,,physics ,,tower1 ,,smith1 ,,turton1 ,,and ,,cope ,illustration3 7,see p4#dda7 ,,three-,,color ,,printing ,y4 ,yellow impression2 negative made through a blue-violet filter4 ,r4 ,crimson impression2 negative made through a green filter4 ,,ry4 ,crimson on yellow4 ,b4 ,blue impression2 negative made through a red filter4 ,,yrb4 ,yellow1 crimson1 and blue combined2 the final product4 7,courtesy of ,phototype ,engraving ,co41 ,philadelphia47 ,,physics ,,by ,,willis ,e4 ,,tower1 ,m4 ,,sci4 7,univ4 of ,illinois7 ,,head ,,of ,,the ,,department ,,of ,,physics1 ,,englewood ,,high ,,school1 ,,chicago ,,charles ,h4 ,,smith1 ,m4 ,e4 7,cornell7 ,,head ,,of ,,the ,,department ,,of ,,physics ,,and ,,assistant ,,principal1 ,,hyde ,,park ,,school1 ,,chicago ,,charles ,m4 ,,turton1 ,a4 ,m4 7,syracuse7 ,,head ,,of ,,the ,,department ,,of ,,physics1 ,,bowen ,,high ,,school1 ,,chicago ,,in ,,collaboration ,,with ,,thomas ,d4 ,,cope1 ,ph4,d4 7,pennsylvania7 ,,assistant ,,professor ,,of ,,physics1 ,,university ,,of ,,pennsylvania ,,based ,,upon ,,principles ,,of ,,physics ,,by ,,tower1 ,,smith and ,,turton ,,with #g ,,plates ,,and #ddh ,,other ,,illustrations ,,philadelphia ,p4 ,,blakiston',s ,,son ,,co4 #ajab ,,walnut ,,street ,,copyright1 #aibj1 ,,by ,p4 ,,blakiston',s ,,son ,,co4 ,,preface ,in the preparation of this text1 the pupil1 his experience1 needs1 and interests have been constantly kept in mind4 ,the order of topics1 illustrations1 and problems have been selected with the purpose of leading the pupil into a clear understanding of the physical phenomena continually taking place about him4 ,the recommendations and conclusions reached by the ,new ,movement in the ,teaching of ,physics have been incorporated into the book as a whole4 ,these conclusions indicate that the most efficient teaching in physics involves a departure from the quantitative1 mathematical methods of presentation that were in general use a dozen or more years ago1 toward a method better adapted to the capabilities1 interests1 and requirements of the young people in our physics classes4 ,the older methods are effective with a portion of the student body which has the greater mathematical ability and training1 but they discourage a large majority of the pupils who are not gifted or prepared for severe mathematical analysis4 ,for this reason1 many of the more difficult mathematical demonstrations often given in physics texts are omitted4 ,most of the problems involve only the units employed in practical every-day measurements4 ,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 subject4 ,the pupil comes to the study of physics with a great number of experiences and impressions of physical phenomena continually occurring about him4 ,in recognition of this fact1 it has been thought best to consider first the explanation of common things well known to all pupils1 such as the diffusion of gases1 evaporation of liquids1 expansion of bodies when heated1 and capillary action4 ,since the molecular theory of matter is now supported by so many conclusive evidences1 we have not hesitated to make free use of it in the early chapters4 ,the applications of this theory are extremely helpful in explaining every-day phenomena4 ,our experience shows that beginners in physics understand and apply this theory without difficulty4 ,the illustrations and drawings have been selected from a pedagogical rather than a spectacular point of view4 ,practically all of them are new4 ,the problems and exercises have been selected for the distinct purpose of illustrating the principles taught in the text and for their practical applications4 ,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 phenomena4 ,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 analysis4 ,some of the special features of the text may be briefly summarized as follows3 7,a7 ,simplicity of presentation is emphasized4 ,the methods of attack1 the illustrations and examples employed in developing the subjects are particularly adapted to beginners in physics4 7,b7 ,the text is divided into some seventy-seven sections1 each containing material enough for one recitation4 7,c7 ,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 attention4 ,the lists of important topics are also of assistance to the teacher in assigning recitations4 7,d7 ,the problems and practical exercises emphasize physical principles as distinguished from mathematical training4 ,a list of exercises is placed at the end of the several sections4 ,they are in sufficient number to permit testing at many points and of a choice of problems by teachers4 ,the authors wish to express their appreciation for suggestions and helpful criticisms to many who have read the text in manuscript or proof4 ,especially to ,professor ,a4 ,p4 ,carman of the ,university of ,illinois and his associate1 ,professor ,f4 ,r4 ,watson1 who have gone carefully over the whole text2 and to ,mr4 ,chas4 ,m4 ,brunson1 ,scott ,high ,school1 ,toledo1 ,ohio1 ,mr4 ,frank ,e4 ,goodell1 ,north ,high ,school1 ,des ,moines1 ,iowa1 and to ,mr4 ,walter ,r4 ,ahrens1 ,englewood ,high ,school1 ,chicago1 for assistance in reading the proofs4 ,also to ,mr4 ,w4 ,h4 ,collins1 ,jr41 ,bowen ,high ,school1 ,chicago1 who supervised the preparation of drawings for the diagrams and figures2 and to many firms and individuals that have courteously furnished material for illustrations4 ,,willis ,e4 ,,tower4 ,,charles ,h4 ,,smith4 ,,charles ,m4 ,,turton4 ,,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 science4 ,he has learned to throw a ball and can tell how a thrown ball moves4 ,he has drawn out nails with a claw hammer4 ,he has seen wood float and iron sink4 ,he has sucked liquids up through straws4 ,in his mother's kitchen1 he sees water as ice1 liquid1 and steam4 ,on a wintry day he reads the temperature on a thermometer4 ,he sees sparks fly from car wheels when the brakes are applied4 ,he has played with a horseshoe magnet1 and has found the north by means of a compass4 ,the telephone1 the electric light and the motor he sees1 and perhaps uses1 many times a day4 ,he dresses before a mirror1 focuses his camera1 watches the images at a moving picture show1 and admires the colors of the rainbow4 ,he has cast stones into water to watch the ripples spread1 has shouted to hear the echo1 and perhaps plays some musical instrument4 ,these1 and a thousand other things1 are known to the intelligent and normal boy or girl who has reached the age at which the study of ,physics is properly begun4 ,to a great extent even the terms used in the science are familiar to the beginner4 ,he speaks of the horse-power of an engine1 reads kilowatt-hours from the meter in the cellar1 and may know that illuminating gas costs one dollar per thousand cubic feet4 ,ampere and volt are words he frequently hears and sees4 ,when he takes up the study of ,physics1 the attitude of the student toward these familiar things and words must undergo a change4 ,casual information about them must be changed to sound knowledge1 purposely acquired4 ,hazy notions about the meanings of words must be replaced by exact definitions4 ,bits of knowledge must be built into a structure in which each fact finds its proper place in relation to the others4 ,the only agent which can accomplish these changes is the student himself4 ,he must consciously and purposely seek the truth and must reflect upon it until he sees it in its relation to other truth4 ,upon him1 and upon him alone1 rests the final responsibility for the success or failure of his study4 ,but the student is not without assistance4 ,in his teacher he finds a guide to stimulate1 to direct1 and to aid his efforts1 and a critic to point out wherein his efforts have failed and wherein they have succeeded4 ,weights1 measures1 and other apparatus are furnished to enable him to answer for himself questions which have arisen in his studies4 ,in addition to these the student has his text book1 his teacher for his hours of private study4 ,a good text book is an inspiring teacher in print4 ,it directs attention to things familiar to the student through long experience1 and inspires him to make a closer scrutiny of them4 ,it invites him to observe1 to analyze1 to compare1 to discover likenesses and differences in behavior4 ,it questions him at every turn4 ,its ever repeated challenge reads1 ,weigh and consider4 ,it furnishes him needed information that he cannot otherwise acquire4 ,it satisfies his desire to know1 ,by whom1 where1 when1 and how was this first discovered8 ,the student of ,physics must never forget that he is studying not pages of text but the behavior and properties of iron1 water1 mica1 moving balls1 pumps1 boiling liquids1 compressed air1 mirrors1 steam engines1 magnets1 dynamos1 violins1 flutes1 and a host of other things4 ,his studies should1 whenever possible1 be made first hand upon the things themselves4 ,the text is an aid to study1 never a substitute for the thing studied4 ,it is an excellent plan for each student to select some one thing for special study1 the telephone for example4 ,by observation1 experiment1 and reading1 he may acquire a large amount of valuable information about such a subject while pursuing his course in ,physics4 ,every part of the science will be found to bear some relation to it4 ,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 lives4 ,by virtue of this knowledge he will be better able to enjoy the world1 to control it1 and to use it4 ,,thomas ,d4 ,,cope4 ,,philadelphia4 ,,contents ,,chapter ,i4 ,,introduction ,,and ,,measurement4 ,,page 7#a7 ,introduction #a 7#b7 ,states of ,matter #d 7#c7 ,the ,metric ,system #h ,,chapter ,,ii4 ,,molecular ,,forces ,,and ,,motions4 7#a7 ,molecular ,motions in ,gases #ac 7#b7 ,molecular ,motions in ,liquids #ah 7#c7 ,molecular ,forces in ,liquids #ba 7#d7 ,molecular ,forces in ,liquids and ,solids #bg 7#e7 ,molecular ,forces in ,solids #ca ,,chapter ,,iii4 ,,mechanics ,,of ,,liquids4 7#a7 ,liquid ,pressure #cf 7#b7 ,transmission of ,liquid ,pressure #da 7#c7 ,archimedes' ,principle #dg 7#d7 ,density and ,specific ,gravity #eb ,,chapter ,,iv4 ,,mechanics ,,of ,,gases4 7#a7 ,weight and ,pressure of the ,air #ee 7#b7 ,compressibility and ,expansibility of the ,air #fb 7#c7 ,pneumatic ,appliances #ff ,,chapter ,v4 ,,force ,,and ,,motion4 7#a7 ,force1 how ,measured and ,represented #gi 7#b7 ,motion4 ,newton's ,laws #he 7#c7 ,resolution of ,forces #if 7#d7 ,moment of ,force and ,parallel ,forces #ii 7#e7 ,gravitation and ,gravity #ajc 7#f7 ,falling ,bodies #aji 7#g7 ,the ,pendulum #aae ,,chapter ,,vi4 ,,work ,,and ,,energy4 7#a7 ,work and ,energy #aai 7#b7 ,power and ,energy #abc 7#c7 ,the ,lever and ,simple ,machines #abi 7#d7 ,wheel and ,axle and ,pulley #acf 7#e7 ,efficiency and the ,inclined ,plane #adb 7#f7 ,friction and its ,uses #adg 7#g7 ,water ,power #aeb ,,chapter ,,vii4 ,,heat1 ,,its ,,production ,,and ,,transmission4 7#a7 ,sources and ,effects of ,heat #aei 7#b7 ,temperature and ,expansion #afb 7#c7 ,expansion of ,gases1 ,liquids and ,solids #afg 7#d7 ,modes of ,transmitting ,heat #agc 7#e7 ,convection1 ,heating and ,ventilation #agi 7#f7 ,the ,moisture in the ,air1 ,hygrometry #aia 7#g7 ,evaporation #aif ,,chapter ,,viii4 ,,heat ,,and ,,work4 7#a7 ,heat ,measurement and ,specific ,heat #bjj 7#b7 ,heat and ,changes of ,state #bje 7#c7 ,heat and ,work #bab 7#d7 ,heat ,engines #bbb ,,chapter ,,ix4 ,,magnetism4 7#a7 ,general ,properties of ,magnets #bbh 7#b7 ,theory of ,magnetism1 ,magnetic ,fields #bcb 7#c7 ,the ,earth's ,magnetism #bch ,,chapter ,,xi4 ,,static ,,electricity4 7#a7 ,electrification and ,electrical ,charges #bdc 7#b7 ,electric ,fields and ,electrostatic ,induction #bdg 7#c7 ,electric ,theories1 ,distribution and ,electric ,charges #beb 7#d7 ,potential1 ,capacity1 and the ,electric ,condenser #beg 7#e7 ,electrostatic ,generators #bfb ,,chapter ,,xi4 ,,electric ,,currents ,,produced ,,by ,,voltaic ,,cells4 7#a7 ,electrical ,currents and ,circuits #bfg 7#b7 ,the ,simple ,voltaic ,cell and its ,action #bgj 7#c7 ,practical ,voltaic ,cells #bgd ,,chapter ,,xii4 ,,magnetic ,,effects ,,of ,,electric ,,currents1 ,,and ,,electrical ,,measurements4 7#a7 ,the ,magnetic ,effect of ,electric ,currents #bgi 7#b7 ,electrical ,measurements #bhi 7#c7 ,ohm's ,law and ,electrical ,circuits #bih 7#d7 ,grouping of ,cells and ,measuring ,resistance #cjb ,,chapter ,,xiii4 ,,chemical ,,and ,,heat ,,effects ,,of ,,electric ,,currents4 7#a7 ,the ,chemical ,effect of ,electric ,currents #cjg 7#b7 ,the ,storage ,battery and ,electric ,power #cab 7#c7 ,the ,heat ,effect of ,electric ,currents #cah ,,chapter ,,xiv4 ,,induced ,,currents4 7#a7 ,electromagnetic ,induction #cbf 7#b7 ,the ,dynamo and the ,motor #cce 7#c7 ,the ,induction ,coil and the ,transformer #cdc 7#d7 ,the ,telephone #cdi ,,chapter ,,xv4 ,,sound4 7#a7 ,sound1 ,source1 ,speed1 ,media #ced 7#b7 ,waves and ,wave ,motion #ceg 7#c7 ,intensity and ,pitch of ,sound #cfc 7#d7 ,musical ,scales and ,resonance #cfh 7#e7 ,interference1 ,beats1 ,vibration of ,strings #cgd 7#f7 ,tone ,quality1 ,vibrating ,plates and ,air ,columns #chd ,,chapter ,,xvi4 ,,light4 7#a7 ,rectilinear ,propagation of ,light #chh 7#b7 ,photometry and ,law of ,reflection #cic 7#c7 ,mirrors and ,formation of ,images #djj 7#d7 ,refraction of ,light #daj 7#e7 ,the ,formation of ,images by ,lenses #daf 7#f7 ,optical ,instruments #dbc 7#g7 ,color and ,spectra #dcj 7#h7 ,nature of ,light #ddb ,,chapter ,,xvii4 ,,invisible ,,radiations4 7#a7 ,electric waves and ,radioactivity #ddh ,,chapter ,,xviii4 ,,wireless ,,telephony ,,and ,,alternating ,,currents4 7#a7 ,wireless ,telephony #dfj 7#b7 ,alternating ,currents #dff ,,index #dhg ,,physics ,,chapter ,i ,,introduction ,,and ,,measurement 7#a7 ,,introduction #a4 ,physics1 an ,explanation of ,common ,things4--,many students take up the study of physics expecting to see wonderful experiments with the ,x rays1 wireless telegraphy1 dynamos1 and other interesting devices4 ,others are dreading to begin a study that to them seems strange and difficult1 because they fear it deals with ideas and principles that are beyond their experience and hard to comprehend4 ,each of these classes is surprised to learn that physics is mainly an explanation of common things4 ,it is a study that systematizes our knowledge of the forces and changes about us2 such as the pull of the earth1 the formation of dew1 rain and frost1 water pressure and pumps1 echoes and music1 thermometers and engines1 and many other things about us with which people are more or less familiar4 ,physics is like other school subjects1 such as mathematics and language1 in having its own peculiar vocabulary and methods of study2 these will be acquired as progress is made in the course4 ,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 idea4 ,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 association1 but it is of especial help in a subject such as physics1 which deals with the systematic study and explanation of the facts of our every-day experience4 #b4 ,knowledge--,common and ,scientific4--,this leads to the distinction between common knowledge and scientific knowledge4 ,we all possess common knowledge of the things about us1 gained from the impressions received by our senses1 from reading1 and from the remarks of others4 ,scientific knowledge is attained when the bits of common knowledge are connected and explained by other information gained through study or experience4 ,that is1 common knowledge becomes scientific1 when it is organized4 ,this leads to the definition3 ,science is organized knowledge4 ,common knowledge of the forces and objects about us becomes scientific only as we are able to make accurate measurements of these4 ,that is1 science is concerned not only in how things work1 but even more in how much is involved or results from a given activity4 ,for example1 a scientific farmer must be able to compute his costs and results in order to determine accurately his net profits4 ,the business man who is conducting his business with efficiency knows accurately his costs of production and distribution4 ,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 thought4 #c4 ,hypothesis1 ,theory1 and ,law4--,three words that are frequently used in science may be mentioned here3 hypothesis1 theory1 and law4 ,an hypothesis is a supposition advanced to explain some effect1 change1 or condition that has been observed4 ,for example1 the ,nebular ,hypothesis of which many high-school students have heard1 is an attempt to explain the origin of the sun1 the earth1 the planets1 and other solar systems4 ,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 question4 ,the ,molecular ,theory of ,matter which states that matter of all kinds is composed of very small particles called molecules 7see ,art4 #f71 is a familiar example of a theory4 ,a theory becomes a law when it may be definitely proved4 ,many laws are expressed in mathematical language1 e4g41 the law of gravitation4 7,see ,art4 #hh47 ,many of the laws of physics are illustrated by laboratory experiments1 which show in a simple way just what the law means4 ,exercises ,explain what is meant by the following terms and expressions3 #a4 ,common knowledge4 #b4 ,scientific knowledge4 #c4 ,science4 #d4 ,topics in physics4 #e4 ,scientific habit of thought4 #f4 ,value of relating new ideas to former experiences4 #g4 ,hypothesis4 #h4 ,theory4 #i4 ,law4 7#b7 ,,the ,,states ,,of ,,matter #d4 ,physics ,defined4--,in the study of any science or field of knowledge1 it is helpful to have a basis for grouping or classifying the facts studied4 ,in physics we are to study the objects1 forces1 and changes about us1 to understand them and their relations to one another4 ,accordingly1 physics1 dealing with the material world about us1 is often defined as the science of matter and energy1 matter being anything that occupies space and energy the capacity for doing work4 ,this definition of physics while not strictly accurate is sufficiently comprehensive for our present purpose4 #e4 ,the ,three ,states of ,matter4--,our bodies are matter since they occupy space4 ,further1 they possess energy since they are able to do work4 ,in beginning the study of physics it will simplify our work if we study one of these topics before the other4 ,we will therefore begin with matter and consider first its three states4 ,some bodies are solid2 as ice1 iron1 wax4 ,others are liquid2 as water1 mercury1 oil4 ,still others are in the state of gas2 as steam1 air1 and illuminating gas4 ,further we notice that the same substance may be found in any one of the three states4 ,for example water may be either ice1 water or steam2 that is1 either a solid1 a liquid1 or a gas4 ,most persons have heard of liquid air and possibly some know of ice air1 i4e41 air cooled until it not only liquefies1 but is solidified4 ,on the other hand1 iron may be melted and1 if heated hot enough1 may be turned into iron vapor4 ,in fact most substances by heating or cooling sufficiently may be changed into any one of the three states4 ,before defining the three states1 let us consider the structure of matter4 ,this may help us to answer the question3 ,how is it possible to change a hard solid1 such as ice1 into a liquid1 water1 and then into an invisible gas like steam8 ,this is explained by the molecular theory of matter4 #f4 ,the ,molecular ,theory of ,matter4--,it is believed that all bodies are made up of very small particles called molecules1 and that these instead of being packed tightly together like square packages in a box1 are1 strange as it may seem1 very loosely packed even in solids and do not permanently touch their neighbors4 ,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 earth1 the molecules magnified in the same proportion would be in size between a baseball and a football4 ,the air and all other gases are believed to be made up of molecules in rapid motion1 striking and rebounding continually from one another and from any objects in contact with the gas4 #g4 ,states of ,matter ,defined4--,these ideas of the structure of matter assist us in understanding the following definitions3 ,a solid is that state of matter in which the molecules strongly cling together and tend to keep the same relative positions4 7,this of course follows from the tendency of a solid to retain a definite form47 ,a liquid is that state of matter in which the molecules tend to cling together1 yet move about freely4 ,hence a liquid takes the form of any vessel in which it is placed4 ,a gas is that state of matter in which the molecules move about freely and tend to separate indefinitely4 ,hence a gas will fill any space in which it is placed4 #h4 ,effect of ,heat on ,matter4--,it is further believed that when a body is heated1 that the action really consists in making its molecules move or vibrate faster and faster as the heating progresses4 ,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 solid1 liquid1 or gas4 ,fig4 #a shows the expansion of air in an air thermometer4 ,fig4 #b shows the expansion of a solid on heating4 ,illustration3 ,,fig4 #a4--,when the bulb is heated1 the air within expands forcing down the water in the tube4 #i4 ,physical and ,chemical ,changes4 ,a change of state such as the freezing or boiling of water is called a physical change1 for this change has not affected the identity of the substance4 ,it is water even though it has become solid or gaseous4 ,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 before4 ,further if salt or sugar be dissolved in water the act of solution is also a physical change since the identical substance 7salt or sugar7 is in the solution and may be obtained by evaporating the water4 ,illustration3 ,,fig4 #b 7a7 represents a straight bar made of a strip of brass and a strip of iron riveted together and attached to a handle4 ,upon heating the compound bar in a gas flame1 the brass expands faster than the iron causing the bar to bend toward the latter as in ,fig4 #b 7b74 ,if some sugar1 however1 is heated strongly1 say in a test-tube1 it is found to blacken1 some water is driven off and on cooling some black charcoal is found in the tube instead of the sugar4 ,this action which has resulted in a change in the nature of the substance treated is called a chemical change4 ,to illustrate further1 if some magnesium wire is heated strongly in a flame1 it burns1 giving off an intense light and when it cools one finds it changed to a light powdery substance like ashes4 ,chemical changes1 or those that change the nature of the substance affected1 are studied in chemistry4 ,in physics we have to do only with physical changes1 that is1 with those changes that do not affect the nature of the substance4 ,important ,topics #a4 ,physics defined4 #b4 ,the three states of matter2 solid1 liquid1 gas4 #c4 ,molecular theory of matter4 #d4 ,physical and chemical changes4 ,exercises ,write out in your own words your understanding of3 #a4 ,the structure of matter4 #b4 ,some of the differences between solids1 liquids1 and gases4 #c4 ,how to change solids to liquids and gases and vice versa4 #d4 ,the reason for the changes of size of a body on heating4 #e4 ,why cooling a gas tends to change it to a liquid or a solid4 #f4 ,the actual size of molecules4 ,which of the following changes are chemical and which physical8 ,give reasons4 #a4 ,melting of ice4 #b4 ,burning of a candle4 #c4 ,production of steam4 #d4 ,falling of a weight4 #e4 ,drying of clothes4 #f4 ,making an iron casting4 #g4 ,decay of vegetables4 #h4 ,sprouting of seeds4 #i4 ,flying an aeroplane4 #aj4 ,growth of a plant4 #aa4 ,grinding of grain4 #ab4 ,sawing a board4 #ac4 ,pulverizing stone4 #ad4 ,making toast4 #ae4 ,sweetening tea or coffee with sugar4 #af4 ,burning wood or gas4 7#c7 ,,the ,,metric ,,system #aj4 ,the ,metric ,system4--,in order to study the three states of matter with sufficient exactness it is necessary to employ a system of measurement4 ,the system universally employed by scientists is called ,the ,metric ,system4 ,in many respects it is the most convenient for all purposes4 ,every student should therefore become familiar with it and learn to use it4 ,at the present time1 not only do scientists everywhere use it1 but many countries have adopted it and use it in common measurements4 ,it was legalized in the ,united ,states in #ahff4 ,the metric system was originated by the ,french ,academy of ,sciences during the latter part of the #ahth century4 ,there were so many different systems of weights and measures in use1 each country having a system of its own1 that commerce was much hindered4 ,it was therefore decided to make a system based upon scientific principles4 ,the length of the earth's quadrant passing from the equator to the pole was determined by surveying and computation4 ,one-ten-millionth of this distance was selected as the unit of length and called a meter4 ,accurate copies of this meter were made and preserved as standards4 ,later surveys have shown that the original determination of the earth's quadrant was not strictly accurate2 so that after all the meter is not exactly one-ten-millionth of the earth's quadrant4 #aa4 ,the ,standard ,meter4--,the standard unit of length in the metric system is the meter4 ,it is the distance1 at the temperature of melting ice1 between two transverse parallel lines ruled on a bar of platinum 7see ,fig4 #c71 which is kept in the ,palace of the ,archives in ,paris4 ,accurate copies of this and other metric standards are also kept at the ,bureau of ,standards at ,washington1 ,d4 ,c4 ,fig4 #d shows the relation between the inch and the centimeter 7one-hundredth of a meter74 #ab4 ,units and ,tables in the ,metric ,system4--,the metric unit of area commonly used in physics is the square centimeter4 ,illustration3 ,,fig4 #c--,the standard meter4 ,the standard unit of volume or capacity is the liter4 ,it is a cube one-tenth of a meter on each edge4 ,it is equal to #a4jeg quarts4 ,it corresponds1 therefore1 to the quart in ,english measure4 ,illustration3 ,,fig4 #d4--;,centimeter and inch scales4 ,the standard unit of mass is the kilogram4 ,it is the mass of #a liter of pure water at the temperature of its greatest density1 #d;,c4 or #ci4b;,f4 ,the three principal units of the metric system1 the meter1 the liter1 and the kilogram1 are related to one another in a simple manner1 since the liter is a cube one-tenth of a meter in each dimension and the kilogram is the mass of a liter of water4 7,see ,fig4 #e47 ,the metric system is a decimal system that is1 one unit is related to another unit in the ratio of ten or of some power of ten4 ,this is indicated by the following tables3 ,metric ,table of ,length #aj millimeters 7mm47 equal #a centimeter4 #aj centimeters 7cm47 equal #a decimeter4 #aj decimeters 7dm47 equal #a meter4 #aj meters 7m47 equal #a dekameter4 #aj dekameters 7,dm47 equal #a hectometer4 #aj hectometers 7hm47 equal #a kilometer4 #aj kilometers 7km47 equal #a myriameter4 ,the measures commonly used are the centimeter1 meter and kilometer4 ,metric ,table of ,mass 7or ,weight7 #aj milligrams 7mg47 equal #a centigram4 #aj centigrams 7cg47 equal #a decigram4 #aj decigrams 7dg47 equal #a gram4 #aj grams 7g47 equal #a dekagram4 #aj dekagrams 7,dg47 equal #a hectogram4 #aj hectograms 7hg47 equal #a kilogram4 #aj kilograms 7kg47 equal #a myriagram4 ,the masses commonly used are the milligram1 gram and kilogram4 ,notice in these tables the similarity to #aj mills equal #a cent1 #aj cents equal #a dime1 #aj dimes equal #a dollar1 in the table of ,united ,states money4 ,other tables in the metric system are built upon the same plan4 ,learn the prefixes in order thus3 milli1 centi1 deci1 deka1 hecto1 kilo1 myria4 ,the first three prefixes are ,latin numerals and represent divisions of the unit4 ,the last four are ,greek numerals and represent multiples4 ,in these tables1 milli means #a_/ajjj1 centi means #a_/ajj1 deci means #a_/aj1 deka means #aj1 hecto1 #ajj1 kilo1 #ajjj1 myria1 #aj1jjj4 ,two other prefixes are sometimes used1 micro which means #a_/a1jjj1jjj2 as microfarad or microvolt1 and meg which means #a1jjj1jjj1 as megohm meaning #a1jjj1jjj ohms4 #ac4 ,advantages of the ,metric ,system4--,first1 it is a decimal system2 second1 the same form and prefixes are used in every table2 third1 the standards of length 7meter71 volume 7liter71 and mass 7kilogram7 bear a simple relation to one another4 ,this simple relation between the three standard units may be given thus3 first1 the liter is a cubic decimeter1 and second1 the kilogram is the mass of a liter of water4 7,see ,fig4 #e7 ,since the liter is a cubic decimeter1 the length of one side is #aj cm4 ,the liter therefore holds #ajjj ccm4 7#aj #aj #aj74 ,therefore1 #a liter #a cu4 dm4 #ajjj ccm4 and since #a liter of water has a mass of #a kg4 or #ajjj g41 then #ajjj ccm4 of water has a mass of #ajjj g41 or #a ccm4 of water has a mass of #a g4 ,illustration3 ,,fig4 #e4--,one liter of the water has a mass of one kilogram4 ,the following table of equivalents gives the relation between the most common ,english and metric units4 ,those marked 7997 should be memorized4 7997 #a meter #ci4cg inches4 #a cu1 in4 #af4chg ccm4 7997 #a inch #b4ed cm4 #a cu4 ft4 #bhcae cm4 #a foot #cj4dh cm4 #a cu4 m4 #a4cjh cu4 yd4 #a mile #a4fji km4 7997 #a liter #a4jeg qt4 #a sq4 in4 #f4de sq4 cm4 7997 #a kg4 #b4bjd lbs4 #a sq4 cm4 #j4aee sq4 in4 #a g4 #ae4dd grains4 #a sq4 m4 #a4aif sq4 yd4 #a lb4 #j4decf kg4 #a acre #j4dje ha4 #a oz4 #bh4ce g4 #a hectare #b4de acres4 #a g4 #j4jcec oz4 ,,the ,c4 ,g4 ,s4 ,,system4 ,scientists have devised a plan for expressing any measurement in terms of what are called the three fundamental units of length1 mass1 and time4 ,the units used are the centimeter1 the gram and the second4 ,whenever a measurement has been reduced to its equivalent in terms of these units1 it is said to be expressed in ,c4,g4,s4 units4 ,important ,topics #a4 ,the metric system2 how originated4 #b4 ,units2 meter1 liter1 kilogram4 #c4 ,metric tables4 #d4 ,advantages of the metric system4 #e4 ,equivalents4 #f4 ,the ,c4,g4,s4 system4 ,exercises #a4 ,which is cheaper1 milk at #h cents a quart or #h cents a liter8 ,why8 #b4 ,which is more expensive1 cloth at #a4jj a yard or at #a4jj a meter8 ,why8 #c4 ,which is a better bargain1 sugar at #e cents a pound or #aa cents a kilogram8 ,why8 #d4 ,express in centimeters the height of a boy #e ft4 #f in4 tall4 #e4 ,what is the length of this page in centimeters8 ,in inches8 #f4 ,what is the mass of a liter of water8 ,of #ejj ccm48 ,of #a ccm48 #g4 ,from ,chicago to ,new ,york is #idj miles4 ,express in kilometers4 #h4 ,a #aj-;gallon can of milk contains how many liters8 #i4 ,what will #ajj meters of cloth cost at #aj cents a yard8 #aj4 ,what will #d kg4 of beef cost at #ae cents a pound8 #aa4 ,what will #e-a_/b lbs4 of mutton cost at #dj cents a kilogram8 #ab4 ,how can you change the state of a body8 ,give three methods4 #ac4 ,correct the statement #a ccm4 #a g4 #ad4 ,how many liters in #cb quarts8 ,,chapter ,,ii ,,molecular ,,forces ,,and ,,motions 7#a7 ,,evidences ,,of ,,molecular ,,motion ,,in ,,gases #ad4 ,size of ,molecules4--,the difference between solids1 liquids1 and gases has been explained as due to the different behavior of molecules in the three states of matter4 ,that is1 in solids they cling together1 in liquids they move freely1 and in gases they separate4 ,at this time we are to consider the evidences of molecular motion in gases4 ,it must be kept in mind that molecules are exceedingly small4 ,it has been said that if a bottle containing about #a ccm4 of ordinary air has pierced in it a minute opening so that #ajj1jjj1jjj molecules 7a number nearly equal to the population of the ,united ,states7 pass out every second1 it would take1 not minutes or hours1 but nearly #ijjj years for all of the molecules to escape4 ,the number of molecules in #a ccm4 of air at #j;,c4 and #gf cm4 pressure has been calculated by ,professor ,rutherford to be #b4g #aj4 ,it is evident that such minute particles cannot be seen or handled as individuals4 ,we must judge of their size and action by the results obtained from experiments4 #ae4 ,diffusion of ,gases4--,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 room4 ,for example1 if illuminating gas is escaping it soon diffuses and is noticed throughout the room4 ,in fact1 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 kind4 ,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 scattered4 ,when cabbage is boiled in the kitchen soon all in the house know it4 ,other illustrations of the diffusion of gases will occur to anyone from personal experience1 such for instance as the pleasing odor from a field of clover in bloom4 ,the following experiment illustrates the rapid diffusion of gases4 ,illustration3 ,,fig4 #f;a4--,diffusion of gases4 ,illustration3 ,,fig4 #f;b4--,effusion of gases4 ,take two tumblers 7see ,fig4 #f;a71 wet the inside of one with a few drops of strong ammonia water and the other with a little hydrochloric acid4 ,cover each with a sheet of clean paper4 ,nothing can now be seen in either tumbler4 ,invert the second one over the first with the paper between1 placing them so that the edges will match4 ,on removing the paper it is noticed that both tumblers are quickly filled with a cloud of finely divided particles1 the two substances having united chemically to form a new substance1 ammonium chloride4 ,on account of their small size1 molecules of air readily pass through porous solids1 cloth1 unglazed earthenware1 etc4 ,the following experiment shows this fact strikingly4 7,see ,fig4 #f;b47 ,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 7,j74 ,the funnel has cemented in its top an inverted porous clay jar 7,c71 over the top of the latter is placed a beaker 7,b74 ,a piece of flexible rubber tubing 7,h7 leading from a hydrogen generator is brought up to the top of the space between the jar and the beaker4 ,when hydrogen gas is allowed to flow into the space between ,c and ,b1 the level of the water in ,w is seen to lower and a stream of water runs out at ,j spurting up into the air4 ,on stopping the flow of hydrogen and removing ,b1 the water falls rapidly in ,j and bubbles of air are seen to enter the water from the tube4 7,the foregoing steps may be repeated as often as desired74 ,this experiment illustrates the fact that the molecules of some gases move faster than those of some other gases4 ,hydrogen molecules are found to move about four times as fast as air molecules4 ,hence1 while both air and hydrogen molecules are at first going in opposite directions through the walls of ,c1 the hydrogen goes in much faster than the air comes out4 ,in consequence it accumulates1 creates pressure1 and drives down the water in ,w and out at ,j4 ,on removing ,b1 the hydrogen within the porous cup comes out much faster than the air renters4 ,this lessens the pressure within1 so that air rushes in through ,j4 ,this experiment demonstrates not only the fact of molecular motion in gases but also that molecules of hydrogen move much faster than those of air4 7,this experiment will work with illuminating gas but not so strikingly47 ,careful experiments have shown that the speed of ordinary air molecules is #dde meters or #adfj ft4 per second2 while hydrogen molecules move at the rate of #agjj meters or #eege ft4 or more than a mile per second4 #af4 ,expansion of ,gases4--,gases also possess the property of indefinite expansion1 that is1 if a small quantity of gas is placed in a vacuum1 the gas will expand immediately to fill the entire space uniformly4 ,this is shown by an experiment with the air pump4 ,on raising the piston the air follows instantly to fill up the space under it4 ,as the air is removed from the receiver of an air pump the air remaining is uniformly distributed within4 #ag4 ,how ,gases ,exert ,pressure4--,it is further found that air under ordinary conditions exerts a pressure of about #ae lbs4 to the square inch4 ,in an automobile tire the pressure may be #ij lbs4 and in a steam boiler it may be #bjj lbs4 or more to the square inch4 ,how is the pressure produced8 ,the molecules are not packed together solidly in a gas1 for when steam changes to water it shrinks to about #a_/afjj of its former volume4 ,air diminishes to about #a_/hjj of its volume on changing to liquid air4 ,the pressure of a gas is not due then to the gas filling all of the space in which it acts1 but is due rather to the motion of the molecules4 ,the blow of a single molecule is imperceptible1 but when multitudes of molecules strike against a surface their combined effect is considerable4 ,in fact1 this action is known to produce the pressure that a gas exerts against the walls of a containing vessel4 ,naturally if we compress twice as much gas into a given space there will be twice as many molecules striking in a given time1 which will give twice as much pressure4 ,if gas is heated1 it is found that the heat will cause a swifter motion of the molecules4 ,this will also make the molecules strike harder and hence cause the gas to expand or exert more pressure4 #ag;a4 ,brownian ,movements4--,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 air4 ,such drops instead of being at rest are constantly dancing about as if they were continually receiving blows from many directions4 ,these motions have been called ,brownian ,movements 7see ,fig4 #g74 ,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 them4 ,if the drops are made smaller or the gas more dense1 the movements increase in intensity4 ,these effects are especially marked at a pressure of #j4ja of an atmosphere4 ,illustration3 ,,fig4 #g4--,photograph of ,brownian movement4 ,this record is prepared by the aid of ,siedentopf's ultra-microscope and a plate moving uniformly across the field from left to right4 ,important ,topics ,it is assumed that air and all gases are made up of molecules in rapid motion2 that this motion is dependent upon temperature and pressure4 ,evidence of this is shown by 7a7 diffusion1 7b7 expansion1 7c7 pressure4 ,brownian ,movements4 ,questions #a4 ,what is the molecular 7kinetic7 theory of gases8 #b4 ,what three kinds of evidence help to confirm the theory8 #c4 ,what have you seen that seems to show that a gas consists of molecules in motion8 #d4 ,how many meters long is a #aj-;ft4 pole8 #e4 ,a #ej-kg4 boy weighs how many pounds8 #f4 ,what are three advantages of the metric system8 #g4 ,what will #ab qts4 of milk cost at #h cents a liter8 #h4 ,a cube #a meter each way will contain how many cubic centimeters8 ,how many liters8 ,what will a cubic meter of water weigh8 7#b7 ,,molecular ,,motion ,,in ,,liquids #ah4 ,diffusion of ,liquids4--,from the evidence given in ,arts4 #ad-ag1 7a7 of diffusion of odors1 7b7 of the continued expansion of air in the air pump1 and 7c7 of the pressure exerted by a gas in all directions1 one may realize without difficulty that a gas consists of small particles in rapid motion4 ,let us now consider some of the evidence of molecular motion in liquids4 ,if a little vinegar is placed in a pail of water1 all of the water will soon taste sour4 ,a lump of sugar in a cup of tea will sweeten the entire contents4 ,this action is somewhat similar to the diffusion of gases but it takes place much more slowly4 ,it is therefore believed that the motion of liquid molecules is much slower than that of gas molecules4 ,again1 if a dish of water is left standing in the open air in fine weather1 within a few days the dish will become dry though no one has taken anything from it4 ,we say the water has evaporated4 ,what was liquid is now vapor4 ,if we were to observe carefully any dish of water we would find that it continually loses weight on dry days4 ,that is1 there is a constant movement of the molecules of water into the air4 ,this movement of the molecules is explained as follows4 ,there appear to be in the dish of water some molecules that by moving back and forth acquire a greater velocity than their neighbors2 when these reach the surface of the liquid1 some vibration or movement sends them flying into the air above4 ,they are now vapor or gas molecules1 flying1 striking1 and rebounding like the air molecules4 ,sometimes on rebounding1 the water molecules get back into the water again4 ,this is especially apt to happen when the air is damp1 i4e41 when it contains many water molecules4 ,sometimes the air over a dish becomes saturated1 as in the upper part of a corked bottle containing water4 ,although molecules are continually leaving the surface of the water they cannot escape from the bottle1 so in time as many molecules must return to the water from the space above as leave the water in the same time4 ,when this condition exists1 the air above the water is said to be saturated4 ,on very damp days the air is often saturated4 ,the explanation above shows why wet clothes dry so slowly on such a day 7,see ,arts4 #aff-g on ,saturation47 #ai4 ,cooling ,effect of ,evaporation4 ,we have seen that warming a gas increases its volume4 ,this expansion is due to the increased motion of the warmed molecules4 ,now the molecules that escape from a liquid when it evaporates are naturally the fastest moving ones1 i4e41 the hottest ones4 ,the molecules remaining are the slower moving ones or colder molecules4 ,the liquid therefore becomes colder as it evaporates1 unless it is heated4 ,this explains why water evaporating on the surface of our bodies cools us4 ,in evaporating1 the water is continually losing its warm1 fast moving molecules4 ,the cooling effect of evaporation is1 therefore an evidence of molecular motion in liquids4 ,illustration3 ,,fig4 #h4--,osmosis ,shown by carrot placed in water4 #bj4 ,osmosis4--,if two liquids are separated by a membrane or porous partition1 they tend to pass through and mix4 ,this action is called osmose1 or osmosis4 ,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 7see ,fig4 #h7 with a thick syrup4 ,the opening is then closed at the top with a rubber stopper through which passes a long glass tube4 ,if the carrot is immersed in water1 as in ,fig4 #h1 a movement of water through the porous wall to the interior begins at once4 ,here1 as in the experiment of the hydrogen and air passing through the porous cup1 the lighter fluid moves faster4 ,the water collecting in the carrot rises in the tube4 ,this action of liquids passing through porous partitions and mingling is called osmosis4 ,gases and liquids are alike in that each will flow4 ,each is therefore called a fluid4 ,sometimes there is much resistance to the flow of a liquid as in molasses4 ,this resistance is called viscosity4 ,alcohol and gasoline have little viscosity4 ,they are limpid or mobile4 ,air also has some viscosity4 ,for instance1 a stream of air always drags some of the surrounding air along with it4 ,important ,topics #a4 ,liquids behave as if they were composed of small particles in motion4 #b4 ,this is shown by 7#a7 ,diffusion1 7#b7 ,solution1 7#c7 ,evaporation1 7#d7 ,expansion1 7#e7 ,osmosis4 ,exercises #a4 ,give an example or illustration of each of the five evidences of molecular motion in liquids4 #b4 ,when is air saturated8 ,what is the explanation8 #c4 ,why does warming a liquid increase its rate of evaporation8 #d4 ,air molecules are in rapid motion in all directions4 ,do they enter a liquid with a surface exposed to the air8 ,give reason4 #e4 ,what are some of the inconveniences of living in a saturated atmosphere8 #f4 ,fish require oxygen4 ,how is it obtained8 7#c7 ,,molecular ,,forces ,,in ,,liquids #ba4 ,cohesion and ,adhesion4--,in liquids the molecules move about freely yet tend to cling together4 ,this tendency of molecules to cling together which is not noticeable in gases is characteristic of liquids and especially of solids4 ,it is the cause of the viscosity mentioned in the previous section and is readily detected in a variety of ways4 ,for instance1 not only do liquid molecules cling together to form drops and streams1 but they cling to the molecules of solids as well1 as is shown by the wet surface of an object that has been dipped in water4 ,the attraction of like molecules for one another is called cohesion1 while the attraction of unlike molecules is called adhesion1 although the force is the same whether the molecules are alike or unlike4 ,it is the former that causes drops of water to form and that holds iron1 copper1 and other solids so rigidly together4 ,the adhesion of glue to other objects is well known4 ,paint also sticks well4 ,sometimes the joint where two boards are glued together is stronger than the board itself4 ,the force of attraction between molecules has been studied carefully4 ,the attraction acts only through very short distances4 ,the attraction even in liquids is considerable and may be measured4 ,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 measured4 ,illustration3 ,,fig4 #i4--,the water is pulled apart4 ,take a beam balance and suspend from one arm a circular glass plate1 ,fig4 #i4 ,weigh the plate and its support4 ,adjust the glass plate so that it hangs horizontally and just touches the surface of clean water1 the under side being completely wet4 ,now find what additional weight is required to raise the glass plate from the water4 ,just as the plate comes from the water its under side is found to be wet4 ,that is1 the water was pulled apart1 and the plate was not pulled from the water4 ,the cohesion of the water to itself is not so strong as its adhesion to the glass4 ,the cohesion of liquids is further shown by the form a drop of liquid tends to take when left to itself4 ,this is readily seen in small drops of liquids4 ,the spherical shape of drops of water or mercury is an example4 ,a mixture of alcohol and water in proper proportions will just support olive oil within it4 ,by carefully dropping olive oil from a pipette into such a mixture1 a drop of the oil1 an inch or more in diameter suspended in the liquid1 may be formed4 ,it is best to use a bottle with plane or flat sides1 for if a round bottle is used1 the sphere of oil will appear flattened4 ,illustration3 ,,fig4 #aj a4 ,,fig4 #aj b4 ,,figs4 #aj a ,,and b4--,surface tension of a liquid film4 #bb4 ,surface ,tension4--,the cohesion of liquids is also indicated by the tendency of films to assume the smallest possible surface4 ,soap bubble films show this readily4 ,fig4 #aj a represents a circular wire form holding a film in which floats a loop of thread4 ,the tension of the film is shown in ,fig4 #aj b by the circular form of the loop after the film within it has been pierced by a hot wire1 ,fig4 #aa shows a rectangular wire form with a rider4 ,the tension in the film draws the rider forward4 ,illustration3 ,,fig4 #aa4--,the rider is drawn forward4 ,illustration3 ,,fig4 #ab4--,surface tension causes the pointed shape4 ,a soap bubble takes its spherical shape because this form holds the confined air within the smallest possible surface4 ,a drop of liquid is spherical for the same reason4 ,many illustrations of the tension in films may be given4 ,users of water colors notice that a dry camel's-hair brush is bushy4 7,fig4 #ab ,a74 ,when in water it is still bushy4 7,fig4 #ab ,b47 ,but when it is taken from the water and the excess is shaken from it1 it is pointed as in ,fig4 #ab ,c4 ,it is held to the pointed shape by the tension of the liquid film about the brush4 ,illustration3 ,,fig4 #ac4--;,a needle depresses the surface when floating4 ,the surface of water acts as if covered by a film which coheres more strongly than the water beneath it4 ,this is shown by the fact that a steel needle or a thin strip of metal may be floated upon the surface of water4 ,it is supported by the surface film4 7,see ,fig4 #ac47 ,if the film breaks the needle sinks4 ,this film also supports the little water bugs seen running over the surface of a quiet pond in summer4 ,the surface film is stronger in some liquids than in others4 ,this may be shown by taking water1 colored so that it can be seen1 placing a thin layer of it on a white surface and dropping alcohol upon it4 ,wherever the alcohol drops1 the water is seen to pull away from it1 leaving a bare space over which the alcohol has been spread4 ,this indicates that the alcohol has the weaker film4 ,the film of greasy benzine is stronger than the film of the pure material4 ,if one wishes to remove a grease spot and places pure benzine at the center of the spot1 the stronger film of the greasy liquid will pull away from the pure benzine1 and spread out1 making a larger spot than before1 while if pure benzine is placed around the grease spot1 the greasy liquid at the center pulls away from the pure benzine1 drawing more and more to the center1 where it may be wiped up and the grease entirely removed4 ,illustration3 ,,fig4 #ad4--,the molecule at ,a is held differently from one within the liquid4 #bc4 ,explanation of the ,surface ,film4--,beneath the surface of a liquid each molecule is attracted by all the other molecules around it4 ,it is attracted equally in all directions4 ,consequently the interior molecules move very easily over each other in any direction4 ,a molecule at the surface1 as at ,a1 ,fig4 #ad1 is not attracted upward by other liquid molecules4 ,its freedom of motion is thereby hindered with the result that a molecule at the surface behaves differently from one beneath the surface4 ,the surface molecules act as if they form an elastic skin or membrane upon the liquid surface4 ,illustration3 ,,fig4 #ae4--;,capillary attraction in tubes4 #bd4 ,capillarity4--,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 them4 ,if the liquid does not wet the tube1 as when mercury is placed in glass1 the liquid is depressed4 ,it is found in general that3 ,liquids rise in capillary tubes when they wet them and are depressed in tubes which they do not wet2 the smaller the diameter of the tube the greater the change of level4 7,see ,fig4 #ae47 ,this action is explained as follows3 ,the molecules of a liquid have an attraction for each other and also for the sides of a tube4 ,the former is called cohesion for itself1 the latter is called adhesion for the sides of the containing vessel4 ,if the cohesion for itself is greater than the adhesion for the side of the containing vessel1 the liquid is pulled away from the side and is depressed4 ,if the adhesion is greater1 the liquid is elevated4 ,this action is called capillary action from the ,latin word 7capillus7 signifying hair1 since it shows best in fine hairlike tubes4 ,there are many common illustrations of capillary action3 oil rising in a wick2 water rising in a towel or through clothes2 ink in a blotter1 etc4 ,the minute spaces between the fibers composing these objects act as fine tubes4 ,if cloth is treated with a preparation which prevents water from adhering to its fibers1 the material will not be wet when water is poured upon it1 because the water will not run in between the fibers2 a surface film spreads over the cloth so that no water enters it4 ,cravenette cloth has been treated in this way and hence is waterproof4 ,the action of this film may be shown by the following experiment4 ,dip a sieve of fine copper gauze in melted paraffin1 thus coating each wire so that water will not adhere to it4 ,water may now be poured into the sieve1 if a piece of paper is first laid in it to break the force of the water4 ,on carefully removing the paper the surface film of the water will prevent the passage of the water through the sieve4 #be4 ,capillary ,action in ,soils4--,the distribution of moisture in the soil depends largely upon capillary action4 ,when the soil is compact the minute spaces between the soil particles act as capillary tubes1 thus aiding the water to rise to the surface4 ,as the water evaporates from the surface more of it rises by capillary action from the damper soil below4 ,keeping the soil loose by cultivation1 makes the spaces between the particles too large for much capillary action1 thus the moisture is largely prevented from rising to the surface4 ,in the semi-arid regions of the ,west dry farming is successfully practised4 ,this consists in keeping the surface covered with a dust mulch produced by frequent cultivation4 ,in this way the moisture is kept below the surface1 where it can be utilized during the hot dry summer by the roots of growing plants4 ,important ,topics #a4 ,attractive forces between liquid molecules4 #b4 ,cohesion 7like molecules72 adhesion 7unlike molecules74 #c4 ,special effects of this force are classified as 7a7 capillary action1 and 7b7 surface tension4 ,exercises #a4 ,what evidence of capillary action have you seen outside of the laboratory8 #b4 ,what is the explanation for capillary action8 #c4 ,where are surface films found8 #d4 ,what are three common effects of surface films8 #e4 ,explain why cravenette cloth sheds water4 #f4 ,if a circular glass disc #aj cm4 in diameter requires #ej grams of force to draw it from the water1 what is the cohesion of water per square centimeter8 #g4 ,what is the weight in grams of #a ccm4 of water8 of a liter of water8 #h4 ,name five examples of adhesion to be found in your home4 #i4 ,under what conditions will a liquid wet a solid and spread over it8 #aj4 ,when will it form in drops on the surface8 #aa4 ,explain the proper procedure for removing a grease spot with benzine4 #ab4 ,what difference is there between a liquid and a fluid8 #ac4 ,why cannot a soap bubble be blown from pure water8 #ad4 ,which are larger1 the molecules of steam or those of water8 ,why8 #ae4 ,why is the ground likely to be damp under a stone or board when it is dry all around8 #af4 ,why does any liquid in falling through the air assume the globule form8 #ag4 ,give three examples of capillary attraction found in the home4 ,three out of doors4 #ah4 ,why does cultivation of the soil prevent rapid evaporation of water from the ground8 7#d7 ,,evidences ,,of ,,molecular ,,forces ,,in ,,liquids ,,and ,,solids #bf4 ,solutions4--,a crystal of potassium permanganate is placed in a liter of water4 ,it soon dissolves and on shaking the flask each portion of the liquid is seen to be colored red4 ,the dissolving of the permanganate is an illustration of the attraction of the molecules of water for the molecules of the permanganate4 ,we are familiar with this action in the seasoning of food with salt and sweetening with sugar4 ,water will dissolve many substances1 but in varying degrees1 i4e41 of some it will dissolve much1 of others1 little1 and some not at all4 ,further1 different liquids have different solvent powers4 ,alcohol will dissolve resin and shellac1 but it will not dissolve gum arabic1 which is soluble in water4 ,benzine dissolves grease4 ,beeswax is not dissolved by water1 alcohol or benzine1 but is soluble in turpentine4 ,it is found that the temperature of the liquid has a marked effect upon the amount of substance that will dissolve4 ,this is an indication that the motions of the molecules are effective in solution4 ,it appears that dissolving a solid is in some respects similar to evaporation1 and just as at higher temperatures more of the liquid evaporates1 because more of the molecules will escape from the liquid into the air above1 so at higher temperatures1 more molecules of a solid will detach themselves through greater vibration and will move into the liquid4 ,further1 just as an evaporating liquid may saturate the space above it so that any escape of molecules is balanced by those returning1 so with a dissolving solid1 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 condition4 #bg4 ,crystals and ,crystallization4--,this return from the liquid to the solid state1 of molecules that are in solution1 is especially noticeable when the solution is cooling or evaporating and hence is losing its capacity to hold so much of the solid4 ,on returning to the solid1 the molecules attach themselves in a definite manner to the solid portion1 building up regular solid forms4 ,these regular forms are crystals4 ,the action that forms them is called crystallization4 ,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 place4 ,the largest and most symmetrical crystals are those in which the molecules are deposited slowly with no disturbance of the liquid4 ,beautiful crystals of alum may be obtained by dissolving #be g4 of alum in #ej ccm4 of hot water1 hanging two or three threads in the solution and letting it stand over night4 ,the thread fibers provide a foundation upon which crystals grow4 ,when a solution of a solid evaporates1 the molecules of the liquid escape as a gas1 the molecules of the solid remain accumulating as crystals4 ,this principle has many uses3 7a7 sea water is purified by evaporating the water and condensing the vapor1 which of course forms pure water4 7b7 water is forced down to salt beds where it dissolves the salt4 ,the brine is then raised and evaporated1 leaving the salt in the evaporating pans4 #bh4 ,absorption of ,gases by ,solids and ,liquids4--,if a piece of heated charcoal is placed in a test-tube containing ammonia gas1 inverted in mercury1 the ammonia is seen to disappear1 the mercury rising to take its place4 ,the ammonia has been absorbed by the charcoal1 the gas molecules clinging closely to the solid4 ,the charcoal being very porous presents a large surface to the action of the gas4 ,this experiment indicates that attraction exists between gas molecules and other molecules4 ,many porous substances have this power of absorbing gases4 ,we have all noticed that butter has its flavor affected by substances placed near it4 ,that liquids absorb gases is shown by slowly heating cold water in a beaker4 ,small bubbles of air form on the sides and rise before the boiling point is reached4 ,ammonia gas is readily absorbed in water1 the bubbles disappearing almost as soon as they escape into the water from the end of the delivery tube4 ,household ammonia is simply a solution of ammonia gas in water4 ,on warming the solution of ammonia the gas begins to pass off2 thus1 warming a liquid tends to drive off any gas dissolved in it4 ,soda water is made by forcing carbon dioxide gas into water under strong pressure4 ,when placed in a vessel open to the air the pressure is lessened and part of the gas escapes4 ,the dissolved gas gives the characteristic taste to the beverage4 ,important ,topics #a4 ,the solution of solids is increased by heating4 #b4 ,the solution of gases is decreased by heating4 #c4 ,pressure increases the quantity of gas that can be dissolved in a liquid4 #d4 ,the attraction 7cohesion7 of molecules of a dissolved solid for each other is shown by crystallization4 ,exercises #a4 ,how do fish obtain oxygen for breathing8 #b4 ,why does warming water enable it to dissolve more of a salt8 #c4 ,why does warming water lessen the amount of a gas that will stay in solution8 #d4 ,will water absorb gases of strong odor8 ,how do you know8 #e4 ,name three solvents4 ,give a use for each4 #f4 ,what liquids usually contain gases in solution8 ,name some uses for these dissolved gases4 #g4 ,what is the weight of a cubic meter of water8 #h4 ,name three substances obtained by crystallization4 #i4 ,how is maple sugar obtained8 #aj4 ,name five crystalline substances4 7#e7 ,,evidence ,,of ,,molecular ,,forces ,,in ,,solids #bi4 ,differences between ,solids and ,gases4--,in studying gases1 it is seen that they behave as if they were composed of small particles in rapid motion1 continually striking and rebounding1 and separating to fill any space into which they are released4 ,this action indicates that there is practically no attractive force between such molecules4 ,between the molecules of a solid1 however1 the forces of attraction are strong1 as is shown by the fact that a solid often requires a great force to pull it apart2 some1 as steel and iron1 show this property in a superlative degree1 a high-grade steel rod #a cm4 in diameter requiring nearly #i tons to pull it apart4 ,tests show that the breaking strengths of such rods are directly proportional to their areas of cross-section4 ,that is1 twice the area has twice the breaking strength4 ,illustration3 ,,fig4 #af4--;,elasticity of bending4 #cj4 ,elasticity4--,fully as important as a knowledge of the breaking strengths of solids1 is the knowledge of what happens when the forces used are not great enough to break the rods or wires4 ,take a wooden rod 7as a meter stick7 and clamp one end to the table top1 as in ,fig4 #af4 ,at the other end hang a weight4 ,fasten a wire to this end so that it projects out in front of a scale4 ,add successively several equal weights and note the position of the wire each time4 ,remove the weights in order1 noting the positions as before4 ,the rod will probably return to the first position4 ,this simple experiment illustrates a characteristic of solids3 that of changing shape when force is applied and of returning to the original shape when the force is removed4 ,this property is called elasticity4 ,tests of elasticity are made by subjecting wire of different materials but of the same dimensions to the same tension4 ,the one changing least is said to have the greatest elastic force or elasticity4 ,if greater forces are applied to the wire and then removed1 one will finally be found that will permanently stretch the wire so that it will not return exactly to the former length4 ,the wire has now passed its elastic limit and has been permanently stretched4 ,just as there are great differences between the elastic forces of different substances1 so there are great differences in the limits of elasticity4 ,in some substances the limit is reached with slight distortion1 while others are perfectly elastic even when greatly stretched4 ,india rubber is an example of a body having perfect elasticity through wide limits4 ,glass has great elastic force but its limit of elasticity is soon reached4 ,substances like ,india rubber may be said to have great stretchability1 but little elastic force4 ,in physics1 elasticity refers to the elastic force rather than to ability to endure stretching4 #ca4 ,kinds of ,elasticity4--,elasticity may be shown in four ways3 compression1 bending or flexure1 extension or stretching1 twisting or torsion4 ,the first is illustrated by squeezing a rubber eraser1 the second by an automobile spring1 the third by the stretching of a rubber band1 the fourth by the twisting and untwisting of a string by which a weight is suspended4 ,there are two kinds of elasticity3 7#a7 elasticity of form or shape2 7#b7 elasticity of volume4 ,gases and liquids possess elasticity of volume1 but not of shape1 while solids may have both kinds4 ,gases and liquids are perfectly elastic because no matter how great pressure may be applied1 as soon as the pressure is removed they regain their former volume4 ,no solid possesses perfect elasticity1 because sooner or later the limit of elasticity will be reached4 #cb4 ,hooke's ,law4,a--,on examining the successive movements of the end of the rod in ,art4 #cj1 we find that they are approximately equal4 ,carefully conducted experiments upon the elasticity of bodies have shown that the changes in shape are directly proportional to the forces applied1 provided that the limit of elasticity is not reached4 ,this relation1 discovered by ,robert ,hooke1 is sometimes expressed as follows3 ,within the limits of perfect elasticity1 all changes of size or shape are directly proportional to the forces producing them4 ,a ,a law is a statement of a constant mode of behavior4 ,it is often expressed in mathematical language4 #cc4 ,molecular ,forces and ,molecular ,motions4--,if a solid is compressed1 on releasing the pressure the body regains its former shape if it has not been compressed too far4 ,this indicates that at a given temperature the molecules of a solid tend to remain at a fixed distance from each other1 and resist any attempt to decrease or increase this distance4 ,this raises the question1 ,why does not the cohesion pull the molecules tightly together so that compression would be impossible8 ,the reason is that heat affects the size of solid bodies4 ,on lowering the temperature1 bodies do contract1 for as soon as the temperature is lowered the vibration of the molecule is lessened4 ,on raising the temperature the molecules are pushed farther apart4 ,the size of a body1 then1 is the result of a balance of opposing forces4 ,the attractive force between the molecules pulling them together is cohesion1 while the force which pushes them apart is due to the motions of the molecules4 ,raising the temperature and thus increasing the motion causes expansion2 lowering the temperature decreases the molecular motion and so causes contraction4 ,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 motion4 #cd4 ,properties of ,matter4--,many differences in the physical properties of solids are due to differences between the cohesive force of different kinds of molecules4 ,in some substances1 the attraction is such that they may be rolled out in very thin sheets4 ,gold is the best example of this1 sheets being formed #a_/cjj1jjj of an inch thick4 ,this property is called malleability4 ,in other substances the cohesion permits it to be drawn out into fine threads or wire4 ,glass and quartz are examples of this4 ,this property is called ductility4 ,in some1 the cohesion makes the substance excessively hard1 so that it is difficult to work or scratch its surface4 ,the diamond is the hardest substance known4 ,some substances are tough1 others brittle4 ,these are tested by the ability to withstand sudden shocks as the blow of a hammer4 ,important ,topics #a4 ,molecular forces in solids2 7a7 adhesion1 7b7 cohesion4 #b4 ,elasticity1 ,hooke's ,law4 #c4 ,contraction on cooling4 #d4 ,malleability1 ductility1 hardness1 brittleness1 etc4 ,exercises #a4 ,give an illustration of ,hooke's ,law from your own experience4 #b4 ,what devices make use of it8 #c4 ,do solids evaporate4 ,give reasons4 #d4 ,when iron is welded1 is cohesion or adhesion acting8 #e4 ,when a tin basin is soldered1 is cohesion or adhesion acting8 #f4 ,sometimes a spring is made more elastic by tempering and made soft by annealing4 ,look up the two terms4 ,how is each accomplished8 #g4 ,review the definitions3 solid1 liquid1 and gas4 ,why do these definitions mean more to you now than formerly8 #h4 ,if a wire is stretched #j4c cm4 on applying #d kg4 of force1 what force will stretch it #j4ge cm8 ,explain4 #i4 ,how long will it take under ordinary conditions for a gas molecule to cross a room8 ,give reasons for your answer4 #aj4 ,what is meant by the elastic limit of a body8 #aa4 ,without reaching the elastic limit1 if a beam is depressed #d mm4 under a load of #fj kg41 what will be the depression under a load of #djj kg48 ,of #fjj kg48 #ab4 ,name three substances that possess elasticity of volume4 #ac4 ,give three examples of each2 elasticity of 7#a7 compression1 7#b7 stretching1 7#c7 torsion1 7#d7 flexure4 ,review ,outline3 ,introduction and ,molecules ,physics2 definition1 topics considered1 physical and chemical changes4 ,science2 hypothesis1 theory1 law4 ,knowledge2 common1 scientific4 ,matter2 three states1 molecular theory4 ,mass1 weight1 volume4 ,metric system2 units1 tables1 equivalents1 advantages4 ,evidences of molecular motions2 gases 7#c71 liquids 7#e71 solids 7#c74 ,evidences of molecular forces2 liquids 7#c71 solids 7many7 special properties such as3 elasticity1 tenacity1 ductility1 hardness1 etc4 ,hooke's law2 applications4 ,,chapter ,,iii ,,mechanics ,,of ,,liquids 7#a7 ,,the ,,gravity ,,pressure ,,of ,,liquids #ce4 ,pressure of ,liquids against ,surfaces4--,the sight of a great ship1 perhaps built of iron and floating on water1 causes one to wonder at the force that supports it4 ,this same force is noticed when one pushes a light body1 as a cork1 under water4 ,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 surface4 ,even the weight of our bodies is so far supported by water that many persons can float4 ,illustration3 ,,fig4 #ag4--,water forces the card against the chimney4 ,the following experiment provides a means of testing this force3 ,if an empty can is pushed down into water1 we feel at once the force of the liquid acting against the object and tending to push it upward4 ,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 liquid4 ,we may test this action in various ways3 a simple way is to take a cylindrical lamp chimney1 press a card against its lower end and place it in the water in a vertical position4 ,the force of the water will hold the card firmly against the end of the chimney4 7,see ,fig4 #ag47 ,the amount of force may be tested by dropping shot into the tube until the card drops off4 ,at greater depths more shot will be required1 showing that the force of the water increases with the depth4 ,or one may pour water into the chimney4 ,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 outside4 ,that is1 before the card will fall off1 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 water4 #cf4 ,law of ,liquid ,pressure4--,as there is twice as much water or shot in the chimney when it is filled to a depth of #aj cm4 as there is when it is filled to a depth of #e cm4 the force of the water upward on the bottom must be twice as great at a depth of #aj cm4 as at a depth of #e cm4 ,since this reasoning will hold good for a comparison of forces at any two depths1 we have the law3 ,the pressure exerted by a liquid is directly proportional to the depth4 ,the amount of this force may be computed as follows3 ,first1 the card stays on the end of the tube until the weight of water from above equals the force of the water from below1 and second1 the card remains until the water is at the same height inside the tube as it is outside4 ,now if we find the weight of water at a given depth in the tube1 we can determine the force of the water from below4 ,if for instance the chimney has an area of cross-section of #ab sq4 cm4 and is filled with water to a depth of #aj cm41 the volume of the water contained will be #abj ccm4 ,this volume of water will weigh #abj g4 ,this represents then1 not only the weight of the water in the tube1 but also the force of the water against the bottom4 ,in a similar way one may measure the force of water against any horizontal surface4 #cg4 ,force and ,pressure4--,we should now distinguish between force and pressure4 ,pressure refers to the force acting against unit area1 while force refers to the action against the whole surface4 ,thus for example1 the atmospheric pressure is often given as #ae pounds to the square inch or as one kilogram to the square centimeter4 ,on the other hand1 the air may exert a force of more than #cjj pounds upon each side of the hand of a man2 or a large ship may be supported by the force of thousands of tons exerted by water against the bottom of the ship4 ,in the illustration1 given in ,art4 #cf1 the upward force of the water against the end of the tube at a depth of #aj cm4 is computed as #abj grams4 ,the pressure at the same depth will be #aj grams per sq4 cm4 ,what will be the pressure at a depth of #bj cm48 at a depth of #ej cm48 of #ajj cm48 ,compare these answers with the law of liquid pressure in ,art4 #cf4 #ch4 ,density4--,if other liquids1 as alcohol1 mercury1 etc41 were in the jar1 the chimney would need filling to the same level outside1 with the same liquid1 before the card would fall off4 ,this brings in a factor that was not considered before1 that of the mass,b of a cubic centimeter of the liquid4 ,this is called the density of the liquid4 ,alcohol has a density of #j4h g4 per cubic centimeter1 mercury of #ac4f g4 per cubic centimeter1 while water has a density of #a g4 per cubic centimeter4 ,b ,the mass of a body is the amount of matter in it1 the weight is the pull of the earth upon it4 #ci4 ,liquid ,force against ,any ,surface4--,to find the force exerted by a liquid against a surface we must take into consideration the area of the surface1 and the height and the density of the liquid above the surface4 ,the following law1 and the formula representing it1 which concisely expresses the principle by which the force exerted by a liquid against any surface may be computed1 should be memorized3 ,the force which a liquid exerts against any surface1 equals the area of the surface1 times its average depth below the surface of the liquid1 times the weight of unit volume of the liquid4 ,or1 expressed by a formula1 ,f ,ahd4 ,in this formula1 ,f stands for the force which a liquid exerts against any surface1 ,a the area of the surface1 h1 for the average depth 7or height7 of the liquid pressing on the surface1 and d1 for the weight of unit volume of the liquid4 ,this is the first illustration in this text1 of the use of a formula to represent a law4 ,observe how accurately and concisely the law is expressed by the formula4 ,when the formula is employed1 however1 we should keep in mind the law expressed by it4 ,we must remember that a liquid presses not only downward and upward but sideways as well1 as we see when water spurts out of a hole in the side of a vessel4 ,experiments have shown that at a point the pressure in a fluid is the same in all directions1 hence the rule given above may be applied to the pressure of a liquid against the side of a tank1 or boat1 or other object1 provided we are accurate in determining the average depth of the liquid2 ,the following example illustrates the use of the law4 ,for ,example3 ,if the ,english system is used1 the area of the surface should be expressed in square feet1 the depth in feet and the weight of the liquid in pounds per cubic foot4 ,one cubic foot of water weighs #fb4d lbs4 ,suppose that a box #c ft4 square and #d ft4 deep is full of water4 ,what force will be exerted by the water against the bottom and a side8 ,from the law given above1 the force of a liquid against a surface equals the product of the area of the surface1 the depth of the liquid and its weight per unit volume1 or using the formula1 ,f ,ahd4 ,to compute the downward force against the bottom we have the area1 #i1 depth1 #d1 and the weight #fb4d lbs4 per cubic foot4 #i #d #fb4d lbs4 #bbdf4d lbs4 ,to compute the force against a side1 the area is #ab1 the average depth of water on the side is #b1 the weight #fb4d1 #ab #b #fb4d lbs4 #adig4f lbs4 ,important ,topics #a4 ,liquids exert pressure2 the greater the depth the greater the pressure4 #b4 ,difference between force and pressure4 #c4 ,rules for finding upward and horizontal force exerted by a liquid4 ,f ,ahd4 #d4 ,weight1 mass1 density4 ,exercises #a4 ,what is the density of water8 #b4 ,what force is pressing upward against the bottom of a flat boat1 if it is #fj ft4 long1 #ae ft4 wide and sinks to a depth of #b ft4 in the water8 ,what is the weight of the boat8 #c4 ,if a loaded ship sinks in the water to an average depth of #bj ft41 the area of the bottom being #fjjj sq4 ft41 what is the upward force of the water8 ,what is the weight of the ship8 #d4 ,if this ship sinks only #aj ft4 when empty1 what is the weight of the ship alone8 ,what was the weight of the cargo in ,problem #c8 #e4 ,what is the liquid force against one side of an aquarium #aj ft4 long1 #d ft4 deep and full of water8 #f4 ,what is the liquid force on one side of a liter cube full of water8 ,full of alcohol8 ,full of mercury8 ,what force is pressing on the bottom in each case8 #g4 ,what depth of water will produce a pressure of #a g4 per square centimeter8 #aj g4 per square centimeter8 #ajjj g4 per square centimeter8 #h4 ,what depth of water will produce a pressure of #a lb4 per square inch8 #aj lbs4 per square inch8 #ajj lbs4 per square inch8 #i4 ,what will be the force against a vertical dam-breast #cj meters long1 the depth of the water being #aj meters8 #aj4 ,a trap door with an area of #ajj sq4 dcm4 is set in the bottom of a tank containing water #e meters deep4 ,what force does the water exert against the trap door8 #aa4 ,what is the force on the bottom of a conical tank1 filled with water1 the bottom of which is #c meters in diameter1 the depth #a4e meters8 #ab4 ,if alcohol1 density #j4h were used in problem #aa1 what would be the force8 ,what would be the depth of alcohol to have the same force on the bottom as in problem #aa8 #ac4 ,what is the pressure in pounds per square inch at a depth of #a mile in sea water1 density #a4jbf grams per cc48 #ad4 ,find the force on the sides and bottom of a rectangular cistern filled with water1 #bj ft4 long1 #aj ft4 wide1 and #aj ft4 deep8 #ae4 ,find the force on the bottom of a water tank #ad ft4 in diameter when the water is #ae ft4 deep1 when full of water4 #af4 ,find the force on one side of a cistern #h ft4 deep and #aj ft4 square1 when full of water4 #ag4 ,find the force on a vertical dam #cjj ft4 long and #aj ft4 high1 when full of water4 #ah4 ,find the pressure at the bottom of the dam in question #ag4 #ai4 ,why are dams made thicker at the bottom than at the top8 #bj4 ,a ship draws #bf ft4 of water1 i4e41 its keel is #bf ft4 under water4 ,what is the liquid force against a square foot surface of the keel8 ,find the pressure on the bottom4 7#b7 ,,transmission ,,of ,,liquid ,,pressure #dj4 ,pascal's ,principle4--,liquids exert pressure not only due to their own weight1 but when confined1 may be made to transmit pressure to considerable distances4 ,this is a matter of common knowledge wherever a system of waterworks with connections to houses is found1 as in cities4 ,the transmission of liquid pressure has a number of important applications4 ,the principle underlying each of these was first discovered by ,pascal1 a ,french scientist of the seventeenth century4 ,pascal's ,principle1 as it is called1 may be illustrated as follows3 ,suppose a vessel of the shape shown in ,fig4 #ah1 the upper part of which we may assume has an area of #a sq4 cm41 is filled with water up to the level ,,ab4 ,a pressure will be exerted upon each square centimeter of area depending upon the depth4 ,suppose that the height of ,,ab above ,,cd is #aj cm41 then the force upon #a sq4 cm4 of ,,cd is #aj g41 or if the area of ,,cd is #af sq4 cm41 it receives a force of #afj g4 ,illustration3 ,,fig4 #ah4--,the force increases with the depth4 ,if now a cubic centimeter of water be poured upon ,,ab it will raise the level #a cm41 or the head of water exerting pressure upon ,,cd becomes #aa cm41 or the total force in ,,cd is #afaa g41 i4e41 each square centimeter of ,,cd receives an additional force of #a g4 ,hence the force exerted on a unit area at ,,ab is transmitted to every unit area within the vessel4 ,the usual form in which this law is expressed is as follows3 ,pressure applied to any part of a confined liquid is transmitted unchanged1 in all directions1 and adds the same force to all equal surfaces in contact with the liquid4 ,illustration3 ,,fig4 #ai4--,the force is proportional to the area4 ,the importance of this principle1 as ,pascal himself pointed out1 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 liquid1 both areas being in contact with the same liquid4 ,thus in ,fig4 #ai if the area of the surface ,,cd is #bjjj times the area of the surface ,,ab1 then #a lb4 applied to the liquid on ,,ab will exert or sustain a force of #bjjj lbs4 on ,,cd4 #da4 ,hydraulic ,press4--,an important application of ,pascal's principle is the hydraulic press4 ,see ,fig4 #bj4 ,it is used for many purposes where great force is required1 as in pressing paper or cloth1 extracting oil from seeds1 lifting heavy objects1 etc4 ,many high school pupils have been seated in a hydraulic chair used by a dentist or barber4 ,this chair is a modified hydraulic press4 ,illustration3 ,,fig4 #bj4--;,cross-section of a hydraulic press4 ,the hydraulic press contains two movable pistons1 ,p and p 7see ,fig4 #bj74 ,the larger of these1 ,p1 has a cross-sectional area that may be #ajj or #ajjj times that of the smaller4 ,the smaller one is moved up and down by a lever2 on each upstroke1 liquid is drawn in from a reservoir1 while each down-stroke forces some of the liquid into the space about the large piston4 ,valves at ,v and ,v prevent the return of the liquid4 ,if the area of ,p is #a1jjj times that of p1 then the force exerted by ,p is #ajjj times the force employed in moving p4 ,on the other hand1 since the liquid moved by the small piston is distributed over the area of the large one1 the latter will move only #a_/ajjj as far as does the small piston4 ,the relation between the motions of the two pistons and the forces exerted by them may be stated concisely as follows3 ,the motions of the two pistons of the hydraulic press are inversely proportional to the forces exerted by them4 ,the cross-sectional areas of the two pistons are1 on the other hand1 directly proportional to the forces exerted by them4 ,an application of ,pascal's principle often employed in cities is the hydraulic elevator4 ,in this device a long plunger or piston extends downward from the elevator car into a cylinder sunk into the earth1 sometimes to a depth of #cjj ft4 ,water forced into this cylinder pushes the piston upward and when the water is released from the cylinder the piston descends4 ,fig4 #ba represents another form of hydraulic elevator1 where the cylinder and piston are at one side of the elevator shaft4 ,in this type1 to raise the elevator1 water is admitted to the cylinder pushing the piston downward4 #db4 ,artesian ,wells4--,sometimes a porous stratum containing water in the earth's crust is inclined4 ,then if there are impervious strata 7see ,fig4 #bb71 both above and below the water-bearing one1 and the latter comes to the surface so that rain may fill it1 a well sunk to the water-bearing stratum at a point where it is below the surface will usually give an artesian well1 that is1 one in which the water rises to or above the surface4 ,many are found in the ,united ,states4 ,illustration3 ,,fig4 #ba4--;,a hydraulic freight elevator4 ,illustration3 ,,fig4 #bb4--;,conditions producing an artesian well4 ,illustration3 ,,fig4 #bc4--;,a standpipe4 #dc4 ,standpipes and ,air ,cushions4--,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 time4 ,again1 if several persons are using a hose for sprinkling1 the pressure may be lessened so as to be insufficient to force the water above the first floor4 ,in order to allow for these changes some flexibility or spring must be introduced somewhere into the water-pipe system4 ,water is nearly incompressible and if no means were employed to take care of the pressure changes1 the sudden stopping and starting of the flow would cause serious jars and start leaks in the pipes4 ,two common devices for controlling sudden changes in the water pressure are the standpipe and the air cushion4 ,the standpipe is simply a large vertical tube connected to the water mains from which and into which water readily flows4 ,when many faucets are opened the water lowers2 when most faucets are closed the water rises1 giving a simple automatic control of the surplus water and a supply of water for a short time during a shut-down of the pumps4 ,standpipes are often used in towns and small cities4 ,fig4 #bc represents the standpipe at ,jerome1 ,idaho4 ,the air cushion 7,fig4 #bd7 is a metal pipe or dome filled with air attached to a water pipe where sudden changes in pressure are to be controlled4 ,at many faucets in a city water system such an air cushion is employed4 ,it contains air2 this1 unlike water1 is easily compressible and the confined air when the tap is suddenly closed receives and checks gradually the rush of water in the pipe4 ,even with an air cushion1 the pound of the water in the pipe when a tap is suddenly closed is often heard4 ,if air cushions were not provided1 the water hammer would frequently crack or break the pipes4 ,illustration3 ,,fig4 #bd4--,the short pipe above the faucet contains air forming an air cushion4 ,important ,topics #a4 ,pascal's law4 #b4 ,hydraulic press4 #c4 ,artesian wells4 #d4 ,standpipes and air cushions4 ,exercises #a4 ,where have you seen an air cushion8 ,describe it and its use4 #b4 ,where have you seen an hydraulic press8 ,why and how used8 #c4 ,where have you seen hydraulic elevators8 ,what moves them8 #d4 ,where do you know of liquids under pressure8 ,three examples4 #e4 ,what is the pressure in water at a depth of #aejj cm4 ,express in grams per square centimeter and in kilograms per square centimeter4 #f4 ,what head,c of water is required to give a pressure of #bjj g4 per square centimeter8 #b kg4 per square centimeter8 ,c ,head is a term used to express the vertical height of water in pipes4 #g4 ,what pressure will be produced by a head of water of #bj meters8 #h4 ,if #agbh cu4 in4 of water are placed in a vertical tube #a sq4 in4 in cross section to what height would the water rise8 ,it would give how many feet of head8 #i4 ,what would the water in problem #h weigh8 ,what pressure would it produce at the bottom1 in pounds per square inch8 ,from this1 compute how many feet of head of water will produce a pressure of #a lb4 per square inch4 #aj4 ,using the result in problem #i1 what head of water will produce a pressure of #aj lbs4 per square inch8 #ajj lbs4 per square inch8 #aa4 ,from the result in #i1 #ajj ft4 of head of water will produce what pressure8 #ajjj ft4 of head8 #ab4 ,if the diameter of the pump piston in a hydraulic press is #b cm4 and that of the press piston #ej cm4 what will be the force against the latter if the former is pushed down with a force of #dj kg48 7#c7 ,,archimedes' ,,principle #dd4 ,a ,body ,supported by a ,liquid4--,among the applications of the force exerted by a liquid upon a surface1 ,archimedes' ,principle is one of the most important4 ,most persons have noted that a body placed in water is partly or wholly supported by the force of the water upon it4 ,a stone held by a cord and lowered into water is felt to have a part of its weight supported1 while a piece of cork or wood is wholly supported and floats4 ,the human body is almost entirely supported in water1 in fact1 many people can easily float in water4 ,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 liquid4 ,illustration3 ,,fig4 #be4--,theoretical proof of ,archimedes' principle4 #de4 ,archimedes' ,principle4--,a body immersed in a liquid is pushed up by a force equal to the weight of the liquid that it displaces4 ,the proof for this law is simply demonstrated4 ,suppose a cube1 abcd1 is immersed in water 7,fig4 #be74 ,the upward force on cd is equal to the weight of a column of water equal to cdef4 7,see ,art4 #ci47 ,the downward force upon the top of the cube is equal to the weight of the column of water abef4 ,then the net upward force upon the cube1 that is1 the upward force upon the bottom less the downward force upon the top1 or the buoyant force exerted by the liquid is exactly equal to the weight of the displaced water abcd4 #df4 ,law of ,floating ,bodies4--,this same reasoning may be applied to any liquid and to any body immersed to any depth below the surface of the liquid4 ,if the body weighs more than the displaced liquid it will sink4 ,if it weighs less than the displaced liquid it will float or rise in the water4 ,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 displaces4 ,from this we have the law of floating bodies4 ,a floating body displaces its own weight of the liquid in which it floats4 ,illustration3 ,,fig4 #bf4--;,a floating body displaces its own weight of water4 ,to test the law of floating bodies1 take a rod of light wood #a cm4 square and #cj cm4 long 7,fig4 #bf74 ,bore out one end and fill the opening with lead and seal with paraffin so that the rod will float vertically when placed in water4 ,mark upon one side of the rod a centimeter scale1 and dip the rod in hot paraffin to make it waterproof4 ,now find the weight of the stick in grams and note the depth to which it sinks in water in centimeters4 ,compute the weight of the displaced water4 ,it will equal the weight of the rod4 #dg4 ,applications of ,archimedes' ,principle4 ,there are numerous applications of ,archimedes' ,principle and the law of floating bodies4 7a7 ,to ,find the ,weight of a ,floating ,body3 ,problem4--,a boat #bj ft4 long and with an average width of #f ft4 sinks to an average depth of #c ft4 in the water4 ,find the weight of the boat4 ,what weight of cargo will sink it to an average depth of #e ft48 ,solution4--,the volume of the water displaced is #bj #f #c cu4 ft4 #cfj cu4 ft4 ,since #a cu4 ft4 of water weighs #fb4d lbs41 #cfj #fb4d lbs4 #bb1dfd lbs41 the weight of water displaced4 ,by the law of floating bodies this is equal to the weight of the boat4 ,when loaded the volume of water displaced is #bj ft4 #f #e ft4 which equal #fjj cu4 ft4 #fjj #fb4d lbs4 #cg1ddj lbs4 ,this is the weight of the water displaced when loaded4 #cg1ddj lbs4 - #bb1dfd lbs4 #ad1igf lbs41 the weight of the cargo4 7b7 ,to ,find the ,volume of an ,immersed ,solid3 ,problem4--,a stone weighs #ahg4b lbs4 in air and appears to weigh #abd4h lbs4 in water4 ,what is its volume8 ,solution4--#ahg4b lbs4 - #abd4h lbs4 #fb4d lbs41 the buoyant force of the water4 ,by ,archimedes' ,principle1 this equals the weight of the displaced water which has a volume of #a cu4 ft4 which is therefore the volume of the stone4 7c7 ,to ,find the ,density of a ,body3 ,the density of a body is defined as the mass of unit volume4 ,we can easily find the mass of a body by weighing it1 but the volume is often impossible to obtain by measurements1 especially of irregular solids4 ,archimedes' ,principle1 however1 provides a method of finding the volume of a body accurately by weighing it first in air and then in water 7,fig4 #bg71 the apparent loss in weight being equal to the weight of the displaced water4 ,one needs only to find the volume of water having the same weight as the loss of weight to find the volume of the body4 ,if the metric system is used1 #a ccm4 of water weighs #a g41 and the volume is numerically the same as the loss of weight4 ,illustration3 ,,fig4 #bg4--;,a method of weighing a body under water4 ,important ,topics #a4 ,archimedes' ,principle4 #b4 ,law of floating bodies4 #c4 ,the applications of ,archimedes' ,principle are to determine 7a7 the weight of a floating body2 7b7 the volume of an immersed solid1 and 7c7 the density of a body4 ,exercises #a4 ,look up the story of ,archimedes and the crown4 ,write a brief account of it4 #b4 ,why is it easier for a fat man to float in water than for a lean one8 #c4 ,a fish weighing #a lb4 is placed in a pail full of water4 ,will the pail and contents weigh more than before adding the fish8 ,why8 #d4 ,why can a large stone be lifted more easily while under water than when on the land8 #e4 ,why does the air bubble in a spirit level move as one end of the instrument is raised or lowered8 #f4 ,why does a dead fish always float8 #g4 ,a ship is built for use in fresh water4 ,what will be the effect on its water line when passing into the ocean8 #h4 ,why can small bugs walk on water while large animals cannot8 #i4 ,if an object weighing #fb4d lbs4 just floats in water1 what weight of water does it displace8 ,what volume of water is displaced8 ,what is the volume of the body8 #aj4 ,what is the volume of a man who just floats in water if he weighs #abd4h lbs48 ,if he weighs #ahg4b lbs48 #aa4 ,an object weighing #ejj g4 just floats in water4 ,what is its volume8 ,how much water does a floating block of wood displace if it weighs #abe lbs48 #abe g48 #b kg48 #bjjj kg48 #ab4 ,a flat boat #aj #dj ft4 in size will sink how much in the water when #aj horses each weighing #abej lbs4 are placed on board8 #ac4 ,a ship #ijj ft4 long and #hj ft4 average width sinks to an average depth of #be ft4 when empty and #dj ft4 when loaded4 ,what is the weight of the ship and of its load8 #ad4 ,will a #ajjj cc4 block sink or float in water if it weighs #hjj g48 ,if it weighs #abjj g48 ,explain4 #ae4 ,if a #ajjj cc4 block of metal weighing #abjj g4 is placed in the water in mid ocean what will become of it8 #af4 ,prove ,archimedes' ,principle by use of the principles of liquid pressure4 #ag4 ,an irregular stone1 density #b4e g4 per ccm4 displaces #b cu4 ft4 of water4 ,what is its weight8 ,its apparent weight in water8 #ah4 ,will the depth to which a vessel sinks in water change as she sails from ,lake ,ontario into the ,atlantic ,ocean8 ,why8 #ai4 ,if the density of sea water is #a4jbfi g4 per cubic centimeter and that of ice #j4iah g4 per ccm41 what portion of an iceberg is above water8 #bj4 ,in drawing water from a well by means of a bucket1 why is less force used when it is under water than when entirely above8 #ba4 ,a stone which weighs #cjj lbs4 can be lifted under water with a force of #aej lbs4 ,what is the volume of the stone8 #bb4 ,the average density of the human body is #a4jg grams per c4c4 ,how much water will a man who weighs #aej lbs4 displace when diving8 ,how much when floating8 7#d7 ,,density ,,and ,,specific ,,gravity #dh4 ,density4--,the density of a substance is often used as a test of its purity4 ,archimedes in testing ,king ,hiero's crown to find out if it were made of pure gold determined first its density4 ,it is by such tests that the purity of milk1 of alcohol1 of gold1 and a great variety of substances is often determined4 ,knowledge of methods of finding density is of value to everyone and should be included in the education of every student4 ,the density of a substance is the mass of unit volume of the substance4 ,in the metric system1 for example1 the density of a substance is the mass in grams per #a ccm4 ,taking water1 #a ccm4 weighs #a gr4 or its density is therefore #a g4 to the cubic centimeter4 ,a cubic centimeter of aluminium weighs #b4g g4 ,its density therefore is #b4g g4 per ccm4 #di4 ,specific ,gravity4--,specific gravity is the ratio of the weight of any volume of a substance to the weight of an equal volume of water4 ,its meaning is not quite the same as that of density1 since specific gravity is always a ratio1 i4e41 an abstract number1 as #b4g4 ,density of a substance is a concrete number1 as #b4g grams per ccm4 ,in the metric system the density of water is one gram per cubic centimeter1 therefore we have3 ,density 7g4 per ccm47 7numerically7 specific gravity4 ,in the ,english system1 the density of water is #fb4d pounds per cubic foot1 therefore in this system we have3 ,density 7lbs4 per cu4 ft47 7numerically7 #fb4d sp4 gr4 #ej4 ,methods for ,finding ,density and ,specific ,gravity 7a7 ,regular ,solids4--,solids of regular shapes such as cubes1 spheres1 etc41 whose volumes may be readily found by measurement1 may be weighed4 ,the mass divided by the volume gives the density1 or ,d ,m_/v4 7b7 ,irregular ,solids4--with these the volume cannot be found by measurement but may be obtained by ,archimedes' ,principle4 ,weigh the solid first in the air and then in water4 ,the apparent loss of weight equals the weight of the equal volume of water displaced4 ,from this the volume may be found4 ,and then the density equals mass_/volume2 the specific gravity wt4 in air _/ wt4 of equal volume of water wt4 in air _/ 77wt4 in air7 - 7wt4 in water77 mass density equals ------2 the specific gravity volume wt4 in air wt4 in air ---------------------------- ----------------------------- wt4 of equal volume of water 77wt4 in air7 - 7wt4 in water77 7c7 ,solids ,lighter than ,water4--,this will require a sinker to hold the body under water4 ,weigh the solid in air 7w74 ,weigh the sinker in water 7s74 ,attach the sinker to the solid and weigh both in water 7w74 ,the specific gravity equals 7wt4 of solid in air7_/7loss in wt4 of solid in water7 or w_/77w s7 - w7 wt4 of solid in air w --------------------------- or ------------ loss of wt4 of solid in water 7w s7 - 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 water1 less the combined weight of both in water4 7d7 ,the ,density of a ,liquid by a ,hydrometer4--,one may also easily find the density of any liquid by ,archimedes' ,principle4 ,if one takes the rod described in ,art4 #df1 and places it in water1 the number of cubic centimeters of water it displaces indicates its weight in grams4 ,on placing the rod in another liquid in which it floats1 it will of course displace its own weight and the height to which the liquid rises on the scale gives the volume4 ,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 liquid4 ,commercial hydrometers for testing the density of milk1 alcohol and other liquids are made of glass of the form shown in ,fig4 #bh4 ,the long narrow stem permits small differences in volume to be noticed1 hence they are more accurate than the rod described in the preceding paragraph4 ,for convenience this rod contains a paper scale1 so that when the height of the liquid on the stem is noted1 the density is read at once4 ,illustration3 ,,fig4 #bh4--;,a hydrometer used to find the density of a liquid4 ,density of ,liquids by ,loss of ,weight4 ,weigh a piece of glass in air 7,wa71 in water 7,ww71 and in the liquid to be tested 7,wl74 ,then 7,wa - ,ww7gives the weight of the water displaced4 ,and 7,wa - ,wl7 gives the weight of the liquid displaced4 ,hence1 7,wa - ,wl7_/7,wa - ,ww7 equals the specific gravity of the liquid4 ,important ,topics #a4 ,definitions of density and specific gravity4 #b4 ,methods of finding density3 7a7 regular solids2 7b7 irregular solids2 7c7 solids lighter than water2 7d7 liquids by hydrometer2 7e7 liquids by loss of weight4 ,exercises ,note4--,consider that #a cu4 ft4 of water weighs #fb4d lbs4 ,consider that #a ccm4 of water weighs #a g4 #a4 ,what is meant by the statement that a block of wood has a specific gravity of #j4f8 #b4 ,considering that the density of the human body is the same as that of water1 what is the volume of a #abe-lb4 boy8 ,of a #bej-lb4 man8 ,of a #fb4d-lb4 boy8 ,what is the volume of your body8 #c4 ,how is the weight of large ships found8 ,give an example4 #d4 ,mention three cases where determinations of density are important4 #e4 ,a body weighs #dj g4 in air1 #ae g4 in water1 #e g4 in an acid4 ,find 7a7 the density of the body2 7b7 its volume2 7c7 density of the acid4 #f4 ,if the specific gravity of a horse is #a1 what is the volume of a horse weighing #ejj kg48 ,of one weighing #abdh lbs48 #g4 ,a weighted wooden box sinks to a depth of #bj cm4 in water and #bd cm4 in alcohol1 and to a depth of #ah cm4 in brine4 ,what is the density of the alcohol and of the brine8 #h4 ,a glass stopper weighs in the air #be g41 in water #ae g41 in oil #ah g4 ,find the density and volume of the stopper4 ,find the density of the oil4 #i4 ,what would a cubic foot of wood weigh if the specific gravity were #j4e48 #aj4 ,the specific gravity of aluminum is #b4g4 ,find the weight of a cubic foot of it4 #aa4 ,a block of wood weighs #dj g4 ,a piece of lead appears to weigh #gj g4 in water4 ,both together appear to weigh #fj g4 in water4 ,find the density of the wood4 #ab4 ,a stone weighs #cj g4 in air1 #bb g4 in water1 and #bj g4 in salt water4 ,find the density of the salt water4 #ac4 ,will iron sink in mercury8 ,why8 #ad4 ,a submarine boat weighing #bjj tons must have what volume in order to float8 #ae4 ,find the weight of #b cu4 ft4 of copper from its density4 #af4 ,what is the weight in water of a mass whose specific gravity is #c4c and whose weight is #ej kg48 #ag4 ,a block of granite weighs #afef lbs42 its volume is #aj cu4 ft41 what is its density8 #ah4 ,if the specific gravity of hard coal is #a4ge how would you determine how many tons of coal a bin would hold8 #ai4 ,a hollow copper ball weighs #b kg4 ,what must be its volume to enable it to just float in water8 #bj4 ,a mass having a volume of #ajj ccm4 and a specific gravity of #b4fg is fastened to #bjj ccm4 of wood1 specific gravity #j4ee4 ,what will the combination weigh in water8 #ba4 ,a block weighing #d oz4 in air is tied to a sinker which appears to weigh #ad oz4 in water4 ,both together appear to weigh #f oz4 in water4 ,what is the specific gravity of the block8 ,,chapter ,,iv ,,mechanics ,,of ,,gases 7#a7 ,,weight ,,and ,,pressure ,,of ,,the ,,air #ea4 ,weight of ,air4--,it is said that savages are unaware of the presence of air4 ,they feel the wind and hear and see it moving the leaves and branches of the trees1 but of air itself they have little conception4 ,to ordinary observers1 it seems to have no weight1 and to offer little resistance to bodies passing through it4 ,that it has weight may be readily shown as follows3 7,see ,fig4 #bi47 ,if a hollow metal sphere1 or a glass flask1 provided with tube and stopcock1 be weighed when the stopcock is open1 and then after the air has been exhausted from it by an air pump1 a definite loss of weight is noticeable4 ,illustration3 ,,fig4 #bi4--,proof that air has weight4 ,if the volume of the sphere is known and it is well exhausted of air1 a fair approximation of the weight of air may be obtained4 ,under standard conditions1 which means at the freezing temperature and a barometric pressure of #gf cm41 a liter of air weighs #a4bic g4 while #ab cu4 ft4 of air weigh approximately #a lb4 #eb4 ,pressure of ,air4--,since air has weight it may be supposed to exert pressure like a liquid4 ,that it does so may be shown in a variety of ways4 ,if a plunger fitting tightly in a glass cylinder be drawn upward1 while the lower end of the tube is under water1 the water will rise in the tube 7,fig4 #cj74 ,the common explanation of this is that the water rises because of suction4 ,the philosophers of the ancient ,greeks explained it by saying that nature abhors a vacuum1 and therefore the water rises4 ,neither explanation is correct4 ,it was found in #afdj that water would not rise in a pump more than #cb ft4 despite the fact that a vacuum was maintained above the water4 ,galileo was applied to for an explanation4 ,he said1 evidently nature's horror of a vacuum does not extend above #cb ft4 ,galileo began tests upon the power of a vacuum but dying left his pupil ,torricelli to continue the experiment4 ,torricelli reasoned that if water would rise #cb ft41 then mercury1 which is #ac4f times as dense as water1 would rise about #a_/ac as much4 ,to test this1 he performed the following famous experiment4 ,illustration3 ,,fig4 #cj4--;,air pressure forces the liquid up the tube4 #ec4 ,torricelli's ,experiment 7#afdc74--,take a glass tube about #c ft4 long1 sealed at one end1 and fill it with mercury4 ,close the end with the finger and invert1 placing the end closed by the finger under mercury in a dish 7,fig4 #ca74 ,remove the finger and the mercury sinks until the top of the mercury is about #cj in4 above the level of the mercury in the dish4 ,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 dish4 ,to test this1 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 stopper4 7,see ,fig4 #cb47 ,if the air pressure is the cause of the rise of mercury in the tube1 on removing the air from the bell jar the mercury should fall in the tube4 ,this is seen to happen as soon as the pump is started4 ,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 dish4 ,a small tube containing mercury is often attached to air pumps to indicate the degree of exhaustion4 ,such tubes are called manometers4 ,illustration3 ,,fig4 #ca4--,torricelli's experiment4 ,illustration3 ,,fig4 #cb4--,the mercury drops as the air is removed4 #ed4 ,the ,amount of ,atmospheric ,pressure4--,torricelli's experiment enables us to compute readily the pressure of the atmosphere1 since it is the atmospheric pressure that balances the column of mercury in the tube4 ,by ,pascal's ,law1 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 outside4 ,this pressure1 due to the air1 must balance the weight of the column of mercury in the tube4 ,it therefore equals the weight of the column of mercury of unit cross-section4 ,the average height of the column of mercury at sea-level is #gf cm4 ,since the weight of #a cc4 of mercury is #ac4f grams1 the pressure inside the tube at the level of the surface of the mercury in the dish is equal to #a #gf #ac4f or #ajcc4f g4 per square centimeter4 ,therefore the atmospheric pressure on the surface of the mercury in the dish is #ajcc4f g4 per square centimeter1 approximately #a kg4 per square centimeter or #ae lbs4 per square inch4 #ee4 ,pascal's ,experiment4--,pascal tested in another way the action of atmospheric pressure upon the column of mercury by requesting his brother-in-law1 ,perrier1 who lived near a mountain1 to try the experiment on its top4 ,perrier found that on ascending #ajjj meters the mercury fell #h cm4 in the tube4 ,travelers1 surveyors1 and aviators frequently determine the altitude above sea-level by reading the barometer1 an ascent of #aa meters giving a fall of about #a mm4 in the mercury column1 or #j4a in4 for every #ij ft4 of ascent4 ,illustration3 ,,fig4 #cc4--;,a standard barometer4 #ef4 ,the ,barometer4--,the modern barometer 7,fig4 #cc71 consists of a ,torricellian tube properly mounted4 ,reading a barometer consists in accurately reading the height of the mercury column4 ,this height varies from #ge to #gf4e cm4 or #bi to #cj in4 in localities not far from the sea-level4 ,the atmospheric pressure varies because of disturbances in the atmosphere4 ,it is found that these disturbances of the atmosphere pass across the country from west to east in a somewhat regular manner1 hence a series of readings of the barometer may give reliable information of the movement of these disturbances and so assist in forecasting the weather4 ,the weather ,bureau has observations taken at the same moment at various stations over the country4 ,these observations form the basis for the daily forecast of the weather4 ,illustration3 ,,fig4 #cd4--;,an aneroid barometer ,another form of barometer in common use is the ,aneroid ,barometer 7,fig4 #cd74 ,its essential parts are a cylindrical air-tight box with an elastic corrugated cover4 ,inside the box is a partial vacuum4 ,this makes the cover very sensitive to slight changes of pressure4 ,the motion of the top of the box is conveyed by a series of levers to an indicating hand which moves over a dial4 ,this barometer can be made so sensitive as to indicate the change of air pressure from a table top to the floor4 ,it is much used by travelers1 explorers1 surveying parties and aviators1 since the mercurial barometer is inconvenient to carry4 ,important ,topics #a4 ,weight and ,pressure of air in ,english and metric units4 ,how shown4 ,evidences4 #b4 ,work of ,galileo1 ,torricelli1 and ,perrier4 #c4 ,barometer3 construction1 action1 mercurial1 aneroid4 ,illustration3 ,,fig4 #ce4--;,air pressure keeps the water ,in the tumbler4 ,illustration3 ,,fig4 #cf4--;,cross-section of a modern drinking fountain4 ,exercises #a4 ,do you think ,archimedes' ,principle applies to the air8 ,does ,pascal's ,law8 ,why8 #b4 ,find the downward pressure of the mercury in a barometer tube if the cross-section is #a sq4 cm4 and the height #ge cm4 at the level of the mercury surface in contact with the air4 7,the density of mercury is #ac4f grams per cc47 #c4 ,what is the weight of the air in a room if it is #aj #h #d meters8 #d4 ,what weight of air is in a room #aj #ae #aj ft48 #e4 ,when smoke rises in a straight line from chimneys1 is it an indication of a high or low barometric pressure8 ,why8 #f4 ,why does a tumbler filled with water and inverted in a dish with its rim under water remain full8 #g4 ,if the barometer tube is inclined the mercury remains at the same horizontal level4 ,how can this be explained8 #h4 ,when the mercurial barometer stands at #gf cm41 how high would a water barometer stand8 ,explain4 #i4 ,explain why it is possible for one to suck soda water through a tube8 #aj4 ,fill a tumbler with water4 ,place a sheet of paper over the top and invert4 ,the paper clings to the tumbler and prevents the water from escaping4 ,explain4 7,see ,fig4 #ce47 #aa4 ,why must a kerosene oil can have two openings in order to allow the oil to flow freely8 #ab4 ,explain the action of the modern drinking fountain 7,fig4 #cf74 7#b7 ,,compressibility ,,and ,,expansibility ,,of ,,the ,,air #eg4 ,effect of ,pressure on ,liquids and ,gases4--,both classes of fluids1 liquids and gases1 have many characteristics in common4 ,both are composed of molecules that move freely2 hence both flow4 ,at any point within a fluid the pressure is the same in all directions4 ,archimedes' ,principle applies1 therefore1 to both liquids and gases4 ,we now come to an important difference between liquids and gases4 ,liquids are practically incompressible4 ,so much so1 that if water is subjected to a pressure of #cjjj kg4 per sq4 cm41 its volume is reduced only about one-tenth4 ,gases show a very different behavior from liquids on being subjected to pressure4 ,they may readily be compressed to a small fraction of their volume as is noticed on inflating a pneumatic tire4 ,a gas has also the ability to spring back to a larger volume as soon as the pressure is released1 as when a cork is driven from a pop gun4 ,not only is compressed air able to expand1 but air under ordinary conditions will expand if it is released in a space where the pressure is less4 ,hollow bodies1 animals and plants1 are not crushed by atmospheric pressure1 because the air and gases contained within exert as much force outward as the air exerts inward4 #eh4 ,boyle's ,law4--,the relation between the volume and pressure of a gas was first investigated by ,robert ,boyle in the seventeenth century4 ,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 follows3 ,illustration3 ,,fig4 #cg a4 ,,fig4 #cg b4 ,,figs4 #cg a ,,and #cg b4--,boyle's law apparatus4 ,a glass tube is bent in the form of the capital letter ,j1 the short arm being closed4 ,a little mercury is poured in to cover the bend4 7,see ,fig4 #cg a47 ,since the mercury is at the same level in both arms1 the pressure in 7,a7 is the same as in 7,b74 ,mercury is now poured into 7,a7 until it stands in the long tube at a height above that in 7,b7 which is equal to the height of the mercury column of the barometer4 7,see ,fig4 #cg b47 ,the air in 7,,bc7 is now under a pressure of two atmospheres 7one atmosphere is due to the mercury column74 ,on measurement the air in 7,,bc7 will be found to have just one-half of its original volume4 ,thus doubling the pressure to which a gas is subjected reduces its volume to one-half4 ,tripling the pressure1 reduces the volume to one-third and so on4 ,careful experiments reveal the following law3 ,the volume of a given mass of gas at constant temperature is inversely proportional to the pressure to which it is subjected4 ,this law is often expressed mathematically4 ,p_/,p ,v_/,v1 or ,,pv ,p,v4 ,since doubling the pressure reduces the volume one-half1 it doubles the density4 ,tripling the pressure triples the density4 ,we therefore have ,p_/,p ,d_/,d or the density of a gas directly proportional to its pressure4 ,illustration3 ,,fig4 #ch4--;,height and density of the air4 #ei4 ,height of the ,atmosphere4--,from its properties of compression and expansion1 the air varies in density and pressure as one ascends in it4 ,at a height of #c miles the pressure is reduced to about one-half4 ,this is an indication that one-half of the air is below this level4 ,balloonists have gone to a height of #g miles1 ,glaser and ,coxwell in ,england in #ahfb and ,berson in ,france in #aija4 ,the atmosphere has been explored to a height of #cj1ejj meters 7#ah4ie miles7 by sending up self-registering barometers in small balloons which burst at great altitudes4 ,a parachute protects the instruments from breakage from too rapid fall4 ,this height of #cj1ejj meters was reached by a balloon sent up by ,william ,r4 ,blair1 at ,huron1 ,south ,dakota1 ,september #a1 #aiaj4 ,at a height of #ce miles1 the density is estimated at #a_/cj1jjj of its value at sea-level4 7,see ,fig4 #ch47 ,it is believed that some rarefied air exists for a considerable distance above this point1 some estimates placing the extent at #ajj miles1 and others from #bjj to #ejj miles4 ,evidences of some air at such heights are shown by3 7a7 the height at which meteors first appear1 7b7 the height of the ,aurora ,borealis1 and 7c71 the distance that the sun is below the horizon when the last traces of color disappear from the sky in the evening4 ,although the exact limits of the atmosphere are unknown1 the weight of a column of air #a sq4 cm4 in cross-section1 and extending upward as high as the atmosphere1 may be accurately computed4 ,for this column of air exactly balances the column of mercury in the tube of the barometer4 ,below sea-level1 the air increases rapidly in density and it is estimated that at a depth of #ce miles1 the density of the air would be a thousand times that at the earth's surface1 or more than that of water4 ,important ,topics #a4 ,evidence of compressibility of gases and incompressibility of liquids4 #b4 ,boyle's ,law4 ,proof1 applications4 #c4 ,extent of the atmosphere--three evidences4 ,exercises #a4 ,mention three illustrations of the compressibility and expansibility of air that you know from your own experience4 #b4 ,increasing the pressure increases the amount of a gas that will be absorbed by a liquid8 ,explain this4 ,have you ever observed this fact8 ,where8 #c4 ,if a toy balloon containing #bjjj ccm4 of gas at the earth's surface where the barometer reading is #gf cm41 rises to an elevation where the barometer reads #ed cm41 the balloon will tend to expand to what volume8 ,explain4 ,will it attain this volume8 #d4 ,if a gas is compressed1 it changes in temperature4 ,how do you explain this8 #e4 ,what change in temperature will occur when compressed air is allowed to expand8 ,explain4 #f4 ,air blowing up a mountain side has its pressure lessened as it approaches the top4 ,how will this affect the temperature8 ,why8 ,what may result from this change in temperature8 ,explain4 #g4 ,to what pressure must #ejj ccm4 of air be subjected to compress it to #cjj ccm4 the barometer reading at first being #ge cm4 ,explain4 ,illustration3 ,,fig4 #ci4--,the air pump4 7#c7 ,,pneumatic ,,appliances #fj4 ,the ,air ,pump4--,the air pump is used to remove air or other gases from a closed vessel4 ,it was invented about #afej by ,otto ,von ,guericke1 burgomaster of ,magdeburg1 ,germany4 ,one form of air pump is shown in ,fig4 #ci4 ,c is a cylinder within which slides a tightly fitting piston4 ,r is the vessel from which the air is to be exhausted4 r and u are valves opening upward4 ,the action of the pump is as follows3 ,on pushing the piston down1 the air in ,c is compressed4 ,this opens valve r allowing the confined air to escape above the piston4 ,the piston is then raised making the space in ,c a partial vacuum4 ,the pressure in ,r now being greater than in ,c1 u is pushed up and the air from ,r rushes into ,c1 until the pressure is equalized4 ,on pushing down the piston again1 valve u closes and the process is repeated until the pressure in ,r is no longer able to raise the valve u4 ,some air pumps are so constructed that the valves are opened and closed automatically by the movement of the piston4 ,with these pumps a higher degree of rarefaction can be obtained4 ,air is often partially exhausted from receivers or vessels by the use of a filter pump or aspirator4 ,a stream of water flowing through a constriction causes a reduced pressure1 draws in air and carries it away1 and thus produces a partial vacuum4 ,see ,fig4 #dj for a section of the device4 ,illustration3 ,,fig4 #dj4--;,an aspirator4 #fa4 ,the ,condensing ,pump4--,this is like the exhaust pump except that its valves are reversed4 ,it is used in compressing illuminating gases into cylinders for use in lighting vehicles1 stereopticons1 ,pintsch lights1 gas light buoys1 etc41 and also for compressing air to operate air brakes1 pneumatic hammers and drills1 and for other uses4 ,the common condensing pump is the kind used for inflating tires4 7,see ,fig4 #da47 ,in this1 a loosely fitting metal piston is attached to a disc of leather somewhat larger than the cylinder4 ,this device is called a cup valve4 ,on raising the piston1 air rushes in from the top past the valve1 but on pushing the piston down1 the valve is pressed tightly against the sides of the cylinder and prevents the escape of any air4 ,the compressed air pushes open a valve on the tire and enters it4 ,this valve closes as soon as the pressure is lessened from outside4 ,it is well to notice in all of these pumps that two valves are used4 ,one holds the air already secured while the other opens for a new supply4 ,both valves are never open at the same time4 ,illustration3 ,,fig4 #da4--;,condensing pump used in inflating tires4 #fb4 ,water ,pumps4--,the ,common ,lift ,pump4 ,this1 the simplest pump for raising water1 consists of a cylinder ,c 7,fig4 #db7 connected by a pipe ,r to a supply of water as a cistern or well4 ,a valve opening upward is placed at the bottom of the cylinder over the entrance to the pipe4 ,in the cylinder is a tightly fitting piston connected by a rod to a lever for ease in action4 ,the piston contains a valve opening upward4 ,in operating this pump water is usually first poured into the cylinder to prime it4 ,this helps to close the valves and prevents air leaking past them4 ,when the piston is lowered the lower valve closes1 the air in the cylinder being compressed pushes the upper valve open and passes above the piston4 ,on raising the piston the upper valve closes4 ,this forms a partial vacuum in the cylinder4 ,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 vacuum4 ,when the cylinder becomes filled with water1 this is lifted out on the up-stroke1 whence its name1 lift pump4 ,since the atmospheric pressure at sea-level can only support a column of water about #cd ft4 high1 the lower valve must be within this distance of the water surface4 ,in actual practice the limit is about #bg ft4 ,in deeper wells1 the cylinder and valves are placed so that they are within #be or #bg ft4 of the surface of the water in the well1 a long piston rod reaching above the surface of the ground and connected to a pump handle operates the piston4 ,a discharge pipe extends from the cylinder to the surface of the ground above4 ,illustration3 ,,fig4 #db4--,the common lift pump4 ,illustration3 ,,fig4 #dc4--;,a force pump with an air chamber 7,a74 #fc4 ,the ,force ,pump4--,the force pump is used to deliver water under pressure either for spraying or to an elevated reservoir4 ,the piston is solid1 the second valve being placed at the entrance of the discharge pipe4 7,see ,fig4 #dc47 ,the action is the same as that of the lift pump1 with this exception2 the piston in its down stroke forces the water out through the discharge pipe1 the velocity depending upon the pressure exerted4 ,a force pump is usually provided with an air chamber which is connected with the discharge pipe4 ,on the down stroke of the piston1 water is forced into the air chamber4 ,this compresses the air it contains4 ,the compressed air reacts and exerts pressure on the water forcing it out in a steady stream4 ,force pumps are used in deep wells1 being placed at the bottom4 ,the pumps used in city water works1 fire engines1 and all steam pumps1 are force pumps4 7,see ,fig4 #dd47 ,illustration3 ,,fig4 #dd4--;,a steam pump used on a fire engine4 #fd4 ,the ,siphon4--,the siphon is a tube used to convey a liquid from one level over an elevation to a lower level by atmospheric pressure4 ,it is used to remove liquids from tanks or vessels that have no opening at the bottom4 ,the siphon cannot be completely understood until one has mastered the laws of the flow of liquids4 ,the following is offered as an incomplete explanation of its behavior4 ,consider the siphon to be full of water and closed at d 7,fig4 #de74 ,atmospheric pressure on a will hold the siphon full if ab does not exceed #cd feet4 ,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 d4 ,this speed is acquired by all the water in the siphon and results in a drop in pressure throughout it4 ,the pressure at a inside the siphon becomes less than the pressure at the same level outside as soon as the water starts flowing4 ,the water in the vessel then flows into the siphon and out at d4 ,this flow continues as long as there is a fall from the free surface of the water in the vessel to the outlet at d4 ,illustration3 ,,fig4 #de4--;,cross-section of a siphon4 ,illustration3 ,,fig4 #df4--,the ,cartesian diver4 #fe4 ,the ,cartesian ,diver4--,this is a device which illustrates at the same time transmission of pressure by liquids1 ,archimedes' principle1 and compressibility of gases4 ,it was invented by ,des ,cartes 7#aeif-afej74 ,as ordinarily made1 it is a hollow glass image with a small opening in the foot4 ,it contains air and water in such amounts that the average density of image and contents is slightly less than that of water4 ,it is placed in a tall glass jar filled with water and covered with tightly stretched rubber tissue4 7,see ,fig4 #df47 ,by pressing on the rubber cover the diver may be made to sink1 since the air and water transmit the pressure on the cover which compresses the air inside the figure admitting some water to it1 thus making the diver more dense than water4 ,by varying the pressure it can be made to sink1 rise1 or remain stationary at will4,d ,a small vial can be used instead of the image4 ,d ,the position of a submarine in or under water is controlled in a similar manner4 #ff4 ,hydraulic ,ram4--,the hydraulic ram 7see ,fig4 #dg7 is an automatic device that is much used for raising water from springs to houses located on higher ground4 ,water flows through the pipe ,a through the opening at ,b4 ,the pressure closes the valve at ,b4 ,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 ,d4 ,this reduces the pressure against the valve ,b so that it drops and allows a little water to escape4 ,just as this happens1 valve ,c closes4 ,the pressure in the pipe then closes ,b and forces water past ,c4 ,this action being continually repeated1 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 feet4 ,illustration3 ,,fig4 #dg4--;,cross-section of a hydraulic ram4 #fg4 ,the ,balloon4--,since air is a fluid1 ,archimedes' principle applies to it as well as to liquids4 ,therefore any object in the air is lifted up by a force equal to the weight of the air it displaces4 ,the object will rise1 if it weighs less than this displaced air and will continue to rise until both weights are equal4 ,the ,balloon 7,fig4 #dh7 rises because it weighs less than the air it displaces1 and therefore it is pushed up by the heavier air1 the lifting power being the difference between its weight and that of the air displaced4 ,the neck at the bottom is left open to allow for expansion of the gas4 ,when the aeronaut wishes to descend1 he opens a valve at the top allowing some of the gas to escape4 ,illustration3 ,,fig4 #dh4--,winner of international championship race1 ,paris1 #aiac4 ,hydrogen is the lightest gas1 weighing #j4ji kg4 per cubic meter1 and so gives the greatest lifting power1 but as it is expensive to make1 coal gas1 density #j4ge kg4 per cubic meter1 is ordinarily employed4 ,helium has recently been used to fill military balloons because it cannot be set on fire4 ,the ,parachute 7,fig4 #di7 is an umbrella-shaped device for use in descending from a balloon4 ,after falling a few seconds it opens1 the large surface exposed to the air causing it to descend slowly4 ,the hole in the top keeps the parachute upright by allowing the air to escape through it1 thus relieving the pressure4 ,illustration3 ,,fig4 #di4--;,a parachute4 ,illustration3 ,,fig4 #ej4--;,cross-section of a ,westinghouse air brake4 #fh4 ,the ,air ,brake4--,compressed air is used to do work in many machines1 such as pneumatic drills1 hammers1 and air brakes4 ,the ,westinghouse air brake 7,fig4 #ej7 uses air at a pressure of about #gj lbs4 to the square inch4 ,the essential parts as shown are a reservoir ,r1 the brake cylinder ,c and a triple valve ,v1 placed under each car with an air pipe ,p1 leading to the engine4 ,this is connected to ,r by the triple valve ,v4 ,when the pressure in ,p is reduced by the engineer or by accident1 the triple valve operates so as to admit air from ,r into the cylinder ,c pushing the piston ,h to the left4 ,h is connected to the brakes by levers which press the brake shoes strongly against the wheels4 ,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 ,p4 ,the hissing sound heard when a train stops is caused by air escaping from cylinder ,c4 ,the spring in ,c keeps the brakes from the wheels except when the air is on4 ,illustration3 ,,fig4 #ea4--;,cross-section of a gas meter showing its construction and action4 #fi4 ,the ,gas ,meter4--,the gas meter consists of a box divided into two parts by a vertical partition 7,fig4 #ea74 ,two bellows are attached to this partition1 one on each side4 ,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 bellows4 ,these levers also operate the hands upon the dials4 ,when the inlet to the bellows ,b is opened1 the outlet of ,a is also opened4 ,gas entering ,b opens the bellows and forces the gas in ,a out into the house-pipe ,e4 ,when ,b is full its inlet valve closes and its outlet valve opens4 ,the inlet of ,a also opens and its outlet closes4 ,gas now flows into ,a1 compressing the bellows and ,b1 and forcing the gas from it into the house-pipe4 ,at each filling of the bellows ,b there will be displaced from ,a and forced into the house-pipe as much gas as enters ,b4 ,it is evident that at each emptying of ,b an equal amount of gas enters ,a4 ,thus we have ,a and ,b alternately filling and emptying as long as the gas burner is open4 ,to have a continuous flow of gas in the house-pipes two pipes and two chambers are necessary1 one being filled while the other is being emptied4 ,fig4 #eb represents the dials upon a gas meter showing a reading of #ed1fjj cu4 ft4 ,illustration3 ,,fig4 #eb4--;,dials of a gas meter4 #gj4 ,centrifugal ,pumps4 ,fluids1 such as water and air1 are often put in motion by devices called centrifugal pumps 7see ,art4 #gh74 ,these pumps contain a revolving part1 like a wheel without a rim1 whose spokes are replaced by thin blades4 ,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 axle4 ,illustration3 ,,fig4 #ec4--;,a vacuum sweeper4 7,courtesy of the ,hoover ,suction ,sweeper ,co47 ,when the wheel is rapidly revolved1 the fluid is driven out with considerable force through the opening at the rim1 while a partial vacuum is produced at the axle causing a rapid flow into the device at this point4 ,this is the principle of the action of the vacuum cleaner4 ,fig4 #ec 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 rear4 ,centrifugal water pumps work on the same principle and furnish a continuous flow of water1 often large in volume and at considerable pressure4 ,important ,topics #a4 ,air pump4 #b4 ,condensing pump4 #c4 ,lift and force pumps4 #d4 ,siphon4 #e4 ,cartesian diver4 #f4 ,hydraulic ram4 #g4 ,balloon4 #h4 ,air brake4 #i4 ,gas meter4 #aj4 ,vacuum cleaner4 ,exercises #a4 ,explain why smoke settles to the ground before storms4 #b4 ,why does the water rise in the suction pipe of a pump8 #c4 ,why is it easier to float in water when the lungs are filled with air than when they are not filled8 #d4 ,why is it easier to swim in salt water than in fresh water8 #e4 ,how are submarines made to sink8 to rise to the surface8 #f4 ,how can a fish rise or sink in water8 #g4 ,explain why a life preserver made of cork will enable a person to float4 #h4 ,hold the open hand out flat with the fingers together4 ,place underneath the fingers a piece of paper4 ,blow between the first and second fingers against the paper4 ,as long as you blow hard the paper will not fall but will stick to the hand4 ,explain4 #i4 ,why does pressing the bulb of an atomizer force out the liquid in a fine spray8 #aj4 ,why is air that contains a large amount of water vapor lighter than air that only contains a small amount8 #aa4 ,how are heights above sea-level ascertained by a barometer8 #ab4 ,oil floats on water but sinks in alcohol4 ,explain4 #ac4 ,in a balloon the lower end is often open to the air4 ,why does not the gas escape and prevent the balloon from rising8 #ad4 ,how long will a balloon continue to rise8 #ae4 ,if the pressure against the #h-;in4 piston of an air brake is #gj lbs4 per square inch1 how much force does the piston exert8 #af4 ,the capacity of a balloon is #dj1jjj cu4 ft4 ,the weight of the balloon1 car1 etc41 is #fjj lbs42 specific gravity of the gas used is #j4df that of the air4 ,find how much weight the balloon can carry4 #ag4 ,the so-called ,magdeburg hemispheres were invented by ,otto von ,guericke of ,magdeburg1 ,germany4 ,when the hemispheres 7see ,fig4 #ed7 are placed in contact and the air exhausted it is found very difficult to pull them apart4 ,explain4 #ah4 ,von ,guericke's hemispheres had an inside diameter of #bb in4 ,what force would be required to pull them apart if all the air were exhausted from them8 7,find the atmospheric force on a circle1 #bb in4 in diameter47 #ai4 ,von ,guericke made a water barometer whose top extended through the roof of his house4 ,on the top of the water in the tube was placed a wooden image4 ,in fair weather the image appeared above the roof1 but it descended before a storm4 ,explain4 #bj4 ,the balloon ,goodyear 7,fig4 #dh71 which won the ,international championship race at ,paris in #aiac1 has a capacity of #hj1jjj cu4 ft4 ,the gas bag weighs #fec lbs41 the net #bdj lbs4 and the basket #ib lbs4 ,how large a load can it carry when filled with hydrogen specific gravity #j4jfi 7compared with air74 ,illustration3 ,,fig4 #ed4--,magdeburg hemispheres4 ,review ,outline3 ,liquids and ,gases ,liquids3 ,force1 pressure1 and density4 ,floating and immersed bodies4 ,laws3 ,liquid force1 ,f ,a4h4d1 ,pascal's1 ,archimedes4 ,illustrations and ,applications3 ,specific gravity1 ,wa_/7,wa - ,ww71 7,wa - ,wl7_/7,wa - ,ww71 ,boyle's1 ,,pv ,p,v ,devices3 ,hydraulic press1 air cushion1 barometer--mercurial and aneroid4 ,pumps1 lift1 force1 vacuum1 compression1 centrifugal1 balloon1 siphon1 etc4 ,construction and action of each4 ,,chapter ,v ,,force ,,and ,,motion 7#a7 ,,force1 ,,how ,,measured ,,and ,,represented #ga4 ,force4--,we have been studying various forces1 such as air pressure1 pressure in liquids1 and the force of elasticity in solids1 and have considered them simply as pushes or pulls4 ,a more formal study of forces in general and of devices for representing and measuring them will be helpful at this point of the course4 ,a force is that which tends to cause a change in the size or shape of a body or in its state of motion4 ,in other words a force is a push or a pull4 ,that is1 force tends to produce distortion or change of motion in a body4 ,force itself is invisible4 ,we measure it by the effect it produces4 ,forces are usually associated with the objects exerting them4 ,thus we speak of muscular force1 air pressure1 liquid pressure1 the force of a spring1 the force of the earth's attraction and so on4 ,forces are classified in various ways4 ,i4 ,with respect to the duration and steadiness of the force4 7a7 ,constant1 as the earth's attraction4 7b7 ,impulsive1 as the stroke of a bat on a ball4 7c7 ,variable1 as the force of the wind4 ,,ii4 ,with respect to the direction of the force4 7a7 ,attractive1 as the earth's attraction4 7b7 ,repulsive1 as air pressure1 liquid pressure1 etc4 #gb4 ,methods of ,measuring ,force4--,since forces are measured by their effects which are either distortion or change of motion1 either of these effects may be used to measure them4 ,for example1 the force exerted by a locomotive is sometimes computed by the speed it can develop in a train of cars in a given time1 or the force of the blow of a baseball bat is estimated by the distance the ball goes before it strikes the ground4 ,the more common method of measuring force1 however1 is by distortion1 that is1 by measuring the change of shape of a body caused by the force4 ,in doing this1 use is made of ,hooke's ,law 7,art4 #cb71 in which it is stated that within the limits of perfect elasticity1 changes of size or shape are directly proportional to the forces employed4 ,that is1 twice as great a force will produce twice as great a change of shape and so on4 ,illustration3 ,,fig4 #ee4--;,a spring balance4 ,a common contrivance using this principle is the spring balance 7,fig4 #ee71 with which all are familiar1 as ice scales1 meat scales1 postal scales1 etc4 ,the object which changes shape in this device is a coiled spring contained in the case of the instrument4 ,the balance is so constructed that when the spring is pulled out as far as possible it has not reached its limit of elasticity1 since1 if the spring were stretched so as to exceed its elastic limit1 the index would not return to its first position on removing the load4 7,see ,arts4 #cj-cb47 #gc4 ,graphic ,representation of ,forces4--,a force is said to have three elements4 ,these are 7a7 its point of application1 7b7 its direction1 and 7c7 its magnitude4 ,for example1 if there is hung upon the hook of a spring balance a weight of #e lbs41 then we have3 7a7 its point of application on the hook of the balance1 7b7 its downward direction and 7c7 its magnitude1 or #e lbs4 ,these three elements may be represented by a line4 ,thus in ,fig4 #ef;a1 a line ,,ab is drawn as shown1 five units long2 ,a represents the point of application2 ,b1 the arrow head1 shows the direction2 and the length of the line 7five units7 shows the magnitude of the force4 ,this is called a graphic representation since it represents by a line the quantity in question4 ,if another weight of #e lbs4 were hung from the first one1 the graphic representation of both forces would be as in ,fig4 #ef;b4 ,here the first force is represented by ,,ab as before1 ,,bc representing the second force applied4 ,the whole line represents the resultant of the two forces or the result of their combination4 ,if the two weights were hung one at each end of a short stick ,,ac 7,fig4 #ef;c71 and the latter suspended at its center their combined weight or resultant would of course be applied at the center4 ,the direction would be the same as that of the two weights4 ,the resultant therefore is represented by ,,on4 ,in order to exactly balance this resultant ,,on1 a force of equal magnitude but opposite in direction must be applied at the point of application of ,,on1 or ,o4 ,,om then represents a force that will just balance or hold in equilibrium the resultant of the two forces ,,ab and ,,cd4 ,this line ,,om therefore represents the equilibrant of the weights ,,ab and ,,cd4 ,the resultant of two forces at an angle with each other is formed differently1 as in ,fig4 #eg a4 ,here two forces ,,ab and ,,ac act at an angle with each other4 ,lay off at the designated angle the lines ,,ab and ,,ac of such length as will accurately represent the forces4 ,lay off ,,bd equal to ,,ac and ,,cd equal to ,,ab4 ,the figure ,,abcd is then a parallelogram4 ,its diagonal ,,ad represents the resultant of the forces ,,ab and ,,ac acting at the angle ,,bac4 ,if ,,bac equals #ij degrees or is a right angle1 ,,ad may be computed thus3 ,,ab ,,bd ,,ad4 ,why8 and ,,ad 7line,,ab line,,bd74 ,illustration3 ,,fig4 #ef4--;,graphic representation of forces acting along the same or parallel lines4 ,illustration3 ,,fig4 #eg4--;,graphic representation of two forces acting 7a7 at a right angle1 7b7 at an acute angle4 ,this method of determining the resultant by computation may be used when the two forces are at right angles4 7,in any case1 ,,ad may be measured using the same scale that is laid off upon ,,ab and ,,ac1 as shown in ,fig4 #eg b47 ,the three cases of combining forces just given may be classified as follows3 ,the first is that of two forces acting along the same line in the same or opposite direction1 as when two horses are hitched tandem1 or in a tug of war4 ,the second is that of two forces acting along parallel lines1 in the same direction1 as when two horses are hitched side by side or abreast4 ,the third is that of two forces acting at the same point at an angle4 ,it may be represented by the device shown in ,fig4 #eh1 consisting of two spring balances suspended from nails at the top of the blackboard at ,a and ,b4 ,a cord is attached to both hooks and is passed through a small ring at ,o from which is suspended a known weight1 ,w4 ,lines are drawn on the blackboard under the stretched cords1 from ,o toward ,,oa1 ,,ob1 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 ,w4 ,let a parallelogram be constructed on the lines measured off on ,,oa and ,,ob4 ,its diagonal drawn from ,o will be found to be vertical and of the same length as the line measured on ,,ow4 ,the diagonal is the resultant of the two forces and ,,ow is the equilibrant which is equal and opposite to the resultant4 ,illustration3 ,,fig4 #eh4--;,experimental proof of parallelogram of forces4 ,again1 the first case may be represented by a boat moving up or down a stream2 the resultant motion being the combined effect of the boat's motion and that of the stream4 ,the second1 may be represented by two horses attached side by side to the same evener4 ,the resultant force equals the sum of the two component forces4 ,the third1 may be represented by a boat going across a stream1 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 boat4 #gd4 ,units for ,measuring ,force4--,force is commonly measured in units of weight3 in pounds1 kilograms1 and grams4 ,for example1 we speak of #ae lbs4 pressure per square inch and #ajcc4f g4 pressure per square centimeter as representing the air pressure4 ,it should be noted here that the words pound1 kilogram1 and gram are used not only to represent weight or force but also the masses of the objects considered4 ,thus1 one may speak of a pound-mass meaning the amount of material in the object4 ,it will help to avoid confusion if we reserve the simple terms gram and pound to denote exclusively an amount of matter1 that is1 a mass1 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 masses4 ,or1 one may speak of a pound-weight meaning the amount of attraction exerted by the earth upon the object4 ,the same is true of gram-mass and gram-weight4 ,the mass of a body does not change when the body is transferred to another place4 ,the weight1 however1 may vary1 for on moving a body from the equator toward the poles of the earth the weight is known to increase4 ,important ,topics #a4 ,definition of force4 #b4 ,classification of forces4 7a7 ,duration3 constant1 impulsive1 variable4 7b7 ,direction3 attractive1 repulsive4 #c4 ,methods of measuring force4 7a7 ,by distortion4 7b7 ,by change of motion4 #d4 ,graphic representation of forces3 component1 resultant1 equilibrant4 #e4 ,three cases of combining forces4 7#a7 ,two forces acting on the same line4 7#b7 ,two forces acting in parallel lines4 7#c7 ,two forces acting at the same point at an angle4 #f4 ,units for measuring force1 pound1 gram4 ,exercises #a4 ,name five natural forces4 ,which produce a tension8 ,which a pressure8 #b4 ,how much can you lift8 ,express in pounds and kilograms4 #c4 ,show graphically the resultant of two forces at right angles1 one of #ab lbs41 the other of #af lbs4 ,what is the magnitude of this resultant8 ,then determine the answer1 first by measurement and then by computation4 ,which answer is more accurate8 ,why8 #d4 ,represent by a parallelogram the two forces that support a person sitting in a hammock and draw the line representing the resultant4 #e4 ,find graphically the resultant of the pull of two forces1 one of #ejj lbs4 east and one of #fjj lbs4 northwest4 #f4 ,determine the equilibrant of two forces1 one of #hjj lbs4 south and one of #fjj lbs4 west4 #g4 ,would the fact that weight varies on going from the equator to either pole be shown by a spring balance or a beam balance8 ,explain4 7#b7 ,,motion4 ,,newton',s ,,laws ,,of ,,motion #ge4 ,motion a ,change of ,position4--,motion is defined as a continuous change in the position of a body4 ,the position of a body is usually described as its distance and direction from some fixed point4 ,thus a man on a boat may be at rest with respect to the boat and moving with respect to the earth4 ,or1 if he walks toward the stern as fast as the boat moves forward1 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 boat4 ,motion and rest1 therefore1 are relative terms4 ,the earth itself is in motion in turning on its axis1 in moving along its orbit1 and in following the sun in its motion through space4 ,motions are classified in several ways3 7,a7 ,,modes ,,of ,,motion #a4 ,translation4--,a body is said to have motion of translation when every line in it keeps the same direction4 #b4 ,rotation4--,a body has motion of rotation when it turns upon a fixed axis within the body1 as a wheel upon its axle or the earth upon its axis4 #c4 ,vibration or ,oscillation4--,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 path1 e4g41 a pendulum4 7,b7 ,,direction ,,of ,,motion #a4 ,rectilinear4--,a body has rectilinear motion when its path is a straight line4 ,absolute rectilinear motion does not exist1 although the motion of a train on a straight stretch of track is nearly rectilinear4 #b4 ,curvilinear4--,a body has curvilinear motion when its path is a curved line1 e4g41 the path of a thrown ball4 7,c7 ,,uniformity ,,of ,,motion #a4 ,uniform4--,a body has uniform motion when its speed and direction of motion do not change4 ,uniform motion for extended periods is rarely observed4 ,a train may cover1 on an average1 #dj miles per hour but during each hour its speed may rise and fall4 #b4 ,variable4--,a body has variable motion when its speed or direction of motion is continually changing4 ,most bodies have variable motion4 #c4 ,accelerated4--,a body has accelerated motion when its speed or direction of motion continually changes4 ,if the speed changes by the same amount each second1 and the direction of motion does not change the motion is said to be uniformly accelerated1 e4g41 a falling body4 ,uniformly accelerated motion will be studied further under the topic of falling bodies4 ,velocity is the rate of motion of a body in a given direction4 ,for example1 a bullet may have a velocity of #acjj ft4 a second upwards4 ,acceleration is the rate of change of velocity in a given direction1 or the change of velocity in a unit of time4 ,a train starting from a station gradually increases its speed4 ,the gain in velocity during one second is its acceleration4 ,when the velocity is decreasing1 as when a train is slowing down1 the acceleration is opposite in direction to the velocity4 ,a falling body falls faster and faster4 ,it has downward acceleration4 ,a ball thrown upward goes more and more slowly4 ,it also has downward acceleration4 #gf4 ,momentum4--,it is a matter of common observation that a heavy body is set in motion with more difficulty than a light one1 or if the same force is used for the same length of time upon a light and a heavy body1,e the light body will be given a greater velocity4 ,this observation has led to the calculation of what is called the quantity of motion of a body1 or its momentum4 ,it is computed by multiplying the mass by the velocity4 ,if the ,c4,g4,s4 system is used we shall have as the momentum of a #ab g4 body moving #be cm4 a second a momentum of #ab #be or #cjj ,c4,g4,s4 units of momentum4 ,this unit has no name and is therefore expressed as indicated above4 ,the formula for computing momentum is3 ,m mv4 ,e ,by a light body is meant one of small mass1 a heavy body possessing much greater mass4 ,newton's ,laws of ,motion #gg4 ,inertia1 ,first ,law of ,motion4--,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 train1 and apparently are jerked backward4 ,while if the train is stopped suddenly1 the passengers tend to keep in motion4 ,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 inertia4 ,newton's first law of motion1 often called the law of inertia1 describes this property of matter as follows3 ,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 force4 ,this means that if an object like a book is lying on a table it will remain there until removed by some outside force4 ,no inanimate object can move itself or stop itself4 ,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 air4 ,it takes time to put a mass into motion1 a heavy object requiring more time for a change than a light object4 ,as an example of this1 note the movements of passengers in a street car when it starts or stops suddenly4 ,another illustration of the law of inertia is the so-called penny and card experiment4 ,balance a card on the end of a finger4 ,place on it a coin directly over the finger1 snap the card quickly so as to drive the card from beneath the coin4 ,the coin will remain on the finger4 7,see ,fig4 #ei47 ,illustration3 ,,fig4 #ei4--,the ball remains when the card is driven away4 ,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 motion1 and would describe a perfectly straight course4 ,the curved path taken by a baseball when thrown shows that it is acted upon by an outside force4 ,this force1 the attraction of the earth1 is called gravity4 ,illustration3 ,,sir ,,isaac ,,newton ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,sir ,isaac ,newton 7#afdb-agbg7 ,professor of mathematics at ,cambridge university2 discovered gravitation2 invented calculus2 announced the laws of motion2 wrote the ,principia2 made many discoveries in light4 ,illustration3 ,,galileo ,,galilei ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,galileo ,galilei 7#aefd-afdb74 ,italian4 ,founder of experimental science2 ,originator of modern physics2 made the first thermometer2 discovered the laws of falling bodies and the laws of the pendulum2 invented ,galilean telescope4 ,illustration3 ,,fig4 #fj4--;,cross-section of the ,de,laval cream separator4 #gh4 ,curvilinear ,motion4--,curvilinear motion occurs when a moving body is pulled or pushed away from a straight path4 ,the pull or push is called centripetal 7center-seeking7 force4 ,a moving stone on the end of a string when pulled toward the hand moves in a curve4 ,if the string is released the stone moves in a tangent to the curve4 ,the string pulls the hand4 ,this phase of the pull is called centrifugal force4 ,the centripetal force is the pull on the stone4 ,centripetal and centrifugal force together cause a tension in the string4 ,examples of curvilinear motion are very common4 ,the rider and horse in a circus ring lean inward in order to move in a curve4 ,the curve on a running track in a gymnasium is banked for the same reason4 ,mud flying from the wheel of a carriage1 the skidding of an automobile when passing rapidly around a corner1 and sparks flying from an emery wheel1 are illustrations of the ,first ,law of ,motion4 ,cream is separated from milk by placing the whole milk in a rapidly revolving bowl1 the cream being lighter collects in the center and is thrown off at the top4 7,see ,fig4 #fj47 ,clothes in steam laundries are dried by a centrifugal drier4 ,in amusement parks many devices use this principle4 7,see centrifugal pumps1 ,art4 #gj47 ,illustration3 ,,fig4 #fa4--,the two balls reach the floor at the same time4 #gi4 ,the ,second ,law of ,motion1 sometimes called the law of momentum1 leads to the measurement of force1 by the momentum or the quantity of motion1 produced by it4 ,the law is stated as follows3 ,change of motion1 or momentum1 is proportional to the acting force and takes place in the direction in which the force acts4 ,in other words1 if two or more forces act at the same instant upon a body each produces the same effect that it would if acting alone4 ,if a card be supported on two nails driven horizontally close together into an upright board 7see ,fig4 #fa71 and two marbles be so placed on the ends as to balance each other1 when one marble is snapped horizontally by a blow1 the other will fall4 ,both reach the floor at the same time4 ,the two balls are equally pulled down by the earth's attraction and strike the ground at the same time1 though one is shot sidewise1 and the other is dropped vertically4 ,as gravity is a constant force1 while the blow was only a momentary force1 the actual path or resultant motion will be a curved line4 ,the constant relation1 between the acting force and the change of momentum it produces in a body1 has led to the adoption of a convenient ,c4,g4,s4 unit of force called the dyne4 ,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 second4 ,this definition assumes that the body acted upon is free to move without hindrance of any kind1 so that the acting force has to overcome only the inertia of the body4 ,however1 the law applies in every case of application of force1 so that each force produces its full effect independently of other forces that may be acting at the same time upon the body4 #hj4 ,newton's ,third ,law4--,this law has been experienced by everyone who has jumped from a rowboat near the shore4 ,the muscular action that pushes the body forward from the boat also pushes the boat backward1 often with awkward results4 ,the law is stated3 ,to every action1 there is always an opposite and equal reaction1 or the mutual actions of any two bodies are always equal and opposite in direction4 ,many illustrations of this law are in every one's mind3 a stretched rope pulls with the same force in one direction as it does in the opposite direction4 ,if a bat hits a ball1 the ball hits the bat with an equal and opposite force4 ,the third law is therefore sometimes called the law of reaction4 ,when a weight is hung upon a spring balance the action of the weight pulls down the spring until it has stretched sufficiently 7,hooke's ,law7 to produce an elastic reaction that equals and hence supports the weight4 ,when a man stands at the center of a plank supported at its ends1 the action of the man's weight bends the plank until the elastic force developed in the plank equals the weight applied4 ,further1 when a train or a wagon is on a bridge the bridge yields until it has developed an elastic reaction equal to the weight applied4 ,if a person stands in the center of a room1 the floor beams yield until the third law is satisfied4 ,in fact1 whenever a force acts1 a contrary equal force always acts4 #ha4 ,stress and ,strain4--,a pair of forces that constitute an action and a reaction is called a stress4 ,the two forces are two parts of one stress4 ,if the two forces act away from each other1 as in the breaking of a string1 the stress is called a tension1 but if they act toward each other as in crushing anything1 the stress is called a pressure4 ,in order for a body to exert force it must meet with resistance4 ,the force exerted is never greater than the resistance encountered4 ,thus one can exert but little force upon a feather floating in the air or upon other light objects4 ,a fast moving shot exerts no force unless it encounters some resistance4 ,forces1 then1 are always found in pairs4 ,thus to break a string1 to stretch an elastic band1 to squeeze a lemon1 one must exert two equal and opposite forces4 ,such a thing as a single force acting alone is unknown4 ,usually1 however1 we give our attention mainly to one of the forces and ignore the other4 ,when a force acts upon a body the change of shape or size resulting is called a strain4 ,hooke's law 7,art4 #cb7 is often expressed as follows3 ,the strain is proportional to the stress1 e4g41 the stretch of the spring of a spring balance is proportional to the load placed upon it4 ,important ,topics #a4 ,motion a change of position4 ,kinds of motion4 #b4 ,newton's laws of motion4 #c4 ,momentum4 #d4 ,inertia4 ,first law of motion4 ,curvilinear motion4 #e4 ,second law of motion4 #f4 ,third law of motion4 ,action and reaction1 stress and strain4 ,exercises #a4 ,mention three illustrations of the third law1 different from those given4 #b4 ,a rifle bullet thrown against a board standing upon edge will knock it down2 the same bullet fired at the board will pass through it without disturbing its position4 ,explain4 #c4 ,a hammer is often driven on to its handle by striking the end of the latter4 ,explain4 #d4 ,consider a train moving #fj miles an hour1 with a gun on the rear platform pointing straight backward4 ,if a ball is fired from the gun with a speed of #fj miles an hour1 what will happen to the ball8 #e4 ,could one play ball on the deck of an ocean steamer going #be miles an hour without making allowance for the motion of the ship8 ,explain4 #f4 ,on a railroad curve1 one rail is always higher4 ,which8 ,why8 #g4 ,why can a small boy when chased by a big boy often escape by dodging8 #h4 ,will a stone dropped from a moving train fall in a straight line8 ,explain4 #i4 ,a blast of fine sand driven against a sheet of glass soon gives it a rough surface4 ,explain4 #aj4 ,explain the use of fly-wheels in steadying the motion of machinery 7for example1 the sewing machine74 #aa4 ,is it easier to walk to the front or rear of a passenger train when it is stopping8 ,why8 #ab4 ,why does lowering the handles of a wheel-barrow on the instant of striking make it easier to go over a bump8 #ac4 ,why should a strong side wind interfere with a game of tennis8 ,how can it be allowed for8 #ad4 ,on which side of a railroad track at a curve is it the safer to walk while a train is passing8 ,why8 #ae4 ,why does a bullet when fired through a window make a clean round hole in the glass1 while a small stone thrown against the window shatters the glass8 #af4 ,a tallow candle can be fired through a pine board4 ,why8 #ag4 ,in cyclones1 straws are frequently found driven a little distance into trees2 why are the straws not broken and crushed instead of being driven into the tree unbroken8 #ah4 ,a bullet weighing one-half oz4 is fired from a gun weighing #h lb4 ,the bullet has a velocity of #ahjj ft4 per second4 ,find the velocity of the kick or recoil of the gun4 #ah4 ,when football players run into each other which one is thrown the harder8 ,why8 #bj4 ,a railroad train weighing #djj tons has a velocity of #fj miles per hour4 ,an ocean steamer weighing #bj1jjj tons has a velocity of one half mile per hour4 ,how do their momenta compare8 #ba4 ,why is a heavy boy preferable to a lighter weight boy for a football team8 #bb4 ,why does a blacksmith when he desires to strike a heavy blow1 select a heavy sledge hammer and swing it over his head8 #bc4 ,why does the catcher on a baseball team wear a padded glove8 7#c7 ,,resolution ,,of ,,forces #hb4 ,resolution of ,forces4--,we have been studying the effect of forces in producing motion and the results of combining forces in many ways2 in the same line1 in parallel lines1 and in diverging lines4 ,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 acts4 ,this case which is called resolution of forces is frequently used4 ,to illustrate3 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 blowing1 e4g41 when the wind is blowing1 say from the north1 the boat may be driven east1 west1 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 northwest4 ,take a sled drawn by a short rope with the force applied along the line ,,ab 7see ,fig4 #fb72 part of this force tends to lift the front of the sled as ,,ac and a part to draw it forward as ,,ad4 ,hence not all of the force applied along ,,ab is used in drawing the sled forward4 ,its effectiveness is indicated by the relative size of the component ,,ad compared to ,,ab4 ,illustration3 ,,fig4 #fb4--;,,ad is the effective component4 ,the force of gravity acting upon a sphere that is resting on an inclined plane may be readily resolved into two components1 one1 the effective component1 as ,,or1 and the other1 the non-effective as ,,os4 7,see ,fig4 #fc47 ,if the angle ,,acb is #cj degrees1 ,,ab equals #a_/b of ,,ac and ,,or equals #a_/b of ,,og1 so that the speed of the sphere down the plane developed in #a second is less than 7about one-half of7 the speed of a freely falling body developed in the same time4 ,why is ,,os non-effective8 ,illustration3 ,,fig4 #fc4--,the effective component is ,,or4 ,illustration3 ,,fig4 #fd4--,resolution of the forces acting on an aeroplane4 #hc4 ,the ,aeroplane4--,the aeroplane consists of one or two frames ,,abcd 7see ,fig4 #fd71 over which is stretched cloth or thin sheet metal4 ,it is driven through the air by a propeller turned by a powerful gasoline motor4 ,this has the effect of creating a strong breeze coming toward the front of the aeroplane4 ,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 ,,ge1 ,,gc acting to lift the aeroplane vertically and ,,ge opposing the action of the propeller4 ,fig4 #fe represents the ,curtis ,flying ,boat passing over the ,detroit river4 ,illustration3 ,,fig4 #fe4--,the ,curtis hydroplane4 ,exercises4 #a4 ,if a wagon weighing #djjj lbs4 is upon a hill which rises #a ft4 in #f1 what force parallel to the hill will just support the load8 7,find the effective component of the weight down the hill47 #b4 ,if a barrel is being rolled up a #af-;ft4 ladder into a wagon box #c ft4 from the ground1 what force will hold the barrel in place on the ladder1 if the barrel weighs #bdj lbs4 ,show by diagram4 #c4 ,show graphically the components into which a man's push upon the handle of a lawn mower is resolved4 #d4 ,does a man shooting a flying duck aim at the bird8 ,explain4 #e4 ,what are the three forces that act on a kite when it is standing in the air8 #f4 ,what relation does the resultant of any two of the forces in problem five have to the third8 #g4 ,into what two forces is the weight of a wagon descending a hill resolved8 ,explain by use of a diagram4 #h4 ,a wind strikes the sail of a boat at an angle of #fj degrees to the perpendicular with a pressure of #c lbs4 per square foot4 ,what is the effective pressure1 perpendicular to the sail8 ,what would be the effective pressure when it strikes at #cj degrees8 #i4 ,how is the vertical component of the force acting on an aeroplane affected when the front edge of the plane is elevated8 ,show by diagram4 7#d7 ,,moment ,,of ,,force ,,and ,,parallel ,,forces #hd4 ,moment of ,force4--,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 velocity4 ,in the study of parallel forces1 especially such as tend to produce rotation1 we consider a similar quantity4 ,it is called a moment of force1 which is the term applied to the effectiveness of a force in producing change of rotation4 ,it also measured by the product of two quantities2 ,one1 the magnitude of the force itself1 and the other1 the perpendicular distance from the axis about which the rotation takes place to the line representing the direction of the force4 ,illustration3 ,,fig4 #ff4--,the moments about ,s are equal4 ,to illustrate3 ,take a rod1 as a meter stick1 drill a hole at ,s and place through it a screw fastened at the top of the blackboard4 ,attach by cords two spring balances and draw to the right and left1 ,a and ,b as in ,fig4 #ff4 ,draw out the balance ,b about half way1 hold it steadily1 or fasten the cord at the side of the blackboard1 and read both balances4 ,note also the distance ,,as and ,,bs4 ,since the rod is at rest1 the tendency to rotate to the right and left must be equal4 ,that is1 the moments of the forces at ,a and ,b about ,s are equal4 ,since these are computed by the product of the force times the force arm1 multiply ,b by ,,bs and ,a by ,,as and see if the computed moments are equal4 ,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 left4 ,illustration3 ,,fig4 #fg4--,law of parallel forces illustrated4 #he4 ,parallel ,forces4--,objects are frequently supported by two or more upward forces acting at different points and forming in this way a system of parallel forces2 as when two boys carry a string of fish on a rod between them or when a bridge is supported at its ends4 ,the principle of moments just described aids in determining the magnitude of such forces and of their resultant4 ,to illustrate this take a wooden board #d in4 wide and #d ft4 long of uniform dimensions4 7,see ,fig4 #fg47 ,place several screw hooks on one edge with one set at ,o where the board will hang horizontally when the board is suspended there4 ,weigh the board by a spring balance hung at ,o4 ,this will be the resultant in the following tests4 ,now hang the board from two spring balances at ,m and ,n and read both balances4 ,call readings f and f4 ,to test the forces consider ,m as a fixed point 7see ,fig4 #fg7 and the weight of the board to act at ,o4 ,then the moment of the weight of the board should be equal the moment of the force at ,n since the board does not move1 or w times ,,om equals f times ,,nm4 ,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 equal1 or w times ,,on f times ,,nm4 ,keeping this illustration in mind1 the law of parallel forces may be stated at follows3 #a4 ,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 components4 ,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 other4 ,problem4--,if two boys carry a string of fish weighing #dj lbs4 on a rod #h ft4 long between them1 what force must each boy exert if the string is #e ft4 from the rear boy8 ,solution4--,the moment of the force ,f exerted about the opposite end by the rear boy is ,f #h4 ,the moment of the weight about the same point is #dj 7#h - #e7 #abj4 ,therefore ,f #h #abj1 or ,f #ae1 the force exerted by the rear boy4 ,the front boy exerts a force of ,f whose moment about the other end of the rod is ,f #h4 ,the moment of the weight about the same point is #dj #e #bjj4 ,since the moment of ,f equals this1 #bjj ,f #h1 or ,f #be4 ,hence the front boy exerts #be lbs4 and the rear boy #ae lbs4 ,illustration3 ,,fig4 #fh4--;,a couple4 #hf4 ,the ,couple4--,if two equal parallel forces act upon a body along different lines in opposite directions1 as in ,fig4 #fh1 they have no single resultant or there is no one force that will have the same effect as the two components acting together4 ,a combination of forces of this kind is called a couple4 ,its tendency is to produce change of rotation in a body4 ,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 south4 ,important ,topics #a4 ,moment of force1 how measured4 #b4 ,parallel forces4 #c4 ,the two laws of parallel forces4 #d4 ,the couple4 ,exercises #a4 ,show by diagram how to arrange a three-horse evener so that each horse must take one-third of the load4 #b4 ,two boys support a #aj-;ft4 pole on their shoulders with a #dj-lb4 string of fish supported from it #d ft4 from the front boy4 ,what load does each boy carry8 ,work by principle of moments4 #c4 ,if two horses draw a load exerting a combined pull of #cjj lbs41 what force must each exert if one is #bh in4 and the other is #cb in4 from the point of attachment of the evener to the load8 ,illustration3 ,,fig4 #fi4--;,forces acting upon a stretched rope4 ,illustration3 ,,fig4 #gj4--;,a crane with horizontal tie4 #d4 ,a weight of #ajj lbs4 is suspended at the middle of a rope ,,acb #bj ft4 long4 7,see ,fig4 #fi47 ,the ends of the rope are fastened at points ,a and ,b at the same height4 ,consider ,d as the center of the line ,,ab4 ,what is the tension of the rope when ,,cd is #c ft48 ,when ,,cd is #a ft48 ,when ,,cd is #a in48 #e4 ,a crane is set up with the tie horizontal4 7,see ,fig4 #gj47 ,if #ajjj lbs4 is to be lifted1 find the tie stress and the boom stress if the boom angle is #cj degrees8 ,if #de degrees8 #fj degrees8 #f4 ,a ball is placed on a plane inclined at an angle of #cj degrees to the horizontal4 ,what fraction of its weight tends to cause motion down the plane8 ,what effect does the other component of the weight have8 ,why8 #g4 ,a person weighing #aej lbs4 is lying in a hammock4 ,the distance between the supports is #ae ft4 ,the hammock sags #d ft4 ,what is the tension in the supports at each end8 ,what is the tension when the sag is only #a ft48 #h4 ,a ladder #cj ft4 long and weighing #hj lbs4 leans against the side of a building so that it makes an angle of #cj degrees with the building4 ,find the direction and magnitude of the component forces on the ground and at the building4 #i4 ,a traveling crane #ej ft4 long weighing #aj tons moves from one end of a shop to the other1 at the same time a load of #djjj lbs4 moves from end to end of the crane4 ,find the pressure of the trucks of the crane on the track when the load is at a distance of #e1 #aj1 #ae1 and #be ft4 from either end4 ,illustration3 ,,fig4 #ga--;,a truss4 #aj4 ,resolve a force of #ejj lbs4 into two components at right angles to each other1 one of which shall be four times the other4 #aa4 ,a truss 7see ,fig4 #ga71 carries a load of #ajjj lbs4 at ,c4 ,find the forces acting along ,,ac1 ,,bc1 and ,,ab4 ,if ,,ac and ,,bc are each #ab ft4 and ,,ab #bj ft41 which of these forces are tensions and which are pressures8 7#e7 ,,gravitation ,,and ,,gravity #hg4 ,gravitation4--,gravitation is the force of attraction that exists between all bodies of matter at all distances4 ,this attraction exists not only between the heavenly bodies1 the stars and planets1 etc41 but is also found between bodies on the earth4 ,a book attracts all objects in a room and outside of a room as well1 since its weight shows that it is attracted by the earth itself4 ,the gravitational attraction between ordinary bodies is so slight that it requires careful experiments to detect it4 ,in fact1 it is only when one of the attracting bodies is large1 as for example the earth1 that the force becomes considerable4 ,careful studies of the motions of the heavenly bodies1 especially of that of the moon in its orbit about the earth1 led ,sir ,isaac ,newton to the statement of the law of gravitation which is well expressed in the following statement3 #hh4 ,law of ,gravitation4--,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 them4 ,the law may be separated into two parts1 one referring to the masses of the bodies concerned1 the other to the effect of the distance between them4 ,the first part is easily understood since we all know that two quarts of milk will weigh just twice as much as one quart4 ,to illustrate the second part of the law1 suppose that the moon were removed to twice its present distance from the earth1 then the attraction between the earth and the moon would be one-fourth its present attraction4 ,if removed to three times its present distance1 the attraction would be one-ninth1 etc4 ,the attraction of the earth for other bodies on or near it is called gravity4 ,the weight of a body is the measure of the earth's attraction for it2 or it is the force of gravity acting upon it4 ,newton's third law of motion states that every action is accompanied by an equal and opposite reaction 7,art4 #hj74 ,hence1 the attraction of the earth for a book or any other object is accompanied by an equal attraction of the book for the earth4 #hi4 ,weight4--,in advanced physics it is proved that a sphere attracts as if it were concentrated at its center4 ,thus if the earth's radius be considered as #djjj miles1 then a body #djjj miles above the earth's surface would be #hjjj miles above the earth's center1 or twice as far from the center of the earth as is a body upon the earth's surface4 ,a body then #djjj miles above the earth's surface will weigh then but one-fourth as much as it will at the surface of the earth4 ,since the earth is flattened at the poles1 the surface at the equator is farther from the center of the earth than at points north or south4 ,thus a body weighing #a lb4 at the equator weighs #a4jjb lb4 at ,chicago1 or about #a_/ejj more4 ,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 #a_/bhi less than at the pole4 ,both effects1 that of flattening and of rotation1 tend to diminish the weight of bodies at the equator1 so that a body at the latter place weighs about #a_/aib less than at the poles4 ,in studying the effect of the earth's gravity1 the following illustration will be helpful3 ,imagine an open shaft a mile square extending through the earth4 ,what would happen to a stone thrown into the shaft8 ,at first it would have the attraction of the whole earth drawing it and continually increasing its speed downward4 ,as it descends from the surface1 the pull toward the center grows less and less4 ,halfway to the center the body has lost half its weight4 ,when the stone reaches the center1 the pull in all directions is the same1 or in other words1 it has no weight4 ,it would1 however1 continue moving rapidly on account of its inertia1 and as it continues on from the center1 the greater part of the earth being left behind1 the attraction pulling toward the center will gradually stop it4 ,it will then fall again toward the center and be stopped again after passing it1 and after repeatedly moving up and down will finally come to rest at the center of the earth4 ,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 earth4 ,what force brings the body to rest8 #ij4 ,center of ,gravity4--,a body is composed of a great many particles each of which is pulled toward the center of the earth by the force of gravity4 ,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 resultant4 ,the magnitude of this resultant is the weight of the body4 ,the direction of this resultant is in a line passing toward the earth's center1 while the point of application of this resultant is called the center of gravity of the body4 ,the center of gravity of a body may also be briefly defined as the point about which it may be balanced4 ,as the location of this point depends upon the distribution of matter in the body1 the center of gravity is also sometimes called the center of mass of the body4 ,the earth's attraction for a body is considered for the sake of simplicity1 not as a multitude of little forces1 but as a single force applied at its center of gravity4 ,to find the center of gravity of a body find two intersecting lines along which it balances1 see ,fig4 #gb1 and the center of gravity will be at the intersection4 ,a vertical line through this point is sometimes called the line of direction of the weight4 ,illustration3 ,,fig4 #gb4--,the center of gravity is at the intersection of the lines of direction4 #ia4 ,equilibrium of ,bodies4--,equilibrium means equally balanced4 ,a body at rest or in uniform motion is then in equilibrium4 ,an object is in equilibrium under gravity when a vertical line through its center of gravity passes through the point of support4 ,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 rests4 ,work will be necessary to tip the trunk from its position4 ,the amount of work required will depend upon the weight of the body and the location of the center of gravity4 #ib4 ,kinds of ,equilibrium4--7a7 ,stable4--,a body is in stable equilibrium under gravity if its center of gravity is raised whenever the body is displaced4 ,it will return to its first position if allowed to fall after being slightly displaced4 ,in ,fig4 #gc1 a and b if slightly tipped will return to their first position4 ,they are in stable equilibrium4 ,other examples are a rocking chair1 and the combination shown in ,fig4 #gd4 ,illustration3 ,,fig4 #gc4--,stable equilibrium4 7b7 ,unstable4--,a body is in unstable equilibrium under gravity if its center of gravity is lowered whenever the body is slightly displaced4 ,it will fall farther from its first position4 ,a pencil balanced on its point or a broom balanced on the end of the handle are in unstable equilibrium4 ,the slightest disturbance will make the line of direction of the weight fall outside of 7away from7 the point of support 7,fig4 #ge a74 ,illustration3 ,,fig4 #gd--;,an example of stable equilibrium4 ,why8 ,illustration3 ,,fig4 #ge4--,unstable equilibrium a1 neutral equilibrium b4 7c7 ,neutral4--,a body is in neutral equilibrium if its center of gravity is neither raised nor lowered whenever the body is moved4 ,familiar examples are a ball lying on a table 7,fig4 #ge b7 and a wagon moving on a level street 7referring to its forward motion74 ,illustration3 ,,fig4 #gf4--;,b is more stable than ,a4 #ic4 ,stability4--,when a body is in stable equilibrium1 effort must be exerted to overturn it1 and the degree of stability is measured by the effort required to overturn it4 ,to overturn a body1 it must be moved so that the vertical line through its center of gravity will pass outside of its supporting base4 ,this movement in stable bodies necessitates a raising of the center of gravity4 ,the higher this center of gravity must be raised in overturning the body1 the more stable it is1 e4g41 see ,fig4 #gf4 ,thus a wagon on a hillside will not overturn until its weight falls outside of its base1 as in ,fig4 #gg ,b4 ,the stability of a body depends upon the position of its center of gravity and the area of its base4 ,the lower the center of gravity and the larger the base1 the more stable the body4 ,what means are employed to give stability to bodies1 in every-day use 7such as clocks1 ink-stands1 pitchers1 vases1 chairs1 lamps1 etc478 ,illustration3 ,,fig4 #gg4--;,b will overturn2 ,a will not4 ,important ,topics #a4 ,gravitation2 law of gravitation1 gravity1 weight4 #b4 ,center of gravity4 #c4 ,the three states of equilibrium4 ,stability4 ,exercises #a4 ,why is a plumb-line useful in building houses8 #b4 ,what is the center of gravity of a body8 #c4 ,explain the action of a rocking chair that has been tipped forward4 #d4 ,is the stability of a box greater when empty or when filled with sand8 ,explain4 #e4 ,how can you start yourself swinging1 in a swing1 without touching the ground8 #f4 ,is the center of gravity of the beam of a balance above1 below1 or at the point of a support8 ,how did you find it out8 #g4 ,why are some ink bottles cone shaped with thick bottoms8 #h4 ,would an electric fan in motion on the rear of a light boat move it8 ,would it move the boat if revolving under water8 ,explain4 #i4 ,what turns a rotary lawn sprinkler8 #aj4 ,why1 when you are standing erect against a wall and a coin is placed between your feet1 can you not stoop and pick it up unless you shift your feet or fall over8 #aa4 ,what would become of a ball dropped into a large hole bored through the center of the earth8 #ab4 ,when an apple falls to the ground1 does the earth rise to meet it8 #ac4 ,how far from the earth does the force of gravity extend8 #ad4 ,why in walking up a flight of stairs does the body bend forward8 #ae4 ,in walking down a steep hill why do people frequently bend backward8 #af4 ,why is it so difficult for a child to learn to walk1 while a kitten or a puppy has no such difficulty8 #ag4 ,explain why the use of a cane by old people makes it easier for them to walk8 7#f7 ,,falling ,,bodies #id4 ,falling ,bodies4--,one of the earliest physical facts learned by a child is that a body unsupported falls toward the earth4 ,when a child lets go of a toy1 he soon learns to look for it on the floor4 ,it is also of common observation that light objects1 as feathers and paper1 fall much slower than a stone4 ,the information1 therefore1 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 surprise4 ,this fact may be shown by using what is called a coin and feather tube4 ,on exhausting the air from this tube1 the feather and coin within are seen to fall at the same rate4 7,see ,fig4 #gh47 when air is again admitted1 the feather flutters along behind4 ,illustration3 ,,fig4 #gh4--;,bodies fall alike in a vacuum4 #ie4 ,galileo's ,experiment4--,the fact that bodies of different weight tend to fall at the same rate was first experimentally shown by ,galileo by dropping a #a-lb4 and a #ajj-lb4 ball from the top of the leaning tower of ,pisa in ,italy 7represented in ,fig4 #gi74 ,both starting at the same time struck the ground together4 ,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 air4 ,after the invention of the air pump this supposition was verified as just explained4 ,illustration3 ,,fig4 #gi4--,leaning tower of ,pisa4 #if4 ,acceleration ,due to ,gravity4--,if a body falls freely1 that is without meeting a resistance or a retarding influence1 its motion will continually increase4 ,the increase in motion is found to be constant or uniform during each second4 ,this uniform increase in motion or in velocity of a falling body gives one of the best illustrations that we have of uniformly accelerated motion4 7,art4 #ge47 ,on the other hand1 a body thrown upward has uniformly retarded motion1 that is1 its acceleration is downward4 ,the velocity acquired by a falling body in unit time is called its acceleration1 or the acceleration due to gravity1 and is equal to #cb4af ft4 7#ihj cm47 per second1 downward1 each second of time4 ,in one second1 therefore1 a falling body gains a velocity of #cb4af ft4 7#ihj cm47 per second1 downward4 ,in two seconds it gains twice this1 and so on4 ,in formulas1 the acceleration of gravity is represented by g and the number of seconds by t1 therefore the formula for finding the velocity1 ,v1,f of a falling body starting from rest is ,v gt4 ,in studying gravity 7,art4 #hi7 we learned that its force varies as one moves toward or away from the equator4 7,how87 ,in latitude #ch the acceleration of gravity is #ihj cm4 per second each second of time4 ,f ,v represents the velocity of a falling body at the end of t seconds4 #ig4 ,experimental ,study of ,falling ,bodies4--,to study falling bodies experimentally by observing the fall of unobstructed bodies is a difficult matter4 ,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 room4 ,the simplest of these1 and in some respects the most satisfactory1 was used by ,galileo4 ,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 seconds4 ,for illustrating this principle a steel piano wire has been selected as being the simplest and the most easily understood4 ,this wire is stretched taut across a room by a turn-buckle so that its slope is about one in sixteen4 7,see ,fig4 #hj47 ,down this wire a weighted pulley is allowed to run and the distance it travels in #a1 #b1 #c1 and #d seconds is observed4 ,from these observations we can compute the distance covered each second and the velocity at the end of each second4 ,illustration3 ,,fig4 #hj4--;,apparatus to illustrate uniformly accelerated motion4 ,in ,fig4 #fc1 if ,,og represents the weight of the body or the pull of gravity1 then the line ,,or will represent the effective component along the wire1 and ,,os the non-effective component against the wire4 ,since the ratio of the height of the plane to its length is as one to sixteen1 then the motion along the wire in ,fig4 #hj will be one-sixteenth that of a falling body4 #ih4 ,summary of ,results4--,the following table gives the results that have been obtained with an apparatus arranged as shown above4 ,in this table1 column #b is the one which contains the results directly observed by the use of the apparatus4 ,columns1 #c1 #d1 and #e are computed from preceding columns4 7#a7 7#b7 7#c7 7#d7 7#e7 ,no4 of ,total ,distance ,velocity at ,acceleration seconds distance each second end of second each second moved ,per second ,per second #a #cj cm4 #cj cm4 #fj cm4 #fj cm4 #b #abj cm4 #ij cm4 #abj cm4 #fj cm4 #c #bgj cm4 #aej cm4 #ahj cm4 #fj cm4 #d #dhj cm4 #baj cm4 #bdj cm4 #fj cm4 ,column #e shows that the acceleration is uniform1 or the same each second4 ,column #d shows that the velocity increases with the number of seconds or that ,v at4 ,column #c shows that the increase in motion from #a second to the next is just equal to the acceleration or #fj cm4 ,this is represented by the following formula3 s #a_/b a7#bt - #a74 ,the results of the second column1 it may be seen1 increase as #a3d3i3af1 while the number of seconds vary as #a3b3c3d4 ,that is1 the total distance covered is proportional to the square of the number of seconds4 ,this fact expressed as a formula gives3 ,s #a_/b;at4 ,substituting g1 the symbol for the acceleration of gravity1 for a in the above formulas1 we have3 7#a7 ,v gt1 7#b7 ,s #a_/b;gt1 7#c7 s #a_/b;g7#bt - #a74 #ii4 ,laws of ,falling ,bodies4--,these formulas may be stated as follows for a body which falls from rest3 #a4 ,the velocity of a freely falling body at the end of any second is equal to #cb4af ft4 per sec4 or #ihj cm4 per second multiplied by the number of the second4 #b4 ,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 #af4jh ft4 or #dij cm4 #c4 ,the distance passed through by a freely falling body during any second is equal to #af4jh feet or #dij cm4 multiplied by one less than twice the number of the second4 ,important ,topics #a4 ,falling bodies4 #b4 ,galileo's experiment4 #c4 ,acceleration due to gravity4 #d4 ,laws of falling bodies4 ,exercises #a4 ,how far does a body fall during the first second8 ,account for the fact that this distance is numerically equal to half the acceleration4 #b4 7a7 ,what is the velocity of a falling body at the end of the first second8 7b7 ,how far does it fall during the second second8 7c7 ,account for the difference between these numbers4 #c4 ,what is the velocity of a falling body at the end of the fifth second8 #d4 ,how far does a body fall 7a7 in #e seconds 7b7 in #f seconds 7c7 during the sixth second8 #e4 7a7 ,what is the difference between the average velocity during the sixth second and the velocity at the beginning of that second8 7b7 ,is this difference equal to that found in the second problem8 ,why8 #f4 ,a stone dropped from a cliff strikes the foot of it in #e seconds4 ,what is the height of the cliff8 #g4 ,why is it that the increased weight of a body when taken to higher latitudes causes it to fall faster1 while at the same place a heavy body falls no faster than a light one8 #h4 ,when a train is leaving a station its acceleration gradually decreases to zero1 although the engine continues to pull4 ,explain4 #i4 ,would you expect the motion of equally smooth and perfect spheres of different weight and material to be equally accelerated on the same inclined plane8 ,give reason for your answer4 ,try the experiment4 #aj4 ,a body is thrown upward with the velocity of #fd4cb ft4 per sec4 ,how many seconds will it rise8 ,how far will it rise8 ,how many seconds will it stay in the air before striking the ground8 #aa4 #cb4af feet how many centimeters8 #ab4 ,the acceleration of a freely falling body is constant at any one place4 ,what does this show about the pull which the earth exerts on the body8 7#g7 ,,the ,,pendulum #ajj4 ,the ,simple ,pendulum4--,any body suspended so as to swing freely to and fro is a pendulum1 as in ,fig4 #ha4 ,a simple pendulum is defined as a single particle of matter suspended by a cord without weight4 ,it is of course impossible to construct such a pendulum4 ,a small metal ball suspended by a thread is approximately a simple pendulum4 ,when allowed to swing its vibrations are made in equal times4 ,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 ,pisa4 ,illustration3 ,,fig4 #ha--;,a simple pendulum4 #aja4 ,definition of ,terms4 ,the center of suspension is the point about which the pendulum swings4 ,a single vibration is one swing across the arc4 ,a complete or double vibration is the swing across the arc and back again4 ,the time required for a double vibration is called the period4 ,the length of a simple pendulum is approximately the distance from the point of support to the center of the bob4 ,a seconds pendulum is one making a single vibration per second4 ,its length at sea-level1 at ,new ,york is #ii4ca cm4 or #ci4a in41 at the equator #ci4ja in41 at the poles #ci4bb in4 ,a compound pendulum is one having an appreciable portion of its mass elsewhere than in the small compact body or sphere called a bob4 ,the ordinary clock pendulum or a meter stick suspended by one end are examples of compound pendulums4 ,the amplitude of a vibration is one-half the arc through which it swings1 for example1 the arc ,,dc or the angle ,,dac in ,fig4 #ha4 #ajb4 ,laws of the ,pendulum4--,the following laws may be stated3 #a4 ,the period of a pendulum is not affected by its mass or the material of which the pendulum is made4 #b4 ,for small amplitudes1 the period is not affected by the length of the arc through which it swings4 #c4 ,the period is directly proportional to the square root of the length4 ,expressed mathematically1 t_/t l_/l4 #ajc4 ,uses of the ,pendulum4--,the chief use of the pendulum is to regulate motion in clocks4 ,the wheels are kept in motion by a spring or a weight and the regulation is effected by an escapement 7,fig4 #hb74 ,at each vibration of the pendulum one tooth of the wheel ,d slips past the prong at one end of the escapement ,c1 at the same time giving a slight push to the escapement4 ,this push transmitted to the pendulum keeps it in motion4 ,in this way1 the motion of the wheel work and the hands is controlled4 ,another use of the pendulum is in finding the acceleration of gravity1 by using the formula1 t 7l_/g71 in which t is the time in seconds of a single vibration and l the length of the pendulum4 ,if1 for example1 the length of the seconds pendulum is #ii4ca cm41 then #a 7#ii4ca_/;g72 squaring both sides of the equation1 we have #a 7#ii4ca_/;g71 or g #ii4ca_/a #ihj4a cm4 per sec41 per sec4 ,from this it follows that1 since the force of gravity depends upon the distance from the center of the earth1 the pendulum may be used to determine the elevation of a place above sea level and also the shape of the earth4 ,important ,topics #a4 ,simple pendulum4 #b4 ,definitions of terms used4 #c4 ,laws of the pendulum4 #d4 ,uses of the pendulum4 ,exercises #a4 ,what is the usual shape of the bob of a clock pendulum8 ,why is this shape used instead of a sphere8 #b4 ,removing the bob from a clock pendulum has what effect on its motion8 ,also on the motion of the hands8 #c4 ,how does the expansion of the rod of a pendulum in summer and its contraction in winter affect the keeping of time by a clock8 ,how can this be corrected8 #d4 ,master clocks that control the time of a railway system have a cup of mercury for a bob4 ,this automatically keeps the same rate of vibration through any changes of temperature4 ,how8 #e4 ,how will the length of a seconds pendulum at ,denver1 #a mile above sea-level1 compare with one at ,new ,york8 ,why8 ,illustration3 ,,fig4 #hb--;,escapement and pendulum of a clock4 #f4 ,what is the period of a pendulum #i in4 long8 ,note4 ,in problems involving the use of the third law1 use the length of a seconds pendulum for l1 and call its period #a4 #g4 ,a swing is #bj ft4 high1 find the time required for one swing across the arc4 #h4 ,a pendulum is #fj cm4 long4 ,what is its period8 #i4 ,if in a gymnasium a pupil takes #c sec4 to swing once across while hanging from a ring1 how long a pendulum is formed8 #aj4 ,a clock pendulum makes four vibrations a second1 what is its length8 ,review ,outline3 ,force and ,motion ,force2 definition1 elements1 how measured1 units1 dyne4 ,graphic ,representation2 typical examples of finding a component1 a resultant1 or an equilibrant4 ,motion2 ,laws of motion 7#c71 inertia1 curvilinear motion1 centrifugal force1 momentum1 7,m mv71 reaction1 stress and strain4 ,moment of ,force2 parallel forces1 couple1 effective and non-effective component4 ,gravitation2 law2 gravity1 center of2 weight4 ,equilibrium #c forms2 stability1 how increased4 ,falling ,bodies2 velocity1 acceleration1 g1 ,laws2 ,v gt1 ,s 7#a_/b7;gt - s 7#a_/b7;g7#bt - #a74 ,pendulum2 simple1 seconds1 laws 7#c71 t 7l_/g74 ,,chapter ,,vi ,,work ,,and ,,energy #ajd4 ,work4--,whenever a force moves a body upon which it acts1 it is said to do work upon that body4 ,for example1 if a man pushes a wheelbarrow along a path1 he is doing work on it as long as the wheelbarrow moves1 but if the wheelbarrow strikes a stone and the man continues to push and no motion results1 from a scientific point of view he is then doing no work on it4 ,work signifies the overcoming of resistance1 and unless the resistance is overcome no work is done4 ,lifting a weight is doing work on it1 supporting a weight is not1 although the latter may be nearly as tiresome as the former4 ,work as used in science is a technical term4 ,do not attach to it meanings which it has in every-day speech4 #aje4 ,measurement of ,work4--,work is measured by the product of the force by the displacement caused in the direction of the force1 that is ,w fs4 ,therefore if a unit of force acts through a unit of space1 a unit of work will be done4 ,there are naturally several units of work depending upon the units of force and space employed4 ,english ,work ,unit4--,if the force of one pound acts through the distance of one foot1 a foot-pound of work is done4 ,a foot-pound is defined as the work done when #a lb4 is lifted #a ft4 against the force of gravity4 ,metric ,work ,unit4--,if the force is one kilogram and the distance one meter1 one kilogram-meter of work is done4 ,absolute ,work ,unit4--,if the force of one dyne acts through the distance of one centimeter a dyne-centimeter of work is done4 ,this usually is called an i4 ,other work units are sometimes used depending upon the force and distance units employed4 ,one1 the i1 is equal to #aj1jjj1jjj ergs or #aj ergs4 ,problem4--,if a load is drawn #b miles by a team exerting #ejj lbs4 force1 how much work is done8 ,solution4--,since the force employed is #ejj lbs41 and the distance is #b #ebhj ft41 the work done is #ejj #b #ebhj or #e1bhj1jjj ft4-lbs4 #ajf4 ,energy4--,in the various cases suggested in the paragraphs upon work1 an agent1 a man1 an animal or a machine1 was mentioned as putting forth an effort in order to do the work4 ,it is also true that in order to perform work an agent must employ energy1 or the energy of a body is its capacity for doing work4 ,where an agent does work upon a body1 as in winding up a spring or in lifting a weight1 the body upon which the work has been done may acquire energy by having work done upon it4 ,that is1 it may become able to do work itself upon some other body4 ,for instance1 a lifted weight in falling back to its first position may turn wheels1 or drive a post into the ground against resistance2 a coiled spring may run clock work1 strike a blow1 or close a door4 ,hence the energy1 or the capacity for doing work1 is often acquired by a body because work has first been done upon that body4 #ajg4 ,potential ,energy4--,the wound up spring may do work because work has first been done upon it4 ,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 powder1 lift another weight or do some other kind of work4 ,the energy that a body possesses on account of its position or shape and a stress to which it is subjected is called potential energy4 ,the potential energy of a body is measured by the work done in lifting it1 changing its shape1 or by bringing about the conditions by which it can do work4 ,thus if a block of iron weighing #bjjj lbs4 is lifted #bj ft41 it possesses #dj1jjj ft4-lbs4 of potential energy4 ,it is therefore able to do #dj1jjj ft4-lbs4 of work in falling back to its first position4 ,if the block just mentioned should fall from its elevated position upon a post1 it could drive the post into the ground because its motion at the instant of striking enables it to do work4 ,to compute potential energy you compute the work done upon the body4 ,that is1 ,p4,e4 w h or f s4 #ajh4 ,kinetic ,energy4--,the energy due to the motion of a body is called kinetic energy4 ,the amount of kinetic energy in a body may be measured by the amount of work done to put it in motion4 ,it is usually computed1 however1 by using its mass and velocity on striking4 ,to illustrate1 a #ajj-lb4 ball is lifted #af ft4 ,the work done upon it1 and hence its potential energy1 is #afjj ft4-lbs4 ,on falling to the ground again1 this will be changed into kinetic energy1 or there will be #afjj ft4-lbs4 of kinetic energy on striking4 ,it will be noted that since energy is measured by the work it can do1 work units are always used in measuring energy4 ,to compute the kinetic energy of a falling body by simply using its mass and velocity one proceeds as follows1 in solving the above problem3 ,first1 find the velocity of the falling body which has fallen #af ft4 ,a body falls #af ft4 in one second4 ,in this time it gains a velocity of #cb ft4 per second4 ,now using the formula for kinetic energy ,k4,e4 wv_/7#b;g71 we have ,k4,e4 #ajj #cb #cb_/7b #cb7 #afjj ft4-lbs4 as before4 ,the formula1 ,k4,e4 wv_/7#b;g71 may be derived in the following manner3 ,the kinetic energy of a falling body equals the work done in giving it its motion1 that is1 ,k4,e4 w ,s1 in which1 w the weight of the body and ,s the distance the body must fall freely in order to acquire its velocity4 ,the distance fallen by a freely falling body1 ,s1 #a_/b;gt gt_/7#b;g7 7,art4 #ih1 p4 #aaa74 ,now1 v gt and v gt4 ,substituting for gt1 its equal v1 we have ,s v_/7#b;g74 ,substituting this value of ,s in the equation ,k4,e4 w ,s1 we have ,k4,e4 wv_/7#b;g74 ,since the kinetic energy of a moving body depends upon its mass and velocity and not upon the direction of motion1 this formula may be used to find the kinetic energy of any moving body4 ,mass and weight in such problems may be considered numerically equal4 ,important ,topics #a4 ,work defined4 #b4 ,work units1 foot-pound1 kilogram-meter1 erg4 #c4 ,energy defined4 #d4 ,kinds of energy1 potential and kinetic4 ,problems #a4 ,how much work will a #abj-lb4 boy do climbing a mountain #cjjj ft4 high8 ,should the vertical or slant height be used8 ,why8 #b4 ,in a mine #djjj kg4 of coal are lifted #bbc meters3 how much work is done upon the coal8 ,what is the kind and amount of energy possessed by the coal8 #c4 ,a pile driver weighs #dej lbs4 ,it is lifted #af ft4 ,how much work has been done upon it8 ,what kind and amount of energy will it have after falling #af ft4 to the pile8 #d4 ,a train weighing #djj tons is moving #cj miles per hour4 ,compute its kinetic energy4 7,change its weight to pounds and velocity to feet per second47 #e4 ,what would be the kinetic energy of the train in problem #d if it were going #fj miles per hour8 ,if it were going #ij miles per hour8 ,how does doubling or trebling the speed of an object affect its kinetic energy8 ,how does it affect its momentum8 #f4 ,what is the kinetic energy of a #afjj-lb4 cannon ball moving #bjjj ft4 per second8 #g4 ,mention as many kinds of mechanical work as you can and show how each satisfies the definition of work4 #h4 ,a pile driver weighing #cjjj lbs4 is lifted #aj ft4 ,how much work is done upon it8 #i4 ,if the pile driver in problem #h is dropped upon the head of a pile which meets an average resistance of #cj1jjj lbs41 how far will one blow drive it8 #aj4 ,a #dj kg4 stone is placed upon the top of a chimney #ej meters high4 ,compute the work done in kilogram-meters and foot-pounds4 7#b7 ,,power ,,and ,,energy #aji4 ,horse-power4--,in computing work1 no account is taken of the time required to accomplish it4 ,but since the time needed to perform an undertaking is of much importance1 the rate of work1 or the power or activity of an agent is an important factor4 ,thus if one machine can do a piece of work in one-fifth the time required by another machine1 it is said to have five times the power of the other4 ,therefore the power of a machine is the rate at which it can do work4 ,james ,watt 7#agcf-ahai71 the inventor of the steam-engine1 in expressing the power of his engine1 used as a unit a horse-power4 ,he considered that a horse could do #cc1jjj ft4-lbs4 of work a minute4 ,this is equal to #eej ft4-lbs4 per second or #gf4je kg4-m4 per second4 ,this is too high a value but it has been used ever since his time4 ,steam engines usually have their power rated in horse-power4 ,that is1 locomotives produce from #ejj to #aejj horse-power4 ,some stationary and marine engines develop as high as #be1jjj horse-power4 ,the power of an average horse is about #c_/d horse-power and of a man about #a_/g horse-power when working continuously for several hours4 #aaj4 ,the ,watt4--,in the metric system1 the erg as a unit of work would give as a unit of power #a erg per second4 ,this amount is so small1 however1 that a larger unit is usually employed1 the practical unit being #aj1jjj1jjj ergs a second1 that is1 one joule per second4 7,see ,art4 #aje47 ,this practical unit is called a ,watt after ,james ,watt4 ,the power of dynamos is usually expressed in kilowatts1 a kilowatt representing #ajjj watts4 ,steam-engines in modern practice are often rated in kilowatts instead of horse-power4 ,a horse-power is equivalent to #gdf watts1 or is nearly #c_/d of a kilowatt4 #aaa4 ,energy4 ,its ,transference and ,transformation4 ,we have considered energy as the capacity for doing work1 and noted the two kinds1 potential and kinetic1 and the facility with which one may change into another4 ,in fact1 the transference of energy from one body to another1 and its transformation from one form to another is one of the most common processes in nature4 ,take a pendulum in motion1 at the end of a swing1 its energy being entirely due to its elevated position is all potential2 at the lowest point in its path its energy being entirely due to its motion is all kinetic4 ,the change goes on automatically as long as the pendulum swings4 ,a motor attached by a belt to a washing machine is started running4 ,the energy of the motor is transferred by the belt to the washer where it is used in rubbing and moving the clothes4 ,the heat used in warming a house is usually obtained by burning coal or wood4 ,coal is believed to be formed from the remains of plants that grew in former geologic times4 ,these plants grew through the help of the radiant energy of the sun4 ,the following are transformations of energy that have occurred3 ,the radiant energy of sunlight was transformed into the chemical energy of the plants4 ,this remained as chemical energy while the plants were being converted into coal1 was mined1 brought to the stove or furnace and burned4 ,the burning transformed the chemical energy into heat energy in which form we use it for warming rooms4 ,take the energy used in running a street car whose electrical energy comes from a waterfall4 ,the energy of the car itself is mechanical4 ,its motor1 however1 receives electrical energy and transforms it into mechanical4 ,this electrical energy comes along a wire from a dynamo at the waterfall1 where water-wheels and generators transform into electrical energy the mechanical energy of the falling water4 ,the water obtained its energy of position by being evaporated by the heat of the radiant energy of the sun4 ,the vapor rising into the air is condensed into clouds and rain1 and falling on the mountain side1 has1 from its elevated position1 potential energy4 ,the order of transformation1 therefore1 is in this case1 radiant1 heat1 mechanical1 electrical1 and mechanical4 ,can you trace the energy from the sun step by step to the energy you are using in reading this page8 #aab4 ,forms of ,energy4--,a steam-engine attached to a train of cars employs its energy in setting the cars in motion1 i4e41 in giving them kinetic energy and in overcoming resistance to motion4 ,but what is the source of the energy of the engine8 ,it is found in the coal which it carries in its tender4 ,but of what kind8 ,surely not kinetic1 as no motion is seen4 ,it is therefore potential4 ,what is the source of the energy of the coal8 ,this question leads us back to the time of the formation of coal beds1 when plants grew in the sunlight and stored up the energy of the sun's heat and light as chemical energy4 ,the sun's light brings to the earth the energy of the sun1 that central storehouse of energy1 which has supplied nearly all the available energy upon the earth4 ,five forms of energy are known1 viz41 mechanical1 heat1 electrical1 radiant1 and chemical4 #aac4 ,energy ,recognized by its ,effects4--,like force1 energy is invisible and we are aware of the forms only by the effects produced by it4 ,we recognize heat by warming1 by expansion1 by pressure4 ,we recognize light by warming1 by its affecting vision4 ,we recognize electrical energy by its heat1 light1 motion1 or magnetic effect4 ,we recognize mechanical energy by the motion that it produces4 ,we recognize chemical energy by knowing that the source of energy does not belong to any of the foregoing4 ,a boy or girl is able to do considerable work4 ,they therefore possess energy4 ,in what form does the energy of the body mainly occur8 ,one can determine this for himself by applying questions to each form of energy in turn as in ,art4 #aad4 #aad4 ,source of the ,energy of the ,human ,body4--,is the energy of the human body mostly heat8 ,no1 since we are not very warm4 ,is it light or electrical8 ,evidently not since we are neither luminous nor electrical4 ,is it mechanical8 ,no1 since we have our energy even when at rest4 ,is it chemical8 ,it must be since it is none of the others4 ,chemical energy is contained within the molecule4 ,it is a form of potential energy and it is believed to be due to the position of the atoms within the molecule4 ,as a tightly coiled watch spring may have much energy within it1 which is set free on allowing the spring to uncoil1 so the chemical energy is released on starting the chemical reaction4 ,gunpowder and dynamite are examples of substances containing chemical energy4 ,on exploding these1 heat1 light1 and motion are produced4 ,gasoline1 kerosene1 and illuminating gas are purchased because of the potential energy they contain4 ,this energy is set free by burning or exploding them4 ,the source of the energy of our bodies is of course the food we eat4 ,the energy contained in the food is also chemical4 ,vegetables obtain their energy from the sunlight 7radiant energy74 ,this is why plants will not grow in the dark4 ,the available energy is mostly contained in the form of starch1 sugar and oil4 ,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 needed4 ,the energy is set free by oxidation 7burning71 the oxygen needed for this being supplied by breathing4 ,breathing also removes the carbon dioxide1 which results from the combustion4 ,it is for its energy that our food is mostly required4 #aae4 ,conservation of ,energy4--,in the study of matter we learned that it is indestructible4 ,energy is also believed to be indestructible4 ,this principle stated concisely teaches that despite the innumerable changes which energy undergoes the amount in the universe is unchangeable1 and while energy may leave the earth and be lost as far as we are concerned1 that it exists somewhere in some form4 ,the principle which teaches this is called the ,conservation of ,energy4 ,the form into which energy is finally transformed is believed to be heat4 ,important ,topics #a4 ,power defined4 ,units4 ,horse-power4 ,watt4 #b4 ,transference and transformations of energy4 #c4 ,forms of energy2 heat1 electrical1 mechanical1 radiant1 chemical4 #d4 ,effects of the several forms of energy4 #e4 ,energy of the human body4 #f4 ,conservation of energy4 ,exercises #a4 ,a boy weighing #aaj lbs4 ran up a stairs #aj ft4 high1 in #d seconds4 ,how much work was done8 ,what was his rate of work 7foot-pounds per second78 ,express also in horse-power4 #b4 ,a locomotive drawing a train exerts a draw bar pull of #aa1jjj lbs4 ,how much work does it do in moving #c miles8 ,what is its rate of work if it moves #c miles in #e minutes8 ,express in horse-power4,g ,g ,the following formula is of assistance in computing horse-power in problems3 ,h4 p4 7lbs4 ft47_/7#eej sec474 #c4 ,if #djj kg4 are lifted #ce meters in #e seconds what work is done8 ,what is the rate of work8 ,express in horse-power1 watts and kilowatts4 #d4 ,trace the energy of a moving railway train back to its source in the sun4 #e4 ,why does turning the propeller of a motor boat cause the boat to move8 #f4 ,does it require more power to go up a flight of stairs in #e seconds than in #aj seconds8 ,explain4 ,is more work done in one case than in the other8 ,why8 #g4 ,can #a man carrying bricks up to a certain elevation for #abj days do as much work as #abj men carrying up bricks for #a day8 #h4 ,if the #a man and #abj men of problem #g do the same amount of work have they the same power8 ,explain4 #i4 ,if #afj cu4 ft4 of water flow each second over a dam #ae;ft4 high what is the available power8 #aj4 ,what power must an engine have to fill a tank #aa #h #e ft4 with water #abj ft4 above the supply1 in #e minutes8 #aa4 ,a hod carrier weighing #aej lbs4 carries a load of bricks weighing #ajj lbs4 up a ladder #cj ft4 high4 ,how much work does he do8 #ab4 ,how much work can a #d-;horse-power engine do in #e minutes8 #ac4 ,find the horse-power of a windmill that pumps #f tons of water from a well #ij ft4 deep in #cj minutes4 #ad4 ,how many horse-power are there in a waterfall #bj ft4 high over which #ejj cu4 ft4 of water pass in a minute8 #ae4 ,the ,chicago drainage canal has a flow of about #fjjj cu4 ft4 a second4 ,if at the controlling works there is an available fall of #cd ft4 how many horse-power can be developed8 #af4 ,how long will it take a #aj-;horse-power pump to fill a tank of #djjj gallons capacity1 standing #cjj ft4 above the pump8 #ag4 ,a boy weighing #afb lbs4 climbs a stairway a vertical height of #ad ft4 in #ad4f seconds4 ,how much power does he exert8 #ah4 ,the same boy does the same work a second time in #d4b seconds4 ,how much power does he exert this time8 ,what causes the difference8 #ai4 ,what is a horse-power-hour8 a kilowatt-hour8 7#c7 ,,simple ,,machines ,,and ,,the ,,lever #aaf4 ,machines and ,their ,uses4--,a man1 while standing on the ground1 can draw a flag to the top of a pole1 by using a rope passing over a pulley4 ,a boy can unscrew a tightly fitting nut that he cannot move with his fingers1 by using a wrench4 ,a woman can sew a long seam by using a sewing machine in much less time than by hand4 ,a girl can button her shoes much quicker and easier with a button-hook than with her fingers4 ,these illustrations show some of the reasons why machines are used4 ,in fact it is almost impossible to do any kind of work efficiently without using one or more machines4 #aag4 ,advantages of ,machines4--7a7 ,many machines make possible an increased speed as in a sewing machine or a bicycle4 7b7 ,other machines exert an increased force4 ,a rope and a set of pulleys may enable a man to lift a heavy object such as a safe or a piano4 ,by the use of a bar a man can more easily move a large rock4 7,see ,fig4 #hc47 ,illustration3 ,,fig4 #hc4--,the rock is easily moved4 7c7 ,the direction of a force may be changed thus enabling work to be done that could not be readily accomplished otherwise4 ,as1 e4g41 the use of a pulley in raising a flag to the top of a flag pole1 or in raising a bucket of ore from a mine by using a horse attached to a rope passing over two or more pulleys4 7,see ,fig4 #hd47 7d7 ,other agents than man or animals can be used such as electricity1 water power1 the wind1 steam1 etc4 ,fig4 #he represents a windmill often used in pumping water4 ,a machine is a device for transferring or transforming energy4 ,it is usually therefore an instrument for doing work4 ,an electric motor is a machine since it transforms the energy of the electric current into motion or mechanical energy1 and transfers the energy from the wire to the driving pulley4 ,illustration3 ,,fig4 #hd4--,the horse lifts the bucket of ore4 #aah4 ,a ,machine ,cannot ,create ,energy4--,whatever does work upon a machine 7a man1 moving water1 wind1 etc47 loses energy which is employed in doing the work of the machine4 ,a pair of shears is a machine since it transfers energy from the hand to the edges that do the cutting4 ,our own bodies are often considered as machines since they both transfer and transform energy4 ,we must keep in mind that a machine cannot create energy4 ,the principle of ,conservation of ,energy is just as explicit on one side as the other4 ,just as energy1 cannot be destroyed1 so energy cannot be created4 ,a machine can give out no more energy than is given to it4 ,it acts simply as an agent in transferring energy from one body to another4 ,many efforts have been made to construct machines that when once started will run themselves1 giving out more energy than they receive4 ,such efforts1 called seeking for perpetual motion1 have never succeeded4 ,this fact is strong evidence in favor of the principle of the conservation of energy4 ,illustration3 ,,fig4 #he4--;,a windmill4 #aai4 ,law of ,machines4--,when a body receives energy1 work is done upon it4 ,therefore work is done upon a machine when it receives energy and the machine does work upon the body to which it gives the energy4 ,in the operation of a machine1 therefore1 two quantities of work are to be considered and by the principle of the conservation of energy1 these two must be equal4 ,the work done by a machine equals the work done upon it1 or the energy given out by a machine equals the energy received by it4 ,these two quantities of work must each be composed of a force factor and a space factor4 ,therefore two forces and two spaces are to be considered in the operation of a machine4 ,the force factor of the work done on the machine is called the force or effort4 ,it is the force applied to the machine4 ,the force factor of the work done by a machine is called the weight or resistance4 ,it is the force exerted by the machine in overcoming the resistance and equals the resistance overcome4 ,if f represents the force or effort1 and ,df the space it acts through1 and w represents the weight or resistance1 and ,dw the space it acts through1 then the law of machines may be expressed by an equation1 f ,df w ,dw4 ,that is1 the effort times the distance the effort acts equals the resistance times the distance the resistance is moved or overcome4 ,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 proportion4 ,the equation given above may therefore be expressed w3 f ,df3 ,dw4 ,or the resistance is to the effort as the effort distance is to the resistance distance4 ,the law of machines may therefore be expressed in several ways4 ,one should keep in mind1 however1 that the same law of machines is expressed even though the form be different4 ,what two ways of expressing the law are given8 #abj4 ,the ,simple ,machines4--,there are but six simple machines4 ,all the varieties of machines known are simply modifications and combinations of the six simple machines4 ,the six simple machines are more easily remembered if we separate them into two groups of three each4 ,the first or lever group consists of those machines in which a part revolves about a fixed axis4 ,it contains the lever1 pulley and wheel and axle4 ,the second or inclined plane group includes those having a sloping surface4 ,it contains the inclined plane1 the wedge1 and the screw4 #aba4 ,the ,lever4--,the lever is one of the simple machines most frequently used1 being seen in scissors1 broom1 coal shovel1 whip1 wheelbarrow1 tongs1 etc4 ,the lever consists of a rigid bar capable of turning about a fixed axis called the fulcrum4 ,in studying a lever1 one wishes to know what weight or resistance it can overcome when a certain force is applied to it4 ,diagrams of levers1 therefore1 contain the letters w and f4 ,in addition to these1 ,o stands for the fulcrum on which it turns4 ,by referring to ,fig4 #hf1 a1 b1 c1 one may notice that each of these may occupy the middle position between the other two4 ,the two forces 7other than the one exerted by the fulcrum7 acting on a lever always oppose each other in the matter of changing rotation4 ,they may be considered as a pair of parallel forces acting on a body1 each tending to produce rotation4 ,illustration3 ,,fig4 #hf4--,the three classes of levers4 #abb4 ,moment of ,force4--,the effectiveness of each force may therefore be determined by computing its moment about the fixed axis 7see ,art4 #hd71 that is1 by multiplying each force by its distance to the fulcrum or axis of rotation4 ,let a meter stick have a small hole bored through it at the #ej cm4 mark near one edge1 and let it be mounted on a nail driven into a vertical support and balanced by sliding a bent wire along it4 ,suspend by a fine wire or thread a #ajj g4 weight1 #ae cm4 from the nail and a #ej g4 weight #cj cm4 from the nail1 on the other side of the support4 ,these two weights will be found to balance4 ,when viewed from this side ,a 7,fig4 #hg7 tends to turn the lever in a clockwise direction 7down at right71 ,b in the counter-clockwise direction 7down at left74 ,since the lever balances1 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 fulcrum4 ,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 force4 ,illustration3 ,,fig4 #hg4--,the two moments are equal about ,c4 #ajj #ae #ej #cj4 ,from the experiment just described1 the moment of the acting force equals the moment of the weight or f ,df w ,dw1 or the effort times the effort arm equals the weight times the weight arm4 ,this equation is called the law of the lever4 ,it corresponds to the general law of machines and may also be written w3 f ,df3 ,dw4 #abc4 ,mechanical ,advantage4--,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 move4 ,if the lever is used in lifting a stone weighing #ejj lbs41 the force available being only #ajj lbs41 then its mechanical advantage would be #e1 the ratio of w3f4 ,in a similar way1 the mechanical advantage of any machine is found by finding the ratio of the resistance or weight to the effort4 ,what must be the relative lengths of the effort arm and resistance or weight arm in the example just mentioned8 ,since the effort times the effort arm equals the weight times the weight arm1 if f ,df w ,dw1 then ,df is five times ,dw4 ,hence the mechanical advantage of a lever is easily found by finding the ratio of the effort arm to the weight arm4 ,important ,topics #a4 ,advantage of machines4 #b4 ,machines cannot create energy4 #c4 ,law of machines4 #d4 ,six simple machines4 #e4 ,lever and principle of moments4 #f4 ,mechanical advantage of a machine4 ,exercises #a4 ,give six examples of levers you use4 #b4 ,fig4 #hh;a represents a pair of paper shears1 #hh;b a pair of tinner's shears4 ,which has the greater mechanical advantage8 ,why8 ,explain why each has the most effective shape for its particular work4 ,illustration3 ,,fig4 #hh4--7;a7 ,paper shears4 7b7 ,tinner's shears4 #c4 ,find examples of levers in a sewing machine4 #d4 ,what would result if1 in ,art4 #abb1 the #ajj g4 weight were put #be cm4 from ,o and the #ej g4 weight #de cm4 from ,o8 ,why8 ,explain using principle of moments4 #e4 ,how is the lever principle applied in rowing a boat8 #f4 ,when you cut cardboard with shears1 why do you open them wide and cut near the pivot8 #g4 ,in carrying a load on a stick over the shoulder should the pack be carried near the shoulder or out on the stick8 ,why8 #h4 ,how can two boys on a see-saw start it without touching the ground8 #i4 ,in lifting a shovel full of sand do you lift up with one hand as hard as you push down with the other8 ,why8 ,illustration3 ,,fig4 #hi4--,the hammer is a bent lever4 ,what is its mechanical advantage8 #aj4 ,why must the hinges of a gate #c ft4 high and #af ft4 wide be stronger than the hinges of a gate #af ft4 high and #c ft4 wide8 #aa4 ,when one sweeps with a broom do the hands do equal amounts of work8 ,explain4 #ab4 ,a bar #f ft4 long is used as a lever to lift a weight of #ejj lbs4 ,if the fulcrum is placed #f in4 from the weight1 what will be the effort required8 ,note3 two arrangements of weight1 fulcrum and effort are possible4 #ac4 ,the handle of a hammer is #ab in4 long and the claw that is used in drawing a nail is #b4e in4 long4 7,see ,fig4 #hi47 ,a force of #be lbs4 is required to draw the nail4 ,what is the resistance of the nail8 #ad4 ,the effective length of the head of a hammer is #b in4 ,the handle is #ae in4 long and the nail holds in the wood with a force of #ejj lbs4 ,only #fj lbs4 of force is available at the end of the handle4 ,what will be the result8 #ae4 ,if an effort of #ej lbs4 acting on a machine moves #aj ft41 how far can it lift a weight of #ajjj lbs48 #af4 ,a bar #aj ft4 long is to be used as a lever4 ,the weight is kept #b ft4 from the fulcrum4 ,what different levers can it represent8 #ag4 ,the effort arm of a lever is #f ft41 the weight arm #f in4 ,how long will the lever be8 ,give all possible answers4 #ah4 ,two boys carry a weight of #ajj lbs4 on a pole #e ft4 long between them4 ,where should the weight be placed in order that one boy may carry one and one-fourth times as much as the other8 7#d7 ,,the ,,wheel ,,and ,,axle ,,and ,,the ,,pulley #abd4 ,the ,wheel and ,axle4--#a4 ,one of the simple machines most commonly applied in compound machines is the wheel and axle4 ,it consists of a wheel ,h mounted on a cylinder ,y so fastened together that both turn on the same axis4 ,in ,fig4 #ij1 ropes are shown attached to the circumferences of the wheel and axle4 ,sometimes a hand wheel is used as on the brake of a freight or street car1 or simply a crank and handle is used1 as in ,fig4 #ia4 ,the capstan is used in moving buildings4 ,sometimes two or three wheels and axles are geared together as on a derrick or crane as in ,fig4 #ib4 ,illustration3 ,,fig4 #ij4--,the wheel and axle4 ,illustration3 ,,fig4 #ia4--,windlass used in drawing water from a well4 ,illustration3 ,,fig4 #ib4--;,a portable crane4 ,illustration3 ,,fig4 #ic4--,the wheel and axle considered as a lever4 ,illustration3 ,,fig4 #id4--,view of transmission gears in an automobile4 #a1 ,drive gear2 #b1 ,high and intermediate gear2 #c1 ,low and reverse gear2 #d1 #h1 ,reverse idler gears2 #e1 #f1 #g1 ,countershaft gears4 7,courtesy of the ,automobile ,journal47 ,illustration3 ,,fig4 #ie4--,reducing gear of a steam turbine4 ,fig4 #ic is a diagram showing that the wheel and axle acts like a lever4 ,the axis ,d is the fulcrum1 the effort is applied at ,f1 at the extremity of a radius of the wheel and the resisting weight ,w at the extremity of a radius of the axle4 ,hence1 if ,df1 the effort distance1 is three times ,dw1 the weight distance1 the weight that can be supported is three times the effort4 ,here as in the lever1 f ,df w ,dw1 or w3f ,df3,dw1 or the ratio of the weight to the effort equals the ratio of the radius of the wheel to the radius of the axle4 ,this is therefore the mechanical advantage of the wheel and axle4 ,since the diameters or circumferences are in the same ratio as the radii these can be used instead of the radii4 ,sometimes1 when increased speed instead of increased force is desired1 the radius of the wheel or part to which power is applied is less than that of the axle4 ,this is seen in the bicycle1 buzzsaw1 and blower4 ,sometimes geared wheels using the principle of the wheel and axle are used to reduce speed1 as in the transmission of an automobile 7see ,fig4 #id71 or the reducing gear of a steam turbine4 7,see ,figs4 #ie and #bic47 ,a bevel gear is frequently used to change the direction of the force4 7,see ,fig4 #id47 ,illustration3 ,,fig4 #if4--;,a single movable pulley4 ,illustration3 ,,fig4 #ig4--;,block and tackle4 ,illustration3 ,,fig4 #ih4--,the fixed pulley considered as a lever4 ,illustration3 ,,fig4 #ii4--,the movable pulley considered as a lever4 #abe4 ,the ,pulley4--,the pulley consists of a wheel turning on an axis in a frame4 ,the wheel is called a sheave and the frame a block4 ,the rim may be smooth or grooved4 ,the grooved rim is used to hold a cord or rope4 ,one use of the pulley is to change the direction of the acting force as in ,fig4 #hd1 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 ,w4 ,these pulleys are fixed and simply change the direction4 ,without considering the loss by friction1 the pull at ,w will equal that at ,f4 ,sometimes1 a pulley is attached to the weight and is lifted with it4 ,it is then called a movable pulley4 ,in ,fig4 #if the movable pulley is at ,p1 a fixed pulley is at ,f4 ,when fixed pulleys are used1 a single cord runs through from the weight to the effort1 so that if a force of #ajj lbs4 is applied by the effort the same force is received at the weight4 ,but with movable pulleys several sections of cord may extend upward from the weight each with the force of the effort upon it4 ,by this arrangement1 a weight several times larger than the effort can be lifted4 ,fig4 #ig represents what is called a block and tackle4 ,if a force of #ej lbs4 is exerted at ,f1 each section of the rope will have the same tension and hence the six sections of the rope will support #cjj lbs4 weight4 ,the mechanical advantage of the pulley or the ratio of the weight to the effort1 therefore1 equals the number of sections of cord supporting the weight4 ,the fixed pulley represents a lever1 see ,fig4 #ih1 where the effort and weight are equal4 ,in the movable pulley1 the fulcrum 7see ,fig4 #ii7 is at ,d2 the weight1 ,w1 is applied at the center of the pulley and the effort at ,f4 ,the weight distance1 ,dw1 is the radius1 and the effort distance1 ,df1 is the diameter of the pulley4 ,since ,w_/,f ,df _/ ,dw #b in a movable pulley1 the weight is twice the effort1 or its mechanical advantage is #b4 ,important ,topics #a4 ,wheel and ,axle1 ,law of ,wheel and ,axle4 #b4 ,pulley1 ,fixed and ,movable1 ,block and ,tackle1 ,law of ,pulley4 ,exercises #a4 ,why do door knobs make it easier to unlatch doors8 ,what simple machine do they represent8 ,explain4 #b4 ,what combination of pulleys will enable a #afj-lb4 man to raise a #ijj-lb4 piano8 #c4 ,when you pull a nail with an ordinary claw hammer1 what is the effort arm8 the resistance arm8 #d4 ,how much work is done by the machine in problem #b in lifting the piano #bj ft48 ,how much work must be done upon the machine to do this work8 #e4 ,the pilot wheel of a boat has a diameter of #fj in42 the diameter of the axle is #f in4 ,if the resistance is #age lbs41 what force must be applied to the wheel8 #f4 ,four men raise an anchor weighing #a #a_/b tons1 with a capstan 7see ,fig4 #aaj7 having a barrel #i in4 in diameter4 ,the circle described by the hand-spikes is #ac #a_/b ft4 in diameter4 ,how much force must each man exert8 ,illustration3 ,,fig4 #ajj4--,the ,capstan4 #g4 ,a bicycle has a #bh-;in4 wheel4 ,the rear sprocket is #c in4 in diameter1,h the radius of the pedal crank is #g in42 #bd lbs4 applied to the pedal gives what force on the rim of the wheel8 ,what will be the speed of the rim when the pedal makes one revolution a second8 ,h ,consider the diameter of the front sprocket as #f inches4 #h4 ,measure the diameters of the large and small pulleys on the sewing-machine at your home4 ,what mechanical advantage in number of revolutions does it give8 ,verify your computation by turning the wheel and counting the revolutions4 #i4 ,what force is required with a single fixed pulley to raise a weight of #bjj lbs48 ,how far will the effort move in raising the weight #aj ft48 ,what is the mechanical advantage8 #aj4 ,in the above problem substitute a single movable pulley for the fixed pulley and answer the same questions4 #aa4 ,what is the smallest number of pulleys required to lift a weight of #fjj lbs4 with a force of #abj lbs48 ,how should they be arranged8 #ab4 ,a derrick in lifting a safe weighing #b tons uses a system of pulleys employing #c sections of rope4 ,what is the force required8 #ac4 ,name three instances where pulleys are used to do work that otherwise would be difficult to do4 #ad4 ,draw a diagram for a set of pulleys by means of which #ajj lbs4 can lift #djj lbs4 7#e7 ,,the ,,inclined ,,plane4 ,,efficiency #abf4 ,efficiency4--,the general law of machines which states that the work done by a machine equals the work put into it requires a modification1 when we apply the law in a practical way1 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 it4 ,hence the statement of the law that accords with actual working conditions runs somewhat as follows3 ,the work put into a machine equals the useful work done by the machine plus the wasted work done by it4 ,the efficiency of a machine is the ratio of the useful work done by it to the total work done on the machine4 ,if there were no friction or wasted work1 the efficiency would be perfect1 or1 as it is usually expressed1 would be #ajj per cent4 ,consider a system of pulleys into which are put #fjj ft4-lbs4 of work4 ,with #dej ft4-lbs4 of useful work resulting1 the efficiency would be #dej #fjj #c_/d1 or #ge per cent4 ,in this case #be per cent4 of the work done on the machine is wasted4 ,in a simple lever the friction is slight so that nearly #ajj per cent4 efficiency is often secured4 ,some forms of the wheel and axle have high efficiencies as in bicycles with gear wheels4 ,other forms in which ropes are employed have more friction4 ,pulleys have sometimes efficiencies as low as #dj per cent4 when heavy ropes are used4 #abg4 ,inclined ,plane4--,we now come to a type of simple machine of lower efficiency than those previously mentioned4 ,these belong to the inclined plane group1 which includes the inclined plane 7see ,fig4 #aja71 the wedge and the screw4 ,they are extensively used1 however1 notwithstanding their low efficiency1 on account of often giving a high mechanical advantage4 ,the relation between these machines may be easily shown1 as the wedge is obviously a double inclined plane4 ,in ,art4 #hb 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 length4 ,illustration3 ,,fig4 #aja4--;,an inclined plane4 ,or while the weight is being lifted the vertical height ,,bc1 the effort has to move the length of the plane ,,ac4 ,since by the law of machines the effort times its distance equals the weight times its distance1 or the weight is to the effort as the effort distance is to the weight distance1 therefore the mechanical advantage of the inclined plane is the ratio of the length to the height of the inclined plane4 ,inclined planes are used to raise heavy objects short distances1 as barrels into a wagon1 and iron safes into a building4 ,stairways are inclined planes with steps cut into them4 #abh4 ,the ,wedge4--,wedges are used to separate objects1 as in splitting wood 7see ,fig4 #ajb71 cutting wood1 and where great force is to be exerted for short distances4 ,an axe is a wedge1 so is a knife4 ,a fork consists of several round wedges set in a handle4 ,the edge of any cutting tool is either an inclined plane or a wedge4 ,our front teeth are wedges4 ,numerous examples of inclined planes may be seen about us4 ,no definite statement as to the mechanical advantage of the wedge can be given as the work done depends largely on friction4 ,the force used is generally applied by blows on the thick end4 ,in general1 the longer the wedge for a given thickness the greater the mechanical advantage4 ,illustration3 ,,fig4 #ajb4--,one use of the wedge4 #abi4 ,the ,screw4--,the screw is a cylinder around whose circumference winds a spiral groove4 7,see ,fig4 #ajc47 ,the raised part between the two adjacent grooves is the thread of the screw4 ,the screw turns in a block called a nut1 within which is a spiral groove and thread exactly corresponding to those of the screw4 ,the distance between two consecutive threads measured parallel to the axis is called the pitch of the screw4 7,see ,fig4 #ajd47 ,if the thread winds around the cylinder ten times in the space of #a in41 the screw is said to have ten threads to the inch1 the pitch being #a_/aj in4 ,the screw usually is turned by a lever or wheel with the effort applied at the end of the lever1 or at the circumference of the wheel4 ,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 7the pitch of the screw74 ,the work done by the effort therefore equals ,f #br1 r being the radius of the wheel1 and the work done on the weight equals ,w s1 s being the pitch of the screw4 ,by the law of machines ,f #br ,w s or ,w _/ ,f 7#br7 _/ s4 ,therefore the mechanical advantage of the screw equals 7#br7 _/ s4 ,since the distance the weight moves is small compared to that the power travels1 there is a great gain in force4 ,the screw is usually employed where great force is to be exerted through small distances as in the vise 7,fig4 #aje7 the jack screw 7,fig4 #ajf71 screw clamps1 to accurately measure small distances as in the micrometer 7,fig4 #ajg7 and spherometer1 and to lessen the motion in speed-reducing devices4 ,the worm gear 7,fig4 #ajh7 is a modification of the screw that is sometimes used where a considerable amount of speed reduction is required4 ,illustration3 ,,fig4 #ajc4--,the screw is a spiral inclined plane4 ,illustration3 ,,fig4 #ajd4--,the pitch is ,s4 ,illustration3 ,,fig4 #aje4--;,a vise4 ,illustration3 ,,fig4 #ajf4--;,a jack screw4 ,illustration3 ,,fig4 #ajg4--;,a micrometer screw4 ,illustration3 ,,fig4 #ajh4--,this large worm-wheel is a part of the hoisting mechanism employed for the lock gates of the ,sault ,ste4 ,marie ,canal4 ,important ,topics #a4 ,efficiency of machines4 #b4 ,the inclined plane1 wedge and screw4 ,applications4 ,exercises #a4 ,a plank #ab ft4 long is used to roll a barrel weighing #bjj lbs4 into a wagon #c ft4 high4 ,find the force required parallel to the incline4 #b4 ,how long a plank will be needed to roll an iron safe weighing #a-a_/b tons into a wagon #c ft4 high using a pull of #fjj lbs4 parallel to the incline4 #c4 ,an effort of #ej lbs4 acting parallel to the plane prevents a #bjj-lb4 barrel from rolling down an inclined plane4 ,what is the ratio of the length to the height of the plane8 #d4 ,a man can push with a force of #aej lbs4 and wishes to raise a box weighing #abjj lbs4 into a cart #c ft4 high4 ,how long a plank must he use8 #e4 ,the radius of the wheel of a letter press is #f in41 the pitch of its screw is #a_/d in4 ,what pressure is produced by a force of #dj lbs48 #f4 ,the pitch of a screw of a vice is #a_/d in41 the handle is #a ft4 long4 what pressure can be expected if the force used is #ajj lbs48 #g4 ,a jackscrew is used to raise a weight of #b tons4 ,the bar of the jackscrew extends #b ft4 from the center of the screw4 ,there are two threads to the inch4 ,find the force required4 7#f7 ,,friction1 ,,its ,,uses ,,and ,,laws #acj4 ,friction4--,although often inconvenient and expensive1 requiring persistent and elaborate efforts to reduce it to a minimum1 friction has its uses1 and advantages4 ,were it not for friction between our shoes and the floor or sidewalk1 we could not keep our footing4 ,friction is the resistance that must be overcome when one body moves over another4 ,it is of two kinds1 sliding and rolling4 ,if one draws a block and then a car of equal weight along a board1 the force employed in each case being measured by a spring balance1 a large difference in the force required will be noticed1 showing how much less rolling friction is than sliding friction4 #aca4 ,ways of ,reducing ,friction4--7a7 ,friction is often caused by the minute projections of one surface sinking into the depressions of the other surface as one moves over the other4 ,it follows1 therefore1 that if these projections could be made as small as possible that friction would be lessened4 ,consequently polishing is one of the best means for reducing friction4 ,in machines all moving surfaces are made as smooth as possible4 ,in different kinds of materials these little ridges and depressions are differently arranged4 7b7 ,in ,fig4 #aji the friction between ,r and ,s would be greater than between ,r and ,t4 ,in ,r and ,s the surfaces will fit closer together than in ,r and ,t4 ,the use of different materials will reduce friction4 ,the iron axles of car wheels revolve in bearings of brass4 ,jewels are used in watches for the same reason4 7c7 ,another very common method of reducing friction is by the use of lubricants4 ,the oil or grease used fills up the irregularities of the bearing surfaces and separates them4 ,rolling friction is frequently substituted for sliding friction by the use of ball and roller bearings4 ,these are used in many machines as in bicycles1 automobiles1 sewing machines1 etc4 7,see ,fig4 #aaj47 ,illustration3 ,,fig4 #aji4--,the friction between ,r and ,s is greater than between ,r and ,t4 #acb4 ,value of ,friction4--,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 lost4 ,friction is therefore the great obstacle to perfect efficiency in machines4 ,friction1 however1 like most afflictions has its uses4 ,we would find it hard to get along without it4 ,without friction we could neither walk nor run2 no machines could be run by belts2 railroad trains1 street cars1 in fact all ordinary means of travel would be impossible1 since these depend upon friction between the moving power and the road for propulsion4 ,illustration3 ,,fig4 #aaj4--,timken roller bearings4 ,as used in the front wheel of an automobile4 #acc4 ,coefficient of ,friction4--,the ratio between the friction when motion is just starting and the force pushing the surfaces together is called the coefficient of friction4 ,if the block in ,fig4 #aaa is drawn along the board with uniform motion1 the reading of the spring balances indicates the amount of friction4 ,suppose the friction is found to be #ejj g41 and the weight of the block to be #bjjj g4 ,then the coefficient of friction for these two substances will be #ejj_/bjjj #a_/d1 or #be per cent4 #acd4 ,laws of ,friction1 ,law ,i4--,the friction when motion is occurring between two surfaces is proportional to the force holding them together4 ,thus if one measures the friction when a brick is drawn along a board1 he will find that it is doubled if a second brick is placed on the first4 ,on brakes greater pressure causes greater friction4 ,if a rope is drawn through the hands more pressure makes more friction4 ,illustration3 ,,fig4 #aaa4--;,a method for testing the friction between surfaces4 ,law ,,ii4--,friction is independent of the extent of surface in contact4 ,thus a brick has the same friction drawn on its side as on its edge1 since1 although the surface is increased1 the weight is unchanged4 ,law ,,iii4--,friction is greatest at starting1 but after starting is practically the same for all speeds4 #ace4 ,fluid ,friction4--,when a solid moves through a fluid1 as when a ship moves through the water or railroad trains through the air1 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 rate4 ,this is the reason why it costs so much to increase the speed of a fast train1 since the resistance of the air becomes the prominent factor at high speeds4 ,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 great4 ,important ,topics #a4 ,friction3 two kinds2 sliding and rolling4 #b4 ,four ways of reducing friction4 #c4 ,uses of friction4 #d4 ,coefficient of friction4 ,three laws of friction4 #e4 ,fluid friction4 ,exercises #a4 ,how long must an inclined plane be which is #aj meters high to enable a car weighing #bjjj kg4 to be pushed up its length by a force of #ajj kg4 parallel to the incline8 #b4 ,state how and where friction is of use in the operation of the inclined plane1 the wedge1 the screw1 the wheel and axle4 #c4 ,a wheelbarrow has handles #f ft4 long4 ,if a load of #cjj lbs4 is placed #ah in4 from the axis of the wheel1 what force placed at the end of the handles will be required to lift it8 #d4 ,a jackscrew has #c threads to the inch1 and the lever used to turn it is #d ft4 long4 ,if the efficiency of the screw is #fj per cent41 what force must be applied to raise a load of #e tons8 #e4 ,in problem #d how far must the force move in raising the weight #c in4 ,compute the work done upon the weight1 the work done by the power and the efficiency of the machine from these two amounts of work4 #f4 ,what simple machines are represented in a jackknife1 a sewing-machine1 a screw-driver1 a plane1 a saw1 a table fork8 #g4 ,a laborer carries #aejj lbs4 of brick to a platform #dj ft4 high4 ,how much useful work does he do8 #h4 ,if he weighs #aej lbs4 and his hod weighs #aj lbs41 how much useless work does he do in taking #cj trips to carry up the bricks of problem #g8 ,what is his efficiency8 #i4 ,if the laborer hoists the brick of problem #g in a bucket weighing #ej lbs41 using a fixed pulley and rope1 what is the useless work done if it takes #ab trips to carry up the brick8 ,what is the efficiency of the device8 #aj4 ,the efficiency of a set of pulleys is #gj per cent4 ,how much force should be applied if acting through #ajj ft4 it is to raise a load of #djj lbs4 #bj ft48 #aa4 ,the spokes of the pilot wheel of a motor-boat are #a ft4 long1 the axle around which the rudder ropes are wound is #c in4 in diameter4 ,what effort must be applied if the tension in the ropes is #ej lbs48 #ab4 ,why are the elevated railway stations frequently placed at the top of an incline1 the tracks sloping gently away in both directions8 #ac4 ,the screw of a press has #d threads to the inch and is worked by a lever of such length that an effort of #be lbs4 produces a force of #b tons4 ,what is the length of the lever8 #ad4 ,it takes a horizontal force of #aj lbs4 to draw a sled weighing #ej lbs4 along a horizontal surface4 ,what is the coefficient of friction8 #ae4 ,the coefficient of rolling friction of a railroad train on a track is #j4jji4 ,what pull would an engine have to exert to haul a train weighing #ajjj tons along a level track8 #af4 ,how heavy a cake of ice can be dragged over a floor by a horizontal force of #bj lbs41 if the coefficient of friction is #j4jf8 #ag4 ,the coefficient of friction of iron on iron is #j4b4 ,what force can a switch engine weighing #bj tons exert before slipping8 #ah4 ,using a system of pulleys with a double movable block a man weighing #bjj lbs4 is just able to lift #fjj lbs4 ,what is the efficiency of the system8 #ai4 ,what is the horse-power of a pump that can pump out a cellar full of water #dj ft4 #bj ft4 by #aj ft4 deep1 in #cj minutes8 #bj4 ,how many tons of coal can a #e horse-power hoisting engine raise in #cj minutes from a barge to the coal pockets1 a height of #ej ft48 7#g7 ,,water ,,power #acf4 ,energy of ,falling ,water4--,the energy of falling and running water has been used from the earliest times for developing power and running machinery4 ,the energy is derived from the action of the moving water in striking and turning some form of water-wheel1 several varieties of which are described below4 ,the ,overshot ,wheel4--,the overshot wheel 7,fig4 #aab7 is turned by the weight of the water in the buckets4 ,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 water4 ,its efficiency is high1 being from #hj to #ij per cent41 the loss being due to friction and spilling of water from the buckets4 ,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 #hj or #ij ft4 ,illustration3 ,,fig4 #aab4--,overshot water wheel4 ,illustration3 ,,fig4 #aac4--,undershot water wheel4 ,illustration3 ,,fig4 #aad4--;,diagram illustrating the principle of the ,pelton wheel4 ,the ,undershot ,wheel4--,the old style undershot wheel 7,fig4 #aac7 is used in level countries1 where there is little fall1 often to raise water for irrigation4 ,its efficiency is very low1 seldom rising more than #be per cent4 ,the principle of the undershot wheel1 however1 is extensively used in the water motor and the ,pelton wheel 7,fig4 #aad74 ,in these the water is delivered from a nozzle in a jet against the lower buckets of the wheel4 ,they have an efficiency of about #hj per cent4 and are much used in cities for running small machines1 washing machines1 pipe organ blowers1 etc41 and in mountainous districts where the head is great4 ,illustration3 ,,fig4 #aae4--;,diagram of a hydro-electric power house showing a vertical turbine ,a with penstock ,b and tail race ,c4 ,illustration3 ,,fig4 #aaf4--,the outer case of a turbine showing the mechanism for controlling the gates4 ,illustration3 ,,fig4 #aag4--;,inner case of a turbine showing the gates and the lower end of the runner within4 ,illustration3 ,,fig4 #aah4--,the runner of a turbine4 ,illustration3 ,,fig4 #aai4--,turbine and generator of the ,tacoma hydro-electric power plant4 #acg4 ,the ,turbine4--,the turbine is now used more than any other form of water-wheel4 ,it was invented in #ahbg by ,de ,fourneyron in ,france4 ,it can be used with a small or large amount of water1 the power depending on the head 7the height of the water1 in the reservoir above the wheel74 ,it is the most efficient type of water-wheel1 efficiencies of #ij per cent4 often being obtained4 ,the wheel is entirely under water 7,fig4 #aae74 ,it is enclosed in an outer case 7,fig4 #aaf7 which is connected with the reservoir by a penstock or pipe and is always kept full of water4 ,the wheel itself is made in two parts1 a rotating part called the runner 7see ,fig4 #aah7 and an inner case 7,fig4 #aag7 with gates that regulate the amount of water entering the wheel4 ,this case has blades curved so that the water can strike the curved blades of the rotating part 7,fig4 #aah7 at the angle that is best adapted to use the energy of the water4 ,the water then drops through the central opening into the tail race below 7see ,fig4 #aae74 ,the energy available is the product of the weight of the water and the head4 ,the turbine is extensively used to furnish power for generating electricity at places where there is a sufficient fall of water4 ,the electrical energy thus developed is transmitted from #ej to #bjj miles to cities where it is used in running street cars1 electric lighting1 etc4 ,turbines can be made to revolve about either vertical or horizontal axes4 ,fig4 #aai represents a horizontal water turbine connected to a dynamo4 ,compare this with the vertical turbine in ,fig4 #aae4 ,exercises #a4 ,does a person do more work when he goes up a flight of stairs in #e seconds than when he goes up in #ae seconds8 ,explain4 #b4 ,a motorcycle has a #d horse-power motor and can go at a rate of #ej miles per hour4 ,why cannot #d horses draw it as fast8 #c4 ,what is the efficiency of a motor that is running fast but doing no useful work8 #d4 ,what horse-power can be had from a waterfall1 #ab ft4 high1 if #bj cu4 ft4 of water pass over it each second8 #e4 ,what is the horse-power of a fire engine if it can throw #fjj gallons of water a minute to a height of #ajj ft48 #f4 ,why are undershot wheels less efficient than the overshot wheel or turbine8 #g4 ,a revolving electric fan is placed on the stern of a boat4 ,does the boat move8 ,why8 ,place the fan under water4 ,does the boat now move8 ,why8 #h4 ,why does an electric fan produce a breeze8 #i4 ,explain the action of the bellows in an organ4 #aj4 ,at ,niagara ,falls the turbines are #acf ft4 below the surface of the river4 ,their average horse-power is #ejjj each4 #dcj cu4 ft4 of water each second pass through each turbine4 ,find the efficiency4 #aa4 ,at ,laxey on the ,isle of ,man is the largest overshot wheel now in use4 ,it has a horse-power of #aej1 a diameter of #gb4e ft41 a width of #aj ft41 and an efficiency of #he per cent4 ,how many cubic feet of water pass over it each second8 #ab4 ,the power plant at the ,pikes ,peak ,hydro-electric ,company utilizes a head of #baej ft41 which is equal to a pressure of #ice lbs4 per square inch1 to run a ,pelton wheel4 ,if the area of the nozzle is #a sq4 in4 and the jet has a velocity of #bb1cjj ft4 per minute1 what is the horse-power developed if the efficiency is #hj per cent48 #ac4 ,a test made in #aiji of the turbines at the ,centerville power house of the ,california ,gas and ,electric ,corporation showed a maximum horse-power of #igjj1 speed #djj r4p4m4 under a head of #eej ft4 ,the efficiency was #hf4be per cent4 ,how many cubic feet of water passed through the turbines each second8 #ad4 ,the turbine in the ,city of ,tacoma ,power ,plant 7see ,fig4 #abj7 uses a head of #dae ft4 #ade cu4 ft4 a second pass through the turbine4 ,calculate the horse-power4 #ae4 ,in problem #ad1 what is the water pressure per square inch at the turbine8 #af4 ,the power plant mentioned in problem #ac develops #fjjj kw4 ,what is the efficiency8 ,review ,outline3 ,work and ,energy ,work2 how measured1 units1 foot-pound1 kilogram meter1 erg4 ,energy2 how measured1 units1 potential1 ,p4,e4 w h1 or f s4 ,kinetic 7wv7_/7#b;g74 ,power2 how measured1 units1 horse power1 watt1 #e forms of energy1 conservation4 ,h4p4 7lbs4 ft47_/7#eej sec474 ,machines2 #f simple forms1 #b groups1 advantages1 uses1 ,law3 ,w ,dw ,f ,df4 ,lever2 moments1 mechanical advantage1 uses and applications4 ,wheel and ,axle and ,pulley2 common applications1 mechanical advantage4 ,inclined ,plane1 ,wedge1 and ,screw2 mechanical advantage and efficiency4 ,friction2 uses1 how reduced1 coefficient of1 laws 7#c74 ,water ,wheels2 types1 efficiency1 uses4 ,,chapter ,,vii ,,heat1 ,,its ,,production ,,and ,,transmission 7#a7 ,,sources ,,and ,,effects ,,of ,,heat #ach4 ,importance of the ,study of ,heat4--,heat is brought to our attention through the sensations of heat and cold4 ,in winter1 we warm our houses and prevent the escape of heat from them as much as possible4 ,in summer we endeavor to keep our living rooms cool and our bodies from being overheated4 ,a clear understanding of the several sources1 effects1 and modes of transferring heat is of importance to everyone living in our complex civilization1 especially when we consider the multitudes of objects that have as their principal use the production1 transfer or utilization of heat4 #aci4 ,principal ,sources of ,heat4--,first and most important is the ,sun1 which is continually sending to us radiant energy in the form of light and heat waves4 ,these warm the earth1 make plants grow1 evaporate water1 besides producing many other important effects4 ,second1 chemical energy is often transformed into heat4 ,one has but to think of the heat produced by burning coal1 wood1 oil1 and gas1 to recognize the importance of this source4 ,chemical energy is also the source of the heat produced within our bodies4 ,the action of quicklime and water upon each other produces much heat4 ,this action is sometimes employed during balloon trips as a means of warming things4 ,third1 ,electrical ,energy4--,in many cities electric cars are heated by the electric current4 ,we have all heard of electric toasters and other devices for heating by electricity4 ,electric light is produced by the heating of some material to incandescence by an electric current4 ,the electric furnace has a wide application in the preparation and refining of metals4 ,illustration3 ,,fig4 #abj4--;,boy-scout method of making fire by friction4 ,fourth1 heat is also produced whenever mechanical energy of motion is overcome1 whether it be by friction1 concussion1 or compression4 ,friction always results in the production of heat1 as when we warm our hands by rubbing them together4 ,when friction is excessive1 such as in the case of a heavy bearing not properly oiled1 the bearing may get very hot4 ,this is the cause of the hot box on a railway car4 ,friction may produce heat enough to set wood on fire4 ,some fires in mills are believed to be due to this cause4 ,every boy scout must learn how to produce fire by friction4 7,see ,fig4 #abj47 ,concussion may be illustrated by the heating of a piece of metal by hammering it1 while the compression of a gas always makes it warmer1 as those who have used a bicycle pump have observed4 ,the production of heat by compressing a gas is illustrated by the fire syringe 7,fig4 #aba74 ,this consists of a glass tube with a tightly fitted piston4 ,a sudden compression of the air contained may ignite a trace of carbon bisulfid vapor4 ,illustration3 ,,fig4 #aba4--;,a fire syringe4 ,the interior of the earth is hot1 but its heat seldom gets to the surface except at hot springs and volcanoes4 #adj4 ,the ,effects of ,heat4--,there are five important changes produced by heat3 7a7 change of size1 7b7 change of temperature1 7c7 change of state1 as the melting of ice or evaporating of water1 7d7 chemical change1 as the charring of sugar when it is overheated1 and 7e7 electrical change4 ,this is illustrated by the production of an electric current1 by the heating of the junction of two different metals4 ,a thermo-electric generator 7see ,fig4 #abb7 has been constructed upon this principle and works successfully4 ,illustration3 ,,fig4 #abb4--;,a thermo-electric generator4 ,important ,topics #a4 ,importance of a study of heat4 #b4 ,four sources of heat4 #c4 ,five effects of heat4 #d4 ,examples of each4 #e4 ,illustrations of transformation of energy which involve heat4 ,exercises #a4 ,write a list of the sources of heat in the order of their importance to you4 ,state why each is important to you4 #b4 ,which three of the effects of heat do you make most use of8 ,explain what use you make of each of these effects4 #c4 ,which of the forms of energy can be transformed into heat8 ,how in each case8 #d4 ,into what other forms of energy may heat be transformed8 ,name the device or process used in each case4 #e4 ,what five different commodities are purchased by people in your neighborhood for the production of heat8 ,which of these costs least for the amount of heat furnished8 ,which is most expensive8 ,how do you determine these answers8 #f4 ,why do many people buy heat in an expensive form1 as in using an electric toaster1 when they can obtain it in a cheaper form by burning gas or coal8 #g4 ,how many of the five effects of heat have you observed outside of school8 7#b7 ,,temperature ,,and ,,expansion #ada4 ,heat and ,temperature4--,we should now clearly distinguish between the terms1 heat and temperature4 ,heat is a form of energy consisting of molecular motion4 ,the temperature of a body is its degree of hotness4 ,the amount of heat present in a body and its temperature are very different things4 ,the temperature refers to the intensity of the heat in the body4 ,a quart of water and a red hot iron ball may contain equal amounts of heat1 although the ball has a much higher temperature than the water4 ,a cup of boiling water will have the same temperature as a tank full of boiling water1 but the tank will contain more heat4 ,every one knows that it will take longer to boil a kettle full of water than a cupful4 ,a hot-water bag1 holding #b quarts of water will give off heat longer than a #a-quart bag1 both being filled with water at the same temperature4 ,to put it in another way1 more work is done in heating a large amount of water1 than a small amount through the same change of temperature4 #adb4 ,units of ,heat and ,temperature4--,there are two common units for measuring heat3 the ,calorie and the ,british thermal unit4 ,the calorie is the amount of heat required to raise the temperature of a gram of water one centigrade degree4 ,the ,british thermal unit is the amount of heat required to raise the temperature of one pound of water one ,fahrenheit degree4 ,one of the units plainly belongs to the metric system1 the other to the ,english4 ,an instrument for measuring temperature is called a thermometer4 ,various scales are placed upon thermometers4 ,the two thermometer scales most commonly used in this country are the ,centigrade and the ,fahrenheit4 ,the ,fahrenheit thermometer scale has the temperature of melting ice marked #cb4 ,the boiling point or steam temperature of pure water under standard conditions of atmospheric pressure is marked #bab and the space between these two fixed points is divided into #ahj parts4 ,the centigrade thermometer scale has the same fixed points marked #j and #ajj and the space between divided into #ajj parts4 7,see ,fig4 #abc47 ,the centigrade scale is the one used by scientists everywhere4 ,illustration3 ,,fig4 #abc4--;,comparison of centigrade and ,fahrenheit scales4 #adc4 ,comparison of ,thermometer ,scales4--,it is often necessary to express in centigrade degrees a temperature for which the ,fahrenheit reading is given or vice versa4 ,since there are #ahj ,fahrenheit degrees between the fixed points and #ajj centigrade degrees1 the ,fahrenheit degrees are smaller than the centigrade1 or #a;,f4 #e_/i;,c4 and #a;,c4 #i_/e;,f4 ,one must also take into account the fact that the melting point of ice on the ,fahrenheit scale is marked #cb4 ,hence the following rule3 ,to change a ,fahrenheit reading to centigrade subtract #cb and take #e_/i of the remainder1 while to change centigrade to ,fahrenheit multiply the centigrade by #i_/e and add #cb to the product4 ,these two rules are expressed by the following formulas4 7,f4 - #cb7e_/i ,c41 #i;,c4_/#e #cb ,f4 ,another method of changing from one thermometric scale to another is as follows3 ,a temperature of -#dj;,f4 is also represented by -#dj;,c41 therefore to change a ,fahrenheit reading into centigrade1 we add #dj to the given reading1 then divide by #a4h after which subtract #dj4 ,to change from a centigrade to ,fahrenheit reading the only difference in this method is to multiply by #a4h or ,c4 7,f4 #dj7_/a4h - #dj and ,f4 #a4h7;,c4 #dj7 - #dj4 ,illustration3 ,,fig4 #abd--;,comparison of absolute1 centigrade and ,fahrenheit scales4 #add4 ,the ,absolute ,scale of ,temperature4--,one often hears the statement as cold as ice4 ,this expresses the incorrect idea that ice cannot become colder than its freezing temperature4 ,the fact is that ice may be cooled below freezing down to the temperature of its surroundings4 ,if a piece of ice is placed where the temperature is below the melting point1 the ice1 like any other solid1 cools to the temperature of the surrounding space4 ,for example1 a piece of ice out of doors is at #aj;,f4 when the air is at this temperature4 ,it follows then1 that when ice has been cooled below the freezing temperature that heat is required to warm the ice up to its melting point2 or in other words that ice at its melting temperature possesses some heat4 ,the temperature at which absolutely no heat exists is called absolute zero4 ,there has been devised an absolute scale of temperature4 ,this scale is based upon the centigrade scale1 i4e41 with #ajj between the two fixed points2 the scale1 however1 extends down1 below the centigrade zero1 #bgc1 to what is called absolute zero4 ,it follows therefore that upon the absolute scale1 the melting point of ice1 and the boiling point of water are #bgc and #cgc respectively4 7,see ,fig4 #abd47 ,the means employed to find the location of absolute zero are of much interest4 ,it has been observed that when heated a gas tends to expand4 ,if a measured volume of air at #j;,c4 is cooled or heated #a;,c41 it changes its volume #a_/bgc1 the pressure remaining the same4 ,if it is cooled #aj it loses #aj_/bgc1 if cooled #ajj it loses #ajj_/bgc and so on4 ,no matter how far it is cooled the same rate of reduction continues as long as it remains in the gaseous state4 ,from these facts it is concluded that if the cooling could be carried down #bgc that the volume would be reduced #bgc_/bgc or that the volume of the gas would be reduced to nothing4 ,this is believed to mean that the molecular motion constituting heat would cease rather than that the matter composing the gas would disappear4 ,scientists have been able to obtain temperatures of extreme cold far down on the absolute scale4 ,liquid air has a temperature of -#bib;,f41 or -#ahj;,c4 or #ic;,a4 ,the lowest temperature thus far reported is #a4g;,a4 or -#bga4c;,c41 obtained in #aiaa1 by evaporating liquid helium4 #ade4 ,the ,law of ,charles4--,the facts given in the last paragraph mean that if #bgc ccm4 of a gas at #j;,c4 or #bgc ,a4 are cooled #ajj1 or to -#ajj;,c41 or #agc;,a41 then it will lose #ajj_/bgc of its volume or have a volume of #agc ccm4 ,if warmed #ajj1 or up to #ajj;,c41 or #cgc;,a41 it will have a volume of #cgc ccm4 ,it follows then that in every case the volume will correspond to its absolute temperature1 providing the pressure remains unchanged4 ,the expression of this fact in scientific language is called the law of ,charles4 ,at a constant pressure the volume of a given mass of gas is proportional to its absolute temperature4 ,expressed mathematically1 we have ,v#a_/,v#b ,t#a_/,t#b4 ,compare the statement and mathematical expression of the laws of ,charles and ,boyle4 ,the formulas for the laws of ,boyle and ,charles are sometimes combined into one expression as follows3 ,,pv_/,t ,p,v_/,t or the product of the volume and pressure of a constant mass of gas is proportional to its absolute temperature4 ,important ,topics #a4 ,heat units2 calorie1 ,british thermal unit4 #b4 ,three thermometer scales1 fixed points on each4 #c4 ,absolute zero1 how determined4 ,its value on each scale4 #d4 ,law of ,charles1 its meaning4 ,combination of laws of ,boyle and ,charles4 ,exercises #a4 ,does ice melt at the same temperature at which water freezes8 ,express the temperature of freezing water on the three thermometer scales4 #b4 ,a comfortable room temperature is #fh;,f4 ,what is this temperature on the centigrade and absolute scales8 #c4 ,change a temperature of #ae;,c4 to ,f42 #ae;,f4 to ,c42 -#d;,c4 to ,f42 -#bj;,f4 to ,c4 #d4 ,the temperature of the human body is #ih4f;,f4 ,what is this temperature on the absolute and centigrade scales8 #e4 ,the temperature of liquid air is -#ahj;,c4 ,what is it on the ,fahrenheit scale8 #f4 ,mercury is a solid at -#dj;,f4 ,what is this on the centigrade scale8 #g4 ,how much heat will be required to raise the temperature of #h lbs4 of water #cb;,f42 #e lbs4 #aj;,f48 ,illustration3 ,,fig4 #abe4--;,a clinical thermometer used to take the temperature of the body4 #h4 ,how much heat will be required to raise the temperature of #cj g4 of water #dc;,c42 #bj g41 #ej;,c48 #i4 ,compute the temperature of absolute zero on the ,fahrenheit scale4 #aj4 ,take three basins of water1 one hot1 one cold1 and one lukewarm4 ,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 water1 this water will feel cool to one hand and warm to the other4 ,explain4 #aa4 ,if #bjj ccm4 of air at #bjj absolute is heated to #cjj;,a4 under constant pressure1 what volume will the air occupy at the latter temperature8 #ab4 ,how does one change a reading on the centigrade scale to a corresponding reading on the absolute scale8 7#c7 ,,expansion ,,of ,,liquids ,,and ,,solids #adf4 ,expansion of ,gases4--,the law of ,charles is found to apply to all gases4 ,that is1 all gases change in volume in proportion to the change of temperature provided the pressure remains constant4 ,it is for this reason that we have the gas thermometer 7see ,fig4 #abf7 which gives in skillful hands more accurate temperature readings than the best mercurial thermometer4 ,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 water4 7,see ,fig4 #a47 ,the water thermometer consists of a glass bulb filled with water which rises into a tube attached to the bulb4 ,one disadvantage of the water thermometer is its limited range since it cannot be used below #j or above #ajj4 ,why8 #adg4 ,expansion of ,liquids4--,the expansion of liquids differs from that of gases in several important respects3 7a7 ,liquids have a smaller rate of expansion than gases4 ,the rate of expansion per degree is called the ,coefficient of ,expansion4 ,for example1 the coefficient of expansion of a gas under constant pressure at #j;,c4 is #a_/bgc of its volume per degree centigrade4 7b7 ,different liquids expand at wholly different rates1 that is1 their coefficients of expansion differ widely4 ,for example1 the coefficient of expansion of mercury is #j4jjjah per degree centigrade1 of glycerine #j4jjje per degree centigrade1 of petroleum #j4jjji per degree centigrade4 ,illustration3 ,,fig4 #abf4--;,gas thermometer4 7c7 ,the same liquid often has different coefficients of expansion at different temperatures4 ,water between #e;,c4 and #f;,c4 has a coefficient expansion of #j4jjjjb per degree centigrade1 between #h and #ej of #j4jjjf1 between #ii and #ajj of #j4jjjgf4 ,the coefficient of expansion of mercury1 however1 is constant for a wide range of temperature and1 therefore1 it is well adapted for use in thermometers4 #adh4 ,peculiarity in the ,expansion of ,water4--,water has a peculiar rate of expansion4 ,this is illustrated by the following experiment3 ,a test-tube filled with cold water is closed by a stopper containing a small glass tube1 the water extending up into the small tube4 7,see ,fig4 #abg47 ,the test-tube is placed in a freezing mixture of salt and ice contained in a tumbler4 ,as the water cools1 the level of the water in the small tube at first sinks4 ,but before the water freezes it rises again1 showing that after the water cools to a certain temperature that expansion of the water occurs with further cooling4 ,careful tests show that the water on cooling contracts until it reaches #d;,c4 ,on cooling below this temperature it expands4 ,for this reason1 when the water of a lake or river freezes1 the coldest water is at the surface4 ,on account of this the ice forms at the top instead of at the bottom4 ,if water contracted as it cooled to the freezing temperature the coldest water would be at the bottom4 ,freezing would begin at the bottom instead of at the surface4 ,lakes and rivers would freeze solid4 ,in the summer only in shallow waters would all the ice melt4 ,the result would be that fish and other aquatic life would be killed4 ,climate would be so changed that the earth might become uninhabitable4 ,since water is densest at #d;,c4 all the water in a lake or river1 when it is covered with ice1 is at #d;,c4 except that near the surface4 ,illustration3 ,,fig4 #abg4--;,apparatus used in testing the expansion of water4 #adi4 ,the ,expansion ,of ,solids4--,most solids when heated expand less than liquids and gases4 ,careful experiments show that expansion is3 7a7 ,proportional to the change in temperature4 7b7 ,different in different solids4 ,here are a few coefficients of linear 7length7 expansion4 ,brass #j4jjjjah per degree ,c4 ,glass #j4jjjjji per degree ,c4 ,ice #j4jjjjeb per degree ,c4 ,iron #j4jjjjab per degree ,c4 ,platinum #j4jjjjji per degree ,c4 ,zinc #j4jjjjbg per degree ,c4 ,the coefficient of linear expansion is the fraction of its length that a body expands when heated one degree4 ,the coefficient of cubical expansion is the fraction of its volume that a body expands when heated one degree4 ,the expansion of solids is used or allowed for in many cases3 a4 ,joints between the rails on a railroad allow for the expansion of the rails in summer4 b4 ,one end of a steel truss bridge is usually supported on rollers so that it can expand and contract with changing temperatures4 7,see ,fig4 #abh47 ,illustration3 ,,fig4 #abh4--,truss bridge showing roller support at one end4 c4 ,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 temperature4 d4 ,iron tires are heated1 slipped on to wagon wheels and then cooled1 the contraction on cooling setting them tightly in place4 e4 ,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 instrument4 7,see ,fig4 #abi47 f4 ,the wires that are fused into glass in incandescent light bulbs must have the same coefficient of expansion as the glass4 ,platinum has therefore been used for this purpose4 7,see table above47 ,illustration3 ,,fig4 #abi4--,metallic thermometer4 ,important ,topics #a4 ,expansion of ,liquids2 peculiarities4 ,anomalous expansion of water and its results4 #b4 ,expansion of solids2 peculiarities1 applications4 #c4 ,coefficient of linear expansion4 #d4 ,coefficient of cubical expansion4 ,exercises #a4 ,the gas within a partly inflated balloon has a volume of #ajjj cu4 ft4 at a pressure of #gd cm41 and a temperature of #ae;,c4 ,what will be the volume of the gas when its pressure is #cg cm4 and the temperature is -#ag;,c48 #b4 ,a man taking a full breath on the top of a mountain fourteen thousand feet high inhales #d liters of air1 the pressure being #dj cm4 ,what volume would this same mass of air have in a place #fjj ft4 above sea-level when the barometer reads #ge cm4 and the temperature is the same as on the mountain top8 #c4 ,if the coefficient of linear expansion of iron is #j4jjjjab per degree ,c41 how much will an iron bridge #ajjj ft4 long change in length in warming from -#bj;,c4 on a winter day to #cj;,c4 upon a summer day4 #d4 ,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 #d;,c48 #e4 ,mention two instances that you have noticed of expansion occurring when a body is heated8 #f4 ,compare the density of air at #cj;,c4 with that at #aj;,c4 at the same pressure4 ,if both are present in a room1 where will each be found8 ,why8 #g4 ,compare the density of water at #dj;,c4 with that at #aj;,c4 ,if water at the two temperatures are in a tank1 where will each be found8 ,why8 #h4 ,if water at #j;,c4 and at #d;,c4 are both in a tank1 where will each be found8 ,why8 #i4 ,how much heat will be required to raise the temperature of a cubic foot of water #aj;,f48 #aj4 ,how much heat will be required to raise the temperature of #d liters of water #be;,c48 #aa4 ,how much longer would the cables of the ,brooklyn suspension bridge be on a summer's day when the temperature is #cj;,c4 than in winter at -#bj;,c41 the length of cable between the supports being about #afjj ft4 #ab4 ,if #be liters of air at -#bc;,c4 is warmed to #gg;,c4 under constant pressure1 what will be the resulting volume of air8 ,explain4 #ac4 ,white pig iron melts at about #bjjj;,f4 ,express this temperature upon the centigrade and absolute scales4 #ad4 ,if #bjj ccm4 of air at #gf cm4 pressure and #bg;,c4 temperature be heated to #abg;,c4 at a pressure of #ch cm4 what will be the resulting volume8 #ae4 ,a balloon contains #aj1jjj cu4 ft4 of gas at #ge4b cm4 pressure and #bd;,c4 ,it ascends until the pressure is #ah cm4 and the temperature is -#aj;,c4 ,what is the volume of gas it then contains4 #af4 ,a gas holder contains #ej cu4 ft4 of gas at a pressure of one atmosphere and #fb;,f4 ,how much gas will it hold at #aj atmospheres and #cb;,f4 #ag4 ,one thousand cubic feet of illuminating gas has what volume with #ge lbs4 pressure and temperature of #aj;,c4 #ah4 ,define a cubic foot of illuminating gas4 #aej4 ,methods of ,transmitting ,heat4--,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 heat4 ,it should be definitely understood at the beginning that cold signifies the absence of heat1 just as darkness implies the absence of light1 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 heat4 ,there are three distinct methods by which heat energy is transferred from one place to another1 depending upon the medium or substance that transfers the heat4 a4 ,a solid transmits heat by the method called conduction4 b4 ,a fluid1 either a liquid or a gas1 transmits heat mainly by the method called convection4 c4 ,space transmits the energy of hot objects by the method called radiation4 ,illustration3 ,,fig4 #acj4--,solids conduct heat4 #aea4 ,conduction4--,to illustrate conduction1 place in a gas flame the ends of same metal wires supported as in ,fig4 #acj4 ,in a short time the other ends of the wires become hot enough to burn one's hand4 ,this may be explained as follows3 ,the hot gas flame contains molecules in violent vibration and those striking the wire set its molecules rapidly vibrating4 ,since1 in a solid1 the molecules are held in the same relative positions1 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 hot4 ,it is a fortunate circumstance that different substances have different rates of conductivity for heat4 ,to realize this1 suppose that our clothing were as good a conductor as iron1 clothing would then be very uncomfortable both in hot and in cold weather4 ,the best conductors for heat are metals4 ,it is interesting to note that1 as a rule good conductors of heat are also good conductors of electricity1 while poor conductors of heat are also poor electric conductors4 ,careful experiments in testing the rate that heat will be conducted through different substances show the following rates of conductivity4 ,illustration3 ,,fig4 #aca4--,water is a poor conductor of heat4 ,these figures are averages taken mainly from the ,smithsonian ,physical ,tables3 ,silver #ajj ,copper #gd ,aluminum #ce ,brass #bg ,zinc #bf ,iron #ae ,tin #ad4g ,german silver #h4d ,mercury #a4g ,granite #j4ec ,limestone #j4eb ,ice #j4e ,glass #j4b ,water #j4abd ,pine1 with grain #j4jc ,pine1 across grain #j4ja ,felt #j4jjh ,air #j4jje ,to test the conductivity of liquids1 take a test-tube nearly full of cold water1 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 boils4 ,the lower end will be found to remain cold4 7,see ,fig4 #aca47 ,careful measurements of the conductivity of water show that heat is transmitted through it only #a_/hjj as rapidly as in silver1 while air conducts but #a_/be as rapidly as water4 ,illustration3 ,,fig4 #acb4--,wall construction of a refrigerator4 #a1 ,porcelain enamel lining lock joint2 #b1 inside wood lining2 #c1 #c-ply red rope waterproof paper2 #d1 wool felt deafening paper2 #e1 flaxlinum insulation2 #f1 dead air space2 #g1 flaxlinum insulation2 #h1 wool felt deafening paper2 #i1 #c-ply red rope waterproof paper2 #aj1 outside wood case4 ,illustration3 ,,fig4 #acc4--,sectional view of a ,thermos bottle4 #aeb4 ,non-conductors and ,their ,uses4--,many solids1 however1 are poor conductors1 as leather1 fur1 felt1 and woolen cloth4 ,these substances owe their non-conductivity mainly to the fact that they are porous4 ,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 solids4 ,for the same reason loosely packed snow is a protection to vegetation covered by it during a period of severe cold in winter4 ,the efficiency of storm sash or double windows1 and of the double and triple walls of ice-houses and refrigerators 7see ,fig4 #acb7 in preventing the conduction of heat is also largely due to the poor conductivity of the air confined in the spaces between the walls4 ,to prevent the circulation of the air1 sawdust1 charcoal1 and other porous material is often loosely packed into the space between the walls of such structure4 ,other illustrations of effective non-conductors will occur to every one2 such as woolen clothing1 wooden handles for hot objects1 and the packing used in fireless cookers4 ,a ,thermos bottle is effective as a non-conductor of heat because the space between the double walls has the air exhausted from it 7,figs4 #acc and #acd74 ,of several objects in a cold room1 some feel much colder to the touch than others1 thus iron1 marble1 oil cloth1 and earthenware will feel colder than woolen cloth1 carpet1 feathers1 or paper4 ,the first four objects feel cold because they are conductors1 and conduct the heat away from the hand rapidly4 ,the other substances named are non-conductors and hence remove heat from the hand less rapidly1 and therefore do not feel so cold4 ,in a similar way1 if several hot objects are touched by the hand1 the good conductors are the ones which will burn one most quickly by conducting heat rapidly to the hand4 ,the non-conductors1 however1 will rarely burn one4 ,why are the handles of hot utensils often made of non-conducting materials such as wood1 cloth1 asbestos1 etc48 ,illustration3 ,,fig4 #acd4--;,cross-section of the vacuum flask in a ,thermos bottle4 #aec4 ,radiation is the method by which heat comes to us from the sun across space containing no tangible matter4 ,it is also the method by which heat gets to us when we stand near a fire4 ,everyone has noticed that this heat is cut off by holding an object between the person and the fire4 ,this fact indicates that radiant heat travels in straight lines4 ,the radiation of heat is believed to be accomplished by means of waves in a medium called ether1 which is invisible and yet pervades everything4 ,three of the most important characteristics of radiation are first1 heat is transferred by radiation with the speed of light1 or #ahf1jjj miles per second4 ,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 sun4 ,second1 radiant heat,i travels in straight lines1 while other modes of transferring heat may follow irregular paths4 ,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 sheltered4 ,third1 radiant heat may pass through an object without heating it4 ,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 it4 ,i ,radiant heat is really radiant energy and becomes heat when it is absorbed by a body4 ,when radiant energy falls upon any object it may be 7a7 reflected at the surface of the object1 7b7 transmitted through the substance1 7c71 absorbed4 ,all three of these effects occur in different degrees with different portions of the radiation4 ,well-polished surfaces are good reflectors4 ,rough and blackened surfaces are good absorbers4 ,transparent objects are those which transmit light well1 but even they absorb some of the energy4 #aed4 ,the ,radiometer4--,radiant heat may be detected by means of the radiometer 7,fig4 #ace74 ,this consists of a glass bulb from which the air has been nearly exhausted4 ,within it is a wheel with four vanes of mica or of aluminum mounted on a vertical axis4 ,one side of each vane is covered with lampblack1 the other being highly polished4 when exposed to radiant heat from any source the vanes revolve with the bright side in advance4 ,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 molecule4 ,the blackened sides absorb more heat than the highly polished sides4 ,the air molecules striking these blackened sides receive more heat and so rebound with greater velocity than from the other side1 thus exerting greater pressure4 ,the blackened sides therefore are driven backward4 ,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 motion4 ,illustration3 ,,fig4 #ace4--;,a radiometer4 ,sun's ,radiation4--,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 ,mt4 ,wilson in #aiac4 ,the average of #fij observations gave a value of #a4icc calories per minute4 ,these results indicate that the sun's radiation per square centimeter is sufficient to warm #a g4 of water #a4icc;,c4 each minute4 ,although the nature of radiation is not discussed until ,art4 #djh-daa in light1 it should be said here that all bodies are radiating heat waves at all temperatures1 the heat waves from cool bodies being much longer than those from hot bodies4 ,glass allows the short luminous waves to pass through freely but the longer heat waves from objects at the room temperature pass through with difficulty4 ,this is the reason why glass is used in the covering of greenhouses and hot beds4 ,water also absorbs many of the longer heat waves4 ,it is therefore used in stereopticons to prevent delicate lantern slides from being injured by overheating4 ,important ,topics #a4 ,conduction in solids1 liquids1 gases4 #b4 ,non-conductors2 uses1 best non-conductors4 #c4 ,radiation1 three characteristics4 #d4 ,the sun's radiation1 amount4 ,the radiometer4 ,exercises #a4 ,does clothing ever afford us heat in winter8 ,how then does it keep us warm8 #b4 ,why are plants often covered with paper on a night when frost is expected8 #c4 ,will frost form in the fall of the year sooner on a wooden or a cement sidewalk8 ,why8 ,on which does ice remain longer8 ,why8 #d4 ,why in freezing ice-cream do we put the ice in a wooden pail and the cream in a tin one8 #e4 ,is iron better than brick or porcelain as a material for stoves8 ,explain4 #f4 ,which is better1 a good or a poor conductor for keeping a body warm8 for keeping a body cool8 #g4 ,should the bottom of a teakettle be polished8 ,explain4 #h4 ,how are safes made fireproof8 #i4 ,explain the principle of the ,thermos bottle4 #aj4 ,explain why the coiled wire handles of some objects as stove-lid lifters1 oven doors1 etc41 do not get hot4 7#e7 ,,transmission ,,of ,,heat ,,in ,,fluids4 ,,heating ,,and ,,ventilation #aee4 ,convection4--,while fluids are poor conductors1 they may transmit heat more effectively than solids by the mode called convection4 ,to illustrate3 if heat is applied at the top of a test-tube of water1 the hot water being lighter is found at the top1 while at the bottom the water remains cold4 ,on the other hand1 if heat is applied at the bottom of the vessel1 as soon as the water at the bottom is warmed 7above #d;,c47 it expands1 becomes lighter and is pushed up to the top by the colder1 denser water about it4 ,this circulation of water continues as long as heat is applied below1 until all of the water is brought to the boiling temperature4 7,see ,fig4 #acf47 ,when a liquid or a gas is heated in the manner just described1 the heat is said to be transferred by convection4 ,thus the air in the lower part of a room may receive heat by conduction from a stove or radiator4 ,as it expands on being warmed1 it is pushed up by the colder denser air about it1 which takes its place1 thus creating a circulation of the air in the room4 7,see ,fig4 #acg47 ,the heated currents of air give up their heat to the objects in the room as the circulation continues4 ,these air currents may be observed readily by using the smoke from burning touch paper 7unglazed paper that has been dipped into a solution of potassium nitrate saltpeter and dried74 ,illustration3 ,,fig4 #acf4--;,convection in a liquid4 #aef4 ,draft of a ,chimney4--,when a fire is started in a stove or a furnace the air above the fire becomes heated1 expands1 and therefore is less dense than it was before4 ,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 outside4 ,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 air4 ,the chimney soon becomes filled with these heated gases4 7,see ,fig4 #ach47 ,these are pushed upward by the pressure of the colder1 denser air1 because this colder air is pulled downward more strongly by the force of gravity than are the heated gases in the chimney4 ,other things being equal1 the taller the chimney1 the greater the draft1 because there is a greater difference between the weight of the gases inside and the weight of an equal volume of outside air4 ,illustration3 ,,fig4 #acg4--;,convection currents in a room4 ,illustration3 ,,fig4 #ach4--;,fire place showing draft of a chimney4 #aeg4 ,convection ,currents in ,nature4--,winds are produced by differences in the pressure or density of the air1 the movement being from places of high toward places of low pressure4 ,one of the causes of a difference in density of the air is a difference in temperature4 ,this is illustrated by what are called the land and sea breezes along the sea shore or large lakes4 ,during the day1 the temperature of the land becomes higher than that of the sea4 ,the air over the land expands and being lighter is moved back and upward by the colder1 denser air from the sea or lake4 ,this constitutes the sea breezes 7,fig4 #aci74 ,at night the land becomes cooler much sooner than the sea and the current is reversed causing the land breeze4 7,see ,fig4 #adj47 ,illustration3 ,,fig4 #aci4--,sea breeze4 ,illustration3 ,,fig4 #adj4--,land breeze4 ,the trade winds are convection currents moving toward the hot equatorial belt from both the north and the south4 ,in the hot belt the air rises and the upper air flows back to the north and the south4 ,this region of ascending currents of air is a region of heavy rainfall1 since the saturated air rises to cool altitudes where its moisture is condensed4 ,the ocean currents are also convection currents4 ,their motion is due to prevailing winds1 differences in density due to evaporation and freezing1 and to the rotation of the earth1 as well as to changes in temperature4 #aeh4 ,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 zone4 ,not only should the air in living rooms be comfortably heated1 but it should be continually changed especially in the crowded rooms of public buildings1 as those of schools1 churches1 and assembly halls1 so that each person may be supplied with #cj or more cubic feet of fresh air per minute4 ,in the colonial days1 the open fire place afforded the ordinary means for heating rooms4 ,this heated the room mainly by radiation4 ,it was wasteful as most of the heat passed up the chimney4 ,this mode of heating secured ample ventilation4 ,fire places are sometimes built in modern homes as an aid to ventilation4 ,benjamin ,franklin seeing the waste of heat in the open fire places devised an iron box to contain the fire4 ,this was placed in the room and provided heat by conduction1 convection1 and radiation4 ,it was called ,franklin's stove and in many forms is still commonly used4 ,it saves a large part of the heat produced by burning the fuel and some ventilation is provided by its draft4 ,illustration3 ,,fig4 #ada4--;,heating and ventilating by means of a hot-air furnace4 #aei4 ,heating by ,hot ,air4--,the presence of stoves in living rooms of homes is accompanied by the annoyance of scattered fuel1 dust1 ashes1 smoke1 etc4 ,one attempt to remove this inconvenience led to placing a large stove or fire box in the basement or cellar1 surrounding this with a jacket to provide a space for heating air which is then conducted by pipes to the rooms above4 ,this device is called the hot-air furnace4 7,see ,fig4 #ada47 ,the heated air rises because it is pushed up by colder1 denser air which enters through the cold-air pipes4 ,the hot-air furnace provides a good circulation of warm air and also ventilation1 provided some cold air is admitted to the furnace from the outside4 ,one objection to its use is that it may not heat a building evenly1 one part being very hot while another may be cool4 ,to provide even and sufficient heat throughout a large building1 use is made of hot water or steam heating4 ,illustration3 ,,fig4 #adb4--;,a hot-water system of heating4 ,illustration3 ,,fig4 #adc4--,one-pipe system of steam heating4 #afj4 ,hot-water ,heating4--,in hot-water heating a furnace arranged for heating water is placed in the basement4 7,see ,fig4 #adb47 ,attached to the top of the heater are pipes leading to the radiators in the various rooms2 other pipes connect the radiators to the bottom of the boiler4 ,the heater1 pipes1 and radiators are all filled with water before the fire is started4 ,when the water is warmed1 it expands and is pushed up through the pipes by the colder water in the return pipe4 ,the circulation continuing brings hot water to the radiator while the cooled water returns to the heater1 the hot radiators heating the several rooms4 #afa4 ,steam ,heating4--,in steam heating a steam boiler is connected to radiators by pipes4 7,see ,fig4 #adc47 ,the steam drives the air out of the pipes and radiators and serves as an efficient source of heat4 ,heating by steam is quicker than heating with hot water4 ,it is therefore preferred where quick1 efficient heating is required4 ,hot water is less intense and more economical in mild weather and is often used in private homes4 ,illustration3 ,,fig4 #add4--;,heating by an indirect radiator with side-wall register4 #afb4 ,direct and ,indirect ,heating4--,in heating by direct radiation 7,figs4 #adb1 #adc71 the steam or hot-water radiators are placed in the rooms to be heated4 ,with direct radiation1 ventilation must be provided by special means1 such as opening windows1 doors1 and ventilators4 ,sometimes radiators are placed in a box or room in the basement4 ,air from out of doors is then driven by a fan over and about the hot radiators4 ,the air thus heated is conducted by pipes to the several rooms4 ,this arrangement is called indirect heating4 7,see ,fig4 #add47 ,the latter method1 it may be observed1 provides both heat and ventilation1 and hence is often used in schools1 churches1 court houses1 and stores4 ,since heated air1 especially in cold weather1 has a low relative humidity some means of moistening the air of living rooms should be provided4 ,air when too dry is injurious to the health and also to furniture and wood work4 ,the excessive drying of wood and glue in a piece of furniture often causes it to fall apart4 ,illustration3 ,,fig4 #ade4--;,an automatic air valve4 ,illustration3 ,,fig4 #adf4--;,an automatic vacuum valve4 #afc4 ,vacuum ,steam ,heating4--,in steam heating1 air valves 7,fig4 #ade7 are placed on the radiators to allow the air they contain to escape when the steam is turned on4 ,when all the air is driven out the valve closes4 ,automatic vacuum valves 7,fig4 #adf7 are sometimes used4 ,when the fire is low and there is no steam pressure in the radiators the pressure of the air closes the valve1 making a partial vacuum inside4 ,the boiling point of water falls as the pressure upon it is reduced4 ,as water will not boil under ordinary atmospheric pressure until its temperature is #ajj;,c4 7#bab;,f471 it follows that by the use of vacuum systems1 often called vapor systems1 of steam heating1 water will be giving off hot vapor even after the fire has been banked for hours4 ,this results in a considerable saving of fuel4 ,illustration3 ,,fig4 #adg4--,plenum hot-blast system with temperature regulation4 #afd4 ,the ,plenum ,system of ,heating4--,in the plenum system of heating 7see ,fig4 #adg7 fresh air is drawn through a window from outdoors and goes first through tempering coils where the temperature is raised to about #gj4 ,the fan then forces some of the air through heating coils1 where it is reheated and raised to a much higher temperature1 depending upon the weather conditions4 ,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 heated4 ,the foul air is forced out of the room through vent ducts which lead to the attic where it escapes through ventilators in the roof4 ,illustration3 ,,fig4 #adh4--;,a thermostat4 7,johnson ,system47 ,a thermostat is placed in the tempered-air part of the plenum room to maintain the proper temperature of the tempered air4 ,this thermostat operates the by-pass damper under the tempering coils1 and sometimes the valves on the coils4 ,the mixing dampers at the base of the galvanized-iron ducts are controlled by their respective room thermostats4 ,attic-vent1 fresh-air1 and return-air dampers are under pneumatic switch control4 ,a humidifier can be provided readily for this system4 ,this system of heating is designed particularly for school houses where adequate ventilation is a necessity4 #afe4 ,the ,thermostat4--,one of the many examples of the expansion of metals is shown in one form of the thermostat 7,fig4 #adh7 in which two pieces of different metals and of unequal rates of expansion1 as brass and iron1 are securely fastened together4 ,the thermostatic strip ,t moving inward and outward1 as affected by the room temperature1 varies the amount of air which can escape through the small port ,c4 ,when the port ,c is completely closed 7,fig4 #adh;a7 the full air pressure collects on the diaphragm ,b which forces down the main valve1 letting the compressed air from the main pass through the chamber ,d into chamber ,e as the valve is forced off its seat4 ,the air from chamber ,e then passes into the branch to operate the damper4 ,when port ,c is fully open 7,fig4 #adh;b7 the air pressure on diaphragm ,b is relieved1 the back pressure in ,e lifts up the diaphragm and the air from the branch escapes out through the hollow stem of the main valve1 operating the damper in the opposite direction from that when ,c is closed4 ,important ,topics #a4 ,transmission of heat in fluids4 #b4 ,convection4 ,drafts of a chimney4 ,land and sea breezes4 #c4 ,heating and ventilation of buildings4 7a7 ,by hot air4 7b7 ,hot-water heating4 7c7 ,steam heating4 7d7 ,direct and indirect heating4 7e7 ,vacuum steam heating4 7f7 ,the plenum system4 7g7 ,the thermostat4 ,exercises #a4 ,is a room heated mainly by conduction1 convection1 or radiation1 from 7a7 a stove1 7b7 a hot-air furnace1 7c7 a steam radiator8 #b4 ,name three natural convection currents4 #c4 ,explain the draft of a chimney4 ,what is it8 ,why does it occur8 #d4 ,make a cross-section sketch of your living room and indicate the convection currents by which the room is heated4 ,explain the heating of the room4 #e4 ,make a sketch showing how the water in the hot-water tank in the kitchen or laundry is heated4 ,explain your sketch1 indicating convection currents4 #f4 ,is it economical to keep stoves and radiators highly polished8 ,explain4 #g4 ,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 door8 ,explain4 #h4 ,if a hot-water heating system contains #ajj cu4 ft4 of water how much heat will be required to raise its temperature #aej;,f48 #i4 ,why does a tall chimney give a better draft than a short one8 #aj4 ,explain how your school room is heated and ventilated4 #aa4 ,should a steam or hot-water radiator be placed near the floor or near the ceiling of a room8 ,why8 #ab4 ,in a hot-water heating system an open tank connected with the pipes is placed in the attic or above the highest radiator4 ,explain its use4 7#f7 ,,the ,,moisture ,,in ,,the ,,atmosphere1 ,,hygrometry #aff4 ,water ,vapor in the ,air4--,the amount of water vapor present in the air has a marked effect upon the weather and the climate of a locality4 ,the study of the moisture conditions of the atmosphere1 or hygrometry1 is therefore a matter of general interest and importance4 ,the water vapor in the atmosphere is entirely due to evaporation from bodies of water1 or snow1 or ice4 ,in the discussion of evaporation1 it is described as due to the gradual escape of molecules into the air from the surface of a liquid4 ,this description fits exactly the conditions found by all careful observers4 ,since the air molecules are continually striking the surface of the liquid1 many of them penetrate it and become absorbed4 ,in the same manner many vapor molecules reenter the liquid1 and if enough vapor molecules are present in the air so that as many vapor molecules reenter the liquid each second as leave it1 the space above the liquid is said to be saturated as previously described4 7,see ,art4 #ah47 #afg4 ,conditions for ,saturation4--,if a liquid is evaporating into a vacuum1 the molecules on leaving find no opposition until they reach the limits of the vessel containing the vacuum4 ,evaporation under these conditions goes on with great rapidity and the space becomes saturated almost instantly4 ,if1 however1 air be present at ordinary pressure1 many of the ordinary water vapor molecules on leaving are struck and returned to the water by the air molecules directly above4 ,those escaping gradually work their way upward through the air4 ,this explains why it is that our atmosphere is not often saturated even near large bodies of water1 the retarding effect of the air upon the evaporation preventing more than the layers of air near the water surface becoming saturated4 ,just as the amount of salt that can be held in solution in a liquid is lessened by cooling the solution 7,art4 #bf71 so the amount of water vapor that can be held in the air is lessened by lowering its temperature4 ,if air not moist enough to be saturated with water vapor is cooled1 it will1 as the cooling continues1 finally reach a temperature at which it will be saturated or will contain all the water vapor it can hold at this temperature4 ,if the air be still further cooled some of the water vapor will condense and may form fog1 dew1 rain1 snow1 etc41 the form it takes depending upon where and how the cooling takes place4 #afh4 ,the ,formation of ,dew4--,if the cooling of the atmosphere is at the surface of some cold object which lowers the temperature of the air below its saturation point1 some of its moisture condenses and collects upon the cold surface as dew4 ,this may be noticed upon the surface of a pitcher of ice-water in summer4 ,at night1 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 objects4 ,if the temperature falls below the saturation point1 dew will be formed4 ,this natural radiation is hindered when it is cloudy1 therefore little dew forms on cloudy nights4 ,clear nights help radiation1 therefore we have the most dew on nights when the sky is clear4 ,if the temperature is below freezing1 frost forms instead of dew4 #afi4 ,formation of ,fog4--,if the cooling at night is great enough to cool the body of air near the earth below the saturation temperature1 then not only may dew be formed1 but some moisture is condensed in the air itself1 usually upon fine dust particles suspended in it4 ,this constitutes a fog4 ,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 region1 e4g41 moves over the top of a cold mountain1 or into the upper air1 then as this air is cooled below its saturation point1 condensation upon fine suspended dust particles takes place1 and a cloud is formed4 ,if much moisture is present in the cloud1 the drops of water grow in size until they begin to fall and rain results2 or if it is cold enough1 instead of rain1 snowflakes will be formed and fall4 ,sometimes whirling winds in severe thunderstorms carry the raindrops into colder and then warmer regions1 alternately freezing and moistening the drops or bits of ice4 ,it is in this way that hail is said to be formed4 #agj4 ,the ,dew ,point4--,the temperature to which air must be cooled to saturate it or the temperature at which condensation begins is called the dew point4 ,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 surface4 ,the temperature of the surface when the moisture first forms is the dew point4 #aga4 ,the ,humidity of the ,atmosphere4--,after the dew point has been obtained1 one may compute the relative humidity or degree of saturation of the atmosphere1 from the table given below4 ,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 temperature4 ,for example1 if the dew point is #e;,c4 and the temperature of the air is #bb;,c41 we find the densities of the water vapor at the two temperatures1 and find their ratio3 #f4h_/ai4c #ce per cent4 nearly4 ,determinations of humidity may give indication of rain or frost and are regularly made at weather bureau stations4 ,they are also made in buildings such as greenhouses1 hospitals1 and schoolhouses to see if the air is moist enough4 ,for the most healthful conditions the relative humidity should be from #dj per cent4 to #ej per cent4 ,,weight ,,of ,,water 7w7 ,,in ,,grams ,,contained ,,in #a ,,cubic ,,meter ,,of ,,saturated ,,air ,,at ,,various ,,temperatures 7t7,c4 -------------- t,c4 w -------------- -#aj #b4a - #i #b4d - #h #b4g - #g #c4j - #f #c4b - #e #c4e - #d #c4h - #c #d4a - #b #d4d - #a #d4f #j #d4i #a #e4b #b #e4f #c #f4j #d #f4d #e #f4h #f #g4c #g #g4g #h #h4a #i #h4h #aj #i4d #aa #aj4j #ab #aj4f #ac #aa4c #ad #ab4j #ae #ab4h #af #ac4f #ag #ad4e #ah #ae4a #ai #af4b #bj #ag4b #ba #ah4b #bb #ai4c #bc #bj4d #bd #ba4e #be #bb4i #bf #bd4b #bg #be4f #bh #bg4j #bi #bh4f #cj #cj4a -------------- #agb4 ,wet and ,dry ,bulb ,hygrometer4--,a device for indicating the relative humidity of the air is called an hygrometer4 ,there are various forms4 ,the wet and dry bulb hygrometer is shown in ,fig4 #adi4 ,this device consists of two thermometers1 one with its bulb dry and exposed to the air1 the other bulb being kept continually moist by a wick dipping into a vessel of water4 ,an application of the principle of cooling by evaporation is made in this instrument4 ,unless the air is saturated so that evaporation is prevented1 the wet-bulb thermometer shows a lower temperature1 the difference depending upon the amount of moisture in the air1 or upon the relative humidity4 ,most determinations of relative humidity are made with this kind of instrument4 ,it is necessary in order to make an accurate determination1 to fan or set the air in motion about the thermometers for some time before reading them4 ,the relative humidity is then found by using tables giving the relative humidity that corresponds to any reading of the thermometers4 ,illustration3 ,,fig4 #adi4--,wet and dry bulb hygrometer4 ,illustration3 ,,fig4 #aej4--;,a dial hygrometer4 ,a form of hygrometer in common use is shown in ,fig4 #aej4 ,in this device1 a thin strip of hygroscopic material 7as a piece of goose quill7 is formed into a spiral coil4 ,one end of this is fastened to a post4 ,the other end carried a hand or pointer4 ,the latter moves over a printed scale and indicates directly the relative humidity4 ,its indications should be tested by comparing its readings with the results of dew-point determinations4 ,the position of the pointer may be adjusted by turning the post4 ,important ,topics #a4 ,water vapor in the air4 ,cause and effect4 #b4 ,formation of dew1 fog1 rain1 and snow4 #c4 ,dew point1 relative humidity4 #d4 ,use of the dry- and wet-bulb hygrometer4 ,goose-quill hygrometer4 ,exercises #a4 ,how is the relative humidity of the air affected by warming it8 ,explain4 #b4 ,how does the white cloud of steam seen about a locomotive in cold weather differ from fog8 ,explain4 #c4 ,in cold weather is the relative humidity of air out of doors and indoors the same8 ,explain4 #d4 ,compare the relative humidity of air in a desert and near the ocean4 #e4 ,look up the derivation of the term hygrometer4 ,give the use of the instrument4 #f4 ,find the relative humidity of air at #bj;,c4 if its dew point is at #aj;,c4 #g4 ,how may the relative humidity of the air in a home be increased8 #h4 ,what is the effect of high humidity in the summer upon human beings8 ,how do you explain this8 #i4 ,does dew fall8 ,explain how dew is formed8 #aj4 ,in what respects is a cloud similar to a fog8 ,in what respects different8 #aa4 ,why are icebergs frequently enveloped in fog8 #ab4 ,does dew form in the day time8 ,explain4 7#g7 ,,evaporation #agc4 ,effects of ,evaporation4--,in ,art4 #ai the cooling effect of evaporation is mentioned and some explanation is made of the cooling effect observed4 ,since evaporation is employed in so many ways1 and since its action is simply explained by the study we have made of molecular motions and molecular forces1 it may be well to consider this subject further4 ,take three shallow dishes1 and place in one a little water1 in another some alcohol1 and some ether in the third1 the liquids being taken from bottles that have stood several hours in the room so that all are at the same temperature4 ,after a short time take the temperature of the three liquids4 ,each will be at a lower temperature than at first1 but of the three the ether will be found to be the coolest1 alcohol next1 and the water nearest its first temperature4 ,it will be noticed also that the ether has evaporated most in the same time4 ,similar effects may be observed by placing a few drops of each of these three liquids upon the back of one's hand1 or by placing a few drops in turn upon the bulb of a simple air thermometer4 #agd4 ,cooling ,effect of ,evaporation4--,the molecules that leave an evaporating liquid are naturally the swiftest moving ones1 that is1 the ones having the highest temperature1 so their escape leaves the liquids cooler than before1 and the one whose molecules leave fastest is naturally the one that becomes coldest1 that is1 the ether1 in the experiment of ,art4 #agc4 ,if no air pressure were exerted upon the surface of the liquid1 the escape of the molecules would be much increased and the temperature of the liquid would be lowered rapidly4 ,to test this1 fill a thin watch glass with ether and place it over a thin slip of glass with a drop of cold water between the two4 ,now place this apparatus under the receiver of an air pump and exhaust the air4 ,the rapid evaporation of the ether so lowers its temperature1 that often the drop of water is frozen4 ,the lowest temperatures are obtained by evaporating liquids at reduced pressure4 ,onnes by evaporating liquid helium at a pressure of about #a4b mm4 reached the lowest temperature yet attained1 -#def;,f41 or -#bga4c;,c4 ,if four thermometers are taken1 the bulbs of three being wetted respectively with ether1 alcohol1 and water the fourth being dry1 on vigorously fanning these1 the moistened thermometers show that they have been cooled while the dry one is unaffected4 ,this indicates that fanning a dry body at the temperature of the air does not change its temperature4 ,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 liquid4 ,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 place4 ,application of this is made at salt works where the brine is spread out in shallow pans4 #age4 ,rate of ,evaporation4--,the rate of evaporation is affected by several factors4 ,these have been illustrated in the preceding paragraphs4 ,to briefly summarize3 ,the rate of evaporation of a liquid is affected by-- 7a7 ,the nature of the liquid4 7b7 ,the temperature of the liquid4 7c7 ,the pressure upon its evaporating surface4 7d7 ,the degree of saturation of the space into which the liquid is evaporating4 7e7 ,the rate of circulation of air over its surface4 7f7 ,the extent of surface exposed to evaporation4 #agf4 ,molecular ,motion in ,solids4--,evidence of molecular motion in liquids is given by expansion on heating1 evaporation1 and diffusion4 ,do any of these lines of evidence apply to solids8 ,it is a fact of common experience that solids do become larger on heating4 ,spaces are left between the ends of rails on railroads so that when they expand in summer they will not distort the track4 ,iron tires are placed on wheels by heating them until they slip on easily4 ,then on cooling1 the iron shrinks and presses the wheel tightly4 ,many common demonstrations of expansion are found in lecture rooms4 ,the fact of the evaporation of a solid is often detected by noticing the odor of a substance4 ,the odor of moth balls is one example4 ,camphor also evaporates4 ,heated tin has a characteristic odor noted by many4 ,ice and snow disappear in winter even though the temperature is below freezing4 ,wet clothes1 freeze dry1 that is1 dry after freezing1 by evaporation4 ,a few crystals of iodine placed in a test-tube and gently heated form a vapor easily seen1 even though none of the iodine melts4 ,where the vapor strikes the side of the tube1 it condenses back to dark gray crystals of iodine4 ,this change from solid directly to gas and back again without becoming liquid is called sublimation4 ,a number of solids are purified by this process4 ,important ,topics #a4 ,cooling effect of evaporation1 rate of evaporation affected by six conditions4 #b4 ,effects of molecular motion in solids3 7a7 ,expansion1 7b7 ,evaporation1 7c7 ,sublimation4 ,exercises #a4 ,does sprinkling the streets or sidewalks cool the air8 ,why8 #b4 ,give an illustration for each of the factors affecting evaporation4 #c4 ,give an illustration for each of the three evidences of molecular motions in solids4 #d4 ,since three-quarters of the earth's surface is covered with water1 why is not the air constantly saturated8 #e4 ,if the air has the temperature of the body1 will fanning the perfectly dry face cool one8 ,explain4 ,will the effect be the same if the face is moist8 ,explain4 #f4 ,what is the cause of ,cloud ,capped mountains8 #g4 ,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 summer8 #h4 ,what causes an unfrozen pond or lake to steam on a very cold day in winter1 or on a very cool morning in summer8 #i4 ,as the air on a mountain top settles down the sides to places of greater pressure1 how will its temperature be affected8 its relative humidity8 ,explain4 #aj4 ,on our ,pacific coast1 moist winds blow from the west over the mountains4 ,where will it rain8 ,where be dry8 ,explain4 ,,chapter ,,viii ,,heat ,,and ,,work 7#a7 ,,heat ,,measurement ,,and ,,specific ,,heat #agg4 ,specific ,heat4--,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 volumes1 e4g41 lead is much denser than water4 ,the study of the relative densities of substance is usually considered under the subject of specific gravity4 ,specific heat as distinguished from specific gravity is concerned with the capacity for heat possessed by different substances4 ,the definition for specific heat is3 ,the ratio of the amount of heat required to change the temperature of a given mass of a substance #a ,c4 degree to the amount of heat required to change the temperature of the same mass of water #a ,c4 degree4 ,by definition1 it requires #a calorie to raise the temperature of the gram of water #a;,c4 ,the specific heat therefore of water is taken as one4 ,the specific heat of most substances except hydrogen1 is less than that of water1 and as a rule1 the denser the body the less its specific heat1 as may be observed in the following table3 ----------------------------- ,specific ,specific gravity heat ----------------------------- ,gold #ai4c #j4jcb ,mercury #ac4f #j4jcc ,copper #h4i #j4jic ,brass #h4d-h4i #j4jid ,nickel #h4eg #j4aa ,iron #g4e #j4aabe ,aluminum #b4fg #j4bah ,glass #b4e-c4f #j4ai ,ice #j4iah #j4ejd ,air #j4jjabi #j4bcg ,steam #j4jjjfa #j4dhj ,hydrogen #j4jjjji #c4dji ----------------------------- #agh4 ,method of ,determining ,specific ,heat4--,the specific heat of a body is usually determined by what is called the method of mixtures4 ,for example1 a definite weight of a substance1 say a #bjj-;g4 iron ball1 is placed in boiling water until it has the temperature of the hot water1 #ajj;,c4 ,suppose that #cjj g4 of water at #ah;,c4 be placed in a calorimeter1 and that the hot iron ball on being placed in the water raises its temperature to #bc4e;,c4 ,the heat received by the water equals #e4e #cjj #afej calories4 ,this must have come from the heated iron ball4 #bjj g4 of iron then in cooling #gf4e;,c4 7#ajj-bc4e7 gave out #afej calories4 ,then #a g4 of iron in cooling #gf4e;,c4 ,would give out #h4be calories or #a g4 of iron cooling #a;,c4 would yield about #j4aa calorie4 ,the specific heat of the iron is then #j4aa4 ,for accurate determination the heat received by the calorimeter must be considered4 #agi4 ,heat ,capacity of ,water4--,the large capacity for heat shown by water is useful in regulating the temperature of the air near lakes and the ocean4 ,in hot weather the water rises slowly in temperature absorbing heat from the warm winds blowing over it4 ,in winter the large amount of heat stored in the water is slowly given out to the air above4 ,thus the climate near the ocean is made more moderate both in winter and summer by the large capacity of water for heat4 ,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 boiling4 ,however1 it is this capacity that makes hot-water bottles and hot-water heating effective4 ,if one takes a pound of ice at #j;,c4 in one dish and a pound of water at #j;,c4 in another1 and warms the dish of ice by a ,bunsen flame until the ice is just melted1 and then warms the water in the other dish for the same time1 the water will be found to be hot and at a temperature #hj;,c41 or #agf;,f4 #ahj4 ,the ,heat of ,fusion of ,ice4--,this experiment indicates the large amount of heat required to change the ice to water without changing its temperature4 ,as indicated by the experiment1 it requires #hj calories to melt #a g4 of ice without changing its temperature or1 in other words1 if one placed #a g4 of ice at #j;,c4 in #a g4 of water at #hj;,c41 the ice would be melted and the water would be cooled to #j;,c4 #aha4 ,heat ,given out by ,freezing water4--,just as #hj calories of heat are required to melt #a g4 of ice1 so in freezing #a g4 of water1 #hj calories of heat are given out4 ,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 acetate4 ,on allowing this to cool quietly it will come to the room temperature and remain liquid4 ,if now a small crystal of sodium acetate is dropped into the liquid the latter quickly becomes a solid mass of crystals1 at the same time rising markedly in temperature4 ,the amount of heat now liberated must enter the sodium acetate when the mass of crystals is melted again4 ,the large amount of heat that must be liberated before water freezes accounts for the slowness of the formation of ice4 ,it is also the reason why the temperature never falls so low in the vicinity of large lakes as it does far inland1 the heat given out by the freezing water warming the surrounding air4 ,the heat that disappears on melting and reappears on solidifying is called the heat of fusion4 ,it is sometimes called latent heat since the heat seems to become hidden or latent4 ,it is now believed that the heat energy that disappears when a body melts has been transformed into the potential energy of partially separated molecules4 ,the heat of fusion therefore represents the work done in changing a solid to a liquid without a change of temperature4 #ahb4 ,melting of ,crystalline and ,amorphous ,substances4--,if a piece of ice is placed in boiling hot water and then removed1 the temperature of the unmelted ice is still #j;,c4 ,there is no known means of warming ice under atmospheric pressure above its melting point and maintaining its solid state4 ,ice being composed of ice crystals is called a crystalline body4 ,all crystalline substances have fixed melting points4 ,for example1 ice always melts at #j;,c4 ,the melting points of some common crystalline substances are given below3 ,melting ,points of ,some ,crystalline ,substances #a4 ,aluminum #feh ,c4 #b4 ,cast iron #abjj ,c4 #c4 ,copper #ajhc ,c4 #d4 ,ice #j ,c4 #e4 ,lead #cbg ,c4 #f4 ,mercury -#ci ,c4 #g4 ,phenol 7carbolic acid7 #dc ,c4 #h4 ,platinum #agee ,c4 #i4 ,salt 7sodium chloride7 #gie ,c4 #aj4 ,saltpeter 7potassium nitrate7 #cdj ,c4 #aa4 ,silver #ifa ,c4 #ab4 ,sodium hyposulphite 7hypo7 #dg ,c4 #ac4 ,zinc #dai ,c4 ,non-crystalline or amorphous substances such as glass1 tar1 glue1 etc41 do not have well defined melting points as do crystalline bodies4 ,when heated they gradually soften and become fluid4 ,for this reason glass can be pressed and molded4 #ahc4 ,change of ,volume ,during ,solidification4--,the fact that ice floats and that it breaks bottles and pipes in which it freezes shows that water expands on freezing4 ,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 crystals4 7,see ,fig4 #aea47 ,the formation of these crystals must leave unoccupied spaces between them in the ice4 ,when liquefied1 however1 no spaces are left and the substance occupies less volume4 ,most substances contract upon solidifying4 ,antimony and bismuth1 however1 expand on solidifying while iron changes little in volume4 ,only those bodies that expand1 or else show little change of volume on solidifying1 can make sharp castings1 for if they contract they will not completely fill the mold4 ,for this reason gold and silver coins must be stamped and not cast4 ,type metal1 an alloy of antimony and lead1 expands on solidifying to form the sharp outlines of good type4 ,several important effects of the expansion of water when freezing should be noted4 7a7 ,ice floats1 7b7 if it sank as soon as formed1 lakes and rivers would freeze solid1 7c7 freezing water is one of the active agents in the disintegration of rocks4 ,illustration3 ,,fig4 #aea4--;,ice crystals4 ,illustration3 ,,fig4 #aeb4--,melting ice by pressure4 ,since water expands on freezing1 pressure would on compressing ice at #j;,c41 tend to turn it into water4 ,pressure does lower the melting point of ice1 so that a little ice may melt when it is subjected to pressure4 ,on removing the pressure the water freezes4 ,this may be shown by placing a loop of fine piano wire 7see ,fig4 #aeb7 over a piece of ice supported so that a weight may be hung upon the wire4 ,the wire will be found to gradually cut through the ice1 the melted ice refreezing above the wire4 ,important ,topics #a4 ,specific heat4 #b4 ,heat of fusion of ice4 #c4 ,crystalline substances have fixed melting points4 #d4 ,expansion on freezing1 importance4 ,exercises #a4 ,what are two advantages in the high heat of fusion of ice8 #b4 ,what are two advantages in the expansion of water while freezing8 #c4 ,how much heat will be required to melt #ajjj g4 of ice and warm the water to #bj;,c48 #d4 ,how many grams of ice at #j;,c4 can be melted by #djj g4 of water at #ee;,c48 #e4 ,what are two advantages of the high specific heat of water8 ,two disadvantages8 #f4 ,if the specific heat of iron is #j4aabe1 how much ice at #j;,c4 can be melted by a #bjj-;g4 ball of iron heated to #cjj;,c8 #g4 ,what is the temperature of a hot ball of iron weighing #hj g41 if when placed on a piece of ice at #j;,c4 it melts #ij g4 of ice8 #h4 ,if #ejj g4 of copper at #djj;,c4 are placed into #cjjj g4 of water at #aj;,c4 what will be the resulting temperature8 #i4 ,what weight of water at #ij;,c4 will just melt #aj kg4 of ice at #j;,c48 #aj4 ,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 piece4 ,explain4 #aa4 ,tubs of hot water are sometimes placed in vegetable cellars to prevent the vegetables from freezing4 ,explain4 #ab4 ,how many ,b4t4u4 are given out when #b lbs4 of water freeze8 7#b7 ,,heat ,,and ,,change ,,of ,,state ,illustration3 ,,fig4 #aec4--,the black cube in the upper corner represents one cubic inch of water4 ,the entire cube represents the space occupied by the cubic inch of water in the form of steam4 ,the reduced spaces at the bottom and sides show how much short the cube is of being one cubic foot4 7,american ,radiator ,co47 #ahd4 ,heat of ,vaporization4--,in our study of evaporation in ,art4 #agd 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 liquid2 this means that a loss of heat will result upon evaporation1 the liquid remaining becoming cooler as the process continues4 ,now just as a ball thrown up in the air loses its kinetic energy as it rises1 and acquires energy of position or potential energy1 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 energy4 ,conversely1 as the ball returns to the ground its potential energy is changed to kinetic energy4 ,similarly when vapor molecules return to the liquid condition they lose their energy of position and acquire kinetic energy4 ,in other words1 when a liquid evaporates a certain amount of heat disappears1 or becomes latent and when the vapor condenses the heat reappears1 or becomes sensible heat4 ,the amount of heat that disappears when #a g4 of a substance is vaporized is called the heat of vaporization4 ,in the case of water at its boiling point1 #ecf calories of heat disappear when #a g4 of water turns to vapor1 and this same amount of heat reappears when the vapor condenses4 ,the change of volume of water on turning to steam is shown in ,fig4 #aec4 ,illustration3 ,,fig4 #aed4--;,effect of pressure on the boiling point4 #ahe4 ,the ,boiling ,point4--,the boiling temperature depends upon the pressure4 ,the boiling point may be defined as the temperature at which bubbles of vapor are formed within the liquid4 ,these bubbles increase the surface at which evaporation can take place in the liquid1 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 cooling4 ,the variation of the boiling temperature with changing pressure may be shown by partly filling a strong #g_/h-;in4 test-tube with water4 ,close the neck with a one-hole rubber stopper through which passes a glass tube to which is attached a soft rubber tube4 7,see ,fig4 #aed47 ,support the tube by a holder1 heat the water and boil until all the air is driven from the tube1 then close the soft rubber tube with a pinch cock and hold the tube in an inverted position4 ,on cooling the end of the tube above the water with cold water or snow1 the vapor within is condensed and the pressure upon the water is reduced4 ,vigorous boiling begins at once4 ,by condensing the vapor repeatedly the water may be made to boil at the room temperature4 ,at the top of ,mt4 ,blanc water boils at #hd;,c4 ,while in steam boilers at #bbe lbs4 pressure to the square inch the boiling point is nearly #bjj;,c4 #ahf4 ,laws of ,boiling4--,the following statements have been found by experiments to be true4 #a4 ,every liquid has its own boiling point which under the same conditions of pressure is always the same4 #b4 ,the temperature of the boiling liquid remains at the boiling point until all the liquid is changed into vapor4 #c4 ,the boiling point rises with increased pressure and falls if the pressure is diminished4 #d4 ,a boiling liquid and the vapor formed from it have the same temperature4 ,on cooling1 a vapor will liquefy at the boiling point4 ,illustration3 ,,fig4 #aee4--;,distilling apparatus4 #e4 ,the solution of solid substances in a liquid raises its boiling point1 additional energy being needed to overcome the adhesion involved in the solution4 ,the boiling point is also affected by the character of the vessel containing the liquid4 ,in glass the boiling point is #aja4 ,illustration3 ,,fig4 #aef4--;,a vacuum pan4 #ahg4 ,distillation of ,water4--,usually when solids are dissolved in liquids the vapor coming from the liquid contains none of the dissolved solid4 ,thus by evaporating salt sea water1 and collecting and condensing the vapor1 pure water is obtained4 ,distillation is the process of boiling a liquid and condensing the vapor formed back again into a liquid4 7,see ,fig4 #aee47 ,the liquid to be distilled is placed in vessel ,f and boiled4 ,the vapor is conducted into the tube ,j which is surrounded by a larger tube containing cold water4 ,the vapor is condensed on the cold walls of the tube4 ,the resulting liquid is collected in the vessel ,r4 ,distillation is employed for two purposes3 7a7 ,to remove impurities from a liquid 7water is purified in this way74 7b7 ,mixtures of different liquids having different boiling points may be separated by distillation4 ,the one having the lower boiling point will be vaporized first4 ,thus a mixture of alcohol and water1 on distillation yields a distillate having a much larger percentage of alcohol than at first4 ,repeating this process which is called fractional distillation yields alcohol of increasing strength of purity4 ,distilled liquor such as alcohol1 brandy1 and whisky are made by distilling fermented liquor1 alcohol being made from fermented grains4 ,gasoline and kerosene are distilled from crude petroleum4 ,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 material4 ,since the two substances named are injured by heating1 the syrup1 or milk is evaporated under reduced pressure in a vacuum pan1 that is in a boiler from which air and vapor are removed by an air pump4 7,see ,fig4 #aef47 #ahh4 ,artificial ,cooling4--,the fact has been brought out that when a solid is melted1 a certain amount of heat1 called the heat of fusion1 is absorbed or disappears4 ,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 heat4 ,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 used4 ,the liquefaction or solution of the salt has been accompanied by an absorption or disappearance of heat4 ,this heat has been taken from the salt and from the water1 resulting in a lowered temperature4 ,sal ammoniac or ammonium nitrate when dissolved in water produce a much more marked cooling effect than does table salt4 ,the dissolving of a crystal in a liquid is something like evaporation1 except that the molecules of the liquid attract the molecules of the solid and thus assist the change of state4 #ahi4 ,freezing ,mixtures4--,if one attempts to freeze a solution of salt and water1 ice will not form at #j;,c4 but several degrees lower4 ,the ice formed however is pure4 ,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 water4 ,as the temperature of freezing water is that of melting ice1 ice in a salt solution melts at lower temperature than in pure water4 ,in a saturated salt solution this temperature is -#bb;,c4 ,it is for this reason that the mixture of ice and salt used in freezing cream is so effective1 the salt water in melting the ice1 being cooled to a temperature many degrees below the freezing point of the cream4 ,the best proportion for a freezing mixture of salt and ice is one part salt to three parts of finely powdered or shaved ice4 #aij4 ,refrigeration by ,evaporation4--,intense cold is also produced by permitting the rapid evaporation of liquids under pressure4 ,carbon dioxide under high pressure is a liquid1 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 -#hj ,c4 ,the evaporation of liquid ammonia by permitting it to escape into a pipe1 under reduced pressure1 is used on a large scale as a means of producing cold in cold storage and refrigeration plants4 7,see ,fig4 #aeg47 ,illustration3 ,,fig4 #aeg4--;,diagram of a refrigerating system4 ,the essential parts of the refrigerating system employing ammonia is represented in ,fig4 #aeg4 ,the compressor exhausts ammonia gas from the coiled pipe in ,e and compresses the gas in ,c1 where under #aej pounds pressure and the cooling effect of water it condenses to liquid ammonia4 ,this is allowed to pass slowly through the regulating valve1 whereupon it evaporates and expands in the long coiled pipe in ,e on its way back to the compressor4 ,this evaporation and expansion causes a large amount of heat to be absorbed from the brine1 cooling the latter below the freezing point of pure water and thus permitting the freezing of cans of water suspended in the brine4 ,the chilled brine may also be sent through pipes in order to cool storage rooms containing meat or other food products4 ,the ammonia absorbs heat when it vaporizes and gives up heat when it is compressed and liquified4 ,important ,topics #a4 ,heat of vaporization1 of water #ecf calories per gram4 #b4 ,boiling point1 effect of pressure upon boiling point1 laws of boiling4 #c4 ,distillation1 artificial cooling1 freezing mixtures1 refrigeration by evaporation4 ,exercises #a4 ,how much heat is required 7a7 to melt #a g4 of ice at #j;,c41 7b7 to raise the temperature of the water resulting to #ajj;,c41 7c7 to change this water to steam8 #b4 ,if the water leaving a steam radiator is as hot as the steam how is the room warmed8 #c4 ,what is the effect of placing salt upon icy sidewalks in cold weather8 #d4 ,is rain water distilled water8 ,is it perfectly pure8 #e4 ,what are two advantages of the high heat of vaporization of water8 #f4 ,if the heat from #a g4 of steam at #ajj;,c4 in changing to water and cooling to #j;,c4 could be used in melting ice at #j;,c4 how much ice would be melted8 7#c7 ,,heat ,,and ,,work #aia4 ,necessity for ,heat ,energy4--,from early times man has been able to transform motion into heat1 and has used this ability in many directions as in starting fires and warming himself by friction4 ,it took man many centuries1 however1 to devise an effective machine for transforming heat into mechanical energy or to use it in doing work4 ,the power of a man is small and as long as the work of the world had to be done by man power1 progress was retarded4 ,when man began the use of beasts of burden1 he took a long step in advance since one man could then employ and direct the power of many men in the animals he controlled4 ,man also built water-wheels and windmills thus gaining power directly from the forces of nature and these added much to his working ability4 ,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 machines4 #aib4 ,heat ,engines4--,at the present time there is a great variety of heat engines in use such as steam1 hot air1 gas1 and gasoline engines1 all using heat energy to produce motion4 ,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 work4 ,illustration3 ,,fig4 #aeh4--;,cross-section view of cylinder and steam chest of a steam engine4 ,illustration3 ,,fig4 #aei4--,the steam drives the piston to the left4 ,illustration3 ,,fig4 #afj4--;,external view of steam engine4 #aic4 ,the ,steam-engine4--,the man who perfected the steam-engine1 and devised its modern form was ,james ,watt 7#agcf-ahai74 ,the essential parts and the action of the steam engine may be readily understood by studying a diagram4 ,in ,fig4 #aeh1 ,s stands for steam chest1 ,c for cylinder1 ,p for piston and v for slide valve4 ,the first two are hollow iron boxes1 the latter are parts that slide back and forth within them4 ,the action of the steam engine is as follows3 ,steam under pressure enters the steam chest1 passes into the cylinder and pushes the piston to the other end4 ,the slide valve is moved to its position in ,fig4 #aei4 ,steam now enters the right end of the cylinder1 driving the piston to the left1 the dead steam in the left end of the cylinder escaping at ,e to the air4 ,the slide valve is now shifted to its first position and the process is repeated4 ,it will assist the student to understand this action if he makes a cardboard model of these parts1 the piston and slide valve being movable4 ,in practical steam-engines1 the piston rod is attached to a crank rod fastened to a crank which turns a wheel4 7,see ,fig4 #afj47 ,the back and forth1 or reciprocating motion of the piston is by this means transformed into rotary motion1 just as in the sewing-machine the back-and-forth motion of the treadle produces rotary motion of the large wheel4 ,upon the shaft of the steam engine is fastened an eccentric 7see ,fig4 #afc7 which moves the slide valve4 ,the steam engine acts continuously as long as steam is supplied to it4 ,since it shifts the position of the slide valve automatically1 it is called an automatic steam engine4 ,and because the team drives the piston both ways1 it is called a double-acting steam engine4 ,see ,fig4 #afa for a length-section of a modern locomotive4 ,illustration3 ,,fig4 #afa4--,length-section of modern1 fast-passenger locomotive4 ,a1 cylinder valve--piston type valve2 ,b1 cylinder--piston at out end of stroke2 ,c1 boiler tubes--flues from fire-box2 ,d1 fire-tube type superheater2 ,e1 draught screen2 ,f-,a1 fire-brick arch to protect tubes from direct heat2 ,f-,b1 firebox2 ,g1 grate2 ,h1 exhaust nozzle2 ,i1 safety valve nest2 ,t1 throttle lever2 ,r1 throttle rod2 ,y1 throttle valve4 #aid4 ,the ,mechanical ,equivalent of ,heat4--,while watching workmen bore holes in cannon1 ,count ,rumford1 #agec-ahad1 noticed with much interest the large amount of heat produced in the process4 ,he observed that the heat developed seemed to have some relation to the work done upon the drill in boring the holes4 ,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 friction4 ,this discovery indicates that in some way heat is related to energy and that heat is probably a form of energy4 ,later experiments have confirmed this idea1 and it is now considered well established that heat is a form of energy4 ,many attempts have been made to discover the relation between the units of heat energy and the units of mechanical energy4 ,to illustrate one method employed1 suppose one measures a given length in inches and in centimeters2 on dividing one result by the other1 it will be found that a certain relation exists between the two sets of measurements1 and that in every case that #a in4 equals #b4ed cm4 ,similarly1 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 employed4 ,one ,b4,t4,u4 is found equivalent to #ggh ft4-lbs4 #a calorie being equivalent to #db1gjj g4 cm4 7#dbg g4 m474 ,this relation is called the mechanical equivalent of heat1 or in other words it represents the number of work units equivalent to one heat unit4 ,illustration3 ,,fig4 #afb4--;,apparatus for determining the mechanical equivalent of heat4 ,illustration3 ,william ,gilbert 7#aedj-afjc71 ,father of magnetic philosophy4 ,especially noted for his experiments and discoveries in magnetism2 first to use the word electricity4 ,first man to practically emphasize experimental science4 ,,dr4 ,,william ,,gilbert 7,popular ,science ,monthly7 ,illustration3 ,james ,prescott ,joule 7#ahah-ahhi71 ,england1 determined the mechanical equivalent of heat2 discovered the relation between an electric current and the heat produced2 first proved experimentally the identity of various forms of energy4 ,,james ,,prescott ,,joule 7,popular ,science ,monthly7 ,one of the first successful experiments in determining the relation between work units and heat units was devised by ,joule in ,england4 7,see portrait p4 #bag47 ,the experiment consisted in taking a can of metal containing water 7,fig4 #afb7 in which was placed a thermometer1 and a rod carrying paddles4 ,the rod was turned by a cord connected through suitable apparatus to heavy weights1 ,w and ,w4 ,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 temperature4 ,careful experiments showed that when #ggh ft4-lbs4 of work had been done by the moving weights the heat produced at the same time would warm one pound of water #a ,fahrenheit degree4 ,if the experiment was performed using metric units1 it was found that the expenditure of #db1gjj gram centimeters 7#dbg gram meters7 would result in producing enough heat to warm one gram of water one centigrade degree4 ,the facts just given may be summarized as follows3 #ggh foot-pounds of energy are equivalent to #a ,british thermal unit and #db1gjj gram centimeters1 or #dbg gram meters1 of energy are equivalent to #a calorie4 ,this relation of work units to heat units is called the mechanical equivalent of heat4 #aie4 ,the ,heat ,equivalent of ,fuels and ,efficiency ,tests of ,engines4--,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 gas2 #a lb4 of average soft coal should produce about #ab1fjj ,b4t4u4 ,now since #ggh ft4-lbs4 are equivalent to one ,b4t4u4 the energy produced when #b lbs4 of average soft coal is burned is #ggh #ab1fjj #b #ai1fje1fjj ft4-lbs4 ,in actual practice #b lbs4 of average soft coal burned will develop about #a horse-power for #a hour4 #a horse-power-hour #cc1jjj ft4-lbs4 #fj #a1ihj1jjj ft4-lbs4 ,now efficiency equals 7work out7_/7work in7 #a1ihj1jjj_/ai1fje1fjj #a_/aj or #aj per cent44 ,this is the efficiency of a good steam engine4 ,ordinary ones require #c lbs4 of coal burned to each horse-power-hour produced or they are but #b_/c as efficient or have but about #g per cent4 efficiency4 ,,heat ,,of ,,combustion ,,of ,,various ,,fuels ,data in this table are taken from ,u4 ,s4 ,geological ,survey1 ,bulletin ,no4 #ccb1 and ,u4 ,s4 ,bureau of ,mines1 ,bulletin ,no4 #bc4 ---------------------------------------- ----- ,b4,t4,u4 ,calories per lb4 per gram ---------------------------------------- ----- ,alcohol1 denatured #aa1fjj #f1dej ,coal1 anthracite1 average #ab1fjj #g1ejj ,coal1 bituminous1 average #ai1jjj #g1jjj ,gasoline #ai1jjj #aj1eej ,illuminating gas #ah1jjj #aj1jjj ,kerosene #ai1iij #aa1jej ---------------------------------------- ----- ,,constants ,,for ,,heat ,,transmission ,data from ,ideal ,fitter1 ,american ,radiator ,co4 ,b4t4u4 transmitted per square foot per hour per degree 7,fahrenheit7 difference in temperature between inside and outside air4 ,brick work #d in4 thick #j4fh concrete #h in4 thick #j4df cement #ej per cent4 more than brick4 #ab in4 thick #j4cc stone #cc-a_/c per cent4 more than brick4 ,window #a4jij ,wood as wall #j4bbj concrete #bj per cent4 more than ,double window #j4efj reinforced brick4 ,important ,topics #a4 ,heat a manifestation of energy4 #b4 ,steam-engine and its action4 #c4 ,mechanical equivalent of heat and heat equivalent of fuels and efficiency of engines4 ,exercises #a4 ,construct a working model of the cylinder and steam chest of a steam engine and be prepared to explain its action4 #b4 ,at #e4jj per ton how many ,b4,t4,u4's should be produced from #a cent's worth of bituminous coal8 #c4 ,try the following experiment3 ,place a quart of water in a teakettle and place it over the fire for #e minutes1 and note the rise in temperature and compute the number of ,b4,t4,u4's entering the water4 ,place another quart of water at the same temperature in an aluminum or tin dish and heat for #e minutes1 note the rise in temperature and compute the heat used before4 ,which of the dishes shows the greater efficiency8 ,how do the efficiencies of the two dishes compare8 ,how do you account for any differences in the efficiencies found8 #d4 ,how high would #h cu4 ft4 of water be lifted if all of the energy produced by burning #a lb4 of coal were used in raising it8 #e4 ,what is the mechanical equivalent of a pound of coal expressed in horse-power hours8 #f4 ,if a furnace burns #ajj lbs4 of coal a day and its efficiency is #ej per cent4 how many ,b4,t4,u4's are used in warming the house8 #g4 ,how many ,b4,t4,u4's can be obtained by burning #a_/b ton of bituminous coal8 #h4 when a pound of water is heated from #dj;,f4 to #bab;,f41 how many foot-pounds of energy are absorbed by the water8 #i4 ,how many loads of coal each weighing #b tons1 could be lifted #ab ft4 by the energy put into the water in problem #h8 ,illustration3 ,,fig4 #afc4--;,an eccentric4 #aj4 ,when #c cu4 ft4 of water are used for a hot bath and the water has been heated from #ej;,f4 to #aab;,f41 how many ,b4,t4,u4's have been absorbed by the water8 #aa4 ,if the average temperature of water at the surface of ,lake ,michigan is #ej;,f41 how many ,b4,t4,u4's would be given off by each cubic foot of water at the surface1 if the temperature of the water should drop #e;,f48 #ab4 ,in a cold storage plant carbon dioxide gas is used4 ,the pipe leading from the compression pump to the expansion valve passes through a condensing tank of cold water4 ,why8 #ac4 ,when the gas is compressed in a cold storage plant1 what becomes of the energy used by the compression pump8 #ad4 ,an eccentric 7,fig4 #afc71 is a round disc mounted a little to one side of its center1 ,a1 on the engine shaft ,b4 ,a band1 ,c1 on the circumference of the disc is connected by a rod1 ,d1 with the slide valve in the steam chest4 ,how is the rotary motion of the shaft changed into a backward and forward motion of the slide valve8 7#d7 ,,heat ,,engines #aif4 ,the ,gas ,engine4--,one of the heat engines in common use to-day is the gasoline engine4 ,it is used to propel automobiles and motor boats1 to drive machinery1 etc4 ,the construction and action of a gasoline engine may be understood by studying a working model1 or by proper diagrams4 ,illustration3 ,,fig4 #afd4--;,cut away view of a modern automobile engine1 with parts requiring attention most frequently1 indicated4 7,courtesy of the ,automobile ,journal7 ,the common gasoline or gas engine is called a four-cycle 7better four-part cycle7 engine 7see ,fig4 #afd71 since it requires four movements of the piston to complete one cycle or series of changes4 ,this is illustrated in ,fig4 #afe #a1 which represents a cross-section of the cylinder of the gasoline engine with the piston moving downward4 ,at the upper end of the cylinder are two ports or openings4 ,one1 the exhaust port1 is closed1 the inlet port is open and a mixture of gas and air is entering4 ,fig4 #afe #b shows the piston returning2 both ports are closed and the charge of air and gas is being compressed4 ,as the piston reaches the end of its stroke in compressing the charge1 an electric spark explodes or fires the charge of gas and air4 ,the hot burning gas expands suddenly driving the piston downward with great force 7,fig4 #afe #c74 ,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 strokes4 ,fig4 #afe #d represents the returning piston pushing out the burnt charge through the open exhaust valve e4 ,on the next downward motion of the piston the valve e closes4 ,it opens1 and new charges of gas and air enter and the cycle is repeated4 ,illustration3 ,,fig4 #afe4--,the four strokes of a gas engine cycle4 ,in order to make the motion more even and continuous and also to secure more power1 more than one cylinder is attached to the same shaft and fly-wheel4 ,two1 three1 four1 six1 eight and even more cylinders have been attached to one shaft4 ,four or six cylinders are commonly used in automobile gasoline motors4 ,to lessen the sound of the exhaust1 the latter is sent through a muffler which often reduces the noise to a low throbbing4 7,see ,fig4 #aff47 ,the gasoline engine is more efficient than the steam-engine1 since the fuel1 gas1 is burned in the cylinder and not in a separate furnace4 ,the combustion of the fuel in the cylinders makes some special cooling device necessary to prevent their overheating4 ,this usually consists of a casing about the cylinders4 ,between the cylinder and this casing is water which on being heated passes to a tank or radiator4 ,in the radiator the water cools and then returns to the space between the cylinders and casing thus keeping up the circulation4 ,illustration3 ,,fig4 #aff4--;,an efficient automobile muffler4 7,courtesy ,popular ,science ,monthly47 #aig4 ,efficiency of ,gas ,engines4--,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 burned4 ,illuminating gas is sometimes employed to drive gas engines4 ,one cubic foot of illuminating gas should produce #fjj ,b4,t4,u4 when burned4 ,the efficiency of the gas or gasoline engines is sometimes as high as #be per cent4 ,this engine is free from smoke and is also compact and quickly started4 ,while the fuel1 gas or gasoline1 is somewhat expensive it is light and easily carried4 ,suppose a gas engine produces #a horse-power and uses #bj cu4 ft4 of gas an hour1 what is its efficiency8 #a horse-power-hour #eej #fj #fj #a1ihj1jjj ft4-lbs4 #bj cu4 ft4 of gas #bj #fjj #ggh #i1ccf1jjj ft4-lbs4 ,efficiency work out_/work in #a1ihj1jjj_/i1ccf1jjj #ba4b per cent4 ,illustration3 ,,fig4 #afg4--,the principle of the steam turbine4 ,illustration3 ,,fig4 #afh4--,path of steam in ,de,laval steam turbine4 7a7 and 7c7 movable blades1 7b7 stationary4 #aih4 ,the ,steam ,turbine4 ,one form of the steam-engine that is coming into general use is the turbine4 7,see ,fig4 #afg47 ,this consists of a shaft to which are attached blades1 the shaft and blades being contained in a closed case4 ,steam is admitted by nozzles and strikes the blades so as to set them and the shaft in motion4 ,there are also stationary blades 7see ,fig4 #afh71 which assist in directing the steam effectively against the rotating parts4 ,the steam turbine is used for large power plants4 7,see ,fig4 #bic47 ,it is very efficient1 makes very little vibration1 and occupies about one-tenth the floor space that a reciprocating engine of equal power uses4 ,some large ocean steamers are now driven by steam turbines4 ,important ,topics #a4 ,the gas engine1 its construction1 action and efficiency4 #b4 ,the steam turbine4 ,exercises #a4 ,if coal costs #d4jj a ton1 and gas1 #j4hj per #ajjj cu4 ft4 what amounts of heat can be secured from #a cent's worth of each8 #b4 ,what will it cost to heat #cj gallons of water 7#a gal4 of water weighs about #h-a_/c lbs47 from #dj;,f4 to #aij;,f4 with coal costing #d4jj per ton and yielding #ab1jjj ,b4,t4,u4 per lb4 if the heater has an efficiency of #ej per cent4 #c4 ,what will it cost to heat #cj gallons of water from #dj;,f4 to #aij;,f4 with gas at #j4hj per #ajjj cu4 ft4 if the heating device has an efficiency of #ge per cent4 #d4 ,construct a cardboard working-model showing the action of the gas engine and be prepared to explain the action of the various parts4 #e4 ,if #ejj lbs4 of iron should fall #bjjj ft4 and all of the resulting mechanical kinetic energy should be transformed into heat1 what would be the amount of heat produced8 #f4 ,what are the special advantages of 7a7 the gasoline engine8 7b7 the turbine8 7c7 the reciprocating steam engine8 #g4 ,do you burn coal or gas in your kitchen stove at home8 ,which is for you the more economical8 ,why8 #h4 ,what are the advantages of using a fireless cooker8 #i4 ,what is the efficiency of a locomotive that burns #c4b lbs4 of coal per horse-power-hour8 #aj4 ,a gas engine developed in a test #j4cd horse-power for #a minute4 and #ej seconds1 #j4e cu4 ft4 of gas being used4 ,the heat of combustion of the gas was #fjj ,b4,t4,u4 per cu4 ft4 ,find the efficiency of the engine4 #aa4 ,find the horse-power of an engine1 the diameter of the piston being #ai in41 stroke #bf in42 it uses steam at an average pressure of #bjj lbs4 per square4 inch and makes #ajj strokes a minute4 #ab4 ,what is the efficiency of an engine and boiler that develops #bjj horse-power1 while burning #cij lbs4 of soft coal per hour8 #ac4 ,if a locomotive has an efficiency of #f per cent4 and develops #agjj horse-power how much coal is burned in an hour8 #ad4 ,if an automobile engine burns #a gallon of gasoline in an hour and develops #aj horse-power1 what is its efficiency8 #ae4 ,the ,a4,l4,a4,m4,j formula for horse-power is 7,n ,b7_/#b4e when the piston speed is #ajjj ft4 per minute1 ,n being the number of cylinders and ,b1 their diameter4 ,find the horse-power of a #d-;cylinder engine1 the cylinders having a diameter of #d in4 ,j ,american ,league of ,automobile ,manufacturers4 #af4 ,find the horse-power of a #f-;cylinder automobile engine1 if the cylinder diameter is #d4e in4 #ag4 ,a #d-;cylinder automobile having #d-;in4 cylinders1 uses #a gallon of gasoline in #a hour4 ,find its efficiency1 if its average horse-power developed is #f4 #ah4 ,the motor boat ,disturber ,,iii1 has #bd cylinders each with diameter #c4e in4 ,if the piston speed is #ajjj ft4 per minute1 what is the horse-power8 7,see problem #ae47 ,review ,outline3 ,heat ,heat2 sources 7#d71 effects 7#e71 units 7#b74 ,temperature2 thermometer scales 7#c71 absolute temperature1 #i;,c_/#e #cb ,f4 ,expansion2 gases1 ,law of ,charles 7,v#a_/,v#b ,t#a_/,t#b71 liquids1 peculiarity of water1 solids1 coefficient of expansion1 uses1 results4 ,heat ,transference2 conduction1 uses of good and poor conductors1 convection1 in nature1 heating and ventilating systems1 radiation1 #c peculiarities1 value of sun's radiation4 ,heat and ,moisture2 relative humidity1 dew point1 formation of dew1 fog1 rain1 snow1 etc41 evaporation1 effects1 conditions4 ,heat ,measurement2 specific heat1 heat of fusion1 of vaporization1 combustion4 ,vaporization2 ,boiling point1 laws of boiling1 distillation1 artificial cooling4 ,heat ,engines2 steam1 gas4--construction1 action1 efficiency1 mechanical equivalent of heat4 ,heat equivalent of fuels4 ,,chapter ,,ix ,,magnetism 7#a7 ,,general ,,properties ,,of ,,magnets #aii4 ,magnets4--,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 steel4 ,such stones are called natural magnets4 ,it is thought by many that the name magnet is derived from ,magnesia in ,asia ,minor1 where these stones are abundant1 though this is but tradition4 ,it was also learned long ago that iron and steel objects when rubbed with natural magnets become magnetized1 that is1 acquire the properties of magnets4 ,these are said to be artificial magnets4 ,illustration3 ,,fig4 #afi4--;,a bar magnet4 ,illustration3 ,,fig4 #agj4--;,a horseshoe magnet4 ,some #hjj years ago it was discovered that magnets1 natural or artificial1 when suspended so as to turn freely1 always come to rest in a definite position pointing approximately north or south4 ,this is especially noticeable when the magnet is long and narrow4 ,because of this property of indicating direction1 natural magnets were given the name of lodestone 7lode-leading74 ,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 flowing4 ,the magnetized steel bars may have any form1 usually they are either straight or bent into a ,u shape4 ,these forms are known as bar and horseshoe magnets4 7,see ,figs4 #afi and #agj47 ,magnets retain their strength best when provided with soft-iron keepers1 as in ,fig4 #aga4 ,illustration3 ,,fig4 #aga4--;,bar magnets with keepers4 #bjj4 ,magnetic ,poles4--,if a magnet is placed in iron filings and removed1 the filings will be found to cling strongly at places near the ends of the magnet1 but for a portion of its length near the middle no attraction is found4 7,see ,fig4 #agb47 ,these places of greatest attraction on a magnet are called poles4 ,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 pole2 at the other end1 is the south-seeking pole4 ,in most places the needle does not point to the true north1 but somewhat to the east or west of north4 ,the direction taken by a magnetic needle is parallel to the magnetic meridian4 ,illustration3 ,,fig4 #agb4--;,iron filings attracted to the poles of a magnet4 #bja4 ,law of ,magnetic ,action4--,the north pole of a magnet is usually marked4 ,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 magnet1 the two poles will be found to repel each other1 as will also two south-seeking poles1 while a north-seeking and a south-seeking pole attract each other4 7,see ,fig4 #agc47 ,this action leads to the statement of the ,law of ,magnetic ,action3 ,like poles repel1 while unlike poles attract each other4 ,the force of attraction or repulsion lessens as the distance increases4 ,the force of the action between magnetic poles is inversely proportional to the square of the distance between them4 ,compare this with the law of gravitation 7,art4 #hh74 ,illustration3 ,,fig4 #agc4--,like poles of two magnets repel4 ,illustration3 ,,fig4 #agd4--;,a magnetoscope4 #bjb4 ,magnetic ,substances and ,properties4--,it is found that if an iron or steel magnet is heated red hot that its magnetic properties disappear4 ,accordingly one method of demagnetizing a magnet is to raise it to a red heat4 ,if a magnet that has been heated red hot and then cooled is brought near a suspended bar magnet1 it is found to attract either end1 showing that it has regained magnetic properties even though it has lost its magnetic polarity4 ,a suspended bar magnet used to test the magnetic properties of a body is called a magnetoscope4 7,see ,fig4 #agd47 ,the needle of a magnetic compass serves very well as a magnetoscope4 ,magnetic properties are most strongly exhibited by iron and steel1 though nickel and cobalt show some magnetic effects4 ,there is a peculiar alloy of copper1 aluminum1 and manganese1 known as ,heusler's ,alloy1 that is also magnetic4 ,however1 of all substances1 iron and steel show the strongest magnetic effects4 #bjc4 ,magnetic ,induction4--,let the north-seeking pole of a bar magnet support an iron nail by its head4 7,see ,fig4 #age47 ,test the point of the nail for polarity4 ,see whether a second nail can be attached by its head to the point of the first4 ,test the polarity of the point of this nail4 ,find by trial how many nails can be suspended in succession from the magnet4 ,test in each case for polarity4 ,withdraw carefully the magnet from the first nail--the string of nails will fall apart4 ,repeat the test with a thickness of paper between the magnet and the first nail4 ,results similar to those secured at first will be found1 though probably fewer nails will be supported4 ,the presence of paper between the magnet and nails simply weakens the action4 ,test the action of the magnet upon the nail when there is between them a piece of glass1 one's thumb1 thin pieces of wood1 copper1 zinc1 etc4 ,the magnetizing of a piece of iron or steel by a magnet near or touching it is called magnetic induction4 ,this action takes place through all substances except large bodies of iron or steel hence these substances are often used as magnetic screens4 ,the pole of the new induced magnet adjacent to the bar magnet is just opposite to the pole used4 ,thus the ,n4-pole of the magnet used will produce a ,s4-pole at the near end of the nail and a ,n4-pole at the end farther away4 7,see ,fig4 #age47 ,on removing the magnet1 the nails are found to retain a part of their induced magnetism4 ,illustration3 ,,fig4 #age4--,nails magnetized by induction4 #bjd4 ,retentivity4--,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 removed4 ,different pieces of iron and steel vary greatly in this respect1 some remaining strongly magnetized1 others losing much of their magnetism4 ,this property of retaining magnetism is called retentivity4 ,hardened steel has a high degree of retentivity1 while soft iron retains but little magnetism4 ,important ,topics #a4 ,magnet2 natural1 artificial1 bar1 horseshoe4 #b4 ,magnetic poles2 north seeking1 south seeking4 #c4 ,law of action1 magnetoscope1 retentivity1 induced magnet4 ,exercises #a4 ,make a summary of the facts of magnetism presented in this lesson4 #b4 ,is magnetism matter1 force1 or energy8 ,how do you decide8 ,to what other phenomenon that we have studied is it similar8 ,how8 #c4 ,make a simple magnetoscope for yourself by suspending a thin steel needle or rod #e to #aj cm4 long1 with a light thread or silk fiber at its center1 so that it will hang level4 ,then magnetize the needle1 and keep the magnetoscope in your book4 #d4 ,name three uses for magnets or magnetism4 #e4 ,mention three uses for a magnetoscope4 #f4 ,are all magnets produced by induction8 ,explain4 #g4 ,in what magnetic devices is a high retentivity desirable8 7#b7 ,,the ,,theory ,,of ,,magnetism ,,and ,,magnetic ,,fields #bje4 ,the ,theory of ,magnetism4--,if a magnetized watch spring is broken in two1 each part is found to be a magnet4 ,if one of these parts be broken and this process of breaking be continued as far as possible1 the smallest part obtained has two poles and is in fact a complete magnet4 7,see ,fig4 #agf47 ,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 magnet4 ,in other words1 magnetism is believed to be molecular4 ,other evidence supporting this idea is found in the fact that when a magnet is heated red hot1 to a temperature of violent molecular motion1 its magnetism disappears4 ,also if a long1 fine soft iron wire be strongly magnetized1 a light jar causes its magnetism to disappear4 ,this would lead us to believe that magnetism is not a property of the surface of the body1 but that it depends upon molecular structure or the arrangement of the molecules4 ,illustration3 ,,fig4 #agf4--;,effect of breaking a magnet4 ,illustration3 ,,fig4 #agg4--,possible arrangement of molecules in an unmagnetized iron bar4 ,it is believed also that the molecules of a magnetic substance are magnets at all times2 that before the body is magnetized the molecules are arranged haphazard 7see ,fig4 #agg7 but that when a magnet is brought near1 the molecules tend to arrange themselves in line1 with their north-seeking poles pointing in the same direction4 7,see ,fig4 #agh47 ,if the magnet is jarred some of the molecules tend to get out of line1 perhaps to form little closed chains of molecules4 7,see ,fig4 #agg47 ,illustration3 ,,fig4 #agh4--;,arrangement of molecules in a saturated magnet4 #bjf4 ,magnetic ,fields and ,lines of ,force4--,the behavior of magnets is better understood after observing and studying the lines of force of a magnet4 ,the earliest descriptions of these are by ,william ,gilbert1 the first ,englishman to appreciate fully the value of making experimental observations4 ,he wrote a book in #afjj called ,de ,magnete in which he published his experiments and discoveries in magnetism4 7,see p4 #bag47 ,magnetic lines of force may be observed by placing a magnet upon the table1 then laying upon it a sheet of paper and sprinkling over the latter fine iron filings4 ,on gently tapping the paper1 the filings arrange themselves along curved lines extending from one end of the magnet to the other4 ,these are called the magnetic lines of force4 7,see ,fig4 #agi47 ,the space about a magnet in which the magnetic lines are found is called the magnetic field4 7,see ,fig4 #ahj47 ,illustration3 ,,fig4 #agi4--;,iron filings on paper over a bar magnet4 ,many interesting things have been discovered concerning the lines of force4 ,some of the facts of magnetic action are given a simple explanation if we think of them as due to the magnetic lines of force4 ,a summary of several discoveries concerning magnetic fields follows3 7,a7 ,magnetic lines of force run side by side and do not cross one another4 7,see magnetic fields47 7,b7 ,magnetic lines of force are believed to form closed curves or to be continuous4 ,the part outside of the magnet is a continuation of the part within the magnet4 7,see ,fig4 #ahj47 ,illustration3 ,,fig4 #ahj4--;,diagram of the field of a bar magnet4 7,c7 ,the attraction of a magnet is strongest where the magnetic lines are thickest1 hence they are believed to be the means by which a magnet attracts4 7,d7 ,since like poles repel and unlike poles attract1 it is known that the action along a line of force is not the same in both directions4 ,it has therefore been agreed by physicists to indicate by an arrow head 7,fig4 #ahj71 the direction that a north-seeking pole tends to move along a line of force4 ,the lines of force are considered as leaving the north-seeking pole of a magnet and entering the south-seeking pole4 7,see ,figs4 #aha and #ahb47 ,illustration3 ,,fig4 #aha4--,magnetic field between like poles showing repulsion4 7,e7 ,a freely suspended small magnet in a magnetic field places itself parallel to the lines of force4 7,test this by holding a magnetic compass in different portions of a magnetic field74 ,note the position of the needle and the lines of force4 ,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 held4 ,illustration3 ,,fig4 #ahb4--,magnetic field between unlike poles showing attraction4 7,f7 ,each magnet is accompanied by its own magnetic field4 ,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 iron4 #bjg4 ,magnetic ,induction4--,the action of magnetic lines of force in magnetizing iron when they pass through it1 is called ,magnetic ,induction4 ,this may now be defined as the production of magnetism in a body by placing it within a magnetic field4 ,freely suspended magnets place themselves parallel to the lines of force in a magnetic field1 therefore when an iron rod is placed in a weak field1 or one with few lines of force1 the iron is but slightly magnetized2 that is1 but few molecules are brought into line4 ,increasing the strength of the magnetizing field1 gives stronger magnetization to the iron up to a certain point4 ,after this1 stronger fields give no increase in magnetizing effect4 ,when iron exhibits its greatest magnetization it is said to be saturated4 ,illustration3 ,,fig4 #ahc4--;,effect of a piece of iron in a magnetic field4 #bjh4 ,permeability4--,if a piece of iron is placed between the poles of a horseshoe magnet1 the field obtained by sprinkling iron filings upon a sheet of paper over the magnet resembles that shown in ,fig4 #ahc4 ,the lines in the space between the poles of the magnet seem to crowd in to the piece of iron4 ,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 permeability4 ,soft iron shows high permeability4 ,marked differences in behavior are shown by different kinds of iron and steel when placed in a magnetic field4 ,very pure iron1 or soft iron1 is strongly magnetized by a magnetic field of medium strength4 ,its magnetism1 however1 is quickly lost when the magnetizing field is removed4 ,this indicates that soft-iron molecules are easily swung into line1 but also disarrange themselves as easily when removed from a magnetizing force4 ,soft-iron magnets having high permeability quickly lose their magnetism4 ,they are therefore called temporary magnets4 ,on the other hand a hardened steel bar is difficult to magnetize1 but when once magnetized retains its magnetism permanently1 unless some action weakens the magnet4 ,such magnets are called permanent magnets4 ,,note4--,the term line of force as used in this text means the same as line of induction as used in more advanced texts4 ,important ,topics #a4 ,molecular theory of magnetism1 saturation1 permeability4 #b4 ,magnetic fields and lines of force4 #c4 ,six facts concerning magnetic fields4 ,exercises #a4 ,name an object whose usefulness depends upon its retentivity4 ,explain4 #b4 ,how do you explain the retentivity of hard steel8 #c4 ,are the molecules of a piece of iron magnetized at all times8 ,explain4 #d4 ,when a piece of iron is magnetized by induction does any magnetism enter the iron from the magnet8 ,does the magnet lose as the iron gains magnetism8 ,explain4 #e4 ,have all magnets been produced by induction8 ,explain4 #f4 ,why will tapping a piece of iron when in a magnetic field increase the amount it will be magnetized8 #g4 ,express in your own words the theory of magnetism4 #h4 ,place two bar magnets in a line #e cm4 apart1 unlike poles adjacent2 obtain the magnetic field with iron filings4 ,sketch it4 #i4 ,repeat ,exercise ,no4 #h using like poles4 ,describe the appearance of a field that gives attraction2 of a field that gives repulsion4 7#c7 ,,the ,,earth',s ,,magnetism #bji4 ,the ,earth's ,magnetic ,field4--,dr4 ,william ,gilbert's famous book1 ,de ,magnete1 contains many helpful and suggestive ideas1 none perhaps more important than his explanation of the behavior of the compass needle4 ,he assumed that the earth is a magnet1 with a south-seeking pole near the geographical north pole1 and with a north-seeking pole near the geographical south pole4 ,this idea has since been shown to be correct4 ,the north magnetic 7or south-seeking7 pole was found in #ahca1 by ,sir ,james ,ross in ,boothia ,felix1 ,canada4 ,its approximate present location as determined by ,captain ,amundsen in #aije is latitude #gj #e ,n4 and longitude #if #df ,w4 ,the south magnetic pole is in latitude #gb ,s41 longitude #aee #af ,e4 ,the north magnetic pole is continually changing its position4 ,at present it is moving slowly westward4 ,illustration3 ,,fig4 #ahd4--,magnetic map of the earth for #aiaj4 ,isogonic lines ------ ,isoclinic lines - - - - #baj4 ,direction of the ,earth's ,magnetic ,field4--,reference has been made to the fact that the compass does not always point exactly north4 ,this indicates that the earth's magnetic field varies in its direction4 ,columbus discovered this fact upon his first voyage4 ,the discovery alarmed the sailors since they feared they might come to a place where the compass would be unreliable4 ,this variation is called declination4 ,it is defined as the angle between the direction of the needle and the geographical meridian4 ,declination is due to the fact that the geographical and magnetic poles do not coincide4 ,what is meant by a declination of #ij8 ,lines drawn upon a map so as to pass through places of the same declination are called isogonic lines4 ,the line passing through points where the needle points north1 without declination1 is the agonic line4 ,the agonic line is slowly moving westward4 ,it now passes near ,lansing1 ,michigan2 ,cincinnati1 ,ohio2 and ,charleston1 ,s4 ,carolina4 7,see ,fig4 #ahd47 ,at all points in the ,united ,states and ,canada east of the agonic line the declination is west1 at points west of the agonic line the declination is east4 #baa4 ,the ,dipping ,needle4--,mount an unmagnetized steel needle on a horizontal axis so as to be in neutral equilibrium1 that is1 so as to remain balanced in any position in which it is left4 ,upon being magnetized and placed so that it can swing in a north and south plane1 the north-seeking pole will now be found to be depressed1 the needle forming an angle of nearly #gj with the horizontal4 7,see ,fig4 #ahe47 ,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 #gj4 ,over the magnetic pole1 the dipping needle as it is called1 is vertical4 ,at the earth's equator it is nearly horizontal4 ,the angle between a horizontal plane and the earth's magnetic lines of force is called the inclination or dip4 ,illustration3 ,,fig4 #ahe4--;,a dipping needle4 #bab4 ,inductive ,effect of the ,earth's ,magnetic ,field4--,the earth's magnetic lines of force are to be considered as filling the space above the earth1 passing through all objects on the surface and into and through the earth's interior4 ,the direction of the earth's field is shown by the compass and the dipping needle4 ,magnetic lines of force tend to crowd into and follow iron and steel objects on account of their permeability4 ,therefore1 iron or steel objects1 such as posts1 columns1 etc41 are permeated by the earth's lines of force1 which in the ,united ,states enter at the top of these objects and leave at the bottom4 ,the lines of force passing through these bodies arrange their molecules in line or magnetize the bodies4 ,the inductive effect of the earth's magnetism indicates how lodestones or natural magnets acquire their magnetized condition4 ,so far as is known1 magnetism produces no effect upon the human body4 ,it can therefore be studied only by observing its effects upon magnets or bodies affected by it4 ,important ,topics ,the earth's magnetic field1 dip1 declination1 agonic line1 induction by the earth's field4 ,exercises #a4 ,how would a dipping needle be of assistance in locating the magnetic poles of the earth8 #b4 ,will a dipping needle weigh more before or after it is magnetized8 ,explain4 #c4 ,it is said that induction precedes attraction4 ,using this idea1 explain how a magnet attracts a piece of soft iron4 #d4 ,devise an experiment to show that a piece of iron attracts a magnet just as a magnet attracts a piece of iron4 #e4 ,give two methods for determining the poles of a magnet4 #f4 ,state three of the most important points in the theory of magnetism4 ,what evidence supports each8 #g4 ,why is a permanent magnet injured when it is dropped8 #h4 ,name two important uses of the earth's magnetic field4 #i4 ,what magnetic pole would you find at the top of an iron post that has stood for some time in the ground8 ,what pole at the bottom8 ,how would you test this8 ,,chapter ,x ,,static ,,electricity 7#a7 ,,electrification ,,and ,,electrical ,,charges #bac4 ,electrical ,charges4--,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 bodies4 ,the process of electrifying a body is very different from that of magnetizing it4 ,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 paper1 thread1 etc4 ,this peculiar attraction was noticed and recorded by the ancient ,greeks1 #fjj ,b4,c41 when it was found that amber when rubbed would attract light objects to itself4 ,for a long time it was supposed that amber was the only substance showing this property4 ,dr4 ,william ,gilbert1 however1 discovered that the electrified condition could be produced by rubbing a great variety of substances4 ,he named the result produced1 electrification1 after the ,greek name for amber 7elektron74 ,a body like hard rubber or amber which will attract light objects when rubbed is said to be electrified1 or to have been given a charge of electricity4 #bad4 ,law of ,electric ,action4--,let a vulcanite rod be electrified by rubbing with a woolen cloth until it will attract light objects2 then place it in a wire stirrup suspended by a silk thread4 ,if a second vulcanite rod is similarly electrified and brought near the first1 the two will be found to repel4 7,see ,fig4 #ahf47 ,if now a glass rod be rubbed with silk and brought near the suspended rod1 the two will attract4 ,this difference in behavior indicates a difference in the electrification or charge upon the rods4 ,the two charged vulcanite rods repelling and the charged glass and vulcanite attracting indicate the law of electric action4 ,like charges repel each other and unlike charges attract each other4 ,extensive experiments with all kinds of substances indicate that there are but two kinds of electrical charges4 ,the electrical charge upon glass when rubbed with silk or wool is called positive1 and that upon hard rubber or vulcanite when rubbed with wool is called negative4 ,illustration3 ,,fig4 #ahf4--,repulsion of like charges4 ,illustration3 ,,fig4 #ahg4--;,an aluminum foil electroscope4 ,illustration3 ,,fig4 #ahh4--;,a proof plane4 #bae4 ,the ,electroscope and its ,uses4--,an electroscope is a device employed to test the presence of an electrical charge4 ,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-foil4 ,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 bottom4 7,see ,fig4 #ahg47 ,the kind of charge upon a body may be determined with an electroscope as follows3 ,make a proof-plane by sealing a small metal disc on the end of a hard rubber rod4 7,see ,fig4 #ahh47 ,touch the disc of the proof-plane first to a charged rubber rod and then to the top of the electroscope4 ,the leaves of the latter will separate showing that the electroscope is charged4 ,this charge remains after the proof-plane is removed4 ,if the charged vulcanite rod is brought near the electroscope1 the leaves separate further ,that is1 a charge like that on the electroscope makes the leaves separate further4 ,but if an unlike charge1 as that on a positively charged glass rod1 is cautiously brought near1 the leaves will be seen to move together4 ,illustration3 ,,fig4 #ahi4--,rod with woolen cap4 #baf4 ,two ,charges are ,produced at the ,same ,time4--,a closely fitting woolen cover or cap some #c in4 long is made for the end of a vulcanite rod4 ,a silk thread attached to the cap enables one to hold the latter while the rod is turned within it4 7,see ,fig4 #ahi47 ,if the rod bearing the cap is held near a charged electroscope little or no effect is noticed4 ,if now the cap is removed by the silk thread and held near the electroscope1 it will be found to be positively charged while the rod is negatively charged4 ,the fact that no result is seen when the cap and rod are together1 indicates that one charge neutralizes the other4 ,in other words1 the charges must be equal4 ,this illustrates the truth that when electrification is produced by friction1 the two objects rubbed together acquire equal and opposite charges4 #bag4 ,charging by ,contact and ,conduction4--,if a small pith ball is suspended by a silk thread1 a charged rod brought near is at first attracted1 but after contact is repelled 7see ,fig4 #aij7 showing that the ball has become charged with the same kind of electrification that is upon the rod4 ,that is1 a charge given to an object by contact with a charged body is of the same kind as that upon the charged one4 ,the proof-plane in ,art4 #bae carries the same kind of charge that is upon the rod it is charged from4 ,some substances have the ability to transfer charges of electrification4 ,these are called conductors1 those that do not conduct electrification are insulators4 ,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 support1 as in ,fig4 #aia4 ,if now a charge be put in contact with the body of a1 the electroscope will show by its leaves whether the rod tested conducts or not4 ,the leaves separate instantly when conducting substances are tested1 while no action results with insulators4 ,in testing some materials for conductivity the leaves are found to diverge gradually4 ,such bodies are said to be poor conductors4 ,all degrees of conductivity are found4 ,the metals are the best conductors4 ,the best insulators are rubber1 mica1 shellac1 glass1 silk1 porcelain1 paraffin1 and oils4 ,illustration3 ,,fig4 #aij4--,the pith ball charged by contact is repelled4 ,illustration3 ,,fig4 #aia4--,testing for conductivity4 ,important ,topics #a4 ,positive and negative changes4 ,law of electric action4 #b4 ,electroscope and its uses4 #c4 ,conductors and insulators4 ,exercises #a4 ,is air a conductor8 ,give reasons for your answer4 #b4 ,mention two points of likeness and two points of difference between magnetism and electrification4 #c4 ,if you were testing the electrification of a body with a charged pith ball suspended by a silk thread1 would attraction or repulsion be the better test8 ,give reasons4 #d4 ,have you ever produced electrification by friction outside of a laboratory8 ,explain4 #e4 ,are the rods upon which we produce electrification by friction1 conductors or insulators8 ,how do you explain this8 #f4 ,are conductors or insulators of the greater importance in practical electricity8 ,explain4 7#b7 ,,electric ,,fields ,,and ,,electrostatic ,,induction ,illustration3 ,,fig4 #aib4--;,an electric field about a positively charged shell4 ,illustration3 ,,fig4 #aic4--;,a detector4 #bah4 ,electrical ,fields4--,in our study of magnetism we learned that a magnet affects objects about it by its magnetic lines of force4 ,in a similar way it is assumed that a charged body produces electrical effects upon its surroundings by electric lines of force4 ,for example1 the attraction that a charged body exerts upon light objects through short distances or the influence of a charge upon an electroscope several feet away1 is said to be due to the electric field about the charged body4 7,see ,fig4 #aib47 ,the presence of the electric lines of force may be shown by placing a perforated1 slender1 diamond-shaped piece of tissue paper upon a light glass pointer 7,fig4 #aic74 ,when placed in an electric field the tissue paper detector places itself parallel to the lines of force4 ,electric lines of force are said to extend from a positive to a negative charge4 7,see ,fig4 #aid47 ,the direction shown by the arrow upon the lines is that along which a small positive charge tends to move4 ,electric lines of force unlike those from magnets are not continuous4 ,they extend from a positive charge to a negative charge4 ,therefore each positive charge is connected by lines of force to a negative charge somewhere4 ,these ideas of electric fields are of much assistance in explaining many electrical effects4 ,electrical fields between oppositely charged shells will be found similar to ,fig4 #aid1 while between shells with like charges1 fields are found as in ,fig4 #aie4 ,illustration3 ,,fig4 #aid4--;,electric field between unlike charges4 ,illustration3 ,,fig4 #aie4--;,electric field between like charges4 #bai4 ,electrostatic ,induction4--,if a charged body is brought near an aluminum-foil electroscope1 the leaves separate4 7,see ,fig4 #aih47 ,the nearer the charge is brought the wider the leaves spread1 but when the charge is removed1 the leaves collapse showing that nothing was given to the electroscope4 ,it was simply affected by the charge in its vicinity4 ,this production of an electrified condition in a body by the influence of a charge near it is called electrostatic induction4 ,placing insulators1 such as a sheet of glass1 between the charge and the electroscope does not affect the result1 which is apparently brought about by the action of the electric lines of force4 ,these lines of force extend without difficulty through uncharged insulators and terminate often at the surface of a conductor1 where their influence causes a charge to accumulate4 ,charged insulators1 however1 do affect inductive action4 ,this may be noticed by using a sensitive electroscope4 ,illustration3 ,,fig4 #aif4--,production of two charges by the influence of a third charge4 ,illustration3 ,,fig4 #aig4--,the two charges separated4 #bbj4 ,electrical ,separation by ,induction4--,the action just described may be illustrated further by taking two insulated1 uncharged brass shells1 ,a and ,b4 7,see ,fig4 #aif47 ,bring a charged vulcanite rod near shell ,a while the shells are touching each other4 ,then remove shell ,b 7,fig4 #aig7 while the rod remains near ,a4 ,on testing the shells for electrification1 ,a is found to possess a positive charge4 ,this action is in some respects similar to magnetic induction1 for if one places a north-seeking pole near a piece of iron1 the iron develops by induction a south-seeking pole at the end nearest the magnet and a north-seeking at the other end4 ,there is1 however1 one striking difference4 ,if the magnetized iron be separated into two parts1 each part is a complete magnet possessing two unlike poles2 while if the object affected by electrostatic induction is separated into two parts one part has a positive charge and the other a negative charge4 ,illustration3 ,,fig4 #aih4--;,effect of a charged rod near an electroscope4 ,illustration3 ,,fig4 #aii4--,when a finger is touched to the top of the electroscope1 the repelled negative charge escapes4 ,illustration3 ,,fig4 #bjj4--,the electroscope is now positively charged4 #bba4 ,charging a body by induction is easily accomplished4 ,to charge an aluminum-foil electroscope by induction bring near 7say #aj cm47 from the top of the electroscope a charged rubber rod4 7,see ,fig4 #aih47 ,the separated leaves show the presence of the repelled or negative charge1 the positive charge being on the disc at the top4 ,if while the charged rod is held near1 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 7,fig4 #aii74 ,on removing first the finger and next the charged rod1 the positive charge spreads over the metal parts of the electroscope1 as is shown by the separation of the leaves 7,fig4 #bjj74 ,the electroscope is now charged positively by induction4 ,if the charged rubber rod is brought to about #cj cm4 from the electroscope1 its leaves tend to move together4 ,if a body charged similarly to the electroscope or positively1 is moved toward the electroscope the leaves separate further4 ,this behavior of the electroscope enables one to determine the kind of charge upon a body4 ,two principles of electrostatic induction may now be stated3 7#a7 ,two equal1 unlike charges are always produced by electrostatic induction4 7#b7 ,if the body affected by induction is connected to the earth by a conductor1 the repelled or free charge is conducted away from the body while the bound charge is held by the inducing charge4 ,these principles apply in every case of induction4 ,important ,topics #a4 ,electric lines of force4 ,characteristics 7#c74 #b4 ,electrostatic induction4 ,principles 7#b74 #c4 ,charging by induction4 ,explanation4 ,exercises #a4 ,what are electric lines of force8 ,where are they found8 ,what does the arrow mean upon the lines8 #b4 ,name three effects produced by electric fields4 #c4 ,does electrostatic induction occur outside of laboratories8 ,where8 ,when8 #d4 ,given a charged rubber rod1 how may one charge from it by induction1 insulated brass shells1 giving some a positive and some a negative charge8 #e4 ,how may the charges upon the shells be tested8 #f4 ,in charging an electroscope by induction1 why must the finger be removed before the glass rod8 #g4 ,why is it best to have the rubber and glass rods1 used in electrification1 warmer than the air of the room in which the experiments are being performed8 #h4 ,when a sharp metallic point is held near the knob of a charged electroscope the leaves quickly come together4 ,explain4 #i4 ,might one of the members of your class in physics be charged with electricity1 if he should stand on a board supported by dry glass insulators8 ,explain4 #aj4 ,if a metal can is charged strongly while standing on an insulator1 tests made by means of the proof-plane and electroscope show no charge on the inside4 ,explain4 7#c7 ,,electrical ,,theories ,,and ,,distribution ,,of ,,charges #bbb4 ,franklin's ,theory of ,electricity4--,we have studied the production of electrification by friction and induction4 ,it will be helpful now to consider some of the theories of electricity4 ,from the ease with which electrification moves1 along a conductor1 many have imagined that electricity is a fluid4 ,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 amount4 ,this theory led to representing positive electrification by a plus 77 sign and negative1 by a minus 7-7 sign4 ,these signs are in general use to-day4 ,the use and significance of these signs should be clearly fixed in mind4 #bbc4 ,the ,electron ,theory4--,various discoveries and experiments made in recent years indicate1 however1 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 prevented4 ,this theory1 sometimes called the ,electron ,theory1 holds that each atom of a substance has as a nucleus a corpuscle of positive electricity1 and surrounding it1 minute negative corpuscles or electrons4 ,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 rapidity4 ,ordinarily1 the positive and negative charges are equal so that the atom is in a neutral or uncharged condition4 ,by the action of various forces some of the negative corpuscles within a conductor may be moved from molecule to molecule4 ,thus if a negatively charged rod is brought near a conductor1 many electrons stream away to the far end charging it negatively1 while the nearer end of the conductor is left with fewer electrons than usual along with the fixed positive corpuscles4 ,hence the near end is positively charged4 7,see ,fig4 #aih47 ,on the other hand1 if a positive charge is used1 it attracts the electrons from the far end1 leaving the immovable positive corpuscles there1 and that end becomes positively electrified1 while the nearer end with its surplus of electrons is1 of course1 negatively electrified4 ,the ,electron ,theory is considered well founded since the electrons have 7a7 had their mass determined1 7b7 their speed measured1 7c7 their electric charge determined1 7d7 and their behavior while passing through magnetic and electric fields observed4 ,these facts and other experimental evidence have demonstrated the existence of electrons4 ,the positive corpuscle has not been directly observed but is assumed to exist to account for the effects observed in induction1 charging by friction1 etc4 #bbd4 ,distribution of an ,electric ,charge upon a ,conductor4--,we have applied the electron theory in explaining the phenomenon of electrostatic induction4 ,let us now use it in studying the distribution of an electric charge upon a conductor4 ,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 it4 7,see ,fig4 #bja47 ,on now taking a proof plane and attempting to obtain a charge from the interior of the vessel no result is found1 while a charge is readily obtained from the outside of the dish4 ,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 vessel4 ,this same condition is also true of a dish made of woven wire4 ,if the charged conductor is not spherical in outline1 an uneven distribution of the charge is observed4 ,thus if an egg-shaped conductor is insulated and charged 7see ,fig4 #bjb71 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 latter4 ,if now a charge be taken from the pointed end by the proof plane to the uncharged electroscope1 a greater spreading of the leaves than before will be noticed4 ,this indicates that the electricity may be unevenly distributed over the surface of a body4 ,it is found that the electric density1 as it is called1 is greatest where the surface curves most sharply4 ,at a very sharp curve1 as at a point1 the electric density may be so great that a part of the charge escapes into the air4 7,see ,fig4 #bjc47 ,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 avoided4 ,while conductors1 such as lightning rods1 which are designed to facilitate the escape of electric charges1 are provided with a number of sharp points at the end or elsewhere4 ,at such points1 air particles are drawn forcibly against the point and after being charged are driven away strongly1 creating the so-called electrical wind which carries away the charge at a rapid rate4 7,see ,fig4 #bjc47 ,illustration3 ,,fig4 #bja4--,no charge is found inside a hollow vessel4 ,illustration3 ,,fig4 #bjb4--,more charge at the pointed end4 #bbe4 ,lightning and ,electricity4--,the fact that lightning is an electrical discharge was first shown in #ageb by ,benjamin ,franklin1 who drew electric charges from a cloud by flying a kite in a thunderstorm4 ,with the electricity which passed down the kite string he performed a number of electrical experiments4 ,this discovery made ,franklin famous among scientific men everywhere4 ,franklin then suggested the use of lightning rods to protect buildings from lightning4 ,these rods act as conductors for the electric discharge and thus prevent it from passing through the building1 with the risk of overheating some part and setting the latter on fire4 ,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 beneath4 ,illustration3 ,,fig4 #bjc4--;,electrical wind produced by a pointed conductor4 ,illustration3 ,,fig4 #bjd4--;,electrical whirl4 ,the reaction from the electrical wind causes it to revolve4 ,illustration3 ,,fig #bje4 ,the wire screen protects the electroscope4 ,the charge in an electrified cloud acts inductively upon the earth beneath1 attracting an opposite charge to the objects below4 ,the discharge from the cloud often passes to the objects beneath1 such as trees or buildings4 ,thunder is believed to be due to the sudden expansion of the air when intensely heated by the electric discharge and its sudden contraction1 like a slap1 as the track instantly cools4 ,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 surfaces4 #bbf4 ,an electric screen is a device for cutting off the influence of an electric charge4 ,faraday found that if a sensitive electroscope is surrounded by a wire mesh screen 7see ,fig4 #bje71 no evidence of electrification could be found inside4 ,in other words1 a network of conductors on a building makes the best protection against lightning1 provided it is connected to the earth by good conductors at several places4 ,important ,topics #a4 ,electrical theories4 ,evidences for electron theory4 #b4 ,how is the theory used in explaining induction8 #c4 ,charges1 and distribution on conductors 7effect of shape74 #d4 ,lightning3 cause1 effects1 lightning rods4 ,exercises #a4 ,in what respects is ,franklin's one-fluid theory like the electron theory8 ,in what respects different8 #b4 ,consider two shells charged by induction from an electrified rubber rod1 one positively and one negatively4 ,explain the process1 using the ideas of the electron theory4 #c4 ,should the metal top of an electroscope have sharp corners8 ,explain4 #d4 ,would a tall steel tower have the same need of a lightning rod as a brick chimney of the same height8 ,explain4 #e4 ,will a solid sphere hold a greater charge of electricity than a hollow one of the same diameter8 ,explain4 #f4 ,if a positively charged cloud floats over a tree which is a good conductor of electricity will the tree be charged8 ,show diagram4 ,explain4 7#d7 ,,potential1 ,,capacity ,,and ,,the ,,electric ,,condenser #bbg4 ,conditions ,causing a ,movement of ,electricity4--,in the study of conductors and insulators it was observed that an electric charge moved along the conducting rod to the electroscope4 ,this movement of electricity along a conductor is a result of great practical importance4 ,we will now consider the conditions that produce the flow or current of electricity4 ,let two electroscopes stand near each other4 ,charge one1 ,c 7,fig4 #bjf71 strongly and charge the other slightly4 ,if now a light stiff wire attached to a stick of sealing wax be placed so as to connect the tops of the electroscopes1 the leaves of ,c will partly close while those of ,d will open slightly1 thus indicating a movement of electricity from ,c to ,d along the wire4 ,the movement was from a place of greater degree of electrification to one of less4 ,illustration3 ,,fig4 #bjf4--;,electricity flows from high to low potential4 #bbh4 ,potential4--,the potential of an electrified body is its degree of electrification4 ,therefore1 it is said that electroscope ,c mentioned above has a greater potential than electroscope ,d4 ,the movement of electricity is from a place of greater or high potential to one of lesser or low potential4 ,if two bodies are at the same potential there will be found no movement of electricity between them4 ,a difference of potential between two points connected by a conductor is therefore the necessary condition for an electric current4 ,just as heat is transmitted along a conductor from a place of high to one of lower temperature1 so electricity is transmitted along a conductor from a place of high to one of low potential4 ,thus potential in electricity corresponds to temperature in heat4 ,one is the degree of electrification1 the other1 the degree of hotness4 ,illustration3 ,,fig4 #bjg4--;,air pressure apparatus to illustrate electrical pressure4 #bbi4 ,electrical pressure is a term sometimes used for difference of potential4 ,to better understand electrical pressure consider three round tanks 7,fig4 #bjg7 containing air4 ,a is a tank holding air at #aj lbs4 pressure per square inch1 above atmospheric pressure1 ,b is open to the air and hence is at atmospheric pressure while ,c has a partial vacuum1 with #aj lbs4 less pressure than that of the atmosphere4 ,if the valve at ,d or ,e is opened a flow of air sets up until the pressures are equalized4 ,while if the pump at ,p is working a difference in pressure is easily maintained4 ,tank ,a corresponds to an insulated body charged to a high positive potential2 tank ,b1 open to the air1 a body connected to the earth2 while tank ,c represents a body having a negative potential4 ,the earth is said to have zero potential4 ,now just as compressed air will be pushed into the atmosphere 7as from ,a to ,b7 while air at atmospheric pressure will if possible be forced itself into a partial vacuum 7as from ,b to ,c71 so electricity at a positive potential will tend to move to a place at zero potential1 while that at zero potential tends to move to a place of negative potential4 ,bodies at the same potential as the earth1 or at zero potential1 are also said to be neutral4 ,those positively electrified have a positive potential1 those negatively electrified have a negative potential4 ,as in gases1 movement always tends from higher pressure 7potential7 to lower pressure 7potential74 ,illustration3 ,,fig4 #bjh4--,the metal plate gives the electroscope a greater surface and hence greater capacity4 #bcj4 ,capacity4--,if we have a #ajj-;gallon tank and a #aj-;gallon tank connected by a pipe both filled with compressed air1 the larger tank will contain ten times as much air as the smaller at the same pressure since it has ten times the capacity1 or1 if the two tanks are separated and the same amount of air is contained in each1 the pressure of the air contained in the small tank will be ten times that in the large one4 ,the electrical capacity of a conductor is in some respects similar to the capacity of a tank for air4 ,since1 however1 electrical charges are upon the surface of a body1 its capacity depends in part upon the extent of surface4 ,for example1 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 noticed4 ,if a circular metal plate several times the diameter of the top of the electroscope is laid upon the latter 7see ,fig4 #bjh71 and a charge equal to that used before is brought to the electroscope1 the leaves show less divergence than before1 showing that the same charge gives a lower potential when placed upon a body of greater capacity4 ,illustration3 ,,fig4 #bji4--;,a plate condenser4 ,illustration3 ,,fig4 #baj4--;,a condenser of several plates4 #bca4 ,the electric condenser is a device having a large electrical capacity consisting of parallel conductors separated by good insulators4 ,it has been devised to enable one to obtain a large electrical charge upon a body of convenient size4 ,such an apparatus is of great practical value in many experiments and operations4 ,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 it4 ,in its simplest form it consists of two parallel conductors separated from each other 7,fig4 #bji74 ,the upper plate has been charged negatively4 ,this has given the lower plate a positive charge by induction1 since the latter is connected to the earth4 ,these positive and negative charges hold or bind each other so that a large quantity may be accumulated4 ,to increase the capacity of a condenser1 several plates are used connected as in ,fig4 #baj4 ,it is a curious fact that the kind of insulator between the charged conductors of a condenser affects its capacity4 ,thus if glass1 paraffine1 or beeswax is between the plates instead of air1 the plates will hold more electricity at the same potential4 ,for this reason condenser plates are often separated by sheets of glass1 paraffined paper1 or mica4 ,illustration3 ,,fig4 #baa4--;,a ,leyden jar and a discharger4 #bcb4 ,the ,leyden ,jar4--,a convenient form of condenser1 used as long ago as #agde1 is the ,leyden jar4 ,it consists of a glass jar 7,fig4 #baa7 coated part way up1 inside and out1 with tinfoil4 ,the inner coating is connected by a chain to a knob at the top4 ,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 electricity4 ,the other kind of charge is developed by induction upon the outer coating1 and each charge binds the other4 ,to discharge a jar1 a conductor1 as a wire1 is connected first to the outer coating and held there while the other end is brought to the knob at the top4 ,a bright spark is produced when the two charges combine4 ,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 present4 #bcc4 ,oscillatory ,discharge4--,the discharge from a ,leyden jar is an interesting phenomenon4 ,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 first1 then a rush of electricity in the opposite direction occurs4 ,this alternation continues several times and constitutes what is called the oscillatory discharge4 7,see ,fig4 #dad47 ,this oscillatory discharge sets up waves in the ether4 ,these are called ,hertzian waves in honor of their discoverer1 ,heinrich ,hertz4 ,they are the ether waves used in wireless telegraphy4 ,a lightning flash has been shown by photographs and by other means to be oscillatory4 ,this fact supports the idea that the electrical conditions just preceding the stroke of lightning reproduce a condenser on a large scale4 ,the charged cloud is the upper charged plate1 the earth beneath1 charged by induction from the cloud1 is the lower charged plate1 while the air between is the insulator or dielectric as it is sometimes called4 ,important ,topics #a4 ,potential3 high1 low1 zero1 positive1 negative1 similar to temperature and air pressure4 #b4 ,capacity affected by 7#a7 area1 7#b7 induction4 #c4 ,condensers1 ,leyden jar1 parallel plate4 #d4 ,oscillatory discharge1 conditions1 results4 ,exercises #a4 ,is the air a conductor8 ,explain4 #b4 ,can the ,leyden jar be strongly charged if the outer coat is insulated8 ,explain4 #c4 ,upon what two conditions does the capacity of a body depend8 ,how in each case8 #d4 ,would a lightning discharge produce wireless waves8 ,explain4 #e4 ,if a sharp tack be dropped point up on the plate of an electroscope the latter is quickly discharged4 ,explain4 7#e7 ,,electrostatic ,,generators #bcd4 ,static ,electric ,machines4--,many machines have been invented to produce larger quantities of static electricity than we have used in the experiments previously described4 ,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 it4 ,this machine was capable of producing powerful effects1 but it took much work to turn it1 and it has been abandoned for a more efficient device1 the static induction machine4 #bce4 ,the electrophorus is the simplest static induction generator1 consisting simply of a flat circular plate of some insulating material1 as paraffine1 shellac1 or rosin contained in a metal pan1 and a flat circular metal disc having an insulating handle4 ,illustration3 ,,fig4 #bab4--;,an electrophorus4 ,the electrophorus is used as follows3 ,the plate is first electrified by rubbing or beating with fur or a woolen cloth4 ,the plate will be found to be charged negatively4 ,the metal disc is placed upon the plate by holding the insulating handle4 ,the upper surface of the charged body is slightly uneven so that the disc touches but a few high points4 ,the greater part of the charged surface is separated from the metal disc by air1 a good insulator4 ,the charge therefore acts inductively upon the disc repelling negative electricity to the upper surface of the disc1 leaving the lower surface charged positively 7,fig4 #bab74 ,if now the finger is touched to the disc the repelled negative charge escapes and the whole disc is left positively charged4 ,the disc is now removed 7,fig4 #bac7 and the charge upon it may be tested or used in any desired manner4 ,the disc may be recharged many times without rubbing the plate again4 ,illustration3 ,,fig4 #bac4--;,electrophorus charged4 ,these electrical charges possess energy4 ,what is the source of this energy8 ,the answer may be determined by the following experiment4 ,place the disc upon the charged plate4 ,touch the disc with the finger to remove the repelled charge4 ,connect an electroscope to the disc by a fine wire4 ,nothing appears on the electroscope1 since the disc has been connected to the earth1 and is therefore at zero potential4 ,if now the disc is lifted slowly1 the leaves of the electroscope gradually separate1 showing that a charge of electricity appears when the disc is being lifted against the force of attraction between the two charges4 ,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 plate4 ,the electrical energy of the charge is therefore due to the work done in separating the two charges4 ,this electrical energy appears as heat and light1 when the disc is discharged4 ,it may be employed to ignite gas1 gunpowder1 etc4 #bcf4 ,the ,toepler-,holtz ,induction ,machine4--,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 machines1 in lecture demonstrations1 etc4 ,this machine 7,fig4 #bad7 consists of two discs3 one fixed1 the other mounted so as to revolve4 ,upon the back of the fixed plate are two sectors of tinfoil which become charged oppositely4 ,upon the revolving plate are six metallic discs4 ,these discs act like the discs of the electrophorus4 ,they become charged by induction from the charges upon the sectors fastened to the fixed plate4 ,the brushes held by a rod touch the discs at just the right time to take off the repelled charge4 ,the charges induced upon the discs are taken off by two metal combs whose points are held close to the revolving disc4 ,the ,leyden jars assist in accumulating a good strong charge before a spark passes between the terminal knobs4 ,some machines are built up of several pairs of plates and give correspondingly large amounts of electricity4 ,illustration3 ,,fig4 #bad4--,the ,toepler-,holtz induction machine4 ,important ,topics ,static ,electric ,generators4--7a7 plate friction machine1 7b7 electrophorus1 7c7 induction or influence machine4 ,exercises #a4 ,potential is similar to what other terms that we have studied8 #b4 ,what three electrical phenomena are better understood from a study of the lines of force8 #c4 ,how many charges may be produced by an electrophorus before the plate needs to be electrified again8 ,explain4 #d4 ,the static induction machine is often called a continuous electrophorous4 ,why8 #e4 ,the ,leyden jars used with the induction machine cause much brighter sparks to be produced than without them4 ,explain4 #f4 ,with the ,leyden jars removed1 would the frequency with which the sparks pass between the knobs be increased or decreased8 ,explain4 #g4 ,mention three likenesses and three differences between magnetism and static electricity4 #h4 ,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 glass8 ,explain4 #i4 ,in what way may an electric charge be divided into three equal parts8 ,review ,outline3 ,magnetism and ,static ,electricity ,comparison between ,magnetism and ,static ,electricity4 ,substances are3 magnetic1 conductors1 non-magnetic4 insulators4 ,produced by3 induction4 friction1 or induction4 ,theory3 molecular4 electron4 7fluid7 attraction1 attraction1 ,fields of ,force repulsion1 repulsion1 ,explain3 induction1 induction4 action of compass4 magnetoscope1 dip1 electroscope1 electron1 declination1 pole1 positive1 negative1 retentivity1 potential1 capacity1 ,terms3 permeability1 condenser1 electrophorus1 lodestone1 oscillatory discharge1 magnetic meridian4 lightning4 ,likeness3 a--produced by induction1 b--attract both are3 and repel1 c--have fields of force4 a--electricity can be conducted1 magnetism cannot4 ,differences3 b--electricity in all substances1 magnetism in few4 c--magnetism with the compass indicates direction4 ,,chapter ,,xi ,,current ,,electricity 7#a7 ,,electrical ,,currents ,,and ,,circuits #bcg4 ,sources of ,electric ,currents4--,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 wire4 ,this movement of electricity is called an electric current 7,art4 #bbg74 ,a difference of potential is therefore often called an electromotive force 7,e4,m4,f471 since it produces the movement of electricity in a conductor4 ,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 bodies4 ,that is1 some device must be used to restore the difference in potential as fast as the conducting wire equalizes it4 ,the continual charging of the bodies takes work4 ,in other words1 it requires a continual expenditure of some form of energy 7which is converted into electrical energy7 to produce the electric current4 ,two forms of energy are commonly used for this purpose4 7,a7 ,chemical energy is employed in voltaic cells for producing electric currents4 7,b7 ,mechanical energy is used for the same purpose in the dynamo and similar devices4 #bch4 ,the voltaic cell is named after ,volta1 an ,italian physicist1 who in #ahjj invented it4 ,in its simplest form it consists of a strip of copper and a strip of zinc placed in dilute sulphuric acid 7one part acid to fifteen or twenty of water7 7,fig4 #bae74 ,by the use of sensitive apparatus1 it can be shown that the copper plate of the voltaic cell has a positive charge and the zinc plate a negative charge4 ,for example1 let a flat plate #aj cm4 in diameter be placed upon the knob of an electroscope and a similar plate1 coated with shellac and provided with an insulating handle1 be set upon it to form a condenser4 7,see ,fig4 #baf47 ,if now wires from the two plates of a simple voltaic cell be respectively connected to the plates of the condenser1 charges from the copper and zinc plates will accumulate upon the two condenser plates4 ,now remove the wires and lift the upper plate4 ,the bound charge upon the lower plate will spread over the leaves and cause them to separate4 ,upon testing1 the charge from the zinc plate will be found to be negative and that from the copper plate1 positive4 ,since a positive charge is found upon the copper plate it is called the positive electrode2 the zinc plate is called the negative electrode4 ,illustration3 ,,fig4 #bae4--;,cross-section of a simple voltaic cell4 ,illustration3 ,,fig4 #baf4--,testing the charges upon the plates of a simple voltaic cell4 #bci4 ,test for an ,electric ,current4--,if the copper and zinc plates of a voltaic cell are connected by a wire1 a current of electricity is set up in the conductor4 ,evidence of the current may be obtained by holding the conducting wire over and parallel to the needle of a magnetoscope4 ,the needle is deflected by the action of the current parallel to it 7,fig4 #bag74 ,this magnetic effect of a current is the means usually employed for the detection and measurement of an electric current4 ,such a device which detects an electric current by its magnetic effect is called a galvanoscope1 in honor of ,galvani1 who in #aghf was the first to discover how to produce an electric current4 ,illustration3 ,,fig4 #bag4--,the magnetic needle is deflected by the current4 ,illustration3 ,,fig4 #bah4--;,diagram of an electric bell circuit4 #bdj4 ,the ,electric ,circuit4--,the entire conducting path along which a current of electricity flows is called an electric circuit4 ,in the case of a voltaic cell1 the circuit includes not only the wires connecting the plates but also the plates themselves and the liquid between them4 ,when some device or apparatus is to receive current from the cell1 it is attached to the plates and wires so that the device is a part of the electric circuit4 ,separating the circuit at any point is called breaking or opening the circuit1 while connecting the ends of an open circuit is called making or closing the circuit4 ,a device for opening and closing a circuit is called a key or switch4 ,the electric circuit used in ringing a door bell is familiar to most boys and girls4 ,this circuit is open most of the time4 ,it is closed by pressing the push-button at the door1 and the flow of current through the electric bell causes the latter to ring4 ,such a circuit is represented in ,fig4 #bah4 ,here ,c is the voltaic cell1 the two lines representing the plates of the cell4 ,a cross-section view of the push-button 7,p71 shows how the circuit is closed1 7,b7 is the bell4 ,wherever current electricity is used the device in which it is employed forms a part of an electric circuit extending back to some electric generator4 ,this generator must be able to continually produce an ,e4,m4,f41 or a difference of potential between its terminals1 in order that the movement of electricity may be continuous4 ,important ,topics 7a7 ,electric generators3 7#a7 voltaic cell uses chemical energy2 7#b7 dynamo uses mechanical energy4 7b7 ,electric circuits3 7#a7 open1 7#b7 closed1 7#c7 key and switch4 7c7 ,voltaic and galvanic electricity 7names74 7d7 ,galvanoscope1 uses4 ,exercises #a4 ,in what two ways are static and current electricity alike8 ,in what two different8 #b4 ,draw a diagram of an electric bell circuit at your home4 ,give the location of the electric bell1 the electric generator and the push-button4 ,show the connecting wires1 and explain briefly how the circuit is operated4 #c4 ,represent some other electric circuit1 naming the generator and other devices in the circuit4 #d4 ,look up the work of ,volta and ,galvani and write a statement of the electrical discoveries and inventions made by them4 7#b7 ,,the ,,voltaic ,,cell ,,and ,,its ,,action #bda4 ,the simple voltaic cell consists of a strip of copper and a strip of zinc placed in dilute sulphuric acid4 7,see ,fig4 #bai47 ,a short time after placing the plates in the acid1 bubbles of a gas 7hydrogen7 appear on the surface of the zinc4 ,these bubbles increase in size and some rise to the surface of the liquid4 ,nothing appears upon the copper plate4 ,if the tops of the plates are connected by a wire1 an electric current is set up through the wire and the cell1 and bubbles of gas also appear upon the copper as well as on the zinc4 ,in a short time the surface of the copper becomes coated with bubbles and the current becomes much weaker4 ,if the plates are left in the acid for some time the zinc is found to be eaten away1 having been dissolved in the acid through chemical action4 ,the copper1 however1 remains practically unaffected4 ,illustration3 ,,fig4 #bai4--;,a simple voltaic cell4 #bdb4 ,how the ,current is ,produced4--,to maintain the electric current a continual supply of energy is required4 ,this is furnished by the chemical action of the acid upon the zinc4 ,the chemical action is in several respects like combustion or burning1 by means of which chemical energy is transformed into heat energy4 ,in the voltaic cell the chemical action of the acid upon the zinc transforms chemical energy into electrical energy4 ,the ,e4,m4,f4 or difference of potential may be considered as originating at the surface of the zinc where the chemical action takes place4 ,at this point the zinc has the lower and the liquid in contact with it the higher potential4 ,the molecules of the acid are believed to be separated or broken up into two parts called ions2 one ion1 the ,,so#d or sulphion1 combines with the zinc forming zinc sulphate1 the other1 or hydrogen 7,h7 ion1 passes over to the copper plate1 and accumulates on the surface of this plate giving it a positive charge4 ,it is therefore called the positive ion4 ,the sulphion ion1 or ,,so#d ion1 carries a negative charge to the zinc4 ,it is therefore called the negative ion4 #bdc4 ,the ,direction of the ,current4,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 plate1 to the wire1 to the zinc plate1 to the starting point1 thus completing the electric circuit4 ,when the circuit is closed it is found that the movement of electricity starts in all parts of the circuit at practically the same instant4 ,k ,many scientists consider that current in a conductor consists of negative electrons flowing in a direction opposite to that described in ,art4 #bdc4 ,this is called the electron current1 as distinguished from the electric current described above4 ,illustration3 ,,fig4 #bbj4--;,a comparison of a voltaic cell and circuit to a water pump and connecting pipes4 #bdd4 ,the production of the current may be illustrated by describing a device for producing a continuous circulation of water4 ,thus let ,cu and ,zn represent two pipes connected by two horizontal tubes1 one at ,v provided with a valve and one at ,p with a rotary ,pump4 7,see ,fig4 #bbj47 ,suppose the pipes filled to the level of ,v and the pump started4 ,the pump will force water from ,zn to ,cu1 through ,p1 the level falling in ,zn and rising in ,cu4 ,if the valve ,v is open the water will flow back through ,v as long as the pump is working4 ,if ,v is closed1 the level in ,cu will rise as high as the driving force of the pump can send it4 ,if now ,v is opened1 the pump will maintain the water in circulation from ,cu to ,zn through ,v4 ,in the illustration1 the tubes ,cu and ,zn correspond to the conducting plates of copper and zinc of a voltaic cell4 ,the pump ,p represents the chemical action which produces the electrical pressure4 ,the upper pipe represents the part of the circuit outside of the cell1 the valve ,v corresponds to an electric key or switch which is used to open and close the electric circuit4 #bde4 ,polarization4--,in the simple voltaic cell1 after the circuit is closed1 bubbles of hydrogen collect upon the copper plate4 ,this accumulation of hydrogen gas is called polarization4 ,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 well4 ,some voltaic cells are made entirely free from this defect1 either 7a7 by the removal of the hydrogen as fast as it is formed1 or 7b7 by the use of such chemicals that no hydrogen is produced4 #bdf4 ,local ,action4--,it is noticed that when a strip of zinc is placed in dilute acid that bubbles appear upon the surface of the zinc4 ,the appearance of these bubbles indicates that some of the hydrogen ions carrying positive electricity have moved to the zinc plate4 ,careful examination of the plate after it has been in acid shows numerous black spots upon it4 ,these are bits of carbon4 ,they are always found in ordinary zinc4 ,small electric currents are set up which run from molecules of pure zinc into the liquid and back to the carbon particles1 thus forming small closed circuits4 7,see ,fig4 #bba47 ,the formation of these circuits from and to the zinc is called local action4 ,this action is a defect in voltaic cells since a part of the current is thus kept from passing through the main outside circuit1 and the zinc may be consumed even when no outside current is flowing4 ,illustration3 ,,fig4 #bba4--,local action4 #bdg4 ,amalgamation4--,local action is prevented by coating the zinc with mercury4 ,this process is called amalgamation4 ,the mercury covers the entire surface of the plate in the acid4 ,its action is to dissolve pure zinc and bring it to the outer surface where it is acted upon by the acid4 ,the carbon particles are kept covered so that no local currents can be formed as long as the bits of carbon are below the surface4 ,amalgamation therefore prevents local action4 ,important ,topics ,the ,simple ,voltaic ,cell #a4 ,two plates3 zinc1 copper2 electrolyte1 dilute sulphuric acid4 #b4 ,ions3 hydrogen1 positive3 sulphion1 negative4 #c4 ,current1 where and how produced1 direction1 illustration4 #d4 ,polarization3 cure1 local action1 cure4 ,exercises #a4 ,write in your own words an account of the production of an electric current by the simple voltaic cell4 ,use sketches4 #b4 ,which plate has the higher potential8 ,how is it produced8 #c4 ,would you expect to get an ,e4,m4,f4 by forming a cell of two copper plates8 ,why8 7#c7 ,,practical ,,voltaic ,,cells #bdh4 ,advantages of ,voltaic ,cells4--,many forms of voltaic cells have been devised4 ,several of the more common of these will be described and their electro-chemical action explained4 ,at the present time voltaic cells are employed only where small currents are needed1 such as for electric bells and induction coils4 ,where more than a small amount of current is required1 the dynamo and the storage battery have generally taken their place as sources of electric current4 ,the advantages of voltaic cells as electric generators are3 7a7 they are inexpensive1 7b7 they are easily taken from place to place1 7c7 they may be ready for instant use4 ,the most desirable voltaic cell would be one having the following qualities3 7a7 ,high electromotive force1 7b7 no polarization or local action1 7c7 very low internal resistance1 7d7 small expense1 both as to first cost and upkeep4 ,illustration3 ,,fig4 #bbb4--,the ,leclanch cell1 wet type4 #bdi4 ,the ,leclanch cell is the one commonly used for ringing door bells4 ,it has two plates3 one of zinc and the other of carbon4 ,these are placed in a solution of sal ammoniac 7,fig4 #bbb74 ,take up the desirable qualities mentioned at the end of the preceding paragraph4 7a7 ,it may be shown that this cell has a good ,e4,m4,f4 about #a4e volts4 7b7 ,it polarizes easily yet it recovers well when left upon open circuit4 ,usually a substance called manganese dioxide is mixed with the carbon4 ,this acts as a depolarizer1 that is1 it combines with the hydrogen to form water4 7c7 ,its resistance varies and is often considerable4 7d7 ,the expense for upkeep is small1 since a #e-;cent rod of zinc1 and a #e-;cent charge of sal ammoniac will keep the cell in action on a bell circuit from six months to a year or more4 ,it is well suited for use on open circuits that is1 where the circuit is open the greater part of the time and is closed only occasionally2 as in ringing door bells1 operating telephones1 and other devices whose circuits are usually open4 #bej4 ,the ,dry ,cell4--,many forms of ,leclanch cells are made4 ,one of these is called the dry cell 7,see ,fig4 #bbc47 ,in this cell the zinc plate is made into a jar or can and contains the other materials4 ,at the center of the cell is a rod of carbon and manganese dioxide4 ,the space between the carbon and zinc is filled with a porous material such as sawdust or plaster of ,paris4 ,a strong solution of sal ammoniac fills the porous material4 ,the top of the cell is sealed with pitch or wax to prevent evaporation4 ,the great advantage of this cell is that it may be used or carried in any position without danger of spilling its contents4 ,dry cells are often used to operate the spark coils of gas and gasoline engines4 ,the ,leclanch cell described in ,art4 #bdi is commonly known as the wet cell4 ,illustration3 ,,fig4 #bbc4--,the ,leclanch cell1 dry type4 ,illustration3 ,,fig4 #bbd4--,the ,daniell cell4 #bea4 ,the ,daniell ,cell4--,this cell is often used in laboratories1 and on closed circuits such as those connected with fire and burglar alarms and telegraph lines4 ,it has two plates of zinc and copper placed in two different liquids which are kept separated by a porous clay cup 7,fig4 #bbd74 ,the zinc rod is kept in a solution of zinc sulphate contained in the porous cup4 ,the copper plate is in a solution of copper sulphate filling the rest of the glass jar4 ,unlike the ,leclanch cell1 this one must be kept upon a closed circuit to do its best work1 as the two liquids mix when the circuit is open4 ,taking its qualities in order1 7a7 its ,e4,m4,f4 is about one volt1 7b7 it has no polarization since copper instead of hydrogen is deposited upon the copper plate4 ,therefore a uniform ,e4,m4,f4 may be obtained from it1 making it especially useful in laboratory experiments and tests4 7c7 ,its resistance is considerable and 7d7 it is more expensive to operate than the ,leclanch4 ,it is sometimes used upon closed circuits outside of laboratories as in burglar and fire alarms1 although in recent years1 the storage battery is taking its place for these purposes4 #beb4 ,the ,gravity ,cell4--,fig4 #bbe is like the ,daniell cell in most respects1 except that in this cell1 the zinc plate is held at the top of the jar in a solution of zinc sulphate while the copper plate is at the bottom1 surrounded by a solution of copper sulphate4 ,the solutions mix but slowly as the copper sulphate solution is denser and remains at the bottom4 ,this cell like the ,daniell must also be kept upon closed circuit4 ,on account of its simplicity and economy it is often used to operate telegraph instruments4 ,its qualities are similar to those of the ,daniell cell4 ,illustration3 ,,fig4 #bbe4--,the gravity cell4 #bec4 ,symbol for ,voltaic ,cells4--,in electrical diagrams1 the symbol employed to represent a voltaic cell is a short thick line near to and parallel to a longer thin one4 ,as in ,fig4 #bbf4 ,if several cells are to be represented the conventional symbol of the combination is represented as in ,fig4 #bbg4 ,a single cell and a group of cells are each frequently called a battery4 ,illustration3 ,,fig4 #bbf4--;,diagram of a single cell4 ,illustration3 ,,fig4 #bbg4--;,diagram of a group of cells4 #bed4 ,effects of ,electric ,currents4--,having studied some of the devices for producing an electric current1 let us now consider some of the effects caused by it4 ,these effects will be studied under three heads3 7a7 ,magnetic1 7b7 ,chemical1 and 7c7 ,heat effects4 ,devices or articles showing these effects known to most high school students are respectively3 7a7 the electromagnet 7b7 electro-plated silver ware and 7c7 electric heaters1 such as electric flat irons1 electric toasters1 etc4 ,the magnetic effect of an electric current was first detected by ,oersted at the ,university of ,copenhagen in #ahai4 ,it may be observed by holding a wire carrying a current from a voltaic cell above and parallel to the needle of a magnetoscope4 ,the needle is at once deflected 7,fig4 #bbh74 ,if the current is reversed in direction the magnetoscope needle is deflected in the reverse direction4 ,this simple device is the most common means for detecting an electric current4 ,it therefore constitutes a galvanoscope4 7,see ,art4 #bci47 ,illustration3 ,,fig4 #bbh4--;,a galvanoscope4 ,important ,topics #a4 ,leclanch cells1 7a71 wet1 7b71 dry1 construction1 advantages1 uses4 #b4 ,daniell and gravity cells1 construction1 advantages1 uses4 #c4 ,three effects of electric currents1 illustrations4 #d4 ,the galvanoscope1 uses4 ,exercises #a4 ,explain how the direction of current in a wire can be determined by a compass4 #b4 ,would you expect to obtain a current from a zinc and copper cell containing a solution of common salt8 ,perform the experiment4 #c4 ,what conditions in a voltaic cell will give a steady electromotive force4 #d4 ,what conditions in a voltaic cell will give a strong electromotive force4 #e4 ,name three different electric circuits that you know exist4 ,which are open and which are closed circuits8 #f4 ,are voltaic cells used in your home8 ,if so1 for what purpose are they used8 ,on open or closed circuits8 ,have you seen them8 what kind are they8 ,,chapter ,,xii ,,the ,,magnetic ,,effect ,,of ,,electric ,,currents4 ,,electrical ,,measurements 7#a7 ,,the ,,magnetic ,,effect ,,of ,,electric ,,currents #bee4 ,the ,magnetic ,effect4--,of all the effects of electric currents1 it is generally conceded that the magnetic effect is the one of greatest practical importance1 and it is also the one most extensively used4 ,an experiment illustrating this effect has been described in ,art4 #bci4 ,this experiment shows that an electric current1 if parallel to a magnetic needle1 and near it will deflect the north-seeking pole of the needle to the right or left depending upon the direction of the current flow4 ,this deflection of the magnetic needle is due to the fact that surrounding every electric current are magnetic lines of force4 ,it is this magnetic field of the current that causes the needle to turn4 ,the position taken by the needle is the resultant of the forces of two magnetic fields2 one1 the earth's field1 the other1 that of the current4 #bef4 ,right-hand ,rule for a ,conductor4--,to show the presence of the magnetic field about a current1 pass a thick copper wire vertically through a sheet of paper1 and connect the ends of the wire to a source of current4 ,while the current 7this should be as much as #aj amperes if possible7 is flowing1 sprinkle iron filings upon the paper and tap gently4 ,the filings will arrange themselves in circles about the wire showing the magnetic field4 7,see ,fig4 #bbi47 ,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 determined4 ,the following rule is helpful and should be memorized3 ,grasp the conductor with the right hand with the outstretched thumb in the direction that the current is flowing4 ,the fingers will then encircle the wire in the direction of the lines of force4 ,this rule may be reversed1 for1 if the fingers of the right hand grasp the wire so as to point with the magnetic field1 then the current flows in the direction in which the thumb points4 7,see ,fig4 #bcj47 ,illustration3 ,,fig4 #bbi4--,magnetic field about a wire carrying an electric current4 ,illustration3 ,,fig4 #bcj4--,right-hand rule for the magnetic field of a current4 #beg4 ,magnetic ,field of a ,helix4--,if a wire be wound about a cylinder to form a cylindrical coil with parallel turns1 it forms a helix or solenoid4 ,the shape of the magnetic field about a current depends upon the form of the conductor4 ,if the latter is in the form of a helix its magnetic field resembles that of a straight bar magnet4 7,see ,fig4 #bca74 ,in fact the helix has the properties of a magnet with north- and south-seeking poles while a current is flowing through it4 ,if such a coil is suspended so as to turn freely1 it tends to turn until the field within it is parallel to the earth's magnetic field4 ,such a suspended helix may therefore be used as a compass4 ,in order to strengthen the magnetic field of a helix or solenoid1 the space within its turns is filled with iron1 often in the form of small soft-iron wires4 ,this bundle of iron wire is called the core of the helix4 ,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 stopped4 ,the direction of the current in a helix 7,fig4 #bcb7 or the polarity of its core may be determined by another right-hand rule4 ,if the helix is grasped with the right hand so that the fingers point in the direction in which the current is flowing1 the extended thumb will point in the direction of the north pole of the helix4 ,on the other hand1 if the poles of the helix are known1 then1 when the helix is grasped with the right hand so that the thumb points to the north-seeking pole1 the current is flowing in the wires in the direction that the fingers point4 ,illustration3 ,,fig4 #bca4--,the magnetic field of a helix4 ,illustration3 ,,fig4 #bcb4--,right-hand rule for a helix4 #beh4 ,the ,electromagnet4--,these right-hand rules are applied in many different devices4 ,among these1 perhaps the most important is the electromagnet1 which is used in the electric bell1 the telegraph1 the telephone1 the dynamo1 the motor1 and many other electric contrivances4 ,the electromagnet is defined as a mass of iron around which is placed a helix for conducting an electric current4 ,on account of its large permeability1 the iron core of the helix adds greatly to the effectiveness of the electromagnet1 since the magnetism of the iron is added to that of the current in the helix4 ,the magnetism remaining in the iron after the current stops is called the residual magnetism4 ,the residual magnetism is small when the core is made of small wires or thin plates1 but is larger when the iron core is solid4 ,like artificial steel magnets1 electromagnets are usually of two forms1 bar and horseshoe4 7,see ,figs4 #bcc and #bcd47 ,for most purposes the horseshoe form is the more effective since it permits a complete iron circuit for the magnetic lines of force4 7,see ,fig4 #bce47 ,this is the form used in the electric bell1 in the telegraph sounder1 and in lifting magnets4 7,see ,fig4 #bcf47 ,illustration3 ,,fig4 #bcc4--;,a bar electromagnet4 ,illustration3 ,,fig4 #bcd4--;,a horseshoe electromagnet4 ,illustration3 ,,fig4 #bce4--;,a horseshoe electromagnet may have a complete iron circuit for its lines of force4 ,illustration3 ,,fig4 #bcf4--;,a lifting magnet4 #bei4 ,effective ,electromagnets4--,the magnetic effect of a current in a helix is small1 hence the force usually is increased by inserting a core of iron4 ,when at first man tried to signal with electromagnets at a distance it was found that the current would not work the electromagnet4 ,an ,american by the name of ,joseph ,henry discovered the remedy for this condition4 ,he found that if the copper wire was insulated by wrapping silk thread about it1 and then many layers of the silk insulated wire were wound upon a spool with an iron core1 that the magnet would work at a great distance from the source of current4 ,if the current is increased1 the magnet is stronger than at first4 ,thus an electromagnet may be made stronger by 7a7 increasing the number of turns of wire in its coils and by 7b7 sending a stronger current through it4 ,illustration3 ,,fig4 #bcg4--;,a simple telegraph circuit4 #bfj4 ,the ,telegraph4--,the invention of an effective electromagnet by ,henry made possible the electric telegraph4 ,in its simplest form it consists of a battery1 ,c1 a key1 ,k1 and a sounder1 ,s1 with connecting wires4 7,see ,fig4 #bcg47 ,the sounder 7,fig4 #bch7 contains a horseshoe electromagnet and a bar of soft iron across its poles called an armature1 ,a1 attached to a lever ,l4 ,when the key is closed1 the electromagnet draws down the armature and lever until the latter hits a stop ,o1 making a click4 ,when the key is raised1 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 click4 ,closing and opening the circuit at ,k will start and stop the current which operates ,s which may be #ajj miles or more from ,k4 ,one voltaic cell will work a sounder in the same room4 ,but if many miles of wire are in the circuit1 the ,e4,m4,f4 of a single cell will not force sufficient current through the long wire to operate the sounder4 ,illustration3 ,,fig4 #bch4--;,a telegraph sounder4 ,illustration3 ,,fig4 #bci4--;,a telegraph relay4 ,illustration3 ,,fig4 #bdj4--;,how the relay is used4 ,illustration3 ,samuel ,f4 ,b4 ,morse 7#agia-ahgb74 ,inventor of the electromagnetic recording telegraph and of the dot and dash alphabet4 ,,samuel ,f4 ,b4 ,,morse ,from ,appleton's ,cyclopedia of ,american ,biography1 ,copyright #ahhh by ,d4 ,appleton ,co4 ,illustration3 ,thomas ,a4 ,edison1 ,orange1 ,new ,jersey4 ,invented the incandescent lamp2 phonograph2 moving picture2 most noted inventor of electrical appliances of the present day4 ,,thomas ,a4 ,,edison ,copyright1 ,photographische ,gessellschaft1 and ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,a battery of several cells is then required4 ,even a large battery is insufficient to operate a long line containing many sounders in circuit4 ,recourse is therefore usually made to a more sensitive device called a relay4 7,see ,fig4 #bci47 ,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 battery4 7,see ,fig4 #bdj47 when the current in the main circuit is stopped1 the armature of the relay is drawn back by a light spring4 ,this opens the local circuit4 ,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 line4 ,it is thus possible for a small current in the main line by the use of a relay1 to close and open a second local circuit containing a local battery and sounder4 ,modern telegraph lines are operated in this manner4 ,illustration3 ,,fig4 #bda4--;,an electric bell and its circuit4 #bfa4 ,the electric bell 7see ,fig4 #bda71 consists of an electromagnet1 ,m1 a soft iron armature1 ,a1 attached to the tapper1 ,t1 and a post1 ,r4 ,when no current is flowing a spring at ,s holds the armature against the post ,r4 ,when current flows through the helix1 its core becomes magnetized and attracts the armature1 drawing it away from the post1 ,r1 and causing the tapper to hit the bell4 ,drawing ,a away from the post1 however1 breaks the circuit at ,r and the current stops4 ,the magnetism in the core disappears releasing the armature1 which is then pulled back by the spring ,s against the post ,r4 ,this completes the circuit and the process repeats itself several times a second as long as the current flows4 ,illustration3 ,,fig4 #bdb4--,magnetizing by the discharge of a ,leyden jar4 #bfb4 ,static and ,current ,electricity ,compared4--,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 needle4 ,if a ,leyden jar 7see ,fig4 #bdb7 is discharged through the coil the steel needle is usually found to be magnetized1 showing that the discharge of the static electricity has a magnetic effect similar to that of an electric current4 ,sometimes a given end of the needle has a north pole and at other times a south pole4 ,this is believed to indicate that the charge of the ,leyden jar is oscillatory1 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 needle4 ,compare this action with that described in ,art4 #bcc4 ,important ,topics #a4 ,right-hand rules1 for conductor1 for helix4 #b4 ,the electromagnet1 two forms1 where used8 #c4 ,likeness between static and current electricity4 #d4 ,the electric bell1 parts1 action4 #e4 ,the telegraph1 key1 sounder1 relay4 ,exercises #a4 ,what is the difference between an electric charge and a current8 #b4 ,how can a magnetic effect be produced from an electric charge8 #c4 ,what is a magnetic field8 ,give two evidences of a magnetic field about a current in a wire8 #d4 ,a current is flowing north in trolley wire1 what is the direction of the magnetic field under the wire8 ,explain4 #e4 ,what would be the result if a hard steel core were placed in the electromagnet8 ,explain4 #f4 ,if the north-seeking pole of a helix is facing you1 does the current in the coils before you move in a clockwise or in a counter-clockwise direction8 ,explain4 #g4 ,a helix is placed horizontally with its north-seeking pole toward the north4 ,does the current in the wire at the top of the helix move east or west8 ,explain4 #h4 ,state at least six conditions any one of which will put an electric bell circuit out of commission4 #i4 ,if one desires to insert a battery into a telegraph circuit already in operation1 how will he determine the direction of the current in the wire8 #aj4 ,if a boy who had magnetized his knife blade in a physics laboratory1 pointed end south-seeking1 should lose his way in the woods on a cloudy day1 how could he determine his way out8 #aa4 ,at a certain point the earth's field acts north1 that of an electric current1 east4 ,the magnetoscope needle points exactly northeast when placed at that point4 ,how do the two magnetic fields compare8 7#b7 ,,electrical ,,measurements #bfc4 ,galvanometers4--,in using electric currents it is often necessary or desirable to be able to know not only that a given current is weak or strong1 but precisely what its strength is4 ,we can determine the relative strengths of two currents by the use of a galvanometer4 ,illustration3 ,,fig4 #bdc4--,the magnet is at the center of the coil4 ,illustration3 ,,fig4 #bdd4--;,a moving-magnet 7tangent7 galvanometer4 ,the older or moving-magnet type of galvanometer is similar to the galvanoscope mentioned in ,art4 #bci4 ,it consists of a magnetic needle mounted at the center of a coil of wire4 ,the coil is placed facing east and west1 so that the needle will be held by the earth's magnetic field parallel to the plane of the coil4 ,when a current is sent through the coil a magnetic field is produced within it4 ,this deflects the needle1 its north end turning east or west depending upon the direction of the current4 7,see ,fig4 #bdc47 ,the coils of a moving-magnet or tangent galvanometer 7see ,fig4 #bdd7 are large and firmly fastened to the base1 while the magnet is small4 ,the moving-coil type of galvanometer 7see ,fig4 #bde7 consists of a large magnet fastened to the frame of the device4 ,the magnet usually has a horseshoe form to produce as strong a field as possible4 ,the coil is wound on a light rectangular frame and is suspended between the two poles of the magnet4 ,to concentrate the magnetic field1 a cylinder of soft iron is usually placed within the coil4 ,fig4 #bdf represents a common form of moving-coil galvanometer4 ,illustration3 ,,fig4 #bde4--,to illustrate the principle of the moving-coil galvanometer4 ,illustration3 ,,fig4 #bdf4--;,a moving-coil 7,d',arsonval7 galvanometer4 #bfd4 ,measurement of ,electric ,currents4--,a galvanometer enables one to compare electric currents4 ,to measure electric currents it is necessary to employ a unit of electrical quantity1 just as in measuring the quantity of water delivered by a pipe1 a unit of liquid measure is employed2 thus1 e4g41 the current delivered by a given pipe may be #b gallons of water per second1 so in measuring the flow of an electric current one may speak of two coulombs per second4 ,the coulomb is the unit quantity of electricity just as the unit of quantity of water is the gallon4 ,for most practical purposes1 however1 we are more interested in the rate or intensity of flow of current than in the actual quantity delivered4 ,the unit of rate of flow or current is called the ampere4 ,in determining the exact quantity of an electric current1 physicists make use of a device called a coulomb meter4 7,see ,fig4 #bdg47 ,this contains a solution of silver nitrate in which are placed two silver plates4 ,the current to be measured is sent through the solution1 in at one plate and out at the other4 ,the plate where the current goes in1 the anode1 ,a 7,fig4 #bdg71 loses in weight since some of the silver is dissolved4 ,the plate where the current goes out1 the cathode1 ,c1 increases in weight since some of the silver is deposited4 ,by an international agreement1 the intensity of the current which deposits silver at the rate of #j4jjaaah g4 per second is #a ampere4 ,this is equal to #d4jbe g4 per hour4 ,illustration3 ,,fig4 #bdg4--;,a coulomb meter1 the anode ,a is separated from the cathode ,c by a porous cup4 ,the coulomb is defined as the quantity of electricity delivered by a current of one ampere during one second4 ,a #dj-watt-incandescent lamp takes about #j4d ampere of current4 ,an arc lamp takes from #f to #ae amperes4 ,a new dry cell may send #bj amperes through a testing meter4 ,a street car may take from #ej to #ajj amperes4 #bfe4 ,the ,ammeter4--,the method described above is not used ordinarily for measuring current strengths on account of its inconvenience4 ,the usual device employed is an ammeter4 ,this instrument is a moving-coil galvanometer4 ,it contains1 wound on a light form1 a coil of fine copper wire4 ,the form is mounted on jewel bearings between the poles of a strong permanent horseshoe magnet4 7,see ,fig4 #bdh47 ,as in other moving-coil galvanometers1 a soft iron cylinder within the form concentrates the field of the magnet4 ,the form and its coil is held in balance by two spiral springs which also conduct current into and out of the coil4 ,only a small part of the whole current measured1 in some cases only #j4jjja passes through the coil1 the larger part of the current passing through a metal wire or strip called a shunt,l 7see ,fig4 #bdh7 connecting the binding posts of the instrument4 ,a fixed fraction of the whole current flows through the coil4 ,its field crossing the field of the horseshoe magnet1 tends to turn until its turning force is balanced by the spiral springs4 ,as the coil turns it moves a pointer attached to it across a scale graduated to indicate the number of amperes in the whole current4 ,l ,a shunt is a conductor or coil connected in parallel with another conductor or circuit4 ,it carries a part of the current4 ,illustration3 ,,fig4 #bdh4--;,diagram of a commercial ammeter4 ,s is the shunt4 ,it should be noted that while all of the current measured passed through the ammeter1 but a small part goes through the coil4 #bff4 ,resistance of ,conductors4--,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 current4 ,for example1 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 wire1 it will be seen that less current flows when the long piece is used4 ,that is1 the long wire seems to hinder or to resist the passing of the current more than the short piece4 ,in other words1 the long wire is said to have more resistance4 ,the resistance of a conducting body is affected by several conditions4 7a7 ,it is directly proportional to the length of the conductor1 one hundred feet of wire having twice the resistance of fifty feet4 7b7 ,it is inversely proportional to the square of the diameter2 a wire #j4a inch in diameter has four times the resistance of a wire #j4b inch in diameter4 7c7 ,it differs with different substances1 iron having about six times as much as copper4 7d7 ,it varies with the temperature1 metals having greater resistance at a higher temperature4 ,since silver is the best conductor known1 the resistances of other substances are compared with it as a standard4 ,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 resistance4 ,purified substances arranged in order of increasing resistance for the same length and sectional area 7,ayrton-,mather7 are given on p4 #bid4 ,silver annealed #a4jj ,copper annealed from #a4jd to #a4ji ,aluminum annealed #a4fd ,nickel annealed #d4fi ,platinum annealed #f4ji ,iron annealed #f4ef ,german ,silver from #ab4hj to #bj4bj ,mercury #fc4cj ,nichrome #fg4ej ,carbon from #bgjj4jj to #fgjj4jj #bfg4 ,the ohm1 the unit of resistance1 is defined by international agreement as follows3 ,an ohm is the resistance of a column of pure mercury1 #ajf4c cm4 long with a cross-section of a square millimeter and at a temperature of #j;,c4 ,it should be noted that each of the four conditions affecting resistance is mentioned in the definition1 viz41 length1 cross-section1 material1 and temperature4 ,since it is inconvenient to handle mercury1 standard resistance coils1 made of an alloy of high resistance are used in comparing and measuring resistances4 ,a piece of copper wire ,no4 #bb 7diameter #j4fdd mm47 #fj4 #e ft4 long has a resistance of #a ohm4 ,see table p4 #bif4 ,the resistance of some telephone receivers is #ge ohms1 of a telegraph sounder1 #d ohms1 of a relay #bjj ohms4 #bfh4 ,resistance of ,circuits4--,every part of an electrical circuit possesses resistance4 ,in an electric-bell circuit1 for instance1 the wires1 the bell1 the push-button1 and the cell itself1 each offers a definite resistance to the passage of the current4 ,the resistance within the cell is termed internal resistance1 while the resistance of the parts outside of the electric generator is called external resistance4 #bfi4 ,electromotive ,force4--,in order to set in motion anything1 some force must be applied4 ,this is as true of electricity as of solids1 liquids1 or gases4 ,by analogy that which is exerted by a battery or by a dynamo in causing current to flow is called an electromotive force4 ,the unit of electromotive force1 the volt1 may be defined as the electromotive force that will drive a current of #a ampere through the resistance of #a ohm4 ,the electromotive force of a dry cell is about #a4e volts1 of a ,daniell cell #a4jh volts4 ,most electric light circuits in buildings carry current at #aaj or #bbj volts pressure4 ,currents for street cars have an electromotive force of from #eej to #ffj volts4 ,illustration3 ,,fig4 #bdi4--;,diagram of a commercial voltmeter4 #bgj4 ,the ,voltmeter4--,an instrument for measuring the electromotive force of electric currents is called a voltmeter 7,fig4 #bdi74 ,it is usually a moving-coil galvanometer1 and is always of high resistance4 ,it is like an ammeter in construction and appearance4 ,in fact1 a voltmeter is an ammeter which has had its shunt removed or disconnected4 ,in place of a shunt1 the voltmeter uses a coil of wire of high resistance 7see ,r1 ,fig4 #bdi7 in series with the galvanometer coil4 ,the high resistance of the voltmeter permits but a very small current to flow through it4 ,hence a voltmeter must be placed across a circuit and not in it4 ,in other words a voltmeter is connected in shunt1 while an ammeter is in series with the circuit as is shown in ,fig4 #bej4 ,,dimensions ,,and ,,functions ,,of ,,copper ,,wires ,column headings3 ,b3 ,b4 ,s4 gauge number ,,mm3 ,millimeters ,,sa3 ,sectional area in square millimeters ,,wl3 ,weight and length1 ,density #h4i1 feet per pound ,r3 ,resistance at #bd;,c41 feet per ohm ,c3 ,capacity in amperes ---------------------------------------- ---------------------- ,diameter ,b ------------- ,circular ,,sa ,,wl ,r ,c ,mils ,,mm mils ---------------------------------------- --------------------- #jjjjdfj4jjjaa4fhdbaa1fjj4jjajg4bai #a4efai1ibi4gjjcab4j #jjjdji4fdjaj4djeafg1hje4jj #he4jbh #a4igae1hjd4ijjbfb4j #jjcfd4hjj #i4bffacc1jgi4dj #fg4dca #b4diab1ecd4bjjbbj4j #jcbd4iej #h4bedaje1eib4ej #ec4dgj #c4ac #i1ide4cjjahe4j #bbeg4fcj #f4edd #ff1cgc4jj #cc4fca #d4ii #f1bea4djjaca4j #dbjd4caj #e4ahi #da1gdb4jj #ba4aea #g4ic #c1ica4fjj #ib4c #fafb4jbj #d4aae #bf1bej4ej #ac4cja #ab4fa #b1dgb4djj #fe4b #habh4dij #c4bfd #af1eji4jj #h4cff #bj4je #a1eee4jjj #df4a #ajaja4hij #b4ehh #aj1cha4jj #e4bfj #ca4ch #igg4hjj #cb4e #ab #hj4hjh #b4jec #f1ebi4ij #c4cji #ej4fi #fae4jbj #bc4j #ad #fd4jhd #a4fbh #d1ajf4hj #b4jha #hj4ei #chf4hjj #af4b #af #ej4hbj #a4bia #b1ehb4ij #a4cji #abh4ad #bdc4bej #aa4e #ah #dj4cjc #a4jbd #a1fbd4cj #j4hbc #bjc4gf #aeb4iij #h4a #bj #ca4ifa #j4hab #a1jba4ej #j4eagf #cbd4jj #if4baj #e4g #bb #be4cdg #j4fdd #fdb4gj #j4cbee #eae4ae #fj4eaj #d4j #bd #bj4ajj #j4eaa #ejd4ja #j4bjdg #hai4ba #ch4jej #b4h #bf #ae4idj #j4dje #bed4ja #j4abhh #a1cjb4fa #bc4icj #b4j #bh #ab4fda #j4cba #aei4gi #j4jhjig #b1jga4bb #ae4jej #a4d #cj #aj4jbe #j4bee #ajj4ej #j4jejib #c1bic4ig #i4dff #a4j #cb #g4iej #j4bjb #fc4bj #j4jcbjc #e1bcf4ff #e4ieb #j4gj #cd #f4cjd #j4afj #ci4gd #j4jbjad #h1cbh4cj #c4gdc #j4ej #cf #e4jjj #j4abg #be4jj #j4jabfgac1bch4hc #b4cee #j4ce #ch #c4ife #j4aja #ae4gb #j4jjgigbj1hed4fe #a4dha #j4be #dj #c4add #j4jhj #i4hi #j4jjejacc1age4id #j4ica #j4ag ---------------------------------------- --------------------- ,important ,topics 7#a7 ,galvanometers3 7#a7 moving magnet1 fixed coil2 7#b7 moving coil1 fixed magnet1 ammeter1 voltmeter4 7#b7 ,unit of quantity1 coulomb4 7#c7 ,unit of current1 ampere4 7#d7 ,unit of resistance1 ohm4 7#e7 ,unit of electromotive force1 volt4 ,exercises #a4 ,how will the resistance of #bj ft4 of ,no4 #bb ,german silver wire compare with that of #aj ft4 of ,no4 #bb copper wire8 ,explain4 #b4 ,where in a circuit is copper wire desirable8 ,where should ,german silver wire be used8 #c4 ,explain the action of the ammeter4 ,why does not the needle or coil swing the full distance with a small current8 #d4 ,why is a telegraph sounder more apt to work on a short line than upon a long one8 ,illustration3 ,,fig4 #bej4--,the ammeter is connected in series and the voltmeter in shunt4 #e4 ,find the resistance of #ae miles of copper telephone wire ,no4 #ab4 7,see table p4 #bif47 #f4 ,what will be the weight and resistance of #a1jjj feet of ,no4 #bj copper wire8 #g4 ,a storage battery sends #d amperes of current through a plating solution4 ,how much silver will it deposit in #b hours8 #h4 7a7 ,compare the diameters of ,no4 #bb and ,no4 #af copper wire4 7b7 ,compare the lengths of the same wires giving #a ohm resistance4 7c7 ,what relation exists between 7a7 and 7b78 #i4 ,why is an electric bell circuit usually open while a telegraph line circuit is usually closed8 #aj4 ,a copper wire and an iron wire of the same length are found to have the same resistance4 ,which is thicker8 ,why8 #aa4 ,why are electric bells usually arranged in parallel instead of in series8 #ab4 ,what would happen if a voltmeter were put in series in a line8 7#c7 ,,ohm',s ,,law ,,and ,,electrical ,,circuits #bga4 ,conditions ,affecting ,current ,flow4--,sometimes over a long circuit one cell will not work a telegraph sounder4 ,in such a case1 two1 three1 or more cells are connected so that the zinc of one is joined to the copper plate of the other4 ,when connected in this way the cells are said to be in series 7,fig4 #bea74 ,in the figure ,a represents a voltmeter4 ,it is found that when cells are in series the ,e4,m4,f4 of the battery is the sum of the electromotive forces of the cells4 ,an ammeter in the circuit shows increased current as the cells are added4 ,hence if the resistance of the circuit remains unchanged1 the greater the ,e4,m4,f4 the greater is the current strength4 ,in this respect1 the movement of electricity in a circuit is similar to the flow of water in a small pipe under pressure1 as in the latter the flow of water increases as the pressure becomes greater4 ,the current in a circuit may also be increased by lessening the resistance1 since the current through a long wire is less than that through a short one1 just as the flow of water will be greater through a short pipe than through a long one4 ,to increase the current flowing in an electric circuit1 one may therefore either increase the ,e4,m4,f4 or decrease the resistance4 ,illustration3 ,,fig4 #bea4--;,diagram of cells connected in series4 #bgb4 ,ohm's ,law4--,the relation between the electromotive force applied to a circuit1 its resistance1 and the current produced was discovered in #ahbg by ,george ,ohm4 ,ohm's law1 one of the most important laws of electricity1 states that1 in any circuit1 the current in amperes equals the electromotive force in volts divided by the resistance in ohms4 ,this principle is usually expressed thus3 ,current intensity electromotive force_/resistance or ,amperes volts_/ohms or ,i ,e_/,r ,illustration3 ,,fig4 #beb4--,the street cars are connected in parallel with each other4 #bgc4 ,resistance of ,conductors in ,series4--,a study of the resistance of conductors when alone and when grouped in various ways is of importance since1 the current flow through any circuit is dependent upon its resistance4 ,the two most common methods of combining several conductors in a circuit are in series and in parallel4 ,conductors are in series when all of the current passes through each of the conductors in turn 7,fig4 #bah71 thus the cell1 push-button1 wires1 and electric bell in an electric-bell circuit are in series4 ,conductors are in parallel when they are so connected that they are side by side and a part of the whole current goes through each4 ,none of the current that passes through one conductor can go through the conductors in parallel with it4 ,thus the electric street cars are in parallel with each other4 7,see ,fig4 #beb47 ,it is easily seen that none of the current passing through one car can go through any of the others4 ,when the conductors are in series the combined resistance is the sum of the several resistances4 ,thus in an electric-bell circuit if the battery has a resistance of #a ohm1 the bell of #b ohms1 and the wire #a ohm1 the total resistance in the circuit is #d ohms4 ,when conductors are in parallel the combined resistance is always less than the separate resistances4 ,just as a crowd of people meets less resistance in leaving a building through several exits1 so electricity finds less resistance in moving from one point to another along several parallel lines1 than along one of the lines4 #bgd4 ,resistance of ,conductors in ,parallel4--,if three conductors of equal resistance are in parallel1 the combined resistance is just one-third the resistance of each separately 7,fig4 #bec74 ,the rule that states the relation between the combined resistance of conductors in parallel and the separate resistances is as follows3,the combined resistance of conductors in parallel is the reciprocal of the sum of the reciprocals of the several resistances4 ,for example1 find the combined resistance of three unequal resistances in parallel2 the first being #d ohms1 the second1 #f ohms1 and third #c ohms4 ,the reciprocals of the three resistances are #a_/d1 #a_/f1 and #a_/c4 ,their sum equals #f_/bd #d_/bd #h_/bd #ah_/bd4 ,the reciprocal of this is #bd_/ah which equals #a-a_/c ohms1 the combined resistance4 ,,fig4 #bec4--,the three conductors are connected in parallel4 ,this rule may be understood better if we consider the conductance of the conductors in parallel4 ,since the conductance of a two ohm wire is just one-half that of a one-ohm wire1 we say that the conductance of a body is inversely as the resistance1 or that it is the reciprocal of the resistance4 ,the conductance of the #d-1 #f-1 and #c-ohm coils will therefore be respectively #a_/d1 #a_/f1 and #a_/c1 and since the combined conductance is the sum of the several conductances1 the total conductance is #ah_/bd4 ,also since this is the reciprocal of the total resistance1 the latter is #bd_/ah or #a-a_/c ohms4 ,when two or more conductors are connected in parallel each one is said to be a shunt of the others4 ,many circuits are connected in shunt or in parallel4 ,fig4 #bed represents four lamps in parallel4 ,incandescent lamps in buildings are usually connected in parallel1 while arc lamps are usually connected in series4 ,fig4 #bee represents four lamps in series4 ,important ,topics #a4 ,conditions affecting current flow1 7a7 ,e4,m4,f41 7b7 resistance4 #b4 ,ohm's law1 three forms for formula4 #c4 ,resistance of conductors3 7a7 in series1 7b7 in parallel2 how computed1 illustrations4 ,illustration3 ,,fig4 #bed4--,the four lamps are connected in parallel4 ,illustration3 ,,fig4 #bee4--,the four lamps are connected in series4 ,exercises #a4 ,what current flows through a circuit if its ,e4,m4,f4 is #aaj volts and the resistance is #bbj ohms8 #b4 ,a circuit contains four conductors in series with resistances of #aj1 #ae1 #f1 and #i ohms respectively4 ,what current will flow through this circuit at #aaj volts pressure8 ,what will be the resistance of these four conductors in parallel8 #c4 ,what is the combined resistance of #h conductors in parallel if each is #bbj ohms8 ,what current will flow through these #h conductors at #aaj volts pressure8 #d4 ,what is the resistance of a circuit carrying #bb amperes1 if the ,e4,m4,f4 is #bj volts8 #e4 ,what ,e4,m4,f4 will send #h amperes of current through a circuit of #ge ohms resistance8 #f4 ,how does the voltmeter differ from the ammeter8 #g4 ,how can one determine the resistance of a conductor8 #h4 ,the resistance of a hot incandescent lamp is #ajj ohms4 ,the current used is #a4a amperes4 ,find the ,e4,m4,f4 applied4 #i4 ,what is the resistance of the wires in an electric heater if the current used is #aj amperes1 the voltage being #aaj8 #aj4 ,the resistance of #ajjj ft4 of ,no4 #cf copper wire is #dbd ohms4 ,how many feet should be used in winding a #bjj ohms relay8 #aa4 ,the resistance of ,no4 #jj trolley wire is #j4hj ohm per #ajjj ft4 ,what is the resistance of a line #a mile long8 #ab4 ,a wire has a resistance of #bj ohms4 ,it is joined in parallel with another wire of #f ohms1 find their combined resistance4 #ac4 ,the separate resistances of two incandescent lamps are #bjj ohms and #gj ohms4 ,what is their combined resistance when joined in parallel8 ,when joined in series8 7#d7 ,,methods ,,of ,,grouping ,,cells ,,and ,,measuring ,,resistance #bge4 ,internal ,resistance of a ,voltaic ,cell4--,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 cell4 ,this is called the internal resistance of the cell4 ,a ,daniell cell has several 7#a-e7 ohms internal resistance4 ,the resistance of dry cells varies from less than #j4a of an ohm when new to several ohms when old4 ,if cells are joined together their combined internal resistance depends upon the method of grouping the cells4 ,illustration3 ,,fig4 #bef4--,the four cans exert four times the water pressure that one can will exert4 #bgf4 ,cells ,grouped in ,series and in ,parallel4--,when in series the copper or carbon plate of one cell is joined to the zinc of another and so on4 7,see ,fig4 #bea47 ,the effect of connecting1 say four cells1 in series may be illustrated by taking four cans of water1 placed one above another4 7,see ,fig4 #bef47 ,the combined water pressure of the series is the sum of the several pressures of the cans of water1 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 cans4 ,in applying this illustration to the voltaic cell1 we make use of ,ohm's law4 ,let ,e represent the e4m4f4 of a single cell1 r the internal resistance of the cell1 and ,r the external resistance or the resistance of the rest of the circuit4 ,consider a group of cells in series4 ,if n represents the number of cells in series1 then ,ohm's law becomes ,i n,e_/7nr ,r74 ,cells are grouped in series when large ,e4,m4,f4 is required to force a current through a large external resistance such as through a long telegraph line4 ,cells are connected in parallel when it is desired to send a large current through a small external resistance4 ,to connect cells in parallel all the copper plates are joined and also all the zinc plates4 7,see ,fig4 #beg47 ,to illustrate the effect of this mode of grouping cells1 suppose several cans of water are placed side by side 7,fig4 #beh74 ,it is easily seen that the pressure of the group is the same as that of a single cell1 while the resistance to the flow is less than that of a single cell4 ,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_/77r_/n7 ,r74 ,illustration3 ,,fig4 #beg4--;,four cells connected in parallel4 ,illustration3 ,,fig4 #beh4--,the water pressure of the group in parallel is the same as that of one4 #bgg4 ,illustrative ,problems4--,suppose that four cells are grouped in parallel1 each with an ,e4,m4,f4 of #a4e volts and an internal resistance of #b ohms4 ,what current will flow in the circuit if the external resistance is #b4e ohms8 ,substitute in the formula for cells in parallel the values given above1 and we have ,i #a4e_/7j4e #b4e7 #a4e_/c #j4e ampere4 ,suppose again that these four cells were grouped in series with the same external resistance1 substituting the values in the formula for cells in series we have ,i #d7a4e7_/7d #b #b4e7 #f_/aj4e #j4eg ampere4 #bgh4 ,volt-ammeter ,method for ,finding ,resistance4--,measurements of the resistance of conductors are often made4 ,one of these methods depends upon an application of ,ohm's law4 ,it is called the volt-ammeter method since it employs both a voltmeter and an ammeter4 ,if the conductor whose resistance is to be measured is made a part of an electric circuit1 being connected in series with the ammeter and in shunt with the voltmeter1 the resistance may easily be determined1 since ,r ,e_/,i4 7,see ,fig4 #bej47 ,if1 for example1 the difference in ,e4,m4,f41 or as it is often called1 the fall of potential between the ends of the wire as read on the voltmeter is #b volts1 and the current is #j4e ampere1 then the resistance of the wire is #d ohms4 ,this method may be readily applied to find the resistance of any wire that is a part of an electric circuit4 #bgi4 ,the ,wheatstone ,bridge4--,to find the resistance of a separate wire or of an electrical device another method devised by an ,englishman named ,wheatstone is commonly employed4 ,this method requires that three known resistances1 a1 b1 c1 in addition to the unknown resistance x be taken4 ,these four resistances are arranged in the form of a parallelogram4 7,see ,fig4 #bei47 ,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 diagonal4 ,the known resistances are changed until when on pressing the keys at ,e and ,k no current flows through the galvanometer4 when this condition is reached1 the four resistances form a true proportion1 thus a3 b c3 x4 ,since the values of a1 b1 and c are known1 x is readily computed4 ,thus if a #aj1 b #ajj1 and c #a4h ohms1 then x1 the unknown resistance1 equals #ah ohms1 since #aj3 #ajj #a4h3 #ah4 ,this method devised by ,wheatstone may be employed to find the resistance of a great variety of objects4 ,it is the one most commonly employed by scientists and practical electricians4 ,illustration3 ,,fig4 #bei4--;,diagram of a ,wheatstone bridge4 ,important ,topics #a4 ,the internal resistance of voltaic cells4 #b4 ,ohm's law applied to groups of cells4 7a7 ,cells in series1 7b7 cells in parallel4 #c4 ,measurement of resistance3 7a7 volt-ammeter method1 7b7 ,wheatstone bridge method4 ,exercises #a4 ,what is the resistance of an electric bell circuit where the ,e4,m4,f4 is #c volts and the current is #j4f ampere8 #b4 ,a telegraph wire is broken somewhere1 the ends lying upon damp ground4 ,if an ,e4,m4,f4 of #cj volts is applied from the ground to the wire and a current of #j4a of an ampere flows1 what is the resistance of the part connected to the ammeter4 7,the earth which completes the circuit from the end of the wire has very small resistance47 ,why8 #c4 ,how far away is the break in the wire if the latter has a resistance of #hj ohms to the mile8 ,diagram4 #d4 ,what current will flow through a bell circuit of #h ohms resistance if it contains three cells in series each with an ,e4,m4,f4 of #a4e volts and an internal resistance of #a_/c ohm8 #e4 ,if the same three cells are connected in parallel on the same circuit what current flows8 ,is the current in problem #d or #e the larger8 ,why8 #f4 ,if four cells each with #a4e volts ,e4,m4,f4 and an internal resistance of #j4d ohm are connected with a circuit having an external resistance of #j4h ohm1 what current will the parallel connection give8 ,the series connection8 ,which gives the larger current8 ,why8 #g4 ,four ,daniell cells each having #a volt ,e4,m4,f4 and #c ohms internal resistance are connected in series with #b telegraph sounders of #d ohms each4 ,the connecting wires have #f ohms resistance4 ,find the current intensity4 #h4 ,a battery of #b cells arranged in series is used to ring a door bell4 ,the ,e4,m4,f4 of each cell is #a4e volts1 internal resistance #j4c ohm1 and the resistance of the bell is #d ohms4 ,what is the current in amperes8 #i4 ,in the above problem find the current if the cells are connected in parallel4 ,,chapter ,,xiii ,,the ,,chemical ,,and ,,heat ,,effects ,,of ,,electric ,,currents 7#a7 ,,the ,,chemical ,,effect ,,of ,,an ,,electric ,,current #bhj4 ,electroplating4--,if two carbon rods 7electric light carbons answer very well7 are placed in a solution of copper sulphate 7,fig4 #bfj7 and then connected by wires to the binding posts of an electric battery1 one of the rods soon becomes covered with a coating of metallic copper while bubbles of gas may be seen upon the other carbon4 ,if a solution of lead acetate is used in the same way a deposit of metallic lead is secured1 while a solution of silver nitrate gives silver4 ,illustration3 ,,fig4 #bfj4--,two carbons placed in a solution of copper sulphate4 ,illustration3 ,,fig4 #bfa4--;,an electroplating bath4 ,this process of depositing metals upon the surface of solids by an electric current is called electroplating4 ,everyone has seen electroplated articles such as silver plated knives1 forks1 and spoons1 and nickel-plated rods1 handles1 etc4 ,copper electrotype plates such as are used in printing school books are made by this process4 ,in practical electroplating a solution of the metal to be deposited is placed in a tank2 across the top of this tank are placed copper rods to act as conducting supports4 ,from one of these rods1 the cathode1 objects to be plated are hung so as to be immersed in the liquid4 ,from other rods1 the anodes1 are hung plates of the metal to be deposited4 ,these are dissolved as the current deposits a coating upon the articles1 thus keeping the solution up to its proper strength4 7,see ,fig4 #bfa47 ,illustration3 ,,fig4 #bfb4--,the current is carried through the solution by ions4 #bha4 ,electrolysis4--,a solution from which a deposit is made by an electric current is called an electrolyte4 ,the plates or other objects by which the current enters or leaves the electrolyte are called the electrodes4 ,the electrode by which the current enters is called the anode 7an in7 while the electrode by which it leaves is the cathode 7cath away74 ,the process by which an electric current decomposes a solution and deposits a substance upon an electrode is called electrolysis4 ,the current always flows within the cell from anode to the cathode4 7,see ,fig4 #bfb47 ,the metal goes with the current and is found deposited upon the cathode4 #bhb4 ,theory of ,electrolysis4--,the action going on in an electrolytic cell has been carefully studied4 ,the theory of electrolysis1 which is supported by much experimental evidence1 supposes that many of the molecules in a dilute solution of a substance split up into two parts called ions1 one ion having a positive1 the other a negative charge4 ,in a dilute solution of sulphuric acid1 the positive ion is of hydrogen1 while the negative ion is the 7,,so#d7 or sulphion4 ,these ions bearing electric charges are believed to be the carriers of the electric current through the electrolyte4 ,the positive ions move with the current from the anode to the cathode1 while the negative ions apparently are repelled by the cathode and appear upon the anode4 ,evidence of the accumulation of the two kinds of ions at the two electrodes is furnished by the electrolysis of water1 described below4 #bhc4 ,electrolysis of ,water4--,two glass tubes 7,fig4 #bfc71 ,h and ,o1 are attached at the bottom to a horizontal glass tube4 ,to the latter is also connected an upright tube ,t4 ,at the lower ends of ,h and ,o are inserted1 fused in the glass1 platinum wires1 ,a and ,c4 ,the tubes are filled with a weak solution of sulphuric acid4 ,the tops of ,h and ,o are closed with stopcocks1 ,t being open2 a current of electricity is sent in at ,a and out at ,c4 ,a movement of the ions at once begins1 the positive hydrogen ions appearing at ,c4 ,these accumulate as bubbles of hydrogen which rise to the top of ,h and displace the liquid4 ,at the same time bubbles of oxygen appear at ,a4 ,these rise in ,o and also displace the liquid which rises in ,t4 ,after the action has continued some time it may be noticed that the volume of hydrogen is just twice that of the oxygen4 ,this was to have been expected since the formula for water is ,h#b,o4 ,the nature of the gas in ,h or ,o may be tested by opening the stopcock and allowing the gas to escape slowly4 ,the hydrogen gas can be lighted by a flame while the oxygen gas will cause a spark upon a piece of wood to glow brightly1 but does not burn itself4 ,illustration3 ,,fig4 #bfc4-;,electrolysis of water2 oxygen collects in ,o1 hydrogen in ,h4 #bhd4 ,evidence that ions are necessary to conduct a current in a liquid is furnished by the following experiment4 ,a quart jar is carefully cleaned1 and half filled with distilled water4 ,two pieces of zinc #e cm4 square are soldered to pieces of rubber-insulated ,no4 #ad copper wire4 ,the zincs are placed in the distilled water 7,fig4 #bfd7 and the wires are connected to a #aaj volt circuit with a #af candle-power incandescent lamp in series with the cell1 as in the figure4 ,if the zincs have been carefully cleansed and the water is pure1 no current flows as is shown by the lamp remaining dark4 ,if a minute quantity of sulphuric acid or of common salt is placed in the water the lamp at once begins to glow4 ,ions are now present in the liquid and conduct the current4 ,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 sugar1 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 sugar4 ,the acid and salt are of mineral origin while the glycerine and sugar are vegetable products4 ,this experiment illustrates the principle that the water will conduct only when it contains ions4 ,illustration3 ,,fig4 #bfd4--,the current passes only when ions are present in the liquid4 #bhe4 ,laws of ,electrolysis4--,these were discovered by ,faraday in #ahcc1 and may be stated as follows3 ,i4 ,the mass of a substance deposited by an electric current from an electrolyte is proportional to the intensity of current which passes through it4 ,,ii4 ,the mass of any substance deposited by a current of uniform intensity is directly proportional to the time the current flows4 ,these laws have been used as a basis for defining and measuring the unit of current flow1 the ampere4 7,see ,art4 #bfd47 #bhf4 ,instances of ,electrolysis4--7a7 ,medicines1 especially those containing a mineral substance1 are sometimes introduced into the human body by electrolysis4 7b7 ,water and gas pipes are sometimes much weakened by the effects of electric currents in the earth1 especially return currents from street railways4 ,such currents use the metal pipes as a conductor4 ,at the place where the current leaves the metal and enters the ground1 it removes metallic ions from the pipe4 ,this process continuing1 the pipe becomes weakened and at length breaks4 7c7 ,copper is purified by the use of electric currents that remove the copper from ore or from other metals and deposit it upon electrodes4 ,electrolytic copper is the purest known4 7d7 ,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 electrolysis4 ,these results are called chemical effects of the current since by the use of electric currents substances are changed chemically1 that is1 they are separated into different chemical substances4 ,important ,topics #a4 ,electrolysis1 electroplating1 anode1 cathode1 ion4 #b4 ,theory of electrolysis--evidence3 7a7 electrolysis of water2 7b7 conductivity of acid and water4 #c4 ,laws of electrolysis4 #d4 ,practical use of electrolysis4 ,exercises #a4 ,a dynamo has an ,e4,m4,f4 of #aj volts4 ,what is the resistance in the circuit when #bj amperes are flowing8 #b4 ,how much silver will be deposited in an hour by this current8 #c4 ,name five objects outside of the laboratory that have been acted upon by electrolysis4 ,how in each case8 #d4 ,why is table ware silver plated8 ,why are many iron objects nickel plated8 #e4 ,how is the electrolysis of water pipes prevented8 #f4 ,two grams of silver are to be deposited on a spoon by a current of #a ampere4 ,find the time required4 #g4 ,how long will it take to deposit #bj g4 of silver in an electroplating bath if a current of #bj amperes is used8 #h4 ,if #ajjj g4 of silver are deposited on the cathode of an electrolytic reduction plant in #aj minutes1 what is the current intensity employed8 7#b7 ,,the ,,storage ,,battery ,,and ,,electric ,,power #bhg4 ,differences ,between ,voltaic and ,storage ,cells4 ,voltaic cells in which electric currents are produced by the chemical action between metal plates and an electrolyte are often called primary batteries4 ,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 material1 the chemical energy of the electrolyte and of one of the plates having been transformed into electrical energy4 ,a different proceeding obtains with another type of cell4 ,this is called a storage battery1 or an accumulator4 ,in these cells1 the same plates and electrolyte are used without change for extended periods1 sometimes for a number of years4 ,for this reason storage batteries have displaced many other types of cells1 and they are now used 7a7 to operate many telephone1 telegraph1 and fire-alarm circuits1 7b7 to work the spark coils of gas and gasoline engines1 7c7 to help carry the peak load upon lighting and power circuits and 7d7 to furnish power for electric automobiles4 ,since a storage battery can deliver an electric current only after an electric current from an outside source has first been sent through it1 they are often called secondary batteries4 #bhh4 ,construction and ,action of a ,storage ,cell4--,the common type of storage cells consists of a number of perforated plates made of an alloy of lead and a little antimony4 7,see ,figs4 #bfe1 #bff1 #bfg47 ,into the perforations is pressed a paste of red lead and litharge mixed with sulphuric acid4 ,the plates are placed in a strong solution 7#bj to #be per cent47 of sulphuric acid4 ,the plates are now ready to be charged4 ,this is accomplished by sending a direct current from an electric generator through the cell4 ,the hydrogen ions are moved by the current to one set of plates and change the paste to spongy metallic lead4 ,the sulphions move to the other set of plates and change the paste to lead oxide4 ,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 cell1 in having plates that are different chemically4 ,it has1 when fully charged1 an ,e4,m4,f4 of about #b4b volts4 ,the several plates of a cell being in parallel and close together1 the cell has but small internal resistance4 ,consequently a large current is available4 ,illustration3 ,,fig4 #bfe4--,the positive plate of a storage cell4 ,illustration3 ,,fig4 #bff4--,the negative plate of a storage cell4 ,illustration3 ,,fig4 #bfg4--;,a complete storage cell4 ,illustration3 ,,fig4 #bfh4 ,about #ge per cent4 of the energy put into the storage cell in charging can be obtained upon discharging4 ,therefore the efficiency of a good storage cell is about #ge per cent4 ,fig4 #bfh represents a storage battery connected to charging and discharging circuits4 ,the lower is the charging circuit4 ,it contains a dynamo and a resistance 7neither of which are shown in the figure7 to control the current sent into the cell4 ,the charging current enters the positive pole and leaves by the negative pole4 ,the current produced by the cell1 however1 flows in the opposite direction through it1 that is1 out from the positive and in at the negative pole4 ,this current may be controlled by a suitable resistance and measured by an ammeter4 ,storage cells have several advantages3 7a7 ,they can be charged and discharged a great many times before the material placed in the perforations in the plates falls out4 7b7 ,the electrical energy used in charging the plates costs less than the plates and electrolyte of voltaic cells4 7c7 ,charging storage cells takes much less labor than replacing the electrolyte and plates of voltaic cells4 7d7 ,storage cells produce larger currents than voltaic cells4 ,the two principal disadvantages of storage cells are that 7a7 they are very heavy1 and 7b7 their initial cost is considerable4 ,illustration3 ,,fig4 #bfi4--,the ,edison storage cell4 ,illustration3 ,,fig4 #bgj4--,the plates of the ,edison storage cell4 #bhi4 ,the ,edison storage cell 7,figs4 #bfi and #bgj7 has plates of iron and nickel oxide4 ,the electrolyte is a strong solution of potassium hydroxide4 ,these cells are lighter than lead cells of the same capacity and they are claimed to have a longer life4 #bij4 ,energy and ,power of a ,storage ,cell4--,in a storage cell1 the electrical energy of the charging current is transformed into chemical energy by the action of electrolysis4 ,it is this chemical energy that is transformed into the energy of the electric current when the cell is discharged4 ,the capacity of storage cells is rated in ampere hours1 a #dj ampere hour cell being capable of producing a current of #a ampere for #dj hours1 or #e amperes for #h hours1 etc4 ,the production and extensive use of electric currents have made necessary accurate methods for measuring the energy and power of these currents4 ,to illustrate how this is accomplished1 let us imagine an electric circuit as represented in ,fig4 #bfh4 ,here four storage cells in series have an ,e4,m4,f4 of #h volts and in accordance with ,ohm's law produce a current of #b amperes through a resistance in the circuit of #d ohms4 ,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 7#a7 the ,e4,m4,f4 or potential difference2 7#b7 the current intensity and 7#c7 the time4 ,the energy is measured by their product4 ,that is1 electrical energy potential difference current intensity time4 ,this represents the electrical energy in joules1 or ,joules volts amperes seconds1 or j ,e ,i t4 ,in the circuit represented in ,fig4 #bfh the energy expended between the points ,m and ,n in #a minute 7#fj seconds7 is #h #b #fj #ifj joules4 #bia4 ,electric ,power4--,since power refers to the time rate at which work is done or energy expended1 it may be computed by dividing the electrical energy by the time1 or the electrical power volts amperes4 ,the power of #a joule per second is called a watt4 ,therefore1 ,watts volts amperes1 or ,watts ,e ,i4 ,other units of power are the kilowatt #ajjj watts and the horse-power #gdf watts4 ,in the example given in ,art4 #bij the power of the current is #h #b #af watts1 or if the energy of the current expended between the joints ,m and ,n were converted into mechanical horse-power it would equal #af_/gdf of a horse-power4 ,electrical energy is usually sold by the kilowatt-hour1 or the amount of electrical energy that would exert a power of #ajjj watts for one hour1 or of #ajj watts for #aj hours1 or of #ej watts for #bj hours1 etc4 ,important ,topics #a4 ,the storage battery1 its construction1 electrolyte1 action1 uses1 advantages1 disadvantages4 #b4 ,electric energy1 unit value1 how computed8 #c4 ,electric power1 three units1 value1 how computed1 how sold8 ,exercises #a4 ,in what three respects are voltaic and storage cells alike8 ,in what two ways different8 #b4 ,name the four advantages of storage cells in the order of their importance4 ,give your reasons for choosing this order4 #c4 ,why are dry cells more suitable for operating a door-bell circuit1 than a storage battery8 ,give two reasons4 #d4 ,the current for a city telephone system is provided by a storage battery4 ,why is this better than dry cells at each telephone8 #e4 ,an incandescent lamp takes #j4e ampere at #aaj volts4 ,what power is required to operate it8 ,how much energy will it transform in #a minute8 #f4 ,how long would it take for this lamp to use a kilowatt hour of energy8 #g4 ,a street car used #ajj amperes at #fjj volts pressure4 ,what power was delivered to it8 ,express also in kilowatts and horse-power4 #h4 ,an electric toaster takes #e amperes at #aaj volts4 ,if it toasts a slice of bread in #b minutes1 what is the cost at #aj cents a kilowatt hour8 #i4 ,an electric flat iron takes #e amperes at #aaj volts4 ,find the cost of using it for #b hours at #ab cents a kilowatt hour4 #aj4 ,a #a_/d kilowatt motor is used to run a washing-machine for #e hours4 ,what is the expense for this power at #aj cents a kilowatt hour8 #aa4 ,what is the efficiency of a motor that takes #gcij watts and develops #i horse-power8 #ab4 ,how many horse-power are there in a water-fall #bab ft4 high over which flows #hjj cu4 ft4 of water per second8 ,express this power in kilowatts4 #ac4 ,what horse-power must be applied to a dynamo having an efficiency of go per cent4 if it is to light #bj arc lamps in series1 each taking #aj amperes at #fj volts8 7#c7 ,,the ,,heat ,,effect ,,of ,,electric ,,currents #bib4 ,the ,production of ,heat by an ,electric ,current4--,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 heat4 ,this effect has many practical applications and some disadvantages4 ,many devices employ the heating effect of electric currents1 7a7 the electric furnace1 7b7 electric lights1 7c7 heating coils for street cars1 7d7 devices about the home1 as flat irons1 toasters1 etc4 ,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 employed4 ,unusually heavy currents have been known to melt the conducting wires of circuits and electrical devices4 ,hence all circuits for electric power as well as many others that ordinarily carry small currents are protected by fuses4 ,an electric fuse is a short piece of wire that will melt and break the circuit if the current exceeds a determined value4 ,the fuse wire is usually enclosed in an incombustible holder4 ,fuse wire is frequently made of lead or of an alloy of lead and other easily fusible metals4 7,see ,figs4 #bga and #bgb47 ,illustration3 ,,fig4 #bga4--;,a type of enclosed fuse4 ,illustration3 ,,fig4 #bgb4--;,a link fuse 7above72 plug fuses 7below74 #bic4 ,heat ,developed in a ,conductor4--,a rule for computing the amount of heat produced in an electric circuit by a given current has been accurately determined by experiment4 ,it has been found that #a calorie of heat 7,art4 #adb71 is produced by an expenditure of #d4b joules of electrical 7or other7 energy4 ,in other words1 #a joule will produce #a_/d4b or #j4bd calorie4 ,now the number of joules of electrical energy in an electric circuit is expressed by the following formula3 ,joules volts amperes seconds1 or since #a joule #j4bd calorie1 ,calories volts amperes seconds #j4bd or ,h ,,ei t #j4bd 7#a7 ,by ,ohm's law1 ,i ,e_/,r or ,e ,i ,r1 substituting in equation 7#a7 ,,ir for its equal ,e we have ,h ,i,r t #j4bd 7#b7 ,also since ,i ,e_/,r substitute ,e_/,r for ,i in equation 7#a7 and we have ,h ,e_/,r t #j4bd 7#c7 ,to illustrate the use of these formulas by a problem suppose that a current of #aj amperes is flowing in a circuit having a resistance of #aa ohms1 for #a minute4 ,the heat produced will be by formula 7#b7 7#aj7 #aa #fj #j4bd equals #ae1hdj calories4 ,illustration3 ,,fig4 #bgc4--;,a carbon filament incandescent lamp4 ,illustration3 ,,fig4 #bgd4--;,a tungsten lamp4 #bid4 ,the ,incandescent ,lamp4--,one of the most common devices employing the heat effect of an electric current is the incandescent lamp4 7,see ,fig4 #bgc47 ,in this lamp the current is sent through a carbon filament1 which is heated to incandescence4 ,in order to keep the filament from burning as well as to prevent loss of heat by convection1 it is placed in a glass bulb from which the air is exhausted4 ,two platinum wires fused in the glass connect the carbon filament with the grooved rim and the end piece of the base4 ,the end piece and rim connect with the socket so that an electric current may flow through the filament of the lamp4 ,the carbon incandescent lamp has a low efficiency4 ,it takes #j4e ampere of current at #aaj volts or in other words it requires #ee watts to cause a #af-;candle-power lamp to glow brightly1 hence #a candle power in this lamp takes #ee_/af #c4dc watts4 ,the efficiency of electric lamps is measured by the number of watts per candle power4 ,this is a peculiar use of the term efficiency1 as the larger the number the less efficient is the lamp4 ,more efficient lamps have been devised with filaments of the metals tantalum and tungsten 7,fig4 #bgd74 ,these give a whiter light than do carbon lamps1 and consume but about #a4be watts per candle power4 ,,comparative ,,efficiency ,,of ,,electric ,,lamps ---------------------------------------- ---------------- ,watts per ,watts per ,name of lamp candle ,name of lamp candle power power ---------------------------------------- ---------------- ,carbon filament #c to #d ,arc lamp #j4e to #j4h ,metallized carbon #b4e ,mercury arc #j4f ,tantalum #b4j ,flaming arc #j4d ,tungsten #a4j to ,nitrogen-filled #j4f to #j4g #a4e tungsten ---------------------------------------- ---------------- ,incandescent lamps are connected in parallel 7see ,fig4 #bed7 to wires that are kept at a constant difference of potential of #aaj or #aae volts4 ,it is customary to place not more than twelve lamps upon one circuit1 each circuit being protected by a fuse and controlled by one or more switches4 #bie4 ,the ,arc ,light4--,the electric arc light 7see ,fig4 #bge7 is extensively used for lighting large rooms1 also in stereopticons and motion picture machines4 ,the light is intense1 varying from #ejj to #agjj candle power4 ,the so-called mean spherical candle power of the arc light is about #eaj4 ,the candle power in the direction of greatest intensity is about #abjj4 ,it is produced at an expenditure of about #ejj watts4 ,it is therefore more efficient than the incandescent lamp1 often taking less than #j4e watt per candle power produced4 ,the arc light was first devised by ,sir ,humphrey ,davy in #ahji1 who used two pieces of charcoal connected to #bjjj voltaic cells4 ,the arc light requires so much power that its production by voltaic cells is very expensive4 ,consequently it did not come into common use until the dynamo had been perfected4 ,fig4 #bgf shows the appearance of the two carbons in an arc light4 ,if a direct current is used the positive carbon is heated more intensely1 and gives out the greater part of the light4 ,the positive carbon is consumed about twice as fast as the negative and its end is concave1 the negative remaining pointed4 ,illustration3 ,,fig4 #bge4--;,an electric arc light4 ,illustration3 ,,fig4 #bgf4--,the appearance of a pair of used carbons4 ,with alternating currents1 the rods are equally consumed and produce equal amounts of light4 ,in the stereopticon1 the carbons are usually placed at right angles as in ,fig4 #bgg4 ,in the stereopticon as well as in outdoor lighting the direct current is more effective1 although the alternating current is often used1 since the latter can be produced and distributed more cheaply than can direct currents4 ,in arc lamps1 placing an inner glass globe 7,fig4 #bgh7 about the carbons1 decreases the consumption of the carbons materially4 ,the carbon rods of enclosed arc lamps often last #fj to #ajj hours4 ,illustration3 ,,fig4 #bgg4--;,a right-angle electric arc lamp for a stereopticon4 ,illustration3 ,,fig4 #bgh4--;,an enclosed arc lamp4 ,the reason why an open arc lamp needs to be retrimmed oftener than the enclosed lamp1 that is1 have new carbons placed in it1 is because the carbons burn freely1 that is unite with the oxygen of the air4 ,in the enclosed arc lamp1 the supply of oxygen in the inner globe is limited and is soon consumed1 therefore the carbons last many times longer in such lamps4 ,some carbon rods have soft cores containing calcium salts4 ,these vaporize in the arc producing the flaming arc light of a bright yellow color1 and give more light than the ordinary lamp4 ,important ,topics #a4 ,heat effects of electric currents1 uses and applications4 #b4 ,computation of the heat developed in a circuit4 ,three formulas4 #c4 ,electric lamps2 incandescent and arc2 construction1 uses1 efficiency4 ,exercises #a4 ,sketch a circuit containing #aj incandescent lamps in parallel4 ,if each lamp when hot has a resistance of #bbj ohms1 and the ,e4,m4,f4 is #ajj volts1 what current will flow8 #b4 ,what will it cost to use these lights for #c hours a day for #cj days at #aj cents a kilowatt hour8 #c4 ,how much heat will these lamps produce per minute8 #d4 ,how could you connect #aaj-volt lamps to a street car circuit of #ffj volts8 ,explain this arrangement and draw a diagram4 #e4 ,a certain arc lamp required #aj amperes of current at #de volts pressure4 ,what would it cost at #aj cents per kilowatt hour if used #c hours a day for #cj days8 #f4 ,show a diagram of #c arc lamps in series4 ,if each takes #de volts and #aj amperes1 how much ,e4,m4,f4 and current will they require8 #g4 ,if an electric toaster uses #e amperes at #aae volts1 how much heat will this develop in half an hour8 #i4 ,how much heat is developed in an electric toaster in #b minutes1 if it uses #e amperes at #ajj volts8 #aj4 ,how many ,b4t4u4's are given off in an electric oven that takes #aj amperes at #aaj volts for #a hour8 7#a ,b4t4u4 equals #beb calories47 #aa4 ,an electric heater supplies heat at the rate of #gjj ,b4t4u4's an hour4 ,how much power does it require8 #ab4 ,how many watts are required to operate #abj incandescent lamps in parallel if each takes #j4e amperes at #aaj volts8 #ac4 ,an electric lamp takes #ab amperes at a ,p4,d4 of #aaj volts4 ,how many ,b4t4u4's are radiated from it each second8 ,how many calories8 #ad4 ,if a #aaj-volt incandescent lamp is submerged for #aj minutes in #djj gr4 of cold water while a current of #j4e amperes is flowing1 how many degrees centigrade will the water be warmed8 #ae4 ,in an electric furnace a current of #cjjj amperes is used at a ,p4,d4 of #aj volts4 ,find the heat developed in #a minute4 #af4 ,how many candle power should a #bj-watt tungsten lamp give if its efficiency is one watt per candle power8 #ag4 ,what is the efficiency of a #dj-watt tungsten lamp if it gives #cd candle power8 ,review ,outline3 ,current ,electricity ,produced by--,chemical action2 voltaic and storage cells4 ,three ,magnetic1 electromagnet1 uses and applications4 ,principal ,chemical1 electrolysis1 applications4 ,effects3 ,heat1 lighting and heating devices4 ,theories3 7a7 of voltaic cells1 7b7 of electrolysis4 ,units3 ,ampere1 ohm1 volt1 watt1 joule1 kilowatt1 horse power4 ,measurement--7a7 magnetic effect2 galvanometer1 ammeter1 voltmeter1 wattmeter1 ,wheatstone bridge1 construction and use4 7b7 chemical effect2 voltameter4 ,laws3 7a7 ,right hand rules1 for conductor and helix4 7b7 ,resistance1 ,conductors in series and parallel4 7c7 ,ohm's law1 heat law1 power law1 #c forms for each4 7d7 ,cells in parallel and series4 ,problems3 ,upon applications of the laws and formulas studied4 ,devices4 ,voltaic cells2 wet1 dry1 and ,daniell4 and ,electrolysis and the storage battery4 ,instruments3 ,measuring instruments1 electric bell1 sounder1 heating and lighting devices4 ,terms3 ,anode1 cathode1 electrolyte1 ion1 circuit switch1 current1 e4m4f41 resistance1 potential4 ,,chapter ,,xiv ,,induced ,,currents 7#a7 ,,electromagnetic ,,induction #bif4 ,current ,induced by a ,magnet4--,the discovery in #ahai that a current in a conductor can deflect a magnetic needle or that it has a magnetic effect1 led to many attempts to produce an electric current by means of a magnet4 ,it was not until about #ahca1 however1 that ,joseph ,henry in ,america and ,michael ,faraday in ,england1 independently discovered how to accomplish this important result4 ,at the present time1 voltaic cells produce but a very small part of the current electricity used4 ,practically all that is employed for power1 light1 heat1 and electrolysis is produced by the use of magnetic fields1 or by electromagnetic induction4 #big4 ,laws of ,induced ,currents4,m--,to illustrate how a current can be produced by electromagnetic induction3 ,m ,an induced current is one produced by changing the number of magnetic lines of force passing through a coil4 ,connect a coil of #djj or more turns of ,no4 #bb insulated copper wire to a sensitive galvanometer4 7,see ,fig4 #bgi47 ,now insert a bar magnet in the coil4 ,a sudden movement of the galvanometer will be noticed1 indicating the production of a current4 ,when the magnet stops moving1 however1 the current stops1 and the coil of the galvanometer returns to its first position4 ,if now the magnet is removed1 a movement of the galvanometer coil in the opposite direction is noticed4 ,this action may be repeated as often as desired with similar results4 ,careful experiments have shown that it is the magnetic field of the magnet that produces the action1 and that only when the number of lines of force in the coil is changing do we find a current produced in the coil4 ,these facts lead to ,law ,i4 ,any change in the number of magnetic lines of force passing through or cut by a coil will produce an electromotive force in the coil4 ,in the account of the experiment just given1 electric currents are produced1 while in ,law ,i1 electromotive forces are mentioned4 ,this difference is due to the fact that an ,e4,m4,f4 is always produced in a coil when the magnetic field within it is changed1 while a current is found only when the coil is part of a closed circuit4 ,the inductive action of the earth's magnetic field 7see ,fig4 #bhj71 may be shown by means of a coil of #djj to #ejj turns a foot in diameter4 ,illustration3 ,,fig4 #bgi4--,the moving magnet induces a current in the coil4 ,illustration3 ,,fig4 #bhj4--;,a current may be induced by turning the coil in the earth's magnetic field4 ,connect its ends to a sensitive galvanometer and hold it at right angles to the earth's field4 ,then quickly revolve the coil through #ahj degrees and note the movement of the galvanometer4 ,reverse the coil and the galvanometer swings in the opposite direction4 ,if the magnet in ,fig4 #bgi is moved in and out of the coil at first slowly and later swiftly1 small and large deflections of the galvanometer coil are noticed4 ,the quicker the movement of the magnetic field the greater are the galvanometer deflections produced4 ,this leads to ,law ,,ii4 ,the electromotive forces produced are proportional to the number of lines of force cut per second4 #bih4 ,the magneto is a device that illustrates the laws of induced currents stated in ,art4 #big4 ,the magneto 7see ,fig4 #bha71 consists of several permanent1 ,u-shaped magnets placed side by side4 ,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 ,fig4 #bhb4 ,the cylinder and coil form what is called an armature4 ,the armature is mounted so as to be revolved between the poles of the ,u-shaped magnets by means of a handle4 ,as the armature revolves1 the lines of force from the magnets pass through the coil first in one direction and then in the other4 ,this repeated change in the lines of force passing through the coil produces an ,e4,m4,f4 which may be felt by holding in the hands the two wires leading from the armature coil4 ,on turning the armature faster the current is felt much stronger1 showing that the ,e4,m4,f4 in the coil increases as the rate of cutting the magnetic lines of force by the coils increases4 ,illustration3 ,,fig4 #bha4--;,a magneto4 ,illustration3 ,,fig4 #bhb4--;,a shuttle armature4 ,illustration3 ,,fig4 #bhc4--,the induced current has a field which opposes the motion of the magnet4 ,the heavy line represents the direction of the induced current4 #bii4 ,lenz's ,law4--,while one is turning the armature of a magneto if the two wires leading from its coil are connected1 forming what is called a short circuit1 the difficulty of turning the armature is at once increased4 ,if now the circuit is broken1 the armature turns as easily as at first4 ,the increased difficulty in turning the armature is due to the current produced in the coil4 ,this current sets up a magnetic field of its own that opposes the field from the steel magnets4 ,this opposition makes it necessary for work to be done to keep up the motion of the coil when a current is passing through it4 ,this fact is called ,lenz's ,law4 ,it may be expressed as follows3 ,whenever a current is induced by the relative motion of a magnetic field and a conductor1 the direction of the induced current is always such as to set up a magnetic field that opposes the motion4 ,lenz's ,law follows from the principle of conservation of energy1 that energy can be produced only from an expenditure of other energy4 ,now since an electric current possesses energy1 such a current can be produced only by doing mechanical work or by expending some other form of energy4 ,to illustrate ,lenz's ,law1 suppose that the north-seeking pole of a bar magnet be inserted in a closed coil of wire4 7,see ,fig4 #bhc47 ,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 magnet1 when the north pole of the magnet is inserted so as to point to the left4 ,that is1 the north pole of the helix is at the right4 ,applying the right-hand rule to the coil1 its current will then be counter clockwise4 ,on withdrawing the magnet1 the current reverses1 becoming clockwise with its field passing to the left within the coil4 ,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 7see ,fig4 #bhd7 and suspending a sheet of copper so as to swing freely between the poles4 ,when no current flows through the magnet the sheet swings easily for some time4 ,when1 however1 the coils are magnetized1 the copper sheet has induced within it1 currents that set up magnetic fields strongly opposing the motion1 the swinging being stopped almost instantly4 ,the principle is applied in good ammeters and voltmeters to prevent the swinging of the needle when deflected4 ,the current induced in the metal form on which is wound the galvanometer coil is sufficient to make the needle practically dead beat4 ,illustration3 ,,fig4 #bhd4--,the magnetic field stops the swinging of the sheet of copper4 #cjj4 ,the ,magneto and the ,dynamo4--,magnetos are used to develop small currents1 such as are used for telephone signals1 and for operating the sparking devices of gasoline engines4 ,they are therefore found in automobiles containing gasoline motors4 ,the most important device for producing electric currents by electromagnetic induction1 however1 is the dynamo4 ,it is employed whenever large currents are desired4 ,the principle of this device is similar to that of the magneto except that it contains an electromagnet for producing the magnetic field4 ,since the electromagnet can develop a much stronger field than a permanent magnet1 the dynamo can produce a higher ,e4,m4,f4 and a much larger current than the magneto4 ,illustration3 ,,lord ,,kelvin ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,lord ,kelvin 7,sir ,william ,thomson71 7#ahbd-aijg74 ,professor of ,physics1 ,glasgow ,university4 ,invented the absolute scale of temperature3 also many practical electrical measuring instruments4 ,the foremost physicist of the latter part of the nineteenth century4 ,illustration3 ,,michael ,,faraday ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,michael ,faraday 7#agia-ahfg74 ,famous ,english ,physicist4 ,made many discoveries in electricity and magnetism2 ,greatest experimentalist of the nineteenth century4 #cja4 ,the ,magnetic ,fields of ,generators4--,in the magneto1 the magnetic field is produced by permanent steel magnets4 ,in dynamos powerful electromagnets are used4 ,the latter are sometimes excited by currents from some other source1 but usually current from the armature is sent around the field coils to produce the magnetic fields4 ,dynamos are classified according to the manner in which the current is sent to their field coils4 ,illustration3 ,,fig4 #bhe4--;,a series-wound dynamo4 ,illustration3 ,,fig4 #bhf4--;,a shunt-wound dynamo4 ,illustration3 ,,fig4 #bhg4--;,a compound-wound dynamo4 ,a4 ,the series wound dynamo 7see ,fig4 #bhe7 is arranged so that all of the current produced by the armature is sent through coils of coarse wire upon the fields1 after flowing through the external circuit4 ,b4 ,the shunt wound dynamo 7see ,fig4 #bhf7 sends a part only of the current produced through the field coils4 ,the latter are of many turns of fine wire so as to use as little current as possible4 ,the greater part of the current goes to the main circuit4 ,if the number of lamps or motors connected to the main circuit is increased1 the voltage is lessened which weakens the current in the field coils1 causing a weaker field and still lower voltage1 producing a fluctuating ,e4,m4,f4 which is unsatisfactory for many purposes4 ,this fault is overcome by ,c4 the compound wound dynamo4 ,this dynamo has both shunt and series coils upon its fields4 7,see ,fig4 #bhg47 ,if more current is drawn into the main circuit with this dynamo1 the series coils produce a stronger field compensating for the weaker field of the shunt coils1 so that uniform voltage is maintained4 ,the compound wound generator is therefore the one most commonly employed4 ,important ,topics #a4 ,laws of electromagnetic induction 7a7 conditions1 7b7 ,e4,m4,f41 7c7 direction4 #b4 ,devices1 7a7 magneto1 7b7 dynamo3 series1 shunt1 compound4 #c4 ,illustrations of the laws4 ,exercises #a4 ,under what conditions may an electric current be produced by a magnet8 #b4 ,show how ,lenz's ,law1 follows from the principle of conservation of energy4 #c4 ,a bar magnet is fixed upright with its north-seeking pole upward4 ,a coil is thrust down over the magnet4 ,what is the direction of the current induced in the coil8 ,explain4 #d4 ,in what two ways may a current be induced in a closed coil8 #e4 ,what method is employed in the magneto8 ,in the dynamo8 #f4 ,what is the nature of the current produced in the armature coil of a magneto1 that is1 is it direct or alternating8 ,why8 #g4 ,what is the resistance of a #bj-watt tungsten lamp if the ,e4,m4,f4 is #aae volts8 #h4 ,find the resistance of a #dj-watt tungsten lamp when the voltage is #aae8 ,how much heat will it produce per minute8 #i4 ,an ,edison storage battery cell on a test gave a discharge of #cj amperes4 ,the average voltage was #a4ai4 ,what was the resistance of the cell8 #aj4 ,eight storage cells are connected in series4 ,each has an ,e4,m4,f4 of #a4b volts and an internal resistance of #j4jc ohms4 ,what will be the current flowing through a voltmeter having #ejj ohms resistance in circuit with them8 7#b7 ,,the ,,dynamo ,,and ,,the ,,motor #cjb4 ,the ,dynamo may be defined as a machine for transforming mechanical energy into the energy of electric currents by electromagnetic induction4 ,although electromagnetic induction was discovered in #ahba1 practical dynamos were not built for about #dj years or until between #ahfj and #ahgj4 ,the great development in the production and use of electric currents has come since the latter date4 ,the principle parts of the dynamo are 7a7 the field magnet1 7b7 the armature1 7c7 the commutator or collecting rings1 7d7 the brushes4 ,fig4 #bhh shows several common methods of arranging the field coils and the armature4 ,illustration3 ,,fig4 #bhh4--,several methods of arranging the field coils and the armature of a dynamo4 ,illustration3 ,,fig4 #bhi4--;,a drum armature4 ,the field coils vary in number and position4 ,the purpose of their construction is always to send the largest possible number of lines of force through the armature4 ,some dynamos are bipolar1 or have two poles1 others are multipolar or have more than two4 ,in ,fig4 #bhh ,no4 #d has four poles4 ,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 iron4 ,fig4 #bhi shows a side view of the iron core of such an armature4 ,iron is used to form the body of the armature since the magnetic lines of force flow easily through the iron4 ,the iron by its permeability also concentrates and increases the magnetic flux4 ,the best armatures are made of many thin sheets of soft iron4 ,these are called laminated armatures4 ,an armature made of a solid piece of iron becomes hot when revolving in a magnetic field4 ,this is due to electric currents induced in the iron itself4 ,this heating is largely reduced by laminating the armature4 ,why8 ,illustration3 ,,fig4 #bij4--;,armature connected to slip rings producing an alternating current4 #cjc4 ,methods of ,collecting ,current from the ,armature4--,the electric currents produced in the armature are conducted away by special sliding contacts4 ,the stationary part of the sliding contact is called a brush4 ,the moving part is a slip ring or a commutator4 ,fig4 #bij shows an armature coil connected to slip rings4 ,as the armature revolves1 the coils and slip rings revolve with it4 ,the two ends of the armature coils are connected to the two rings respectively4 ,now as the armature revolves it cuts the lines of force first in one direction and then in the other4 ,this produces in the coils an ,e4,m4,f4 first one way and then the other4 ,this ,e4,m4,f4 sets up a current which is conducted to the outside circuits through the slip rings and brushes4 ,such a current which repeatedly reverses its direction is called an alternating current4 ,fig4 #bia 7#a7 indicates graphically how the current moves alternately one way and then the other4 ,alternating currents are extensively used for electric light1 heat1 and power4 ,direct currents or those going continuously in one direction are however in much demand especially for street car service1 for electrolysis1 and for charging storage batteries4 #cjd4 ,the ,commutator4--,for a dynamo to deliver a direct current it must carry upon the shaft of the armature a commutator4 ,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 armature4 ,this reversal of connection when the direction of current changes1 keeps the current in the outside circuit flowing in the same direction4 ,fig4 #bia is a diagram of an armature with a commutator4 ,the commutator is a split ring1 having as many parts or segments as there are coils upon the armature4 ,the brushes touch opposite points upon the commutator as they slide over the surface of the latter4 ,suppose that the armature viewed from the commutator end rotates in a counter-clockwise direction1 also that the currents from the upper part move toward the commutator and out the top brush4 ,illustration3 ,,fig4 #bia4--,the armature coils are connected to a commutator producing a direct current4 ,as the armature revolves1 its coils soon begin to cut the force lines in the opposite direction4 ,this change in the direction of cutting the lines of force causes the current to reverse in the coils of the armature4 ,at the instant the current changes in direction1 what was the upper segment of the commutator slips over into contact with the lower brush1 and the other segment swings over to touch the upper brush4 ,since the current has reversed in the coils it continues to flow out of the upper brush4 ,this change in connection at the brushes takes place at each half turn of the armature1 just as the current changes in direction in the coils4 ,this is the manner in which the commutator of a dynamo changes the alternating current produced in the armature coils1 into a direct current in the external circuit4 ,fig4 #bib 7#a7 represents graphically an alternating current1 7#b7 of the same figure shows current taken from the brushes of the commutator of a dynamo with one coil on the armature4 ,illustration3 ,,fig4 #bib4--;,graphic representation of 7#a7 an alternating current2 7#b7 a pulsating current2 7#c7 a continuous current4 ,illustration3 ,,fig4 #bic4--;,de,laval multi-stage turbine and gear driving #gej-kw41 #gej-r4p4m41 #fjj-volt direct-current generator4 ,a practical dynamo1 however1 has many coils upon its armature with a corresponding number of segments upon the commutator4 7,see ,figs4 #bhi and #bic47 ,as each coil and commutator segment passes a brush1 it contributes an impulse to the current with the result that armatures with many coils produce currents that flow quite evenly4 7,see ,fig4 #bib1 #c47 ,the current represented in ,fig4 #bib 7#b7 is called a pulsating current4 ,illustration3 ,,fig4 #bid4--;,a wire carrying a current across a magnetic field is pushed sideways by the field4 #cje4 ,the electric motor is a machine which transforms the energy of an electric current into mechanical energy or motion4 ,the direct current motor consists of the same essential parts as a direct current dynamo1 viz41 the field magnet1 armature1 commutator and brushes4 ,its operation is readily comprehended after one understands the following experiment3 ,set up two bar electromagnets with unlike poles facing each other about an inch apart4 ,a wire connected to a source of current is hung loosely between the poles as in ,fig4 #bid4 ,the circuit through the wire should contain a key or switch4 ,if a current is sent through the electromagnets and then another is sent through the wire1 the latter will be found to be pushed either up or down1 while if the current is reversed through the wire it is pushed in the opposite direction4 ,these results may be explained as follows3 ,consider the magnetic field about a wire carrying a current 7,see ,fig4 #bie47 ,if such a wire is placed in the magnetic field between two opposite poles of an electromagnet 7,fig4 #bif71 the wire will be moved either up or down4 ,the reason for this is shown by the diagram in ,fig4 #big4 ,here a wire carrying a current and therefore surrounded by a magnetic field passes across another magnetic field4 ,the two fields affect each other causing a crowding of the force lines either above or below the wire4 ,the wire at once tends to move sideways across the field away from the crowded side4 ,in the figure1 the wire tends to move downward4 ,illustration3 ,,fig4 #bie4--,the magnetic field about a wire carrying a current4 ,illustration3 ,,fig4 #bif4--,the magnetic field between two unlike poles4 ,illustration3 ,,fig4 #big4--,the crowding of the lines of force above the wire1 pushes it downward4 ,in a practical motor1 the wires upon the armature are so connected that those upon one side 7see ,fig4 #bih71 carry currents that pass in1 while on the other side they pass out4 ,to represent the direction of the current in the wires1 the following device is employed2 a circle with a cross 7to represent the feather in the tail of an arrow7 indicates a current going away from the observer1 while a circle with a dot at its center 7to represent the tip of an arrow7 indicates a current coming toward the observer4 ,illustration3 ,,fig4 #bih4--,the crowding of the lines of force causes the armature to revolve in a clockwise direction4 ,in ,fig4 #bih the north pole is at the left and the south pole at the right4 ,the field of the magnets therefore passes from left to right as indicated in the figure4 ,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 away4 ,applying the right-hand rule1 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 side4 ,this will cause a rotation up on the left side and down on the right1 or in a clockwise direction4 ,illustration3 ,,fig4 #bii4--,view of a one-half horse-power motor4 ,if the current in the armature is reversed 7in on the left and out on the right71 the lines of force will crowd the armature around in the opposite direction or counter clockwise4 ,the rotation of the armature will also be reversed if1 while the current in the armature is unchanged in direction1 the poles of the magnet are changed thus reversing the magnetic field4 ,the motorman of a street car reverses the motion of his car by reversing the direction of the current in the armature of the motor4 ,illustration3 ,,fig4 #cjj4--,the frame and electromagnet 7at left71 front bracket and brush holder 7at right7 of the motor shown in ,fig4 #bii4 ,illustration3 ,,fig4 #cja4--,the armature of a motor4 #cjf4 ,practical motors have many coils upon the armature with a corresponding number of segments upon the commutator4 ,a large number of coils and commutator segments enables some one of the coils to exert its greatest efficiency at each instant1 hence a steady force is provided for turning the armature which causes it to run smoothly4 ,fig4 #bii represents a #a_/b horse-power motor ready for use while ,fig4 #cjj shows the frame and poles and the front bracket and brush holder1 and ,fig4 #cja represents the armature4 ,important ,topics #a4 ,the dynamo1 four essential parts1 action 7a7 for alternating currents1 7b7 for direct currents4 #b4 ,the electric motor3 7a7 essential parts1 7b7 action4 ,exercises #a4 ,why is an alternating current produced in the armature of a dynamo8 #b4 ,how is this current produced8 ,give careful explanations4 #c4 ,what is the result of ,lenz's law as applied to the dynamo8 #d4 ,apply the first two laws of electromagnetic induction to the dynamo4 #e4 ,what is the power of a dynamo if it produces #dj amperes of current at #aaj volts8 #f4 ,how much power must be applied to this dynamo if its efficiency is #ij per cent48 #g4 ,a motor takes #aj amperes of current at #bbj volts2 what is the power of the current in watts8 ,if this motor has an efficiency of #ie per cent41 how many horse-power of mechanical energy can it develop8 #h4 ,explain why reversing the current in the armature of a motor reverses the direction of rotation4 #i4 ,find the cost of running a washing machine using a #a_/b-;horsepower motor #b hours if the cost of the electricity is #aj cents a kilowatt hour4 #aj4 ,a #a_/h-;horse-power motor is used to run a sewing machine4 ,if used for #c hours what will be the cost at #aa cents a kilowatt hour8 7#c7 ,,the ,,induction ,,coil ,,and ,,the ,,transformer #cjg4 ,the ,induction ,coil4--,practically all electric currents are produced either by voltaic cells or by dynamos4 ,it is frequently found1 however1 that it is desirable to change the ,e4,m4,f4 of the current used1 either for purposes of effectiveness1 convenience1 or economy4 ,the induction coil and the transformer1 devices for changing the ,e4,m4,f4 of electric currents1 are therefore in common use4 ,the induction coil 7see ,fig4 #cjb7 consists of a primary coil of coarse wire ,p 7,fig4 #cjc7 wound upon a core of soft iron wire1 and a secondary coil1 ,s1 of several thousand turns of fine wire4 ,in circuit with the primary coil is a battery1 ,b1 and a current interrupter1 ,k1 which works like the interrupter upon an electric bell4 ,the ends of the secondary coil are brought to binding posts or spark points as at ,d4 ,illustration3 ,,fig4 #cjb4--;,an induction coil4 ,the current from the battery flows through the primary coil magnetizing the iron core4 ,the magnetism in the core attracts the soft-iron end of the interrupter1 drawing the latter over and breaking the circuit at the screw contact1 ,k4 ,this abruptly stops the current and at once the core loses its magnetism4 ,the spring support of the interrupter now draws the latter back to the contact1 ,t1 again completing the circuit4 ,the whole operation is repeated1 the interrupter vibrating rapidly continually opening and closing the circuit4 ,illustration3 ,,fig4 #cjc4--;,diagram showing the parts of an induction coil4 #cjh4 ,the ,production of ,induced ,currents in the ,secondary ,coil4--,when the current flows through the primary it sets up a magnetic field in the core4 ,when the current is interrupted1 the field disappears4 ,the increase and decrease in the field of the core induces an ,e4,m4,f4 in the secondary coil1 in accordance with the first law of electromagnetic induction4 ,the ,e4,m4,f4 produced depends upon 7a7 the number of turns in the secondary1 7b7 the strength of the magnetic field and 7c7 the rate of change of the field4 ,the rate of change in the field is more rapid at the break than at the make4 ,when the circuit is closed it takes perhaps #a_/aj of a second for the current to build up to its full strength while at a break the current stops in perhaps #j4jjjja of a second1 so that the induced ,e4,m4,f4 is perhaps #aj1jjj times as great at break as at make4 ,to increase the suddenness of the make and break1 a condenser is often connected in the primary circuit1 in parallel1 with the interrupter4 7,see ,fig4 #cjc1 ,c47 ,this condenser provides a place to hold the rush of current at the instant that the interrupter breaks the circuit4 ,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 ,e4,m4,f4 ,the induced currents from induction coils are sometimes called faradic currents in honor of ,faraday who discovered electromagnetic induction4 ,they are used to operate sparking devices upon gas and gasoline engines and in many devices and experiments in which high-tension electricity is employed4 ,illustration3 ,,fig4 #cjd4--,the transformer has a closed core2 the induction coil1 an open core4 ,illustration3 ,,fig4 #cje4--,the laminated iron core of a transformer4 ,illustration3 ,,fig4 #cjf4--;,cross-section of the transformer shown in ,fig4 #cje showing the magnetic field around the primary and secondary coils4 #cji4 ,the ,transformer4--,this is like the induction coil in that it uses a primary and a secondary coil1 and an iron core to carry the magnetic field4 7,see ,fig4 #cjd47 ,they differ in that the transformer has a closed core or one forming a continuous iron circuit1 while the induction coil has an open core1 or one in which the magnetic field must travel in air from the north to the south poles of the core4 ,the transformer must always be used with an alternating current while the induction coil may use either a direct or an alternating current4 ,further1 the induction coil always produces a higher ,e4,m4,f4 while the transformer may produce an ,e4,m4,f4 in its secondary coil that is either higher or lower than the one in the primary4 ,the former is called step-up while the latter is a step-down transformer4 ,the alternating current in the primary coil of the transformer produces an alternating magnetic flux in the iron core4 ,this iron core is laminated 7see ,fig4 #cje7 to prevent the heating that would result if a solid core were used4 ,the alternating magnetic flux induces in the secondary coil an ,e4,m4,f4 in accordance with the following rule4 ,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 coils4 ,if the secondary coil has #h turns while the primary has #d1 the ,e4,m4,f4 of the secondary will be just twice that of the primary4 ,or1 if in the primary coil of the transformer ,fig4 #cjf is an ,e4,m4,f4 of #aaj volts1 in the secondary will be found an ,e4,m4,f4 of #bbj volts4 ,illustration3 ,,fig4 #cjg4--;,a commercial transformer4 #caj4 ,uses of ,transformers4--,in electric lighting systems1 dynamos often produce alternating currents at #ajjj to #ab1jjj volts pressure4 ,it is very dangerous to admit currents at this pressure into dwellings and business houses1 so that transformers are installed just outside of buildings to step-down the high voltage currents to #aaj or #bbj volts4 ,the lighting current that enters a house does not come directly from a dynamo4 ,it is an induced current produced by a transformer placed near the house4 7,see ,fig4 #cjg47 ,in a perfect transformer the efficiency would be #ajj per cent4 ,this signifies that the energy that is sent into the primary coil of the transformer exactly equals the energy in the secondary coil4 ,the best transformers actually show efficiencies better than #ig per cent4 ,the lost energy appears as heat in the transformer4 ,the transfer of great power in a large transformer from one circuit to another circuit entirely separate and distinct1 without any motion or noise and almost without loss1 is one of the most wonderful phenomena under the control of man4 #caa4 ,the mercury arc rectifier is a device for changing an alternating current into a direct current4 ,it is frequently used for charging storage batteries where only alternating current is supplied by the electric power company4 ,it consists of an exhausted bulb containing two carbon or graphite electrodes marked ,g in ,fig4 #cjh and a mercury electrode marked ,m4 ,it is found that current will pass through such a bulb only from the graphite to the mercury but not in the reverse direction4 ,in operating the device1 the secondary terminals of an alternating current transformer ,t are connected to the graphite terminals of the rectifier4 ,a wire connected to the center of the secondary of the transformer at ,c is attached to the negative terminal of the storage battery ,,sb4 ,the positive terminal of the battery is connected to the mercury electrode of the rectifier tube through a reactance or choke coil ,r4 ,this coil serves to sustain the arc between the alternations4 ,sw is a starting switch1 used only in striking the arc4 ,it is opened immediately after the tube begins to glow4 ,illustration3 ,,fig4 #cjh4--;,diagram of a mercury arc rectifier4 ,important ,topics ,transformer1 induction coil1 mercury arc rectifier1 construction1 action2 uses of each4 ,exercises #a4 ,does the spark of an induction coil occur at make or at break8 ,why8 #b4 ,what must be the relative number of turns upon the primary and secondary coils of a transformer if it receives current at #bbj volts and delivers current at #aaj8 ,also show by diagram4 #c4 ,would the transformer work upon a direct current8 ,why8 #d4 ,explain why the interrupter is a necessary part of the induction coil and not of the transformer4 #e4 ,if a building used eighty #aaj-volt incandescent lamps1 what would be necessary to light them if they were joined in series8 ,why would this not be practical8 #f4 ,if a #af-;candle-power lamp requires #j4e ampere upon a #aaj-volt circuit what current and voltage will be needed to operate #ab such lamps in parallel8 #g4 ,what will it cost to run these lamps #d hours a night for #cj days at #aj cents per kilowatt hour8 #h4 ,if a mercury arc rectifier uses #e amperes of current at #aaj volts alternating current to produce #e amperes of direct current at #gj volts1 what is the efficiency of the rectifier8 #i4 ,compute the heat produced in a #dj watt tungsten lamp in #a minute4 #aj4 ,compute the heat produced in a #fj watt carbon incandescent lamp in #a hour4 7#d7 ,,the ,,telephone #cab4 ,the ,electric ,telephone4--,this is an instrument for reproducing the human voice at a distance by an electric current4 ,the modern electric telephone consists of at least four distinct parts 7see ,fig4 #cab72 viz41 a transmitter1 an induction coil1 an electric battery1 and a receiver4 ,the first three of these are concerned in sending1 or transmitting over the connecting wires a fluctuating electric current1 which has been modified by the waves of a human voice4 ,the receiver1 is affected by the fluctuating current and reproduces the voice4 ,it will be considered first1 in our study4 #cac4 ,the telephone receiver was invented in #ahgf by ,alexander ,graham ,bell4 ,it consists of a permanent steel magnet1 ,u shaped1 with a coil of fine insulated copper wire about each pole4 7,see ,fig4 #caj47 ,a disc of thin sheet iron is supported so that its center does not quite touch the poles of the magnet4 ,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 place4 ,illustration3 ,,fig4 #cji4--,the simplest telephone system4 ,it consists of two telephone receivers connected in series on a circuit4 ,it will work1 but not satisfactorily4 ,the action of the receiver may be understood from the following explanation3 ,the electric current sent to the receiver1 comes from the secondary coil of the induction coil2 it is an alternating current1 fluctuating back and forth just in time with the waves of the voice affecting it at the transmitter4 ,this alternating current flows around the coils on the poles of the permanent magnet4 ,when this current flows in one direction1 its magnetic field assists the field of the permanent magnet1 strengthening it4 ,this stronger magnetic field draws the thin iron disc in front of the poles of the magnet a little closer to them4 ,when the current in the coils flows the other way1 its magnetic field weakens the field of the steel magnet1 and the disc is drawn back by the force of its own elasticity4 ,thus the disc of the receiver vibrates with the alternations of the current1 and reproduces the same sounds that were spoken into the transmitter4 ,illustration3 ,,fig4 #caj4--;,a telephone receiver4 ,this receiver has a permanent horseshoe magnet with a coil about each pole4 #cad4 ,the ,telephone ,transmitter4--,the telephone receiver just described has great sensitiveness in reproducing sound1 but it is not satisfactory as a transmitter or sending apparatus4 ,the transmitter commonly used is represented in cross-section in ,fig4 #caa4 ,in this figure1 back of the mouthpiece1 is a thin carbon disc1 ,d4 ,back of this disc is a circular compartment containing granular carbon1 g4 ,the wires of the circuit are connected to the carbon disc and to the back of the case containing granular carbon4 ,the circuit through the transmitter also includes a voltaic or storage cell and the primary coil of an induction coil4 7,see ,fig4 #cab47 ,illustration3 ,,fig4 #caa4--;,a telephone transmitter4 ,illustration3 ,,fig4 #cab4--,telephone instruments at one end of a talking circuit4 #cae4 ,the action of the transmitter is explained as follows3 ,when the sound waves of the voice strike upon the carbon disc1 the latter vibrates1 alternately increasing and decreasing the pressure upon the granular carbon4 ,when the pressure increases1 the electrical resistance of the granular carbon is lessened1 and when the pressure upon it is decreased1 its resistance increases4 ,this changing resistance causes fluctuations in the electric current that correspond exactly with the sound waves of the voice affecting it4 #caf4 ,a complete telephone system operating with a local battery is shown in ,fig4 #cab4 ,a person speaking into the transmitter causes a fluctuation in the electric current in the transmitter as described in ,art4 #cae4 ,this fluctuating current passes through the primary coil of the induction coil ,ic4 ,this fluctuating current produces a fluctuating magnetic field in its core4 ,this fluctuating field induces an alternating current in the secondary coil which alternates just as the primary current fluctuates1 but with a much higher ,e4,m4,f4 than the latter4 ,the alternating current passes to the receiver which reproduces the speech as described in ,art4 #cac4 ,the line circuit includes the secondary of the induction coil1 the receiving instrument and the receiver of the sending instrument so that the voice is reproduced in both receivers4 ,an electric bell is placed at each station to call the attention of parties wanted4 ,the movement of the receiver hook when the receiver is lifted1 disconnects the bell and closes the talking circuit4 ,the latter is opened and the bell connected when the receiver is hung up again4 ,illustration3 ,,fig4 #cac4--;,diagram of a telephone system as used in a large exchange4 ,in cities and towns1 the telephone system in use differs from the one described in usually having one large battery placed in the central exchange1 instead of dry cells at each instrument4 7,see ,fig4 #cac47 ,also the operator at central is called by simply taking the receiver from the hook instead of being rung up by the subscriber4 ,the operations of the transmitter1 induction coil and receiver1 however1 are the same in all telephones4 ,important ,topics #a4 ,receiver3 parts1 action4 #b4 ,transmitter3 parts1 action4 #c4 ,induction coil1 bell1 line wires1 etc4 #d4 ,action of the whole device4 ,exercises #a4 ,state three important electrical laws or principles that are employed in the operation of the telephone4 ,what is the application of each8 #b4 ,connect the binding posts of a telephone receiver with a sensitive galvanometer and press on the diaphragm of the receiver2 a deflection of the galvanometer will be noticed4 ,release the diaphragm and a reflection in the opposite direction is seen4 ,explain4 #c4 ,is the current passing through the transmitter the one going to the receiver of the instrument8 ,explain4 #d4 ,does the receiver at the telephone used by a person repeat the speech of the person8 ,explain4 #e4 ,how many #j4e ampere lamps can be used with a #f ampere fuse8 #f4 ,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 doors8 #g4 ,how many candle power should a #fj watt carbon incandescent lamp give1 if its efficiency is #c4d watts per candle power8 #h4 ,three incandescent lamps having resistances of #ajj1 #aej1 and #bdj ohms1 respectively1 are connected in parallel4 ,what is their combined resistance8 ,review ,outline3 ,induced ,currents ,induced currents2 #c laws1 illustrations4 ,construction1 action1 and uses of--magneto1 dynamo1 induction coil1 transformer1 motor1 telephone4 ,mercury arc rectifier4 ,terms--primary1 secondary1 for coils and currents1 armature1 commutator1 slip ring1 brush1 rectifier1 open core1 series1 shunt1 and compound connections for dynamos4 ,,chapter ,,xv ,,sound 7#a7 ,,sound ,,and ,,wave ,,motion #cag4 ,what is a ,sound8--,this question has two answers1 which may be illustrated as follows3 ,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 away4 ,if when the tapper strikes the bell at the end of the week no ear is within a hundred miles1 is any sound produced8 ,the two view-points are now made evident1 for some will answer no others yes4 ,those answering no hold that sound is a sensation which would not be produced if no ear were at hand to be affected4 ,those answering yes understand1 by the term sound1 a mode of motion capable of affecting the auditory nerves1 and that sound exists wherever such motions are present4 ,this latter point of view is called the physical and is the one we are to use in this study4 ,illustration3 ,,fig4 #cad4--,the tuning fork is vibrating4 #cah4 ,source of ,sound4--,if we trace any sound to its source1 it will be found to originate in a body in rapid motion usually in what is called a state of vibration4 ,to illustrate1 take a tuning fork1 strike it to set it in vibration and place its stem firmly against a thin piece of wood2 the sound will be strengthened materially by the vibration of the wood4 ,if now the vibrating fork is placed with the tips of the prongs in water1 the vibration is plainly shown by the spattering of the water 7,fig4 #cad74 ,when one speaks1 the vibrating body is in the larynx at the top of the windpipe4 ,its vibration may be plainly felt by the hand placed upon the throat while speaking4 #cai4 ,sound ,media4--,usually sounds reach the ear through the air4 ,the air is then said to be a medium for sound4 ,other substances may serve as a sound medium1 for if the head is under water and two stones1 also under water1 are struck together a sharp sound is heard4 ,also if one end of a wooden rod is held at the ear and the other end of the rod is scratched by a pin1 the sound is more plainly perceived through the wood than through the air4 ,think of some illustration from your own experience of a solid acting as medium for sound4 ,if an electric bell is placed in a bell jar attached to an air pump1 as in ,fig4 #cae1 on exhausting the air the loudness of the sound is found to diminish1 indicating that in a perfect vacuum no sound would be transmitted4 ,this effect of a vacuum upon the transmission of sound is very different from its effect upon radiation of heat and light4 ,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 matter4 ,sound differs from this in that it is always transmitted by some material body and cannot exist in a vacuum4 ,illustration3 ,,fig4 #cae4--,sound does not travel in a vacuum4 #cbj4 ,speed of ,sound4--,everyone has noticed that it takes time for sound to travel from one place to another4 ,if we see a gun fired at a distance1 the report is heard a few seconds after the smoke or flash is seen4 ,the time elapsing between a flash of lightning and the thunder shows that sound takes time to move from one place to another4 ,careful experiments to determine the speed of sound have been made4 ,one method measures accurately the time required for the sound of a gun to pass between two stations several miles apart4 ,a gun or cannon is placed at each station4 ,these are fired alternately1 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 wind4 ,this mode of determining the speed of sound is not accurate4 ,other methods1 more refined than the one just described have given accurate values for the speed of sound4 ,the results of a number of experiments show that1 at the freezing temperature1 #j;,c41 the speed of sound in air is #ccb meters or #ajij ft4 a second4 ,the speed of sound in air is affected by the temperature1 increasing #b ft4 or #j4f meter per second for each degree that the temperature rises above #j;,c4 ,the speed decreases the same amount for each degree ,c4 that the air is cooled below the freezing point4 ,the speed of sound in various substances has been carefully determined4 ,it is greater in most of them than in air4 ,in water the speed is about #adjj meters a second2 in wood1 while its speed varies with different kinds1 it averages about #djjj meters a second2 in brass the speed is about #cejj meters2 while in iron it is about #eajj meters a second4 #cba4 ,the ,nature of ,sound4--,we have observed that sound originates at a vibrating body1 that it requires a medium in order to be transmitted from one place to another1 and that it travels at a definite speed in a given substance4 ,nothing has been said1 however1 of the mode of transmission1 or of the nature of sound4 ,sounds continue to come from an alarm clock even though it is placed under a bell jar4 ,it is certain that nothing material can pass through the glass of the jar4 ,if1 however1 we consider that sound is transmitted by waves through substances the whole matter can be given a simple explanation4 ,in order to better understand the nature of sound a study of waves and wave motion will be taken up in the next section4 ,important ,topics ,sound3 two definitions1 source1 medium1 speed1 nature4 ,exercises #a4 ,give two illustrations from outside the laboratory of the fact that sound is transmitted by other materials than air4 #b4 ,name the vibrating part that is the source of the sound in three different musical instruments4 #c4 ,is sound transmitted more strongly in solids1 liquids or gases8 ,how do you explain this8 #d4 ,how far away is a steamboat if the sound of its whistle is heard #aj seconds after the steam is seen1 the temperature being #bj;,c48 ,compute in feet and in meters4 #e4 ,how many miles away is lightning if the thunder is heard #ab seconds after the flash in seen1 the temperature being #be;,c48 #f4 ,four seconds after a flash of lightning is seen the thunder clap is heard4 ,the temperature is #ij;,f4 ,how far away was the discharge8 #g4 ,the report of a gun is heard #c seconds after the puff of smoke is seen4 ,how far away is the gun if the temperature is #bj;,c48 #h4 ,an explosion takes place #aj miles away4 ,how long will it take the sound to reach you1 the temperature being #hj;,f84 ,how long at #j;,f48 #i4 ,how long after a whistle is sounded will it be heard if the distance away is #a_/d mile1 the temperature being #ij;,f48 #aj4 ,the report of an explosion of dynamite is heard #b minutes after the puff of smoke is seen4 ,how far away is the explosion the temperature being #gg;,f48 7#b7 ,,waves,n ,,and ,,wave ,,motion ,n ,a wave is a disturbance in a substance or medium that is transmitted through it4 #cbb4 ,visible ,waves4--,it is best to begin the study of wave motion by considering some waves which are familiar to most persons4 ,take for example the waves that move over the surface of water 7,fig4 #caf74 ,these have an onward motion1 yet boards or chips upon the surface simply rise and fall as the waves pass them4 ,they are not carried onward by the waves4 ,the water surface simply rises and falls as the waves pass by4 ,consider also the waves that may be seen to move across a field of tall grass or grain4 ,such waves are produced by the bending and rising of the stalks as the wind passes over them4 ,again1 waves may be produced in a rope fastened at one end1 by suddenly moving the other end up and down4 ,these waves move to the end of the rope where they are reflected and return4 ,the three types of waves just mentioned are illustrations of transverse waves1 the ideal case being that in which the particles move at right angles to the path or course of the wave4 ,such waves are therefore called transverse waves4 ,illustration3 ,,fig4 #caf4--,water waves4 #cbc4 ,longitudinal waves4--,another kind of wave is found in bodies that are elastic and compressible and have inertia1 such as gases and coiled wire springs4 ,such waves may be studied by considering a wire spring as the medium through which the waves pass4 7,see ,fig4 #cah47 ,illustration3 ,,fig4 #cag4--,the compression wave travels through the spring4 ,if the end of the wire spring shown in ,fig4 #cag is struck the first few turns of the spring will be compressed4 ,since the spring possesses elasticity1 the turns will move forward a little and compress those ahead1 these will press the next in turn and so on4 ,thus a compression wave will move to the end of the spring1 where it will be reflected and return4 ,consider the turns of the spring as they move toward the end4 ,on account of their inertia they will continue moving until they have separated from each other more than at first1 before returning to their usual position4 ,this condition of a greater separation of the turns of the spring than usual is called a rarefaction4 ,it moves along the spring following the wave of compression4 ,the condensation and rarefaction are considered as together forming a complete wave4 ,since the turns of wire move back and forth in a direction parallel to that in which the wave is traveling1 these waves are called longitudinal4 ,illustration3 ,,fig4 #cah4--,longitudinal waves 7#a7 in a spring1 7#b7 in air1 and 7#c7 graphic representation showing wave length1 condensations1 and rarefactions4 #cbd4 ,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 spring4 ,consider a light spring 7,fig4 #cah1 #a7 attached at the end of a vibrating tuning fork1 ,k1 and also to a diaphragm1 ,d4 ,each vibration of the fork will first compress and then separate the coils of the spring4 ,these impulses will be transmitted by the spring as described in ,art4 #cae1 and cause the diaphragm to vibrate at the same rate as the tuning fork4 ,the diaphragm will then give out a sound similar to that of the tuning fork4 ,suppose that the spring is replaced by air1 and the diaphragm1 by the ear of a person1 ,e1 7,fig4 #cah1 #b47 when the prong of the fork moves toward the ear it starts a compression and when it moves back a rarefaction4 ,the fork continues vibrating and these impulses move onward like those in the spring at a speed of about #aabj ft4 in a second4 ,they strike the diaphragm of the ear causing it to move back and forth or to vibrate at the same rate as the tuning fork1 just as in the case of the diaphragm attached to the spring4 #cbe4 ,graphic ,representation of ,sound waves4--,it is frequently desirable to represent sound waves graphically4 ,the usual method is to use a curve like that in 7,fig4 #cah1 #c74 ,this curve is considered as representing a train of waves moving in the same direction as those in ,fig4 #cah #a and #b1 and also having the same length4 ,the part of the wave ,a-,b represents a condensation of the sound wave and the part ,b-,c represents a rarefaction4 ,a complete wave consisting of a condensation and a rarefaction is represented by that portion of the curve ,a-,c4 ,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 waves4 ,the curve1 ,fig4 7#cah1 #c7 represents not only the wave length1 but also the height of the wave or the amount of movement of the particles along the wave4 ,this is called the amplitude and is indicated by the distance ,a-b4 ,since the loudness or intensity of a sound is found to depend upon the amount of movement of the particles along the wave1 the amplitude of the curve is used to indicate the loudness of the sound represented4 ,all of the characteristics of a sound wave may be graphically represented by curves4 ,such curves will be used frequently as an aid in explaining the phenomena of wave motion both in sound and in light4 #cbf4 ,reflections of ,sound4--,it is found that a wave moving along a wire spring is reflected when it reaches the end and returns along the spring4 ,similarly a sound wave in air is reflected upon striking the surface of a body4 ,if the wave strikes perpendicularly it returns along the line from which it comes1 if1 however1 it strikes at some other angle it does not return along the same line1 but as in other cases of reflected motion1 the direction of the reflected wave is described by the ,law of ,reflected ,motion as follows3 ,the angle of reflection is always equal to the angle of incidence4 ,this law is illustrated in ,fig4 #cai4 ,suppose that a series of waves coming from a source of sound move from ,h to ,o4 ,after striking the surface ,,ij the waves are reflected and move toward ,l along the line ,,ol4 ,let ,,po be perpendicular to the surface ,,ij at ,o4 ,then ,,hop is the angle of incidence and ,,lop is the angle of reflection4 ,by the law of reflected motion these angles are equal4 ,in an ordinary room when a person speaks the sound waves reflected from the smooth walls reinforce the sound waves moving directly to the hearers4 ,it is for this reason that it is usually easier to speak in at room than in the open air4 ,other illustrations of the reinforcement of sound by reflection are often seen4 ,thus an ear trumpet 7,fig4 #cbj71 uses the principle of reflection and concentration of sound4 ,so-called sounding boards are sometimes placed back of speakers in large halls to reflect sound waves to the audience4 ,illustration3 ,,fig4 #cai4--,law of reflection4 ,illustration3 ,,fig4 #cbj4--;,an ear trumpet4 #cbg4 ,echoes4--,an echo is the repetition of a sound caused by its reflection from some distant surface such as that of a building1 cliff1 clouds1 trees1 etc4 ,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 listener4 ,experiments have shown that the sensation of a sound persists about one-tenth of a second4 ,since the velocity of sound at #bj;,c4 is about #aacj ft4 per second1 during one-tenth of a second the sound wave will travel some #aac ft4 ,if the reflecting surface is about #ef ft4 distant a short sound will be followed immediately by its echo as it is heard one-tenth of a second after the original sound4 ,the reflected sound tends to strengthen the original one if the reflecting surface is less than #ef ft4 away4 ,if the distance of the reflecting surface is much more than #ef ft4 however1 the reflected sound does not blend with the original one but forms a distinct echo4 ,the echoes in large halls especially those with large smooth walls may very seriously affect the clear perception of the sound4 ,such rooms are said to have poor acoustic properties4 ,furniture1 drapery1 and carpets help to deaden the echo because of diffused reflection4 ,the ,mormon ,tabernacle at ,salt ,lake ,city1 ,utah1 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 remarkable1 a pin dropped at one end being plainly heard at the other end about #bjj ft4 away4 ,important ,topics #a4 ,waves3 transverse1 longitudinal2 wave length1 condensation1 rarefaction4 #b4 ,wave motion3 in coiled spring1 in air1 on water4 #c4 ,reflection of waves3 law1 echoes4 ,exercises #a4 ,a hunter hears an echo in #h seconds after firing his gun4 ,how far is the reflecting surface if the temperature is #bj;,c48 #b4 ,how far is the reflecting surface of a building if the echo of one's footsteps returns in #a second at #aj;,c48 #c4 ,why is it easier to speak or sing in a room than out of doors8 #d4 ,draw a curve that represents wave motion4 ,make it exactly three full wave lengths1 and state why your curve shows this length4 ,indicate the parts of the curve that correspond to a condensation and to a rarefaction4 #e4 ,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 ,art4 #cbg8 #f4 ,an echo is heard after #f seconds4 ,how far away is the reflecting surface1 the temperature being #gj;,f48 #g4 ,why are outdoor band-stands generally made with the back curving over the band8 #h4 ,a man near a forest calls to a friend4 ,in #d seconds the echo comes back4 ,how far away is he from the forest8 #i4 ,would it be possible for us ever to hear a great explosion upon the moon8 ,explain4 #aj4 ,if a sunset gun was fired exactly at #f3jj ,p4,m4 at a fort1 at what time was the report heard by a man #be miles away1 if the temperature was #aj;,c48 7#c7 ,,intensity ,,and ,,pitch ,,of ,,sounds ,illustration3 ,,fig4 #cba4--;,graphic representations of 7a7 a noise1 7b7 a musical sound4 #cbh4 ,musical ,sounds and ,noises ,distinguished4--,the question is sometimes raised1 what is the difference between a noise and a musical sound8 ,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 string4 ,a noise on the other hand is characterized by sudden or irregular vibrations such as those produced by a wagon bumping over a stony street4 ,these differences may be represented graphically as in ,fig4 #cba1 7a7 represents a noise1 7b7 a musical tone4 ,illustration3 ,,fig4 #cbb4--;,curve b represents a tone of greater intensity4 #cbi4 ,characteristics of ,musical ,sounds4--,musical tones differ from one another in three ways or are said to have three characteristics1 viz41 intensity1 pitch1 and quality4 ,thus two sounds may differ only in intensity or loudness1 that is1 be alike in all other respects except this one1 as when a string of a piano is struck at first gently1 and again harder4 ,the second sound is recognized as being louder4 ,the difference is due to the greater amplitude of vibration caused by more energy being used4 ,fig4 #cbb shows these differences graphically4 ,curve b represents the tone of greater intensity or loudness1 since its amplitude of vibration is represented as being greater4 #ccj4 ,conditions ,affecting the ,intensity of ,sound4--,the intensity of sounds is also affected by the area of the vibrating body4 ,this is shown by setting a tuning fork in vibration4 ,the area of the vibrating part being small1 the sound is heard but a short distance from the fork4 ,if1 however1 the stem of the vibrating fork is pressed against the panel of a door or the top of a box1 the sound may be heard throughout a room4 ,the stem of the fork has communicated its vibrations to the wood4 ,the vibrating area1 being greater1 the sound is thereby much increased in intensity1 producing a wave of greater amplitude4 ,the same principle is employed in the sounding boards of musical instruments as in the piano1 violin1 etc4 ,it is a common observation that sounds decrease in loudness as the distance from the source increases4 ,this is due to the increase of the surface of the spherical sound waves spreading in all directions from the source4 ,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 source4 ,if a sound is confined so that it cannot spread1 such as the sound moving through a speaking tube1 it maintains its intensity for a considerable distance4 ,an ear trumpet 7see ,fig4 #cbj7 also applies this principle4 ,it is constructed so that sound from a given area is concentrated by reflection to a much smaller area with a corresponding increase in intensity4 ,the megaphone 7,fig4 #cbc71 and the speaking trumpet start the sound waves of the voice in one direction so that they are kept from spreading widely1 consequently by its use the voice may be heard several times the usual distance4 ,the intensity of a sound is also affected by the density of the transmitting medium4 ,thus a sound produced on a mountain top is fainter and thinner than one produced in a valley4 ,the sound of a bell in the receiver of an air pump becomes weaker as the air is exhausted from the latter4 ,four factors thus influence the intensity of a sound1 the area of the vibrating body1 its amplitude of vibration1 the distance of the source and the density of the transmitting medium4 ,it is well to fix in mind the precise effect of each of these factors4 ,illustration3 ,,fig4 #cbc4--,the megaphone4 #cca4 ,pitch4--,the most characteristic difference between musical sounds is that of pitch4 ,some sounds have a high pitch1 such as those produced by many insects and birds4 ,others have a low pitch as the notes of a bass drum or the sound of thunder4 ,how notes of different pitch are produced may be shown by the siren 7,fig4 #cbd74 ,this is a disc mounted so as to be rotated on an axis4 ,several rows of holes are drilled in it in concentric circles4 ,the number of holes in successive rows increases from within outward4 ,if when the siren is rapidly rotated air is blown through a tube against a row of holes a clear musical tone is heard4 ,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 intervals4 ,if the blast is directed against a row of holes nearer the circumference the pitch is higher1 if against a row nearer the center the pitch is lower4 ,or if the blast is sent against the same row of holes the pitch rises when the speed increases and lowers when the speed lessens4 ,these facts indicate that the pitch of a tone is due to the number of pulses or vibrations that strike the ear each second2 also that the greater the rate of vibration1 the higher the pitch4 ,illustration3 ,,fig4 #cbd4--;,a siren4 #ccb4 ,the ,major ,scale4--,if a siren is made with eight rows of holes1 it may indicate the relation between the notes of a major scale4 ,to accomplish this1 the number of holes in the successive rows should be #bd1 #bg1 #cj1 #cb1 #cf1 #dj1 #de1 #dh4 ,if a disc so constructed is rapidly rotated at a uniform rate1 a blast of air sent against all of the rows in succession produces the tones of the scale4 ,these facts indicate that the relative vibration numbers of the notes of any major scale have the same relation as the numbers #bd1 #bg1 #cj1 #cb1 #cf1 #dj1 #de1 #dh4 ,the note called middle ,c is considered by physicists as having #bef vibrations a second4 ,this would give the following actual vibration numbers to the remaining notes of the major scale that begins with ,middle ,c ,d4-#bhh1 ,e4-#cbj1 ,f4-#cda4c1 ,g4-#chd1 ,a4-#dbf4f1 ,b4-#dhj1 ,c'4-#eab4 ,musicians1 however1 usually make use of a scale of slightly higher pitch4 ,the international standard of pitch in this country and in ,europe is that in which ,a has #dce vibrations per second4 ,this corresponds to #bfa vibrations for middle ,c4 #ccc4 ,the ,relation between ,speed1 ,wave ,length1 and ,number of ,vibrations per ,second4--,since the notes from the various musical instruments of an orchestra are noticed to harmonize as well at a distance as at the place produced1 it is evident that notes of all pitches travel at the same rate1 or have the same speed4 ,notes of high pitch1 having a high vibration rate produce more waves in a second than notes of low pitch1 consequently the former are shorter than the latter4 ,the following formula gives the relation between the speed 7v71 wave length 7l71 and number of vibrations per sec4 7n73 v l n1 or l v_/n that is1 the speed of a sound wave is equal to the number of vibrations per second times the wave length1 or the wave length is equal to the speed divided by the number of vibrations per second4 ,this formula may also be employed to find the number of vibrations when the wave length and speed are given4 ,important ,topics #a4 ,difference between noise and music4 #b4 ,factors affecting intensity3 area1 amplitude1 density1 distance4 #c4 ,pitch1 major scale1 relative vibration numbers4 #d4 ,relation between speed1 wave length and vibration rate4 ,exercises #a4 ,give an illustration from your own experience of each of the factors affecting intensity4 #b4 ,write the relative vibration numbers of a major scale in which do has #abj vibrations4 #c4 ,what is the wave length of the ,a of international concert pitch at #be;,c48 ,compute in feet and centimeters4 #d4 ,at what temperature will sound waves in air in unison with ,middle ,c be exactly #d ft4 long8 #e4 ,explain the use of a megaphone4 #f4 ,what tone has waves #c ft4 long at #be;,c48 #g4 ,what is the purpose of the sounding board of a piano8 #h4 ,two men are distant #ajjj and #cjjj ft4 respectively from a fog horn4 ,what is the relative intensity of the sounds heard by the two men8 #i4 ,the speaking tone of the average man's voice has #afj vibrations per second4 ,how long are the waves produced by him at #bj;,c48 7#d7 ,,musical ,,scales ,,and ,,resonance #ccd4 ,a musical interval refers to the ratio between the pitches,o of two notes as indicated by the results of the siren experiment4 ,the simplest interval1 or ratio between two notes is the octave1 ,c'3,c1 or #b3a 7#dh3bd74 ,other important intervals with the corresponding ratios are the fifth1 ,g3,c1 or #c3b 7#cf3bd72 the sixth1 ,a3,c1 or #e3c 7#dj3bd72 the fourth1 ,f3,c1 #d3c 7#cb3bd72 the major third1 ,e3,c1 or #e3d 7#cj3bd72 and the minor third1 ,g3,e1 #f3e4 ,the interval between any two notes may be determined by finding the ratio between the vibration numbers of the two notes4 ,thus1 if one note is produced by #fjj vibrations a second and another by #djj1 the interval is #c3b1 or a fifth1 and this would be recognized by a musician who heard the notes sounded together or one after the other4 ,below is a table of musical nomenclatures1 showing various relations between the notes of the major scale4 ,o ,pitch as used here1 means vibration rate4 ,,table ,,of ,,musical ,,nomenclatures ---------------------------------------- ------------------------- ,name of note ,c ,d ,e ,f ,g ,a ,b ,c ----------------------------- ----- ----------------------------- ,frequency in terms ofn#i_/hn#e_/dn#d_/cn#c_/bn#e_/cn#ae_/hn #bn do ---------------------------------------- ------------------- ,intervals #i_/h #aj_/i #af_/ae #i_/h #aj_/i #i_/h #af_/ae ---------------------------------------- ------------------- ,name of note in vocaldo re mi fa sol la ti do music ---------------------------------------- ------------------------- ,treble clef4 ,music ,bass clef4 ,music ---------------------------------------- ------------------------- ,international pitch of treble clef #bfa #bic4f #cbf4c #cdh4 #cia4e #dce #dhi4d #ebb ---------------------------------------- ------------------------- ,scientific scale #bef #bhh #cbj #cda4c #chd #dbf4f #dhj #eab ---------------------------------------- ------------------------- ,relative vibration #bd #bg #cj #cb #cf #dj #de #dh numbers ---------------------------------------- ------------------------- #cce4 ,major and ,minor ,triads4--,the notes ,c1 ,e1 ,g 7do1 mi1 sol7 form what is called a major triad4 ,the relative vibration numbers corresponding are #bd1 #cj1 #cf4 ,these in simplest terms have ratios of #d3e3f4 ,any three other tones with vibration ratios of #d3e3f will also form a major triad4 ,if the octave of the lower tone is added1 the four make a major chord4 ,thus3 ,f1 ,a1 ,c 7fa1 la1 do71 #cb3dj3dh1 or #d3e3f1 also form a major triad as do ,g1 ,b1 ,d 7sol1 ti1 re71 #cf3de3ed1 or #d3e3f4 ,inspection will show that these three major triads comprise all of the tones of the major scale ,d being the octave of ,d4 ,it is1 therefore1 said that the major scale is based1 or built1 upon these three major triads4 ,the examples just given indicate the mathematical basis for harmony in music4 ,three notes having vibration ratios of #aj3ab3ae are called minor triads4 ,these produce a less pleasing effect than those having ratios of #d3e3f4 #ccf4 ,the ,need for ,sharps and ,flats4--,we have considered the key of ,c4 ,this is represented upon the piano or organ by white keys only 7,fig4 #cbe74 ,now in order 7a7 to give variety to instrumental selections1 and 7b7 to accommodate instruments to the range of the human voice1 it has been necessary to introduce other notes in musical instruments4 ,these are represented by the black keys upon the piano and organ and are known as sharps and flats4 ,to illustrate the necessity for these additional notes take the major scale starting with ,b4 ,this will give vibration frequencies of #bdj1 #bgj1 #cjj1 #cbj1 #cfj1 #djj1 #dej1 and #dhj4 ,the only white keys that may be used with this scale are ,e #cbj and ,b #dhj vibrations4 ,since the second note on this scale requires #bgj vibrations about halfway between ,c and ,d the black key ,c sharp is inserted4 ,other notes must be inserted between ,d and ,e 7,d sharp71 between ,f and ,g 7,f sharp71 also ,g and ,a sharps4 ,illustration3 ,,fig4 #cbe4--,section of a piano keyboard4 #ccg4 ,tempered ,scales4--,in musical instruments with fixed notes1 such as the harp1 organ1 or piano1 complications were early recognized when an attempt was made to adapt these instruments so that they could be played in all keys4 ,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 key4 ,in using the various notes as the keynote for a major scale1 #gb different notes in the octave would be required4 ,this would make it more difficult for such instruments as the piano to be played4 ,to avoid these complications as much as possible1 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 case4 ,the differences between semitones are abolished so that1 for example1 ,c sharp and ,d flat become the same tone instead of two different tones4 ,such a scale is called a tempered scale4 ,the tempered scale has #ac notes to the octave1 with #ab equal intervals1 the ratio between two successive notes being the #b or #a4jei4 ,that is1 any vibration rate on the tempered scale may be computed by multiplying the vibration rate of the preceding note by #a4jei4 ,while this is a necessary arrangement1 there is some loss in perfect harmony4 ,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 piano1 since the simple harmonious ratios may be employed when the voices are alone4 ,the imperfection introduced by equal temperament tuning is illustrated by the following table3 ,c ,d ,e ,f ,g ,a ,b ,c ,perfect ,scale of ,c #bef4j #bhh4j #cbj4j #cda4c #chd4j #dbf4f #dhj4j #eab4j ,tempered ,scale #bef4j #bhg4c #cbb4e #cda4g #chc4f #dcj4e #dhc4c #eab4j #cch4 ,resonance4--,if two tuning forks of the same pitch are placed near each other1 and one is set vibrating1 the other will soon be found to be in vibration4 ,this result is said to be due to sympathetic vibration1 and is an example of resonance 7,fig4 #cbf74 ,if water is poured into a glass tube while a vibrating tuning fork is held over its top1 when the air column has a certain length it will start vibrating1 reinforcing strongly the sound of the tuning fork4 7,see ,fig4 #cbg47 ,this is also an example of resonance4 ,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 vibration4 ,most persons will recall illustrations of this effect from their own experience4 ,illustration3 ,,fig4 #cbf4--,one tuning fork will vibrate in sympathy with the other1 if they have exactly equal rates of vibration4 ,illustration3 ,,fig4 #cbg4--;,an air column of the proper length reinforces the sound of the tuning fork4 #cci4 ,sympathetic vibration is explained as follows3 ,sound waves produce very slight motions in objects affected by them2 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 latter4 ,this action continuing1 the body soon acquires a motion sufficient to produce audible waves4 ,a good illustration of sympathetic vibration is furnished by the bell ringer1 who times his pulls upon the bell rope with the vibration rate of the swing of the bell4 ,in the case of the resonant air column over which is held a vibrating tuning fork 7see ,fig4 #cbh71 when the prong of the fork starts downward from #a to #b1 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 #b to #a2 also when the prong starts upward from #b to #a1 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 returns4 ,while the prong is making a single movement1 up or down1 it is plain that the air wave moves twice the length of the open tube4 ,during a complete vibration of the fork1 therefore1 the sound wave moves four times the length of the air column4 ,in free air1 the sound progresses a wave length during a complete vibration1 hence the resonant air column is one-fourth the length of the sound wave to which it responds4 ,experiments with tubes cf different lengths show that the diameter of the air column has some effect upon the length giving best resonance4 ,about #be per cent4 of the diameter of the tube must be added to the length of the air column to make it just one-fourth the wave length4 ,the sound heard in seashells and in other hollow bodies is due to resonance4 ,vibrations in the air too feeble to affect the ear are intensified by sympathetic vibration until they can be heard4 ,a tuning fork is often mounted upon a box called a resonator1 which contains an air column of such dimensions that it reinforces the sound of the fork's sympathetic vibration4 ,illustration3 ,,fig4 #cbh4--;,explanation of resonance4 ,important ,topics #a4 ,musical intervals3 octave1 sixth1 fifth1 fourth1 third4 #b4 ,major chord1 #d3e3f4 #c4 ,use of sharps and flats4 ,tempered scale4 #d4 ,resonance1 sympathetic vibration1 explanation1 examples4 ,exercises #a4 ,what is a major scale8 ,why is a major scale said to be built upon three triads8 #b4 ,why are sharps and flats necessary in music8 #c4 ,what is the tempered scale and why is it used8 ,what instruments need not use it8 ,why8 #d4 ,mention two examples of resonance or sympathetic vibration from your own experience out of school4 #e4 ,an air column #b ft4 long closed at one end is resonant to what wave length8 ,what number of vibrations will this sound have per second at #be;,c48 #f4 ,at #bd;,c4 ,what length of air column closed at one end will be resonant to a sound having #bg vibrations a second8 #g4 ,a given note has #cjj vibrations a second4 ,what will be the number of vibrations of its 7a7 octave1 7b7 fifth1 7c7 sixth1 7d7 major third8 #h4 ,in the violin or guitar what takes the place of the sounding board of the piano8 #i4 ,can you explain why the pitch of the bell on a locomotive rises as you rapidly approach it and falls as you recede from it8 #aj4 ,do notes of high or low pitch travel faster8 ,explain4 #aa4 ,an ,a tuning fork on the international scale makes #dce vibrations per second4 ,what is the length of the sound waves produced8 7#e7 ,,wave ,,interference1 ,,beats1 ,,vibration ,,of ,,strings #cdj4 ,interference of waves4--,the possibility of two trains of waves combining so as to produce a reduced motion or a complete destruction of motion may be shown graphically4 ,suppose two trains of waves of equal wave length and amplitude as in ,fig4 #cbi meet in opposite phases4 ,that is1 the parts corresponding to the crests of ,a coincide with the troughs of ,b1 also the troughs of ,a with the crests of ,b2 when this condition obtains1 the result is that shown at ,c1 the union of the two waves resulting in complete destruction of motion4 ,the more or less complete destruction of one train of waves by another similar train is an illustration of interference4 ,if two sets of water waves so unite as to entirely destroy each other the result is a level water surface4 ,if two trains of sound waves combine they may so interfere that silence results4 ,the conditions for securing interference of sound waves may readily be secured by using a tuning fork and a resonating air column4 ,if the tuning fork is set vibrating and placed over the open end of the resonating air column 7see ,fig4 #cbh71 an increase in the sound through resonance may be heard4 ,if the fork is rotated about its axis1 in some positions no sound is heard while in other positions the sound is strongly reinforced4 ,similar effects may be perceived by holding a vibrating fork near the ear and slowly rotating as before4 ,in some positions interference results while in other positions the sound is plainly heard4 ,the explanation of interference may be made clear by the use of a diagram4 7,see ,fig4 #ccj47 ,let us imagine that we are looking at the two square ends of a tuning fork4 ,when the fork is vibrating the two prongs approach each other and then recede4 ,as they approach1 a condensation is produced at #b and rarefactions at #a and #c4 ,as they separate1 a rarefaction is produced at #b and condensations at #a and #c4 ,now along the lines at which the simultaneously produced rarefactions and condensations meet there is more or less complete interference4 7,see ,fig4 #cca47 ,these positions have been indicated by dotted lines extending through the ends of the prongs4 ,as indicated above1 these positions may be easily found by rotating a vibrating fork over a resonant air column1 or near the ear4 ,illustration3 ,,fig4 #cbi4--;,interference of sound waves4 ,illustration3 ,,fig4 #ccj4--;,at #b is a condensation2 at #a and #c are rarefactions4 ,illustration3 ,,fig4 #cca4--,the condensations and rarefactions meet along the dotted lines producing silence4 ,illustration3 ,,fig4 #ccb4--;,diagram illustrating the formations of beats4 #cda4 ,beats4--,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 board1 so that the sounds may be intensified1 a peculiar pulsation of the sound may be noticed4 ,this phenomenon is known as beats4 ,its production may be easily understood by considering a diagram 7,fig4 #ccb74 ,let the curve ,a represent the sound wave sent out by one tuning fork and ,b1 that sent out by the other4 ,c represents the effect produced by the combination of these waves4 ,at ,r the two sound waves meet in the same phase and reinforce each other4 ,this results in a louder sound than either produces alone4 ,now since the sounds are of slightly different pitch1 one fork sends out a few more vibrations per second than the other4 ,the waves from the first fork are therefore a little shorter than those from the other4 ,consequently1 although the two waves are at one time in the same phase1 they must soon be in opposite phases as at ,i4 ,here interference occurs1 and silence results4 ,immediately the waves reinforce1 producing a louder sound and so on alternately4 ,the resulting rise and fall of the sound are known as beats4 ,the number of beats per second must1 of course1 be the same as the difference between the numbers of vibrations per second of the two sounds4 ,one effect of beats is discord4 ,this is especially noticeable when the number of beats per second is between #cj and #abj4 ,strike the two lowest notes on a piano at the same time4 ,the beats are very noticeable4 ,illustration3 ,,fig4 #ccc4--,turkish cymbals4 ,illustration3 ,,fig4 #ccd4--,the cornet4 #cdb4 ,three ,classes of ,musical ,instruments4--,there are three classes or groups of musical instruments1 if we consider the vibrating body that produces the sound in each3 7,a7 ,those in which the sound is produced by a vibrating plate or membrane1 as the drum1 cymbals 7,fig4 #ccc71 etc42 7,b7 those with vibrating air columns1 as the flute1 pipe organ1 and cornet 7,fig4 #ccd71 and 7,c7 with vibrating wires or strings1 as the piano1 violin1 and guitar4 ,it is worth while to consider some of these carefully4 ,we will begin with a consideration of vibrating wires and strings1 these often producing tones of rich quality4 ,let us consider the strings of a piano4 7,if possible1 look at the strings in some instrument47 ,the range of the piano is #g-a_/c octaves4 ,its lowest note1 ,a#d1 has about #bg vibrations per second4 ,its highest1 ,c1 about #dagf4 ,this great range in vibration rate is secured by varying the length1 the tension1 and the diameter of the strings4 #cdc4 ,the ,laws of ,vibrating ,strings4--,the relations between the vibration rate1 the length1 the tension and the diameter1 of vibrating strings have been carefully studied with an instrument called a sonometer 7,fig4 #cce74 ,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-half4 ,by determining the vibration rate of many lengths1 the following law has been derived3 7,law ,i7 ,the rate of vibration of a string is inversely proportional to its length4 ,illustration3 ,,fig4 #cce4--;,a sonometer4 ,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 doubled1 and if it is increased nine times its rate is tripled1 that is3 7,law ,,ii7 ,the vibration rates of strings are directly proportional to the square roots of their tensions4 ,tests of the effects of diameter are made by taking wires of equal length and tension and of the same material but of different diameter4 ,suppose one is twice as thick as the other4 ,this string has a tone an octave lower or vibrates one-half as fast as the first4 ,therefore3 7,law ,,iii7 ,the vibration rates of strings are inversely proportional to the diameters4 ,these laws may be expressed by a formula n 7t7_/dl4 ,the vibration of a string is rarely a simple matter4 ,it usually vibrates in parts at the same time that it is vibrating as a whole4 ,the tone produced by a string vibrating as a whole is called its fundamental4 ,the vibrating parts of a string are called loops or segments 7see ,fig4 #ccf71 while the points of least or no vibration are nodes4 ,segments are often called antinodes4 ,illustration3 ,,fig4 #ccf4--;,a string yielding its fundamental and its first overtone4 #cdd4 ,overtones4--,the quality of the tone produced by a vibrating string is affected by its vibration in parts when it is also vibrating as a whole4 7,see ,fig4 #ccf47 ,the tones produced by the vibration in parts are called overtones or partial tones4 ,the presence of these overtones may often be detected by the sympathetic vibration of other wires near-by4 ,what is called the first overtone is produced by a string vibrating in two parts1 the second overtone by a string vibrating in three parts1 the third overtone by its vibration in four parts and so on4 ,in any overtone1 the number of the parts or vibrating segments of the string is one more than the number of the overtone4 ,for example1 gently press down the key of middle ,c of a piano4 ,this will leave the string free to vibrate4 ,now strongly strike the ,c an octave lower and then remove the finger from this key4 ,the middle ,c string will be heard giving its tone4 ,in like manner try ,e and ,g1 with ,c4 ,this experiment shows that the sound of the ,c string contains these tones as overtones4 ,it also illustrates sympathetic vibration4 ,important ,topics #a4 ,interference1 beats1 production1 effects4 #b4 ,vibration of strings1 three laws4 #c4 ,three classes of musical instruments4 #d4 ,fundamental and overtones1 nodes1 segments1 how produced8 ,results4 ,exercises #a4 ,what different means are employed to produce variation of the pitch of piano strings8 ,for violin strings8 #b4 ,how many beats per second will be produced by two tuning forks having #eab and #eji vibrations per second respectively8 #c4 ,a wire #ahj cm4 long produces middle ,c4 ,show by a diagram1 using numbers1 where a bridge would have to be placed to cause the string to emit each tone of the major scale4 #d4 ,how can a violinist play a tune on a single string8 #e4 ,what are the frequencies of the first #e overtones of a string whose fundamental gives #bef vibrations per second8 #f4 ,one person takes #aab steps a minute and another #aaf4 ,how many times a minute will the two walkers be in step8 ,how many times a minute will one be advancing the left foot just when the other advances the right8 #g4 ,why is it necessary to have a standard pitch8 #h4 ,how can the pitch of the sounds given by a phonograph be lowered8 #i4 ,how many beats per second will occur when two tuning forks having frequencies of #eab and #eae respectively1 are sounded together8 #aj4 ,which wires of a piano give the highest pitch8 ,why8 7#f7 ,,tone ,,quality1 ,,vibrating ,,air ,,columns1 ,,plates #cde4 ,quality4--,the reason for the differences in tone quality between notes of the same pitch and intensity as produced1 e4g41 by a violin and a piano1 was long a matter of conjecture4 ,helmholtz1 a ,german physicist 7see p4 #cig7 first definitely proved that tone quality is due to the various overtones present along with the fundamental and their relative intensities4 ,if a tuning fork is first set vibrating by drawing a bow across it and then by striking it with a hard object1 a difference in the quality of the tones produced is noticeable4 ,it is thus evident that the manner of setting a body in vibration affects the overtones produced and thus the quality4 ,piano strings are struck by felt hammers at a point about one-seventh of the length of the string from one end4 ,this point has been selected by experiment1 it having been found to yield the best combination of overtones as shown by the quality of the tone resulting4 ,illustration3 ,,fig4 #ccg4--;,chladni's plate4 ,illustration3 ,,fig4 #cch4--;,chladni's figures4 #cdf4 ,chladni's ,plate4--,the fact that vibrating bodies are capable of many modes of vibration is well illustrated by what is known as ,chladni's plate4 ,this consists of a circular or square sheet of brass attached to a stand at its center so as to be held horizontally4 7,see ,fig4 #ccg47 ,fine sand is sprinkled over its surface and the disc is set vibrating by drawing a violin bow across its edge4 ,the mode of vibration of the disc is indicated by the sand accumulating along the lines of least vibration1 called nodal lines4 ,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 disc4 ,they are known as ,chladni's figures4 7,see ,fig4 #cch47 ,illustration3 ,,fig4 #cci4--,manometric flame apparatus4 #cdg4 ,manometric ,flames4--,the actual presence of overtones along with the fundamental may be made visible by the manometric flame apparatus4 ,this consists of a wooden box1 ,c1 mounted upon a stand4 7,see ,fig4 #cci47 ,the box is divided vertically by a flexible partition or diaphragm4 ,two outlets are provided on one side of the partition1 one1 ,c1 leads to a gas pipe1 the other is a glass tube1 ,d4 ,on the other side of the partition a tube1 ,e1 leads to a mouthpiece4 ,a mirror1 ,m1 is mounted so as to be rotated upon a vertical axis in front of ,f and near it4 ,gas is now turned on and lighted at ,f4 ,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 it4 ,this action affects the flame which rises and falls4 ,if now the mirror is rotated1 the image of the flame seen in the mirror rises and falls1 showing not only the fundamental or principal vibrations but also the overtones4 ,if the different vowel sounds are uttered in succession in the mouthpiece1 each is found to be accompanied by its characteristic wave form 7,fig4 #cdj74 ,in some1 the fundamental is strongly prominent1 while in others1 the overtones produce marked modifications4 ,other devices have been invented which make possible the accurate analysis of sounds into their component vibrations1 while still others unite simple tones to produce any complex tone desired4 #cdh4 ,the ,phonograph4--,the graphophone or phonograph provides a mechanism for cutting upon a disc or cylinder a groove that reproduces1 in the varying form or depth of the tracing1 every peculiarity of the sound waves affecting it4 ,the reproducer consists of a sensitive diaphragm to which is attached a needle4 ,the disc or cylinder is rotated under the reproducing needle4 ,the irregularities of the bottom of the tracing cause corresponding movements of the needle and the attached diaphragm1 which start waves that reproduce the sounds that previously affected the recorder4 ,the construction of the phonograph has reached such perfection that very accurate reproduction of a great variety of sounds is secured4 ,illustration3 ,,fig4 #cdj4--;,characteristic forms of manometric flames4 #cdi4 ,wind ,instruments4--,in many musical instruments as the cornet1 pipe-organ1 flute1 etc41 and also in whistles1 the vibrating body that serves as a source of sound is a column of air1 usually enclosed in a tube4 ,unlike vibrating strings1 this vibrating source of sound changes but little in tension or density1 hence changes in the pitch of air columns is secured by changing their length4 ,the law being similar to that with strings1 the vibration rates of air columns are inversely proportional to their lengths4 ,illustration3 ,,fig4 #cda4--7,r7 ,cross-section of an organ pipe showing action of tongue at ,c4 7a7 ,the fundamental tone in a closed pipe has a wave length four times the length of the pipe2 7b7 and 7c7 how the first and second overtones are formed in a closed pipe2 7d7 the fundamental tone of an open pipe has a wave length equal to twice the length of the pipe2 7e7 and 7f7 first and second overtones of open pipe4 ,if an open organ pipe be sounded by blowing gently through it1 a tone of definite pitch is heard4 ,now if one end is closed1 on being sounded again the pitch is found to be an octave lower4 ,therefore1 the pitch of a closed pipe is an octave lower than that of an open one of the same length4 #cej4 ,nodes in ,organ ,pipes4--,fig4 #cda1 ,r represents a cross-section of a wooden organ pipe4 ,air is blown through ,a1 and strikes against a thin tongue of wood ,c4 ,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 ,a4 ,to understand the mode of vibration of the air column a study of the curve that represents wave motion 7,fig4 #cdb7 is helpful ,let ,,ab represent such a curve1 in this #b1 #d and #f represent nodes or points of least vibration1 while #a1 #c and #e are antinodes or places of greatest motion4 ,a full wave length extends from #a-e1 or #b-f4 ,now in the open organ pipe 7,fig4 #cda;d71 the end of the air column d is a place of great vibration or is an antinode4 ,at the other end also occurs another place of great vibration or an antinode2 between these two antinodes must be a place of least vibration or a node4 ,the open air column therefore extends from antinode to antinode 7or from #a-c7 or is one-half a wave length4 ,the closed air column 7,fig4 #cda;a7 extends from a place of great vibration at a to a place of no vibration at the closed end4 ,the distance from an antinode to a node is that from #a-b on the curve and is one-fourth a wave length4 ,illustration3 ,,fig4 #cdb4--;,graphic representation of sound waves4 ,illustration3 ,,fig4 #cdc4--;,a clarinet4 ,when a pipe is blown strongly it yields overtones4 ,the bugle is a musical instrument in which notes of different pitch are produced by differences in blowing4 7,see ,fig4 #cda47 7d71 7e71 7f74 ,in playing the cornet different pitches are produced by differences in blowing1 and by valves which change the length of the vibrating air column4 7,see ,fig4 #ccd47 ,the clarinet has a mouthpiece containing a reed similar to that made by cutting a tongue on a straw or quill4 ,the length of the vibrating air column in the clarinet is changed by opening holes in the sides of the tube4 7,see ,fig4 #cdc47 #cea4 ,how we ,hear4--,our hearing apparatus is arranged in three parts4 7,see ,fig4 #cdd47 ,the external ear leads to the tympanum4 ,the middle ear contains three bones that convey the vibrations of the tympanum to the internal ear4 ,the latter is filled with a liquid which conveys the vibrations to a part having a coiled shell-like structure called the ,cochlea4 ,stretched across within the cochlea are some #cjjj fibers or strings4 ,it is believed that each is sensitive to a particular vibration rate and that each is also attached to a nerve fiber4 ,the sound waves of the air transmitted by the tympanum1 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 hear4 ,the highest tones perceptible by the human ear are produced by from #bd1jjj to #dj1jjj vibrations per second4 ,the average person cannot hear sounds produced by more than about #bh1jjj vibrations4 ,the usual range of hearing is about #aa octaves4 ,the tones produced by higher vibrations than about #dajj per second are shrill and displeasing4 ,in music the range is #g-a_/c octaves1 the lowest tone being produced by #bg4e vibrations1 the highest by about #dajj per second4 ,illustration3 ,,fig4 #cdd4--,the human ear4 ,the tones produced by men are lower than those of women and boys4 ,in men the vocal cords are about #ah mm4 long2 in women they are #ab mm4 long4 ,the compass of the human voice is about two octaves1 although some noted singers have a range of two and one-half octaves4 ,in ordinary conversation the wave length of sounds produced by a man's voice is from #h to #ab ft4 and that of a woman's voice is from #b to #d ft4 ,important ,topics #a4 ,tone quality4 ,fundamental and overtones4 ,chladni's plate4 #b4 ,manometric flame apparatus4 #c4 ,phonograph recorder and reproducer4 #d4 ,air columns and wind instruments4 #e4 ,how we hear4 ,exercises #a4 ,what determines the pitch of the note of a toy whistle8 #b4 ,the lowest note of the organ has a wave length of about #fd ft4 ,what is the length of a closed pipe giving this note8 ,of an open pipe8 #c4 ,what is the first overtone of ,c8 ,what are the second and third overtones8 ,give vibration numbers and pitch names or letters4 #d4 ,why is the music of a band just as harmonious at a distance of #djj ft4 as at #ajj ft48 #e4 ,a resonant air column #fj cm4 long closed at one end will respond to what rate of vibration at #aj;,c48 #f4 ,can you find out how the valves on a cornet operate to change the pitch of the tone8 #g4 ,how is the trombone operated to produce tones of different pitch8 #h4 ,the lowest note on an organ has a wave length of about #fd ft4 ,what must be the length of a closed pipe giving this note8 #i4 ,what is the approximate length of an open organ pipe which sends out waves #d ft4 long8 ,review ,outline3 ,sound ,sound--definition1 source1 medium1 speed1 nature4 ,waves--longitudinal1 transverse1 illustrations4 ,characteristics of intensity--area1 amplitude1 density1 distance4 ,musical ,sounds3 pitch--scales2 major1 tempered1 triads1 ,n ,v_/,l quality--fundamental and overtones4 ,sympathetic ,vibrations--resonance1 interference1 beats1 discord4 ,musical ,instruments--string1 air column1 membrane or plate4 ,laws of2 7a7 vibrating strings 7#c71 7b7 vibrating air columns 7#b74 ,,chapter ,,xvi ,,light 7#a7 ,,light1 ,,its ,,rectilinear ,,propagation1 ,,shadows #ceb4 ,a ,comparison of ,sound and ,light4--,light from the standpoint of physics is considered much as is sound1 as a mode of motion2 one affecting the ear1 the other producing the result called vision4 ,there are other differences also worth considering4 7a7 ,while sound travels as vibrations of some material medium1 light travels only as vibrations of the ether2 solids1 liquids1 and gases act so as to hinder rather than to assist in its movement4 ,that is1 light travels best in a vacuum or in a space devoid of ordinary matter4 7b7 ,the speed of light is so great that at ordinary distances on the earth its motion is practically instantaneous4 ,experiments have shown that its speed is about #ahf1jjj miles to #cjj1jjj kilometers a second4 #cec4 ,luminous and ,illuminated ,bodies4--,if we consider the objects within a room1 some of them1 as books and furniture1 would be invisible if all light from external sources were excluded4 ,on the other hand1 some other objects1 such as a lighted lamp1 a burning coal1 or a red hot iron1 would be seen if no outside light were present4 ,such bodies are said to be luminous4 ,most luminous bodies are hot and become non-luminous on cooling4 ,there are1 however1 some bodies that are luminous at ordinary room temperatures1 as the firefly and some phosphorescent paints4 ,when light emitted by a luminous body strikes an object1 a portion of it is always reflected4 ,it is this reflected light that makes the illuminated object visible4 ,if the object is a sheet of glass1 some of the light is transmitted4 ,if a substance is so clear that objects can be seen through it1 the substance is transparent1 but if objects cannot be seen through it1 the substance is said to be translucent4 ,objects transmitting no light are opaque4 ,some of the light falling upon a body is neither reflected nor transmitted1 but is absorbed and tends to warm the body4 ,the light falling upon a body is therefore either reflected1 transmitted1 or absorbed4 ,thus ,fig4 #cde represents light coming from ,s to a piece of glass ,,gl4 ,a portion of the light represented by ,r is reflected4 ,another part ,a is absorbed and disappears1 while still another part ,t is transmitted and passes on4 ,illustration3 ,,fig4 #cde4--,the light is transmitted 7,t71 reflected 7,r71 or absorbed 7,a74 ,there is no sharply drawn line between transparent and opaque bodies4 ,very thin sheets of gold transmit a greenish light1 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 found4 ,all light whether from luminous bodies or reflected from non-luminous objects shows certain properties which will now be considered4 #ced4 ,the ,rectilinear ,propagation of ,light4--,if a beam of light passes through a hole in a window shade into a darkened room1 it is seen to follow a perfectly straight course4 ,if a person while coughing holds a book before the face1 the sound passes around the book and is heard at any point in the room while the face is hidden by the book4 ,in other words1 light ordinarily does not pass around corners as sound does1 but travels in straight lines4 ,this fact is made use of when one aims a gun or merely looks at an object4 ,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 it1 that we are sometimes deceived as to the real position of an object1 when the course of the light from it has been changed by a mirror or some other reflecting surface4 ,many illusions are produced in this way1 of which the mirage of the desert is one example4 7,see ,art4 #cha47 ,illustration3 ,,fig4 #cdf4--,shadow from a small source of light4 ,illustration3 ,,fig4 #cdg4--,shadow when source of light is large4 #cee4 ,shadows4--,a shadow is the space from which light is cut off by an opaque body4 ,thus if a book 7see ,fig4 #cdf7 is held between a screen1 ,n1 and a small source of light1 ,l1 a shadow is produced which extends from the book to the screen4 ,notice that the shadow is a space and not an area4 ,if a large gas flame 7see ,fig4 #cdg7 is used as the source of light1 the shadow of the book is no longer clear cut at the edges as before1 but has a darker central part with a lighter fringe of partial shadow at the edges4 ,the dark portion within the shadow has all the light excluded from it and is called the umbra4 ,the lighter portion of the shadow at the edges has only a part of the light from the flame cut off4 ,this portion is called the penumbra4 when one stands in sunlight his shadow extends from his body to the ground or object on which the shadow falls4 ,at night we are in the earth's shadow1 which extends out into space beyond the earth4 ,illustration3 ,,fig4 #cdh4--;,character of the earth's shadow4 #cef4 ,eclipses4--,since the sun is a very large object the shadow cast by the earth contains both umbra and penumbra4 7,see ,fig4 #cdh47 ,when the moon passes into the shadow of the earth1 there is said to be an eclipse of the moon1 while if the moon's shadow falls upon the earth1 the portion of the earth cut off from the sun's light has an eclipse of the sun4 #ceg4 ,images by ,small ,apertures4--,the straight line movement of light makes possible the pin-hole camera1 by which satisfactory photographs have been made4 ,the action of this device may be illustrated by placing a luminous body1 a lighted candle1 an incandescent lamp1 or a gas flame1 in front of a piece of cardboard1 ,s1 which has a small opening in it4 ,light from the object 7see ,fig4 #cdi7 falls upon a screen1 ,s#b1 so as to produce an inverted image4 ,other applications of this principle will be given later4 ,in ,fig4 #cdi let ,,pq represent a gas flame1 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#b at the bottom of the illuminated spot upon the screen4 ,light from ,q passing in straight lines through the aperture will strike at ,q#b at the top of the lighted space4 ,this spot of light will have the same outlines as the luminous body ,,pq and being formed as just described will be inverted4 ,illustration3 ,,fig4 #cdi4--;,image formed by a small aperture is inverted4 ,this spot of light1 resembling in its outlines the flame1 is called an image4 ,an image is defined as an optical counterpart of an object4 ,images are formed in a variety of devices1 such as apertures1 mirrors1 and lenses4 ,the pin-hole camera is simply a light-tight box with a small aperture in one side4 ,light passing through this aperture forms an image upon the opposite side of the interior of the box1 of whatever object is in front of the camera4 ,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 surface4 ,important ,topics #a4 ,light contrasted with sound 7three differences74 #b4 ,bodies3 transparent1 translucent1 opaque4 #c4 ,light3 reflected1 transmitted1 absorbed4 #d4 ,light travels in straight lines1 evidence1 shadows1 umbra1 penumbra4 #e4 ,formation of images by small apertures4 ,exercises #a4 ,consider the circumference of the earth as #be1jjj miles4 ,how many times would the speed of light cover this distance in a second8 #b4 ,how soon after any great disturbance takes place on the sun1 #ic1jjj1jjj miles distant1 can it be seen upon the earth8 #c4 ,construct a diagram of the moon's shadow4 ,how much of the sun can one see when in the moon's umbra8 ,when in its penumbra8 ,have you ever been in either8 ,when8 ,have you ever been in the earth's umbra8 ,in its penumbra8 #d4 ,explain1 using a diagram1 the formation of an inverted image by a small aperture4 #e4 ,if the sun is #de degrees above the horizon1 what is the height of a pole casting a shadow #fj ft4 long8 #f4 ,if a shadow #f ft4 long is cast by a #aj-;ft4 pole standing vertically upon a walk1 how tall is the tree whose shadow is #db ft4 long1 both measurements being made at the same time8 #g4 ,why are the shadows caused by an electric arc lamp so sharply defined8 #h4 ,why should schoolroom windows be all on one side and reach to the ceiling8 #i4 ,what is the relation between the size of an image and its distance from the aperture forming it8 ,can you prove this by geometry8 #aj4 ,what are silhouettes and how are they produced8 7#b7 ,,photometry ,,and ,,the ,,law ,,of ,,reflection #ceh4 ,photometry4--,it is desirable at times to compare the intensities of illumination produced by light from different sources4 ,this is done to determine the relative cost or effectiveness of various illuminants such as candles1 kerosene and gas lamps1 and electric lights ,the process of determining the relative intensity of lights or lamps is called photometry4 7,photos light47 ,the unit for measuring the power of light is called a candle power4 ,it is the light produced by a sperm candle burning #abj grains per hour4 ,an ordinary gas light burns #e or more cubic feet of gas per hour and yields from #ae to #be candle power4 ,a ,welsbach gas lamp1 consuming #c cu4 ft4 per hour1 produces #ej to #ajj candle power4 ,instead of using candles1 for practical photometry1 incandescent lamps standardized by the ,bureau of ,standards are used for testing or calibration purposes4 ,it is necessary to distinguish between the intensity of a luminous body1 i4e41 as a source of light1 and the intensity of illumination upon some surface produced by a light4 ,it is considered that two sources of light are of equal intensity if they produce equal illumination at equal distances4 #cei4 ,law of ,intensity of ,light4--,a device for measuring the candle power of a light is called a photometer4 ,its use is based upon the law of intensity of light4 ,the intensity of illumination of a surface is inversely proportional to the square of its distance from the source of light4 ,this relation is similar to that existing between the intensity of a sound and the distance from its source4 ,the following device illustrates the truth of this law in a simple manner4 ,illustration3 ,,fig4 #cej4--,the light spreads over four times the area at twice the distance4 ,cut a hole #a in4 square in a large sheet of cardboard 7,k7 and place the card in an upright position #a meter from an arc light or other point source of light 7,l74 ,now rule inch squares upon another card 7,m7 and place it parallel to the first card and #b meters from it4 7,see ,fig4 #cej47 ,the light that passed through the hole of #a sq4 in4 at a distance of #a meter is spread over #d sq4 in4 at a distance of #b meters4 ,therefore1 the intensity of illumination on each square inch of ,m is one-fourth that upon the surface of ,k4 ,if ,m is placed #c meters from the light1 #i sq4 in4 are illuminated1 or the intensity is one-ninth that at #a meter distance4 ,illustration3 ,,fig4 #cea4--,the ,bunsen photometer4 ,these relations show that the intensity of illumination is inversely proportional to the square of the distance from the source of light4 ,an application of the law of intensity is made in using a simple 7,bunsen7 photometer4 ,this consists of a card containing a spot soaked with oil or melted wax4 7,see ,fig4 #cea47 ,the lights whose intensities are to be compared are placed upon opposite sides of the card4 ,the card is then adjusted so that the spot appears the same on both sides4 ,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 card4 ,the simple device just described will give approximate results only4 ,for accurate results more elaborate apparatus is required4 #cfj4 ,measurement of the ,intensity of ,illumination4--,a standard candle 7,art4 #ceh7 produces when lighted #a candle power4 ,the illumination caused by this upon a surface #a ft4 away and at right angles to the light rays is called a foot-candle4 ,it is the unit of intensity of illumination4 ,a #d-;candle-power lamp1 at a distance of #a ft41 produces #d foot-candles4 ,a #af-;candle-power lamp at a distance of #b ft4 also produces #d foot-candles--7#af #b74 ,the intensity of illumination required for a good light for seeing varies with the conditions4 ,thus1 for stage and store lighting about #d foot-candles are needed1 while homes and churches may require but #a foot-candle4 ,too great an intensity of illumination is as harmful as not enough4 ,exposed lights having an intensity of more than #e candle power per square inch are often a cause of eye trouble4 ,such lights should be protected by frosted globes4 ,a pleasing form of lighting for large halls and public buildings is the indirect system4 ,in this1 the lamps are hidden by reflectors which throw the light upon the ceiling from which it is diffused over the room4 ,this form of lighting is more expensive than other systems since but a part of the light is reflected4 ,its cost therefore is an important factor when considering its use4 #cfa4 ,the ,reflection of ,light4--,the light reflected from the surfaces of bodies about us gives us information concerning our surroundings4 ,a knowledge of the behavior of light undergoing reflection is not usually gained from ordinary observation4 ,the law of reflection of light may be shown1 however1 by an experiment4 ,illustration3 ,,fig4 #ceb4--;,b is as far back of the mirror as ,b is in front of it4 ,illustration3 ,,christian ,,huygens 7,popular ,science ,monthly7 ,christian ,huygens 7#afbi-afie74 ,dutch physicist2 invented the pendulum clock 7#afef72 developed the wave theory of light2 discovered polarization of light 7#afij74 ,illustration3 ,h4 ,v4 ,,helmholtz ,by ,permission of the ,berlin ,photographic ,co41 ,new ,york4 ,hermann von ,helmholtz 7#ahba-ahid7 ,germany4 ,established the doctrine of conservation of energy2 made many discoveries in sound2 invented the ophthalmoscope2 established the physical basis of tone quality4 ,a plane mirror1 ,m1 is held in a vertical position resting upon a sheet of paper4 7,see ,fig4 #ceb47 ,pins are set upright in the paper at ,a and ,b4 ,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 surface4 ,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 line4 ,this indicates that the light from ,a and ,c passing along ,,ca toward ,o is reflected back along the light ,,cbd4 ,by means of a ruler1 draw lines through ,,bd and ,,ac till they intersect at ,o4 ,also draw ,,po perpendicular to the mirror at ,o4 ,then the angles ,,aop and ,,bop will be found equal4 ,these are called the angles of incidence and reflection respectively4 ,the law of reflection is therefore stated3 ,the angle of reflection is equal to the angle of incidence4 ,these angles are in the same plane1 that of the paper4 ,this law applies in all cases of reflection of light4 ,it is similar to the law of reflection of sound 7,art4 #cbf47 ,important ,topics #a4 ,photometry1 law of intensity1 candle power1 foot-candle4 #b4 ,intensity of illumination4 #c4 ,reflected light and law of reflection4 ,exercises #a4 ,both sides of a card are equally illuminated when two lights are on opposite sides of it and #aj and #cj cm4 respectively from it4 what are their relative intensities8 #b4 ,what are the relative intensities of illumination from a gas light upon a book #f ft4 and #b ft4 respectively from the light8 #c4 ,which is more expensive per candle power8 ,how many times as expensive8 ,a #ej-watt #af-;candle-power incandescent lamp at #aj cents per kilowatt-hour or a #ajj-;candle-power ,welsbach light burning #e cu4 ft4 of gas per hour at #hj cents per #ajjj cu4 ft4 of gas4 7,find cost of each per hour1 and then the cost of #a candle power hour for each47 #d4 ,why are not ordinary shadows perfectly dark8 #e4 ,at what distance will a #af-;candle-power lamp give the same illumination as a single candle at #aj in48 #f4 ,if the sun is at an elevation of #cj degrees what is the angle of incidence at which it strikes the surface of water8 ,what is the angle between the incident and the reflected rays8 #g4 ,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 glass8 #h4 ,a horizontal ray of light1 traveling due east1 strikes a vertical mirror so that after reflection it is traveling due north4 ,if the mirror be now turned #aj degrees about a vertical axis1 the north edge moving east1 what will be the direction of the reflected ray8 #i4 ,the necessary illumination for reading is about #b foot-candles4 ,how far away may an #h-;candle-power lamp be placed8 #aj4 ,what is the illumination in foot-candles upon a surface #bj ft4 from an arc lamp having an intensity of #ajjj candle power8 #aa4 ,how far from a #ajj-;candle-power ,welsbach light would the illumination be #b foot-candles8 7#c7 ,,mirrors ,,and ,,the ,,formation ,,of ,,images ,illustration3 ,,fig4 #cec4--,reflection of light1 7a7 diffused1 7b7 regular4 #cfb4 ,mirrors4--,the many purposes served by mirrors in our every-day life has made their use familiar to everyone4 ,yet without study and experiment few understand their properties and action4 ,any smooth surface may serve as a mirror1 as that of glass1 water1 polished wood1 or metal4 ,most objects1 unlike mirrors1 have irregular surfaces2 these scatter or diffuse the light that falls upon them4 7,see ,fig4 #cec;a47 ,this is called diffused or irregular reflection4 ,the reflection of light from the smooth surface of a mirror is regular4 7,see ,fig4 #cec;b47 ,in every case of reflected light1 however1 the angle of reflection equals the angle of incidence1 diffusion being due to the irregularity of the surface4 ,it is by means of the light diffused from the surface of illuminated bodies1 such as plants1 animals1 food1 and manufactured articles1 that we see the various objects about us1 and it is this light that enables us to judge of their distance1 size1 form1 color1 etc4 ,the moon is seen by the sunlight reflected from its surface4 ,moonlight is therefore sunlight diffused by reflection4 ,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 earth4 ,at the time of the full moon the whole illuminated surface is seen4 #cfc4 ,images ,formed by a ,plane ,mirror4--,the most common use of mirrors is in the formation of images4 ,the way in which images are formed by a plane mirror may be illustrated by diagrams4 ,thus in ,fig4 #ced1 let ,l represent a luminous body and ,e and ,e two positions of the observer's eye4 ,take any line or ray as ,,lo along which the light from ,l strikes the mirror ,o-,o4 ,it will be reflected so that angle ,,lop equals angle ,,poe4 ,similarly with any other ray1 as ,,lo1 the reflected ray ,o,e has a direction such as that angle ,l,o,e equals angle ,p,o,e4 ,any other rays will be reflected in a similar manner1 each of the reflected rays appearing to the eye to come from a point ,l behind the mirror4 ,illustration3 ,,fig4 #ced4--,the virtual image of a fixed object as seen in a plane mirror1 has the same location from every position of the observer's eye4 #cfd4 ,light ,waves and ,wave ,diagrams4--,just as a stick continually moved at the surface of a body of water sets up a series of waves spreading in all directions1 so one may imagine a train of waves sent out by a luminous body ,l 7as in ,fig4 #cee7 to the mirror ,,mn4 ,these waves will be reflected from the mirror as if the source of light were at ,l4 ,it is much simpler and more convenient to locate the position of the image of a point by the use of lines or rays 7as in ,fig4 #ced7 than by the wave diagram 7as in ,fig4 #cee74 ,in all ray diagrams1 however1 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 wave4 ,thus in ,fig4 #ced1 the light from ,l moving toward ,o is reflected to ,e along the line ,,oe1 the heavy lines representing rays4 ,illustration3 ,,fig4 #cee4--,wave diagram of image formed in a plane mirror4 #cfe4 ,to locate the image of an object formed by a plane mirror requires simply an application of the law of reflection4 ,thus in ,fig4 #cef let ,,ab represent an object and ,,mn a plane mirror4 ,let ,,aa be a ray from ,a striking the mirror perpendicularly4 ,it is therefore reflected back along the same line toward ,a4 ,let ,,ao represent any other ray from ,a4 ,it will be reflected along ,,oe so that angle r equals i4 ,the intersection of ,,ac and ,,oe at ,a behind the mirror locates the image of the point ,a1 as seen by reflection from the mirror4 ,the triangles ,,aco and ,a,,co may be proved equal by geometry4 ,therefore ,a,c equals ,,ac4 ,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 it4 ,this principle may be used in locating the image of point ,b at ,b4 ,locating the position of the end points of an image determines the position of the whole image as ,a,b4 ,illustration3 ,,fig4 #cef4--,the image ,a,b is as far back of the mirror ,m ,n as the object ,a ,b is in front of the mirror4 #cff4 ,how the ,image is ,seen4--,suppose the eye to be placed at ,e4 ,it will receive light from ,a by reflection as if it came from ,a4 ,similarly light starting from ,b reaches the eye from the direction of ,b4 ,there is nothing back of the mirror in reality that affects our sight1 the light traveling only in the space in front of the mirror4 ,yet the action of the reflected light is such that it produces the same effect as if it came from behind the mirror4 ,images such as are seen in plane mirrors are called virtual to distinguish them from real images1 in which light actually comes to the eye from the various parts of the visible image1 as from the real image formed by a projecting lantern upon a screen1 or by an aperture as in the pin-hole camera4 ,real images therefore are those that can be obtained upon a screen while virtual images cannot4 #cfg4 ,multiple ,reflection4--,if the light from an object is reflected by two or more mirrors various effects may be produced1 as may be illustrated by the kaleidoscope4 ,this consists of three plane mirrors so arranged that a cross-section of the three forms an equilateral triangle4 ,the mirrors are placed in a tube across the end of which is a compartment with a translucent cover containing pieces of colored glass4 ,on looking through the tube1 the reflections from the several surfaces produce beautiful hexagonal designs4 ,illustration3 ,,fig4 #ceg4--,perspective view of ,pepper's ghost4 ,illustration3 ,,fig4 #ceh4--;,diagram of the ,pepper ,ghost illusion4 #cfh4 ,optical ,illusions by a ,plane ,mirror4--,the illusion called ,pepper's ,ghost is typical of many illusions produced by reflection4 ,it may be illustrated by taking a piece of plate glass1 ,m-,n1 a tumbler of water1 ,w1 and a lighted candle1 ,c1 placed in a box1 ,b1 having one side open and arranged as shown in perspective in ,fig4 #ceg1 and in section in ,fig4 #ceh4 ,if the effect is produced in a darkened room1 the observer at ,e sees a virtual image of the lighted candle as if it were in the glass of water1 the water being seen by transmitted light through the plate glass1 the latter forming a virtual image of the candle by reflection4 ,some of the illusions produced by this means are3 7a7 the figure suspended in mid air2 7b7 the bust of a person without a trunk2 7c7 the stage ghost2 7d7 the disappearing bouquet4 ,illustration3 ,,fig4 #cei4--;,action of a concave mirror on parallel rays of light4 ,illustration3 ,,fig4 #cfj4--,real image formed by a concave mirror4 #cfi4 ,concave ,mirrors4--,another useful piece of physical apparatus is the concave spherical mirror4 ,it is frequently made from plano-convex lenses by silvering the convex surface of the lens1 thus making a concave reflecting surface from the inner surface of the silvered part2 they are also made by polishing the inner surfaces of metallic spherical shells4 ,the concave mirror is represented in section in ,fig4 #cei by the curve ,,mn2 ,c is the center of curvature or the center of the surface of which this mirror ,,mn is a part2 the line ,,vc through the center ,v of the mirror is called the principal axis2 while any other line passing through ,c is called a secondary axis4 ,the point midway between the vertex ,v and center of curvature ,c is called the principal focus1 ,f4 ,it is the point through which parallel incident rays pass after reflection4 ,the angle ,,mcn which the curve of the mirror subtends at the center is called the aperture of the mirror4 ,we learned in ,art4 #cfa1 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 be4 ,if the reflecting surface is a regular concave surface1 like the inner surface of a sphere1 the rays of light coming from a point source may after reflection come to a focus1 forming a real image4 ,the two extreme points of an object should be selected for locating its image2 ,fig4 #cfj shows the construction4 ,the real images formed by concave mirrors are always inverted4 ,the principal focus of a concave mirror may be observed by holding the mirror in a beam of sunlight entering a darkened room4 ,the sun's rays after reflection converge to form a small1 round1 intense spot of light1 which is a real image of the sun1 located at the principal focus of the mirror4 ,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 mirror4 #cgj4 ,virtual ,images by ,concave ,mirrors4--,when light comes from a small point situated between a concave mirror and its principal focus1 the reflected rays are divergent and hence no real image of the object can be found in front of the mirror4 ,but if the rays are extended behind the mirror they will meet in a point called the virtual focus4 ,this is the point from which they appear to come4 ,any image of an object situated between the principal focus and a concave mirror is therefore a virtual image1 erect and larger than the object4 7,see ,fig4 #cfa47 ,illustration3 ,,fig4 #cfa4--,virtual image formed by a concave mirror4 #cga4 ,construction of ,real ,images4--,there are five positions at which an object may be situated in front of a concave mirror1 namely3 7#a7 beyond ,c2 7#b7 at ,c2 7#c7 between ,c and ,f2 7#d7 at ,f and 7#e7 between ,f and ,v4 ,there are two ways by means of which the image formed at each of these positions may be located1 namely2 7#a7 experimentally1 by allowing the rays of light from a luminous body to focus on a screen and 7#b7 diagrammatically4 ,by the latter method the two rays of light are considered the course of each of which may easily be determined2 first1 the ray which strikes the mirror parallel to its principal axis and which after reflection passes through the principal focus2 second1 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 path4 ,where these two reflected rays intersect is located the real image of the object4 ,whenever these two rays of light do actually intersect1 as in ,fig4 #cfj1 a real image 7ab7 is formed of the object ,,ab4 ,the points ,a and a1 ,b and b and others similarly situated on an axis extending through the center of curvature ,c are called conjugate foci1 for they are so related that an object being at either one1 its image will be found at the other4 ,illustration3 ,,fig4 #cfb4--;,action of a convex mirror upon parallel rays of light4 #cgb4 ,the ,convex ,mirror4--,there are few practical uses to which convex mirrors can be put4 ,they are sometimes used to give the chauffeur of an automobile a view of the road behind him4 ,it is then attached to the wind shield by a short rod4 ,the reflected rays coming from a ,convex mirror are always divergent 7see ,fig4 #cfb71 hence the image is always virtual and located behind the reflecting surface4 ,the method of construction for images formed by a convex mirror is similar to that for concave mirrors4 7,see ,fig4 #cfc47 ,the center of curvature and principal focus are behind the mirror and consequently the reflected rays have to be produced backward until they meet4 ,the images are always virtual1 erect and smaller than the object4 ,illustration3 ,,fig4 #cfc4--;,construction of an image by a convex mirror4 ,illustration3 ,,fig #cfd4--;,illustrations of ,spherical ,aberration4 #cgc4 ,spherical ,aberration4 ,sometimes in a concave mirror when the aperture ,,mcn 7,fig4 #cfd7 is large the images are blurred or indistinct4 ,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 vertex1 but cross the principal axis at points between the mirror and principal focus as is shown in ,fig4 #cfd2 this result is called spherical aberration4 ,the larger the aperture of the mirror the more the image is blurred4 ,concave mirrors in practical use do not have an aperture much greater than #aj degrees4 ,this non-focusing of the rays of light by curved reflecting surfaces may be noticed in many places1 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 paper4 ,the pupil will note other instances4 ,this curve of light observed is called the caustic by reflection4 #cgd4 ,parabolic ,mirrors4--,the best possible surface to give to concave mirrors is parabolic4 ,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 equal4 ,if a source of light is placed at ,f the rays after reflection are rendered parallel4 ,see ,fig4 #cfe4 ,this reflector is used in automobile lamps1 headlights of locomotives1 search-lights1 etc4 ,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 focus4 ,such mirrors may be made exceedingly accurate4 ,illustration3 ,,fig4 #cfe4--,parabolic mirror4 ,important ,topics #a4 ,reflection3 regular1 diffused2 plane mirrors2 laws of reflection4 #b4 ,formation and location of images by plane mirrors4 ,wave and ray diagrams4 #c4 ,multiple reflection1 illusions4 #d4 ,curved mirrors1 uses2 concave1 convex1 parabolic4 ,exercises #a4 ,distinguish between regular and diffused reflection4 ,by means of which do we see non-luminous bodies8 #b4 ,could a perfect reflecting surface be seen8 ,explain4 #c4 ,a pencil is stood upright in front of a plane mirror set at an angle of #de degrees to the vertical4 ,shown by a diagram the location and position of the image4 #d4 ,show by diagrams the position and location of the images of a pencil 7a7 when standing erect and in front of a vertical mirror4 7b7 when standing upon a horizontal mirror4 #e4 ,what is the difference between a real and a virtual image8 #f4 ,a standard candle and a lamp give equal illuminations to a screen that is #a ft4 from the candle and #f ft4 from the lamp4 ,what is the candle power of the lamp8 ,explain4 #g4 ,why are walls finished in rough plaster or painted with soft tones without gloss better for schoolrooms than glossy paints or smooth white plaster8 #h4 ,try to read a printed page by looking at its image in a mirror4 write your name backward on a sheet of paper1 and then look at the image of the writing in a mirror4 ,what effect is produced by the mirror in each case8 #i4 ,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 mirror4 ,explain4 #aj4 ,given a small lighted candle1 a concave mirror1 a meter stick1 and a white screen1 how would you prove the statements made in ,arts4 #cfi and #cgj concerning the location of images formed by concave mirrors8 ,make the diagram in each case4 #aa4 ,why do images seen in a quiet pond of water appear inverted8 ,explain by a diagram4 7#d7 ,,refraction ,,of ,,light #cge4 ,common ,examples of ,refraction4--,everyone has noticed the apparent bending of an oar1 of a stick1 or of a spoon when placed in water 7see ,fig4 #cff71 while many have observed that the bottom of a pond or stream looks nearer to the surface than it really is4 ,these and similar illusions are due to the refraction or bending of light rays as they pass from one medium to another4 ,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 instruments1 such as the camera1 microscope1 telescope1 and the eye4 ,illustration3 ,,fig4 #cff4--,the stick appears to be bent on account of refraction4 #cgf4 ,action of ,light ,undergoing ,refraction4--,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 jar1 a part of the beam may be seen to be reflected while another portion is transmitted through the water 7,fig4 #cfg74 ,the reflected beam follows the law of reflection while the transmitted beam is seen to be refracted1 or to have its courses slightly changed in direction upon entering the water4 ,if the mirror is turned so that the angle at which the light strikes the water is changed1 the amount of refraction or change of course of the light is varied4 ,when the light strikes the water perpendicularly there is no refraction4 ,on the other hand1 the greater the angle at which the light strikes the water the greater the bending4 ,illustration3 ,,fig4 #cfg4--,part of the ray is reflected and part passes into the water and is refracted4 ,illustration3 ,,fig4 #cfh4--;,illustrating the laws of refraction of light4 #cgg4 ,laws of ,refraction4 ,the action of light on entering1 passing through1 and leaving a great variety of substances has been carefully studied4 ,a summary of the results of these observations is given in the following laws of refraction3 ,i4 ,when light enters a transparent body1 perpendicularly1 it passes on without changing its direction4 ,,ii4 ,when light enters a denser transparent body obliquely1 it is bent toward the perpendicular2 when light enters a less dense body obliquely1 it is bent away from the perpendicular4 7,see ,fig4 #cfh47 #cgh4 ,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 #a1 #b1 #c1 etc41 indicated in ,fig4 #cfi4 ,suppose that the upper and lower parts of the field have a smooth hard surface1 while at the center is a strip of newly ploughed ground4 ,the line will move more slowly over the ploughed field than over the hard field4 ,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 line1 toward the perpendicular to the edge of the field 7on entering the place of more difficult travel71 and away from the perpendicular on moving into a place where increased speed results4 ,illustration3 ,,fig4 #cfi4--;,diagram illustrating the cause of refraction4 #cgi4 ,index of ,refraction4--,by studying the change of direction of the marching men as shown in ,fig4 #cfi it is evident first that it is due to a difference in speed in the two media4 ,it is not easy to measure the speed of light in a medium4 ,however1 the amount of refraction may be determined easily and from this the relative speed may be computed4 ,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 medium4 ,the relative speeds of light1 or the indices of refraction for some substances1 are3 water1 #a4cc1 crown glass1 #a4ea1 flint glass1 #a4fa1 diamond1 #b4dg1 carbon bisulphide1 #a4fd4 ,illustration3 ,,fig4 #cgj4--,the incident ray and the emergent rays are parallel4 #chj4 ,plates1 ,prisms1 ,lenses4--,the refraction of light is usually observed when it is passing through a plate1 a prism1 or a lens4 ,the important differences between the effects of each in refracting light are illustrated in ,figs4 #cgj1 #cga and #cgb4 ,in ,fig4 #cgj it is seen that the refraction of the ray on entering the glass is counteracted by the refraction away from the perpendicular upon leaving it4 ,so that the entering and emergent rays are parallel4 ,in ,fig4 #cga the refraction at the two surfaces of the prism results in a change of direction of the ray1 the course being bent toward the thicker part of the prism4 ,in ,fig4 #cgb it may be noticed that the convex lens resembles two prisms with their bases together4 ,since all parts of the lens refract light toward the thicker part1 the center1 the effect of the convex lens is to bring the rays of light to a focus1 at ,f4 ,illustration3 ,,fig4 #cga4--;,effect of a prism upon a ray of light4 ,illustration3 ,,fig4 #cgb4--,the convex lens brings the rays of light to a focus4 #cha4 ,total ,reflection4--,it has been shown that when light passes from a denser to a lighter medium1 as from glass or water to air1 that the beam is refracted away from the perpendicular4 ,this is illustrated in ,fig4 #cgc4 ,the diagram represents the change in the course of a ray of light that passes through water to a surface with air above it4 ,a ray striking perpendicularly passes through without refraction4 ,other rays show increasing refraction with increasing angle of incidence4 ,for one ray the angle of refraction is so large that the refracted ray is parallel to the surface4 ,when this condition is reached1 the angle of incidence is called the critical angle4 ,any increase in the angle of incidence causes all of the light to be reflected as is the beam ,e4 ,this action is called total reflection1 the course of the reflected ray being according to the law of reflection4 ,a right-angle prism 7see ,fig4 #cgd7 is often used where a mirror would ordinarily be employed1 the total reflection occurring within the prism giving more satisfactory results than a mirror4 ,see ,art4 #cih for a description of the ,zeiss binocular field-glass for an example of this use of total reflection4 ,illustration3 ,,fig4 #cgc4--;,an example of total reflection4 ,illustration3 ,,fig4 #cgd4--,total reflection in a right-angle prism4 ,the mirage 7see ,fig4 #cge7 is an optical illusion by which distant objects1 below the horizon1 are sometimes plainly seen4 ,this phenomenon is most frequently observed in hot1 desert regions1 when the air conditions are such that the lower strata near the ground are very much hotter than those above4 ,these lower strata1 having expanded the most1 are less dense than the cooler ones above4 ,hence a ray of light traveling obliquely downward is refracted more and more until total reflection takes place4 ,the images seen are inverted giving a representation of trees or other objects reflected on the surface of still water4 ,the mirage is also frequently seen at sea1 ships being observed1 sometimes erect1 sometimes inverted1 apparently sailing in the clouds near the horizon4 ,over the ,great ,lakes1 trees1 boats1 and towns on the opposite shore1 sixty or seventy miles away1 can sometimes be plainly seen1 apparently but a few miles out4 ,in this case the images are erect1 the total reflection being from warm1 still layers of air over colder layers near the water4 ,illustration3 ,,fig4 #cge4--;,diagram of a mirage4 ,important ,topics 7,a7 ,refraction3 cause1 illustration1 two principles4 7,b7 ,index of refraction1 meaning4 7,c7 ,plates1 prisms1 lenses1 action of each4 7,d7 ,total reflection1 uses4 ,exercises #a4 ,compute the speed of light in water1 the index of refraction being #a4cc4 #b4 ,if one wished to shoot a fish under water1 should he aim at the apparent location of the fish as viewed from the air8 ,explain1 using a diagram4 #c4 ,define refraction4 ,mention two illustrations of this action that you have observed out of school4 #d4 ,why does the moon look larger near the horizon8 #e4 ,is your reflection seen in a pool of water upside down8 ,why8 #f4 ,why does it whiten molasses candy to pull it8 #g4 ,when looking at a building through the ordinary glass of a window why do straight lines of the building appear to be so distorted8 ,what makes them appear to move as you move your head slightly8 #h4 ,explain the phenomenon which one observes when looking at an object through the air arising from a hot stove or radiator4 #i4 ,frequently the horizontal diameter of the setting sun appears to be greater than the vertical4 ,explain4 #aj4 ,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 eye1 the angle of reflection being large4 7#e7 ,,the ,,formation ,,of ,,images ,,by ,,lenses #chb4 ,uses of ,lenses in ,optical ,instruments4--,the use of instruments that employ lenses in their operation1 such as spectacles1 reading and opera glasses1 and the camera1 microscope1 and telescope1 is familiar to most students of physics4 ,the part played by the lenses1 however1 is not generally understood4 ,consequently the study of the formation of images by lenses is of general interest and importance4 #chc4 ,forms of ,lenses4--,while a lens may be formed from any transparent solid it is commonly made of glass4 ,it may have two curved surfaces or one curved and one plane surface4 ,most lenses are spherical lenses1 since their curved surfaces form a part of the surface of a sphere4 ,fig4 #cgf represents a spherical lens with a curved surface coinciding with that of a sphere whose center is at ,c4 ,this center is called the center of curvature1 while the radius of the sphere ,r1 is the radius of curvature4 ,illustration3 ,,fig4 #cgf4--;,formation of a spherical lens4 ,there are two classes of lenses3 those thick in the middle are called convex1 while those thick at the edges are concave4 ,the mode of constructing the six forms of spherical lenses is shown in ,fig4 #cgg4 ,these are named as follows3 7#a7 double convex1 7#b7 plano convex1 7#c7 concavo-convex1 7#d7 double concave1 7#e7 plano concave1 7#f7 convexo-concave4 ,illustration3 ,,fig4 #cgg4--;,forms of ,lenses4 #a4 double convex2 #b4 plano convex2 #c4 concavo convex2 #d4 double concave2 #e4 plano concave2 #f4 convexo concave4 ,illustration3 ,,fig4 #cgh4--,the action of a burning glass4 #chd4 ,effect of ,lenses upon ,light4--,the most important characteristic of a lens is its effect upon a beam of light4 ,most persons have seen a burning glass1 a double convex lens1 used to bring to a point1 or focus1 a beam of sunlight4 ,to show the action of a burning glass send a beam of light into a darkened room1 and place in its path a double convex lens4 7,see ,fig4 #cgh47 ,if two blackboard erasers are struck together near the lens1 the chalk particles in the path of the light are strongly illuminated1 showing that the light after passing through the lens it brought to a focus and that it spreads out beyond this point4 ,this point to which the cone of light rays converges after passing through the convex lens is called the principal focus of the lens4 ,the distance from the principal focus to the center of the lens is the focal length or principal focal distance of the lens4 ,the focal length of double convex lenses of crown glass is about the same as the radius of curvature of either surface4 ,the action of a convex or converging lens upon light may be better understood by studying ,fig4 #cgi in which light is passing from ,s to ,f4 ,the successive positions and shape of the advancing light waves are indicated by lines drawn across the beam4 ,the light being retarded more in the thicker part of the lens1 the light waves on leaving the lens have a concave front4 ,since light waves tend to move at right angles to the front of the wave1 the light is brought to a focus4 ,after passing the focus the waves have a convex front1 forming a diverging cone4 ,illustration3 ,,fig4 #cgi4--,wave diagram of light passing through a convex lens4 #che4 ,concave ,lenses4--,when sunlight passes through a concave lens a diverging cone of light is formed4 7,see ,fig4 #chj47 ,this is caused by the edges of the wave being retarded more than the center1 producing a convex wave front4 ,this diverging cone of light acts as if it had proceeded from a luminous point at ,f4 ,this point is called a virtual focus and is nearly at the center of the curvature of the nearer surface4 ,illustration3 ,,fig4 #chj4--,wave diagram of light passing through a concave lens4 #chf4 ,the ,formation of ,images by ,lenses4--,if a beam composed of parallel rays of light1 as sunlight1 is sent in turn through three convex lenses of the same diameter but of different thickness1 it is found that the thicker the lens the greater is its converging power1 or the shorter is its focal length4 7,see ,fig4 #cha47 ,now if a luminous body1 such as a lighted candle1 be placed near the convex lens but beyond its focal length1 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 point4 7,see ,fig4 #chb47 ,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 foci4 ,illustration3 ,,fig4 #cha4--,the thicker the lens1 the shorter is its focal length4 ,illustration3 ,,fig4 #chb4--;,c and ,s are at conjugate foci4 ,it will be helpful to compare the images formed of a candle by an aperture and by a convex lens4 ,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 candle4 ,this image is rather hazy in outline4 ,each cone of rays from luminous points of the flame is brought by the lens to a focus on the screen1 producing a sharp image4 ,it is the converging power of convex lenses that enables them to produce clear images4 ,illustration3 ,,fig4 #chc4--;,construction of a real image by a convex lens4 #chg4 ,the ,construction of ,diagrams to ,represent the ,formation of ,images by ,lenses4--,just as the earth has an axis at right angles to its equator to which are referred positions and distances1 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 ,fig4 #chc4 ,let ,,mn be the principal axis of a convex lens1 ,p and ,p are principal foci on either side of the lens1 ,s and ,s are secondary foci4 ,these are at points on the principal axis that are twice as far from ,o1 the center of the lens1 as are the principal foci4 ,in the formation of images by a convex lens1 several distinct cases may be noticed3 7,a7 ,if a luminous body is at a great distance at the left1 its light is brought to a focus at ,p1 or its image is formed at ,p4 7,b7 ,as the object approaches the lens the image gradually recedes until the object and image are at ,s and ,s1 equally distant from ,o and of equal size 7as in ,fig4 #chc74 ,the object and image are now said to be at the secondary foci of the lens4 7,c7 ,as the object moves from ,s to ,p the image recedes1 rapidly increasing in size until 7,d7 when the object is at ,p the rays become parallel and no image is formed4 7,e7 ,when the object is between ,p and the lens1 the rays appear to proceed from points back of the object1 thus forming an erect1 larger1 virtual image of the object4 7,see ,fig4 #chd47 ,this last arrangement illustrates the simple microscope4 ,with a concave lens but one case is possible1 that corresponding to the one last mentioned with convex lenses2 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 virtual1 erect1 smaller image of the object is formed4 ,this virtual image may be seen by looking through the lens toward the object4 7,see ,fig4 #che47 ,illustration3 ,,fig4 #chd4--;,construction of a virtual image by a convex lens4 ,illustration3 ,,fig4 #che4--;,construction of a virtual image by a concave lens4 #chh4 ,the ,lens ,equation4--,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 known4 ,this is accomplished by the use of a formula #a_/;,f #a_/;,d#j #a_/;,d#a in which ,f represents the focal length and ,d#j and ,d#a the distance from the lens of the object and the image respectively4 ,thus if an object is placed #cj cm4 from a lens of #aj cm4 focal length1 where will the image be formed8 ,thus3 #a_/aj #a_/cj #a_/;,d and #c;,d#a ,d#a #cj1 or #b;,d#a #cj ,d#a #ae4 ,this result indicates that a real image will be #ae cm4 from the lens4 ,a minus value would indicate a virtual image4 ,important ,topics 7,a7 ,lenses3 convex1 concave1 six forms1 center and radius of curvature4 7,b7 ,principal focus1 focal length1 virtual focus1 conjugate foci4 7,c7 ,principal axis1 images formed when object is in various locations4 7,d7 ,computation of location of images4 ,exercises #a4 ,why is an image of a candle formed by an aperture1 not sharply defined8 #b4 ,when a photographer takes your picture and moves the camera nearer you1 must he move the ground glass screen toward the lens or away from it8 ,explain4 #c4 ,how can you find the principal focal length of a lens4 #d4 ,how can you test a spectacle lens to see whether it is convex concave8 #e4 ,when will a convex lens produce a virtual image8 ,have you ever seen one8 ,where8 #f4 ,when a photographer wishes to obtain a full length view of a person1 where does he place the camera8 #g4 ,the focal length of the lens is #bd cm4 ,how far from the lens must an object be placed in order that a real image may be three times as long as the object8 #h4 ,there is a perfect image of an object on the ground glass of a camera4 ,the center of the lens is #bj cm4 in front of the image and the object #ge cm4 from the lens4 ,what is the focal length of the lens8 #i4 ,an object is #fj cm4 from the lens1 the image #abj cm4 from it4 ,find the focal length4 #aj4 ,how can you find experimentally the principal focal length of a lens8 #aa4 ,a lens is used to project an enlarged image of a candle upon a screen4 ,which is farther from the lens1 the candle or the image8 ,explain4 7#f7 ,,optical ,,instruments #chi4 ,the ,eye4--,the most common optical instrument is the eye4 ,while the structure of the eye is complicated1 the principle of it is simple1 involving the formation of an image by a double convex lens4 7,see ,fig4 #chf1 in which is shown a front to back1 vertical cross-section of the eye47 ,the eye appears to be made of portions of two spheres1 one of which1 smaller than the other1 is placed in front4 ,this projecting part is transparent1 but refracts the light which strikes it obliquely1 so as to turn it into the eye4 ,this enables us to see objects at the side when looking straight ahead4 ,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 hand4 ,illustration3 ,,fig4 #chf4--;,cross-section of the eye4 #cij4 ,action of the ,eye in ,vision4--,when we look at an object1 a small1 real1 inverted image is formed upon the retina at the back of the interior of the eye4 ,the retina is an expansion of the optic nerve and covers the inner surface at the back of the eyeball4 ,seeing is due to the action of light in forming images upon the retina4 ,our eyes are so constructed that when they are relaxed the lens is adjusted to form clear images of distant objects upon the retina4 ,if we look from distant to near objects without changing the shape of the eye lens1 a sharp image of the latter cannot be formed and we get a blurred impression4 ,it is difficult1 however1 to look at objects without automatically adjusting the eye lens so that it will make a sharp image4 ,test this by looking out of a window at a distant object1 then without moving the head or eyes look at the glass of the window2 you will notice a slight change of some sort in the eye itself as the vision is adjusted4 ,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 ones4 ,the eye ordinarily does not see objects nearer than #aj in4 clearly4 ,this means that the greatest possible thickening of lens will not form clear images upon the retina if the object is nearer than #aj in4 7#be cm474 ,illustration3 ,,fig4 #chg4--,the visual angle1 ,,aob is greater at ,,ab than at ,a,b4 #cia4 ,the ,visual ,angle4--,to examine objects carefully we usually bring them as close to the eye as possible1 for the nearer to the eye the object is brought1 the larger is the visual angle formed by it 7see ,fig4 #chg71 and the larger is its image upon the retina4 ,the visual angle of an object is the angle at the eye lens between the rays that have come from the ends of the object4 ,consequently the more distant the object1 the smaller is its visual angle4 ,now if we wish to examine small objects with great care1 we frequently find that it is necessary to bring them close to the eye so that they have a visual angle of adequate size4 ,if they must be brought closer than #aj in4 a double convex lens is placed in front of the eye4 ,this assists the eye lens in converging the light so that a clear image may be formed when the object is close1 say an inch or so from the eye4 ,this is the principle of the magnifying glass used by watch-makers and of the simple microscope4 ,the action of the latter is illustrated by ,fig4 #chh4 ,the convex lens forms a virtual1 enlarged image ,a-,b of the object ,a-,b which it observed instead of the object itself4 ,illustration3 ,,fig4 #chh4--;,action of the simple microscope4 ,illustration3 ,,fig4 #chi4--,near sightedness1 or myopia4 ,parallel rays come to a focus at ,f2 emerging rays focus at ,a1 the far point4 #cib4 ,defects of ,vision4--,there are several defects of vision that may be corrected by spectacles or eye-glasses4 ,one of these is near-sightedness4 ,it is due either to an eyeball that is elongated1 or to an eye lens that is too convex1 or to both conditions4 ,this condition brings light from distant objects to a focus too soon 7as shown in ,fig4 #chi74 ,only light from near objects will focus upon the retina in such cases4 ,with normal vision light from distant or near objects may be focused without unusual effort upon the retina1 see ,fig4 #cij4 ,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 7,fig4 #cia74 ,far-sightedness is the reverse of near-sightedness2 the eyeball is either too short1 or the lens too flat1 or both conditions obtain1 so that the light entering the eye is brought to a focus behind the eyeball 7,fig4 #cib74 ,the remedy is convex lenses which will assist in properly converging the light1 see ,fig4 #cic4 ,a third defect is called astigmatism4 ,this is caused by some irregularity or lack of symmetry in the eye4 ,it is corrected by a cylindrical lens that compensates for this defect of the eye4 ,a diagram similar to ,fig4 #cid is used as a test for astigmatism4 ,if the lines appear with unequal distinctness1 some irregularity of refraction 7astigmatism7 is indicated4 ,illustration3 ,,fig4 #cij4--,the normal eye4 ,the parallel rays ,a ,b focus without accommodative effort at ,c4 ,illustration3 ,,fig4 #cia4--;,correction of near-sightedness by concave lens4 ,illustration3 ,,fig4 #cib4--;,far-sightedness or hyperopia4 ,parallel rays focused behind the retina4 ,illustration3 ,,fig4 #cic4--;,correction of far-sightedness by a convex lens4 ,illustration3 ,,fig4 #cid4--,test card for astigmatism4 #cic4 ,the ,photographic ,camera4--,this is a light-tight box1 provided with a convex lens in front1 covering an aperture and a ground glass screen at the back4 ,the distance between the lens and the screen is adjusted until a sharp image is obtained upon the latter1 which is then replaced by a sensitive plate or film4 ,the sensitized surface of the plate or film contains a salt of silver which is changed by the action of light4 ,after the plate has been exposed to the action of light1 it is developed by the use of chemicals producing a negative image4 ,from negative1 by the use of sensitized paper1 positive prints may be secured which resemble the object photographed4 ,illustration3 ,,fig4 #cie4--;,diagram of the projecting lantern4 #cid4 ,the projecting lantern 7see ,fig4 #cie7 employs a strong source of light1 as an electric arc lamp ,l1 to strongly illuminate a transparent picture1 or lantern slide1 ,s1 a real image 7,i7 of which is formed upon a large screen4 ,two large plano-convex lenses 7,c71 called condensing lenses1 are placed near the lamp to concentrate the light upon the slide ,s4 ,the convex lens forming the image is called the objective 7,o74 #cie4 ,the compound microscope consists of two lenses4 ,one called the objective is placed near the object to be viewed4 ,this lens has a short focal length usually less than a centimeter4 ,it forms a real image of the object4 ,a-,b4 ,the other lens1 the eyepiece forms a virtual image of this real image4 ,a-,b4 7,see ,fig4 #cif47 #cif4 ,the telescope consists of two lenses1 the eyepiece and the objective4 ,as in the compound microscope1 the objective of the telescope forms a real image of the distant object1 the eyepiece forming an enlarged virtual image of the real image4 ,it is the virtual image that is viewed by the observer4 7,see ,fig4 #cig47 ,in order to collect sufficient light from distant stars the objective is made large1 sometimes #ej in4 in diameter4 ,illustration3 ,,fig4 #cif4--;,formation of an image by a microscope4 ,a-,b is the object4 ,b-,a the real image formed by the objective4 ,b-,a is the virtual image formed by the eyepiece4 ,the eye sees the virtual image4 ,the length of the telescope tube depends upon the focal length of the objective1 since the distance between the two lenses must equal the sum of their focal lengths4 ,illustration3 ,,fig4 #cig4--;,formation of an image by a telescope4 b-a is the real image2 d-c is the virtual image seen by the observer4 #cig4 ,the opera glass consists of a convex lens as objective and a concave lens as an eyepiece4 ,the former tends to form a real image but the latter diverges the rays before a real image can be formed1 the action of the two lenses producing an enlarged virtual image 7as in ,fig4 #cih7 which is viewed by the one using the glass4 ,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 lengths4 ,illustration3 ,,fig4 #cih4--;,formation of an image by an opera-glass4 a-b is the virtual image4 ,illustration3 ,,fig4 #cii4--;,diagram of the ,zeiss binocular or prism field glass4 #cih4 ,the ,prism ,field ,glass or ,binocular4--,this instrument4 has come into use in recent years4 ,it possesses the wide field of view of the spy glass but is as compact as the opera glass4 ,this compact form is secured by causing the light to pass back and forth between two right-angle prisms 7as shown in ,fig4 #cii74 ,this device permits the use of an objective lens with a focal length three times that of the tube1 securing much greater magnifying power than the short instrument would otherwise possess4 ,a further advantage is secured by the total reflection from the two prisms1 one of which is placed so as to reverse the image right for left and the other inverts it1 so that when viewed in the eyepiece it is in its proper position4 ,important ,topics #a4 ,the eye3 parts1 formation of image1 kind1 how1 where4 #b4 ,eye defects1 how remedied4 ,visual angle4 #c4 ,simple microscope1 camera2 images1 kind1 how formed4 #d4 ,compound microscope1 telescope and opera glass2 images1 action of each lens4 ,exercises #a4 ,name three instruments in which lenses form virtual images and three in which real images are formed4 #b4 ,in what direction is an oar in water apparently bent8 ,explain by a diagram4 #c4 ,what optical instruments have you used8 ,is the visible image formed by each of these real or virtual8 #d4 ,the focal length of a copying camera lens is #ad in4 ,where must a drawing be placed so that an image of the same size may be formed upon the ground glass screen8 ,what must be the distance of the screen from the lens8 #e4 ,what are two methods by which you can determine the focal lengths of the lens of a photographic camera8 #f4 ,the critical angle for water is #dh-a_/b degrees4 ,show by a diagram how much of the sky can be seen by a diver who looks upward through the water4 #g4 ,how is near-sightedness caused8 ,how is it corrected8 ,illustrate by a diagram4 #h4 ,how is the eye accommodated 7focused7 as an object gradually approaches it8 #i4 ,explain why a simple microscope assists in looking at the parts of a flower or insect4 #aj4 ,why do people who have good eyesight when young require glasses as they grow old8 7#g7 ,,color ,,and ,,spectra ,illustration3 ,,guglielmo ,,marconi ,copyright by ,underwood ,underwood1 ,n4 ,y4 ,guglielmo ,marconi 7,italy74 ,inventor of wireless telegraphy4 ,illustration3 ,,alexander ,,graham ,,bell ,copyright by ,underwood ,underwood1 ,n4 ,y4 ,alexander ,graham ,bell1 ,washington1 ,d4 ,c4 ,inventor of the telephone4 #cii4 ,color4--,much of the pleasure experienced in gazing at beautiful objects is due to the color shown by them4 ,the blue sky1 the green grass1 and the varied tints of flowers1 and of the rainbow all excite our admiration ,the study of color begins naturally with the production of the spectrum1 the many-colored image upon a screen produced by passing a beam of light through a prism4 ,the spectrum is best shown when the light enters by a narrow slit 7,fig4 #djj74 ,the spectrum was first produced by ,sir ,isaac ,newton in #afge by the means just described4 ,the names usually given to the more prominent colors of the spectrum are violet1 indigo1 blue1 green1 yellow1 orange1 and red4 ,the initials of these names1 combined1 spell vibgyor1 a word without meaning except to assist in remembering the order of the colors in a spectrum4 ,if the light that has passed through a prism is sent through a second prism placed in reverse position 7see ,fig4 #dja71 the light passing through both prisms is found to be white4 ,this experiment indicates that white light is composed of light of all colors4 ,illustration3 ,,fig4 #djj4--;,formation of the spectrum by a prism4 ,illustration3 ,,fig4 #dja4--,the colors of the spectrum recombine to form white light4 #djj4 ,dispersion4--,the separation of the colors by a prism is called dispersion4 ,in experimenting to find a reason for dispersion1 it has been learned that lights of different colors are of different wave lengths4 ,color in light is therefore analogous to pitch in sound4 ,we hear through many octaves1 but we see through about one octave4 ,that is1 the shortest visible waves of violet light are about #j4jjjjch cm4 in length while the longest visible red rays are #j4jjjjgf cm41 or the longest visible light waves are about twice the length of the shortest visible ones4 ,it appears from the evidence of experiments upon dispersion that light waves of different lengths are refracted differently4 ,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 outline1 since the violet light is brought to a focus sooner than the red4 7,see ,fig4 #djb47 ,this seriously affects the value of such lenses for optical purposes4 ,fortunately it is found that different kinds of glass have a different rate of dispersion for the same amount of refraction4 ,illustration3 ,,fig4 #djb4--,violet light comes to a focus sooner than red4 #dja4 ,the ,achromatic ,lens4--,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 refraction4 ,such a combination is shown in ,fig4 #djc4 ,it is called an achromatic lens1 since images formed by it are not colored but white 7a without1 chroma color74 ,the achromatic lens consists of a double convex lens of crown glass combined with a plano-concave lens of flint glass4 ,achromatic lenses are used in all high-grade optical instruments such as telescopes and microscopes4 ,the colored images that are sometimes seen in cheap opera glasses show the result of not using achromatic lenses4 ,illustration3 ,,fig4 #djc4--;,an achromatic lens4 ,c is of crown glass2 ,f1 of flint glass4 #djb4 ,the ,color of ,bodies4--,project the spectrum of sunlight upon a white surface in a darkened room4 ,now place in different parts of the spectrum objects of various colors4 ,red objects will show brilliant red when at the red end of the spectrum but look black at the blue end1 while blue objects appear blue only at the blue end4 ,these facts indicate that the color of an object depends upon two things3 7a7 the light that falls upon it and 7b7 the light which it sends to the eye4 ,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 it4 ,a white object will appear red in red light1 and blue in blue light since it reflects both of these4 ,a colored object reflects light of its own color but absorbs all others4 ,the color then of a body is due to the light which it does not absorb1 but which comes from it to the eye4 #djc4 ,the color of transparent bodies1 such as colored glass1 is due to the presence of a dye or pigment contained in the body4 ,this pigment absorbs a part of the light1 the part transmitted giving the color4 ,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 prism4 ,some colors1 as red1 may be found to be nearly pure1 only the red passing through1 while green glass often transmits in addition to the green some yellow and some red light4 #djd4 ,complementary ,colors4--,if two prisms are placed in reversed position near each other 7see ,fig4 #dja71 a beam of light dispersed by one is recombined into white light by the other4 ,if now a card is held between the two prisms so as to cut off some of the colored light1 say the red1 the remaining light will be found to form a greenish blue4 ,if the card is removed1 the light becomes white again4 ,that is1 red and peacock blue light together form white4 ,any two colors that together form white light are called complementary4 ,other complementary colors are light yellow and blue1 green and crimson1 orange and greenish blue1 violet and greenish yellow4 ,we must not confuse the combining of colors 7light7 and the combining of pigments1 the latter consisting of bodies that absorb light4 ,yellow pigment absorbs all but yellow and some green1 while blue pigment absorbs all but blue and some green4 ,mixing these two pigments causes the absorption of all colors but green4 ,blue and yellow paint mixed produce green1 while blue and yellow light give white4 #dje4 ,the solar spectrum1 as the spectrum of sunlight is called1 may be observed in the rainbow4 ,the latter is produced through the dispersion of light by spherical raindrops4 ,its formation may be imitated by sending a small circular beam of light through a screen against a round glass flask filled with water4 7,see ,fig4 #djd47 ,the light passes through the water and is dispersed when it enters and when it leaves1 producing a color upon the screen at ,r-,v4 ,the course of the light within the drop is indicated in ,fig4 #dje4 ,the violet ray comes to the eye more nearly horizontal and is therefore below red1 as we look at the rainbow4 #djf4 ,fraunhofer ,lines4--,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 screen4 ,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 lines4 ,these are called ,fraunhofer lines1 to honor the ,german scientist who in #ahad first accurately determined their position4 ,two experiments with a spectroscope will help to make clear the meaning of the ,fraunhofer lines4 ,illustration3 ,,fig4 #djd4--;,a rainbow formed by a beam of light striking a flask of water4 ,illustration3 ,,fig4 #dje4--,the course of a beam of light within a drop of water4 #djg4 ,the ,spectroscope and ,its ,uses4--,the spectroscope 7,fig4 #djf7 is an instrument for observing spectra4 ,it consists of a prism1 a slit1 and a convex lens ,t for focusing an image of the slit accurately upon a screen 7,fig4 #djg7 where the spectrum is observed through the eyepiece ,e4 ,illustration3 ,,fig4 #djf4--,the spectroscope4 7,a7 ,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 flame2 the latter becomes yellow and a vivid yellow line is observed on the screen in the spectroscope4 ,other substances1 as barium and strontium salts1 when heated to incandescence in the ,bunsen flame1 give characteristic bright lines4 ,in fact each element has been found to have its own characteristic set of colored lines4 ,this fact is made use of in spectrum analysis1 by which the presence of certain elements in a substance can be definitely proved upon the appearance of its particular lines in the spectrum4 ,illustration3 ,,fig4 #djg4--;,diagram of a spectroscope4 ,illustration3 ,,fig4 #djh4--,the bright line spectrum of iron and its coincidences with some of the dark lines of the solar spectrum4 7,b7 ,if light from1 for example1 an arc light is sent over a gas flame containing sodium vapor1 a dark line appears in the spectrum--in the exact position in which the yellow sodium line appeared4 ,it seems that the sodium vapor removes from white light the same wave lengths that it itself produces4 ,this absorption is supposed to be due to sympathetic vibration2 just as a tuning fork is set in vibration by the waves of another fork in unison with it1 at the same time absorbing the wave energy1 so in the gas flame the sodium particles absorb the wave motion of the same vibration rate as that emitted by them4 ,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 itself4 ,by comparing the dark lines of the solar spectrum with the bright-line spectra of various substances found in the earth1 such an exact correspondence of the lines is found that the presence of the vapor of these substances about the sun is considered proved4 7,see ,fig4 #djh 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 spectrum47 ,the spectra of the stars also contain certain dark lines4 ,thus the presence of the corresponding substances in distant stars is considered as determined4 #djh4 ,theory of ,color ,vision4--,by combining light of the three colors red1 green and blue-violet in proper proportions1 it has been found possible to produce any color effect1 even white4 ,this leads to the conclusion that in the retina of the eye are three different kinds or sets of sensitive nerve endings1 sensitive respectively to red1 to green1 and to blue light4 ,this idea is given corroboration by some facts of color blindness4 ,thus some persons have no sensation of red1 this color not being distinguished from green4 ,others are color blind to green or blue4 ,it is supposed that in color blind persons one of the sets of nerve endings sensitive to one of these three colors is lacking4 #dji4 ,three-color ,printing4--,since all colors may be produced by mixing the three colors1 light red1 green1 and blue-violet1 these are called the three primary colors4 ,the so-called primary pigments or paints are simply the complements of the three primary colors4 ,they are1 in order1 peacock blue1 crimson1 and light yellow4 ,the three pigments when mixed yield black1 since combined they absorb all kinds of visible light4 ,the process of three-color printing1 now so generally employed in printing colored pictures for books1 calendars1 etc41 consists in combining upon white paper three colored impressions1 using successively the three primary pigments 7yellow1 crimson and blue7 from plates prepared as follows3 ,three photographs of a given colored object are taken1 each through a different sheet of gelatine called a filter1 stained the color of one of the primary colors4 ,from these photographs half-tone blocks are made in the usual way4 ,the colored picture is made by carefully superposing impressions from these blocks1 using in each case an ink whose color is the complement of the filter through which the original picture was taken4 ,an illustration of the process is given upon the plate in the frontispiece of this book4 ,important ,topics #a4 ,color1 due to wave length2 dispersion by prism1 sphere in rainbow1 complementary colors1 color of opaque and transparent bodies4 #b4 ,spectra1 solar2 formation of rainbow2 bright-line spectra1 how formed1 how used2 dark-line1 how formed1 used4 #c4 ,theory of color vision4 ,three color printing4 ,exercises #a4 ,how does a white flower look when viewed through a blue glass8 ,through a red glass8 ,through a red and blue glass at the same time8 #b4 ,why does a red ribbon appear black when seen by blue light and red when seen by red light8 #c4 ,in what part of the sky must you look to see a rainbow in the morning8 ,in the afternoon8 ,explain4 #d4 ,how would you arrange two similar prisms so as to produce double the deviation produced by one8 #e4 ,the color of an object depends upon what two things8 #f4 ,what kind of a spectrum should moonlight give8 ,why8 #g4 ,a mixture of green and red lights gives a sensation of yellow4 ,can you suggest why a mixture of blue and yellow lights gives the sensation of white8 7#h7 ,,nature ,,of ,,light1 ,,interference1 ,,polarization #daj4 ,the ,corpuscular ,theory4--,the theory of the nature of light that was most generally accepted until about the year #ahjj1 held that light consists of streams of minute particles1 called corpuscles1 moving at enormous velocities4 ,this corpuscular theory was in accord with the facts of reflection and the rectilinear motion of light1 but was abandoned after the discovery of the interference of light1 as it could not account for the latter phenomenon4 #daa4 ,the ,wave ,theory of ,light4--,the theory that light is a form of wave motion was first advanced by ,huygens1 a ,dutch physicist1 in the seventeenth century4 ,this theory was opposed at the start since 7,a7 no medium was known to exist which would convey wave motion through space1 as from the sun to the earth1 and 7,b7 the rectilinear motion of light was unlike that of any other form of known wave motions1 such as that of water or of sound waves which are able to bend around corners4 ,in answer to the first objection1 ,huygens assumed the presence of a medium which he named ether1 while the second objection has been completely overcome during the past century by the discovery that light may deviate from a straight line4 ,it is now known that the excessive shortness of light waves is the reason for its straight-line motion4 ,further1 long ether waves1 as those of wireless telegraphy1 are found to bend around obstacles in a manner similar to those of water or sound4 ,illustration3 ,,fig4 #dji4--,two plates pressed together by a screw clamp4 ,illustration3 ,,fig4 #daj4--;,illustrating the interference of light by a thin film of air4 #dab4 ,the interference of light is one of the phenomena for which the wave theory offers the only satisfactory explanation4 ,interference of light may be shown by taking two pieces of plate glass and forcibly pressing them together by a screw clamp1 as shown in ,fig4 #dji4 ,after a certain pressure has been reached1 colored rings will appear about the compressed spot when viewed by light reflected from the upper surface of the glass4 ,if light of one color1 such as that transmitted by red glass1 falls upon the apparatus1 the rings are seen to be alternately red and dark bands4 ,the explanation of this phenomenon according to the wave theory is as follows3 ,the two sheets of glass1 although tightly pressed together1 are separated in most places by a thin wedge of air 7see ,fig4 #daj71 which represents in an exaggerated form the bending of the plates when pressed by the clamp4 ,several waves are represented as coming from the right and entering the glass4 ,now the wave moving from ,r to the plates has some of its light reflected from each glass surface4 ,consider the two portions of the wave reflected at each of the surfaces between the plates1 i4e41 from the two surfaces of the wedge of air4 ,if the portion of the wave reflected from the second surface of the air wedge combines with that reflected from the first surface1 in the same phase as at ,c1 the two reflected waves strengthen each other4 ,while if the two reflected portions of the wave meet in opposite phases as at ,a and ,b1 a decrease or a complete extinction of the light results4 ,this is called interference4 ,if light of one wave length is used1 as red light1 the regions of reinforcement and interference are shown by red and dark rings1 while if white light is used1 the ring where red light interferes1 yields its complementary color1 greenish blue4 ,where interference of greenish blue occurs1 red is found1 etc4 ,many phenomena are due to interference1 such as 7,a7 the color of thin films of oil on water1 where the portions of light reflected from the two surfaces of the oil film interfere resulting in the production of color2 7,b7 the color of soap bubbles4 ,when first formed1 soap-bubble films are not thin enough to show interference well1 but as the bubbles increase in size or become thinner on standing1 the conditions for interference are reached and1 as the film becomes thinner1 a regular succession of colors is noticed4 #dac4 ,differences ,between ,light and ,sound4--,among the important differences between light and sound that have been considered are the following3 the former are 7a7 waves in the ether1 7b7 of very short wave length1 and 7c7 their motion is in straight lines4 ,another difference 7d7 is in the mode of vibration4 ,sound waves are longitudinal1 while light waves are transverse4 ,light waves consist of vibrations of the ether at right angles to the line of motion4 ,to illustrate the reasoning that has led to this conclusion1 suppose a rope to be passed through two vertical gratings4 7,see ,fig4 #daa1 #a47 ,if the rope be set in transverse vibration by a hand1 the waves produced will readily pass through to the gratings ,p and ,q and continue in the part extending beyond ,q4 ,if1 however1 ,q is at right angles to ,p1 no motion will be found beyond ,q4 ,now if a stretched coiled spring with longitudinal vibrations should take the place of the rope1 it is evident that the crossed position of the two gratings would offer no obstacles to the movement of the vibration4 ,in other words1 crossed gratings offer no obstruction to longitudinal vibrations1 while they may completely stop transverse vibrations4 ,illustration3 ,,fig4 #daa4--,transverse waves will pass through both gratings in 7#a7 where the openings in the two gratings are at right angles4 ,the waves passing ,p are stopped by ,q 7#b74 ,illustration3 ,,fig4 #dab4--;,effect of tourmaline crystals on light4 #dad4 ,polarization of ,light4--,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 rope4 ,thus1 if a small opening in a screen is covered with a tourmaline crystal1 light comes through but slightly diminished in intensity4 ,if a second crystal is placed over the first one so that the two axes are in the same direction as in ,fig4 #dab,p1 light is as freely transmitted through the second crystal as through the first1 but if the crystals are crossed 7,fig4 #dab,s7 no light passes the second crystal4 ,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 position1 hence it is believed that a tourmaline crystal is capable of transmitting light that is vibrating in one particular plane4 ,the direct conclusion from this is that light waves are transverse rather than longitudinal4 ,the experiment just described illustrates what is called polarization of light4 ,the beam that after passing through a 7,fig4 #dab7 is unable to pass through b1 if the two axes are crossed1 is called a polarized beam4 ,the conclusion that light waves are transverse is therefore based upon the phenomenon of the polarization of light4 ,this was first discovered by ,huygens in #afij4 ,important ,topics #a4 ,interference of light3 evidence1 reasoning involved1 illustration4 #b4 ,polarization of light3 evidence1 reasoning involved4 #c4 ,nature of light1 differences between sound and light4 ,exercises #a4 ,make a list of the differences between sound and light and state briefly the evidence upon which the knowledge of these differences is based4 #b4 ,why will a thickness of film that will produce interference of red light be different from that producing interference for green or blue8 #c4 ,using the formula n v_/l compute the vibration rate for violet light if its wave length is considered as #j4jjjjd cm4 #d4 ,explain how the fact of polarization affects the wave theory of light4 #e4 ,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 earth4 ,review ,outline3 ,light ,light2 speed1 source1 medium4 ,straight ,line ,motion2 shadow1 umbra1 penumbra1 eclipse1 image4 ,photometry2 ,law of intensity1 candle power1 foot-candle4 ,mirrors2 ,law of reflection2 image--real1 virtual2 plane1 curved1 parabolic1 mirrors4 ,refraction2 cause and effects2 plate1 prism1 lens2 total reflection4 ,lenses2 six forms1 principal focus1 center1 lens equation1 #a_/;,f #a_/;,do #a_/;,di4 ,optical instruments2 eye1 defects and correction1 camera1 microscope1 etc4 ,spectra2 #c kinds1 dispersion1 production of color effects1 spectroscope1 uses4 ,nature of ,light2 wave theory1 interference1 polarization1 significance4 ,,chapter ,,xvii ,,invisible ,,radiations 7#a7 ,,electric ,,waves ,,and ,,radio-,,activity #dae4 ,oscillatory ,nature of the ,spark from a ,leyden ,jar4--,in studying sound 7,art4 #cci71 the sympathetic vibration of two tuning forks having the same rate of vibration was given as an illustration of resonance4 ,the conditions for obtaining electrical resonance by the use of two ,leyden jars are given in the following experiment4 ,join the two coats of a ,leyden jar 7,fig4 #dac7 to a loop of wire ,l1 the sliding crosspiece ,m being arranged so that the length of the loop may be changed as desired4 ,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 ,g4 ,now join the outer coating of another exactly similar jar ,a to a wire loop of fixed length1 the end of the loop being separated from the knob connected to the inner coating1 a short distance at ,p4 ,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 coil4 ,at each discharge between the knobs at ,p1 a spark will appear in the other jar at ,g1 if the crosspiece ,m is so adjusted that the areas of the two loops are exactly equal4 ,when the wire ,m is moved so as to make the areas of the two loops quite unequal1 the spark at ,g disappears4 ,illustration3 ,,fig4 #dac4 ,the experiment just described shows that two electrical circuits can be tuned by adjusting their lengths1 just as two tuning forks may be made sympathetic by adjusting their lengths4 ,this fact indicates that the discharge of the ,leyden jar is oscillatory1 since resonance can plainly not be secured except between bodies having natural periods of vibration4 ,this same fact is also shown by examining the discharge of a ,leyden jar as it appears when viewed in a rapidly revolving mirror4 7,see ,fig4 #dad47 ,the appearance in the mirror shows that the discharge is made up of a number of sparks1 often a dozen or more1 vibrating back and forth until they finally come to rest4 ,the time of one vibration varies from one millionth to one hundred millionth of a second1 depending on the space between the discharging balls and the size of the jars4 ,illustration3 ,,fig4 #dad4--,photograph of the oscillatory discharge of a ,leyden jar4 ,the discharge of a ,leyden jar or of another condenser sets up ether waves that have the speed of light4 ,heinrich ,hertz in ,germany first proved this in #ahhh4 ,these waves are now known as ,hertzian waves4 ,the length of these varies from #c cm4 to several miles1 depending upon the size and conditions of the discharging circuit4 ,illustration3 ,,fig4 #dae4--;,a coherer4 #daf4 ,the ,coherer4--,the coherer is a device for detecting electric waves4 ,it consists of a glass tube with metal filings loosely packed between two metal plugs that fit the tube closely4 7,see ,fig4 #dae47 ,these filings offer a high resistance to the passage of an electric current1 but when electric waves pass through the filings these cohere and allow a weak current to pass through4 ,this current may be strong enough to operate a relay connected with a sounder or bell that gives audible signals4 ,if the tube be tapped the filings will be disturbed and the resistance again made so high that no current can pass through4 #dag4 ,wireless ,telegraphy4--,in #ahid ,marconi1 then a young man of twenty1 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 relay4 ,at present the coherer is used principally in laboratory apparatus1 as much more sensitive detectors are now available for commercial work4 ,the essential parts of a modern wireless telegraph apparatus as used in many commercial stations are shown in ,fig4 #daf4 ,alternating current at #aaj volts is sent into the primary1 ,p1 of a transformer1 the secondary1 ,s1 of which produces a potential of #ejjj to #bj1jjj volts4 ,the secondary charges a condenser until its potential becomes high enough to produce a discharge across a spark gap1 ,,sg4 ,this discharge is oscillatory1 the frequency being at the rate of about one million a second1 depending upon the capacity of the condenser and the induction of the circuit4 ,these oscillations pass through the primary of the oscillation transformer1 inducing in the secondary1 electric oscillations which surge back and forth through the antenn1 or aerial wires1 ,a4 ,these oscillations set up the wireless waves4 ,the production of these waves is explained as follows3 ,an electric current in a wire sets up a magnetic field spreading out about the conductor2 when the current stops the field returns to the conductor and disappears4 ,the oscillations in the antenn1 however1 have such a high frequency1 of the order of a million a second1 that when one surge of electricity sets up a magnetic field1 the reverse surge immediately following sets up an opposite magnetic field before the first field can return to the wire4 ,under these conditions a succession of oppositely directed magnetic fields are produced which move out from the antenn with the speed of light and induce electric oscillations in any conductors cut by them4 ,illustration3 ,,fig4 #daf4--;,diagram of a commercial wireless telegraph apparatus4 ,while the electric waves are radiated in all directions from the aerial1 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 transformer4 ,the electric waves induce effective electrical oscillations in the aerial of the receiving station1 even at distances of hundreds of miles1 provided the receiving transformer1 ,,rt1 is tuned in resonance with the transmitting apparatus by adjustments of the variable condenser1 ,,vc1 and the loading coil1 ,l4 ,the detector of these oscillations in the receiving transformer is simply a crystal of silicon or carborundum1 ,d1 in series with two telephone receivers1 ,ph4 ,the crystal detector permits the electric oscillations to pass through it in one direction only4 ,if the crystal did not possess this property1 the telephone could not be used as a receiver as it cannot respond to high frequency oscillations4 ,while one spark passes at ,,sg1 an intermittent current passes through the receiver in one direction4 ,since some #cjj to #abjj sparks pass each second at ,,sg while the key1 ,k1 is closed1 the operator at ,ph hears a musical note of this frequency as long as ,k is depressed4 ,short and long tones then correspond to the dots and dashes of ordinary telegraphy4 ,in order to maintain a uniform tone a rotary spark gap1 as shown1 is often used4 ,this insures a tone of fixed pitch by making uniform the rate of producing sparks4 ,the ,continental instead of the ,morse code of signals is generally employed in wireless telegraphy1 since the former employs only dots and dashes4 ,the latter code employs1 in addition to dots and dashes1 spaces which have sometimes caused confusion in receiving wireless messages4 ,the ,united ,states government has adopted the regulations of the ,international ,radio ,congress which directs that commercial companies shall use wave lengths between #cjj and #fjj or above #afjj meters4 ,amateurs may use wave lengths less than #bjj meters and no others1 while the government reserves the right to wave lengths of #fjj to #afjj meters4 ,see p4 #dei for ,continental telegraph code4 #dah4 ,discharges in ,rarefied ,air4--,fig4 #dag represents a glass tube #fj or more centimeters long1 attached to an air pump4 ,connect the ends of the tube to the terminals of a static machine or of an induction coil1 a-b4 ,at first no sparks will pass between a and f1 because of the high resistance of the air in the tube4 ,upon exhausting the air in the tube1 however1 the discharge begins to pass through it instead of between a and b4 ,this shows that an electrical discharge will pass more readily through a partial vacuum than through air at ordinary pressure4 ,as the air becomes more and more exhausted1 the character of the discharge changes4 ,at first it is a faint spark1 gradually changing until it becomes a glow extending from one terminal to the other and nearly filling the tube4 ,illustration3 ,,fig4 #dag4--;,an ,aurora tube4 ,geissler tubes are tubes like the above4 ,they are usually made of different kinds of glass twisted into various shapes to produce beautiful color effects4 ,the aurora borealis or northern light is supposed to be electric discharges through rarefied air at the height of from #fj to #ajj miles above the earth's magnetic poles4 7,see ,fig4 #dah47 ,illustration3 ,,fig4 #dah4--;,aurora ,borealis4 #dai4 ,cathode ,rays4--,when the tube in ,art4 #dbj is exhausted to a pressure of #j4jja mm41 or a little less than one millionth of an atmosphere1 the character of the discharge is entirely changed4 ,the tube becomes filled with a yellowish green phosphorescent light4 ,this is produced by what are called cathode rays striking the glass walls of the tube4 ,these rays are called cathode rays because they come from the cathode of the tube4 ,they are invisible and that they travel in straight lines is shown by the shadow obtained by using a tube with a screen 7,fig4 #dai74 ,illustration3 ,,fig4 #dai4--;,a cathode ray tube4 #dbj4 ,x ,rays4--,in #ahie1 ,professor ,rntgen of ,wurtzburg1 ,germany1 discovered that when the cathode rays strike the walls of the tube or any solid within it they excite a form of invisible radiation4 ,this radiation is called ,rntgen rays1 or more commonly1 ,x rays4 ,careful experiments show that they travel in straight lines1 and that they can not be reflected or refracted as light waves are4 ,they pass through glass and opaque objects such as flesh1 cardboard1 cloth1 leather1 etc41 but not through metallic substances4 ,the tube in ,fig4 #dbj has a screen covered with crystals which become luminous when struck by the cathode rays4 ,on bringing a magnet near the tube the luminous line is raised or lowered showing that the magnetic field affects the stream of cathode rays1 attracting it when in one position but repelling it when in the reverse direction4 ,the cathode rays which cause the bright line possess a negative charge of electricity4 ,they are now believed to be electrons shot off from the surface of the cathode with speeds that may reach #ajj1jjj miles a second4 ,x rays possess no electrical charge whatever and cannot be deflected by a magnet4 ,they produce the same effect on a photograph plate as light does1 only more slowly4 ,hence1 they can be used in taking ,x ray photographs4 ,certain crystals1 like barium platinum cyanide1 fluoresce when struck by the ,x rays4 ,the fluoroscope is the name given to a light-tight box closed at one end by a cardboard covered with these crystals 7,fig4 #dba74 ,on looking into the fluoroscope with an opaque object such as the hand placed between the screen and the ,x ray tube1 a shadow of the bones of the hand can be seen upon the screen of the fluoroscope4 7,see ,fig4 #dbb47 ,illustration3 ,,fig4 #dbj4--,the stream of cathode rays is deflected by a magnet4 ,illustration3 ,,fig4 #dba4--;,a fluoroscope4 ,illustration3 ,,fig4 #dbb4--;,a view of the shadow of a hand as seen in a fluoroscope4 ,a special form of the tube is used4 7,see ,fig4 #dbc47 ,in this tube a platinum disc is placed at the focus of the concave cathode4 ,this concentrates the ,x rays in one direction4 ,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 anode4 ,illustration3 ,,fig4 #dbc4--;,an ,x ray tube4 #dba4 ,the ,electromagnetic ,theory of ,light4--,the study of electric waves has shown that they are similar to light waves in many respects3 7a7 they have the same velocity2 7b7 they can be reflected and refracted4 ,the main difference is in their length1 light waves being very much shorter4 ,in #ahfd ,james ,clerk ,maxwell1 an ,english physicist1 proposed the theory that ether waves could be produced by electrical means and that light waves are electromagnetic4 ,in #ahhh ,hertz proved by his experiments that ether waves having the same velocity as light could be produced in this way4 ,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 ether4 #dbb4 ,radio-activity4--,in #ahif ,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 rays4 ,these rays are often called ,becquerel rays in honor of their discoverer4 ,the property of emitting such rays is called radio-activity1 and the substances producing them are called radio-active4 ,in #ahih1 ,professor and ,mme4 ,curie after an investigation of all the elements found that thorium1 one of the chief constituents of incandescent gas mantles1 together with its compounds1 was also radio-active4 ,this may be shown by the following experiment3 ,place a flattened gas mantle upon a photographic plate and leave in a light tight-box for several days4 ,upon developing the plate in the usual way a distinct image of the mantle will be found upon the plate4 #dbc4 ,radium4--,mme4 ,curie discovered also that pitch-blende possessed much greater radio-active power than either thorium or uranium4 ,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 uranium4 ,she called this new substance radium4 ,radium is continually being decomposed1 this decomposition being accompanied by the production of a great deal of heat4 ,it has been calculated that it will take about #cjj years for a particle of radium to be entirely decomposed and separated into other substances4 ,it is also believed that radium itself is the product of the decomposition of uranium1 atomic weight #bch1 and that the final product of successive decompositions may be some inert metal1 like lead1 atomic weight #bjg4 ,the radiation given off by radio-active substances consists of three kinds3 7,a7 ,positively charged particles of helium called alpha rays3 7,b7 negatively charged particles called beta rays3 7,c7 gamma rays4 ,the alpha rays have little penetrating power1 a sheet of paper or a sheet of aluminum #j4je mm4 stopping them4 ,upon losing their charges they become atoms of helium4 ,their velocity is about #a_/aj of that of light or #ah1jjj miles a second4 ,the spinthariscope is a little instrument devised by ,sir ,williams ,crookes in #aijc to show direct evidence that particles are continually being shot off from radium4 ,in this instrument 7,fig4 #dbd71 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 sulphide4 ,looking in the dark at this screen through the lens ,l1 a continuous succession of sparks is seen like a swarm of fireflies on a warm summer night4 ,each flash is due to an alpha particle striking the screen4 ,the beta rays are supposed to be cathode rays or electrons with velocities of from #dj1jjj to #agj1jjj miles a second4 ,the gamma rays are supposed to be ,x rays produced by the beta rays striking solid objects4 ,illustration3 ,,fig4 #dbd4--;,a spinthariscope4 #dbd4 ,the discovery of radio-activity has revolutionized the ideas of the constitution of matter4 ,further1 the results of experiments upon radio-active materials reveals the presence of immense quantities of sub-atomic energy4 ,if man ever discovers a means of utilizing this1 he will enter a storehouse of energy of far greater extent and value than any of which he has as yet made use4 ,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 nature4 ,important ,topics #a4 ,oscillatory nature of discharge of ,leyden jar4 ,proofs4 #b4 ,wireless telegraphy and telephony4 #c4 ,electrical discharges in rarefied gases4 #d4 ,cathode and ,x rays4 #e4 ,electromagnetic theory of light4 #f4 ,radio activity and radium4 ,illustration3 ,,continental ,,telegraph ,,code ,a 4 - ,j 4 - - - ,s 4 4 4 ,b - 4 4 4 ,k - 4 - ,t - ,c - 4 - 4 ,l 4 - 4 4 ,u 4 4 - ,d - 4 4 ,m - - ,v 4 4 4 - ,e 4 ,n - 4 ,w 4 - - ,f 4 4 - 4 ,o - - - ,x - 4 4 - ,g - - 4 ,p 4- - 4 ,y - 4 - - ,h 4 4 4 4 ,q - - 4 - ,z - - 4 4 ,i 4 4 ,r 4 - 4 ,,period ,,interrogation ,,exclamation 4 4 4 4 4 4 4 4 - - 4 4 - - 4 4 - - #a 4 - - - - #b 4 4 - - - #c 4 4 4 - - #d 4 4 4 4 - #e 4 4 4 4 4 #f - 4 4 4 4 #g - - 4 4 4 #h - - - 4 4 #i - - - - 4 #j - - - - - ,,chapter ,,xviii ,,wireless ,,telephony ,,and ,,alternating ,,currents ,the developments in wireless communication have been so rapid during recent years that a more extended account1 than that given in ,art4 #dag of the apparatus and methods used at the present time1 seems desirable4 ,the study of ,alternating ,currents is also included with the idea that it will make the text more complete and of wider usefulness4 ,,wireless ,,telephony #dbe4 ,the ,wireless ,telephone4--,one of the most important developments in wireless communication in recent years has been in wireless telephony4 ,we realize its possibilities1 when we hear of the achievements of talking across an ocean or between airplanes and the ground4 ,the wireless telephone can be best understood by comparing it with the common telephone4 ,when the latter is in use1 a direct current flows continually through the instrument4 7,see ,arts4 #cab-caf47 ,when a person speaks into the transmitter1 the sound waves of the voice cause the diaphragm to vibrate1 this action causes rapid changes in the resistance of the transmitter1 which in turn causes the direct current to fluctuate just in step with the pulses of the voice waves4 ,this fluctuating direct current passes through the primary of an induction coil1 producing in the secondary an intensified alternating current4 ,this passes over the line wires to the receiver where it produces variations in the magnetic field affecting the receiver diaphragm1 causing the latter to reproduce the voice of the person speaking in the transmitter4 ,now to make the comparison clear1 two facts must be noted with regard to the wire telephone3 first1 there must be an action in the transmitter which causes variations in a current through the instrument2 second1 this fluctuating current produces a more intense alternating current which flows over the line and affects the receiver diaphragm1 producing there sound vibrations of greater intensity than those used at the transmitter4 ,this added energy comes from the current flowing through the transmitter4 ,the case is analogous to that of an electric bell4 ,the armature of the bell vibrates with greater energy than is required to push the button1 the extra energy being derived from the battery4 #dbf4 ,the ,action of the ,wireless ,telephone4--,in the wireless telephone we have a continuous stream of electric waves of high frequency4 7,see ,fig4 #dbe;,a47 ,this stream of electric waves corresponds to the current that flows through the transmitter in the wire telephone4 ,these waves are of such high frequency that even though we had a receiver diaphragm vibrating in step with the waves1 we could not hear the sound because the human ear cannot hear a sound which consists of more than about #dj1jjj vibrations per second4 ,the sound waves act upon this stream of waves very much1 as in the wire telephone1 the transmitter acts to modify the line current4 ,the impulses caused by the voice are much slower than the electric waves first mentioned and these slower impulses are reproduced in the receiver4 ,not only are these slower impulses reproduced but they are amplified1 that is1 produced with greater energy than the impulses impressed on the stream of waves4 ,fig4 #dbe;,a represents as nearly as is possible in a diagram the continuous stream of electric waves4 ,fig4 #dbf;,b1 represents the impulses produced by the sound alone1 and ,fig4 #dbf;,c1 shows how these voice impulses are impressed on the stream of waves4 ,illustration3 ,,fig4 #dbe4--;,a1 unmodified high frequency waves2 ,b1 waves of voice frequency2 ,c1 high frequency waves modified by waves of voice frequency4 ,illustration3 ,,fig4 #dbf4--,vacuum tube1 transmitting type4 7,western ,electric ,co47 ,illustration3 ,,fig4 #dbg4--,vacuum tube1 receiving type4 7,western ,electric ,co47 ,illustration3 ,,fig4 #dbh4--;,diagram of wireless telephone transmitting set4 #dbg4 ,the ,vacuum ,tube or ,audion4--,the device by which all of this is accomplished is the vacuum tube4 7,see ,fig4 #dbf47 ,this tube contains three electrodes4 ,first1 a filament 7,f1 in ,fig4 #dbh7 which is heated by a current from a battery 7,b#a1 ,fig4 #dbh7 and because it is heated1 sends out a stream of electrons4 ,second1 the plate which forms the anode of the circuit from battery1 ,b#b4 ,this plate receives the electrons which are thrown off by the heated filament1 hence a current flows through the circuit of ,b#b2 the discharge through the tube depending on the e4m4f4 between the filament and the plate4 ,third1 a grid is placed between the filament and the plate and is connected to the secondary of the induction coil1 the primary of which is connected to the transmitter4 ,when the transmitter diaphragm is vibrating1 the e4m4f4 induced in the secondary of the induction coil causes a variation in the potential of the grid4 ,this means a variation in the electric field between the filament and the plate4 7,see ,fig4 #dbh47 ,the changing electric field causes a variation in the discharge of electrons through the tube2 the variation corresponds to the vibrations of the transmitter diaphragm4 ,this produces a surging current of the frequency of the sound waves in the primary of the transformer 7,t1 ,fig4 #dbh74 ,the secondary of this transformer is connected to the antenn 7,a7 and the earth 7,e74 ,by means of the transformer1 rapid surgings are set up in the antenn and these surgings produce a continuous stream of electromagnetic waves which goes out in space4 7,like ,fig4 #dbf;,c47 ,these electromagnetic waves produce oscillations in the antenn of a receiving station4 ,the antenn transmit the impulses to a tube 7,fig4 #dbg7 which acts as a detector1 and makes possible the reproduction of the sound by an ordinary telephone receiver4 ,illustration3 ,,fig4 #dbi4--,view of wireless telephone set4 ,the vacuum tube in the transmitting circuit also amplifies the impulses1 that is1 the energy of the waves given out is greater than that of the impulses which produce them1 the additional energy being derived from the battery sending current through the plate and filament4 ,in operation1 the filament and the plate are connected to a battery with a condenser 7,,vc7 and an inductance coil 7,i7 in the circuit1 as shown in ,fig4 #dbh4 ,photograph of a complete modern wireless telephone set is shown in ,fig4 #dbi4 ,,alternating ,,currents #dbh4 ,alternating currents are of interest to us because of their general commercial use4 ,to understand the reason for the extensive application of alternating currents it is necessary to learn the fundamental principles which pertain to them4 ,the production of such currents has already been explained in ,arts4 #cjj-cjd4 ,it should be remembered that the current developed in the armature of a dynamo is alternating4 ,a dynamo may deliver a direct or an alternating current1 depending on the method of collecting the current from the armature4 ,if a commutator is used1 the machine delivers direct current1 if slip rings are employed1 an alternating current is delivered4 #dbi4 ,the ,magnetic ,field of an ,alternating ,current4--,the magnetic field of a direct current has been considered in ,arts4 #bee-bef4 ,it has been shown to be arranged in circles about the conductor1 according to the ,right ,hand ,rule4 7,see ,figs4 #bbi and #bcj47 ,these facts will help one to understand the following experiment3 ,if a number of magnetic compasses be arranged in a circle about a straight vertical wire carrying a direct current1 the compass needles will point out a circle about the wire4 7,see ,fig4 #dcj1 ,a47 ,if now the current be reversed the compass needles will reverse themselves and point in a direction just opposite to that taken at first4 7,see ,fig4 #dcj1 ,b47 ,this will be clear if you imagine yourself walking around the wire in the direction the compass needles pointed at first1 and then walking around the wire in the reverse direction4 ,this illustrates what happens in the field of an alternating current4 ,the field reverses each time the current reverses4 ,the magnetic field of an alternating current not only rapidly reverses itself1 but also continually changes in intensity4 ,at the instant when the current reverses1 the force of the magnetic field is zero since the current at that instant is zero4 ,as the current begins flowing and increases to its maximum intensity1 the magnetic field appears and increases in intensity2 and as the current decreases to zero1 the magnetic field changes in a similar manner4 ,the field as it grows in strength extends farther and farther from the wire1 as it decreases in strength it contracts or draws closer to the wire4 ,thus the magnetic field may be said to expand and contract4 ,we may picture the lines of force as continually moving4 ,in a typical a4-c4 circuit1 the complete series of changes takes place in a small fraction of a second1 and is repeated many times over in a second4 ,contrast this with the magnetic field of a constant direct current4 ,here the magnetic field has the same direction as long as the current flows and does not change in strength4 ,this comparison is important because most of the differences between direct and alternating currents depend on differences in the action of their magnetic fields4 ,illustration3 ,,fig4 #dcj4--;,arrangement of compasses about a wire carrying an alternating current4 #dcj4 ,transformers4--,the transformer has been described in ,arts4 #cji-caj4 ,the principle of the transformer may be illustrated by the following experiment3 ,a coil having several hundred turns of ,no4 #ah d4c4c4 copper wire is placed over one arm of a ,u shaped iron core 7see ,fig4 #dca7 and then connected to a #aaj volt a4-c4 lighting circuit4 ,another coil 7,s7 having about #ej turns of ,no4 #bb d4c4c4 copper wire is connected to an electric bell or buzzer1 or a low voltage electric light bulb4 ,when the small coil is held over the other arm of the ,u shaped iron core1 the bell rings or the bulb glows4 ,it is evident that the electromotive force developed in the small coil 7,s7 is due to the alternating magnetic field surging back and forth through the iron core4 ,in ,fig4 #dca the core is open since the magnetic field must pass through the air from one end of the core to the other4 ,a typical transformer has a closed core to provide a closed magnetic circuit4 ,to secure this1 take a suitable bar of iron and lay across the end of the ,u shaped core1 and notice any change in the induced current produced in the small coil1 due to increased movement of magnetism through the closed iron core4 ,illustration3 ,,fig4 #dca4--;,diagram of a transformer4 ,this experiment illustrates the construction and action of a transformer4 ,in a commercial transformer1 the two windings are on a closed magnetic circuit4 7,see ,figs4 #cjd and #cje1 p4 #cdf47 ,to keep the coils insulated1 the transformer is placed in an iron housing and covered with oil4 ,these housings1 or transformer cases are generally attached to poles near buildings in which alternating current is used4 #dca4 ,voltage ,relation in a ,transformer4--,in the experiment described above1 a bell was rung by an induced current produced in the secondary coil4 ,the induced e4m4f4 was less than the voltage of the primary coil partly because there was some magnetic leakage1 but mainly because there were fewer turns of wire on the secondary4 ,in a commercial transformer the magnetic leakage is practically zero4 ,in such a case1 the ratio of the number of turns on the primary coil to the number on the secondary equals the ratio of the e4m4f4 induced in the primary to the e4m4f4 induced in the secondary4 ,suppose1 for example1 we wish to make a bell ringing transformer to use on a #aaj volt lighting circuit1 #aj volts being required for the bell2 the secondary will then need one-eleventh of the number of turns of the primary4 ,so that if #eej turns are on the primary1 then #ej turns will be needed for the secondary4 ,this will be a step-down transformer4 ,on the other hand1 suppose we wish to step-up the voltage as is done in a certain power station where the voltage of the generators is #fjjj volts1 the voltage being stepped up to #dd1jjj by means of large transformers4 ,this means that the secondary coils have approximately #g-a_/c times as many turns as the primary4 #dcb4 ,power ,loss in a ,transformer4--,when the voltage is stepped up in a transformer1 do we gain power8 ,to answer this question we must remember that electric power does not depend on voltage alone but on the product of e4m4f4 and current intensity4 7,see ,art4 #bia47 ,by tests with a4-c4 voltmeters and ammeters1 we find that when the secondary e4m4f4 is greater than the primary e4m4f41 the secondary current intensity is less than that in the primary4 ,it is also found that the power developed is less than the power received by the transformer1 i4e41 the output is less than the input as we would expect from the law of machines4 ,the power loss is mainly due to the work required to reverse the magnetism1 that is1 to continually reverse the position of the iron molecules4 7,see ,art4 #bje47 ,the energy lost in this manner is known as core loss since it occurs in the iron core4 ,the lost energy appears as heat4 ,so much heat is developed in large transformers that special means of cooling are provided4 ,in order to make the heat developed as small as possible1 the cores are laminated 7see ,fig4 #cje1 p4 #cdf71 that is1 built up of thin sheets of iron1 because if the iron cores were solid1 the changing magnetic fields would induce electric currents in the iron cores1 which would produce an excessive amount of heat with a correspondingly large power loss4 ,illustration3 ,,fig4 #dcb4--;,diagram of bell-ringing transformer4 #dcc4 ,choke ,coils and ,inductance4--,if we refer to ,fig4 #dcb we see that the primary winding of the bell ringing transformer is connected across the line4 ,this winding forms a closed circuit whether the bell is ringing or not4 ,the resistance of this winding is small4 ,let us assume it to be one ohm4 ,with a one ohm resistance connected across a #aaj volt line we might expect a current of #aaj amperes4 ,this is certainly what we should get if we were to connect a one ohm resistance across a line having #aaj volts direct4 ,the primary would form a short circuit if the current were direct4 ,but the fact is that practically no current flows through the primary winding when the bell is not ringing4 ,herein lies one of the important differences between alternating and direct currents4 ,with an alternating current the primary winding of our transformer acts as a choke coil and chokes down the current almost to zero4 ,let us see how this is done4 ,illustration3 ,,fig4 #dcc4--;,a circuit containing a choke coil4 ,let ,fig4 #dcc represent a choke coil4 ,since alternating current is used1 the magnetic field is continually changing4 ,each turn of wire has its own magnetic field4 ,the lines of force of turn number #a expand and contract and as they do so they move across turns #b1 #c and so on4 ,in like manner the lines of force from each turn of wire move across the other turns4 ,in other words the coil is cutting its own lines of force4 ,now whenever an electric conductor cuts magnetic lines of force an electromotive force is induced in the conductor4 ,there is then an e4m4f4 induced in the coil by its own magnetic field4 ,this induced e4m4f4 on the whole opposes the applied e4m4f42 in the primary of our bell ringing transformer the induced e4m4f4 opposes the e4m4f4 of the line to such an extent as to reduce the current almost to zero4 ,inductance is the action of an alternating current in inducing an opposing e4m4f4 in the coil in which the current is flowing4 ,since this opposing e4m4f4 is induced in the coil by its own magnetic field this action is also called self-induction4 ,in a transformer the action of the field of the primary upon the secondary is mutual induction2 while the action of the field of the primary in choking the current in the primary itself is self-induction or inductance4 ,a coil having a single winding and used to introduce inductance in a circuit is called a choke coil4 ,a choke coil inserted in a lamp circuit in series with the lamps dims the lamps because it reduces the intensity of the current4 ,illustration3 ,,fig4 #dcd4--;,diagram showing graphically an alternating current with a lag of #cj behind its electromotive force4 ,self-induction causes the current to lag1 that is1 the current does not quite reach its maximum at the instant the voltage reaches its maximum4 ,fig4 #dcd shows graphically an e4m4f4 and a lagging current4 ,in this figure the maximum current is shown following the maximum voltage at an interval of #cj degrees4 ,in other words the armature in a two-pole field must turn #cj degrees from the position of maximum voltage before the current in the coil1 where the self-induction occurs1 reaches its maximum4 #dcd4 ,reactance and ,impedance4--,a choke coil has resistance as well as inductance4 ,its resistance can be found by the voltmeter-ammeter method1 using a direct current4 7,see ,art4 #bgh47 ,let us take for example the primary winding of a bell ringing transformer4 ,using a direct current and testing the coil with a voltmeter and ammeter we find its resistance to be1 let us say1 one ohm4 ,if we connect the same coil across a #aaj volt a4-c4 line we find the current to be very small1 say #j4je ampere4 ,the coil now has resistance and reactance4 ,reactance is the effect of self-induction in hindering the flow of current4 ,it is measured in ohms4 ,the combined effect of resistance and reactance is called impedance4 ,in the example above1 the coil has #aaj 7volts7_/#j4je 7ampere7 #bbjj ohms of impedance4 ,in applying ,ohm's law to an alternating current circuit1 impedance must be substituted for resistance4 ,ohm's law as applied to an a-c4 circuit should be stated3 ,current intensity equals e4m4f4 divided by impedance1 or ,i ,e_/,z4 7,z impedance47 ,illustration3 ,,fig4 #dce4--,the relation between resistance1 reactance and impedance4 ,impedance1 however1 does not equal the sum of resistance and reactance4 ,the relation between these three quantities is similar to that between the three sides of a right triangle1 in which the impedance represents the hypotenuse1 and the resistance and reactance the other two sides4 ,see ,fig4 #dce which indicates that ,resistance ,reactance ,impedance1 or 7,r ,x ,z74 7,x reactance47 ,to illustrate this relation2 suppose the primary of a transformer has #aj ohms impedance and #h ohms resistance1 then the reactance equals #aj - #h #f1 or the reactance is #f ohms4 ,exercises #a4 ,find the reactance of a choke coil having a resistance of #aj ohms1 when its impedance is #ej ohms4 ,how great a current flows through this coil if the terminal voltage is #aaj volts8 #b4 ,when the bell is ringing1 the primary of a bell ringing transformer has an appreciable current4 ,suppose this current is #j4b ampere4 ,what is the impedance if the voltage of the line is #aae volts8 ,what is the reactance if the resistance is #a ohm8 #c4 ,the primary of a large transformer has a terminal voltage of #fjjj volts and a current of #fjj amperes4 ,what is the impedance8 ,if the resistance is #f ohms1 what is the reactance8 ,illustration3 ,,fig4 #dcf4--;,a telephone set showing a condenser used in the circuit of the ringer4 #dce4--,the electric condenser 7see ,art4 #bca7 is a very useful device in a4-c4 circuits2 e4g41 in telephone sets used in cities1 a condenser is used in the ringing circuit1 as shown in ,fig4 #dcf4 ,alternating current is required to ring such a bell and a condenser permits an a4-c4 current to act through it1 although it entirely prevents the flow of a direct current4 ,this peculiar action will now be explained4 #dcf4 ,the action of a condenser in an alternating current circuit may be illustrated by the following experiment4 ,connect twelve1 #a m4f4 7microfarad7 condensers1 in parallel1 and then attach them to a #aaj volt a4-c4 line so that an incandescent lamp is in circuit as shown in ,fig4 #dcg4 ,the lamp will be found to glow brightly1 although there is no electrical connection between the two sets of condenser plates4 ,if the same arrangement is connected to a #aaj volt direct current circuit1 the lamp does not glow because it is really an open circuit4 ,the lamp glows on an a4-c4 circuit because1 although no electricity flows through the condenser1 it does flow into and out of the condenser1 surging back and forth through the lamp with sufficient intensity to cause it to glow brightly4 ,when the a4-c4 current moves one way in the circuit1 one set of plates of the condensers becomes charged positively1 the other1 negatively4 ,when the a4-c4 current reverses1 the charges on the condenser plates reverse4 ,in the ordinary lighting circuit #abj reversals take place each second1 so that electricity rapidly flows into and out of the condensers4 ,on removing one condenser after another from the circuit1 the lamp is found to glow less and less1 till when but one condenser is left1 no glowing is observed1 since one small condenser does not have sufficient capacity4 ,illustration3 ,,fig4 #dcg4--,twelve condensers in circuit with an incandescent lamp4 ,the unit of capacity is the ,farad4 ,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 second4 ,if a change of one volt per second causes one coulomb to flow per second1 that is1 a current of one ampere1 the capacity is one farad4 ,the condensers used in the above experiment have a capacity of one microfarad1 or one millionth of a farad4 ,a condenser1 on account of its capacity1 causes an a4-c4 current to lead the voltage1 that is the current reaches its maximum value before the voltage does4 ,in this respect a condenser has an effect opposite to that of the self-induction of a choke coil 7the latter causing the current to lag74 7,see ,fig4 #dce47 #dcg4 ,transmission of ,electric ,power4--,a field of peculiar usefulness for a4-c4 currents is in the economical transmission of electric power4 ,this fact is due to the following reasons3 7a7 ,the loss of electrical power in a transmission line is due to the production of heat2 the heat produced being proportional to ,i,r1 or to the square of the current intensity4 ,any lessening of the current flow required to transmit a given power will therefore increase the efficiency of transmission4 7b7 ,in order to employ a small current in transmitting a large amount of power1 we must use a very high e4m4f4 ,such high electromotive forces1 say from #fj1jjj to #ajj1jjj volts1 can be obtained only by the use of a4-c4 transformers1 since it is not practicable to build a direct current generator capable of producing #fj1jjj volts4 ,in large power transmission systems1 a4-c4 generators are used to produce powerful alternating currents4 ,the e4m4f4 is then stepped up to a suitable voltage 7#bcjj-ajj1jjj7 by transformers and sent over transmission lines to the various places where the power is to be used2 at these places suitable transformers step-down the e4m4f4 to a convenient or safe voltage for use4 7,see ,fig4 #ddb of a transmission line and ,fig4 #dch of a large power transmission system1 and ,fig4 #dci of an a4-c4 generator and power plant47 ,illustration3 ,,fig4 #dch4--;,diagram of an alternating current high tension power system4 7,a7 ,alternator1 7,tu7 water turbine1 direct connected to alternator1 7,e7 exciter1 7,t#a7 step-up transformers in power station1 7,t#b7 step-down transformers in substation1 7,m7 motor1 7,l7 lamps1 single-phase1 three-wire system1 7,t#c7 step-down transformers delivering three-phase current to rotary converter 7,r7 which delivers direct current to the trolley line4 #dch4 ,power ,factor4--,the power factor is a matter of interest and importance in the use of a4-c4 machines4 ,its meaning and use may be learned from the following explanation3 ,in a direct current circuit1 watts equals volts times amperes4 ,in an alternating current circuit1 this equation is true only when the current is in step with the voltage1 that is1 only when there is no inductance or capacity in the circuit4 ,if current and voltage are out of step1 i4e41 if there is lag or lead 7see ,fig4 #dcd71 the product of volts and amperes gives only the apparent power1 the ratio between true and apparent power depending on the amount of lag or lead4 ,this ratio is called the power factor4 ,in an a4-c4 circuit1 then1 the power equation is3 watts volts amperes power factor1 or power factor true power_/apparent power4 ,the product of volts and amperes is the apparent power and is called volt-amperes in distinction from the true power or watts4 ,therefore the following is true3 power factor true watts_/volt-amperes4 ,illustration3 ,,fig4 #dci4--,power house showing alternators1 direct connected to horizontal hydraulic turbines4 ,note the direct current exciter on end of shaft of alternator4 7,courtesy of ,general ,electric ,co47 #dci4 ,single-phase ,currents4--,there are several kinds of a4-c4 currents4 ,one of the most common is the single-phase4 ,it is simply the common a4-c4 current used for light and power in the average home1 and uses a two-wire circuit around which the current is rapidly alternating4 ,fig4 #ddj illustrates the changes of e4m4f4 in an a4-c4 single-phase current4 ,it may be produced by a single coil rotating in a magnetic field4 ,the curve of ,fig4 #ddj represents one cycle1 that is1 one complete series of changes in the electromotive forces4 ,at the end of the cycle the armature is in the same condition as at the beginning so far as the magnetic field is concerned4 ,it then begins a new cycle4 ,the ordinary commercial alternating current has a frequency of #fj1 that is #fj cycles per second4 ,one rotation produces as many cycles as there are pairs of poles4 ,for example1 if there are #dh poles in the generator field1 one rotation produces #bd cycles4 ,illustration3 ,,fig4 #ddj4--;,graph showing the e4m4f4 changes of a single-phase current for one cycle4 #ddj4 ,three-phase ,currents4--,now suppose we have three coils as in ,fig4 #dda1 the coils being evenly spaced1 or #abj degrees apart1 at ,a1 ,b1 and ,c4 ,if the coils are rotated in a magnetic field1 each will produce an electromotive force4 ,the result produced by three such coils is called a three-phase current4 ,ordinarily six wires1 or three circuits1 would be required to carry the current produced by three separate coils2 for when coil ,c is in the #ij degree position1 where its e4m4f4 is a maximum1 coil ,b is #abj degrees past its maximum1 and coil ,a is #bdj degrees past its maximum4 ,the graph 7,fig4 #dda7 shows the maximum points of the three e4m4f's4 separated by intervals of #abj degrees4 ,in practice1 however1 it is found possible to use three wires instead of six1 as explained in ,art4 #dda4 ,illustration3 ,,fig4 #dda4--;,graph showing the e4m4f4 changes of a three-phase current for one cycle4 #dda4 ,three-wire ,transmission4--,the currents produced in the three coils just described undergo precisely the same changes as those represented in the graph 7,fig4 #dda7 for the three electromotive forces4 ,careful examination of the graph will show that at any point the sum of the plus e4m4f's4 equals the sum of the minus e4m4f's4 ,in other words the algebraic sum of the three e4m4f's4 is zero4 ,therefore if we properly connect a transmission line of three wires to the generator1 the sum of the currents leaving the generator will equal the sum of the currents returning to it4 ,since the algebraic sum of the currents produced by the three coil combination described in ,art4 #ddj is always zero1 it is possible to use three wires on three-phase transmission lines4 ,fig4 #ddb shows a tower carrying three1 three-wire transmission lines4 ,long distance1 high tension transmission lines are generally three-wire lines carrying three-phase a4-c4 currents4 ,illustration3 ,,fig4 #ddb4--;,a tower supporting three1 three-phase circuits of a high tension transmission line4 #ddb4 ,alternators4--,a dynamo which delivers alternating current is known as an alternator4 ,commercial alternators have many pairs of poles in the field and as a rule the field rotates while the armature is stationary4 ,the field must be supplied with direct current for the polarity of each coil in the field must remain unchanged4 ,usually a separate exciter is used1 which is a small direct current generator4 ,the current from this exciter is fed into the rotating field by means of slip rings4 ,fig4 #dci shows a d4-c4 7direct current7 exciter on the end of the armature shaft of the large alternator4 ,illustration3 ,,fig4 #ddc4--;,diagram of a ,series ,motor4 #ddc4 ,the ,a4-,c4 ,series ,motors4--,the only type of motor that will run on either alternating or direct current is the series motor4 ,the universal motor used in household appliances such as electric fans1 vacuum cleaners1 etc41 is a series motor4 ,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 7a7 the direction of the current in the armature1 and 7b7 the polarity of the field4 ,reversing either of these alone1 reverses the direction of rotation of the armature1 while reversing both at the same instant leaves the direction of rotation unchanged4 ,fig4 #ddc is a diagram of a series motor since the field coils and armature are connected in series4 ,on an a4-c4 line1 both field and armature current must therefore reverse at the same instant4 ,in a shunt motor 7similar to ,fig4 #bhf7 we have a divided circuit1 and the greater self-induction of the field coils causes an a4-c4 current through these coils to lag behind that flowing in the armature so that the two currents do not reverse at the same instant4 ,illustration3 ,,fig4 #ddd4--;,diagram of a gramme ring4 ,it is shown connected to a single-phase current so as to produce a rotating magnetic field1 similar to that obtained with a three-phase current4 7,ahrens1 ,harley and ,burns47 ,illustration3 ,,fig4 #dde4--,the stator of an induction motor4 #ddd4 ,the ,induction ,motor4--,another common type of a4-c4 motor is the induction motor4 ,its advantage lies in its simplicity4 ,it has neither commutator nor brushes1 the armature having no connection with an external circuit4 ,if the wires of a three-phase line be connected to a coil wound in the form of a gramme ring1 the connections being #abj degrees apart as in ,fig4 #ddd1 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 coil4 ,suppose the ,n pole at one instant is at ,a1 in one-third of a cycle it moves to ,b1 in another third to ,c1 and in one cycle it makes a complete revolution4 ,thus we have a rotating magnetic field4 ,if a cup of some non-magnetic metal such as aluminium or copper be placed on a pivot in the center of this coil1 the cup is cut by the moving lines of force and currents are induced in it4 ,because of these currents1 the cup has a magnetic field of its own1 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 rotates4 ,the coil represents the stationary part1 the stator 7,fig4 #dde7 and the cup the rotating part1 the rotor1 of an induction motor4 ,while the cup rotates in the same direction1 it does not rotate so rapidly as the magnetic field4 ,if it should it is plain that it would not cut the lines of force4 ,the difference between the rate of rotation of the rotor and that of the magnetic field is called the slip4 ,the rotating part in small induction motors is frequently made in a single casting4 ,in large motors1 it is built up of heavy copper bars4 ,thus1 from its appearance the common form of rotor is known as the squirrel cage rotor4 7,see ,fig4 #ddf47 ,illustration3 ,,fig4 #ddf4--,the rotor of an induction motor4 ,illustration3 ,,fig4 #ddg4--;,diagram illustrating the principle of the synchronous motor4 ,the armature coil passes the position shown in the figure at the instant the current in the line reverses4 ,thus the armature keeps with the line current1 making one revolution with each cycle4 #dde4 ,a synchronous motor is one that keeps step with the alterations of an alternating current4 ,the line current is fed into the armature by means of two slip rings and brushes4 ,the principle of the synchronous motor is illustrated in ,fig4 #ddg4 ,this shows a motor having a two-pole field4 ,the armature current must be reversed twice in each revolution4 ,the reversal must take place when the armature winding is perpendicular to the lines of force of the field4 ,in a direct current motor this reversal is brought about by the commutator4 ,in a synchronous motor the armature reaches the #ij degree position at the exact instant at which the current reverses in the line4 ,thus in the case of a two-pole motor the armature must make exactly one revolution for each cycle2 it is1 therefore1 a constant speed motor4 ,such motors are frequently employed in converter stations where alternating current is converted into direct current by what are called rotary converters4 ,in practice the synchronous motor has a number of pairs of field poles4 ,it is essentially an alternating current generator running as a motor4 ,one of the principal uses of the synchronous motor is that of a converter1 receiving alternating current and delivering direct current4 ,synchronous motors are also used in transmission lines to aid in maintaining constant voltage4 ,important ,topics ,the wireless telephone1 essential parts1 action1 arrangement4 ,alternating currents1 alternating fields4 ,transformers1 voltage relation of coils1 power and core losses4 ,self-induction1 inductance1 and coke coils1 uses1 applications4 ,impedance1 reactance1 and resistance2 relation and effects4 ,condensers1 uses and applications with a-c4 circuits4 ,alternating current power transmission2 uses1 advantages4 ,power factor1 lag1 lead1 volt-amperes1 true watts4 ,single- and three-phase currents2 uses and nature of each4 ,three-wire transmission systems1 alternators1 construction1 and action4 ,a-c4 motors1 series1 induction1 synchronous4 ,,index ,aberration1 spherical1 #djh ,absolute scale of temperature1 #afd ,absorptions of gases by solids and liquids1 #bi ,accelerated motion1 #hf ,acceleration1 #hg ,adhesion1 #ba ,aeroplane1 #ig ,air1 aspirator1 #fg brake1 #gd cushion1 #df height 7of atmosphere71 #fd pressure1 #ef pump1 #ff weight1 #ef ,alternators1 #dha ,alternating current1 #ccg1 #dff ,amalgamation1 #bgc ,ammeter1 #bia ,ampere1 #bia ,archimedes' principle1 #dh ,arc light1 #cba ,armature1 #cce ,artesian wells1 #dd ,audion1 #dfc ,aurora borealis1 #dec ,balloon1 #gb ,barometer1 #ei ,beats1 #cgf ,boiling1 laws1 #bjh point1 #bjg ,boyle's ,law1 #fc ,breezes1 land and sea1 #aha ,british thermal unit1 #afb ,brownian movements1 #af ,calorie1 defined1 #afb ,camera1 #dbf ,candlepower1 #cid ,capillary action1 #be ,cartesian diver1 #ga ,cathode rays1 #dec ,centrifugal force1 #ia ,charles' ,law1 #afe ,chladni's figures1 #cha ,choke coils1 #dgj ,coefficient of expansion1 definitions1 #agj gases1 #afg liquids1 #afh solids1 #afi ,coherer1 #ddi ,cohesion1 #ba1 #cc ,color1 #dce bodies1 #dce complementary1 #dcf primary1 #ddj prismatic1 #dcc theory of color vision1 #ddj three-color printing1 #ddj ,commutator1 #cce1 #ccf ,compass1 #bcj1 #bdj ,concave lens1 #dah ,condenser1 #bfj1 #dgd ,conductors1 #bdf ,conservation of energy1 #abg ,continental code1 #dei compared with the ,morse1 #deb ,convection1 #agi currents in nature1 #aha draft of a chimney1 #ahj ,convex lens1 #daf ,cooling1 artificial1 #baj ,corpuscular theory1 #ddb ,coulomb1 #bij meter1 #bia ,couple1 #aja ,critical angle1 #dad ,crookes' tube1 #def ,crystallization1 #bh melting point of some crystalline substances1 #bjc ,daniel cell1 #bgf ,declination1 #bdj ,density1 #ch1 #eb methods for finding1 #ec ,dew1 #aib ,dew point1 #aic ,diffusion of gases1 #ac ,dipping needle1 #bdj ,direct ,current1 #ccg ,dispersion1 #dcc ,distillation1 #bjh ,draft of a chimney1 #ahj ,dry cell1 #bge ,dynamo1 #ccj1 #ccc ,dyne1 #ic ,eye1 the1 #dbc action of1 in vision1 #dbc defects of1 #dbe ,ear1 the1 #chf trumpet1 #cfa ,earth's magnetism1 #bch ,echoes1 #cfb ,eclipses1 #cia ,efficiency1 #adb engines 7tests71 #bai machines1 #adb ,elasticity1 #ca ,electric bell1 #bfi1 #bhg charge1 distribution of1 upon a conductor1 #bec circuit1 #bfi currents1 #bfg single phase1 #dgi three phase1 #dgi effects1 #bgg induced1 #cbf discharge in rarefied air1 #deb motor1 #cci screen1 #bef ,electrical capacity1 #bei fields1 #bdg ,electrification1 #bdc ,electrolysis1 #cjh laws1 #caa practical uses1 #caa ,electromagnet1 #bha ,electromagnetic theory of light1 #def ,electromotive force1 #bfg unit of1 #bie ,electron theory1 #beb ,electrophorus1 #bfc ,electroplating1 #cjg ,electroscope1 #bdd ,electrostatic induction1 #bdh ,energy1 #abj conservation1 #abg falling water1 #aeb forms1 #abe human body1 #abf ,energy1 kinetic1 #aba potential1 #abj transference and transformation1 #abd ,engines1 #bac ,engines1 gas1 #bbb steam1 #bac turbine1 #bbe ,equilibrant1 #ha ,equilibrium1 #ajf neutral1 #ajg stable1 #ajf stability1 #ajh unstable1 #ajg ,erg1 #aai ,ether1 #agg ,evaporation1 #ah cooling effect1 #ai1 #aig rate1 #aih ,expansion1 coefficient1 #afh gases1 #afg liquids1 #afh peculiarity1 in water1 #afh solids1 #afi water1 on turning to steam1 #bjf ,falling bodies1 #aji experimental study1 #aaa laws1 #aac ,floating bodies1 #dh ,fluoroscope1 #dee ,foot candle1 #cif ,force1 #gi dyne1 #ic effectiveness1 #acd graphic representation1 #hj liquid1 against any surface1 #ch measuring1 #gi moment1 #ii parallel1 #ajj resolution1 #if units1 #hc ,forces1 parallel1 #ajj ,franklin's theory of electricity1 #beb ,fraunhofer lines1 #dci ,freezing1 evaporation1 #aig1 #aii mixtures1 #baj ,friction1 #adg1 coefficient1 #adi fluid1 #aej kinds1 #adg ,friction1 laws1 #aej reducing1 #adh uses1 #adi ,galvanometers1 #bhi ,galvanoscope1 #bfi ,gas engine1 #bbb efficiency of1 #bbd ,gas meter1 #ge ,geissler tubes1 #dec ,gravitation1 #ajc law1 #ajd ,gravity1 #hh1 #ajd acceleration due to1 #aaa cell1 #bgg center of1 #aje ,hail1 #aic ,hearing1 #chf ,heat1 capacity for water1 #bja conduction1 #agc constants for transmission1 #bbj convection1 #agi effects1 #afa engines1 #bac1 #bbb equivalent of fuels1 #bai fusion1 #bja measurement1 #bjj methods of transmitting1 #agc produced by electric current1 #cah radiation1 #agf sources1 #aei units1 #afb vaporization1 #bje work1 #bab ,heating of buildings1 #ahb direct and indirect radiation1 #ahf hot air1 #ahc water1 #ahf plenum system1 #ahg steam1 #ahf vacuum steam1 #ahg vapor steam1 #ahg ,hertzian waves1 #bfb1 #ddi ,hooke's law1 #cc ,horse power1 #abc electric equivalent of1 #abc ,humidity1 #aid ,hydraulic press1 #db elevator1 #dd ram1 #gb ,hygrometers1 #aid ,hygrometry1 #aia conditions for saturation1 #aib dew point1 #aic fog1 #aic formation1 of dew1 #aib humidity1 #aid hygrometers1 #aid importance1 #aia ,hypothesis1 #c ,images1 concave mirrors1 #dje construction1 #dje definition1 #cib plain mirror1 #dja small apertures1 #cia ,impedance1 #dgb ,incandescent lamp1 #cbj ,inclined plane1 #adc ,inductance1 #dga ,induction coil1 #cdc ,inertia1 #hg ,insulators1 #bdf ,intensity of sound1 #cfc ,interference1 light1 #ddb sound1 #cgd ,joule1 #abj1 #cai ,laws1 boiling1 #bjh ,boyle's #fc ,charles'1 #afe electric action1 #bdc falling bodies1 #aac floating bodies1 #dh gravitation1 #ajd ,hooke's1 #cc induced currents1 #cbf intensity of light1 #cid ,lenz's1 #cbh liquid pressure1 #cg machines1 #aca magnetic action1 #bbi motion1 #hg ,ohm's1 #bih pendulum1 #aaf reflection1 #cii refraction of light1 #daa vibration of strings1 #cgh ,lenses1 achromatic1 #dcd effect on light1 #dag equation1 #dba formation of images1 #dah forms1 #daf ,leclanch cell1 #bge ,lever1 #acb ,leyden jar1 #bfa oscillatory nature of the discharge1 #ddh ,light1 compared with sound1 #chh1 #ddd electromagnetic theory1 #def intensity1 #cid interference1 #ddb polarization1 #dde rectilinear propagation1 #chi reflection1 #cif total reflection1 #dac ,lightning1 #bed ,lines1 of force1 #bcc agonic1 #bdj isogonic1 #bdj ,liquids1 pressure1 #cf ,local action1 #bgc ,luminous and illuminated bodies1 #chh ,machines1 #abi advantages1 #abi cannot create energy1 #acj efficiency1 #adb law1 #aca mechanical advantage1 #acd the six simple1 #acb uses1 #abi ,magnetic action1 #bbi fields1 #bcc1 #dff induction1 #bca1 #bcf permeability1 #bcg poles1 #bbi properties1 #bcj retentivity1 #bca substances1 #bcj effect of electric current1 #bgi ,magnetism1 #bbh ,magnetism1 theory1 #bcb ,major and minor triads1 #cfi ,magneto1 #cbh ,magnetoscope1 #bcj ,magnets1 #bbh poles1 #bbi ,major scale1 #cff ,manometric flames1 #chb ,matter1 #d effect of heat1 #e molecular theory1 #e properties1 #cd states of1 #d states of1 defined1 #e ,mechanical advantage1 #acd ,megaphone1 #cfe ,melting points1 #bjc ,mercury arc rectifier1 #cdg ,metric system1 #h ,microscope1 #dbg ,mirage1 #dad ,mirrors1 #djj concave1 #dje convex1 #djg parabolic1 #dji plane1 #dja ,molecular motion in liquids1 #ah in gases1 #ac in liquids and solids1 #bg in solids1 #ca ,molecules1 motion1 #af size1 #ac ,moment of force1 #ii1 #acc ,momentum1 #hg law of1 #ib ,motion1 #he accelerated1 #hf curvilinear1 #hh direction1 #hf first law1 #hg modes1 #he second law1 #ib third law1 #ic uniformity1 #hf ,motor 7electric71 #cci ,a4 ,c4 series1 #dhb induction1 #dhc synchronous1 #dhe ,muffler1 #bbd ,musical instruments1 #cgg interval1 #cfh nomenclatures1 table1 #cfi ,musical sounds1 characteristics #cfd ,newton's ,laws of motion1 #hg ,nodes1 in pipes1 #chd in strings1 #cgi ,noise and music1 #cfc ,ohm1 #bid ,ohm's ,law1 #bih ,opera glass1 #dbh ,optical illusions1 #cij1 #djd instruments1 #dbc camera1 #dbf eye1 #dbc microscope1 #dbg opera glass1 #dbh prism field glass1 #dbi projecting lantern1 #dbg telescope1 #dbh ,organ pipes1 closed1 #chd nodes1 #chd open1 #chd ,oscillatory discharge1 #ddh ,osmosis1 #ai ,outline ,review1 current electricity1 #cbe force and motion1 #aah heat1 #bbg induced currents1 #cec light1 #ddf magnetism and static electricity1 #bff sound1 #chg work and energy1 #aeh ,overtones1 #cgi ,pascal's principle1 #da ,pendulum1 compound1 #aae laws1 #aaf simple1 #aae uses1 #aaf ,pepper's ghost1 #djd ,permeability1 #bcg ,phonograph1 #chc ,physics1 definition1 #d ,photometer1 #cid ,photometry1 #cic ,pitch1 #cfe ,polarization1 of light1 #dde of voltaic cells1 #bgc ,portraits1 ,bell1 #dca ,edison1 #bhe ,faraday1 #cca ,galileo1 #hi ,gilbert1 #bag ,helmholtz1 #cig ,huygens1 #cig ,joule1 #bag ,kelvin1 #cca ,marconi1 #dca ,morse1 #bhe ,newton1 #hi ,potential1 #beg ,power1 #abc electric1 #caf power factor1 #dgf transmission of electric1 #dgf water1 #aeb ,pressure1 air1 #ef atmospheric1 #eh ,pressure1 definition1 #cg effect on liquids and gases1 #fb law of liquid1 #cg ,prism field glass1 #dbi ,projecting lantern1 #dbg ,proof-plane1 #bdd ,pulley1 #aci ,pumps1 air1 #ff condensing1 #fg water 7lift1 #fh1 force1 #fi7 ,quality of musical tones1 #chj ,radiation1 #agf sun's1 #agh ,radio-activity1 #deg ,radiometer1 #agg ,radium1 #deg ,rainbow1 #dcf ,reactance1 #dgb ,reflection1 light1 #cif multiple1 #djd sound1 #cfj total of light1 #dac ,refraction1 #daj cause1 #dab index1 #dab light1 #daj in plates1 prisms1 and lenses1 #dac ,resolution of forces1 #if ,resistance1 cells in series1 and parallel1 #cjb conductors1 #bic in series and parallel1 #bii1 #cjj unit1 #bid volt-ammeter method for finding1 #cjd ,resonance1 #cga ,resonator1 #cgc ,resultant1 #ha ,retentivity1 #bca ,right hand rule1 #bgi ,rotary converter1 #dhf ,science1 definition1 #b ,screw1 #add ,shadows1 #cij ,single phase currents1 #dgi ,siphon1 #gj ,siren1 #cff ,solidification1 change of volume during1 #bjc ,solutions1 #bg ,sound1 compared with light1 #chh interference1 #cgd media1 #cee nature1 #cef reflection1 #cfj rule for finding velocity1 #cfg source1 #ced speed1 #cee transmission in air1 #cei ,specific heat1 #bjj method of determining1 #bja ,spectroscope1 #dch ,spectrum1 #dcc ,spherical aberration1 #djh ,spinthariscope1 #deh ,stability1 #ajh ,standpipe1 #df ,static and current electricity compared1 #bhg electrical machines1 #bfb ,steam engine1 #bac turbine1 #bbe ,storage battery1 #cab ,stress and strain1 #id ,sublimation1 #aii ,surface tension1 #bb ,sympathetic vibration1 #cgb ,telegraph1 #bhc wireless1 #dej ,telephone1 #cdi receiver1 #cdi transmitter1 #cej wireless1 #dfj ,telescope1 #dbh ,temperature1 #afb absolute scale1 #afd ,tempered scale1 #cgj ,theory1 #c ,thermometer1 air1 #afg centigrade1 ,fahrenheit1 #afc gas1 #afg ,thermos bottle1 #agf ,thermostat1 #ahh ,three-color printing1 #ddj ,three-phase currents1 #dgi ,three wire transmission1 #dhj ,torricelli's experiment1 #eg ,trade winds1 #ahb ,transformer1 #cde1 #dfg uses1 #cdg ,turbine1 steam1 #bbe water1 #aed ,vacuum cleaner1 #gf pan1 #baj ,velocity1 #hf ,vibration strings1 #cgh sympathetic1 #cgb ,visual angle1 #dbd ,viscosity1 #bj ,volt1 #bie ,voltaic cell1 #bgj advantages1 #bgd amalgamation1 #bgc local action1 #bgc polarization1 #bgc simple1 #bgj ,voltmeter1 #bie ,water wheels1 #aeb overshot1 #aeb turbine1 #aed undershot1 #aec ,watt1 #abc1 #cag ,wave theory1 of light1 #ddb ,waves1 beats1 #cgf interference1 #cgd longitudinal1 #ceh sound1 #ceh transverse1 #ceh visible1 #ceg ,wedge1 #add ,weight1 #ajd ,wheatstone bridge1 #cjd ,wheel and axle1 #acf ,wind instruments1 #chc ,wireless telegraphy1 #dej telephony1 #dfj ,work1 #aai units1 #aai ,x rays #ded ,transcriber's ,note3 ,this book uses ,b4,t4,u4 and ,b4t4u41 electrophorous and electrophorus1 e4m4f4 and ,e4,m4,f4 and this has been left as written4 ,hyphenation is also inconsistent1 e4g4 electro-plated and electroplated4 ,on page #cbd1 ,exercise number #h was not used in the original4 ,the exercises have not been renumbered4