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diff --git a/40175-8.txt b/40175-8.txt deleted file mode 100644 index 2f02f51..0000000 --- a/40175-8.txt +++ /dev/null @@ -1,16632 +0,0 @@ -The Project Gutenberg EBook of Physics, by -Willis Eugene Tower and Charles Henry Smith and Charles Mark Turton and Thomas Darlington Cope - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -Title: Physics - -Author: Willis Eugene Tower - Charles Henry Smith - Charles Mark Turton - Thomas Darlington Cope - -Release Date: July 9, 2012 [EBook #40175] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK PHYSICS *** - - - - -Produced by Anna Hall, Albert László and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - - PHYSICS - - TOWER, SMITH, TURTON, - AND - COPE - - - [Illustration: (_See p.441_) - - THREE-COLOR PRINTING - - _Y._ Yellow impression; negative made through a blue-violet filter. _R._ - Crimson impression; negative made through a green filter. _RY._ Crimson - on yellow. _B._ Blue impression; negative made through a red filter. - _YRB._ Yellow, crimson, and blue combined; the final product. (Courtesy - of Phototype Engraving Co., Philadelphia.)] - - - PHYSICS - - BY - - WILLIS E. TOWER, M. SCI. (Univ. of Illinois) - HEAD OF THE DEPARTMENT OF PHYSICS, ENGLEWOOD - HIGH SCHOOL, CHICAGO - - CHARLES H. SMITH, M. E. (Cornell) - HEAD OF THE DEPARTMENT OF PHYSICS AND ASSISTANT - PRINCIPAL, HYDE PARK SCHOOL, CHICAGO - - CHARLES M. TURTON, A. M. (Syracuse) - HEAD OF THE DEPARTMENT OF PHYSICS, BOWEN - HIGH SCHOOL, CHICAGO - - IN COLLABORATION WITH - - THOMAS D. COPE, Ph.D. (Pennsylvania) - ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY - OF PENNSYLVANIA - - BASED UPON - PRINCIPLES OF PHYSICS - BY - TOWER, SMITH and TURTON - - WITH 7 PLATES AND 448 OTHER ILLUSTRATIONS - - PHILADELPHIA - P. BLAKISTON'S SON & CO. - 1012 WALNUT STREET - - - COPYRIGHT, 1920, BY P. BLAKISTON'S SON & CO. - - - - -PREFACE - - -In the preparation of this text, the _pupil_, his experience, needs, and -interests have been constantly kept in mind. The order of topics, -illustrations, and problems have been selected with the purpose of -leading the _pupil_ into a clear understanding of the physical phenomena -continually taking place about him. - -The recommendations and conclusions reached by the "New Movement in the -Teaching of Physics" have been incorporated into the book as a whole. -These conclusions indicate that the most efficient teaching in physics -involves a departure from the quantitative, mathematical methods of -presentation that were in general use a dozen or more years ago, toward -a method better adapted to the capabilities, interests, and requirements -of the young people in our physics classes. - -The older methods are effective with a portion of the student body which -has the greater mathematical ability and training, but they discourage a -large majority of the pupils who are not gifted or prepared for severe -mathematical analysis. For this reason, many of the more difficult -mathematical demonstrations often given in physics texts are omitted. -Most of the problems involve only the units employed in practical -every-day measurements. - -The portions of Mechanics that are ordinarily so difficult for the -average pupil are not taken up until he has covered considerable ground -with which he is more or less familiar and not until he has become -somewhat accustomed to the methods of study and the technical terms of -the subject. - -The pupil comes to the study of physics with a great number of -experiences and impressions of physical phenomena continually occurring -about him. In recognition of this fact, it has been thought best to -consider first the explanation of common things well known to all -pupils, such as the diffusion of gases, evaporation of liquids, -expansion of bodies when heated, and capillary action. Since the -molecular theory of matter is now supported by so many conclusive -evidences, we have not hesitated to make free use of it in the early -chapters. The applications of this theory are extremely helpful in -explaining every-day phenomena. Our experience shows that beginners in -physics understand and apply this theory without difficulty. - -The illustrations and drawings have been selected from a pedagogical -rather than a spectacular point of view. Practically all of them are -new. The problems and exercises have been selected for the distinct -purpose of illustrating the principles taught in the text and for their -practical applications. - -Many direct applications to common every-day experiences are given in -order to connect the subject matter with the home environment and daily -observation of physical phenomena. Some phenomena are mentioned without -detailed explanation as it is felt that the presentation of these -subjects in this manner is better for this grade of student than a -complete analysis. - -Some of the special features of the text may be briefly summarized as -follows: - -(A) _Simplicity of presentation_ is emphasized. The methods of attack, -the illustrations and examples employed in developing the subjects are -particularly adapted to beginners in physics. - -(B) The text is divided into some _seventy-seven sections_, each -containing material enough for one recitation. - -(C) Each of these sections is summarized by a list of _important topics_ -which point out to the pupil the principles and subject matter requiring -most careful attention. The lists of important topics are also of -assistance to the teacher in assigning recitations. - -(D) The _problems and practical exercises_ emphasize physical principles -as distinguished from mathematical training. A list of exercises is -placed at the end of the several sections. They are in sufficient number -to permit testing at many points and of a choice of problems by -teachers. - -The authors wish to express their appreciation for suggestions and -helpful criticisms to many who have read the text in manuscript or -proof. Especially to Professor A. P. Carman of the University of -Illinois and his associate, Professor F. R. Watson, who have gone -carefully over the whole text; and to Mr. Chas. M. Brunson, Scott High -School, Toledo, Ohio, Mr. Frank E. Goodell, North High School, Des -Moines, Iowa, and to Mr. Walter R. Ahrens, Englewood High School, -Chicago, for assistance in reading the proofs. Also to Mr. W. H. -Collins, Jr., Bowen High School, Chicago, who supervised the preparation -of drawings for the diagrams and figures; and to many firms and -individuals that have courteously furnished material for illustrations. - - WILLIS E. TOWER. - CHARLES H. SMITH. - CHARLES M. TURTON. - - - - -ON THE STUDY OF PHYSICS - - -When a pupil begins the study of Physics he has in his possession many -bits of knowledge which are fundamental in the science. He has learned -to throw a ball and can tell how a thrown ball moves. He has drawn out -nails with a claw hammer. He has seen wood float and iron sink. He has -sucked liquids up through straws. In his mother's kitchen, he sees water -as ice, liquid, and steam. On a wintry day he reads the temperature on a -thermometer. He sees sparks fly from car wheels when the brakes are -applied. He has played with a horseshoe magnet, and has found the north -by means of a compass. The telephone, the electric light and the motor -he sees, and perhaps uses, many times a day. He dresses before a mirror, -focuses his camera, watches the images at a moving picture show, and -admires the colors of the rainbow. He has cast stones into water to -watch the ripples spread, has shouted to hear the echo, and perhaps -plays some musical instrument. These, and a thousand other things, are -known to the intelligent and normal boy or girl who has reached the age -at which the study of Physics is properly begun. - -To a great extent even the terms used in the science are familiar to the -beginner. He speaks of the horse-power of an engine, reads -kilowatt-hours from the meter in the cellar, and may know that -illuminating gas costs one dollar per thousand "cubic feet." "Ampere" -and "volt" are words he frequently hears and sees. - -When he takes up the study of Physics, the attitude of the student -toward these familiar things and words must undergo a change. Casual -information about them must be changed to sound knowledge, purposely -acquired. Hazy notions about the meanings of words must be replaced by -exact definitions. Bits of knowledge must be built into a structure in -which each fact finds its proper place in relation to the others. - -The only agent which can accomplish these changes is the student -himself. He must consciously and purposely seek the truth and must -reflect upon it until he sees it in its relation to other truth. Upon -him, and upon him alone, rests the final responsibility for the success -or failure of his study. - -But the student is not without assistance. In his teacher he finds a -guide to stimulate, to direct, and to aid his efforts, and a critic to -point out wherein his efforts have failed and wherein they have -succeeded. Weights, measures, and other apparatus are furnished to -enable him to answer for himself questions which have arisen in his -studies. - -In addition to these the student has his text book, his teacher for his -hours of private study. A good text book is an inspiring teacher in -print. It directs attention to things familiar to the student through -long experience, and inspires him to make a closer scrutiny of them. It -invites him to observe, to analyze, to compare, to discover likenesses -and differences in behavior. It questions him at every turn. Its ever -repeated challenge reads, "Weigh and consider." It furnishes him needed -information that he cannot otherwise acquire. It satisfies his desire to -know, "By whom, where, when, and how was this first discovered?" - -The student of Physics must never forget that he is studying not pages -of text but the behavior and properties of iron, water, mica, moving -balls, pumps, boiling liquids, compressed air, mirrors, steam engines, -magnets, dynamos, violins, flutes, and a host of other things. His -studies should, whenever possible, be made first hand upon the things -themselves. The text is an aid to study, never a substitute for the -thing studied. - -It is an excellent plan for each student to select some one thing for -special study, the telephone for example. By observation, experiment, -and reading, he may acquire a large amount of valuable information about -such a subject while pursuing his course in Physics. Every part of the -science will be found to bear some relation to it. - -The student who takes up the study of Physics in the way suggested will -find himself at the end of a year of study in possession of much new and -valuable knowledge about the physical world in which he lives. By virtue -of this knowledge he will be better able to enjoy the world, to control -it, and to use it. - - THOMAS D. COPE. - - PHILADELPHIA. - - - - -CONTENTS - - CHAPTER I. INTRODUCTION AND MEASUREMENT. PAGE - - (1) Introduction 1 - (2) States of Matter 4 - (3) The Metric System 8 - - CHAPTER II. MOLECULAR FORCES AND MOTIONS. - - (1) Molecular Motions in Gases 13 - (2) Molecular Motions in Liquids 18 - (3) Molecular Forces in Liquids 21 - (4) Molecular Forces in Liquids and Solids 27 - (5) Molecular Forces in Solids 31 - - CHAPTER III. MECHANICS OF LIQUIDS. - - (1) Liquid Pressure 36 - (2) Transmission of Liquid Pressure 41 - (3) Archimedes' Principle 47 - (4) Density and Specific Gravity 52 - - CHAPTER IV. MECHANICS OF GASES. - - (1) Weight and Pressure of the Air 55 - (2) Compressibility and Expansibility of the Air 62 - (3) Pneumatic Appliances 66 - - CHAPTER V. FORCE AND MOTION. - - (1) Force, how Measured and Represented 79 - (2) Motion. Newton's Laws 85 - (3) Resolution of Forces 96 - (4) Moment of Force and Parallel Forces 99 - (5) Gravitation and Gravity 103 - (6) Falling Bodies 109 - (7) The Pendulum 115 - - CHAPTER VI. WORK AND ENERGY. - - (1) Work and Energy 119 - (2) Power and Energy 123 - (3) The Lever and Simple Machines 129 - (4) Wheel and Axle and Pulley 136 - (5) Efficiency and the Inclined Plane 142 - (6) Friction and its Uses 147 - (7) Water Power 152 - - CHAPTER VII. HEAT, ITS PRODUCTION AND TRANSMISSION. - - (1) Sources and Effects of Heat 159 - (2) Temperature and Expansion 162 - (3) Expansion of Gases, Liquids and Solids 167 - (4) Modes of Transmitting Heat 173 - (5) Convection, Heating and Ventilation 179 - (6) The Moisture in the Air, Hygrometry 191 - (7) Evaporation 196 - - CHAPTER VIII. HEAT AND WORK. - - (1) Heat Measurement and Specific Heat 200 - (2) Heat and Changes of State 205 - (3) Heat and Work 212 - (4) Heat Engines 222 - - CHAPTER IX. MAGNETISM. - - (1) General Properties of Magnets 228 - (2) Theory of Magnetism, Magnetic Fields 232 - (3) The Earth's Magnetism 238 - - CHAPTER XI. STATIC ELECTRICITY. - - (1) Electrification and Electrical Charges 243 - (2) Electric Fields and Electrostatic Induction 247 - (3) Electric Theories, Distribution and Electric Charges 252 - (4) Potential, Capacity, and the Electric Condenser 257 - (5) Electrostatic Generators 262 - - CHAPTER XI. ELECTRIC CURRENTS PRODUCED BY VOLTAIC - CELLS. - - (1) Electrical Currents and Circuits 267 - (2) The Simple Voltaic Cell and its Action 270 - (3) Practical Voltaic Cells 274 - - CHAPTER XII. MAGNETIC EFFECTS OF ELECTRIC CURRENTS, - AND ELECTRICAL MEASUREMENTS. - - (1) The Magnetic Effect of Electric Currents 279 - (2) Electrical Measurements 289 - (3) Ohm's Law and Electrical Circuits 298 - (4) Grouping of Cells and Measuring Resistance 302 - - CHAPTER XIII. CHEMICAL AND HEAT EFFECTS OF ELECTRIC - CURRENTS. - - (1) The Chemical Effect of Electric Currents 307 - (2) The Storage Battery and Electric Power 312 - (3) The Heat Effect of Electric Currents 318 - - CHAPTER XIV. INDUCED CURRENTS. - - (1) Electromagnetic Induction 326 - (2) The Dynamo and the Motor 335 - (3) The Induction Coil and the Transformer 343 - (4) The Telephone 349 - - CHAPTER XV. SOUND. - - (1) Sound, Source, Speed, Media 354 - (2) Waves and Wave Motion 357 - (3) Intensity and Pitch of Sound 363 - (4) Musical Scales and Resonance 368 - (5) Interference, Beats, Vibration of Strings 374 - (6) Tone Quality, Vibrating Plates and Air Columns 384 - - CHAPTER XVI. LIGHT. - - (1) Rectilinear Propagation of Light 388 - (2) Photometry and Law of Reflection 393 - (3) Mirrors and Formation of Images 400 - (4) Refraction of Light 410 - (5) The Formation of Images by Lenses 416 - (6) Optical Instruments 423 - (7) Color and Spectra 430 - (8) Nature of Light 442 - - CHAPTER XVII. INVISIBLE RADIATIONS. - - (1) Electric waves and Radioactivity 448 - - CHAPTER XVIII. WIRELESS TELEPHONY AND ALTERNATING - CURRENTS. - - (1) Wireless Telephony 460 - (2) Alternating Currents 466 - - INDEX 487 - - - - -PHYSICS - - - - -CHAPTER I - -INTRODUCTION AND MEASUREMENT - - -(1) INTRODUCTION - - -=1. Physics, an Explanation of Common Things.=--Many students take up -the study of physics expecting to see wonderful experiments with the "X" -rays, wireless telegraphy, dynamos, and other interesting devices. -Others are dreading to begin a study that to them seems strange and -difficult, because they fear it deals with ideas and principles that are -beyond their experience and hard to comprehend. - -Each of these classes is surprised to learn that _physics is mainly an -explanation of common things_. It is a study that systematizes our -knowledge of the forces and changes about us; such as the pull of the -earth, the formation of dew, rain and frost, water pressure and pumps, -echoes and music, thermometers and engines, and many other things about -us with which people are more or less familiar. Physics is like other -school subjects, such as mathematics and language, in having its own -peculiar vocabulary and methods of study; these will be acquired as -progress is made in the course. - -The most useful habit that the student of physics can form is that of -connecting or relating each _new idea_ or _fact_ that is presented to -him to _some observation_ or _experience_ that will illustrate the new -idea. This relating or connecting of the new ideas to one's own personal -experience is not only one of the best known means of cultivating the -memory and power of association, but it is of especial help in a subject -such as physics, which deals with the systematic study and explanation -of the facts of our every-day experience. - -=2. Knowledge--Common and Scientific.=--This leads to the distinction -between _common knowledge and scientific knowledge_. We all possess -common knowledge of the things about us, gained from the impressions -received by our senses, from reading, and from the remarks of others. -_Scientific_ knowledge is attained when the bits of common knowledge are -connected and explained by other information gained through study or -experience. That is, common knowledge becomes scientific, when it is -_organized_. This leads to the definition: _Science is organized -knowledge_. - -Common knowledge of the forces and objects about us becomes scientific -only as we are able to make accurate measurements of these. That is, -science is concerned not only in _how_ things work, but even more in -_how much_ is involved or results from a given activity. For example, a -scientific farmer must be able to compute his costs and results in order -to determine accurately his net profits. The business man who is -conducting his business with efficiency knows accurately his costs of -production and distribution. - -This book is written in the hope that it will make more scientific the -student's common knowledge of the forces and changes in the world about -him and will give him many ideas and principles that will help him to -acquire the habit of looking from effects to their natural causes and -thus tend to develop what is called the _scientific habit of thought_. - -=3. Hypothesis, Theory, and Law.=--Three words that are frequently used -in science may be mentioned here: _hypothesis_, _theory_, and _law_. An -hypothesis is a supposition advanced to explain some effect, change, or -condition that has been observed. For example, the Nebular Hypothesis of -which many high-school students have heard, is an attempt to explain the -origin of the sun, the earth, the planets, and other solar systems. - -A theory is an hypothesis which has been tested in a variety of ways and -which seems to fit the conditions and results so that it is generally -accepted as giving a satisfactory explanation of the matter in question. -The Molecular Theory of Matter which states that matter of all kinds is -composed of very small particles called molecules (see Art. 6), is a -familiar example of a theory. - -A theory becomes a law when it may be definitely proved. Many laws are -expressed in mathematical language, e.g., the law of gravitation. (See -Art. 88.) Many of the laws of physics are illustrated by laboratory -experiments, which show in a simple way just what the law means. - - -Exercises - -Explain what is meant by the following terms and expressions: - -1. Common knowledge. - -2. Scientific knowledge. - -3. Science. - -4. Topics in physics. - -5. Scientific habit of thought. - -6. Value of relating new ideas to former experiences. - -7. Hypothesis. - -8. Theory. - -9. Law. - - -(2) THE STATES OF MATTER - -=4. Physics Defined.=--In the study of any science or field of -knowledge, it is helpful to have a basis for grouping or classifying the -facts studied. In physics we are to study the objects, forces, and -changes about us, to understand them and their relations to one another. -Accordingly, physics, dealing with the material world about us, is often -defined as _the science of matter and energy_, _matter_ being _anything -that occupies space_ and _energy_ the _capacity for doing work_. This -definition of physics while not strictly accurate is sufficiently -comprehensive for our present purpose. - -=5. The Three States of Matter.=--Our bodies are _matter_ since they -occupy space. Further, they possess _energy_ since they are able to do -work. In beginning the study of physics it will simplify our work if we -study one of these topics before the other. We will therefore begin with -matter and consider first its three states. - -Some bodies are _solid_; as ice, iron, wax. Others are _liquid_; as -water, mercury, oil. Still others are in the state of _gas_; as steam, -air, and illuminating gas. Further we notice that the same substance may -be found in any one of the three states. For example water may be either -ice, water or steam; that is, either a solid, a liquid, or a gas. - -Most persons have heard of _liquid air_ and possibly some know of _ice -air_, _i.e._, air cooled until it not only liquefies, but is solidified. -On the other hand, iron may be melted and, if heated hot enough, may be -turned into iron vapor. In fact most substances by heating or cooling -sufficiently may be changed into any one of the three states. - -Before defining the three states, let us consider the _structure_ of -matter. This may help us to answer the question: How is it possible to -change a hard solid, such as ice, into a liquid, water, and then into -an invisible gas like steam? This is explained by the molecular theory -of matter. - -=6. The Molecular Theory of Matter.=--It is believed that all bodies are -made up of very small particles called _molecules_, and that these -instead of being packed tightly together like square packages in a box, -are, strange as it may seem, very loosely packed even in solids and do -not _permanently_ touch their neighbors. The size of these molecules is -so minute that it has been estimated that if a drop of water could be -magnified to the size of the earth, the molecules magnified in the same -proportion would be in size between a baseball and a football. The air -and all other gases are believed to be made up of molecules in _rapid -motion_, striking and rebounding continually from one another and from -any objects in contact with the gas. - -=7. States of Matter Defined.=--These ideas of the structure of matter -assist us in understanding the following definitions: _A solid is that -state of matter in which the molecules strongly cling together and tend -to keep the same relative positions_. (This of course follows from the -tendency of a solid to retain a definite form.) _A liquid is that state -of matter in which the molecules tend to cling together, yet move about -freely._ Hence a liquid takes the form of any vessel in which it is -placed. _A gas is that state of matter in which the molecules move about -freely and tend to separate indefinitely._ Hence a gas will fill any -space in which it is placed. - -=8. Effect of Heat on Matter.=--It is further believed that when a body -is heated, that the action really consists in making its molecules move -or vibrate faster and faster as the heating progresses. This increase of -motion causes the molecules to push apart from one another and this -separation of the molecules causes an expansion of the body whether it -be solid, liquid, or gas. Fig. 1 shows the expansion of air in an air -thermometer. Fig. 2 shows the expansion of a solid on heating. - -[Illustration: FIG. 1.--When the bulb is heated, the air within expands -forcing down the water in the tube.] - -=9. Physical and Chemical Changes.= A change of state such as the -freezing or boiling of water is called a _physical_ change, for this -change has not affected the identity of the substance. It is water even -though it has become solid or gaseous. Heating a platinum wire red hot -is also a physical change for the wire when on cooling is found to be -the same substance as before. Further if salt or sugar be dissolved in -water the act of _solution_ is also a physical change since the -identical substance (salt or sugar) is in the solution and may be -obtained by evaporating the water. - -[Illustration: FIG. 2 (_a_) represents a straight bar made of a strip of -brass and a strip of iron riveted together and attached to a handle. -Upon heating the compound bar in a gas flame, the brass expands faster -than the iron causing the bar to bend toward the latter as in Fig. 2 -(_b_).] - -If some sugar, however, is heated strongly, say in a test-tube, it is -found to blacken, some water is driven off and on cooling _some black -charcoal is found in the tube instead of the sugar_. This action which -has resulted in a _change in the nature of the substance_ treated is -called a _chemical_ change. To illustrate further, if some magnesium -wire is heated strongly in a flame, it burns, giving off an intense -light and when it cools one finds it changed to a light powdery -substance like ashes. Chemical changes, or those that change the nature -of the substance affected, are studied in _chemistry_. In _physics_ we -have to do only with physical changes, that is, with those changes that -do not affect the nature of the substance. - - -Important Topics - -1. Physics defined. - -2. The three states of matter; solid, liquid, gas. - -3. Molecular theory of matter. - -4. Physical and chemical changes. - - -Exercises - -Write out in your own words your understanding of: - -1. The structure of matter. - -2. Some of the differences between solids, liquids, and gases. - -3. How to change solids to liquids and gases and _vice versa_. - -4. The reason for the changes of size of a body on heating. - -5. Why cooling a gas tends to change it to a liquid or a solid. - -6. The actual size of molecules. - -Which of the following changes are chemical and which physical? - -Give reasons. - -1. Melting of ice. - -2. Burning of a candle. - -3. Production of steam. - -4. Falling of a weight. - -5. Drying of clothes. - -6. Making an iron casting. - -7. Decay of vegetables. - -8. Sprouting of seeds. - -9. Flying an aeroplane. - -10. Growth of a plant. - -11. Grinding of grain. - -12. Sawing a board. - -13. Pulverizing stone. - -14. Making toast. - -15. Sweetening tea or coffee with sugar. - -16. Burning wood or gas. - - -(3) THE METRIC SYSTEM - -=10. The Metric System.=--In order to study the three states of matter -with sufficient exactness it is necessary to employ a system of -measurement. The system universally employed by scientists is called -_The Metric System_. In many respects it is the most convenient for all -purposes. Every student should therefore become familiar with it and -learn to use it. At the present time, not only do scientists everywhere -use it, but many countries have adopted it and use it in common -measurements. It was legalized in the United States in 1866. The metric -system was originated by the French Academy of Sciences during the -latter part of the 18th century. There were so many different systems of -weights and measures in use, each country having a system of its own, -that commerce was much hindered. It was therefore decided to make a -system based upon scientific principles. The length of the earth's -quadrant passing from the equator to the pole was determined by -surveying and computation. One-ten-millionth of this distance was -selected as the unit of length and called a _meter_. Accurate copies of -this meter were made and preserved as standards. - -Later surveys have shown that the original determination of the earth's -quadrant was not strictly accurate; so that after all the meter is not -exactly one-ten-millionth of the earth's quadrant. - -=11. The Standard Meter.=--The standard unit of _length_ in the metric -system is the _meter_. It is the distance, at the temperature of melting -ice, between two transverse parallel lines ruled on a bar of platinum -(see Fig. 3), which is kept in the Palace of the Archives in Paris. -Accurate copies of this and other metric standards are also kept at the -Bureau of Standards at Washington, D. C. Fig. 4 shows the relation -between the inch and the centimeter (one-hundredth of a meter). - -=12. Units and Tables in the Metric System.=--The metric unit of _area_ -commonly used in physics is the _square centimeter_. - -[Illustration: FIG. 3--The standard meter.] - -The standard unit of _volume_ or capacity is the _liter_. It is a cube -one-tenth of a meter on each edge. It is equal to 1.057 quarts. It -corresponds, therefore, to the quart in English measure. - -[Illustration: FIG. 4.--Centimeter and inch scales.] - -The standard unit of _mass_ is the _kilogram_. It is the mass of 1 liter -of pure water at the temperature of its greatest density, 4°C. or -39.2°F. - -The three principal units of the metric system, the _meter_, the -_liter_, and the _kilogram_, are related to one another in a simple -manner, since the liter is a cube one-tenth of a meter in each dimension -and the kilogram is the mass of a liter of water. (See Fig. 5.) - -The metric system is a _decimal_ system that is, one unit is related to -another unit in the ratio of _ten_ or of some power of ten. This is -indicated by the following tables: - - _Metric Table of Length_ - - 10 millimeters (mm.) equal 1 centimeter. - 10 centimeters (cm.) equal 1 decimeter. - 10 decimeters (dm.) equal 1 meter. - 10 meters (m.) equal 1 dekameter. - 10 dekameters (Dm.) equal 1 hectometer. - 10 hectometers (hm.) equal 1 kilometer. - 10 kilometers (km.) equal 1 myriameter. - -The measures commonly used are the _centimeter_, _meter_ and -_kilometer_. - - _Metric Table of Mass_ (_or Weight_) - - 10 milligrams (mg.) equal 1 centigram. - 10 centigrams (cg.) equal 1 decigram. - 10 decigrams (dg.) equal 1 gram. - 10 grams (g.) equal 1 dekagram. - 10 dekagrams (Dg.) equal 1 hectogram. - 10 hectograms (hg.) equal 1 kilogram. - 10 kilograms (kg.) equal 1 myriagram. - -The masses commonly used are the _milligram_, _gram_ and _kilogram_. - -Notice in these tables the similarity to 10 mills equal 1 cent, 10 cents -equal 1 dime, 10 dimes equal 1 dollar, in the table of United States -money. - -Other tables in the metric system are built upon the same plan. Learn -the prefixes in order thus: milli, centi, deci, deka, hecto, kilo, -myria. The first three prefixes are Latin numerals and represent -divisions of the unit. The last four are Greek numerals and represent -multiples. In these tables, milli means 1/1000, centi means 1/100, deci -means 1/10, deka means 10, hecto, 100, kilo, 1000, myria, 10,000. Two -other prefixes are sometimes used, _micro_ which means 1/1,000,000; as -microfarad or microvolt, and _meg_ which means 1,000,000, as megohm -meaning 1,000,000 ohms. - -=13. Advantages of the Metric System.=--_First_, it is a decimal system; -_second_, the same form and prefixes are used in every table; _third_, -the standards of length (meter), volume (liter), and mass (kilogram) -bear a simple relation to one another. This simple relation between the -three standard units may be given thus: _first_, the liter is a cubic -decimeter, and _second_, the kilogram is the mass of a liter of water. -(See Fig. 5) Since the liter is a cubic decimeter, the length of one -side is 10 cm. The liter therefore holds 1000 ccm. (10 × 10 × 10). -Therefore, 1 liter = 1 cu. dm. = 1000 ccm. and since 1 liter of water -has a mass of 1 kg. or 1000 g., then 1000 ccm. of water has a mass of -1000 g., or _1 ccm. of water has a mass of 1 g._ - -[Illustration: FIG. 5.--One liter of the water has a mass of one -kilogram.] - -The following table of equivalents gives the relation between the most -common English and metric units. Those marked (*) should be memorized. - - (*) 1 meter = 39.37 inches. 1 cu, in. = 16.387 ccm. - (*) 1 inch = 2.54 cm. 1 cu. ft. = 28315 cm. - 1 foot = 30.48 cm. 1 cu. m. = 1.308 cu. yd. - 1 mile = 1.609 km. (*) 1 liter = 1.057 qt. - 1 sq. in. = 6.45 sq. cm. (*) 1 kg. = 2.204 lbs. - 1 sq. cm. = 0.155 sq. in. 1 g. = 15.44 grains. - 1 sq. m. = 1.196 sq. yd. 1 lb. = 0.4536 kg. - 1 acre = 0.405 ha. 1 oz. = 28.35 g. - 1 hectare = 2.45 acres. 1 g. = 0.0353 oz. - -THE C. G. S. SYSTEM. Scientists have devised a plan for expressing any -measurement in terms of what are called the _three fundamental units of -length_, _mass_, and _time_. The units used are the _centimeter_, the -_gram_ and the _second_. Whenever a measurement has been reduced to its -equivalent in terms of these units, it is said to be expressed in -_C.G.S._ units. - - -Important Topics - -1. The metric system; how originated. - -2. Units; meter, liter, kilogram. - -3. Metric tables. - -4. Advantages of the metric system. - -5. Equivalents. - -6. The C.G.S. system. - - -Exercises - -1. Which is cheaper, milk at 8 cents a quart or 8 cents a liter? Why? - -2. Which is more expensive, cloth at $1.00 a yard or at $1.00 a meter? -Why? - -3. Which is a better bargain, sugar at 5 cents a pound or 11 cents a -kilogram? Why? - -4. Express in centimeters the height of a boy 5 ft. 6 in. tall. - -5. What is the length of this page in centimeters? In inches? - -6. What is the mass of a liter of water? Of 500 ccm.? Of 1 ccm.? - -7. From Chicago to New York is 940 miles. Express in kilometers. - -8. A 10-gallon can of milk contains how many liters? - -9. What will 100 meters of cloth cost at 10 cents a yard? - -10. What will 4 kg. of beef cost at 15 cents a pound? - -11. What will 5-1/2 lbs. of mutton cost at 40 cents a kilogram? - -12. How can you change the state of a body? Give three methods. - -13. Correct the statement 1 ccm. = 1 g. - -14. How many liters in 32 quarts? - - - - -CHAPTER II - -MOLECULAR FORCES AND MOTIONS - - -(1) EVIDENCES OF MOLECULAR MOTION IN GASES - - -=14. Size of Molecules.=--The difference between solids, liquids, and -gases has been explained as due to the different behavior of molecules -in the three states of matter. That is, in solids they cling together, -in liquids they move freely, and in gases they separate. At this time we -are to consider the _evidences_ of molecular motion in gases. It must be -kept in mind that molecules are exceedingly small. It has been said that -if a bottle containing about 1 ccm. of ordinary air has pierced in it a -minute opening so that 100,000,000 molecules (a number nearly equal to -the population of the United States) pass out every second, it would -take, not minutes or hours, but nearly 9000 years for all of the -molecules to escape. The number of molecules in 1 ccm. of air at 0°C. -and 76 cm. pressure has been calculated by Professor Rutherford to be -2.7 × 10¹{~SUPERSCRIPT NINE~}. It is evident that such minute particles cannot be seen or -handled as _individuals_. We must judge of their size and action by the -results obtained from experiments. - -=15. Diffusion of Gases.=--One line of evidence which indicates that a -gas consists of moving particles is the rapidity with which a gas having -a strong odor penetrates to all parts of a room. For example, if -illuminating gas is escaping it soon diffuses and is noticed throughout -the room. In fact, the common experience of the diffusion of gases -having a strong odor is such that we promptly recognize that it is due -to motion of some kind. The gas having the odor consists of little -particles that are continually hitting their neighbors and are being -struck and buffeted in turn until the individual molecules are widely -scattered. When cabbage is boiled in the kitchen soon all in the house -know it. Other illustrations of the _diffusion_ of gases will occur to -anyone from personal experience, such for instance as the pleasing odor -from a field of clover in bloom. - -The following experiment illustrates the rapid diffusion of gases. - -[Illustration: FIG. 6_a_.--Diffusion of gases.] - -[Illustration: FIG. 6_b_.--Effusion of gases.] - - Take two tumblers (see Fig. 6_a_), wet the inside of one with a few - drops of strong ammonia water and the other with a little - hydrochloric acid. Cover each with a sheet of clean paper. Nothing - can now be seen in either tumbler. Invert the second one over the - first with the paper between, placing them so that the edges will - match. On removing the paper it is noticed that both tumblers are - quickly filled with a cloud of finely divided particles, the two - substances having united chemically to form a new substance, - ammonium chloride. - -On account of their small size, molecules of air readily pass through -porous solids, cloth, unglazed earthenware, etc. The following -experiment shows this fact strikingly. (See Fig. 6_b_.) - - A flask containing water is closed by a rubber stopper through - which pass the stem of a glass funnel and a bent glass tube that - has been drawn out to a small opening (_J_). The funnel has - cemented in its top an inverted porous clay jar (_C_), over the top - of the latter is placed a beaker (_B_). A piece of flexible rubber - tubing (_H_) leading from a hydrogen generator is brought up to the - top of the space between the jar and the beaker. When hydrogen gas - is allowed to flow into the space between _C_ and _B_, the level of - the water in _W_ is seen to lower and a stream of water runs out at - _J_ spurting up into the air. - - On stopping the flow of hydrogen and removing _B_, the water falls - rapidly in _J_ and bubbles of air are seen to enter the water from - the tube. (The foregoing steps may be repeated as often as - desired). - - This experiment illustrates the fact that the molecules of some - gases move faster than those of some other gases. Hydrogen - molecules are found to move about four times as fast as air - molecules. Hence, while both air and hydrogen molecules are at - first going in opposite directions through the walls of _C_, the - hydrogen goes in much faster than the air comes out. In consequence - it accumulates, creates pressure, and drives down the water in _W_ - and out at _J_. On removing _B_, the hydrogen within the porous cup - comes out much faster than the air reënters. This lessens the - pressure within, so that air rushes in through _J_. This experiment - demonstrates not only the fact of molecular motion in gases but - also that molecules of hydrogen move much faster than those of air. - (This experiment will work with illuminating gas but not so - strikingly.) - -Careful experiments have shown that the speed of ordinary air molecules -is 445 meters or 1460 ft. per second; while hydrogen molecules move at -the rate of 1700 meters or 5575 ft. or more than a mile per second. - -=16. Expansion of Gases.=--Gases also possess the property of indefinite -expansion, that is, if a small quantity of gas is placed in a vacuum, -the gas will expand immediately to fill the entire space uniformly. This -is shown by an experiment with the air pump. On raising the piston the -air follows instantly to fill up the space under it. As the air is -removed from the receiver of an air pump the air remaining is uniformly -distributed within. - -=17. How Gases Exert Pressure.=--It is further found that air under -ordinary conditions exerts a pressure of about 15 lbs. to the square -inch. In an automobile tire the pressure may be 90 lbs. and in a steam -boiler it may be 200 lbs. or more to the square inch. - -How is the pressure produced? The molecules are not packed together -solidly in a gas, for when steam changes to water it shrinks to about -1/1600 of its former volume. Air diminishes to about 1/800 of its volume -on changing to liquid air. The pressure of a gas is not due then to the -gas filling all of the space in which it acts, but is due rather to the -_motion_ of the molecules. The blow of a single molecule is -imperceptible, but when multitudes of molecules strike against a surface -their combined effect is considerable. In fact, this action is known to -produce the pressure that a gas exerts against the walls of a containing -vessel. Naturally if we compress twice as much gas into a given space -there will be twice as many molecules striking in a given time, which -will give twice as much pressure. - -If gas is heated, it is found that the heat will cause a swifter motion -of the molecules. This will also make the molecules strike harder and -hence cause the gas to expand or exert more pressure. - -=17a. Brownian Movements.=--Direct photographic evidence of the motion -of molecules in gases has been obtained by studying the behavior of -minute drops of oil suspended in stagnant air. Such drops instead of -being at rest are constantly dancing about as if they were continually -receiving blows from many directions. These motions have been called -_Brownian Movements_ (see Fig. 7). - -It has been proved that these movements are due to the blows that these -small drops receive from the swiftly moving molecules of the gas about -them. If the drops are made smaller or the gas more dense, the movements -increase in intensity. These effects are especially marked at a pressure -of 0.01 of an atmosphere. - -[Illustration: FIG. 7.--Photograph of Brownian movement. This record is -prepared by the aid of Siedentopf's ultra-microscope and a plate moving -uniformly across the field from left to right.] - - -Important Topics - -It is assumed that air and all gases are made up of molecules in rapid -motion; that this motion is dependent upon temperature and pressure. -Evidence of this is shown by (a) diffusion, (b) expansion, (c) pressure. -Brownian Movements. - - -Questions - -1. What is the molecular (kinetic) theory of gases? - -2. What three kinds of evidence help to confirm the theory? - -3. What have you seen that seems to show that a gas consists of -molecules in motion? - -4. How many meters long is a 10-ft. pole? - -5. A 50-kg. boy weighs how many pounds? - -6. What are three advantages of the metric system? - -7. What will 12 qts. of milk cost at 8 cents a liter? - -8. A cube 1 meter each way will contain how many cubic centimeters? How -many liters? What will a cubic meter of water weigh? - - -(2) MOLECULAR MOTION IN LIQUIDS - -=18. Diffusion of Liquids.=--From the evidence given in Arts. 14-17, (a) -of diffusion of odors, (b) of the continued _expansion_ of air in the -air pump, and (c) of the pressure exerted by a gas in all directions, -one may realize without difficulty that a _gas consists of small -particles in rapid motion_. Let us now consider some of the evidence of -molecular motion in liquids. If a little vinegar is placed in a pail of -water, all of the water will soon taste sour. A lump of sugar in a cup -of tea will sweeten the entire contents. This action is somewhat similar -to the diffusion of gases but it takes place much more slowly. It is -therefore believed that the motion of liquid molecules is much slower -than that of gas molecules. - -Again, if a dish of water is left standing in the open air in fine -weather, within a few days the dish will become dry though no one has -taken anything from it. We say the water has _evaporated_. What was -liquid is now _vapor_. If we were to observe carefully any dish of water -we would find that it continually loses weight on dry days. That is, -there is a constant movement of the molecules of water into the air. -This movement of the molecules is explained as follows. There appear to -be in the dish of water some molecules that by moving back and forth -acquire a greater velocity than their neighbors; when these reach the -surface of the liquid, some vibration or movement sends them flying into -the air above. They are now vapor or gas molecules, flying, striking, -and rebounding like the air molecules. Sometimes on rebounding, the -water molecules get back into the water again. This is especially apt to -happen when the air is damp, _i.e._, when it contains many water -molecules. Sometimes the air over a dish becomes _saturated_, as in the -upper part of a corked bottle containing water. Although molecules are -continually leaving the surface of the water they cannot escape from the -bottle, so in time as many molecules must return to the water from the -space above as leave the water in the same time. When this condition -exists, the air above the water is said to be _saturated_. On very damp -days the air is often saturated. The explanation above shows why wet -clothes dry so slowly on such a day (See Arts. 166-7 on Saturation.) - -=19. Cooling Effect of Evaporation.= We have seen that warming a gas -increases its volume. This expansion is due to the increased motion of -the warmed molecules. Now the molecules that escape from a liquid when -it evaporates are naturally the fastest moving ones, _i.e._, the hottest -ones. The molecules remaining are the slower moving ones or colder -molecules. The liquid therefore becomes colder as it evaporates, unless -it is heated. This explains why water evaporating on the surface of our -bodies cools us. In evaporating, the water is continually losing its -warm, fast moving molecules. The _cooling effect_ of evaporation is, -therefore an evidence of molecular motion in liquids. - -[Illustration: FIG. 8.--Osmosis Shown by carrot placed in water.] - -=20. Osmosis.=--If two liquids are separated by a membrane or porous -partition, they tend to pass through and mix. This action is called -osmose, or _osmosis_. - - Such a movement of liquid molecules in osmosis may be illustrated - by filling a beet or carrot that has had its interior cut out to - form a circular opening (see Fig. 8) with a thick syrup. The - opening is then closed at the top with a rubber stopper through - which passes a long glass tube. - - If the carrot is immersed in water, as in Fig. 8, a movement of - water through the porous wall to the interior begins at once. Here, - as in the experiment of the hydrogen and air passing through the - porous cup, the lighter fluid moves faster. The water collecting in - the carrot rises in the tube. This action of liquids passing - through porous partitions and mingling is called _osmosis_. - -Gases and liquids are alike in that each will _flow_. Each is therefore -called a _fluid_. Sometimes there is much resistance to the flow of a -liquid as in molasses. This resistance is called _viscosity_. Alcohol -and gasoline have little viscosity. They are _limpid_ or _mobile_. Air -also has some viscosity. For instance, a stream of air always drags some -of the surrounding air along with it. - - -Important Topics - -1. Liquids behave as if they were composed of small particles in motion. - -2. This is shown by (1) Diffusion, (2) Solution, (3) Evaporation, (4) -Expansion, (5) Osmosis. - - -Exercises - -1. Give an example or illustration of each of the five evidences of -molecular motion in liquids. - -2. When is air saturated? What is the explanation? - -3. Why does warming a liquid increase its rate of evaporation? - -4. Air molecules are in rapid motion in all directions. Do they enter a -liquid with a surface exposed to the air? Give reason. - -5. What are some of the inconveniences of living in a saturated -atmosphere? - -6. Fish require oxygen. How is it obtained? - - -(3) MOLECULAR FORCES IN LIQUIDS - -=21. Cohesion and Adhesion.=--In liquids "the molecules move about -freely yet tend to cling together." This tendency of molecules to cling -together which is not noticeable in gases is characteristic of =liquids= -and especially of =solids=. It is the cause of the viscosity mentioned -in the previous section and is readily detected in a variety of ways. -For instance, not only do liquid molecules cling together to form drops -and streams, but they cling to the molecules of solids as well, as is -shown by the wet surface of an object that has been dipped in water. The -attraction of like molecules for one another is called _cohesion_, while -the attraction of =unlike molecules= is called _adhesion_, although the -force is the same whether the molecules are alike or unlike. It is the -former that causes drops of water to form and that holds iron, copper, -and other solids so rigidly together. The adhesion of glue to other -objects is well known. Paint also "sticks" well. Sometimes the "joint" -where two boards are glued together is stronger than the board itself. -The force of attraction between molecules has been studied carefully. -The attraction acts only through very short distances. The attraction -even in liquids is considerable and may be measured. The cohesion of -water may be shown by an experiment where the force required to pull a -glass plate from the surface of water is measured. - -[Illustration: FIG. 9.--The water is pulled apart.] - - Take a beam balance and suspend from one arm a circular glass - plate, Fig. 9. Weigh the plate and its support. Adjust the glass - plate so that it hangs horizontally and just touches the surface of - clean water, the under side being completely wet. Now find what - additional weight is required to raise the glass plate from the - water. - -Just as the plate comes from the water its under side is found to be -wet. That is, _the water was pulled apart_, and the plate was not pulled -from the water. The cohesion of the water to itself is not so strong as -its adhesion to the glass. - -The cohesion of liquids is further shown by the form a drop of liquid -tends to take when left to itself. This is readily seen in small drops -of liquids. The spherical shape of drops of water or mercury is an -example. A mixture of alcohol and water in proper proportions will just -support olive oil within it. By carefully dropping olive oil from a -pipette into such a mixture, a drop of the oil, an inch or more in -diameter suspended in the liquid, may be formed. It is best to use a -bottle with plane or flat sides, for if a round bottle is used, the -sphere of oil will appear flattened. - -[Illustration: FIG. 10 _a_. - -FIG. 10 _b_. - -FIGS. 10 _a_ AND _b_.--Surface tension of a liquid film.] - -=22. Surface Tension.=--The cohesion of liquids is also indicated by the -tendency of films to assume the smallest possible surface. Soap bubble -films show this readily. Fig. 10 _a_ represents a circular wire form -holding a film in which floats a loop of thread. The tension of the -film is shown in Fig. 10 _b_ by the circular form of the loop after the -film within it has been pierced by a hot wire, Fig. 11 shows a -rectangular wire form with a "rider." The tension in the film draws the -rider forward. - -[Illustration: FIG. 11.--The rider is drawn forward.] - -[Illustration: FIG. 12.--Surface tension causes the pointed shape.] - -A soap bubble takes its spherical shape because this form holds the -confined air within the smallest possible surface. A drop of liquid is -spherical for the same reason. Many illustrations of the tension in -films may be given. Users of water colors notice that a dry camel's-hair -brush is bushy. (Fig. 12 _A_). When in water it is still bushy. (Fig. 12 -_B_.) But when it is taken from the water and the excess is shaken from -it, it is pointed as in Fig. 12 _C_. It is held to the pointed shape by -the tension of the liquid film about the brush. - -[Illustration: FIG. 13.--A needle depresses the surface when floating.] - -The surface of water acts as if covered by a film which coheres more -strongly than the water beneath it. This is shown by the fact that a -steel needle or a thin strip of metal may be floated upon the surface of -water. It is supported by the surface film. (See Fig. 13.) If the film -breaks the needle sinks. This film also supports the little water bugs -seen running over the surface of a quiet pond in summer. The surface -film is stronger in some liquids than in others. This may be shown by -taking water, colored so that it can be seen, placing a thin layer of it -on a white surface and dropping alcohol upon it. Wherever the alcohol -drops, the water is seen to pull away from it, leaving a bare space over -which the alcohol has been spread. This indicates that the alcohol has -the weaker film. The _film of greasy benzine is stronger_ than the film -of the pure material. If one wishes to remove a grease spot and places -pure benzine at the center of the spot, the stronger film of the greasy -liquid will pull away from the pure benzine, and spread out, making a -larger spot than before, while if pure benzine is placed _around the -grease spot_, the greasy liquid at the center pulls away from the pure -benzine, drawing more and more to the center, where it may be wiped up -and the grease entirely removed. - -[Illustration: FIG. 14.--The molecule at _A_ is held differently from -one within the liquid.] - -=23. Explanation of the Surface Film.=--Beneath the surface of a liquid -each molecule is attracted by all the other molecules around it. It is -attracted equally in all directions. Consequently the interior molecules -move very easily over each other in any direction. A molecule at the -surface, as at _A_, Fig. 14, is not attracted _upward_ by other liquid -molecules. Its freedom of motion is thereby hindered with the result -that a molecule at the surface behaves differently from one beneath the -surface. The surface molecules act as if they form an elastic skin or -membrane upon the liquid surface. - -[Illustration: FIG. 15.--Capillary attraction in tubes.] - -=24. Capillarity.=--A striking action of the surface film of a liquid is -seen in the rise of liquids in tubes of small bore when the liquid -_wets_ them. If the liquid _does not wet_ the tube, as when mercury is -placed in glass, the liquid is depressed. It is found in general that: -_Liquids rise in capillary tubes when they wet them and are depressed in -tubes which they do not wet; the smaller the diameter of the tube the -greater the change of level._ (See Fig. 15.) This action is explained as -follows: The molecules of a liquid have an attraction for each other and -also for the sides of a tube. The former is called "cohesion for -itself," the latter is called "adhesion for the sides of the containing -vessel." If the cohesion for itself is greater than the adhesion for the -side of the containing vessel, the liquid is pulled away from the side -and is depressed. If the adhesion is greater, the liquid is elevated. -This action is called "capillary action" from the Latin word -(_capillus_) signifying hair, since it shows best in fine hairlike -tubes. - -There are many common illustrations of capillary action: oil rising in a -wick; water rising in a towel or through clothes; ink in a blotter, etc. -The minute spaces between the fibers composing these objects act as fine -tubes. If cloth is treated with a preparation which prevents water from -adhering to its fibers, the material will not be wet when water is -poured upon it, because the water will not run in between the fibers; a -surface film spreads over the cloth so that no water enters it. -_Cravenette cloth_ has been treated in this way and hence is waterproof. - - The action of this film may be shown by the following experiment. - Dip a sieve of fine copper gauze in melted paraffin, thus coating - each wire so that water will not adhere to it. Water may now be - poured into the sieve, if a piece of paper is first laid in it to - break the force of the water. On carefully removing the paper the - surface film of the water will prevent the passage of the water - through the sieve. - -=25. Capillary Action in Soils.=--The distribution of moisture in the -soil depends largely upon capillary action. When the soil is compact the -minute spaces between the soil particles act as capillary tubes, thus -aiding the water to rise to the surface. As the water evaporates from -the surface more of it rises by capillary action from the damper soil -below. Keeping the soil loose by cultivation, makes the spaces between -the particles too large for much capillary action, thus the moisture is -largely prevented from rising to the surface. - -In the semi-arid regions of the West "_dry farming_" is successfully -practised. This consists in keeping the surface covered with a "dust -mulch" produced by frequent cultivation. In this way the moisture is -kept below the surface, where it can be utilized during the hot dry -summer by the roots of growing plants. - - -Important Topics - -1. Attractive forces between liquid molecules. - -2. Cohesion (like molecules); adhesion (unlike molecules). - -3. Special effects of this force are classified as (a) capillary action, -and (b) surface tension. - - -Exercises - -1. What evidence of capillary action have you seen outside of the -laboratory? - -2. What is the explanation for capillary action? - -3. Where are surface films found? - -4. What are three common effects of surface films? - -5. Explain why cravenette cloth sheds water. - -6. If a circular glass disc 10 cm. in diameter requires 50 grams of -force to draw it from the water, what is the cohesion of water per -square centimeter? - -7. What is the weight in grams of 1 ccm. of water? of a liter of water? - -8. Name five examples of adhesion to be found in your home. - -9. Under what conditions will a liquid wet a solid and spread over it? - -10. When will it form in drops on the surface? - -11. Explain the proper procedure for removing a grease spot with -benzine. - -12. What difference is there between a liquid and a fluid? - -13. Why cannot a "soap bubble" be blown from pure water? - -14. Which are larger, the molecules of steam or those of water? Why? - -15. Why is the ground likely to be damp under a stone or board when it -is dry all around? - -16. Why does any liquid in falling through the air assume the globule -form? - -17. Give three examples of capillary attraction found in the home. Three -out of doors. - -18. Why does cultivation of the soil prevent rapid evaporation of water -from the ground? - - -(4) EVIDENCES OF MOLECULAR FORCES IN LIQUIDS AND SOLIDS - -=26. Solutions.=--A crystal of potassium permanganate is placed in a -liter of water. It soon dissolves and on shaking the flask each portion -of the liquid is seen to be colored red. The dissolving of the -permanganate is an illustration of the attraction of the molecules of -water for the molecules of the permanganate. We are familiar with this -action in the seasoning of food with salt and sweetening with sugar. - -Water will dissolve many substances, but in varying degrees, _i.e._, of -some it will dissolve much, of others, little, and some not at all. -Further, different liquids have different solvent powers. Alcohol will -dissolve resin and shellac, but it will not dissolve gum arabic, which -is soluble in water. Benzine dissolves grease. Beeswax is not dissolved -by water, alcohol or benzine, but is soluble in turpentine. - -It is found that the _temperature_ of the liquid has a marked effect -upon the amount of substance that will dissolve. This is an indication -that the _motions_ of the molecules are effective in solution. It -appears that dissolving a solid is in some respects similar to -evaporation, and just as at higher temperatures more of the liquid -evaporates, because more of the molecules will escape from the liquid -into the air above, so at higher temperatures, more molecules of a solid -will detach themselves through greater vibration and will move into the -liquid. - -Further, just as an evaporating liquid may saturate the space above it -so that any escape of molecules is balanced by those returning, so with -a dissolving solid, the liquid may become _saturated_ so that the -solution of more of the solid is balanced by the return of the molecules -from the liquid to the solid condition. - -=27. Crystals and Crystallization.=--This return from the liquid to the -solid state, of molecules that are in solution, is especially noticeable -when the solution is cooling or evaporating and hence is losing its -capacity to hold so much of the solid. On returning to the solid, the -molecules attach themselves in a definite manner to the solid portion, -building up regular solid forms. These regular forms are _crystals_. The -action that forms them is called _crystallization_. - -Each substance seems to have its own _peculiar form of crystal_ due to -the manner in which the molecules attach themselves to those previously -in place. The largest and most _symmetrical crystals are_ those in which -the molecules are deposited slowly with no disturbance of the liquid. -Beautiful crystals of alum may be obtained by dissolving 25 g. of alum -in 50 ccm. of hot water, hanging two or three threads in the solution -and letting it stand over night. The thread fibers provide a foundation -upon which crystals grow. - -When a _solution_ of a solid evaporates, the molecules of the _liquid_ -escape as a gas, the molecules of the _solid_ remain accumulating as -crystals. This principle has many uses: (a) sea water is purified by -_evaporating the water and condensing the vapor_, which of course forms -pure water. (b) water is forced down to _salt_ beds where it dissolves -the salt. The brine is then raised and evaporated, leaving the salt in -the evaporating pans. - - =28. Absorption of Gases by Solids and Liquids.=--If a piece of - heated charcoal is placed in a test-tube containing ammonia gas, - inverted in mercury, the ammonia is seen to disappear, the mercury - rising to take its place. The ammonia has been absorbed by the - charcoal, the gas molecules clinging closely to the solid. The - charcoal being very porous presents a large surface to the action - of the gas. - -This experiment indicates that attraction exists between gas molecules -and other molecules. Many porous substances have this power of absorbing -gases. We have all noticed that butter has its flavor affected by -substances placed near it. - -That _liquids absorb gases_ is shown by slowly heating cold water in a -beaker. Small bubbles of air form on the sides and rise before the -boiling point is reached. Ammonia gas is readily absorbed in water, the -bubbles disappearing almost as soon as they escape into the water from -the end of the delivery tube. _Household ammonia_ is simply a solution -of ammonia gas in water. On warming the solution of ammonia the gas -begins to pass off; thus, warming a liquid tends to drive off any gas -dissolved in it. - -_Soda water_ is made by forcing carbon dioxide gas into water under -strong pressure. When placed in a vessel open to the air the pressure is -lessened and part of the gas escapes. The dissolved gas gives the -characteristic taste to the beverage. - - -Important Topics - -1. The solution of solids is increased by heating. - -2. The solution of gases is decreased by heating. - -3. Pressure increases the quantity of gas that can be dissolved in a -liquid. - -4. The attraction (cohesion) of molecules of a dissolved solid for each -other is shown by crystallization. - - -Exercises - -1. How do fish obtain oxygen for breathing? - -2. Why does warming water enable it to dissolve more of a salt? - -3. Why does warming water lessen the amount of a gas that will stay in -solution? - -4. Will water absorb gases of strong odor? How do you know? - -5. Name three solvents. Give a use for each. - -6. What liquids usually contain gases in solution? Name some uses for -these dissolved gases. - -7. What is the weight of a cubic meter of water? - -8. Name three substances obtained by crystallization. - -9. How is maple sugar obtained? - -10. Name five crystalline substances. - - -(5) EVIDENCE OF MOLECULAR FORCES IN SOLIDS - -=29. Differences between Solids and Gases.=--In studying gases, it is -seen that they behave as if they were composed of small particles in -rapid motion, continually striking and rebounding, and separating to -fill any space into which they are released. This action indicates that -there is practically no attractive force between such molecules. - -Between the molecules of a solid, however, the forces of attraction are -strong, as is shown by the fact that a solid often requires a great -force to pull it apart; some, as steel and iron, show this property in a -superlative degree, a high-grade steel rod 1 cm. in diameter requiring -nearly 9 tons to pull it apart. Tests show that the breaking strengths -of such rods are directly proportional to their areas of cross-section. -That is, twice the area has twice the breaking strength. - -[Illustration: FIG. 16.--Elasticity of bending.] - -=30. Elasticity.=--Fully as important as a knowledge of the breaking -strengths of solids, is the knowledge of what happens when the forces -used are not great enough to break the rods or wires. - - Take a wooden rod (as a meter stick) and clamp one end to the table - top, as in Fig. 16. At the other end hang a weight. Fasten a wire - to this end so that it projects out in front of a scale. Add - successively several equal weights and note the position of the - wire each time. Remove the weights in order, noting the positions - as before. The rod will probably return to the first position. - -This simple experiment illustrates a characteristic of solids: that of -changing shape when force is applied and of returning to the original -shape when the force is removed. This property is called _elasticity_. - -Tests of elasticity are made by subjecting wire of different materials -but of the same dimensions to the same tension. The one changing least -is said to have the greatest _elastic force_ or elasticity. If greater -forces are applied to the wire and then removed, one will finally be -found that will permanently stretch the wire so that it will not return -exactly to the former length. The wire has now passed its _elastic -limit_ and has been permanently stretched. - -Just as there are great differences between the _elastic forces_ of -different substances, so there are great differences in the _limits of -elasticity_. In some substances the limit is reached with slight -distortion, while others are _perfectly elastic_ even when greatly -stretched. India rubber is an example of a body having _perfect_ -elasticity through wide limits. Glass has great _elastic force_ but its -_limit_ of _elasticity_ is soon reached. Substances like India rubber -may be said to have great "_stretchability_," but little elastic force. -In physics, elasticity refers to the elastic force rather than to -ability to endure stretching. - -=31. Kinds of Elasticity.=--_Elasticity may be shown in four ways_: -_compression_, _bending_ or _flexure_, _extension_ or _stretching_, -_twisting_ or _torsion_. The first is illustrated by squeezing a rubber -eraser, the second by an automobile spring, the third by the stretching -of a rubber band, the fourth by the twisting and untwisting of a string -by which a weight is suspended. - -_There are two kinds of elasticity_: (1) elasticity of form or shape; -(2) elasticity of volume. Gases and liquids possess elasticity of -volume, but not of shape, while solids may have both kinds. Gases and -liquids are perfectly elastic because no matter how great pressure may -be applied, as soon as the pressure is removed they regain their former -volume. No solid possesses perfect elasticity, because sooner or later -the limit of elasticity will be reached. - -=32. Hooke's Law.=[A]--On examining the successive movements of the end -of the rod in Art. 30, we find that they are approximately equal. -Carefully conducted experiments upon the elasticity of bodies have shown -that the changes in shape are _directly proportional_ to the forces -applied, provided that the limit of elasticity is not reached. This -relation, discovered by Robert Hooke, is sometimes expressed as follows: -"_Within the limits of perfect elasticity, all changes of size or shape -are directly proportional to the forces producing them._" - - [A] A law is a statement of a constant mode of behavior. It is - often expressed in mathematical language. - -=33. Molecular Forces and Molecular Motions.=--If a solid is compressed, -on releasing the pressure the body regains its former shape if it has -not been compressed too far. This indicates that at a given temperature -the "molecules of a solid tend to remain at a fixed distance from each -other, and resist any attempt to decrease or increase this distance." -This raises the question, Why does not the cohesion pull the molecules -tightly together so that compression would be impossible? The reason is -that heat affects the size of solid bodies. On lowering the temperature, -bodies do contract, for as soon as the temperature is lowered the -vibration of the molecule is lessened. On raising the temperature the -molecules are pushed farther apart. - -The size of a body, then, is the result of a balance of opposing forces. -The attractive force between the molecules pulling them together is -_cohesion_, while the force which pushes them apart is due to the -motions of the molecules. Raising the temperature and thus increasing -the motion causes expansion; lowering the temperature decreases the -molecular motion and so causes contraction. If an outside force tries to -pull the body apart or to compress it this change of size is resisted by -either cohesion or molecular motion. - -=34. Properties of Matter.=--Many differences in the physical properties -of solids are due to differences between the cohesive force of different -kinds of molecules. In some substances, the attraction is such that they -may be rolled out in very thin sheets. Gold is the best example of this, -sheets being formed 1/300,000 of an inch thick. This property is called -_malleability_. In other substances the cohesion permits it to be drawn -out into fine threads or wire. Glass and quartz are examples of this. -This property is called _ductility_. In some, the cohesion makes the -substance excessively _hard_, so that it is difficult to work or scratch -its surface. The diamond is the hardest substance known. Some substances -are _tough_, others _brittle_. These are tested by the ability to -withstand sudden shocks as the blow of a hammer. - - -Important Topics - -1. Molecular forces in solids; (_a_) adhesion, (_b_) cohesion. - -2. Elasticity, Hooke's Law. - -3. Contraction on cooling. - -4. Malleability, ductility, hardness, brittleness, etc. - - -Exercises - -1. Give an illustration of Hooke's Law from your own experience. - -2. What devices make use of it? - -3. Do solids evaporate. Give reasons. - -4. When iron is welded, is cohesion or adhesion acting? - -5. When a tin basin is soldered, is cohesion or adhesion acting? - -6. Sometimes a spring is made more elastic by _tempering_ and made soft -by _annealing_. Look up the two terms. How is each accomplished? - -7. Review the definitions: solid, liquid, and gas. Why do these -definitions mean more to you now than formerly? - -8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what force -will stretch it 0.75 cm? Explain. - -9. How long will it take under ordinary conditions for a gas molecule to -cross a room? Give reasons for your answer. - -10. What is meant by the elastic limit of a body? - -11. Without reaching the elastic limit, if a beam is depressed 4 mm. -under a load of 60 kg., what will be the depression under a load of 400 -kg.? Of 600 kg.? - -12. Name three substances that possess elasticity of volume. - -13. Give three examples of each; elasticity of (1) compression, (2) -stretching, (3) torsion, (4) flexure. - - -Review Outline: Introduction and Molecules - -Physics; definition, topics considered, physical and chemical changes. - -Science; hypothesis, theory, law. Knowledge; common, scientific. - -Matter; three states, molecular theory. Mass, weight, volume. - -Metric system; units, tables, equivalents, advantages. - -Evidences of molecular motions; gases (3), liquids (5), solids (3). - -Evidences of molecular forces; liquids (3), solids (many) special -properties such as: elasticity, tenacity, ductility, hardness, etc. - -Hooke's law; applications. - - - - -CHAPTER III - -MECHANICS OF LIQUIDS - - -(1) THE GRAVITY PRESSURE OF LIQUIDS - - -=35. Pressure of Liquids against Surfaces.=--The sight of a great ship, -perhaps built of iron and floating on water, causes one to wonder at the -force that supports it. This same force is noticed when one pushes a -light body, as a cork, under water. It is quite evident in such a case -that a force exists sufficient to overcome the weight of the cork so -that it tends to rise to the surface. Even the weight of our bodies is -so far supported by water that many persons can float. - -[Illustration: FIG. 17.--Water forces the card against the chimney.] - -The following experiment provides a means of testing this force: - - If an empty can is pushed down into water, we feel at once the - force of the liquid acting against the object and tending to push - it upward. It may be noticed also that so long as the can is not - completely submerged the deeper the can is pushed into the water - the greater is the upward force exerted by the liquid. - - We may test this action in various ways: a simple way is to take a - cylindrical lamp chimney, press a card against its lower end and - place it in the water in a vertical position. The force of the - water will hold the card firmly against the end of the chimney. - (See Fig. 17.) The amount of force may be tested by dropping shot - into the tube until the card drops off. At greater depths more shot - will be required, showing that the force of the water increases - with the depth. Or one may pour water into the chimney. It will - then be found that the card does not drop until the level of the - water inside the chimney is the same as on the outside. That is, - before the card will fall off, the water must stand as high within - the chimney as without no matter to what depth the lower end of the - chimney is thrust below the surface of the water. - -=36. Law of Liquid Pressure.=--As there is twice as much water or shot -in the chimney when it is filled to a depth of 10 cm. as there is when -it is filled to a depth of 5 cm. the force of the water upward on the -bottom must be twice as great at a depth of 10 cm. as at a depth of 5 -cm. Since this reasoning will hold good for a comparison of forces at -any two depths, we have the law: "_The pressure exerted by a liquid is -directly proportional to the depth_." - -The amount of this force may be computed as follows: First, the card -stays on the end of the tube until the _weight_ of water from above -equals the force of the water from below, and second, the card remains -until the water is at the same _height_ inside the tube as it is -outside. Now if we find the weight of water at a given depth in the -tube, we can determine the force of the water from below. If for -instance the chimney has an area of cross-section of 12 sq. cm. and is -filled with water to a depth of 10 cm., the volume of the water -contained will be 120 ccm. This volume of water will weigh 120 g. This -represents then, not only the weight of the water in the tube, but also -the force of the water against the bottom. In a similar way one may -measure the force of water against any horizontal surface. - -=37. Force and Pressure.=--We should now distinguish between _force_ and -_pressure_. Pressure refers to the force acting against _unit area_, -while force refers to the action against the whole surface. Thus for -example, the atmospheric _pressure_ is often given as 15 pounds to the -square inch or as one kilogram to the square centimeter. On the other -hand, the air may exert a _force_ of more than 300 pounds upon each side -of the hand of a man; or a large ship may be supported by the _force_ of -thousands of tons exerted by water against the bottom of the ship. - -In the illustration, given in Art. 36, the upward _force_ of the water -against the end of the tube at a depth of 10 cm. is computed as 120 -grams. The _pressure_ at the _same_ depth will be 10 grams per sq. cm. -What will be the pressure at a depth of 20 cm.? at a depth of 50 cm.? of -100 cm.? Compare these answers with the law of liquid pressure in Art. -36. - -=38. Density.=--If other liquids, as alcohol, mercury, etc., were in the -jar, the chimney would need filling to the same level outside, with the -_same_ liquid, before the card would fall off. This brings in a factor -that was not considered before, _that of the mass[B] of a cubic -centimeter of the liquid_. This is called the _density_ of the liquid. -Alcohol has a density of 0.8 g. per cubic centimeter, mercury of 13.6 g. -per cubic centimeter, while water has a density of 1 g. per cubic -centimeter. - - [B] The _mass_ of a body is the _amount of matter in it_, the - _weight_ is the _pull of the earth upon it_. - -=39. Liquid Force against Any Surface.=--To find the force exerted by a -liquid against a surface we must take into consideration the area of the -surface, and the height and the =density= of the liquid above the -surface. The following law, and the formula representing it, which -concisely expresses the principle by which the force exerted by a liquid -against any surface may be computed, should be memorized: - - _The force which a liquid exerts against any surface, equals the - area of the surface, times its average depth below the surface of - the liquid, times the weight of unit volume of the liquid._ - -Or, expressed by a formula, _F = Ahd_. In this formula, "F" stands for -_the force which a liquid exerts against any surface_, "A" _the area -of the surface_, "h," for _the average depth (or height) of the liquid -pressing on the surface_, and "d", for _the weight of unit volume of the -liquid_. This is the first illustration in this text, of the use of a -formula to represent a law. Observe how accurately and concisely the law -is expressed by the formula. When the formula is employed, however, we -should keep in mind the law expressed by it. - -We must remember that a liquid presses not only downward and upward but -sideways as well, as we see when water spurts out of a hole in the side -of a vessel. Experiments have shown that at a point the pressure in a -fluid is the same in all directions, hence the rule given above may be -applied to the pressure of a liquid against the side of a tank, or boat, -or other object, provided we are accurate in determining the _average -depth of the liquid_; The following example illustrates the use of the -law. - - _For Example_: If the English system is used, the area of the - surface should be expressed in square feet, the depth in feet and - the weight of the liquid in pounds per cubic foot. One cubic foot - of water weighs 62.4 lbs. - - Suppose that a box 3 ft. square and 4 ft. deep is full of water. - What force will be exerted by the water against the bottom and a - side? - - From the law given above, the force of a liquid against a surface - equals the product of the _area_ of the surface, the _depth_ of the - liquid and its weight per unit volume, or using the formula, _F = - Ahd_. To compute the downward force against the bottom we have the - area, 9, depth, 4, and the weight 62.4 lbs. per cubic foot. 9 × 4 × - 62.4 lbs. = 2246.4 lbs. To compute the force against a side, the - area is 12, the average depth of water on the side is 2, the weight - 62.4, 12 × 2 × 62.4 lbs. = 1497.6 lbs. - - -Important Topics - -1. Liquids exert pressure; the greater the depth the greater the -pressure. - -2. Difference between force and pressure. - -3. Rules for finding upward and horizontal force exerted by a liquid. _F -= Ahd._ - -4. Weight, mass, density. - - -Exercises - -1. What is the density of water? - -2. What force is pressing upward against the bottom of a flat boat, if -it is 60 ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the -water? What is the weight of the boat? - -3. If a loaded ship sinks in the water to an average depth of 20 ft., -the area of the bottom being 6000 sq. ft., what is the upward force of -the water? What is the weight of the ship? - -4. If this ship sinks only 10 ft. when empty, what is the weight of the -ship alone? What was the weight of the cargo in Problem 3? - -5. What is the liquid force against one side of an aquarium 10 ft. long, -4 ft. deep and full of water? - -6. What is the liquid force on one side of a liter cube full of water? -Full of alcohol? Full of mercury? What force is pressing on the bottom -in each case? - -7. What depth of water will produce a pressure of 1 g. per square -centimeter? 10 g. per square centimeter? 1000 g. per square centimeter? - -8. What depth of water will produce a pressure of 1 lb. per square inch? -10 lbs. per square inch? 100 lbs. per square inch? - -9. What will be the force against a vertical dam-breast 30 meters long, -the depth of the water being 10 meters? - -10. A trap door with an area of 100 sq. dcm. is set in the bottom of a -tank containing water 5 meters deep. What force does the water exert -against the trap door? - -11. What is the force on the bottom of a conical tank, filled with -water, the bottom of which is 3 meters in diameter, the depth 1.5 -meters? - -12. If alcohol, density 0.8 were used in problem 11, what would be the -force? What would be the depth of alcohol to have the same force on the -bottom as in problem 11? - -13. What is the pressure in pounds per square inch at a depth of 1 mile -in sea water, density 1.026 grams per cc.? - -14. Find the force on the sides and bottom of a rectangular cistern -filled with water, 20 ft. long, 10 ft. wide, and 10 ft. deep? - -15. Find the force on the bottom of a water tank 14 ft. in diameter when -the water is 15 ft. deep, when full of water. - -16. Find the force on one side of a cistern 8 ft. deep and 10 ft. -square, when full of water. - -17. Find the force on a vertical dam 300 ft. long and 10 ft. high, when -full of water. - -18. Find the pressure at the bottom of the dam in question 17. - -19. Why are dams made thicker at the bottom than at the top? - -20. A ship draws 26 ft. of water, _i.e._, its keel is 26 ft. under -water. What is the liquid force against a square foot surface of the -keel? Find the pressure on the bottom. - - -(2) TRANSMISSION OF LIQUID PRESSURE - -=40. Pascal's Principle.=--Liquids exert pressure not only due to their -own weight, but when confined, may be made to transmit pressure to -considerable distances. This is a matter of common knowledge wherever a -system of waterworks with connections to houses is found, as in cities. -The transmission of liquid pressure has a number of important -applications. The principle underlying each of these was first -discovered by Pascal, a French scientist of the seventeenth century. -Pascal's Principle, as it is called, may be illustrated as follows: - - Suppose a vessel of the shape shown in Fig. 18, the upper part of - which we may assume has an area of 1 sq. cm., is filled with water - up to the level _AB_. A pressure will be exerted upon each square - centimeter of area depending upon the depth. Suppose that the - height of _AB_ above _CD_ is 10 cm., then the force upon 1 sq. cm. - of _CD_ is 10 g., or if the area of _CD_ is 16 sq. cm., it receives - a force of 160 g. - -[Illustration: FIG. 18.--The force increases with the depth.] - - If now a cubic centimeter of water be poured upon _AB_ it will - raise the level 1 cm., or the head of water exerting pressure upon - _CD_ becomes 11 cm., or the total force in _CD_ is 16×11 g., - _i.e._, each square centimeter of _CD_ receives an additional force - of 1 g. _Hence the force exerted on a unit area at_ _AB_ _is - transmitted to every unit area within the vessel._ - -The usual form in which this law is expressed is as follows: _Pressure -applied to any part of a confined liquid is transmitted unchanged, in -all directions, and adds the same force to all equal surfaces in contact -with the liquid_. - -[Illustration: FIG. 19.--The force is proportional to the area.] - -The importance of this principle, as Pascal himself pointed out, lies in -the fact that by its aid we are able to exert a great force upon a large -area by applying a small force upon a small area of a confined liquid, -both areas being in contact with the same liquid. Thus in Fig. 19 if the -area of the surface _CD_ is 2000 times the area of the surface _AB_, -then 1 lb. applied to the liquid on _AB_ will exert or sustain a force -of 2000 lbs. on _CD_. - -=41. Hydraulic Press.=--An important application of Pascal's principle -is the _hydraulic press_. See Fig. 20. It is used for many purposes -where great force is required, as in pressing paper or cloth, extracting -oil from seeds, lifting heavy objects, etc. Many high school pupils have -been seated in a _hydraulic chair_ used by a dentist or barber. This -chair is a modified hydraulic press. - -[Illustration: FIG. 20.--Cross-section of a hydraulic press.] - -The hydraulic press contains two movable pistons, _P_ and _p_ (see Fig. -20). The larger of these, _P_, has a cross-sectional area that may be -100 or 1000 times that of the smaller. The smaller one is moved up and -down by a lever; on each upstroke, liquid is drawn in from a reservoir, -while each down-stroke forces some of the liquid into the space about -the large piston. Valves at _V_ and _V´_ prevent the return of the -liquid. If the area of _P_ is 1,000 times that of _p_, then the force -exerted by _P_ is 1000 times the force employed in moving _p_. On the -other hand, since the liquid moved by the small piston is distributed -over the area of the large one, the latter will move only 1/1000 as far -as does the small piston. The relation between the motions of the two -pistons and the forces exerted by them may be stated concisely as -follows: The _motions_ of the two _pistons_ of the hydraulic press are -inversely proportional to the forces exerted by them. The -_cross-sectional areas_ of the two pistons are, on the other hand, -directly proportional to the forces exerted by them. - -An application of Pascal's principle often employed in cities is the -hydraulic elevator. In this device a long plunger or piston extends -downward from the elevator car into a cylinder sunk into the earth, -sometimes to a depth of 300 ft. Water forced into this cylinder pushes -the piston upward and when the water is released from the cylinder the -piston descends. - - Fig. 21 represents another form of hydraulic elevator, where the - cylinder and piston are at one side of the elevator shaft. In this - type, to raise the elevator, water is admitted to the cylinder - pushing the piston downward. - -=42. Artesian Wells.=--Sometimes a porous stratum containing water in -the earth's crust is inclined. Then if there are impervious strata (see -Fig. 22), both above and below the water-bearing one, and the latter -comes to the surface so that rain may fill it, a well sunk to the -water-bearing stratum at a point where it is below the surface will -usually give an artesian well, that is, one in which the water rises to -or above the surface. Many are found in the United States. - -[Illustration: FIG. 21.--A hydraulic freight elevator.] - -[Illustration: FIG. 22.--Conditions producing an artesian well.] - -[Illustration: FIG. 23.--A standpipe.] - -=43. Standpipes and Air Cushions.=--Many who have lived in cities where -water is pumped into houses under pressure know that the water pressure -is changed when several faucets are opened at the same time. Again, if -several persons are using a hose for sprinkling, the pressure may be -lessened so as to be insufficient to force the water above the first -floor. In order to allow for these changes some flexibility or spring -must be introduced somewhere into the water-pipe system. Water is -nearly incompressible and if no means were employed to take care of the -pressure changes, the sudden stopping and starting of the flow would -cause serious jars and start leaks in the pipes. Two common devices for -controlling sudden changes in the water pressure are the _standpipe_ and -the _air cushion_. - - The _standpipe_ is simply a large vertical tube connected to the - water mains from which and into which water readily flows. When - many faucets are opened the water lowers; when most faucets are - closed the water rises, giving a simple automatic control of the - surplus water and a supply of water for a short time during a - shut-down of the pumps. Standpipes are often used in towns and - small cities. Fig. 23 represents the standpipe at Jerome, Idaho. - - The _air cushion_ (Fig. 24) is a metal pipe or dome filled with air - attached to a water pipe where sudden changes in pressure are to be - controlled. At many faucets in a city water system such an air - cushion is employed. It contains air; this, unlike water, is easily - compressible and the confined air when the tap is suddenly closed - receives and checks gradually the rush of water in the pipe. Even - with an air cushion, the "pound" of the water in the pipe when a - tap is suddenly closed is often heard. If air cushions were not - provided, the "water hammer" would frequently crack or break the - pipes. - -[Illustration: FIG. 24.--The short pipe above the faucet contains air -forming an air cushion.] - - -Important Topics - -1. Pascal's law. - -2. Hydraulic press. - -3. Artesian wells. - -4. Standpipes and air cushions. - - -Exercises - -1. Where have you _seen_ an air cushion? Describe it and its use. - -2. Where have you _seen_ an hydraulic press? Why and how used? - -3. Where have you _seen_ hydraulic elevators? What moves them? - -4. Where do you know of liquids under pressure? Three examples. - -5. What is the pressure in water at a depth of 1500 cm. Express in grams -per square centimeter and in kilograms per square centimeter. - -6. What head[C] of water is required to give a pressure of 200 g. per -square centimeter? 2 kg. per square centimeter? - - [C] "Head" is a term used to express the vertical height of water - in pipes. - -7. What _pressure_ will be produced by a "head" of water of 20 meters? - -8. If 1728 cu. in. of water are placed in a vertical tube 1 sq. in. in -cross section to what height would the water rise? It would give how -many feet of _head_? - -9. What would the water in problem 8 weigh? What pressure would it -produce at the bottom, in pounds per square inch? From this, compute how -many feet of "head" of water will produce a pressure of 1 lb. per square -inch. - -10. Using the result in problem 9, what "head" of water will produce a -pressure of 10 lbs. per square inch? 100 lbs. per square inch? - -11. From the result in 9, 100 ft. of "head" of water will produce what -pressure? 1000 ft. of "head?" - -12. If the diameter of the pump piston in a hydraulic press is 2 cm. and -that of the press piston 50 cm. what will be the force against the -latter if the former is pushed down with a force of 40 kg.? - - -(3) ARCHIMEDES' PRINCIPLE - -=44. A Body Supported by a Liquid.=--Among the applications of the force -exerted by a liquid upon a surface, Archimedes' Principle is one of the -most important. - -Most persons have noted that a body placed in water is partly or wholly -supported by the force of the water upon it. A stone held by a cord and -lowered into water is felt to have a part of its weight supported, -while a piece of cork or wood is wholly supported and floats. - -The human body is almost entirely supported in water, in fact, many -people can easily float in water. It was the consideration of this fact -that led the Greek philosopher Archimedes to discover and state the -principle that describes the supporting of a body in a liquid. - -[Illustration: FIG. 25.--Theoretical proof of Archimedes' principle.] - -=45. Archimedes' Principle.=--"_A body immersed in a liquid is pushed up -by a force equal to the weight of the liquid that it displaces._" The -proof for this law is simply demonstrated. Suppose a cube, _abcd_, is -immersed in water (Fig. 25). The upward force on _cd_ is equal to the -weight of a column of water equal to _cdef_. (See Art. 39.) The downward -force upon the top of the cube is equal to the weight of the column of -water _abef_. Then the net upward force upon the cube, that is, the -upward force upon the bottom less the downward force upon the top, or -the buoyant force exerted by the liquid is exactly equal to the weight -of the displaced water _abcd_. - -=46. Law of Floating Bodies.=--This same reasoning may be applied to any -liquid and to any body immersed to any depth below the surface of the -liquid. If the body weighs more than the displaced liquid it will sink. -If it weighs less than the displaced liquid it will float or rise in the -water. A block of wood rises out of the water in which it floats until -its own weight just equals the weight of the water it displaces. From -this we have the law of floating bodies. - -_A floating body displaces its own weight of the liquid in which it -floats._ - -[Illustration: FIG. 26.--A floating body displaces its own weight of -water.] - -To test the law of floating bodies, take a rod of light wood 1 cm. -square and 30 cm. long (Fig. 26). Bore out one end and fill the opening -with lead and seal with paraffin so that the rod will float vertically -when placed in water. Mark upon one side of the rod a centimeter scale, -and dip the rod in hot paraffin to make it waterproof. Now find the -weight of the stick in grams and note the depth to which it sinks in -water in centimeters. Compute the weight of the displaced water. It will -equal the weight of the rod. - -=47. Applications of Archimedes' Principle.= There are numerous -applications of Archimedes' Principle and the law of floating bodies. - - =(a) To Find the Weight of a Floating Body: Problem.=--A boat 20 - ft. long and with an average width of 6 ft. sinks to an average - depth of 3 ft. in the water. Find the weight of the boat. What - weight of cargo will sink it to an average depth of 5 ft.? - - =Solution.=--The volume of the water displaced is 20 × 6 × 3 cu. - ft. = 360 cu. ft. Since 1 cu. ft. of water weighs 62.4 lbs., 360 × - 62.4 lbs. = 22,464 lbs., the weight of water displaced. By the law - of floating bodies this is equal to the weight of the boat. When - loaded the volume of water displaced is 20 ft. × 6 × 5 ft. which - equal 600 cu. ft. 600 × 62.4 lbs. = 37,440 lbs. This is the weight - of the water displaced when loaded. 37,440 lbs. - 22,464 lbs. = - 14,976 lbs., the weight of the cargo. - - =(b) To Find the Volume of an Immersed Solid: Problem.=--A stone - weighs 187.2 lbs. in air and appears to weigh 124.8 lbs. in water. - What is its volume? - - =Solution.=--187.2 lbs. - 124.8 lbs. = 62.4 lbs., the buoyant force - of the water. By Archimedes' Principle, this equals the weight of - the displaced water which has a volume of 1 cu. ft. which is - therefore the volume of the stone. - - =(c) To Find the Density of a Body:= The density of a body is - defined as the mass of unit volume. - - We can easily find the mass of a body by weighing it, but the - volume is often impossible to obtain by measurements, especially of - irregular solids. - -Archimedes' Principle, however, provides a method of finding the volume -of a body accurately by weighing it first in air and then in water (Fig. -27), the apparent loss in weight being equal to the weight of the -displaced water. One needs only to find the volume of water having the -same weight as the loss of weight to find the volume of the body. - -If the metric system is used, 1 ccm. of water weighs 1 g., and the -volume is numerically the same as the loss of weight. - -[Illustration: FIG. 27.--A method of weighing a body under water.] - - -Important Topics - -1. Archimedes' Principle. - -2. Law of floating bodies. - -3. The applications of Archimedes' Principle are to determine (a) the -weight of a floating body; (b) the volume of an immersed solid, and (c) -the density of a body. - - -Exercises - -1. Look up the story of Archimedes and the crown. Write a brief account -of it. - -2. Why is it easier for a fat man to float in water than for a lean -one? - -3. A fish weighing 1 lb. is placed in a pail full of water. Will the -pail and contents weigh more than before adding the fish? Why? - -4. Why can a large stone be lifted more easily while under water than -when on the land? - -5. Why does the air bubble in a spirit level move as one end of the -instrument is raised or lowered? - -6. Why does a dead fish always float? - -7. A ship is built for use in fresh water. What will be the effect on -its water line when passing into the ocean? - -8. Why can small bugs walk on water while large animals cannot? - -9. If an object weighing 62.4 lbs. just floats in water, what weight of -water does it displace? What volume of water is displaced? What is the -volume of the body? - -10. What is the volume of a man who just floats in water if he weighs -124.8 lbs.? If he weighs 187.2 lbs.? - -11. An object weighing 500 g. just floats in water. What is its volume? -How much water does a floating block of wood displace if it weighs 125 -lbs.? 125 g.? 2 kg.? 2000 kg.? - -12. A flat boat 10 × 40 ft. in size will sink how much in the water when -10 horses each weighing 1250 lbs. are placed on board? - -13. A ship 900 ft. long and 80 ft. average width sinks to an average -depth of 25 ft. when empty and 40 ft. when loaded. What is the weight of -the ship and of its load? - -14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? If -it weighs 1200 g.? Explain. - -15. If a 1000 cc. block of metal weighing 1200 g. is placed in the water -in mid ocean what will become of it? - -16. Prove Archimedes' Principle by use of the principles of liquid -pressure. - -17. An irregular stone, density 2.5 g. per ccm. displaces 2 cu. ft. of -water. What is its weight? Its apparent weight in water? - -18. Will the depth to which a vessel sinks in water change as she sails -from Lake Ontario into the Atlantic Ocean? Why? - -19. If the density of sea water is 1.0269 g. per cubic centimeter and -that of ice 0.918 g. per ccm., what portion of an iceberg is above -water? - -20. In drawing water from a well by means of a bucket, why is less force -used when it is under water than when entirely above? - -21. A stone which weighs 300 lbs. can be lifted under water with a force -of 150 lbs. What is the volume of the stone? - -22. The average density of the human body is 1.07 grams per c.c. How -much water will a man who weighs 150 lbs. displace when diving? How much -when floating? - - -(4) DENSITY AND SPECIFIC GRAVITY - -=48. Density.=--The density of a substance is often used as a test of -its purity. Archimedes in testing King Hiero's crown to find out if it -were made of pure gold determined first its density. It is by such tests -that the purity of milk, of alcohol, of gold, and a great variety of -substances is often determined. - -Knowledge of methods of finding density is of value to everyone and -should be included in the education of every student. _The density of a -substance is the mass of unit volume of the substance._ In the metric -system, for example, the density of a substance is the mass in grams per -1 ccm. Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1 -g. to the cubic centimeter. A cubic centimeter of aluminium weighs 2.7 -g. Its density therefore is 2.7 g. per ccm. - -=49. Specific Gravity.=--_Specific gravity is the ratio of the weight of -any volume of a substance to the weight of an equal volume of water._ -Its meaning is not quite the same as that of density, since specific -gravity is always a _ratio_, _i.e._, an _abstract_ number, as 2.7. -Density of a substance is a _concrete_ number, as 2.7 grams per ccm. In -the metric system the density of water is one gram per cubic centimeter, -therefore we have: - -Density (g. per ccm.) = (numerically) specific gravity. - -In the English system, the density of water is 62.4 pounds per cubic -foot, therefore in this system we have: - -Density (lbs. per cu. ft.) = (numerically) 62.4 × sp. gr. - -=50. Methods for Finding Density and Specific Gravity= - -=(a) Regular Solids.=--Solids of regular shapes such as cubes, spheres, -etc., whose volumes may be readily found by measurement, may be weighed. -The mass divided by the volume gives the density, or _D = M{~GREEK SMALL LETTER MU~}/v_. - -=(b) Irregular Solids.=--with these the volume cannot be found by -measurement but may be obtained by Archimedes' Principle. Weigh the -solid first in the air and then in water. The apparent loss of weight -equals the weight of the equal volume of water displaced. From this the -volume may be found. And then the - -density equals mass/volume; the specific gravity = - -wt. in air / wt. of equal volume of water = wt. in air / ((wt. in air) - -(wt. in water)) - - mass - density equals ------; the specific gravity = - volume - - wt. in air wt. in air - ---------------------------- = ----------------------------- - wt. of equal volume of water ((wt. in air) - (wt. in water)) - -=(c) Solids Lighter than Water.=--This will require a sinker to hold the -body under water. Weigh the solid in air (_w_). Weigh the sinker in -water (_s_). Attach the sinker to the solid and weigh both in water -(w´). The specific gravity equals - - (wt. of solid in air)/(loss in wt. of solid in water) or _w/((w + - s) - w´)_ - - wt. of solid in air _w_ - --------------------------- or ------------ - loss of wt. of solid in water (_w + s_) - _w´_ - -The apparent loss of weight of the solid is equal to the sum of its -weight in air plus the weight of the sinker in water, less the combined -weight of both in water. - -=(d) The Density of a Liquid by a Hydrometer.=--One may also easily find -the density of any liquid by Archimedes' Principle. If one takes the rod -described in Art. 46, and places it in water, the number of cubic -centimeters of water it displaces indicates its weight in grams. On -placing the rod in another liquid in which it floats, it will of course -displace its own weight and the height to which the liquid rises on the -scale gives the volume. By dividing the _weight_ of the rod as shown by -its position in _water_ by the _volume_ of the _liquid_ displaced we -obtain the density of the liquid. Commercial hydrometers for testing the -density of milk, alcohol and other liquids are made of glass of the form -shown in Fig. 28. The long narrow stem permits small differences in -volume to be noticed, hence they are more accurate than the rod -described in the preceding paragraph. For convenience this rod contains -a paper scale, so that when the height of the liquid on the stem is -noted, the density is read at once. - -[Illustration: FIG. 28.--A hydrometer used to find the density of a -liquid.] - -=Density of Liquids by Loss of Weight.= Weigh a piece of glass in air -(_W_{a}_), in water (_W_{w}_), and in the liquid to be tested (_W_{l}_). - -Then (_W_{a}_ - _W_{w}_)gives the weight of the water displaced. - -And (_W_{a}_ - _W_{l}_) gives the weight of the liquid displaced. - -Hence, (_W_{a}_ - _W_{l}_)/(_W_{a}_ - _W_{w}_) equals the specific -gravity of the liquid. - - -Important Topics - -1. Definitions of density and specific gravity. - -2. Methods of finding density: (a) regular solids; (b) irregular solids; -(c) solids lighter than water; (d) liquids by hydrometer; (e) liquids by -loss of weight. - - -Exercises - -_Note._--Consider that 1 cu. ft. of water weighs 62.4 lbs. Consider that -1 ccm. of water weighs 1 g. - -1. What is meant by the statement that a block of wood has a specific -gravity of 0.6? - -2. Considering that the density of the human body is the same as that of -water, what is the volume of a 125-lb. boy? Of a 250-lb. man? Of a -62.4-lb. boy? What is the volume of your body? - -3. How is the weight of large ships found? Give an example. - -4. Mention three cases where determinations of density are important. - -5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find (a) -the density of the body; (b) its volume; (c) density of the acid. - -6. If the specific gravity of a horse is 1, what is the volume of a -horse weighing 500 kg.? Of one weighing 1248 lbs.? - -7. A weighted wooden box sinks to a depth of 20 cm. in water and 24 cm. -in alcohol, and to a depth of 18 cm. in brine. What is the density of -the alcohol and of the brine? - -8. A glass stopper weighs in the air 25 g., in water 15 g., in oil 18 g. -Find the density and volume of the stopper. Find the density of the oil. - -9. What would a cubic foot of wood weigh if the specific gravity were -0.5.? - -10. The specific gravity of aluminum is 2.7. Find the weight of a cubic -foot of it. - -11. A block of wood weighs 40 g. A piece of lead appears to weigh 70 g. -in water. Both together appear to weigh 60 g. in water. Find the density -of the wood. - -12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt -water. Find the density of the salt water. - -13. Will iron sink in mercury? Why? - -14. A submarine boat weighing 200 tons must have what volume in order to -float? - -15. Find the weight of 2 cu. ft. of copper from its density. - -16. What is the weight in water of a mass whose specific gravity is 3.3 -and whose weight is 50 kg.? - -17. A block of granite weighs 1656 lbs.; its volume is 10 cu. ft., what -is its density? - -18. If the specific gravity of hard coal is 1.75 how would you determine -how many tons of coal a bin would hold? - -19. A hollow copper ball weighs 2 kg. What must be its volume to enable -it to just float in water? - -20. A mass having a volume of 100 ccm. and a specific gravity of 2.67 is -fastened to 200 ccm. of wood, specific gravity 0.55. What will the -combination weigh in water? - -21. A block weighing 4 oz. in air is tied to a sinker which appears to -weigh 14 oz. in water. Both together appear to weigh 6 oz. in water. -What is the specific gravity of the block? - - - - -CHAPTER IV - -MECHANICS OF GASES - - -(1) WEIGHT AND PRESSURE OF THE AIR - - -=51. Weight of Air.=--It is said that savages are unaware of the -presence of _air_. They feel the _wind_ and hear and see it moving the -leaves and branches of the trees, but of air itself they have little -conception. - -To ordinary observers, it seems to have no weight, and to offer little -resistance to bodies passing through it. That it has weight may be -readily shown as follows: (See Fig. 29.) If a hollow metal sphere, or a -glass flask, provided with tube and stopcock, be weighed when the -stopcock is open, and then after the air has been exhausted from it by -an air pump, a definite loss of weight is noticeable. - -[Illustration: FIG. 29.--Proof that air has weight.] - -If the volume of the sphere is known and it is well exhausted of air, a -fair approximation of the weight of air may be obtained. Under -"_standard conditions_," which means _at the freezing temperature_ and a -barometric pressure of 76 cm., a liter of air weighs 1.293 g. while 12 -cu. ft. of air weigh approximately 1 lb. - -=52. Pressure of Air.=--Since air has weight it may be supposed to exert -pressure like a liquid. That it does so may be shown in a variety of -ways. - -If a plunger fitting tightly in a glass cylinder be drawn upward, while -the lower end of the tube is under water, the water will rise in the -tube (Fig. 30). The common explanation of this is that the water rises -because of "suction." The philosophers of the ancient Greeks explained -it by saying that "nature abhors a vacuum," and therefore the water -rises. Neither explanation is correct. It was found in 1640 that water -would not rise in a pump more than 32 ft. despite the fact that a vacuum -was maintained above the water. Galileo was applied to for an -explanation. He said, "evidently nature's horror of a vacuum does not -extend above 32 ft." Galileo began tests upon "the power of a vacuum" -but dying left his pupil Torricelli to continue the experiment. -Torricelli reasoned that if water would rise 32 ft., then mercury, which -is 13.6 times as dense as water, would rise about 1/13 as much. To test -this, he performed the following famous experiment. - -[Illustration: FIG. 30.--Air pressure forces the liquid up the tube.] - -=53. Torricelli's Experiment (1643).=--Take a glass tube about 3 ft. -long, sealed at one end, and fill it with mercury. Close the end with -the finger and invert, placing the end closed by the finger under -mercury in a dish (Fig. 31). Remove the finger and the mercury sinks -until the top of the mercury is about 30 in. above the level of the -mercury in the dish. Torricelli concluded that the rise of liquids in -exhausted tubes is due to the pressure of the atmosphere acting on the -surface of the mercury in the dish. - -To test this, place the tube with its mercury upon the plate of an air -pump and place a tubulated bell jar over the apparatus so that the tube -projects through a tightly fitting stopper. (See Fig. 32.) If the air -pressure is the cause of the rise of mercury in the tube, on removing -the air from the bell jar the mercury should fall in the tube. This is -seen to happen as soon as the pump is started. It is difficult to remove -all the air from the receiver so the mercury rarely falls to the same -level in the tube as in the dish. A small tube containing mercury is -often attached to air pumps to indicate the degree of exhaustion. Such -tubes are called _manometers_. - -[Illustration: FIG. 31.--Torricelli's experiment.] - -[Illustration: FIG. 32.--The mercury drops as the air is removed.] - -=54. The Amount of Atmospheric Pressure.=--Torricelli's experiment -enables us to compute readily the pressure of the atmosphere, since it -is the atmospheric pressure that balances the column of mercury in the -tube. By Pascal's Law, the pressure of the atmosphere on the surface of -the mercury in the dish is transmitted as an exactly equal pressure on -the mercury column in the tube at the same level as the mercury -outside. - -This pressure, due to the air, must balance the weight of the column of -mercury in the tube. It therefore equals the weight of the column of -mercury of unit cross-section. The average height of the column of -mercury at sea-level is 76 cm. Since the weight of 1 cc. of mercury is -13.6 grams, the pressure inside the tube at the level of the surface of -the mercury in the dish is equal to 1 × 76 × 13.6 or 1033.6 g. per -square centimeter. Therefore the _atmospheric pressure_ on the surface -of the mercury in the dish is 1033.6 g. per square centimeter, -approximately _1 kg. per square centimeter or 15 lbs. per square inch_. - -=55. Pascal's Experiment.=--Pascal tested in another way the action of -atmospheric pressure upon the column of mercury by requesting his -brother-in-law, Perrier, who lived near a mountain, to try the -experiment on its top. Perrier found that on ascending 1000 meters the -mercury fell 8 cm. in the tube. Travelers, surveyors, and aviators -frequently determine the altitude above sea-level by reading the -barometer, an ascent of 11 meters giving a fall of about 1 mm. in the -mercury column, or 0.1 in. for every 90 ft. of ascent. - -[Illustration: FIG. 33.--A standard barometer.] - -_56. The Barometer._--The modern barometer (Fig. 33), consists of a -Torricellian tube properly mounted. Reading a barometer consists in -accurately reading the height of the mercury column. This height varies -from 75 to 76.5 cm. or 29 to 30 in. in localities not far from the -sea-level. The atmospheric pressure varies because of disturbances in -the atmosphere. It is found that these disturbances of the atmosphere -pass across the country from west to east in a somewhat regular manner, -hence a series of readings of the barometer may give reliable -information of the movement of these disturbances and so assist in -forecasting the weather. The weather Bureau has observations taken at -the same moment at various stations over the country. These observations -form the basis for the daily forecast of the weather. - -[Illustration: FIG. 34.--An aneroid barometer] - - Another form of barometer in common use is the _Aneroid Barometer_ - (Fig. 34). Its essential parts are a cylindrical air-tight box with - an elastic corrugated cover. Inside the box is a partial vacuum. - This makes the cover very sensitive to slight changes of pressure. - The motion of the top of the box is conveyed by a series of levers - to an indicating hand which moves over a dial. This barometer can - be made so sensitive as to indicate the change of air pressure from - a table top to the floor. It is much used by travelers, explorers, - surveying parties and aviators, since the mercurial barometer is - inconvenient to carry. - - -Important Topics - -1. _Weight_ and _Pressure_ of air in English and metric units. How -shown. Evidences. - -2. Work of Galileo, Torricelli, and Perrier. - -3. Barometer: construction, action, mercurial, aneroid. - -[Illustration: FIG. 35.--Air pressure keeps the water In the tumbler.] - -[Illustration: FIG. 36.--Cross-section of a modern drinking fountain.] - - -Exercises - -1. Do you think Archimedes' Principle applies to the air? Does Pascal's -Law? Why? - -2. Find the downward pressure of the mercury in a barometer tube if the -cross-section is 1 sq. cm. and the height 75 cm. at the level of the -mercury surface in contact with the air. (The density of mercury is 13.6 -grams per cc.) - -3. What is the weight of the air in a room if it is 10 × 8 × 4 meters? - -4. What weight of air is in a room 10 × 15 × 10 ft.? - -5. When smoke rises in a straight line from chimneys, is it an -indication of a high or low barometric pressure? Why? - -6. Why does a tumbler filled with water and inverted in a dish with its -rim under water remain full? - -7. If the barometer tube is inclined the mercury remains at the same -horizontal level. How can this be explained? - -8. When the mercurial barometer stands at 76 cm., how high would a water -barometer stand? Explain. - -9. Explain why it is possible for one to suck soda water through a tube? - -10. Fill a tumbler with water. Place a sheet of paper over the top and -invert. The paper clings to the tumbler and prevents the water from -escaping. Explain. (See Fig. 35.) - -11. Why must a kerosene oil can have two openings in order to allow the -oil to flow freely? - -12. Explain the action of the modern drinking fountain (Fig. 36). - - -(2) COMPRESSIBILITY AND EXPANSIBILITY OF THE AIR - -=57. Effect of Pressure on Liquids and Gases.=--Both classes of fluids, -liquids and gases, have many characteristics in common. Both are -composed of molecules that move freely; hence both _flow_. At any point -within a fluid the _pressure is the same in all directions_. Archimedes' -Principle applies, therefore, to both liquids and gases. - -We now come to an important _difference_ between liquids and gases. -_Liquids_ are _practically incompressible_. "So much so, that if water -is subjected to a pressure of 3000 kg. per sq. cm., its volume is -reduced only about one-tenth." Gases show a very different behavior from -liquids on being subjected to pressure. They may readily be compressed -to a small fraction of their volume as is noticed on inflating a -pneumatic tire. A gas has also the _ability to spring back_ to a larger -volume as soon as the pressure is released, as when a cork is driven -from a pop gun. Not only is compressed air able to expand, but air -under ordinary conditions will expand if it is released in a space where -the pressure is less. - -Hollow bodies, animals and plants, are not crushed by atmospheric -pressure, because the air and gases contained within exert as much force -outward as the air exerts inward. - -=58. Boyle's Law.=--The relation between the volume and pressure of a -gas was first investigated by Robert Boyle in the seventeenth century. -The experiment by which he first discovered the law or the relation -between the volume and the pressure of a gas is briefly described as -follows: - -[Illustration: FIG. 37 _a_. - -FIG. 37 _b_. - -FIGS. 37 _a_ AND 37 _b_.--Boyle's law apparatus.] - - A glass tube is bent in the form of the capital letter J, the short - arm being closed. A little mercury is poured in to cover the bend. - (See Fig. 37 _a_.) Since the mercury is at the _same level in both - arms_, the pressure in (_A_) is the same as in (_B_). Mercury is - now poured into (_A_) until it stands in the long tube at a height - above that in (B) which is equal to the height of the mercury - column of the barometer. (See Fig. 37 _b_.) The air in (_BC_) is - now under a pressure of two atmospheres (one atmosphere is due to - the mercury column). On measurement the air in (_BC_) will be found - to have just one-half of its original volume. - -Thus doubling the pressure to which a gas is subjected reduces its -volume to one-half. Tripling the pressure, reduces the volume to -one-third and so on. - -Careful experiments reveal the following law: _The volume of a given -mass of gas at constant temperature is inversely proportional to the -pressure to which it is subjected_. - -This law is often expressed mathematically. _P/P´ = V´/V_, or _PV = -P´V´_. Since doubling the pressure reduces the volume one-half, it -doubles the density. Tripling the pressure triples the density. We -therefore have _P/P´ = D/D´_ or the density of a gas directly -proportional to its pressure. - -[Illustration: FIG. 38.--Height and density of the air.] - -=59. Height of the Atmosphere.=--From its properties of _compression_ -and _expansion_, the air varies in density and pressure as one ascends -in it. At a height of 3 miles the pressure is reduced to about one-half. -This is an indication that one-half of the air is below this level. -Balloonists have gone to a height of 7 miles, Glaser and Coxwell in -England in 1862 and Berson in France in 1901. The atmosphere has been -explored to a height of 30,500 meters (18.95 miles) by sending up -self-registering barometers in small balloons which burst at great -altitudes. A parachute protects the instruments from breakage from too -rapid fall. This height of 30,500 meters was reached by a balloon sent -up by William R. Blair, at Huron, South Dakota, September 1, 1910. - -At a height of 35 miles, the density is estimated at 1/30,000 of its -value at sea-level. (See Fig. 38.) It is believed that some rarefied air -exists for a considerable distance above this point, some estimates -placing the extent at 100 miles, and others from 200 to 500 miles. -Evidences of some air at such heights are shown by: (a) the height at -which meteors first appear, (b) the height of the Aurora Borealis, and -(c), the distance that the sun is below the horizon when the last traces -of color disappear from the sky in the evening. - -Although the exact limits of the atmosphere are unknown, the weight of a -column of air 1 sq. cm. in cross-section, and extending _upward as high -as the atmosphere_, may be accurately computed. For this column of air -exactly balances the column of mercury in the tube of the barometer. - -Below sea-level, the air increases rapidly in density and it is -estimated that at a depth of 35 miles, the density of the air would be a -thousand times that at the earth's surface, or more than that of water. - - -Important Topics - -1. Evidence of compressibility of gases and incompressibility of -liquids. - -2. Boyle's Law. Proof, applications. - -3. Extent of the atmosphere--three evidences. - - -Exercises - -1. Mention three illustrations of the compressibility and expansibility -of air that you know from your own experience. - -2. Increasing the pressure increases the amount of a gas that will be -absorbed by a liquid? Explain this. Have you ever observed this fact? -Where? - -3. If a toy balloon containing 2000 ccm. of gas at the earth's surface -where the barometer reading is 76 cm., rises to an elevation where the -barometer reads 54 cm., the balloon will tend to expand to what volume? -Explain. Will it attain this volume? - -4. If a gas is compressed, it changes in temperature. How do you explain -this? - -5. What change in temperature will occur when compressed air is allowed -to expand? Explain. - -6. Air blowing up a mountain side has its pressure lessened as it -approaches the top. How will this affect the temperature? Why? What may -result from this change in temperature? Explain. - -7. To what pressure must 500 ccm. of air be subjected to compress it to -300 ccm. the barometer reading at first being 75 cm. Explain. - -[Illustration: FIG. 39.--The air pump.] - - -(3) PNEUMATIC APPLIANCES - -=60. The Air Pump.=--The air pump is used to remove air or other gases -from a closed vessel. It was invented about 1650 by Otto Von Guericke, -burgomaster of Magdeburg, Germany. One form of air pump is shown in -Fig. 39. _C_ is a cylinder within which slides a tightly fitting piston. -_R_ is the vessel from which the air is to be exhausted. _r_ and _u_ are -valves opening upward. The action of the pump is as follows: - -On pushing the piston down, the air in _C_ is compressed. This opens -valve _r_ allowing the confined air to escape above the piston. The -piston is then raised making the space in _C_ a partial vacuum. The -pressure in _R_ now being greater than in _C_, _u_ is pushed up and the -air from _R_ rushes into _C_, until the pressure is equalized. On -pushing down the piston again, valve _u_ closes and the process is -repeated until the pressure in _R_ is no longer able to raise the valve -_u_. Some air pumps are so constructed that the valves are opened and -closed automatically by the movement of the piston. With these pumps a -higher degree of rarefaction can be obtained. - -Air is often partially exhausted from receivers or vessels by the use of -a filter pump or _aspirator_. A stream of water flowing through a -constriction causes a reduced pressure, draws in air and carries it -away, and thus produces a partial vacuum. See Fig. 40 for a section of -the device. - -[Illustration: FIG. 40.--An aspirator.] - -=61. The Condensing Pump.=--This is like the exhaust pump except that -its valves are reversed. It is used in compressing illuminating gases -into cylinders for use in lighting vehicles, stereopticons, Pintsch -lights, gas light buoys, etc., and also for compressing air to operate -air brakes, pneumatic hammers and drills, and for other uses. - -The common condensing pump is the kind used for inflating tires. (See -Fig. 41.) In this, a loosely fitting metal piston is attached to a disc -of leather somewhat larger than the cylinder. This device is called a -_cup valve_. On raising the piston, air rushes in from the top past the -valve, but on pushing the piston down, the valve is pressed tightly -against the sides of the cylinder and prevents the escape of any air. -The compressed air pushes open a valve on the tire and enters it. This -valve closes as soon as the pressure is lessened from outside. It is -well to notice in all of these pumps that _two_ valves are used. One -holds the air already secured while the other opens for a new supply. -Both valves are never open at the same time. - -[Illustration: FIG. 41.--Condensing pump used in inflating tires.] - -=62. Water Pumps.--The Common Lift Pump.= This, the simplest pump for -raising water, consists of a cylinder _C_ (Fig. 42) connected by a pipe -_R_ to a supply of water as a cistern or well. A valve opening upward is -placed at the bottom of the cylinder over the entrance to the pipe. In -the cylinder is a tightly fitting piston connected by a rod to a lever -for ease in action. The piston contains a valve opening upward. In -operating this pump water is usually first poured into the cylinder to -"prime" it. This helps to close the valves and prevents air leaking past -them. When the piston is lowered the lower valve closes, the air in the -cylinder being compressed pushes the upper valve open and passes above -the piston. On raising the piston the upper valve closes. This forms a -partial vacuum in the cylinder. - -The air pressing on the surface of the water below forces the water and -air that may be in the tube upward through the lower valve to fill this -partial vacuum. - -When the cylinder becomes filled with water, this is lifted out on the -up-stroke, whence its name, "lift pump." Since the atmospheric pressure -at sea-level can only support a column of water about 34 ft. high, the -lower valve must be within this distance of the water surface. In actual -practice the limit is about 27 ft. In deeper wells, the cylinder and -valves are placed so that they are within 25 or 27 ft. of the surface of -the water in the well, a long piston rod reaching above the surface of -the ground and connected to a pump handle operates the piston. A -discharge pipe extends from the cylinder to the surface of the ground -above. - -[Illustration: FIG. 42.--The common lift pump.] - -[Illustration: FIG. 43.--A force pump with an air chamber (_A_).] - -=63. The Force Pump.=--The force pump is used to deliver water under -pressure either for spraying or to an elevated reservoir. The piston is -solid, the second valve being placed at the entrance of the discharge -pipe. (See Fig. 43.) The action is the same as that of the lift pump, -with this exception; the piston in its down stroke forces the water out -through the discharge pipe, the velocity depending upon the pressure -exerted. - -A force pump is usually provided with an air chamber which is connected -with the discharge pipe. On the down stroke of the piston, water is -forced into the air chamber. This compresses the air it contains. The -compressed air reacts and exerts pressure on the water forcing it out in -a steady stream. - -Force pumps are used in deep wells, being placed at the bottom. - -The pumps used in city water works, fire engines, and all steam pumps, -are force pumps. (See Fig. 44.) - -[Illustration: FIG. 44.--A steam pump used on a fire engine.] - -=64. The Siphon.=--The siphon is a tube used to convey a liquid from one -level over an elevation to a lower level by atmospheric pressure. It is -used to remove liquids from tanks or vessels that have no opening at the -bottom. - -The siphon cannot be completely understood until one has mastered the -laws of the flow of liquids. The following is offered as an incomplete -explanation of its behavior. Consider the siphon to be full of water -and closed at _d_ (Fig. 45). Atmospheric pressure on _a_ will hold the -siphon full if _ab_ does not exceed 34 feet. If _d_ is opened the water -falls out with a speed equal to that acquired in falling from the level -of _a_ to that of _d_. This speed is acquired by all the water in the -siphon and results in a drop in pressure throughout it. The pressure at -_a_ inside the siphon becomes less than the pressure at the same level -outside as soon as the water starts flowing. The water in the vessel -then flows into the siphon and out at _d_. This flow continues as long -as there is a fall from the free surface of the water in the vessel to -the outlet at _d_. - -[Illustration: FIG. 45.--Cross-section of a siphon.] - -[Illustration: FIG. 46.--The Cartesian diver.] - -=65. The Cartesian Diver.=--This is a device which illustrates at the -same time transmission of pressure by liquids, Archimedes' principle, -and compressibility of gases. It was invented by Des Cartes (1596-1650). -As ordinarily made, it is a hollow glass image with a small opening in -the foot. It contains air and water in such amounts that the average -density of image and contents is slightly less than that of water. It is -placed in a tall glass jar filled with water and covered with tightly -stretched rubber tissue. (See Fig. 46.) By pressing on the rubber cover -the diver may be made to sink, since the air and water transmit the -pressure on the cover which compresses the air inside the figure -admitting some water to it, thus making the diver more dense than -water. By varying the pressure it can be made to sink, rise, or remain -stationary at will.[D] A small vial can be used instead of the image. - - [D] The position of a submarine in or under water is controlled in - a similar manner. - -=66. Hydraulic Ram.=--The hydraulic ram (see Fig. 47) is an automatic -device that is much used for raising water from springs to houses -located on higher ground. Water flows through the pipe _A_ through the -opening at _B_. The pressure closes the valve at _B_. The increased -pressure in the pipe due to the closing of _B_ opens the valve _C_ and -some of the water flows into the air chamber _D_. This reduces the -pressure against the valve _B_ so that it drops and allows a little -water to escape. Just as this happens, valve _C_ closes. The pressure in -the pipe then closes _B_ and forces water past _C_. This action being -continually repeated, the air in _D_ becomes so compressed that it has -elastic force enough to raise the water in a steady stream to a height -of many feet. - -[Illustration: FIG. 47.--Cross-section of a hydraulic ram.] - -=67. The Balloon.=--Since air is a fluid, Archimedes' principle applies -to it as well as to liquids. Therefore any object in the air is lifted -up by a force equal to the weight of the air it displaces. The object -will rise, if it weighs less than this displaced air and will continue -to rise until both weights are equal. - -_The Balloon_ (Fig. 48) rises because it weighs less than the air it -displaces, and therefore it is pushed up by the heavier air, the -"lifting power" being the difference between its weight and that of the -air displaced. The neck at the bottom is left open to allow for -expansion of the gas. When the aeronaut wishes to descend, he opens a -valve at the top allowing some of the gas to escape. - -[Illustration: FIG. 48.--Winner of international championship race, -Paris, 1913.] - -_Hydrogen_ is the lightest gas, weighing 0.09 kg. per cubic meter, and -so gives the greatest lifting power, but as it is expensive to make, -coal gas, density 0.75 kg. per cubic meter, is ordinarily employed. -Helium has recently been used to fill military balloons because it -cannot be set on fire. - -_The Parachute_ (Fig. 49) is an umbrella-shaped device for use in -descending from a balloon. After falling a few seconds it opens, the -large surface exposed to the air causing it to descend slowly. The hole -in the top keeps the parachute upright by allowing the air to escape -through it, thus relieving the pressure. - -[Illustration: FIG. 49.--A parachute.] - -[Illustration: FIG. 50.--Cross-section of a Westinghouse air brake.] - -=68. The Air Brake.=--Compressed air is used to do work in many -machines, such as pneumatic drills, hammers, and air brakes. The -Westinghouse air brake (Fig. 50) uses air at a pressure of about 70 lbs. -to the square inch. The essential parts as shown are a reservoir _R_, -the brake cylinder _C_ and a triple valve _V_, placed under each car -with an air pipe _P_, leading to the engine. This is connected to _R_ by -the triple valve _V_. When the pressure in _P_ is reduced by the -engineer or by accident, the triple valve operates so as to admit air -from _R_ into the cylinder _C_ pushing the piston _H_ to the left. _H_ -is connected to the brakes by levers which press the brake shoes -strongly against the wheels. When the air pressure in _P_ is restored -the triple valve acts so as to permit the air in _C_ to escape while _R_ -is filled again from _P_. The hissing sound heard when a train stops is -caused by air escaping from cylinder _C_. The spring in _C_ keeps the -brakes from the wheels except when the "air is on." - -[Illustration: FIG. 51.--Cross-section of a gas meter showing its -construction and action.] - -=69. The Gas Meter.=--The gas meter consists of a box divided into two -parts by a vertical partition (Fig. 51). Two bellows are attached to -this partition, one on each side. The valves that regulate the flow of -gas to and from the bellows and the chambers _A_ and _D_ are opened and -closed by levers connected with the bellows. These levers also operate -the hands upon the dials. When the inlet to the bellows _B_ is opened, -the outlet of _A_ is also opened. Gas entering _B_ opens the bellows and -forces the gas in _A_ out into the house-pipe _E_. When _B_ is full its -inlet valve closes and its outlet valve opens. The inlet of _A_ also -opens and its outlet closes. Gas now flows into _A_, compressing the -bellows and _B_, and forcing the gas from it into the house-pipe. At -each filling of the bellows _B_ there will be displaced from _A_ and -forced into the house-pipe as much gas as enters _B_. It is evident that -at each emptying of _B_ an equal amount of gas enters _A_. Thus we have -_A_ and _B_ alternately filling and emptying as long as the gas burner -is open. To have a continuous flow of gas in the house-pipes two pipes -and two chambers are necessary, one being filled while the other is -being emptied. - -Fig. 52 represents the dials upon a gas meter showing a reading of -54,600 cu. ft. - -[Illustration: FIG. 52.--Dials of a gas meter.] - -=70. Centrifugal Pumps.= Fluids, such as water and air, are often put in -motion by devices called _centrifugal pumps_ (see Art. 78). These pumps -contain a revolving part, like a wheel without a rim, whose spokes are -replaced by thin blades. This revolving part resembles the paddle wheel -of some steam boats and is enclosed in a case or cover having one -opening at the rim and another opening on one side about the axle. - -[Illustration: FIG. 53.--A vacuum sweeper. (_Courtesy of the Hoover -Suction Sweeper Co._)] - -When the wheel is rapidly revolved, the fluid is driven out with -considerable force through the opening at the rim, while a partial -vacuum is produced at the axle causing a rapid flow into the device at -this point. - -This is the principle of the action of the _vacuum cleaner_. Fig. 53 is -a section of a vacuum sweeper showing the revolving wheel and the -current of air passing into the wheel at the lower side and out of the -rim of the case at the rear. - -_Centrifugal water pumps_ work on the same principle and furnish a -continuous flow of water, often large in volume and at considerable -pressure. - - -Important Topics - -1. Air pump. - -2. Condensing pump. - -3. Lift and force pumps. - -4. Siphon. - -5. Cartesian diver. - -6. Hydraulic ram. - -7. Balloon. - -8. Air brake. - -9. Gas meter. - -10. Vacuum cleaner. - - -Exercises - -1. Explain why smoke settles to the ground before storms. - -2. Why does the water rise in the suction pipe of a pump? - -3. Why is it easier to float in water when the lungs are filled with air -than when they are not filled? - -4. Why is it easier to swim in salt water than in fresh water? - -5. How are submarines made to sink? to rise to the surface? - -6. How can a fish rise or sink in water? - -7. Explain why a life preserver made of cork will enable a person to -float. - -8. Hold the open hand out flat with the fingers together. Place -underneath the fingers a piece of paper. Blow between the first and -second fingers against the paper. As long as you blow hard the paper -will not fall but will stick to the hand. Explain. - -9. Why does pressing the bulb of an atomizer force out the liquid in a -fine spray? - -10. Why is air that contains a large amount of water vapor lighter than -air that only contains a small amount? - -11. How are heights above sea-level ascertained by a barometer? - -12. Oil floats on water but sinks in alcohol. Explain. - -13. In a balloon the lower end is often open to the air. Why does not -the gas escape and prevent the balloon from rising? - -14. How long will a balloon continue to rise? - -15. If the pressure against the 8-in. piston of an air brake is 70 lbs. -per square inch, how much force does the piston exert? - -16. The capacity of a balloon is 40,000 cu. ft. The weight of the -balloon, car, etc., is 600 lbs.; specific gravity of the gas used is -0.46 that of the air. Find how much weight the balloon can carry. - -17. The so-called Magdeburg hemispheres were invented by Otto von -Guericke of Magdeburg, Germany. When the hemispheres (see Fig. 54) are -placed in contact and the air exhausted it is found very difficult to -pull them apart. Explain. - -18. Von Guericke's hemispheres had an inside diameter of 22 in. What -force would be required to pull them apart if all the air were exhausted -from them? (Find the atmospheric force on a circle, 22 in. in diameter.) - -19. Von Guericke made a water barometer whose top extended through the -roof of his house. On the top of the water in the tube was placed a -wooden image. In fair weather the image appeared above the roof, but it -descended before a storm. Explain. - -20. The balloon "Goodyear" (Fig. 48), which won the International -championship race at Paris in 1913, has a capacity of 80,000 cu. ft. The -gas bag weighs 653 lbs., the net 240 lbs. and the basket 92 lbs. How -large a load can it carry when filled with hydrogen specific gravity -0.069 (compared with air). - -[Illustration: FIG. 54.--Magdeburg hemispheres.] - - -Review Outline: Liquids and Gases - -Liquids: Force, pressure, and density. Floating and immersed bodies. -Laws: Liquid force, _F = A.h.d_, Pascal's, Archimedes. Illustrations and -Applications: - - Specific gravity, _W_{a}/(W_{a} - W_{w})_, _(W_{a} - W_{l})/(W_{a} - - W_{w})_, Boyle's, _PV = P´V´_ - -Devices: Hydraulic press, air cushion, barometer--mercurial and aneroid. -Pumps, lift, force, vacuum, compression, centrifugal, balloon, siphon, -etc. Construction and action of each. - - - - -CHAPTER V - -FORCE AND MOTION - - -(1) FORCE, HOW MEASURED AND REPRESENTED - -=71. Force.=--We have been studying various forces, such as air -pressure, pressure in liquids, and the force of elasticity in solids, -and have considered them simply as pushes or pulls. A more formal study -of forces in general and of devices for representing and measuring them -will be helpful at this point of the course. - -_A force is that which tends to cause a change in the size or shape of a -body or in its state of motion._ In other words a force is a push or a -pull. That is, force tends to produce distortion or change of motion in -a body. Force itself is invisible. We measure it by the effect it -produces. Forces are usually associated with the objects exerting them. -Thus we speak of _muscular force_, _air pressure_, _liquid pressure_, -the force of a spring, the force of the earth's attraction and so on. - -Forces are classified in various ways. - -I. With respect to the _duration and steadiness_ of the force. - -(a) Constant, as the earth's attraction. (b) Impulsive, as the stroke of -a bat on a ball. (c) Variable, as the force of the wind. - -II. With respect to the _direction_ of the force. - -(a) Attractive, as the earth's attraction. (b) Repulsive, as air -pressure, liquid pressure, etc. - -=72. Methods of Measuring Force.=--Since forces are measured by their -effects which are either distortion or change of motion, either of these -effects may be used to measure them. For example, the force exerted by -a locomotive is sometimes computed by the _speed_ it can develop in a -train of cars in a given time, or the force of the blow of a baseball -bat is estimated by the _distance_ the ball goes before it strikes the -ground. - -The more common method of measuring force, however, is by _distortion_, -that is, by measuring the change of shape of a body caused by the force. -In doing this, use is made of Hooke's Law (Art. 32), in which it is -stated that "within the limits of perfect elasticity," changes of size -or shape are directly proportional to the forces employed. That is, -twice as great a force will produce twice as great a change of shape and -so on. - -[Illustration: FIG. 55.--A spring balance.] - -A common contrivance using this principle is the spring balance (Fig. -55), with which all are familiar, as ice scales, meat scales, postal -scales, etc. The object which changes shape in this device is a coiled -spring contained in the case of the instrument. The balance is so -constructed that when the spring is pulled out as far as possible it has -not reached its limit of elasticity, since, if the spring were stretched -so as to exceed its elastic limit, the index would not return to its -first position on removing the load. (See Arts. 30-32.) - -=73. Graphic Representation of Forces.=--A force is said to have three -elements. These are (a) _its point_ of _application_, (b) _its -direction_, and (c) _its magnitude_. For example, if there is hung upon -the hook of a spring balance a weight of 5 lbs., then we have: (a) its -point of application on the hook of the balance, (b) its downward -direction and (c) its magnitude, or 5 lbs. These three elements may be -represented by a line. Thus in Fig. 56_a_, a line _AB_ is drawn as -shown, five units long; _A_ represents the point of application; _B_, -the arrow head, shows the direction; and the length of the line (five -units) shows the magnitude of the force. - -This is called a _graphic representation_ since it represents by a line -the quantity in question. If another weight of 5 lbs. were hung from the -first one, the graphic representation of both forces would be as in Fig. -56_b_. Here the first force is represented by _AB_ as before, _BC_ -representing the second force applied. The whole line represents the -_resultant_ of the two forces or the result of their combination. If the -two weights were hung one at each end of a short stick _AC_ (Fig. -56_c_), and the latter suspended at its center their combined weight or -_resultant_ would of course be applied at the center. The direction -would be the same as that of the two weights. The resultant therefore is -represented by _ON_. In order to exactly balance this resultant _ON_, a -force of equal magnitude but opposite in direction must be applied at -the point of application of _ON_, or _O_. _OM_ then represents a force -that will just balance or hold in equilibrium the resultant of the two -forces _AB_ and _CD_. This line _OM_ therefore represents the -_equilibrant_ of the weights _AB_ and _CD_. The resultant of two forces -at an angle with each other is formed differently, as in Fig. 57 _a_. -Here two forces _AB_ and _AC_ act at an angle with each other. Lay off -at the designated angle the lines _AB_ and _AC_ of such length as will -accurately represent the forces. Lay off _BD_ equal to _AC_ and _CD_ -equal to _AB_. The figure _ABCD_ is then a parallelogram. Its diagonal -_AD_ represents the resultant of the forces _AB_ and _AC_ acting at the -angle _BAC_. If _BAC_ equals 90 degrees or is a right angle, _AD_ may be -_computed_ thus: _AB² + BD² = AD²_. Why? - - and _AD_ = {~SQUARE ROOT~}_([line]AB² + [line]BD²)._ - -[Illustration: FIG. 56.--Graphic representation of forces acting along -the same or parallel lines.] - -[Illustration: FIG. 57.--Graphic representation of two forces acting -(_a_) at a right angle, (_b_) at an acute angle.] - -This method of determining the resultant by _computation_ may be used -when the two forces are at right angles. (In any case, _AD may be -measured_ using the same scale that is laid off upon _AB_ and _AC_, as -shown in Fig. 57 _b_.) The three cases of combining forces just given -may be classified as follows: The _first_ is that of _two forces acting -along the same line_ in the same or opposite direction, as when two -horses are hitched tandem, or in a tug of war. The _second_ is that of -_two forces acting along parallel lines_, in the same direction, as when -two horses are hitched side by side or abreast. The _third_ is that of -_two forces acting at the same point at an angle_. It may be represented -by the device shown in Fig. 58, consisting of two spring balances -suspended from nails at the top of the blackboard at _A_ and _B_. A cord -is attached to both hooks and is passed through a small ring at _O_ from -which is suspended a known weight, _W_. Lines are drawn on the -blackboard under the stretched cords, from _O_ toward _OA_, _OB_, and -_OW_ and distances measured on each from _O_ to correspond to the three -forces as read on balance _A_ and _B_ and the weight _W_. Let a -parallelogram be constructed on the lines measured off on _OA_ and _OB_. -Its diagonal drawn from _O_ will be found to be vertical and of the same -length as the line measured on _OW_. The diagonal is the _resultant_ of -the two forces and _OW_ is the equilibrant which is equal and opposite -to the resultant. - -[Illustration: FIG. 58.--Experimental proof of parallelogram of forces.] - -Again, the _first_ case may be represented by a boat moving up or down a -stream; the resultant motion being the combined effect of the boat's -motion and that of the stream. The _second_, may be represented by two -horses attached side by side to the same evener. The resultant force -equals the sum of the two component forces. The _third_, may be -represented by a boat going across a stream, the resultant motion being -represented by the diagonal of the parallelogram formed by using the -lines that represent the motion of the stream and of the boat. - -=74. Units for Measuring Force.=--Force is commonly measured in units of -weight: in pounds, kilograms, and grams. For example, we speak of 15 -lbs. pressure per square inch and 1033.6 g. pressure per square -centimeter as representing the air pressure. It should be noted here -that the words pound, kilogram, and gram are used not only to represent -_weight_ or _force_ but also the masses of the objects considered. Thus, -one may speak of a pound-mass meaning the amount of material in the -object. - -It will help to avoid confusion if we reserve the simple terms "gram" -and "pound" to denote exclusively an amount of matter, that is, a mass, -and to use the full expression "gram of force" or "pound of force" -whenever we have in mind the pull of the earth upon these masses. Or, -one may speak of a _pound-weight_ meaning the amount of attraction -exerted by the earth upon the object. The same is true of _gram-mass_ -and _gram-weight_. The mass of a body does not change when the body is -transferred to another place. The weight, however, may vary, for on -moving a body from the equator toward the poles of the earth the weight -is known to increase. - - -Important Topics - -1. Definition of force. - -2. Classification of forces. (a) Duration: constant, impulsive, -variable. (b) Direction: attractive, repulsive. - -3. Methods of measuring force. (a) By distortion. (b) By change of -motion. - -4. Graphic representation of forces: component, resultant, equilibrant. - -5. Three cases of combining forces. (1) Two forces acting on the same -line. (2) Two forces acting in parallel lines. (3) Two forces acting at -the same point at an angle. - -6. Units for measuring force, pound, gram. - - -Exercises - -1. Name five natural forces. Which produce a tension? Which a pressure? - -2. How much can you lift? Express in pounds and kilograms. - -3. Show graphically the resultant of two forces at right angles, one of -12 lbs., the other of 16 lbs. What is the magnitude of this resultant? -Then determine the answer, first by measurement and then by computation. -Which answer is more accurate? Why? - -4. Represent by a parallelogram the two forces that support a person -sitting in a hammock and draw the line representing the resultant. - -5. Find graphically the resultant of the pull of two forces, one of 500 -lbs. east and one of 600 lbs. northwest. - -6. Determine the equilibrant of two forces, one of 800 lbs. south and -one of 600 lbs. west. - -7. Would the fact that weight varies on going from the equator to either -pole be shown by a spring balance or a beam balance? Explain. - - -(2) MOTION. NEWTON'S LAWS OF MOTION - -=75. Motion a Change of Position.=--Motion is defined as a continuous -_change in the position_ of a body. The _position_ of a body is usually -described as its _distance_ and _direction_ from some fixed point. Thus -a man on a boat may be at rest with respect to the boat and moving with -respect to the earth. Or, if he walks toward the stern as fast as the -boat moves forward, he may keep directly over a rock on the bottom of -the lake and hence not be moving with reference to the rock and yet be -in motion with respect to the boat. Motion and rest, therefore, are -_relative_ terms. The earth itself is in motion in turning on its axis, -in moving along its orbit, and in following the sun in its motion -through space. Motions are classified in several ways: - - -(A) MODES OF MOTION - -1. _Translation._--A body is said to have motion of _translation_ when -every line in it keeps the same direction. - -2. _Rotation._--A body has motion of _rotation_ when it turns upon a -fixed axis within the body, as a wheel upon its axle or the earth upon -its axis. - -3. _Vibration_ or _Oscillation_.--A body is said to have _vibratory_ or -_oscillatory_ motion when it returns to the same point at regular -intervals by reversals of motion along a given path, _e.g._, a pendulum. - - -(B) DIRECTION OF MOTION - -1. _Rectilinear._--A body has rectilinear motion when its path is a -straight line. Absolute rectilinear motion does not exist, although the -motion of a train on a straight stretch of track is nearly rectilinear. - -2. _Curvilinear._--A body has _curvilinear_ motion when its path is a -curved line, _e.g._, the path of a thrown ball. - - -(C) UNIFORMITY OF MOTION - -1. _Uniform._--A body has uniform motion when its speed and direction of -motion do not change. Uniform motion for extended periods is rarely -observed. A train may cover, on an average, 40 miles per hour but during -each hour its speed may rise and fall. - -2. _Variable._--A body has variable motion when its speed or direction -of motion is continually changing. Most bodies have variable motion. - -3. _Accelerated._--A body has accelerated motion when its speed or -direction of motion continually changes. If the speed changes by the -same amount each second, _and the direction of motion does not change_ -the motion is said to be _uniformly_ accelerated, _e.g._, a falling -body. - -Uniformly accelerated motion will be studied further under the topic of -falling bodies. - -_Velocity_ is _the rate of motion_ of a body in a given direction. For -example, a bullet may have a velocity of 1300 ft. a second upwards. -_Acceleration_ is _the rate of change of velocity_ in a given direction, -or the change of velocity in a unit of time. A train starting from a -station gradually increases its speed. The gain in velocity during one -second is its acceleration. When the velocity is decreasing, as when a -train is slowing down, the acceleration is opposite in direction to the -velocity. A falling body falls faster and faster. It has _downward -acceleration_. A ball thrown upward goes more and more slowly. It also -has _downward acceleration_. - -=76. Momentum.=--It is a matter of common observation that a heavy body -is set in motion with more difficulty than a light one, or if the same -force is used for the same length of time upon a light and a heavy -body,[E] the light body will be given a greater velocity. This -observation has led to the _calculation_ of what is called the "quantity -of motion" of a body, or its _momentum_. It is computed by multiplying -the mass by the velocity. If the C.G.S. system is used we shall have as -the momentum of a 12 g. body moving 25 cm. a second a momentum of 12 × -25 or 300 C.G.S. units of momentum. This unit has no name and is -therefore expressed as indicated above. The formula for computing -momentum is: _M = mv_. - - [E] By a light body is meant one of small mass, a heavy body - possessing much greater mass. - - -Newton's Laws of Motion - -=77. Inertia, First Law of Motion.=--One often observes when riding in a -train that if the train moves forward suddenly the passengers do not get -into motion as soon as the train, and apparently are jerked backward. -While if the train is stopped suddenly, the passengers tend to keep in -motion. This tendency of matter to keep moving when in motion and to -remain at rest when at rest is often referred to as the property of -_inertia_. _Newton's first law of motion_, often called the _law of -inertia_, describes this property of matter as follows: - -_Every body continues in a state of rest or of uniform motion in a -straight line unless it is compelled to change that state by some -external force._ This means that if an object like a book is lying on a -table it will remain there until removed by some outside force. No -inanimate object can move itself or stop itself. If a ball is thrown -into the air it would move on forever if it were not for the _force_ of -attraction of the earth and the resistance of the air. - -It takes time to put a mass into motion, a heavy object requiring more -time for a change than a light object. As an example of this, note the -movements of passengers in a street car when it starts or stops -suddenly. Another illustration of the law of inertia is the so-called -"penny and card" experiment. Balance a card on the end of a finger. -Place on it a coin directly over the finger, snap the card quickly so as -to drive the card from beneath the coin. The coin will remain on the -finger. (See Fig. 59.) - -[Illustration: FIG. 59.--The ball remains when the card is driven away.] - -According to Newton's first law of motion a moving body which could be -entirely freed from the action of all external forces would have uniform -motion, and would describe a perfectly straight course. The curved path -taken by a baseball when thrown shows that it is acted upon by an -outside force. This force, the attraction of the earth, is called -_gravity_. - -[Illustration: SIR ISAAC NEWTON "By Permission of the Berlin -Photographic Co., New York." - -Sir Isaac Newton (1642-1727) Professor of mathematics at Cambridge -university; discovered gravitation; invented calculus; announced the -laws of motion; wrote the Principia; made many discoveries in light.] - -[Illustration: GALILEO GALILEI "By Permission of the Berlin Photographic -Co., New York." - -Galileo Galilei (1564-1642). Italian. "Founder of experimental science"; -"Originator of modern physics"; made the first thermometer; discovered -the laws of falling bodies and the laws of the pendulum; invented -Galilean telescope.] - -[Illustration: FIG. 60.--Cross-section of the DeLaval cream separator.] - -=78. Curvilinear Motion.=--Curvilinear motion occurs when a moving body -is pulled or pushed away from a straight path. The pull or push is -called _centripetal_ (center-seeking) force. A moving stone on the end -of a string when pulled toward the hand moves in a curve. If the string -is released the stone moves in a tangent to the curve. The string pulls -the hand. This phase of the pull is called _centrifugal_ force. The -_centripetal_ force is the pull on the stone. Centripetal and -centrifugal force together cause a tension in the string. Examples of -curvilinear motion are very common. The rider and horse in a circus ring -lean inward in order to move in a curve. The curve on a running track in -a gymnasium is "banked" for the same reason. Mud flying from the wheel -of a carriage, the skidding of an automobile when passing rapidly around -a corner, and sparks flying from an emery wheel, are illustrations of -the First Law of Motion. - -Cream is separated from milk by placing the whole milk in a rapidly -revolving bowl, the cream being lighter collects in the center and is -thrown off at the top. (See Fig. 60.) Clothes in steam laundries are -dried by a centrifugal drier. In amusement parks many devices use this -principle. (See centrifugal pumps, Art. 70.) - -[Illustration: FIG. 61.--The two balls reach the floor at the same -time.] - -=79. The Second Law of Motion,= sometimes called the _law of momentum_, -leads to the _measurement of force_, by the momentum or the quantity of -motion, produced by it. The law is stated as follows: - -_Change of motion, or momentum, is proportional to the acting force and -takes place in the direction in which the force acts._ In other words, -if two or more forces act at the same instant upon a body each produces -the same effect that it would if acting alone. If a card be supported on -two nails driven horizontally close together into an upright board (see -Fig. 61), and two marbles be so placed on the ends as to balance each -other, when one marble is snapped horizontally by a blow, the other will -fall. Both reach the floor at the same time. The two balls are equally -pulled down by the earth's attraction and strike the ground at the same -time, though one is shot sidewise, and the other is dropped vertically. - -As gravity is a constant force, while the blow was only a momentary -force, the actual path or resultant motion will be a curved line. - -The constant relation, between the acting force and the change of -momentum it produces in a body, has led to the adoption of a convenient -C.G.S. unit of force called the _dyne_. _The dyne is that force which -can impart to a mass of one gram a change of velocity at the rate of one -centimeter per second every second._ This definition assumes that the -body acted upon is free to move without hindrance of any kind, so that -the acting force has to overcome only the _inertia_ of the body. -_However_, the _law_ applies in every case of application of force, so -that each force produces its full effect independently of other forces -that may be acting at the same time upon the body. - -=80. Newton's Third Law.=--This law has been experienced by everyone who -has jumped from a rowboat near the shore. The muscular action that -pushes the body forward from the boat also pushes the boat backward, -often with awkward results. The law is stated: _To every action, there -is always an opposite and equal reaction, or the mutual actions of any -two bodies are always equal and opposite in direction_. Many -illustrations of this law are in every one's mind: a stretched rope -pulls with the same force in one direction as it does in the opposite -direction. If a bat hits a ball, the ball hits the bat with an equal and -opposite force. The third law is therefore sometimes called the law of -_reaction_. When a weight is hung upon a spring balance the action of -the weight pulls down the spring until it has stretched sufficiently -(Hooke's Law) to produce an elastic _reaction_ that equals and hence -supports the weight. When a man stands at the center of a plank -supported at its ends, the action of the man's weight bends the plank -until the elastic force developed in the plank equals the weight -applied. Further, when a train or a wagon is on a bridge the bridge -yields until it has developed an elastic reaction equal to the weight -applied. If a person stands in the center of a room, the floor beams -yield until the third law is satisfied. In fact, whenever a force acts, -a contrary equal force always acts. - -=81. Stress and Strain.=--A pair of forces that constitute an action and -a reaction is called a _stress_. The two forces are two parts of one -_stress_. If the two forces act away from each other, as in the breaking -of a string, the stress is called a _tension_, but if they act toward -each other as in crushing anything, the stress is called a _pressure_. -In order for a body to exert force it must meet with resistance. The -force exerted is never greater than the resistance encountered. Thus one -can exert but little force upon a feather floating in the air or upon -other light objects. A fast moving shot exerts no force unless it -encounters some resistance. - -Forces, then, are always found in pairs. Thus to break a string, to -stretch an elastic band, to squeeze a lemon, one must exert two equal -and opposite forces. Such a thing as a single force acting alone is -unknown. Usually, however, we give our attention mainly to one of the -forces and ignore the other. When a force acts upon a body the change of -shape or size resulting is called a _strain_. Hooke's law (Art. 32) is -often expressed as follows: "The strain is proportional to the stress," -_e.g._, the stretch of the spring of a spring balance is proportional to -the load placed upon it. - - -Important Topics - -1. Motion a change of position. Kinds of motion. - -2. Newton's laws of motion. - -3. Momentum. - -4. Inertia. First law of motion. Curvilinear motion. - -5. Second law of motion. - -6. Third law of motion. Action and reaction, stress and strain. - - -Exercises - -1. Mention three illustrations of the third law, different from those -given. - -2. A rifle bullet thrown against a board standing upon edge will knock -it down; the same bullet fired at the board will pass through it without -disturbing its position. Explain. - -3. A hammer is often driven on to its handle by striking the end of the -latter. Explain. - -4. Consider a train moving 60 miles an hour, with a gun on the rear -platform pointing straight backward. If a ball is fired from the gun -with a speed of 60 miles an hour, what will happen to the ball? - -5. Could one play ball on the deck of an ocean steamer going 25 miles an -hour without making allowance for the motion of the ship? Explain. - -6. On a railroad curve, one rail is always higher. Which? Why? - -7. Why can a small boy when chased by a big boy often escape by dodging? - -8. Will a stone dropped from a moving train fall in a straight line? -Explain. - -9. A blast of fine sand driven against a sheet of glass soon gives it a -rough surface. Explain. - -10. Explain the use of fly-wheels in steadying the motion of machinery -(for example, the sewing machine). - -11. Is it easier to walk to the front or rear of a passenger train when -it is stopping? Why? - -12. Why does lowering the handles of a wheel-barrow on the instant of -striking make it easier to go over a bump? - -13. Why should a strong side wind interfere with a game of tennis? How -can it be allowed for? - -14. On which side of a railroad track at a curve is it the safer to walk -while a train is passing? Why? - -15. Why does a bullet when fired through a window make a clean round -hole in the glass, while a small stone thrown against the window -shatters the glass? - -16. A tallow candle can be fired through a pine board. Why? - -17. In cyclones, straws are frequently found driven a little distance -into trees; why are the straws not broken and crushed instead of being -driven into the tree unbroken? - -18. A bullet weighing one-half oz. is fired from a gun weighing 8 lb. -The bullet has a velocity of 1800 ft. per second. Find the velocity of -the "kick" or recoil of the gun. - -18. When football players run into each other which one is thrown the -harder? Why? - -20. A railroad train weighing 400 tons has a velocity of 60 miles per -hour. An ocean steamer weighing 20,000 tons has a velocity of one half -mile per hour. How do their momenta compare? - -21. Why is a heavy boy preferable to a lighter weight boy for a football -team? - -22. Why does a blacksmith when he desires to strike a heavy blow, select -a heavy sledge hammer and swing it over his head? - -23. Why does the catcher on a baseball team wear a padded glove? - - -(3) RESOLUTION OF FORCES - -=82. Resolution of Forces.=--We have been studying the effect of forces -in producing motion and the results of combining forces in _many_ ways; -in the _same line_, in _parallel lines_, and in _diverging lines_. -Another case of much interest and importance is _the determination of -the effectiveness of a force in a direction different from the one in -which it acts_. This case which is called _resolution of forces_ is -frequently used. To illustrate: one needs but to recall that a sailor -uses this principle in a practical way whenever he sails his boat in any -other direction than the one in which the wind is blowing, _e.g._, when -the wind is blowing, say from the north, the boat may be driven east, -west, or to any point south between the east and west and it is even -possible to beat back against the wind toward the northeast or -northwest. Take a sled drawn by a short rope with the force applied -along the line _AB_ (see Fig. 62); part of this force tends to lift the -front of the sled as _AC_ and a part to draw it forward as _AD_. Hence -not all of the force applied along _AB_ is used in drawing the sled -forward. Its effectiveness is indicated by the relative size of the -component _AD_ compared to _AB_. - -[Illustration: FIG. 62.--_AD_ is the effective component.] - -The force of gravity acting upon a sphere that is resting on an -_inclined plane_ may be readily resolved into two components, one, the -_effective_ component, as _OR_, and the other, the _non-effective_ as -_OS_. (See Fig. 63.) If the angle _ACB_ is 30 degrees, _AB_ equals 1/2 -of _AC_ and _OR_ equals 1/2 of _OG_, so that the speed of the sphere -down the plane developed in 1 second is less than (about one-half of) -the speed of a freely falling body developed in the same time. Why is -_OS_ non-effective? - -[Illustration: FIG. 63.--The effective component is _OR_.] - -[Illustration: FIG. 64.--Resolution of the forces acting on an -aeroplane.] - -=83. The Aeroplane.=--The aeroplane consists of one or two frames _ABCD_ -(see Fig. 64), over which is stretched cloth or thin sheet metal. It is -driven through the air by a propeller turned by a powerful gasoline -motor. This has the effect of creating a strong breeze coming toward the -front of the aeroplane. As in the case of the sailboat a pressure is -created at right angles to the plane along _GF_ and this may be resolved -into two components as _GC_ and _GE_, _GC_ acting to lift the aeroplane -vertically and _GE_ opposing the action of the propeller. Fig. 65 -represents the Curtis Flying Boat passing over the Detroit river. - -[Illustration: FIG. 65.--The Curtis hydroplane.] - - -Exercises. - -1. If a wagon weighing 4000 lbs. is upon a hill which rises 1 ft. in 6, -what force parallel to the hill will just support the load? (Find the -effective component of the weight down the hill.) - -2. If a barrel is being rolled up a 16-ft. ladder into a wagon box 3 ft. -from the ground, what force will hold the barrel in place on the ladder, -if the barrel weighs 240 lbs. Show by diagram. - -3. Show graphically the components into which a man's push upon the -handle of a lawn mower is resolved. - -4. Does a man shooting a flying duck aim at the bird? Explain. - -5. What are the three forces that act on a kite when it is "standing" in -the air? - -6. What relation does the resultant of any two of the forces in problem -five have to the third? - -7. Into what two forces is the weight of a wagon descending a hill -resolved? Explain by use of a diagram. - -8. A wind strikes the sail of a boat at an angle of 60 degrees to the -perpendicular with a pressure of 3 lbs. per square foot. What is the -effective pressure, perpendicular to the sail? What would be the -effective pressure when it strikes at 30 degrees? - -9. How is the vertical component of the force acting on an aeroplane -affected when the front edge of the plane is elevated? Show by diagram. - - -(4) MOMENT OF FORCE AND PARALLEL FORCES - -=84. Moment of Force.=--In the study of motion we found that the -quantity of motion is called _momentum_ and is measured by the product -of the _mass times the velocity_. In the study of _parallel forces_, -especially such as tend to produce _rotation_, we consider a similar -quantity. It is called a _moment of force_, which is the term applied to -the _effectiveness_ of a force in producing change of rotation. It also -measured by the product of two quantities; _One, the magnitude of the -force itself_, and the other, _the perpendicular distance from the axis -about which the rotation takes place to the line representing the -direction of the force_. - -[Illustration: FIG. 66.--The moments about _S_ are equal.] - -_To illustrate:_ Take a rod, as a meter stick, drill a hole at _S_ and -place through it a screw fastened at the top of the blackboard. Attach -by cords two spring balances and draw to the right and left, _A_ and _B_ -as in Fig. 66. Draw out the balance _B_ about half way, hold it -steadily, or fasten the cord at the side of the blackboard, and read -both balances. Note also the distance _AS_ and _BS_. Since the rod is at -rest, the tendency to rotate to the right and left must be equal. That -is, the moments of the forces at _A_ and _B_ about _S_ are equal. Since -these are computed by the product of the _force times the force_ arm, -multiply _B_ by _BS_ and _A_ by _AS_ and see if the computed moments are -equal. _Hence a force that tends to turn or rotate a body to the right -can be balanced by another of equal moment that acts toward the left._ - -[Illustration: FIG. 67.--Law of parallel forces illustrated.] - -=85. Parallel Forces.=--Objects are frequently supported by two or more -upward forces acting at different points and forming in this way a -system of parallel forces; as when two boys carry a string of fish on a -rod between them or when a bridge is supported at its ends. The -principle of moments just described aids in determining the magnitude of -such forces and of their resultant. To illustrate this take a wooden -board 4 in. wide and 4 ft. long of uniform dimensions. (See Fig. 67.) -Place several screw hooks on one edge with one set at _O_ where the -board will hang horizontally when the board is suspended there. Weigh -the board by a spring balance hung at _O_. This will be the resultant in -the following tests. Now hang the board from two spring balances at _M_ -and _N_ and read both _balances_. Call readings _f_ and _f´_. To test -the forces consider _M_ as a fixed point (see Fig. 67) and the weight of -the board to act at _O_. Then the moment of the weight of the board -should be equal the moment of the force at _N_ since the board does not -move, or _w_ times _OM_ equals _f´_ times _NM_. If _N_ is considered the -fixed point then the moment of the weight of the board and of _f with -reference to the point N_ should be equal, or _w_ times _ON_ = _f_ times -_NM_. Keeping this illustration in mind, the law of parallel forces may -be stated at follows: 1. _The resultant of two parallel forces acting in -the same direction at different points in a body is equal to their sum -and has the same direction as the components._ - -_The moment of one of the components about the point of application of -the other is equal and opposite to the moment of the supported weight -about the other._ - - =Problem.=--If two boys carry a string of fish weighing 40 lbs. on - a rod 8 ft. long between them, what force must each boy exert if - the string is 5 ft. from the rear boy? - - =Solution.=--The moment of the force _F_ exerted about the opposite - end by the rear boy is _F_ × 8. The moment of the weight about the - same point is 40 × (8 - 5) = 120. Therefore _F_ × 8 = 120, or _F_ = - 15, the force exerted by the rear boy. The front boy exerts a force - of _F_ whose moment about the other end of the rod is _F_ × 8. The - moment of the weight about the same point is 40 × 5 = 200. Since - the moment of _F_ equals this, 200 = _F_ × 8, or _F_ = 25. Hence - the front boy exerts 25 lbs. and the rear boy 15 lbs. - -[Illustration: FIG. 68.--A couple.] - -=86. The Couple.=--If two equal parallel forces act upon a body along -different lines in opposite directions, as in Fig. 68, they have no -single resultant or there is no one force that will have the same effect -as the two components acting together. A combination of forces of this -kind is called a _couple_. Its tendency is to produce change of rotation -in a body. An example is the action upon a compass needle which is -rotated by a force which urges one end toward the north and by an equal -force which urges the other end toward the south. - - -Important Topics - -1. Moment of force, how measured. - -2. Parallel forces. - -3. The two laws of parallel forces. - -4. The couple. - - -Exercises - -1. Show by diagram how to arrange a three-horse evener so that each -horse must take one-third of the load. - -2. Two boys support a 10-ft. pole on their shoulders with a 40-lb. -string of fish supported from it 4 ft. from the front boy. What load -does each boy carry? Work by principle of moments. - -3. If two horses draw a load exerting a combined pull of 300 lbs., what -force must each exert if one is 28 in. and the other is 32 in. from the -point of attachment of the evener to the load? - -[Illustration: FIG. 69.--Forces acting upon a stretched rope.] - -[Illustration: FIG. 70.--A crane with horizontal tie.] - -4. A weight of 100 lbs. is suspended at the middle of a rope _ACB_ 20 -ft. long. (See Fig. 69.) The ends of the rope are fastened at points _A_ -and _B_ at the same height. Consider _D_ as the center of the line _AB_. -What is the tension of the rope when _CD_ is 3 ft.? When _CD_ is 1 ft.? -When _CD_ is 1 in.? - -5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000 -lbs. is to be lifted, find the tie stress and the boom stress if the -boom angle is 30 degrees? If 45 degrees? 60 degrees? - -6. A ball is placed on a plane inclined at an angle of 30 degrees to the -horizontal. What fraction of its weight tends to cause motion down the -plane? What effect does the other component of the weight have? Why? - -7. A person weighing 150 lbs. is lying in a hammock. The distance -between the supports is 15 ft. The hammock sags 4 ft. What is the -tension in the supports at each end? What is the tension when the sag is -only 1 ft.? - -8. A ladder 30 ft. long and weighing 80 lbs. leans against the side of a -building so that it makes an angle of 30 degrees with the building. Find -the direction and magnitude of the component forces on the ground and at -the building. - -9. A traveling crane 50 ft. long weighing 10 tons moves from one end of -a shop to the other, at the same time a load of 4000 lbs. moves from end -to end of the crane. Find the pressure of the trucks of the crane on the -track when the load is at a distance of 5, 10, 15, and 25 ft. from -either end. - -[Illustration: FIG. 71--A truss.] - -10. Resolve a force of 500 lbs. into two components at right angles to -each other, one of which shall be four times the other. - -11. A truss (see Fig. 71), carries a load of 1000 lbs. at _C_. Find the -forces acting along _AC_, _BC_, and _AB_. If _AC_ and _BC_ are each 12 -ft. and _AB_ 20 ft., which of these forces are tensions and which are -pressures? - - -(5) GRAVITATION AND GRAVITY - -=87. Gravitation.=--Gravitation is the force of attraction that exists -between all bodies of matter at all distances. This attraction exists -not only between the heavenly bodies, the stars and planets, etc., but -is also found between bodies on the earth. A book attracts all objects -in a room and outside of a room as well, since its weight shows that it -is attracted by the earth itself. The gravitational attraction between -ordinary bodies is so slight that it requires careful experiments to -detect it. In fact, it is only when one of the attracting bodies is -large, as for example the earth, that the force becomes considerable. -Careful studies of the motions of the heavenly bodies, especially of -that of the moon in its orbit about the earth, led Sir Isaac Newton to -the statement of the _law of gravitation_ which is well expressed in the -following statement: - -=88. Law of Gravitation.=--_Every particle of matter in the universe -attracts every other particle with a force that is directly proportional -to the product of their masses and inversely proportional to the square -of the distance between them._ - -The law may be separated into two parts, one referring to the masses of -the bodies concerned, the other to the effect of the distance between -them. The first part is easily understood since we all know that two -quarts of milk will weigh just twice as much as one quart. To illustrate -the second part of the law, suppose that the moon were removed to -_twice_ its present distance from the earth, then the attraction between -the earth and the moon would be _one-fourth_ its present attraction. If -removed to _three_ times its present distance, the attraction would be -_one-ninth_, etc. - -The attraction of the earth for other bodies on or near it is called -_gravity_. The _weight_ of a body is the measure of the earth's -attraction for it; or it is the force of gravity acting upon it. -Newton's third law of motion states that every action is accompanied by -an equal and opposite reaction (Art. 80). Hence, the attraction of the -earth for a book or any other object is accompanied by an equal -attraction of the book for the earth. - -=89. Weight.=--In advanced physics it is proved that a sphere attracts -as if it were concentrated at its center. Thus if the earth's radius be -considered as 4000 miles, then a body 4000 miles above the earth's -surface would be 8000 miles above the earth's center, or twice as far -from the center of the earth as is a body upon the earth's surface. A -body then 4000 miles above the earth's surface will weigh then but -one-fourth as much as it will at the surface of the earth. - -Since the earth is flattened at the poles, the surface at the equator -is farther from the center of the earth than at points north or south. -Thus a body weighing 1 lb. at the equator weighs 1.002 lb. at Chicago, -or about 1/500 more. The rotation of the earth also affects the weight -of a body upon it so that at the equator the weight of a body is 1/289 -less than at the pole. Both effects, that of flattening and of rotation, -tend to diminish the weight of bodies at the equator, so that a body at -the latter place weighs about 1/192 less than at the poles. - - In studying the effect of the earth's gravity, the following - illustration will be helpful: Imagine an open shaft a mile square - extending through the earth. What would happen to a stone thrown - into the shaft? At first it would have the attraction of the whole - earth drawing it and continually increasing its speed downward. As - it descends from the surface, the pull toward the center grows less - and less. Halfway to the center the body has lost half its weight. - When the stone reaches the center, the pull in all directions is - the same, or in other words, _it has no weight_. It would, however, - continue moving rapidly on account of its inertia, and as it - continues on from the center, the greater part of the earth being - left behind, the attraction pulling toward the center will - gradually stop it. It will then fall again toward the center and be - stopped again after passing it, and after repeatedly moving up and - down will finally come to rest at the center of the earth. At this - point it will be found to be a body without weight since it is - pulled equally in all directions by the material of the earth. What - force brings the body to rest? - -=90. Center of Gravity.=--A body is composed of a great many particles -each of which is pulled toward the center of the earth by the force of -gravity. A single force that would exactly equal the combined effect of -the pull of the earth for all the particles of a body would be their -resultant. The _magnitude_ of this resultant is the weight of the body. -The _direction_ of this resultant is in a line passing toward the -earth's center, while the _point of application_ of this resultant is -called the _center of gravity_ of the body. The center of gravity of a -body may also be briefly defined as _the point about which it may be -balanced_. As the location of this point depends upon the distribution -of matter in the body, the center of gravity is also sometimes called -the _center of mass_ of the body. - -The earth's attraction for a body is considered for the sake of -simplicity, not as a multitude of little forces, but as a single force -applied at its center of gravity. To find the center of gravity of a -body find two intersecting lines along which it balances, see Fig. 72, -and the center of gravity will be at the intersection. A vertical line -through this point is sometimes called the _line of direction of the -weight_. - -[Illustration: FIG. 72.--The center of gravity is at the intersection of -the lines of direction.] - -=91. Equilibrium of Bodies.=--Equilibrium means equally balanced. A body -at rest or in uniform motion is then in equilibrium. An object is in -equilibrium under gravity when a vertical line through its center of -gravity passes through the point of support. A trunk is an example of a -body in equilibrium since a vertical line from its center of gravity -falls within the base formed by the area upon which it rests. Work will -be necessary to tip the trunk from its position. The amount of work -required will depend upon the weight of the body and the location of the -center of gravity. - -=92. Kinds of Equilibrium.--(a) Stable.=--A body is in stable -equilibrium under gravity if its center of gravity is raised whenever -the body is displaced. It will return to its first position if allowed -to fall after being slightly displaced. In Fig. 73, _a_ and _b_ if -slightly tipped will return to their first position. They are in stable -equilibrium. Other examples are a rocking chair, and the combination -shown in Fig. 74. - -[Illustration: FIG. 73.--Stable equilibrium.] - -=(b) Unstable.=--A body is in unstable equilibrium under gravity if its -center of gravity is lowered whenever the body is slightly displaced. It -will fall farther from its first position. A pencil balanced on its -point or a broom balanced on the end of the handle are in unstable -equilibrium. The slightest disturbance will make the line of direction -of the weight fall outside of (away from) the point of support (Fig. 75 -_a_). - -[Illustration: FIG. 74--An example of stable equilibrium. Why?] - -[Illustration: FIG. 75.--Unstable equilibrium _a_, neutral equilibrium -_b_.] - -=(c) Neutral.=--A body is in neutral equilibrium if its center of -gravity is neither raised nor lowered whenever the body is moved. -Familiar examples are a ball lying on a table (Fig. 75 _b_) and a wagon -moving on a level street (referring to its forward motion). - -[Illustration: FIG. 76.--_B_ is more stable than _A_.] - -=93. Stability.=--When a body is in stable equilibrium, effort must be -exerted to overturn it, and the degree of stability is measured by the -effort required to overturn it. To overturn a body, it must be moved so -that the vertical line through its center of gravity will pass outside -of its supporting base. This movement in stable bodies necessitates a -raising of the center of gravity. The higher this center of gravity must -be raised in overturning the body, the more stable it is, _e.g._, see -Fig. 76. Thus a wagon on a hillside will not overturn until its weight -falls outside of its base, as in Fig. 77 _B_. The stability of a body -depends upon the position of its center of gravity and the area of its -base. _The lower the center of gravity and the larger the base_, the -more stable the body. What means are employed to give stability to -bodies, in every-day use (such as clocks, ink-stands, pitchers, vases, -chairs, lamps, etc.)? - -[Illustration: FIG. 77.--_B_ will overturn; _A_ will not.] - - -Important Topics - -1. Gravitation; law of gravitation, gravity, weight. - -2. Center of gravity. - -3. The three states of equilibrium. Stability. - - -Exercises - -1. Why is a plumb-line useful in building houses? - -2. What is the center of gravity of a body? - -3. Explain the action of a rocking chair that has been tipped forward. - -4. Is the stability of a box greater when empty or when filled with -sand? Explain. - -5. How can you start yourself swinging, in a swing, without touching the -ground? - -6. Is the center of gravity of the beam of a balance above, below, or at -the point of a support? How did you find it out? - -7. Why are some ink bottles cone shaped with thick bottoms? - -8. Would an electric fan in motion on the rear of a light boat move it? -Would it move the boat if revolving under water? Explain. - -9. What turns a rotary lawn sprinkler? - -10. Why, when you are standing erect against a wall and a coin is placed -between your feet, can you not stoop and pick it up unless you shift -your feet or fall over? - -11. What would become of a ball dropped into a large hole bored through -the center of the earth? - -12. When an apple falls to the ground, does the earth rise to meet it? - -13. How far from the earth does the force of gravity extend? - -14. Why in walking up a flight of stairs does the body bend forward? - -15. In walking down a steep hill why do people frequently bend backward? - -16. Why is it so difficult for a child to learn to walk, while a kitten -or a puppy has no such difficulty? - -17. Explain why the use of a cane by old people makes it easier for them -to walk? - - -(6) FALLING BODIES - -=94. Falling Bodies.=--One of the earliest physical facts learned by a -child is that a body unsupported falls toward the earth. When a child -lets go of a toy, he soon learns to look for it on the floor. It is also -of common observation that light objects, as feathers and paper, fall -much slower than a stone. The information, therefore, that all bodies -actually fall at the same rate in a vacuum or when removed from the -retarding influence of the air is received with surprise. - -This fact may be shown by using what is called a coin and feather tube. -On exhausting the air from this tube, the feather and coin within are -seen to fall at the same rate. (See Fig. 78.) when air is again -admitted, the feather flutters along behind. - -[Illustration: FIG. 78.--Bodies fall alike in a vacuum.] - -=95. Galileo's Experiment.=--The fact that bodies of different weight -tend to fall at the same rate was first experimentally shown by Galileo -by dropping a 1-lb. and a 100-lb. ball from the top of the leaning tower -of Pisa in Italy (represented in Fig. 79). Both starting at the same -time struck the ground together. Galileo inferred from this that -feathers and other light objects would fall at the same rate as iron or -lead were it not for the resistance of the air. After the invention of -the air pump this supposition was verified as just explained. - -[Illustration: FIG. 79.--Leaning tower of Pisa.] - -=96. Acceleration Due to Gravity.=--If a body falls freely, that is -without meeting a resistance or a retarding influence, its motion will -continually increase. The _increase_ in motion is found to be constant -or uniform during each second. This uniform increase in motion or in -velocity of a falling body gives one of the best illustrations that we -have of uniformly accelerated motion. (Art. 75.) On the other hand, a -body thrown upward has uniformly retarded motion, that is, its -acceleration is downward. The velocity acquired by a falling body in -unit time is called its _acceleration_, or the _acceleration due to -gravity_, and is equal to 32.16 ft. (980 cm.) per second, downward, each -second of time. In one second, therefore, a falling body gains a -velocity of 32.16 ft. (980 cm.) per second, downward. In two seconds it -gains twice this, and so on. - -In formulas, the acceleration of gravity is represented by "_g_" and the -number of seconds by _t_, therefore the formula for finding the -velocity, _V_,[F] of a falling body starting from rest is _V_ = _gt_. In -studying gravity (Art. 89) we learned that its force varies as one moves -toward or away from the equator. (How?) In latitude 38° the acceleration -of gravity is 980 cm. per second each second of time. - - [F] _V_ represents the velocity of a falling body at the end of _t_ - seconds. - -=97. Experimental Study of Falling Bodies.=--To study falling bodies -experimentally by observing the fall of unobstructed bodies is a -difficult matter. Many devices have been used to reduce the motion so -that the action of a falling body may be observed within the limits of a -laboratory or lecture room. The simplest of these, and in some respects -the most satisfactory, was used by Galileo. It consists of an inclined -plane which reduces the effective component of the force of gravity so -that the motion of a body rolling down the plane may be observed for -several seconds. For illustrating this principle a steel piano wire has -been selected as being the simplest and the most easily understood. This -wire is stretched taut across a room by a turn-buckle so that its slope -is about one in sixteen. (See Fig. 80.) Down this wire a weighted pulley -is allowed to run and the distance it travels in 1, 2, 3, and 4 seconds -is observed. From these observations we can compute the distance covered -each second and the velocity at the end of each second. - -[Illustration: FIG. 80.--Apparatus to illustrate uniformly accelerated -motion.] - -In Fig. 63, if _OG_ represents the weight of the body or the pull of -gravity, then the line _OR_ will represent the effective component along -the wire, and _OS_ the non-effective component against the wire. Since -the ratio of the height of the plane to its length is as one to sixteen, -then the motion along the wire in Fig. 80 will be one-sixteenth that of -a falling body. - -=98. Summary of Results.=--The following table gives the results that -have been obtained with an apparatus arranged as shown above. - -In this table, column 2 is the one which contains the results directly -observed by the use of the apparatus. Columns, 3, 4, and 5 are computed -from preceding columns. - - (1) (2) (3) (4) (5) - No. of Total Distance Velocity at Acceleration - seconds distance each second end of second each second - moved - - Per second Per second - 1 30 cm. 30 cm. 60 cm. 60 cm. - 2 120 cm. 90 cm. 120 cm. 60 cm. - 3 270 cm. 150 cm. 180 cm. 60 cm. - 4 480 cm. 210 cm. 240 cm. 60 cm. - -Column 5 shows that the acceleration is uniform, or the same each -second. Column 4 shows that the velocity increases with the number of -seconds or that _V_ = _at_. Column 3 shows that the increase in motion -from 1 second to the next is just equal to the acceleration or 60 cm. -This is represented by the following formula: _s_ = 1/2 _a_(2_t_ - 1). - -The results of the second column, it may be seen, increase as 1:4:9:16, -while the number of seconds vary as 1:2:3:4. That is, _the total -distance covered is proportional to the square of the number of -seconds_. - -This fact expressed as a formula gives: _S_ = 1/2_at_². - -Substituting _g_, the symbol for the acceleration of gravity, for _a_ in -the above formulas, we have: (1) _V_ = _gt_, (2) _S_ = 1/2_gt_², (3) _s_ -= 1/2_g_(2_t_ - 1). - -=99. Laws of Falling Bodies.=--These formulas may be stated as follows -for a body which falls from rest: - -1. The velocity of a freely falling body at the end of any second is -equal to 32.16 ft. per sec. or 980 cm. per second multiplied by the -number of the second. - -2. The distance passed through by a freely falling body during any -number of seconds is equal to the square of the number of seconds -multiplied by 16.08 ft. or 490 cm. - -3. The distance passed through by a freely falling body during any -second is equal to 16.08 feet or 490 cm. multiplied by one less than -twice the number of the second. - - -Important Topics - -1. Falling bodies. - -2. Galileo's experiment. - -3. Acceleration due to gravity. - -4. Laws of falling bodies. - - -Exercises - -1. How far does a body fall during the first second? Account for the -fact that this distance is numerically equal to half the acceleration. - -2. (a) What is the velocity of a falling body at the end of the first -second? (b) How far does it fall during the second second? (c) Account -for the difference between these numbers. - -3. What is the velocity of a falling body at the end of the fifth -second? - -4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during -the sixth second? - -5. (a) What is the difference between the average velocity during the -sixth second and the velocity at the beginning of that second? - -(b) Is this difference equal to that found in the second problem? Why? - -6. A stone dropped from a cliff strikes the foot of it in 5 seconds. -What is the height of the cliff? - -7. Why is it that the increased weight of a body when taken to higher -latitudes causes it to fall faster, while at the same place a heavy body -falls no faster than a light one? - -8. When a train is leaving a station its acceleration gradually -decreases to zero, although the engine continues to pull. Explain. - -9. Would you expect the motion of equally smooth and perfect spheres of -different weight and material to be equally accelerated on the same -inclined plane? Give reason for your answer. Try the experiment. - -10. A body is thrown upward with the velocity of 64.32 ft. per sec. How -many seconds will it rise? How far will it rise? How many seconds will -it stay in the air before striking the ground? - -11. 32.16 feet = how many centimeters? - -12. The acceleration of a freely falling body is constant at any one -place. What does this show about the pull which the earth exerts on the -body? - - -(7) THE PENDULUM - -=100. The Simple Pendulum.=--Any body suspended so as to swing freely to -and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a -single particle of matter suspended by a cord without weight. It is of -course impossible to construct such a pendulum. A small metal ball -suspended by a thread is approximately a simple pendulum. When allowed -to swing its vibrations are made in equal times. This feature of the -motion of a pendulum was first noticed by Galileo while watching the -slow oscillations of a bronze chandelier suspended in the Cathedral in -Pisa. - -[Illustration: FIG. 81--A simple pendulum.] - -=101. Definition of Terms.= _The center of suspension_ is the point -about which the pendulum swings. A _single vibration_ is one swing -across the arc. A _complete_ or _double_ vibration is the swing across -the arc and back again. The time required for a double vibration is -called the _period_. The _length_ of a simple pendulum is approximately -the distance from the point of support to the center of the bob. - -A _seconds pendulum_ is one making a single vibration per second. Its -length at sea-level, at New York is 99.31 cm. or 39.1 in., at the -equator 39.01 in., at the poles 39.22 in. - -A _compound pendulum_ is one having an appreciable portion of its mass -elsewhere than in the small compact body or sphere called a bob. The -ordinary clock pendulum or a meter stick suspended by one end are -examples of compound pendulums. - -The _amplitude_ of a vibration is one-half the arc through which it -swings, for example, the arc _DC_ or the angle _DAC_ in Fig. 81. - -=102. Laws of the Pendulum.=--The following laws may be stated: - -1. The period of a pendulum is not affected by its mass or the material -of which the pendulum is made. - -2. For small amplitudes, the period is not affected by the length of the -arc through which it swings. - -3. The period is directly proportional to the square root of the length. -Expressed mathematically, _t_/_t´_ = {~SQUARE ROOT~}_l_/{~SQUARE ROOT~}_l´_. - -=103. Uses of the Pendulum.=--The chief use of the pendulum is to -regulate motion in clocks. The wheels are kept in motion by a spring or -a weight and the regulation is effected by an escapement (Fig. 82). At -each vibration of the pendulum one tooth of the wheel _D_ slips past the -prong at one end of the escapement _C_, at the same time giving a slight -push to the escapement. This push transmitted to the pendulum keeps it -in motion. In this way, the motion of the wheel work and the hands is -controlled. Another use of the pendulum is in finding the acceleration -of gravity, by using the formula, _t_ = {~GREEK SMALL LETTER PI~}{~SQUARE ROOT~}(_l_/_g_), in which _t_ is the -time in seconds of a single vibration and _l_ the length of the -pendulum. If, for example, the length of the seconds pendulum is 99.31 -cm., then 1 = {~GREEK SMALL LETTER PI~}{~SQUARE ROOT~}(99.31/_g_); squaring both sides of the equation, we -have 1² = {~GREEK SMALL LETTER PI~}²(99.31/_g_), or _g_ = {~GREEK SMALL LETTER PI~}² × 99.31/1² = 980.1 cm. per sec., -per sec. From this it follows that, since the force of gravity depends -upon the distance from the center of the earth, the pendulum may be used -to determine the elevation of a place above sea level and also the shape -of the earth. - - -Important Topics - -1. Simple pendulum. - -2. Definitions of terms used. - -3. Laws of the pendulum. - -4. Uses of the pendulum. - - -Exercises - -1. What is the usual shape of the bob of a clock pendulum? Why is this -shape used instead of a sphere? - -2. Removing the bob from a clock pendulum has what effect on its motion? -Also on the motion of the hands? - -3. How does the expansion of the rod of a pendulum in summer and its -contraction in winter affect the keeping of time by a clock? How can -this be corrected? - -4. Master clocks that control the time of a railway system have a cup of -mercury for a bob. This automatically keeps the same rate of vibration -through any changes of temperature. How? - -5. How will the length of a seconds pendulum at Denver, 1 mile above -sea-level, compare with one at New York? Why? - -[Illustration: FIG. 82--Escapement and pendulum of a clock.] - -6. What is the period of a pendulum 9 in. long? _Note._ In problems -involving the use of the third law, use the length of a seconds pendulum -for _l_, and call its period 1. - -7. A swing is 20 ft. high, find the time required for one swing across -the arc. - -8. A pendulum is 60 cm. long. What is its period? - -9. If in a gymnasium a pupil takes 3 sec. to swing once across while -hanging from a ring, how long a pendulum is formed? - -10. A clock pendulum makes four vibrations a second, what is its -length? - - -Review Outline: Force and Motion - -Force; definition, elements, how measured, units, dyne. - -Graphic Representation; typical examples of finding a component, a -resultant, or an equilibrant. - -Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal -force, momentum, (_M = mv_), reaction, stress and strain. - -Moment of Force; parallel forces, couple, effective and non-effective -component. - -Gravitation; law; gravity, center of; weight. Equilibrium 3 forms; -stability, how increased. - -Falling Bodies; velocity, acceleration, "g," Laws; _V_ = _gt_, _S_ = -(1/2)_gt_² - _s_ = (1/2)_g_(2_t_ - 1). - -Pendulum; simple, seconds, laws (3), _t_ = {~GREEK SMALL LETTER PI~}{~SQUARE ROOT~}(_l_/_g_). - - - - -CHAPTER VI - -WORK AND ENERGY - - -_104. Work._--"Whenever a force moves a body upon which it acts, it is -said to do work upon that body." For example, if a man pushes a -wheelbarrow along a path, he is doing work on it as long as the -wheelbarrow moves, but if the wheelbarrow strikes a stone and the man -continues to push and no motion results, from a scientific point of view -he is then doing no work on it. - -"Work signifies the overcoming of resistance," and unless the resistance -is overcome no work is done. Lifting a weight is doing work on it, -supporting a weight is not, although the latter may be nearly as -tiresome as the former. Work as used in science is a technical term. Do -not attach to it meanings which it has in every-day speech. - -=105. Measurement of Work.=--Work is measured by the product of the -force by the displacement caused in the direction of the force, that is -_W_ = _fs_. Therefore if a unit of force acts through a unit of space, a -unit of work will be done. There are naturally several units of work -depending upon the units of force and space employed. - -_English Work Unit._--If the force of one _pound_ acts through the -distance of one _foot_, a _foot-pound_ of work is done. A foot-pound is -defined as the work done when 1 lb. is lifted 1 ft. against the force of -gravity. - -_Metric Work Unit._--If the force is one _kilogram_ and the distance one -_meter_, _one kilogram-meter_ of work is done. - -_Absolute Work Unit._--If the force of one _dyne_ acts through the -distance of one _centimeter_ a _dyne-centimeter_ of work is done. This -usually is called an i. Other work units are sometimes used depending -upon the force and distance units employed. One, the i, is equal to -10,000,000 ergs or 10{~SUPERSCRIPT SEVEN~} ergs. - - =Problem.=--If a load is drawn 2 miles by a team exerting 500 lbs. - force, how much work is done? - - =Solution.=--Since the force employed is 500 lbs., and the distance - is 2 × 5280 ft., the work done is 500 × 2 × 5280 or 5,280,000 - ft.-lbs. - -=106. Energy.=--In the various cases suggested in the paragraphs upon -work, an agent, a man, an animal or a machine, was mentioned as putting -forth an effort in order to do the work. It is also true that in order -to perform work an agent must employ _energy, or the energy of a body is -its capacity for doing work_. Where an agent does work upon a body, as -in winding up a spring or in lifting a weight, the body upon which the -work has been done may acquire energy by having work done upon it. That -is, it may become able to do work itself upon some other body. For -instance, a lifted weight in falling back to its first position may turn -wheels, or drive a post into the ground against resistance; a coiled -spring may run clock work, strike a blow, or close a door. Hence the -energy, or the capacity for doing work, is often acquired by a body -because work has first been done upon that body. - -=107. Potential Energy.=--The wound up spring may do work because work -has first been done upon it. The lifted weight may also do work because -work has first been done in raising it to its elevated position since in -falling it may grind an object to powder, lift another weight or do some -other kind of work. _The energy that a body possesses on account of its -position or shape and a stress to which it is subjected is called -potential energy._ The potential energy of a body is measured by the -work done in lifting it, changing its shape, or by bringing about the -conditions by which it can do work. Thus if a block of iron weighing -2000 lbs. is lifted 20 ft., it possesses 40,000 ft.-lbs. of potential -energy. It is therefore able to do 40,000 ft.-lbs. of work in falling -back to its first position. If the block just mentioned should fall from -its elevated position upon a post, it could drive the post into the -ground because its motion at the instant of striking enables it to do -work. To compute potential energy you compute the work done upon the -body. That is, _P.E._ = _w_ × _h_ or _f_ × _s_. - -=108. Kinetic Energy.=--_The energy due to the motion of a body is -called kinetic energy_. The amount of kinetic energy in a body may be -measured by the amount of work done to put it in motion. It is usually -computed, however, by using its mass and velocity on striking. To -illustrate, a 100-lb. ball is lifted 16 ft. The work done upon it, and -hence its potential energy, is 1600 ft.-lbs. On falling to the ground -again, this will be changed into kinetic energy, or there will be 1600 -ft.-lbs. of kinetic energy on striking. It will be noted that since -energy is measured by the work it can do, work units are always used in -measuring energy. To compute the kinetic energy of a falling body by -simply using its mass and velocity one proceeds as follows, in solving -the above problem: - - First, find the velocity of the falling body which has fallen 16 - ft. A body falls 16 ft. in _one_ second. In this time it gains a - velocity of 32 ft. per second. Now using the formula for kinetic - energy _K.E._ = _wv_²/(2_g_), we have _K.E._ = 100 × 32 × 32/(2 × - 32) = 1600 ft.-lbs. as before. The formula, _K.E._ = _wv_²/(2_g_), - may be derived in the following manner: - - The kinetic energy of a falling body equals the work done in giving - it its motion, that is, _K.E._ = _w_ × _S_, in which, _w_ = the - weight of the body and _S_ = the distance the body must fall freely - in order to acquire its velocity. The distance fallen by a freely - falling body, _S_, = 1/2_gt_² = _g_²_t_²/(2_g_) (Art. 98, p. 111). - Now, _v_ = _gt_ and _v_² = _g_²_t_². - - Substituting for _g_²_t_², its equal _v_², we have _S_ = - _v_²/(2_g_). Substituting this value of S in the equation _K.E._ = - _w_ × _S_, we have _K.E._ = _wv_²/(2_g_). - - Since the kinetic energy of a moving body depends upon its mass and - velocity and not upon the _direction_ of motion, this formula may - be used to find the kinetic energy of any moving body. Mass and - weight in such problems may be considered numerically equal. - - =Important Topics= - - 1. Work defined. - - 2. Work units, foot-pound, kilogram-meter, erg. - - 3. Energy defined. - - 4. Kinds of energy, potential and kinetic. - - =Problems= - - 1. How much work will a 120-lb. boy do climbing a mountain 3000 ft. - high? Should the vertical or slant height be used? Why? - - 2. In a mine 4000 kg. of coal are lifted 223 meters: how much work - is done upon the coal? What is the kind and amount of energy - possessed by the coal? - - 3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work - has been done upon it? What kind and amount of energy will it have - after falling 16 ft. to the pile? - - 4. A train weighing 400 tons is moving 30 miles per hour. Compute - its kinetic energy. (Change its weight to pounds and velocity to - feet per second.) - - 5. What would be the kinetic energy of the train in problem 4 if it - were going 60 miles per hour? If it were going 90 miles per hour? - How does doubling or trebling the speed of an object affect its - kinetic energy? How does it affect its momentum? - - 6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 - ft. per second? - - 7. Mention as many kinds of mechanical work as you can and show how - each satisfies the definition of work. - - 8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work - is done upon it? - - 9. If the pile driver in problem 8 is dropped upon the head of a - pile which meets an average resistance of 30,000 lbs., how far will - one blow drive it? - - 10. A 40 kg. stone is placed upon the top of a chimney 50 meters - high. Compute the work done in kilogram-meters and foot-pounds. - - (2) POWER AND ENERGY - -=109. Horse-power.=--In computing work, no account is taken of the time -required to accomplish it. But since the time needed to perform an -undertaking is of much importance, the rate of work, or the _power or -activity_ of an agent is an important factor. Thus if one machine can do -a piece of work in one-fifth the time required by another machine, it is -said to have five times the power of the other. Therefore the power of a -machine is _the rate at which it can do work_. James Watt (1736-1819), -the inventor of the steam-engine, in _expressing_ the power of his -engine, used as a unit a _horse-power_. He considered that a horse could -do 33,000 ft.-lbs. of work a minute. This is equal to 550 ft.-lbs. per -second or 76.05 kg.-m. per second. This is too high a value but it has -been used ever since his time. Steam engines usually have their power -rated in horse-power. That is, locomotives produce from 500 to 1500 -horse-power. Some stationary and marine engines develop as high as -25,000 horse-power. The power of an average horse is about 3/4 -horse-power and of a man about 1/7 horse-power when working continuously -for several hours. - -=110. The Watt.=--In the metric system, the erg as a unit of work would -give as a unit of power 1 erg per second. This amount is so small, -however, that a larger unit is usually employed, the practical unit -being 10,000,000 ergs a second, that is, one joule per second. (See Art. -105.) This practical unit is called a _Watt_ after James Watt. The -power of dynamos is usually expressed in kilowatts, a kilowatt -representing 1000 watts. Steam-engines in modern practice are often -rated in kilowatts instead of horse-power. A horse-power is equivalent -to 746 watts, or is nearly 3/4 of a kilowatt. - -=111. Energy. Its Transference and Transformation.= We have considered -energy as the capacity for doing work, and noted the two kinds, -potential and kinetic, and the facility with which one may change into -another. In fact, the transference of energy from one body to another, -and its transformation from one form to another is one of the most -common processes in nature. Take a pendulum in motion, at the _end_ of a -swing, its energy being entirely due to its elevated position is all -_potential_; at the _lowest_ point in its path its energy being entirely -due to its motion is all _kinetic_. The change goes on automatically as -long as the pendulum swings. A motor attached by a belt to a washing -machine is started running. The energy of the motor is transferred by -the belt to the washer where it is used in rubbing and moving the -clothes. - -The heat used in warming a house is usually obtained by burning coal or -wood. Coal is believed to be formed from the remains of plants that grew -in former geologic times. These plants grew through the help of the -radiant energy of the sun. The following are transformations of energy -that have occurred: The radiant energy of sunlight was transformed into -the _chemical_ energy of the plants. This remained as chemical energy -while the plants were being converted into coal, was mined, brought to -the stove or furnace and burned. The burning transformed the chemical -energy into heat energy in which form we use it for warming rooms. Take -the energy used in running a street car whose electrical energy comes -from a waterfall. The energy of the car itself is mechanical. Its -motor, however, receives electrical energy and transforms it into -mechanical. This electrical energy comes along a wire from a dynamo at -the waterfall, where water-wheels and generators transform into -electrical energy the mechanical energy of the falling water. The water -obtained its energy of position by being evaporated by the heat of the -radiant energy of the sun. The vapor rising into the air is condensed -into clouds and rain, and falling on the mountain side, has, from its -elevated position, potential energy. The order of transformation, -therefore, is in this case, radiant, heat, mechanical, electrical, and -mechanical. Can you trace the energy from the sun step by step to the -energy you are using in reading this page? - -=112. Forms of Energy.=--A steam-engine attached to a train of cars -employs its energy in setting the cars in motion, _i.e._, in giving them -kinetic energy and in overcoming resistance to motion. But what is the -source of the energy of the engine? It is found in the coal which it -carries in its tender. But of what kind? Surely not kinetic, as no -motion is seen. It is therefore potential. What is the source of the -energy of the coal? This question leads us back to the time of the -formation of coal beds, when plants grew in the sunlight and stored up -the energy of the sun's heat and light as _chemical_ energy. The sun's -light brings to the earth the energy of the sun, that central storehouse -of energy, which has supplied nearly all the available energy upon the -earth. Five _forms_ of energy are known, viz., mechanical, heat, -electrical, radiant, and chemical. - -=113. Energy Recognized by its Effects.=--Like force, energy is -invisible and we are aware of the forms only by the effects produced by -it. - -We recognize _heat_ by _warming_, by expansion, by pressure. - -We recognize _light_ by _warming_, by its affecting vision. - -We recognize _electrical_ energy by its heat, light, motion, or magnetic -effect. We recognize _mechanical_ energy by the _motion_ that it -produces. We recognize _chemical_ energy by knowing that the source of -energy does not belong to any of the foregoing. - -A boy or girl is able to do considerable work. They therefore possess -energy. In what form does the energy of the body mainly occur? One can -determine this for himself by applying questions to each form of energy -in turn as in Art. 114. - -_114. Source of the Energy of the Human Body._--Is the energy of the -human body mostly heat? No, since we are not very warm. Is it light or -electrical? Evidently not since we are neither luminous nor electrical. -Is it mechanical? No, since we have our energy even when at rest. Is it -chemical? It must be since it is none of the others. Chemical energy is -contained within the molecule. - -It is a form of potential energy and it is believed to be due to the -position of the atoms within the molecule. As a tightly coiled watch -spring may have much energy within it, which is set free on allowing the -spring to uncoil, so the chemical energy is released on starting the -chemical _reaction_. Gunpowder and dynamite are examples of substances -containing chemical energy. On exploding these, heat, light, and motion -are produced. Gasoline, kerosene, and illuminating gas are purchased -because of the potential energy they contain. This energy is set free by -burning or exploding them. - -The source of the energy of our bodies is of course the food we eat. The -energy contained in the food is also chemical. Vegetables obtain their -energy from the sunlight (radiant energy). This is why plants will not -grow in the dark. The available energy is mostly contained in the form -of starch, sugar and oil. Digestion is employed principally to dissolve -these substances so that the blood may absorb them and carry them to the -tissues of the body where they are needed. The energy is set free by -oxidation (burning), the oxygen needed for this being supplied by -breathing. Breathing also removes the carbon dioxide, which results from -the combustion. It is for its energy that our food is mostly required. - -=115. Conservation of Energy.=--In the study of matter we learned that -it is indestructible. Energy is also believed to be indestructible. This -principle stated concisely teaches that _despite the innumerable changes -which energy undergoes the amount in the universe is unchangeable_, and -while energy may leave the earth and be lost as far as we are concerned, -that it exists somewhere in some form. The principle which teaches this -is called the "Conservation of Energy." The form into which energy is -finally transformed is believed to be heat. - - -Important Topics - -1. Power defined. Units. Horse-power. Watt. - -2. Transference and transformations of energy. - -3. Forms of energy; heat, electrical, mechanical, radiant, chemical. - -4. Effects of the several forms of energy. - -5. Energy of the human body. - -6. Conservation of energy. - - -Exercises - -1. A boy weighing 110 lbs. ran up a stairs 10 ft. high, in 4 seconds. -How much work was done? What was his _rate_ of work (foot-pounds per -second)? Express also in horse-power. - -2. A locomotive drawing a train exerts a draw bar pull of 11,000 lbs. -How much work does it do in moving 3 miles? What is its _rate_ of work -if it moves 3 miles in 5 minutes? Express in horse-power.[G] - - [G] The following formula is of assistance in computing - _horse-power_ in problems: H. p. = (lbs. × ft.)/(550 × sec.). - -3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? What -is the rate of work? Express in horse-power, watts and kilowatts. - -4. Trace the energy of a moving railway train back to its source in the -sun. - -5. Why does turning the propeller of a motor boat cause the boat to -move? - -6. Does it require more power to go up a flight of stairs in 5 seconds -than in 10 seconds? Explain. Is more work done in one case than in the -other? Why? - -7. Can 1 man carrying bricks up to a certain elevation for 120 days do -as much work as 120 men carrying up bricks for 1 day? - -8. If the 1 man and 120 men of problem 7 do the same amount of work have -they the same power? Explain. - -9. If 160 cu. ft. of water flow each second over a dam 15ft. high what -is the available power? - -10. What power must an engine have to fill a tank 11 × 8 × 5 ft. with -water 120 ft. above the supply, in 5 minutes? - -11. A hod carrier weighing 150 lbs. carries a load of bricks weighing -100 lbs. up a ladder 30 ft. high. How much work does he do? - -12. How much work can a 4-horse-power engine do in 5 minutes? - -13. Find the horse-power of a windmill that pumps 6 tons of water from a -well 90 ft. deep in 30 minutes. - -14. How many horse-power are there in a waterfall 20 ft. high over which -500 cu. ft. of water pass in a minute? - -15. The Chicago drainage canal has a flow of about 6000 cu. ft. a -second. If at the controlling works there is an available fall of 34 ft. -how many horse-power can be developed? - -16. How long will it take a 10-horse-power pump to fill a tank of 4000 -gallons capacity, standing 300 ft. above the pump? - -17. A boy weighing 162 lbs. climbs a stairway a vertical height of 14 -ft. in 14.6 seconds. How much power does he exert? - -18. The same boy does the same work a second time in 4.2 seconds. How -much power does he exert this time? What causes the difference? - -19. What is a horse-power-hour? a kilowatt-hour? - - -(3) SIMPLE MACHINES AND THE LEVER - -=116. Machines and Their Uses.=--A man, while standing on the ground, -can draw a flag to the top of a pole, by using a rope passing over a -pulley. - -A boy can unscrew a tightly fitting nut that he cannot move with his -fingers, by using a wrench. - -A woman can sew a long seam by using a sewing machine in much less time -than by hand. - -A girl can button her shoes much quicker and easier with a button-hook -than with her fingers. - -These illustrations show some of the reasons why machines are used. In -fact it is almost impossible to do any kind of work efficiently without -using one or more machines. - -=117. Advantages of Machines.=--(a) Many machines make possible an -_increased speed_ as in a sewing machine or a bicycle. - -(b) Other machines exert an _increased force_. A rope and a set of -pulleys may enable a man to lift a heavy object such as a safe or a -piano. By the use of a bar a man can more easily move a large rock. (See -Fig. 83.) - -[Illustration: FIG. 83.--The rock is easily moved.] - -(c) The _direction_ of a force may be changed thus enabling work to be -done that could not be readily accomplished otherwise. As, e.g., the use -of a pulley in raising a flag to the top of a flag pole, or in raising a -bucket of ore from a mine by using a horse attached to a rope passing -over two or more pulleys. (See Fig. 84.) - -(d) _Other agents_ than man or animals _can be used_ such as -electricity, water power, the wind, steam, etc. Fig. 85 represents a -windmill often used in pumping water. - -_A machine is a device for transferring or transforming energy._ It is -usually therefore an instrument for doing work. An electric motor is a -machine since it _transforms_ the energy of the electric current into -motion or mechanical energy, and _transfers_ the energy from the wire to -the driving pulley. - -[Illustration: FIG. 84.--The horse lifts the bucket of ore.] - -=118. A Machine Cannot Create Energy.=--Whatever does work upon a -machine (a man, moving water, wind, etc.) loses energy which is employed -in doing the work of the machine. A pair of shears is a machine since it -transfers energy from the hand to the edges that do the cutting. Our own -bodies are often considered as machines since they both transfer and -transform energy. - -We must keep in mind that _a machine cannot create energy_. The -principle of "Conservation of Energy" is just as explicit on one side as -the other. Just as energy, cannot be destroyed, so energy cannot be -created. A machine can give out no more energy than is given to it. It -acts simply as an agent in transferring energy from one body to -another. Many efforts have been made to construct machines that when -once started will run themselves, giving out more energy than they -receive. Such efforts, called seeking for _perpetual motion_, have never -succeeded. This fact is strong evidence in favor of the principle of the -conservation of energy. - -[Illustration: FIG. 85.--A windmill.] - -=119. Law of Machines.=--When a body receives energy, work is done upon -it. Therefore work is done upon a machine when it receives energy and -the machine does work upon the body to which it gives the energy. In the -operation of a machine, therefore, two quantities of work are to be -considered and by the principle of the conservation of energy, these two -must be equal. _The work done by a machine equals the work done upon it, -or the energy given out by a machine equals the energy received by it._ -These two quantities of work must each be composed of a _force_ factor -and a _space_ factor. Therefore two forces and two spaces are to be -considered in the operation of a machine. The force factor of the work -done on the machine is called the _force_ or _effort_. It is the force -applied to the machine. The force factor of the work done by a machine -is called the _weight or resistance_. It is the force exerted by the -machine in overcoming the resistance and equals the resistance -overcome. - -If _f_ represents the force or effort, and _D_{f}_ the space it acts -through, and _w_ represents the weight or resistance, and _D_{w}_ the -space it acts through, then the law of machines may be expressed by an -equation, _f × D_{f} = w × D_{w}_. That is, _the effort times the -distance the effort acts equals the resistance times the distance the -resistance is moved or overcome_. When the product of two numbers equals -the product of two other numbers either pair may be made the means and -the other the extremes of a proportion. The equation given above may -therefore be expressed _w: f = D_{f}: D_{w}_. Or the resistance is to -the effort as the effort distance is to the resistance distance. The law -of machines may therefore be expressed in several ways. One should keep -in mind, however, that the _same_ law of machines is expressed even -though the form be different. What two ways of expressing the law are -given? - -=120. The Simple Machines.=--There are but six _simple machines_. All -the varieties of machines known are simply modifications and -combinations of the six simple machines. The six simple machines are -more easily remembered if we separate them into two groups of three -each. The first or _lever_ group consists of those machines in which a -part revolves about a fixed axis. It contains the _lever_, _pulley_ and -_wheel and axle_. The second or _inclined plane group_ includes those -having a sloping surface. It contains the _inclined plane_, the _wedge_, -and the _screw_. - -=121. The Lever.=--The _lever_ is one of the simple machines most -frequently used, being seen in scissors, broom, coal shovel, whip, -wheelbarrow, tongs, etc. _The lever consists of a rigid bar capable of -turning about a fixed axis called the fulcrum._ In studying a lever, one -wishes to know what weight or resistance it can overcome when a certain -force is applied to it. Diagrams of levers, therefore, contain the -letters _w_ and _f_. In addition to these, _O_ stands for the fulcrum -on which it turns. By referring to Fig. 86, _a_, _b_, _c_, one may -notice that each of these may occupy the middle position between the -other two. The two forces (other than the one exerted by the fulcrum) -acting on a lever always oppose each other in the matter of changing -rotation. They may be considered as a pair of parallel forces acting on -a body, each tending to produce rotation. - -[Illustration: FIG. 86.--The three classes of levers.] - -=122. Moment of Force.=--The _effectiveness_ of each force may therefore -be determined by computing its _moment_ about the fixed axis (see Art. -84), that is, by multiplying each force by its distance to the fulcrum -or axis of rotation. Let a meter stick have a small hole bored through -it at the 50 cm. mark near one edge, and let it be mounted on a nail -driven into a vertical support and balanced by sliding a bent wire along -it. Suspend by a fine wire or thread a 100 g. weight, 15 cm. from the -nail and a 50 g. weight 30 cm. from the nail, on the other side of the -support. These two weights will be found to balance. When viewed from -this side _A_ (Fig. 87) tends to turn the lever in a clockwise direction -(down at right), _B_ in the counter-clockwise direction (down at left). -Since the lever balances, the forces have equal and opposite effects in -changing its rotation as may also be computed by determining the moment -of each force by multiplying each by its distance from the fulcrum. -Therefore the _effectiveness_ of a force in changing rotation depends -upon the distance from it to the axis as well as upon the magnitude of -the force. - -[Illustration: FIG. 87.--The two moments are equal about _C_. 100 × 15 = -50 × 30.] - -From the experiment just described, the moment of the acting force -equals the moment of the weight or _f × D_{f} = w × D_{w}_, or the -effort times the effort arm equals the weight times the weight arm. This -equation is called the law of the lever. It corresponds to the general -law of machines and may also be written _w: f = D_{f}: D_{w}_. - -=123. Mechanical Advantage.=--A lever often gives an advantage because -by its use one may lift a stone or weight which the unaided strength of -man could not move. If the lever is used in lifting a stone weighing 500 -lbs., the force available being only 100 lbs., then its _mechanical -advantage_ would be 5, the ratio of _w:f_. In a similar way, the -mechanical advantage of any machine is found by finding the ratio of the -resistance or weight to the effort. What must be the relative lengths of -the effort arm and resistance or weight arm in the example just -mentioned? Since the effort times the effort arm equals the weight times -the weight arm, if _f × D_{f} = w × D_{w}_, then _D_{f}_ is five times -_D_{w}_. Hence the mechanical advantage of a lever is easily found by -finding the ratio of the effort arm to the weight arm. - - -Important Topics - -1. Advantage of machines. - -2. Machines cannot create energy. - -3. Law of machines. - -4. Six simple machines. - -5. Lever and principle of moments. - -6. Mechanical advantage of a machine. - - -Exercises - -1. Give six examples of levers you use. - -2. Fig. 88_a_ represents a pair of paper shears, 88_b_ a pair of -tinner's shears. Which has the greater mechanical advantage? Why? -Explain why each has the most effective shape for its particular work. - -[Illustration: FIG. 88.--(_a_) Paper shears. (_b_) Tinner's shears.] - -3. Find examples of levers in a sewing machine. - -4. What would result if, in Art. 122, the 100 g. weight were put 25 cm. -from O and the 50 g. weight 45 cm. from O? Why? Explain using principle -of moments. - -5. How is the lever principle applied in rowing a boat? - -6. When you cut cardboard with shears, why do you open them wide and cut -near the pivot? - -7. In carrying a load on a stick over the shoulder should the pack be -carried near the shoulder or out on the stick? Why? - -8. How can two boys on a see-saw start it without touching the ground? - -9. In lifting a shovel full of sand do you lift up with one hand as hard -as you push down with the other? Why? - -[Illustration: FIG. 89.--The hammer is a bent lever. What is its -mechanical advantage?] - -10. Why must the hinges of a gate 3 ft. high and 16 ft. wide be stronger -than the hinges of a gate 16 ft. high and 3 ft. wide? - -11. When one sweeps with a broom do the hands do equal amounts of work? -Explain. - -12. A bar 6 ft. long is used as a lever to lift a weight of 500 lbs. If -the fulcrum is placed 6 in. from the weight, what will be the effort -required? Note: two arrangements of weight, fulcrum and effort are -possible. - -13. The handle of a hammer is 12 in. long and the claw that is used in -drawing a nail is 2.5 in. long. (See Fig. 89.) A force of 25 lbs. is -required to draw the nail. What is the resistance of the nail? - -14. The effective length of the head of a hammer is 2 in. The handle is -15 in. long and the nail holds in the wood with a force of 500 lbs. Only -60 lbs. of force is available at the end of the handle. What will be the -result? - -15. If an effort of 50 lbs. acting on a machine moves 10 ft., how far -can it lift a weight of 1000 lbs.? - -16. A bar 10 ft. long is to be used as a lever. The weight is kept 2 ft. -from the fulcrum. What different levers can it represent? - -17. The effort arm of a lever is 6 ft., the weight arm 6 in. How long -will the lever be? Give all possible answers. - -18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between -them. Where should the weight be placed in order that one boy may carry -one and one-fourth times as much as the other? - - -(4) THE WHEEL AND AXLE AND THE PULLEY - -=124. The Wheel and Axle.=--1. One of the simple machines most commonly -applied in compound machines is the _wheel_ and _axle_. It consists of a -wheel _H_ mounted on a cylinder _Y_ so fastened together that both turn -on the same axis. In Fig. 90, ropes are shown attached to the -circumferences of the wheel and axle. Sometimes a hand wheel is used as -on the brake of a freight or street car, or simply a crank and handle is -used, as in Fig. 91. The _capstan_ is used in moving buildings. -Sometimes two or three wheels and axles are geared together as on a -derrick or crane as in Fig. 92. - -[Illustration: FIG. 90.--The wheel and axle.] - -[Illustration: FIG. 91.--Windlass used in drawing water from a well.] - -[Illustration: FIG. 92.--A portable crane.] - -[Illustration: FIG. 93.--The wheel and axle considered as a lever.] - -[Illustration: FIG. 94.--View of transmission gears in an automobile. 1, -Drive gear; 2, High and intermediate gear; 3, Low and reverse gear; 4, -8, Reverse idler gears; 5, 6, 7, Countershaft gears. (_Courtesy of the -Automobile Journal_.)] - -[Illustration: FIG. 95.--Reducing gear of a steam turbine.] - -Fig. 93 is a diagram showing that the wheel and axle acts like a lever. -The axis _D_ is the fulcrum, the effort is applied at _F_, at the -extremity of a radius of the wheel and the resisting weight _W_ at the -extremity of a radius of the axle. Hence, if _D_{f}_, the effort -distance, is three times _D_{w}_, the weight distance, the weight that -can be supported is three times the effort. Here as in the lever, _f × -D_{f} = w × D_{w}_, or _w:f = D_{f}:D_{w}_, or _the ratio of the weight -to the effort equals the ratio of the radius of the wheel to the radius -of the axle_. This is therefore the mechanical advantage of the wheel -and axle. Since the diameters or circumferences are in the same ratio as -the radii these can be used instead of the radii. Sometimes, when -_increased speed_ instead of increased force is desired, the radius of -the wheel or part to which power is applied is less than that of the -axle. This is seen in the bicycle, buzzsaw, and blower. Sometimes geared -wheels using the principle of the wheel and axle are used to reduce -speed, as in the _transmission_ of an automobile (see Fig. 94), or the -reducing gear of a steam turbine. (See Figs. 95 and 293.) - -A _bevel gear_ is frequently used to change the direction of the force. -(See Fig. 94.) - -[Illustration: FIG. 96.--A single movable pulley.] - -[Illustration: FIG. 97.--Block and tackle.] - -[Illustration: FIG. 98.--The fixed pulley considered as a lever.] - -[Illustration: FIG. 99.--The movable pulley considered as a lever.] - -=125. The Pulley.=--The _pulley_ consists of a wheel turning on an axis -in a frame. The wheel is called a sheave and the frame a block. The rim -may be smooth or grooved. The grooved rim is used to hold a cord or -rope. One use of the pulley is to change the _direction_ of the acting -force as in Fig. 84, where pulley _B_ changes a horizontal pull at _H_ -to a downward force and pulley _A_ changes this into an upward force -lifting the weight _W_. These pulleys are fixed and simply change the -direction. Without considering the loss by friction, the pull at _W_ -will equal that at _F_. Sometimes, a pulley is attached to the weight -and is lifted with it. It is then called a _movable pulley_. In Fig. 96 -the _movable pulley_ is at _P_, a fixed pulley is at _F_. When _fixed -pulleys_ are used, a single cord runs through from the weight to the -effort, so that if a force of 100 lbs. is applied by the effort the same -force is received at the weight. But with movable pulleys several -sections of cord may extend upward from the weight each with the force -of the effort upon it. By this arrangement, a weight several times -larger than the effort can be lifted. Fig. 97 represents what is called -a _block and tackle_. If a force of 50 lbs. is exerted at _F_, each -section of the rope will have the same tension and hence the six -sections of the rope will support 300 lbs. weight. The _mechanical -advantage of the pulley_ or the _ratio of the weight_ to the effort, -therefore, _equals the number of sections of cord supporting the -weight_. The fixed pulley represents a lever, see Fig. 98, where the -effort and weight are equal. In the movable pulley, the fulcrum (see -Fig. 99) is at _D_; the weight, _W_, is applied at the center of the -pulley and the effort at _F_. The weight distance, _D_{w}_, is the -radius, and the effort distance, _D_{f}_, is the diameter of the -pulley. Since _W/F = D_{f} / D_{w} = 2_ in a movable pulley, the weight -is twice the effort, or its mechanical advantage is 2. - - -Important Topics - -1. Wheel and Axle, Law of Wheel and Axle. - -2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley. - - -Exercises - -1. Why do door knobs make it easier to unlatch doors? What simple -machine do they represent? Explain. - -2. What combination of pulleys will enable a 160-lb. man to raise a -900-lb. piano? - -3. When you pull a nail with an ordinary claw hammer, what is the effort -arm? the resistance arm? - -4. How much work is done by the machine in problem 2 in lifting the -piano 20 ft.? How much work must be done upon the machine to do this -work? - -5. The pilot wheel of a boat has a diameter of 60 in.; the diameter of -the axle is 6 in. If the resistance is 175 lbs., what force must be -applied to the wheel? - -6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see -Fig. 110) having a barrel 9 in. in diameter. The circle described by the -hand-spikes is {13 1/2} ft. in diameter. How much force must each man -exert? - -[Illustration: FIG. 100.--The Capstan.] - -7. A bicycle has a 28-in. wheel. The rear sprocket is 3 in. in -diameter,[H] the radius of the pedal crank is 7 in.; 24 lbs. applied to -the pedal gives what force on the rim of the wheel? What will be the -speed of the rim when the pedal makes one revolution a second? - - [H] Consider the diameter of the front sprocket as 6 inches. - -8. Measure the diameters of the large and small pulleys on the -sewing-machine at your home. What mechanical advantage in number of -revolutions does it give? Verify your computation by turning the wheel -and counting the revolutions. - -9. What force is required with a single fixed pulley to raise a weight -of 200 lbs.? How far will the effort move in raising the weight 10 ft.? -What is the mechanical advantage? - -10. In the above problem substitute a single movable pulley for the -fixed pulley and answer the same questions. - -11. What is the smallest number of pulleys required to lift a weight of -600 lbs. with a force of 120 lbs.? How should they be arranged? - -12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys -employing 3 sections of rope. What is the force required? - -13. Name three instances where pulleys are used to do work that -otherwise would be difficult to do. - -14. Draw a diagram for a set of pulleys by means of which 100 lbs. can -lift 400 lbs. - - -(5) THE INCLINED PLANE. EFFICIENCY - -=126. Efficiency.=--The general law of machines which states that the -work done by a machine equals the work put into it requires a -modification, when we apply the law in a practical way, for the reason -that in using any machine there is developed more or less friction due -to parts of the machine rubbing on each other and to the resistance of -the air as the parts move through it. Hence the statement of the law -that accords with actual working conditions runs somewhat as follows: -_The work put into a machine equals the useful work done by the machine -plus the wasted work done by it._ The _efficiency_ of a machine is the -ratio of the _useful_ work done by it to the _total_ work done on the -machine. If there were no friction or wasted work, the efficiency would -be perfect, or, as it is usually expressed, would be 100 per cent. -Consider a system of pulleys into which are put 600 ft.-lbs. of work. -With 450 ft.-lbs. of useful work resulting, the efficiency would be 450 -÷ 600 = {3/4}, or 75 per cent. In this case 25 per cent. of the work -done on the machine is wasted. In a simple lever the friction is slight -so that nearly 100 per cent. efficiency is often secured. - -Some forms of the wheel and axle have high efficiencies as in bicycles -with gear wheels. Other forms in which ropes are employed have more -friction. Pulleys have sometimes efficiencies as low as 40 per cent. -when heavy ropes are used. - -=127. Inclined Plane.=--We now come to a type of _simple machine of -lower efficiency_ than those previously mentioned. These belong to the -inclined plane group, which includes the inclined plane (see Fig. 101), -the wedge and the screw. They are extensively used, however, -notwithstanding their low efficiency, on account of often giving a high -mechanical advantage. The _relation between these machines may be easily -shown_, as the _wedge_ is obviously _a double inclined plane_. In Art. -82 it is shown that the effort required to hold a weight upon an -inclined plane is to the _weight_ supported as the _height_ of the plane -is to its _length_. - -[Illustration: FIG. 101.--An inclined plane.] - -Or while the weight is being lifted the vertical height _BC_, the effort -has to move the length of the plane _AC_. Since by the law of machines -the effort times its distance equals the weight times its distance, or -the weight is to the effort as the effort distance is to the weight -distance, therefore the mechanical advantage of the inclined plane is -the ratio of the length to the height of the inclined plane. - -_Inclined planes_ are used to raise heavy objects short distances, as -barrels into a wagon, and iron safes into a building. Stairways are -inclined planes with steps cut into them. - -=128. The Wedge.=--Wedges are used to separate objects, as in splitting -wood (see Fig. 102), cutting wood, and where great force is to be -exerted for short distances. An axe is a wedge, so is a knife. A fork -consists of several round wedges set in a handle. The edge of any -cutting tool is either an inclined plane or a wedge. Our front teeth are -wedges. Numerous examples of inclined planes may be seen about us. - -No definite statement as to the mechanical advantage of the wedge can be -given as the work done depends largely on friction. The force used is -generally applied by blows on the thick end. In general, the longer the -wedge for a given thickness the greater the mechanical advantage. - -[Illustration: FIG. 102.--One use of the wedge.] - -=129. The Screw.=--The screw is a cylinder around whose circumference -winds a spiral groove. (See Fig. 103.) The raised part between the two -adjacent grooves is the =thread= of the screw. The screw turns in a -block called a =nut=, within which is a spiral groove and thread exactly -corresponding to those of the screw. The distance between two -consecutive threads measured parallel to the axis is called the =pitch= -of the screw. (See Fig. 104.) If the thread winds around the cylinder -ten times in the space of 1 in., the screw is said to have ten threads -to the inch, the pitch being {1/10} in. The screw usually is turned by -a lever or wheel with the effort applied at the end of the lever, or at -the circumference of the wheel. While the effort moves once about the -circumference of the wheel the weight is pushed forward a distance equal -to the distance between two threads (the pitch of the screw). The work -done by the effort therefore equals _F × 2{~GREEK SMALL LETTER PI~}r_, _r_ being the radius of -the wheel, and the work done on the weight equals _W × s_, _s_ being the -pitch of the screw. By the law of machines _F × 2{~GREEK SMALL LETTER PI~}r = W × s_ or _W / F = -(2{~GREEK SMALL LETTER PI~}r) / s_. Therefore the mechanical advantage of the screw equals -_(2{~GREEK SMALL LETTER PI~}r) / s_. Since the distance the weight moves is small compared to -that the power travels, there is a great gain in force. The screw is -usually employed where _great force_ is to be exerted through small -distances as in the vise (Fig. 105) the jack screw (Fig. 106), screw -clamps, to accurately measure small distances as in the micrometer (Fig. -107) and spherometer, and to lessen the motion in speed-reducing -devices. The worm gear (Fig. 108) is a modification of the screw that is -sometimes used where a considerable amount of speed reduction is -required. - -[Illustration: FIG. 103.--The screw is a spiral inclined plane.] - -[Illustration: FIG. 104.--The pitch is _S_.] - -[Illustration: FIG. 105.--A vise.] - -[Illustration: FIG. 106.--A jack screw.] - -[Illustration: FIG. 107.--A micrometer screw.] - -[Illustration: FIG. 108.--This large worm-wheel is a part of the -hoisting mechanism employed for the lock gates of the Sault Ste. Marie -Canal.] - - -Important Topics - -1. Efficiency of machines. - -2. The inclined plane, wedge and screw. Applications. - - -Exercises - -1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a -wagon 3 ft. high. Find the force required parallel to the incline. - -2. How long a plank will be needed to roll an iron safe weighing 1-1/2 -tons into a wagon 3 ft. high using a pull of 600 lbs. parallel to the -incline. - -3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb. -barrel from rolling down an inclined plane. What is the ratio of the -length to the height of the plane? - -4. A man can push with a force of 150 lbs. and wishes to raise a box -weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use? - -5. The radius of the wheel of a letter press is 6 in., the pitch of its -screw is 1/4 in. What pressure is produced by a force of 40 lbs.? - -6. The pitch of a screw of a vice is 1/4 in., the handle is 1 ft. long. -what pressure can be expected if the force used is 100 lbs.? - -7. A jackscrew is used to raise a weight of 2 tons. The bar of the -jackscrew extends 2 ft. from the center of the screw. There are two -threads to the inch. Find the force required. - - -(6) FRICTION, ITS USES AND LAWS - -=130. Friction.=--Although often inconvenient and expensive, requiring -persistent and elaborate efforts to reduce it to a minimum, friction has -its uses, and advantages. Were it not for friction between our shoes and -the floor or sidewalk, we could not keep our footing. _Friction is the -resistance that must be overcome when one body moves over another._ It -is of two kinds, _sliding_ and _rolling_. If one draws a block and then -a car of equal weight along a board, the force employed in each case -being measured by a spring balance, a large difference in the force -required will be noticed, showing how much less rolling friction is than -sliding friction. - -=131. Ways of Reducing Friction.=--(a) Friction is often caused by the -minute projections of one surface sinking into the depressions of the -other surface as one moves over the other. It follows, therefore, that -if these projections could be made as small as possible that friction -would be lessened. Consequently _polishing_ is one of the best means for -reducing friction. In machines all moving surfaces are made as smooth as -possible. In different kinds of materials these little ridges and -depressions are differently arranged. (b) In Fig. 109 the friction -between _R_ and _S_ would be greater than between _R_ and _T_. In _R_ -and _S_ the surfaces will fit closer together than in _R_ and _T_. The -_use of different materials will reduce friction_. The iron axles of car -wheels revolve in bearings of brass. Jewels are used in watches for the -same reason. (c) Another very common method of reducing friction is by -the use of _lubricants_. The oil or grease used fills up the -irregularities of the bearing surfaces and separates them. _Rolling -friction_ is frequently substituted for sliding friction by the use of -ball and roller bearings. These are used in many machines as in -bicycles, automobiles, sewing machines, etc. (See Fig. 110.) - -[Illustration: FIG. 109.--The friction between _R_ and _S_ is greater -than between _R_ and _T_.] - -=132. Value of Friction.=--_Friction always hinders motion_ and whenever -one body moves over or through another the energy used in overcoming the -friction is transformed into heat which is taken up by surrounding -bodies and usually lost. Friction is therefore the great obstacle to -perfect efficiency in machines. Friction, however, like most afflictions -_has its uses_. We would find it hard to get along without it. Without -friction we could neither walk nor run; no machines could be run by -belts; railroad trains, street cars, in fact all ordinary means of -travel would be impossible, since these depend upon friction between the -moving power and the road for propulsion. - -[Illustration: FIG. 110.--Timken roller bearings. As used in the front -wheel of an automobile.] - -=133. Coefficient of Friction.=--The ratio between the friction when -motion is just starting and the force pushing the surfaces together is -called the _coefficient of friction_. - -If the block in Fig. 111 is drawn along the board with uniform motion, -the reading of the spring balances indicates the amount of friction. -Suppose the friction is found to be 500 g., and the weight of the block -to be 2000 g. Then the coefficient of friction for these two substances -will be {500/2000} = {1/4}, or 25 per cent. - -=134. Laws of Friction, Law I.=--_The friction when motion is occurring -between two surfaces is proportional to the force holding them -together._ Thus if one measures the friction when a brick is drawn along -a board, he will find that it is doubled if a second brick is placed on -the first. On brakes greater pressure causes greater friction. If a rope -is drawn through the hands more pressure makes more friction. - -[Illustration: FIG. 111.--A method for testing the friction between -surfaces.] - -=Law II.=--_Friction is independent of the extent of surface in -contact._ Thus a brick has the same friction drawn on its side as on its -edge, since, although the surface is increased, the weight is unchanged. - -=Law III.=--Friction is greatest at starting, but after starting is -practically the same for all speeds. - -=135. Fluid Friction.=--When a solid moves through a fluid, as when a -ship moves through the water or railroad trains through the air, the -resistance encountered is not the same as with solids but increases with -the square of the velocity for slow speeds and for high speeds at a -higher rate. This is the reason why it costs so much to increase the -speed of a fast train, since the resistance of the air becomes the -prominent factor at high speeds. The resistance to the motion of a ship -at high speed is usually considered to increase as the cube of the -velocity so that to double the speed of a boat its driving force must be -eight times as great. - - -Important Topics - -1. Friction: two kinds; sliding and rolling. - -2. Four ways of reducing friction. - -3. Uses of friction. - -4. Coefficient of friction. Three laws of friction. - -5. Fluid friction. - - -Exercises - -1. How long must an inclined plane be which is 10 meters high to enable -a car weighing 2000 kg. to be pushed up its length by a force of 100 kg. -parallel to the incline? - -2. State how and where friction is of use in the operation of the -inclined plane, the wedge, the screw, the wheel and axle. - -3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is placed -18 in. from the axis of the wheel, what force placed at the end of the -handles will be required to lift it? - -4. A jackscrew has 3 threads to the inch, and the lever used to turn it -is 4 ft. long. If the efficiency of the screw is 60 per cent., what -force must be applied to raise a load of 5 tons? - -5. In problem 4 how far must the force move in raising the weight 3 in. -Compute the work done upon the weight, the work done by the power and -the efficiency of the machine from these two amounts of work. - -6. What simple machines are represented in a jackknife, a -sewing-machine, a screw-driver, a plane, a saw, a table fork? - -7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. How -much useful work does he do? - -8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much useless -work does he do in taking 30 trips to carry up the bricks of problem 7? -What is his efficiency? - -9. If the laborer hoists the brick of problem 7 in a bucket weighing 50 -lbs., using a fixed pulley and rope, what is the useless work done if it -takes 12 trips to carry up the brick? What is the efficiency of the -device? - -10. The efficiency of a set of pulleys is 70 per cent. How much force -should be applied if acting through 100 ft. it is to raise a load of 400 -lbs. 20 ft.? - -11. The spokes of the pilot wheel of a motor-boat are 1 ft. long, the -axle around which the rudder ropes are wound is 3 in. in diameter. What -effort must be applied if the tension in the ropes is 50 lbs.? - -12. Why are the elevated railway stations frequently placed at the top -of an incline, the tracks sloping gently away in both directions? - -13. The screw of a press has 4 threads to the inch and is worked by a -lever of such length that an effort of 25 lbs. produces a force of 2 -tons. What is the length of the lever? - -14. It takes a horizontal force of 10 lbs. to draw a sled weighing 50 -lbs. along a horizontal surface. What is the coefficient of friction? - -15. The coefficient of rolling friction of a railroad train on a track -is 0.009. What pull would an engine have to exert to haul a train -weighing 1000 tons along a level track? - -16. How heavy a cake of ice can be dragged over a floor by a horizontal -force of 20 lbs., if the coefficient of friction is 0.06? - -17. The coefficient of friction of iron on iron is 0.2. What force can a -switch engine weighing 20 tons exert before slipping? - -18. Using a system of pulleys with a double movable block a man weighing -200 lbs. is just able to lift 600 lbs. What is the efficiency of the -system? - -19. What is the horse-power of a pump that can pump out a cellar full of -water 40 ft. × 20 ft. by 10 ft. deep, in 30 minutes? - -20. How many tons of coal can a 5 horse-power hoisting engine raise in -30 minutes from a barge to the coal pockets, a height of 50 ft.? - - -(7) WATER POWER - -=136. Energy of Falling Water.=--The energy of falling and running water -has been used from the earliest times for developing power and running -machinery. The energy is derived from the action of the moving water in -striking and turning some form of _water-wheel_, several varieties of -which are described below. - -=The Overshot Wheel.=--The overshot wheel (Fig. 112) is turned by the -weight of the water in the buckets. It was formerly much used in the -hilly and mountainous sections of this country for running sawmills and -grist mills as it is very easily made and requires only a small amount -of water. Its efficiency is high, being from 80 to 90 per cent., the -loss being due to friction and spilling of water from the buckets. To -secure this high efficiency the overshot wheel must have a diameter -equal to the height of the fall which may be as much as 80 or 90 ft. - -[Illustration: FIG. 112.--Overshot water wheel.] - -[Illustration: FIG. 113.--Undershot water wheel.] - -[Illustration: FIG. 114.--Diagram illustrating the principle of the -Pelton wheel.] - -=The Undershot Wheel.=--The old style undershot wheel (Fig. 113) is used -in level countries, where there is little fall, often to raise water for -irrigation. Its efficiency is very low, seldom rising more than 25 per -cent. The principle of the undershot wheel, however, is extensively used -in the water motor and the Pelton wheel (Fig. 114). In these the water -is delivered from a nozzle in a jet against the lower buckets of the -wheel. They have an efficiency of about 80 per cent. and are much used -in cities for running small machines, washing machines, pipe organ -blowers, etc., and in mountainous districts where the head is great. - -[Illustration: FIG. 115.--Diagram of a hydro-electric power house -showing a vertical turbine _A_ with penstock _B_ and tail race _C_.] - -[Illustration: FIG. 116.--The outer case of a turbine showing the -mechanism for controlling the gates.] - -[Illustration: FIG. 117.--Inner case of a turbine showing the gates and -the lower end of the runner within.] - -[Illustration: FIG. 118.--The runner of a turbine.] - -[Illustration: FIG. 119.--Turbine and generator of the Tacoma -hydro-electric power plant.] - -=137. The Turbine.=--The turbine is now used more than any other form of -water-wheel. It was invented in 1827 by De Fourneyron in France. It can -be used with a small or large amount of water, the power depending on -the head (the height of the water, in the reservoir above the wheel). It -is the most efficient type of water-wheel, efficiencies of 90 per cent. -often being obtained. The wheel is entirely under water (Fig. 115). It -is enclosed in an outer case (Fig. 116) which is connected with the -reservoir by a penstock or pipe and is always kept full of water. The -wheel itself is made in two parts, a rotating part called the runner -(see Fig. 118) and an inner case (Fig. 117) with gates that regulate -the amount of water entering the wheel. This case has blades curved so -that the water can strike the curved blades of the rotating part (Fig. -118) at the angle that is best adapted to use the energy of the water. -The water then drops through the central opening into the tail race -below (see Fig. 115). The energy available is the product of the weight -of the water and the head. The turbine is extensively used to furnish -power for generating electricity at places where there is a sufficient -fall of water. The electrical energy thus developed is transmitted from -50 to 200 miles to cities where it is used in running street cars, -electric lighting, etc. Turbines can be made to revolve about either -vertical or horizontal axes. Fig. 119 represents a _horizontal_ water -turbine connected to a dynamo. Compare this with the _vertical_ turbine -in Fig. 115. - - -Exercises - -1. Does a person do more work when he goes up a flight of stairs in 5 -seconds than when he goes up in 15 seconds? Explain. - -2. A motorcycle has a 4 horse-power motor and can go at a rate of 50 -miles per hour. Why cannot 4 horses draw it as fast? - -3. What is the efficiency of a motor that is running fast but doing no -useful work? - -4. What horse-power can be had from a waterfall, 12 ft. high, if 20 cu. -ft. of water pass over it each second? - -5. What is the horse-power of a fire engine if it can throw 600 gallons -of water a minute to a height of 100 ft.? - -6. Why are undershot wheels less efficient than the overshot wheel or -turbine? - -7. A revolving electric fan is placed on the stern of a boat. Does the -boat move? Why? Place the fan under water. Does the boat now move? Why? - -8. Why does an electric fan produce a breeze? - -9. Explain the action of the bellows in an organ. - -10. At Niagara Falls the turbines are 136 ft. below the surface of the -river. Their average horse-power is 5000 each. 430 cu. ft. of water each -second pass through each turbine. Find the efficiency. - -11. At Laxey on the Isle of Man is the largest overshot wheel now in -use. It has a horse-power of 150, a diameter of 72.5 ft., a width of 10 -ft., and an efficiency of 85 per cent. How many cubic feet of water pass -over it each second? - -12. The power plant at the Pikes Peak Hydro-electric Company utilizes a -head of 2150 ft., which is equal to a pressure of 935 lbs. per square -inch, to run a Pelton wheel. If the area of the nozzle is 1 sq. in. and -the jet has a velocity of 22,300 ft. per minute, what is the horse-power -developed if the efficiency is 80 per cent.? - -13. A test made in 1909 of the turbines at the Centerville power house -of the California Gas and Electric Corporation showed a maximum -horse-power of 9700, speed 400 r.p.m. under a head of 550 ft. The -efficiency was 86.25 per cent. How many cubic feet of water passed -through the turbines each second? - -14. The turbine in the City of Tacoma Power Plant (see Fig. 120) uses a -head of 415 ft. 145 cu. ft. a second pass through the turbine. Calculate -the horse-power. - -15. In problem 14, what is the water pressure per square inch at the -turbine? - -16. The power plant mentioned in problem 13 develops 6000 kw. What is -the efficiency? - - -Review Outline: Work and Energy - -Work; how measured, units, foot-pound, kilogram meter, erg. - -Energy; how measured, units, potential, _P.E._ = _w × h_, or _f × s_. -Kinetic = _(wv²)/(2g)_. - -Power; how measured, units, horse power, watt, 5 forms of energy, -conservation. H.p. = (lbs. × ft.)/(550 × sec.). - -Machines; 6 simple forms, 2 groups, advantages, uses, Law: _W × D_{w}_ = -_F × D_{f}_. - -Lever; moments, mechanical advantage, uses and applications. - -Wheel and Axle and Pulley; common applications, mechanical advantage. - -Inclined Plane, Wedge, and Screw; mechanical advantage and efficiency. - -Friction; uses, how reduced, coefficient of, laws (3). - -Water Wheels; types, efficiency, uses. - - - - -CHAPTER VII - -HEAT, ITS PRODUCTION AND TRANSMISSION - - -(1) SOURCES AND EFFECTS OF HEAT - -=138. Importance of the Study of Heat.=--Heat is brought to our -attention through the sensations of heat and cold. In winter, we warm -our houses and prevent the escape of heat from them as much as possible. -In summer we endeavor to keep our living rooms cool and our bodies from -being overheated. - -A clear understanding of the several _sources_, _effects_, and _modes of -transferring_ heat is of importance to everyone living in our complex -civilization, especially when we consider the multitudes of objects that -have as their principal use the _production, transfer or utilization_ of -heat. - -=139. Principal Sources of Heat.=--_First_ and most important is the -_Sun_, which is continually sending to us _radiant energy_ in the form -of light and heat waves. These warm the earth, make plants grow, -evaporate water, besides producing many other important effects. - -_Second_, _chemical energy_ is often transformed into heat. One has but -to think of the heat produced by burning coal, wood, oil, and gas, to -recognize the importance of this source. Chemical energy is also the -source of the heat produced within our bodies. The action of quicklime -and water upon each other produces much heat. This action is sometimes -employed during balloon trips as a means of warming things. - -_Third_, _Electrical Energy_.--In many cities electric cars are heated -by the electric current. We have all heard of electric toasters and -other devices for heating by electricity. _Electric_ light is produced -by the heating of some material to incandescence by an electric current. -The _electric furnace_ has a wide application in the preparation and -refining of metals. - -[Illustration: FIG. 120.--Boy-scout method of making fire by friction.] - -_Fourth_, heat is also produced whenever _mechanical energy_ of motion -is overcome, whether it be by _friction_, _concussion_, or -_compression_. Friction _always_ results in the production of heat, as -when we warm our hands by rubbing them together. When friction is -excessive, such as in the case of a heavy bearing not properly oiled, -the bearing may get very hot. This is the cause of the "hot box" on a -railway car. Friction may produce heat enough to set wood on fire. Some -fires in mills are believed to be due to this cause. Every _boy scout_ -must learn how to produce fire by friction. (See Fig. 120.) _Concussion_ -may be illustrated by the heating of a piece of metal by hammering it, -while the compression of a gas always makes it warmer, as those who have -used a bicycle pump have observed. The production of heat by compressing -a gas is illustrated by the "fire syringe" (Fig. 121). This consists of -a glass tube with a tightly fitted piston. A sudden compression of the -air contained may ignite a trace of carbon bisulfid vapor. - -[Illustration: FIG. 121.--A fire syringe.] - -The _interior of the earth_ is hot, but its heat seldom gets to the -surface except at _hot springs_ and _volcanoes_. - -=140. The Effects of Heat.=--There are five important changes produced -by heat: (a) change of _size_, (b) change of _temperature_, (c) change -of _state_, as the melting of ice or evaporating of water, (d) -_chemical_ change, as the charring of sugar when it is overheated, and -(e) _electrical_ change. This is illustrated by the production of an -electric current, by the heating of the junction of two different -metals. A thermo-electric generator (see Fig. 122) has been constructed -upon this principle and works successfully. - -[Illustration: FIG. 122.--A thermo-electric generator.] - - -Important Topics - -1. Importance of a study of heat. - -2. Four sources of heat. - -3. Five effects of heat. - -4. Examples of each. - -5. Illustrations of transformation of energy which involve heat. - - -Exercises - -1. Write a list of the _sources_ of heat in the order of their -importance to you. State why each is important to you. - -2. Which _three_ of the _effects_ of heat do _you_ make most use of? -Explain what use you make of each of these effects. - -3. Which of the forms of energy can be transformed into heat? How in -each case? - -4. Into what other forms of energy may heat be transformed? Name the -device or process used in each case. - -5. What five different commodities are purchased by people in your -neighborhood for the production of heat? Which of these costs least for -the amount of heat furnished? Which is most expensive? How do you -determine these answers? - -6. Why do many people buy heat in an expensive form, as in using an -electric toaster, when they can obtain it in a cheaper form by burning -gas or coal? - -7. How many of the five effects of heat have you observed outside of -school? - - -(2) TEMPERATURE AND EXPANSION - -=141. Heat and Temperature.=--We should now clearly distinguish between -the terms, _heat_ and _temperature_. Heat is _a form of energy -consisting of molecular motion_. The temperature of a body is its -_degree of hotness_. The _amount of heat_ present in a body and its -_temperature_ are very different things. The temperature refers to the -intensity of the heat in the body. A quart of water and a red hot iron -ball may contain _equal amounts_ of heat, although the ball has a _much -higher temperature_ than the water. A cup of boiling water will have the -same temperature as a tank full of boiling water, but the tank will -contain more heat. Every one knows that it will take longer to boil a -kettle full of water than a cupful. A hot-water bag, holding 2 quarts of -water will give off heat longer than a 1-quart bag, both being filled -with water at the same temperature. To put it in another way, more work -is done in heating a large amount of water, than a small amount through -the same change of temperature. - -=142. Units of Heat and Temperature.=--There are two common units for -measuring heat: the _Calorie_ and the _British thermal unit_. The -_calorie is the amount of heat required to raise the temperature of a -gram of water one centigrade degree_. The British thermal unit is _the -amount of heat required to raise the temperature of one pound of water -one Fahrenheit degree_. One of the units plainly belongs to the metric -system, the other to the English. - -An instrument for measuring temperature is called a _thermometer_. -Various scales are placed upon thermometers. The two thermometer scales -most commonly used in this country are the _Centigrade_ and the -_Fahrenheit_. The _Fahrenheit thermometer scale_ has the temperature of -melting ice marked 32°. The boiling point or steam temperature of pure -water under standard conditions of atmospheric pressure is marked 212° -and the space between these two fixed points is divided into 180 parts. - -The centigrade thermometer scale has the same fixed points marked 0 and -100 and the space between divided into 100 parts. (See Fig. 123.) The -centigrade scale is the one used by scientists everywhere. - -[Illustration: FIG. 123.--Comparison of centigrade and Fahrenheit -scales.] - -=143. Comparison of Thermometer Scales.=--It is often necessary to -express in centigrade degrees a temperature for which the Fahrenheit -reading is given or _vice versa_. Since there are 180 Fahrenheit degrees -between the "fixed points" and 100 centigrade degrees, the Fahrenheit -degrees are smaller than the centigrade, or 1°F. = 5/9°C. and 1°C. = -9/5°F. One must also take into account the fact that the melting point -of ice on the Fahrenheit scale is marked 32°. Hence the following rule: -To change a Fahrenheit reading to centigrade subtract 32 and take 5/9 -of the remainder, while to change centigrade to Fahrenheit multiply the -centigrade by 9/5 and add 32 to the product. These two rules are -expressed by the following formulas. - - (F.° - 32)5/9 = C.°, 9C.°/5 + 32° = F.° - -Another method of changing from one thermometric scale to another is as -follows: - -A temperature of -40°F. is also _represented_ by -40°C., therefore to -change a Fahrenheit reading into centigrade, we add 40 to the given -reading, then divide by 1.8 after which subtract 40. To change from a -centigrade to Fahrenheit reading the only difference in this method is -to multiply by 1.8 or - - C. = (F. + 40)/1.8 - 40 and F. = 1.8(C. + 40) - 40. - -[Illustration: FIG. 124--Comparison of absolute, centigrade and -Fahrenheit scales.] - -=144. The Absolute Scale of Temperature.=--One often hears the statement -"as cold as ice." This expresses the incorrect idea that ice cannot -become colder than its freezing temperature. The fact is that ice _may -be cooled_ below freezing down to the temperature of its surroundings. -If a piece of ice is placed where the temperature is below the melting -point, the ice, like any other solid, cools to the temperature of the -surrounding space. For example, a piece of ice out of doors is at 10°F. -when the air is at this temperature. It follows then, that when ice has -been cooled below the freezing temperature that heat is required to -warm the ice up to its melting point; or in other words that ice at its -melting temperature possesses some heat. The temperature at which -absolutely no heat exists is called _absolute zero_. There has been -devised an _absolute scale of_ temperature. This scale is based upon the -centigrade scale, _i.e._, with 100° between the two fixed points; the -scale, however, extends down, below the centigrade zero, 273°, to what -is called _absolute zero_. It follows therefore that upon the absolute -scale, the melting point of ice, and the boiling point of water are 273° -and 373° respectively. (See Fig. 124.) - -The means employed to find the location of absolute zero are of much -interest. It has been observed that when heated a gas tends to expand. -If a measured volume of air at 0°C. is cooled or heated 1°C., it changes -its volume 1/273, the pressure remaining the same. If it is cooled 10° -it loses 10/273, if cooled 100° it loses 100/273 and so on. No matter -how far it is cooled the same rate of reduction continues as long as it -remains in the gaseous state. From these facts it is concluded that if -the cooling could be carried down 273° that the volume would be reduced -273/273 or that the volume of the gas would be reduced to nothing. This -is believed to mean that the molecular motion constituting heat would -cease rather than that the matter composing the gas would disappear. -Scientists have been able to obtain temperatures of extreme cold far -down on the absolute scale. Liquid air has a temperature of -292°F., or --180°C. or 93°A. The lowest temperature thus far reported is 1.7°A. or --271.3°C., obtained in 1911, by evaporating liquid helium. - -=145. The Law of Charles.=--The facts given in the last paragraph mean -that if 273 ccm. of a gas at 0°C. or 273° A. are cooled 100°, or to --100°C., or 173°A., then it will lose 100/273 of its volume or have a -volume of 173 ccm. If warmed 100°, or up to 100°C., or 373°A., it will -have a volume of 373 ccm. It follows then that in every case the volume -will correspond to its absolute temperature, providing the pressure -remains unchanged. The expression of this fact in scientific language is -called the law of _Charles_. _At a constant pressure the volume of a -given mass of gas is proportional to its absolute temperature._ - -Expressed mathematically, we have _V_{1}/V_{2} = T_{1}/T_{2}_. Compare -the statement and mathematical expression of the laws of Charles and -Boyle. - -The formulas for the laws of Boyle and Charles are sometimes combined -into one expression as follows: - - _PV/T = P´V´/T´_ - -or the product of the volume and pressure of a constant mass of gas is -proportional to its absolute temperature. - - -Important Topics - -1. Heat units; calorie, British thermal unit. - -2. Three thermometer scales, fixed points on each. - -3. Absolute zero, how determined. Its value on each scale. - -4. Law of Charles, its meaning. Combination of laws of Boyle and -Charles. - - -Exercises - -1. Does ice melt at the same temperature at which water freezes? Express -the temperature of freezing water on the three thermometer scales. - -2. A comfortable room temperature is 68°F. What is this temperature on -the centigrade and absolute scales? - -3. Change a temperature of 15°C. to F.; 15°F. to C.; -4°C. to F.; -20°F. -to C. - -4. The temperature of the human body is 98.6°F. What is this temperature -on the absolute and centigrade scales? - -5. The temperature of liquid air is -180°C. What is it on the Fahrenheit -scale? - -6. Mercury is a solid at -40°F. What is this on the centigrade scale? - -7. How much heat will be required to raise the temperature of 8 lbs. of -water 32°F.; 5 lbs. 10°F.? - -[Illustration: FIG. 125.--A clinical thermometer used to take the -temperature of the body.] - -8. How much heat will be required to raise the temperature of 30 g. of -water 43°C.; 20 g., 50°C.? - -9. Compute the temperature of absolute zero on the Fahrenheit scale. - -10. Take three basins of water, one hot, one cold, and one lukewarm. If -one hand be placed in the hot water while the other is placed in the -cold and after a few minutes both are placed in the lukewarm water, this -water will feel cool to one hand and warm to the other. Explain. - -11. If 200 ccm. of air at 200° absolute is heated to 300°A. under -constant pressure, what volume will the air occupy at the latter -temperature? - -12. How does one change a reading on the centigrade scale to a -corresponding reading on the absolute scale? - - -(3) EXPANSION OF LIQUIDS AND SOLIDS - -=146. Expansion of Gases.=--The law of Charles is found to apply to all -gases. That is, all gases change in volume in proportion to the change -of temperature provided the pressure remains constant. It is for this -reason that we have the _gas thermometer_ (see Fig. 126) which gives in -skillful hands more accurate temperature readings than the best -mercurial thermometer. Galileo devised and used the first _air -thermometer_ which consisted of a hollow bulb blown on a glass tube and -inverted in a dish of water. (See Fig. 1.) The _water thermometer_ -consists of a glass bulb filled with water which rises into a tube -attached to the bulb. One disadvantage of the water thermometer is its -limited range since it cannot be used below 0° or above 100°. Why? - -=147. Expansion of Liquids.=--The expansion of liquids differs from that -of gases in several important respects: - -(a) Liquids have a smaller rate of expansion than gases. The _rate_ of -expansion per degree is called the _Coefficient of Expansion_. For -example, the coefficient of expansion of a gas under constant pressure -at 0°C. is {1/273} of its volume per degree centigrade. - -(b) Different liquids expand at wholly different rates, that is, their -coefficients of expansion differ widely. For example, the coefficient of -expansion of mercury is 0.00018 per degree centigrade, of glycerine -0.0005 per degree centigrade, of petroleum 0.0009 per degree centigrade. - -[Illustration: FIG. 126.--Gas thermometer.] - -(c) The same liquid often has different coefficients of expansion at -different temperatures. Water between 5°C. and 6°C. has a coefficient -expansion of 0.00002 per degree centigrade, between 8° and 50° of -0.0006, between 99° and 100° of 0.00076. The coefficient of expansion of -mercury, however, is constant for a wide range of temperature and, -therefore, it is well adapted for use in thermometers. - -=148. Peculiarity in the Expansion of Water.=--Water has a peculiar rate -of expansion. This is illustrated by the following experiment: - - A test-tube filled with cold water is closed by a stopper - containing a small glass tube, the water extending up into the - small tube. (See Fig. 127.) The test-tube is placed in a freezing - mixture of salt and ice contained in a tumbler. As the water cools, - the level of the water in the small tube at first _sinks_. But - before the water freezes it _rises_ again, showing that after the - water cools to a certain temperature that _expansion of the water - occurs with further cooling_. - -Careful tests show that the water on cooling contracts until it reaches -4°C. On cooling below this temperature it expands. For this reason, when -the water of a lake or river freezes, the coldest water is at the -surface. On account of this the ice forms at the top instead of at the -bottom. If water contracted as it cooled to the freezing temperature the -coldest water would be at the bottom. Freezing would begin at the bottom -instead of at the surface. Lakes and rivers would freeze solid. In the -summer only in shallow waters would all the ice melt. The result would -be that fish and other aquatic life would be killed. Climate would be so -changed that the earth might become uninhabitable. Since water is -densest at 4°C. all the water in a lake or river, when it is covered -with ice, is at 4°C. except that near the surface. - -[Illustration: FIG. 127.--Apparatus used in testing the expansion of -water.] - -=149. The Expansion Of Solids.=--Most solids when heated expand less -than liquids and gases. Careful experiments show that expansion is: - -(a) Proportional to the change in temperature. - -(b) Different in different solids. - -Here are a few coefficients of linear (length) expansion. - - Brass 0.000018 per degree C. - Glass 0.000009 per degree C. - Ice 0.000052 per degree C. - Iron 0.000012 per degree C. - Platinum 0.000009 per degree C. - Zinc 0.000027 per degree C. - -_The coefficient of linear expansion is the fraction of its length that -a body expands when heated one degree._ - -_The coefficient of cubical expansion is the fraction of its volume that -a body expands when heated one degree._ - -The expansion of solids is used or allowed for in many cases: - -a. Joints between the rails on a railroad allow for the expansion of the -rails in summer. - -b. One end of a steel truss bridge is usually supported on rollers so -that it can expand and contract with changing temperatures. (See Fig. -128.) - -[Illustration: FIG. 128.--Truss bridge showing roller support at one -end.] - -c. Suspension bridges have expansion joints where the ends of the iron -girders can move in or out of an expansion joint thus making the bridge -longer or shorter according to the temperature. - -d. Iron tires are heated, slipped on to wagon wheels and then cooled, -the contraction on cooling setting them tightly in place. - -e. Metallic thermometers depend upon the movement due to the expansion -of a coiled strip of metal which turns a pointer on the dial of the -instrument. (See Fig. 129.) - -f. The wires that are fused into glass in incandescent light bulbs must -have the same coefficient of expansion as the glass. Platinum has -therefore been used for this purpose. (See table above.) - -[Illustration: FIG. 129.--Metallic thermometer.] - - -Important Topics - -1. Expansion of Liquids; peculiarities. Anomalous expansion of water and -its results. - -2. Expansion of solids; peculiarities, applications. - -3. Coefficient of linear expansion. - -4. Coefficient of cubical expansion. - - -Exercises - -1. The gas within a partly inflated balloon has a volume of 1000 cu. ft. -at a pressure of 74 cm., and a temperature of 15°C. What will be the -volume of the gas when its pressure is 37 cm. and the temperature is --17°C.? - -2. A man taking a full breath on the top of a mountain fourteen thousand -feet high inhales 4 liters of air, the pressure being 40 cm. What volume -would this same mass of air have in a place 600 ft. above sea-level when -the barometer reads 75 cm. and the temperature is the same as on the -mountain top? - -3. If the coefficient of linear expansion of iron is 0.000012 per -degree C., how much will an iron bridge 1000 ft. long change in length -in warming from -20°C. on a winter day to 30°C. upon a summer day. - -4. What are some of the results that would follow in freezing weather if -water continually contracted on being cooled to zero instead of -beginning to expand when cooled below 4°C.? - -5. Mention two instances that you have noticed of expansion occurring -when a body is heated? - -6. Compare the density of air at 30°C. with that at 10°C. at the same -pressure. If both are present in a room, where will each be found? Why? - -7. Compare the density of water at 40°C. with that at 10°C. If water at -the two temperatures are in a tank, where will each be found? Why? - -8. If water at 0°C. and at 4°C. are both in a tank, where will each be -found? Why? - -9. How much heat will be required to raise the temperature of a cubic -foot of water 10°F.? - -10. How much heat will be required to raise the temperature of 4 liters -of water 25°C.? - -11. How much longer would the cables of the Brooklyn suspension bridge -be on a summer's day when the temperature is 30°C. than in winter at --20°C., the length of cable between the supports being about 1600 ft. - -12. If 25 liters of air at -23°C. is warmed to 77°C. under constant -pressure, what will be the resulting volume of air? Explain. - -13. White pig iron melts at about 2000°F. Express this temperature upon -the centigrade and absolute scales. - -14. If 200 ccm. of air at 76 cm. pressure and 27°C. temperature be -heated to 127°C. at a pressure of 38 cm. what will be the resulting -volume? - -15. A balloon contains 10,000 cu. ft. of gas at 75.2 cm. pressure and -24°C. It ascends until the pressure is 18 cm. and the temperature is --10°C. What is the volume of gas it then contains. - -16. A gas holder contains 50 "cu. ft." of gas at a pressure of one -atmosphere and 62°F. How much gas will it hold at 10 atmospheres and -32°F. - -17. One thousand "cubic feet" of illuminating gas has what volume with -75 lbs. pressure and temperature of 10°C. - -18. Define a "cubic foot" of illuminating gas. - -=150. Methods of Transmitting Heat.=--One of the most practical benefits -of the study of heat is clearer understanding of the different methods -by which heat is transferred from one place to another and an -intelligent idea of the means employed to prevent the transfer of heat. - -It should be definitely understood at the beginning that _cold signifies -the absence of heat_, just as darkness implies the absence of light, so -when one speaks of cold getting into a house what is really meant is -either the entrance of cold air by some opening or else the escape of -the heat. - -There are three distinct methods by which heat energy is transferred -from one place to another, depending upon the medium or substance that -transfers the heat. - -a. A solid transmits heat by the method called _conduction_. - -b. A fluid, either a liquid or a gas, transmits heat mainly by the -method called _convection_. - -c. Space transmits the energy of hot objects by the method called -_radiation_. - -[Illustration: FIG. 130.--Solids conduct heat.] - -=151. Conduction.=--To illustrate conduction, place in a gas flame the -ends of same metal wires supported as in Fig. 130. In a short time the -other ends of the wires become hot enough to burn one's hand. This may -be explained as follows: The hot gas flame contains molecules in violent -vibration and those striking the wire set its molecules rapidly -vibrating. Since, in a solid, the molecules are held in the same -relative positions, when one end of a wire is heated the rapidly -vibrating molecules at the hot end set their neighbors vibrating and -these the next in turn and so on until the whole wire is hot. It is a -fortunate circumstance that different substances have different rates of -conductivity for heat. To realize this, suppose that our clothing were -as good a conductor as iron, clothing would then be very uncomfortable -both in hot and in cold weather. The best conductors for heat are -metals. It is interesting to note that, as a rule good conductors of -heat are also good conductors of electricity, while poor conductors of -heat are also poor electric conductors. Careful experiments in testing -the rate that heat will be conducted through different substances show -the following rates of conductivity. - -[Illustration: FIG. 131.--Water is a poor conductor of heat.] - -These figures are averages taken mainly from the Smithsonian Physical -Tables: - - Silver 100 - Copper 74 - Aluminum 35 - Brass 27 - Zinc 26 - Iron 15 - Tin 14.7 - German silver 8.4 - Mercury 1.7 - Granite 0.53 - Limestone 0.52 - Ice 0.5 - Glass 0.2 - Water 0.124 - Pine, with grain 0.03 - Pine, across grain 0.01 - Felt 0.008 - Air 0.005 - -To test the conductivity of _liquids_, take a test-tube nearly full of -cold water, hold the lower end in the hand while the tube is inclined so -that the upper end is heated by a gas flame until the water boils. The -lower end will be found to remain cold. (See Fig. 131.) Careful -measurements of the conductivity of water show that heat is transmitted -through it only {1/800} as rapidly as in silver, while air conducts but -{1/25} as rapidly as water. - -[Illustration: FIG. 132.--Wall construction of a refrigerator. 1, -Porcelain enamel lining lock joint; 2, inside wood lining; 3, 3-ply red -rope waterproof paper; 4, wool felt deafening paper; 5, flaxlinum -insulation; 6, dead air space; 7, flaxlinum insulation; 8, wool felt -deafening paper; 9, 3-ply red rope waterproof paper; 10, outside wood -case.] - -[Illustration: FIG. 133.--Sectional view of a Thermos bottle.] - -=152. Non-conductors and Their Uses.=--Many solids, however, are poor -conductors, as leather, fur, felt, and woolen cloth. These substances -owe their non-conductivity mainly to the fact that they are porous. The -air which fills the minute spaces of these substances is one of the -poorest conductors known and hinders the transfer of heat through these -solids. For the same reason loosely packed snow is a protection to -vegetation covered by it during a period of severe cold in winter. The -efficiency of storm sash or double windows, and of the double and -triple walls of ice-houses and refrigerators (see Fig. 132) in -preventing the conduction of heat is also largely due to the poor -conductivity of the air confined in the spaces between the walls. To -prevent the circulation of the air, sawdust, charcoal, and other porous -material is often loosely packed into the space between the walls of -such structure. - -Other illustrations of effective non-conductors will occur to every one; -such as _woolen_ clothing, _wooden_ handles for hot objects, and the -_packing_ used in fireless cookers. A _Thermos_ bottle is effective as a -non-conductor of heat because the space between the double walls has the -air exhausted from it (Figs. 133 and 134). - -Of several objects in a cold room, some feel much colder to the touch -than others, thus iron, marble, oil cloth, and earthenware will feel -colder than woolen cloth, carpet, feathers, or paper. The first four -objects feel cold because they are conductors, and conduct the heat away -from the hand rapidly. The other substances named are non-conductors and -hence remove heat from the hand less rapidly, and therefore do not feel -so cold. In a similar way, if several hot objects are touched by the -hand, the good conductors are the ones which will burn one most quickly -by conducting heat rapidly to the hand. The non-conductors, however, -will rarely burn one. Why are the handles of hot utensils often made of -non-conducting materials such as wood, cloth, asbestos, etc.? - -[Illustration: FIG. 134.--Cross-section of the vacuum flask in a Thermos -bottle.] - -=153. Radiation= is the method by which heat comes to us from the sun -across space containing no tangible matter. It is also the method by -which heat gets to us when we stand near a fire. Everyone has noticed -that this heat is cut off by holding an object between the person and -the fire. This fact indicates that radiant heat travels in _straight_ -lines. - -_The radiation of heat_ is believed to be accomplished by means of waves -in a medium called _ether_, which is invisible and yet pervades -everything. Three of the most important characteristics of radiation are -_first, heat is transferred by radiation with the speed of light_, or -186,000 miles per second. This fact is shown by the cutting off of both -the sun's heat and light at the same instant during an eclipse of the -sun. _Second, radiant heat[I] travels in straight lines_, while other -modes of transferring heat may follow irregular paths. The straight line -motion of radiant heat is shown by its being cut off where a screen is -placed between the source of heat and the object sheltered. _Third, -radiant heat may pass through an object without heating it._ This is -shown by the coldness of the upper layers of the atmosphere and also by -the fact that a pane of glass may not be heated appreciably by the heat -and light from the sun which passes through it. - - [I] Radiant heat is really _radiant energy_ and becomes heat when - it is absorbed by a body. - -When radiant energy falls upon any object it may be (a) _reflected_ at -the surface of the object, (b) _transmitted_ through the substance, (c), -absorbed. All three of these effects occur in different degrees with -different portions of the radiation. _Well-polished surfaces are good -reflectors._ Rough and blackened surfaces are _good absorbers_. -Transparent objects are those which transmit light well, but even they -absorb some of the energy. - -=154. The Radiometer.=--Radiant heat may be detected by means of the -radiometer (Fig. 135). This consists of a glass bulb from which the air -has been nearly exhausted. Within it is a wheel with four vanes of mica -or of aluminum mounted on a vertical axis. One side of each vane is -covered with lampblack, the other being highly polished. when exposed to -radiant heat from any source the vanes revolve with the bright side in -advance. - -The bulb is so nearly exhausted of air that a single molecule remaining -may travel from the walls of the bulb to the vanes without coming in -contact with another molecule. - -The blackened sides absorb more heat than the highly polished sides. The -air molecules striking these blackened sides receive more heat and so -rebound with greater velocity than from the other side, thus exerting -greater pressure. The blackened sides therefore are driven backward. If -the air were not so rarified the air molecules would hit each other so -frequently as to equalize the pressure and there would be no motion. - -[Illustration: FIG. 135.--A radiometer.] - -_Sun's Radiation._--Accurate tests of the amount of the sun's radiation -received upon a square centimeter of the earth's surface perpendicular -to the sun's rays were made at Mt. Wilson in 1913. The average of 690 -observations gave a value of 1.933 calories per minute. These results -indicate that the sun's radiation per square centimeter is sufficient to -warm 1 g. of water 1.933°C. each minute. Although the _nature_ of -_radiation_ is not discussed until Art. 408-411 in light, it should be -said here that all bodies are radiating heat waves at all temperatures, -the heat waves from cool bodies being much longer than those from hot -bodies. Glass allows the short luminous waves to pass through freely but -the longer heat waves from objects at the room temperature pass through -with difficulty. This is the reason why glass is used in the covering of -greenhouses and hot beds. Water also absorbs many of the longer heat -waves. It is therefore used in stereopticons to prevent delicate lantern -slides from being injured by overheating. - - -Important Topics - -1. Conduction in solids, liquids, gases. - -2. Non-conductors; uses, best non-conductors. - -3. Radiation, three characteristics. - -4. The sun's radiation, amount. The radiometer. - - -Exercises - -1. Does clothing ever afford us heat in winter? How then does it keep us -warm? - -2. Why are plants often covered with paper on a night when frost is -expected? - -3. Will frost form in the fall of the year sooner on a wooden or a -cement sidewalk? Why? On which does ice remain longer? Why? - -4. Why in freezing ice-cream do we put the ice in a wooden pail and the -cream in a tin one? - -5. Is iron better than brick or porcelain as a material for stoves? -Explain. - -6. Which is better, a good or a poor conductor for keeping a body warm? -for keeping a body cool? - -7. Should the bottom of a teakettle be polished? Explain. - -8. How are safes made fireproof? - -9. Explain the principle of the Thermos bottle. - -10. Explain why the coiled wire handles of some objects as stove-lid -lifters, oven doors, etc., do not get hot. - - -(5) TRANSMISSION OF HEAT IN FLUIDS. HEATING AND VENTILATION - -=155. Convection.=--While fluids are poor conductors, they may transmit -heat more effectively than solids by the mode called _convection_. To -illustrate: if heat is applied at the _top_ of a test-tube of water, -the hot water being lighter is found at the top, while at the bottom the -water remains cold. On the other hand, if heat is applied at the -_bottom_ of the vessel, as soon as the water at the bottom is warmed -(above 4°C.) it expands, becomes lighter and is pushed up to the top by -the colder, denser water about it. This circulation of water continues -as long as heat is applied below, until all of the water is brought to -the boiling temperature. (See Fig. 136.) - -When a liquid or a gas is heated in the manner just described, the heat -is said to be transferred by _convection_. Thus the air in the lower -part of a room may receive heat by conduction from a stove or radiator. -As it expands on being warmed, it is pushed up by the colder denser air -about it, which takes its place, thus creating a circulation of the air -in the room. (See Fig. 137.) The heated currents of air give up their -heat to the objects in the room as the circulation continues. These air -currents may be observed readily by using the smoke from burning "touch -paper" (unglazed paper that has been dipped into a solution of potassium -nitrate ["saltpeter"] and dried). - -[Illustration: FIG. 136.--Convection in a liquid.] - -=156. Draft of a Chimney.=--When a fire is started in a stove or a -furnace the air above the fire becomes heated, expands, and therefore is -less dense than it was before. This warm air and the heated gases which -are the products of the combustion of the fuel weigh less than an equal -volume of the colder air outside. Therefore they are pushed upward by a -force equal to the difference between their weight and the weight of an -equal volume of the colder air. - -The chimney soon becomes filled with these heated gases. (See Fig. 138.) -These are pushed upward by the pressure of the colder, denser air, -because this colder air is pulled downward more strongly by the force of -gravity than are the heated gases in the chimney. - -Other things being equal, the taller the chimney, the greater the draft, -because there is a greater difference between the weight of the gases -inside and the weight of an equal volume of outside air. - -[Illustration: FIG. 137.--Convection currents in a room.] - -[Illustration: FIG. 138.--Fire place showing draft of a chimney.] - -=157. Convection Currents in Nature.=--Winds are produced by differences -in the _pressure_ or _density_ of the air, the movement being from -places of high toward places of low pressure. One of the causes of a -difference in density of the air is a difference in temperature. This -is illustrated by what are called the _land_ and _sea breezes_ along the -sea shore or large lakes. During the day, the temperature of the land -becomes higher than that of the sea. The air over the land expands and -being lighter is moved back and upward by the colder, denser air from -the sea or lake. This constitutes the _sea breezes_ (Fig. 139). At night -the land becomes cooler much sooner than the sea and the current is -reversed causing the _land breeze_. (See Fig. 140.) - -[Illustration: FIG. 139.--Sea breeze.] - -[Illustration: FIG. 140.--Land breeze.] - -The _trade winds_ are convection currents moving toward the hot -equatorial belt from both the north and the south. In the hot belt the -air rises and the upper air flows back to the north and the south. This -region of ascending currents of air is a region of heavy rainfall, since -the saturated air rises to cool altitudes where its moisture is -condensed. The _ocean currents_ are also convection currents. Their -motion is due to prevailing winds, differences in density due to -evaporation and freezing, and to the rotation of the earth, as well as -to changes in temperature. - -=158. The heating and ventilation of buildings= and the problems -connected therewith are matters of serious concern to all who live in -winter in the temperate zone. Not only should the air in living rooms be -comfortably heated, but it should be continually changed especially in -the crowded rooms of public buildings, as those of schools, churches, -and assembly halls, so that each person may be supplied with 30 or more -cubic feet of fresh air per minute. In the colonial days, the _open fire -place_ afforded the ordinary means for heating rooms. This heated the -room mainly by _radiation_. It was wasteful as most of the heat passed -up the chimney. This mode of heating secured ample _ventilation_. Fire -places are sometimes built in modern homes as an aid to ventilation. - -Benjamin Franklin seeing the waste of heat in the open fire places -devised an iron box to contain the fire. This was placed in the room and -provided heat by conduction, convection, and radiation. It was called -_Franklin's stove_ and in many forms is still commonly used. It saves a -large part of the heat produced by burning the fuel and some ventilation -is provided by its draft. - -[Illustration: FIG. 141.--Heating and ventilating by means of a hot-air -furnace.] - -=159. Heating by Hot Air.=--The presence of stoves in living rooms of -homes is accompanied by the annoyance of scattered fuel, dust, ashes, -smoke, etc. One attempt to remove this inconvenience led to placing a -large stove or fire box in the basement or cellar, surrounding this with -a jacket to provide a space for heating air which is then conducted by -pipes to the rooms above. This device is called the hot-air furnace. -(See Fig. 141.) The heated air rises because it is pushed up by colder, -denser air which enters through the cold-air pipes. The _hot-air -furnace_ provides a good circulation of warm air and also ventilation, -provided some cold air is admitted to the furnace from the outside. One -objection to its use is that it may not heat a building evenly, one part -being very hot while another may be cool. To provide even and sufficient -heat throughout a large building, use is made of _hot water_ or _steam -heating_. - -[Illustration: FIG. 142.--A hot-water system of heating.] - -[Illustration: FIG. 143.--One-pipe system of steam heating.] - -=160. Hot-water Heating.=--In hot-water heating a furnace arranged for -heating water is placed in the basement. (See Fig. 142.) Attached to the -top of the heater are pipes leading to the radiators in the various -rooms; other pipes connect the radiators to the bottom of the boiler. -The heater, pipes, and radiators are all filled with water before the -fire is started. When the water is warmed, it expands and is pushed up -through the pipes by the colder water in the return pipe. The -circulation continuing brings hot water to the radiator while the cooled -water returns to the heater, the hot radiators heating the several -rooms. - -=161. Steam Heating.=--In _steam heating_ a steam boiler is connected to -radiators by pipes. (See Fig. 143.) The steam drives the air out of the -pipes and radiators and serves as an efficient source of heat. Heating -by steam is _quicker_ than heating with hot water. It is therefore -preferred where quick, efficient heating is required. Hot water is less -intense and more economical in mild weather and is often used in private -homes. - -[Illustration: FIG. 144.--Heating by an indirect radiator with side-wall -register.] - -=162. Direct and Indirect Heating.=--In heating by _direct radiation_ -(Figs. 142, 143), the steam or hot-water radiators are placed in the -rooms to be heated. With direct radiation, ventilation must be provided -by special means, such as opening windows, doors, and ventilators. -Sometimes radiators are placed in a box or room in the basement. Air -from out of doors is then driven by a fan over and about the hot -radiators. The air thus heated is conducted by pipes to the several -rooms. This arrangement is called _indirect heating_. (See Fig. 144.) -The latter method, it may be observed, provides both heat and -ventilation, and hence is often used in schools, churches, court houses, -and stores. Since heated air, especially in cold weather, has a low -_relative humidity_ some means of moistening the air of living rooms -should be provided. Air when too dry is injurious to the health and also -to furniture and wood work. The excessive drying of wood and glue in a -piece of furniture often causes it to fall apart. - -[Illustration: FIG. 145.--An automatic air valve.] - -[Illustration: FIG. 146.--An automatic vacuum valve.] - -=163. Vacuum Steam Heating.=--In steam heating, air valves (Fig. 145) -are placed on the radiators to allow the air they contain to escape when -the steam is turned on. When all the air is driven out the valve closes. -Automatic vacuum valves (Fig. 146) are sometimes used. When the fire is -low and there is no steam pressure in the radiators the pressure of the -air closes the valve, making a partial vacuum inside. The boiling point -of water falls as the pressure upon it is reduced. As water will not -boil under ordinary atmospheric pressure until its temperature is 100°C. -(212°F.), it follows that by the use of vacuum systems, often called -vapor systems, of steam heating, water will be giving off hot vapor even -after the fire has been banked for hours. This results in a considerable -saving of fuel. - -[Illustration: FIG. 147.--Plenum hot-blast system with temperature -regulation.] - -=164. The Plenum System of Heating.=--In the plenum system of heating -(see Fig. 147) fresh air is drawn through a window from outdoors and -goes first through tempering coils where the temperature is raised to -about 70°. The fan then forces some of the air through heating coils, -where it is reheated and raised to a much higher temperature, depending -upon the weather conditions. Both the hot and tempered air are kept -under pressure by the fan in the plenum room and are forced from this -room through galvanized iron ducts to the various rooms to be heated. -The foul air is forced out of the room through vent ducts which lead to -the attic where it escapes through ventilators in the roof. - -[Illustration: FIG. 148.--A thermostat. (Johnson System.)] - -A thermostat is placed in the tempered-air part of the plenum room to -maintain the proper temperature of the tempered air. This thermostat -operates the by-pass damper under the tempering coils, and sometimes the -valves on the coils. The mixing dampers at the base of the -galvanized-iron ducts are controlled by their respective room -thermostats. Attic-vent, fresh-air, and return-air dampers are under -pneumatic switch control. A humidifier can be provided readily for this -system. This system of heating is designed particularly for school -houses where adequate ventilation is a necessity. - -=165. The Thermostat.=--One of the many examples of the expansion of -metals is shown in one form of the thermostat (Fig. 148) in which two -pieces of different metals and of unequal rates of expansion, as brass -and iron, are securely fastened together. - -The thermostatic strip _T_ moving inward and outward, as affected by the -room temperature, varies the amount of air which can escape through the -small port _C_. When the port _C_ is completely closed (Fig. 148_a_) the -full air pressure collects on the diaphragm _B_ which forces down the -main valve, letting the compressed air from the main pass through the -chamber _D_ into chamber _E_ as the valve is forced off its seat. The -air from chamber _E_ then passes into the branch to operate the damper. - -When port _C_ is fully open (Fig. 148_b_) the air pressure on diaphragm -_B_ is relieved, the back pressure in _E_ lifts up the diaphragm and the -air from the branch escapes out through the hollow stem of the main -valve, operating the damper in the opposite direction from that when _C_ -is closed. - - -Important Topics - -1. Transmission of heat in fluids. - -2. Convection. Drafts of a chimney. Land and sea breezes. - -3. Heating and ventilation of buildings. - - (a) By hot air. - (b) Hot-water heating. - (c) Steam heating. - (d) Direct and indirect heating. - (e) Vacuum steam heating. - (f) The plenum system. - (g) The thermostat. - - -Exercises - -1. Is a room heated mainly by conduction, convection, or radiation, from -(a) a stove, (b) a hot-air furnace, (c) a steam radiator? - -2. Name three natural convection currents. - -3. Explain the _draft_ of a chimney. _What_ is it? _Why_ does it occur? - -4. Make a _cross-section_ sketch of your living room and indicate the -convection currents by which the room is heated. _Explain_ the heating -of the room. - -5. Make a sketch showing how the water in the hot-water tank in the -kitchen or laundry is heated. Explain your sketch, indicating convection -currents. - -6. Is it economical to keep stoves and radiators highly polished? -Explain. - -7. If you open the door between a warm and a cool room what will be the -direction of the air currents at the top and at the bottom of the door? -Explain. - -8. If a hot-water heating system contains 100 cu. ft. of water how much -heat will be required to raise its temperature 150°F.? - -9. Why does a tall chimney give a better draft than a short one? - -10. Explain how your school room is heated and ventilated. - -11. Should a steam or hot-water radiator be placed near the floor or -near the ceiling of a room? Why? - -12. In a hot-water heating system an open tank connected with the pipes -is placed in the attic or above the highest radiator. Explain its use. - - -(6) THE MOISTURE IN THE ATMOSPHERE, HYGROMETRY - -=166. Water Vapor in the Air.=--The amount of water vapor present in the -air has a marked effect upon the weather and the climate of a locality. -The study of the moisture conditions of the atmosphere, or hygrometry, -is therefore a matter of general interest and importance. The water -vapor in the atmosphere is entirely due to evaporation from bodies of -water, or snow, or ice. In the discussion of evaporation, it is -described as due to the gradual escape of molecules into the air from -the surface of a liquid. This description fits exactly the conditions -found by all careful observers. Since the air molecules are continually -striking the surface of the liquid, many of them penetrate it and become -absorbed. In the same manner many vapor molecules reenter the liquid, -and if enough vapor molecules are present in the air so that as many -vapor molecules reenter the liquid each second as leave it, the space -above the liquid is said to be _saturated_ as previously described. (See -Art. 18.) - -=167. Conditions for Saturation.=--If a liquid is evaporating into a -vacuum, the molecules on leaving find no opposition until they reach the -limits of the vessel containing the vacuum. Evaporation under these -conditions goes on with great rapidity and the space becomes saturated -almost instantly. If, however, air be present at ordinary pressure, many -of the ordinary water vapor molecules on leaving are struck and returned -to the water by the air molecules directly above. Those escaping -gradually work their way upward through the air. This explains why it is -that our atmosphere is not often saturated even near large bodies of -water, the retarding effect of the air upon the evaporation preventing -more than the layers of air near the water surface becoming saturated. - -Just as the amount of salt that can be held in solution in a liquid is -lessened by cooling the solution (Art. 26), so the amount of water vapor -that can be held in the air is lessened by lowering its temperature. If -air not moist enough to be saturated with water vapor is cooled, it -will, as the cooling continues, finally reach a temperature at which it -will be saturated or will contain all the water vapor it can hold at -this temperature. If the air be still further cooled some of the water -vapor will condense and may form fog, dew, rain, snow, etc., the form it -takes depending upon where and how the cooling takes place. - -=168. The Formation of Dew.=--If the cooling of the atmosphere is at the -surface of some cold object which lowers the temperature of the air -below its saturation point, some of its moisture condenses and collects -upon the cold surface as _dew_. This may be noticed upon the surface of -a pitcher of ice-water in summer. At night, the temperature of grass and -other objects near or on the ground may fall much faster than that of -the atmosphere owing to the radiation of heat from these objects. If the -temperature falls below the saturation point, dew will be formed. This -natural radiation is hindered when it is cloudy, therefore little dew -forms on cloudy nights. Clear nights help radiation, therefore we have -the most dew on nights when the sky is clear. If the temperature is -below freezing, _frost_ forms instead of dew. - -=169. Formation of Fog.=--If the cooling at night is great enough to -cool the body of air near the earth below the saturation temperature, -then not only may dew be formed, but some moisture is condensed in the -air itself, usually upon fine dust particles suspended in it. This -constitutes a _fog_. If the cooling of the body of air takes place above -the earth's surface as when a warm moist current of air enters a colder -region, _e.g._, moves over the top of a cold mountain, or into the upper -air, then as this air is cooled below its saturation point, condensation -upon fine suspended dust particles takes place, and a _cloud_ is formed. -If much moisture is present in the cloud, the drops of water grow in -size until they begin to fall and _rain_ results; or if it is cold -enough, instead of rain, snowflakes will be formed and fall. Sometimes -whirling winds in severe thunderstorms carry the raindrops into colder -and then warmer regions, alternately freezing and moistening the drops -or bits of ice. It is in this way that _hail_ is said to be formed. - -=170. The Dew Point.=--The temperature to which air must be cooled to -saturate it or the temperature at which condensation begins is called -the _dew point_. This is often determined in the laboratory by partly -filling a polished metal vessel with water and cooling the water by -adding ice until a thin film of moisture is formed upon the outer -surface. The temperature of the surface when the moisture first forms is -the dew point. - -=171. The Humidity of the Atmosphere.=--After the dew point has been -obtained, one may compute the _relative humidity_ or _degree of -saturation of the atmosphere_, from the table given below. This is -defined as the _ratio of the amount of water vapor present in the air to -the amount that would be present if the air were saturated at the same -temperature_. - - For example, if the dew point is 5°C. and the temperature of the - air is 22°C., we find the densities of the water vapor at the two - temperatures, and find their ratio: 6.8/19.3 = 35 per cent. nearly. - Determinations of humidity may give indication of rain or frost and - are regularly made at weather bureau stations. They are also made - in buildings such as greenhouses, hospitals, and schoolhouses to - see if the air is moist enough. For the most healthful conditions - the relative humidity should be from 40 per cent. to 50 per cent. - -WEIGHT OF WATER (_w_) IN GRAMS CONTAINED IN 1 CUBIC METER OF SATURATED -AIR AT VARIOUS TEMPERATURES (_t_°)C. - - --------+------ - _t_°C. | _w_ - --------+------ - -10 | 2.1 - - 9 | 2.4 - - 8 | 2.7 - - 7 | 3.0 - - 6 | 3.2 - - 5 | 3.5 - - 4 | 3.8 - - 3 | 4.1 - - 2 | 4.4 - - 1 | 4.6 - 0 | 4.9 - 1 | 5.2 - 2 | 5.6 - 3 | 6.0 - 4 | 6.4 - 5 | 6.8 - 6 | 7.3 - 7 | 7.7 - 8 | 8.1 - 9 | 8.8 - 10 | 9.4 - 11 | 10.0 - 12 | 10.6 - 13 | 11.3 - 14 | 12.0 - 15 | 12.8 - 16 | 13.6 - 17 | 14.5 - 18 | 15.1 - 19 | 16.2 - 20 | 17.2 - 21 | 18.2 - 22 | 19.3 - 23 | 20.4 - 24 | 21.5 - 25 | 22.9 - 26 | 24.2 - 27 | 25.6 - 28 | 27.0 - 29 | 28.6 - 30 | 30.1 - --------+------ - -=172. Wet and Dry Bulb Hygrometer.=--A device for indicating the -relative humidity of the air is called an _hygrometer_. There are -various forms. The _wet_ and _dry bulb hygrometer_ is shown in Fig. 149. -This device consists of two thermometers, one with its bulb dry and -exposed to the air, the other bulb being kept continually moist by a -wick dipping into a vessel of water. An application of the principle of -cooling by evaporation is made in this instrument. Unless the air is -saturated so that evaporation is prevented, the wet-bulb thermometer -shows a lower temperature, the difference depending upon the amount of -moisture in the air, or upon the relative humidity. Most determinations -of relative humidity are made with this kind of instrument. It is -necessary in order to make an accurate determination, to fan or set the -air in motion about the thermometers for some time before reading them. -The relative humidity is then found by using tables giving the relative -humidity that corresponds to any reading of the thermometers. - -[Illustration: FIG. 149.--Wet and dry bulb hygrometer.] - -[Illustration: FIG. 150.--A dial hygrometer.] - - A form of hygrometer in common use is shown in Fig. 150. In this - device, a thin strip of hygroscopic material (as a piece of goose - quill) is formed into a spiral coil. One end of this is fastened to - a post. The other end carried a hand or pointer. The latter moves - over a printed scale and indicates directly the relative humidity. - Its indications should be tested by comparing its readings with the - results of dew-point determinations. The position of the pointer - may be adjusted by turning the post. - - -Important Topics - -1. Water vapor in the air. Cause and effect. - -2. Formation of dew, fog, rain, and snow. - -3. Dew point, relative humidity. - -4. Use of the dry- and wet-bulb hygrometer. Goose-quill hygrometer. - - -Exercises - -1. How is the relative humidity of the air affected by warming it? -Explain. - -2. How does the white cloud of steam seen about a locomotive in cold -weather differ from fog? Explain. - -3. In cold weather is the relative humidity of air out of doors and -indoors the same? Explain. - -4. Compare the relative humidity of air in a desert and near the ocean. - -5. Look up the derivation of the term "hygrometer." Give the use of the -instrument. - -6. Find the relative humidity of air at 20°C. if its dew point is at -10°C. - -7. How may the relative humidity of the air in a home be increased? - -8. What is the effect of high humidity in the summer upon human beings? -How do you explain this? - -9. Does dew fall? Explain how dew is formed? - -10. In what respects is a cloud similar to a fog? In what respects -different? - -11. Why are icebergs frequently enveloped in fog? - -12. Does dew form in the day time? Explain. - - -(7) EVAPORATION - -=173. Effects of Evaporation.=--In Art. 19 the cooling effect of -evaporation is mentioned and some explanation is made of the cooling -effect observed. Since evaporation is employed in so many ways, and -since its action is simply explained by the study we have made of -molecular motions and molecular forces, it may be well to consider this -subject further. - - Take three shallow dishes, and place in one a little water, in - another some alcohol, and some ether in the third, the liquids - being taken from bottles that have stood several hours in the room - so that all are at the same temperature. After a short time take - the temperature of the three liquids. Each will be at a lower - temperature than at first, but of the three the ether will be found - to be the coolest, alcohol next, and the water nearest its first - temperature. It will be noticed also that the ether has evaporated - most in the same time. Similar effects may be observed by placing a - few drops of each of these three liquids upon the back of one's - hand, or by placing a few drops in turn upon the bulb of a simple - air thermometer. - -=174. Cooling Effect of Evaporation.=--The molecules that leave an -evaporating liquid are naturally the swiftest moving ones, that is, the -ones having the highest temperature, so their escape leaves the liquids -cooler than before, and the one whose molecules leave fastest is -naturally the one that becomes coldest, that is, the ether, in the -experiment of Art. 173. If no air pressure were exerted upon the surface -of the liquid, the escape of the molecules would be much increased and -the temperature of the liquid would be lowered rapidly. - - To test this, fill a thin watch glass with ether and place it over - a thin slip of glass with a drop of cold water between the two. Now - place this apparatus under the receiver of an air pump and exhaust - the air. The rapid evaporation of the ether so lowers its - temperature, that often the drop of water is frozen. The lowest - temperatures are obtained by evaporating liquids at reduced - pressure. - -Onnes by evaporating liquid helium at a pressure of about 1.2 mm. -reached the lowest temperature yet attained, -456°F., or -271.3°C. - - If four thermometers are taken, the bulbs of three being wetted - respectively with ether, alcohol, and water the fourth being dry, - on vigorously fanning these, the moistened thermometers show that - they have been cooled while the dry one is unaffected. - -This indicates that fanning a dry body at the temperature of the air -does not change its temperature. Fanning does increase evaporation by -removing the air containing the evaporated molecules near the surface of -the liquid so that unsaturated air is continually over the liquid. If a -pint of water is placed in a bottle and another pint in a wide pan the -latter will become dry much sooner because of the greater surface over -which evaporation can take place. Application of this is made at salt -works where the brine is spread out in shallow pans. - -=175. Rate of Evaporation.=--The rate of evaporation is affected by -several factors. These have been illustrated in the preceding -paragraphs. To briefly summarize: - -The rate of evaporation of a liquid is affected by-- - -(a) The nature of the liquid. - -(b) The temperature of the liquid. - -(c) The pressure upon its evaporating surface. - -(d) The degree of saturation of the space into which the liquid is -evaporating. - -(e) The rate of circulation of air over its surface. - -(f) The extent of surface exposed to evaporation. - -=176. Molecular Motion in Solids.=--Evidence of molecular motion in -liquids is given by expansion on heating, evaporation, and diffusion. Do -any of these lines of evidence apply to solids? It is a fact of common -experience that solids do become larger on heating. Spaces are left -between the ends of rails on railroads so that when they expand in -summer they will not distort the track. Iron tires are placed on wheels -by heating them until they slip on easily. Then on cooling, the iron -shrinks and presses the wheel tightly. Many common demonstrations of -expansion are found in lecture rooms. The fact of the evaporation of a -solid is often detected by noticing the odor of a substance. The odor of -moth balls is one example. Camphor also evaporates. Heated tin has a -characteristic odor noted by many. Ice and snow disappear in winter even -though the temperature is below freezing. Wet clothes, "freeze dry," -that is, dry after freezing, by evaporation. A few crystals of iodine -placed in a test-tube and gently heated form a vapor easily seen, even -though none of the iodine melts. Where the vapor strikes the side of the -tube, it condenses back to dark gray crystals of iodine. This change -from solid directly to gas and back again without becoming liquid is -called _sublimation_. A number of solids are purified by this process. - - -Important Topics - -1. Cooling effect of evaporation, rate of evaporation affected by six -conditions. - -2. Effects of molecular motion in solids: (a) Expansion, (b) -Evaporation, (c) Sublimation. - - -Exercises - -1. Does sprinkling the streets or sidewalks cool the air? Why? - -2. Give an illustration for each of the factors affecting evaporation. - -3. Give an illustration for each of the three evidences of molecular -motions in solids. - -4. Since three-quarters of the earth's surface is covered with water, -why is not the air constantly saturated? - -5. If the air has the temperature of the body, will fanning the -perfectly dry face cool one? Explain. Will the effect be the same if the -face is moist? Explain. - -6. What is the cause of "Cloud Capped" mountains? - -7. Why does the exhaust steam from an engine appear to have so much -greater volume on a cold day in winter than on a warm one in summer? - -8. What causes an unfrozen pond or lake to "steam" on a very cold day in -winter, or on a very cool morning in summer? - -9. As the air on a mountain top settles down the sides to places of -greater pressure, how will its temperature be affected? its relative -humidity? Explain. - -10. On our Pacific coast, moist winds blow from the west over the -mountains. Where will it rain? Where be dry? Explain. - - - - -CHAPTER VIII - -HEAT AND WORK - - -(1) HEAT MEASUREMENT AND SPECIFIC HEAT - -=177. Specific Heat.=--In the study of density and specific gravity it -is made clear that different substances differ widely in the amount of -matter contained in equal volumes, _e.g._, lead is much denser than -water. The study of the relative densities of substance is usually -considered under the subject of _specific gravity_. - -_Specific heat_ as distinguished from specific gravity is concerned with -the _capacity_ for heat possessed by different substances. The -definition for specific heat is: _The ratio of the amount of heat -required to change the temperature of a given mass of a substance 1 C. -degree to the amount of heat required to change the temperature of the -same mass of water 1 C. degree._ By definition, it requires 1 calorie to -raise the temperature of the gram of water 1°C. The _specific heat_ -therefore of water is taken as one. The specific heat of most substances -except hydrogen, is _less_ than that of water, and as a rule, the denser -the body the less its specific heat, as may be observed in the following -table: - - ---------+----------+---------- - | Specific | Specific - | gravity | heat - ---------+----------+---------- - Gold | 19.3 | 0.032 - Mercury | 13.6 | 0.033 - Copper | 8.9 | 0.093 - Brass | 8.4-8.9 | 0.094 - Nickel | 8.57 | 0.11 - Iron | 7.5+ | 0.1125 - Aluminum | 2.67 | 0.218 - Glass | 2.5-3.6 | 0.19 - Ice | 0.918 | 0.504 - Air | 0.00129 | 0.237 - Steam | 0.00061 | 0.480 - Hydrogen | 0.00009 | 3.409 - ---------+----------+---------- - -=178. Method of Determining Specific Heat.=--The specific heat of a body -is usually determined by what is called the _method of mixtures_. - - For example, a definite weight of a substance, say a 200-g. iron - ball, is placed in boiling water until it has the temperature of - the hot water, 100°C. Suppose that 300 g. of water at 18°C. be - placed in a calorimeter, and that the hot iron ball on being placed - in the water raises its temperature to 23.5°C. The heat received by - the water equals 5.5 × 300 = 1650 calories. This must have come - from the heated iron ball. 200 g. of iron then in cooling 76.5°C. - (100°-23.5°) gave out 1650 calories. Then 1 g. of iron in cooling - 76.5°C. Would give out 8.25 calories or 1 g. of iron cooling 1°C. - would yield about 0.11 calorie. The specific heat of the iron is - then 0.11. For accurate determination the heat received by the - calorimeter must be considered. - -=179. Heat Capacity of Water.=--The large capacity for heat shown by -water is useful in regulating the temperature of the air near lakes and -the ocean. In hot weather the water rises slowly in temperature -absorbing heat from the warm winds blowing over it. In winter the large -amount of heat stored in the water is slowly given out to the air above. -Thus the climate near the ocean is made more moderate both in winter and -summer by the large capacity of water for heat. This large heat capacity -of water may seem to be a disadvantage when one is warming it for -domestic purposes since it requires so much heat to warm water to -boiling. However, it is this capacity that makes hot-water bottles and -hot-water heating effective. - - If one takes a pound of ice at 0°C. in one dish and a pound of - water at 0°C. in another, and warms the dish of ice by a Bunsen - flame until the ice is just melted, and then warms the water in the - other dish for the same time, the water will be found to be _hot_ - and at a temperature 80°C., or 176°F. - -=180. The Heat of Fusion of Ice.=--This experiment indicates the large -amount of heat required to change the ice to water without changing its -temperature. As indicated by the experiment, it requires 80 calories to -melt 1 g. of ice without changing its temperature or, in other words, if -one placed 1 g. of ice at 0°C. in 1 g. of water at 80°C., the ice would -be melted and the water would be cooled to 0°C. - -=181. Heat Given out by Freezing water.=--Just as 80 calories of heat -are required to melt 1 g. of ice, so in freezing 1 g. of water, 80 -calories of heat are given out. - - The fact that heat is set free or given out when a liquid - solidifies may be strikingly shown by making a strong solution of - sodium acetate. On allowing this to cool quietly it will come to - the room temperature and remain liquid. If now a small crystal of - sodium acetate is dropped into the liquid the latter quickly - becomes a solid mass of crystals, at the same time rising markedly - in temperature. The amount of heat now liberated must enter the - sodium acetate when the mass of crystals is melted again. - -The large amount of heat that must be liberated before water freezes -accounts for the slowness of the formation of ice. It is also the reason -why the temperature never falls so low in the vicinity of large lakes as -it does far inland, the heat given out by the freezing water warming the -surrounding air. - -The heat that disappears on melting and reappears on solidifying is -called the _heat of fusion_. It is sometimes called _latent heat_ since -the heat seems to become hidden or latent. It is now believed that the -heat energy that disappears when a body melts has been transformed into -the _potential energy_ of partially separated molecules. The heat of -fusion therefore represents the work done in changing a solid to a -liquid without a change of temperature. - -=182. Melting of Crystalline and Amorphous Substances.=--If a piece of -ice is placed in boiling hot water and then removed, the temperature of -the unmelted ice is still 0°C. There is no known means of warming ice -under atmospheric pressure above its melting point and maintaining its -solid state. Ice being composed of ice crystals is called a crystalline -body. All crystalline substances have fixed melting points. For example, -ice always melts at 0°C. The melting points of some common crystalline -substances are given below: - -_Melting Points of Some Crystalline Substances_ - - 1. Aluminum 658 C. - 2. Cast iron 1200 C. - 3. Copper 1083 C. - 4. Ice 0 C. - 5. Lead 327 C. - 6. Mercury -39 C. - 7. Phenol (carbolic acid) 43 C. - 8. Platinum 1755 C. - 9. Salt (sodium chloride) 795 C. - 10. Saltpeter (potassium nitrate) 340 C. - 11. Silver 961 C. - 12. Sodium hyposulphite (hypo) 47 C. - 13. Zinc 419 C. - -_Non-crystalline or amorphous substances_ such as glass, tar, glue, -etc., do not have well defined melting points as do crystalline bodies. -When heated they gradually soften and become fluid. For this reason -glass can be pressed and molded. - -=183. Change of Volume During Solidification.=--The fact that ice floats -and that it breaks bottles and pipes in which it freezes shows that -water expands on freezing. How a substance may occupy more space when -solid than when liquid may be understood when we learn that ice consists -of masses of star-shaped crystals. (See Fig. 151.) The formation of -these crystals must leave unoccupied spaces between them in the ice. -When liquefied, however, no spaces are left and the substance occupies -less volume. Most substances contract upon solidifying. Antimony and -bismuth, however, expand on solidifying while iron changes little in -volume. Only those bodies that expand, or else show little change of -volume on solidifying, can make sharp castings, for if they contract -they will not completely fill the mold. For this reason gold and silver -coins must be stamped and not cast. Type metal, an alloy of antimony and -lead, expands on solidifying to form the sharp outlines of good type. -Several important effects of the expansion of water when freezing should -be noted. (a) Ice floats, (b) if it sank as soon as formed, lakes and -rivers would freeze solid, (c) freezing water is one of the active -agents in the disintegration of rocks. - -[Illustration: FIG. 151.--Ice crystals.] - -[Illustration: FIG. 152.--Melting ice by pressure.] - -Since water expands on freezing, pressure would on compressing ice at -0°C., tend to turn it into water. Pressure does lower the melting point -of ice, so that a little ice may melt when it is subjected to pressure. -On removing the pressure the water freezes. This may be shown by placing -a loop of fine piano wire (see Fig. 152) over a piece of ice supported -so that a weight may be hung upon the wire. The wire will be found to -gradually cut through the ice, the melted ice refreezing above the wire. - - -Important Topics - -1. Specific heat. - -2. Heat of fusion of ice. - -3. Crystalline substances have fixed melting points. - -4. Expansion on freezing, importance. - - -Exercises - -1. What are two advantages in the high heat of fusion of ice? - -2. What are two advantages in the expansion of water while freezing? - -3. How much heat will be required to melt 1000 g. of ice and warm the -water to 20°C.? - -4. How many grams of ice at 0°C. can be melted by 400 g. of water at -55°C.? - -5. What are two advantages of the high specific heat of water? Two -disadvantages? - -6. If the specific heat of iron is 0.1125, how much ice at 0°C. can be -melted by a 200-g. ball of iron heated to 300°C? - -7. What is the temperature of a hot ball of iron weighing 80 g., if when -placed on a piece of ice at 0°C. it melts 90 g. of ice? - -8. If 500 g. of copper at 400°C. are placed into 3000 g. of water at -10°C. what will be the resulting temperature? - -9. What weight of water at 90°C. will just melt 10 kg. of ice at 0°C.? - -10. If the smooth dry surface of two pieces of ice are pressed together -for a short time the two pieces will be frozen into one piece. Explain. - -11. Tubs of hot water are sometimes placed in vegetable cellars to -prevent the vegetables from freezing. Explain. - -12. How many B.t.u. are given out when 2 lbs. of water freeze? - - -(2) HEAT AND CHANGE OF STATE - -[Illustration: FIG. 153.--The black cube in the upper corner represents -one cubic inch of water. The entire cube represents the space occupied -by the cubic inch of water in the form of steam. The reduced spaces at -the bottom and sides show how much short the cube is of being one cubic -foot. (American Radiator Co.)] - -=184. Heat of Vaporization.=--In our study of evaporation in Art. 174 we -considered the more rapidly moving or vibrating molecules in the liquid -escaping to the air above and the slower moving molecules being left -behind in the liquid; this means that a loss of heat will result upon -evaporation, the liquid remaining becoming cooler as the process -continues. Now just as a ball thrown up in the air loses its kinetic -energy as it rises, and acquires energy of position or potential energy, -so molecules escaping from a liquid lose a certain amount of kinetic -energy or heat and acquire a corresponding amount of _energy of -position_ or potential energy. _Conversely_, as the ball returns to the -ground its potential energy is changed to kinetic energy. Similarly when -vapor molecules return to the liquid condition they lose their energy of -position and acquire kinetic energy. In other words, when a liquid -evaporates a certain amount of heat disappears, or becomes _latent_ and -when the vapor condenses the heat reappears, or becomes _sensible_ heat. -_The amount of heat that disappears when 1 g. of a substance is -vaporized is called the heat of vaporization._ In the case of water at -its boiling point, 536 calories of heat disappear when 1 g. of water -turns to vapor, and this same amount of heat reappears when the vapor -condenses. - -The change of volume of water on turning to steam is shown in Fig. 153. - -[Illustration: FIG. 154.--Effect of pressure on the boiling point.] - -=185. The Boiling Point.=--The boiling temperature depends upon the -pressure. The boiling point may be defined as _the temperature at which -bubbles of vapor are formed within the liquid_. These bubbles increase -the surface at which evaporation can take place in the liquid, and the -principal reason why rapid application of heat to a liquid does not -raise its temperature above the boiling point is that as more heat is -applied more bubbles form so that the increase of evaporating surface -supplies a correspondingly greater surface for cooling. The variation of -the boiling temperature with changing pressure may be shown by partly -filling a strong 7/8-in. test-tube with water. Close the neck with a -one-hole rubber stopper through which passes a glass tube to which is -attached a soft rubber tube. (See Fig. 154.) Support the tube by a -holder, heat the water and boil until all the air is driven from the -tube, then close the soft rubber tube with a pinch cock and hold the -tube in an inverted position. On cooling the end of the tube above the -water with cold water or snow, the vapor within is condensed and the -pressure upon the water is reduced. Vigorous boiling begins at once. By -condensing the vapor repeatedly the water may be made to boil at the -room temperature. At the top of Mt. Blanc water boils at 84°C. While in -steam boilers at 225 lbs. pressure to the square inch the boiling point -is nearly 200°C. - -=186. Laws of Boiling.=--The following statements have been found by -experiments to be true. - -1. Every liquid has its own _boiling_ point which under the same -conditions of _pressure_ is always the same. - -2. The temperature of the boiling liquid remains at the boiling point -until all the liquid is changed into vapor. - -3. The boiling point rises with increased pressure and falls if the -pressure is diminished. - -4. A boiling liquid and the vapor formed from it have the same -temperature. On cooling, a vapor will liquefy at the boiling point. - -[Illustration: FIG. 155.--Distilling apparatus.] - -5. The solution of solid substances in a liquid raises its boiling -point, additional energy being needed to overcome the adhesion involved -in the solution. The boiling point is also affected by the character of -the vessel containing the liquid. In glass the boiling point is 101°. - -[Illustration: FIG. 156.--A vacuum pan.] - -=187. Distillation of Water.=--Usually when solids are dissolved in -liquids the vapor coming from the liquid contains none of the dissolved -solid. Thus by evaporating salt sea water, and collecting and condensing -the vapor, pure water is obtained. _Distillation_ is the process of -boiling a liquid and condensing the vapor formed back again into a -liquid. (See Fig. 155.) The liquid to be distilled is placed in vessel -_F_ and boiled. The vapor is conducted into the tube _J_ which is -surrounded by a larger tube containing cold water. The vapor is -condensed on the cold walls of the tube. The resulting liquid is -collected in the vessel _R_. Distillation is employed for two purposes: -(a) To remove impurities from a liquid (water is purified in this way). -(b) Mixtures of different liquids having different boiling points may be -separated by distillation. The one having the lower boiling point will -be vaporized first. Thus a mixture of alcohol and water, on distillation -yields a distillate having a much larger percentage of alcohol than at -first. Repeating this process which is called _fractional distillation_ -yields alcohol of increasing strength of purity. Distilled liquor such -as alcohol, brandy, and whisky are made by distilling fermented liquor, -alcohol being made from fermented grains. Gasoline and kerosene are -distilled from crude petroleum. Sometimes as in the production of sugar -or evaporated milk the object is to remove the water by evaporation in -order to obtain the solid material. Since the two substances named are -injured by heating, the syrup, or milk is evaporated under reduced -pressure in a _vacuum pan_, that is in a boiler from which air and vapor -are removed by an air pump. (See Fig. 156.) - -=188. Artificial Cooling.=--The fact has been brought out that when a -solid is melted, a certain amount of heat, called the heat of fusion, is -absorbed or disappears. This absorption of heat is also noticed when a -solid is liquefied by dissolving it in a liquid as well as when it is -liquefied by simply applying heat. Thus if some table salt is placed in -a tumbler of water the temperature of the solution is lowered several -degrees below that of the salt and water used. The liquefaction or -solution of the salt has been accompanied by an absorption or -disappearance of heat. This heat has been taken from the salt and from -the water, resulting in a lowered temperature. Sal ammoniac or ammonium -nitrate when dissolved in water produce a much more marked cooling -effect than does table salt. The dissolving of a crystal in a liquid is -something like evaporation, except that the molecules of the liquid -attract the molecules of the solid and thus assist the change of state. - -=189. Freezing Mixtures.=--If one attempts to freeze a solution of salt -and water, ice will not form at 0°C. but several degrees lower. The ice -formed however is pure. Evidently the attraction of the molecules of -salt for the water molecules prevented the formation of ice until the -motions of the water molecules had been reduced more than is necessary -in pure water. As the temperature of freezing water is that of melting -ice, ice in a salt solution melts at lower temperature than in pure -water. In a saturated salt solution this temperature is -22°C. It is -for this reason that the mixture of ice and salt used in freezing cream -is so effective, the salt water in melting the ice, being cooled to a -temperature many degrees below the freezing point of the cream. The best -proportion for a freezing mixture of salt and ice is one part salt to -three parts of finely powdered or shaved ice. - -=190. Refrigeration by Evaporation.=--Intense cold is also produced by -permitting the rapid evaporation of liquids under pressure. Carbon -dioxide under high pressure is a liquid, but when allowed to escape into -the air evaporates so rapidly that a portion of the liquid is frozen -into solid carbon dioxide which has a temperature of -80° C. The -evaporation of liquid ammonia by permitting it to escape into a pipe, -under reduced pressure, is used on a large scale as a means of producing -cold in cold storage and refrigeration plants. (See Fig. 157.) - -[Illustration: FIG. 157.--Diagram of a refrigerating system.] - -The essential parts of the refrigerating system employing ammonia is -represented in Fig. 157. The _compressor_ exhausts ammonia gas from the -coiled pipe in "_E_" and compresses the gas in "_C_," where under 150 -pounds pressure and the cooling effect of water it condenses to liquid -ammonia. This is allowed to pass slowly through the regulating valve, -whereupon it evaporates and expands in the long coiled pipe in "_E_" on -its way back to the compressor. This evaporation and expansion causes a -large amount of heat to be absorbed from the brine, cooling the latter -below the freezing point of pure water and thus permitting the freezing -of cans of water suspended in the brine. The chilled brine may also be -sent through pipes in order to cool storage rooms containing meat or -other food products. The ammonia absorbs heat when it vaporizes and -gives up heat when it is compressed and liquified. - - -Important Topics - -1. Heat of vaporization, of water 536 calories per gram. - -2. Boiling point, effect of pressure upon boiling point, laws of -boiling. - -3. Distillation, artificial cooling, freezing mixtures, refrigeration by -evaporation. - - -Exercises - -1. How much heat is required (a) to melt 1 g. of ice at 0°C., (b) to -raise the temperature of the water resulting to 100°C., (c) to change -this water to steam? - -2. If the water leaving a steam radiator is as hot as the steam how is -the room warmed? - -3. What is the effect of placing salt upon icy sidewalks in cold -weather? - -4. Is rain water distilled water? Is it perfectly pure? - -5. What are two advantages of the high heat of vaporization of water? - -6. If the heat from 1 g. of steam at 100°C. in changing to water and -cooling to 0°C. could be used in melting ice at 0°C. how much ice would -be melted? - - -(3) HEAT AND WORK - -=191. Necessity for Heat Energy.=--From early times man has been able to -transform motion into heat, and has used this ability in many directions -as in starting fires and warming himself by friction. It took man many -centuries, however, to devise an effective machine for transforming heat -into mechanical energy or to use it in doing work. - -The _power_ of a man is small and as long as the work of the world had -to be done by man power, progress was retarded. When man began the use -of beasts of burden, he took a long step in advance since one man could -then employ and direct the power of many men in the animals he -controlled. Man also built water-wheels and windmills thus gaining power -directly from the forces of nature and these added much to his working -ability. But he took the greatest step in gaining control over his -surroundings when he learned to use heat energy and to make it drive his -machines. - -=192. Heat Engines.=--At the present time there is a great variety of -_heat engines_ in use such as _steam_, _hot air_, _gas_, and _gasoline_ -engines, all using _heat energy_ to produce motion. The expansive power -of steam when confined has been observed for hundreds of years and many -different machines have been invented to use it in doing work. - -[Illustration: FIG. 158.--Cross-section view of cylinder and steam chest -of a steam engine.] - -[Illustration: FIG. 159.--The steam drives the piston to the left.] - -[Illustration: FIG. 160.--External view of steam engine.] - -=193. The Steam-engine.=--The man who perfected the steam-engine, and -devised its modern form was _James Watt_ (1736-1819). The essential -parts and the action of the steam engine may be readily understood by -studying a diagram. In Fig. 158, _S_ stands for _steam chest_, _C_ for -_cylinder_, _P_ for _piston_ and _v_ for _slide valve_. The first two -are hollow iron boxes, the latter are parts that slide back and forth -within them. The action of the steam engine is as follows: Steam under -pressure enters the steam chest, passes into the cylinder and pushes the -piston to the other end. The slide valve is moved to its position in -Fig. 159. Steam now enters the right end of the cylinder, driving the -piston to the left, the "dead" steam in the left end of the cylinder -escaping at _E_ to the air. The slide valve is now shifted to its first -position and the process is repeated. It will assist the student to -understand this action if he makes a cardboard model of these parts, the -piston and slide valve being movable. In practical steam-engines, the -piston rod is attached to a _crank rod_ fastened to a crank which turns -a wheel. (See Fig. 160.) The back and forth, or _reciprocating_ motion -of the piston is by this means transformed into _rotary_ motion, just as -in the sewing-machine the back-and-forth motion of the treadle produces -rotary motion of the large wheel. Upon the shaft of the steam engine is -fastened an _eccentric_ (see Fig. 163) which moves the slide valve. The -steam engine acts continuously as long as steam is supplied to it. Since -it shifts the position of the slide valve automatically, it is called an -automatic steam engine. And because the team drives the piston both -ways, it is called a _double-acting_ steam engine. See Fig. 161 for a -length-section of a modern locomotive. - -[Illustration: FIG. 161.--Length-section of modern, fast-passenger -locomotive. _A_, cylinder valve--piston type valve; _B_, -cylinder--piston at out end of stroke; _C_, boiler tubes--flues from -fire-box; _D_, fire-tube type superheater; _E_, draught screen; _F-A_, -fire-brick arch to protect tubes from direct heat; _F-B_, firebox; _G_, -grate; _H_, exhaust nozzle; _I_, safety valve nest; _T_, throttle lever; -_R_, throttle rod; _Y_, throttle valve.] - -=194. The Mechanical Equivalent of Heat.=--While watching workmen bore -holes in cannon, Count Rumford, 1753-1814, noticed with much interest -the large amount of heat produced in the process. He observed that the -heat developed seemed to have some relation to the work done upon the -drill in boring the holes. Later experiments performed by many men -indicated that a definite relation exists between the heat produced by -friction and the amount of work done in overcoming the friction. This -discovery indicates that in some way heat is related to energy and that -heat is probably a form of energy. Later experiments have confirmed this -idea, and it is now considered well established that _heat is a form of -energy_. Many attempts have been made to discover the relation between -the units of heat energy and the units of mechanical energy. To -illustrate one method employed, suppose one measures a given _length_ in -inches and in centimeters; on dividing one result by the other, it will -be found that a certain relation exists between the two sets of -measurements, and that in every case that 1 in. equals 2.54 cm. -Similarly, when the same amount of _energy_ is measured both in heat -units and in work units a constant relation is always found between the -units employed. _One B.T.U. is found equivalent to 778 ft.-lbs. 1 -calorie being equivalent to 42,700 g. cm. (427 g. m.)._ This relation is -called the _mechanical equivalent of heat_, or in other words it -represents the number of work units equivalent to one heat unit. - -[Illustration: FIG. 162.--Apparatus for determining the mechanical -equivalent of heat.] - -[Illustration: William Gilbert (1540-1603), "Father of magnetic -philosophy." Especially noted for his experiments and discoveries in -magnetism; first to use the word "electricity." First man to practically -emphasize experimental science. - - DR. WILLIAM GILBERT - (Popular Science Monthly)] - -[Illustration: James Prescott Joule (1818-1889), England, determined the -mechanical equivalent of heat; discovered the relation between an -electric current and the heat produced; first proved experimentally the -identity of various forms of energy. - - JAMES PRESCOTT JOULE - (Popular Science Monthly)] - -One of the first successful experiments in determining the relation -between work units and heat units was devised by Joule in England. (See -portrait p. 217.) The experiment consisted in taking a can of metal -containing water (Fig. 162) in which was placed a thermometer, and a rod -carrying paddles. The rod was turned by a cord connected through -suitable apparatus to heavy weights, _W_ and _W_. The energy represented -by the downward motion of the weights through a given distance was -compared with the heat energy developed in the water as shown by its -rise in temperature. Careful experiments showed that when 778 ft.-lbs. -of work had been done by the moving weights the heat produced at the -same time would warm one pound of water 1 Fahrenheit degree. If the -experiment was performed using metric units, it was found that the -expenditure of 42,700 gram centimeters (427 gram meters) would result in -producing enough heat to warm one gram of water one centigrade degree. -The facts just given may be summarized as follows: _778 foot-pounds of -energy are equivalent to 1 British thermal unit and 42,700 gram -centimeters, or 427 gram meters, of energy are equivalent to 1 calorie_. -This relation of work units to heat units is called the _mechanical -equivalent of heat_. - -=195. The Heat Equivalent of Fuels and Efficiency Tests of Engines.=--To -determine the efficiency of a steam engine it is necessary to know not -only the mechanical equivalent of heat but also the heat produced by -burning coal or gas; 1 lb. of average soft coal should produce about -12,600 B.t.u. Now since 778 ft.-lbs. are equivalent to one B.t.u. the -energy produced when 2 lbs. of average soft coal is burned is 778 × -12,600 × 2 = 19,605,600 ft.-lbs. In actual practice 2 lbs. of average -soft coal burned will develop about 1 horse-power for 1 hour. 1 -horse-power-hour = 33,000 ft.-lbs. × 60 = 1,980,000 ft.-lbs. Now -efficiency equals (work out)/(work in) 1,980,000/19,605,600 = 1/10 or 10 -per cent.. This is the efficiency of a good steam engine. Ordinary ones -require 3 lbs. of coal burned to each horse-power-hour produced or they -are but 2/3 as efficient or have but about 7 per cent. efficiency. - -HEAT OF COMBUSTION OF VARIOUS FUELS - - Data in this table are taken from U. S. Geological Survey, Bulletin - No. 332, and U. S. Bureau of Mines, Bulletin No. 23. - - --------------------------+---------+---------- - | B.T.U. | Calories - | per lb. | per gram - --------------------------+---------+---------- - Alcohol, denatured | 11,600 | 6,450 - Coal, anthracite, average | 12,600 | 7,500 - Coal, bituminous, average | 19,000 | 7,000 - Gasoline | 19,000 | 10,550 - Illuminating gas | 18,000 | 10,000 - Kerosene | 19,990 | 11,050 - --------------------------+---------+---------- - -CONSTANTS FOR HEAT TRANSMISSION - - Data from "Ideal Fitter," American Radiator Co. - -B.t.u. transmitted per square foot per hour per degree (Fahrenheit) -difference in temperature between inside and outside air. - - _Brick work_ - - 4 in. thick = 0.68 { concrete } - 8 in. thick = 0.46 { cement } 50 per cent. more than brick. - 12 in. thick = 0.33 { - - stone 33-1/3 per cent. more than brick. - - Window = 1.090 { - Wood as wall = 0.220 { concrete } 20 per cent. more than - Double window = 0.560 { reinforced } brick. - - -Important Topics - -1. Heat a manifestation of energy. - -2. Steam-engine and its action. - -3. Mechanical equivalent of heat and heat equivalent of fuels and -efficiency of engines. - - -Exercises - -1. Construct a working model of the cylinder and steam chest of a steam -engine and be prepared to explain its action. - -2. At $5.00 per ton how many B.T.U.'s should be produced from 1 cent's -worth of bituminous coal? - -3. Try the following experiment: Place a quart of water in a teakettle -and place it over the fire for 5 minutes, and note the rise in -temperature and compute the number of B.T.U.'s entering the water. Place -another quart of water at the same temperature in an aluminum or tin -dish and heat for 5 minutes, note the rise in temperature and compute -the heat used before. Which of the dishes shows the greater efficiency? -How do the efficiencies of the two dishes compare? How do you account -for any differences in the efficiencies found? - -4. How high would 8 cu. ft. of water be lifted if all of the energy -produced by burning 1 lb. of coal were used in raising it? - -5. What is the mechanical equivalent of a pound of coal expressed in -horse-power hours? - -6. If a furnace burns 100 lbs. of coal a day and its efficiency is 50 -per cent. how many B.T.U.'s are used in warming the house? - -7. How many B.T.U.'s can be obtained by burning 1/2 ton of bituminous -coal? - -8. when a pound of water is heated from 40°F. to 212°F., how many -foot-pounds of energy are absorbed by the water? - -9. How many loads of coal each weighing 2 tons, could be lifted 12 ft. -by the energy put into the water in problem 8? - -[Illustration: FIG. 163.--An eccentric.] - -10. When 3 cu. ft. of water are used for a hot bath and the water has -been heated from 50°F. to 112°F., how many B.T.U.'s have been absorbed -by the water? - -11. If the average temperature of water at the surface of Lake Michigan -is 50°F., how many B.T.U.'s would be given off by each cubic foot of -water at the surface, if the temperature of the water should drop 5°F.? - -12. In a cold storage plant carbon dioxide gas is used. The pipe -leading from the compression pump to the expansion valve passes through -a condensing tank of cold water. Why? - -13. When the gas is compressed in a cold storage plant, what becomes of -the energy used by the compression pump? - -14. An eccentric (Fig. 163), is a round disc mounted a little to one -side of its center, _A_, on the engine shaft _B_. A band, _C_, on the -circumference of the disc is connected by a rod, _D_, with the slide -valve in the steam chest. How is the rotary motion of the shaft changed -into a backward and forward motion of the slide valve? - - -(4) HEAT ENGINES - -=196. The Gas Engine.=--One of the heat engines in common use to-day is -the gasoline engine. It is used to propel automobiles and motor boats, -to drive machinery, etc. The construction and action of a gasoline -engine may be understood by studying a working model, or by proper -diagrams. - -[Illustration: FIG. 164.--Cut away view of a modern automobile engine, -with parts requiring attention most frequently, indicated. (Courtesy of -the "Automobile Journal")] - -The common gasoline or gas engine is called a four-cycle (better -four-part cycle) engine (see Fig. 164), since it requires four -movements of the piston to complete one cycle or series of changes. This -is illustrated in Fig. 165 =1=, which represents a cross-section of the -_cylinder_ of the gasoline engine with the _piston_ moving downward. At -the upper end of the cylinder are two _ports_ or openings. One, the -_exhaust_ port, is closed, the _inlet_ port is open and a mixture of gas -and air is entering. Fig. 165 =2= shows the piston returning; both ports -are closed and the "charge" of air and gas is being compressed. As the -piston reaches the end of its stroke in compressing the charge, an -electric spark explodes or "fires" the charge of gas and air. The hot -burning gas expands suddenly driving the piston downward with great -force (Fig. 165 =3=). The piston rod is attached to the crank of a heavy -fly-wheel and this is given sufficient energy or momentum to keep it -going through the next three strokes. Fig. 165 =4= represents the -returning piston pushing out the burnt "charge" through the open exhaust -valve _e_. On the next downward motion of the piston the valve _e_ -closes. It opens, and new charges of gas and air enter and the "cycle" -is repeated. - -[Illustration: FIG. 165.--The four strokes of a gas engine cycle.] - -In order to make the motion more even and continuous and also to secure -more power, more than one cylinder is attached to the same shaft and -fly-wheel. Two, three, four, six, eight and even more cylinders have -been attached to one shaft. Four or six cylinders are commonly used in -automobile gasoline motors. To lessen the sound of the "exhaust," the -latter is sent through a "muffler" which often reduces the noise to a -low throbbing. (See Fig. 166.) The gasoline engine is more efficient -than the steam-engine, since the fuel, gas, is burned in the cylinder -and not in a separate furnace. The combustion of the fuel in the -cylinders makes some special cooling device necessary to prevent their -overheating. This usually consists of a casing about the cylinders. -Between the cylinder and this casing is water which on being heated -passes to a tank or radiator. In the radiator the water cools and then -returns to the space between the cylinders and casing thus keeping up -the circulation. - -[Illustration: FIG. 166.--An efficient automobile muffler. (_Courtesy -Popular Science Monthly._)] - -=197. Efficiency of Gas Engines.=--One may test the _efficiency_ of a -gas engine by determining the amount of power developed and comparing it -with the mechanical equivalent of the fuel burned. Illuminating gas is -sometimes employed to drive gas engines. One cubic foot of illuminating -gas should produce 600 B.T.U. when burned. The efficiency of the gas or -gasoline engines is sometimes as high as 25 per cent. This engine is -free from smoke and is also compact and quickly started. While the fuel, -gas or gasoline, is somewhat expensive it is light and easily carried. -Suppose a gas engine produces 1 horse-power and uses 20 cu. ft. of gas -an hour, what is its efficiency? 1 horse-power-hour = 550 × 60 × 60 = -1,980,000 ft.-lbs. 20 cu. ft. of gas = 20 × 600 × 778 = 9,336,000 -ft.-lbs. - -Efficiency = work out/work in = 1,980,000/9,336,000 = 21.2 per cent. - -[Illustration: FIG. 167.--The principle of the steam turbine.] - -[Illustration: FIG. 168.--Path of steam in DeLaval steam turbine. (_a_) -and (_c_) movable blades, (_b_) stationary.] - -=198. The Steam Turbine.= One form of the steam-engine that is coming -into general use is the turbine. (See Fig. 167.) This consists of a -shaft to which are attached blades, the shaft and blades being contained -in a closed case. Steam is admitted by nozzles and strikes the blades so -as to set them and the shaft in motion. There are also stationary blades -(see Fig. 168), which assist in directing the steam effectively against -the rotating parts. The steam turbine is used for large power plants. -(See Fig. 293.) It is very efficient, makes very little vibration, and -occupies about one-tenth the floor space that a reciprocating engine of -equal power uses. Some large ocean steamers are now driven by steam -turbines. - - -Important Topics - -1. The gas engine, its construction, action and efficiency. - -2. The steam turbine. - - -Exercises - -1. If coal costs $4.00 a ton, and gas, $0.80 per 1000 cu. ft. what -amounts of heat can be secured from 1 cent's worth of each? - -2. What will it cost to heat 30 gallons of water (1 gal. of water weighs -about 8-1/3 lbs.) from 40°F. to 190°F. with coal costing $4.00 per ton -and yielding 12,000 B.T.U. per lb. if the heater has an efficiency of 50 -per cent. - -3. What will it cost to heat 30 gallons of water from 40°F. to 190°F. -with gas at $0.80 per 1000 cu. ft. if the heating device has an -efficiency of 75 per cent. - -4. Construct a cardboard working-model showing the action of the gas -engine and be prepared to explain the action of the various parts. - -5. If 500 lbs. of iron should fall 2000 ft. and all of the resulting -mechanical kinetic energy should be transformed into heat, what would be -the amount of heat produced? - -6. What are the special advantages of (a) the gasoline engine? (b) the -turbine? (c) the reciprocating steam engine? - -7. Do you burn coal or gas in your kitchen stove at home? Which is for -you the more economical? Why? - -8. What are the advantages of using a fireless cooker? - -9. What is the efficiency of a locomotive that burns 3.2 lbs. of coal -per horse-power-hour? - -10. A gas engine developed in a test 0.34 horse-power for 1 minute. and -50 seconds, 0.5 cu. ft. of gas being used. The heat of combustion of the -gas was 600 B.T.U. per cu. ft. Find the efficiency of the engine. - -11. Find the horse-power of an engine, the diameter of the piston being -19 in., stroke 26 in.; it uses steam at an average pressure of 200 lbs. -per square. inch and makes 100 strokes a minute. - -12. What is the efficiency of an engine and boiler that develops 200 -horse-power, while burning 390 lbs. of soft coal per hour? - -13. If a locomotive has an efficiency of 6 per cent. and develops 1700 -horse-power how much coal is burned in an hour? - -14. If an automobile engine burns 1 gallon of gasoline in an hour and -develops 10 horse-power, what is its efficiency? - -15. The A.L.A.M.[J] formula for horse-power is (_N_ _B_²)/2.5 when the -piston speed is 1000 ft. per minute, _N_ being the number of cylinders -and _B_, their diameter. Find the horse-power of a 4-cylinder engine, -the cylinders having a diameter of 4 in. - - [J] American League of Automobile Manufacturers. - -16. Find the horse-power of a 6-cylinder automobile engine, if the -cylinder diameter is 4.5 in. - -17. A 4-cylinder automobile having 4-in. cylinders, uses 1 gallon of -gasoline in 1 hour. Find its efficiency, if its average horse-power -developed is 6. - -18. The motor boat Disturber III, has 24 cylinders each with diameter -3.5 in. If the piston speed is 1000 ft. per minute, what is the -horse-power? (See problem 15.) - - -Review Outline: Heat - -Heat; sources (4), effects (5), units (2). - -Temperature; thermometer scales (3), absolute temperature, 9C°/5 + 32° = -F°. - -Expansion; gases, Law of Charles (V_{1}/V_{2} = T_{1}/T_{2}), liquids, -peculiarity of water, solids, coefficient of expansion, uses, results. - -Heat Transference; conduction, uses of good and poor conductors, -convection, in nature, heating and ventilating systems, radiation, 3 -peculiarities, value of sun's radiation. - -Heat and Moisture; relative humidity, dew point, formation of dew, fog, -rain, snow, etc., evaporation, effects, conditions. - -Heat Measurement; specific heat, heat of fusion, of vaporization, -combustion. - -Vaporization; Boiling point, laws of boiling, distillation, artificial -cooling. - -Heat Engines; steam, gas.--construction, action, efficiency, mechanical -equivalent of heat. Heat equivalent of fuels. - - - - -CHAPTER IX - -MAGNETISM - - -(1) GENERAL PROPERTIES OF MAGNETS - -=199. Magnets.=--Since the times of the early Greek philosophers men -have known of certain stones that have the property of attracting to -themselves objects of iron and steel. Such stones are called _natural -magnets_. It is thought by many that the name magnet is derived from -Magnesia in Asia Minor, where these stones are abundant, though this is -but tradition. - -It was also learned long ago that iron and steel objects when rubbed -with natural magnets become magnetized, that is, acquire the properties -of magnets. These are said to be _artificial magnets_. - -[Illustration: FIG. 169.--A bar magnet.] - -[Illustration: FIG. 170.--A horseshoe magnet.] - -Some 800 years ago it was discovered that magnets, natural or -artificial, when suspended so as to turn freely, always come to rest in -a definite position pointing approximately north or south. This is -especially noticeable when the magnet is long and narrow. Because of -this property of indicating direction, natural magnets were given the -name of _lodestone_ (lode-leading). - -Artificial magnets are made by rubbing steel bars with a magnet or by -placing the steel bar in a coil of wire through which a current of -electricity is flowing. The magnetized steel bars may have any form, -usually they are either straight or bent into a "U" shape. These forms -are known as _bar_ and _horseshoe_ magnets. (See Figs. 169 and 170.) -Magnets retain their strength best when provided with soft-iron -"_keepers_," as in Fig. 171. - -[Illustration: FIG. 171.--Bar magnets with keepers.] - -=200. Magnetic Poles.=--If a magnet is placed in iron filings and -removed, the filings will be found to cling strongly at places near the -ends of the magnet, but for a portion of its length near the middle no -attraction is found. (See Fig. 172.) These places of greatest attraction -on a magnet are called _poles_. If a bar magnet is suspended so as to -swing freely about a vertical axis the magnetic pole at the end pointing -north is called the _north-seeking_ pole; at the other end, is the -_south-seeking_ pole. In most places the needle does not point to the -true north, but somewhat to the east or west of north. The direction -taken by a magnetic needle is parallel to the _magnetic meridian_. - -[Illustration: FIG. 172.--Iron filings attracted to the poles of a -magnet.] - -=201. Law of Magnetic Action.=--The north pole of a magnet is usually -marked. If a marked bar magnet be held in the hand and its north-seeking -pole be brought near the north-seeking pole of a freely suspended bar -magnet, the two poles will be found to repel each other, as will also -two south-seeking poles, while a north-seeking and a south-seeking pole -attract each other. (See Fig. 173.) This action leads to the statement -of the _Law of Magnetic Action_: _Like poles repel, while unlike poles -attract each other._ The force of attraction or repulsion lessens as the -distance increases. _The force of the action between magnetic poles is -inversely proportional to the square of the distance between them._ -Compare this with the law of gravitation (Art. 88). - -[Illustration: FIG. 173.--Like poles of two magnets repel.] - -[Illustration: FIG. 174.--A magnetoscope.] - -=202. Magnetic Substances and Properties.=--It is found that if an iron -or steel magnet is heated _red hot_ that its magnetic properties -disappear. Accordingly one method of _demagnetizing_ a magnet is to -raise it to a red heat. If a magnet that has been heated red hot and -then cooled is brought near a suspended bar magnet, it is found to -_attract either_ end, showing that it has regained _magnetic properties_ -even though it has lost its _magnetic polarity_. A suspended bar magnet -used to test the magnetic properties of a body is called a -_magnetoscope_. (See Fig. 174.) The needle of a _magnetic compass_ -serves very well as a magnetoscope. Magnetic properties are most -strongly exhibited by iron and steel, though nickel and cobalt show some -magnetic effects. There is a peculiar alloy of copper, aluminum, and -manganese, known as _Heusler's Alloy_, that is also magnetic. However, -of all substances, iron and steel show the strongest magnetic effects. - -=203. Magnetic Induction.=--Let the north-seeking pole of a bar magnet -support an iron nail by its head. (See Fig. 175.) Test the point of the -nail for polarity. See whether a second nail can be attached by its head -to the point of the first. Test the polarity of the point of this nail. -Find by trial how many nails can be suspended in succession from the -magnet. Test in each case for polarity. Withdraw carefully the magnet -from the first nail--the string of nails will fall apart. Repeat the -test with a thickness of paper between the magnet and the first nail. -Results similar to those secured at first will be found, though probably -fewer nails will be supported. The presence of paper between the magnet -and nails simply weakens the action. Test the action of the magnet upon -the nail when there is between them a piece of glass, one's thumb, thin -pieces of wood, copper, zinc, etc. _The magnetizing of a piece of iron -or steel by a magnet near or touching it is called magnetic induction._ -This action takes place through all substances except large bodies of -iron or steel hence these substances are often used as _magnetic -screens_. The pole of the new _induced magnet_ adjacent to the bar -magnet is just opposite to the pole used. Thus the N.-pole of the magnet -used will produce a S.-pole at the near end of the nail and a N.-pole at -the end farther away. (See Fig. 175.) On removing the magnet, the nails -are found to retain a part of their induced magnetism. - -[Illustration: FIG. 175.--Nails magnetized by induction.] - -=204. Retentivity.=--In several of the foregoing paragraphs it has been -seen that a piece of iron or steel when once magnetized does not -entirely lose its magnetism when the magnetizing force is removed. -Different pieces of iron and steel vary greatly in this respect, some -remaining strongly magnetized, others losing much of their magnetism. -_This property of retaining magnetism is called retentivity._ Hardened -steel has a high degree of retentivity, while soft iron retains but -little magnetism. - - -Important Topics - -1. Magnet; natural, artificial, bar, horseshoe. - -2. Magnetic poles; north seeking, south seeking. - -3. Law of action, magnetoscope, retentivity, induced magnet. - - -Exercises - -1. Make a summary of the facts of magnetism presented in this lesson. - -2. Is magnetism matter, force, or energy? How do you decide? To what -other phenomenon that we have studied is it similar? How? - -3. Make a simple magnetoscope for yourself by suspending a thin steel -needle or rod 5 to 10 cm. long, with a light thread or silk fiber at its -center, so that it will hang level. Then magnetize the needle, and keep -the magnetoscope in your book. - -4. Name three uses for magnets or magnetism. - -5. Mention three uses for a magnetoscope. - -6. Are all magnets produced by induction? Explain. - -7. In what magnetic devices is a high retentivity desirable? - - -(2) THE THEORY OF MAGNETISM AND MAGNETIC FIELDS - -=205. The Theory of Magnetism.=--If a magnetized watch spring is broken -in two, _each part_ is found to be a magnet. If one of these parts be -broken and this process of breaking be continued as far as possible, the -smallest part obtained has two poles and is in fact a complete magnet. -(See Fig. 176.) It is supposed that if the division could be continued -far enough that each of the _molecules of the steel spring_ would be -found to have _two poles_ and to be a magnet. In other words, magnetism -is believed to be _molecular_. Other evidence supporting this idea is -found in the fact that when a magnet is heated red hot, to a temperature -of violent molecular motion, its magnetism disappears. Also if a long, -fine soft iron wire be strongly magnetized, a light jar causes its -magnetism to disappear. This would lead us to believe that magnetism is -not a property of the surface of the body, but that it depends upon -molecular structure or the arrangement of the molecules. - -[Illustration: FIG. 176.--Effect of breaking a magnet.] - -[Illustration: FIG. 177.--Possible arrangement of molecules in an -unmagnetized iron bar.] - -It is believed also that the _molecules_ of a magnetic substance are -magnets at all times; that before the body is magnetized the molecules -are arranged haphazard (see Fig. 177) but that when a magnet is brought -near, the molecules tend to arrange themselves in line, with their -north-seeking poles pointing in the same direction. (See Fig. 178.) If -the magnet is jarred some of the molecules tend to get out of line, -perhaps to form little closed chains of molecules. (See Fig. 177.) - -[Illustration: FIG. 178.--Arrangement of molecules in a saturated -magnet.] - -=206. Magnetic Fields and Lines of Force.=--The behavior of magnets is -better understood after observing and studying the _lines of force_ of -a magnet. The earliest descriptions of these are by William Gilbert, the -first Englishman to appreciate fully the value of making experimental -observations. He wrote a book in 1600 called _De Magnete_ in which he -published his experiments and discoveries in magnetism. (See p. 217.) - -Magnetic lines of force may be observed by placing a magnet upon the -table, then laying upon it a sheet of paper and sprinkling over the -latter fine iron filings. On gently tapping the paper, the filings -arrange themselves along curved lines extending from one end of the -magnet to the other. These are called the _magnetic lines of force_. -(See Fig. 179.) The space about a magnet in which the magnetic lines are -found is called the _magnetic field_. (See Fig. 180.) - -[Illustration: FIG. 179.--Iron filings on paper over a bar magnet.] - -Many interesting things have been discovered concerning the lines of -force. Some of the facts of magnetic action are given a simple -explanation if we think of them as due to the magnetic lines of force. A -summary of several discoveries concerning magnetic fields follows: - -(A) Magnetic lines of force run side by side and do not cross one -another. (See magnetic fields.) - -(B) Magnetic lines of force are believed to form "_closed curves_" or to -be continuous. The part outside of the magnet is a continuation of the -part within the magnet. (See Fig. 180.) - -[Illustration: FIG. 180.--Diagram of the field of a bar magnet.] - -(C) The attraction of a magnet is strongest where the magnetic lines are -thickest, hence they are believed to be the means by which a magnet -attracts. - -(D) Since like poles repel and unlike poles attract, it is known that -the action along a line of force is not the same in both directions. It -has therefore been agreed by physicists to indicate by an arrow head -(Fig. 180), the direction that a north-seeking pole tends to move along -a line of force. The lines of force are considered as leaving the -north-seeking pole of a magnet and entering the south-seeking pole. (See -Figs. 181 and 182.) - -[Illustration: FIG. 181.--Magnetic field between like poles showing -repulsion.] - -(E) A freely suspended small magnet in a magnetic field places itself -parallel to the lines of force. (Test this by holding a magnetic compass -in different portions of a magnetic field). Note the position of the -needle and the lines of force. This fact indicates that the compass -needle points north on account of its tendency to turn so as to be -parallel to the earth's magnetic held. - -[Illustration: FIG. 182.--Magnetic field between unlike poles showing -attraction.] - -(F) Each magnet is accompanied by its own magnetic field. When a piece -of iron is brought within the field of a magnet the lines of force -passing through the iron tend to arrange the iron molecules in line or -to magnetize the iron. - -=207. Magnetic Induction.=--The action of magnetic lines of force in -magnetizing iron when they pass through it, is called _Magnetic -Induction_. This may now be defined as _the production of magnetism in a -body by placing it within a magnetic field_. Freely suspended magnets -place themselves parallel to the lines of force in a magnetic field, -therefore when an iron rod is placed in a weak field, or one with few -lines of force, the iron is but slightly magnetized; that is, but few -molecules are brought into line. Increasing the strength of the -magnetizing field, gives stronger magnetization to the iron up to a -certain point. After this, stronger fields give no increase in -magnetizing effect. When iron exhibits its greatest magnetization it is -said to be _saturated_. - -[Illustration: FIG. 183.--Effect of a piece of iron in a magnetic -field.] - -=208. Permeability.=--If a piece of iron is placed between the poles of -a horseshoe magnet, the "field" obtained by sprinkling iron filings upon -a sheet of paper over the magnet resembles that shown in Fig. 183. The -lines in the space between the poles of the magnet seem to crowd in to -the piece of iron. The _property_ of the iron by which it tends to -concentrate and increase the number of lines of force of a magnetic -field is called _permeability_. Soft iron shows high permeability. -Marked differences in behavior are shown by different kinds of iron and -steel when placed in a magnetic field. Very pure iron, or _soft_ iron, -is strongly magnetized by a magnetic field of medium strength. Its -magnetism, however, is quickly lost when the magnetizing field is -removed. This indicates that soft-iron molecules are easily swung into -line, but also disarrange themselves as easily when removed from a -magnetizing force. Soft-iron magnets having high permeability quickly -lose their magnetism. They are therefore called temporary magnets. On -the other hand a hardened steel bar is difficult to magnetize, but when -once magnetized retains its magnetism permanently, unless some action -weakens the magnet. Such magnets are called _permanent_ magnets. - - NOTE.--The term "line of force" as used in this text means the same - as "line of induction" as used in more advanced texts. - - -Important Topics - -1. Molecular theory of magnetism, saturation, permeability. - -2. Magnetic fields and lines of force. - -3. Six facts concerning magnetic fields. - - -Exercises - -1. Name an object whose usefulness depends upon its retentivity. -Explain. - -2. How do you explain the retentivity of hard steel? - -3. Are the molecules of a piece of iron magnetized at all times? -Explain. - -4. When a piece of iron is magnetized by induction does any magnetism -enter the iron from the magnet? Does the magnet lose as the iron gains -magnetism? Explain. - -5. Have all magnets been produced by induction? Explain. - -6. Why will tapping a piece of iron when in a magnetic field increase -the amount it will be magnetized? - -7. Express in your own words the theory of magnetism. - -8. Place two bar magnets in a line 5 cm. apart, _unlike_ poles adjacent; -obtain the magnetic field with iron filings. Sketch it. - -9. Repeat Exercise No. 8 using _like_ poles. Describe the appearance of -a field that gives attraction; of a field that gives repulsion. - - -(3) THE EARTH'S MAGNETISM - -=209. The Earth's Magnetic Field.=--Dr. William Gilbert's famous book, -_De Magnete_, contains many helpful and suggestive ideas, none perhaps -more important than his explanation of the behavior of the compass -needle. He assumed that the earth is a magnet, with a _south-seeking_ -pole near the geographical north pole, and with a _north-seeking_ pole -near the geographical south pole. This idea has since been shown to be -correct. The north magnetic (or south-seeking) pole was found in 1831, -by Sir James Ross in Boothia Felix, Canada. Its approximate present -location as determined by Captain Amundsen in 1905 is latitude 70° 5´ -N. and longitude 96° 46´ W. The south magnetic pole is in latitude 72° -S., longitude 155° 16´ E. The north magnetic pole is continually -changing its position. At present it is moving slowly westward. - -[Illustration: FIG. 184.--Magnetic map of the earth for 1910. Isogonic -lines ------ Isoclinic lines - - - -] - -=210. Direction of the Earth's Magnetic Field.=--Reference has been made -to the fact that the compass does not always point exactly north. This -indicates that the earth's magnetic field varies in its direction. -Columbus discovered this fact upon his first voyage. The discovery -alarmed the sailors since they feared they might come to a place where -the compass would be unreliable. This variation is called _declination_. -It is defined as the _angle between the direction of the needle and the -geographical meridian_. Declination is due to the fact that the -geographical and magnetic poles do not coincide. What is meant by a -declination of 90°? Lines drawn upon a map so as to pass through places -of the same declination are called _isogonic_ lines. The line passing -through points where the needle points north, without declination, is -the _agonic_ line. The agonic line is slowly moving westward. It now -passes near Lansing, Michigan; Cincinnati, Ohio; and Charleston, S. -Carolina. (See Fig. 184.) At all points in the United States and Canada -east of the agonic line the declination is _west_, at points west of the -agonic line the declination is _east_. - -=211. The Dipping Needle.=--Mount an unmagnetized steel needle on a -_horizontal_ axis so as to be in neutral equilibrium, that is, so as to -remain balanced in any position in which it is left. Upon being -magnetized and placed so that it can swing in a north and south plane, -the north-seeking pole will now be found to be depressed, the needle -forming an angle of nearly 70° with the horizontal. (See Fig. 185.) The -position assumed by the needle indicates that the earth's magnetic field -instead of being horizontal in the United States _dips_ down at an -angle of about 70°. Over the magnetic pole, the _dipping needle_ as it -is called, is vertical. At the earth's equator it is nearly horizontal. -_The angle between a horizontal plane and the earth's magnetic lines of -force is called the inclination or dip._ - -[Illustration: FIG. 185.--A dipping needle.] - -=212. Inductive Effect of the Earth's Magnetic Field.=--The earth's -magnetic lines of force are to be considered as filling the space above -the earth, passing through all objects on the surface and into and -through the earth's interior. The _direction_ of the earth's field is -shown by the compass and the dipping needle. Magnetic lines of force -tend to crowd into and follow iron and steel objects on account of their -permeability. Therefore, iron or steel objects, such as posts, columns, -etc., are permeated by the earth's lines of force, which in the United -States enter at the top of these objects and leave at the bottom. The -lines of force passing through these bodies arrange their molecules in -line or magnetize the bodies. The _inductive effect_ of the earth's -magnetism indicates how lodestones or natural magnets acquire their -magnetized condition. So far as is known, magnetism produces no effect -upon the human body. It can therefore be studied only by observing its -effects upon magnets or bodies affected by it. - - -Important Topics - -The earth's magnetic field, dip, declination, agonic line, induction by -the earth's field. - - -Exercises - -1. How would a dipping needle be of assistance in locating the magnetic -poles of the earth? - -2. Will a dipping needle weigh more before or after it is magnetized? -Explain. - -3. It is said that _induction precedes attraction_. Using this idea, -explain how a magnet attracts a piece of soft iron. - -4. Devise an experiment to show that a piece of iron attracts a magnet -just as a magnet attracts a piece of iron. - -5. Give two methods for determining the poles of a magnet. - -6. State three of the most important points in the theory of magnetism. -What evidence supports each? - -7. Why is a permanent magnet injured when it is dropped? - -8. Name two important uses of the earth's magnetic field. - -9. What magnetic pole would you find at the top of an iron post that has -stood for some time in the ground? What pole at the bottom? How would -you test this? - - - - -CHAPTER X - -STATIC ELECTRICITY - - -(1) ELECTRIFICATION AND ELECTRICAL CHARGES - -=213. Electrical Charges.=--The ideas gained in the study of magnetism -are of assistance in the study of electricity in giving some fundamental -ideas and principles that will often be referred to as a basis for -comparing the actions of magnetized and electrified bodies. The process -of electrifying a body is very different from that of magnetizing it. -Thus if a rubber comb or rod be rubbed with a woolen cloth the object -rubbed is able to attract to itself light bits of paper, thread, etc. -This peculiar attraction was noticed and recorded by the ancient Greeks, -600 B.C., when it was found that amber when rubbed would attract light -objects to itself. For a long time it was supposed that amber was the -only substance showing this property. Dr. William Gilbert, however, -discovered that the electrified condition could be produced by rubbing a -great variety of substances. He named the _result_ produced, -_electrification_, after the Greek name for amber (_elektron_). A body -like hard rubber or amber which will attract light objects when rubbed -is said to be _electrified_, or to have been given a _charge_ of -electricity. - -=214. Law of Electric Action.=--Let a vulcanite rod be electrified by -rubbing with a woolen cloth until it will attract light objects; then -place it in a wire stirrup suspended by a silk thread. If a second -vulcanite rod is similarly electrified and brought near the first, the -two will be found to repel. (See Fig. 186.) If now a glass rod be -rubbed with silk and brought near the suspended rod, the two will -_attract_. This difference in behavior indicates a difference in the -electrification or charge upon the rods. The two charged vulcanite rods -repelling and the charged glass and vulcanite attracting indicate _the -law of electric action_. _Like charges repel each other and unlike -charges attract each other._ Extensive experiments with all kinds of -substances indicate that there are but two kinds of electrical charges. -The electrical charge upon glass when rubbed with silk or wool is called -_positive_, and that upon hard rubber or vulcanite when rubbed with wool -is called _negative_. - -[Illustration: FIG. 186.--Repulsion of like charges.] - -[Illustration: FIG. 187.--An aluminum foil electroscope.] - -[Illustration: FIG. 188.--A proof plane.] - -=215. The Electroscope and its Uses.=--An electroscope is a device -employed to test the presence of an electrical charge. The _aluminum -foil electroscope_ consists of a flask closed by a rubber stopper -through which passes a rod which ends at the top in a ball or plate and -below is attached two narrow leaves of thin aluminum-foil. Ordinarily -the two leaves hang close together and parallel but if a charged body is -brought near the electroscope the leaves spread apart at the bottom. -(See Fig. 187.) The _kind of charge_ upon a body may be determined with -an electroscope as follows: Make a _proof-plane_ by sealing a small -metal disc on the end of a hard rubber rod. (See Fig. 188.) Touch the -disc of the proof-plane first to a charged rubber rod and then to the -top of the electroscope. The leaves of the latter will separate showing -that the electroscope is charged. This charge remains after the -proof-plane is removed. If the charged vulcanite rod is brought near the -electroscope, the leaves separate further That is, a charge _like_ that -on the electroscope makes the leaves separate further. But if an -_unlike_ charge, as that on a positively charged glass rod, is -cautiously brought near, the leaves will be seen to move together. - -[Illustration: FIG. 189.--Rod with woolen cap.] - -=216. Two Charges are Produced at the Same Time.=--A closely fitting -woolen cover or cap some 3 in. long is made for the end of a vulcanite -rod. A silk thread attached to the cap enables one to hold the latter -while the rod is turned within it. (See Fig. 189.) If the rod bearing -the cap is held near a charged electroscope little or no effect is -noticed. If now the cap is removed by the silk thread and held near the -electroscope, it will be found to be positively charged while the rod is -negatively charged. The fact that no result is seen when the cap and rod -are together, indicates that one charge neutralizes the other. In other -words, _the charges_ must _be equal_. This illustrates the truth that -_when electrification is produced by friction, the two objects rubbed -together acquire equal and opposite charges_. - -=217. Charging by Contact and Conduction.=--If a small pith ball is -suspended by a silk thread, a charged rod brought near is at first -attracted, but after contact is repelled (see Fig. 190) showing that the -ball has become charged with the same kind of electrification that is -upon the rod. That is, a charge given to an object by _contact_ with a -charged body is of the _same kind_ as that upon the charged one. The -proof-plane in Art. 215 carries the same kind of charge that is upon the -rod it is charged from. Some substances have the ability to transfer -charges of electrification. These are called _conductors_, those that do -not conduct electrification are _insulators_. The conducting power of a -body is readily tested by placing one end of a rod of the material upon -the top of an electroscope and the other end upon an insulated support, -as in Fig. 191. If now a charge be put in contact with the body of _a_, -the electroscope will show by its leaves whether the rod tested conducts -or not. The leaves separate instantly when conducting substances are -tested, while no action results with insulators. In testing some -materials for conductivity the leaves are found to diverge gradually. -Such bodies are said to be _poor_ conductors. All degrees of -conductivity are found. The metals are the best conductors. The best -insulators are rubber, mica, shellac, glass, silk, porcelain, paraffin, -and oils. - -[Illustration: FIG. 190.--The pith ball charged by contact is repelled.] - -[Illustration: FIG. 191.--Testing for conductivity.] - - -Important Topics - -1. Positive and negative changes. Law of electric action. - -2. Electroscope and its uses. - -3. Conductors and insulators. - - -Exercises - -1. Is air a conductor? Give reasons for your answer. - -2. Mention two points of likeness and two points of difference between -magnetism and electrification. - -3. If you were testing the electrification of a body with a charged pith -ball suspended by a silk thread, would attraction or repulsion be the -better test? Give reasons. - -4. Have you ever produced electrification by friction outside of a -laboratory? Explain. - -5. Are the rods upon which we produce electrification by friction, -conductors or insulators? How do you explain this? - -6. Are conductors or insulators of the greater importance in practical -electricity? Explain. - - -(2) ELECTRIC FIELDS AND ELECTROSTATIC INDUCTION - -[Illustration: FIG. 192.--An electric field about a positively charged -shell.] - -[Illustration: FIG. 193.--A "detector."] - -=218. Electrical Fields.=--In our study of magnetism we learned that a -magnet affects objects about it by its magnetic lines of force. In a -similar way it is assumed that a charged body produces electrical -effects upon its surroundings by _electric lines of force_. For example, -the attraction that a charged body exerts upon light objects through -short distances or the influence of a charge upon an electroscope -several feet away, is said to be due to the _electric field_ about the -charged body. (See Fig. 192.) The presence of the electric lines of -force may be shown by placing a perforated, slender, diamond-shaped -piece of tissue paper upon a light glass pointer (Fig. 193). When -placed in an electric field the tissue paper "detector" places itself -parallel to the lines of force. Electric lines of force are said to -extend from a positive to a negative charge. (See Fig. 194.) The -direction shown by the arrow upon the lines is that along which a small -positive charge tends to move. Electric lines of force unlike those from -magnets are _not_ continuous. They extend from a positive charge to a -negative charge. Therefore each positive charge is connected by lines of -force to a negative charge somewhere. These ideas of electric fields are -of much assistance in explaining many electrical effects. Electrical -fields between _oppositely_ charged shells will be found similar to Fig. -194, while between shells with like charges, fields are found as in Fig. -195. - -[Illustration: FIG. 194.--Electric field between unlike charges.] - -[Illustration: FIG. 195.--Electric field between like charges.] - -=219. Electrostatic Induction.=--If a charged body is brought near an -aluminum-foil electroscope, the leaves separate. (See Fig. 198.) The -nearer the charge is brought the wider the leaves spread, but when the -charge is removed, the leaves collapse showing that nothing was given to -the electroscope. It was simply affected by the charge in its vicinity. -_This production of an electrified condition in a body by the influence -of a charge near it is called electrostatic induction._ Placing -insulators, such as a sheet of glass, between the charge and the -electroscope does not affect the result, which is apparently brought -about by the action of the electric lines of force. These lines of force -extend without difficulty _through uncharged insulators_ and terminate -often at the surface of a conductor, where their influence causes a -charge to accumulate. _Charged insulators_, however, do affect inductive -action. This may be noticed by using a sensitive electroscope. - -[Illustration: FIG. 196.--Production of two charges by the influence of -a third charge.] - -[Illustration: FIG. 197.--The two charges separated.] - -=220. Electrical Separation by Induction.=--The action just described -may be illustrated further by taking two insulated, uncharged brass -shells, _A_ and _B_. (See Fig. 196.) Bring a charged vulcanite rod near -shell "_A_" while the shells are touching each other. Then remove shell -_B_ (Fig. 197) while the rod remains near _A_. On testing the shells for -electrification, _A_ is found to possess a positive charge. This action -is in some respects similar to magnetic induction, for if one places a -north-seeking pole near a piece of iron, the iron develops by induction -a south-seeking pole at the end nearest the magnet and a north-seeking -at the other end. There is, however, one striking difference. If the -magnetized iron be separated into two parts, each part is a complete -magnet possessing two unlike poles; while if the object affected by -electrostatic induction is separated into two parts _one part_ has a -_positive_ charge and the other a _negative_ charge. - -[Illustration: FIG. 198.--Effect of a charged rod near an electroscope.] - -[Illustration: FIG. 199.--When a finger is touched to the top of the -electroscope, the repelled negative charge escapes.] - -[Illustration: FIG. 200.--The electroscope is now positively charged.] - -=221. Charging a body by induction= is easily accomplished. To charge an -aluminum-foil electroscope by induction bring _near_ (say 10 cm.) from -the top of the electroscope a charged rubber rod. (See Fig. 198.) The -separated leaves show the presence of the repelled or _negative_ charge, -the _positive_ charge being on the disc at the top. If while the charged -rod is held near, the metal top of the electroscope is touched by the -finger the leaves at once fall together showing that the repelled -negative charge has escaped from the electroscope (Fig. 199). On -removing _first_ the _finger_ and next the charged rod, the positive -charge spreads over the metal parts of the electroscope, as is shown by -the separation of the leaves (Fig. 200). The electroscope is now -_charged positively_ by induction. If the charged rubber rod is brought -to about 30 cm. from the electroscope, its leaves tend to move -together. If a body charged similarly to the electroscope or -_positively_, is moved toward the electroscope the leaves separate -further. This behavior of the electroscope enables one to determine the -_kind_ of charge upon a body. - -Two principles of _electrostatic_ induction may now be stated: (1) Two -_equal_, _unlike_ charges are always produced by _electrostatic_ -induction. - -(2) If the body affected by induction is connected to the earth by a -conductor, the repelled or "_free_" charge is conducted away from the -body while the "_bound_" charge is held by the inducing charge. - -These principles apply in every case of induction. - - -Important Topics - -1. Electric lines of force. Characteristics (3). - -2. Electrostatic induction. Principles (2). - -3. Charging by induction. Explanation. - - -Exercises - -1. What are electric lines of force? Where are they found? What does the -arrow mean upon the lines? - -2. Name three effects produced by electric fields. - -3. Does electrostatic induction occur outside of laboratories? Where? -When? - -4. Given a charged rubber rod, how may one charge from it by induction, -insulated brass shells, giving some a positive and some a negative -charge? - -5. How may the charges upon the shells be tested? - -6. In charging an electroscope by induction, why must the finger be -removed before the glass rod? - -7. Why is it best to have the rubber and glass rods, used in -electrification, warmer than the air of the room in which the -experiments are being performed? - -8. When a sharp metallic point is held near the knob of a charged -electroscope the leaves quickly come together. Explain. - -9. Might one of the members of your class in physics be charged with -electricity, if he should stand on a board supported by dry glass -insulators? Explain. - -10. If a metal can is charged strongly while standing on an insulator, -tests made by means of the proof-plane and electroscope show no charge -on the inside. Explain. - - -(3) ELECTRICAL THEORIES AND DISTRIBUTION OF CHARGES - -=222. Franklin's Theory of Electricity.=--We have studied the production -of electrification by friction and induction. It will be helpful now to -consider some of the theories of electricity. From the ease with which -electrification moves, along a conductor, many have imagined that -electricity is a fluid. Benjamin Franklin's _One Fluid Theory_ held that -a _positive_ charge consisted in an accumulation or an excess of -electricity while a _negative_ charge implies a deficiency or less than -the usual amount. This theory led to representing positive -electrification by a plus (+) sign and _negative_, by a minus (-) sign. -These signs are in general use to-day. The use and significance of these -signs should be clearly fixed in mind. - -=223. The Electron Theory.=--Various discoveries and experiments made in -recent years indicate, however, that _negative_ electricity consists of -little _corpuscles_ or _electrons_ which may pass readily from one -molecule of a conductor to another while their movement through an -insulator is much retarded if not entirely prevented. This theory, -sometimes called the _Electron Theory_, holds that each atom of a -substance has as a nucleus a corpuscle of _positive_ electricity, and -surrounding it, minute negative corpuscles or electrons. It is thought -that the electrons in the atom are very much smaller than the positive -charges and are revolving about the latter with great rapidity. -Ordinarily, the positive and negative charges are equal so that the atom -is in a neutral or uncharged condition. By the action of various forces -some of the _negative_ corpuscles within a conductor may be moved from -molecule to molecule. Thus if a negatively charged rod is brought near a -conductor, many electrons stream away to the far end charging it -_negatively_, while the nearer end of the conductor is left with fewer -electrons than usual along with the fixed positive corpuscles. Hence the -near end is positively charged. (See Fig. 198.) On the other hand, if a -positive charge is used, it attracts the electrons from the far end, -leaving the immovable positive corpuscles there, and that end becomes -positively electrified, while the nearer end with its surplus of -electrons is, of course, negatively electrified. - -The Electron Theory is considered well founded since the electrons have -(a) had their _mass_ determined, (b) their _speed_ measured, (c) their -_electric charge_ determined, (d) and their _behavior_ while _passing -through magnetic_ and _electric fields_ observed. These facts and other -experimental evidence have demonstrated the existence of electrons. The -positive corpuscle has not been directly observed but is assumed to -exist to account for the effects observed in induction, charging by -friction, etc. - -=224. Distribution of an Electric Charge upon a Conductor.=--We have -applied the electron theory in explaining the phenomenon of -electrostatic induction. Let us now use it in studying the distribution -of an electric charge upon a conductor. Let a cylindrical metal vessel -open at the top and insulated by being placed upon pieces of sealing wax -have a charge of negative electricity given it. (See Fig. 201.) On now -taking a proof plane and attempting to obtain a charge from the -_interior_ of the vessel no result is found, while a charge is readily -obtained from the _outside_ of the dish. This result is explained by -considering that the electrons are mutually self-repellent and in their -attempt to separate as widely as possible pass to the outer surface of -the vessel. This same condition is also true of a dish made of woven -wire. If the charged conductor is not spherical in outline, an uneven -distribution of the charge is observed. Thus if an _egg-shaped_ -conductor is insulated and charged (see Fig. 202), a proof plane touched -to the broad end of the body and then to an electroscope causes a -certain divergence of the leaves of the latter. If now a charge be taken -from the _pointed_ end by the proof plane to the uncharged electroscope, -a greater spreading of the leaves than before will be noticed. This -indicates that the electricity may be unevenly distributed over the -surface of a body. It is found that the _electric density_, as it is -called, is greatest where the surface curves most sharply. At a very -sharp curve, as at a point, the electric density may be so great that a -part of the charge escapes into the air. (See Fig. 203.) For this reason -electric conductors on which it is desired to _keep_ an electric charge -have round surfaces and all sharp points and corners are avoided. While -conductors, such as lightning rods, which are designed to facilitate the -escape of electric charges, are provided with a number of sharp points -at the end or elsewhere. At such points, air particles are drawn -forcibly against the point and after being charged are driven away -strongly, creating the so-called _electrical wind_ which carries away -the charge at a rapid rate. (See Fig. 203.) - -[Illustration: FIG. 201.--No charge is found inside a hollow vessel.] - -[Illustration: FIG. 202.--More charge at the pointed end.] - -=225. Lightning and Electricity.=--The fact that lightning is an -electrical discharge was first shown in 1752 by Benjamin Franklin, who -drew electric charges from a cloud by flying a kite in a thunderstorm. -With the electricity which passed down the kite string he performed a -number of electrical experiments. This discovery made Franklin famous -among scientific men everywhere. Franklin then suggested the use of -lightning rods to protect buildings from lightning. These rods act as -conductors for the electric discharge and thus prevent it from passing -through the building, with the risk of overheating some part and setting -the latter on fire. The points provided at the top of lightning rods are -believed to aid in preventing strokes of lightning by the _silent -discharge_ of the so-called electric wind which tends to quietly unite -the charges in the clouds and on the earth beneath. - -[Illustration: FIG. 203.--Electrical wind produced by a pointed -conductor.] - -[Illustration: FIG. 204.--Electrical whirl. The reaction from the -electrical wind causes it to revolve.] - -[Illustration: FIG 205. The wire screen protects the electroscope.] - -The charge in an electrified cloud acts inductively upon the earth -beneath, attracting an opposite charge to the objects below. The -discharge from the cloud often passes to the objects beneath, such as -trees or buildings. _Thunder_ is believed to be due to the sudden -expansion of the air when intensely heated by the electric discharge -and its sudden contraction, like a _slap_, as the track instantly cools. -Thunder at a distance is usually followed by rumblings due to changes in -the intensity of the sound mainly due to reflections of sound waves from -clouds and other reflecting surfaces. - -=226. An electric screen= is a device for cutting off the influence of -an electric charge. Faraday found that if a sensitive electroscope is -surrounded by a wire mesh screen (see Fig. 205), no evidence of -electrification could be found inside. In other words, a network of -conductors on a building makes the best protection against lightning, -provided it is connected to the earth by good conductors at several -places. - - -Important Topics - -1. Electrical theories. Evidences for electron theory. - -2. How is the theory used in explaining induction? - -3. Charges, and distribution on conductors (effect of shape). - -4. Lightning: cause, effects, lightning rods. - - -Exercises - -1. In what respects is Franklin's one-fluid theory like the electron -theory? In what respects different? - -2. Consider two shells charged by induction from an electrified rubber -rod, one positively and one negatively. Explain the process, using the -ideas of the electron theory. - -3. Should the metal top of an electroscope have sharp corners? Explain. - -4. Would a tall steel tower have the same need of a lightning rod as a -brick chimney of the same height? Explain. - -5. Will a solid sphere hold a greater charge of electricity than a -hollow one of the same diameter? Explain. - -6. If a positively charged cloud floats over a tree which is a good -conductor of electricity will the tree be charged? Show diagram. -Explain. - - -(4) POTENTIAL, CAPACITY AND THE ELECTRIC CONDENSER - -=227. Conditions Causing a Movement of Electricity.=--In the study of -conductors and insulators it was observed that an electric charge moved -along the conducting rod to the electroscope. This _movement_ of -_electricity_ along a conductor is a result of great practical -importance. We will now consider the conditions that produce the "flow" -or "current" of electricity. Let two electroscopes stand near each -other. Charge one, _C´_ (Fig. 206), strongly and charge the other -slightly. If now a light stiff wire attached to a stick of sealing wax -be placed so as to connect the tops of the electroscopes, the leaves of -_C_ will partly close while those of _D_ will open slightly, thus -indicating a movement of electricity from _C_ to _D_ along the wire. The -movement was from a place of greater degree of electrification to one of -less. - -[Illustration: FIG. 206.--Electricity flows from high to low potential.] - -=228. Potential.=--The _potential_ of an electrified body is its -_degree_ of _electrification_. Therefore, it is said that electroscope -_C_ mentioned above has a greater potential than electroscope _D_. The -movement of electricity is from a place of greater or _high_ potential -to one of lesser or _low_ potential. If two bodies are at the _same_ -potential there will be found no movement of electricity between them. A -_difference_ of _potential_ between two points connected by a conductor -is therefore the _necessary condition_ for an electric current. Just as -heat is transmitted along a conductor from a place of high to one of -lower temperature, so electricity is transmitted along a conductor from -a place of high to one of low potential. Thus potential in electricity -corresponds to temperature in heat. One is the "degree of -electrification," the other, "the degree of hotness." - -[Illustration: FIG. 207.--Air pressure apparatus to illustrate -electrical pressure.] - -=229. Electrical pressure= is a term sometimes used for difference of -potential. To better understand electrical pressure consider three round -tanks (Fig. 207) containing air. _A_ is a tank holding air at 10 lbs. -pressure per square inch, above atmospheric pressure, _B_ is open to the -air and hence is at atmospheric pressure while _C_ has a partial vacuum, -with 10 lbs. less pressure than that of the atmosphere. If the valve at -_D_ or _E_ is opened a flow of air sets up until the pressures are -equalized. While if the pump at _P_ is working a difference in pressure -is easily maintained. Tank _A_ corresponds to an insulated body charged -to a high _positive_ potential; tank _B_, open to the air, a body -connected to the earth; while tank _C_ represents a body having a -_negative_ potential. The earth is said to have _zero potential_. - -Now just as compressed air will be pushed into the atmosphere (as from -_A_ to _B_) while air at atmospheric pressure will if possible be forced -itself into a partial vacuum (as from _B_ to _C_), so electricity at a -positive potential will tend to move to a place at zero potential, while -that at zero potential tends to move to a place of negative potential. -Bodies at the _same_ potential as the earth, or at zero potential, are -also said to be _neutral_. Those positively electrified have a positive -potential, those negatively electrified have a negative potential. As in -gases, movement always tends from higher pressure (potential) to lower -pressure (potential). - -[Illustration: FIG. 208.--The metal plate gives the electroscope a -greater surface and hence greater capacity.] - -=230. Capacity.=--If we have a 100-gallon tank and a 10-gallon tank -connected by a pipe both filled with compressed air, the larger tank -will contain ten times as much air as the smaller at the _same pressure_ -since it has ten times the capacity, or, if the two tanks are separated -and the same amount of air is contained in each, the pressure of the air -contained in the small tank will be ten times that in the large one. - -The _electrical capacity_ of a conductor is in some respects similar to -the capacity of a tank for air. Since, however, electrical charges are -upon the surface of a body, its capacity depends in part upon the extent -of surface. For example, if a charge is taken from a charged rubber rod -by a proof plane to an electroscope a certain divergence of the leaves -will be noticed. If a circular metal plate several times the diameter of -the top of the electroscope is laid upon the latter (see Fig. 208), and -a charge equal to that used before is brought to the electroscope, the -leaves show less divergence than before, showing that the _same charge -gives a lower potential when placed upon a body of greater capacity_. - -[Illustration: FIG. 209.--A plate condenser.] - -[Illustration: FIG. 210.--A condenser of several plates.] - -=231. The electric condenser= is a device having a large electrical -capacity consisting of parallel conductors separated by good insulators. -It has been devised to enable one to obtain a large electrical charge -upon a body of convenient size. Such an apparatus is of great practical -value in many experiments and operations. Its construction involves the -principle of electrostatic induction in which a charge of one kind -attracts and "holds" strongly a charge of opposite kind near it. In its -simplest form it consists of two parallel conductors separated from each -other (Fig. 209). The upper plate has been charged negatively. This has -given the lower plate a positive charge by induction, since the latter -is connected to the earth. These positive and negative charges hold or -"bind" each other so that a large quantity may be accumulated. To -increase the capacity of a condenser, several plates are used connected -as in Fig. 210. - -It is a curious fact that the kind of insulator between the charged -conductors of a condenser affects its capacity. Thus if glass, -paraffine, or beeswax is between the plates instead of air, the plates -will "hold" more electricity at the same potential. For this reason -condenser plates are often separated by sheets of glass, paraffined -paper, or mica. - -[Illustration: FIG. 211.--A Leyden jar and a discharger.] - -=232. The Leyden Jar.=--A convenient form of condenser, used as long ago -as 1745, is the Leyden jar. It consists of a glass jar (Fig. 211) coated -part way up, inside and out, with tinfoil. The inner coating is -connected by a chain to a knob at the top. The Leyden jar is charged by -connecting the outer coating to the earth while to the inner coating is -given a charge of either kind of electricity. The other kind of charge -is developed by induction upon the outer coating, and each charge binds -the other. To discharge a jar, a conductor, as a wire, is connected -first to the outer coating and held there while the other end is brought -to the knob at the top. A bright spark is produced when the two charges -combine. It is best not to let the discharge from the jar pass through -the body unless one is certain that only a very small charge is present. - -=233. Oscillatory Discharge.=--The discharge from a Leyden jar is an -interesting phenomenon. The rush of electricity from one coat to the -other does not stop when the two coats are exactly neutralized but -continues until the two plates are charged just oppositely to their -condition at first, then a rush of electricity in the opposite direction -occurs. This alternation continues several times and constitutes what is -called the _oscillatory discharge_. (See Fig. 414.) This oscillatory -discharge sets up waves in the ether. These are called _Hertzian_ waves -in honor of their discoverer, Heinrich Hertz. They are the ether waves -used in wireless telegraphy. A _lightning flash_ has been shown by -photographs and by other means to be oscillatory. This fact supports the -idea that the electrical conditions just preceding the stroke of -lightning reproduce a condenser on a large scale. The charged cloud is -the upper charged plate, the earth beneath, charged by induction from -the cloud, is the lower charged plate, while the air between is the -insulator or _dielectric_ as it is sometimes called. - - -Important Topics - -1. Potential: high, low, zero, positive, negative, similar to -temperature and air pressure. - -2. _Capacity_ affected by (1) area, (2) induction. - -3. Condensers, Leyden jar, parallel plate. - -4. Oscillatory discharge, conditions, results. - - -Exercises - -1. Is the air a conductor? Explain. - -2. Can the Leyden jar be strongly charged if the outer coat is -insulated? Explain. - -3. Upon what two conditions does the capacity of a body depend? How in -each case? - -4. Would a lightning discharge produce wireless waves? Explain. - -5. If a sharp tack be dropped point up on the plate of an electroscope -the latter is quickly discharged. Explain. - - -(5) ELECTROSTATIC GENERATORS - -=234. Static Electric Machines.=--Many machines have been invented to -produce larger quantities of static electricity than we have used in the -experiments previously described. One of the earlier of these was the -_plate friction machine_ in which a large circular glass plate was -rotated while a pad of some material was held against it. This machine -was capable of producing powerful effects, but it took much work to -turn it, and it has been abandoned for a more efficient device, the -_static induction machine_. - -=235. The electrophorus= is the simplest static induction generator, -consisting simply of a flat circular plate of some insulating material, -as paraffine, shellac, or rosin contained in a metal pan, and a flat -circular metal _disc_ having an insulating handle. - -[Illustration: FIG. 212.--An electrophorus.] - -_The electrophorus is used as follows_: The plate is first electrified -by rubbing or beating with fur or a woolen cloth. The plate will be -found to be charged negatively. The metal disc is placed upon the plate -by holding the insulating handle. The upper surface of the charged body -is slightly uneven so that the disc touches but a few high points. The -greater part of the charged surface is separated from the metal disc by -air, a good insulator. The charge therefore acts inductively upon the -disc _repelling negative_ electricity to the upper surface of the disc, -leaving the lower surface charged positively (Fig. 212). If now the -finger is touched to the disc the repelled negative charge escapes and -the whole disc is left positively charged. The disc is now removed (Fig. -213) and the charge upon it may be tested or used in any desired manner. -The disc may be recharged many times without rubbing the plate again. - -[Illustration: FIG. 213.--Electrophorus charged.] - -These electrical charges possess _energy_. What is the source of this -energy? The answer may be determined by the following experiment. Place -the disc upon the charged plate. Touch the disc with the finger to -remove the repelled charge. Connect an electroscope to the disc by a -fine wire. Nothing appears on the electroscope, since the disc has been -connected to the earth, and is therefore at zero potential. If now the -disc is lifted slowly, the leaves of the electroscope gradually -separate, showing that a charge of electricity appears when the disc is -being lifted against the force of attraction between the two charges. -Just as potential energy is developed in a weight when it is lifted -against the earth's attraction so electrical energy appears in the disc -while it is being separated from the plate. The electrical energy of the -charge is therefore due to the work done in separating the two charges. -This electrical energy appears as heat and light, when the disc is -discharged. It may be employed to ignite gas, gunpowder, etc. - -=236. The Toepler-Holtz Induction Machine.=--This is a type of induction -or influence machine that is often used for producing a continuous -supply of electricity as in the operation of "X" ray machines, in -lecture demonstrations, etc. This machine (Fig. 214) consists of two -discs: one fixed, the other mounted so as to revolve. Upon the back of -the fixed plate are two sectors of tinfoil which become charged -oppositely. Upon the revolving plate are six metallic discs. These discs -act like the discs of the electrophorus. They become charged by -induction from the charges upon the sectors fastened to the fixed plate. -The brushes held by a rod touch the discs at just the right time to take -off the repelled charge. The charges induced upon the discs are taken -off by two metal combs whose points are held close to the revolving -disc. The Leyden jars assist in accumulating a good strong charge -before a spark passes between the terminal knobs. Some machines are -built up of several pairs of plates and give correspondingly large -amounts of electricity. - -[Illustration: FIG. 214.--The Toepler-Holtz induction machine.] - - -Important Topics - -_Static Electric Generators._--(a) plate friction machine, (b) -electrophorus, (c) induction or influence machine. - - -Exercises - -1. Potential is similar to what other terms that we have studied? - -2. What three electrical phenomena are better understood from a study of -the lines of force? - -3. How many charges may be produced by an electrophorus before the plate -needs to be electrified again? Explain. - -4. The static induction machine is often called a "continuous -electrophorous." Why? - -5. The Leyden jars used with the induction machine cause much brighter -sparks to be produced than without them. Explain. - -6. With the Leyden jars removed, would the frequency with which the -sparks pass between the knobs be increased or decreased? Explain. - -7. Mention three likenesses and three differences between magnetism and -static electricity. - -8. Will you receive a greater shock by touching a knob of a charged -Leyden jar when it is held in the hand or when it is standing on a sheet -of glass? Explain. - -9. In what way may an electric charge be divided into three equal -parts? - - -Review Outline: Magnetism and Static Electricity - -Comparison between Magnetism and Static Electricity. - - Substances are: { magnetic, { conductors, - { non-magnetic. { insulators. - - Produced by: induction. friction, or induction. - - Theory: molecular. electron. (fluid) - - { attraction, { attraction, - Fields of Force { repulsion, { repulsion, - Explain: { induction, { induction. - { action of compass. - - { magnetoscope, dip, { electroscope, electron, - { declination, pole, { positive, negative, - { retentivity, { potential, capacity, - Terms: { permeability, { condenser, electrophorus, - { lodestone, { oscillatory discharge, - { magnetic meridian. { lightning. - - Likeness: { _a_--produced by induction, _b_--attract - both are: { and repel, _c_--have fields of force. - - { _a_--electricity can be _conducted_, - { magnetism cannot. - { - Differences: { _b_--electricity in _all substances_, - { magnetism in few. - { - { _c_--magnetism with the compass indicates - { direction. - - - - -CHAPTER XI - -CURRENT ELECTRICITY - - -(1) ELECTRICAL CURRENTS AND CIRCUITS - -=237. Sources of Electric Currents.=--In studying the production and -distribution of static electricity it was seen that if two bodies at -_different potentials_ are connected by a copper wire a _movement of -electricity to the body_ having the _lower potential_ occurred along the -conducting wire. This movement of electricity is called an _electric -current_ (Art. 227). _A difference of potential_ is therefore often -called an _electromotive force_ (E.M.F.), since it produces the movement -of electricity in a conductor. The current between two _oppositely -charged_ bodies lasts for so short a time as to be of little or no -practical value unless some means are found for continually recharging -the bodies. That is, some device must be used to restore the difference -in potential as fast as the conducting wire equalizes it. The continual -charging of the bodies takes work. In other words, it requires a -continual expenditure of some form of energy (which is converted into -electrical energy) to produce the electric current. Two forms of energy -are commonly used for this purpose. - -(A) _Chemical energy_ is employed in _voltaic cells_ for producing -electric currents. (B) _Mechanical energy_ is used for the same purpose -in the _dynamo_ and similar devices. - -=238. The voltaic cell= is named after Volta, an Italian physicist, who -in 1800 invented it. In its simplest form it consists of a strip of -copper and a strip of zinc placed in dilute sulphuric acid (one part -acid to fifteen or twenty of water) (Fig. 215). By the use of sensitive -apparatus, it can be shown that the copper plate of the voltaic cell has -a positive charge and the zinc plate a negative charge. For example, let -a flat plate 10 cm. in diameter be placed upon the knob of an -electroscope and a similar plate, coated with shellac and provided with -an insulating handle, be set upon it to form a condenser. (See Fig. -216.) If now wires from the two plates of a simple voltaic cell be -respectively connected to the plates of the condenser, charges from the -copper and zinc plates will accumulate upon the two condenser plates. -Now remove the wires and lift the upper plate. The "bound" charge upon -the lower plate will spread over the leaves and cause them to separate. -Upon testing, the charge from the zinc plate will be found to be -_negative_ and that from the copper plate, _positive_. Since a positive -charge is found upon the copper plate it is called the _positive -electrode_; the zinc plate is called the _negative electrode_. - -[Illustration: FIG. 215.--Cross-section of a simple voltaic cell.] - -[Illustration: FIG. 216.--Testing the charges upon the plates of a -simple voltaic cell.] - -=239. Test for an Electric Current.=--If the copper and zinc plates of a -voltaic cell are connected by a wire, a current of electricity is set -up in the conductor. Evidence of the current may be obtained by holding -the conducting wire over and parallel to the needle of a magnetoscope. -The needle is deflected by the action of the current parallel to it -(Fig. 217). This _magnetic effect_ of a current is the means usually -employed for the _detection_ and _measurement_ of an electric current. -Such a device which detects an electric current by its _magnetic effect -is called a galvanoscope_, in honor of Galvani, who in 1786 was the -first to discover how to produce an electric current. - -[Illustration: FIG. 217.--The magnetic needle is deflected by the -current.] - -[Illustration: FIG. 218.--Diagram of an electric bell circuit.] - -=240. The Electric Circuit.=--_The entire conducting path along which a -current of electricity flows is called an electric circuit._ In the case -of a voltaic cell, the circuit includes not only the wires connecting -the plates but also the plates themselves and the liquid between them. -When some device or apparatus is to receive current from the cell, it is -attached to the plates and wires so that the device is a part of the -electric circuit. Separating the circuit at any point is called -_breaking_ or _opening_ the circuit, while connecting the ends of an -open circuit is called _making_ or _closing_ the circuit. A device for -opening and closing a circuit is called a _key_ or _switch_. The -electric circuit used in ringing a door bell is familiar to most boys -and girls. This circuit is _open_ most of the time. It is closed by -pressing the _push-button_ at the door, and the flow of current through -the _electric bell_ causes the latter to ring. Such a circuit is -represented in Fig. 218. Here _C_ is the voltaic cell, the two lines -representing the plates of the cell. A cross-section view of the -push-button (_P_), shows how the circuit is closed, (_B_) is the bell. -Wherever current electricity is used the device in which it is employed -forms a part of an electric circuit extending back to some electric -generator. This generator must be able to continually produce an E.M.F., -or a difference of potential between its terminals, in order that the -movement of electricity may be continuous. - - -Important Topics - -(a) Electric generators: (1) voltaic cell uses chemical energy; (2) -dynamo uses mechanical energy. - -(b) Electric circuits: (1) open, (2) closed, (3) key and switch. - -(c) Voltaic and galvanic electricity (names). - -(d) Galvanoscope, uses. - - -Exercises - -1. In what _two_ ways are static and current electricity alike? In what -two different? - -2. Draw a diagram of an electric bell circuit at your home. Give the -location of the electric bell, the electric generator and the -push-button. Show the connecting wires, and explain briefly how the -circuit is operated. - -3. Represent some other electric circuit, naming the generator and other -devices in the circuit. - -4. Look up the work of Volta and Galvani and write a statement of the -electrical discoveries and inventions made by them. - - -(2) THE VOLTAIC CELL AND ITS ACTION - -=241. The simple voltaic cell= consists of a strip of copper and a strip -of zinc placed in dilute sulphuric acid. (See Fig. 219.) A short time -after placing the plates in the acid, bubbles of a gas (hydrogen) appear -on the surface of the zinc. These bubbles increase in size and some rise -to the surface of the liquid. Nothing appears upon the copper plate. If -the tops of the plates are connected by a wire, an electric current is -set up through the wire and the cell, and bubbles of gas also appear -upon the _copper_ as well as on the zinc. In a short time the surface of -the copper becomes coated with bubbles and the current becomes much -_weaker_. If the plates are left in the acid for some time the zinc is -found to be eaten away, having been dissolved in the acid through -chemical action. The copper, however, remains practically unaffected. - -[Illustration: FIG. 219.--A simple voltaic cell.] - -=242. How the Current is Produced.=--To maintain the electric current a -continual supply of energy is required. This is furnished by the -_chemical action_ of the acid upon the zinc. The chemical action is in -several respects like _combustion_ or _burning_, by means of which -chemical energy is transformed into heat energy. In the voltaic cell the -chemical action of the acid upon the zinc _transforms_ chemical energy -into electrical energy. The E.M.F. or _difference of potential_ may be -considered as originating at the surface of the zinc where the chemical -action takes place. At this point the zinc has the lower and the liquid -in contact with it the higher potential. The molecules of the acid are -believed to be separated or broken up into two parts called _ions_; one -ion, the SO_{4} or _sulphion_, combines with the zinc forming zinc -sulphate, the other, or hydrogen (H) ion, passes over to the copper -plate, and accumulates on the surface of this plate giving it a positive -charge. It is therefore called the _positive ion_. The sulphion ion, or -SO_{4} ion, carries a negative charge to the zinc. It is therefore -called the _negative ion_. - -=243. The Direction of the Current.=[K]--Beginning at the surface of the -zinc the _direction_ of the movement of _positive_ electricity may be -traced through the liquid to the copper plate, to the wire, to the zinc -plate, to the starting point, thus completing the electric circuit. When -the circuit is closed it is found that the movement of electricity -starts in _all_ parts of the circuit at practically _the same instant_. - - [K] Many scientists consider that current in a conductor consists - of _negative electrons_ flowing in a direction _opposite_ to that - described in Art. 243. This is called the _electron current_, as - distinguished from the _electric current_ described above. - -[Illustration: FIG. 220.--A comparison of a voltaic cell and circuit to -a water pump and connecting pipes.] - -=244. The production of the current= may be illustrated by describing a -device for producing a continuous circulation of water. Thus let _Cu_ -and _Zn_ represent two pipes connected by two horizontal tubes, one at -_V_ provided with a valve and one at _P_ with a rotary _Pump_. (See Fig. -220.) Suppose the pipes filled to the level of _V_ and the pump started. -The pump will force water from _Zn_ to _Cu_, through _P_, the level -falling in _Zn_ and rising in _Cu_. If the valve _V_ is open the water -will flow back through _V_ as long as the pump is working. If _V_ is -closed, the level in _Cu_ will rise as high as the driving force of the -pump can send it. If now _V_ is opened, the pump will maintain the water -in circulation from _Cu_ to _Zn_ through _V_. In the illustration, the -tubes _Cu_ and _Zn_ correspond to the conducting plates of _copper_ and -_zinc_ of a voltaic cell. The pump _P_ represents the chemical action -which produces the electrical pressure. The upper pipe represents the -part of the circuit outside of the cell, the valve _V_ corresponds to an -electric key or switch which is used to open and close the electric -circuit. - -=245. Polarization.=--In the simple voltaic cell, after the circuit is -closed, bubbles of hydrogen collect upon the copper plate. This -accumulation of hydrogen gas is called _polarization_. It acts as a -non-conducting layer upon the surface of the plate and seriously -interferes with the movement of electricity from the liquid to the -copper plate not only in the simple voltaic cell but in many others as -well. Some voltaic cells are made entirely free from this defect, either -(a) _by the removal of the hydrogen as fast as it is formed_, or (b) _by -the use of such chemicals that no hydrogen is produced_. - -=246. Local Action.=--It is noticed that when a strip of zinc is placed -in dilute acid that bubbles appear upon the surface of the zinc. The -appearance of these bubbles indicates that some of the hydrogen ions -carrying positive electricity have moved to the zinc plate. Careful -examination of the plate after it has been in acid shows numerous black -spots upon it. These are bits of carbon. They are always found in -ordinary zinc. Small electric currents are set up which run from -molecules of pure zinc into the liquid and back to the carbon particles, -thus forming small closed circuits. (See Fig. 221.) The formation of -these circuits from and to the zinc is called _local_ action. This -action is a defect in voltaic cells since a part of the current is thus -kept from passing through the main outside circuit, and the zinc may be -consumed even when no outside current is flowing. - -[Illustration: FIG. 221.--Local action.] - -=247. Amalgamation.=--Local action is prevented by coating the zinc with -mercury. This process is called _amalgamation_. The mercury covers the -entire surface of the plate in the acid. Its action is to dissolve pure -zinc and bring it to the outer surface where it is acted upon by the -acid. The carbon particles are kept covered so that no local currents -can be formed as long as the bits of carbon are below the surface. -Amalgamation therefore prevents local action. - - -Important Topics - -_The Simple Voltaic Cell_ - -1. Two plates: zinc, copper; electrolyte, dilute sulphuric acid. - -2. Ions: hydrogen, positive: sulphion, negative. - -3. Current, where and how produced, direction, illustration. - -4. Polarization: cure, local action, cure. - - -Exercises - -1. Write in your own words an account of the production of an electric -current by the simple voltaic cell. Use sketches. - -2. Which plate has the higher potential? How is it produced? - -3. Would you expect to get an E.M.F. by forming a cell of two copper -plates? Why? - - -(3) PRACTICAL VOLTAIC CELLS - -=248. Advantages of Voltaic Cells.=--Many forms of voltaic cells have -been devised. Several of the more common of these will be described and -their electro-chemical action explained. - -At the present time voltaic cells are employed only where small currents -are needed, such as for electric bells and induction coils. Where more -than a small amount of current is required, the dynamo and the storage -battery have generally taken their place as sources of electric current. - -The advantages of voltaic cells as electric generators are: (a) they are -inexpensive, (b) they are easily taken from place to place, (c) they may -be ready for instant use. - -The most desirable voltaic cell would be one having the following -qualities: (a) High electromotive force, (b) no polarization or local -action, (c) very low internal resistance, (d) small expense, both as to -first cost and upkeep. - -[Illustration: FIG. 222.--The Leclanché cell, "wet" type.] - -=249. The Leclanché cell= is the one commonly used for ringing door -bells. It has two plates: one of zinc and the other of _carbon_. These -are placed in a solution of sal ammoniac (Fig. 222). Take up the -desirable qualities mentioned at the end of the preceding paragraph. (a) -It may be shown that this cell has a good E.M.F. about 1.5 volts. (b) It -_polarizes_ easily yet it recovers well when left upon open circuit. -Usually a substance called manganese dioxide is mixed with the carbon. -This acts as a _depolarizer_, that is, it combines with the hydrogen to -form water. (c) Its resistance varies and is often considerable. (d) The -expense for upkeep is small, since a 5-cent rod of zinc, and a 5-cent -charge of sal ammoniac will keep the cell in action on a bell circuit -from six months to a year or more. It is well suited for use on _open -circuits_ that is, where the circuit is open the greater part of the -time and is closed only occasionally; as in ringing door bells, -operating telephones, and other devices whose circuits are usually open. - -=250. The Dry Cell.=--Many forms of Leclanché cells are made. One of -these is called the _dry cell_ (See Fig. 223.) In this cell the zinc -plate is made into a jar or can and contains the other materials. At the -center of the cell is a rod of carbon and manganese dioxide. The space -between the carbon and zinc is filled with a porous material such as -sawdust or plaster of Paris. A strong solution of sal ammoniac fills the -porous material. The top of the cell is sealed with pitch or wax to -prevent evaporation. The great advantage of this cell is that it may be -used or carried in any position without danger of spilling its contents. -Dry cells are often used to operate the spark coils of gas and gasoline -engines. The Leclanché cell described in Art. 249 is commonly known as -the "wet cell." - -[Illustration: FIG. 223.--The Leclanché cell, "dry" type.] - -[Illustration: FIG. 224.--The Daniell cell.] - -=251. The Daniell Cell.=--This cell is often used in laboratories, and -on closed circuits such as those connected with fire and burglar alarms -and telegraph lines. It has two plates of zinc and copper placed in two -different liquids which are kept separated by a porous clay cup (Fig. -224). The zinc rod is kept in a solution of zinc sulphate contained in -the porous cup. The copper plate is in a solution of copper sulphate -filling the rest of the glass jar. Unlike the Leclanché cell, this one -must be kept upon a _closed circuit_ to do its best work, as the two -liquids mix when the circuit is open. Taking its qualities in order, (a) -its E.M.F. is about one volt, (b) it has no polarization since copper -instead of hydrogen is deposited upon the copper plate. Therefore a -uniform E.M.F. may be obtained from it, making it especially useful in -laboratory experiments and tests. (c) Its resistance is considerable and -(d) it is more expensive to operate than the Leclanché. It is sometimes -used upon closed circuits outside of laboratories as in burglar and -fire alarms, although in recent years, the storage battery is taking its -place for these purposes. - -=252. The Gravity Cell.=--Fig. 225 is like the Daniell cell in most -respects, except that in this cell, the zinc plate is held at the top of -the jar in a solution of zinc sulphate while the copper plate is at the -bottom, surrounded by a solution of copper sulphate. The solutions mix -but slowly as the copper sulphate solution is denser and remains at the -bottom. This cell like the Daniell must also be kept upon closed -circuit. On account of its simplicity and economy it is often used to -operate telegraph instruments. Its qualities are similar to those of the -Daniell cell. - -[Illustration: FIG. 225.--The gravity cell.] - -=253. Symbol for Voltaic Cells.=--In electrical diagrams, the symbol -employed to represent a voltaic cell is a short thick line near to and -parallel to a longer thin one. As in Fig. 226. If several cells are to -be represented the conventional symbol of the combination is represented -as in Fig. 227. A single cell and a group of cells are each frequently -called a battery. - -[Illustration: FIG. 226.--Diagram of a single cell.] - -[Illustration: FIG. 227.--Diagram of a group of cells.] - -=254. Effects of Electric Currents.=--Having studied some of the devices -for producing an electric current, let us now consider some of the -_effects_ caused by it. These effects will be studied under three heads: -(a) _Magnetic_, (b) _Chemical_, and (c) _Heat_ effects. Devices or -articles showing these effects known to most high school students are -respectively: (a) the _electromagnet_ (b) _electro-plated silver ware_ -and (c) _electric heaters_, such as electric flat irons, electric -toasters, etc. The _magnetic_ effect of an electric current was first -detected by Oersted at the University of Copenhagen in 1819. It may be -observed by holding a wire carrying a current from a voltaic cell above -and _parallel_ to the needle of a _magnetoscope_. The needle is at once -deflected (Fig. 228). If the current is reversed in direction the -magnetoscope needle is deflected in the reverse direction. This simple -device is the most common means for detecting an electric current. It -therefore constitutes a _galvanoscope_. (See Art. 239.) - -[Illustration: FIG. 228.--A galvanoscope.] - - -Important Topics - -1. Leclanché cells, (a), wet, (b), dry, construction, advantages, uses. - -2. Daniell and gravity cells, construction, advantages, uses. - -3. Three effects of electric currents, illustrations. - -4. The galvanoscope, uses. - - -Exercises - -1. Explain how the direction of current in a wire can be determined by a -compass. - -2. Would you expect to obtain a current from a zinc and copper cell -containing a solution of common salt? Perform the experiment. - -3. What conditions in a voltaic cell will give a steady electromotive -force. - -4. What conditions in a voltaic cell will give a strong electromotive -force. - -5. Name three different electric circuits that you know exist. Which are -_open_ and which are _closed_ circuits? - -6. Are voltaic cells used in your home? If so, for what purpose are they -used? On open or closed circuits? Have you seen them? what kind are -they? - - - - -CHAPTER XII - -THE MAGNETIC EFFECT OF ELECTRIC CURRENTS. ELECTRICAL MEASUREMENTS - - -(1) THE MAGNETIC EFFECT OF ELECTRIC CURRENTS - -=255. The Magnetic Effect.=--Of all the effects of electric currents, it -is generally conceded that the _magnetic effect_ is the one of _greatest -practical importance_, and it is also the one most extensively used. An -experiment illustrating this effect has been described in Art. 239. This -experiment shows that an electric current, if _parallel_ to a magnetic -needle, and _near it_ will deflect the north-seeking pole of the needle -to the right or left depending upon the _direction_ of the current flow. -This _deflection_ of the magnetic needle is due to the fact that -surrounding every electric current are magnetic lines of force. It is -this magnetic field of the current that causes the needle to turn. The -position taken by the needle is the resultant of the forces of two -magnetic fields; one, the earth's field, the other, that of the current. - -=256. Right-hand Rule for a Conductor.=--To show the presence of the -magnetic field about a current, pass a thick copper wire vertically -through a sheet of paper, and connect the ends of the wire to a source -of current. While the current (this should be as much as 10 amperes if -possible) is flowing, sprinkle iron filings upon the paper and tap -gently. The filings will arrange themselves in circles about the wire -showing the magnetic field. (See Fig. 229.) The needle of a magnetoscope -tends to place itself parallel to the lines of force of this field and -from this action or tendency the _direction_ of the magnetic lines -about a current may be determined. The following rule is helpful and -should be memorized: _Grasp the conductor with the right hand with the -outstretched thumb in the direction that the current is flowing. The -fingers will then encircle the wire in the direction of the lines of -force._ This rule may be reversed, for, if the fingers of the right hand -grasp the wire so as to point with the magnetic field, then the current -flows in the direction in which the thumb points. (See Fig. 230.) - -[Illustration: FIG. 229.--Magnetic field about a wire carrying an -electric current.] - -[Illustration: FIG. 230.--Right-hand rule for the magnetic field of a -current.] - -=257. Magnetic Field of a Helix.=--If a wire be wound about a cylinder -to form a cylindrical coil with parallel turns, it forms a _helix_ or -_solenoid_. The shape of the magnetic field about a current depends upon -the _form_ of the conductor. If the latter is in the form of a _helix_ -its magnetic field resembles that of a straight bar magnet. (See Fig. -231). In fact the helix _has the properties of a magnet_ with north- and -south-seeking poles while a _current_ is _flowing_ through it. If such a -coil is suspended so as to turn freely, it tends to turn until the field -within it is parallel to the earth's magnetic field. Such a suspended -helix may therefore be used as a compass. In order to strengthen the -magnetic field of a helix or solenoid, the space within its turns is -filled with iron, often in the form of small soft-iron wires. This -bundle of iron wire is called the _core_ of the helix. The core becomes -strongly magnetized by the field of the helix while the current is -flowing and quickly loses its magnetic force when the current is -stopped. _The direction of the current in a helix_ (Fig. 232) or the -_polarity_ of its core may be determined by another _right-hand rule_. -_If the helix is grasped with the right hand so that the fingers point -in the direction in which the current is flowing, the extended thumb -will point in the direction of the north pole of the helix._ On the -other hand, if the poles of the helix are known, then, when the helix is -grasped with the right hand so that the thumb points to the -north-seeking pole, the current is flowing in the wires in the direction -that the fingers point. - -[Illustration: FIG. 231.--The magnetic field of a helix.] - -[Illustration: FIG. 232.--Right-hand rule for a helix.] - -=258. The Electromagnet.=--These "right-hand" rules are applied in many -different devices. Among these, perhaps the most important is the -electromagnet, which is used in the electric bell, the telegraph, the -telephone, the dynamo, the motor, and many other electric contrivances. - -The electromagnet is defined as a _mass of iron around which is placed a -helix for conducting an electric current_. On account of its large -permeability, the iron core of the helix adds greatly to the -effectiveness of the electromagnet, since the magnetism of the iron is -added to that of the current in the helix. The magnetism remaining in -the iron after the current stops is called the _residual_ magnetism. The -residual magnetism is small when the core is made of small wires or thin -plates, but is larger when the iron core is solid. Like artificial steel -magnets, electromagnets are usually of two forms, _bar_ and _horseshoe_. -(See Figs. 233 and 234.) For most purposes the horseshoe form is the -more effective since it permits a complete iron circuit for the magnetic -lines of force. (See Fig. 235.) This is the form used in the electric -bell, in the telegraph sounder, and in lifting magnets. (See Fig. 236.) - -[Illustration: FIG. 233.--A bar electromagnet.] - -[Illustration: FIG. 234.--A horseshoe electromagnet.] - -[Illustration: FIG. 235.--A horseshoe electromagnet may have a complete -iron circuit for its lines of force.] - -[Illustration: FIG. 236.--A lifting magnet.] - -=259. Effective Electromagnets.=--The _magnetic_ effect of a current in -a helix is small, hence the force usually is increased by inserting a -core of iron. When at first man tried to signal with electromagnets at -a distance it was found that the current would not work the -electromagnet. An American by the name of Joseph Henry discovered the -remedy for this condition. He found that if the copper wire was -insulated by wrapping silk thread about it, and then many layers of the -silk insulated wire were wound upon a spool with an iron core, that the -magnet would work at a great distance from the source of current. If the -current is increased, the magnet is stronger than at first. Thus an -_electromagnet may be made stronger by_ (a) _increasing the number of -turns of wire in its coils_ and by (b) _sending a stronger current -through it_. - -[Illustration: FIG. 237.--A simple telegraph circuit.] - -=260. The Telegraph.=--The invention of an effective electromagnet by -Henry made possible the _electric telegraph_. In its simplest form it -consists of a battery, _C_, a key, _K_, and a sounder, _S_, with -connecting wires. (See Fig. 237.) The _sounder_ (Fig. 238) contains a -_horseshoe electromagnet_ and a bar of soft iron across its poles called -an armature, _A_, attached to a lever _L_. When the key is closed, the -electromagnet draws down the armature and lever until the latter hits a -stop _O_, making a click. When the key is raised, the magnet releases -the armature which is raised by the action of a spring at _S_ until the -lever hits a stop at _T_ making another click. Closing and opening the -circuit at _K_ will start and stop the current which operates _S_ which -may be 100 miles or more from _K_. One voltaic cell will work a sounder -in the same room. But if many miles of wire are in the circuit, the -E.M.F. of a single cell will not force sufficient current through the -long wire to operate the sounder. - -[Illustration: FIG. 238.--A telegraph sounder.] - -[Illustration: FIG. 239.--A telegraph relay.] - -[Illustration: FIG. 240.--How the relay is used.] - -[Illustration: Samuel F. B. Morse (1791-1872). Inventor of the -electromagnetic recording telegraph and of the dot and dash alphabet. - -SAMUEL F. B. MORSE - -"From Appleton's Cyclopedia of American Biography, Copyright 1888 by D. -Appleton & Co."] - -[Illustration: Thomas A. Edison, Orange, New Jersey. Invented the -incandescent lamp; phonograph; moving picture; most noted inventor of -electrical appliances of the present day. - -THOMAS A. EDISON - -"Copyright, Photographische Gessellschaft," and "By Permission of the -Berlin Photographic Co., New York."] - -A battery of several cells is then required. Even a large battery is -insufficient to operate a long line containing many sounders in circuit. -Recourse is therefore usually made to a more sensitive device called a -_relay_. (See Fig. 239.) In the relay a very small current will -magnetize its electromagnet enough to draw toward it the delicately hung -armature thereby closing a second circuit which contains a sounder and a -battery. (See Fig. 240.) when the current in the main circuit is -stopped, the armature of the relay is drawn back by a light spring. This -opens the _local_ circuit. Thus the local circuit is closed and opened -by the relay just in time with the starting and stopping of the current -in the main line. It is thus possible for a small current in the main -line by the use of a relay, to close and open a second local circuit -containing a local battery and sounder. Modern telegraph lines are -operated in this manner. - -[Illustration: FIG. 241.--An electric bell and its circuit.] - -=261. The electric bell= (see Fig. 241), consists of an electromagnet, -_M_, a soft iron _armature_, _A_, attached to the _tapper_, _T_, and a -post, _R_. When no current is flowing a spring at _S_ holds the armature -against the post _R_. When current flows through the helix, its core -becomes magnetized and attracts the armature, drawing it away from the -post, _R_, and causing the tapper to hit the bell. Drawing _A_ away from -the post, however, breaks the circuit at _R_ and the current stops. The -magnetism in the core disappears releasing the armature, which is then -pulled back by the spring _S_ against the post _R_. This completes the -circuit and the process repeats itself several times a second as long as -the current flows. - -[Illustration: FIG. 242.--Magnetizing by the discharge of a Leyden jar.] - -=262. Static and Current Electricity Compared.=--The likeness between a -discharge of static electricity and an electric current may be shown by -winding a coil of insulated wire about a glass tube which contains a -steel needle. If a Leyden jar (see Fig. 242) is discharged through the -coil the steel needle is usually found to be magnetized, showing that -the discharge of the static electricity has a magnetic effect similar to -that of an electric current. Sometimes a given end of the needle has a -north pole and at other times a south pole. This is believed to -indicate that the charge of the Leyden jar is _oscillatory_, and that -in different discharges sometimes a surge in one direction and at other -times a surge in the reverse direction has been most effective in -magnetizing the needle. Compare this action with that described in Art. -233. - - -Important Topics - -1. Right-hand rules, for conductor, for helix. - -2. The electromagnet, two forms, where used? - -3. Likeness between static and current electricity. - -4. The electric bell, parts, action. - -5. The telegraph, key, sounder, relay. - - -Exercises - -1. What is the difference between an electric charge and a current? - -2. How can a magnetic effect be produced from an electric charge? - -3. What is a magnetic field? Give two evidences of a magnetic field -about a current in a wire? - -4. A current is flowing north in trolley wire, what is the direction of -the magnetic field under the wire? Explain. - -5. What would be the result if a hard steel core were placed in the -electromagnet? Explain. - -6. If the north-seeking pole of a helix is facing you, does the current -in the coils before you move in a clockwise or in a counter-clockwise -direction? Explain. - -7. A helix is placed horizontally with its north-seeking pole toward the -north. Does the current in the wire at the top of the helix move east or -west? Explain. - -8. State at least six conditions any one of which will put an electric -bell circuit out of commission. - -9. If one desires to insert a battery into a telegraph circuit already -in operation, how will he determine the direction of the current in the -wire? - -10. If a boy who had magnetized his knife blade in a physics laboratory, -pointed end south-seeking, should lose his way in the woods on a cloudy -day, how could he determine his way out? - -11. At a certain point the earth's field acts north, that of an electric -current, east. The magnetoscope needle points exactly northeast when -placed at that point. How do the two magnetic fields compare? - - -(2) ELECTRICAL MEASUREMENTS - -=263. Galvanometers.=--In using electric currents it is often necessary -or desirable to be able to know not only that a given current is weak or -strong, but precisely what its strength is. We can determine the -relative strengths of two currents by the use of a _galvanometer_. - -[Illustration: FIG. 243.--The magnet is at the center of the coil.] - -[Illustration: FIG. 244.--A moving-magnet (tangent) galvanometer.] - -The older or _moving-magnet_ type of galvanometer is similar to the -galvanoscope mentioned in Art. 239. It consists of a magnetic needle -mounted at the center of a coil of wire. The coil is placed facing east -and west, so that the needle will be held by the earth's magnetic field -parallel to the plane of the coil. When a current is sent through the -coil a magnetic field is produced within it. This deflects the needle, -its north end turning east or west depending upon the direction of the -current. (See Fig. 243.) The _coils_ of a moving-magnet or _tangent_ -galvanometer (see Fig. 244) are _large_ and firmly fastened to the base, -while the _magnet_ is _small_. - -The _moving-coil_ type of galvanometer (see Fig. 245) consists of a -_large magnet_ fastened to the frame of the device. The magnet usually -has a horseshoe form to produce as strong a field as possible. The -_coil_ is wound on a _light_ rectangular frame and is suspended between -the two poles of the magnet. To concentrate the magnetic field, a -cylinder of soft iron is usually placed within the coil. Fig. 246 -represents a common form of moving-coil galvanometer. - -[Illustration: FIG. 245.--To illustrate the principle of the moving-coil -galvanometer.] - -[Illustration: FIG. 246.--A moving-coil (D'Arsonval) galvanometer.] - -=264. Measurement of Electric Currents.=--A galvanometer enables one to -_compare_ electric currents. To _measure_ electric currents it is -necessary to employ a _unit_ of electrical quantity, just as in -measuring the quantity of water delivered by a pipe, a unit of liquid -measure is employed; thus, _e.g._, the current delivered by a given pipe -may be 2 gallons of water per second, so in measuring the flow of an -electric current one may speak of two _coulombs_ per second. The -_coulomb_ is the unit quantity of electricity just as the unit of -quantity of water is the gallon. - -For most practical purposes, however, we are more interested in the -_rate_ or _intensity_ of flow of current than in the actual _quantity_ -delivered. The unit of rate of flow or current is called the _ampere_. - -In determining the exact _quantity_ of an electric current, physicists -make use of a device called a _coulomb meter_. (See Fig. 247.) This -contains a solution of silver nitrate in which are placed two silver -plates. The current to be measured is sent through the solution, in at -one plate and out at the other. The plate where the current goes _in_, -the _anode_, _A_ (Fig. 247), loses in weight since some of the silver is -dissolved. The plate where the current goes _out_, the _cathode_, _C_, -increases in weight since some of the silver is deposited. By an -international agreement, _the intensity of the current which deposits -silver at the rate of 0.001118 g. per second is 1 ampere_. This is equal -to 4.025 g. per hour. - -[Illustration: FIG. 247.--A coulomb meter, the anode _A_ is separated -from the cathode _C_ by a porous cup.] - -The _coulomb_ is defined as the quantity of electricity delivered by a -current of one ampere during one second. - -A 40-watt-incandescent lamp takes about 0.4 ampere of current. An arc -lamp takes from 6 to 15 amperes. A new dry cell may send 20 amperes -through a testing meter. A street car may take from 50 to 100 amperes. - -=265. The Ammeter.=--The method described above is not used ordinarily -for measuring current strengths on account of its inconvenience. The -usual device employed is an _ammeter_. This instrument is a _moving-coil -galvanometer_. It contains, wound on a light form, a coil of fine -copper wire. The form is mounted on jewel bearings between the poles of -a strong permanent horseshoe magnet. (See Fig. 248.) As in other -moving-coil galvanometers, a soft iron cylinder within the form -concentrates the field of the magnet. The form and its coil is held in -balance by two spiral springs which also conduct current into and out of -the coil. - -Only a small part of the whole current measured, in some cases only -0.0001 passes through the coil, the larger part of the current passing -through a metal wire or strip called a _shunt_[L] (see Fig. 248) -connecting the binding posts of the instrument. A fixed fraction of the -whole current flows through the coil. Its field crossing the field of -the horseshoe magnet, tends to turn until its turning force is balanced -by the spiral springs. As the coil turns it moves a pointer attached to -it across a scale graduated to indicate the number of amperes in the -whole current. - - [L] A shunt is a conductor or coil connected in parallel with - another conductor or circuit. It carries a part of the current. - -[Illustration: FIG. 248.--Diagram of a commercial ammeter. _S_ is the -shunt.] - -It should be noted that while _all_ of the current measured passed -through the ammeter, but a small _part_ goes through the coil. - -=266. Resistance of Conductors.=--With an ammeter one may study the -change produced in the amount of current flowing in a wire when a change -is made in the wire conducting the current. For example, if one measures -with an ammeter the current flowing from a dry cell through a long and -then through a short piece of fine copper wire, it will be seen that -less current flows when the long piece is used. That is, the long wire -seems to hinder or to _resist_ the passing of the current more than the -short piece. In other words, the long wire is said to have more -_resistance_. - -The resistance of a conducting body is affected by several conditions. - -(a) It is _directly_ proportional to the _length_ of the conductor, one -hundred feet of wire having twice the resistance of fifty feet. - -(b) It is _inversely_ proportional to the _square of the diameter_; a -wire 0.1 inch in diameter has four times the resistance of a wire 0.2 -inch in diameter. - -(c) It differs with different substances, iron having about six times as -much as copper. - -(d) It varies with the temperature, metals having greater resistance at -a higher temperature. - -Since silver is the best conductor known, the resistances of other -substances are compared with it as a standard. - -The ratio of the resistance of a wire of any substance as compared to -the resistance of a silver wire of exactly the same diameter and length -is called its _relative_ resistance. - -Purified substances arranged in order of increasing resistance for the -same length and sectional area (Ayrton-Mather) are given on p. 294. - - Silver annealed 1.00 - Copper annealed { from 1.04 - { to 1.09 - Aluminum annealed 1.64 - Nickel annealed 4.69 - Platinum annealed 6.09 - Iron annealed 6.56 - German Silver { from 12.80 - { to 20.20 - Mercury 63.30 - Nichrome 67.50 - Carbon { from 2700.00 - { to 6700.00 - -=267. The ohm, the unit of resistance=, is defined by international -agreement as follows: _An ohm is the resistance of a column of pure -mercury, 106.3 cm. long with a cross-section of a square millimeter and -at a temperature of 0°C._ - -It should be noted that each of the four conditions affecting resistance -is mentioned in the definition, viz., length, cross-section, material, -and temperature. Since it is inconvenient to handle mercury, _standard -resistance coils_, made of an alloy of high resistance are used in -comparing and measuring resistances. - -A piece of copper wire No. 22 (diameter 0.644 mm.) 60. 5 ft. long has a -resistance of 1 ohm. See table p. 296. - -The resistance of some telephone receivers is 75 ohms, of a telegraph -sounder, 4 ohms, of a relay 200 ohms. - -=268. Resistance of Circuits.=--Every part of an electrical circuit -possesses resistance. In an electric-bell circuit, for instance, the -wires, the bell, the push-button, and the cell itself, each offers a -definite resistance to the passage of the current. The resistance -_within the cell_ is termed _internal resistance_, while the resistance -of the parts outside of the electric generator is called _external -resistance_. - -=269. Electromotive Force.=--In order to set in motion anything, some -_force_ must be applied. This is as true of electricity as of solids, -liquids, or gases. By analogy that which is exerted by a battery or by a -dynamo in causing current to flow is called an _electromotive force_. -The unit of electromotive force, the _volt_, may be defined as _the -electromotive force that will drive a current of 1 ampere through the -resistance of 1 ohm_. The electromotive force of a dry cell is about 1.5 -volts, of a Daniell cell 1.08 volts. Most electric light circuits in -buildings carry current at 110 or 220 volts pressure. Currents for -street cars have an electromotive force of from 550 to 660 volts. - -[Illustration: FIG. 249.--Diagram of a commercial voltmeter.] - -=270. The Voltmeter.=--An instrument for measuring the electromotive -force of electric currents is called a _voltmeter_ (Fig. 249). It is -usually a moving-coil galvanometer, and is always of _high resistance_. -It is like an ammeter in construction and appearance. In fact, a -voltmeter is an ammeter which has had its shunt removed or disconnected. -In place of a shunt, the voltmeter uses a coil of wire of high -resistance (see _R_, Fig. 249) _in series_ with the galvanometer coil. -The high resistance of the voltmeter permits but a very small current to -flow through it. Hence a voltmeter must be placed _across_ a circuit -and not in it. In other words _a voltmeter is connected in shunt_, -while _an ammeter is in series with the circuit_ as is shown in Fig. -250. - -DIMENSIONS AND FUNCTIONS OF COPPER WIRES - - Column headings: - - B: B. & S. gauge number - MM: Millimeters - SA: Sectional area in square millimeters - WL: Weight and length, Density = 8.9, feet per pound - R: Resistance at 24°C., feet per ohm - C: Capacity in amperes - - ----+--------------+----------+---------+---------+----------+------ - | Diameter | | | | | - B +-------+------+ Circular | SA | WL | R | C - | Mils | MM | mils | | | | - ----+-------+------+----------+---------+---------+----------+------ - 0000|460.000|11.684|211,600.00|107.219 | 1.56|19,929.700|312.0 - 000|409.640|10.405|167,805.00| 85.028 | 1.97|15,804.900|262.0 - 00|364.800| 9.266|133,079.40| 67.431 | 2.49|12,534.200|220.0 - 0|324.950| 8.254|105,592.50| 53.470 | 3.13| 9,945.300|185.0 - 2|257.630| 6.544| 66,373.00| 33.631 | 4.99| 6,251.400|131.0 - 4|204.310| 5.189| 41,742.00| 21.151 | 7.93| 3,931.600| 92.3 - 6|162.020| 4.115| 26,250.50| 13.301 | 12.61| 2,472.400| 65.2 - 8|128.490| 3.264| 16,509.00| 8.366 | 20.05| 1,555.000| 46.1 - 10|101.890| 2.588| 10,381.00| 5.260 | 31.38| 977.800| 32.5 - 12| 80.808| 2.053| 6,529.90| 3.309 | 50.69| 615.020| 23.0 - 14| 64.084| 1.628| 4,106.80| 2.081 | 80.59| 386.800| 16.2 - 16| 50.820| 1.291| 2,582.90| 1.309 | 128.14| 243.250| 11.5 - 18| 40.303| 1.024| 1,624.30| 0.823 | 203.76| 152.990| 8.1 - 20| 31.961| 0.812| 1,021.50| 0.5176 | 324.00| 96.210| 5.7 - 22| 25.347| 0.644| 642.70| 0.3255 | 515.15| 60.510| 4.0 - 24| 20.100| 0.511| 504.01| 0.2047 | 819.21| 38.050| 2.8 - 26| 15.940| 0.405| 254.01| 0.1288 | 1,302.61| 23.930| 2.0 - 28| 12.641| 0.321| 159.79| 0.08097| 2,071.22| 15.050| 1.4 - 30| 10.025| 0.255| 100.50| 0.05092| 3,293.97| 9.466| 1.0 - 32| 7.950| 0.202| 63.20| 0.03203| 5,236.66| 5.952| 0.70 - 34| 6.304| 0.160| 39.74| 0.02014| 8,328.30| 3.743| 0.50 - 36| 5.000| 0.127| 25.00| 0.01267|13,238.83| 2.355| 0.35 - 38| 3.965| 0.101| 15.72| 0.00797|20,854.65| 1.481| 0.25 - 40| 3.144| 0.080| 9.89| 0.00501|33,175.94| 0.931| 0.17 - ----+-------+------+----------+---------+---------+----------+------ - - -Important Topics - -(1) _Galvanometers_: (1) moving magnet, fixed coil; (2) moving coil, -fixed magnet, ammeter, voltmeter. - -(2) _Unit of quantity, coulomb._ - -(3) _Unit of current, ampere._ - -(4) _Unit of resistance, ohm._ - -(5) _Unit of electromotive force, volt._ - - -Exercises - -1. How will the resistance of 20 ft. of No. 22 German silver wire -compare with that of 10 ft. of No. 22 copper wire? Explain. - -2. Where in a circuit is copper wire desirable? Where should German -silver wire be used? - -3. Explain the action of the ammeter. Why does not the needle or coil -swing the full distance with a small current? - -4. Why is a telegraph sounder more apt to work on a short line than upon -a long one? - -[Illustration: FIG. 250.--The ammeter is connected in series and the -voltmeter in shunt.] - -5. Find the resistance of 15 miles of copper telephone wire No. 12. (See -table p. 296.) - -6. What will be the weight and resistance of 1,000 feet of No. 20 copper -wire? - -7. A storage battery sends 4 amperes of current through a plating -solution. How much silver will it deposit in 2 hours? - -8. (a) Compare the diameters of No. 22 and No. 16 copper wire. - -(b) Compare the lengths of the same wires giving 1 ohm resistance. - -(c) What relation exists between (a) and (b)? - -9. Why is an electric bell circuit usually open while a telegraph line -circuit is usually closed? - -10. A copper wire and an iron wire of the same length are found to have -the same resistance. Which is thicker? Why? - -11. Why are electric bells usually arranged in parallel instead of in -series? - -12. What would happen if a voltmeter were put in series in a line? - - -(3) OHM'S LAW AND ELECTRICAL CIRCUITS - -=271. Conditions Affecting Current Flow.=--Sometimes over a long circuit -one cell will not work a telegraph sounder. In such a case, two, three, -or more cells are connected so that the zinc of one is joined to the -copper plate of the other. When connected in this way the cells are said -to be _in series_ (Fig. 251). In the figure _A_ represents a voltmeter. -It is found that _when cells are in series the E.M.F. of the battery is -the sum of the electromotive forces of the cells_. An ammeter in the -circuit shows increased current as the cells are added. Hence _if the -resistance of the circuit remains unchanged, the greater the E.M.F. the -greater is the current strength_. In this respect, the movement of -electricity in a circuit is similar to the flow of water in a small pipe -under pressure, as in the latter the flow of water increases as the -pressure becomes greater. The current in a circuit may also be increased -by lessening the resistance, since the current through a long wire is -less than that through a short one, just as the flow of water will be -greater through a short pipe than through a long one. To increase the -current flowing in an electric circuit, one may therefore either -increase the E.M.F. or decrease the resistance. - -[Illustration: FIG. 251.--Diagram of cells connected in series.] - -=272. Ohm's Law.=--The relation between the electromotive force applied -to a circuit, its resistance, and the current produced was discovered in -1827 by George Ohm. Ohm's law, one of the most important laws of -electricity, states that, in any circuit, _the current in amperes equals -the electromotive force in volts divided by the resistance in ohms_. - -This principle is usually expressed thus: - - Current intensity = electromotive force/resistance or - - Amperes = volts/ohms or _I_ = _E_/_R_ - -[Illustration: FIG. 252.--The street cars are connected in parallel with -each other.] - -=273. Resistance of Conductors in Series.=--A study of the _resistance_ -of conductors when alone and when grouped in various ways is of -importance _since, the current flow through any circuit is dependent -upon its resistance_. The two most common methods of combining several -conductors in a circuit are in _series_ and in _parallel_. Conductors -are in _series_ when all of the current passes through each of the -conductors in turn (Fig. 218), thus the cell, push-button, wires, and -electric bell in an electric-bell circuit are in series. Conductors are -in _parallel_ when they are so connected that they are side by side and -a part of the whole current goes through each. None of the current that -passes through one conductor can go through the conductors in parallel -with it. Thus the electric street cars are in _parallel_ with each -other. (See Fig. 252.) It is easily seen that none of the current -passing through one car can go through any of the others. When the -conductors are in _series_ the combined resistance is the _sum_ of the -several resistances. Thus in an electric-bell circuit if the battery has -a resistance of 1 ohm, the bell of 2 ohms, and the wire 1 ohm, the total -resistance in the circuit is 4 ohms. When conductors are in _parallel_ -the combined resistance is always _less_ than the separate resistances. -Just as a crowd of people meets less resistance in leaving a building -through several exits, so electricity finds less resistance in moving -from one point to another along several parallel lines, than along one -of the lines. - -=274. Resistance of Conductors in Parallel.=--If three conductors of -equal resistance are in parallel, the combined resistance is just -one-third the resistance of each separately (Fig. 253). The rule that -states the relation between the combined resistance of conductors in -parallel and the separate resistances is as follows:_The combined -resistance of conductors in parallel is the reciprocal of the sum of the -reciprocals of the several resistances_. For example, find the combined -resistance of three unequal resistances in parallel; the first being 4 -ohms, the second, 6 ohms, and third 3 ohms. The reciprocals of the three -resistances are 1/4, 1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 = -18/24. The reciprocal of this is 24/18 which equals 1-1/3 ohms, the -combined resistance. - -FIG. 253.--The three conductors are connected in parallel. - - This rule may be understood better if we consider the _conductance_ - of the conductors in parallel. Since the conductance of a two ohm - wire is just one-half that of a one-ohm wire, we say that the - conductance of a body is inversely as the resistance, or that it is - the _reciprocal of the resistance_. The conductance of the 4-, 6-, - and 3-ohm coils will therefore be respectively 1/4, 1/6, and 1/3, - and since the combined conductance is the sum of the several - conductances, the total conductance is 18/24. Also since this is - the reciprocal of the total resistance, the latter is 24/18 or - 1-1/3 ohms. - -When two or more conductors are connected in parallel each one is said -to be a _shunt_ of the others. Many circuits are connected in _shunt_ or -in parallel. Fig. 254 represents four lamps in parallel. Incandescent -lamps in buildings are usually connected in parallel, while arc lamps -are usually connected in series. Fig. 255 represents four lamps in -series. - - -Important Topics - -1. Conditions affecting current flow, (a) E.M.F., (b) resistance. - -2. Ohm's law, three forms for formula. - -3. Resistance of conductors: (a) in series, (b) in parallel; how -computed, illustrations. - -[Illustration: FIG. 254.--The four lamps are connected in parallel.] - -[Illustration: FIG. 255.--The four lamps are connected in series.] - - -Exercises - -1. What current flows through a circuit if its E.M.F. is 110 volts and -the resistance is 220 ohms? - -2. A circuit contains four conductors in series with resistances of 10, -15, 6, and 9 ohms respectively. What current will flow through this -circuit at 110 volts pressure? What will be the resistance of these four -conductors in parallel? - -3. What is the combined resistance of 8 conductors in parallel if each -is 220 ohms? What current will flow through these 8 conductors at 110 -volts pressure? - -4. What is the resistance of a circuit carrying 22 amperes, if the -E.M.F. is 20 volts? - -5. What E.M.F. will send 8 amperes of current through a circuit of 75 -ohms resistance? - -6. How does the voltmeter differ from the ammeter? - -7. How can one determine the resistance of a conductor? - -8. The resistance of a hot incandescent lamp is 100 ohms. The current -used is 1.1 amperes. Find the E.M.F. applied. - -9. What is the resistance of the wires in an electric heater if the -current used is 10 amperes, the voltage being 110? - -10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How -many feet should be used in winding a 200 ohms relay? - -11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What -is the resistance of a line 1 mile long? - -12. A wire has a resistance of 20 ohms. It is joined in parallel with -another wire of 6 ohms, find their combined resistance. - -13. The separate resistances of two incandescent lamps are 200 ohms and -70 ohms. What is their combined resistance when joined in parallel? When -joined in series? - - -(4) METHODS OF GROUPING CELLS AND MEASURING RESISTANCE - -=275. Internal Resistance of a Voltaic Cell.=--The current produced by a -voltaic cell is affected by the resistance that the current meets in -passing from one plate to another through the liquid of the cell. This -is called the _internal resistance_ of the cell. A Daniell cell has -several (1-5) ohms internal resistance. The resistance of dry cells -varies from less than 0.1 of an ohm when new to several ohms when old. -If cells are joined together their combined internal resistance depends -upon the method of grouping the cells. - -[Illustration: FIG. 256.--The four cans exert four times the water -pressure that one can will exert.] - -=276. Cells Grouped in Series and in Parallel.=--When in _series_ the -copper or carbon plate of one cell is joined to the zinc of another and -so on. (See Fig. 251.) The effect of connecting, say four cells, in -series may be illustrated by taking four cans of water, placed one above -another. (See Fig. 256.) The combined water pressure of the series is -the sum of the several pressures of the cans of water, while the -opposition offered to the movement of a quantity of water through the -group of cans is the sum of the several resistances of the cans. In -applying this illustration to the voltaic cell, we make use of Ohm's -law. Let _E_ represent the e.m.f. of a single cell, _r_ the internal -resistance of the cell, and _R_ the external resistance or the -resistance of the rest of the circuit. Consider a group of cells in -series. If _n_ represents the _number_ of cells in _series_, then Ohm's -law becomes - - _I_ = _nE_/(_nr_ + _R_). - -Cells are grouped in _series_ when large E.M.F. is required to force a -current through a large external resistance such as through a long -telegraph line. Cells are connected in _parallel_ when it is desired to -send a large current through a small external resistance. To connect -cells in parallel all the copper plates are joined and also all the zinc -plates. (See Fig. 257.) To illustrate the effect of this mode of -grouping cells, suppose several cans of water are placed side by side -(Fig. 258). It is easily seen that the pressure of the group is the same -as that of a single cell, while the resistance to the flow is less than -that of a single cell. Applying this reasoning to the electric circuit -we have by Ohm's law the formula for the current flow of a group of - - _n_ cells arranged in parallel _I_ = _E_/((_r/n_) + _R_). - -[Illustration: FIG. 257.--Four cells connected in parallel.] - -[Illustration: FIG. 258.--The water pressure of the group in parallel is -the same as that of one.] - -=277. Illustrative Problems.=--Suppose that four cells are grouped in -parallel, each with an E.M.F. of 1.5 volts and an internal resistance of -2 ohms. What current will flow in the circuit if the external resistance -is 2.5 ohms? Substitute in the formula for cells in parallel the values -given above, and we have _I_ = 1.5/(0.5 + 2.5) = 1.5/3 = 0.5 ampere. -Suppose again that these four cells were grouped in series with the same -external resistance, substituting the values in the formula for cells in -series we have _I_ = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere. - -=278. Volt-ammeter Method for Finding Resistance.=--Measurements of the -resistance of conductors are often made. One of these methods depends -upon an application of Ohm's law. It is called the volt-ammeter method -since it employs both a voltmeter and an ammeter. If the conductor whose -resistance is to be measured is made a part of an electric circuit, -being connected _in series with the ammeter_ and _in shunt with the -voltmeter_, the resistance may easily be determined, since _R_ = _E/I_. -(See Fig. 250.) If, for example, the difference in E.M.F., or as it is -often called, the _fall of potential_ between the ends of the wire as -read on the voltmeter is 2 volts, and the current is 0.5 ampere, then -the resistance of the wire is 4 ohms. This method may be readily applied -to find the resistance of any wire that is a part of an electric -circuit. - -=279. The Wheatstone Bridge.=--To find the resistance of a separate wire -or of an electrical device another method devised by an Englishman named -Wheatstone is commonly employed. This method requires that three known -resistances, _a_, _b_, _c_, in addition to the unknown resistance _x_ -be taken. These four resistances are arranged in the form of a -parallelogram. (See Fig. 259.) A voltaic cell is joined to the -parallelogram at the extremities of one diagonal while a moving-coil -galvanometer is connected across the extremities of the other diagonal. -The known resistances are changed until when on pressing the keys at _E_ -and _K_ no current flows through the galvanometer. when this condition -is reached, the four resistances form a true proportion, thus _a_: _b_ = -_c_: _x_. - -Since the values of _a_, _b_, and _c_ are known, _x_ is readily -computed. Thus if _a_ = 10, _b_ = 100, and _c_ = 1.8 ohms, then _x_, the -unknown resistance, equals 18 ohms, since 10: 100 = 1.8: 18. This method -devised by Wheatstone may be employed to find the resistance of a great -variety of objects. It is the one most commonly employed by scientists -and practical electricians. - -[Illustration: FIG. 259.--Diagram of a Wheatstone bridge.] - - -Important Topics - -1. The internal resistance of voltaic cells. - -2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells -in parallel. - -3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone -bridge method. - - -Exercises - -1. What is the resistance of an electric bell circuit where the E.M.F. -is 3 volts and the current is 0.6 ampere? - -2. A telegraph wire is broken somewhere, the ends lying upon damp -ground. If an E.M.F. of 30 volts is applied from the ground to the wire -and a current of 0.1 of an ampere flows, what is the resistance of the -part connected to the ammeter. (The earth which completes the circuit -from the end of the wire has very small resistance.) Why? - -3. How far away is the break in the wire if the latter has a resistance -of 80 ohms to the mile? Diagram. - -4. What current will flow through a bell circuit of 8 ohms resistance if -it contains three cells _in series_ each with an E.M.F. of 1.5 volts and -an internal resistance of 1/3 ohm? - -5. If the same three cells are connected in parallel on the same circuit -what current flows? Is the current in problem 4 or 5 the larger? Why? - -6. If four cells each with 1.5 volts E.M.F. and an internal resistance -of 0.4 ohm are connected with a circuit having an external resistance of -0.8 ohm, what current will the parallel connection give? The series -connection? Which gives the larger current? Why? - -7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal -resistance are connected in series with 2 telegraph sounders of 4 ohms -each. The connecting wires have 6 ohms resistance. Find the current -intensity. - -8. A battery of 2 cells arranged in series is used to ring a door bell. -The E.M.F. of each cell is 1.5 volts, internal resistance 0.3 ohm, and -the resistance of the bell is 4 ohms. What is the current in amperes? - -9. In the above problem find the current if the cells are connected in -parallel. - - - - -CHAPTER XIII - -THE CHEMICAL AND HEAT EFFECTS OF ELECTRIC CURRENTS - - -(1) THE CHEMICAL EFFECT OF AN ELECTRIC CURRENT - - -=280. Electroplating.=--If two carbon rods (electric light carbons -answer very well) are placed in a solution of _copper sulphate_ (Fig. -260) and then connected by wires to the binding posts of an electric -battery, one of the rods soon becomes covered with a coating of -_metallic copper_ while bubbles of gas may be seen upon the other -carbon. If a solution of _lead acetate_ is used in the same way a -deposit of _metallic lead_ is secured, while a solution of _silver -nitrate_ gives silver. - -[Illustration: FIG. 260.--Two carbons placed in a solution of copper -sulphate.] - -[Illustration: FIG. 261.--An electroplating bath.] - -This process of depositing metals upon the surface of solids by an -electric current is called _electroplating_. Everyone has seen -_electroplated_ articles such as silver plated knives, forks, and -spoons, and nickel-plated rods, handles, etc. _Copper electrotype_ -plates such as are used in printing school books are made by this -process. In practical electroplating a solution of the metal to be -deposited is placed in a tank; across the top of this tank are placed -copper rods to act as conducting supports. From one of these rods, the -cathode, objects to be plated are hung so as to be immersed in the -liquid. From other rods, the anodes, are hung plates of the metal to be -deposited. These are dissolved as the current deposits a coating upon -the articles, thus keeping the solution up to its proper strength. (See -Fig. 261.) - -[Illustration: FIG. 262.--The current is carried through the solution by -ions.] - -=281. Electrolysis.=--A solution from which a deposit is made by an -electric current is called an _electrolyte_. The plates or other objects -by which the current enters or leaves the electrolyte are called the -_electrodes_. The electrode by which the current enters is called the -_anode_ (_an_ = in) while the electrode by which it leaves is the -cathode (_cath_ = away). The process by which an electric current -decomposes a solution and deposits a substance upon an electrode is -called _electrolysis_. The _current_ always flows within the cell from -_anode to the cathode_. (See Fig. 262.) The metal goes with the current -and is found deposited upon the cathode. - -=282. Theory of Electrolysis.=--The action going on in an _electrolytic_ -cell has been carefully studied. The _theory of electrolysis_, which is -supported by much experimental evidence, supposes that many of the -molecules in a _dilute_ solution of a substance "split up" into two -parts called "ions," one ion having a positive, the other a negative -charge. In a dilute solution of sulphuric acid, the _positive_ ion is of -hydrogen, while the _negative_ ion is the (SO_{4}) or sulphion. These -ions bearing electric charges are believed to be the _carriers of the -electric current_ through the electrolyte. - -The positive ions move with the current from the anode to the cathode, -while the negative ions apparently are repelled by the cathode and -appear upon the anode. Evidence of the accumulation of the two kinds of -ions at the two electrodes is furnished by the _electrolysis_ of water, -described below. - -=283. Electrolysis of Water.=--Two glass tubes (Fig. 263), _H_ and _O_, -are attached at the bottom to a horizontal glass tube. To the latter is -also connected an upright tube _T_. At the lower ends of _H_ and _O_ are -inserted, fused in the glass, platinum wires, _A_ and _C_. The tubes are -filled with a weak solution of sulphuric acid. The tops of _H_ and _O_ -are closed with stopcocks, _T_ being open; a current of electricity is -sent in at _A_ and out at _C_. A movement of the ions at once begins, -the positive hydrogen ions appearing at _C_. These accumulate as bubbles -of hydrogen which rise to the top of _H_ and displace the liquid. At the -same time bubbles of oxygen appear at _A_. These rise in _O_ and also -displace the liquid which rises in _T_. After the action has continued -some time it may be noticed that the volume of hydrogen is just twice -that of the oxygen. This was to have been expected since the formula -for water is H_{2}O. The nature of the gas in _H_ or _O_ may be tested -by opening the stopcock and allowing the gas to escape slowly. The -hydrogen gas can be lighted by a flame while the oxygen gas will cause a -spark upon a piece of wood to glow brightly, but does not burn itself. - -[Illustration: FIG. 263.-Electrolysis of water; oxygen collects in _O_, -hydrogen in _H_.] - -=284. Evidence that ions are necessary to conduct a current in a liquid= -is furnished by the following experiment. A quart jar is carefully -cleaned, and half filled with distilled water. Two pieces of zinc 5 cm. -square are soldered to pieces of rubber-insulated No. 14 copper wire. -The zincs are placed in the distilled water (Fig. 264) and the wires are -connected to a 110 volt circuit with a 16 candle-power incandescent lamp -in _series_ with the cell, as in the figure. If the zincs have been -carefully cleansed and the water is pure, no current flows as is shown -by the lamp remaining dark. If a minute quantity of sulphuric acid or of -common salt is placed in the water the lamp at once begins to glow. Ions -are now present in the liquid and conduct the current. That some -substances in solution do not form ions may be shown by adding to -another jar of pure water some glycerine and some cane sugar, substances -resembling the acid and salt in external appearance but which do not -_ionize_ when dissolved as is shown by the lamp remaining dark after -adding the glycerine and sugar. The acid and salt are of _mineral_ -origin while the glycerine and sugar are _vegetable_ products. This -experiment illustrates the principle that the water will conduct only -when it contains ions. - -[Illustration: FIG. 264.--The current passes only when ions are present -in the liquid.] - -=285. Laws of Electrolysis.=--These were discovered by Faraday in 1833, -and may be stated as follows: _I. The mass of a substance deposited by -an electric current from an electrolyte is proportional to the intensity -of current which passes through it._ - -_II. The mass of any substance deposited by a current of uniform -intensity is directly proportional to the time the current flows._ - -These laws have been used as a basis for defining and measuring the unit -of current flow, the _ampere_. (See Art. 264.) - -=286. Instances of Electrolysis.=--(a) Medicines, especially those -containing a mineral substance, are sometimes introduced into the human -body by electrolysis. (b) Water and gas pipes are sometimes much -weakened by the effects of electric currents in the earth, especially -return currents from street railways. Such currents use the metal pipes -as a conductor. At the place where the current leaves the metal and -enters the ground, it removes metallic ions from the pipe. This process -continuing, the pipe becomes weakened and at length breaks. (c) _Copper_ -is purified by the use of electric currents that remove the copper from -ore or from other metals and deposit it upon electrodes. _Electrolytic_ -copper is the purest known. (d) _Aluminum_ is obtained by the use of -large currents of electricity that first heat the material used until it -melts and then deposit the metal from the fluid material by -electrolysis. These results are called chemical effects of the current -since by the use of electric currents substances are changed chemically, -that is, they are separated into different chemical substances. - - -Important Topics - -1. Electrolysis, electroplating, anode, cathode, ion. - -2. Theory of electrolysis--evidence: (a) electrolysis of water; (b) -conductivity of acid and water. - -3. Laws of electrolysis. - -4. Practical use of electrolysis. - - -Exercises - -1. A dynamo has an E.M.F. of 10 volts. What is the resistance in the -circuit when 20 amperes are flowing? - -2. How much silver will be deposited in an hour by this current? - -3. Name five objects outside of the laboratory that have been acted upon -by electrolysis. How in each case? - -4. Why is table ware silver plated? Why are many iron objects nickel -plated? - -5. How is the electrolysis of water pipes prevented? - -6. Two grams of silver are to be deposited on a spoon by a current of 1 -ampere. Find the time required. - -7. How long will it take to deposit 20 g. of silver in an electroplating -bath if a current of 20 amperes is used? - -8. If 1000 g. of silver are deposited on the cathode of an electrolytic -reduction plant in 10 minutes, what is the current intensity employed? - - -(2) THE STORAGE BATTERY AND ELECTRIC POWER - -=287. Differences Between Voltaic and Storage Cells.= Voltaic cells in -which electric currents are produced by the chemical action between -metal plates and an electrolyte are often called _primary batteries_. In -voltaic cells one or both plates and the electrolyte are used up or lose -their chemical energy in producing the current and after a time need to -be replaced by new material, the _chemical energy_ of the electrolyte -and of one of the plates having been _transformed_ into electrical -energy. - -A different proceeding obtains with another type of cell. This is -called a _storage battery_, or an accumulator. In these cells, the same -_plates_ and electrolyte are _used_ without change _for extended -periods_, sometimes for a number of years. For this reason storage -batteries have displaced many other types of cells, and they are now -used (a) to operate many telephone, telegraph, and fire-alarm circuits, -(b) to work the spark coils of gas and gasoline engines, (c) to help -carry the "peak" load upon lighting and power circuits and (d) to -furnish power for electric automobiles. Since a storage battery can -deliver an electric current only after an electric current from an -outside source has first been sent through it, they are often called -_secondary batteries_. - -=288. Construction and Action of a Storage Cell.=--The common type of -storage cells consists of a _number of perforated_ plates made of an -alloy of lead and a little antimony. (See Figs. 265, 266, 267.) Into the -perforations is pressed a paste of red lead and litharge mixed with -sulphuric acid. The plates are placed in a strong solution (20 to 25 per -cent.) of sulphuric acid. The plates are now ready to be charged. This -is accomplished by sending a direct current from an electric generator -through the cell. The hydrogen ions are moved by the current to one set -of plates and change the paste to _spongy_ metallic lead. The sulphions -move to the other set of plates and change the paste to lead oxide. This -electrolytic action causes the two plates to become quite different -chemically so that when the cell is fully charged it is like a voltaic -cell, in having plates that are different chemically. It has, when fully -charged, an E.M.F. of about 2.2 volts. The several plates of a cell -being in parallel and close together, the cell has but small internal -resistance. Consequently a large current is available. - -[Illustration: FIG. 265.--The positive plate of a storage cell.] - -[Illustration: FIG. 266.--The negative plate of a storage cell.] - -[Illustration: FIG. 267.--A complete storage cell.] - -[Illustration: FIG. 268.] - -About 75 per cent. of the energy put into the storage cell in charging -can be obtained upon _discharging_. Therefore the _efficiency_ of a good -storage cell is about 75 per cent. Fig. 268 represents a storage battery -connected to charging and discharging circuits. The lower is the -charging circuit. It contains a dynamo and a resistance (neither of -which are shown in the figure) to control the current sent into the -cell. The charging current enters the positive pole and leaves by the -negative pole. The current produced by the cell, however, flows in the -_opposite_ direction through it, that is, out from the positive and in -at the negative pole. This current may be controlled by a suitable -resistance and measured by an ammeter. Storage cells have several -advantages: (a) They can be charged and discharged a great many times -before the material placed in the perforations in the plates falls out. -(b) The electrical energy used in charging the plates _costs less_ than -the plates and electrolyte of voltaic cells. (c) Charging storage cells -takes much _less labor_ than replacing the electrolyte and plates of -voltaic cells. (d) Storage cells produce _larger currents_ than voltaic -cells. The two principal _disadvantages_ of storage cells are that (a) -they are _very heavy_, and (b) their initial _cost_ is _considerable_. - -[Illustration: FIG. 269.--The Edison storage cell.] - -[Illustration: FIG. 270.--The plates of the Edison storage cell.] - -=289. The Edison storage cell= (Figs. 269 and 270) has plates of iron -and nickel oxide. The electrolyte is a strong solution of potassium -hydroxide. These cells are lighter than lead cells of the same capacity -and they are claimed to have a longer life. - -=290. Energy and Power of a Storage Cell.=--In a storage cell, the -electrical energy of the charging current is transformed into _chemical_ -energy by the action of electrolysis. It is this chemical energy that is -transformed into the energy of the electric current when the cell is -discharged. The _capacity_ of storage cells is rated in "ampere hours," -a 40 ampere hour cell being capable of producing a current of 1 ampere -for 40 hours, or 5 amperes for 8 hours, etc. The production and -extensive use of electric currents have made necessary accurate methods -for measuring the _energy_ and _power_ of these currents. To illustrate -how this is accomplished, let us imagine an electric circuit as -represented in Fig. 268. Here four storage cells in series have an -E.M.F. of 8 volts and in accordance with Ohm's law produce a current of -2 amperes through a resistance in the circuit of 4 ohms. Now the work -done or energy expended by the current in passing through the resistance -between the points _M_ and _N depends_ upon three factors (1) the E.M.F. -or _potential difference_; (2) the _current intensity_ and (3) the -_time_. The energy is measured by their product. That is, _electrical -energy_ = _potential difference_ × _current intensity_ × _time_. This -represents the electrical energy in _joules_, or - - Joules = volts × amperes × seconds, or - _j_ = _E_ × _I_ × _t_. - -In the circuit represented in Fig. 268 the energy expended between the -points _M_ and _N_ in 1 minute (60 seconds) is 8 × 2 × 60 = 960 joules. - -=291. Electric Power.=--Since power refers to the _time rate_ at which -work is done or energy expended, it may be computed by dividing the -electrical energy by the time, or the _electrical power_ = _volts_ × -_amperes_. The power of 1 joule per second is called a _watt_. -Therefore, - - Watts = volts × amperes, or - Watts = _E_ × _I_. - -Other units of power are the _kilowatt_ = 1000 watts and the -_horse-power_ = 746 watts. In the example given in Art. 290 the power of -the current is 8 × 2 = 16 watts, or if the energy of the current -expended between the joints _M_ and _N_ were converted into mechanical -horse-power it would equal 16/746 of a horse-power. Electrical energy is -usually sold by the _kilowatt-hour_, or the amount of electrical energy -that would exert a power of 1000 watts for one hour, or of 100 watts for -10 hours, or of 50 watts for 20 hours, etc. - - -Important Topics - -1. The storage battery, its construction, electrolyte, action, uses, -advantages, disadvantages. - -2. Electric energy, unit value, how computed? - -3. Electric power, three units, value, how computed, how sold? - - -Exercises - -1. In what three respects are voltaic and storage cells alike? In what -two ways different? - -2. Name the four advantages of storage cells in the order of their -importance. Give your reasons for choosing this order. - -3. Why are dry cells more suitable for operating a door-bell circuit, -than a storage battery? Give two reasons. - -4. The current for a city telephone system is provided by a storage -battery. Why is this better than dry cells at each telephone? - -5. An incandescent lamp takes 0.5 ampere at 110 volts. What power is -required to operate it? How much _energy_ will it transform in 1 minute? - -6. How long would it take for this lamp to use a kilowatt hour of -energy? - -7. A street car used 100 amperes at 600 volts pressure. What power was -delivered to it? Express also in kilowatts and horse-power. - -8. An electric toaster takes 5 amperes at 110 volts. If it toasts a -slice of bread in 2 minutes, what is the cost at 10 cents a kilowatt -hour? - -9. An electric flat iron takes 5 amperes at 110 volts. Find the cost of -using it for 2 hours at 12 cents a kilowatt hour. - -10. A 1/4 kilowatt motor is used to run a washing-machine for 5 hours. -What is the expense for this power at 10 cents a kilowatt hour? - -11. What is the efficiency of a motor that takes 7390 watts and develops -9 horse-power? - -12. How many horse-power are there in a water-fall 212 ft. high over -which flows 800 cu. ft. of water per second? Express this power in -kilowatts. - -13. What horse-power must be applied to a dynamo having an efficiency of -go per cent. if it is to light 20 arc lamps in series, each taking 10 -amperes at 60 volts? - - -(3) THE HEAT EFFECT OF ELECTRIC CURRENTS - -=292. The Production of Heat by an Electric Current.=--When no chemical -or mechanical work is done by an electric current its energy is employed -in overcoming the resistance of the conducting circuit and is -transformed into _heat_. This effect has many practical applications and -some disadvantages. Many devices employ the heating effect of electric -currents, (a) the electric furnace, (b) electric lights, (c) heating -coils for street cars, (d) devices about the home, as flat irons, -toasters, etc. Sometimes the heat produced by an electric current in the -wires of a device such as a transformer is so large in amount that -especial means of cooling are employed. Unusually heavy currents have -been known to melt the conducting wires of circuits and electrical -devices. Hence all circuits for electric power as well as many others -that ordinarily carry small currents are protected by _fuses_. An -_electric fuse_ is a short piece of wire that will melt and break the -circuit if the current exceeds a determined value. The fuse wire is -usually enclosed in an incombustible holder. Fuse wire is frequently -made of lead or of an alloy of lead and other easily fusible metals. -(See Figs. 271 and 272.) - -[Illustration: FIG. 271.--A type of enclosed fuse.] - -[Illustration: FIG. 272.--A link fuse (above); plug fuses (below).] - -=293. Heat Developed in a Conductor.=--A rule for computing the amount -of heat produced in an electric circuit by a given current has been -accurately determined by experiment. It has been found that 1 _calorie_ -of heat (Art. 142), is produced by an expenditure of 4.2 joules of -electrical (or other) energy. In other words, 1 joule will produce 1/4.2 -or 0.24 calorie. Now the number of joules of electrical energy in an -electric circuit is expressed by the following formula: - -Joules = volts × amperes × seconds, or since 1 joule = 0.24 calorie, - - Calories = volts × amperes × seconds × 0.24 or - _H_ = _EI_ × _t_ × 0.24 (1) - -By Ohm's law, _I_ = _E_/_R_ or _E_ = _I_ × _R_, substituting in equation -(1) _IR_ for its equal _E_ we have - - _H_ = _I²R_ × _t_ × 0.24 (2) - -Also since _I_ = _E_/_R_ substitute _E_/_R_ for _I_ in equation (1) and -we have - - _H_ = _E²_/_R_ _t_ × 0.24 (3) - -To illustrate the use of these formulas by a problem suppose that a -current of 10 amperes is flowing in a circuit having a resistance of 11 -ohms, for 1 minute. The heat produced will be by formula (2) = (10)² × -11 × 60 × 0.24 equals 15,840 calories. - -[Illustration: FIG. 273.--A carbon filament incandescent lamp.] - -[Illustration: FIG. 274.--A tungsten lamp.] - -=294. The Incandescent Lamp.=--One of the most common devices employing -the heat effect of an electric current is the _incandescent lamp_. (See -Fig. 273.) In this lamp the current is sent through a carbon filament, -which is heated to incandescence. In order to keep the filament from -burning as well as to prevent loss of heat by convection, it is placed -in a glass bulb from which the air is exhausted. Two platinum wires -fused in the glass connect the carbon filament with the grooved rim and -the end piece of the base. The end piece and rim connect with the socket -so that an electric current may flow through the filament of the lamp. -The carbon incandescent lamp has a low efficiency. It takes 0.5 ampere -of current at 110 volts or in other words it requires 55 watts to cause -a 16-candle-power lamp to glow brightly, hence 1 candle power in this -lamp takes 55/16 = 3.43 watts. - -The _efficiency of electric lamps_ is measured by the _number of watts -per candle power_. This is a peculiar use of the term efficiency, as the -larger the number the less efficient is the lamp. More efficient lamps -have been devised with filaments of the metals _tantalum_ and _tungsten_ -(Fig. 274). These give a whiter light than do carbon lamps, and consume -but about 1.25 watts per candle power. - - -COMPARATIVE "EFFICIENCY" OF ELECTRIC LAMPS - - ------------------+----------+----------------+------------ - |Watts per | | Watts per - Name of lamp | candle | Name of lamp | candle - | power | | power - ------------------+----------+----------------+------------ - Carbon filament | 3 to 4 |Arc lamp | 0.5 to 0.8 - Metallized carbon | 2.5 |Mercury arc | 0.6 - Tantalum | 2.0 |Flaming arc | 0.4 - Tungsten | 1.0 to |Nitrogen-filled | 0.6 to 0.7 - | 1.5 | tungsten | - ------------------+----------+----------------+------------ - -Incandescent lamps are connected in parallel (see Fig. 254) to wires -that are kept at a constant difference of potential of 110 or 115 volts. -It is customary to place not more than twelve lamps upon one circuit, -each circuit being protected by a fuse and controlled by one or more -switches. - -=295. The Arc Light.=--The electric _arc_ light (see Fig. 275) is -extensively used for lighting large rooms, also in stereopticons and -motion picture machines. The light is intense, varying from 500 to 1700 -candle power. The so-called mean spherical candle power of the arc light -is about 510. The candle power in the direction of greatest intensity is -about 1200. It is produced at an expenditure of about 500 watts. It is -therefore more efficient than the incandescent lamp, often taking less -than 0.5 watt per candle power produced. The arc light was first devised -by Sir Humphrey Davy in 1809, who used two pieces of charcoal connected -to 2000 voltaic cells. The arc light requires so much power that its -production by voltaic cells is very expensive. Consequently it did not -come into common use until the dynamo had been perfected. Fig. 276 shows -the appearance of the two carbons in an arc light. If a direct current -is used the positive carbon is heated more intensely, and gives out the -greater part of the light. The positive carbon is consumed about twice -as fast as the negative and its end is concave, the negative remaining -pointed. - -[Illustration: FIG. 275.--An electric arc light.] - -[Illustration: FIG. 276.--The appearance of a pair of used carbons.] - -With alternating currents, the rods are equally consumed and produce -equal amounts of light. In the stereopticon, the carbons are usually -placed at right angles as in Fig. 277. In the stereopticon as well as -in outdoor lighting the direct current is more effective, although the -alternating current is often used, since the latter can be produced and -distributed more cheaply than can direct currents. In arc lamps, placing -an inner glass globe (Fig. 278) about the carbons, decreases the -consumption of the carbons materially. The carbon rods of _enclosed_ arc -lamps often last 60 to 100 hours. - -[Illustration: FIG. 277.--A right-angle electric arc lamp for a -stereopticon.] - -[Illustration: FIG. 278.--An enclosed arc lamp.] - - The reason why an _open_ arc lamp needs to be "retrimmed" oftener - than the _enclosed_ lamp, that is, have new carbons placed in it, - is because the carbons "burn" freely, that is unite with the oxygen - of the air. In the enclosed arc lamp, the supply of oxygen in the - inner globe is limited and is soon consumed, therefore the carbons - last many times longer in such lamps. - -Some carbon rods have soft cores containing calcium salts. These -vaporize in the arc producing the _flaming arc light_ of a bright yellow -color, and give more light than the ordinary lamp. - - -Important Topics - -1. Heat effects of electric currents, uses and applications. - -2. Computation of the heat developed in a circuit. Three formulas. - -3. Electric lamps; incandescent and arc; construction, uses, -efficiency. - - -Exercises - -1. Sketch a circuit containing 10 incandescent lamps in parallel. If -each lamp when hot has a resistance of 220 ohms, and the E.M.F. is 100 -volts, what current will flow? - -2. What will it cost to use these lights for 3 hours a day for 30 days -at 10 cents a kilowatt hour? - -3. How much heat will these lamps produce per minute? - -4. How could you connect 110-volt lamps to a street car circuit of 660 -volts? Explain this arrangement and draw a diagram. - -5. A certain arc lamp required 10 amperes of current at 45 volts -pressure. What would it cost at 10 cents per kilowatt hour if used 3 -hours a day for 30 days? - -6. Show a diagram of 3 arc lamps in series. If each takes 45 volts and -10 amperes, how much E.M.F. and current will they require? - -7. If an electric toaster uses 5 amperes at 115 volts, how much heat -will this develop in half an hour? - -9. How much heat is developed in an electric toaster in 2 minutes, if it -uses 5 amperes at 100 volts? - -10. How many B.t.u.'s are given off in an electric oven that takes 10 -amperes at 110 volts for 1 hour? (1 B.t.u. equals 252 calories.) - -11. An electric heater supplies heat at the rate of 700 B.t.u.'s an -hour. How much power does it require? - -12. How many watts are required to operate 120 incandescent lamps in -parallel if each takes 0.5 amperes at 110 volts? - -13. An electric lamp takes 12 amperes at a P.D. of 110 volts. How many -B.t.u.'s are radiated from it each second? How many calories? - -14. If a 110-volt incandescent lamp is submerged for 10 minutes in 400 -gr. of cold water while a current of 0.5 amperes is flowing, how many -degrees centigrade will the water be warmed? - -15. In an electric furnace a current of 3000 amperes is used at a P.D. -of 10 volts. Find the heat developed in 1 minute. - -16. How many candle power should a 20-watt tungsten lamp give if its -efficiency is one watt per candle power? - -17. What is the "efficiency" of a 40-watt tungsten lamp if it gives 34 -candle power? - - -Review Outline: Current Electricity - -Produced by--Chemical action; voltaic and storage cells. - - Three { Magnetic, electromagnet, uses and applications. - Principal { Chemical, electrolysis, applications. - Effects: { Heat, lighting and heating devices. - -Theories: (a) of voltaic cells, (b) of electrolysis. - -Units: Ampere, ohm, volt, watt, joule, kilowatt, horse power. - - Measurement--(a) magnetic effect; galvanometer, ammeter, voltmeter, - wattmeter, Wheatstone bridge, construction - and use. - - (b) chemical effect; voltameter. - - Laws: (a) Right hand rules, for conductor and helix. - (b) Resistance, Conductors in series and parallel. - (c) Ohm's law, heat law, power law, 3 forms for each. - (d) Cells in parallel and series. - -Problems: Upon applications of the laws and formulas studied. - - Devices. { Voltaic cells; wet, dry, and Daniell. - and { Electrolysis and the storage battery. - Instruments: { Measuring instruments, electric bell, sounder, - { heating and lighting devices. - -Terms: Anode, cathode, electrolyte, ion, circuit switch, current, -e.m.f., resistance, potential. - - - - -CHAPTER XIV - -INDUCED CURRENTS - - -(1) ELECTROMAGNETIC INDUCTION - -=296. Current Induced by a Magnet.=--The discovery in 1819 that a -current in a conductor can deflect a magnetic needle or that it has a -magnetic effect, led to many attempts _to produce an electric current by -means of a magnet_. It was not until about 1831, however, that _Joseph -Henry_ in America and _Michael Faraday_ in England, independently -discovered how to accomplish this important result. - -At the present time, voltaic cells produce but a very small part of the -current electricity used. Practically all that is employed for _power, -light, heat, and electrolysis is produced by the use of magnetic fields, -or by electromagnetic induction_. - -=297. Laws of Induced Currents.=[M]--To illustrate how a current can be -produced by electromagnetic induction: - - [M] An induced current is one produced by changing the number of - magnetic lines of force passing through a coil. - - Connect a coil of 400 or more turns of No. 22 insulated copper wire - to a sensitive galvanometer. (See Fig. 279.) Now insert a bar - magnet in the coil. A sudden movement of the galvanometer will be - noticed, indicating the _production of a current_. When the magnet - stops moving, however, the current stops, and the coil of the - galvanometer returns to its first position. If now the magnet is - removed, a movement of the galvanometer coil _in the opposite - direction is_ noticed. This action may be repeated as often as - desired with similar results. - -Careful experiments have shown that it is the _magnetic field_ of the -magnet that produces the action, and that only when the _number of -lines of force in the coil is changing_ do we find a current produced in -the coil. These facts lead to _Law I_. _Any change in the number of -magnetic lines of force passing through or cut by a coil will produce an -electromotive force in the coil._ In the account of the experiment just -given, _electric currents_ are produced, while in Law I, _electromotive -forces_ are mentioned. This difference is due to the fact that an E.M.F. -is _always_ produced in a coil when the magnetic field within it is -changed, while a current is found only when the coil is part of a -_closed circuit_. The inductive action of the earth's magnetic field -(see Fig. 280), may be shown by means of a coil of 400 to 500 turns a -foot in diameter. - -[Illustration: FIG. 279.--The moving magnet induces a current in the -coil.] - -[Illustration: FIG. 280.--A current may be induced by turning the coil -in the earth's magnetic field.] - - Connect its ends to a sensitive galvanometer and hold it at right - angles to the earth's field. Then quickly revolve the coil through - 180 degrees and note the movement of the galvanometer. Reverse the - coil and the galvanometer swings in the opposite direction. - -If the magnet in Fig. 279 is moved _in_ and _out_ of the coil at first -_slowly_ and _later swiftly_, _small and large_ deflections of the -galvanometer coil are noticed. The quicker the movement of the magnetic -field the greater are the galvanometer deflections produced. This leads -to _Law II_. _The electromotive forces produced are proportional to the -number of lines of force cut per second._ - -=298. The magneto= is a device that illustrates the laws of induced -currents stated in Art. 297. The magneto (see Fig. 281), consists of -several permanent, "U"-shaped magnets placed side by side. Between the -poles of these magnets is placed a slotted iron cylinder having a coil -of many turns of fine insulated copper wire wound in the slot as in Fig. -282. The cylinder and coil form what is called an _armature_. The -armature is mounted so as to be revolved between the poles of the -"U"-shaped magnets by means of a handle. As the armature revolves, the -lines of force from the magnets pass through the coil first in one -direction and then in the other. This repeated change in the lines of -force passing through the coil produces an E.M.F. which may be felt by -holding in the hands the two wires leading from the armature coil. On -turning the armature _faster_ the current is felt _much stronger_, -showing that the E.M.F. in the coil increases as the rate of cutting the -magnetic lines of force by the coils increases. - -[Illustration: FIG. 281.--A magneto.] - -[Illustration: FIG. 282.--A shuttle armature.] - -[Illustration: FIG. 283.--The induced current has a field which opposes -the motion of the magnet. The heavy line represents the direction of the -induced current.] - -=299. Lenz's Law.=--While one is turning the armature of a magneto if -the two wires leading from its coil are connected, forming what is -called a "short circuit," the difficulty of turning the armature is at -once increased. If now the circuit is broken, the armature turns as -easily as at first. The increased difficulty in turning the armature is -due to the _current_ produced in the coil. This current sets up a -magnetic field of its own that opposes the field from the steel magnets. -This opposition makes it necessary for _work_ to be done to keep up the -motion of the coil when a current is passing through it. This fact is -called _Lenz's Law_. It may be expressed as follows: _Whenever a current -is induced by the relative motion of a magnetic field and a conductor, -the direction of the induced current is always such as to set up a -magnetic field that opposes the motion._ Lenz's Law follows from the -principle of conservation of energy, that energy can be produced only -from an expenditure of other energy. Now since an electric current -possesses energy, such a current can be produced only by doing -mechanical work or by expending some other form of energy. To illustrate -Lenz's Law, suppose that the north-seeking pole of a bar magnet be -inserted in a closed coil of wire. (See Fig. 283.) The current induced -in the coil has a direction such that its lines of force will pass -within the coil so as to _oppose_ the field of the bar magnet, when the -north pole of the magnet is inserted so as to point to the left. That -is, the north pole of the helix is at the right. Applying the right-hand -rule to the coil, its current will then be _counter clockwise_. On -withdrawing the magnet, the current reverses, becoming _clockwise_ with -its field passing to the left within the coil. - -A striking illustration of the opposition offered by the field of the -induced current to that of the inducing field is afforded by taking a -strong electromagnet (see Fig. 284) and suspending a sheet of copper so -as to swing freely between the poles. When no current flows through the -magnet the sheet swings easily for some time. When, however, the coils -are magnetized, the copper sheet has induced within it, currents that -set up magnetic fields strongly opposing the motion, the swinging being -stopped almost instantly. The principle is applied in good ammeters and -voltmeters to prevent the swinging of the needle when deflected. The -current induced in the metal form on which is wound the galvanometer -coil is sufficient to make the needle practically "dead beat." - -[Illustration: FIG. 284.--The magnetic field stops the swinging of the -sheet of copper.] - -=300. The Magneto and the Dynamo.=--Magnetos are used to _develop small_ -currents, such as are used for telephone signals, and for operating the -_sparking_ devices of gasoline _engines_. They are therefore found in -automobiles containing gasoline motors. The most important device for -producing electric currents by electromagnetic induction, however, is -the _dynamo_. It is employed whenever large currents are desired. The -principle of this device is similar to that of the magneto except that -it contains an _electromagnet_ for producing the magnetic field. -Since the electromagnet can develop a much stronger field than a -permanent magnet, the dynamo can produce a higher E.M.F. and a much -larger current than the magneto. - -[Illustration: LORD KELVIN - -"By Permission of the Berlin Photographic Co., New York." - -Lord Kelvin (Sir William Thomson), (1824-1907). Professor of Physics, -Glasgow University. Invented the absolute scale of temperature: also -many practical electrical measuring instruments. The foremost physicist -of the latter part of the nineteenth century.] - -[Illustration: MICHAEL FARADAY - -"By Permission of the Berlin Photographic Co., New York." - -Michael Faraday (1791-1867). Famous English Physicist. Made many -discoveries in electricity and magnetism; "Greatest experimentalist of -the nineteenth century."] - -=301. The Magnetic Fields of Generators.=--In the magneto, the magnetic -field is produced by _permanent_ steel magnets. In dynamos powerful -_electromagnets_ are used. The latter are sometimes excited by currents -from some other source, but usually current from the armature is sent -around the field coils to produce the magnetic fields. Dynamos are -classified according to the manner in which the current is sent to their -field coils. - -[Illustration: FIG. 285.--A series-wound dynamo.] - -[Illustration: FIG. 286.--A shunt-wound dynamo.] - -[Illustration: FIG. 287.--A compound-wound dynamo.] - -_A._ The _series wound dynamo_ (see Fig. 285) is arranged so that _all_ -of the current produced by the armature is sent through coils of coarse -wire upon the fields, after flowing through the external circuit. - -_B._ The _shunt wound dynamo_ (see Fig. 286) sends a part only of the -current produced through the field coils. The latter are of many turns -of fine wire so as to use as little current as possible. The greater -part of the current goes to the main circuit. If the number of lamps or -motors connected to the main circuit is increased, the voltage is -lessened which weakens the current in the field coils, causing a weaker -field and still lower voltage, producing a fluctuating E.M.F. which is -unsatisfactory for many purposes. This fault is overcome by - -_C._ the _compound wound dynamo_. This dynamo has both shunt and series -coils upon its fields. (See Fig. 287.) If more current is drawn into the -main circuit with this dynamo, the series coils produce a stronger field -compensating for the weaker field of the shunt coils, so that uniform -voltage is maintained. The compound wound generator is therefore the one -most commonly employed. - - -Important Topics - -1. Laws of electromagnetic induction (a) conditions, (b) E.M.F., (c) -direction. - -2. Devices, (a) magneto, (b) dynamo: series, shunt, compound. - -3. Illustrations of the laws. - - -Exercises - -1. Under what conditions may an electric current be produced by a -magnet? - -2. Show how Lenz's Law, follows from the principle of conservation of -energy. - -3. A bar magnet is fixed upright with its north-seeking pole upward. A -coil is thrust down over the magnet. What is the direction of the -current induced in the coil? Explain. - -4. In what two ways may a current be induced in a closed coil? - -5. What method is employed in the magneto? In the dynamo? - -6. What is the nature of the current produced in the armature coil of a -magneto, that is, is it direct or alternating? Why? - -7. What is the resistance of a 20-watt tungsten lamp if the E.M.F. is -115 volts? - -8. Find the resistance of a 40-watt tungsten lamp when the voltage is -115? How much heat will it produce per minute? - -9. An Edison storage battery cell on a test gave a discharge of 30 -amperes. The average voltage was 1.19. What was the resistance of the -cell? - -10. Eight storage cells are connected in series. Each has an E.M.F. of -1.2 volts and an internal resistance of 0.03 ohms. What will be the -current flowing through a voltmeter having 500 ohms resistance in -circuit with them? - - -(2) THE DYNAMO AND THE MOTOR - -=302. The Dynamo= may be defined as a machine for transforming -mechanical energy into the energy of electric currents by -electromagnetic induction. Although electromagnetic induction was -discovered in 1821, practical dynamos were not built for about 40 years -or until between 1860 and 1870. The great development in the production -and use of electric currents has come since the latter date. The -principle parts of the dynamo are (a) the _field magnet_, (b) the -_armature_, (c) the _commutator_ or _collecting rings_, (d) the -_brushes_. Fig. 288 shows several common methods of arranging the field -coils and the armature. - -[Illustration: FIG. 288.--Several methods of arranging the field coils -and the armature of a dynamo.] - -[Illustration: FIG. 289.--A drum armature.] - -The field coils vary in number and position. The purpose of their -construction is always to send the largest possible number of lines of -force through the armature. Some dynamos are _bipolar_, or have _two_ -poles, others are multipolar or have more than two. In Fig. 288 No. 4 -has four poles. The _armature_ of a dynamo differs from a magneto -armature in that it consists of a series of coils of insulated copper -wire wound in numerous slots cut in the surface of a cylindrical piece -of iron. Fig. 289 shows a _side_ view of the iron core of such an -armature. Iron is used to form the body of the armature since the -magnetic lines of force flow easily through the iron. The iron by its -permeability also concentrates and increases the magnetic flux. The best -armatures are made of many thin sheets of soft iron. These are called -_laminated_ armatures. An armature made of a solid piece of iron becomes -hot when revolving in a magnetic field. This is due to electric currents -induced in the iron itself. This heating is largely reduced by -_laminating_ the armature. Why? - -[Illustration: FIG. 290.--Armature connected to slip rings producing an -alternating current.] - -=303. Methods of Collecting Current from the Armature.=--The electric -currents produced in the armature are conducted away by _special sliding -contacts_. The stationary part of the sliding contact is called a -_brush_. The moving part is a _slip ring_ or a _commutator_. Fig. 290 -shows an armature coil connected to slip rings. As the armature -revolves, the coils and slip rings revolve with it. The two ends of the -armature coils are connected to the two rings respectively. Now as the -armature revolves it cuts the lines of force first in one direction and -then in the other. This produces in the coils an E.M.F. first one way -and then the other. This E.M.F. sets up a current which is conducted to -the outside circuits through the slip rings and brushes. Such a current -which repeatedly reverses its direction is called an _alternating -current_. Fig. 291 (1) indicates graphically how the current moves -alternately one way and then the other. Alternating currents are -extensively used for electric _light, heat, and power_. _Direct -currents_ or those going continuously in one direction are however in -much demand especially for _street car service_, _for electrolysis_, and -for _charging storage batteries_. - -=304. The Commutator.=--For a dynamo to deliver a _direct current_ it -must carry upon the shaft of the armature a _commutator_. The commutator -is used to _reverse_ the connections of the ends of the armature coils -at the instant that the current changes its direction in the armature. -This reversal of connection when the direction of current changes, keeps -the current in the outside circuit flowing in the same direction. Fig. -291 is a diagram of an armature with a commutator. The commutator is a -_split ring_, having as many parts or _segments_ as there are coils upon -the armature. The brushes touch opposite points upon the commutator as -they slide over the surface of the latter. Suppose that the armature -viewed from the commutator end rotates in a counter-clockwise direction, -also that the currents from the upper part move toward the commutator -and out the top brush. - -[Illustration: FIG. 291.--The armature coils are connected to a -commutator producing a direct current.] - -As the armature revolves, its coils soon begin to cut the force lines in -the opposite direction. This change in the direction of cutting the -lines of force causes the current to reverse in the coils of the -armature. At the instant the current changes in direction, what was the -upper segment of the commutator slips over into contact with the lower -brush, and the other segment swings over to touch the upper brush. Since -the current has reversed in the coils it continues to flow out of the -upper brush. This change in connection at the brushes takes place at -each half turn of the armature, just as the current changes in direction -in the coils. This is the manner in which the commutator of a dynamo -changes the alternating current produced in the armature coils, into a -direct current in the external circuit. Fig. 292 (1) represents -graphically an alternating current, (2) of the same figure shows current -taken from the brushes of the commutator of a dynamo with one coil on -the armature. - -[Illustration: FIG. 292.--Graphic representation of (1) an alternating -current; (2) a pulsating current; (3) a continuous current.] - -[Illustration: FIG. 293.--DeLaval multi-stage turbine and gear driving -750-kw., 750-r.p.m., 600-volt direct-current generator.] - -A practical dynamo, however, has many coils upon its armature with a -corresponding number of segments upon the commutator. (See Figs. 289 and -293.) As each coil and commutator segment passes a brush, it contributes -an impulse to the current with the result that armatures with many coils -produce currents that flow quite evenly. (See Fig. 292, 3.) - -The current represented in Fig. 292 (2) is called a _pulsating_ current. - -[Illustration: FIG. 294.--A wire carrying a current across a magnetic -field is pushed sideways by the field.] - -=305. The electric motor= is a machine which transforms the energy of an -electric current into mechanical energy or motion. The _direct current -motor_ consists of the same essential parts as a direct current dynamo, -viz., the field magnet, armature, commutator and brushes. Its operation -is readily comprehended after one understands the following experiment: - -Set up two bar electromagnets with unlike poles facing each other about -an inch apart. A wire connected to a source of current is hung loosely -between the poles as in Fig. 294. The circuit through the wire should -contain a key or switch. If a current is sent through the electromagnets -and then another is sent through the wire, the latter will be found to -be pushed either up or down, while if the current is reversed through -the wire it is pushed in the opposite direction. These results may be -explained as follows: - -Consider the magnetic field about a wire carrying a current (See Fig. -295.) If such a wire is placed in the magnetic field between two -opposite poles of an electromagnet (Fig. 296), the wire will be moved -either up or down. The reason for this is shown by the diagram in Fig. -297. Here a wire carrying a current and therefore surrounded by a -magnetic field passes across another magnetic field. The two fields -affect each other causing a crowding of the force lines either above or -below the wire. The wire at once tends to move sideways across the field -away from the crowded side. In the figure, the wire tends to move -downward. - -[Illustration: FIG. 295.--The magnetic field about a wire carrying a -current.] - -[Illustration: FIG. 296.--The magnetic field between two unlike poles.] - -[Illustration: FIG. 297.--The crowding of the lines of force above the -wire, pushes it downward.] - -In a practical motor, the wires upon the armature are so connected that -those upon one side (see Fig. 298), carry currents that pass in, while -on the other side they pass out. To represent the direction of the -current in the wires, the following device is employed; a circle with a -cross (to represent the feather in the tail of an arrow) indicates a -current going away from the observer, while a circle with a dot at its -center (to represent the tip of an arrow) indicates a current coming -toward the observer. - -[Illustration: FIG. 298.--The crowding of the lines of force causes the -armature to revolve in a clockwise direction.] - -In Fig. 298 the north pole is at the left and the south pole at the -right. The field of the magnets therefore passes from left to right as -indicated in the figure. Now in the armature the currents in the wires -on the left half of the armature are coming toward the observer while -those on the right move away. Applying the right-hand rule, the magnetic -lines will crowd _under_ the wires on the left side of the armature -while they will crowd _over_ the wires on the right side. This will -cause a rotation up on the left side and down on the right, or in a -_clockwise_ direction. - -[Illustration: FIG. 299.--View of a one-half horse-power motor.] - -If the current in the armature is reversed (in on the left and out on -the right), the lines of force will crowd the armature around in the -opposite direction or _counter clockwise_. The rotation of the armature -will also be reversed if, while the current in the armature is unchanged -in direction, the poles of the magnet are changed thus reversing the -magnetic field. - -The motorman of a street car reverses the motion of his car by reversing -the direction of the current in the _armature_ of the motor. - -[Illustration: FIG. 300.--The frame and electromagnet (at left), front -bracket and brush holder (at right) of the motor shown in Fig. 299.] - -[Illustration: FIG. 301.--The armature of a motor.] - -=306. Practical motors= have many coils upon the armature with a -corresponding number of segments upon the commutator. A large number of -coils and commutator segments enables some one of the coils to exert its -greatest efficiency at each instant, hence a steady force is provided -for turning the armature which causes it to run smoothly. Fig. 299 -represents a 1/2 horse-power motor ready for use while Fig. 300 shows -the frame and poles and the front bracket and brush holder, and Fig. 301 -represents the armature. - - -Important Topics - -1. The dynamo, four essential parts, action (a) for alternating -currents, (b) for direct currents. - -2. The electric motor: (a) essential parts, (b) action. - - -Exercises - -1. _Why_ is an alternating current produced in the armature of a dynamo? - -2. _How_ is this current produced? Give careful explanations. - -3. What is the result of Lenz's law as applied to the dynamo? - -4. Apply the first two laws of electromagnetic induction to the dynamo. - -5. What is the power of a dynamo if it produces 40 amperes of current at -110 volts? - -6. How much power must be applied to this dynamo if its efficiency is 90 -per cent.? - -7. A motor takes 10 amperes of current at 220 volts; what is the _power_ -of the current in _watts_? If this motor has an efficiency of 95 per -cent., how many horse-power of mechanical energy can it develop? - -8. Explain why reversing the current in the armature of a motor reverses -the direction of rotation. - -9. Find the cost of running a washing machine using a 1/2-horsepower -motor 2 hours if the cost of the electricity is 10 cents a kilowatt -hour. - -10. A 1/8-horse-power motor is used to run a sewing machine. If used for -3 hours what will be the cost at 11 cents a kilowatt hour? - - -(3) THE INDUCTION COIL AND THE TRANSFORMER - -=307. The Induction Coil.=--Practically all electric currents are -produced either by voltaic cells or by dynamos. It is frequently found, -however, that it is desirable to change the E.M.F. of the current used, -either for purposes of _effectiveness_, _convenience_, _or economy_. The -_induction coil_ and the _transformer_, devices for changing the E.M.F. -of electric currents, are therefore in common use. _The induction coil_ -(see Fig. 302) consists of a _primary_ coil of coarse wire _P_ (Fig. -303) wound upon a core of soft iron wire, and a _secondary_ coil, _S_, -of several thousand turns of fine wire. In circuit with the primary coil -is a battery, _B_, and a current interrupter, _K_, which works like the -interrupter upon an electric bell. The ends of the secondary coil are -brought to binding posts or spark points as at _D_. - -[Illustration: FIG. 302.--An induction coil.] - -The current from the battery flows through the primary coil magnetizing -the iron core. The magnetism in the core attracts the soft-iron end of -the interrupter, drawing the latter over and breaking the circuit at the -screw contact, _K_. This abruptly stops the current and at once the core -loses its magnetism. The spring support of the interrupter now draws the -latter back to the contact, _T_, again completing the circuit. The whole -operation is repeated, the interrupter vibrating rapidly continually -opening and closing the circuit. - -[Illustration: FIG. 303.--Diagram showing the parts of an induction -coil.] - -=308. The Production of Induced Currents in the Secondary Coil.=--When -the current flows through the _primary_ it sets up a magnetic field in -the _core_. When the current is interrupted, the field disappears. The -increase and decrease in the field of the core induces an E.M.F. in the -secondary coil, in accordance with the first law of electromagnetic -induction. The E.M.F. produced depends upon (a) the number of turns in -the secondary, (b) the strength of the magnetic field and (c) the rate -of change of the field. The rate of change in the field is more rapid at -the break than at the make. When the circuit is closed it takes perhaps -1/10 of a second for the current to build up to its full strength while -at a break the current stops in perhaps 0.00001 of a second, so that the -induced E.M.F. is perhaps 10,000 times as great at "break" as at make. -To increase the suddenness of the "make" and "break," a condenser is -often connected in the primary circuit, in parallel, with the -interrupter. (See Fig. 303, _C._) This condenser provides a place to -hold the rush of current at the instant that the interrupter breaks the -circuit. This stored up charge reinforces the current at the make -producing a much more sudden change in the magnetic field with a -corresponding increase in the E.M.F. The induced currents from induction -coils are sometimes called _faradic currents_ in honor of Faraday who -discovered electromagnetic induction. They are used to operate sparking -devices upon gas and gasoline engines and in many devices and -experiments in which high-tension electricity is employed. - -[Illustration: FIG. 304.--The transformer has a closed core; the -induction coil, an open core.] - -[Illustration: FIG. 305.--The laminated iron core of a transformer.] - -[Illustration: FIG. 306.--Cross-section of the transformer shown in Fig. -305 showing the magnetic field around the primary and secondary coils.] - -=309. The Transformer.=--This is like the induction coil in that it uses -a _primary_ and a _secondary_ coil, and an iron core to carry the -magnetic field. (See Fig. 304.) They differ in that the transformer has -a _closed_ core or one forming a continuous iron circuit, while the -induction coil has an _open_ core, or one in which the magnetic field -must travel in air from the north to the south poles of the core. The -transformer must always be used with an _alternating_ current while the -induction coil may use either a direct or an alternating current. -Further, the _induction_ coil always produces a higher E.M.F. while the -transformer may produce an E.M.F. in its secondary coil that is either -higher or lower than the one in the primary. The former is called -"_step-up_" while the latter is a "_step-down_" transformer. The -alternating current in the primary coil of the transformer produces an -_alternating magnetic flux_ in the iron core. This iron core is -_laminated_ (see Fig. 305) to prevent the heating that would result if a -solid core were used. The alternating magnetic flux induces in the -secondary coil an E.M.F. in accordance with the following rule. The -ratio of the _number_ of _turns_ in the _primary_ to the _number_ of the -_turns_ in the _secondary_ coil equals the ratio of the electromotive -forces in these respective coils. If the secondary coil has 8 turns -while the primary has 4, the E.M.F. of the secondary will be just twice -that of the primary. Or, if in the primary coil of the transformer Fig. -306 is an E.M.F. of 110 volts, in the secondary will be found an E.M.F. -of 220 volts. - -[Illustration: FIG. 307.--A commercial transformer.] - -=310. Uses of Transformers.=--In electric lighting systems, dynamos -often produce alternating currents at 1000 to 12,000 volts pressure. It -is very dangerous to admit currents at this pressure into dwellings and -business houses, so that transformers are installed just outside of -buildings to "step-down" the high voltage currents to 110 or 220 volts. -The lighting current that enters a house does not come directly from a -dynamo. It is an induced current produced by a transformer placed near -the house. (See Fig. 307.) In a perfect transformer the efficiency would -be 100 per cent. This signifies that the energy that is sent into the -primary coil of the transformer exactly equals the energy in the -secondary coil. The best transformers actually show efficiencies better -than 97 per cent. The lost energy appears as heat in the transformer. -"The transfer of great power in a large transformer from one circuit to -another circuit entirely separate and distinct, without any motion or -noise and almost without loss, is one of the most wonderful phenomena -under the control of man." - -=311. The mercury arc rectifier= is a device for changing an alternating -current into a direct current. It is frequently used for charging -storage batteries where only alternating current is supplied by the -electric power company. It consists of an exhausted bulb containing two -carbon or graphite electrodes marked _G_ in Fig. 308 and a mercury -electrode marked _M_. It is found that current will pass through such a -bulb only from the graphite to the mercury but not in the reverse -direction. In operating the device, the secondary terminals of an -alternating current transformer _T_ are connected to the graphite -terminals of the rectifier. A wire connected to the center of the -secondary of the transformer at _C_ is attached to the _negative_ -terminal of the storage battery _SB_. The _positive_ terminal of the -battery is connected to the mercury electrode of the rectifier tube -through a reactance or choke coil _R_. This coil serves to sustain the -arc between the alternations. _Sw_ is a starting switch, used only in -striking the arc. It is opened immediately after the tube begins to -glow. - -[Illustration: FIG. 308.--Diagram of a mercury arc rectifier.] - - -Important Topics - -Transformer, induction coil, mercury arc rectifier, construction, -action; uses of each. - - -Exercises - -1. Does the spark of an induction coil occur at "make" or at "break?" -Why? - -2. What must be the relative number of turns upon the primary and -secondary coils of a transformer if it receives current at 220 volts -and delivers current at 110? Also show by diagram. - -3. Would the transformer work upon a direct current? Why? - -4. Explain why the interrupter is a necessary part of the induction coil -and not of the transformer. - -5. If a building used eighty 110-volt incandescent lamps, what would be -necessary to light them if they were joined in series? Why would this -not be practical? - -6. If a 16-candle-power lamp requires 0.5 ampere upon a 110-volt circuit -what current and voltage will be needed to operate 12 such lamps in -parallel? - -7. What will it cost to run these lamps 4 hours a night for 30 days at -10 cents per kilowatt hour? - -8. If a mercury arc rectifier uses 5 amperes of current at 110 volts -alternating current to produce 5 amperes of direct current at 70 volts, -what is the efficiency of the rectifier? - -9. Compute the heat produced in a 40 watt tungsten lamp in 1 minute. - -10. Compute the heat produced in a 60 watt carbon incandescent lamp in 1 -hour. - - -(4) THE TELEPHONE - -=312. The Electric Telephone.=--This is an instrument for reproducing -the human voice at a distance by an electric current. The modern -electric telephone consists of at least four distinct parts (see Fig. -312); viz., a _transmitter_, an induction coil, an electric battery, and -a _receiver_. The first three of these are concerned in sending, or -_transmitting_ over the connecting wires a fluctuating electric current, -which has been modified by the waves of a human voice. The receiver, is -affected by the fluctuating current and reproduces the voice. It will be -considered first, in our study. - -=313. The telephone receiver= was invented in 1876 by Alexander Graham -Bell. It consists of a permanent steel magnet, U shaped, with a coil of -fine insulated copper wire about each pole. (See Fig. 310.) A disc of -thin sheet iron is supported so that its center does not quite touch -the poles of the magnet. A hard rubber cap or ear piece with an opening -at its center is screwed on so as to hold the iron disc firmly in place. - -[Illustration: FIG. 309.--The simplest telephone system. It consists of -two telephone receivers connected in series on a circuit. It will work, -but not satisfactorily.] - -_The action of the receiver_ may be understood from the following -explanation: The electric current sent to the receiver, comes from the -secondary coil of the induction coil; it is an alternating current, -fluctuating back and forth just in time with the waves of the voice -affecting it at the transmitter. This alternating current flows around -the coils on the poles of the permanent magnet. When this current flows -in one direction, its magnetic field assists the field of the permanent -magnet, strengthening it. This stronger magnetic field draws the thin -iron disc in front of the poles of the magnet a little closer to them. -When the current in the coils flows the other way, its magnetic field -weakens the field of the steel magnet, and the disc is drawn back by the -force of its own elasticity. Thus the disc of the receiver vibrates with -the alternations of the current, and reproduces the same sounds that -were spoken into the transmitter. - -[Illustration: FIG. 310.--A telephone receiver. This receiver has a -permanent horseshoe magnet with a coil about each pole.] - -=314. The Telephone Transmitter.=--The telephone receiver just described -has great sensitiveness in reproducing sound, but it is not satisfactory -as a transmitter or sending apparatus. The _transmitter_ commonly used -is represented in cross-section in Fig. 311. In this figure, back of the -mouthpiece, is a thin carbon disc, _D_. Back of this disc is a circular -compartment containing granular carbon, _g_. The wires of the circuit -are connected to the carbon disc and to the back of the case containing -granular carbon. The circuit through the transmitter also includes a -voltaic or storage cell and the primary coil of an induction coil. (See -Fig. 312.) - -[Illustration: FIG. 311.--A telephone transmitter.] - -[Illustration: FIG. 312.--Telephone instruments at one end of a talking -circuit.] - -=315. The action of the transmitter= is explained as follows: When the -sound waves of the voice strike upon the carbon disc, the latter -vibrates, alternately increasing and decreasing the pressure upon the -granular carbon. When the pressure _increases_, the electrical -resistance of the granular carbon is _lessened_, and when the pressure -upon it is _decreased_, its resistance _increases_. This changing -resistance causes fluctuations in the electric current _that_ correspond -exactly with the sound waves of the voice affecting it. - -=316. A complete telephone system= operating with a local battery is -shown in Fig. 312. A person speaking into the transmitter causes a -fluctuation in the electric current in the transmitter as described in -Art. 315. This fluctuating current passes through the primary coil of -the induction coil _Ic_. This fluctuating current produces a fluctuating -magnetic field in its core. This fluctuating field induces an -_alternating_ current in the secondary coil which alternates just as the -primary current fluctuates, but with a much higher E.M.F. than the -latter. The alternating current passes to the receiver which reproduces -the speech as described in Art. 313. The line circuit includes the -secondary of the induction coil, the receiving instrument and the -receiver of the sending instrument so that the voice is reproduced in -both receivers. An electric bell is placed at each station to call the -attention of parties wanted. The movement of the receiver hook when the -receiver is lifted, disconnects the bell and closes the talking circuit. -The latter is opened and the bell connected when the receiver is hung up -again. - -[Illustration: FIG. 313.--Diagram of a telephone system as used in a -large exchange.] - -In cities and towns, the telephone system in use differs from the one -described in usually having one large battery placed in the central -exchange, instead of dry cells at each instrument. (See Fig. 313.) Also -the operator at _central_ is called by simply taking the receiver from -the hook instead of being "rung up" by the subscriber. The operations of -the transmitter, induction coil and receiver, however, are the same in -all telephones. - - -Important Topics - -1. Receiver: parts, action. - -2. Transmitter: parts, action. - -3. Induction coil, bell, line wires, etc. - -4. Action of the whole device. - - -Exercises - -1. State three important electrical laws or principles that are employed -in the operation of the telephone. What is the application of each? - -2. Connect the binding posts of a telephone receiver with a sensitive -galvanometer and press on the diaphragm of the receiver; a deflection of -the galvanometer will be noticed. Release the diaphragm and a reflection -in the opposite direction is seen. Explain. - -3. Is the current passing through the transmitter the one going to the -receiver of the instrument? Explain. - -4. Does the receiver at the telephone used by a person repeat the speech -of the person? Explain. - -5. How many 0.5 ampere lamps can be used with a 6 ampere fuse? - -6. Why is it necessary to have a rheostat connected in series with a -stereopticon or moving picture machine while a rheostat is not used with -arc lights out doors? - -7. How many candle power should a 60 watt carbon incandescent lamp give, -if its efficiency is 3.4 watts per candle power? - -8. Three incandescent lamps having resistances of 100, 150, and 240 -ohms, respectively, are connected in parallel. What is their combined -resistance? - - -Review Outline: Induced Currents - -Induced currents; 3 laws, illustrations. - -Construction, action, and uses of--magneto, dynamo, induction coil, -transformer, motor, telephone. Mercury arc rectifier. - -Terms--primary, secondary, for coils and currents, armature, commutator, -slip ring, brush, rectifier, open core, series, shunt, and compound -connections for dynamos. - - - - -CHAPTER XV - -SOUND - - -(1) SOUND AND WAVE MOTION - -=317. What is a Sound?=--This question has two answers, which may be -illustrated as follows: Suppose that an alarm clock is set so that it -will strike in one week and that it is placed upon a barren rock in the -Pacific Ocean by sailors who immediately sail away. If when the tapper -strikes the bell at the end of the week no ear is within a hundred -miles, is any sound produced? The two view-points are now made evident, -for some will answer "no" others "yes." Those answering "no" hold that -sound is a _sensation_ which would not be produced if no ear were at -hand to be affected. Those answering "yes" understand, by the term -sound, _a mode of motion capable of affecting the auditory nerves_, and -that sound exists wherever such motions are present. This latter point -of view is called the _physical_ and is the one we are to use in this -study. - -[Illustration: FIG. 314.--The tuning fork is vibrating.] - -=318. Source of Sound.=--If we trace any sound to its source, it will be -found to originate in a body in rapid motion usually in what is called a -state of _vibration_. To illustrate, take a tuning fork, strike it to -set it in vibration and place its stem firmly against a thin piece of -wood; the sound will be strengthened materially by the vibration of the -wood. If now the vibrating fork is placed with the tips of the prongs in -water, the vibration is plainly shown by the spattering of the water -(Fig. 314). When one _speaks_, the vibrating body is in the _larynx_ at -the top of the windpipe. Its vibration may be plainly felt by the hand -placed upon the throat while speaking. - -=319. Sound Media.=--Usually sounds reach the ear through the air. The -air is then said to be a _medium for sound_. Other substances may serve -as a sound medium, for if the head is under water and two stones, also -under water, are struck together a sharp sound is heard. Also if one end -of a wooden rod is held at the ear and the other end of the rod is -scratched by a pin, the sound is more plainly perceived through the wood -than through the air. Think of some illustration from your own -experience of a solid acting as medium for sound. If an electric bell is -placed in a bell jar attached to an air pump, as in Fig. 315, on -exhausting the air the loudness of the sound is found to diminish, -indicating that in a perfect vacuum no sound would be transmitted. This -effect of a vacuum upon the transmission of sound is very different from -its effect upon radiation of heat and light. Both heat and light are -known to pass through a vacuum since both come to the earth from the sun -through space that so far as we know contains no air or other matter. -Sound differs from this in that it is always transmitted by some -material body and cannot exist in a vacuum. - -[Illustration: FIG. 315.--Sound does not travel in a vacuum.] - -=320. Speed of Sound.=--Everyone has noticed that it takes time for -sound to travel from one place to another. If we see a gun fired at a -distance, the report is heard a few seconds after the smoke or flash is -seen. The time elapsing between a flash of lightning and the thunder -shows that sound takes time to move from one place to another. Careful -experiments to determine the speed of sound have been made. One method -measures accurately the time required for the sound of a gun to pass -between two stations several miles apart. A gun or cannon is placed at -each station. These are fired alternately, first the one at one station -and then the one at the other so as to avoid an error in computation due -to the motion of wind. This mode of determining the speed of sound is -not accurate. Other methods, more refined than the one just described -have given accurate values for the speed of sound. The results of a -number of experiments show that, at the freezing temperature, 0°C., the -speed of sound in air is 332 meters or 1090 ft. a second. The speed of -sound in air is affected by the temperature, increasing 2 ft. or 0.6 -meter per second for each degree that the temperature rises above 0°C. -The speed decreases the same amount for each degree C. that the air is -cooled below the freezing point. The speed of sound in various -substances has been carefully determined. It is greater in most of them -than in air. In water the speed is about 1400 meters a second; in wood, -while its speed varies with different kinds, it averages about 4000 -meters a second; in brass the speed is about 3500 meters; while in iron -it is about 5100 meters a second. - -=321. The Nature of Sound.=--We have observed that sound originates at a -vibrating body, that it requires a medium in order to be transmitted -from one place to another, and that it travels at a definite speed in a -given substance. Nothing has been said, however, of the _mode_ of -transmission, or of the _nature_ of _sound_. Sounds continue to come -from an alarm clock even though it is placed under a bell jar. It is -certain that nothing material can pass through the glass of the jar. -If, however, we consider that _sound is transmitted by waves through -substances_ the whole matter can be given a simple explanation. In order -to better understand the nature of sound a study of waves and wave -motion will be taken up in the next section. - - -Important Topics - -Sound: two definitions, source, medium, speed, nature. - - -Exercises - -1. Give two illustrations from outside the laboratory of the fact that -sound is transmitted by other materials than air. - -2. Name the vibrating part that is the source of the sound in three -different musical instruments. - -3. Is sound transmitted more strongly in solids, liquids or gases? How -do you explain this? - -4. How far away is a steamboat if the sound of its whistle is heard 10 -seconds after the steam is seen, the temperature being 20°C.? Compute in -feet and in meters. - -5. How many miles away is lightning if the thunder is heard 12 seconds -after the flash in seen, the temperature being 25°C.? - -6. Four seconds after a flash of lightning is seen the thunder clap is -heard. The temperature is 90°F. How far away was the discharge? - -7. The report of a gun is heard 3 seconds after the puff of smoke is -seen. How far away is the gun if the temperature is 20°C.? - -8. An explosion takes place 10 miles away. How long will it take the -sound to reach you, the temperature being 80°F?. How long at 0°F.? - -9. How long after a whistle is sounded will it be heard if the distance -away is 1/4 mile, the temperature being 90°F.? - -10. The report of an explosion of dynamite is heard 2 minutes after the -puff of smoke is seen. How far away is the explosion the temperature -being 77°F.? - - -(2) WAVES[N] AND WAVE MOTION - - [N] A wave is a disturbance in a substance or medium that is - transmitted through it. - -=322. Visible Waves.=--It is best to begin the study of wave motion by -considering some waves which are familiar to most persons. Take for -example the waves that move over the surface of water (Fig. 316). These -have an onward motion, yet boards or chips upon the surface simply rise -and fall as the waves pass them. They are not carried onward by the -waves. The water surface simply rises and falls as the waves pass by. -Consider also the waves that may be seen to move across a field of tall -grass or grain. Such waves are produced by the bending and rising of the -stalks as the wind passes over them. Again, waves may be produced in a -rope fastened at one end, by suddenly moving the other end up and down. -These waves move to the end of the rope where they are _reflected_ and -return. The three types of waves just mentioned are illustrations of -_transverse_ waves, the ideal case being that in which the particles -move at _right angles_ to the path or course of the wave. Such waves are -therefore called _transverse_ waves. - -[Illustration: FIG. 316.--Water waves.] - -=323. Longitudinal waves.=--Another kind of wave is found in bodies that -are elastic and compressible and have inertia, such as gases and coiled -wire springs. Such waves may be studied by considering a wire spring as -the medium through which the waves pass. (See Fig. 318.) - -[Illustration: FIG. 317.--The compression wave travels through the -spring.] - -If the end of the wire spring shown in Fig. 317 is struck the first few -turns of the spring will be compressed. Since the spring possesses -elasticity, the turns will move forward a little and compress those -ahead, these will press the next in turn and so on. Thus a _compression_ -wave will move to the end of the spring, where it will be reflected and -return. Consider the turns of the spring as they move toward the end. -On account of their _inertia_ they will continue moving until they have -separated from each other _more_ than at first, before returning to -their usual position. This condition of a greater separation of the -turns of the spring than usual is called a _rarefaction_. It moves along -the spring following the wave of compression. The condensation and -rarefaction are considered as together forming a complete wave. Since -the turns of wire move back and forth in a direction parallel to that in -which the wave is traveling, these waves are called _longitudinal_. - -[Illustration: FIG. 318.--Longitudinal waves (1) in a spring, (2) in -air, and (3) graphic representation showing wave length, condensations, -and rarefactions.] - -=324. The transmission of a sound by the air= may be understood by -comparing it with the process by which a _wave is transmitted by a wire -spring_. Consider a light spring (Fig. 318, 1) attached at the end of a -vibrating tuning fork, _K_, and also to a diaphragm, _D_. Each vibration -of the fork will first compress and then separate the coils of the -spring. These impulses will be transmitted by the spring as described in -Art. 315, and cause the diaphragm to vibrate _at the same rate_ as the -tuning fork. The diaphragm will then give out a sound similar to that of -the tuning fork. Suppose that the spring is replaced by air, and the -diaphragm, by the ear of a person, _E_, (Fig. 318, 2.) when the prong -of the fork moves toward the ear it starts a compression and when it -moves back a rarefaction. The fork continues vibrating and these -impulses move onward like those in the spring at a speed of about 1120 -ft. in a second. They strike the diaphragm of the ear causing it to move -back and forth or to vibrate at the same rate as the tuning fork, just -as in the case of the diaphragm attached to the spring. - -=325. Graphic Representation of Sound waves.=--It is frequently -desirable to represent sound waves graphically. The usual method is to -use a curve like that in (Fig. 318, 3). This curve is considered as -representing a train of waves moving in the same direction as those in -Fig. 318 1 and 2, and also having the same length. The part of the wave -_A-B_ represents a condensation of the sound wave and the part _B-C_ -represents a rarefaction. A complete wave consisting of a condensation -and a rarefaction is represented by that portion of the curve _A-C_. The -portion of the curve _B-D_ also represents a _full wave length_ as the -latter is defined as _the distance between two corresponding parts of -the adjacent waves_. The curve, Fig. (318, 3) represents not only the -wave length, but also the height of the wave or the amount of movement -of the particles along the wave. This is called the _amplitude_ and is -indicated by the distance _A-b_. Since the _loudness_ or intensity of a -sound is found to depend upon the amount of movement of the particles -along the wave, the _amplitude_ of the curve is used to indicate the -loudness of the sound represented. All of the characteristics of a sound -wave may be graphically represented by curves. Such curves will be used -frequently as an aid in explaining the phenomena of wave motion both in -sound and in light. - -=326. Reflections of Sound.=--It is found that a wave moving along a -wire spring is reflected when it reaches the end and returns along the -spring. Similarly a sound wave in air is reflected upon striking the -surface of a body. If the wave strikes perpendicularly it returns along -the line from which it comes, if, however, it strikes at some other -angle it does not return along the same line, but as in other cases of -reflected motion, the _direction_ of the _reflected_ wave is described -by the _Law of Reflected Motion_ as follows: _The angle of reflection is -always equal to the angle of incidence_. This law is illustrated in Fig. -319. Suppose that a series of waves coming from a source of sound move -from _H_ to _O_. After striking the surface _IJ_ the waves are reflected -and move toward _L_ along the line _OL_. Let _PO_ be perpendicular to -the surface _IJ_ at _O_. Then _HOP_ is _the angle_ of incidence and -_LOP_ is the _angle of reflection_. By the law of reflected motion these -angles are equal. In an ordinary room when a person speaks the sound -waves reflected from the smooth walls reinforce the sound waves moving -directly to the hearers. It is for this reason that it is usually easier -to speak in at room than in the open air. Other illustrations of the -reinforcement of sound by reflection are often seen. Thus an _ear -trumpet_ (Fig. 320), uses the principle of reflection and concentration -of sound. So-called _sounding boards_ are sometimes placed back of -speakers in large halls to reflect sound waves to the audience. - -[Illustration: FIG. 319.--Law of reflection.] - -[Illustration: FIG. 320.--An ear trumpet.] - -=327. Echoes.=--_An echo is the repetition of a sound caused by its -reflection from some distant surface_ such as that of a building, cliff, -clouds, trees, etc. The interval of time between the production of a -sound and the perception of its echo is the time that the sound takes to -travel from its source to the reflecting body and back to the listener. -Experiments have shown that the sensation of a sound persists about -one-tenth of a second. Since the velocity of sound at 20°C. is about -1130 ft. per second, during one-tenth of a second the sound wave will -travel some 113 ft. If the reflecting surface is about 56 ft. distant a -_short_ sound will be followed immediately by its echo as it is heard -one-tenth of a second after the original sound. The reflected sound -tends to strengthen the original one if the reflecting surface is less -than 56 ft. away. If the distance of the reflecting surface is much more -than 56 ft. however, the reflected sound does not blend with the -original one but forms a distinct echo. The echoes in large halls -especially those with large smooth walls may very seriously affect the -clear perception of the sound. Such rooms are said to have poor -_acoustic_ properties. Furniture, drapery, and carpets help to deaden -the echo because of diffused reflection. The Mormon Tabernacle at Salt -Lake City, Utah, is a fine example of a building in which the reflecting -surfaces of the walls and ceiling are of such shape and material that -its acoustic properties are remarkable, a pin dropped at one end being -plainly heard at the other end about 200 ft. away. - - -Important Topics - -1. Waves: transverse, longitudinal; wave length, condensation, -rarefaction. - -2. Wave motion: in coiled spring, in air, on water. - -3. Reflection of waves: law, echoes. - - -Exercises - -1. A hunter hears an echo in 8 seconds after firing his gun. How far is -the reflecting surface if the temperature is 20°C.? - -2. How far is the reflecting surface of a building if the echo of one's -footsteps returns in 1 second at 10°C.? - -3. Why is it easier to speak or sing in a room than out of doors? - -4. Draw a curve that represents wave motion. Make it exactly three full -wave lengths, and state why your curve shows this length. Indicate the -parts of the curve that correspond to a condensation and to a -rarefaction. - -5. How long does it take the sound of the "pin drop" to reach a person -at the farther end of the building mentioned at the end of Art. 327? - -6. An echo is heard after 6 seconds. How far away is the reflecting -surface, the temperature being 70°F.? - -7. Why are outdoor band-stands generally made with the back curving over -the band? - -8. A man near a forest calls to a friend. In 4 seconds the echo comes -back. How far away is he from the forest? - -9. Would it be possible for us ever to hear a great explosion upon the -moon? Explain. - -10. If a sunset gun was fired exactly at 6:00 P.M. at a fort, at what -time was the report heard by a man 25 miles away, if the temperature was -10°C.? - - -(3) INTENSITY AND PITCH OF SOUNDS - -[Illustration: FIG. 321.--Graphic representations of (_a_) a noise, -(_b_) a musical sound.] - -=328. Musical Sounds and Noises Distinguished.=--The question is -sometimes raised, what is the difference between a _noise_ and a -_musical sound_? The latter has been found to be produced by an even and -regular vibration such as that of a tuning fork or of a piano string. A -noise on the other hand is characterized by sudden or irregular -vibrations such as those produced by a wagon bumping over a stony -street. These differences may be represented graphically as in Fig. 321, -(a) represents a noise, (b) a musical tone. - -[Illustration: FIG. 322.--Curve _b_ represents a tone of greater -intensity.] - -=329. Characteristics of Musical Sounds.=--Musical tones differ from one -another in three ways or are said to have _three characteristics_, viz., -_intensity_, _pitch_, and _quality_. Thus two sounds may differ only in -intensity or _loudness_, that is, be alike in all other respects except -this one, as when a string of a piano is struck at first gently, and -again harder. The second sound is recognized as being louder. The -difference is due to the greater _amplitude_ of vibration caused by more -energy being used. Fig. 322 shows these differences graphically. Curve -_b_ represents the tone of greater intensity or loudness, since its -amplitude of vibration is represented as being greater. - -=330. Conditions Affecting the Intensity of Sound.=--The intensity of -sounds is also affected by the _area_ of the vibrating body. This is -shown by setting a tuning fork in vibration. The area of the vibrating -part being small, the sound is heard but a short distance from the fork. -If, however, the stem of the vibrating fork is pressed against the panel -of a door or the top of a box, the sound may be heard throughout a room. -The stem of the fork has communicated its vibrations to the wood. The -vibrating area, being greater, the sound is thereby much increased in -intensity, producing a wave of greater amplitude. The same principle is -employed in the sounding boards of musical instruments as in the piano, -violin, etc. It is a common observation that sounds decrease in -loudness as the distance from the source increases. This is due to the -increase of the surface of the spherical sound waves spreading in all -directions from the source. Careful experiments have shown that in a -uniform medium _the intensity of a sound is inversely proportional to -the square of the distance from its source_. If a sound is confined so -that it cannot spread, such as the sound moving through a speaking tube, -it maintains its intensity for a considerable distance. An _ear trumpet_ -(see Fig. 320) also applies this principle. It is constructed so that -sound from a given area is _concentrated_ by reflection to a much -smaller area with a corresponding increase in intensity. The _megaphone_ -(Fig. 323), and the _speaking trumpet_ start the sound waves of the -voice in one direction so that they are kept from spreading widely, -consequently by its use the voice may be heard several times the usual -distance. The intensity of a sound is also affected by the _density_ of -the transmitting medium. Thus a sound produced on a mountain top is -fainter and thinner than one produced in a valley. The sound of a bell -in the receiver of an air pump becomes weaker as the air is exhausted -from the latter. _Four_ factors thus influence the intensity of a sound, -the _area_ of the vibrating body, its _amplitude_ of vibration, the -_distance_ of the source and the _density_ of the transmitting medium. -It is well to fix in mind the precise effect of each of these factors. - -[Illustration: FIG. 323.--The megaphone.] - -=331. Pitch.=--The most characteristic difference between musical sounds -is that of _pitch_. Some sounds have a high pitch, such as those -produced by many insects and birds. Others have a low pitch as the notes -of a bass drum or the sound of thunder. How notes of different pitch -are produced may be shown by the siren (Fig. 324). This is a disc -mounted so as to be rotated on an axis. Several rows of holes are -drilled in it in concentric circles. The number of holes in successive -rows increases from within outward. If when the siren is rapidly rotated -air is blown through a tube against a row of holes a clear musical tone -is heard. The tone is due to the succession of pulses in the air -produced by the row of holes in the rotating disc alternately cutting -off and permitting the air blast to pass through at very short -intervals. If the blast is directed against a row of holes nearer the -circumference the pitch is higher, if against a row nearer the center -the pitch is lower. Or if the blast is sent against the same row of -holes the pitch rises when the speed increases and lowers when the speed -lessens. These facts indicate that the pitch of a tone is due to the -number of pulses or vibrations that strike the ear each second; also -that _the greater the rate of vibration, the higher the pitch_. - -[Illustration: FIG. 324.--A siren.] - -=332. The Major Scale.=--If a siren is made with eight rows of holes, it -may indicate the relation between the notes of a _major scale_. To -accomplish this, the number of holes in the successive rows should be -24, 27, 30, 32, 36, 40, 45, 48. If a disc so constructed is rapidly -rotated at a uniform rate, a blast of air sent against all of the rows -in succession produces the tones of the scale. These facts indicate that -the relative vibration numbers of the notes of any _major scale_ have -the same relation as the numbers 24, 27, 30, 32, 36, 40, 45, 48. - -The note called middle C is considered by physicists as having 256 -vibrations a second. This would give the following _actual vibration_ -numbers to the remaining notes of the major scale that begins with -"Middle C" D.-288, E.-320, F.-341.3, G.-384, A.-426.6, B.-480, C'.-512. -Musicians, however, usually make use of a scale of slightly higher -pitch. The _international_ standard of pitch in this country and in -Europe is that in which "A" has 435 vibrations per second. This -corresponds to 261 vibrations for middle C. - -=333. The Relation between Speed, Wave Length, and Number of Vibrations -per Second.=--Since the notes from the various musical instruments of an -orchestra are noticed to harmonize as well at a distance as at the place -produced, it is evident that notes of all pitches travel at the same -rate, or have the _same speed_. Notes of high pitch, having a high -vibration rate produce more waves in a second than notes of low pitch, -consequently the former are shorter than the latter. The following -formula gives the relation between the speed (_v_), wave length (_l_), -and number of vibrations per sec. (_n_): - - _v_ = _l_ × _n_, or _l_ = _v/n_ - -that is, _the speed of a sound wave is equal to the number of vibrations -per second times the wave length, or the wave length is equal to the -speed divided by the number of vibrations per second_. This formula may -also be employed to find the _number_ of vibrations when the wave length -and speed are given. - - -Important Topics - -1. Difference between noise and music. - -2. Factors affecting intensity: area, amplitude, density, distance. - -3. Pitch, major scale, relative vibration numbers. - -4. Relation between speed, wave length and vibration rate. - - -Exercises - -1. Give an illustration from your own experience of each of the factors -affecting intensity. - -2. Write the relative vibration numbers of a major scale in which _do_ -has 120 vibrations. - -3. What is the wave length of the "A" of international concert pitch at -25°C.? Compute in feet and centimeters. - -4. At what temperature will sound waves in air in unison with "Middle C" -be exactly 4 ft. long? - -5. Explain the use of a megaphone. - -6. What tone has waves 3 ft. long at 25°C.? - -7. What is the purpose of the "sounding board" of a piano? - -8. Two men are distant 1000 and 3000 ft. respectively from a fog horn. -What is the relative intensity of the sounds heard by the two men? - -9. The speaking tone of the average man's voice has 160 vibrations per -second. How long are the waves produced by him at 20°C.? - - -(4) MUSICAL SCALES AND RESONANCE - -=334. A musical interval= _refers to the ratio between the pitches[O] of -two notes_ as indicated by the results of the siren experiment. The -simplest interval, or ratio between two notes is the _octave_, C':C, or -2:1 (48:24). Other important intervals with the corresponding ratios are -the _fifth_, G:C, or 3:2 (36:24); the _sixth_, A:C, or 5:3 (40:24); the -_fourth_, F:C, 4:3 (32:24); the _major third_, E:C, or 5:4 (30:24); and -the _minor third_, G:E, 6:5. The interval between any two notes may be -determined by finding the ratio between the vibration numbers of the two -notes. Thus, if one note is produced by 600 vibrations a second and -another by 400, the interval is 3:2, or a _fifth_, and this would be -recognized by a musician who heard the notes sounded together or one -after the other. Below is a table of musical nomenclatures, showing -various relations between the notes of the major scale. - - [O] Pitch as used here, means _vibration rate_. - -TABLE OF MUSICAL NOMENCLATURES - - ---------------------+---+------+------+------+------+------+-------+---- - Name of note | C | D | E | F | G | A | B | C´ - ---------------------+---+----- +----- +------+------+------+-------+---- - Frequency in terms of|_n_|9/8_n_|5/4_n_|4/3_n_|3/2_n_|5/3_n_|15/8_n_|2_n_ - "do" | | | | | | | | - ---------------------+---+--+---+--+---+--+---+--+---+--+---+---+---+---- - Intervals | 9/8 | 10/9 | 16/15| 9/8 | 10/9 | 9/8 | 16/15 - ---------------------+---+--+---+--+---+--+---+--+---+--+---+---+---+---- - Name of note in vocal|do | re | mi | fa | sol | la | ti | do - music | | | | | | | | - ---------------------+---+------+------+------+------+------+-------+---- - Treble clef. - [Music] - - Bass clef. - [Music] - ---------------------+---+------+------+------+------+------+-------+---- - International pitch | | | | | | | | - of treble clef |261| 293.6| 326.3| 348. | 391.5| 435 | 489.4 | 522 - ---------------------+---+------+------+------+------+------+-------+---- - Scientific scale |256| 288 | 320 | 341.3| 384 | 426.6| 480 | 512 - ---------------------+---+------+------+------+------+------+-------+---- - Relative vibration | 24| 27 | 30 | 32 | 36 | 40 | 45 | 48 - numbers | | | | | | | | - ---------------------+---+------+------+------+------+------+-------+---- - -=335. Major and Minor Triads.=--The notes C, E, G (_do_, _mi_, _sol_) -form what is called a _major triad_. The _relative vibration numbers_ -corresponding are 24, 30, 36. These in simplest terms have ratios of -4:5:6. Any three other tones with vibration ratios of 4:5:6 will also -form a major triad. If the octave of the lower tone is added, the four -make a major chord. Thus: F, A, C´ (_fa_, _la_, _do_), 32:40:48, or -4:5:6, also form a major triad as do G, B, D´ (_sol_, _ti_, _re_), -36:45:54, or 4:5:6. Inspection will show that these three major triads -comprise all of the tones of the major scale D´ being the octave of D. -It is, therefore, said that the major scale is based, or built, upon -these three major triads. The examples just given indicate the -mathematical basis for harmony in music. Three notes having vibration -ratios of 10:12:15 are called _minor triads_. These produce a less -pleasing effect than those having ratios of 4:5:6. - -=336. The Need for Sharps and Flats.=--We have considered the key of C. -This is represented upon the piano or organ by white keys only (Fig. -325). Now in order (a) to give variety to instrumental selections, and -(b) to accommodate instruments to the range of the human voice, it has -been necessary to introduce other notes in musical instruments. These -are represented by the _black keys_ upon the piano and organ and are -known as _sharps_ and _flats_. To illustrate the necessity for these -additional notes take the major scale starting with B. This will give -vibration frequencies of 240, 270, 300, 320, 360, 400, 450, and 480. The -only white keys that may be used with this scale are E 320 and B 480 -vibrations. Since the second note on this scale requires 270 vibrations -about halfway between C and D the black key C sharp is inserted. Other -notes must be inserted between D and E (D sharp), between F and G (F -sharp), also G and A sharps. - -[Illustration: FIG. 325.--Section of a piano keyboard.] - -=337. Tempered Scales.=--In musical instruments with fixed notes, such -as the harp, organ, or piano, complications were early recognized when -an attempt was made to adapt these instruments so that they could be -played in all keys. For the vibration numbers that would give a perfect -major scale starting at C are not the same as will give a perfect major -scale beginning with any other key. In using the various notes as the -keynote for a major scale, 72 different notes in the octave would be -required. This would make it more difficult for such instruments as the -piano to be played. To avoid these complications as much as possible, it -has been found necessary to abandon the simple ratios between successive -notes and to substitute another ratio in order that the vibration ratio -between any two successive notes will be equal in every case. The -differences between semitones are abolished so that, for example, C -sharp and D flat become the same tone instead of two different tones. -Such a scale is called a _tempered scale_. The tempered scale has 13 -notes to the octave, with 12 equal intervals, the ratio between two -successive notes being the ¹²{~SQUARE ROOT~}2 or 1.059. That is, any vibration rate on -the tempered scale may be computed by multiplying the vibration rate of -the preceding note by 1.059. While this is a necessary arrangement, -there is some loss in perfect harmony. It is for this reason that a -quartette or chorus of voices singing without accompaniment is often -more harmonious and satisfactory than when accompanied with an -instrument of fixed notes as the piano, since the simple harmonious -ratios may be employed when the voices are alone. The imperfection -introduced by _equal temperament tuning_ is illustrated by the following -table: - - C D E F G A B C - Perfect Scale of C 256.0 288.0 320.0 341.3 384.0 426.6 480.0 512.0 - Tempered Scale 256.0 287.3 322.5 341.7 383.6 430.5 483.3 512.0 - -=338. Resonance.=--If two tuning forks of the same pitch are placed near -each other, and one is set vibrating, the other will soon be found to be -in vibration. This result is said to be due to _sympathetic vibration_, -and is an example of _resonance_ (Fig. 326). If water is poured into a -glass tube while a vibrating tuning fork is held over its top, when the -air column has a certain length it will start vibrating, reinforcing -strongly the sound of the tuning fork. (See Fig. 327.) This is also an -example of resonance. These and other similar facts indicate that _sound -waves started by a vibrating body will cause another body near it to -start vibrating if the two have the same rate of vibration_. Most -persons will recall illustrations of this effect from their own -experience. - -[Illustration: FIG. 326.--One tuning fork will vibrate in sympathy with -the other, if they have exactly equal rates of vibration.] - -[Illustration: FIG. 327.--An air column of the proper length reinforces -the sound of the tuning fork.] - -=339. Sympathetic vibration= is explained as follows: Sound waves -produce very slight motions in objects affected by them; if the -vibration of a given body is exactly in time with the vibrations of a -given sound each impulse of the sound wave will strike the body so as to -increase the vibratory motion of the latter. This action continuing, the -body soon acquires a motion sufficient to produce audible waves. A good -illustration of sympathetic vibration is furnished by the bell ringer, -who times his pulls upon the bell rope with the vibration rate of the -swing of the bell. In the case of the resonant air column over which is -held a vibrating tuning fork (see Fig. 328), when the prong of the fork -starts downward from 1 to 2, a condensation wave moves down to the water -surface and back just in time to join the condensation wave _above_ the -fork as the prong begins to move from 2 to 1; also when the prong -starts upward from 2 to 1, the rarefaction produced under it moves to -the bottom of the air column and back so as to join the rarefaction -_above_ the fork as the prong returns. While the prong is making a -_single_ movement, up or down, it is plain that the air wave moves twice -the length of the open tube. During a _complete_ vibration of the fork, -therefore, the sound wave moves four times the length of the air column. -In free air, the sound progresses a wave length during a complete -vibration, hence the resonant air column is one-fourth the length of the -sound wave to which it responds. Experiments with tubes cf different -lengths show that the diameter of the air column has some effect upon -the length giving best resonance. About 25 per cent. of the diameter of -the tube must be added to the length of the air column to make it just -one-fourth the wave length. The sound heard in seashells and in other -hollow bodies is due to resonance. Vibrations in the air too feeble to -affect the ear are intensified by sympathetic vibration until they can -be heard. A tuning fork is often mounted upon a box called a -_resonator_, which contains an air column of such dimensions that it -reinforces the sound of the fork's sympathetic vibration. - -[Illustration: FIG. 328.--Explanation of resonance.] - - -Important Topics - -1. Musical intervals: octave, sixth, fifth, fourth, third. - -2. Major chord, 4:5:6. - -3. Use of sharps and flats. Tempered scale. - -4. Resonance, sympathetic vibration, explanation, examples. - - -Exercises - -1. What is a major scale? Why is a major scale said to be built upon -three triads? - -2. Why are sharps and flats necessary in music? - -3. What is the tempered scale and why is it used? What instruments need -not use it? Why? - -4. Mention two examples of resonance or sympathetic vibration from your -own experience out of school. - -5. An air column 2 ft. long closed at one end is resonant to what wave -length? What number of vibrations will this sound have per second at -25°C.? - -6. At 24°C. What length of air column closed at one end will be resonant -to a sound having 27 vibrations a second? - -7. A given note has 300 vibrations a second. What will be the number of -vibrations of its (a) octave, (b) fifth, (c) sixth, (d) major third? - -8. In the violin or guitar what takes the place of the sounding board of -the piano? - -9. Can you explain why the pitch of the bell on a locomotive rises as -you rapidly approach it and falls as you recede from it? - -10. Do notes of high or low pitch travel faster? Explain. - -11. An "A" tuning fork on the "international" scale makes 435 vibrations -per second. What is the length of the sound waves produced? - - -(5) WAVE INTERFERENCE, BEATS, VIBRATION OF STRINGS - -=340. Interference of waves.=--The possibility of two trains of waves -combining so as to produce a reduced motion or a _complete destruction_ -of motion may be shown graphically. Suppose two trains of waves of equal -wave length and amplitude as in Fig. 329 meet in _opposite phases_. That -is, the parts corresponding to the _crests_ of _A_ coincide with the -_troughs_ of _B_, also the troughs of _A_ with the crests of _B_; when -this condition obtains, the result is that shown at _C_, the union of -the two waves resulting in complete destruction of motion. _The more or -less complete destruction of one train of waves by another similar train -is an illustration of_ =interference=. If two sets of water waves so -unite as to entirely destroy each other the result is a level water -surface. If two trains of sound waves combine they may so interfere that -silence results. The conditions for securing interference of sound waves -may readily be secured by using a tuning fork and a resonating air -column. If the tuning fork is set vibrating and placed over the open end -of the resonating air column (see Fig. 328), an increase in the sound -through resonance may be heard. If the fork is rotated about its axis, -in some positions no sound is heard while in other positions the sound -is strongly reinforced. Similar effects may be perceived by holding a -vibrating fork near the ear and slowly rotating as before. In some -positions interference results while in other positions the sound is -plainly heard. The explanation of interference may be made clear by the -use of a diagram. (See Fig. 330.) Let us imagine that we are looking at -the two square ends of a tuning fork. When the fork is vibrating the two -prongs approach each other and then recede. As they approach, a -condensation is produced at 2 and rarefactions at 1 and 3. As they -separate, a rarefaction is produced at 2 and condensations at 1 and 3. -Now along the lines at which the simultaneously produced rarefactions -and condensations meet there is more or less complete interference. (See -Fig. 331.) These positions have been indicated by dotted lines extending -through the ends of the prongs. As indicated above, these positions may -be easily found by rotating a vibrating fork over a resonant air column, -or near the ear. - -[Illustration: FIG. 329.--Interference of sound waves.] - -[Illustration: FIG. 330.--At 2 is a condensation; at 1 and 3 are -rarefactions.] - -[Illustration: FIG. 331.--The condensations and rarefactions meet along -the dotted lines producing silence.] - -[Illustration: FIG. 332.--Diagram illustrating the formations of beats.] - -=341. Beats.=--If two tuning forks of slightly different pitch are set -vibrating and placed over resonating air columns or with the stem of -each fork upon a sounding board, so that the sounds may be intensified, -a peculiar pulsation of the sound may be noticed. This phenomenon is -known as _beats_. Its production may be easily understood by considering -a diagram (Fig. 332). Let the curve _A_ represent the sound wave sent -out by one tuning fork and _B_, that sent out by the other. _C_ -represents the effect produced by the combination of these waves. At _R_ -the two sound waves meet in the _same phase_ and reinforce each other. -This results in a louder sound than either produces alone. Now since the -sounds are of slightly different pitch, one fork sends out a few more -vibrations per second than the other. The waves from the first fork are -therefore a little shorter than those from the other. Consequently, -although the two waves are at one time in the _same_ phase, they must -soon be in opposite phases as at _I_. Here interference occurs, and -silence results. Immediately the waves reinforce, producing a louder -sound and so on alternately. The resulting rise and fall of the sound -are known as _beats_. The number of beats per second must, of course, be -the same as the difference between the numbers of vibrations per second -of the two sounds. One effect of beats is _discord_. This is especially -noticeable when the number of beats per second is between 30 and 120. -Strike the two lowest notes on a piano at the same time. The beats are -very noticeable. - -[Illustration: FIG. 333.--Turkish cymbals.] - -[Illustration: FIG. 334.--The cornet.] - -=342. Three Classes of Musical Instruments.=--There are three classes or -groups of musical instruments, if we consider the vibrating body that -produces the sound in each: (A) Those in which the sound is produced by -a vibrating _plate_ or _membrane_, as the drum, cymbals (Fig. 333), -etc.; (B) those with vibrating _air columns_, as the flute, pipe organ, -and cornet (Fig. 334), and (C) with vibrating _wires_ or _strings_, as -the piano, violin, and guitar. It is worth while to consider some of -these carefully. We will begin with a consideration of vibrating wires -and strings, these often producing tones of rich quality. - -Let us consider the strings of a piano. (If possible, look at the -strings in some instrument.) The range of the piano is 7-1/3 octaves. -Its lowest note, A_{4}, has about 27 vibrations per second. Its highest, -C{~SUPERSCRIPT FOUR~}, about 4176. This great range in vibration rate is secured by varying -the length, the tension, and the diameter of the strings. - -=343. The Laws of Vibrating Strings.=--The relations between the -vibration rate, the length, the tension and the diameter, of vibrating -strings have been carefully studied with an instrument called a -_sonometer_ (Fig. 335). By this device it is found that the pitch of a -vibrating string is raised one octave when its vibrating length is -reduced to one-half. By determining the vibration rate of many lengths, -the following law has been derived: (Law I) _The rate of vibration of a -string is inversely proportional to its length._ - -[Illustration: FIG. 335.--A sonometer.] - -Careful tests upon the change of vibration rate produced by a change of -_tension_ or pull upon the strings show that if the pull is increased -four times its vibrations rate is _doubled_, and if it is increased nine -times its rate is tripled, that is: (Law II) _The vibration rates of -strings are directly proportional to the square roots of their -tensions._ - -Tests of the effects of diameter are made by taking wires of equal -length and tension and of the same material but of different diameter. -Suppose one is twice as thick as the other. This string has a tone an -octave lower or vibrates one-half as fast as the first. Therefore: (Law -III) _The vibration rates of strings are inversely proportional to the -diameters._ These laws may be expressed by a formula _n_ {~PROPORTIONAL TO~}{~SQUARE ROOT~}(_t_)/_dl_. - -The vibration of a string is rarely a simple matter. It usually vibrates -in parts at the same time that it is vibrating as a whole. The tone -produced by a string vibrating as a whole is called its _fundamental_. -The vibrating parts of a string are called _loops_ or _segments_ (see -Fig. 336), while the points of least or no vibration are _nodes_. -Segments are often called _antinodes_. - -[Illustration: FIG. 336.--A string yielding its fundamental and its -first overtone.] - -=344. Overtones.=--The _quality_ of the tone produced by a vibrating -string is affected by its vibration in parts when it is also vibrating -as a whole. (See Fig. 336.) The tones produced by the vibration in parts -are called _overtones_ or _partial_ tones. The presence of these -overtones may often be detected by the sympathetic vibration of other -wires near-by. What is called the _first_ overtone is produced by a -string vibrating in _two_ parts, the _second_ overtone by a string -vibrating in _three parts_, the _third_ overtone by its vibration in -_four_ parts and so on. In any overtone, the number of the parts or -vibrating segments of the string is one more than the number of the -overtone. For example, gently press down the key of middle C of a piano. -This will leave the string free to vibrate. Now strongly strike the C an -octave lower and then remove the finger from this key. The middle C -string will be heard giving its tone. In like manner try E¹ and G¹, -with C. This experiment shows that the sound of the C string contains -these tones as overtones. It also illustrates sympathetic vibration. - - -Important Topics - -1. Interference, beats, production, effects. - -2. Vibration of strings, three laws. - -3. Three classes of musical instruments. - -4. Fundamental and overtones, nodes, segments, how produced? Results. - - -Exercises - -1. What different means are employed to produce variation of the pitch -of piano strings? For violin strings? - -2. How many beats per second will be produced by two tuning forks having -512 and 509 vibrations per second respectively? - -3. A wire 180 cm. long produces middle C. Show by a diagram, using -numbers, where a bridge would have to be placed to cause the string to -emit each tone of the major scale. - -4. How can a violinist play a tune on a single string? - -5. What are the frequencies of the first 5 overtones of a string whose -fundamental gives 256 vibrations per second? - -6. One person takes 112 steps a minute and another 116. How many times a -minute will the two walkers be in step? How many times a minute will one -be advancing the left foot just when the other advances the right? - -7. Why is it necessary to have a standard pitch? - -8. How can the pitch of the sounds given by a phonograph be lowered? - -9. How many beats per second will occur when two tuning forks having -frequencies of 512 and 515 respectively, are sounded together? - -10. Which wires of a piano give the highest pitch? Why? - - -(6) TONE QUALITY, VIBRATING AIR COLUMNS, PLATES - -=345. Quality.=--The reason for the _differences in tone quality_ -between notes of the same pitch and intensity as produced, _e.g._, by a -violin and a piano, was long a matter of conjecture. Helmholtz, a German -physicist (see p. 397) first definitely proved that tone quality is due -to the _various overtones_ present along with the fundamental and _their -relative intensities_. If a tuning fork is first set vibrating by -drawing a bow across it and then by striking it with a hard object, a -difference in the _quality_ of the tones produced is noticeable. It is -thus evident that the manner of setting a body in vibration affects the -overtones produced and thus the quality. Piano strings are struck by -felt hammers at a point about one-seventh of the length of the string -from one end. This point has been selected by experiment, it having been -found to yield the best combination of overtones as shown by the quality -of the tone resulting. - -[Illustration: FIG. 337.--Chladni's plate.] - -[Illustration: FIG. 338.--Chladni's figures.] - -=346. Chladni's Plate.=--The fact that vibrating bodies are capable of -many modes of vibration is well illustrated by what is known as -Chladni's plate. This consists of a circular or square sheet of brass -attached to a stand at its center so as to be held horizontally. (See -Fig. 337.) Fine sand is sprinkled over its surface and the disc is set -vibrating by drawing a violin bow across its edge. The mode of -vibration of the disc is indicated by the sand accumulating along the -lines of least vibration, called _nodal lines_. A variety of nodal lines -each accompanied by its characteristic tone may be obtained by changing -the position of the bow and by touching the fingers at different points -at the edge of the disc. They are known as Chladni's figures. (See Fig. -338.) - -[Illustration: FIG. 339.--Manometric flame apparatus.] - -=347. Manometric Flames.=--The actual presence of overtones along with -the fundamental may be made _visible_ by the _manometric flame -apparatus_. This consists of a wooden box, _C_, mounted upon a stand. -(See Fig. 339.) The box is divided vertically by a flexible partition or -diaphragm. Two outlets are provided on one side of the partition, one, -_C_, leads to a gas pipe, the other is a glass tube, _D_. On the other -side of the partition a tube, _E_, leads to a mouthpiece. A mirror, _M_, -is mounted so as to be rotated upon a vertical axis in front of _F_ and -near it. Gas is now turned on and lighted at _F_. The sound of the voice -produced at the mouthpiece sends sound waves through the tube and -against the diaphragm which vibrates back and forth as the sound waves -strike it. This action affects the flame which rises and falls. If now -the mirror is rotated, the image of the flame seen in the mirror rises -and falls, showing not only the fundamental or principal vibrations but -also the overtones. If the different vowel sounds are uttered in -succession in the mouthpiece, each is found to be accompanied by its -characteristic wave form (Fig. 340). In some, the fundamental is -strongly prominent, while in others, the overtones produce marked -modifications. Other devices have been invented which make possible the -accurate analysis of sounds into their component vibrations, while still -others unite simple tones to produce any complex tone desired. - -=348. The Phonograph.=--The _graphophone_ or _phonograph_ provides a -mechanism for cutting upon a disc or cylinder a groove that reproduces, -in the varying form or depth of the tracing, every peculiarity of the -sound waves affecting it. The reproducer consists of a sensitive -diaphragm to which is attached a needle. The disc or cylinder is rotated -under the reproducing needle. The irregularities of the bottom of the -tracing cause corresponding movements of the needle and the attached -diaphragm, which start waves that reproduce the sounds that previously -affected the recorder. The construction of the phonograph has reached -such perfection that very accurate reproduction of a great variety of -sounds is secured. - -[Illustration: FIG. 340.--Characteristic forms of manometric flames.] - -=349. Wind Instruments.=--In many musical instruments as the _cornet_, -_pipe-organ_, _flute_, etc., and also in _whistles_, the vibrating body -that serves as a source of sound is _a column of air_, usually enclosed -in a tube. Unlike vibrating strings, this vibrating source of sound -changes but little in tension or density, hence changes in the pitch of -air columns is secured by changing their length. The law being similar -to that with strings, _the vibration rates of air columns are inversely -proportional to their lengths_. - -[Illustration: FIG. 341.--(_R_) Cross-section of an organ pipe showing -action of tongue at _C_. (_a_) The fundamental tone in a closed pipe has -a wave length four times the length of the pipe; (_b_) and (_c_) how the -first and second overtones are formed in a closed pipe; (_d_) the -fundamental tone of an open pipe has a wave length equal to twice the -length of the pipe; (_e_) and (_f_) first and second overtones of open -pipe.] - -If an _open_ organ pipe be sounded by blowing gently through it, a tone -of definite pitch is heard. Now if one end is closed, on being sounded -again the pitch is found to be an octave lower. Therefore, _the pitch of -a closed pipe is an octave lower than that of an open one of the same -length_. - -=350. Nodes in Organ Pipes.=--Fig. 341, _R_ represents a cross-section -of a wooden organ pipe. Air is blown through _A_, and strikes against a -thin tongue of wood _C_. This starts the jet of air vibrating thus -setting the column of air in vibration so that the sound is kept up as -long as air is blown through _A_. To understand the mode of vibration of -the air column a study of the curve that represents wave motion (Fig. -342) is helpful Let _AB_ represent such a curve, in this 2, 4 and 6 -represent nodes or points of least vibration, while 1, 3 and 5 are -antinodes or places of greatest motion. A full wave length extends from -1-5, or 2-6. Now in the open organ pipe (Fig. 341_d_), the end of the -air column _d_ is a place of great vibration or is an antinode. At the -other end also occurs another place of great vibration or an antinode; -between these two antinodes must be a place of least vibration or a -node. The open air column therefore extends from antinode to antinode -(or from 1-3) or is _one-half_ a wave length. _The closed air column_ -(Fig. 341_a_) extends from a place of _great_ vibration at _a_ to a -place of _no_ vibration at the closed end. The distance from an antinode -to a node is that from 1-2 on the curve and is _one-fourth_ a wave -length. - -[Illustration: FIG. 342.--Graphic representation of sound waves.] - -[Illustration: FIG. 343.--A clarinet.] - -When a pipe is blown strongly it yields overtones. The _bugle_ is a -musical instrument in which notes of different pitch are produced by -differences in blowing. (See Fig. 341.) (_d_), (_e_), (_f_). In playing -the _cornet_ different pitches are produced by differences in blowing, -and by valves which change the length of the vibrating air column. (See -Fig. 334.) The _clarinet_ has a mouthpiece containing a reed similar to -that made by cutting a tongue on a straw or quill. The length of the -vibrating air column in the clarinet is changed by opening holes in the -sides of the tube. (See Fig. 343.) - -=351. How we Hear.=--Our hearing apparatus is arranged in three parts. -(See Fig. 344.) _The external ear_ leads to the _tympanum_. _The middle -ear_ contains three bones that convey the vibrations of the tympanum to -the _internal ear_. The latter is filled with a liquid which conveys the -vibrations to a part having a coiled shell-like structure called the -_Cochlea_. Stretched across within the cochlea are some 3000 fibers or -strings. It is believed that each is sensitive to a particular vibration -rate and that each is also attached to a nerve fiber. The sound waves of -the air transmitted by the tympanum, the ear bones and the liquid of the -internal ear start sympathetic vibrations in the strings of the cochlea -which affect the auditory nerve and we hear. The highest tones -perceptible by the human ear are produced by from 24,000 to 40,000 -vibrations per second. The average person cannot hear sounds produced by -more than about 28,000 vibrations. The usual range of hearing is about -11 octaves. The tones produced by higher vibrations than about 4100 per -second are shrill and displeasing. In music the range is 7-1/3 octaves, -the lowest tone being produced by 27.5 vibrations, the highest by about -4100 per second. - -[Illustration: FIG. 344.--The human ear.] - -The tones produced by men are lower than those of women and boys. In men -the vocal cords are about 18 mm. long; in women they are 12 mm. long. - -The compass of the human voice is about two octaves, although some -noted singers have a range of two and one-half octaves. In ordinary -conversation the wave length of sounds produced by a man's voice is from -8 to 12 ft. and that of a woman's voice is from 2 to 4 ft. - - -Important Topics - -1. Tone quality. Fundamental and overtones. Chladni's plate. - -2. Manometric flame apparatus. - -3. Phonograph recorder and reproducer. - -4. Air columns and wind instruments. - -5. How we hear. - - -Exercises - -1. What determines the pitch of the note of a toy whistle? - -2. The lowest note of the organ has a wave length of about 64 ft. What -is the length of a closed pipe giving this note? Of an open pipe? - -3. What is the first overtone of C? What are the second and third -overtones? Give vibration numbers and pitch names or letters. - -4. Why is the music of a band just as harmonious at a distance of 400 -ft. as at 100 ft.? - -5. A resonant air column 60 cm. long closed at one end will respond to -what rate of vibration at 10°C.? - -6. Can you find out how the valves on a cornet operate to change the -pitch of the tone? - -7. How is the trombone operated to produce tones of different pitch? - -8. The lowest note on an organ has a wave length of about 64 ft. What -must be the length of a closed pipe giving this note? - -9. What is the approximate length of an open organ pipe which sends out -waves 4 ft. long? - - -Review Outline: Sound - -Sound--definition, source, medium, speed, nature. - -Waves--longitudinal, transverse, illustrations. - - Characteristics of { intensity--area, amplitude, density, distance. - Musical Sounds: { pitch--scales; major, tempered, triads, _N_ = - { _V_/_L_ quality--fundamental and overtones. - -Sympathetic Vibrations--resonance, interference, beats, discord. - -Musical Instruments--string, air column, membrane or plate. - -Laws of; (a) vibrating strings (3), (b) vibrating air columns (2). - - - - -CHAPTER XVI - -LIGHT - - -(1) LIGHT, ITS RECTILINEAR PROPAGATION, SHADOWS - -=352. A Comparison of Sound and Light.=--Light from the standpoint of -physics is considered much as is _sound_, as a _mode_ of _motion_; one -affecting the ear, the other producing the result called _vision_. There -are other differences also worth considering. (a) While sound travels as -vibrations of some _material_ medium, light travels only as vibrations -of the _ether_; solids, liquids, and gases act so as to hinder rather -than to assist in its movement. That is, light travels best in a vacuum -or in a space devoid of ordinary matter. (b) The _speed_ of light is so -great that at ordinary distances on the earth its motion is practically -instantaneous. Experiments have shown that its speed is about 186,000 -miles to 300,000 kilometers a second. - -=353. Luminous and Illuminated Bodies.=--If we consider the objects -within a room, some of them, as books and furniture, would be invisible -if all light from external sources were excluded. On the other hand, -some other objects, such as a lighted lamp, a burning coal, or a red hot -iron, would be seen if no outside light were present. Such bodies are -said to be luminous. Most luminous bodies are hot and become -non-luminous on cooling. There are, however, some bodies that are -luminous at ordinary room temperatures, as the firefly and some -phosphorescent paints. When light emitted by a luminous body strikes an -object, a portion of it is always _reflected_. It is this reflected -light that makes the illuminated object _visible_. If the object is a -sheet of glass, some of the light is _transmitted_. If a substance is so -clear that objects can be seen through it, the substance is -_transparent_, but if objects cannot be seen through it, the substance -is said to be _translucent_. Objects transmitting no light are _opaque_. -Some of the light falling upon a body is neither reflected nor -transmitted, but is _absorbed_ and tends to warm the body. The light -falling upon a body is therefore either _reflected_, _transmitted_, or -_absorbed_. Thus Fig. 345 represents light coming from _S_ to a piece of -glass _GL_. A portion of the light represented by _R_ is reflected. -Another part _A_ is absorbed and disappears, while still another part -_T_ is transmitted and passes on. - -[Illustration: FIG. 345.--The light is transmitted (_T_), reflected -(_R_), or absorbed (_A_).] - -There is no sharply drawn line between transparent and opaque bodies. -Very thin sheets of gold transmit a greenish light, and experiments have -shown that substances as transparent as clear water absorb enough light -so that at considerable depths in an ocean or lake little or no light is -ever found. All light whether from luminous bodies or reflected from -non-luminous objects shows certain properties which will now be -considered. - -=354. The Rectilinear Propagation of Light.=--If a beam of light passes -through a hole in a window shade into a darkened room, it is seen to -follow a perfectly straight course. If a person while coughing holds a -book before the face, the sound passes around the book and is heard at -any point in the room while the face is hidden by the book. In other -words, light ordinarily does not pass around corners as sound does, but -travels in _straight lines_. This fact is made use of when one aims a -gun or merely looks at an object. So well established in our minds is -the idea that an _object_ is in the direction from which we see the -light coming to us from it, that we are sometimes deceived as to the -real position of an object, when the course of the light from it has -been changed by a mirror or some other reflecting surface. Many -_illusions_ are produced in this way, of which the _mirage_ of the -desert is one example. (See Art. 381.) - -[Illustration: FIG. 346.--Shadow from a small source of light.] - -[Illustration: FIG. 347.--Shadow when source of light is large.] - -=355. Shadows.=--_A shadow is the space from which light is cut off by -an opaque body._ Thus if a book (see Fig. 346) is held between a screen, -_N_, and a _small_ source of light, _L_, a shadow is produced which -extends from the book to the screen. Notice that the shadow is a _space_ -and not an _area_. If a _large_ gas flame (see Fig. 347) is used as the -source of light, the shadow of the book is no longer clear cut at the -edges as before, but has a darker central part with a lighter fringe of -partial shadow at the edges. The dark portion within the shadow has all -the light excluded from it and is called the _umbra_. The lighter -portion of the shadow at the edges has only a part of the light from the -flame cut off. This portion is called the _penumbra_. when one stands in -sunlight his shadow extends from his body to the ground or object on -which the shadow falls. At night we are in the earth's shadow, which -extends out into space beyond the earth. - -[Illustration: FIG. 348.--Character of the earth's shadow.] - -=356. Eclipses.=--Since the sun is a very large object the shadow cast -by the earth contains both umbra and penumbra. (See Fig. 348.) When the -moon passes into the shadow of the earth, there is said to be an eclipse -of the moon, while if the moon's shadow falls upon the earth, the -portion of the earth cut off from the sun's light has an eclipse of the -sun. - -=357. Images by Small Apertures.=--The straight line movement of light -makes possible the _pin-hole_ camera, by which satisfactory photographs -have been made. The action of this device may be illustrated by placing -a luminous body, a lighted candle, an incandescent lamp, or a gas flame, -in front of a piece of cardboard, _S_, which has a small opening in it. -Light from the object (see Fig. 349) falls upon a screen, _S_{2}_, so as -to produce an _inverted image_. Other applications of this principle -will be given later. - - In Fig. 349 let _PQ_ represent a gas flame, then light from point - _P_ at the _top_ of the flame will pass in a straight line through - the opening or aperture of the cardboard and strike at _P_{2}_ at - the _bottom_ of the illuminated spot upon the screen. Light from - _Q_ passing in straight lines through the aperture will strike at - _Q_{2}_ at the top of the lighted space. This spot of light will - have the same outlines as the luminous body _PQ_ and being formed - as just described will be _inverted_. - -[Illustration: FIG. 349.--Image formed by a small aperture is inverted.] - -This spot of light, resembling in its outlines the flame, is called an -_image_. _An image is defined as an optical counterpart of an object_. -Images are formed in a variety of devices, such as _apertures_, -_mirrors_, and _lenses_. The _pin-hole camera_ is simply a light-tight -box with a small aperture in one side. Light passing through this -aperture forms an image upon the opposite side of the interior of the -box, of whatever object is in front of the camera. Light entering a room -through a _large_ aperture such as a window produces a multitude of -overlapping images which blend to form a somewhat evenly illuminated -surface. - - -Important Topics - -1. Light contrasted with sound (three differences). - -2. Bodies: transparent, translucent, opaque. - -3. Light: reflected, transmitted, absorbed. - -4. Light travels in straight lines, evidence, shadows, umbra, penumbra. - -5. Formation of images by small apertures. - - -Exercises - -1. Consider the circumference of the earth as 25,000 miles. How many -times would the speed of light cover this distance in a second? - -2. How soon after any great disturbance takes place on the sun, -93,000,000 miles distant, can it be seen upon the earth? - -3. Construct a diagram of the moon's shadow. How much of the sun can one -see when in the moon's umbra? When in its penumbra? Have you ever been -in either? When? Have you ever been in the earth's umbra? In its -penumbra? - -4. Explain, using a diagram, the formation of an inverted image by a -small aperture. - -5. If the sun is 45 degrees above the horizon, what is the height of a -pole casting a shadow 60 ft. long? - -6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically -upon a walk, how tall is the tree whose shadow is 42 ft. long, both -measurements being made at the same time? - -7. Why are the shadows caused by an electric arc lamp so sharply -defined? - -8. Why should schoolroom windows be all on one side and reach to the -ceiling? - -9. What is the relation between the size of an image and its distance -from the aperture forming it? Can you prove this by geometry? - -10. What are silhouettes and how are they produced? - - -(2) PHOTOMETRY AND THE LAW OF REFLECTION - -=358. Photometry.=--It is desirable at times to compare the intensities -of illumination produced by light from different sources. This is done -to determine the _relative cost or effectiveness_ of various illuminants -such as candles, kerosene and gas lamps, and electric lights The process -of determining the relative intensity of lights or lamps is called -photometry. (_Photos_ = light.) - -The unit for measuring the power of light is called a _candle power_. It -is the light produced by a sperm candle burning 120 grains per hour. An -ordinary gas light burns 5 or more cubic feet of gas per hour and yields -from 15 to 25 candle power. A Welsbach gas lamp, consuming 3 cu. ft. per -hour, produces 50 to 100 candle power. - -Instead of using candles, for practical photometry, incandescent lamps -standardized by the Bureau of Standards are used for testing or -calibration purposes. - -It is necessary to distinguish between the intensity of a _luminous_ -body, _i.e._, as a source of light, and the _intensity_ of -_illumination_ upon some surface produced by a light. It is considered -that two sources of light are of _equal intensity_ if they produce equal -illumination at equal distances. - -=359. Law of Intensity of Light.=--A device for measuring the candle -power of a light is called a _photometer_. Its use is based upon the -_law of intensity of light_. _The intensity of illumination of a surface -is inversely proportional to the square of its distance from the source -of light._ This relation is similar to that existing between the -intensity of a sound and the distance from its source. The following -device illustrates the truth of this law in a simple manner. - -[Illustration: FIG. 350.--The light spreads over four times the area at -twice the distance.] - - Cut a hole 1 in. square in a large sheet of cardboard (_K_) and - place the card in an upright position 1 meter from an arc light or - other _point source_ of light (_L_). Now rule inch squares upon - another card (_M_) and place it parallel to the first card and 2 - meters from it. (See Fig. 350.) The light that passed through the - hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq. - in. at a distance of 2 meters. Therefore, the intensity of - illumination on each square inch of _M_ is one-fourth that upon the - surface of _K_. If _M_ is placed 3 meters from the light, 9 sq. in. - are illuminated, or the intensity is one-ninth that at 1 meter - distance. - -[Illustration: FIG. 351.--The Bunsen photometer.] - -These relations show that the intensity of illumination is inversely -proportional to the square of the distance from the source of light. An -application of the law of intensity is made in using a simple (Bunsen) -photometer. This consists of a card containing a spot soaked with oil or -melted wax. (See Fig. 351.) The lights whose intensities are to be -compared are placed upon opposite sides of the card. The card is then -adjusted so that the spot appears the same on both sides. The -illumination is now equal on both sides of the card and the _candle -powers of the two lights are proportional to the squares of their -distances from the card_. The simple device just described will give -approximate results only. For accurate results more elaborate apparatus -is required. - -=360. Measurement of the Intensity of Illumination.=--A standard candle -(Art. 358) produces when lighted 1 candle power. The illumination caused -by this upon a surface 1 ft. away and at right angles to the light rays -is called a =foot-candle=. It is the unit of intensity of illumination. -A 4-candle-power lamp, at a distance of 1 ft., produces 4 foot-candles. -A 16-candle-power lamp at a distance of 2 ft. also produces 4 -foot-candles--(16 ÷ 2²). - -The intensity of illumination required for a good light for seeing -varies with the conditions. Thus, for stage and store lighting about 4 -foot-candles are needed, while homes and churches may require but 1 -foot-candle. - -Too great an intensity of illumination is as harmful as not enough. -Exposed lights having an intensity of more than 5 candle power per -square inch are often a cause of eye trouble. Such lights should be -protected by frosted globes. - -A pleasing form of lighting for large halls and public buildings is the -_indirect system_. In this, the lamps are hidden by reflectors which -throw the light upon the ceiling from which it is diffused over the -room. This form of lighting is more expensive than other systems since -but a part of the light is reflected. Its cost therefore is an important -factor when considering its use. - -=361. The Reflection of Light.=--The light reflected from the surfaces -of bodies about us gives us information concerning our surroundings. A -knowledge of the behavior of light undergoing reflection is not usually -gained from ordinary observation. The law of reflection of light may be -shown, however, by an experiment. - -[Illustration: FIG. 352.--_B´_ is as far back of the mirror as _B_ is in -front of it.] - -[Illustration: CHRISTIAN HUYGENS - -(Popular Science Monthly) - -Christian Huygens (1629-1695). Dutch physicist; invented the pendulum -clock (1656); developed the wave theory of light; discovered -polarization of light (1690).] - -[Illustration: H. V. HELMHOLTZ - -"By Permission of the Berlin Photographic Co., New York." - -Hermann von Helmholtz (1821-1894) Germany. Established the doctrine of -conservation of energy; made many discoveries in sound; invented the -ophthalmoscope; established the physical basis of tone quality.] - - A plane mirror, _M_, is held in a vertical position resting upon a - sheet of paper. (See Fig. 352.) Pins are set upright in the paper - at _A_ and _B_. On placing the eye along the line _AC_ and looking - toward the mirror an image of _B_ may be seen in the mirror due to - the light reflected from its surface. Pins _C_ and _D_ are now set - in the paper so that when one looks along the line _BD_ toward the - mirror one may see all four pins apparently in one line. This - indicates that the light from _A_ and _C_ passing along _CA_ toward - _O_ is reflected back along the light _CBD_. By means of a ruler, - draw lines through _BD_ and _AC_ till they intersect at _O_. Also - draw _PO_ perpendicular to the mirror at _O_. - -Then the angles _AOP_ and _BOP_ will be found equal. These are called -the angles of _incidence_ and _reflection_ respectively. _The law of -reflection_ is therefore stated: _The angle of reflection is equal to -the angle of incidence._ These angles are in the same plane, that of the -paper. This law applies in all cases of reflection of light. It is -similar to the law of reflection of sound (Art. 326.) - - -Important Topics - -1. Photometry, law of intensity, candle power, foot-candle. - -2. Intensity of illumination. - -3. Reflected light and law of reflection. - - -Exercises - -1. Both sides of a card are equally illuminated when two lights are on -opposite sides of it and 10 and 30 cm. respectively from it. what are -their relative intensities? - -2. What are the relative intensities of illumination from a gas light -upon a book 6 ft. and 2 ft. respectively from the light? - -3. Which is more expensive per candle power? How many times as -expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per -kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of -gas per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per -hour, and then the cost of 1 candle power hour for each.) - -4. Why are not ordinary shadows perfectly dark? - -5. At what distance will a 16-candle-power lamp give the same -illumination as a single candle at 10 in.? - -6. If the sun is at an elevation of 30 degrees what is the angle of -incidence at which it strikes the surface of water? What is the angle -between the incident and the reflected rays? - -7. What is the difference between the phenomena of reflection of light -from a white sheet of writing paper and from a piece of clear window -glass? - -8. A horizontal ray of light, traveling due east, strikes a vertical -mirror so that after reflection it is traveling due north. If the mirror -be now turned 10 degrees about a vertical axis, the north edge moving -east, what will be the direction of the reflected ray? - -9. The necessary illumination for reading is about 2 foot-candles. How -far away may an 8-candle-power lamp be placed? - -10. What is the illumination in foot-candles upon a surface 20 ft. from -an arc lamp having an intensity of 1000 candle power? - -11. How far from a 100-candle-power Welsbach light would the -illumination be 2 foot-candles? - - -(3) MIRRORS AND THE FORMATION OF IMAGES - -[Illustration: FIG. 353.--Reflection of light, (_a_) diffused, (_b_) -regular.] - -=362. Mirrors.=--The many purposes served by mirrors in our every-day -life has made their use familiar to everyone. Yet without study and -experiment few understand their properties and action. _Any smooth_ -surface may serve as a mirror, as that of glass, water, polished wood, -or metal. Most objects, unlike mirrors, have irregular surfaces; these -scatter or diffuse the light that falls upon them. (See Fig. 353_a_.) -This is called _diffused or irregular reflection_. The reflection of -light from the smooth surface of a mirror is _regular_. (See Fig. -353_b_.) In every case of reflected light, however, the angle of -reflection equals the angle of incidence, diffusion being due to the -irregularity of the surface. It is by means of the light "diffused" -from the surface of illuminated bodies, such as plants, animals, food, -and manufactured articles, that we "see" the various objects about us, -and it is this light that enables us to judge of their distance, size, -form, color, etc. The moon is seen by the sunlight reflected from its -surface. Moonlight is therefore sunlight diffused by reflection. The -_new moon_ is that phase or condition of the moon when only a narrow -strip of the moon's illuminated surface is turned toward the earth. At -the time of the _full moon_ the whole illuminated surface is seen. - -=363. Images Formed by a Plane Mirror.=--The most common use of mirrors -is in the formation of images. The way in which images are formed by a -plane mirror may be illustrated by diagrams. Thus in Fig. 354, let _L_ -represent a luminous body and _E_ and _E´_ two positions of the -observer's eye. Take any line or ray as _LO_ along which the light from -_L_ strikes the mirror _O-O´_. It will be reflected so that angle _LOP_ -equals angle _POE_. Similarly with any other ray, as _LO´_, the -reflected ray _O´E´_ has a direction such as that angle _L´O´E´_ equals -angle _P´O´E´_. Any other rays will be reflected in a similar manner, -each of the reflected rays appearing to the eye to come from a point -_L´_ behind the mirror. - -[Illustration: FIG. 354.--The virtual image of a fixed object as seen in -a plane mirror, has the same location from every position of the -observer's eye.] - -=364. Light Waves and Wave Diagrams.=--Just as a stick continually moved -at the surface of a body of water sets up a series of waves spreading in -all directions, so one may imagine a train of waves sent out by a -luminous body _L_ (as in Fig. 355) to the mirror _MN_. These waves will -be reflected from the mirror as if the source of light were at _L´_. It -is much simpler and more convenient to locate the position of the image -of a point by the use of lines or "rays" (as in Fig. 354) than by the -wave diagram (as in Fig. 355). In all _ray diagrams_, however, it should -be kept in mind that the _so-called_ ray is a symbol used to represent -the direction taken by a part of a light wave. Thus in Fig. 354, the -light from _L_ moving toward _O_ is reflected to _E_ along the line -_OE_, the heavy lines representing rays. - -[Illustration: FIG. 355.--Wave diagram of image formed in a plane -mirror.] - -=365. To locate the image of an object formed by a plane mirror= -_requires_ simply an application of the law of reflection. Thus in Fig. -356 let _AB_ represent an object and _MN_ a plane mirror. Let _AA´_ be a -ray from _A_ striking the mirror _perpendicularly_. It is therefore -reflected back along the same line toward _A_. Let _AO_ represent any -other ray from _A_. It will be reflected along _OE_ so that angle _r_ -equals _i_. The intersection of _AC_ and _OE_ at _A´_ behind the mirror -locates the image of the point _A_, as seen by reflection from the -mirror. The triangles _ACO_ and _A´CO_ may be proved equal by geometry. -Therefore _A´C_ equals _AC_. This indicates that _the image of a point -formed by a plane mirror is the same distance back of the mirror as the -point itself is in front of it_. This principle may be used in locating -the image of point _B_ at _B´_. Locating the position of the _end -points_ of an image determines the position of the whole image as -_A´B´_. - -[Illustration: FIG. 356.--The image _A´B´_ is as far back of the mirror -_M N_ as the object _A B_ is in front of the mirror.] - -=366. How the Image is Seen.=--Suppose the eye to be placed at _E_. It -will receive light from _A_ by reflection as if it came from _A´_. -Similarly light starting from _B_ reaches the eye from the direction of -_B´_. There is nothing back of the mirror _in reality_ that affects our -sight, the light traveling only in the space in front of the mirror. Yet -the action of the reflected light is such that it produces the same -effect as if it came from behind the mirror. Images such as are seen in -plane mirrors are called _virtual_ to distinguish them from _real_ -images, in which light actually comes to the eye from the various parts -of the visible image, as from the real image formed by a projecting -lantern upon a screen, or by an aperture as in the pin-hole camera. -Real images therefore are those that can be obtained upon a screen while -virtual images cannot. - -=367. Multiple Reflection.=--If the light from an object is reflected by -two or more mirrors various effects may be produced, as may be -illustrated by the _kaleidoscope_. This consists of three plane mirrors -so arranged that a cross-section of the three forms an equilateral -triangle. The mirrors are placed in a tube across the end of which is a -compartment with a translucent cover containing pieces of colored glass. -On looking through the tube, the reflections from the several surfaces -produce beautiful hexagonal designs. - -[Illustration: FIG. 357.--Perspective view of "Pepper's ghost."] - -[Illustration: FIG. 358.--Diagram of the "Pepper Ghost" illusion.] - -=368. Optical Illusions by a Plane Mirror.=--The _illusion_ called -_Pepper's Ghost_ is typical of many illusions produced by reflection. It -may be illustrated by taking a piece of plate glass, _M-N_, a tumbler of -water, _W_, and a lighted candle, _C_, placed in a box, _B_, having one -side open and arranged as shown in perspective in Fig. 357, and in -section in Fig. 358. If the effect is produced in a darkened room, the -observer at _E_ sees a virtual image of the lighted candle as if it were -in the glass of water, the water being seen by transmitted light -_through_ the plate glass, the latter forming a virtual image of the -candle by reflection. Some of the illusions produced by this means are: -(_a_) the figure suspended in mid air; (_b_) the bust of a person -without a trunk; (_c_) the stage ghost; (_d_) the disappearing bouquet. - -[Illustration: FIG. 359.--Action of a concave mirror on parallel rays of -light.] - -[Illustration: FIG. 360.--Real image formed by a concave mirror.] - -=369. Concave Mirrors.=--Another useful piece of physical apparatus is -the concave spherical mirror. It is frequently made from plano-convex -lenses by silvering the convex surface of the lens, thus making a -concave reflecting surface from the inner surface of the silvered part; -they are also made by polishing the inner surfaces of metallic spherical -shells. The concave mirror is represented in section in Fig. 359 by the -curve _MN_; _C_ is the _center of curvature_ or the center of the -surface of which this mirror _MN_ is a part; the line _VC_ through the -center _V_ of the mirror is called the _principal axis_; while any other -line passing through _C_ is called a _secondary axis_. The point midway -between the vertex _V_ and center of curvature _C_ is called the -_principal focus_, _F_. It is the point through which parallel incident -rays pass after reflection. The angle _MCN_ which the curve of the -mirror subtends at the center is called the aperture of the mirror. We -learned in Art. 361, the angle of reflection of a ray of light is always -equal to the angle of incidence no matter what the nature of the -reflecting surface may be. If the reflecting surface is a regular -concave surface, like the inner surface of a sphere, the rays of light -coming from a point source may after reflection come to a focus, forming -a real image. The two extreme points of an object should be selected for -locating its image; Fig. 360 shows the construction. The real images -formed by concave mirrors are always inverted. The principal focus of a -concave mirror may be observed by holding the mirror in a beam of -sunlight entering a darkened room. The sun's rays after reflection -converge to form a small, round, intense spot of light, which is a real -image of the sun, located at the principal focus of the mirror. The -distance of the principal focus from the mirror is the least distance -that a real image can be formed in front of a concave mirror. - -=370. Virtual Images by Concave Mirrors.=--When light comes from a small -point situated between a concave mirror and its principal focus, the -reflected rays are divergent and hence no real image of the object can -be found in front of the mirror. But if the rays are extended behind the -mirror they will meet in a point called the _virtual focus_. This is the -point from which they appear to come. Any image of an object situated -between the principal focus and a concave mirror is therefore a virtual -image, erect and larger than the object. (See Fig. 361.) - -[Illustration: FIG. 361.--Virtual image formed by a concave mirror.] - -=371. Construction of Real Images.=--There are five positions at which -an object may be situated in front of a concave mirror, namely: (1) -_beyond C_; (2) at _C_; (3) _between C and F_; (4) _at F_ and (5) -_between F_ and _V_. There are two ways by means of which the image -formed at each of these positions may be located, namely; (1) -_experimentally_, by allowing the rays of light from a luminous body to -focus on a screen and (2) _diagrammatically_. By the latter method the -two rays of light are considered the course of each of which may easily -be determined; first, the ray which strikes the mirror parallel to its -principal axis and which after reflection passes through the principal -focus; second, the ray which passing through the center of curvature -strikes the mirror at right angles and therefore after reflection must -pass directly back along its incident path. Where these two reflected -rays intersect is located the real image of the object. Whenever these -two rays of light do actually intersect, as in Fig. 360, a real image -(_ab_) is formed of the object _AB_. - -The points _A_ and _a_, _B_ and _b_ and others similarly situated on an -axis extending through the center of curvature _C_ are called _conjugate -foci_, for they are so related that an object being at either one, its -image will be found at the other. - -[Illustration: FIG. 362.--Action of a convex mirror upon parallel rays -of light.] - -=372. The Convex Mirror.=--There are few practical uses to which convex -mirrors can be put. They are sometimes used to give the chauffeur of an -automobile a view of the road behind him. It is then attached to the -wind shield by a short rod. The reflected rays coming from a Convex -mirror are always divergent (see Fig. 362), hence the image is always -virtual and located behind the reflecting surface. The method of -construction for images formed by a convex mirror is similar to that for -concave mirrors. (See Fig. 363.) The center of curvature and principal -focus are behind the mirror and consequently the reflected rays have to -be produced backward until they meet. The images are always _virtual_, -_erect_ and _smaller_ than the object. - -[Illustration: FIG. 363.--Construction of an image by a convex mirror.] - -[Illustration: FIG 364.--Illustrations of Spherical Aberration.] - -=373. Spherical Aberration.= Sometimes in a concave mirror when the -aperture _MCN_ (Fig. 364) is large the images are blurred or indistinct. -This is due to the fact that the incident rays near the outer edge of -the mirror do not focus after reflection at the same point as those -which pass into the mirror near the vertex, but cross the principal axis -at points between the mirror and principal focus as is shown in Fig. -364; this result is called _spherical aberration_. The larger the -aperture of the mirror the more the image is blurred. Concave mirrors in -practical use do not have an aperture much greater than 10 degrees. This -non-focusing of the rays of light by curved reflecting surfaces may be -noticed in many places, as when light is reflected from the inside of a -cup that contains milk or from the inside of a wide gold ring placed on -top of a piece of white paper. The pupil will note other instances. -This curve of light observed is called the _caustic by reflection_. - -=374. Parabolic Mirrors.=--The best possible surface to give to concave -mirrors is parabolic. This is a curve which may be generated by moving a -point so that its distance from a fixed point and a fixed line are -always equal. If a source of light is placed at _F_ the rays after -reflection are rendered parallel. See Fig. 365. This reflector is used -in automobile lamps, headlights of locomotives, search-lights, etc. It -is also used in large reflecting astronomical telescopes to collect as -large an amount of light as possible from distant stars and bring it to -a focus. Such mirrors may be made exceedingly accurate. - -[Illustration: FIG. 365.--Parabolic mirror.] - - -Important Topics - -1. Reflection: regular, diffused; plane mirrors; laws of reflection. - -2. Formation and location of images by plane mirrors. Wave and ray -diagrams. - -3. Multiple reflection, illusions. - -4. Curved mirrors, uses; concave, convex, parabolic. - - -Exercises - -1. Distinguish between regular and diffused reflection. By means of -which do we see non-luminous bodies? - -2. Could a perfect reflecting surface be seen? Explain. - -3. A pencil is stood upright in front of a plane mirror set at an angle -of 45 degrees to the vertical. Shown by a diagram the location and -position of the image. - -4. Show by diagrams the position and location of the images of a pencil -(a) when standing erect and in front of a _vertical_ mirror. (b) when -standing upon a horizontal mirror. - -5. What is the difference between a real and a virtual image? - -6. A standard candle and a lamp give equal illuminations to a screen -that is 1 ft. from the candle and 6 ft. from the lamp. What is the -candle power of the lamp? Explain. - -7. Why are walls finished in rough plaster or painted with soft tones -without gloss better for schoolrooms than glossy paints or smooth white -plaster? - -8. Try to read a printed page by looking at its image in a mirror. write -your name backward on a sheet of paper, and then look at the image of -the writing in a mirror. What effect is produced by the mirror in each -case? - -9. If the point of a pencil is held to the surface of a piece of -plate-glass mirror two or more images may be seen in the mirror. -Explain. - -10. Given a small lighted candle, a concave mirror, a meter stick, and a -white screen, how would you prove the statements made in Arts. 369 and -370 concerning the location of images formed by concave mirrors? Make -the diagram in each case. - -11. Why do images seen in a quiet pond of water appear inverted? Explain -by a diagram. - - -(4) REFRACTION OF LIGHT - -=375. Common Examples of Refraction.=--Everyone has noticed the apparent -bending of an oar, of a stick, or of a spoon when placed in water (see -Fig. 366), while many have observed that the bottom of a pond or stream -looks nearer to the surface than it really is. These and similar -illusions are due to the _refraction_ or bending of light rays as they -pass from one medium to another. The principles of refraction are among -the most useful found in the study of light since application is made of -them in the construction and use of important optical instruments, such -as the camera, microscope, telescope, and the eye. - -[Illustration: FIG. 366.--The stick appears to be bent on account of -refraction.] - -=376. Action of Light Undergoing Refraction.=--If a beam of sunlight be -admitted to a darkened room and reflected by a mirror so that it strikes -the surface of water in a glass jar, a part of the beam may be seen to -be reflected while another portion is transmitted through the water -(Fig. 367). The reflected beam follows the law of reflection while the -transmitted beam is seen to be _refracted_, or to have its courses -slightly changed in direction upon entering the water. If the mirror is -turned so that the angle at which the light strikes the water is -changed, the amount of refraction or change of course of the light is -varied. When the light strikes the water perpendicularly there is no -refraction. On the other hand, the greater the angle at which the light -strikes the water the greater the bending. - -[Illustration: FIG. 367.--Part of the ray is reflected and part passes -into the water and is refracted.] - -[Illustration: FIG. 368.--Illustrating the laws of refraction of light.] - -=377. Laws of Refraction.= The action of light on entering, passing -through, and leaving a great variety of substances has been carefully -studied. A summary of the results of these observations is given in the -following _laws of refraction_: I. _When light enters a transparent -body, perpendicularly, it passes on without changing its direction._ -II. _When light enters a denser transparent body obliquely, it is bent -toward the perpendicular; when light enters a less dense body obliquely, -it is bent away from the perpendicular._ (See Fig. 368.) - -=378. The cause of refraction= may be illustrated by considering a line -of men moving across a field and occupying at equal time intervals the -successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that -the upper and lower parts of the field have a smooth hard surface, while -at the center is a strip of newly ploughed ground. The line will move -more slowly over the ploughed field than over the hard field. This will -result in a retardation of the end of the line first striking the soft -ground with a resulting change of direction of the line, _toward_ the -perpendicular to the edge of the field (_on entering the place of more -difficult travel_), and _away_ from the perpendicular on moving into a -place where _increased speed results_. - -[Illustration: FIG. 369.--Diagram illustrating the cause of refraction.] - -=379. Index of Refraction.=--By studying the change of direction of the -marching men as shown in Fig. 369 it is evident _first_ that it is due -to a difference in speed in the two media. It is not easy to measure the -speed of light in a medium. However, the amount of refraction may be -determined easily and from this the _relative_ speed may be computed. -The _number that expresses the ratio of the speed of light in air to its -speed in another medium is called the index of refraction of that -medium_. The relative speeds of light, or the indices of refraction for -some substances, are: water, 1.33, crown glass, 1.51, flint glass, -1.61, diamond, 2.47, carbon bisulphide, 1.64. - -[Illustration: FIG. 370.--The incident ray and the emergent rays are -parallel.] - -=380. Plates, Prisms, Lenses.=--The refraction of light is usually -observed when it is passing through a plate, a prism, or a lens. The -important differences between the effects of each in refracting light -are illustrated in Figs. 370, 371 and 372. In Fig. 370 it is seen that -the refraction of the ray on entering the glass is counteracted by the -refraction away from the perpendicular upon leaving it. So that the -entering and emergent rays are _parallel_. In Fig. 371 the refraction at -the two surfaces of the prism results in a change of direction of the -ray, the course being bent toward the _thicker_ part of the _prism_. In -Fig. 372 it may be noticed that the convex lens resembles two prisms -with their bases together. Since all parts of the lens refract light -toward the thicker part, the center, the effect of the convex lens is to -bring the rays of light to a focus, at _F_. - -[Illustration: FIG. 371.--Effect of a prism upon a ray of light.] - -[Illustration: FIG. 372.--The convex lens brings the rays of light to a -focus.] - -=381. Total Reflection.=--It has been shown that when light passes from -a _denser to a lighter_ medium, as from glass or water to air, that the -beam is refracted _away_ from the perpendicular. This is illustrated in -Fig. 373. The diagram represents the change in the course of a ray of -light that passes through water to a surface with air above it. A ray -striking perpendicularly passes through without refraction. Other rays -show increasing refraction with increasing angle of incidence. For one -ray the angle of refraction is so large that the refracted ray is -parallel to the surface. When this condition is reached, the _angle of -incidence_ is called the _critical angle_. Any increase in the angle of -incidence causes all of the light to be reflected as is the beam _E_. -This action is called _total reflection_, the course of the reflected -ray being according to the law of reflection. _A right-angle prism_ (see -Fig. 374) is often used where a mirror would ordinarily be employed, the -total reflection occurring within the prism giving more satisfactory -results than a mirror. See Art. 398 for a description of the Zeiss -binocular field-glass for an example of this use of total reflection. - -[Illustration: FIG. 373.--An example of total reflection.] - -[Illustration: FIG. 374.--Total reflection in a right-angle prism.] - - The mirage (see Fig. 375) is an optical illusion by which distant - objects, below the horizon, are sometimes plainly seen. This - phenomenon is most frequently observed in hot, desert regions, when - the air conditions are such that the lower strata near the ground - are very much hotter than those above. These lower strata, having - expanded the most, are less dense than the cooler ones above. Hence - a ray of light traveling obliquely downward is refracted more and - more until total reflection takes place. The images seen are - inverted giving a representation of trees or other objects - reflected on the surface of still water. The mirage is also - frequently seen at sea, ships being observed, sometimes erect, - sometimes inverted, apparently sailing in the clouds near the - horizon. Over the Great Lakes, trees, boats, and towns on the - opposite shore, sixty or seventy miles away, can sometimes be - plainly seen, apparently but a few miles out. In this case the - images are erect, the total reflection being from warm, still - layers of air over colder layers near the water. - -[Illustration: FIG. 375.--Diagram of a mirage.] - - -Important Topics - -(A) Refraction: cause, illustration, two principles. - -(B) Index of refraction, meaning. - -(C) Plates, prisms, lenses, action of each. - -(D) Total reflection, uses. - - -Exercises - -1. Compute the speed of light in water, the index of refraction being -1.33. - -2. If one wished to shoot a fish under water, should he aim at the -apparent location of the fish as viewed from the air? Explain, using a -diagram. - -3. Define refraction. Mention two illustrations of this action that you -have observed out of school. - -4. Why does the moon look larger near the horizon? - -5. Is your reflection seen in a pool of water upside down? Why? - -6. Why does it whiten molasses candy to pull it? - -7. When looking at a building through the ordinary glass of a window why -do straight lines of the building appear to be so distorted? What makes -them appear to move as you move your head slightly? - -8. Explain the phenomenon which one observes when looking at an object -through the air arising from a hot stove or radiator. - -9. Frequently the horizontal diameter of the setting sun appears to be -greater than the vertical. Explain. - -10. Explain why one observes several images of a luminous body like a -lighted candle when the reflected light from a thick glass mirror enters -the eye, the angle of reflection being large. - - -(5) THE FORMATION OF IMAGES BY LENSES - -=382. Uses of Lenses in Optical Instruments.=--The use of instruments -that employ lenses in their operation, such as spectacles, reading and -opera glasses, and the camera, microscope, and telescope, is familiar to -most students of physics. The part played by the lenses, however, is not -generally understood. Consequently the study of the formation of images -by lenses is of general interest and importance. - -=383. Forms of Lenses.=--While a lens may be formed from any transparent -solid it is commonly made of glass. It may have two curved surfaces or -one curved and one plane surface. Most lenses are _spherical lenses_, -since their curved surfaces form a part of the surface of a sphere. Fig. -376 represents a spherical lens with a curved surface coinciding with -that of a sphere whose center is at _C_. This center is called the -_center of curvature_, while the radius of the sphere _R_, is the -_radius of curvature_. - -[Illustration: FIG. 376.--Formation of a spherical lens.] - -There are two classes of lenses: those thick in the middle are called -_convex_, while those thick at the edges are _concave_. The mode of -constructing the six forms of spherical lenses is shown in Fig. 377. -These are named as follows: (1) double convex, (2) plano convex, (3) -concavo-convex, (4) double concave, (5) plano concave, (6) -convexo-concave. - -[Illustration: FIG. 377.--Forms of Lenses. 1. double convex; 2. plano -convex; 3. concavo convex; 4. double concave; 5. plano concave; 6. -convexo concave.] - -[Illustration: FIG. 378.--The action of a burning glass.] - -=384. Effect of Lenses upon Light.=--The most important characteristic -of a lens is its effect upon a beam of light. Most persons have seen a -"burning glass," a double convex lens, used to bring to a point, or -focus, a beam of sunlight. To show the action of a burning glass send a -beam of light into a darkened room, and place in its path a double -convex lens. (See Fig. 378.) If two blackboard erasers are struck -together near the lens, the chalk particles in the path of the light are -strongly illuminated, showing that the light after passing through the -lens it brought to a focus and that it spreads out beyond this point. -This point to which the cone of light rays converges after passing -through the convex lens is called the _principal_ focus of the lens. The -distance from the principal focus to the center of the lens is the -_focal length_ or _principal focal distance_ of the lens. _The focal -length of double convex lenses of crown glass is about the same as the -radius of curvature of either surface._ The action of a convex or -converging lens upon light may be better understood by studying Fig. 379 -in which light is passing from _S_ to _F_. The successive positions and -shape of the advancing light waves are indicated by lines drawn across -the beam. The light being retarded more in the thicker part of the lens, -the light waves on leaving the lens have a concave front. Since light -waves tend to move at right angles to the front of the wave, the light -is brought to a focus. After passing the focus the waves have a convex -front, forming a diverging cone. - -[Illustration: FIG. 379.--Wave diagram of light passing through a convex -lens.] - -=385. Concave Lenses.=--When sunlight passes through a _concave_ lens a -diverging cone of light is formed. (See Fig. 380.) This is caused by the -edges of the wave being retarded more than the center, producing a -convex wave front. This diverging cone of light acts as if it had -proceeded from a luminous point at _F_. - -This point is called a _virtual_ focus and is nearly at the center of -the curvature of the nearer surface. - -[Illustration: FIG. 380.--Wave diagram of light passing through a -concave lens.] - -=386. The Formation of Images by Lenses.=--If a beam composed of -_parallel_ rays of light, as sunlight, is sent in turn through three -convex lenses of the same diameter but of different thickness, it is -found that the _thicker the lens the greater is its converging power, or -the shorter is its focal_ length. (See Fig. 381.) Now if a luminous -body, such as a lighted candle, be placed near the convex lens but -_beyond its focal length_, the light will be brought to a focus upon the -other side of the lens and an image of the candle may be clearly seen -upon the screen placed at this point. (See Fig. 382.) _The two points so -situated on opposite sides of a lens that an object at one will form an -image at the other are called conjugate foci._ - -[Illustration: FIG. 381.--The thicker the lens, the shorter is its focal -length.] - -[Illustration: FIG. 382.--_C_ and _S_ are at conjugate foci.] - -It will be helpful to compare the images formed of a candle by an -_aperture_ and by a _convex_ lens. Rays of light from each point of the -luminous body pass through the aperture in straight lines and produce -upon the screen a lighted space of the same shape as the candle. This -image is rather _hazy_ in outline. Each cone of rays from luminous -points of the flame is brought by the lens to a focus on the screen, -producing a _sharp image_. It is the converging power of convex lenses -that enables them to produce clear images. - -[Illustration: FIG. 383.--Construction of a real image by a convex -lens.] - -=387. The Construction of Diagrams to Represent the Formation of Images -by Lenses.=--Just as the earth has an axis at right angles to its -equator to which are referred positions and distances, so a lens has a -_principal axis_ at right angles to its greatest diameter and along this -axis are certain definite positions as shown in Fig. 383. Let _MN_ be -the _principal axis_ of a convex lens, _P_ and _P´_ are _principal foci_ -on either side of the lens, _S_ and _S´_ are _secondary foci_. These are -at points on the principal axis that are twice as far from _O_, the -center of the lens, as are the principal foci. In the formation of -images by a convex lens, several distinct cases may be noticed: - -(A) If a luminous body is at a _great distance_ at the left, its light -is brought to a _focus_ at _P_, or its _image is formed at P_. (B) As -the _object approaches_ the lens the _image gradually recedes_ until the -object and image are at _S_ and _S´_, _equally distant from O and of -equal size_ (as in Fig. 383). The object and image are now said to be at -the _secondary foci_ of the lens. (C) As the _object moves from S to P_ -the image recedes, rapidly increasing in size until (D) when the object -is at _P_ the rays become parallel and no image is formed. (E) When the -object is between _P_ and the lens, the rays _appear to proceed from -points back of the object_, thus forming an _erect, larger, virtual -image_ of the object. (See Fig. 384.) This last arrangement illustrates -the _simple microscope_. - -With a concave lens but one case is possible, that corresponding to the -one last mentioned with convex lenses; since the rays from a body are -divergent after passing through a concave lens they appear to proceed -from points _nearer_ the lens than the object and hence a _virtual, -erect, smaller image_ of the object is formed. This virtual image may be -seen by looking _through_ the lens toward the object. (See Fig. 385.) - -[Illustration: FIG. 384.--Construction of a virtual image by a convex -lens.] - -[Illustration: FIG. 385.--Construction of a virtual image by a concave -lens.] - -=388. The Lens Equation.=--The location of either the object or of the -image upon the principal axis of the lens may be calculated if the -position of one of these and the focal length are known. This is -accomplished by the use of a formula 1/_F_ = 1/_D_{0}_ + 1/_D_{1}_ in -which _F_ represents the focal length and _D_{0}_ and _D_{1}_ the -distance from the lens of the object and the image respectively. Thus if -an object is placed 30 cm. from a lens of 10 cm. focal length, where -will the image be formed? Thus: 1/10 = 1/30 + 1/_D_ and 3_D_{1}_ = -_D_{1}_ + 30, or 2_D_{1}_ = 30 _D_{1}_ = 15. This result indicates that -a real image will be 15 cm. from the lens. A minus value would indicate -a virtual image. - - -Important Topics - -(A) Lenses: convex, concave, six forms, center and radius of curvature. - -(B) Principal focus, focal length, virtual focus, conjugate foci. - -(C) Principal axis, images formed when object is in various locations. - -(D) Computation of location of images. - - -Exercises - -1. Why is an image of a candle formed by an aperture, not sharply -defined? - -2. When a photographer takes your picture and moves the camera nearer -you, must he move the ground glass screen toward the lens or away -from it? Explain. - -3. How can you find the principal focal length of a lens. - -4. How can you test a spectacle lens to see whether it is convex -concave? - -5. When will a convex lens produce a virtual image? Have you ever seen -one? Where? - -6. When a photographer wishes to obtain a full length view of a person, -where does he place the camera? - -7. The focal length of the lens is 24 cm. How far from the lens must an -object be placed in order that a real image may be three times as long -as the object? - -8. There is a perfect image of an object on the ground glass of a -camera. The center of the lens is 20 cm. in front of the image and the -object 75 cm. from the lens. What is the focal length of the lens? - -9. An object is 60 cm. from the lens, the image 120 cm. from it. Find -the focal length. - -10. How can you find experimentally the principal focal length of a -lens? - -11. A lens is used to project an enlarged image of a candle upon a -screen. Which is farther from the lens, the candle or the image? -Explain. - - -(6) OPTICAL INSTRUMENTS - -=389. The Eye.=--The most common optical instrument is the _eye_. While -the structure of the eye is complicated, the principle of it is simple, -involving the formation of an image by a double convex lens. (See Fig. -386, in which is shown a front to back, vertical cross-section of the -eye.) The eye appears to be made of portions of two spheres, one of -which, smaller than the other, is placed in front. This projecting part -is transparent, but refracts the light which strikes it obliquely, so as -to turn it into the eye. This enables us to see objects at the side when -looking straight ahead. Test this by looking directly in front of you -and see how far back on each side of the head you can notice a movement -of the forefinger of each hand. - -[Illustration: FIG. 386.--Cross-section of the eye.] - -=390. Action of the Eye in Vision.=--When we look at an object, a small, -real, inverted image is formed upon the _retina_ at the back of the -interior of the eye. The retina is an expansion of the optic nerve and -covers the inner surface at the back of the eyeball. Seeing is due to -the action of light in forming images upon the retina. Our eyes are so -constructed that when they are relaxed the lens is adjusted to form -clear images of _distant_ objects upon the retina. If we look from -distant to near objects without changing the shape of the eye lens, a -sharp image of the latter cannot be formed and we get a blurred -impression. It is difficult, however, to look at objects without -automatically adjusting the eye lens so that it will make a sharp image. -Test this by looking out of a window at a distant object, then without -moving the head or eyes look at the glass of the window; you will notice -a slight change of some sort _in_ the eye itself as the vision is -adjusted. This adjustment is made by muscles that pull or compress the -eye lens so as to make it thicker for near objects and thinner for -distant ones. The eye ordinarily does not see objects nearer than 10 in. -clearly. This means that the greatest possible thickening of lens will -not form clear images upon the retina if the object is nearer than 10 -in. (25 cm.). - -[Illustration: FIG. 387.--The visual angle, _AOB_ is greater at _AB_ -than at _A´B´_.] - -=391. The Visual Angle.=--To examine objects carefully we usually bring -them as close to the eye as possible, for the nearer to the eye the -object is brought, the larger is the visual angle formed by it (see Fig. -387), and the larger is its image upon the retina. _The visual angle of -an object is the angle at the eye lens between the rays that have come -from the ends of the object._ Consequently the more distant the object, -the smaller is its visual angle. Now if we wish to examine small objects -with great care, we frequently find that it is necessary to bring them -close to the eye so that they have a visual angle of adequate size. If -they must be brought closer than 10 in. a double convex lens is placed -in front of the eye. This assists the eye lens in converging the light -so that a clear image may be formed when the object is close, say an -inch or so from the eye. This is the principle of the magnifying glass -used by watch-makers and of the _simple microscope_. The action of the -latter is illustrated by Fig. 388. The convex lens forms a virtual, -enlarged image "_A´-B´_" of the object "_A-B_" which it observed instead -of the object itself. - -[Illustration: FIG. 388.--Action of the simple microscope.] - -[Illustration: FIG. 389.--"Near sightedness", or myopia. Parallel rays -come to a focus at _F_; emerging rays focus at _A_, the far point.] - -=392. Defects of Vision.=--There are several defects of vision that may -be corrected by spectacles or eye-glasses. One of these is -"near-sightedness." It is due either to an eyeball that is elongated, or -to an eye lens that is too convex, or to both conditions. This condition -brings light from distant objects to a focus too soon (as shown in Fig. -389). Only light from near objects will focus upon the retina in such -cases. With _normal_ vision light from _distant_ or _near_ objects may -be focused without unusual effort upon the retina, see Fig. 390. The -remedy for near-sightedness is to use concave lenses which will assist -in properly refracting the light so the focus will be formed on the -retina (Fig. 391). "Far-sightedness" is the reverse of near-sightedness; -the eyeball is either too short, or the lens too flat, or both -conditions obtain, so that the light entering the eye is brought to a -focus behind the eyeball (Fig. 392). The remedy is convex lenses which -will assist in properly converging the light, see Fig. 393. A third -defect is called _astigmatism_. This is caused by some irregularity or -lack of symmetry in the eye. It is corrected by a _cylindrical_ lens -that compensates for this defect of the eye. A diagram similar to Fig. -394 is used as a test for astigmatism. If the lines appear with unequal -distinctness, some irregularity of refraction (astigmatism) is -indicated. - -[Illustration: FIG. 390.--The normal eye. The parallel rays _A B_ focus -without accommodative effort at _C_.] - -[Illustration: FIG. 391.--Correction of near-sightedness by concave -lens.] - -[Illustration: FIG. 392.--Far-sightedness or hyperopia. Parallel rays -focused behind the retina.] - -[Illustration: FIG. 393.--Correction of far-sightedness by a convex -lens.] - -[Illustration: FIG. 394.--Test card for astigmatism.] - -=393. The Photographic Camera.=--This is a light-tight box, provided -with a convex lens in front, covering an aperture and a ground glass -screen at the back. The distance between the lens and the screen is -adjusted until a sharp image is obtained upon the latter, which is then -replaced by a sensitive plate or film. The sensitized surface of the -plate or film contains a salt of silver which is changed by the action -of light. After the plate has been "exposed" to the action of light, it -is "developed" by the use of chemicals producing a _negative_ image. -From "negative," by the use of sensitized paper, "positive" prints may -be secured which resemble the object photographed. - -[Illustration: FIG. 395.--Diagram of the projecting lantern.] - -=394. The projecting lantern= (see Fig. 395) employs a strong source of -light, as an electric arc lamp _L_, to strongly illuminate a transparent -picture, or _lantern slide_, _S_, a real image (_I_) of which is formed -upon a large screen. Two large plano-convex lenses (_C_), called -condensing lenses, are placed near the lamp to concentrate the light -upon the "slide" _S_. The convex lens forming the image is called the -"objective" (_O_). - -=395. The compound microscope= consists of two lenses. One called the -_objective_ is placed near the object to be viewed. This lens has a -short focal length usually less than a centimeter. It forms a _real -image_ of the object. _A´_-_B´_. The other lens, the _eyepiece_ forms a -virtual image of this real image. _A´´_-_B´´_. (See Fig. 396.) - -=396. The telescope= consists of two lenses, the eyepiece and the -objective. As in the compound microscope, the objective of the telescope -forms a real image of the distant object, the eyepiece forming an -enlarged virtual image of the real image. It is the virtual image that -is viewed by the observer. (See Fig. 397.) In order to collect -sufficient light from distant stars the objective is made large, -sometimes 50 in. in diameter. - -[Illustration: FIG. 396.--Formation of an image by a microscope. _A_-_B_ -is the object. _B´_-_A´_ the real image formed by the "objective." -_B´´_-_A´´_ is the virtual image formed by the eyepiece. The eye sees -the virtual image.] - -The length of the telescope tube depends upon the focal length of the -objective, since the distance between the two lenses must equal the -_sum_ of their focal lengths. - -[Illustration: FIG. 397.--Formation of an image by a telescope. _b_-_a_ -is the real image; _d_-_c_ is the virtual image seen by the observer.] - -=397. The opera glass= consists of a convex lens as objective and a -_concave_ lens as an eyepiece. The former tends to form a real image but -the latter diverges the rays before a real image can be formed, the -action of the two lenses producing an enlarged virtual image (as in Fig. -398) which is viewed by the one using the glass. The compact size of -the opera glass is due to the fact that the distance between the two -lenses is the _difference_ of the focal lengths. - -[Illustration: FIG. 398.--Formation of an image by an opera-glass. -_a_-_b_ is the virtual image.] - -[Illustration: FIG. 399.--Diagram of the Zeiss binocular or prism field -glass.] - -=398. The Prism Field Glass or Binocular.=--This instrument. has come -into use in recent years. It possesses the wide field of view of the spy -glass but is as compact as the opera glass. This compact form is secured -by causing the light to pass back and forth between two right-angle -prisms (as shown in Fig. 399). This device permits the use of an -objective lens with a focal length three times that of the tube, -securing much greater magnifying power than the short instrument would -otherwise possess. A further advantage is secured by the total -reflection from the two prisms, one of which is placed so as to reverse -the image right for left and the other inverts it, so that when viewed -in the eyepiece it is in its proper position. - - -Important Topics - -1. The eye: parts, formation of image, kind, how, where. - -2. Eye defects, how remedied. Visual angle. - -3. Simple microscope, camera; images, kind, how formed. - -4. Compound microscope, telescope and opera glass; images, action of -each lens. - - -Exercises - -1. Name three instruments in which lenses form virtual images and three -in which _real_ images are formed. - -2. In what direction is an oar in water apparently bent? Explain by a -diagram. - -3. What optical instruments have you used? Is the _visible_ image formed -by each of these _real_ or _virtual_? - -4. The focal length of a copying camera lens is 14 in. Where must a -drawing be placed so that an image of the same size may be formed upon -the ground glass screen? What must be the distance of the screen from -the lens? - -5. What are two methods by which you can determine the focal lengths of -the lens of a photographic camera? - -6. The critical angle for water is 48-1/2 degrees. Show by a diagram how -much of the sky can be seen by a diver who looks upward through the -water. - -7. How is near-sightedness caused? How is it corrected? Illustrate by a -diagram. - -8. How is the eye accommodated (focused) as an object gradually -approaches it? - -9. Explain why a simple microscope assists in looking at the parts of a -flower or insect. - -10. Why do people who have good eyesight when young require glasses as -they grow old? - - -(7) COLOR AND SPECTRA - -[Illustration: GUGLIELMO MARCONI - -"Copyright by Underwood & Underwood, N. Y." - -Guglielmo Marconi (Italy). Inventor of wireless telegraphy.] - -[Illustration: ALEXANDER GRAHAM BELL - -"Copyright by Underwood & Underwood, N. Y." - -Alexander Graham Bell, Washington, D. C. Inventor of the telephone.] - -=399. Color.=--Much of the pleasure experienced in gazing at beautiful -objects is due to the _color_ shown by them. The blue sky, the green -grass, and the varied tints of flowers, and of the rainbow all excite -our admiration The study of color begins naturally with the production -of the _spectrum_, the many-colored image upon a screen produced by -passing a beam of light through a prism. The spectrum is best shown when -the light enters by a narrow slit (Fig. 400). The spectrum was first -produced by Sir Isaac Newton in 1675 by the means just described. The -names usually given to the more prominent colors of the spectrum are -violet, indigo, blue, green, yellow, orange, and red. The initials of -these names, combined, spell _vibgyor_, a word without meaning except to -assist in remembering the order of the colors in a spectrum. If the -light that has passed through a prism is sent through a second prism -placed in reverse position (see Fig. 401), the light passing through -both prisms is found to be white. This experiment _indicates that white -light is composed of light of all colors_. - -[Illustration: FIG. 400.--Formation of the spectrum by a prism.] - -[Illustration: FIG. 401.--The colors of the spectrum recombine to form -white light.] - -=400. Dispersion.=--The separation of the colors by a prism is called -dispersion. In experimenting to find a reason for dispersion, it has -been learned that lights of different colors are of different wave -lengths. Color in light is therefore analogous to pitch in sound. We -hear through many octaves, but we see through about one octave. That is, -the shortest visible waves of violet light are about 0.000038 cm. in -length while the longest visible red rays are 0.000076 cm., or the -longest visible light waves are about twice the length of the shortest -visible ones. It appears from the evidence of experiments upon -dispersion that _light waves of different lengths are refracted -differently_. This causes the images formed by refraction through simple -glass lenses to be fringed with color and to lose some of their -sharpness and definiteness of outline, since the violet light is brought -to a focus sooner than the red. (See Fig. 402.) This seriously affects -the value of such lenses for optical purposes. Fortunately it is found -that _different kinds of glass have a different rate of dispersion for -the same amount of refraction_. - -[Illustration: FIG. 402.--Violet light comes to a focus sooner than -red.] - -=401. The Achromatic Lens.=--The existence of these different kinds of -glass makes possible a combination of lenses in which dispersion is -entirely overcome with the loss of only about one-half of the -refraction. Such a combination is shown in Fig. 403. It is called an -_achromatic lens_, since images formed by it are not colored but white -(_a_ = without, _chroma_ = color). _The achromatic lens consists of a -double convex lens of crown glass combined with a plano-concave lens of -flint glass._ Achromatic lenses are used in all high-grade optical -instruments such as telescopes and microscopes. The colored images that -are sometimes seen in cheap opera glasses show the result of not using -achromatic lenses. - -[Illustration: FIG. 403.--An achromatic lens. _C_ is of crown glass; -_F_, of flint glass.] - -=402. The Color of Bodies.=--Project the spectrum of sunlight upon a -white surface in a darkened room. - - Now place in different parts of the spectrum objects of various - colors. Red objects will show brilliant red when at the red end of - the spectrum but look black at the blue end, while blue objects - appear blue only at the blue end. - -These facts indicate that the color of an object depends upon two -things: (a) _the light that falls upon it and_ (b) _the light which it -sends to the eye_. A _black_ surface absorbs all color while a _white_ -one reflects all wave lengths to the eye in the same proportion that -they come to it. A white object will appear red in red light, and blue -in blue light since it reflects both of these. A _colored_ object -reflects light of its own color but absorbs all others. The color then -of a body is due to the light which it does not absorb, but which comes -from it to the eye. - -_403. The color of transparent bodies_, such as colored glass, is due to -the presence of a _dye_ or _pigment_ contained in the body. This pigment -absorbs a part of the light, the part transmitted giving the color. This -may be shown by holding a sheet of colored glass in a beam of light -either before or after it has passed through a prism. Some colors, as -red, may be found to be nearly _pure_, only the red passing through, -while green glass often transmits in addition to the green some yellow -and some red light. - -=404. Complementary Colors.=--If two prisms are placed in reversed -position near each other (see Fig. 401), a beam of light dispersed by -one is recombined into white light by the other. If now a card is held -between the two prisms so as to cut off some of the colored light, say -the red, the remaining light will be found to form a _greenish blue_. If -the card is removed, the light becomes _white_ again. That is, red and -_peacock blue_ light together form white. Any two colors that together -form white light are called _complementary_. Other complementary colors -are light yellow and blue, green and crimson, orange and greenish blue, -violet and greenish yellow. We must not confuse the combining of colors -(light) and the combining of _pigments_, the latter consisting of bodies -that absorb light. Yellow pigment absorbs all but yellow and some green, -while blue pigment absorbs all but blue and some green. Mixing these two -pigments causes the absorption of all colors but _green_. Blue and -yellow _paint_ mixed produce _green_, while blue and yellow _light_ give -white. - -=405. The solar spectrum=, as the spectrum of sunlight is called, may be -observed in the _rainbow_. The latter is produced through the dispersion -of light by spherical raindrops. Its formation may be imitated by -sending a small circular beam of light through a screen against a round -glass flask filled with water. (See Fig. 404.) The light passes through -the water and is dispersed when it enters and when it leaves, producing -a color upon the screen at _R_-_V_. The course of the light within the -drop is indicated in Fig. 405. The violet ray comes to the eye more -nearly horizontal and is therefore below red, as we look at the rainbow. - -=406. Fraunhofer Lines.=--Some of the most important features of the -solar spectrum are not seen in the rainbow or in the band of light -usually observed upon a screen. By the use of a narrow slit and a -convex lens to carefully focus the slit upon a white screen it is seen -that the solar spectrum is crossed by many _dark_ lines. These are -called Fraunhofer lines, to honor the German scientist who in 1814 first -accurately determined _their_ position. Two experiments _with a -spectroscope_ will help to make clear the meaning of the Fraunhofer -lines. - -[Illustration: FIG. 404.--A rainbow formed by a beam of light striking a -flask of water.] - -[Illustration: FIG. 405.--The course of a beam of light within a drop of -water.] - -=407. The Spectroscope and Its Uses.=--The spectroscope (Fig. 406) is an -instrument for observing spectra. It consists of a prism, a slit, and a -convex lens _T_ for focusing an image of the slit accurately upon a -screen (Fig. 407) where the spectrum is observed through the eyepiece -_E_. - -[Illustration: FIG. 406.--The spectroscope.] - -(A) A Bunsen flame is placed in front of the slit and a heated platinum -wire which has been dipped in common salt or some sodium compound placed -in the Bunsen flame; the latter becomes yellow and a vivid yellow line -is observed on the screen in the spectroscope. Other substances, as -barium and strontium salts, when heated to incandescence in the Bunsen -flame, give characteristic bright lines. In fact each _element_ has been -found to have its own characteristic set of colored lines. This fact is -made use of in _spectrum analysis_, by which the presence of certain -elements in a substance can be definitely proved upon the appearance of -its particular lines in the spectrum. - -[Illustration: FIG. 407.--Diagram of a spectroscope.] - -[Illustration: FIG. 408.--The bright line spectrum of iron and its -coincidences with some of the dark lines of the solar spectrum.] - -(B) If light from, for example, an arc light is sent over a gas flame -containing _sodium_ vapor, a _dark line_ appears in the spectrum--in -the exact position in which the yellow sodium line appeared. It seems -that the sodium vapor removes from white light the same wave lengths -that it itself produces. This absorption is supposed to be due to -sympathetic vibration; just as a tuning fork is set in vibration by the -waves of another fork in unison with it, at the same time absorbing the -wave energy, so in the gas flame the sodium particles absorb the wave -motion of the same vibration rate as that emitted by them. The fact that -the spectrum of sunlight contains a great many dark lines is believed to -indicate that the sun is surrounded by clouds formed by the vaporization -of the various substances in the sun itself. By comparing the dark lines -of the solar spectrum with the _bright-line spectra_ of various -substances found in the earth, such an exact correspondence of the lines -is found that the presence of the vapor of these substances about the -sun is considered proved. (See Fig. 408 which shows the exact -correspondence between the bright-line spectrum of iron vapor and the -dark lines appearing in a portion of the sun's spectrum.) The spectra of -the stars also contain certain dark lines. Thus the presence of the -corresponding substances in distant stars is considered as determined. - -=408. Theory of Color Vision.=--By combining light of the _three colors_ -_red_, _green_ and _blue-violet_ in proper proportions, it has been -found possible to produce any color effect, even white. This leads to -the conclusion that in the retina of the eye are three different kinds -or sets of sensitive nerve endings, sensitive respectively to red, to -green, and to blue light. This idea is given corroboration by some facts -of color blindness. Thus some persons have no sensation of _red_, this -color not being distinguished from green. Others are color blind to -green or blue. It is supposed that in color blind persons one of the -sets of nerve endings sensitive to one of these three colors is lacking. - -=409. Three-color Printing.=--Since all colors may be produced by mixing -the three colors, light red, green, and blue-violet, these are called -_the three primary colors_. The so-called primary pigments or paints are -simply the complements of the three primary colors. They are, in order, -peacock blue, crimson, and light yellow. The three pigments when mixed -yield black, since combined they absorb all kinds of visible light. The -process of three-color printing, now so generally employed in printing -colored pictures for books, calendars, etc., consists in combining upon -white paper three colored impressions, using successively the three -primary pigments (yellow, crimson and blue) from plates prepared as -follows: - -Three photographs of a given colored object are taken, each through a -different sheet of gelatine called a filter, stained the color of one of -the primary colors. From these photographs half-tone blocks are made in -the usual way. The colored picture is made by carefully superposing -impressions from these blocks, using in each case an ink whose color is -the complement of the "filter" through which the original picture was -taken. An illustration of the process is given upon the plate in the -frontispiece of this book. - - -Important Topics - -1. Color, due to wave length; dispersion by prism, sphere in rainbow, -complementary colors, color of opaque and transparent bodies. - -2. Spectra, solar; formation of rainbow; bright-line spectra, how -formed, how used; dark-line, how formed, used. - -3. Theory of color vision. Three color printing. - - -Exercises - -1. How does a white flower look when viewed through a blue glass? -Through a red glass? Through a red and blue glass at the same time? - -2. Why does a red ribbon appear black when seen by blue light and red -when seen by red light? - -3. In what part of the sky must you look to see a rainbow in the -morning? In the afternoon? Explain. - -4. How would you arrange two similar prisms so as to produce double the -deviation produced by one? - -5. The color of an object depends upon what two things? - -6. What kind of a spectrum should moonlight give? Why? - -7. A mixture of green and red lights gives a sensation of yellow. Can -you suggest why a mixture of blue and yellow lights gives the sensation -of white? - - -(8) NATURE OF LIGHT, INTERFERENCE, POLARIZATION - -=410. The Corpuscular Theory.=--The theory of the nature of light that -was most generally accepted until about the year 1800, held that light -consists of streams of minute particles, called corpuscles, moving at -enormous velocities. This _corpuscular theory_ was in accord with the -facts of reflection and the _rectilinear_ motion of light, but was -abandoned after the discovery of the _interference of light_, as it -could not account for the latter phenomenon. - -=411. The Wave Theory of Light.=--The theory that _light is_ a _form of -wave motion_ was first advanced by Huygens, a Dutch physicist, in the -seventeenth century. This theory was opposed at the start since (A) _no -medium_ was known to exist which would convey wave motion through space, -as from the sun to the earth, and (B) the _rectilinear motion_ of light -was _unlike_ that of any _other_ form of known wave motions, such as -that of water or of sound waves which are able to bend around corners. -In answer to the first objection, Huygens assumed the presence of a -medium which he named _ether_, while the second objection has been -completely overcome during the past century by the discovery that _light -may deviate from a straight line_. It is now known that the _excessive -shortness_ of light waves is the reason for its straight-line motion. -Further, long ether waves, as those of wireless telegraphy, are found to -bend around obstacles in a manner similar to those of water or sound. - -[Illustration: FIG. 409.--Two plates pressed together by a screw clamp.] - -[Illustration: FIG. 410.--Illustrating the interference of light by a -thin film of air.] - -=412. The interference of light= is one of the phenomena for which the -wave theory offers the only satisfactory explanation. Interference of -light may be shown by taking two pieces of plate glass and forcibly -pressing them together by a screw clamp, as shown in Fig. 409. After a -certain pressure has been reached, colored rings will appear about the -compressed spot when viewed by light _reflected_ from the upper surface -of the glass. If light of one color, such as that transmitted by red -glass, falls upon the apparatus, the rings are seen to be alternately -red and dark bands. The explanation of this phenomenon according to the -wave theory is as follows: The two sheets of glass, although tightly -pressed together, are separated in most places by a thin wedge of air -(see Fig. 410), which represents in an exaggerated form the bending of -the plates when pressed by the clamp. Several waves are represented as -coming from the right and entering the glass. Now the wave moving from -_R_ to the plates has some of its light reflected from each glass -surface. Consider the two portions of the wave reflected at each of the -surfaces between the plates, _i.e._, from the two surfaces of the wedge -of air. If the portion of the wave reflected from the second surface of -the air wedge combines with that reflected from the first surface, in -the _same phase_ as at _C_, the two reflected waves strengthen each -other. While if the two reflected portions of the wave meet in opposite -phases as at _A_ and _B_, a decrease or a complete extinction of the -light results. This is called _interference_. If light of one wave -length is used, as red light, the regions of reinforcement and -interference are shown by red and dark rings, while if white light is -used, the ring where red light interferes, yields its complementary -color, greenish blue. Where interference of greenish blue occurs, red is -found, etc. Many phenomena are due to interference, such as (A) the -color of thin films of oil on water, where the portions of light -reflected from the two surfaces of the oil film interfere resulting in -the production of color; (B) the color of soap bubbles. When first -formed, soap-bubble films are not thin enough to show interference well, -but as the bubbles increase in size or become thinner on standing, the -conditions for interference are reached and, as the film becomes -thinner, a regular succession of colors is noticed. - -=413. Differences Between Light and Sound.=--Among the important -differences between light and sound that have been considered are the -following: the former are (a) _waves_ in the ether, (b) _of very short -wave length_, and (c) their _motion is in straight lines_. Another -difference (d) is in _the mode of vibration_. - -Sound waves are _longitudinal, while light waves are transverse_. Light -waves consist of vibrations of the ether at right angles to the line of -motion. To illustrate the reasoning that has led to this conclusion, -suppose a rope to be passed through two vertical gratings. (See Fig. -411, 1.) If the rope be set in _transverse_ vibration by a hand, the -waves produced will readily pass through to the gratings _P_ and _Q_ and -continue in the part extending beyond _Q_. If, however, _Q_ is at right -angles to _P_, no motion will be found beyond _Q_. Now if a stretched -coiled spring with longitudinal vibrations should take the place of the -rope, it is evident that the crossed position of the two gratings would -offer no obstacles to the movement of the vibration. In other words, -crossed gratings offer no obstruction to longitudinal vibrations, while -they may completely stop transverse vibrations. - -[Illustration: FIG. 411.--Transverse waves will pass through both -gratings in (1) where the openings in the two gratings are at right -angles. The waves passing _P_ are stopped by _Q_ (2).] - -[Illustration: FIG. 412.--Effect of tourmaline crystals on light.] - -=414. Polarization of Light.=--It is found that two crystals of -tourmaline behave toward light just as the two gratings behave with -respect to the transverse waves of the rope. Thus, if a small opening in -a screen is covered with a _tourmaline_ crystal, light comes through but -slightly diminished in intensity. If a second crystal is placed over the -first one so that the two axes are in the same direction as in Fig. -412_P_, light is as freely transmitted through the second crystal as -through the first, but if the crystals are crossed (Fig. 412_S_) no -light passes the second crystal. This experiment shows that the light -which has passed through one tourmaline crystal will pass through -another only when the latter is held in a certain position, hence it is -believed that a tourmaline crystal is capable of transmitting light -that is vibrating in one particular plane. The direct conclusion from -this is that _light waves_ are _transverse rather than longitudinal_. -The experiment just described illustrates what is called _polarization -of light_. The beam that after passing through _a_ (Fig. 412) is unable -to pass through _b_, if the two axes are crossed, is called a _polarized -beam_. The conclusion that light waves are transverse is therefore based -upon the phenomenon of the polarization of light. This was first -discovered by Huygens in 1690. - - -Important Topics - -1. Interference of light: evidence, reasoning involved, illustration. - -2. Polarization of light: evidence, reasoning involved. - -3. Nature of light, differences between sound and light. - - -Exercises - -1. Make a list of the differences between sound and light and state -briefly the evidence upon which the knowledge of these differences is -based. - -2. Why will a thickness of film that will produce interference of red -light be different from that producing interference for green or blue? - -3. Using the formula _n_ = _v_/_l_ compute the vibration rate for violet -light if its wave length is considered as 0.00004 cm. - -4. Explain how the fact of polarization affects the wave theory of -light. - -5. Show how it is possible by comparing the spectrum of the sun with -that of a star to tell whether the star is approaching or receding from -the earth. - - -Review Outline: Light - -Light; speed, source, medium. - -Straight Line Motion; shadow, umbra, penumbra, eclipse, image. - -Photometry; Law of intensity, candle power, foot-candle. - -Mirrors; Law of reflection; image--real, virtual; plane, curved, -parabolic, mirrors. - -Refraction; cause and effects; plate, prism, lens; total reflection. - -Lenses; six forms, principal focus, center, lens equation, 1/_F_ = -1/_D_{o}_ + 1/_D_{i}_. - -Optical instruments; eye, defects and correction, camera, microscope, -etc. - -Spectra; 3 kinds, dispersion, production of color effects, spectroscope, -uses. - -Nature of Light; wave theory, interference, polarization, significance. - - - - -CHAPTER XVII - -INVISIBLE RADIATIONS - - -(1) ELECTRIC WAVES AND RADIO-ACTIVITY - -=415. Oscillatory Nature of the Spark from a Leyden Jar.=--In studying -sound (Art. 339), the sympathetic vibration of two tuning forks having -the same rate of vibration was given as an illustration of resonance. -The conditions for obtaining _electrical resonance_ by the use of two -Leyden jars are given in the following experiment. - - Join the two coats of a Leyden jar (Fig. 413) to a loop of wire - _L_, the sliding crosspiece _M_ being arranged so that the length - of the loop may be changed as desired. Also place a strip of - tinfoil in contact with the inner coating and bring it over to - within about a millimeter of the outer coating as indicated at _G_. - Now join the outer coating of another exactly similar jar _A_ to a - wire loop of fixed length, the end of the loop being separated from - the knob connected to the inner coating, a short distance at _P_. - Place the jars near each other with the wire loops parallel and - connect coatings of _A_ to the terminals of a static machine or an - induction coil. At each discharge between the knobs at _P_, a spark - will appear in the other jar at _G_, if the crosspiece _M_ is so - adjusted that the areas of the two loops are exactly equal. When - the wire _M_ is moved so as to make the areas of the two loops - quite unequal, the spark at _G_ disappears. - -[Illustration: FIG. 413.] - -The experiment just described shows that two electrical circuits can be -_tuned_ by adjusting their lengths, just as two tuning forks may be -made sympathetic by adjusting their lengths. This fact indicates that -the discharge of the Leyden jar is _oscillatory_, since resonance can -plainly not be secured except between bodies having natural periods of -vibration. This same fact is also shown by examining the discharge of a -Leyden jar as it appears when viewed in a rapidly revolving mirror. (See -Fig. 414.) The appearance in the mirror shows that the discharge is made -up of a number of sparks, often a dozen or more, vibrating back and -forth until they finally come to rest. The time of one vibration varies -from one millionth to one hundred millionth of a second, depending on -the space between the discharging balls and the size of the jars. - -[Illustration: FIG. 414.--Photograph of the oscillatory discharge of a -Leyden jar.] - -The discharge of a Leyden jar or of another condenser sets up ether -waves that have the speed of light. Heinrich Hertz in Germany first -proved this in 1888. These waves are now known as Hertzian waves. The -length of these varies from 3 cm. to several miles, depending upon the -size and conditions of the discharging circuit. - -[Illustration: FIG. 415.--A coherer.] - -=416. The Coherer.=--The coherer is a device for detecting electric -waves. It consists of a glass tube with metal filings loosely packed -between two metal plugs that fit the tube closely. (See Fig. 415.) These -filings offer a _high_ resistance to the passage of an electric current, -but when electric waves pass through the filings these _cohere_ and -allow a weak current to pass through. This current may be strong enough -to operate a relay connected with a sounder or bell that gives audible -signals. If the tube be tapped the filings will be disturbed and the -resistance again made so high that no current can pass through. - -=417. Wireless Telegraphy.=--In 1894 Marconi, then a young man of -twenty, while making some experiments with electrical discharges -discovered that the coherer would detect electrical waves at a -considerable distance from their source and that by the use of a -telegraph key the "dots and dashes" of the telegraph code could be -reproduced by a sounder attached to a relay. At present the coherer is -used principally in laboratory apparatus, as much more sensitive -detectors are now available for commercial work. The essential parts of -a modern wireless telegraph apparatus as used in many commercial -stations are shown in Fig. 416. - - Alternating current at 110 volts is sent into the primary, _P_, of - a transformer, the secondary, _S_, of which produces a potential of - 5000 to 20,000 volts. The secondary charges a condenser until its - potential becomes high enough to produce a discharge across a spark - gap, _SG_. This discharge is oscillatory, the frequency being at - the rate of about one million a second, depending upon the capacity - of the condenser and the induction of the circuit. - - These oscillations pass through the primary of the oscillation - transformer, inducing in the secondary, electric oscillations which - surge back and forth through the antennæ, or aerial wires, _A_. - These oscillations set up the "wireless waves." The production of - these waves is explained as follows: An electric current in a wire - sets up a magnetic field spreading out about the conductor; when - the current stops the field returns to the conductor and - disappears. The oscillations in the antennæ, however, have such a - high frequency, of the order of a million a second, that when one - surge of electricity sets up a magnetic field, the reverse surge - immediately following sets up an opposite magnetic field before the - first field can return to the wire. Under these conditions a - succession of oppositely directed magnetic fields are produced - which move out from the antennæ with the speed of light and induce - electric oscillations in any conductors cut by them. - -[Illustration: FIG. 416.--Diagram of a commercial wireless telegraph -apparatus.] - - While the electric waves are radiated in all directions from the - aerial, the _length_ of the waves set up is approximately four - times the combined length of the aerial wires and the "lead in" - connection to the oscillation transformer. - - The electric waves induce effective electrical oscillations in the - aerial of the receiving station, even at distances of hundreds of - miles, provided the receiving transformer, _RT_, is "tuned" in - resonance with the transmitting apparatus by adjustments of the - variable condenser, _VC_, and the loading coil, _L_. The _detector_ - of these oscillations in the receiving transformer is simply a - crystal of silicon or carborundum, _D_, in series with two - telephone receivers, _Ph_. The crystal detector permits the - electric oscillations to pass through it in one direction only. If - the crystal did not possess this property, the telephone could not - be used as a receiver as it cannot respond to high frequency - oscillations. While one spark passes at _SG_, an intermittent - current passes through the receiver in one direction. Since some - 300 to 1200 sparks pass each second at _SG_ while the key, _K_, is - closed, the operator at _Ph_ hears a musical note of this frequency - as long as _K_ is depressed. Short and long tones then correspond - to the dots and dashes of ordinary telegraphy. In order to maintain - a _uniform tone a rotary spark gap_, as shown, is often used. This - insures a tone of fixed pitch by making uniform the rate of - producing sparks. - -The _Continental_ instead of the _Morse_ code of signals is generally -employed in wireless telegraphy, since the former employs only _dots_ -and _dashes_. The latter code employs, in addition to dots and dashes, -_spaces_ which have sometimes caused confusion in receiving wireless -messages. The United States government has adopted the regulations of -the _International Radio Congress_ which directs that commercial -companies shall use wave lengths between 300 and 600 or above 1600 -meters. Amateurs may use wave lengths less than 200 meters and no -others, while the government reserves the right to wave lengths of 600 -to 1600 meters. See p. 459 for Continental telegraph code. - -=418. Discharges in Rarefied Air.=--Fig. 417 represents a glass tube 60 -or more centimeters long, attached to an air pump. Connect the ends of -the tube to the terminals of a static machine or of an induction coil, -_a-b_. At first no sparks will pass between _a_ and _f_, because of the -high resistance of the air in the tube. Upon exhausting the air in the -tube, however, the discharge begins to pass through it instead of -between _a_ and _b_. This shows that an electrical discharge will pass -more readily through a partial vacuum than through air at ordinary -pressure. As the air becomes more and more exhausted, the character of -the discharge changes. At first it is a faint spark, gradually changing -until it becomes a glow extending from one terminal to the other and -nearly filling the tube. - -[Illustration: FIG. 417.--An Aurora tube.] - -_Geissler tubes_ are tubes like the above. They are usually made of -different kinds of glass twisted into various shapes to produce -beautiful color effects. The _aurora borealis_ or northern light is -supposed to be electric discharges through rarefied air at the height of -from 60 to 100 miles above the earth's magnetic poles. (See Fig. 418.) - -[Illustration: FIG. 418.--Aurora Borealis.] - -=419. Cathode Rays.=--When the tube in Art. 420 is exhausted to a -pressure of 0.001 mm., or a little less than one millionth of an -atmosphere, the character of the discharge is entirely changed. The -tube becomes filled with a yellowish green phosphorescent light. This is -produced by what are called cathode rays striking the glass walls of the -tube. These rays are called cathode rays because they come from the -cathode of the tube. They are invisible and that they travel in straight -lines is shown by the shadow obtained by using a tube with a screen -(Fig. 419). - -[Illustration: FIG. 419.--A cathode ray tube.] - -=420. "X" Rays.=--In 1895, Professor Röntgen of Wurtzburg, Germany, -discovered that when the cathode rays strike the walls of the tube or -any solid within it they excite a form of invisible radiation. This -radiation is called Röntgen rays, or more commonly, "X" rays. Careful -experiments show that they travel in straight lines, and that they can -not be reflected or refracted as light waves are. They pass through -glass and opaque objects such as flesh, cardboard, cloth, leather, etc., -but not through metallic substances. The tube in Fig. 420 has a screen -covered with crystals which become luminous when struck by the cathode -rays. On bringing a magnet near the tube the luminous line is raised or -lowered showing that the magnetic field affects the stream of cathode -rays, attracting it when in one position but repelling it when in the -reverse direction. The cathode rays which cause the bright line possess -a negative charge of electricity. They are now believed to be electrons -shot off from the surface of the cathode with speeds that may reach -100,000 miles a second. "X" rays possess no electrical charge whatever -and cannot be deflected by a magnet. They produce the same effect on a -photograph plate as light does, only more slowly. Hence, they can be -used in taking "X" ray photographs. Certain crystals, like barium -platinum cyanide, fluoresce when struck by the "X" rays. The -_fluoroscope_ is the name given to a light-tight box closed at one end -by a cardboard covered with these crystals (Fig. 421). On looking into -the fluoroscope with an opaque object such as the hand placed between -the screen and the "X" ray tube, a shadow of the bones of the hand can -be seen upon the screen of the fluoroscope. (See Fig. 422.) - -[Illustration: FIG. 420.--The stream of cathode rays is deflected by a -magnet.] - -[Illustration: FIG. 421.--A fluoroscope.] - -[Illustration: FIG. 422.--A view of the "shadow" of a hand as seen in a -fluoroscope.] - -A special form of the tube is used. (See Fig. 423.) In this tube a -platinum disc is placed at the focus of the concave cathode. This -concentrates the "X" rays in one direction. It is now generally believed -that "X" rays are waves in the ether set up by the sudden stoppage of -the cathode rays at the platinum anode. - -[Illustration: FIG. 423.--An "X" ray tube.] - -=421. The Electromagnetic Theory of Light.=--The study of electric waves -has shown that they are similar to light waves in many respects: (a) -they have the same velocity; (b) they can be reflected and refracted. -The main difference is in their length, light waves being very much -shorter. In 1864 James Clerk Maxwell, an English physicist, proposed the -theory that ether waves could be produced by electrical means and that -light waves are electromagnetic. In 1888 Hertz proved by his experiments -that ether waves having the same velocity as light could be produced in -this way. It is now the general belief that light waves are ether waves -produced by the vibrations of the electrons within the atoms and that -they consist of electromagnetic waves in the ether. - -=422. Radio-activity.=--In 1896 Henri Becquerel of Paris discovered that -uranium and its compounds emit a form of radiation that produces an -effect upon a photographic plate that is similar to that resulting from -the action of "X" rays. These rays are often called _Becquerel_ rays in -honor of their discoverer. The property of emitting such rays is called -=radio-activity=, and the substances producing them are called -=radio-active=. - -In 1898, Professor and Mme. Curie after an investigation of all the -elements found that _thorium_, one of the chief constituents of -incandescent gas mantles, together with its compounds, was also -radio-active. This may be shown by the following experiment: - - Place a flattened gas mantle upon a photographic plate and leave in - a light tight-box for several days. Upon developing the plate in - the usual way a distinct image of the mantle will be found upon the - plate. - -=423. Radium.=--Mme. Curie discovered also that pitch-blende possessed -much greater radio-active power than either thorium or uranium. After -prolonged chemical experiments she obtained from several tons of the ore -a few milligrams of a substance more than a million times as active as -thorium or uranium. She called this new substance _radium_. Radium is -continually being decomposed, this decomposition being accompanied by -the production of a great deal of heat. It has been calculated that it -will take about 300 years for a particle of radium to be entirely -decomposed and separated into other substances. It is also believed that -radium itself is the product of the decomposition of uranium, atomic -weight 238, and that the final product of successive decompositions may -be some inert metal, like lead, atomic weight 207. - -The radiation given off by radio-active substances consists of three -kinds: (A) Positively charged particles of helium called _alpha_ rays: -(B) negatively charged particles called _beta_ rays: (C) _gamma_ rays. - -The alpha rays have little penetrating power, a sheet of paper or a -sheet of aluminum 0.05 mm. stopping them. Upon losing their charges they -become atoms of helium. Their velocity is about 1/10 of that of light or -18,000 miles a second. The _spinthariscope_ is a little instrument -devised by Sir Williams Crookes in 1903 to show direct evidence that -particles are continually being shot off from radium. In this instrument -(Fig. 424), a speck of radium _R_ is placed on the under side of a wire -placed a few millimeters above a screen _S_ covered with crystals of -zinc sulphide. Looking in the dark at this screen through the lens _L_, -a continuous succession of sparks is seen like a swarm of fireflies on a -warm summer night. Each flash is due to an alpha particle striking the -screen. The beta rays are supposed to be cathode rays or electrons with -velocities of from 40,000 to 170,000 miles a second. The gamma rays are -supposed to be "X" rays produced by the beta rays striking solid -objects. - -[Illustration: FIG. 424.--A spinthariscope.] - -=424. The discovery of radio-activity= has revolutionized the ideas of -the constitution of matter. Further, the results of experiments upon -radio-active materials reveals the presence of immense quantities of -sub-atomic energy. If man ever discovers a means of utilizing this, he -will enter a storehouse of energy of far greater extent and value than -any of which he has as yet made use. A consideration of this unexplored -region gives zest to the work of those who day by day are striving to -understand and control forces of nature. - - -Important Topics - -1. Oscillatory nature of discharge of Leyden jar. Proofs. - -2. Wireless telegraphy and telephony. - -3. Electrical discharges in rarefied gases. - -4. Cathode and "X" rays. - -5. Electromagnetic theory of light. - -6. Radio activity and radium. - -[Illustration: CONTINENTAL TELEGRAPH CODE - - A . - J . - - - S . . . - B - . . . K - . - T - - C - . - . L . - . . U . . - - D - . . M - - V . . . - - E . N - . W . - - - F . . - . O - - - X - . . - - G - - . P .- - . Y - . - - - H . . . . Q - - . - Z - - . . - I . . R . - . - - PERIOD INTERROGATION EXCLAMATION - . . . . . . . . - - . . - - . . - - - - 1 . - - - - 2 . . - - - 3 . . . - - - 4 . . . . - 5 . . . . . 6 - . . . . 7 - - . . . - 8 - - - . . 9 - - - - . 0 - - - - -] - - - - -CHAPTER XVIII - -WIRELESS TELEPHONY AND ALTERNATING CURRENTS - - The developments in wireless communication have been so rapid - during recent years that a more extended account, than that given - in Art. 417 of the apparatus and methods used at the present time, - seems desirable. The study of Alternating Currents is also included - with the idea that it will make the text more complete and of wider - usefulness. - - -WIRELESS TELEPHONY - -=425. The Wireless Telephone.=--One of the most important developments -in wireless communication in recent years has been in wireless -telephony. We realize its possibilities, when we hear of the -achievements of talking across an ocean or between airplanes and the -ground. - -The wireless telephone can be best understood by comparing it with the -common telephone. When the latter is in use, a direct current flows -continually through the instrument. (See Arts. 312-316.) When a person -speaks into the transmitter, the sound waves of the voice cause the -diaphragm to vibrate, this action causes rapid changes in the -_resistance_ of the transmitter, which in turn causes the direct current -to fluctuate just in step with the pulses of the voice waves. This -fluctuating direct current passes through the primary of an induction -coil, producing in the secondary an intensified alternating current. -This passes over the line wires to the receiver where it produces -variations in the magnetic field affecting the receiver diaphragm, -causing the latter to reproduce the voice of the person speaking in the -transmitter. Now to make the comparison clear, two facts must be noted -with regard to the wire telephone: first, there must be an action in the -transmitter which causes variations in a current through the instrument; -second, this fluctuating current produces a more intense alternating -current which flows over the line and affects the receiver diaphragm, -producing there sound vibrations of greater intensity than those used at -the transmitter. This added energy comes from the current flowing -through the transmitter. The case is analogous to that of an electric -bell. The armature of the bell vibrates with greater energy than is -required to push the button, the extra energy being derived from the -battery. - -=426. The Action of the Wireless Telephone.=--In the wireless telephone -we have a continuous stream of electric waves of high frequency. (See -Fig. 425_A_.) This stream of electric waves corresponds to the current -that flows through the transmitter in the wire telephone. These waves -are of such high frequency that even though we had a receiver diaphragm -vibrating in step with the waves, we could not hear the sound because -the human ear cannot hear a sound which consists of more than about -40,000 vibrations per second. The sound waves act upon this stream of -waves very much, as in the wire telephone, the transmitter acts to -modify the line current. The impulses caused by the voice are much -slower than the electric waves first mentioned and these slower impulses -are reproduced in the receiver. Not only are these slower impulses -reproduced but they are _amplified_, that is, produced with greater -energy than the impulses impressed on the stream of waves. Fig. 425_A_ -represents as nearly as is possible in a diagram the continuous stream -of electric waves. Fig. 426_B_, represents the impulses produced by the -sound alone, and Fig. 426_C_, shows how these voice impulses are -impressed on the stream of waves. - -[Illustration: FIG. 425.--_A_, unmodified high frequency waves; _B_, -waves of voice frequency; _C_, high frequency waves modified by waves of -voice frequency.] - -[Illustration: FIG. 426.--Vacuum tube, transmitting type. (_Western -Electric Co._)] - -[Illustration: FIG. 427.--Vacuum tube, receiving type. (_Western -Electric Co._)] - -[Illustration: FIG. 428.--Diagram of wireless telephone transmitting -set.] - -=427. The Vacuum Tube or Audion.=--The device by which all of this is -accomplished is the _vacuum tube_. (See Fig. 426.) This tube contains -three electrodes. _First_, a _filament_ (_F_, in Fig. 428) which is -heated by a current from a battery (_B_{1}_, Fig. 428) and because it is -heated, sends out a stream of electrons. _Second_, the _plate_ which -forms the anode of the circuit from battery, _B_{2}_. This plate -receives the electrons which are thrown off by the heated filament, -hence a current flows through the circuit of _B_{2}_; the discharge -through the tube depending on the e.m.f. between the filament and the -plate. _Third_, a _grid_ is placed between the filament and the plate -and is connected to the _secondary_ of the induction coil, the primary -of which is connected to the transmitter. When the transmitter diaphragm -is vibrating, the e.m.f. induced in the secondary of the induction coil -causes a variation in the potential of the grid. This means a variation -in the electric field between the filament and the plate. (See Fig. -428.) The changing electric field causes a variation in the discharge of -electrons through the tube; the variation corresponds to the vibrations -of the transmitter diaphragm. This produces a surging current of the -frequency of the sound waves in the primary of the transformer (_T_, -Fig. 428). The secondary of this transformer is connected to the antennæ -(_A_) and the earth (_E_). By means of the transformer, rapid surgings -are set up in the antennæ and these surgings produce a continuous stream -of electromagnetic waves which goes out in space. (Like Fig. 426_C_.) -These electromagnetic waves produce oscillations in the antennæ of a -receiving station. The antennæ transmit the impulses to a _tube_ (Fig. -427) which acts as a _detector_, and makes possible the reproduction of -the sound by an ordinary telephone receiver. - -[Illustration: FIG. 429.--View of wireless telephone set.] - -The _vacuum tube_ in the transmitting circuit also _amplifies_ the -impulses, that is, the energy of the waves given out is greater than -that of the impulses which produce them, the additional energy being -derived from the battery sending current through the plate and filament. -In operation, the filament and the plate are connected to a battery with -a _condenser_ (_VC_) and an _inductance coil_ (_I_) in the circuit, as -shown in Fig. 428. Photograph of a complete modern wireless telephone -set is shown in Fig. 429. - - -ALTERNATING CURRENTS - -=428. Alternating currents= are of interest to us because of their -general commercial use. To understand the reason for the extensive -application of alternating currents it is necessary to learn the -fundamental principles which pertain to them. The production of such -currents has already been explained in Arts. 300-304. It should be -remembered that the current developed in the armature of a dynamo is -alternating. A dynamo may _deliver_ a direct or an alternating current, -depending on the method of collecting the current from the armature. If -a _commutator_ is used, the machine delivers _direct_ current, if _slip -rings_ are employed, an _alternating_ current is delivered. - -=429. The Magnetic Field of an Alternating Current.=--The magnetic field -of a direct current has been considered in Arts. 255-256. It has been -shown to be arranged in circles about the conductor, according to the -_Right Hand Rule_. (See Figs. 229 and 230.) These facts will help one to -understand the following experiment: - - If a number of magnetic compasses be arranged in a circle about a - straight vertical wire carrying a direct current, the compass - needles will point out a circle about the wire. (See Fig. 430, - _A_.) If now the current be reversed the compass needles will - reverse themselves and point in a direction just opposite to that - taken at first. (See Fig. 430, _B_.) This will be clear if you - imagine yourself walking around the wire in the direction the - compass needles pointed at first, and then walking around the wire - in the reverse direction. This illustrates what happens in the - field of an alternating current. The field reverses each time the - current reverses. - -The magnetic field of an alternating current not only rapidly reverses -itself, but also continually _changes in intensity_. At the instant when -the current reverses, the force of the magnetic field is zero since the -current at that instant is zero. As the current begins flowing and -increases to its maximum intensity, the magnetic field appears and -increases in intensity; and as the current decreases to zero, the -magnetic field changes in a similar manner. The field as it grows in -strength extends farther and farther from the wire, as it decreases in -strength it contracts or draws closer to the wire. Thus the magnetic -field may be said to expand and contract. We may picture the lines of -force as continually moving. In a typical a.-c. circuit, the complete -series of changes takes place in a small fraction of a second, and is -repeated many times over in a second. Contrast this with the magnetic -field of a constant direct current. Here the magnetic field has the same -direction as long as the current flows and does not change in strength. -This comparison is important because most of the differences between -direct and alternating currents depend on differences in the action of -their magnetic fields. - -[Illustration: FIG. 430.--Arrangement of compasses about a wire carrying -an alternating current.] - -=430. Transformers.=--The transformer has been described in Arts. -309-310. The principle of the transformer may be illustrated by the -following experiment: - - A coil having several hundred turns of No. 18 d.c.c. copper wire is - placed over one arm of a "U" shaped iron core (see Fig. 431) and - then connected to a 110 volt a.-c. lighting circuit. Another coil - (_S_) having about 50 turns of No. 22 d.c.c. copper wire is - connected to an electric bell or buzzer, or a low voltage electric - light bulb. When the small coil is held over the other arm of the - "U" shaped iron core, the bell rings or the bulb glows. It is - evident that the electromotive force developed in the small coil - (_S_) is due to the alternating magnetic field surging back and - forth through the iron core. In Fig. 431 the core is "open" since - the magnetic field must pass through the air from one end of the - core to the other. A typical transformer has a _closed core_ to - provide a _closed magnetic circuit_. To secure this, take a - suitable bar of iron and lay across the end of the "U" shaped core, - and notice any change in the induced current produced in the small - coil, due to increased movement of magnetism through the closed - iron core. - -[Illustration: FIG. 431.--Diagram of a transformer.] - -This experiment illustrates the construction and action of a -transformer. In a commercial transformer, the two windings are on a -closed magnetic circuit. (See Figs. 304 and 305, p. 346.) To keep the -coils insulated, the transformer is placed in an iron "housing" and -covered with oil. These "housings," or transformer cases are generally -attached to poles near buildings in which alternating current is used. - -=431. Voltage Relation in a Transformer.=--In the experiment described -above, a bell was rung by an induced current produced in the secondary -coil. The induced e.m.f. was less than the voltage of the primary coil -partly because there was some magnetic leakage, but mainly because -there were fewer turns of wire on the secondary. In a commercial -transformer the magnetic leakage is practically zero. In such a case, -the ratio of the number of turns on the primary coil to the number on -the secondary equals the ratio of the e.m.f. induced in the primary to -the e.m.f. induced in the secondary. Suppose, for example, we wish to -make a bell ringing transformer to use on a 110 volt lighting circuit, -10 volts being required for the bell; the secondary will then need -one-eleventh of the number of turns of the primary. So that if 550 turns -are on the primary, then 50 turns will be needed for the secondary. This -will be a "step-down" transformer. On the other hand, suppose we wish to -"step-up" the voltage as is done in a certain power station where the -voltage of the generators is 6000 volts, the voltage being stepped up to -44,000 by means of large transformers. This means that the secondary -coils have approximately 7-1/3 times as many turns as the primary. - -=432. Power Loss in a Transformer.=--When the voltage is "stepped up" in -a transformer, do we gain power? To answer this question we must -remember that electric power does not depend on voltage alone but on the -_product_ of e.m.f. and current intensity. (See Art. 291.) By tests with -a.-c. voltmeters and ammeters, we find that when the secondary e.m.f. is -_greater_ than the primary e.m.f., the secondary current intensity is -_less_ than that in the primary. It is also found that the _power_ -developed is less than the power received by the transformer, _i.e._, -the "output" is less than the "input" as we would expect from the law of -machines. The power loss is mainly due to the work required to reverse -the magnetism, that is, to continually reverse the position of the iron -molecules. (See Art. 205.) The energy lost in this manner is known as -"core loss" since it occurs in the iron core. The lost energy appears -as heat. So much heat is developed in large transformers that special -means of cooling are provided. In order to make the heat developed as -small as possible, the cores are "laminated" (see Fig. 305, p. 346), -that is, built up of thin sheets of iron, because if the iron cores were -solid, the changing magnetic fields would induce electric currents in -the iron cores, which would produce an excessive amount of heat with a -correspondingly large power loss. - -[Illustration: FIG. 432.--Diagram of "bell-ringing" transformer.] - -=433. Choke Coils and Inductance.=--If we refer to Fig. 432 we see that -the primary winding of the bell ringing transformer is connected across -the line. This winding forms a closed circuit whether the bell is -ringing or not. The resistance of this winding is small. Let us assume -it to be one ohm. With a one ohm resistance connected across a 110 volt -line we might expect a current of 110 amperes. This is certainly what we -should get if we were to connect a one ohm resistance across a line -having 110 volts direct. The primary would form a short circuit if the -current were direct. But the fact is that practically no current flows -through the primary winding when the bell is not ringing. Herein lies -one of the important differences between alternating and direct -currents. With an alternating current the primary winding of our -transformer acts as a _choke coil_ and "chokes" down the current almost -to zero. Let us see how this is done. - -[Illustration: FIG. 433.--A circuit containing a choke coil.] - -Let Fig. 433 represent a choke coil. Since alternating current is used, -the magnetic field is continually changing. Each turn of wire has its -own magnetic field. The lines of force of turn number 1 expand and -contract and as they do so they move across turns 2, 3 and so on. In -like manner the lines of force from each turn of wire move across the -other turns. In other words the coil is cutting its own lines of force. -Now whenever an electric conductor cuts magnetic lines of force an -electromotive force is induced in the conductor. There is then an e.m.f. -induced in the coil by its own magnetic field. This induced e.m.f. on -the whole opposes the applied e.m.f.; in the primary of our bell ringing -transformer the induced e.m.f. opposes the e.m.f. of the line to such an -extent as to reduce the current almost to zero. _Inductance_ is the -action of an alternating current in inducing an opposing e.m.f. in the -coil in which the current is flowing. Since this opposing e.m.f. is -induced in the coil by its own magnetic field this action is also called -_self-induction_. In a transformer the action of the field of the -primary upon the secondary is _mutual induction_; while the action of -the field of the primary in choking the current in the primary itself is -self-induction or inductance. A coil having a single winding and used to -introduce inductance in a circuit is called a _choke coil_. A choke -coil inserted in a lamp circuit in series with the lamps dims the lamps -because it reduces the intensity of the current. - -[Illustration: FIG. 434.--Diagram showing graphically an alternating -current with a "lag" of 30° behind its electromotive force.] - -Self-induction causes the current to _lag_, that is, the current does -not quite reach its maximum at the instant the voltage reaches its -maximum. Fig. 434 shows graphically an e.m.f. and a lagging current. In -this figure the maximum current is shown following the maximum voltage -at an interval of 30 degrees. In other words the armature in a two-pole -field must turn 30 degrees from the position of maximum voltage before -the current in the coil, where the self-induction occurs, reaches its -maximum. - -=434. Reactance and Impedance.=--A choke coil has resistance as well as -inductance. Its resistance can be found by the voltmeter-ammeter method, -using a direct current. (See Art. 278.) Let us take for example the -primary winding of a bell ringing transformer. Using a direct current -and testing the coil with a voltmeter and ammeter we find its resistance -to be, let us say, one ohm. If we connect the same coil across a 110 -volt a.-c. line we find the current to be very small, say 0.05 ampere. -The coil now has resistance and _reactance_. Reactance is the effect of -self-induction in hindering the flow of current. It is measured in ohms. -The combined effect of resistance and reactance is called _impedance_. -In the example above, the coil has 110 (volts)/0.05 (ampere) = 2200 ohms -of impedance. In applying Ohm's law to an alternating current circuit, -impedance must be substituted for resistance. Ohm's law as applied to an -a-c. circuit should be stated: "Current intensity equals e.m.f. divided -by impedance", or _I_ = _E_/_Z_. (_Z_ = impedance.) - -[Illustration: FIG. 435.--The relation between resistance, reactance and -impedance.] - -Impedance, however, does not equal the _sum_ of resistance and -reactance. The relation between these three quantities is similar to -that between the three sides of a right triangle, in which the impedance -represents the hypotenuse, and the resistance and reactance the other -two sides. See Fig. 435 which indicates that Resistance² + Reactance² = -Impedance², or (_R²_ + _X²_ = _Z²_). (_X_ = reactance.) To illustrate -this relation; suppose the primary of a transformer has 10 ohms -impedance and 8 ohms resistance, then the reactance equals 10² - 8² = -6², or the reactance is 6 ohms. - - -Exercises - -1. Find the reactance of a choke coil having a resistance of 10 ohms, -when its impedance is 50 ohms. How great a current flows through this -coil if the terminal voltage is 110 volts? - -2. When the bell is ringing, the primary of a bell ringing transformer -has an appreciable current. Suppose this current is 0.2 ampere. What is -the impedance if the voltage of the line is 115 volts? What is the -reactance if the resistance is 1 ohm? - -3. The primary of a large transformer has a terminal voltage of 6000 -volts and a current of 600 amperes. What is the impedance? If the -resistance is 6 ohms, what is the reactance? - -[Illustration: FIG. 436.--A telephone set showing a condenser used in -the circuit of the "ringer."] - -=435.--The electric condenser= (see Art. 231) is a very useful device in -a.-c. circuits; _e.g._, in telephone sets used in cities, a condenser is -used in the ringing circuit, as shown in Fig. 436. Alternating current -is required to ring such a bell and a condenser permits an a.-c. current -to act through it, although it entirely prevents the flow of a direct -current. This peculiar action will now be explained. - -=436. The action of a condenser= in an alternating current circuit may -be illustrated by the following experiment. Connect twelve, 1 m.f. -(microfarad) condensers, in parallel, and then attach them to a 110 volt -a.-c. line so that an incandescent lamp is in circuit as shown in Fig. -437. The lamp will be found to glow brightly, although there is no -electrical connection between the two sets of condenser plates. If the -same arrangement is connected to a 110 volt direct current circuit, the -lamp does not glow because it is really an open circuit. The lamp glows -on an a.-c. circuit because, although no electricity flows _through_ the -condenser, it does flow _into and out of_ the condenser, surging back -and forth through the lamp with sufficient intensity to cause it to glow -brightly. When the a.-c. current moves one way in the circuit, one set -of plates of the condensers becomes charged positively, the other, -negatively. When the a.-c. current reverses, the charges on the -condenser plates reverse. In the ordinary lighting circuit 120 reversals -take place each second, so that electricity rapidly flows into and out -of the condensers. On removing one condenser after another from the -circuit, the lamp is found to glow less and less, till when but one -condenser is left, no glowing is observed, since one small condenser -does not have sufficient _capacity_. - -[Illustration: FIG. 437.--Twelve condensers in circuit with an -incandescent lamp.] - -The unit of capacity is the _Farad_. Capacity is defined as the quantity -of electricity per second that flows into a condenser when the voltage -at the terminals changes at the rate of one volt per second. If a change -of one volt per second causes one coulomb to flow per second, that is, a -current of one ampere, the capacity is one _farad_. The condensers used -in the above experiment have a capacity of one microfarad, or one -millionth of a farad. - -A condenser, on account of its capacity, causes an a.-c. current to -_lead_ the voltage, that is the current reaches its maximum value before -the voltage does. In this respect a condenser has an effect opposite to -that of the self-induction of a choke coil (the latter causing the -current to "lag"). (See Fig. 435.) - -=437. Transmission of Electric Power.=--A field of peculiar usefulness -for a.-c. currents is in the economical transmission of electric power. -This fact is due to the following reasons: (_a_) The loss of electrical -power in a transmission line is due to the production of heat; the heat -produced being proportional to _I²R_, or to the _square_ of the _current -intensity_. Any lessening of the current flow required to transmit a -given power will therefore increase the efficiency of transmission. -(_b_) In order to employ a small current in transmitting a large amount -of power, we must use a very high e.m.f. Such high electromotive forces, -say from 60,000 to 100,000 volts, can be obtained only by the use of -a.-c. transformers, since it is not practicable to build a direct -current generator capable of producing 60,000 volts. In large power -transmission systems, a.-c. generators are used to produce powerful -alternating currents. The e.m.f. is then stepped up to a suitable -voltage (2300-100,000) by transformers and sent over transmission lines -to the various places where the power is to be used; at these places -suitable transformers "step-down" the e.m.f. to a convenient or safe -voltage for use. (See Fig. 442 of a transmission line and Fig. 438 of a -large power transmission system, and Fig. 439 of an a.-c. generator and -power plant.) - -[Illustration: FIG. 438.--Diagram of an alternating current high tension -power system. (_A_) Alternator, (_Tu_) water turbine, direct connected -to alternator, (_E_) exciter, (_T_{1}_) step-up transformers in power -station, (_T_{2}_) step-down transformers in substation, (_M_) motor, -(_L_) lamps, single-phase, three-wire system, (_T_{3}_) step-down -transformers delivering three-phase current to rotary converter (_R_) -which delivers direct current to the trolley line.] - -=438. Power Factor.=--The _power factor_ is a matter of interest and -importance in the use of a.-c. machines. Its meaning and use may be -learned from the following explanation: In a direct current circuit, -watts equals volts times amperes. In an alternating current circuit, -this equation is true only when the current is "in step" with the -voltage, that is, only when there is no _inductance_ or _capacity_ in -the circuit. If current and voltage are out of step, _i.e._, if there is -_lag_ or _lead_ (see Fig. 434), the product of volts and amperes gives -only the _apparent power_, the ratio between true and apparent power -depending on the amount of lag or lead. This ratio is called the power -factor. In an a.-c. circuit, then, the power equation is: watts = volts -× amperes × power factor, or power factor = true power/apparent power. -The product of volts and amperes is the _apparent power_ and is called -volt-amperes in distinction from the true power or watts. Therefore the -following is true: power factor = true watts/volt-amperes. - -[Illustration: FIG. 439.--Power house showing alternators, direct -connected to horizontal hydraulic turbines. Note the direct current -"exciter" on end of shaft of alternator. (_Courtesy of General Electric -Co._)] - -=439. Single-phase Currents.=--There are several kinds of a.-c. -currents. One of the most common is the _single-phase_. It is simply the -common a.-c. current used for light and power in the average home, and -uses a two-wire circuit around which the current is rapidly alternating. -Fig. 440 illustrates the changes of e.m.f. in an a.-c. single-phase -current. It may be produced by a single coil rotating in a magnetic -field. The curve of Fig. 440 represents one _cycle_, that is, one -complete series of changes in the electromotive forces. At the end of -the cycle the armature is in the same condition as at the beginning so -far as the magnetic field is concerned. It then begins a new cycle. The -ordinary commercial alternating current has a frequency of 60, that is -60 cycles per second. One rotation produces as many cycles as there are -pairs of poles. For example, if there are 48 poles in the generator -field, one rotation produces 24 cycles. - -[Illustration: FIG. 440.--Graph showing the e.m.f. changes of a -single-phase current for one "cycle."] - -=440. Three-phase Currents.=--Now suppose we have three coils as in Fig. -441, the coils being evenly spaced, or 120 degrees apart, at _A_, _B_, -and _C_. If the coils are rotated in a magnetic field, each will produce -an electromotive force. The result produced by three such coils is -called a _three-phase_ current. Ordinarily six wires, or three circuits, -would be required to carry the current produced by three separate coils; -for when coil "_C_" is in the 90 degree position, where its e.m.f. is a -maximum, coil "_B_" is 120 degrees past its maximum, and coil "_A_" is -240 degrees past its maximum. The graph (Fig. 441) shows the maximum -points of the three e.m.f's. separated by intervals of 120 degrees. In -practice, however, it is found possible to use _three wires_ instead of -six, as explained in Art. 441. - -[Illustration: FIG. 441.--Graph showing the e.m.f. changes of a -three-phase current for one "cycle."] - -=441. Three-wire Transmission.=--The currents produced in the three -coils just described undergo precisely the same changes as those -represented in the _graph_ (Fig. 441) for the three electromotive -forces. Careful examination of the graph will show that at any point the -sum of the _plus_ e.m.f's. equals the sum of the _minus_ e.m.f's. In -other words the algebraic sum of the three e.m.f's. is zero. Therefore -if we properly connect a transmission line of three wires to the -generator, the sum of the currents leaving the generator will equal the -sum of the currents returning to it. Since the algebraic sum of the -currents produced by the three coil combination described in Art. 440 is -always zero, it is possible to use three wires on three-phase -transmission lines. Fig. 442 shows a "tower" carrying three, three-wire -transmission lines. Long distance, high tension transmission lines are -generally three-wire lines carrying three-phase a.-c. currents. - -[Illustration: FIG. 442.--A "tower" supporting three, three-phase -circuits of a high tension transmission line.] - -=442. Alternators.=--A dynamo which delivers alternating current is -known as an _alternator_. Commercial alternators have many pairs of -poles in the field and as a rule the field rotates while the armature is -stationary. The field must be supplied with _direct_ current for the -polarity of each coil in the field must remain unchanged. Usually a -separate "exciter" is used, which is a small direct current generator. -The current from this exciter is fed into the rotating field by means of -slip rings. Fig. 439 shows a d.-c. (direct current) exciter on the end -of the armature shaft of the large alternator. - -[Illustration: FIG. 443.--Diagram of a "Series Motor."] - -=443. The A.-C. Series Motors.=--The only type of motor that will run on -either alternating or direct current is the _series motor_. The -"universal" motor used in household appliances such as electric fans, -vacuum cleaners, etc., is a series motor. The reason a series motor will -run on either direct or alternating current is because the direction of -rotation of the armature of a motor depends on (_a_) the direction of -the current in the armature, and (_b_) the polarity of the field. -Reversing either of these alone, reverses the direction of rotation of -the armature, while reversing both at the same instant leaves the -direction of rotation unchanged. Fig. 443 is a diagram of a series motor -since the field coils and armature are connected in series. On an a.-c. -line, both field and armature current must therefore reverse at the same -instant. In a shunt motor (similar to Fig. 286) we have a divided -circuit, and the greater self-induction of the field coils causes an -a.-c. current through these coils to lag behind that flowing in the -armature so that the two currents do not reverse at the same instant. - -[Illustration: FIG. 444.--Diagram of a gramme ring. It is shown -connected to a single-phase current so as to produce a rotating magnetic -field, similar to that obtained with a three-phase current. (_Ahrens, -Harley and Burns._)] - -[Illustration: FIG. 445.--The "stator" of an induction motor.] - -=444. The Induction Motor.=--Another common type of a.-c. motor is the -_induction motor_. Its advantage lies in its simplicity. It has neither -commutator nor brushes, the armature having no connection with an -external circuit. If the wires of a three-phase line be connected to a -coil wound in the form of a _gramme ring_, the connections being 120 -degrees apart as in Fig. 444, the magnetic field within this coil will -change in the same manner as if a magnet were spinning upon a pivot at -the center of the coil. Suppose the _N_ pole at one instant is at _A_, -in one-third of a cycle it moves to _B_, in another third to _C_, and in -one cycle it makes a complete revolution. Thus we have a _rotating -magnetic field_. If a cup of some non-magnetic metal such as aluminium -or copper be placed on a pivot in the center of this coil, the cup is -cut by the moving lines of force and currents are induced in it. -Because of these currents, the cup has a magnetic field of its own, and -the action of the two magnetic fields is such as to pull the cup around -and cause it to rotate in the same direction as that in which the field -of the coil rotates. The coil represents the stationary part, the -_stator_ (Fig. 445) and the cup the rotating part, the _rotor_, of an -induction motor. While the cup rotates in the same direction, it does -not rotate so rapidly as the magnetic field. If it should it is plain -that it would not cut the lines of force. The difference between the -rate of rotation of the rotor and that of the magnetic field is called -the "slip." The rotating part in small induction motors is frequently -made in a single casting. In large motors, it is built up of heavy -copper bars. Thus, from its appearance the common form of rotor is -known as the "squirrel cage" rotor. (See Fig. 446.) - -[Illustration: FIG. 446.--The "rotor" of an induction motor.] - -[Illustration: FIG. 447.--Diagram illustrating the principle of the -synchronous motor. The armature coil passes the position shown in the -figure at the instant the current in the line reverses. Thus the -armature keeps with the line current, making one revolution with each -"cycle."] - -=445. A synchronous motor= is one that keeps step with the alterations -of an alternating current. The line current is fed into the armature by -means of two slip rings and brushes. The principle of the synchronous -motor is illustrated in Fig. 447. This shows a motor having a two-pole -field. The armature current must be reversed twice in each revolution. -The reversal must take place when the armature winding is perpendicular -to the lines of force of the field. In a direct current motor this -reversal is brought about by the commutator. In a synchronous motor the -armature reaches the 90 degree position at the exact instant at which -the current reverses in the line. Thus in the case of a two-pole motor -the armature must make exactly one revolution for each cycle; it is, -therefore, a constant speed motor. Such motors are frequently employed -in converter stations where alternating current is converted into direct -current by what are called _rotary converters_. - -In practice the synchronous motor has a number of pairs of field poles. -It is essentially an alternating current generator running as a motor. -One of the principal uses of the synchronous motor is that of a -converter, receiving alternating current and delivering direct current. -Synchronous motors are also used in transmission lines to aid in -maintaining constant voltage. - - -Important Topics - -The wireless telephone, essential parts, action, arrangement. - -Alternating currents, alternating fields. - -Transformers, voltage relation of coils, power and core losses. - -Self-induction, inductance, and coke coils, uses, applications. - -Impedance, reactance, and resistance; relation and effects. - -Condensers, uses and applications with a-c. circuits. - -Alternating current power transmission; uses, advantages. - -Power factor, lag, lead, volt-amperes, true watts. - -Single- and three-phase currents; uses and nature of each. - -Three-wire transmission systems, alternators, construction, and action. - -A-c. motors, series, induction, synchronous. - - - - -INDEX - - -Aberration, spherical, 408 - -Absolute scale of temperature, 164 - -Absorptions of gases by solids and liquids, 29 - -Accelerated motion, 86 - -Acceleration, 87 - -Adhesion, 21 - -Aeroplane, 97 - -Air, aspirator, 67 - brake, 74 - cushion, 46 - height (of atmosphere), 64 - pressure, 56 - pump, 66 - weight, 56 - -Alternators, 481 - -Alternating current, 337, 466 - -Amalgamation, 273 - -Ammeter, 291 - -Ampere, 291 - -Archimedes' principle, 48 - -Arc light, 321 - -Armature, 335 - -Artesian wells, 44 - -Audion, 463 - -Aurora borealis, 453 - - -Balloon, 72 - -Barometer, 59 - -Beats, 376 - -Boiling, laws, 208 - point, 207 - -Boyle's Law, 63 - -Breezes, land and sea, 181 - -British thermal unit, 162 - -Brownian movements, 16 - - -Calorie, defined, 162 - -Camera, 426 - -Candlepower, 394 - -Capillary action, 25 - -Cartesian diver, 71 - -Cathode rays, 453 - -Centrifugal force, 91 - -Charles' Law, 165 - -Chladni's figures, 381 - -Choke coils, 470 - -Coefficient of expansion, definitions, 170 - gases, 167 - liquids, 168 - solids, 169 - -Coherer, 449 - -Cohesion, 21, 33 - -Color, 435 - bodies, 435 - complementary, 436 - primary, 440 - prismatic, 433 - theory of color vision, 440 - three-color printing, 440 - -Commutator, 335, 336 - -Compass, 230, 240 - -Concave lens, 418 - -Condenser, 260, 474 - -Conductors, 246 - -Conservation of energy, 127 - -Continental code, 459 - compared with the Morse, 452 - -Convection, 179 - currents in nature, 181 - draft of a chimney, 180 - -Convex lens, 416 - -Cooling, artificial, 210 - -Corpuscular theory, 442 - -Coulomb, 290 - meter, 291 - -Couple, 101 - -Critical angle, 414 - -Crookes' tube, 456 - -Crystallization, 28 - melting point of some crystalline substances, 203 - - -Daniel cell, 276 - -Declination, 240 - -Density, 38, 52 - methods for finding, 53 - -Dew, 192 - -Dew point, 193 - -Diffusion of gases, 13 - -Dipping needle, 240 - -Direct Current, 337 - -Dispersion, 433 - -Distillation, 208 - -Draft of a chimney, 180 - -Dry cell, 275 - -Dynamo, 330, 333 - -Dyne, 93 - - -Eye, the, 423 - action of, in vision, 423 - defects of, 425 - -Ear, the, 386 - trumpet, 361 - -Earth's magnetism, 238 - -Echoes, 362 - -Eclipses, 391 - -Efficiency, 142 - engines (tests), 219 - machines, 142 - -Elasticity, 31 - -Electric bell, 269, 287 - charge, distribution of, upon a conductor, 253 - circuit, 269 - currents, 267 - single phase, 479 - three phase, 479 - effects, 277 - induced, 326 - discharge in rarefied air, 452 - motor, 339 - screen, 256 - -Electrical capacity, 259 - fields, 247 - -Electrification, 243 - -Electrolysis, 308 - laws, 311 - practical uses, 311 - -Electromagnet, 281 - -Electromagnetic theory of light, 456 - -Electromotive force, 267 - unit of, 295 - -Electron theory, 252 - -Electrophorus, 263 - -Electroplating, 307 - -Electroscope, 244 - -Electrostatic induction, 248 - -Energy, 120 - conservation, 127 - falling water, 152 - forms, 125 - human body, 126 - -Energy, kinetic, 121 - potential, 120 - transference and transformation, 124 - -Engines, 213 - -Engines, gas, 222 - steam, 213 - turbine, 225 - -Equilibrant, 81 - -Equilibrium, 106 - neutral, 107 - stable, 106 - stability, 108 - unstable, 107 - -Erg, 119 - -Ether, 177 - -Evaporation, 18 - cooling effect, 19, 197 - rate, 198 - -Expansion, coefficient, 168 - gases, 167 - liquids, 168 - peculiarity, in water, 168 - solids, 169 - water, on turning to steam, 206 - - -Falling bodies, 109 - experimental study, 111 - laws, 113 - -Floating bodies, 48 - -Fluoroscope, 455 - -Foot candle, 396 - -Force, 79 - dyne, 93 - effectiveness, 134 - graphic representation, 80 - liquid, against any surface, 38 - measuring, 79 - moment, 99 - parallel, 100 - resolution, 96 - units, 83 - -Forces, parallel, 100 - -Franklin's theory of electricity, 252 - -Fraunhofer lines, 439 - -Freezing, evaporation, 197, 199 - mixtures, 210 - -Friction, 147, - coefficient, 149 - fluid, 150 - kinds, 147 - -Friction, laws, 150 - reducing, 148 - uses, 149 - - -Galvanometers, 289 - -Galvanoscope, 269 - -Gas engine, 222 - efficiency of, 224 - -Gas meter, 75 - -Geissler tubes, 453 - -Gravitation, 103 - law, 104 - -Gravity, 88, 104 - acceleration due to, 111 - cell, 277 - center of, 105 - - -Hail, 193 - -Hearing, 386 - -Heat, capacity for water, 201 - conduction, 173 - constants for transmission, 220 - convection, 179 - effects, 161 - engines, 213, 222 - equivalent of fuels, 219 - fusion, 201 - measurement, 200 - methods of transmitting, 173 - produced by electric current, 318 - radiation, 176 - sources, 159 - units, 162 - vaporization, 205 - work, 212 - -Heating of buildings, 182 - direct and indirect radiation, 186 - hot air, 183 - water, 186 - plenum system, 187 - steam, 186 - vacuum steam, 187 - vapor steam, 187 - -Hertzian waves, 262, 449 - -Hooke's law, 33 - -Horse power, 123 - electric equivalent of, 123 - -Humidity, 194 - -Hydraulic press, 42 - elevator, 44 - ram, 72 - -Hygrometers, 194 - -Hygrometry, 191 - conditions for saturation, 192 - dew point, 193 - fog, 193 - formation, of dew, 192 - humidity, 194 - hygrometers, 194 - importance, 191 - -Hypothesis, 3 - - -Images, concave mirrors, 405 - construction, 405 - definition, 392 - plain mirror, 401 - small apertures, 391 - -Impedance, 472 - -Incandescent lamp, 320 - -Inclined plane, 143 - -Inductance, 471 - -Induction coil, 343 - -Inertia, 87 - -Insulators, 246 - -Intensity of sound, 363 - -Interference, light, 442 - sound, 374 - - -Joule, 120, 319 - - -Laws, boiling, 208 - Boyle's 63 - Charles', 165 - electric action, 243 - falling bodies, 113 - floating bodies, 48 - gravitation, 104 - Hooke's, 33 - induced currents, 326 - intensity of light, 394 - Lenz's, 328 - liquid pressure, 37 - machines, 131 - magnetic action, 229 - motion, 87 - Ohm's, 298 - pendulum, 116 - reflection, 399 - refraction of light, 411 - vibration of strings, 378 - -Lenses, achromatic, 434 - effect on light, 417 - equation, 421 - formation of images, 418 - forms, 416 - -Leclanché cell, 275 - -Lever, 132 - -Leyden jar, 261 - oscillatory nature of the discharge, 448 - -Light, compared with sound, 388, 444 - electromagnetic theory, 456 - intensity, 394 - interference, 442 - polarization, 445 - rectilinear propagation, 389 - reflection, 396 - total reflection, 413 - -Lightning, 254 - -Lines, of force, 233 - agonic, 240 - isogonic, 240 - -Liquids, pressure, 36 - -Local action, 273 - -Luminous and illuminated bodies, 388 - - -Machines, 129 - advantages, 129 - cannot create energy, 130 - efficiency, 142 - law, 131 - mechanical advantage, 134 - the six simple, 132 - uses, 129 - -Magnetic action, 229 - fields, 233, 466 - induction, 231, 236 - permeability, 237 - poles, 229 - properties, 230 - retentivity, 231 - substances, 230 - effect of electric current, 279 - -Magnetism, 228 - -Magnetism, theory, 232 - -Major and minor triads, 369 - -Magneto, 328 - -Magnetoscope, 230 - -Magnets, 228 - poles, 229 - -Major scale, 366 - -Manometric flames, 382 - -Matter, 4 - effect of heat, 5 - molecular theory, 5 - properties, 34 - states of, 4 - states of, defined, 5 - -Mechanical advantage, 134 - -Megaphone, 365 - -Melting points, 203 - -Mercury arc rectifier, 347 - -Metric system, 8 - -Microscope, 427 - -Mirage, 414 - -Mirrors, 400 - concave, 405 - convex, 407 - parabolic, 409 - plane, 401 - -Molecular motion in liquids, 18 - in gases, 13 - in liquids and solids, 27 - in solids, 31 - -Molecules, motion, 16 - size, 13 - -Moment of force, 99, 133 - -Momentum, 87 - law of, 92 - -Motion, 85 - accelerated, 86 - curvilinear, 88 - direction, 86 - first law, 87 - modes, 85 - second law, 92 - third law, 93 - uniformity, 86 - -Motor (electric), 339 - A. C. series, 482 - induction, 483 - synchronous, 485 - -Muffler, 224 - -Musical instruments, 377 - interval, 368 - nomenclatures, table, 369 - -Musical sounds, characteristics 364 - - -Newton's Laws of motion, 87 - -Nodes, in pipes, 384 - in strings, 379 - -Noise and music, 363 - - -Ohm, 294 - -Ohm's Law, 298 - -Opera glass, 428 - -Optical illusions, 390, 404 - instruments, 423 - camera, 426 - eye, 423 - microscope, 427 - opera glass, 428 - prism field glass, 429 - projecting lantern, 427 - telescope, 428 - -Organ pipes, closed, 384 - nodes, 384 - open, 384 - -Oscillatory discharge, 448 - -Osmosis, 19 - -Outline Review, - current electricity, 325 - force and motion, 118 - heat, 227 - induced currents, 353 - light, 446 - magnetism and static electricity, 266 - sound, 387 - work and energy, 158 - -Overtones, 379 - - -Pascal's principle, 41 - -Pendulum, compound, 115 - laws, 116 - simple, 115 - uses, 116 - -Pepper's ghost, 404 - -Permeability, 237 - -Phonograph, 383 - -Physics, definition, 4 - -Photometer, 394 - -Photometry, 393 - -Pitch, 365 - -Polarization, of light, 445 - of voltaic cells, 273 - -Portraits, - Bell, 431 - Edison, 285 - Faraday, 331 - Galileo, 89 - Gilbert, 217 - Helmholtz, 397 - Huygens, 397 - Joule, 217 - Kelvin, 331 - Marconi, 431 - Morse, 285 - Newton, 89 - -Potential, 257 - -Power, 123 - electric, 316 - power factor, 476 - transmission of electric, 476 - water, 152 - -Pressure, air, 56 - atmospheric, 58 - -Pressure, definition, 37 - effect on liquids and gases, 62 - law of liquid, 37 - -Prism field glass, 429 - -Projecting lantern, 427 - -Proof-plane, 244 - -Pulley, 139 - -Pumps, air, 66 - condensing, 67 - water (lift, 68, force, 69) - - -Quality of musical tones, 380 - - -Radiation, 176 - sun's, 178 - -Radio-activity, 457 - -Radiometer, 177 - -Radium, 457 - -Rainbow, 436 - -Reactance, 472 - -Reflection, light, 396 - multiple, 404 - sound, 360 - total of light, 413 - -Refraction, 410 - cause, 412 - index, 412 - light, 410 - in plates, prisms, and lenses, 413 - -Resolution of forces, 96 - -Resistance, cells in series, and parallel, 302 - conductors, 293 - in series and parallel, 299, 300 - unit, 294 - volt-ammeter method for finding, 304 - -Resonance, 371 - -Resonator, 373 - -Resultant, 81 - -Retentivity, 231 - -Right hand rule, 279 - -Rotary converter, 486 - - -Science, definition, 2 - -Screw, 144 - -Shadows, 390 - -Single phase currents, 479 - -Siphon, 70 - -Siren, 366 - -Solidification, change of volume during, 203 - -Solutions, 27 - -Sound, compared with light, 388 - interference, 374 - media, 355 - nature, 356 - reflection, 360 - rule for finding velocity, 367 - source, 354 - speed, 355 - transmission in air, 359 - -Specific heat, 200 - method of determining, 201 - -Spectroscope, 438 - -Spectrum, 433 - -Spherical aberration, 408 - -Spinthariscope, 458 - -Stability, 108 - -Standpipe, 46 - -Static and current electricity compared, 287 - electrical machines, 262 - -Steam engine, 213 - turbine, 225 - -Storage battery, 312 - -Stress and strain, 94 - -Sublimation, 199 - -Surface tension, 22 - -Sympathetic vibration, 372 - - -Telegraph, 283 - wireless, 450 - -Telephone, 349 - receiver, 349 - transmitter, 350 - wireless, 460 - -Telescope, 428 - -Temperature, 162 - absolute scale, 164 - -Tempered scale, 370 - -Theory, 3 - -Thermometer, air, 167 - centigrade, Fahrenheit, 163 - gas, 167 - -Thermos bottle, 176 - -Thermostat, 188 - -Three-color printing, 440 - -Three-phase currents, 479 - -Three wire transmission, 480 - -Torricelli's experiment, 57 - -Trade winds, 182 - -Transformer, 345, 467 - uses, 347 - -Turbine, steam, 225 - water, 154 - - -Vacuum cleaner, 76 - pan, 210 - -Velocity, 86 - -Vibration strings, 378 - sympathetic, 372 - -Visual angle, 424 - -Viscosity, 20 - -Volt, 295 - -Voltaic cell, 270 - advantages, 274 - amalgamation, 273 - local action, 273 - polarization, 273 - simple, 270 - -Voltmeter, 295 - - -Water wheels, 152 - overshot, 152 - turbine, 154 - undershot, 153 - -Watt, 123, 317 - -Wave theory, of light, 442 - -Waves, beats, 376 - interference, 374 - longitudinal, 358 - sound, 358 - transverse, 358 - visible, 357 - -Wedge, 144 - -Weight, 104 - -Wheatstone bridge, 304 - -Wheel and axle, 136 - -Wind instruments, 383 - -Wireless telegraphy, 450 - telephony, 460 - -Work, 119 - units, 119 - - -"X" rays 454 - - - Transcriber's Note: - - This book uses B.T.U. and B.t.u., electrophorous and electrophorus, - e.m.f. and E.M.F. and this has been left as written. - - Hyphenation is also inconsistent, e.g. electro-plated and - electroplated. - - On page 324, Exercise number 8 was not used in the original. The - exercises have not been renumbered. - - - - - -End of the Project Gutenberg EBook of Physics, by -Willis Eugene Tower and Charles Henry Smith and Charles Mark Turton and Thomas Darlington Cope - -*** END OF THIS PROJECT GUTENBERG EBOOK PHYSICS *** - -***** This file should be named 40175-8.txt or 40175-8.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/0/1/7/40175/ - -Produced by Anna Hall, Albert László and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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