MINE GASES AND VENTILATION 
 

 PUBLISHERS OF BOOKS, FOR/ 
 
 Coal Age * Electric Railway Journal 
 
 Electrical \Xforld ^ Engineering News -Record 
 
 American Machinist v Ingenieria Interaacional 
 
 Engineering 8 Mining Journal ^ p o we r 
 
 Chemical, & MetallurgicallEngineering 
 
 Electrical Merchandising 
 
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- 
 tingTheoretical 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 the 5 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 . per cent. 
 
 Nitrogen 79 . 1 per cent. 77 . per cent. ' 
 
 100 . per cent. 100 . per cent. 
 
 Air also contains 0.04 per cent, of carbon dioxide (CO 2 ), 
 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 (32F.) 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 
 
 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 
 
 
 
 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/ 
 
 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 
 
 
 
 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 
 
 
 
 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. 
 
 B h = 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 - P er sc l- 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"> 
 
 ;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 w x at the altitude x, we have 
 
 8p x = w x 5x (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, w x , 
 and p x , we have 
 
 W x p x W 
 
 = ; and w x = ~p x (2) 
 
 W Po Po 
 
 Substituting this value in equation 1 and dividing both mem- 
 bers of the equation by p x , 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* = - 5 X ; or 5 X = -^ d log p x (4) 
 
 PO o 
 
 Then integrating between the limits x = 0, and x = h, remem- 
 bering that when x = 0, p x = p ; and when x = h, p x = p^ 
 and subtracting the lower integral from the higher, 
 
 fc-0=(logp -logp ft ) (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 = 53.28T 7 (log po - log Ph ) (7) 
 
 Or, expressed in common logarithms, 
 
 h = 122.687 7 (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 p h ) 
 Or, log p h = 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 deg. C., the rise 
 in temperature is 20 = 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 ( 273C.) 
 or 492 deg. below freezing (-460F.). 
 
 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 ( 273C.), 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 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 p 2 = Tz 
 
 vi T l vi p 2 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 = W g (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 
 
 = 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 
 11 .0 
 79.92 
 112.4 
 132.81 
 40.09 
 12 
 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 
 
 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 
 96.0 
 58.68 
 14.01 
 190.9 
 16 
 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 
 
 y lron 
 
 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., 4C.). 
 
 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, 4C.) 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. 
 
 w z 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, w m j 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 
 
 793 
 
 49 5 
 
 commercial 
 Aluminum 
 
 0.834 
 2 66 
 
 52.1 
 166 
 
 Asphalt (1 to 1.8) 
 
 1 4 
 
 87 
 
 Brass, east (7.8 to 8.4) 
 
 8.1 
 
 506 
 
 rolled 
 
 8 4 
 
 525 
 
 Brick, pressed 
 
 2 4 
 
 150 
 
 common, hard 
 
 2.0 
 
 125 
 
 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 
 
 Concrete 
 
 2.3 
 
 144.0 
 
 Copper, cast (8.6 to 8.8) 
 rolled (8.8 to 9) 
 
 8.7 
 8 9 
 
 543.0 
 556 
 
 Earth, dry, loose to well rammed 
 moist, loose to well rammed. . . . 
 wet, flowing mud 
 
 
 76 to 95 . 
 78 to 96.0 
 105 to 115 
 
 Granite (2 56 to 2 88) 
 
 2 72 
 
 170 
 
 Gold, cast (18.29 to 19.37) 
 
 18 83 
 
 1176 
 
 Gravel, loose 
 
 
 95 to 100 
 
 Gypsum, ground or calcined, loose 
 well shaken 
 Ice 
 
 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 . 
 
 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, 4C.) 1.0 62.428 
 
 (pure, 62F.) 0.999 62.366 
 
 (pure, 212F.) . 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) 
 
 . . 880 
 
 7.34 
 
 whale 
 
 0.925 
 
 7.72 
 
 Vegetable cottonseed 
 
 .... 0.923 
 
 7.70 
 
 linseed (raw) 
 
 . 933 
 
 7.79 
 
 (boiled) 
 
 0.780 
 
 6.51 
 
 olive 
 
 0.917 
 
 7.65 
 
 rape (colza) 
 
 0.915 
 
 7.63 
 
 Mineral petroleum (crude) 
 
 . 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 (60F., bar. 30 in.) 
 as 0.0766 Ib., since the specific gravity of carb.on dioxide (CO 2 ) 
 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 (CH 4 ); 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 (CO 2 ); sp. gr., 1.529; v = , = 0.808 
 
 *- 529 (Air = l) 
 
 Methane (CH 4 ); 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 
 (CH 4 ), carbon monoxide (CO), carbon dioxide (CO 2 ), 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 (CH 4 ) 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 (CH 4 ) 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 (H 4 ) ; 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 (CO 2 ) 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 (O 2 ); 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 (CH 4 ) to each 1000 volumes of carbon dioxide 
 (CO-.). The process is as follows: 
 
 Volume Sq.gr.^I 6 ^ 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 =* ~ - 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 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 
 
 
 
 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 = 104F. 
 
 F = % ( - 10) + 32 = 14F. 
 
 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 32F 144 B.t.u. 
 
 Sensible heat absorbed by water, 32 to 212F 180 B.t.u. 
 
 Latent heat of vaporization, from and at 212F. . . 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 (32F.). 
 
 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 
 
 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 ioilj j 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 . 324 . 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 
 
 1050-0 1989 
 
 Lead 
 
 60- 600 
 
 0.0299-0.0338 
 
 Lead (at melting point, 610F.) 
 Mercury 
 
 610- 680 
 32- 500 
 
 0.0356-0.0410 
 0334-0 0320 
 
 Platinum 
 Silver 
 Tin 
 
 60- 210 
 32-1200 
 32- 210 
 
 0.0324 
 0.0559-0.0750 
 0545 
 
 Zinc 
 
 32- 700 
 
 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 
 
 . 2374 
 
 . 1689 
 
 0.2374 
 
 Methane 
 
 0.5929 
 
 0.4219 
 
 0.3314 
 
 Olefiant gas 
 
 0.4040 . 
 
 2875 
 
 3951 
 
 Carbon monoxide 
 Carbon dioxide 
 Hydrogen sulphide 
 
 0.2450 
 0.2163 
 2432 
 
 0.1743 
 0.1539 
 1731 
 
 . 2369 
 . 3307 
 
 2897 
 
 Oxygen 
 
 2175 
 
 1548 
 
 2405 
 
 Nitrogen 
 Hydrogen. ... 
 
 0.2438 
 3 4090 
 
 0.1735 
 2 4260 
 
 0.2368 
 2361 
 
 Water vapor 
 Ammonia 
 
 0.4805 
 5080 
 
 0.3419 
 3615 
 
 0.2996 
 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 
 C 2 ; oxygen, O 2 ; 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 
 2H 2 + O 2 = 2H 2 O. 
 
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. 
 
 H 2 + C1 2 = 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 : 
 
 Ca 2 + O 2 = 2CaO 
 Ca 2 + 2C1 2 = 2CaCl 2 . 
 
 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: 
 
 N 2 0, N 2 2 , N 2 3 , N 2 4 , N 2 5 . 
 
 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 (H 2 S). 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 (H 2 0) to an anhydrous 
 acid (anhydride). 
 
 In the first instance, the formation is as follows: 
 
 Hydrogen radical (hydroxyl) 2(HO) 
 
 Acid radical . . SO, 
 
 Sulphuric acid H 2 SO4 
 
 Or, again, the formation may be regarded thus: 
 
 Water H 2 O 
 
 Sulphuric anhydride SO 3 
 
 Sulphuric acid H 2 SO 4 
 
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 (CO 2 ). 
 
 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, C 2 , H 2 , N 2 , 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 
 
 C 2 + 2O 2 = 2CO 2 
 
 The expression 2CO 2 should be interpreted to mean two mole- 
 cules of CO 2 , 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 (C 2 ) takes up two atoms of 
 oxygen to form the molecule of carbon dioxide (CO 2 ), 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 (NH 8 ) by electrolysis, forming free nitrogen (N) and 
 hydrogen (H) gases, placing below each molecular formula its 
 relative or molecular volume ; thus, 
 
 2NH 3 = N 2 + 3H 2 
 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 (CH 4 ) is exploded in a plentiful supply of normal 
 air, and the methane is completely burned, forming only car- 
 bon dioxide (CO 2 ) and water (H 2 O). The nitrogen of the air 
 being unchanged it may be omitted in writing the equation 
 expressing this reaction, which is as follows: 
 
 CH 4 + 2O 2 = CO 2 + 2H 2 O 
 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 + O 2 + 4N 2 - 2CO 2 + 4N 2 . 
 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 (CH 4 ), 
 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.-ca 1 . 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 .... 
 
 CH 4 
 C 2 H 2 
 C 2 H 4 
 C 2 H 6 
 CO 
 CO 2 
 H 2 S 
 S0 2 
 H 2 O 
 H 2 O 
 H 2 
 H 2 O 
 
 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 (32F.) 
 
 Water (32F.) 
 
 Water (212F ) 
 
 Steam (212F ) 
 
 
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 
 
 CH 4 + 2 O 2 = CO 2 + 2 H 2 O - x 
 
 39,060 + = 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 (CH 4 ) 
 is written thus: 
 
 CH 4 + 2O 2 = CO 2 + 2H 2 O - 388,116 B.t.u. 
 Or, in the French system, 
 
 CH 4 + 20 2 = C0 2 + 2H 2 O - 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 + O 2 = CO 2 - 174,600 B.t.u. 
 or C + O 2 = C0 2 - 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 (p v ) 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 t v = 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 8 g 7 X x 5 3 3 6 Q 02 - 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; p w and pd the respective 
 saturated vapor pressures of the tables, for the corresponding 
 wet-and-dry-bulb temperatures t w 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 
 
 
 
 '?, 
 
 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 70F., 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<* t w ) and the 
 
76 MINE GASES AND VENTILATION 
 
 barometric pressure (B), in inches of mercury, first find the 
 saturated vapor pressure (p w ), 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 = p w ( d ocT^ ) 
 
 oU \ oo / 
 
 Example. Find the actual vapor pressure when the dry bulb reads 
 60 and the wet bulb 54F., the barometric pressure being B = 30 in., 
 and the saturated vapor pressure for the wet-bulb temperature (54F.) 
 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 (60F.) is 0.5183 in., the relative humidity in the above ex- 
 ample is 
 
 TT P* ^ inn 0.3497 X 100 __ . 
 H= p d Xl = -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 
 (32F.) in. 
 
 Pressure, 
 pounds per 
 square inch 
 
 ! 
 
 Degrees, 
 Fahr 
 
 Barometric 
 pressure, 
 mercury 
 (32F.) in. 
 
 Pressure, 
 pounds per 
 square inch 
 
 -30 0.0099 
 
 0.0049 
 
 70 
 
 0.7335 
 
 . 3602 
 
 -20 0.0168 
 
 0.0082 
 
 71 
 
 0.7587 
 
 0.3726 
 
 -10 0.0276 0.0136 
 
 72 
 
 0.7848 
 
 0.3854 
 
 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 
 
 . 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 
 
 . 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 
 
 . 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 
 
 . 4826 
 
 . 2370 
 
 155 
 
 8.535 
 
 4.1914 
 
 59 
 
 0.5001 
 
 . 2456 
 
 160 
 
 9.630 
 
 4.7292 
 
 60 
 
 0.5183 
 
 0.2545 
 
 165 
 
 10.841 
 
 5.324 
 
 61 
 
 0.5370 
 
 . 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 p v (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 
 (p M = 0.4178 in.), is 
 
 , = 0.4178 - 
 
HEAT 79 
 
 The saturated vapor pressure for the given temperature 
 (see Table) is p Q2 = 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) 
 
 p a . r 
 Air fully saturated, w = - - Q (4) 
 
 w = weight (Ib. per cu. ft.) 
 
 c = degree of saturation, expressed as a decimal 
 
 p a = atmospheric pressure (Ib. per sq. in.) 
 
 p v = 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.82757cp v 
 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 - 0.3765p v ) (8) 
 
 It is evident that when air is fully saturated, c = 1, and 
 disappears from the formula. The values of p v 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 p a = p a cp v ; 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 p v , 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. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^f 
 
 -^* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ; 
 
 \>t 
 
 &'<> 
 
 ; 
 
 ^ 
 
 
 
 
 
 
 *" 
 
 
 
 L 
 
 r?. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o^ 
 
 ^ 
 
 ^ 
 
 ** 
 
 
 
 
 
 
 
 
 .Q 
 
 
 
 -N 
 
 X 
 
 ** 
 
 , 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 11 OK 
 
 360 
 
 
 
 
 
 
 
 'p. 
 
 
 
 
 
 
 
 
 ( x 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 ^x 
 
 
 a 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 ^ 
 
 X 
 
 
 
 
 
 
 
 ^ 
 
 
 
 S* 
 
 x 
 
 
 
 890 s 350 
 
 
 
 
 
 
 
 
 
 Xj 
 
 fc 
 
 ^, 
 
 / 
 
 
 
 
 
 
 
 
 \* 
 
 
 X 1 
 
 
 
 
 
 
 4* 
 
 
 
 
 
 
 
 
 
 
 X 
 
 "v 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 (X 
 
 ^ 
 
 
 w 
 
 
 
 
 
 
 
 
 ^ 
 
 / 
 
 
 
 
 "^ 
 
 s s 
 
 
 
 ^ 
 
 X 
 
 
 
 
 
 ^x 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 " > - 
 
 *^ 
 
 
 
 
 
 ^ 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 ^J 
 
 < 
 
 
 
 
 
 
 
 
 -$ 
 
 
 
 
 
 ^ 
 
 / 
 
 
 
 
 
 
 
 X 
 
 ** 
 
 
 
 x 
 
 X 
 
 
 
 ** 
 
 r^. 
 
 
 
 
 
 
 Is 
 
 *" 360 o 320 
 
 
 
 / 
 
 ' 
 
 
 
 
 
 
 J 
 
 x 
 
 
 ^1 
 
 
 X 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 W g 
 
 2 ^ 
 
 
 / 
 
 
 
 
 
 
 
 s 
 
 
 O e 
 
 V^J 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 HQC O 
 
 5 SCO ^ 310 
 
 / 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 ^ 
 
 ^ 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 s 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 13 3 
 
 ^340 --300 
 
 
 
 
 ^ 
 
 / 
 
 
 ^ 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 g 
 
 S ^ 
 
 
 
 / 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 H p^ 
 
 H S3 o *o 290 
 
 
 / 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1180 
 
 
 ' 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 820 W 280 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 900 
 
 880 . 
 
 860 s 
 
 840 
 
 70 80 90 100 110 120 130 140 150 160 170 180 190 200 
 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) 
 
 CH 4 
 C 2 H 4 
 
 16 
 
 28 
 
 8 
 14 
 
 0.559 
 
 978 
 
 Ethane 
 Carbon monoxide 
 Carbon dioxide . . ... 
 
 C 2 H 6 
 CO 
 CO 2 
 
 30 
 
 28 
 44 
 
 15 
 14 
 
 22 
 
 1 . 0366 
 0.967 
 1 529 
 
 Hydrogen sulphide 
 
 H 2 S 
 
 34 
 
 17 
 
 1 1912 
 
 Oxygen 
 
 O 2 
 
 32 
 
 10 
 
 1 . 1056 
 
 Nitrogen .... 
 
 N 2 
 
 28 
 
 14 
 
 9713 
 
 Hydrogen 
 
 H 2 
 
 2 
 
 1 
 
 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 
 
 N 2 
 
 C0 2 
 
 0-2 
 
 .C 2 H 6 
 
 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 
 
 CH 4 
 
 N, 
 
 C0 2 
 
 O 2 
 
 CO 
 
 C 2 H 4 
 
 Austria 
 
 88 9 
 
 10 8 
 
 1 
 
 3 
 
 
 
 Austria 
 
 99 1 
 
 7 
 
 2 
 
 
 
 
 Austria 
 
 90 
 
 9 2 
 
 2 
 
 6 
 
 
 
 Germany 
 
 87 2 
 
 11 7 
 
 1 l 
 
 
 
 
 Germany 
 
 77 7 
 
 18 5 
 
 3 7 
 
 1 
 
 
 
 South Wales 
 
 96 7 
 
 2 8 
 
 5 
 
 
 
 
 Wallsend, England 
 
 92 8 
 
 6 9 
 
 3 
 
 
 
 
 Jarrow, England 
 Oakwellgate, England 
 
 83.1 
 
 98 2 
 
 14.2 
 1 3 
 
 2.1 
 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 C n H 2n+2 ; 
 the "defines," C n H 2n ; the "acetylenes," C n H 2n _ 2 ; and 
 other compounds of less importance in mining, as the " ben- 
 zenes," "naphthalines," etc. 
 
 Occurrence and Formation. Methane or light carbureted 
 hydrogen (CH 4 ) and ethane (C 2 H 6 ), belong to the paraffin 
 or fatty group, while olefiant gas (C 2 H 4 ) 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, (C 2 H 4 ); sp. gr., 0.978; 
 
 Ethane, (C 2 H 6 ); 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 (C 2 H 6 ) 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 (CH 4 ) is shown by the relative weights of these 
 gases in the following reaction : 
 
 CH 4 + 2O 2 = CO 2 + 2H 2 O 
 
 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. 
 
 it 
 
 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 212F. is 970.4 B.t.u. The 
 heat absorbed by the products of combustion, for a rise of 
 1200 - 32 = 1168F., 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. CH 4 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 60F., 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 (CH 4 ) 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, 
 
 CH 4 + 2O 2 = CO 2 + 2H 2 O 
 Molecular volumes, 1212 
 
 It should be observed that when the symbol of each gas 
 is written as a molecule (oxygen = O 2 ) 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 
 (2O 2 ) are required to completely burn one volume of methane 
 (CH 4 ); and there are formed one volume of carbon dioxide 
 (CO 2 ) and two volumes of water (2H 2 O). 
 
 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 (CH 4 ) and carbon dioxide (CO 2 ), 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. 
 
 CH 4 = VL529 L236 = 
 C0 2 ~ 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: 
 
 CH 4 /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 (CH 4 ) : 
 
 Q = 1 X 12 = 12 
 H 4 = 4 X 1 = 4 
 
 Molecular wt. ==16; density, 16 -r- 2 = 8 
 Carbon dioxide (CO 2 ) : 
 
 C = 1 X 12 = 12 
 2 = 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 (CH 4 ) ................. .............. ____ 1658 volumes; 
 
 Carbon dioxide (CO 2 ) ......................... .... 1000 volumes; 
 
 Total . . ........................................ 2658 volumes. 
 
 Percentage, by volume, 
 
 Methane, 165 ^ Q 100 = 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 
 (CH 4 ), carbon monoxide (CO), ethane (C 2 H 6 ), ethene or olefi- 
 ant gas (C 2 H 4 ), hydrogen (H 2 ) and hydrogen sulphide (H 2 S). 
 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 . 
 
 9.5 
 
 29.5 
 
 66.3 
 
 72.0 
 
 The same data, in reference to olefiant gas (ethene or ethy- 
 lene), C 2 H 4 , 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 (1200F.), 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 + H 2 O = CO 2 + H 2 
 2H 2 + O 2 = 2H 2 O 
 
 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 PR 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 
 
 BUKNEDTOH t O 
 
 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 . 
 
 CH 4 
 
 1212 
 
 Ethane 
 
 C 2 H 6 
 
 1140 
 
 Ethene (olefiant gas) 
 
 C 2 H 4 
 
 1124 
 
 Hydrogen . 
 
 H 2 
 
 1077 
 
 Acetylene 
 
 C 2 H 2 
 
 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 . 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 + O 2 = 2CO 2 
 
 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 .... . 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, H 2 O) 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 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 w T hen 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 
 
 C0 2 
 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 . . . 
 
 237 
 
 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 + CO 2 = Na 2 CO 3 + H 2 O 
 
 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 = 1 MoJ an d the 4 Ib. of caustic soda, if completely 
 utilized, would absorb 4( 1 ^ ) = 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 V 2 , 
 the exhalation bagL 2 , 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 = W h = 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 Q m (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 
 
 Q m t 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, w u = .' ^D 
 
 Uait pressure, p = 1.3273 
 
 which can be written 
 
 1.3273B (T -- t) D 
 P " (460+ T} (460 + 
 
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 (h d ) in terms of the downcast air, 
 divide the above expression for unit ventilating pressure by the 
 weight (w d ) 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 
 w u 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 ( 10F.); 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 
 
 p n = 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), w = 
 
 ~~" JLU 
 
 1.3273 X 30 v 
 Slope column (positive), w, = ~ X 525 
 
 1 ^97*? V ^0 
 
 Shaft column (negative), w u = 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 
 p n = 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 p 2 , 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 = a v = 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, 2 2 = 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 (d 2 ) and the perimeter varies as the diameter (d) ; hence, 
 
 a 3 . d 6 
 - vanes as -p or simply as d 5 
 
 Hence, 
 
 q 2 varies as d 5 
 
 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, 
 
 8 V-/ 4 V 
 ~\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 = v 2 ), 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 
 (y 2 ); the final product will be the total resistance (R), in 
 pounds, as expressed by the formula 
 
 R = ksv 2 
 
 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 800 2 = 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, 
 X p = pressure potential, 
 X u = 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%, q 3 , 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, X z , X 3 , etc.; or X a , X b , 
 X c , 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 X pa 
 or the power potential X ua - The general potential, in a split 
 circulation, is written X Q ; or X p0 and X U Q 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 X a + Xb + X c . 
 
 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 X , X a o, 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= ksv 2 
 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 (ksv 2 ) 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 (v 2 ) 
 of the air current. 
 
 For the same total pressure (pa) , in an airway, k being 
 constant, the square of the velocity (v 2 ) 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 
 
 _ ksv 2 
 
 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 = ksv 2 
 Power on the air, u = pav = ksv 3 
 
 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 R A = 500 /^ P Cr 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, X p = X u \/X~u = 373.45 \/373.45 = 7217, nearly 
 Pressure potential, 
 
 X n = 
 
 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 = X u \/u q = 373.45 \/300,000 
 
 = 25,000 cu.ft. per min. 
 
 q = X p \/p q = 7217A/12 =25,000 cu.ft. per min 
 
 ksv 2 0.00000002 X 120,000 X 500 2 
 
 Pressure, p = p = 5Q 
 
 = 12 lb. per sq. ft. 
 _ ksq 2 _ 0.00000002 X 120,000 X 25,000 2 
 
 p ~ : T 3 ~ p = 50 3 
 
 = 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 = ksv 2 R = 0.00000002 X 120,000 X 500 2 
 
 = 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^ -- 
 
 a 3 50 3 
 
 = 300,000 ft.-lb. permin. 
 
 u = qp u= 25,000 X 12 
 
 = 300,000 ft.-lb. permin. 
 
 permin. 
 
 u = p av 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 /60,000 2 
 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 ' } = 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 = \ = A l- 
 
 \ 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 
 
 
 
 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, 
 
 Q 2 120,000 2 
 
 = 
 
 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 = 1.414 3 = 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 (X u ) and a pressure potential (X p ). 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 = X u \/u 
 q = X p \/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 
 
 X u = ,, = . , = 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* 75,000 2 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 = = sa y 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 = X u \/^ = 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 
 
 X p = V~X* U = A/429. 1 3 = 8890, nearly 
 
 Then, q = X p 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, 
 
 g 2 30, OOP 2 
 
 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, X u 
 
 Mine pressure potential, X p = \/ 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: 
 
 kO 3 
 
 H = 
 
 I 1 1 1 \ 
 
 \YT 3 + xT 3 + !x7 3+ etc v 
 
 #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 
 
 Q 3 1 
 
 ~ #33,000 \ Xj #33,000 X u 3 
 
 But, since l/X u z = k s/a 3 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 X u = -=; and _1_ = JL 
 
 Now, calculating the value of l/X u 3 = s/a 3 , 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 
 
 I 1 
 
 80 X 80 X 80 
 120,000 
 
 .l/Oo 
 
 = 0.5555 
 n ft '-i '-in 
 
 1 
 
 60 X 60 X 60 
 70,000 
 
 I 3 
 
 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 
 
 X = -. -. = 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 
 
 kQ 3 _1_ _ 0.00000002 X 30,000* 1 , 
 
 " #33,000 *o 3 " 0.60 X 33,000 X 0.7716 3 
 
 (b) The mine water gage due to this circulation is 
 
 kQ* 0.00000002 X 30,000 2 
 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/X U Z = s/a 3 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, 
 
 Xi 3 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/X 3 0.4635 
 
 For the horsepower and water gage, we have 
 
 kQ* 1 0.00000002 X 50,000 3 x 
 H = f = 33,000 - X 
 
 = kQ^ J_ = 0.00000002 X 50, OOP 2 
 W ' 9 ' ~ 5.2 X 3 ~ 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, X 2 , X 3 , etc.; and the 
 corresponding unit pressures and powers on the air by pi, p 2 , 
 p 3 , etc.; and MI, M 2 , M 3 , 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 U Q . 
 
 Mine pressure, p (} = Q 2 l^-r + -^- + etc 
 
 \A "i A 2 
 
 = Q 2 (w~ + vT" + etc ') 
 \A tt i A 3 u2 / 
 
 or 7>o 
 
 \ tt i u2 
 
 These formulas may be written more simply by indicating 
 the summation of the potential factors by the character ; 
 thus, 
 
 Mine pressure, p Q = 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, U Q = Q 3 ( -^g~~ H~ ^T 
 
 \A u i A 
 
 or u = Q 8 -- 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 u = Q s 
 
 
 In a tandem circulation, if desired, the general mine po- 
 
216 MINE GASES AND VENTILATION 
 
 tentials for power (X u0 ) and for pressure (X p0 ) can be calcu- 
 lated by the formulas 
 
 X ua = -T7 =; and X vo = 
 
 "*' 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 
 
 .A M a .A i yo 
 
 70 3 
 90,000 
 
 152,000 = 
 
 = 0.0900 
 
 oo 8 
 
 Potential factors for entire mine, 2 (ip-J = 1-0170 
 
 Mine part % = ^ = = 9944 
 
 potentials, " \/S(l/^ u 3 ) " ^1.0170 
 
 X po = - L = , l = 0.9916 
 
 vsa/Xp 2 ) v i.oi7o 
 
 fcQ 2 0.00000002 X 30,000 2 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 _ fcQ 3 _ 0.00000002 X 3Q,000 3 
 
 the air, = X * uo ~ .994 4 3 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, 
 
 k Q 3 ^/ 1 \ 0.00000002 X 60,000 3 X 0.1723 
 H *" 3^000 S feV = 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 60,000 2 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 X u i and X pi , respectively; and designating 
 
220 MINE GASES AND VENTILATION 
 
 these factors after splitting, by Q 2) X u2 and X p2 , respectively, 
 we have the following formulas: 
 
 ~ X u2 ~ -3 \ /X n $ 
 Power constant, Q 2 = Qi -^ ; or Q 2 = Qi 
 
 3 
 
 Pressure constant,Q 2 = Qi ^^; or Q 2 = Qi 
 
 A p i \ \^\ u i/ 
 
 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 X p i = 0.6708, 
 and after splitting X p2 = 0.8554: 
 
 Hence, Q 2 = 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, 
 
 kloq 2 , 9 p/a 3 \ 
 
 P 11 an d q = T (r-J 
 
 a 3 k \lo I 
 
 Then, since p and k are both constant, q z varies as a 3 /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 (X p ) is equal to the cube of the power 
 potential (X u ); 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\, q z , 
 q 3 , etc., and the corresponding split potentials Xi, X^ X 3 , 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+ X 2 + X 3 + 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 X p i, X p2 , 
 X p3 , 'etc.; the corresponding powers on the air by MI, u 2 , u 3 , 
 etc.; and the total power on the air by M O , 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 : 
 
 u = MI+ u 2 + etc. (1) 
 
 But, MI = JT-; u 2 = --; etc. (2) 
 
 A p i 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 : 
 
 /cO 3 
 Horsepower on the air, H = - 
 
 The formula for calculating the water gage, in like manner, is 
 
 kQ 2 
 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 60,000 2 
 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, _ kQ 3 _ 0.00000002 X 60,000 3 
 
 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, 2X P ........................... 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, SX P 4.636 
 
 kQ 2 7 / Q \ 2 
 Pressure, p -^ . 2 = k ( j 
 
 p. = 0.00000002 (-^ 3 6 ) 2 = 5.2 Ib. per sq. ft. 
 
 Horsepower on the air, 
 
 feQ 3 0.00000002 X 75,OOQ 3 
 
 - oo / v, v N9. - 33^00 X 4.636 2 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.; 
 
 
 
 = 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.; 
 
 
 
 = 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 (X p ), 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, q a = ^ggy X 100,000 = 34,570 cu. ft. per min. 
 
 SQ^ 
 Split B, q b = ^^ X 100,000 = 29,960 cu. ft. per min. 
 
 Split C, q e = 7 X 100,000 = 20,500 cu. ft. per min. 
 
 ^.9o7 
 
 Split D, q d = ^^ 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 
 
 = kloq 2 
 a 3 
 
 Thus, taking split A, 
 
 0.00000002 X 6000 X 40 X 34,570 2 
 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\/ ^ ^ = 1.920 
 
 120 
 
 r~i2 
 
 Split U, X p , - 12 \62p5a = L664 
 
 Split C, X p3 = 72X^7^ =1-138 
 
 Split D, X p t - 
 
 Sum of part pressure potentials (2Z P ) 5.553 
 
228 MINE GASES AND VENTILATION 
 
 Substituting this value for SZ P , in the formulas for finding the horse- 
 power on the air and water gage, in natural splitting, 
 
 0.00000002 X 100,000 3 
 Horsepower on air, H = 33>0 oo x 5.5532 = 19-6 hp 
 
 0.00000002 X 100,000 2 
 Unit pressure, p = - - - P . 2 - =6.48 Ib. per sq. ft. 
 
 0.00000002 X|100,000 2 
 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 3 M = ; or A M = 
 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 /100,000 2 
 
 Mine power potential, A M =\ = \/ 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; 
 
 X l 
 
 x a 
 x b 
 x c 
 x d 
 
 = 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 
 
 Q07 
 
 J 
 
 24 
 
 
 o = 18; Z - 
 
 90 
 
 \840 
 
 X 
 
 20 
 
 = 0.786 
 
 J 
 
 20 
 
 
 
 \720 
 
 X 
 
 IS 
 
 The general split potential (X Q ) is equal to the sum of the potentials 
 for the four splits; thus, 
 
 X Q = 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,< i tU 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 X p by combining, in tan- 
 dem, the main-airway potential (Xi) and the general split 
 potential (X ) 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 .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 \X V -] ~ 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 20,000 2 
 Split A, p = - 96 x 96 x 96 = 2.17 Ib. per *q. ft. 
 
 0.00000002 X 12,000 X 52 X 40,000 2 
 Spht B, p = - 12 Q X 120 X 120 ~ = 1L55 lb ' per * *' 
 
 0.00000002 X 8000 X 36 X 30,000 2 
 Split C, p = 72 X 72 X 72 = 3 ' 89 l per sq ' &' 
 
 0.00000002 X 1000 X 20 X 10,000 2 
 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 (p r ) 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 = 
 A d = 
 
 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 X a , Xb, X c , etc. 
 
 Secondary splits are designated AI, A 2) etc., and BI, B%, 
 etc., depending on the primary split from which they branch; 
 and the corresponding split potentials by X a i, X a 2, Xbi, Xbt, 
 etc. The general potential for a primary split is designated 
 XQ, and for a secondary split X ao , 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, A 2 , 
 etc., or Bi, B z , etc. 
 
 The corresponding split potentials are indicated thus: 
 
 i 
 
 Primary potentials, X a , Xb, X c , etc. 
 
 Secondary potentials, X a \, X a z; Xbi XL?; X c \ X c i; etc. 
 
 General split potentials, X ao , Xio, X co 
 
 General mine potentials, X 
 
 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 C 8 , 800 ft. long. 
 The part potential values for the splits are, then, 
 
 Split A, X p = eu/p X a (as before) = 1.837 
 
 Split 5, X b (as before) = 1.623 
 
 Split C, 'x.- 48^1-^ = 2.629 
 
 " 48 "=1.697 
 
 Split Ci, X e i = 48 J 
 
 Split C 2 , X cZ = 48 J, 
 
 1200 X 32 
 
 = 2.078 
 
 800 X 32 
 General split potential, SX C = 1.697 + 2.078 = 3.775 
 
 Combining this general potential for Splits Ci and C 2 with 
 the potential for Split C, in tandem, we have, 
 
 Part potential factors, 
 
 
 (Tandem circulation) X 2 C 2.629 2 
 
 = - 0702 
 
 Tandem value, X f0 = S (l/X 2 c ) ..... 0.2149 
 
 General part potential, 
 
 (Primary split C) X co = ^A^ = 2.157 
 
 Part potential, Split A, X a = 1.837 
 
 Part potential, Split B, X b = 1.623 
 
 Mine pressure potential, X po ..... 5.617 
 
238 MINE GASES AND VENTILATION 
 
 Mine power potential, (After splitting) 
 
 = 3.160 
 
 Mine power potential, (Before splitting, p. 225) 
 
 X ul = \/4i636 2 = 2.780 
 
 For a constant power, the quantity ratio is equal to the 
 power-potential ratio; thus, 
 
 Q* = X*_ 2 . ( 
 ~' 
 
 X ul ' 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, C 2 , 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.) 
 
 X a = 1.837; q a = X 85,240 = 27,880 20,240 
 
 O. 
 
 X b = 1.623; q b = X 85,240 = 24,630 16,000 
 
 X co = 2.157; q c = l~~ X 85,240 = 32,730 40,000 
 o . 
 
 2X P = 5.617 Q= ...... 85,240 85,240 
 
 Secondary splits, 
 
 X el = 1.697; q el = \^ X 32,730 = 14.710 25,000 
 
 o . / O 
 
 X cZ = 2.078; q c2 = = X 32,730 = 18.020 15,000 
 
 o . 775 
 
 SX P = 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. 
 
 p c . = 0.00000002 (^-^g) 2 = 1 -042 Ib. per sq. ft. 
 
 Tandem p c = 0.00000002 ' ' = 4 . 630 Ib. per sq. ft. 
 
 Primary pressures, p c0 = 2p c 8.971/6. per sq.ft. 
 
 /2Q 240\ 2 
 p a = 0.00000002 (y^) =5.067 Ib. per sq. ft. 
 
 p b = 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 C 2 , 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 C 2 , 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 _ . 
 A a = 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 ,, 
 A c2 = - 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 
 
 A a = - . - = 8Asq.fi. 
 
 V0.751 
 
 0.00025 X 16,000 
 
 VI. 351 
 
 = .3 A sq.ft. 
 
 0.00025 X 15,000 . _ A 
 
 A c2 = - 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 C 2 
 
 
 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 A z . 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 
 
 = 1 
 
 I = 20 
 
 a = 1 
 
 = 1 
 
 I = 5 
 
 a = 1 
 
 = 1 
 
 I = 4 
 
 a = 1 
 
 = 1 
 
 I = 5 
 
 a = 1 
 
 = 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 (X a and A' o) : 
 
 = = 0.4082 
 
 + 1/A 2 00 Vl/0.5 2 + 1/6.707* 
 A 2 = A, + X b = 0.4082 + 0.4472 = 0.8554 
 
 Since the power is the same, before and after division and calling these 
 respective general potentials X it A 2 , we have 
 
 jOil = Q*. f , 120,000 3 = _Q,_ 
 (Xi) 2 A 2 2 ' 0.6708 2 0.8554* 
 
 Q 2 = 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 
 
 ksq 2 u ksq* 
 
 a 3 a a 4 
 
 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, Q 3 varies as n 3 , 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 (V G ) 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 (s ) 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 = nA ; (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 = ksv 3 , 
 
 u = k(s v 3 + s^i 3 ) (4) 
 
 Substituting for Si and Vi 3 the values given in Equations 1 
 and 2, gives after simplifying 
 
 o 
 
 u = fcWl + - 3 = fcWr- (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 n 3 + m 
 
 and, observing Equation 2, 
 
 vi varies as 3/ __ =: ( 7) 
 
 \/n 3 + 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 v ; or, for a 
 constant power (u) on the air, 
 
 Q varies as 3/ = (8) 
 
 V ft 3 + 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 i 2 ) (9) 
 
 and R 
 
 Finally, from Equations 6 and 10 is derived 
 
 n 2 + 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 25,000 2 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 X u the quantity varies as the 4/5 power of that 
 potential. 
 
 The mine potentials, in this case, are, 
 
 Before splitting Since l/X 3 i = 2.2449; X ui = . 1 = 0.7637 
 
 After splitting Since 1/X 3 2 = 0.6892; X ut = . 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 34,250 2 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 
 
 A p * \ po l 
 
 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 
 
 X u 
 
 Quantity, Q varies as X 
 
 Power Applied to Fan Shaft Constant (U) 
 
 Efficiency, 1/K* varies as X u 3 = X p 2 = a z 
 
 Effective power, u varies as K 
 
 Quantity, Q & varies as AV 
 
 Mine Potential Constant (X u 3 = X p 2 = a 3 /s) 
 
 Effective power, u varies as Q 3 
 
 Quantity, Q 6 varies as n 4 
 
 Water eage, (w.g.) & varies as n 8 
 
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 
 Deputy 7 ' 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 
 | .f or 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 
 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 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 (CaC 2 ) 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 (CaC 2 ), the 
 remainder of the carbon taking up the oxygen and passing off 
 as carbon dioxide (CO*), according to- the reaction, 
 
 4CaO + 5C 2 = 4CaC 2 + 2CO 2 
 
 When water comes in contact with calcium carbide, calcium 
 hydroxide, Ca(OH) 2 , is formed and acetylene gas (C 2 H 2 ) is 
 set free according to the equation. 
 
 CaC 2 + 2H 2 O = Ca(OH) 2 + O 2 H 2 
 
 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. 
 
 2C 2 H 2 + 5O 2 = 4CO 2 + 2H 2 O 
 
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 
 (CaC 2 ) being 40 + 2(12) = 64; and that of acetylene (C 2 H 2 ), 
 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. 
 
 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 
 
 (n 4 ) of the fan varies as the fifth power of the quantity (q r ) of air in circula- 
 tion ; which is expressed as follows : 
 
 n - 4 varies as q 5 
 
 or n varies as q*; or r/'- 25 
 
 and q varies as n 5 ; or n - 8 
 
 The expression n or the fourth-fifths power of n is identical with 
 V/rt 4 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 - . 30103 = . 69897 
 Characteristic of antilog, + 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 . 60206 = . 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: 
 
 _ ksq 2 _ 0.00000002 X 40,000 X 50,000 2 
 
 a 3 ~ 50 3 
 
 Solution. log 0.00000002 , 8.30103 
 
 log 40,000 4 . 60206 
 
 log 50,000 2 (4.69897 X 2) 9.39794 
 
 antilog 50 3 , (log 50 3 = 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. 
 
 
 
 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 
 
 
 
 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 
 & 
 
 
 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 
 
 
 
 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 
 8 1 '' 
 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 
 
 > 
 
 ( 
 
 > 
 
 
 
 
 { 
 
 IP 
 
 9 
 
 
 
 / 
 
 
 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 
 
 ] 
 
 
 
 1 
 
 1 
 
 ] 
 
 2 
 
 1 
 
 3 
 
 ] 
 
 4 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosine 
 
 
 
 
 .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 
 
 
 
 
 OMift* 
 
 fiiac 
 
 Coaina 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Coein* 
 
 Sine 
 
 
 
 79 
 
 
 
 7S 
 
 9 ' 
 
 77 
 
 5 
 
 76< 
 
 > 
 
 75 C 
 
 
 
 
SINES AND COSINES 
 
 357 
 
 / 
 
 1 
 
 5 
 
 1 
 
 5 
 
 1 
 
 7 
 
 1 
 
 } 
 
 1< 
 
 ) 
 
 / 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .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 
 
 
 
 70 
 
 
 
 
358 
 
 MINE GASES AND VENTILATION 
 
 
 2 
 
 
 
 2 
 
 1 
 
 2 
 
 2 
 
 2 
 
 >o 
 
 Z 
 
 1 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .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 
 
 
 
 66 
 
 
 
 65 
 
 
 
 / 
 
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 
 
 
 
 
 
 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 
 
 
 
 
 .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 
 
 
 
 
 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 
 
 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .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 
 
 
 
 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 
 
 
 
 
 .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 
 
 .03114 
 
 32.1181 
 
 .04862 
 
 20.5691 
 
 .06613 
 
 15.1222 
 
 .08368 
 
 11.9504 
 
 13 
 
 48 
 
 .01396 
 
 71.6151 
 
 .03143 
 
 31.8205 
 
 .04891 
 
 20.4465 
 
 .06642 
 
 15.0557 
 
 .08397 
 
 11.9087 
 
 12 
 
 49 
 
 .01425 
 
 70.1533 
 
 .03172 
 
 31.5284 
 
 .04920 
 
 20.3253 
 
 .06671 
 
 14.9898 
 
 .08427 
 
 11.8673 
 
 11 
 
 50 
 
 .01455 
 
 68.7501 
 
 .03201 
 
 31.2416 
 
 .04949 
 
 20.2056 
 
 .06700 
 
 14.9244 
 
 .08456 
 
 11.8262 
 
 10 
 
 51 
 
 .01484 
 
 67.4019 
 
 .03230 
 
 30.9599 
 
 .04978 
 
 20.0872 
 
 .06730 
 
 14.8596 
 
 .08485 
 
 11.7853 
 
 
 52 
 
 .01513 
 
 66.1055 
 
 .03259 
 
 30.6833 
 
 .05007 
 
 19.9702 
 
 .06759 
 
 14.7954 
 
 .08514 
 
 11.7448 
 
 
 53 
 
 .01542 
 
 64.8580 
 
 .03288 
 
 30.4116 
 
 .05037 
 
 19.8546 
 
 .06788 
 
 14.7317 
 
 .08544 
 
 11.7045 
 
 
 54 
 
 .01571 
 
 63.6567 
 
 .03317 
 
 30.1446 
 
 .05066 
 
 19.7403 
 
 .06817 
 
 14.6685 
 
 .08573 
 
 11.6645 
 
 
 55 
 
 .01600 
 
 62.4992 
 
 .03346 
 
 29.8823 
 
 .05095 
 
 19.6273 
 
 .06847 
 
 14.6059 
 
 .08602 
 
 11.6248 
 
 
 56 
 
 .01629 
 
 61.3829 
 
 .03376 
 
 29.6245 
 
 .05124 
 
 19.5156 
 
 .06876 
 
 14.5438 
 
 .08632 
 
 11.5853 
 
 
 57 
 
 .01658 
 
 60.3058 
 
 .03405 
 
 29.3711 
 
 .05153 
 
 19.4051 
 
 .06905 
 
 14.4823 
 
 .08661 
 
 11.5461 
 
 
 58 
 
 .01687 
 
 59.2659 
 
 .03434 
 
 29.1220 
 
 .05182 
 
 19.2959 
 
 .06934 
 
 14.4212 
 
 .08690 
 
 11.5072 
 
 
 59 
 
 .01716 
 
 58.2612 
 
 .03463 
 
 28.8771 
 
 .05212 
 
 19.1879 
 
 .06963 
 
 14.3607 
 
 .08720 
 
 11.4685 
 
 
 60 
 
 .01748 
 
 57.2900 
 
 .03492 
 
 28.6363 
 
 .05241 
 
 19.0811 
 
 .06993 
 
 14.3007 
 
 .08749 
 
 11.4301 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 / 
 
 8 
 
 9 
 
 8 
 
 8 
 
 8 
 
 7 
 
 8 
 
 6 
 
 8 
 
 5 
 
 
TANGENTS AND COTANGENTS 
 
 365 
 
 
 5 
 
 o . 
 
 6 
 
 S 
 
 
 D 
 
 8 
 
 3 
 
 9 
 
 
 
 
 
 - 
 
 
 
 Tan <T 
 
 Cotan" 
 
 TttTlW 
 
 
 Tftn<* 
 
 Cotang 
 
 
 
 
 
 
 o ang 
 
 
 
 i an 
 
 > ang 
 
 l atl 
 
 
 
 
 .08749 
 
 11.4301 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 .14054 
 
 7.11537 
 
 .15838 
 
 6.31375 
 
 60 
 
 
 .08778 
 
 11.3919 
 
 .10540 
 
 9.48781 
 
 .12308 
 
 8.12481 
 
 .14084 
 
 7.10038 
 
 .15868 
 
 6.30189 
 
 59 
 
 
 .08807 
 
 11.3540 
 
 .10569 
 
 9.46141 
 
 .12338 
 
 8.10536 
 
 .14113 
 
 7.08546 
 
 .15898 
 
 6.29007 
 
 58 
 
 
 .08837 
 
 11.3163 
 
 .10599 
 
 9.43515 
 
 .12367 
 
 8.08600 
 
 .14143 
 
 7.07059 
 
 .15928 
 
 6.27829 
 
 57 
 
 
 .08866 
 
 11.2789 
 
 .10628 
 
 9.40904 
 
 .12397 
 
 8.06674 
 
 .14173 
 
 7.05579 
 
 .15958 
 
 6.26655 
 
 56 
 
 
 .08895 
 
 11.2417 
 
 .10657 
 
 9.38307 
 
 .12426 
 
 8.04756 
 
 .14202 
 
 7.04105 
 
 .15988 
 
 6.25486 
 
 55 
 
 
 .08925 
 
 11.2048 
 
 .10687 
 
 9.35724 
 
 .12456 
 
 8.02848 
 
 .14232 
 
 7.02637 
 
 .16017 
 
 6.24321 
 
 54 
 
 
 .08954 
 
 11.1681 
 
 .10716 
 
 9.33155 
 
 .12485 
 
 8.00948 
 
 .14262 
 
 7.01174 
 
 .16047 
 
 6.23160 
 
 53 
 
 
 .08983 
 
 11.1316 
 
 .10746 
 
 9.30599 
 
 .12515 
 
 7.99058 
 
 .14291 
 
 6.99718 
 
 .16077 
 
 6.22003 
 
 52 
 
 
 .09013 
 
 11.0954 
 
 .10775 
 
 9.28058 
 
 .12544 
 
 7.97176 
 
 .14321 
 
 6.98268 
 
 .16107 
 
 6.20851 
 
 51 
 
 10 
 
 .09042 
 
 11.0594 
 
 .10805 
 
 9.25530 
 
 .12574 
 
 7.95302 
 
 .14351 
 
 6.96823 
 
 .16137 
 
 6.19703 
 
 50 
 
 11 
 
 .09071 
 
 11.0237 
 
 .10834 
 
 9.23016 
 
 .12603 
 
 7.93438 
 
 .14381 
 
 6.95385 
 
 .16167 
 
 6.18559 
 
 49 
 
 12 
 
 .09101 
 
 10.9882 
 
 .10863 
 
 9.20516 
 
 .12633 
 
 7.91582 
 
 .14410 
 
 6.93952 
 
 .16196 
 
 6.17419 
 
 48 
 
 13 
 
 .09130 
 
 10.9529 
 
 .10893 
 
 9.18028 
 
 .12662 
 
 7.89734 
 
 .14440 
 
 6.92525 
 
 .16226 
 
 6.16283 
 
 47 
 
 14 
 
 .09159 
 
 10.9178 
 
 .10922 
 
 9.15554 
 
 .12692 
 
 7.87895 
 
 .14470 
 
 6.91104 
 
 .16256 
 
 6.15151 
 
 46 
 
 15 
 
 .09189 
 
 10.8829 
 
 .10952 
 
 9.13093 
 
 .12722 
 
 7.86064 
 
 .14499 
 
 6.89688 
 
 .16286 
 
 6.14023 
 
 45 
 
 16 
 
 .09218 
 
 10.8483 
 
 .10981 
 
 9.10646 
 
 .12751 
 
 7.84242 
 
 .14529 
 
 6.88278 
 
 .16316 
 
 6.12899 
 
 44 
 
 17 
 
 .09247 
 
 10.8139 
 
 .11011 
 
 9.08211 
 
 .12781 
 
 7.82428 
 
 .14559 
 
 6.86874 
 
 .16346 
 
 6.11779 
 
 43 
 
 18 
 
 .09277 
 
 10.7797 
 
 .11040 
 
 9.05789 
 
 .12810 
 
 7.80622 
 
 .14588 
 
 6.85475 
 
 .16376 
 
 6.10664 
 
 42 
 
 19 
 
 .09306 
 
 10.7457 
 
 .11070 
 
 9.03379 
 
 .12840 
 
 7.78825 
 
 .14618 
 
 6.84082 
 
 .16405 
 
 6.09552 
 
 41 
 
 20 
 
 .09335 
 
 10.7119 
 
 .11099 
 
 9.00983 
 
 .12869 
 
 7.77035 
 
 .14648 
 
 6.82694 
 
 .16435 
 
 6.08444 
 
 40 
 
 21 
 
 .09365 
 
 10.6783 
 
 .11128 
 
 8.98598 
 
 .12899 
 
 7.75254 
 
 .14678 
 
 6.81312 
 
 .16465 
 
 6.07340 
 
 39 
 
 22 
 
 .09394 
 
 10.6450 
 
 .11158 
 
 8.96227 
 
 .12929 
 
 7.73480 
 
 .14707 
 
 6.79936 
 
 .16495 
 
 6.06240 
 
 38 
 
 23 
 
 .09423 
 
 10.6118 
 
 .11187 
 
 8.93867 
 
 .12958 
 
 7.71715 
 
 .14737 
 
 6.78564 
 
 .16525 
 
 6.05143 
 
 37 
 
 24 
 
 .09453 
 
 10.5789 
 
 .11217 
 
 8.91520 
 
 .12988 
 
 7.69957 
 
 .14767 
 
 6.77199 
 
 .16555 
 
 6.04051 
 
 36 
 
 25 
 
 .09482 
 
 10.5462 
 
 .11246 
 
 8.89185 
 
 .13017 
 
 7.68208 
 
 .14796 
 
 6.75838 
 
 .16585 
 
 6.02962 
 
 35 
 
 26 
 
 .09511 
 
 10.5136 
 
 .11276 
 
 8.86862 
 
 .13047 
 
 7.66466 
 
 .14826 
 
 6.74483 
 
 .16615 
 
 6.01878 
 
 34 
 
 27 
 
 .09541 
 
 10.4813 
 
 .11305 
 
 8.84551 
 
 .13076 
 
 7.64732 
 
 .14856 
 
 6.73133 
 
 .16645 
 
 6.00797 
 
 33 
 
 28 
 
 .09570 
 
 10.4491 
 
 .11335 
 
 8.82252 
 
 .13106 
 
 7.63005 
 
 .14886 
 
 6.71789 
 
 .16674 
 
 5.99720 
 
 32 
 
 29 
 
 .09600 
 
 10.4172 
 
 .11364 
 
 8.79964 
 
 .13136 
 
 7.61287 
 
 .14915 
 
 6.70450 
 
 .16704 
 
 5.98646 
 
 31 
 
 30 
 
 .09629 
 
 10.3854 
 
 .11394 
 
 8.77689 
 
 .13165 
 
 7.59575 
 
 .14945 
 
 6.69116 
 
 .16734 
 
 5.97576 
 
 30 
 
 31 
 
 .09658 
 
 10.3538 
 
 .11423 
 
 8.75425 
 
 .13195 
 
 7.57872 
 
 .14975 
 
 6.67787 
 
 .16764 
 
 5.96510 
 
 29 
 
 32 
 
 .09688 
 
 10.3224 
 
 .11452 
 
 8.73172 
 
 .13224 
 
 7.56176 
 
 .15005 
 
 6.66463 
 
 .16794 
 
 5.95448 
 
 28 
 
 33 
 
 .09717 
 
 10.2913 
 
 .11482 
 
 8.70931 
 
 .13254 
 
 7.54487 
 
 .15034 
 
 6.65144 
 
 .16824 
 
 5.94390 
 
 27 
 
 34 
 
 .09746 
 
 10.2602 
 
 .11511 
 
 8.68701 
 
 .13284 
 
 7.52806 
 
 .15064 
 
 6.63831 
 
 .16854 
 
 5.93335 
 
 26 
 
 35 
 
 .09776 
 
 10.2294 
 
 .11541 
 
 8.66482 
 
 .13313 
 
 7.51132 
 
 .15094 
 
 6.62523 
 
 .16884 
 
 5.92283 
 
 25 
 
 36 
 
 .09805 
 
 10.1988 
 
 .11570 
 
 8.64275 
 
 .13343 
 
 7.49465 
 
 .15124 
 
 6.61219 
 
 .16914 
 
 5.91236 
 
 24 
 
 37 
 
 .09834 
 
 10.1683 
 
 .11600 
 
 8.62078 
 
 .13372 
 
 7.47806 
 
 .15153 
 
 6.59921 
 
 .16944 
 
 5.90191 
 
 23 
 
 38 
 
 .09864 
 
 10.1381 
 
 .11629 
 
 8.59893 
 
 .13402 
 
 7.46154 
 
 .15183 
 
 6.58627 
 
 .16974 
 
 5.89151 
 
 22 
 
 39 
 
 .09893 
 
 10.1080 
 
 .11659 
 
 8.57718 
 
 .13432 
 
 7.44509 
 
 .15213 
 
 6.57339 
 
 .17004 
 
 5.88114 
 
 21 
 
 40 
 
 .09923 
 
 10.0780 
 
 .11688 
 
 8.55555 
 
 .13461 
 
 7.42871 
 
 .15243 
 
 6.56055 
 
 .17033 
 
 5.87080 
 
 20 
 
 41 
 
 .09952 
 
 10.0483 
 
 .11718 
 
 8.53402 
 
 .13491 
 
 7.41240 
 
 .15272 
 
 6.54777 
 
 .17063 
 
 5.86051 
 
 19 
 
 42 
 
 .09981 
 
 10.0187 
 
 .11747 
 
 8.51259 
 
 .13521 
 
 7.39616 
 
 .15302 
 
 6.53503 
 
 .17093 
 
 5.85024 
 
 18 
 
 43 
 
 .10011 
 
 9.98931 
 
 .11777 
 
 8.49128 
 
 .13550 
 
 7.37999 
 
 .15332 
 
 6.52234 
 
 .17123 
 
 5.84001 
 
 17 
 
 44 
 
 .10040 
 
 9.96007 
 
 .11806 
 
 8.47007 
 
 .13580 
 
 7.36389 
 
 .15362 
 
 6.50970 
 
 .17153 
 
 5.82982 
 
 16 
 
 45 
 
 .10069 
 
 9.93101 
 
 .11836 
 
 8.44896 
 
 .13609 
 
 7.34786 
 
 .15391 
 
 6.49710 
 
 .17183 
 
 5.81966 
 
 15 
 
 46 
 
 .10099 
 
 9.90211 
 
 .11865 
 
 8.42795 
 
 .13639 
 
 7.33190 
 
 .15421 
 
 6.48456 
 
 .17213 
 
 5.80953 
 
 14 
 
 47 
 
 .10128 
 
 9.87338 
 
 .11895 
 
 8.40705 
 
 .13669 
 
 7.31600 
 
 .15451 
 
 6.47206 
 
 .17243 
 
 5.79944 
 
 13 
 
 48 
 
 .10158 
 
 9.84482 
 
 .11924 
 
 8.38625 
 
 .13698 
 
 7.30018 
 
 .15481 
 
 6.45961 
 
 .17273 
 
 5.78938 
 
 12 
 
 49 
 
 .10187 
 
 9.81641 
 
 .119f4 
 
 8.36555 
 
 .13728 
 
 7.28442 
 
 .15511 
 
 6.44720 
 
 .17303 
 
 5.77936 
 
 11 
 
 50 
 
 .10216 
 
 9.78817 
 
 .11983 
 
 8.34496 
 
 .13758 
 
 7.26873 
 
 .15540 
 
 6.43484 
 
 .17333 
 
 5.76937 
 
 10 
 
 51 
 
 .10246 
 
 9.76009 
 
 .12013 
 
 8,32446 
 
 .13787 
 
 7.25310 
 
 .15570 
 
 6.42253 
 
 .17363 
 
 5.75941 
 
 9 
 
 52 
 
 .10275 
 
 9.73217 
 
 .12042 
 
 8.30406 
 
 .13817 
 
 7.23754 
 
 .15600 
 
 6.41026 
 
 .17393 
 
 5.74949 
 
 8 
 
 53 
 
 .10305 
 
 9.70441 
 
 .12072 
 
 8.28376 
 
 .13846 
 
 7.22204 
 
 .15630 
 
 6.39804 
 
 .17423 
 
 5.73960 
 
 7 
 
 54 
 
 .10334 
 
 9.67680 
 
 .12101 
 
 8.26355 
 
 .13876 
 
 7.20661 
 
 .15660 
 
 6.38587 
 
 .17453 
 
 5.72974 
 
 
 55 
 
 .10363 
 
 9.64935 
 
 .12131 
 
 8.24345 
 
 .13906 
 
 7.19125 
 
 .15689 
 
 6.37374 
 
 .17483 
 
 5.71992 
 
 
 56 
 
 .10393 
 
 9.62205 
 
 .12160 
 
 8.22344 
 
 .13935 
 
 7.17594 
 
 .15719 
 
 6.36165 
 
 .17513 
 
 5.71013 
 
 
 57 
 
 .10422 
 
 9.59490 
 
 .12190 
 
 8.20352 
 
 .13965 
 
 7.16071 
 
 .15749 
 
 6.34961 
 
 .17543 
 
 5.70037 
 
 
 58 
 
 .10452 
 
 9.56791 
 
 .12219 
 
 8.18370 
 
 .13995 
 
 7.14553 
 
 .15779 
 
 6.33761 
 
 .17573 
 
 5.69064 
 
 
 59 
 
 .10481 
 
 9.54106 
 
 .12249 
 
 8.16398 
 
 .14024 
 
 7.13042 
 
 .15809 
 
 6.32566 
 
 .17603 
 
 5.68094 
 
 
 60 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 .14054 
 
 7.11537 
 
 .15838 
 
 6.31375 
 
 .17633 
 
 5.67128 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 / 
 
 8- 
 
 1 
 
 85 
 
 * 
 
 8 
 
 2 
 
 
 
 L 
 
 8 
 
 
 
 t 
 
366 
 
 MINE GASES AND VENTILATION 
 
 
 1( 
 
 IP 
 
 1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 JP 
 
 ] 
 
 40 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 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 
 
 .24964 
 
 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 
 
 .25026 
 
 3.99592 
 
 57 
 
 
 .17753 
 
 5.63295 
 
 .19559 
 
 5.11279 
 
 .21377 
 
 4.67786 
 
 .23209 
 
 4.308CO 
 
 .25056 
 
 3.99099 
 
 56 
 
 
 .17783 
 
 5.62344 
 
 .19589 
 
 5.10490 
 
 .21408 
 
 4.67121 
 
 .23240 
 
 4.30291 
 
 .25087 
 
 3.98607 
 
 55 
 
 
 .17813 
 
 5.61397 
 
 .19619 
 
 5.09704 
 
 .21438 
 
 4.66458 
 
 .23271 
 
 4.29724 
 
 .25118 
 
 3.98117 
 
 54 
 
 
 .17843 
 
 5.60452 
 
 .19(549 
 
 5.08921 
 
 .21469 
 
 4.G5797 
 
 .23301 
 
 4.29159 
 
 .25149 
 
 3.97627 
 
 53 
 
 
 .17873 
 
 5.59511 
 
 .19680 
 
 5.08139 
 
 .21499 
 
 4.65138 
 
 .23332 
 
 4.28595 
 
 .25180 
 
 3.97139 
 
 52 
 
 
 .17903 
 
 5.58573 
 
 .19710 
 
 5.07360 
 
 .21529 
 
 4.64480 
 
 .23363 
 
 4.28032 
 
 .25211 
 
 3.96651 
 
 51 
 
 10 
 
 .17933 
 
 5.57638 
 
 .19740 
 
 5.06584 
 
 .21560 
 
 4.63825 
 
 .23393 
 
 4.27471 
 
 .25242 
 
 3.96165 
 
 50 
 
 11 
 
 .17963 
 
 5.56706 
 
 .19770 
 
 5.05809 
 
 .21590 
 
 4.63171 
 
 .23424 
 
 4.26911 
 
 .25273 
 
 3.95680 
 
 49 
 
 12 
 
 .17993 
 
 5.55777 
 
 .19801 
 
 5.05037 
 
 .21621 
 
 4.62518 
 
 .23455 
 
 4.26352 
 
 .25304 
 
 3.95196 
 
 48 
 
 13 
 
 .18023 
 
 5.54851 
 
 .19831 
 
 5.04267 
 
 .21651 
 
 4.61868 
 
 .23485 
 
 4.25795 
 
 .25335 
 
 3.94713 
 
 47 
 
 14 
 
 .18053 
 
 5.53927 
 
 .19861 
 
 5.03499 
 
 .21682 
 
 4.61219 
 
 .23516 
 
 4.25239 
 
 .25366 
 
 3.94232 
 
 46 
 
 15 
 
 .18083 
 
 5.53007 
 
 .19891 
 
 5.02734 
 
 .21712 
 
 4.60572 
 
 .23547 
 
 4.24685 
 
 .25397 
 
 3.93751 
 
 45 
 
 16 
 
 .18113 
 
 5.52090 
 
 .19921 
 
 5.01971 
 
 .21743 
 
 4.59927 
 
 .23578 
 
 4.24132 
 
 .25428 
 
 3.93271 
 
 44 
 
 17 
 
 .18143 
 
 5.51176 
 
 .19952 
 
 5.01210 
 
 .21773 
 
 4.59283 
 
 .23608 
 
 4.2C530 
 
 .25459 
 
 3.92793 
 
 43 
 
 18 
 
 .18173 
 
 5.50264 
 
 .19982 
 
 5.00451 
 
 .21804 
 
 4.58641 
 
 .23639 
 
 4.23030 
 
 .25490 
 
 3.92316 
 
 42 
 
 19 
 
 .18203 
 
 5.49356 
 
 .20012 
 
 4.99695 
 
 .21834 
 
 4.58001 
 
 .23670 
 
 4.22481 
 
 .25521 
 
 3.91839 
 
 41 
 
 20 
 
 .18233 
 
 5.48451 
 
 .20042 
 
 4.98940 
 
 .21864 
 
 4.57363 
 
 .23700 
 
 4.21933 
 
 .25552 
 
 3.91364 
 
 40 
 
 21 
 
 .1823 
 
 5.47548 
 
 .20073 
 
 4.98188 
 
 .21895 
 
 4.56726 
 
 .23731 
 
 4.21387 
 
 .25583 
 
 3.90890 
 
 39 
 
 22 
 
 .18293 
 
 5.46648 
 
 .20103 
 
 4.97438 
 
 .21925 
 
 4.56091 
 
 .23762 
 
 4.20842 
 
 .25614 
 
 3.90417 
 
 38 
 
 23 
 
 .18323 
 
 5.45751 
 
 .20133 
 
 4.96690 
 
 .21956 
 
 4.55458 
 
 .23793 
 
 4.20298 
 
 .25645 
 
 3.89945 
 
 37 
 
 24 
 
 .18353 
 
 5.44857 
 
 .20164 
 
 4.95945 
 
 .21986 
 
 4.54826 
 
 .23823 
 
 4.19756 
 
 .25676 
 
 3.89474 
 
 36 
 
 25 
 
 .18384 
 
 5.43966 
 
 .20194 
 
 4.95201 
 
 .22017 
 
 4.54196 
 
 .23854 
 
 4.19215 
 
 .25707 
 
 3.89004 
 
 35 
 
 26 
 
 .18414 
 
 5.43077 
 
 .20224 
 
 4.94460 
 
 .22047 
 
 4.53568 
 
 .23885 
 
 4.18675 
 
 .25738 
 
 3.88536 
 
 34 
 
 27 
 
 .18444 
 
 5.42192 
 
 .20254 
 
 4.93721 
 
 .22078 
 
 4.52941 
 
 .23916 
 
 4.18137 
 
 .25769 
 
 3.88068 
 
 33 
 
 28 
 
 .18474 
 
 5.41309 
 
 .20285 
 
 4.92984 
 
 .22108 
 
 4.52316 
 
 .23946 
 
 4.17600 
 
 .25800 
 
 3.87601 
 
 32 
 
 29 
 
 .18504 
 
 5.40429 
 
 .20315 
 
 4.92249 
 
 .22139 
 
 4.51693 
 
 .23977 
 
 4.17064 
 
 .25831 
 
 3.87136 
 
 31 
 
 30 
 
 .18534 
 
 5.39552 
 
 .20345 
 
 4.91516 
 
 .22169 
 
 4.51071 
 
 .24008 
 
 4.16530 
 
 .25862 
 
 3.86671 
 
 30 
 
 31 
 
 .18564 
 
 5.38677 
 
 .20376 
 
 4.90785 
 
 .22200 
 
 4.50451 
 
 .24039 
 
 4.15997 
 
 .25893 
 
 3.86208 
 
 29 
 
 82 
 
 .18594 
 
 5.37805 
 
 .20406 
 
 4.90056 
 
 .22231 
 
 4.49832 
 
 .24069 
 
 4.15465 
 
 .25924 
 
 3.85745 
 
 28 
 
 33 
 
 .18624 
 
 5.36936 
 
 .20436 
 
 4.89330 
 
 .22261 
 
 4.49215 
 
 .24100 
 
 4.14934 
 
 .25955 
 
 3.85284 
 
 27 
 
 34 
 
 .18654 
 
 5.36070 
 
 .20466 
 
 4.88605 
 
 .22292 
 
 4.48600 
 
 .24131 
 
 4.14405 
 
 .25986 
 
 3.84824 
 
 26 
 
 35 
 
 .18684 
 
 5.35206 
 
 .20497 
 
 4.87882 
 
 .22322 
 
 4.47986 
 
 .24162 
 
 4.13877 
 
 .26017 
 
 3.84364 
 
 25 
 
 36 
 
 .18714 
 
 5.34345 
 
 .20527 
 
 4.87162 
 
 .22353 
 
 4.47374 
 
 .24193 
 
 4.13350 
 
 .26048 
 
 3.83906 
 
 24 
 
 87 
 
 .18745 
 
 5.33487 
 
 .20557 
 
 4.86444 
 
 .22383 
 
 4.46764 
 
 .24223 
 
 4.12825 
 
 .26079 
 
 3.83449 
 
 23 
 
 38 
 
 .18775 
 
 5.32631 
 
 .20588 
 
 4.85727 
 
 .22414 
 
 4.46155 
 
 .24254 
 
 4.12301 
 
 .26110 
 
 3.82992 
 
 22 
 
 39 
 
 .18805 
 
 5.31778 
 
 .20618 
 
 4.85013 
 
 .22444 
 
 4.45548 
 
 .24285 
 
 4.11778 
 
 .26141 
 
 3.82537 
 
 21 
 
 40 
 
 .18835 
 
 5.30928 
 
 .20648 
 
 4.84300 
 
 .22475 
 
 4.44942 
 
 .24316 
 
 4.11256 
 
 .26172 
 
 3.82083 
 
 20 
 
 41 
 
 .18865 
 
 5.30080 
 
 .20679 
 
 4.83590 
 
 .22505 
 
 4'.44338 
 
 .24347 
 
 4.10736 
 
 .26203 
 
 3.81630 
 
 19 
 
 42 
 
 .18895 
 
 5.29235 
 
 .20709 
 
 4.82882 
 
 .22536 
 
 4.43735 
 
 .24377 
 
 4.10216 
 
 .26235 
 
 3.81177 
 
 18 
 
 43 
 
 .18925 
 
 5.28393 
 
 .20739 
 
 4.82175 
 
 .22567 
 
 4.43134 
 
 .24408 
 
 4.09699 
 
 .26266 
 
 3.80726 
 
 17 
 
 44 
 
 .18955 
 
 5.27553 
 
 .20770 
 
 4.81471 
 
 .22597 
 
 4.42534 
 
 .24439 
 
 4.09182 
 
 .26297 
 
 3.80276 
 
 16 
 
 45 
 
 .18986 
 
 5.26715 
 
 .20800 
 
 4.80769 
 
 .22628 
 
 4.41936 
 
 .24470 
 
 4.08666 
 
 .26328 
 
 3.79827 
 
 15 
 
 46 
 
 .19016 
 
 5.25880 
 
 .20830 
 
 4.80068 
 
 .22658 
 
 4.41340 
 
 .24501 
 
 4.08152 
 
 .26359 
 
 3.79378 
 
 14 
 
 47 
 
 .19046 
 
 5.25048 
 
 .20861 
 
 4.79370 
 
 .22689 
 
 4.40745 
 
 .24532 
 
 4.07639 
 
 .26390 
 
 3.78931 
 
 13 
 
 48 
 
 .19076 
 
 5.24218 
 
 .20891 
 
 4.78673 
 
 .22719 
 
 4.40152 
 
 .24562 
 
 4.07127 
 
 .26421 
 
 3.78485 
 
 12 
 
 49 
 
 .19106 
 
 5.23391 
 
 .20921 
 
 4.77978 
 
 .22750 
 
 4.39560 
 
 .24593 
 
 4.06616 
 
 .26452 
 
 S. 78040 
 
 11 
 
 50 
 
 .19136 
 
 5.22566 
 
 .20952 
 
 4.77286 
 
 .22781 
 
 4.38969 
 
 .24624 
 
 4.06107 
 
 .26483 
 
 3.77595 
 
 10 
 
 51 
 
 .19166 
 
 5.21744 
 
 .20982 
 
 4.76595 
 
 .22811 
 
 4.38381 
 
 .24655 
 
 4.05599 
 
 .26515 
 
 3.77152 
 
 
 62 
 
 .19197 
 
 5.20925 
 
 .21013 
 
 4.75906 
 
 .22842 
 
 4.37793 
 
 .24686 
 
 4.05092 
 
 .26546 
 
 3.76709 
 
 
 63 
 
 .19227 
 
 5.20107 
 
 .21043 
 
 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 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 T*ng 
 
 
 / 
 
 6< 
 
 ) 
 
 6* 
 
 
 
 6' 
 
 rO 
 
 6f 
 
 o 
 
 6, 
 
 ) 
 
 
TANGENTS AND COTANGENTS 
 
 369 
 
 
 2i 
 
 ) 
 
 2t 
 
 
 
 X 
 
 o 
 
 2 
 
 o 
 
 2 
 
 J 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang. 
 
 Tang 
 
 Cotang 
 
 
 
 .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 
 
 .53620 
 
 1.86499 
 
 .55888 
 
 1.78929 
 
 48 
 
 13 
 
 .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 
 
 .51983 
 
 1.92371 
 
 .54220' 
 
 1.84433 
 
 .56501 
 
 1.76990 
 
 32 
 
 29 
 
 .47662 
 
 2.09811 
 
 .49822 
 
 2.00715 
 
 .52020 
 
 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 
 
 .50004 
 
 1.99986 
 
 .52205 
 
 1.91554 
 
 .54446 
 
 1.83667 
 
 .56731 
 
 1.76271 
 
 26 
 
 35 
 
 .47876 
 
 2.08872 
 
 .50040 
 
 1.99841 
 
 .52242 
 
 1.91418 
 
 .54484 
 
 1.83540 
 
 .56769 
 
 1.76151 
 
 25 
 
 36 
 
 .47912 
 
 2.08716 
 
 .50076 
 
 1.99695 
 
 .52279 
 
 1.91282 
 
 .54522 
 
 1.83413 
 
 .56808 
 
 1.76032 
 
 24 
 
 37 
 
 .47948 
 
 2.08560 
 
 .50113 
 
 1.99550 
 
 .52316 
 
 1.91147 
 
 .54560 
 
 1.83286 
 
 .56846 
 
 1.75913 
 
 23 
 
 38 
 
 .47984 
 
 2.08405 
 
 .50149 
 
 1.99406 
 
 .52353 
 
 1.91012 
 
 .54597 
 
 1.83159 
 
 .56885 
 
 1.75794 
 
 22 
 
 39 
 
 .48019 
 
 2.08250 
 
 .50185 
 
 1.99261 
 
 .52390 
 
 1.90876 
 
 .54635 
 
 1.83033 
 
 .56923 
 
 1.75675 
 
 21 
 
 40 
 
 .48055 
 
 2.08094 
 
 .50222 
 
 1.99116 
 
 .52427 
 
 1.90741 
 
 .54673 
 
 1.82906 
 
 .56962 
 
 1.75556 
 
 20 
 
 41 
 
 .48091 
 
 2.07939 
 
 .50258 
 
 1.98972 
 
 .52464 
 
 1.90607 
 
 .54711 
 
 1.82780 
 
 .57000 
 
 1.75437 
 
 19 
 
 42 
 
 .48127 
 
 2.07785 
 
 .50295 
 
 1.98828 
 
 .52501 
 
 1.90472 
 
 .54748 
 
 1.82654 
 
 .57039 
 
 1.75319 
 
 18 
 
 43 
 
 .48163 
 
 2. 7630 
 
 .50331 
 
 1.98684 
 
 .52538 
 
 1.90337 
 
 .54786 
 
 1.82528 
 
 .57078 
 
 1.75200 
 
 17 
 
 44 
 
 .48198 
 
 2.07476 
 
 .50368 
 
 1.98540 
 
 .52575 
 
 1.90203 
 
 .54824 
 
 1.82402 
 
 .57116 
 
 1.75082 
 
 16 
 
 45 
 
 .48234 
 
 2 07321 
 
 .50404 
 
 1.98396 
 
 .52613 
 
 1.90069 
 
 .54862 
 
 1.82276 
 
 .57155 
 
 1.74964 
 
 15 
 
 46 
 
 .48270 
 
 2.07167 
 
 .50441 
 
 1.98253 
 
 .52650 
 
 1.89935 
 
 .54900 
 
 1.82150 
 
 .57193 
 
 1.74846 
 
 14 
 
 47 
 
 .48306 
 
 2.07014 
 
 .50477 
 
 1.98110 
 
 .52687 
 
 1.89801 
 
 .54938 
 
 1.82025 
 
 .57232 
 
 1.74728 
 
 13 
 
 48 
 
 .48342 
 
 2.06860 
 
 .50514 
 
 1.97966 
 
 .52724 
 
 1.89667 
 
 .54975 
 
 1.81899 
 
 .57271 
 
 1.74610 
 
 12 
 
 49 
 
 .48378 
 
 2.06706 
 
 .50550 
 
 1.97823 
 
 .52761 
 
 1.89533 
 
 .55013 
 
 1.81774 
 
 .57309 
 
 1.74492 
 
 11 
 
 50 
 
 .48414 
 
 2.06553 
 
 .50587 
 
 1.97681 
 
 .52798 
 
 1.89400 
 
 .55051 
 
 1.81649 
 
 .57348 
 
 1.74375 
 
 10 
 
 61 
 
 .48450 
 
 2.06400 
 
 .50623 
 
 1.97538 
 
 .52836 
 
 1.89266 
 
 .55089 
 
 1.81524 
 
 .57386 
 
 1.74257 
 
 
 52 
 
 .48486 
 
 2.06247 
 
 .50660 
 
 1.97395 
 
 .52873 
 
 1.89133 
 
 .55127 
 
 1.81399 
 
 .57425 
 
 1.74140 
 
 
 63 
 
 .48521 
 
 2.06094 
 
 .50696 
 
 1.97253 
 
 .52910 
 
 1.89000 
 
 .55165 
 
 1.81274 
 
 .57464 
 
 1.74022 
 
 
 64 
 
 .48557 
 
 2.05942 
 
 .50733 
 
 1.97111 
 
 .52947 
 
 1.88867 
 
 .55203 
 
 1.81150 
 
 .57503 
 
 1.73905 
 
 
 55 
 
 .48593 ' 
 
 2.05790 
 
 .50769 
 
 1.96969 
 
 .52985 
 
 1.88734 
 
 .55241 
 
 1.81025 
 
 .57541 
 
 1.73788 
 
 
 56 
 
 .48629 
 
 2.05637 
 
 .50806 
 
 1.96827 
 
 .53022 
 
 1.88602 
 
 .55279 
 
 1.80901 
 
 .57580 
 
 1.73671 
 
 
 57 
 
 .48665 
 
 2.05485 
 
 .50843 
 
 1.96685 
 
 .53059 
 
 1.88469 
 
 .55317 
 
 1.80777 
 
 .57619 
 
 1.73565 
 
 
 58 
 
 .48701 
 
 2.05333 
 
 .50879 
 
 1.96544 
 
 .53096 
 
 1.88337 
 
 .55355 
 
 1.80653 
 
 .57657 
 
 1.73438 
 
 
 59 
 
 .48737 
 
 2.05182 
 
 .50916 
 
 1.96402 
 
 .53134 
 
 1.88205 
 
 .55393 
 
 1.80529 
 
 .5769ft 
 
 1.73321 
 
 
 60 
 
 .48773 
 
 2.05030 
 
 .50953 
 
 1.96261 
 
 .53171 
 
 1.88073 
 
 .55431 
 
 1.80406 
 
 .57735 
 
 1.73205 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 / 
 
 fr 
 
 1 
 
 6, 
 
 J 
 
 e: 
 
 >o 
 
 C] 
 
 
 
 8 
 
 y> 
 
 t 
 
370 
 
 MINE GASES AND VENTILATION 
 
 f 
 
 3( 
 
 ) 
 
 3] 
 
 
 
 31 
 
 to 
 
 Si 
 
 5 
 
 & 
 
 1 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .57735 
 
 1.73205 
 
 .60086 
 
 1.66428 
 
 .62487 
 
 1.60033 
 
 .64941 
 
 1.53986 
 
 .67451 
 
 1.48256 
 
 60 
 
 
 .57774 
 
 1.73089 
 
 .60126 
 
 1.66318 
 
 .62527 
 
 1.59930 
 
 .64982 
 
 1.53888 
 
 .67493 
 
 1.48163 
 
 59 
 
 2 
 
 .57813 
 
 1.72973 
 
 .60165 
 
 1.66209 
 
 .62568 
 
 1.59826 
 
 .65024 
 
 1.53791 
 
 .67536 
 
 1.48070 
 
 58 
 
 3 
 
 .57851 
 
 1.72857 
 
 .60205 
 
 1.66099 
 
 .62608 
 
 1.59723 
 
 .65065 
 
 1.53693 
 
 .67578 
 
 1.47977 
 
 57 
 
 4 
 
 .57890 
 
 1.72741 
 
 .60245 
 
 1.65990 
 
 .62649 
 
 1.59620 
 
 .65106 
 
 1.53595 
 
 .67620 
 
 1.47885 
 
 56 
 
 5 
 
 .57929 
 
 1.72625 
 
 .60284 
 
 1.65881 
 
 .62689 
 
 1.59517 
 
 .65148 
 
 1.53497 
 
 .67663 
 
 1.47792 
 
 55 
 
 6 
 
 .57968 
 
 1.72509 
 
 .60324 
 
 1.65772 
 
 .62730 
 
 1.59414 
 
 .65189 
 
 1.53400 
 
 .67705 
 
 1.47699 
 
 54 
 
 7 
 
 .58007 
 
 1.72393 
 
 .60364 
 
 1.65663 
 
 .62770 
 
 1.59311 
 
 .65231 
 
 1.53302 
 
 .67748 
 
 1.47607 
 
 53 
 
 8 
 
 .58046 
 
 1.72278 
 
 .60403 
 
 1.65554 
 
 .62811 
 
 1.59208 
 
 .65272 
 
 1.53205 
 
 .67790 
 
 1.47514 
 
 52 
 
 9 
 
 .58085 
 
 1.72163 
 
 .60443 
 
 1.65445 
 
 .62852 
 
 1.59105 
 
 .65314 
 
 1.53107 
 
 .67832 
 
 1.47422 
 
 51 
 
 10 
 
 .58124 
 
 1.72047 
 
 .60483 
 
 1.65337 
 
 .62892 
 
 1.59002 
 
 .65355 
 
 1.53010 
 
 .67875 
 
 1.47330 
 
 50 
 
 11 
 
 .58162 
 
 1.71932 
 
 .60522 
 
 1.65228 
 
 .62933 
 
 1.58900 
 
 .65397 
 
 1.52913 
 
 .67917 
 
 1.47238 
 
 49 
 
 12 
 
 .58201 
 
 1.71817 
 
 .60562 
 
 1.65120 
 
 .62973 
 
 1.58797 
 
 .65438 
 
 1.52816 
 
 .67960 
 
 1.47146 
 
 48 
 
 13 
 
 .58240 
 
 1.71702 
 
 .60602 
 
 1.65011 
 
 .63014 
 
 1.58695 
 
 .65480 
 
 1.52719 
 
 .68002 
 
 1.47053 
 
 47 
 
 14 
 
 .58279 
 
 1.71588 
 
 .60642 
 
 1.64903 
 
 .63055 
 
 1.58593 
 
 .65521 
 
 1.52622 
 
 .68045 
 
 1.46962 
 
 46 
 
 IS 
 
 .58318 
 
 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 
 
 .68215 
 
 1.46595 
 
 42 
 
 19 
 
 .58474 
 
 1.710,15 
 
 .60841 
 
 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 
 
 .68514 
 
 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 
 
 .68771 
 
 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 
 
 .68985 
 
 1.44958 
 
 24 
 
 37 
 
 .59179 
 
 1.68979 
 
 .61561 
 
 1.62442 
 
 .63994 
 
 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 
 
 .59297 
 
 1.68643 
 
 .61681 
 
 1.62125 
 
 .64117 
 
 1.55966 
 
 .66608 
 
 1.50133 
 
 ".69157 
 
 1.44598 
 
 20 
 
 41 
 
 .59336 
 
 1.68531 
 
 .61721 
 
 1.62019 
 
 .64158 
 
 1.55866 
 
 .66650 
 
 1.50038 
 
 .69200 
 
 1.44508 
 
 19 
 
 42 
 
 .59376 
 
 1.68419 
 
 .61761 
 
 1.61914 
 
 .64199 
 
 1.55766 
 
 .66692 
 
 1.49944 
 
 .69243 
 
 1.44418 
 
 18 
 
 43 
 
 .59415 
 
 1.68308 
 
 .61801 
 
 1.61808 
 
 .64240 
 
 1.55666 
 
 .66734 
 
 1.49849 
 
 .69286 
 
 1.44329 
 
 17 
 
 44 
 
 .59454 
 
 1.68196 
 
 .61842 
 
 1.61703 
 
 .64281 
 
 1.55567 
 
 .66776 
 
 1.49755 
 
 .69329 
 
 1.44239 
 
 16 
 
 45 
 
 .59494 
 
 1.68085 
 
 .61882 
 
 1.61598 
 
 .64322 
 
 1.55467 
 
 .66818 
 
 1.49661 
 
 .69372 
 
 1.44149 
 
 15 
 
 46 
 
 .59533 
 
 1.67974 
 
 .61922 
 
 1.61493 
 
 .64363 
 
 1.55368 
 
 .66860 
 
 1.49566 
 
 .69416 
 
 1.44060 
 
 14 
 
 47 
 
 .59573 
 
 1.67863 
 
 .61962 
 
 1.61388 
 
 .64404 
 
 1.55269 
 
 .66902 
 
 1.49472 
 
 .69459 
 
 1.43970 
 
 13 
 
 48 
 
 .59612 
 
 1.67752 
 
 .62003 
 
 1.61283 
 
 .64446 
 
 1.55170 
 
 .66944 
 
 1.49378 
 
 .69502 
 
 1.43881 
 
 12 
 
 49 
 
 .59651 
 
 1.67641 
 
 .62043 
 
 1.61179 
 
 .64487 
 
 1.55071 
 
 .66986 
 
 1.49284 
 
 .69545 
 
 1.43792 
 
 11 
 
 50 
 
 .59691 
 
 1.67530 
 
 .62083 
 
 1.61074 
 
 .64528 
 
 1.54972 
 
 .67028 
 
 1.49190 
 
 .69588 
 
 1.43703 
 
 10 
 
 51 
 
 .59730 
 
 1.67419 
 
 .62124 
 
 1.60970 
 
 .64569 
 
 1.54873 
 
 .67071 
 
 1.49097 
 
 .69631 
 
 1.43614 
 
 
 52 
 
 .59770 
 
 1.67309 
 
 .62164 
 
 1.60865 
 
 .64610 
 
 1.54774 
 
 .67113 
 
 1.49003 
 
 .69675 
 
 1.43525 
 
 
 53 
 
 .59803 
 
 1.67198 
 
 .62204 
 
 1.60761 
 
 .64652 
 
 1.54675 
 
 .67155 
 
 1.48909 
 
 .69718 
 
 1.43436 
 
 
 54 
 
 .59849 
 
 1.67088 
 
 .62245 
 
 1.60657 
 
 .64693 
 
 1.54576 
 
 .67197 
 
 1.48816 
 
 .69761 
 
 1.43347 
 
 
 55 
 
 .59888 
 
 1.66978 
 
 .62285 
 
 1.60553 
 
 .64734 
 
 1.54478 
 
 .67239 
 
 1.48722 
 
 .69804 
 
 1.43258 
 
 
 56 
 
 .59928 
 
 1.66867 
 
 .62325 
 
 1.60449 
 
 .64775 
 
 1.54379 
 
 .67282 
 
 1.48629 
 
 .69847 
 
 1.43169 
 
 
 57 
 
 .59967 
 
 1.6675T 
 
 .62366 
 
 1.60345 
 
 .64817 
 
 1.54281 
 
 .67324 
 
 1.48536 
 
 .69891 
 
 1.43080 
 
 
 58 
 
 .60007 
 
 1.66647 
 
 .62406 
 
 1.60241 
 
 .64858 
 
 1.54183 
 
 .67366 
 
 1.48442 
 
 .69934 
 
 1.42992 
 
 
 59 
 
 .60046 
 
 1.66538 
 
 .62446 
 
 1.60137 
 
 .64899 
 
 1.54085 
 
 .67409 
 
 1 .48349 
 
 .69977 
 
 1.42903 
 
 1 
 
 60 
 
 .60086 
 
 1.66426 
 
 .62487 
 
 1.60033 
 
 .64941 
 
 1.63986 
 
 .67451 
 
 1.48256 
 
 .70021 
 
 1.42815 
 
 
 
 
 Ootang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 I 
 
 
 
 9 
 
 51 
 
 * 
 
 5 
 
 J. 
 
 5 
 
 5 
 
 5 
 
 5 
 
 / 
 
TANGENTS AND COTANGENTS 
 
 371 
 
 / 
 
 3i 
 
 > 
 
 3C 
 
 
 
 O' 
 
 
 
 38 
 
 
 
 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 
 
 
 .7004 
 
 1.42726 
 
 .72699 
 
 1.37554 
 
 .75401 
 
 1.32624 
 
 .78175 
 
 1.27917 
 
 .81027 
 
 1.23416 
 
 59 
 
 
 .70107 
 
 1.42638 
 
 .72743 
 
 1.37470 
 
 .75447 
 
 1.32544 
 
 .78222 
 
 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 
 
 
 
 
 .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 
 
 
 
 
 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 
 
 ,00a r v47009 
 
 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 
 
 386 S 884 
 
 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 
 
 5 r 
 
 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 
 
 83 L 
 
 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 
 
 74 1 
 
 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 
 
 94 t 
 
 
 
 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 
 
 93 i 
 
 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 18.5 2 ) = 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 inche s 
 
 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., 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 
 (4C.), 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) . 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 (4C.) 
 and weighing exactly 1 oz. avoirdupois. The volume of the fluid ounce 
 is calculated as follows: 
 
 1 cubic centimeter of water (4C.) = 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, mm 2 ; cubic millimeter, mm 3 . 
 Square centimeter, cm 2 ; cubic centimeter, cm 3 . 
 Square decimeter, dm 2 ; cubic decimeter, dm 3 . 
 Square meter, m 2 ; cubic meter, m 3 . 
 
 Square kilometer, km 2 . 
 
 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 
 = 5.644 
 =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 
 
 = 
 
 
 
 0154 
 
 
 
 
 
 
 
 1 centigram 
 
 = 
 
 
 
 154 
 
 
 
 006 
 
 
 
 
 
 1 decigram 
 
 = 
 
 1 
 
 54 
 
 0. 
 
 064 
 
 0. 
 
 0032 
 
 
 
 1 gram 
 
 = 
 
 15. 
 
 43 
 
 0. 
 
 643 
 
 0. 
 
 032 
 
 
 
 1 decagram 
 
 = 
 
 
 
 6. 
 
 430 
 
 
 
 322 
 
 
 
 ,0268 
 
 1 hectogram 
 
 BS 
 
 
 
 64. 
 
 302 
 
 3 
 
 215 
 
 
 
 .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 . 093 
 
 sq. yard = . 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 = . 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 
 
 
 
 .908 
 
 0. 
 
 227 
 
 
 
 ,114 
 
 
 
 .028 
 
 1 
 
 centistere = 
 
 9, 
 
 081 
 
 2. 
 
 270 
 
 1 
 
 .135 
 
 
 
 ,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 
 
 
 
 .022 
 
 
 
 
 
 1 
 
 liter = 7.043 
 
 1.761 0.880 
 
 
 
 .220 
 
 
 
 .110 
 
 
 
 .028 
 
 1 
 
 decaliter = 
 
 8.803 
 
 2 
 
 .201 
 
 1 
 
 .100 
 
 
 
 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.S7 2 -T- 144 = 10.76386736 sq. ft.; 
 
 1 cu. meter = 39.37 3 -=- 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 m 2 
 
 1 ton per sq. ft (0.9072 X 10.764) = 9.765 tonnes per m 2 
 
 1 ton per sq. yd (0.9072 X 1.196) = 1.085 tonnes per m 2 
 
 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 cm 3 
 
 1 oz. per cu .ft (0.0283 X 35.3145) = 1.00 kg. per m 3 
 
 1 Ib. per cu. ft (0.4536 X 35.3145) = 16.0184 kg. per m 3 
 
 1 Ib. per cu. yd. ... (0.4536 X 1.308) = 0.5933 kg. per m 3 
 
 1 ton per cu. yd . . (0.9072 X 1.308) = 1.1866 tonnes per m 3 
 
 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 m 3 = 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 cm 2 
 
 1 Ib. per sq. in (453.59 X 0.155) = 70.306 g. per cm 2 
 
 1 Ib. per sq. ft. . . . (0.4536 X 10.764) = 4.882 kg. per m 2 
 
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 m 3 
 
 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 m 3 
 
 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 . 986) = . 0937 m 2 per cheval 
 
 1 cu. ft. per hp (0. 028 X 0. 986) = 0. 0276 m 3 per cheval 
 
 FUEL OR WATER CONSUMPTION 
 
 1 Ib. per hp.-hr (0 . 4536 X . 986) = . 4472 kg. per cheval-hr. 
 
 1 ton per hp.-hr (0 . 9072 X . 986) = . 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 . 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 m 2 
 
 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 . 0703) = 1 . 033 kg. per cm 2 
 (14.696 -7-0.4911) = 29. 925 in. mercury 
 (29.925 X 25.4) = 760 mm. mercury 
 
 /29.925 X 13. 6\ , 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. 
 
 3 15.60 1.733 
 
 H 0.65 0.072 y 16.90 1.878 
 
 K 1-30 0.144 Y 2 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 Y 2 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 y 2 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^ 
 
 <ifSs 
 
 nml _MO -*55 
 
 4600J _1M -2S5. 
 
 M!^ 
 
 n.ioo : m -* B 
 
 1WLJ&-5 
 
 mat_si5._a5 
 
 7iflo j _iiQ -Ufl 
 
 9?OQ : 4jM "** 
 
 9500 : 4f& 4.15 IIJOQ- 5 
 
 9!L JJO _ 4 j fl 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 
 
YC 33742 
 
 
 UNIVERSITY OF CALIFORNIA LIBRARY