0
.028
1
decaliter =
8.803
2
.201
1
.100
0
275
1
hectoliter =
22
.008
11
.004
2
,751
1
kiloliter =
220
083
110,
042
27
510
1
rnyrialiter =
275.
104
CAPACITY (BRITISH TO METRIC)
(Wet and dry) Ml. Cl. Dl. L. Kl.
1 gill = 142.0 14.199 1.420 0.142
1 pint = 56.797 5.680 0.568
1 quart = 11.359 1.136
1 gallon = 45.437 4.544
1 peck = 90.875 9.087
1 bushel = 36.350 0.036
The conversion factors in these tables have been derived independently
from the following standards:
1 meter (U. S.) = 39.37 in. (1 in. = 25.4 mm.);
1 sq. meter = 39.S72 -T- 144 = 10.76386736 sq. ft.;
1 cu. meter = 39.373 -=- 1728 = 35.31445447 cu. ft.;
1 liter = 61.02338189 cu. in.;
1 U. S. (Winchester) bushel = 2150.4 cu. in.;
1 British (Imperial) bushel = 2218.192 PU. in.
DENOMINATE NUMBERS 411
CONVERSION OF COMPOUND UNITS
In the conversion of compound units from the United States to the
metric system, and vice versa, it is more convenient and saves much
time and frequently avoids error arising from confusion of terms to em-
ploy a single factor. The following are the more common conversion
factors :
WEIGHT PER UNIT LENGTH
1 Ib. per ft (0.4536 X 3.28) = 1.488 kg. per m.
1 Ib. per yd (0.4536 X 1.0936). = 0.496 kg. per m.
1 ton per mi (0.9072 X 0.6214) = 0.5637 tonnes per km.
1 long ton per mi (1.016 X 0.6214) = 0.6313 tonnes per km.
WEIGHT PER UNIT AREA
1 Ib. per sq. ft (0.4536 X 10.764) = 4.882 kg. per m2
1 ton per sq. ft (0.9072 X 10.764) = 9.765 tonnes per m2
1 ton per sq. yd (0.9072 X 1.196) = 1.085 tonnes per m2
1 ton per acre (0.9072 X 2.471) = 2.2417 tonnes per hectare
1 long ton per acre (1.016 X 2.471) = 2.5105 tonnes per hectare
WEIGHT PER UNIT VOLUME
1 oz. per cu. in ... (28.35 X 0.06102) = 1.73 g. per cm3
1 oz. per cu .ft (0.0283 X 35.3145) = 1.00 kg. per m3
1 Ib. per cu. ft (0.4536 X 35.3145) = 16.0184 kg. per m3
1 Ib. per cu. yd. ... (0.4536 X 1.308) = 0.5933 kg. per m3
1 ton per cu. yd . . (0.9072 X 1.308) = 1.1866 tonnes per m3
1 ton per acre-ft. . . (0.9072 X 8.106) = 7.3538 tonnes per hectare-m.
1 long ton per acre-ft (1.016 X 8. 106) = 8. 2357 tonnes per . hectare-m .
It is worthy of note that ounces per cubic foot are equivalent to kilo-
grams per cubic meter, or grams per liter, since 1 m3 = 1000 liters.
WEIGHT PER UNIT CAPACITY — LIQUID
1 gr. per gal.— U. S (64.8 X 0.264) = 17.107 mg. per 1.
1 oz. per gal ( 28.35 X 0.264) = 7.484 g. per 1.
1 Ib. per gal (453.59 X 0.264) = 119.748 g. per 1.
1 gr. per gal.— Gt. Br (64.8 X 0.22). = 14.256 mg. per 1.
1 oz. per gal (28.35 X 0.22) = 6.237 g. per 1.
1 Ib. per gal (453.59 X 0.22) = 99.790 g. per 1-
WEIGHT PER UNIT CAPACITY — DRY
1 Ib. per bu.— U. S (0.4536 X 28.378) = 12.872 kg. per stere
1 Ib. per bu.— Gt. Bt (0.4536 X 27.51) = 12.479 kg. per stere
PRESSURE
1 oz. per sq. in (28.35 X 0.155) = 4.394 g. per cm2
1 Ib. per sq. in (453.59 X 0.155) = 70.306 g. per cm2
1 Ib. per sq. ft. . . . (0.4536 X 10.764) = 4.882 kg. per m2
412 MINE GASES AND VENTILATION
WORK
1 inch-pound (2.54 X 453.59) = 1152.1 gram-centimeters
1 foot-pound (0.3048 X 0.4536) = 0.1383 kilogram meters
1 ton-pound (0-3048 X 0.9072) = 0.2765 tonne-meters
WORK IN HEAT UNITS
1 B.t.u.— 778 ft.-lb (778 X 0.1383) = 107. 564 kg.-m.
1 pound-calorie (107.564 X 1.8) = 193.615 kg.-m.
1 calorie (193.615 X 2.2046) = 426.844 kg.-m.
CALORIFIC OR HEATING VALUE
1 B.t.u. per Ib (0.252 X 2.2046) = 0.55556 cal. per kg.
1 B.t.u. per Ib 5/9(2 . 2046) = 1 . 22478 Ib.-cal. per kg.
1 B.t.u. per cu. ft (0.252 X 35.3145) = 8.89925 cal. per m3
1 Ib.-cal. per Ib (0 . 4536 X 2 . 2046) = 1 . 00000 cal. per kg.
1 Ib.-cal. per Ib = 2.20462 Ib.-cal. per kg.
1 Ib.-cal. per cu. ft (0.4536 X 35.3145) = 16.01866 cal. per m3
POWER
The metric horsepower (force de cheval), which for convenience may
be abbreviated "cheval," is the power capable of performing 75 kg.-m. of
work per second, or 75 X 60 = 4500 kg.-m. per min.
1 horsepower (33,000 X 0.1383) = 4563.9 kg.-m. per min.
1 horsepower (4563 . 9 -r- 4500) = 1 . 0142 chevals
1 cheval (4500 H- 4563.9) = 0.986 hp.
POWER FACTORS
1 sq. ft. per hp (0 . 093 X 0 . 986) = 0 . 0937 m2 per cheval
1 cu. ft. per hp (0. 028 X 0. 986) = 0. 0276 m3 per cheval
FUEL OR WATER CONSUMPTION
1 Ib. per hp.-hr (0 . 4536 X 0 . 986) = 0 . 4472 kg. per cheval-hr.
1 ton per hp.-hr (0 . 9072 X 0 . 986) = 0 . 8945 tonnes per cheval-hr.
1 gal. (U. S.) per hp.-hr . . (3 . 785 XO . 986) = 3 . 7320 liters per cheval-hr.
1 gal. (Gt. Bt.) per hp.-hr. (4 . 544 X 0 . 986) = 4 . 4804 liters per cheval-hr.
EVAPORATION FACTORS
1 gal. per sq. ft.— U. S (3.785 X 10.764) = 40.7417 1. per m.2
1 gal. per Ib. fuel (3. 785 X 2. 2046) = 8. 3444 1. per kg.
1 gal. per B.t.u (3.785 X 3.968) = 15.0189 1. per cal.
1 gal. per B.t.u (3.785X1.8) = 6.8130 1. per Ib.-cal.
1 gal. per sq. ft.— Gt. Bt (4 . 544 X 10 . 764) = 48 . 91 16 1. per m2
1 gal. per Ib. fuel (4.544 X 2.2046) = 10.0177 1. per kg.
1 gal. per B.t.u (4.544 X 3.968) = 18.0306 1. per cal.
1 gal. per B.t.u (4.544 X 1.8) = 8. 1792 1. per Ib.-cal
DENOMINATE NUMBERS 413
EQUIVALENTS IN AIR MEASUREMENTS
Atmospheric pressure, sea, level, normal, 14.696 Ib. per sq. in.
(14 . 696 X 0 . 0703) = 1 . 033 kg. per cm2
(14.696 -7-0.4911) = 29. 925 in. mercury
(29.925 X 25.4) = 760 mm. mercury
/29.925 X 13. 6\ ,0 ft ,,
I — j = 33.9 ft. water column
(33.915 X 0.3048 = 10.34m. water column
The specific gravity of mercury (32 deg. F.) being 13.593, 1 in. ba-
rometer (standard reading) corresponds to 13.6 in. water gage and,
roughly, to (13.6 X 815) -t- 12 = say 900 ft. air-column.
Pressure, in fan ventilation is frequently expressed in ounces per
square inch, instead of in pounds per square inch. The following table
giving the equivalent values in these denominations and inches of water
gage.
Water Lb. per Oz. per Water Lb. per Oz.per
gage sq. ft. sq. in. Gage sq. in. sq. in.
0 3 15.60 1.733
H 0.65 0.072 y± 16.90 1.878
K 1-30 0.144 Y2 18.20 2.022
H 1.95 0.216 Y± 19.50 2.167
H 2.60 0.289 4 20.80 2.311
% 3.25 0.361 y± 22.10 2.456
% 3.90 0.433 Y2 23.40 2.600
% 4.55 0,505 % 24.70 .2.744
1 5.20 0.578 5 26.00 2.889
H 6-50 0-722 y± 27.30 3.033
% 7.80 0.867 % 28.60 3.178
% 9.10 1.011 % 29.90 3.322
2 10.40 1.156 6 31.20 3.467
y± 11.70 1.300 K 32.50 3.611
% . 13.00 1.444 y2 33.80 3.756
% 14.30 1.589 % 35.10 3.900
The table on the following page will be found convenient in comparing
short and long tons. It expresses the decimal equivalent of the short and
long ton, per hundredweight, to 20,000 Ib. or 10 short tons.
414 MINE GASES AND VENTILATION
TABLE OF COMPARATIVE VALUES OF THE SHORT AND LONG TON
POUNDS^
<««i£fSs
nml _MO -*55
4600J _1M -2S5.
M!^
n.ioo: m -*B
1WLJ&-5®
mat_si5._a5
7ifloj _iiQ -Ufl
9?OQ: 4jM "**
9500 : 4f& 4.15 IIJOQ- »5
9«!L JJO _4jfl ll^fifij _S7Q
iQBt JUB JK
INDEX
NOTE. — Numbers refer to pages. Letters are used to abbreviate words in the same
line or in the heading in which they stand. Other abbreviations are those in common
use.
Absolute pressure, 192
A. temperature; A, zero, 18
Rel. of a. p. to a. temp., 20
Acceleration, 26 .
Acetylene gas, Generation of,
Burning a. g. ; Oxygen con-
sumed; Calculation, 310
Chem. reactions, 309
Properties of a. g., 311
Acetylene lamp (See L., Miners'
Carbide)
Acids, Bases, Salts: Nature of a.;
Distinguishing character-
istics, 61
Affinity of atoms, 59
Afterdamp: Composition, etc., Ill
Air, 1 (See Respiration)
Composition of a., 4; Per-
centage c. calculated, 30
Density of a. calculated, 30
Dry a., 4, 70; Formulas, 4,
79, 80
Dry a, vs. wet a., 79 (Sec
Hygrometry)
Early theories of a., 1
Mechanical mixture, 2, 61
Moisture in a. (See Hygrom-
etry)
Normal a., 4, 5; Exhaled a., 3;
Free a., 19; Residual a.,
Tidal a., 133
Weight of a.: Formulas 4,
79, 80
Weight of a.: Dif. altitudes
and temp, (tables) 11, 15
Air bridges: Overcasts; Under-
casts; Natural o., 251
Air crossings, 249
Air columns — Atmospheric (See
Atmos. pressure)
Average temp, (atmos. a. c.)
Calc. of, 14; Observed
temp. Table of, 15
Air columns, in mines:
Estimation of, 166; Condi-
tions affecting; Positive
and negative a.c., 167;
Downcast, Upcast c. 168;
Calculation of a. c.; Ef-
fective depth, 169; Prob-
lems, 170; Relation of
a. c. to unit ventilating
press., 184; Wwater gage,
184; Barom, pres., 185
Air currents, Conducting, 249
(See Mine Ventilation)
Appliances used: Air bridges
(overcasts undercasts),
brattices, doors, stop-
pings, regulators, 249-251
Circulating system : Intake
and discharge openings,
161; Intake and return
airways, 258; Coursing
the a.; Single current not
adequate, 218 -
Distribution of a., 257; A.
splits, 258
Measurement of a. c., 199
Splitting the a. c. (See S. the
A. C.)
Velocity of a. c., 173, Danger
of high v., 179; How v.
is estimated and meas-
ured, 180; Rel. of pres.
and v., 173
415
416
INDEX
Air splits, 258 (See Splitting of the
A. Current)
Airways :
Definition of a., 187; Essen-
tial features; Shape, 188
Intake and return a., 258
Potential of a., 200; Table, 202
Similar a., 189, Principle of
s. a., 191; Rule, 192
Systems of mine a., 262
Resistance of a.; How r.
varies, 191; Unit of r. ;
Coef. of fric.; Calcula-
tion of r. of an a., 192;
Formulas for r. 196, 198
Anemometer, The, 180
Artificial respiration (See R.)
Sylvester method, 158; Schae-
fer method, 159
Ashworth-Hepplewhite-Gray safe-
ty lamp, 283
Atmosphere, The, 5 (See Air)
Constant composition, 61
Pressure expressed in a's, 19
Atmospheric pressure, 5
A. p. at dif. altitudes, Table of,
11; Relation of a. p. to
altitude, temp., etc., Table
of, 15
Calculating a. p. (Differential
method), 15
Measurement of (See Baro-
metric Pressure)
Variation of, Daily and yearly,
6
Atoms, corpuscles, electrons, mole-
cules, 22
Atomic heat, re a. wt., 53
Atomic volume, unit of gaseous
v., 29, 63
Atomic weight, rel. w., 59; A. w.
of elements (table), 28
Attraction, Law of, 22, Terrestrial
a., 23
Authorities: Abel, 122; Atkinson,
191; Avogadro, 29;
Beard, 305; Berzelius,
122; Boyle, 19; Burrell,
296; Cavendish, 1; Cham-
berlin, 90; Charles, 18;
Clowes, 311; Dalton, 22;
Davy, 269; Dulong, 53;
Emich, 113; Fairley, 191;
Favre, 66, 68; Galloway,
304, 305; Gay Lussac,
18; Gibbs, 143; Graham,
37; Haldane, 106, 107,
109; Hopkins, 157; Lav-
oisier, 1 ; LeChatelier, 114,
311; Mallard, 114; Man-
ning, 157; Mariotte, 19;
Paul, 147; Petit, 53;
Priestley, 1; Remsen, 53;
Schaefer, 159; Silber-
mann, 66, 68; Stephen-
son, 268; Stewart, 134;
Stoney, 22 ; Sylvester, 158;
Taffanel, 123; Thomson,
22
Avogadro's law of gaseous vol-
ume, 29
B
Barometer, The, 6
Aneroid b., 9
Mercurial b., 6; Description,
8; Principle of b., 7
Barometric pressure, 6 (See At-
mospheric P.)
Calculation of p. from b.
reading 6; Calculation for
any altitude, 12; Form-
ula, 13
Standard, b. readings, 8
Table of b. p. at dif. altitudes,
11
Bases, in chemistry, 61
Battery, Edison storage, 313
Beard-Mackie sight indicator,
for gas, 297
INDEX
417
Birds, Effect of carbon monoxide
on, 106; Table showing
length of exposure and
recovery, 108
Blackdamp, 110 (See Carbon Diox-
ide)
Carbide lamps in b., 311
Definition; Production in
mines; Effect on human
system, 110
Blood, Circulation of, 3 (See Respi-
ration)
Absorption of carbon mono-
oxide by the b., 103;
Rate of a., 104
B. test for carbon monoxide,
106
Percentage of saturation in
b. re p. c. in air breathed,
105; P. of carbon mon-
oxide fatal to life, 107
Blowers, Gas, 87 (See Geological
Conditions)
Blownout shot, cause of mine ex-
plosion, 127
Boiling, Evaporation, Vaporiza-
tion, 50
B. points of dif. liquids, Table,
51; Effect of pres. on
b. p. and v., 50
Bonnet, Lamp (See L. Mine
Safety)
Box regulator, The, 231 (See
Regulators)
Area of opening, Example,
234, 240
Pres. due to b. r., 232
Brattices, 249; How built, 250
Breathing Apparatus, 132 (See
Respiration)
Design; Development, 135
Permissible b. a.; Definition,
148
. Principle of b. a., 132
Regenerator, 136
Specifications by the Bureau
27
of Mines: Conditions
of testing, 148; Character
of tests, 150; Construc-
tion of b. a., 151; Detail
of procedure in tests,
153; Approval of a., 155
Notification to manufac-
turer; Fees for testing;
Application for test of a.,
156
Testing b. a., 136
Types of b. a., 137:
Draeger b.a., 137; Essen-
tial parts; Capacity, 139
Fleus Proto b. a., 139;
Essential parts, 140; Ca-
pacity, 142
Gibbs b. a., 143; Circu-
lation, 144; Testing 145
Paul b. a., 147
British thermal unit, 51
Burrell gas detector, The, 299
Bureau of Mines, 147
Requirements in breathing
apparatus, 147; Specifica-
tions b. a, 148; Electric
mine lamps, 319; Mine
safety lamps, 288
C
Calorie, 52
Pound, c., 52; Equivalent
B.t.u., etc., 53
Canary, (See Birds etc.)
Cap, Flame, ( See F. C.)
Cap lamp, Electric, (See E. Mine
L.)
Carbide lamps (SeeL. Acetylene C.)
Carbon, Heat of combustion of,
66
Thermochemical equation, 69
Carbon dioxide, 109
Absorption of, in breathing
apparatus, 136
Amount produced in breath-
ing, 134
418
INDEX
Carbon dioxide, Effect on flame;
on life; on respiration;
Production in mines, 109
Reduces poisonous effect of
carbon monoxide, 107
Toxic effect, 2, 109, 312
Treatment of victims, 110
Carbonic acid gas (See Carbon
Dioxide)
Carbon monoxide, 103
Absorption by blood 103;
Rate of a.; Fatal per-
centage, 1G4
Combustion in air (chem.
equa.), 65
Detection in air; Blood test,
106
Effect on birds and mice; on
flame, 106; on life, 103;
Haldane's conclusions,
107
Explosive and inflammable
range (table) ; Effect of
high press, and temp.,
114; Moisture necessary,
114, 121
Flame temp., Calculation of,
120
Production in mines, 105
Properties, 103
Treatment for c. m. poisoning,
103
Catalysis, 122
Centigrade re Fahrenheit scale
(table), 44
Conversion formulas; Ex-
amples, 45
Charts: Explosive mine gases;
E. range; Max. e. point;
Inflammable limits;
Symbols; Molecular wts.,
Densities; Wt. per cu. ft.;
Vol. per pound; Specific
heats; Heat of combustion
in oxygen ; Chem. equation
showing reaction, 115
Flame caps in safety lamps;
Height of f. cap or elon-
gation of f. for dif. illumi-
nants and dif. percentages
of gas; Inflammable and
explosive zones, 303
Humidity of air for dif.
dry-and-wet bulb read-
ings; Percentage and
weight of water vapor in
air, 81; Table, 75
Pressure (atmospheric) at dif.
altitudes; Corresponding
water column and baro-
meter; Mean observed
temp, of atmosphere, 15
Pressure, power, volume: Lb.
p. sq. ft.; Oz. p. sq. in.;
water gage, inches, 184
Temperature : Expansion
curve for air and gases;
Relation of absolute t.
and volume, 19
Chemical affinity, 46, 56
C. change; C. reaction, 56,
62; Examples of c.r.; Effect
of heat 57; C. compound,
60; C. equation; How
written, 62; What it
shows, 67; Use of c. e.,
63; C. symbols, 58
Chemistry of gases, 56
Chesneau safety lamp, 283
Chokedamp, 109 (See Carbon
Dioxide)
Circulation in mines (See M. Venti-
lation)
Flow of air in airways, 172;
Potential of c., 201; P.
values for dif. c., 202;
Table, 203; Pres. pro-
ducing c., 174; Power
required to produce a
given c., 249
Tandem c.; Summation of
potentials, 214; Formulas,
INDEX
419
215; Examples int. c., 216,
237; T. vs. split c., 222
Circulation of blood, 3 (See B., C. of)
Clanny safety lamp, 277
Clowes hydrogen safety lamp, 284
Coal: Condition of gas in c. ;
Escape of g. from c. ;
Gas evolved from c. in
vacuum, 90; Heat value
of some coals (table), 66;
Inflammability of c., 124
Coal dust, 123 (See D., C.)
Coefficient of friction of air:
Atkinson c; Fairley c.,
192
Cohesion, 22
Combustion: A form of oxidation;
Products of C. ; Slow c.;
Supporter of c., 57
Heat of c. (exothermic) ;
Formula; Table of h. of
c'., 66; Calculation of h.
of c., 67
Rapid (active) c. ; Spontaneous
c., 58
Composition, Percentage : By vol-
ume, 40; By weight, 39
Conducting air currents, 249 (See
A. C., C.)
Conduction of heat, 52
Convection, 52
Conversion formulas: Degrees of
temp., 45; Heat units, 52
Conversion tables, 406 (See T.)
Corpuscles, 22
Critical temp, of a liquid, 81
D
Damps, 94
Davy safety lamp, The, 275
Deliquescent, 48
Denominate numbers, 397
Density defined; Formula, 29
Calculation of d. from relative
(atomic) wts., 30
Mass, volume, d., 24
Dew point, 5, 76
D. p. temp., 76
Diffusion of ah- and gases 34, 36
Law of d., 36; Graham's 1.;
Illustration ; Experiment,
37.; Calculation of den-
sity based on 1. of dif-
fusion; Formula, 41
Dip workings, Ventilation of, 162
Distribution of air in mines, 257
Division of air: (See Splitting the
A. Current)
Natural d. 220; Proportionate
d. 230
Door regulator, The, 231;
Area of opening; Use of the
d. r., 235; Example, 240
Doors, Mine, 249
Double -entry system, 263
Draeger breathing apparatus, 137
Drainage, Mine 252
Dust, Coal, 123 (See D. Explosion)
Anthracite d., 124
Effect of c. d. on. flame, 123
Inflammability of c. d., 124
Dust, Shale or Stone,
Barrier to propagation of
explosion, 125
Catalytic action of s. d., 122
Dust explosion, 116 (See E., D.)
Dynamic force, 25
E
Edison storage battery for mine
lamps, 313
Electric mine lamps, 128, 313
(See Incandescent L.)
Battery, Selecting a suitable;
Edison storage b., 313;
Charging the b., 315;
Cap 1. and cable, 314
Permissible e. m. 1.; Defini-
tion, 319
Specifications (Bureau of
Mines) ; Conditions of
testing, 319; Require-
420
INDEX
ments for approval,
320; Tests of design .
and construction;
safety devices, 323;
short circuit ;
— lighting 324; cur-
rent consumption, candle
power, life of bulb;
— leakage of electrolyte;
Approval, 325; Notifica-
tion of manufacturer;
Fees for testing, 326
Use of e.m.l., 317
Electric wires, switches, fuses,
brushes, sparking of, 127
Electrons, 22
Elements, The, 28
Classification of the e., 60
Combining power; Valence,
59
Heat of e. ; in reaction, always
zero, 65
Emission of gases, 34 (See Trans-
piration of G.)
Endothermic reaction, 65, 67
Energy: Definition; Forms of e;
Kinetic e.J Potential e.,
27; Heat e. never lost,
67
Equations: Chemical e., 62; Ther-
mochemical e., 67; E. of
time, 402
Ethane, 89; Occurrence and
properties, 92
Ethene (ethylene), 89 (See Ole-
fiant Gas)
Equivalents hi measurement, 184
Air column re water gage;
re unit of vent, pres.,
184; re barometric pres.,
185
Atmospheric pressure e., 413
Barometric pressure re air
column; re unit of vent.
pres., 185
Power, volume (diagram), 185
Pressure e. (table), 185
Evaporation, 50 (See Boiling, E.
etc.)
Exothermic reaction, 65, 67
Expansion of air and gas ; 17
Adiabatic e. ; Formulas, 21;
Isothermal e., 22
Coefficient of e. or contraction,
17
Effect of press, and temp., 17;
Addition of heat, 20
Pressure re abs. temp., 20;
re volume (Boyle's or
Mariotte's law), 19
Temperature (absolute) re
volume (Charles' or Gay
Lussac's law), 18
Volume, press., abs. temp.,
Rel. of; Formulas, 20
Work of e., calculated in two
ways, 20, 21
Explosion, Dust, 116:
Absence of gas; Character of
d.; Influence of d. on e.;
Pioneering cloud of d. ;
Weight of d. per cu. ft. of
air to render air explosive,
123; Inflammability of
coal d., 124
Anthracite d. not explosive;
Volatile combustible mat-
ter in coal an index of its
explosibility, 124
Incombustible d, Influence
of, 125 (See D., Shale or
Stone)
Explosion, Gas (See Mine Gases;
E., Mine)
Definition of g. e., 116
E. of g.; Influence of pres.
and temp, on e., 121; I. of
catalysis, initial impulse,
moisture, volume and in-
tensity of flame, 122; I. of
coal dust on e., 123; I. of
rock dust to arrest e., 125
Peculiarities of e. of methane,
114
INDEX
421
Explosion, Mine, 126 (See E.,
Dust; E., Gas)
Causes of m. e., 127
Definition of a m. e., 116
Development of the e., 126
Propagation of an e. in a m.;
Pioneering cloud, 123
Prevention of m. e., 129; Shale
or stone dust (See D.,
S. or S.)
Rescue and first-aid work;
Entering a. m. after an e.,
131;
F-a. suggestions, 132 (See
F-A. W.; Breathing Ap-
paratus)
Explosive Mine Gases, 112, 115
(See M. G.; Firedamp)
Chart showing e. range, etc.
of m. g., 115
Effect of high pres. and temp.
on e. range, 114
E. and inflammable limits;
E. range of g. ; Maximum
e. point ; Lower and higher
limits; Degree of explo-
siveness, how affected,
113; Table, 114
Inflammation of gas; Theory
of, 116 (See Inflammable
M. G.)
Fahrenheit scale, 43
F. re centigrade, s. (table),
44; Conversion formulas;
Examples, 45
Faults in mining (See Geological
Conditions)
Feeders, Gas; Blowers, 87; Com-
position of f. g., 91; Oc-
currence, 87
Federal Bureau of Mines (See
B. of M.)
Firedamp, 94
Definition, 94
Firedamp, Effect of dust and other
gases, 95
F. is a mechanical mixture, 38
Inflammable and explosive
range, Table of, 101;
Lower i. limit, 95; Cal-
culating the 1. i. 1., 96;
Percentage of gas, 98; L.
e. limit; Max. e. point,
98; Percentage of gas, 99;
Higher e. limit, 99; Per-
centage of gas, 100; High-
er i. limit, 100
Fitst-aid work, 157 (See Artificial
Respiration; Breathing
Apparatus)
Resuscitation, 157
Suggestions on f.— a. to ex-
plosion victims, 132
Flame, Nature and temperature of,
117
Effect of coal dust on f., 123; E.
of carbon dioxide on f . , 109 ;
E. of c. monoxide on f ., 106
Extinction of lamp f. in car-
bon dioxide, 109; E. of
carbide f . by depletion of
oxygen, 312
Kinds of f. : Gas-fed f.; Oil-fed
f., 109, 312
Lamp f., Chart of, 303
Temp, of f., Theoretical; Cal-
culation of f. t., 118;
Methane in air, 119;
Carbon monoxide in air,
120; Temp, of f. re
temp, of ignition of
gas, 118
Volatile-oil f . sensitive to gas,
288
Volume of f., Estimated, 121
Zones inf., 118,301
Flame caps: Fuel c.; Gas c., 302
Calculation of height of f. c.
304; Formulas, 305
Chart of f. c., 303
422
INDEX
Flame caps : Height of f .% c. re
percentage of gas, 303,
305
Flame test, The, 301 (See Testing
for Gas)
Flashdamp: Definition; Calcula-
tion of composition of
f., 101; Percentage com-
position, 102
Fleuss Proto Breathing Apparatus,
139
Flow of air in airways, 172 (See
Air Currents, ; Conduct-
ing; Airways).
Appliances for conducting the
a., 249
Coefficients of friction : Atkin-
son jFairley, 192
Pressure producing circula-
tion, 174; Power required
to produce c., 249
Resistance of a.; How r.
varies, 191; Unit of r.,
192
Fluid ounce, The, 405
Fluid state, 23
Force: Measurement of f.; Static
f.; Dynamic f., 25
Formulas and symbols, 192
Basal f . ; Important principles,
196
How factors vary, 195
Use of f., 194; Illustration of
f., 197
Free air, 19
Free split, 233
Freezing points of liquids (table), 51
Difference bet, melting and
f. p.; Effect of pres., 49
French thermal unit, 52
Friction, Coefficient of; Atkinson c. ;
Fairley c., 192
Fuel cap in testing for gas, 302
Furnace ventilation; Principle of
f. v.; Location of a mine
furnace; Construction of
f., 164; Area of grate;
Wt. of coal burned per
hr., 165; Formula; Ex-
ample, 166
Fusion, Heat of, 48; Table of h.
of f., 50
Effect of pressure on f ., 49
G
Gas cap, in testing for g., 302 (See
Flame C.)
Gases, 23 (See Mine G.; Geologi-
cal conditions)
Blower g., 87 (See Feeder G.)
Composition of g. ; Simple or
elementary; Compound,
38
Density, Standard for g., 31
Expansion and contraction of
g.; Coef. of e. or c.
17
Gaseous state, 23; Distribu-
tion of heat by convection
in, g., 52
Hydrocarbon g. (See H. G.)
Natural g., 87;
Gases, Olefines; Paraffins, 92 (See
Hydrocarbon Gases)
Vapors and g., Difference, 24
Gas explosion, 116 (See E., G.)
Gas feeders, 87 (See F., G.; Geo-
logical conditions)
Gas indicators, 296; Beard-Mack-
ie, 297; Burrell, 299;
Liveing, 296
Geological conditions, 86
Condition of gas in coal; Es-
cape of g. ; Composition
of g. evolved, 90
Effect of faults, 87
Gas feeders, Blowers, 87;
Composition of f. g.
(table), 91
Gas, oil and water in the
strata, 86
INDEX
423
Geological conditions, Natural
gas, 87
Occluded gases; Pressure of
o. g., 35, 88
Outbursts of gas, 88
Water level in strata, 87
Gibbs breathing apparatus, 143
Gram-atom, 53; G. -calorie, 67;
G.-molecule, 47, 54
Gravitation : Gravity, 23
H
Haemoglobin or red corpuscles of
the blood, 3; Affinity of
h. for carbon monoxide,
103
Haulage, as affecting plan of mine,
253
Direction of road for given
grade; inclined seam ; Rule
and formula, 254
Heat, 42
Definition; Theory of h.;
H. in bodies, 42; Ab-
sorption of h., 47; Dis-
appearance of h.; Total
h. in a body, 48; H. cal-
culation, 67; H. changes;
H. of decomposition;
H. of elements, H. of
formation or combi-
nation, 65; H. of fusion;
h. of vaporization; H. of
condensation, 48; H. of
reaction, positive h., nega-
tive h., 67
H. energy, 20; No h. e. lost,
67; Transformation of h.
e., 47
H. re temp., 43; Sensible h.;
Latent h., 46
Kinds of h. : Atomic h., 53;
Chemical h. ; Molecular
h., 46;
Combining h. ; H. due to fric-
tion, impact, pressure, 47;
Heat, H. of combustion, 66; Spe-
cific h. or relative h. ca-
pacity, 54
Measurement of h., 51 (See
M. of H.)
Mechanical equivalent of .h,
53
Sources of h., 46
Tables: H. of combustion, 66;
H. of formation or com-
bination, 68; H. of fusion,
50
Specific h., solids and liq-
uids; S. h., gases and
vapors, 55
Transmission of h.; Radia-
tion ; conduction ; con-
vection. 52
Units of h., 51; Conversion
formulas, 52; Definition
of a u. of h., 54
Horsepower in mine ventilation:
Calculation of h. from mine
potential, 207, 212, 213;
C. of h. in natural division
of air, 227; Proportionate
div. of air, 232; secondary
splitting, 239
Humidity (Relative) of air, 74;
How measured 71; Tables,
75, 81
Hydrocarbon gases, 91; Acety-
lenes; Olefines; Paraffins,
92
General formulas for h. g.,
91
Heavy h. g.; Ethane; Ethene,
ethylene or olefiant g.
92
Light carbureted hydrogen,
methane, 92
Occurrence and formation, 92
Hydrogen: Symbol, mol. wt.,
density, sp. gr. (table) 89
Explosive range, Inflammable
limits (table) 114
424
INDEX
Hygrometer, The (Psychrometer) ,
71
Indicates degree of saturation
of air, 74
Principle of the h., 73
Swing p., 73
Wet-and-dry-bulb h., 72
Hygrometry, 70
Calculation of wt. of moisture
in air, 70; Formulas, 79,
80; Caution, 78
Dew point, The, 76
Dry vs. wet air, Deg. of
saturation, 70 D. and
w. a compared, 79; For-
mulas, 79, 80
Humidity (Relative) of air,
74; How measured, 71
Tables, 75, 81
Vapor pressure, Actual; How
calculated, 75; Saturated
(table), 77
Vapors, Laws of, 80
Illuminants for safety lamps, 307
Light volatile oils: Benzine,
gasoline, naphtha, 308
Mineral oils: Crude petroleum
(rock o..), 307; Coal o.
(kerosene), 308
Incandescent lamps :
Cause of mine explosions,
127
Conditions of breaking, 128
Indicators, Gas (See G. 1.)
Inertia, a property of matter, 23
Inflammable and Explosive Mine
Gases, 112, (See E. M. G.)
1. gases, The, 112; I. limits of
gases (table) 114; range,
112
Inflammation of gases; Theory
of, 116
Lamp flames (chart;, 303
Lamphouse or station, 293
Lamps, Acetylene (Carbide), 308
(See A. Gas)
C. 1. in blackdamp, 311
Extinction of c. L, 312
Precautions in use of c. 1.,
313
Lamps, Electric Mine, 313 (See
E. M. L.)
Lamps, Mine safety,
Bonnet or shield, 271; Effect
on flame cap, 303
Chart of 1. flames, 303
Classification of s. 1., 270
Defective s. L, cause of explo-
sion, 127
Historical grouping of s. L,
286, 287
Illuminating power, 273
Lock fastenings, Lead 1.;
Magnetic 1., 272
Oil-burning 1. ; Non-volatile
o.; Volatile o., 271
Permissible m. s. L; Defini-
tion, 288
Principle of construction ; Pro-
tecting shield ; Stephen-
son L, 268; Wire gauze,
269
Requirements of a good test-
ing 1.; Sensitive to gas,
270; R. of working 1.,
272
Specifications by the Bureau
of Mines, 274; Conditions
of testing, 288; Mechani-
cal tests; Photometric t.
Explosion t., 290; Tests
of glasses; Igniter t., 291;
Approval of s. 1., 292;
Notification to manufac-
turer; Fees for testing,
293
INDEX
425
Lamps, Mine safety:
Types of 1., Characteristic,
275: Davy, 275; Clanny,
277; Marsaut, 278; Mu-
eseler, 279
Types of 1., Special, 281:
Pieler, 282; Chesneau;
Ashworth - Hepplewhite-
Gray, 283; Stokes alco-
hol; Clowes hydrogen,
284, Wolf, 285; Miscella-
neous 1., 286, 287
Use and care of s. 1., 293;
Handling of s. 1., 294
Volume of 1. chimney, 269
Latitude etc., 402
Laws of gases :
Avogadro, law of gaseous
volume, 29; Application, 64
Boyle-Mariotte, law of vol.
re pres., 19
Charles-Gay Lussac law of
vol. re temp., 18
Graham, law of diffusion of
air and g., 36, 37
Liquid state, 23; Liquefaction, 48;
Distribution of heat by
convection, in liquids, 52
Logarithms :
Definition; Systems; Charac-
teristic, Mantissa, 328;
How to find 1. of a number,
329; Use of 1., 330;
Rules; Arithmetical comple-
ment, Antilog. 331; Ex-
amples, 332; Table of 1.
333-351
Lighting, Mine lamps and, 268
Liveing gas indicator, 296
Longwall plans, 256, 257
Ventilation of 1. workings, 256
Longtiude etc. 402
M
Marsant safety lamp, 278
Marsh gas (See Methane)
Mass, property of matter, 22
M., volume, density; Unit
of m., 24; Measure of
force, 25
Matter, 22
Definition; Divisions of m.;
Properties of m., 22
Heat a condition of m., 51
M. is indestructible, 62
Molecular theory of m., 59
Measurement, 25
Distance; Force; Static f.,
Dynamic f.; Formulas,
25; Tine; Special units
of m.; Compound units,
26
Energy; Forms of e.; Kinetic
e.; Potential e. 27
Measurement of air currents, 199
(See Mine Potential)
Measurement of heat, 51
Standards of h. m.; Thermal
units; British t. u., 51;
French t. u. or calorie; Pound
c.; Conversion formulas,
52
Measurement of time, 402
Sun t.; Equation of t.; Sid-
ereal t.; Local t. ; Stand-
ard t., 402; Eastern t.;
Central t., Mountain t.,
Pacific t.; Civil t. ; Astro-
nomical t., 403
Measurement of humidity (See
H. of Air)
Measurement, Relative (See Spe-
cific M.)
Measures, Weights and (tables),
397
U. S. and British system, 398;
Metric system, 403; Me-
, trie abbrevations; Con-
version tables 406; Com-
pound units, 411
Mechanical equivalent of heat,
53
426
INDEX
Melting points of substances, 49
Difference bet. m. p. and
freezing p. ; 49
Table of m. p. of substances,
50
Mercurial barometer, The, 6
Methane (Marsh gas), 93 (See
Firedamp)
Combustion of m. in air or
oxygen, 64; wt. of o.
per Ib. of m., 96; Vol.
of o. per unit vol. of
m., 64; Effect of other
gas.es and dust, 95; Heat
of c. of m. in air (table),
66; Heat of formation of
m. (table), 68; Heat cal-
culation, 67
Explosive limits of m. (table),
114
Flame temp, of m. burning in
air, calculation, 119
Occurrence and properties, 93,
Occluded in coal forma-
tions, 88
Percentage composition of m.,
39
Mine air, 5 (See A.)
Concussion of a. in mines,
127
Mine gases, 86 (See Geological
Conditions)
Chart of m. g., 115
Common m. g. (table), 89
Explosive m. g. (see E. M. G.)
Inflammable m. g. (See 1.
M. G.)
Properties and behavior of
m. g., 93
Mine potential, The, 199 (See P.)
Effect of splitting on m. p.,
203, Illustration, 204 ;
Practical example, 205;
Examples, 209; Formu-
las: M. power p.; M.
pressure p. 211
Mine potential :
Formulas: Power p., 197;
Pressure p., 198
General m. p., 212; G. m. p.,
equal splits, 213; G.m.p.,
natural division of air,
Example, 228
P. of airway, 200; Table of
values, dif. a., 202; P. of
circulation, 201 ; Table of
values, dif. c., 203
Mineral oil, 307
Mine -rescue work and appliances,
131 (See Explosion, M.)
Mine Ventilation, 1G1 (See Fur-
nace V.; V., Practical)
Conducting air currents in
mines (See A. C., C.)
Formulas, 197-199; Basal f.,
196
Kinds of v.; Natural v.;
Slope and dip workings,
162
Power on the air; Work and
p. synonymous, 182; P.-
press.-vol. chart, 185; P.
formulas, 199; P., press.,
quantity, 201
Pressure, Ventilating, 174: P.
producing circulation; P.
how produced, 174; P.
how estimated; P. how
measured, 175; P. formu-
las, 198; unit of v. p.,
177; P. calculated from
m. potential, 206; P.
due to regulator, 232;
P. re velocity; 173;
Equivalents in v. p. (table)
175, 185
Quantity of air, 181: Q. of
a. required; Q. how esti-
mated ; Q. how measured,
181; Q. formulas, 198; Q.
calculated from m. po-
tential, 207
INDEX
427
Mine Ventilation:
Resistance of airways, 191
(See A.)
Requirements in v., 161; R.
of the m. law, 182,
199
Spitting air currents (See S. A.
C.;
Symbols and formulas, 192
Systems of v., 261 : Blowing
s., 174, 262; Exhaust s.,
174, 261; E. vs. B. s. of
v., 261
Variation of factors, 247
Mixed lights in mines, 127
Molecular state, 23
M. forces: M. attraction; M.
repulsion, 23; M. heat,
46; M. h. of reaction, 67;
M. theory, 59; M. volume,
29; M. weight, 59
Molecule, The. — Definition, Sym-
bol; Atoms in a m., 58
Mueseler safety lamp, 279
English and Belgian types,
280
N
Natural division of air, 220 (See
Splitting the A. Current)
Natural gas, 87
Natural overcast, 251
Nitrogen in air: Percentage by
vol., by wt, (table),
4; Rel. veloc, of trans-
piration from coal (table),
35; N. in blackdamp, 110;
N. in afterdamp, 111;
Symbol, mol. wt., den-
sity, sp. gr. (table), 89
Non-volatile oils used in safety
lamps, 307
O
Occlusion of Gases, 34 (See Geo-
logical Conditions)
Occlusion of Gases :
Examples of o.; Pressure of
o. g., 35, 88
Oil -burning lamps, 271
Oils: Non-volatile o. used in safe-
ty lamps ; Animal o. ;
Vegetable o., 307
Mineral o. (rock o.), 307; Coal
o. or kerosene, 308
Volatile o., 271; Benzine,
naphtha, gasoline, 308
Water, gas and o. in strata,
86
Olefiant gas (ethene, ethylene), 92
Composition, 59
Density, sp. gr., mol. wt., sym-
bol, 89; Chart, 115
Inflammable, 112
Occurrence and properties, 92
Rel. rate of transpiration, 35
Olefines, 92
Open lights cause of explosion, 127
Open-flame lamp, (carbide 1.), 308
Ounce, The fluid, 405
Outbursts of gas, 88
Overcasts, 249, 250, 251
Oxides: Monoxide; Dioxide; Tri-
oxide, 62
O. of nitrogen, 60
Oxygen :
Absorption of o. in spontane-
ous combustion, 58; A.
by coal, 111
Consumed in breathing, 3
(See B. Apparatus)
Density, sp. gr., mol. wt., sym-
bol, 89
Depletion of o. in air, 4;
Caused by absorption of
o. Ill; Effect on flame,
312; Effect on life, 4;
Increases poisonous ac-
tion of carbon monoxide,
107
Normal percentage of o. in
air, 4
428
INDEX
Paraffins, 92
Paul breathing apparatus, 147
Percentage composition: By vol-
ume, 40; By wt., 39
Calculation of p. c. of air, 30
Percentage of gas re height of
fame cap; Chart; 303
Calculation of h. of f. c.,
304; Diagram; Formu-
las, 305
Permissible breathing apparatus,
148 (See B. A.)
Permissible electric mine lamps,
319 (See E. M. L.)
Permissible mine safety lamps,
288 (See L., M. S.)
Phlogiston, 1
Physics of air and gases, 17 (See
Expansion of A. and G. ;
Hygrometry)
Tension (pressure) of a., 19
Pieler safety lamp, 282; Chart of
1. flame, 303
Plan of mine, General, 252
Requirements re drainage,
haulage and ventilation;
Economy and efficiency;
Drainage, 252; Haulage,
253; Road angle re grade
in inclined seam; Formu-
las, 254; Distribution of
air, 257
System of mining: Room-and-
pillar, 254, 255; Long-
wall, 256, 257; Single,
Double, Triple-entry sys-
tems, 263; Multiple-entry
system; Economy of m.
main airways, 265
Output, Estimation for given,
266
* Ventilation of longwall work-
ings, 256
Potential (See Mine P.)
Explanation of potential prin-
ciple, 196
Formulas: P. of airway, 200;
Values, dif. a. (table), 202 ;
P. of circulation, 201 ; Val-
ues, dif. c. (table), 203
Pressure p.; Power p. —
Caution, 207; Equivalent
p. f.; Power; Pressure,
208; Quantity, 209; Il-
lustration 197, 198
Part p. values, 212; Illus-
tration, 213, 216
Relative p. values, 221; Illus-
tration, 224
Split p. formula, 204; Ex-
amples, 205-207, 209;
Split power p. and press.
p. f. 211; Ex.; General
s. p., 229
Summation of split p., 232
Tandem circulations, 214:
Summation of p., 214,
215; General t. p. form-
ulas, 216
Use of p. factors, 208
Pound : Unit of mass, 25
Pound -calorie, 52; Value of, 53;
Pound-molecule, 67
Power on the air, 182 (See Mine
Ventilation)
Power, volume, pressure diagram,
185
Practical ventilation (See V. ,P.)
Pressure (See Mine Ventilation)
Effect of p. on air and gas, 17;
E. on freezing, fusion,
melting points, 49; E. on
boiling point and vapori-
zation, 50
Heat due to p., 47
Power, volume, p. diagram,
185
P. re absolute temp. 20
P. of occluded gas, 35
INDEX
429
Pressure :
Primary and secondary splits,
219; P. and s. pressures,
239
Proportionate division of air, 230
(See Splitting the A.
Current)
Regulators required, 219, 230
(See R.)
Psychrometer, 71 (See Hygro-
meter, The)
Pulmotor, 103
Q
Quantity of air, 181 (See Mine
Ventilation)
R
Radiation of heat, 52
Ratios, Solution by (in mine ven-
tilation), 173
Reaction, Chemical, 56
Endothermic; Exothermic, 65,
67
Interchange of atoms, 62
Molecular heat of the r., 67
Regulate the air, To, 230
Regulators (in mine ventilation),
239, 251
Effect of r., 231
Kind: Box r.; Door r., 321
Pressure due to box r., 232;
Area of opening in b. r.,
234; Example, 240; Ve-
locity and quantity of
air passing, 233
Use of the door r. ; Area of
opening; Example, 240;
Quantity of air passing, 235
Rescue work in mines (See Ex-
plosion, M.)
Resistance of airways, 191 (See
A.)
Respiration (See Artificial R.)
Action in r. wearing breathing
apparatus, 133
Respiration :
Capacity of lungs; Rate of
breathing; Quantity of
air exhaled each breath;
Quantity of air inhaled
per min. depending on
exertion; Volume of car-
bon dioxide exhaled about
equal to vol, of oxygen
inhaled, 133
Effect of carbon dioxide on r.,
109, 110
Quantity of oxygen consumed
in breathing, 3
Respiratory action, 3
Origin and regulation at nerve
center; Transmitted to
r. muscles produces
breathing ; Oxygen ab-
sorbed by the blood and
carried in the circulation
oxidizes the impurities,
which are expelled largely
in the carbon dioxide
of the exhaled breath
containing 2 or 3 per
cent, of that gas, 3
Respiratory system, 2
Purpose to oxidize the organic
matter of the body and
accomplish its removal in
form of carbon dioxide
in the exhaled breath.
Safety lamps, Mine (See L., M.
S.)
Salts, in chemistry, 61
Saturation of air (See Hygrometry)
Scale of air, in ventilation, 260
Secondary splitting, 235
Diagram of s. s.; Formulas,
general split potential and
gen. tandem potential;
Illustration of s. s., 236;
430
INDEX
Examples, 237-239; Pri-
mary and s. pressure, 239 ;
Symbols, 236
Secondary splits, Primary and, 219
Shaft columns, in ventilation, 168
(See Air C.)
Slope mines, Natural ventilation
in, 162
Shaw gas machine, 297
Single -entry system, in ventila-
tion, 263
Solids, 23; Conduction of heat in
s., 52; Standard for s.,
31
Solution, Solvent, 48
Specific, Meaning of the term :
S. gravity; S. heat;
S. volume; S. weight;
Relative measurements
referred to adopted
standards, 28
Specific gravity, 30
Definition; General formula,
30; S. g. of substances
(table), 32; Finding s. g.
of gases, liquids; solids —
formulas, 31; Use of s. g.,
33; S. g. of mixed gases;
Calculation, 40; S. g.
caluclated by law of dif-
fusion; Formula, 41; S. g.
of mine gases (table), 89
Specific heat, 54
S. h. per gram-molecule is
molecular h., 47; S. h. of
a substance is its relative
h. capacity, 54; S. h. of
solids, liquids,, gases
(tables), 55; S. h. varies
with temp., 56
Specific measurement: Elements
the basis of relative m.,
30; Relative m. shown by
chemical equation giving
mol. wts. and vol's., 63;
Rel. vol. of a gaseous
atom the unit of vol.,
63, 64; Relative humidity
of air expressed by ratio
of actual vapor pressure
to the saturated v. p., 74
Specific volume (See Atomic V.)
Specific weight (See Atomic W.)
Specifications, by Bureau of
Mines:
Permissible breathing appa-
ratus, 148 (See B. A.); P.
electric mine lamps, 319
(See E. M. L.); P. mine
safety lamps, 288 (See
L., M. S.)
Splitting the air current, 218, 260
A. splits, 258
Effect of s. on mine potential,
203; E. on mine resist-
ance, 245; E. on quan-
tity, 245; E. on velocity,
244
Equal splits; Illustration, 223;
General mine potential,
213; Ex., 214
Formulas Split potential, 204;
S. power and s press, pot.,
211; General tandem
power and press, pot's.
216; Summation of split
pot., 222; Sum. of pot's
in secondary s., 237;
Advantage in sum. of
pot. values, 227
Natural division of a., 220
Ex., 224, 225-230; N. s.;
Proportionate s., 219
Need of s. the a. c., 218;
Method of s., 219
Practical conditions, result
of s., 243; Ex., 245
Primary and secondary splits,
219
Proportionate division of a.,
230 (See Regulators);
Ex., 232
INDEX
431
Splitting the air current :
Quantity, Increase of, 219;
Q. proportional to num-
ber of splits, 243
Theoretical considerations in
8., 242
Unequal splits, illustrated, 224
Spontaneous combustion, 58
Cause of explosion, 127
Standards, Comparison of, 30
Air, hydrogen, water 30, 31
S. for gases; S. for liquids
and solids, 31
Static force, 25
Steam, 82
Definition ; Saturated s. ; Su-
perheated s., 82
Diagram of heat and temp.
curves, 83
Steam tables (Marks and
Davis), by permission of
publishers, Longmans,
Green & Co., 84, 85
Stone Dust (See D., Shale or s.)
Stoppings, in mine ventilation, 249
Stokes alcohol lamp, 284
Sulphuric acid, 61
Symbol, Chemical, 58
S. of a molecule, 58
S's in mine ventilation, 192
Tables:
Circumferences and areas of
circles, 391
Conversion of compound units,
411; Conversion t.;
Weights and measures,
U. S. and metric, 407
Logarithms of numbers, 333
Sines and cosins, 353
Squares, cubes, s. roots, c.
roots and reciprocals of
numbers, 373
Tangents and cotangents, 363
Tandem circulations, 214 (See
C. in mines)
Temperature, 43
Absolute t. Rel. to vol. of
air and gas, 18; Rel. to
press, of air and gas; T.,
press., vol. of air and
gas, 20; Abs. zero, 18;
How t. is measured-two
scales, 43; Table, Fahr.
and centigrade scales, 44
Mean observed t. dif. alti-
tudes (table), 11; Drop
in t. as altidude increases
above sea level (table),
12; Rel. of drop in t. to
alt. (formula), 13; Aver-
age t. of atmos. air col-
umn (formula,) 14
Volume of air and gas, Effect
of t., 17
Temperature of flame (see F.,
Nature and T. of)
Temperature of ignition, 117
Table of t. of i. of gases,
117
Testing for gas, 295 (See Flame
Caps)
Making a test for gas in the
mine, 306; Use of gas in-
dicators (See G. 1.); Use
of lamps in t. for g, (See
L., Mine Safety)
Theory of ventilation, 161 (See
Mine V.)
Thermal units, 51 (See Heat)
Thermochemistry, 65
Writing a thermochemical
equation, 67, 69
Thermometer scales, 43
Comparison of Fahr. and
centigrade s. (table) 44
Time in estimation of velocity and
power, 26
Calendar t. — Day: Solar d.,
Sidereal d.; Month; Year:
432
INDEX
Solar y. ; Sidereal y. ; Com-
mon y. ;Leap y., 401
Measurement of t. : Sun t. ;
Sidereal t. ; Equation of t.,
Local t., Standard t., 402;
Eastern t., Central t.,
Mountain t.; Pacific t. ;
Civil t., Astronomical t.,
403
Transmission of heat, 52 (See H.)
Transpiration of Gases from Coal,
35
Relative velocity of t. (table),
35
Triple-entry system, 263
U
Undercast, in mine ventilation,
249, 251
Units of measurement: Special u.;
Compound u.; U. veloc-
ity; U, work; U. power,
26, 406; Heat u., 51;
Kinds of u., 397; U. of
ventilating press., 177;
U. resistance, 192
Valence, valency, 59
Vaporization, Evaporation, Boil-
ing, 50
Effect of press, on v., 50;
B. points of liquids (table;
51; V. takes place at all
temp., 24, 80
Vapors and Gases, 24 (See Hygrom-
etry)
Definition of a v., 24
Laws of v., 80
Saturated v. press, (table),
77
V. saturates space it occupies,
80
Wt. of water v.; formulas,
79, 80; Diagram, 81
Velocity (See Air Currents, Con-
ducting)
Constant v., 25; Acceleration,
26
Ventilating pressure, 174 (See
Mine Ventilation)
Ventilation, Mine (See M. V.)
Ventilation, Practical, 248 (See
Air Currents, Conducting)
Distribution of air, 257 (See
Splitting the Air Current)
Entry systems : Single, Double,
Triple, 263; Multiple, e. s.,
265;
V. of cross-entries, 259; V.
of mine stables, 260; V. of
longwall workings, 256
Natural v. in slope and dip
workings, 162
Plan of mine (See P. of M.)
Systems of V. (see Mine V.) ;
S. of mine airways, 262
Volume: Atomic or specific v;
Molecular v. ; Avogadro's
law of v., 29; Application
of 1. of v., 64; V. of
atom, unity, 64
Density and v., 29
Mass, v., density, 24
V. re abs. press., 19; re
abs. temp., 18
V., press., temp., 20
Power, v., press, diagram, 185
Volatile oil flame, sensitive to gas,
288
Volatile oils, in safety lamps, (See
Ilium inants for S. L.)
Give fuel cap in testing for
gas, 271
Light v. o., 308
Water: Density referred to air,
31; Unit wt. dif. temp,
(table), 34
INDEX
433
Water column, Calculation of, 6
Water gage, The Mine, 175
Calculation from m. potential,
206
Equivalents in measurement,
175, 185; Diagram, 184
Reading the w. g., 177
Scales, Dif., 176
Use of w. g. in the mine; What
it shows, 178
Water vapor (See Vapors and
Gases)
Weight :
A property of matter, 22
Atomic w., molecular w., 59
W. of air: Formulas, 4, 79, 80;
Dif. altitudes and temp.
(tables), 11, 15; W. of
elements (table), 28; W. of
substances (table), 32; W.
of water, dif. temp., 31, 33;
W.of oils (table), 33; W.
of woods (table) 34
Weights and measures, 397
Systems in use; Standards of
weight, length, capacity,
397
Weights and measures:
U. S. and British systems, 398
Calendar time, 401
Measurement of time, 402
Metric system of w. and m.,
403; Metric abbrevia-
tions, 406 ; Conversion
tables, 406; Compound
units, 411
Wet-and-dry bulb hygrometer, 72
(See H.)
Whitedamp (See Carbon Monoxide)
Wire gauze : Cooling effect ; Prin-
ciple of w. g., Standard
mesh, 269
Windy shot, in blasting, cause of
explosion, 127
Wolf safety lamp, 285 ; Flame-
cap diagram, 303
Wood, Wt., of dif., (table), 34
Work:
Internal w. due to expansion
of air or gas, calculated
in two ways, 20, 21
W., in mine ventilation, syn-
onymous with "power on
the air," 182
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