CIHM Microfiche Series (Monographs) ICMH Collection de microfiches (monographies) Canadian Inatltiita for Historical IMicrorsproductlons / Insthut Canadian da microraproductioiu historiquaa 1995 Technical and Bibliographic Notes / Notes technique et bibliographiques The Institute tias attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significanily change the usual method of filming ara checked below. B Coloured covets / Couverture de couleur I I Covers ds naged / ' — ' Couverture endommagte I I Covers restored and/or laminated/ ' — ' Couverture restauree et/ou pellicula I I Cover title missing /Letltrede couverture manque I I Coloured maps / Cartes gtegraphiques en couleur I I Coioured ink (i.e. other than blue or black)/ — Encre de couleur (i.e. autre que bleue ou noire) FT- Coloured plates and/or iHustratkxis / •-^ Planches et/ou illustratkjns en couleur I I Bound with other material / ' — Relii avec d'autres documents □ Only editk>n available / Seule Mitkin disponlble I I Tight binding may cause shadows or distortion along Interior margin / La reliure serr6e peut causer de I'ombre ou de la distorsbn le long de la marge int6rieure. I j Blank leaves added during res;or.:iions may appear within the text. Whenever possible, these have been omitted from fbnlng / II se peut que cettaines pages blanches ajouttes kirs d'une restauration apparainsnt dans Is texle, mais, kxsque cela Atait possible, ces pages n'ont pas «te fllmtes. L'Institut a microfilm* ie meilleur examplaire qu'il lui a 6t6 possible de se procurer. Les details de cet exem- plaire qui sont peut-6tre uniques du point de vue bibii- ographique, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modifications dans la m6th- ode normale de filmage sont indiqu6s ci-dessous. r~l Cokjured pages/ Pages de couleur I I Pages damaged/ Pages endommag«es I I Pages restored and/or laminated / ' —^ Pages restaureos et/ou pellicuiees r^ Pages discoloured, stained or foxed / Pages dicdorees, tachet^es ou piquees I I Pages detached/ Pages ditach^es r^ Showthtough / Transparence I I Quality of print varies / I — ' Quality Inegale de Pimpressfcin I I Includes supplementaiy material / Comprend du materiel suppieretentaire I I Pages wholly or partially obscured by errata ' — ' slips, tissues, etc., have been refilmed to ensure the best possible image / Les pages totalement ou partiellement obscurcies par un feuillet d'enata, une pelure, etc., ont M filmtes i nouveau de fa;on k obtenir la meilleure image possible. I I Opposing pages with varying colouration or ' — ' discolourations are filmed twfee to ensure the best possible image / Les pages s'opposant ayant des colorations, variables ou des ddcol- oratkins sont filmtes deux fois afin d'obtenir la meitleur Image possible. D AdiMonal comments / Commentalres suppKmentaires: Thii inm is filmad at tlit rtdtietion ratio disdnd iitlaw/ C« doaiiiMiit tst f ilmi lu au« d« rMuction indiqirf ei-dmous. lOX l«x nx 22X »x 12X 1«X Th« copy filmtd hara hM bMO raproduead thank* to tha ganaroaity of: National Llbraxy of Canada L'aaamplaira film* fut roproduit grtea i la g«n4ro«lt« da: Blbllothiqua natlonala du Canada Tha imagaa appaaring hara ara tha bast quality peaaibia sonaidaring tha eandition and logibility of tha original copy and in liaoping with tha filming contract apacif icatiena. Original eopia* in printad papar eovara ara fllmad baginning with tha front covar and anding on tha laat paga with a printad or illuatratad Impraa- aion, or iha bacli covar whan appropriata. All othor original coptaa ara filmad baginning on tha f irat paga with a printad or Illuatratad Impraa- aion, and anding on tha laat paga wWi a printad or Hluauatad •■npraaaion. Tha laat racordad frama on aach microfieha •hall contain tha symbol —^ Imaaning "CON- TINUkD"!, or tha aymbol y Imaaning "END"), whiehavar appliaa. Laa imagaa luivantaa ont M rapreduitai avae la plua grand loin, compta tanu da la condition at da la nattatt da I'aaampiaira film*, at an eonformit* mtae laa condition* du contrat da fUmaga. Laa aiamplairaa originaua dont la eouvartura an papiar aat Imprlmaa aent film** an commandant par la pramiar plat at an tarminant loii par la darnlAra paga qui eompona una amprainta d'Impraaaion ou d'llluatration, loit par la taeond plat, aalon la eaa. Toua laa autras aaamplairas originaua aont filmta an commandant par la pramlAra paga qui eompona una amprainta d'Impraaaion ou d'IMuawatien at an tarminant par la damitr* paga qui comporta una talla amprainta. Un daa symbolaa auivanta apparattra «ur la darnMra imaga da chaqua microfieha. talon la caa: la tymbela •«' tignifia "A SUIVRE". la tymbola ▼ tignifia "FIN". Mapa, plataa. chana. ate. may ba fllmad at diff arant raductien ratioa. Thoaa too larga to ba ontiraiy included in one axpeaura are filmad baginning in tha upper left hand ecmer, left to right and top to bonom. at many framaa aa required. Tha following diagrama illuanata the method: Laa eartaa. planchaa. ubiaaux. etc.. peuvent itre filmto A dee taux da rMuction difftranit. Loraque la document eat trap grand pour itra reproduit en un taul elich*. il aat film* * partir da Tangle tupdrieur gauche, de gauche * droite. et de haut en baa, an prenr t le nombre d'imegea ndceaaaire. Lee diegremmea tuivanit illuatrant la mdthode. 1 2 3 1 2 3 4 5 6 Miaoeofy kisouition tbt chart (ANSI ond ISO TEST CHART No. 2) 123 2J5 U 13.6 lis. 112.0 US 1.8 ^1141^ xIPPLIED IN/HGE In 1653 East Moin Strwt RfHiheiter, New York 14609 USA (716) 482 - 0300 - Phone (716) 288-5989 - Fqk ^.•:.'c «r»-»- -'^- »- < •>,* i c- /(^o\ or. O^^A^ ^ V ^• If; INTRODUCTION TO HYSICAL SCIENCE BY ALFRED PAYSON GAGE, Ph.D Ai-THDR OP "Prisciples of Phyricb," "Elemknth or Physics," Ktc. iiEvrsKn rcn/Tfox AV. J. GAGE & CO., LiMiTKD TORONTO /fox. 251929 Kmtbrkd at STATionss* Hall COPTBIOHT, 1887. 1903, BY ALFRED PATSON OAGB ALL ElOBTI KBSBBVKD GINN * COMPANY • PRO* PKlKTOfcli • BUSTON • U^J^ PEEFACE Methods of teaching elementary physics have undei^ gone, within scarcely more than a decade, many radi- cal changes. The educational pendulum has vibrated between extreme methods of all text-book and no text- book, all laboratory and no laboratory, the inductive method and the deductive method, all oral instruction and little oral instruction. At present it seems to have approached the point of equilibrium where the good in each of these methods is given its due weight. It appears to be the consensus of opinion among teachera of physics that the method of instruction which includes a due proportion of text-book study, lecturfr-room demon- stration, and individual work in the laboratory is the method conducive to the highest order of results from an educational point of view. In revising this book, the attempt is made to emphar size its texUook feature. It has been the author's pui^ pose to place before the pnpU in simple knguage and in logical order, with due regard to chUd psychology, the general principles and the important laws of phys- ical science, and not to allow them to be obscured by a multiplicity of experimental details which would be more appropriate in a teachers' handbook or in a labota- toiy mMinaL Some experiments have been introduced wiai a view to making the presentation of the subjects Ul PREFACE realistic ; but they are, in the main, such as the pupil can perform, and should be encouraged to perform, by himself outside of the class hours. Numerous practice exercises are given, from which selections may be made at the discretion of the teacher. It is generally conceded that nothing else so tends to olaiify the pupil's ideas and to fix scientific principles in his mind as does the solving of problems and ques- tions growing oui; of these principles. Furthermore, since acquaintance with the history of a science helps to make attractive and to humanize that which might otherwise seem IduU and colorless, frequent allusions are made to the great discoveries and researches by means of which the edifice of physical science has been built up, and portraits of some of tho most notable of its master-builders have been interspersed throughout the book. Provision has been made for a year's work, on the sup- position that about one third of the time will be dev^ ted to laboratory practice. For laboratory use the teacher wiU choose from the many excellent manuals now avail- able the one best adapted to his ideas and convenience. Should it seem expedient to use a manual of the same authorship as this text, he will choose between the Phygwal Manual and Note Book and the Physical Experiment*. The latter is especially adapted to meet the requirements for admission to Harvard University. The author desires to acknowledge especial obliga- tions to Arthur W. Goodspeed, Ph.D., and to Clarence G. Hoag, A.M., of the University of Pennsylvania, who have read the manuscript and proof of the entire hook PREFACE and furnished valuable criticisms and suggestions. His thanks are also due to Mr. Albert Perry Walker, English High School, Boston; Mr. Chester B. Curtis, High School, St. Louis ; and Mr. Joseph Sparks, Super- intendent of Schools, Aurora, Neb., for assistance in correcting the proof. ALFRED FAYSON GAGE. Borms, Mass., 1902. CONTENTS CHAPTER I □TTRODUCTIOH rAoifl Domain of phyaics. Some properties of matter. Physical •"*""'*"""'- Force and equilibrium 1.17 CHAPTER II FLUID PKKS8URB Law of tranunlnion of pressure. Pascal's principle. Atmos- plierio pressure. Boyle's Law. Principle of Archimedes. Specific gravity jg_54 CHAPTER III DTHAiacS Motion, velocity, and acceleration. Composition of velocities. ComposiUon of forces. Center of gravity. Momentum. Newton's Laws of Motion. Absolule units of force. Curvilinear motion. Gravitation. The pendulum. Work, energy, and power. Machines. Molecular forces. Cap^ illary phenomena 65-128 CHAPTER IV HEAT Sources of heat Temperature and thermometry. Calorim- etry. Effects of heat Laws of gases. Latent heat Artiflcial cold. Diffusion of heat Thermodynamics. Steam engine I2B.173 vii VUl CONTENTS CHAPTER V SOUHD Wave motion. Origin, tnnamiHlon, Telocity, and energy of •ound waves. Sympathetic Tibrationa. Hualcal aounde. Vibration of atrlnga. Quality of aound. Vocal (oundi, »«dlUon 174-M6 CHAPTER VI LIGHT Radiant energy. Intensity of Illumination. Reflection. Refraction. Prisms and lenses. Prismatic analysis. Color. Optical instruments. Thermal effects of radia- tion 200-263 CHAPTKB VII ELECTROSTATICS Properties of electrified bodle-s. Electrical potential . . . 264-274 CHAPTER VIII ELECTRO-KINETICS Voltaic cells. Effects producible by an electric current. Elec- trical quantities and units. Electrical resistance. Bat- teries. Magnetism. Magnetic relations of the current Electro-dynamics. Induction. Dynamo. Electric motor. Storage cells. Electric light. Electrotyplng and electro- plating. Telegraph. Telephone. RSntgen phenomena. Wireless telegraphy. Maxwell's theory of light . . . 276-347 Appendix 340-353 J™" 366-859 PHYSICAL SCIENCE CHAPTER I INTRODUCTION SECTION I DOMAm OF PHYSICS — SOUK PROPERTIES OP HATTER 1. Physics defined. — As we look around in the world in which we live, we receive impressions from a variety of objects independent of ourselves.' Some of these objects we see, some we hear, othere weleei;' taste, or smell, while many appeal to sevei-al senses. " > £?L.?^3?SS-afeP apprisfiJia that objects undergo many changes jinder varying conditigna. For example"? if a 3trc£ hi sealing wg be rubbed with a dry flannel, it undergoes a change of state by virtue of which it' attrwtejomirdjtself small pieces of paper, t By jhe" *PP!»''."^°ljLe?l^e js.changed to a liquid and even to invisible steam, and a dark gray piece of iron may become re3 or even white . '• Any change in 'an object is called a vhenom^nnn . Both our experience and our reason lead us to conclude JtetAaiejsji c ause for every phenomenon . Our pres- ent study chiefly relates to natural phenomena and pL their_cau8«. Every one who has used his senses to ' ' 1 INTBODUCTIOK any purpom has become acquainted, even before begin- ning the study of our science, with a great many phe- nomena, among them some of the yet unexplained. Thingg that t^eot our senses directly are called mat- tor, «..<;.. stone, water, air, etn. It is Eeirev ed that there _exi8te8ometWng^ that does hot affect the senses directly, jio mething that fill s all the,Bj»ce of the univerae, called the «tW. We^shall find, as we proceed^' that all changra iSJ^e appearance of objectB are accompanied by motion. n£!iXUSLkth?jeis!iee,which treP«rty of matte r in virtue of which a body occu- j)ies space to the exclusion of all oUier bodies is called impenetrab ility. ~ Experiment — Float a cork on a surface of water, cover it with a tumbler as in Fig. 1, and force the tumbler, mouth down- ward, deep into the water. (The cork serves merely to show the boundary surface between the water and the air.) Does water enttr and fiU the tumbler? Wliat property does Uiig experiment show air to possess? What evidence that air is matter do you discover? > <-< SOME PROPERTIES OP MATTER 8 1 Matter u defined m *Wj?«M scggjif , ,;;«« anitHW- f •""Li2£«!?it«W« there exists some particle wUch is the smaUest that can possibly exist Such smallest particle of anyjul^tance wcdled a woWe. Molecules are mu"ch too "small to be seeii.! Their existence is inferred from phenomena which can be explained only on the supposition that they exist. (3)_ Cqmpreuibaity and ei^ar^bility. All bodies are compressible and ex^sJMe. though in v^rfdifferent „,.LMtf'.'** J" ™'*' "" •■" •' • '"""^ « 'wheB in diameter were snail >hot and smaUer tban football.. -Lord Kelvin. INTRODUCTION degrees. Air and gnge ii generally are very comprewible . A proof, though by no means the meet convincing one, of the existence of moleoulea and of the granular struc- ture of bodies may be found in this fact. Matter (e.g., a ^">dy of gold or water) is either continuous as it api>ear> lu the eye, or it is discontinuous, granular, composed of distinct particles (molecules), somewhat as represented in Fig. 2. But bodiei are eompretriblt and expannble. _ On tl)»^'upposition that matter is con- ','•'::■.'■:.'■'.;. tmuous these pRehomena cannot be '""~' •.■.■/•.{• ■.•■.•:; explained ; but on the supposition that matter iscpmposed of disconnected parti- cles they are easily explainable. Accord- ing to tfie latter supposition a changfe of volume by contraction or expansion means a coming together or a teparation of the moleimlei componng the body, as represented in Fig. 2. The property of compren^bH ity " "f ftn^' a cimieo and an evidenee of the molecular constitution of km ria.t 3. Theory of the Constitution of Matter ; Porosity. — For reasons which will appear as our knowledge of matter is extended, physicists have generally adopted the following theory of the constitution of matter: tUveri/ body of matter excejjU^the^ molecule it co mpoud of edir^ly gmall ditconnected particle*, rilled moleculei. 'molecuTes are ever in a state of intense vibr ation,_ _ Tmaking'mang~bilTion» of viFrations per tseeond^ In their to-and-fro motions neighboring mole- Icules hit and rebound from one another; lience, the \ molecules in a bod y are n ever in contact except at the LORD KELVIN (1824- ProbnWy the „,o.t noted of Ifvl,,^ pl,„|„„„ . ..pedally ren„ . o«l I,.,!. , hi. .„.„y „r„l„. r,,.„cbe. an., valuable oo„trlb„.H .7..-!" ,„ tntti^ and fo.- the li.vei,li,.i, of i.iiuiy eiectrlcal derloel of imjat nriu^l^i . j ""OflMg. T«lae. From a photograph. '"■ <" «™« P«rtlo«l and ooinnu.rcl.1 THEORY OP THE CONSTITUTION OF MATTER 6 in ttantt of collm on. WlifM tf i f temperature of a body ri tes, the mo le'^'il'", ffiff?"""y f/yiW/y, 'frikf harder Zto wi and drive one another a little farther apart ; hence, the bodifjx^mids. ' f~li the m nleniilfts ff a h^Ay ■"i^f'\\f and are never in contact except at the instants of collision, it follows that there must be spaces between them^' These spaces are called pore i. The pores of a body are spaces within a body not filled with Uie substance of which the body is composed. V Even in bodies in \™ioh tlie molecules are most compact, such for instance as goliTi jt is estimated tiiat' the average dis - tance bet ween the molecuftp is many times tlie diaineter of tl^p. moleculfl . All matter is porous, pores of iron and gold, i ater may be forced through the trictly Rpeilkinfr' nn/?^ piftlfri^fx pftftf^tf ^ the property of impe.nptrq ^\lii^ The term pores, in physics, is restricted to the invisible spaces that separate molecules and does not inniide such cavities as may be seen with the naked eye in sponges, and with a microscope in wood, etc. 4. Three States of Matter ; Fluidity We recognize three states gr conditions of matter, viz., the solid, the. liquid, and t he gaseou s, represented by earth, water, ana air. In solids tlie molecules offer resistance to change in their relative positions . Hence, solid bodies tend to preserve a definite volume and shape. In liquids the molecules offer little resistance to change of relative ■josition . but glide around and past one another with great freedom. A body of liquid, therefore, as we experience it on the earth, can have INTRODUCTION / no. BhftP« of ite na au bu iLj)n account of its weight ■-^£Sft!i»l*Ji^S8, thejom of Jhe vMMl in wMoHTtlw ^be placed . The distinctive characteristic of a gaa is ita incessan t -at riiggl e to Qcc apy a greater voluniR . or the tendency of Ug molecules to s eparate fromnng annfh^r Hence, both the volume and the shape of a body of gas are deter- mined only by the vessel in which it is inclosed. In consequence of the mobility of their molecules and the ease with which they flow, liquids and gases are called fluids. Susceptibility of motipn of the mole- cules of a body around and among one another is called fluidity. All bodies of matter, including solids, ^n«««», this property, but in very different degrees. It is due to this proi)erty that solids can^be bent, stretched. «nd . compres^d, and that most me iak c^JigjWnjnf^ wires and rolled or hammered intn aY^f^ a JllXcvaX^O^^ EXERCISES 1. How do yon kno^Mhat air is matter ? 2. Give some reason for concluding that all matter is molecuJar in structure. ^^ 8. Can molecules be seen ? Can pores be seen ? 4. Whence do fish obtain the air with which their blood is aerated ? 6. Whence come the bubbles of gas that cause the eflerreecence when soda water is drawn from a fountain ? 6. What Is understood by a molecule of chalk f 7. According to the definition of a molecule, can such a thine exist as a half of a molecule of chalk P 8. (a) In Experiment 1 why does not the water enter the tumbler When it is thrust down into the water f (6) Does the water enter a Uttls way mto the tumbler ? Explain. EXERCISES 9. Explain how the flow of liquid into the bottle through the fun- nel A (Fig. 3), maybe regulated by pleasure on the rubber tube B. 10. (o) We aay that a tumbler ie " f ul 1 of water. " May we not with equal propriety aay that it la at the aanie time ftill of air P (6) If the tumbler be full of both water and air at the same time, shall we aay that these aubatancee do not pos- sess the property of impenetra- bility ? 11. If a block of wood be placed under water in an air-tight vessel (Fig. 4), and the air be removed, air I oblea will form on the surface of the wood and also in mid water and rise to the surface of the water. What do you infer from this respecting the porosity of wood and water ? 13. (a) Give names of at least three substances. (6) Give a name of a body of each subetance named. 13. Prepare a list of (a) several atmospheric phenomena ; (&) aereral phenomena which may occur to water; (c) aeveral phenomena pro- ducible by heatj (d) several p!'^- nomena which may accompany cooling or loss of heat ; (e) aeveral sound phenomena; (/) aeveral phenomena caused by light; (g) several phenomena attrilju- table to electricity. 14. What evidence have you that auch phenomena as you liave specified ever exist ? 16. How may it be shown that water is porous ? 16. What evidence does an air bubble in water fumiah that air ia matter r Fig. 3 Fio. 4 r -■ INTRODUCTION SECTION II \ PHYSICAL HEASUkEIIENTS 5. Units of Measurement. — Physics is often called^a " s cience of measurements ," since most of UiB-truths of which it treats are based- on measurements that have been made from time to time. Measuring c onsists in finHit^g ^H^ y ma ny tjmes a definite quantity, called a unit, is contained in the quantity to be measured. For "^example, should we "wish to measure the length of a tabw we might choose fory unit of me asuremen t the length of a certain pencil and proceed to find how many times this pencil may be laid along the table. If ten times, we say the table is ten pencil-lengths long. The unit of meaturement mu^t be a definite quantit}/ of th e~ iame kind as the thing to be measure^. Thus, a un it f(^^ easuri ng length must jie_a^ certain leng th, a unit for measuring surface must b e a certain qua ntity of surface! and a unk^for_measurmg_volunae_must be "a ge Hnite volu me.. A unit which ha s become legdizfld, either by statute or by common usage, i s called a ttand - ard unit. The expretiion of a physical quantity con- sists of a statement of the concrete unit employed , e.g., pound, foot, quart, etc., with the number of those u nits prefixed. The numerical part, c iJled the numeric , is obtained by measurement. 6. Metric System of Measures. — (In this connection the Table of Metric Meaaui-es, in the Appendix, should be studied, and the pupil should immediately become METRIC SYSTEM OF MEASURES 9 femfliar with metric units, particularly units of lenrth object!..) The tern, metric is derived from the word meter, which is the name of a unit employed LtJ^ system for measuring length. The interJatfonal stanT ard meter is defined by law to bTthTk^thTfiSt ^i^num .pdiilLtheJfimpe«uux^^ a^ilS rod, constructed by Boi-di «. v,^ -^^•'*-'-;- liiis about 17Qfi • ^, \ ' '*°'''* mathematician, W^M '.,,,'** ** *'■' Interaational Bureau o W;eight8.^nd Measures in Paris. unwieldy British units. ^' i™''onal and measure, also for the measurement o[^S^ vessels, _th e.«fe^(^ld„,,) i, genemV^f /• Volume, M^^itensl^^ Weight. -The q„an — ^— "— 'J^'™***'*'^"''**— ^^^'SjUjigs 's "° volume am^^ expressed in cubic centimeters pT; — 5" V ^' "^ The unit of mass^ emn l npo/] ! ! ■ . tW: ■ ^/==? employed m sc ince is the aram i^^SegS... The Wogram is the ^^,-^i^i^^^. 10 INTRODUCTION of platinum in the keeping of the French goyemment at Paris. It is also, with considerable accuracy, repre- sented by the mass of a cubic decimeter of pure water at the temperature of 4° C . Since a cubic decimeter contains 1000 cc, the mass of 1 cc. of wate r IS"! g . ^_ J[ilvj/rrlng balance measure mass 7 9. An electric car Is moving at the rata of 14 km. per hour. What is the rate in miles per hour ? vi- . TIO. A certain man weighs 160 pounds, and a certain boy weighs 30 kg. Express the difference in their weights in pounds. 'I'i', .^lo*^ 11. (a) With a meter stick measure your hight In meters. (6) Express the same In centimeters, (c) In giving your hIght, in each case state the concrete unit and the numeric used. 12. The Eiffel Tower in Fpris is 300 m. high. What is the £ight of the tower In feet ? Fio. 6 EQUILIBRIUM OF FOECE8 18 SECTION III FORCE ASO KQUIUBSIUII 9. Force defined — No body at rest starts to move unless it is made to do so. Whenev er we see a body beenJa-maifi^or a body in motion begin to stop or in anyjvaytaxdiangaits-inQtionrwTretlierirD^ii'diiii^on or injpeedjiTO are sure that there is &caufe. -The cause i sjsalhd force . - - __ J!2r£«J±<'»y eaute^ which tend* to produce moOouina hody at re»t, or to produce change qf motion in a body \tKat ia moving. la Equilibrium of Forces. — Force may act without .ca usmg a change of motion, as whiiTt^o persons puTf a chair equaUy in opposite directions; the chair does not move; nevertheless each pull "tends" to move it. ^J*ii_case^oneJorceJs_said to balance the_othfiu Every change o f jnotion is caused by foree = hence, any change m the motion of a bod^^TISh;^; it be in dii^T i t'oP or m speed, jg gv;^»n»wi;^^^_^ i,^ j^. j^ j^gj^^^jj^^ & by an unbalanced foi ye.. JLiljodj^l^^lrest, or if in motion ite motiondoesjiotdiange, it is an Indication that theforces acting on that body balance one another, or are %n eguOibrium^ That the motion of a body remains unchanged is an indication, not that the body IS free from the action of force, but that the forees acting on it are in equilibrium. IL Gravity There is a variety of forces in nature, the most prominent of which is the force of gravitv 14 INTRODUCTION It i y the forc H tVttt cft"""'' ""■■tBi)orte d bodies to fall to the eart tu It is the force t lmt givea woig ht iQ.iiodieg when their fall i8 resisted. 'J'h'" f"!*;*' iiotiiig between t he Bun and tho_fiuilli cauBes the latter to move in a curviliiienr orbit around the former, instead of moving in a straight path and leaving the sun behind. No body in t he univemojs cvec free from it^action. On a small scale, we have the force ot cohejnon which keeps the molecules of sol "!" iml jiquiilg (ngBthnr and resista attempts to separate them. Jn ga aea there is^iifl cohesion ; on tlie contrary, the particles of gases ever tend to separate more and more widely. 12. Stress and Strain. — ^'orce does not always cause it_change inthe_iiiflti!Jnj^f the lK)dy as a whole. IFmay cause srm])ljr _a relati ve motion ofitSilJituis. In this latter case it causes a'cliaiige in THe size or shape of the body, as it>-th e stretching of a rubber band , the .bending of a ritrip of steel, the compression of air , and the flattenini; of a b all of soft putty . Qhange of size o r _8hgpe by tlia-njipljcfftinii (|f force is calle d a ttrain. In the cases just cited, and in all cases, strain is the result of a pair of balanced forces. A pair of b alanced foiceaxausing a atrain^s^called a strets. If the pair of forces act away from each other, as in the act of stretch- ing a rubber band, the stress is called a pidl, ov a tensile »tre»»; if they act toward each other, as in tlie act of co m- _£ressing air,11re" stress Is cal led a ^ug^, o r a pressu re. A body lying on a table causes a strain {i.e., a compression) in the matter of the table just beneath the body, and the elastic force (§ 13) of this strained or compressed ELASTICITY AND ELASTIC FORCE 15 matter rapporta the liody. The pair of opposing forces, vit., the weight of the body acting downwunl and the elastic force acting upward, gives rino to a pre»$ur« between the body and the table. 13. EUitlcit7 and Elutic Force. _ A strained or stretched rubber band and a strip of htcel that is bent tendjo jticoyer their original dimen sions or shape. JSiajtMt/k the property of a Ixxly by virtue of which it tends to recover fiom a strain. The molecular stress which tends to restore to a strained boi .ai is the force with which the earth attracts a mass of a kilogram when placed at thTsea level in latitude 46° i In ihe untish gravitattonai system the unit of force is the force with which the earth attracts a mass of a pound under similar conditions. We learned (§7) that the attraction exerted by the earth'on a given mass is not thOame at all places ; consequently the for ce with wbich the earUi attracta (i.e., the weight o f) a kil ogr am-maas , for instance, is not _fivggrwhere a kilogram-force. EXKRCISES IT appltad to th. ring to prevent the iton. from moving f , , "*' '""• „rLir.l.^'"\'"i'" '"""' •PP"«' 'o "he .tone (mu«ul.r fore, or gr.rlty doe. th. dynwnooeter meMure In thta c«. r iTuT, -.ould b. th. g«M.r, wh.t wouU happen to th. .ton. f 4. (a) If a fore of 8 kg. »ct on » body In «, MMeriv dl«rtl™ ~.d . fore of 10 kg. .ct .ln,ult««,nriy L thTZ^ LlTn ™ .i«!t 1, 0PP0.1U, dlr«tlon, what wUl h.p^„ ,o L^y tL ho» gmtUth. unbalwcM fore. th.t cuiTthta n^lVT ,') Wh.tT ,<«, oo«cl„,lon ,e.p«,ung th. .««« of « „„^'Jd 1. ^Un^ ^~..^r^J:r" ,'"> ^".ttayourconcl^lorri^ttaVtSf ». How la prMHir. piodncMi r no'.ll^ltjorol''.^""' ""'*^™"' "-• "-"^ "■" <^'»»— 7. Defln.akllogTam.forcej agram-fbro.. to fl'^w'IL't^""~''''''° •'''*• ■'"'"'""'•"'•''""'"o'Hv.,. ^^9^^If a force act, on a body and doe. not move It. what do you \ CHAPTER II FLUID PRESSURE SECTION I TRAKSMISSIBILITY OF FLUID PRESSURE 16. Difference in Respect to Transmission of Pressure between Fluids and Solids. — If a glass globe and cylin- der (Pig. 8) be filled with water, and a piston, P, be thrust into the cylinder, jet« of water willjie tlirown n o t only from the apei v ' tnreA toward which the force is applied and the piston movesj wit equally from al Tthe aperttrrgj ir- « a cylinder of wood fit easily into a vessel (Fig. 9) and D |:^saure as that of a wfii(>ht hfi appliPfl on the top, it causes a pr fSHiir^ t.hmiijT}i tho ^n,i to Ig ^xerted on the bottom of the vesse l ; but^ ihis is the only pressur e exerted o».4im_isssel. This illustrates an important difference between the pressure of one solid on another, which is exerted only in the direction in which the force acts, and 3nid pres-~ sure, which is transmitt ed in every directio n. When pjressureia applied t o a solid bod y, the body is incapable, on account of its rigidity, of transmitting the '% MULTIPLICATION OF PRESSURE 19 pressure in other directions than that in which it is pressed. But fluids, ou accoi . nt of the mnhilify of their molecules, are incapable of resisting IT cljitiige of shape when acted upon at any point by a force; and, hence, r^ y fpy^e iip])lied to a fluid body must ,..aiM.sm;fr ..rl by the fluid in every direc lor. 17. Multiplication of Pressure; Pascal's ^"^•^ ^"^'"g to the transmi,i >,il,ilitj. of pressure any force impressed upon a body , •'f fl"i Fluid pre88ure _ia.^ xpres8ed by stating the force exerted on a unit area, as 2 pounds per square inch, g-~Per SQYrfi t^fiTiti^pt^ etc. It is always exerted in a"direction at right angles to the surface pressed^ uponT Bxperiment 1. — Fig. 12 represents a section of an apparatus called (from the number of uses to which it may be put) the Fio. 12 jnmjn^me_a^aralui. ^ is a hollow cylinder closed at one end. B is a tighUy fitting piston which may be pushed into or drawn out of the cyUnder by the detachable handle C when actemd THE HYDRAULIC PRESS 21 I into the piston. D is another handle permanently connected I with the closed end of the cylinder. £ is a nipple, opening into I the space below the piste n. To this may be attached a thick-walled I rubber tube, F. G is a stojxjock, and // is a funnel, either of which may be inserted at will into the free end of the tube. / Support the seven-in-one apparatus with the ojien end upward, force the piston in, place on it a block of wood, A (Fig. 13), and oil the block a heavy weight. Attach one end of the rubber tube B (12 feet long) to the apparatus and insert a funnel, C, in the other end of the tube. Raise this end as high as practicable and pour water into the tube. Explain how the few ounces of water standing in the tube can exert a pressure of many pounds on the piston and cause it to rise together with the burden that is on it. We thus see that,'paradoxieal as it may seem, a small qua ntity of wat er may be made to suppor t a very great weigHtl Ezperiraent 2 Remove the water from the apparatus, place on the piston a 16-pound weight, and blow (Fig. It) from the lungs into the apparatus. Notwith- standing- that the actual pushing force exerted through the tube by the lungs probably does not exceed a few ounces, the slight increase of pressure caused thereby, when exerted upon the (about) 26 square inches of surface of the pis- ton, causes it to rise together with its burden. 18. The Hydraulic Press Closely allied to the seven-in-one apparatus is t he hydraulic pre a reservoir, A ■ — y- 'g- -to). by a sucfioiTan^ xu worked by a lever , .5, jsTorced along the tuoa -x^-mtn JEe cylinder ^" This cyRSier contains a phmger^^ . Fio. U Water drawn fi-om 'orce Dumr 22 FLUID PRESSURE which wor>' water-tight in the collar F. The plunger carries a jlate, G, upon which are placed objects to be compresseaT The water forced into the cylinder exerts upon the plunger a total upward pres8ure_w hich is as many times greater tHan- lbe downward- ^..... exerted upon the liquid through the plunger i/ ^'the area of [Fm II iffiiFriiiiiliHiiiiiiiiiiBiBiiiw- FlQ. IS aiecro^section of the plunger P isJimeBLgrfiatfit,than^ the_MgajxLthe-i!ro_sg^ section of" the plunger H . To oBtam the entire theoreBcargSnT^ force that may be obtained by th.s machine, the ratio of the cross sec tions of the plungers is multi£lie£b£^^io of the two _arnia_of the lever B. (See § 88.) ~ The pressure that may be exerted by thesp presses is enormous. ^Th e^hand of a child can break a strong iron bar . But observe that, although the pressure exerted is very g^t, the upwud PASCAL'S PRINCIPLE ^movement of the plunger P h very slow. I„ , ,r,Ier that the plunger P may rtse I cm., the plunger H must descend as many centi- meters as the area of the cro ss section of Ph times the area of the cross section.of ff. The disadvantlge arising^fronVsIoW^ess of operatjonjs ofjittle consequence, however, when we MnsVder the great advantage accruing from the fact that one man can pro- duce as great a pressure with the press as many melTJSKithout it. The modern engineer finds it a most efficient machine whenever ^reat^resistances are ifite. moved through shgrt di stimce^, ' \, 19. Pascal's Principle. --Eliiiik_«xeit4irfiaH.iirajlue to their weight. Imagine a vessel filled with shot; the upper la ^r o Lghgt will .press upon tlw lajer next _bdneath with a force equal to its weight, "the s^^d upon the third with a force equal to the sum of the weights of the first two, and so on. You conclude, therefore, that the p ressure_exerted upon the successi ve . _ layers will be exitctly ^i^^^:^Himal to their de pths. In I iiKe "manner, and for the same reason, t^he riLi^ir^ nt different point! in a liauid is prnpnrtim,nl /^ fy ^^pff, Since shot possess a certain degree of mobility o r freedom of motion around one another, their weight will^ause^to some extent, a lateral pressure against one another and against the walls of the containing vessel. In consequence of the extreme mobility of the molecules of fluids, th e downward pressure due to gravitatio n at any point in a fluid gives rise to an equal pressure at (that point in all directions. Hence, the so-called Fagcal's principle: At any point in a Huid m. >../ tJ,. t£um^ equal in al l directions. ^ The oo^lMhydraulie Jack act , on the same principle as the hydraulic press. In fact, theTSaBjn ffu Iil /t U luj.ltcat lon ot Scatter. Ther^tto -~^T m? ° '-^ t^-" P'''°g°" is made so great In some fiSSrCEST- ?»e " gcM l»t a load of mbre Oi an IflQ nrin p^nr, (., •=='- 24 FLUID PRESSURE Fia. 1« Thug, let o, b, e, etc. (Fig. 18), represent imaginary rarfaoea, and (he atrowheads the direction of prewure exerted at points in these surfaces at equal deptlia in a liquid. The^rejauua exerted at these several points are equal. " •I'he truth of this principle is obvious, for if there be any inequality of pressure at any point, the unbalanced force will cause particles at that point to move, which is contrary to the suppositiAii that the fluid is at "r^-- Conversely, when Ihere is moly /n in a bodi/ oT fluid it it gpirfgnce 0^ g n^ i neoiio/i(y ^ presButes. If a glass tube (Fig. 17) be plMed vertically in a streajn of water with ite lower end bent into a horizontal direction so as to face the stream, the water will rise in the tube to a hight, say, AS. This hight, tech'.icaily calle d head, measures the ine- quality of pressures, or the unbalanced force which moves the water. Now the velocity of the stream is jnst that which would be produced by a head of water of the same magnitude. In other words, the vetncity 18 prnimrt.ifmal to thn Jiciui ; hence, this-ingte3inent--inaiy_bS-Ma6d.ior-(1etermining the velocity of a s tream of water. Fig. 18 represents a jar of water having immersed in it several U-tubes with long and short arms. The shorter arms open in different directions, upward, down- ward, and sidewise. The bends of the tubes contain the same amount of mercury, and the openings of the short arms are all brought to the same level or depth in the water. The pressure of the water exerted downward, upward, and laterally forces the mercury to the same Fio. IT 1 PASCAL'S PniNCIPLE £5 hight in all the tubes, thus showing that at tK, ,„^. depth pre^mrej^j^ij^^i^ .fir^il. '^"^ ^ (Fig. 19) is a glass jar containing^ater; B is a cylinder of woyd thrust endwise into the water • C a cyhndncal gla^s vessel filled with water tl' thl mouth downwani into the jar of water, the water in this vessel being sus- tained by atmospheric pressure ; and D Fro. 18 Fia. lit the water m the bend E and causes thp »„f .,. hPDfJ t^ ^=„ k- 1. . i-auses the water in the t^«d tc n^s li i ghf unon e arm than in the other. The 26 FLUID PRESSURE \ distance cd is equal to the depth of point a and me«»- ures the pressure of the water at point a. If the tube be raised so that a, the point where water and air are in contact, shall be at half the depth that it is at present, the distance cd between the two surfaces of the water in the bend will be reduced one half, showing that the pressure is half as great; in other words, that the prt*- ture it proport ional to the depth. ^ ' If, now, t£e tube be moved so that its end shall be under C, and at the same distance below the free sur- face (i.e., the surface in contact with the atmosphere) of the water, the distance cd will be unchanged, although the hight of the water above a, including the water in the vessel C, is now niuch greater. Move the end of the tube under the cylinder B so that the hight of water immediately above shall be much less than at first; no change in pressure, as indicated by the hight cd, will occur. From all this we conclude t.haf^ yr^Murg at any ^ittt in a liquid, du e to its weight, is direeOii^jn-o^ortional to the depth of the point below the free surface of the liquid. 20. Pressure in Liquids is independent of the Shape of the Vessel and of the Quantity of Liquid. — This may be demonstrated with apparatus constructed from a large glass funnel and bent glass tubes, as shown in Fig. 20. If a small quantity of mercury be poured into vessels jl and B so aa to stand at the same hight in the U-tubes of both, and then water be poured upon the mereury so as to stand at the same level, mn, in both A and B, it will be found that the mercury will be raised by the pressure of the superincumbent water to the same level, Fio. ao CALCULATING LIQUID PRESSURE 27 ed, though the shapes of the vesseh and the quantity of water which they contain are very "Afferent aL Methods of calculating Liquid Pressure. — Conceive a square prism of water (Fig. 21) in the miJat of a body of water, its upp r euiface coin- ciding with the free surface of the liquid. Let the prism be 4 cm. deep and 1 cm. square at the end ; then the area of one of its ends is 1 cm.', and the volume of the prism is 4 cc. Now the weight of 4 cc. of water is 4 g. ; hence, this ( prism must exert a down- ward pressure of 4 g. upon an area of 1 cm.* But at same deptli the pressure in all directions is tlie same ; hence, generally, the pressure at any depth in water may be taken as 1 K- per square c entimeter for P.iioh "centune^r'praeDth (= o= 1000 kg. P^' square meter for each meter of aept"ET~or, since the weight of water is about_ eSLS pounds per cubic foot, 62.3 pounds per square fo oTIore ach foot of depth). To determine., the. -pressure at any given dep th in a ny other liquid, thew ater press ureat. the ^ven d epth miiHtJifi multipliBd ^ the specific gravity (see Appendix) of the liquid. Fio. 21 28 FLUID FRKSSURR 33. Rule* for calcuUting Liquid Prewure againtt the Bottom and Sidea of 2 Containing Vesiel. — Ita totfliw- ■u» due to wmytty on any portion of the horiwntal bettoii .of T^^I^^SLil^^jiLiuAJLtoUie weight of 'a eolj^i^ of the Mine liquid whow beee U the Me.'^ft^ pJ^MST'^f^ the bottom jmeeed upon, and whoee Ught (• the tegUi of theUgnid In theneiML " Evidently the lateral pressure at any point of the side of a vessel depends upon tlie depth of that point ; and, aa depth at different points of a side varies, to find the totd jtCHure upon any portion of a side of a veeadTflnd ffie w dght of a colnttn 1^ 'liquia whose base rObCP«iIiLti>f|t portion of We side, and whose hlght is the average depth of that portion. 83. The Surface of a Liquid at Rest is Level. — By jolting a vessel the Surface of a liquid in it may be mnde to assume the forn» ,rpen in Fig. 22. Can it retain -7- this I'o; ;.i / Take two particles of the liquid at the points a and b, on the same level. The total downward prea- sures upon a and 6 are in the ratio of their respective depths, ca and db. But since the pressure at a given depth' is the same in all directions, ea and db represent the lateral pressures at the points a and b, respectively. ^Bflt_rf6 i8_greater than^jsa ; hence, the particles a and b, and those lying in a straight line between them, are acted upon laterally by two unequal fQrces in opposite directions. Hence, the liquid cannot remain at rest in the position assumed ; there will be a - movemen ti n the dir^tion of the greater force, toward a. tiU *%J^^Js^5quiliMumj)f forces, which will occur cmly FiQ. 22 EXERCISES 29 I point, in the *^rface^an_ojuhe^,^^ "- Thiifoct i«coimiionlvHxiw»»oillliii«- .. u--. . • Ifvpl " I„ - . '"'"•""'<"■ seeks its owp«t I w,ll not reman, l,ea,K.d «p. An illu.tration Flo. 23 r.« rr,t;:;.rt,:r. ,rv -r =• - -ioe^ip:,, to t^:;::;;;.;:;™ ix;-"^' ^' ""''''*-"«•' "^ EXERCISES 1. The areas of the bottoms of vessels Ann ^ ^ «e equal. The vessels have the IITe demf' H ^J'"*' '''> water, (a) Which ves- '^P"' ""'' »™ fi"ed with ' ,y sel contains the most water? (6) On the bot- tom of which vessel is the pressure equal to ■ ""» weight of the water which it contains? (c) How does the pres- sare upon the bottoms of vessels Ann j t. fvely. with the weight of theTatr in fhem ? "" "°"»"'' "^ Via. 24 80 FLUID PRESSURE S. Suppon that th« um of tb« bottom of each veael U 100 tqnan InohM, and tb« depth 1* U Inchet, what U the pmtura on tha bottom ofaachr - i >, 3. The bottom of veiiel A ii iqaare. What la the total prawira acainit one of lu Tertlcal aide* r 4. Let A (Fig. 1£) be a cloaed cubical tank wlioae Inalde dlmeoalon la 10 em. Leading from lu aide la a tube, fi, whoae top la 60 cm. abore the Interior top aurfare of the tank, (a) What maw of water will the Unk (not Including the tube) con- tain ? (6) What will be the preaiure on the entire bottom of the Unk ? (c) What on one of Ita ildea f • (d) Will there be any preaaure on the top of the tankr Whyf (<) Suppoae the tank and tube to be filled with water, what preiaure will be exerted upon the entire bottom of the Unk r (/) What upon one of lu aldei r (s) What upon the top of the tank r (A) Suppoae the liquid uaed were alcohol, how would anawera to the above queationa be aacerUlned ? ' 5. Suppoae that the area of the end of the large piaton Fro. 2B o< > hydraulic preea ia 100 square inches, what muat be the area of the end of the amall piaton that a force of 100 pounda applied to It may produce a preanire of 2 tone upon the laiga piston? 6. Take a glass U-tube (Fig. 20) about 40 Inches high, having a stout rubber tube, a, attached, conuining mercury with the surfaoea at the same level In both arms. Blow Into the tube j the surfaces of mercury will at once assume diflerent levels. How will you determine the pressure which you exert through the air In the tube upon the mercury (the tpecyii! gravity of mercury being 13.69) ? 7. (a) Suck air from o. What will happen to the mercury ? (6) How may you determine the j diminution of pressure which you produce by suction 7 8. Take a similar tube conUining water in- j. j. stead of mercury j connect it with a gas jet and turn on the gas. How would you determine how much greater (or less) lu pressure is than that of the atmosphere ? 9. How great Is the pressure in fresh water at the depth of 60 feet f n- EXERCISES 3j cell- th.„ « .^int In .ta^rf M u .r ' '" "".""* '" "" tha urn. ah.« . . ' ' " ""' pre«»urB n the Dim 1 x : .tU r """'"' '"" " """' '" "" ■""- - "' " je^n..,ip,.,,u^-,^. CiL";;::,E;rs-:'t^ SECTION II '-' ATMOSPHEKIC PRK88VU ^■^ since people fully grasped the idealhitl.;riive which foms ite ^^;;;;^in;:;^i:& ~TST:n^ ^ «a. ^The extern.1 pre«iu«, , about 15 pp.«„d, j^^ ^^e-lnl . ' AlitBr.n f rtr y «< n >t<««-lav>l«tthe fa.mn«r.t... „ . 82 FLUID PRESSURE ia balanced by the internal pressure of the gases contained in the pores o^ the flesh and Ji^uida gf Qur bodies^ If we enter a highly rarefied air, the gusgfi within our bodies expand, sometimes burst- Trig "blood vessels. '■^ Bleeding from t he nose or lungs is a familiar occurrence at high altitudes where tlie air is very rare. TOTS JuJlJ Fig. 27 -s- Evide ntly the pressure in t he a tmosphere due to its weight incr e ases wit h_the_depth, or — siijce in our posi- tion we are more accustomed to speak of hiffht in the atmosphere — decreases with the hight.'^ The p ressure loes not dim nish regularly with th g-^lg*''^ aa-in the liquid ocean : hiTT fl,f oT^Yf^ivar, pf^ int it ia en nal in a ll directions. *'Air ^8 _very compressible ; of the atmosphere, which sustain the weight of the ">*' l^z Fia. 28 EXPERIMENTS 33 -ZTJf ""^^ r "''''' ""•npressecUnd are therefore . 'n^^h. deps^r than the upper strata. ^^The density of the air diminishe s more-mpwllj^. ;, -^ the high t abov e sea level in- creas es. ^O wing Jo this fact more than half of the jytmos- pherie matter is/witlim 4 miles o^ the sea level, notwith staiiHing" that the atmosphere extends, it is thought^ 200 mUes above the earth.i Itxperiment 1 — Fill, or partly fill, a tumbler with water, cover the top closely with a card or writing paper, hold the paper in place with the palm of the hand and nn.vi-i .nvert the tumbler (Fig. 28). How U the water .i^rld'"' Experiment 2._F„^e the piston A (Fig. o„) „f j,,, ,^^^„_.„_ one apparatus quite to the closed end of the hollow cylinder, and close the stopcock B. Try to pull the piston out again. Why do you not succeed? Hold the appa- ratus in various positions, so that FiQ. 29 the atmosphere may press down. Yon ^;.„ ,.» ^"'^^'ly- and up, against the piston. a^^ierzLr™""' '" ''- '--' ""-''' " --^- ^^'n n the left margin show the hight in m', .- thosi rt it «;«, T ^'"*' 34 FLUID FRESSUBE 35. How Atmospheric Pressure is measured. ■»P«in»M>t 3. — Take a U-ahaped glaaa tube (Fig. 30), half fill it with water, cIo m one en d •with a thumb^and tilt the tube ro that the water will run into the closed arm and fill it; then _ restore it to its original ver- Un ^S^^lfc^^ tical poaition . Why doe»~' I m J^^^^llllK °°* ^^^ water settle to the I li^^ 91 same level in both arms? ^^il^^^Si***''^! Let Fig. 81 represent Fio. 30 a U-shaped glass tube almy 1 34-i«7^TPiriTrf iighf , closed a t_one end Miid^h^Ymg..aJiere^^f_l_8qiiarerinch 'iectionV Jh©-|yY '" * he. cinnfH^ arm _ — ^ | BJnka about 2 ini^l^ea to A and rises 2 inches in the open arm to C Iftayin g *^'^ g nrfana i 30 UlcheS hiprher than tjln anrfnon C. This can be accounted for only by the atmos- pheric pressure on the surface of mercury at C. The column of mercury BA, contain- ing 30 cubic inches , is an exact counterpoise for a column of air of the same diameter extending from C to the upper limit of the atmospheric ocean. _ J hfi y^i i^tHt of the 3 cubic innhftn of itifliviry ^ \\^f ^olumn B A is 14.7 pnnnHa Hence, the weight of a column of air of 1 square-inch section, extending from the surface of the sea to the upper limit of the atmos- phere, J8_about 14.7 pounds. But in fluids gravitation causes equal pressiure in all directions. Hence, at M« Kig.8t \ STANDARD PRESSURE 85 Uvd^the sea all hodiet are preiied upon in all direc tumTSy IWatmoephere hy a force of about 14.7 poy p^" per tifuare inch: nr nh^., l *^~, j-^r ,quai.- e-/nnf.. 86. Standard Pressure. - Many physical operations require a standard pressure for reference. The standa rd generally adopted is the pressure, per square centimeter, " - equal to % weight of^^^^al^ mn' of mercury 76 cm. in ^'S^^ f^^^ 0» fiWh square c'StSasJer; iUk ?. ' .'t "{g equal, on each square centimeter, to the weight of 76 cm » of mercuiy.i This is equal to the weight of about Jj)83g. of water. Physicists generally express fluid pres- sure in terms of the milli- meters (or centimeters) of mercury at 0° C. that the given pressure would sustain in a vacuum tube. Thus, for example, the average sea- level atmospheric prtwijuiT^ 18 expressed as 76 760 |-©33^ 27. The Barometer The hight of the column of mei^ cuiy supported by atmos- pheric pressure is propor- tional to the pressure per unit area flod-is.quite inde - J)endent of the total area of the surface of the merf-nr r pressed upon ; hence, the apparatus is more conveniently CouoliBcted in the form represented in Fig. 32. •AunitoJpwMureof 16 pounds per square inch isqultegenerallyadopted Ky engineers in expressing very large pressures, and is called an atmo^hm. Fro. 33 86 FLUID PRESSURE ^ __ABtTOight_tul)e about 34 inches long ia closed at nn« flTifl fljifl fillp'i with iiininiiT}r The tube ia inverted, with its open end tig htl y cnyfrftd w i^h a lin p per, and >^.n a.^/1 in ir.ooi^n.1 in^p p ^^)pn^l,(jf mgrniliy- When tKu ger 18 witnarawn the mercui-y sinks until there is equilibrium between the dowrnward pressure qf the Jner- cuTtia"'column AB and the j)r^svire of the atmosphere. The empty space at the top of the tube ia called i^^ar^£Uan^ in apparatus designed to measure atmospheric pressure is called a barometer (gressure measurer). A common and inexpensive form of bivrometer is represented in Fig. 33. To protect the mer - cury from fallinp; dust, the cistern is inclosed in a sm all close^■■ ^ 1. whicli is not, however, air-tigh t. Beoi de the tnlw. and near its top ^ is a s cale. 'graduated in inches or npntimptpra. indicating I the hipiit ^f tlif mprcnria] cnlnmn. For Ordinary purposes this scale needs to have a range of only three or four inches, so as to include the maximum fluctuations of the column. Such a barometer is giihipf-t tp g, ainnii ormi. in iterea^ng, which is eliminated in the more expensive kinds. In refined scientific work it Fia 33 '^ necessary to make suita^jle allowances for" exBaagipn and contraction of the mercury and the scale attending changes of temperature. Fluct uations in barome tric pressure are of^le^ qttent^ occurrence. Some of the many conHTtions which 1 Thfl fimt ^ftfometer was conatmoted by TorriceUi, a Florentine, In 16*3. BXERCISES 87 influence atmospheric presBure are charge, in temper,^ 88. Barometric Measurement of Hlehts ^ Ta''''' " ""f P"""" '» ■'^'^^f:^ZLZT.:j:Z --'«*-'"-. ehieX because an. vary «MeetionLle,lt .h r^IUTmistr;' ""i' ^""^ """'' logical point of view. To form a f^t "f 2T Z^ '""" " "'•'"'"">■ . b^o^eter, a thermometer.™ d r^^tl"; ^t »' ">-- v„„,, one must be familiar with the law. whf* . "onBuHcd, and «««phericpre,.u«Zpe»tJ::^Uwurerer "" '"•"°°' ■«"*«■" 88 FLUID PRESSURE 6. The top of Mt Blanc, In Switzerland, in S^ miles above aea level. The average atmospheric pressure on the summit of this monn- tahi is 38 cm. Only what portion of the matter of tlie atmospheric ocean is above the summit ? (See Fig, 27.) 7. Examine Fig. 27 and determine about what portion of tl^e mass of the atmosphere is within 16 miles of the earth's surface. 8. Is it essential that the barometer tube be of uniform bore ?^lX)> 9. Explain what is meant by (a) a " head " of 10 feet of water j (6) a pressure of 20 inches of mercury. 10. Compute the pressure due to a head of watur of 10.47 m. (34 feet) in kilograms per square decimeter. SECTION III RELATION BETWEEN THE DENSITY, THE TOLUU, AND THE PSESSUKE OF A BODY OF GAS 89. I^ressure of Confined Gases due to Molecular Motion. -t= When a quantity of gas is con fined in a close vessel it ex ert3apressim^nn_alljin.ri-j» of thfiJaterioi of the vesse l, •^rhis pressure is out of all proportiijn fa i t\)g weight of the gas, and in fact is not due to its weight. The pressure may exc eed the weight a million tinaeO Th pressure cann ot be duejQjtny thing similar to the ra(M)tioii~ Ota compressed spring, for the Stftecules Q|^.gaa.aie free rone anothef^^ififluence. It can be accounted fo r mm (if iJHTrnwdcti, of th: »f.jmr>f^. m/?ff(Y^«. impac rd th< I _ yiJii/!^ r" ^tinuou»l^ bombard the gideg (jf the vetse^. W^im the volume of a body of gas is reduced by compression the pressure which it exerts per unit area is increaaed. ^because more molecules now strike a unit area in a unit of time. __ 30. Elasticity of Gageg.^TO« ^Ifutimtif of eituet it peifeet^ ~By this is meant that the force exerted in - BOTLE-8 (OR MABIOTTE'S) LAW 89 jne barometer.^ hich m.I.lT*:^., J J' Fid. 34 ^_ui^^ at the same time thTXtio orce o the ai./. A. Quailed ..<...r! ^^short because it ^ selciiJ^tS to mke mea«uremenfe except" in tok«blr -"• - ^^ ■ g^ apparatus nl«. .d under the r...; ... Igg iiic^me Ih. nltlfiiiMrg oTpressu^ of the airm the recei^^TT^glKS^^^ ae^ree of exhaustion is readily determin^T A »fa-de thf, rfrp,y,r nt n iU ajtiTSSnia^, and after -B. ghauatapn the vacuum gauge inside th.T"^ »*_„ J. „i , „ S»"(ie insifl^i th e recBlv or gtoujg ^t 10 nm. .; then the preasTre ha. bSS, diminished f755» in -\7jK „ „, . ^" that «* of th. i ~J """• Thin indir iO a, _tPat «t of the air-hn- 1.^ „,^^^^ ^ , 3, 31. Boyle's (or Mariotte's) Law. B^riment— Take a bent. ,,1... ...u^ ^^, 3 I winch .hould be at least ,856^715^87^3^ at the top. Pou. me^„nrr„,^^ ,f„'>^ Ji»«ttUaa. between Z^^C^L V^"""'"**'' '''*'' '« iSila. — i._i _g . flence, ita hig^t, g, may represent its Jnn.. 40 FLDID PRESSURE Meantn H (U., the dutance between A and C) and regard the ntmber of centimeters as representing the volume, V. Its pressure. P< evidently in the same as that of the atmospher e at the time. 4tSliHlltkiftJ||2;SSlStSL^"° ascertain tlie hight of the barometrie. column; represent this hight by P. Pour a litUe mercury into the tube; the mercury rises, say, to ^, and B,. Memmn. ^ vertical distoni-a between ^j and C; this number represents the volume F, of the body of air now. Measure the vertical distance between il, and B, ; this number represents the increase in pres- sure, which, added to P, gives its present pressure, />,. Now pour more mercury into the tube, so that it will rise to, say, i4, and B,. Determine aa before the new volume K, and the new pressure />,. So continue to "Mill |11f ""•'8' * t!k'~' '~i\ i fourth time, and get new values for the volume V, and V^ and for the pressure P, and />,. Arrange the results as follows : V =., I'. = . . etc. P =. . p,=.. vie. V y P =. K, X P. = . K,x/'. = . I ^ It will be found that the series of prodnctai in the last column jTB apj>mTiTT[|^^|y c/^ii»l /•/!■■» allowance being made for errors in measurement, etc.); consequently, the product of the volume of a body of gas multiplied by its pressure is constant, and the vol- ume varies inversely as ita pressure. Hence the (Boyle's') law : _, ^The voluine of « body of gaa at a eon t^iHj *«" ««~J '"' ~— =^ EXERCISES 1. If the volume of a certain body of gas be 600 cc. when Its pras- sare is 800 g. per square centimeter, what is the volume of the i body v?hen its pressure is 1200 g. per square centimeter ? 2. If a body of air whose jlnme is 1 m.' and whose pteasure is 700 mm. expands and occupies 4.6 m.*, what will be its pressure Z 3. A bubble of air liberated at a depth of 2 m. In water has • v^nme of ^ cm.*. What will be its volume when it has risen 1 m.f ■-i'^liO.r. •'^^aL^^^-stf^^JlM ^sxcLc- I ■ THK AlB PUMP L> * A nuua of - *lr occupies 160 cc. when the prenun ^ 700 mm. What 37»^""' '^ ">e preg- '^r^TOfo thU it ghaU W occapyoniysocc.r 7. Suppose that, onadaywhentlie pnnure of the air 1» 766 mm., air li ezhaiuted from the receiver of an air Fio. 36 pump until the mercury in the baiimeter FiVlg whatperc«toft on^ 'vi.d ^jtJ^tWj/oU-j 42 FLUID PBESSURE »nd the confined air panel to the upper lide of the piaton. The ■uceeeding upatroke of the piston jjljmfc^liftg B, and opena^ . The upward motion of B ia limited by a ahoulder which it carriaa near ita upper end. The air that paaaei through S ia forced out through an opening (closed by a valve) at the top of the barrel, and the air in R expands and fills again the barrel below D. Thai, at each double stroke a certain fraction of the air remain- ing in R is removed; but, on account of leakage and other imperfections, the pressure of the air left in A can be reduced bv t\^ })Mt BBinp« hilt a. lit.t.lA below 1 mm. of mercury . When a higher degree of exhaustion is required use is made of mercury pumps. (See f U2 of the author's Principki of Phyrict.) Fio.Sg Fia.3S It is obvious that if 5 and A open downward instead of upward, then, as the piston is raised and depressed, air is com- pressed in ij. A condenser ia m^ lf^y * yiiimp yf\tft it. yfiv.^ rrYBriMilr H"-* in llWIfi 33. Lifting Pump for liqnlda The common lifting pump is ''"Mtnir^"'^ '"'" tko baiTri) uf m jiji pmnp fajig. 37 represents the piston B in the act of rising. A4|he air ia rarefied below it, water risea in conaeouenee i^f atmn«ph«in.t Fio. 37 FORCE PUMP 48 £^^°" tho wter in the well and open, the lower valve D WhTBtVp..t.,n..rn,.^dHnwn (Fig. 38) tl^e W£jalvedp«. .^™^JM;^^2^enj, .„d the water between th e bottom of^ .bove thelSlS-n i. raW and dustomlJ^am. • ™^ 34 V«ret Pomp. _ In this pump the ordinary pirton with , valve i. replaced by a »Mcili4r^jMt.l. ^Tk/Io^ c^!5 ^plunger . Thi. paMeaUi^JiiihT ^^ * ^' '""'^ . wumnjt box . D, in which it fits air- t'K'"*- l ^Yea opening upward and outwar d are placed at A and C, " respectively. . When the plungwr i . raised A opens anrf n nl^„ .-. water is raised into the barrel by atmospheric pressure, jyhen the pluniw.- descends A clow. «nH <^ .ogensj and the water is forced up through the pipe E. Anair dome, F, is usually connectecTwiLh f.rAUr P""*?* to regulate the pressure so as to give through the delivery pipe » very steady stream. This dome ' contains air. When the p lnnf^pr descends it fo rces water into tne do me and co mpresses the »i, J^ As soon „ the do;;iJ^oke of" the piston ce««» the I.t fT' 'u *^i2-£gB ffig8«ed air in the dnn,. f^,^^ ^ ^ jv ater out through Jg in a continuous strea HT ^^ 35. Siphon. — Take two vesscis, ^ and * (Fig 41) oontoiniug water (or other liquid). Let the surface of the liquid in one vessel be lo wer than the surf^^i^f. , » The statement that •■ Nature abhors a vacuam " was used a^es a™ .^ ~=»un. f.r varioa. phe„.„eaa, - among them the risT" XTp^,:: 44 FLUID PRESSURE other.. Be iiil J tlltmi '"^'i "' '"1' ''""' i" T ruUwr or glaM) intoliie form <»( the letter U, ftU it with Home of the Baine liquid, cover the eiida ^^=5;^" " with your finger«, iiivert the tuhe, " « (Up the eiulH ofJ liflJufeaifltaihe liquitla and Fio. 41 Liquid will flow from the vemiel in which the liquid has a higher level into the other vessel. The pressure of the atmosphere, per square centimeter, on the free surfaces of the li'■«•> ^ey sin k ni^ j i ji fhay ~»nVi o depth where the upward prewmre is jiia^-. pqijnl to their weight an d the body is in equilibrium. \ Hie wdriit of the lignid diiptoced by » floating body to M ml to 1 the w«l|^ of the tody. This statement may be verified as followi: Jake a vessel like that ahown in Fig. 44 and jll it with water until the water is jQst ready to flow from th« tube A. Take a block of wood that will float in water, weigh it, and also weigh vessel B . Then carefully place tiie block in the water, catching the nverflnw in B. Find Fio. 44 1 PteTiousIy the descent ot heavy bodies and the rUin| ot light tMdies in liquids were explained on the sssomption that " every object se.eigJU^^ equal volume ^ some star^ard substance. The standard adopted for solids and i;q.i:>l« j^ .listined water at some .Ipfinit^ ^mnerature. Hence,lor solids and Uquids, wdqhtofthe body (4) specific gravity = ^^.^^ ^^ ^^ ^^ ^^^^^ (^jggt^ — -?1 J SPECIFIC GRAVITY OF BODIES 49 _ Accord ing to Archimedes' Principle. lou of might in water ^ wnif^hf. nf_a n equal volum e ofmtU^ hence. (5) tpecific gravity - - "* in which u, = weight of the body, tc' = the weight of the body in water, and «,-«,' = the loss of weight in water t.e., the weight of an equal volume of water. It wiU be seen that when the ^ram and th^ ..nhio ..„■ timeter are used as units in ^jfl^higjfensity thelliin;. bers which express the density and the soecifin [rn.vj.y of any substanc e ajejnumericallv p.).,.! tt^, .ArT JgLflfiUaaLPt lead is 11.3 g. pe r^ilbi^ centimeter and the specific gravity of lead is 11.3 (an abstract number). 40. Methods of finding the Specific Gravity of Bodies (1) Solid*. Kxperimmt 1 From a hook beneath a Bcale pan fFig 46^ .UT.end by a fine thread a .mall Jjodj:. of the substance ^hose specific gravity w to be found and weigh it, while diy, in the air. Then immerae aie body in > tumbler of wat^^- f^ ffc-f it ia mv«i^ »ifi. .■■>..- „„^- „ |,„||,^„ ,toiiche« the tumble r^ a nd weiffh it. in ^waier. The difference between its weight in air and its weight in water (w - w,) is the weight of an equal volume of water. Apply formula f .51. § 39. Experiment 2. _ Take a piece of cork or a smaU block of pine or other kind of ^'°°^i »l»o a strip of sheet lead whose ■5^^ ^_»t^'^'>^L l!»l Lt''»t of the block a nd whose length is saffloient for It to be wound once around the block. Weigh the Flu. 46 t; 60 FLUID PRESSURE dor bloc k : »l«n 1j[^ jjy l«iLJ Smpend the lead ginker and weigh it in water. Fold the lead sinker around the block an(^ weigh l y)th when immersed in water. S ubtract their com bined w«^ght jn water trom the su m of theirwei [ ^htg in a ir j this give s the weight of water d iiylmwd by hnth, Subtract from this the weight lost by the lead alone, a nd the remainder is the weight of water displaced ' by tBe cork. Ap ply formula (4). (2) Lijuidt, Izpuiman* 3 Take a so-called tpecific-gra vUg bottle , i.e., a bottle made so as to hold, when the stopple is pressed in, an exact (round) number of grams of water, e.g., 100 g. or 1000 g. Trill ti.^ tw^ttu with t}]g liijiiid whose specific gravity is sought. Place it on a scale pan (Fig. 47), and on the other pan pUce a piece of metal, a, which is an exact counterpoise for the bottle when empty. On the same pan place other weights, b, until there is equilibrium, and thus weigh the liquid contents of the bottle. The water c^Munty of these bottles is usually etohed on the bottles. The weight "» tl^° "T"'' '" **" '"**'' '^'TJllnri V the water capacit y ofthe bottle will givw th^ ip*^**" gf f '"*y "* the given liquid. Kxperimtet 4. — Weigh a pebble in air, also in w ater, and find _tli a_ weight of water dis placed by it: Wipe the'stoSe, weigh i^ in some other liquid w hose specific gravity is sought, and find the wejyht nf thin li quid displace d by the stone. You now have the weights of equal volumes of the two liquids. Compute the specific gravity of the latter liquid by formula (4). 41. The Hydrometer. — One form of this instrument consists of «_nlf^rl f,}yui tn}»,^4 (Fig. 48), ^ nninatin g_ in a bulb loaded with shot or mercury to keep it upright no. 47 EXERCISES 51 when placed in a liquid. It is merely placed in the liquid to be tested, and the specific gmvity i, r..^^ ^ ^ ^^ a graduated scale on the stem at that pomt which is at the surface of the %»id. The less the density of the liquid, t he deeper the instnimRnt. «i>.t-.. Hydrometers are much used for testing t he purity of milk, alcohol, p,tf.. . and are then graduated with special reference to the liquids for which they are to be used, and hence take the special names of lactometeiB, alcoholometers, etc., ' KZERC ms^:-)i (In the Mlution of the following exercises fre- quent reference must be made to the Tables of Specific QraTity in the Appendix.) ^°- ** 1. (a) Why dbes a body immersed In a fluid la«i weight ? lb) How •much weight does it lose r , — ' ^ stwhow 2. A body floating on a liquid displaces how much liquid? J- to tL /"* ^^ ^°^ ' '*"°°° ^ ' <*' ^'^ ""' » *»'"»» "•" 4. Under what conditions will a body sink in a Uquid f , j"; ilK^^i *■ °'*'"' ''y *''* »^«e"'«'>t that the specific giavitr of gold Is 19.S f (6) What is the demiity of gold P \«l • Vv 8. Will ice sink or float in water ? Why ? 7. What is the density of alcohol ? « "o \ tr^ . 1 ^ I declL^'?"'"' """P*"'"™ ^ "■"»' » density of 1 kg. per cubic •.. !' <''>„'^!"'"**°"'y "•«"»»«■»«»'««* the specific gravity of . ^^Z^^V <*>^'"'»"«'<"»™«"y'"henzine?T)Wh^wld ^ a liter of benzine weigh f (d) Would benzine rise or sink in water f -l ^^ Ja^^- °' ""^^ fl>»ting on water duplaces 10 kg. of water. i ■^h'f What is the weij^t of the block f ID '^ 62 FLUID PRES8UKE 11. In which liquid, water or alcohol, would a block of pine wood ilnklartlierf O.' . ^^vV 12. The area of the croia aectlon of a wooden priim la 4 cm.«. Placed vertically In water It alnki 16 cm. What la the weight of the prlun ? (Ji 01^ ^''•V ~- gttO oKo-^VN/" , 13. Fig. 4fl repreeenta a beaker graduated In cubic cenUmeten. Suppoae that when water atanda In the graduate at SO cc. a pebble la dropped Into the water and the water rlaea to 76 cc. (a) What la the Tolurae of the atone r (6) How much lea doea the atone weigh In water than In air ? (c) What la the weight of an equal volume of water fa ) -Jt^ffi^, fcJ--50r- 1<^ Flo, 49 14. If a piece of cork la floated on water In a graduate and displaces (i.e., cauaea the water to rise) 10 CO., what la the weight of the cork f/O"^ 16. You wlah to meaaure out 60 g. of alcohol. To what number on a beaker graduated In cubic centlmetera will you pour the alcohol f^oCC- 16. State how you would meaaure out 60 g. of nitric acid. 17. A measuring beaker contalna 40 cc. of meicnry. What does the mercury weigh ? ^"i% 3S ^ JX, Ov . 1& What Is the volmqe rf 40 g. of gold f o?^ g. of al^nlnum f 19. A sponge throwtf od waterVoats at first, but i^r'a timi linka. Is the specific gravity of the fibe^ of sponge greater or lea than tha; of water? < 20. Why will a tin basin or Iron steamship float on water 21. Find the weight of a cube of aluminum of 1 dm. edge 22. A body weighs 1200 g. In air and 060 g. in water. What Is Its density ? I i ' 23. A piece of metal weighing in air 70.4 g. is placed in a tumbler filled with water. The overflowing water la found to weigh 8.8 g. What is the specific gravity of .iie metal f 24. If 720 g. of silver be suspended in water, what will be the tenalon of the supporting string ? 26. What is the specific gravity of a substance whose draidty la 80 pounds per cubic foot f -M' ^^ u ^•'*4> Vo\ EXERCISES' me oody eipr«wd In grwn. per cubic centimeter T o as. 29. 30. 3i; What What la the yolume of 28 g. of tine t What ia the weight of 40 cc. of zinc ? What aupport will water irlve tn Tf. . „» .■ . weigh in aIrP *' *"*'" "o" "leh does it 34. Find the weight of a liter of olive oil. SB. Find the volume of 60 g. of olive oil weiS.i^ir-rh'^^t.rgTr'-m'rr-''"-"- i. i^-^^^Z^''" "'"' """> "• ™"- -«^er water. Wh« . in ^tef ^°c^m wel^t^; m ''T' '""""^ -"^•' »"« »™ weigh the more in l^t ' ""^ '" "' **'*' ' W '^"'ch will « r^'tl'",'* !!:""«" "''«""'• o'caatironln water, would a cZ ,J^J% Z^'J:£ -^"^ °' ~'^ ' (») ^'-t , 41. Ftod the volume of fiOO g. of lead. ^ ^ ' ' '/ *- **^ 42. Find the weight of 1 1. of water at 20° C 43. («) Find the buoyant force on I dm » of ca«tlmn-k . in water; (i) when Immereed in glycerine °""""""""'™ '"""""ed in :lr^'-* "•' ''"»^'-' '»- ™ > ^- o' ca« iro^l^Z^^^i' buoyant effect Of the waZ^tpo'^ttt.rr^llr^r^r' " "" gravity of the wood? C "mockt (6) What i» the ^)eciflo /I M FLUID PRESSUSE IffllMIMd. . . >laai«S(aii rn.io «r. A ioUd whoM ipcoUlo gnrltjr U O.R and whoM weight in »lr li 80 g. li fuuned to a linker that weigh* lao g. al«ne in wataR How much will both together weigh in water t 48. A pieoe of oork weight in air SM g. It li fattened by a thread to the bottom o( a Teiael ao ai to keep it entirely ImnieiMd. Find the tenaion of the thread. 49. Bow could you find the Tola irregularly ihaped atone ? 50. How could you find the ci^MKslty of an Irregularly shaped cavity in a body f fil. A (Fig. 60) represent* a sink, B a trap, C a pipe leading to open air outside the house, and D a pipe leading to a cesspool or sewer, (a) Ezidain how water mfty flow from the sink to the lewer but sewage gases be prevented from escaping at the sink. (6) Wllat prevents the trap from acting as a siphon within certain limits t 62. Fig. 61 represents two tumblers, A containing water and B containing some other liquid. Dipping into these liquids are the two ends of an inverted glass U-tube. This tube has a branch tube, C, to which is attached a rubber tube, D. X i* a clamp. If air be nicked out of the tube at D and the tube be damped St j;, liquid* will rise in the arms of the glass tube, (a) What causes the Uqnid* to rl*e f (6) The hight* of the liquid column* UN and OP are unequal. Why I* thi* 10 r (c) Which of the two is the denser Uqnid t (d) Having measured the bights of the two Ikinkl col- umns UN and OP, how would you compute the spedfio gravity of the liquid In £? 63. If a glass U-tube (Fig. 62) be parUy filled with water and then some keroeene be poured slowly down one of it* arms on top of the water, the free surface of .BJ..^D the two liquids A and C will not be on the same level, (a) Suppose the tube to be of uniform bore, how doe* the weight of the column of liquid AB compare with the weight of the column CD ? {b) If the hlght of the column of water AB be 14.4 cm. and the hlght of the column CD be 18 cm., what I* the apeciflc gravity of ke w a ne 1 1, CHAPTER in byhamics section i MOnOH, VtlOaTV, AIID ACCTUaiXIOH »„J*;h "!'*?• ^'^0'^—J>ynamic» tmta of the motion and tho tendencies to motion exhibited by matter und^ e^uence of force. Motion is a contLous chl^^ •pace only by determining its direction and distant W some other particle, ar from some point of S ence Hence a change of position of a particle must be a change m either direction or distance in relation to some other particle or point of reference. For thi reason all motion is spoken of aJ. relative motion. A particle moves relatively to a given point when an imagmarjr straight line connecting it with the point changes in either direction or length. A particle is at rest relatively to a given point when a straight line joinmg them changes in neither direction nor length. niMtaitloii.._Whenyouopenor8hutthe I eg8ofai«urofdivider.(Fig.63),thertpaight '' ^ h^ o-J', connecting the pointo »t the end, of "■ " ese pomta. n (Fig. 54) you open th« leg, , uttlo way and, 66 DTKAM1CS Flo.M Azlng the end of one of the legi upon • plane ntrfMe, tnm • oirele with the end of the other leg kiound the former u ■ center, then will be reUtire motion between the two pointi, linoe ■ line joining them, ab, of, etc., chMige* in dine lion. If (Fig. S&) you tredt with the pointa of the open divider* two ■tr»ight parallel linee on a plane torface, the two pointi will be relatively at rert, Juit a* snrely a* if the divider! were lying upor the table, rince in both oaaei a itraight line connecting the points ai, a'b', etc., changei in neither length nor direction. A point may be at the aame inetant at rent with reference to certain pointa and in motion with reference to certain other pointi. For example, while the points of the divider* are tracing itraight lines on the plane surface (Fig. SS) and are relatively at rest, they are in motion with reference to every point in the pUne lurface. A passenger in a railway oar may be at rest relatively to the car and to the other passengers, but in rapid motion relatively to objects by the roadside. In ordinary language the phrase << a body at rest " means a body that does not change its position with reference to that on which it stands, as, for instance, the surface of the earth or the deck of a ship. It can mean nothing else, for both the body said to be " at rest " and all points on the earth's surface are in rapid motion with reference to the sun and other heavenly bodies, and also with reference to the earth's axis. 43. Velocity. — Velocity u rate of change of pontion. It involves units of distance and units of time, and is commonly expressed in unit* qf dittanee per unit of (tm«, VELOCITY 67 *.g., Rieten or feet per iieoond, kilometer» or milei per hour, etc. *^ If the motion of n porticlo be not uniform, - in other word*, if the distances traversed in HUtce«iive equal times continually increase or continually decrease the velocity is said to be accelerated. I .-.rration is the rate at which a particle gains or l(,s-.s , 'oatv. Kveiy youth is familiar with the acceler m.,,, ^.,,;, •,),;« to!,,.^ gan or double runner acquires i., ; . en.Iin. .,1' "o with the retarded motion which .i U.IJ oxp.ri ..».. /ivl.en it is rolled along level ground. Velocity is determined by dividui ; J,e !,.,(, .ee trav- ersed by the time consumed. If a L.kIv ■wmvo « motoni in t^seconds, its velocity, v, is *- meten. per second; i.e., » = -. In case the velocity be not uniform, this result is to be regarded as the average velocity for that distance. The velocity of a body whose motion is not uniform can be given only at some definite instant or at some pomt in ita journey. It denotes tlie number of units of distance the body would traverse in a unit of time in the direction of its motion at that instant, if iu motion tcere continued unchanged for a whole unit of time. A velocity possesses direction as well as speed. The term speed does not take into account the direction of a motion If a stone be thrown obliquely upwaid into the air, both the direction of the motion and the speed continually change. »v1 mn'f ''?'* ^"^ ' ^" '""^'^ ""' """''' ''*^ " ''««"'« "P^^J. y 1000 feet per «cond. At the instant of di«harge it i. mor- iDg in a certain direction, A£ (Fig. 56), «, that if it continued to 68 DYNAMICS move at that ipeed for a whole unit of time it would trareree a distance in that direction that may be represented by the length of the line AB. A velocity, then, can be completely represented by a straight line, inasmuch as a straight line has both magnitude . C Fio.M and direction. When the shot reaches the point C it has a differ- ent speed and a different direction from that at point A. The velocity at this point may be represented by the line CD. The velocity of the shot is continually changing during it« whole flight ; this is called variable velocity. When a particle experiences equal changes of speed in equal units of time, its motion is said to be uniformly/ accelerated, and its change of velocity per unit o^' time is called its acceleration and is represented by the letter a. When the velocity increases, as in the case of a falling stone, its acceleration is said to be positive (+ a) ; when the velocity decreases, as in the case of a stone thrown upward, its acceleration is said to be negative {—a). Negative acceleration is called, in common language, retardation. In the case of a body falling in a vacnnm, and in that of a body projected vertically upward, the acceleration is practically uniform. In the former case it is about 9.8 m. (about 33.2 feet) jier second ; in the latter case it is a negative acceleration of about 9.8 m. per second. The acceleration of a particle in traversing a certain distance in a given time is found by dividing the entii» FOEMULAS FOR ACCELERATED MOTION 69 change in velocity, v, by the units of time, t, consumed in making the change ; «.«., a = -, whence, (i) „ = „(. Thus, if the velocity of a railroad train at a certain instant be 15 mile, per hour, and half an hour hence it be 25 mUes per hour, then the entire change of velocity, v, is 10 miles per hour; hence the average acceleration, i.e., the acceleration if it were uniformi; ist^buted throughout the 30 minutes, is iJ = J of a mUe p^ 44. Pomulas for Accelerated Motion. _ If a particle starting from a state of rest move with uniform accel- eration, a, its velocity, v, at the end of any given number of units of time, t, is found by the equation (1) v = at,aa given in § 43. From this equation we infer that change of velocity it proportional to the acceleration and to the time occupied. But if a particle be in motion, and at a certain instant have a velocity, V, and its acceleration be a, then its velocity at any subsequent instant is expressed as follows : After a lapse of one unit of time, » = F ± (o x 1). " " ' « two units " " f=V±(ax2\ " ' (2)v=r±at. Now, since the velocity of a particle starting from a state of rest increases from zero to at, the average velocity must be -~ = i at. At this rate, in the same time, t, it would traverse a distance, S, equal to iatxt = iafi units; whence, (S)S=iafi, 60 DYNAMICS a formula which enables one to compute the entire dis- tance traversed in a given time by a particle starting from a state of rest and having uniformly accelerated motion. It appears that the entire dUtance traversed in proportional to the acceleration and to the square of the time occupied. If a particle, instead of starting from a state of rest, have an initial velocity V, it would move in t units of time without acceleration a distance Vxt; to this dis- tance must be added the distance it moves in conse- quence of acceleration, in order to obtain the entire distance traversed in t units, and our formula becomes (4) S=Vt + iat\ If it be required to find the distance passed over dur- ing any specified unit of time, we may subtract the dis- tance traversed in ( - 1 units from the disttmce traversed in t units. Thus, representing the required distance traversed during a specified unit of time, t, by g, we have . (5) » = i ai" - i a (« - 1)2 = i a (2 « - 1). EXERCISES 1. When is there relative motion betTeen two particles ? 2. A boy is riding on an electric car along a straight road and hU friend on a bicycle regulates his speed so as to keep constantly by his Bide. Is there relative motion or relative rest between the two ? 3. Suppose the two vehicles named in Exercise 2 are turning a curve ; are the friends in relative motion or at relative rest ? 4. A boat moves away from a wharf at the rate of 5 miles an hour. A person on the boat's deck walks from the prow toward thf, stem at the rate of 4 miles an hour. (,i) What is his rate nf motion t.e., his velocity, with reference to the wharf ? (6) What is his velocity with reference to the boat ? EXERCISSS 81 motion of a body ZeltlTTnZ"'"" " "'■ <*> ""'^ """^ '"« falling bo,Iy ? "^ ^ " ™""*"^ "P"*"! "ifler fron, that of a tion of freely falling bo.iies ? ' * "' "^ ""= accelera- 10. Th« velocity of a partideal a certain instant i8 r. i. fon .a „ What will be it. velocity, „. af ter "ti^ !:/,; -V"'^"- i.. fl-i" !^t;::'t:i::?';'r^'^ ■-' ^ ■ "« ---tion «. »„<. 12 If a hn 1 . '" »'^1'"""g '<^ final velocity ? veiocy^tr; t::^e::::;;r;: -^-'^ »^ --'- - ^ -n^, a 13. If a body move from a state of rest »i.), tion a. wbat space, ., .ill it U-^ZlTLZlnZT ""•^™- 10 seconds hence ? ^ ^^'"" ^.11 be its velocity b; '-2 fXTieid^r ;tr "r,^^"'"'" --"'■'^'^ ^^^^ instant named ? ' '"" *" "^ "'"''"y « '^'"onds after U>e veloc.y at the end of the first second ? (J, Wh^at th- / ." tenth second ? (e) What at the end of J of i ZloLl "' ""' 18. If the initial velocity of a bodv he 1 f<.„t .„ velocity 2fl feet per second, and its accele^tion 2 ,2 r"""' 'T """' wa, the time consumed i„ ac<,uiring theflnnulX'^""''"'' """ 62 DTKAMIC8 19. A bnllet Is projected vertically upvard with an initial Telocltj: of 40 m. per aecond. What will be its velocity at the end of the third second? 20. How long wUl the bullet named in the last exercise rise t 21. What velocity will the bullet have at the end of the sixth second, and in what direction will It be moving? 22. A penon throws a stone vertically upward to a distance of 78.4 m. With what velocity does the stone leave his hand ? 23. Find the depth of a well in which a stone, if dropped, takes 1^ seconds to reach the bottom. 24. A body falls from a state of rest, (a) How many feet does it fall during the fifth second ? (6) How many meters does it fall during the fourth second ? 26. A stone thrown vertically downward is given an Initial velocity of 40 feet per second. How far will it descend in 10 seconds ? 26. (a) A bullet is projected vertically upward withan initial velocity of 225.4 feet per second. How long will it rise ? (6) How far will it rise? 27. (o) A body falls during 2 seconds. What is its final velocity ? (b) How far does it fall ? 28. A body falls 207.6 feet in 4 seconds. What was its initial velocity? Ans. 10 feet per second. 29. What initial velocity must be given a body that it may rise 6 seconds? 30. Afalllngbodyacquiresavelocityof 68.6 m. per second. How long does it fall ? 31. A body acquires in falling a velocity of 98 m. per second. From what hight has it fallen ? SECTION II COMPOSITION Am> KBSOLUTION OF VELOCITIES 4S. Composition of Velocities. — A body may have several velocities in different directions at the same time. For example, a steamer may be moving at the COMPOSITION OF VELOCITIES 68 «te of 8 miles per hour and a pei^on on its deck may be walk»,g toward it« prow at the rate of 4 miles per hJm^ In th.s case the actual or re,ultant velocity of the p.«on 1 sl.n! T^" r" ""' " '^' I'«'^°" ^"Ik toward the stem, his resultant velocity is 4 miles per hour vefrf'"^''°'I '^^ P"^°" ^"^^ '^^'^''^y ^^^^^ the leWV . ''''''"' g^pWcaUy each of his component velocities by straight lines on a scale of 1 cm. = 2 miles. Thus, line All (Fig. 57) may represent his velocity in common with the steamer, and AC his independ- ent velocity. If ,ve complete a paral- lelogram on these two lines and draw a diagonal, AD, from their junction, this diagonal represents the actual or result- ant velocity. For example, if the steamer's course be due north, then the person faces due west as he walks, but his resultant velocity is northwesterly, ».«., m the direction of the line AT>. His actual velocity .8 represented by the length of the line AD. Thi ite measures 4.4 cm. ; consequently it represents a vel^ t^ ^ per scale of (4.4 x 2 =) 8.8 miles per hour in a S^ tion somewhat north of northwesterly. rt»lT«^ ■■ r^ "''"'*^* "^ '^° ^^^■^^ in the «une •t«lght line is the .Igebndc sum of these yelocitier EuLE 2 : If two velocities not in the same stralirht lln. h. ;^ejj»tedj.y the ad^cent sides of a ^..^^^y^^^l "^^ ^wrl^.r^°*1 ^ ""* ^"^ "' "» I««llelog™^ A- represents u lorce of 2 kg. acting parallel to tiie lirst, with its point of application at D. 48. Composition of Forces acting in the Same Line- Equilibrium of Forces ; Balanced Forces. — When one force opposes in any degree another force, each is spoken of as a resistance to the other. Let/represent the nnm- ber of pounds of any given force and let a foitje acting in any given direction be called positive and indicated by the plus ( + ) sign, and a force acting in an opposite direction to the force which we have denominated posi- tive U called negative ami indicated by the minus (-) sig'i. Then, if two forces, +/and -/, acting on a body at the same point or along the same line be equal, they are said to be halam-ed, and the result is that no change of motion is produced. 5* 66 DYNAMICS Viewed algebraically, +/-/= ; or, correctly inter- preted, +/ -/ =0= (is equivalent to) 0, t.e., no force. In all such ca-ses there is said to be an equUibrium of force*, and the body is said to be in a ttate of equilibrium. Equi- librium is the condition of two or more forces which are so opposed that their combined action on a body pro- duces no change in its rest or motion. A force that produces equilibrium \^\u one or more forces is called an equilibrant. 49. Unbalanced Porcei. — If Mie of two opposing forces be greater than the other, the excess is spoken of as an tmbalanced force, and its direction is indicated by one or the other sign, as the case may be. Thus, if a force of -(- 8 pounds act on a body towartl the east, and a force of - 10 pounds act on the sante body along the same line, then the unbalanced force is - 2 pounds ; i.e., the result is the same as if a single force of 2 pouads acted on the body toward the west. Such an equiva lent force is called a resultant. A resultant force it a single force that may he substituted for two or more force* and produce the mme result that the simultaneous action of the several force* would produce. The resultant of any number of forces acting in the same straight line is equal to the algebraic «um of the forces. An equilibrant of several forces is equal in mag- nitude to their resultant, but opposite in direction. An unbalanced force always produces aeetleration. Hence, a body acted on by an unbalanced foree cannot be at rest, nor can its motion be uniform. EXERCISES xxncnn 1. Bzplaln the um of a line to repnnent a tone. 2. (a) When a force of 160 kg. i. repreBented by * line 16 cm long what . the «ale n^d ? (6) On the «m<, ncale, what force wUl » 26 kg , " "'■"*'"' ' <'> "°" '""f "«»"<» » '""' »* »o repre«nt wlU. force., re..peot,VBly, of 60 pounda, 00 pounda, and 70 pound^ A 1. nearest the end of the rope, B next, and C next, (a) Whrt iaU,^ tenaion of the r„p.. bc-ween A and B P (6) What between B «,d C f in^.r?; ' ^""' ''• '"" ^' """" """ » '""'^ <" 75 pound. In the Zo^t^'r ' "" ''■'"" "'"" '^ •^qoU'lTium, what la the ten- r»rf .„ ■ C'P" "'"'■'*" f »"<• "? (/) Write the equation ahowing the algebraic addition of the force. In oa« of equllZZ 4. The hook, of two spring balance, are connected by a string and the balance, are pulled, (a) If one .^tatera 5 pound., what d^^e other reg«ter ? (6) vvh,^ ,, tho tension in the string ? 6. How i. change of motion pi-oduced ? 6. What effect does an unbalanced force alway. produce f SECTION IV CQBPOSITTOH OF PARAIML FWCSt- OF FORCES 50. Composition of Parallel Forces actiag in the Sunt Direction and ia the Same Plane. •xporimMt.-.IB (Fig. 80) represents a rod is , boria>nt»J position with three strings loosely looped around it m> that they may be slid along tl,e rod. Dynamometers are attaebH to the free ends of the strings. The string, are all atrctched in parallel direotioBs 10 a plane parallel m the top of the tdble. (Gnat can 68 DYNAMICS """!.*" "!',''!' '" "" "■" "'•""" '" ''"'P ""e three .tring, exactly parallel. The dynamc.eten, r^^Uter the le„«i,.„, i., t^ •evernl iitringB, i.e., the forces applied through them to tlii' rml. Observe: (1) Wlien tlioio is cquililMium the ilyrmmoinotei' A' I'egiHte-'^ as much aa do F and O added together. But the force iiijpliod iit C ia the — 8 Fill. 110 equ. hbmnt of the other fo,t;es, „„d thi« is equal to their resultant acting in the direction CJ). (2) The point of apphcation of the resultant (..re.,uilibr«nt) is between the points of application of the components. (3) This point 18 nearer the greater force. (4) The distance of this point from the smaller force is as many times gi^ater than its distance from the larger force as the larger force is times greater than the smaller force. For example, if AF be 14 pounds and JiG be 6 pounds (14 : 6 = 7 • 8) then distances CA and VJl will be a.s - : > . I„ other words, the component forces are said to vavff invertely a», or to be mverteli, proportional to, their distances from their resultant. These observations are summarized as fol- ows The w«Utant of two p«^el force, in the same dfaection 1. equal to their sum, ani th€ dUtances of their point, of appU- catton from the point of appli^Uon of the ie.„lta„t vary invert M the intensities of the components. ^^^ 51. Moment of a Force. -The value of a force for producing rotation about a given axis" is called iU ' An ails 18 a line about which a rotating body tunig. KQUILIBUIUM OK MOMKNTS 69 moment with iffcronco to th.it Hxk Point C (Fig (iU may rt.,,.^.«.nt tho extremity .,f the .«i« about which ■1JI IS Bui (Fig. 63) is {[/] 45 + [e] 25 + [a] 30) + ([c] - 30 [d] - 40 [b] -30) = ; the sum of all the moments being zero, there is equi- librium of moments ; consequently there is no tendency to rotation. 53. Dynamical Couple. — Two equal forces applied to the tame body in parallel and opposite directions not in the same straight line constitute what is called a dynamical couple. The effect of a couple is to produce rotation, but no motion of translation. Since the two forces which constitute a couple are equal and opposite, their resultant is zero, and therefore no single force can equilibrate a couple. Examples of couples are forces applied to a screw-driTer, a watch key, and the milled head of a screw. EXKRCISES 71 Fi 1 M. Moment of a Couple. - Tlie moment of a couple, or Its value in producing rotation, is the sum of the moments of ite two components about the axis of rota- tion, or the product of either force by the distance between their directions. Let F and t\ (Fig. 64) constitute a couple whose points of application are A and B. To find the rotating value of the couple, let r be the axis of rotation; then the moments of /'and f\ relatively to P are F x AP, and F^ x PP. The total resultant moment of the two forces is (F x AP) + (Fi X BP), or (since F = F^) F x AB. Fia. 64 EZSRCISES 1. Two parallel forces of 8 pounds and 12 pounds act In the same direction, respectively, at points A and B, 12 inches apart. Find the magnitude and position of their resultant. 2. Two men carry a weight of 100 pounds suspended from a pole 16 feet long ; each man is 18 inches from his end of the pole Where f"^to oflf *" '""''"' '" """' """ """ ""'' "^y •*»' "■"« 3. (a) A plank weighing 40 pounds is placed across a log so as to be balanced A boy weighing 00 pounds site on one end of the plank. Where shall another boy weighing 90 pounds sit that he may balance the first ? (6) What pressure will be exerted upon the log ? 4. Two horses harnessed abreast are plowing. How can von areange that one horse sliall pull only two thirds as much as the 6. The maximum muscular force which a certain man can exert is .aw pounds. With what leverages can he raise a stone weighing a ton f 6. How can pressure be multiplied indefinitely ? 7. Threeforce8of2, 10, and 12 units act on a body along parallel lines. Show how they may be adjusted so as to be in equilibrittm. 72 DYNAMICS SECTION V CENTER OF GRAVITY point ; body. 55. Center of Gravity defined Let fig. 65 represent any body of matter, e.g., a stone. Every particle of the body is acted upon by the force of gravity. The forces of gravity acting on the particles form a set of parallel forces, the resultant of v;hicli equals their sum (§ 60) and has the same downward direction as its components. In v^hatever position the body may be, the resultant passes through a definite this point is called the center of gravity of the The center of gravity (e.g.) of a body is, therefore, the point of application of the resultant of all the forces of gravity ; and for many practical purposes the whole weight of the body may be supposed to be concentrated at this point. Let G (Fig. 65) represent the- e.g. of the stone. For practical purposes we may consider that the force of gravity acts only at this point and in the direction GF. If the stone fall freely, this point cannot deviate from a vertical path, however much other points of the body may rotate about this point during its fall. Inasmuch, then, as the e.g. of a falling body tends to describe a definite path, a line, GF, that represents this path, or the path in which a body supported tends to move, is called the line of direction. It may be defined as the st straight CENTER OF GRAVITY 78 line in which lie the e.g. of the body and the e.g. of the earth ; its direction is always vertical. A vertical line is indicated by a string supporting a small weight, called a phmh line. A line or plane perpendicular to a vertical line is horizontal. To mpport any body, then, it is only necettary to pro- vide a support for it» c.y. The supporting force must le applied somewhere in the line of direction. The difficulty of poising a took, or any other object, on the end of a finger consists in keeping the support under its e.g., i.e., in the line of direction. Fig. 80 repres«iits a tf)y called a •' witch," consisting of a cylin- der of pith terminating in a hemisphere of lead. The toy will not lie in a horizontal pfsition because when it is horizontal the support is not applied immediately under its e.g. at G; but when placed horizontally it immediately assumes a vertical position, A. It appears to rise ; really, however, it falls, because its e.g. takes a lower position. 56. How to find the C.G. of a Body. _ Suspend the body, e.g., a potato, by a string, as in Fig. 67. When the body is at rest there is an equilibrium of forces, , , "'"' ""« e.g. must be somewhere in the ' line of direction nn. Suspend the body from some other point, as h, and the eg. must be somewhere in the new line of direction h». Since the e.g. lies in both the lines an and Is, it must be at c, their point of intersection. It will be found that, from whatever point the body is supported, Fio. 66 Fia.e; 74 DYNAMICS the point c will always be vertically tiuder the (xiint of xupport. In a similar manner the eg. of any bmly may Iih found. But the e.g. of a body may not be coincident with any )>article of the body ; for exanipli-, the e.g. of a ring, of a hollow sphere, etc., is not within the mass itself. 57. Center of Buoyancy. — Tlie upwai-d pressure against the submerged pui-t of a body floating in a fluid, e.g., the hull of a vessel, is an upward force applied at \the e.g. of the displaced fluid. Hence, the e.g. of the aisplaced fluid is called the center of buoyancy. When the floating body is at rest the center of buoy- ancy and the e.g. of the body lie in the same vertical Fig. fi8 line, as shown in A (Fig. 68), in which m represents the e.g. of a vessel and n the center of buoyancy. If the body be disturbed, as in the rolling of a vessel, the center of buoyancy is shifted, as shown in B. In this case the buoyant force of the water acting upward at n and the weight of the body acting downward at m constitute a dynamical couple tending to right the body. 58. Equilibrium of B'jdies. — A body will rest in equi- librium when its line of direction passes through its point of support. A body will be supported at its base when its line of direction falls within its base or lowest side. STABILIT:. OF BODIES 76 (The base of any lx>dy, e.g., a chair, is the polygon formed by joining by straight lines the points of support.) There' are three kinds of equilibrium : 1. A l.o.ly so supported that when slightly disturl«d it tends to return o ,ts original position is suid t*, be in >UMe e.,uUibrium. This W.U he the ca.se whenever such a disturbance raises its c.s ■ for the weight of the l« is made heavy at the bottom, and ihis lowers its e.g. and gives it greater stability. 60. Weight of a Lever. — In practice we consider that the weight of a body is located at its e.g. (§ 65). For erample, let AB (Fig. 70) represent a plank weighing 20 kg., resting on a prop at C. Its e.g. is at D. We have then to consider a force of 20 kg. applied at D in the direction DE. Let the distance AC he 10 dm. and the distance I>C be 25 dm. Then the moment of the weight of the plank located at 2> is (20 X 25 =) 500. To produce equilibrium a force of (500 -i- 10 =) 50 kg. must be applied at A.^- The plank in this case is regarded as a lever. It is evident that when precise results are required the weight of the lever must be taken into account. What is the pressure on the prop C in this case ? A C B D E 11 Flo. 70 EXKKCISES n ZnRCISES 1. In wlilch of the following canes do«j the e.g. lie iiiilde and n which outside, the body : a straight wire, the wuie wire bent Into a circle, .1 tumbler, a baseball, a football ? 2. Why is a i)yrauiid a very stable structiiiT ? 3. What i,s the object of ballast In a vessel ? 4. State sevinil ways of givini; stability to ail inkstand. B. (a) In what i.ositioii would you plat-e a cone on a horizonial plane that it may ho in stable equilibrium ? (6) that it may be in neutral equilibrium ? (c) ihat it may be ill uu.slahle equilibritiin ? 6. In li«ulins a wagon where should the heavy lugga^'o be placed ? Why ? 7. Why are hiiieds slower in learning to walk than quadnqiedK ? 8. Why is mercury placed In the bulb of a hydrometer ? FiQ. 72 *■ ""^^ ™'" " '""" ^y ""'"S in » Iwat affect Its stability ? 10. Which is more liable to bo over- turned, a load of hay or a load of stone of equal weight ? 11 What attitude does a man assume when carrying a heavy load on his bacls ? Why? 12. What position do bodies floating in air or in water take ? 13. (a) Kxplaiii how the toy horse (Fig. 71) stands upon the platform with- out falling off, tb) Explain how the toy may rock upon Its support without falling off. Via. 73 Ji T8 DTlNAMICS 14. It la difficult to balance a lead pencil on the end of a flnger ; but by attaching two knives to it, air in Fig. 72, It may be rocked to and fro without falling. Kxplain. 16. If the end Cof the triangular frame AB (Fig. 73) be railed and allowed to fall, the frame will rock to and fro on ita support and finally come to rest in its original position, (a) Wliat kind of equi- librium has it ? (ft) If the weiglit at the end li be removed, will the frame be supported by the table ? (c) Why ? 16. Suppose the diatance CII (Fig. 70) to be 40 dm., the weight applied at A to be 100 kg., and the other comlitions be the same a* given In } 60, what force applied at B will produce equilibrium f SECTION VI COMPOSITION OF FORCES THAT AKE HOT PASAUEL 61. Parallelogram of Forces. — If two forces whose lines of action pass through the same point act simul- taneously at an angle with each other, then their resultant (or equilibnint) may be ascertained by means of the parallelogram of force*, as the following experiment will illustrate. Experiment. — Stretch over a sheet of white paper three spring balances R, F, and a (Fig. 74) with strings meeting at a common point, A. Drive nails at B, C, and /) so as to hold the balances taut. Place a block with a straight edge against each string and draw lines on the paper showing the directions in which the several forces act. Note the readings of E, F, and G, which in this case we suppose to be, respectively, 30, 13, and 34. Flo. 74 PARALLELOGRAM OF FOKCKS 79 RemoTe the baUncvs and on some convenient icale \aj off on AB,A C, and .1 1) iliatunces to repn-sent thi correii|ionilinK foreei. Complete the parallelogram AllKL and i. • * the diat{»nal ^lA'. Meuure thi« diagonal, and if the work hi- lecn carefully rlone, it will be found that AK and M) are in the same iitraight line and equal in length. Hut AD in the f, and AX. Fia. 76 63. Resolution of a Force. — A single force may be resolved into two or more component fore m acting at angles to one another. We may take, for illustration, a body, B (Fig. 77), supported on an inclined plane, MN. Let the vertical line A W represent the weight W at the body, whose point of applica- tion is at A, its e.g. Construct, the parallelogram AC WD, and the component ^2> represents the force JF, which tends to move the body down the plane, to prevent which requires (friction between the body and the plane beiug disregarded') a force equal to jP acting in the opposite direc- tion, e.^., the weight S. Component AC represents the pressure P of the body upon the plane. > b ynotksc than Is t1w»ya mote or kM fitotloB, wUoIi HiWa in tin ettpon of Um body oo tiw plaiM. Fio. 77 EXERCISES 81 The triangles A WD ud JfML are equianguW »b<' therefore aimilw. Hence, (1) alao, i£-i^ or— h'ght of plane AW yJU' Jf'lei^ofpUne' .>f. WD(orAC) _ML P length of haw AW NM' W length ofliiiii^' Formula (1) tranHliiteii give, ua the following impor- tant kw for the simple machine called the inclined plwie: WtaM a gtvn fcite acta pnaUil to aa i««H«iH l pUm H win sappert a wrigbt as many tlnss itsdf as ths kacth U the plaat la timss tta vertical Ucht. — •" «• un xzncmt t What ii the greatnt and what the leiHt nraltant of two fonM of 16 pooiide and 17 poundi ? ^*" •aeh other a. ^B „d ^ C In the four dlag™™ (We. 78), and having B B about the lame dlrectlou ; auign numerical valuee arMtrarllv to eaeh convonent, drawing to «,ale, and find the direction «>d the numeriori value of the reewltant of each pair of component* """•rtoal to each other, one of the furces to be 16 pounds. ^^ 11 82 DYNAMICS 6. (a) The bue of u> incllued plane Is 12 feet, its hight fi feet, and ite length 18 feet. What force acting parallel to Che plane will nipport on it a weight of 800 pounds ? (6) What will be the praasure on the plane? 6. What force parallel to an inclined plane 50 feet long and 26 feet high will rapport on the plane a body weighing a ton ? SECTION VII hewtoh'S thsxb i^ws of hotioh— momertok The effects of impressed force on the motions of bodies are concisely expressed in what are known as The Thrtt Law* of Motion, first enunciated by Sir Isaac Newton. 64. Newton's First Law of Motion ; Inertia — A body at rest remains at rest, and a body in motion mores withunlionn •peed in a atraiglit line, unless acted upon by some external force. This law is an axiom; it does not admit of, and does not require, direct experimental proof ; its trnth is uni- versally admitted by all who thoroughly understand ita import. It is directly deduced from the fundamental fact that "every effect requires a cause to produce it." Hence, a body unaffected by any force must remain in the state in which it already exists. By the phrase "unless acted upon by some external force" Newton means that the action must be between the body under consideration and some other body, in contradistinction to an action between parts of the same body. Prior to Newton's time (1642-1727) Copernicns had demon- strated that the whole solar system revolves ahout a common center; bat he failed to point out what it is that keeps tlie SIR ISAAC NEWTON (I642-I7i7) Profound i.iatheraaticiaa, "Prinoe of PbiLOKmher." traceil tlic j.rinclple !ii NEWTON'S LAWS OF MOTION li planets in motion.' Newton, in the law given above, showed that a moving hoily " lefl to itself" does not require any force to keep it in motion. If no force act on such a body, it moves at a unifonn rate in a straight line. It is only when the direction or the speed of the body is altered that we know that force is at work; so that the only force required in the case of the planets is one (gravity) to bend or alter the direction of motion. This law is also known as the Law of Inertia, since it states that no body is capable of altering its state of rest or motion without the intervention of some outside influence. We state this fact briefly when we say that every body has inertia. Inertia is the Latin word for " laziness " ; but la/iness in matter is manifested quite as much in its indisposition to stop when in motion as to move when at rest. The state of motion is quite as natiu-al to matter as the state of rest. Examples of Inertia. — In a railway collision the rear cars maintain their inertia of motion and act like battering-rams on the cars in front of them. The body of a person stepping off a moving car retains the motion it had when on the car ; his feet are stopped as they touch the ground, but the rest of his body falls forward unless the person steps lively. (In what direction ought he to step?) A tablecloth may be so quickly drawn from a table as to leave all the dishes, in consequence of their inertia of rest, occupying nearly the same relative positions that they 1 Kepler, who followed Copernicus, attempted an explanation. His thought was pretty nearly this: that the rays of the sun were like the spokes of a wheel, and that they caught tlie planets and carried them round. A little later Descartes propounded a theory that maintained its ground for a very long time and, strange to say, was the theory advanced in a text-book in use in one of our American colleges as late as 1743. He accounted for the planetary motions >>y his " .system of vortices.** Water moving round and round in a whirlpool will carry with it light bodies, such as straws and chips of wood. He supposed that a vortex or swirl of air or ether revolving aljout the sun carried the planets with it round and round in a similar manner. ■i' ii 84 DYNAMICS hurt before the cloth was withdrawn. When a carpet in beaten the carpet is propelled forward, but the dust lags beliind. When water flowing in pipes is suddenly turned off, the shock produced sometimes bursts the pipes. It is only on the assumption of the correctness of the Law of Inertia that it becomes possible to cal- culate the times of eclipses and of tides, the different phases of the moon, and the motions of cek.jtial bodies generally, as given in almanacs. " Uniform velocity " in the case of bodies is nowhere found in nature. Moving bodies always meet with resistances, that is, tiiey are always acted on by external forces ; but the more the resistances are removed, the more nearly uniform is every motion. If a stone were thrown along a surface of perfectly smooth ice without encountering any resistance from friction or from the air, its motion would be uniform and "in a straight line." 65. Momentum. — If two bodies, one of which con- tains twice as much matter as the other, move with equal velocities, it will require twice as great a force to stop the more massive body as to stop the other in the same time; or the same force will require twice as long a time. Hence, we conclude that of two bodies moving with the same velocity the body that has twice the mass has twice the " quantity of motion," or, in scientific lan- guage, twice the momentum. Momentum is not velocity, but involves both mass and velocity. A moving point has velocity but not momentum. The. momentum of a body it a quantity measured by the produ I of its mass and its velocity. A unit of momen- tum is the momentum of a unit mass moving with a NEWTON'S SECOND LAW 85 unit velocity. If a body contains 80 g. ,.f n,atter and moves at 11.0 nUe of 100 c.n. per «ee,md, it l>a« 8000 units ot niomentuni. 66. Newton's Second Law. - Change of momentum take. puce .n the di«ction in which the force acts, .„d 1, p^t^ to its intensity and to the time during which it acts The fi,«t law stated that force alone can j.roduce a change of motion; the second law tells us how the change d..,.ends on the magnitude and the direction of the force. This law (except as rega.xls direction) is expressed in the following formula: ft^mv, in which m is the mass of the body, . the change of velocity, nw the change of momentum, ./-the force that produces the change, and t the time duiing wliich the change is made The prodiut ft signifies that change of momentum .8 proportional to the time, t, during which a force acts and to the intensity, /, of the force. We infer from thus equation (1) that „ definite force acting upon any free body for a i/iven time will came a change of velojy which u inversely proportional to its mass. This law declares, by implication,' (2) that an unbalanced force always produces in a yivcn time exactly the same ehanae of momentum, regardless of the mass of tJce body that an unbalanced force never fails to produce a change of momentum; an.l hence that any force, however small, can move any free body, of however yreat mass. For ex.a,„,,l,, .a d.il.I ca„ n.ove a free l.ody h.,ving .. ,„a„. „f a ton, and the momentum that the child can generate in this > No reference ia luade in the law to the ma., of the body aeted upon. 86 DYNAMICS immense body in a giren time is precisely the same as that which he would generate by the exertion of the same lorce for the same length of time on a body having a mass of, say, 10 pounds. Momentum is the product of mass by velocity; so, of course, as the mass is large, the velocity acquired in a given time will be correspondingly small. The instant the child begins to act, the immense body begins to move. Its velocity, infinitesimally small at the beginning, increases at an almost infinitesimally slow rate, so that it might be many minutes before its motion would become perceptible. This law declares, by implication, (3) that a force acting on a body in motion produces just the same effect as \f it were acting on ihe same body at rest, for no reference is made in the law to the state of the body acted upon. Experiment. — Draw back the rod D (Fig. 70) toward the left, jnd place the detent pin c in one of the slots. Place one of the brass balls on the projecting rod in contact with the end of -: i=-— ■ ,.„^ \ • \ J 1 i i Klo. 7i) the instrument, as at A. Place the other b .11 in the short tube B. Raise the apparatus in as great .in elt^vation as practicable, and place it in a perfectly horizontal position. Release the detent, NEWTON'S THIRD LAW 87 and the rod, prn|»>llp(l by the elastic force of the spring within, will strike the ball /i, projectinK '' "' » horizontal ilirectlon. At the same instant that Ji leaves the tube and is free to fall, the ball A is rulcased from the nxl anil begins to fall. The sounds made on striking the flcM>r reach the ears of the observer at the same 'nstant ; this shows that both balls reach the fliHir in sensibly the same time, and that the horizontal motion which one of the balls has dcM^s not affect the time of its fall, i.e., does not modify the effect of the force of gravity.' - To every action thete ia an 67. Newton's Third Law. equal and opposite reaction. This law virtually states that all forces are of the nature of a stress (§ 12) or a reciprocal action between portions of matter. We are accustomed to say that one of two bodies acts upon the other, and the latter reacts upon the former. Every action is either a /mil or a pmh. We cannot conceive of a pull or a push except between at least two bodies or two parts of the same body ; there is no such thing as a one-sided pull or push. As the Chinese proverb declares, " You can't clap hands with one hand." The wings of a bird act upon the air, giving a certain portion of it a rearward motion ; the air reacts upon the wings, giving the bird a forward motion. The bat strikes the ball, imparting to it an acceleration ; the ball reacts upon the bat, giving it a negative acceleration. If action and reaction were not equal, there might be a possi- bility that a person standing in a basket might raise himself by » This principle ol the imlependence of forces ai;ting simultaneously was an experimental discovery made by Galileo. Before bis time it was held that one cause must cease to act before another can commence to do so ■ and, accordingly, it was believed that when a projectile wag shot into the air the force of projection must be expended before any tendency to fall could assert itself. In reality, however, after a projectile leaves the muzzle of a gun it is unsupported, no amount of velocity in a horizontal direction furnishing any support; consequently the projectile must beirfn to fall the moment it leaves the muzzle. lii DYNAMICS pulling on the handles, that a vessel might be propelled in a calm by blowing against Hs sail with a powerful bellows fixed to the deck of the 8«me vessel, that a person sitting in a buggy might give himself a ride by pressing his feet against the dasher, that a person might advance without pressing the earth benaath him, or that a bird might fly without having the external air to act upon. Ajipearances sometimes seem to contradict the above state- ments. For example, a man stamling on a wharf pulls a distant boat by means of a rope. The boat moves as the rp»alt of the pull, but, though he is bracing himself against the wharf, he is not willing, perhaps, to concede that he is likewise i)ulled. Let him stand in the boat and pull the rope which is attached at the other end to the wharf; both he and the boat move. What body, according to appearancei, is pulled in this case ? What bodies are actually pulled ? A very instructive illustration of the principle of reaction is furnished by the following experiment : Susix^nd by a strong sewing thread, A (Fig. 80), a metal ball, H, weighing from 5 to 10 pounds. To the lower side of the ball attach another thread, C, of the same kind. Now either of the two threads may lie broken at will. If, grasping the lower thread at C, you pull gently and gradually increase the pull, the upper thread will break, because, in addition to yonr pull, it is pulled by the weight of the ball, while the lower thread is affected only by the pull of the hand. But if you pull the lower thread with a sudden jerk, the reaction of the ball due to its inertia will cause the lower thread to break. In the case of action between two free bodies, the law .mplies that the momenta generated by the action and by the reaction are equal. The recoil of a rifle affords a good illustration of this. The gases liberated by the explosion of the powder inside the barrel exert equal and opposite impulses on the ball and on the Fio. 80 EXEBCISE8 go gun and cause them to move in opposite directionH ^utit ;t l';r' ^'^ -'^^•^ °^ ^"^ '^ - ^ - rifia he 10 feet ,.r Jond Th "I " ""'^''^ "' ""' the i„„ta„t is (5 xTo=)'v,?„ tV ;Tr"""" "' *'" """ "' 800 feet per second i, the maximum velocity of the ball. "* EZXRCI8IS .owe'; S TLZ: '"""""" '"" '^^ "■- " --he. .he a Jp a"r,:;,r: r rrsi":: ':i z:::r r "»'« "■-«'- jumping vertically upward ? ^""' '*^""'* "^ """P'? 3. How are we made aware of the existence of foree ? 4. Is perpetual motion possible ? 6. A carriage is suddenly stODped and >h<, ^. be .. thrown out." Are .he/«A"' ' '^"'^" "" "'" '^ 6. (a) Why may a man raise himself by nulling .„»..„< . ■ bar, but not by pulling on any part of his neZ, ? !> t •■"' f "*" is he acted upon by an externa7fo.™;T)Tthe'L JI^'"','":: body receives .he action and which the ti'll; ,d) ^^^T. ^ce.ves t e action in the second case, and what*":::eiv'lheTac«o:' 8. What agent is the immediate cause of motion ? 9 Whatdistinctiondoyoumakebetween velocity and momentum? ™n w ^r" I ^""^ "" "■o"^""''" given to a ball fired from a gnn by the expanding gjises depend ? 11. Inasmuch as the ball and the gun mentioned in Exercise 10 are affected by equal forces and for the «.me length of .ime^„w will the momenta communicated to the two compare ? 90 DYNAMICS 12. If there be 3i ponndi of matter in the gnn and 1 oqhm {ft lb.) in the ball, and the gun acquire a mazlmum Telocity of 3 feet per ncond, what, at that IniUnt, li the Telocity of the ball t 13. Can any body be put in motion in no time, <.e., does It require time to change the motion of a body ? (Demonstrate from formala ft = me.) 14. Compare the momentum of a car weighing 60 tons, moTing 10 feet per minute, with that of a lump of ice weighing & hundred- weight, at the end of the third second of iu fall. 16. With what velocity must a boy weighing 26 kg. move to have the same momentum that a man weighing 80 kg. has when running at the rate of 10 km. per hour ? 16. Since /C = mv, to wtiat is change of momentum proportional ? 17. If the same force act for the same length of time upon bodlea baring different masses, to wliat will the velocities produced be proportional ? I: 18. Two boats of unequal masses are brought together by pulling j] on a rope, (a) Resiaunce being dinregarded, how will their momenta if at any given instant compare? (6) Huw will their Telocitlea at the 1 1 same instants compare ? 19. If the motion of the moon in its orbit about the earth were to cease, these bodies would approach each other. The mass of the earth is about 80 times tliat of the moon. What part of the whole distance between them would the moon move before collision ? 20. (a) Why does not a given force, acting for a given length of time, (five a loaded car as great a velocity as an empty car f (6) After equal forces have acted for the same length of time upon both can, and have given them unequal velocities, which will bo the more difB- cult to stop ? 21. (a) The planets move unceasingly ; Is this evidence that there are forces pushing or pulling them along ? (6) None of their motions are in straight lines ; are they acted upon by external foi'ces ? 22. A certain body is in motion. Suppose that all hindrances to motion and all external forces be withdrawn from it, how long will it move? Why? In what direction? Why? With what kind of motion, i.e., accelerated, retarded, or uniform ? Why ? 23. If one body have four times the mass of another, how must the forces applied to them compare in order to give them equal momenta in equal times P CONSTANT FORCE ^ 86. Which Uw of motion 1. ,„„..„,,d by ,h. .-kick " of . gun f how^uh'e'rrrsr-KS""-''^"^-'''''^---''- SECTION VIII ""ASUMMBT OP FORCE IN ABSOWTE UWITS 68. Constant Force. - A constant foree is a force that acta continuously and with uniform intensity. Such a W IB gravty. We have seen in the case of fin. bodies that a oonHuM force acting on a free hody WuT« uniformly acceUraUd motion. "■y proauett eratlott -Force is known to exist only by its effects • hence, . can be measured only by measuring its effete Newton's Second Law of Motion teaches how f orce m^y te measu^d. We learn from this law that force teZ to produce a change of momentum. From the formula (§66) /. = .„.. eobtain/=^. From the latter for- mula we infer that force is measured by the quotient 2!!, in other words, by the change of momentum it is capable 92 DYNAMICS of producing ia iu line of action per unit of time. But change of velocity per unit of time fie., -) In wpre- sentetl by a; hence, /= — - ma. If the fnctow m, v, and t are each equal to 1, then the force is equal to 1. ^ unit force, theit-fore, i« ajorce tehieli -Ing for a unit of time, will give to a unit mat$ a unit velocity. A constant *orce of the requisite inten- sity to produce in a grnm-hiass a change of velocity of 1 cm. per, Becond, i.e., an acceleration of 1 cm., is called a dgne. The dyne is independent of the force of grav- ity; hence, it is called an abiolute i unit of force. (In this connection § 15 should be reviewed.) Any mass falling freely re- ceives at Paris an acceleration of 980.96 cm. per second; at Boston, 980.4 cm. Cotuequently a gram- mass weighs at Paris 980.96 dynes; at Boston, 980.4 dynes. The letter ^r is usually suijstituted for a in representing the accel- eration produced by the force of gravity at any given locality; so we pay, in general, that the weight of a fjram-m.Tss is g dynes. It is apparent that mass, force, and rate of change of velocity, or acceleration, are quantities closely related to one another. If v ,) wish to measure mass, we can do so by calculating the Fio. 81 GALILEO (1564-1642) MatheniMli-lan, Mlronomer, iibviicint ■■ fn„„.i . > GALILEO'S EXPERIMENT gg acceleration which would be imparted to it by a given force; if we wLsh to measure force, we calculate the acceleration which it would impart to a given mass. 70. Galileo's Experiment with Falling Bodies Gali- leo let fall from the top of the leaning tower at Pisa> iron balls of widely different masses, and found - that they readied the ground at apparently the same instant. This celebrated exiieriment established the important fact that the acceleration of a falling body due to the force of gravity in independent of itg tnass. This proposition is apparently contradicted by every- * day experience, for if a coin and a featl.er be dropped from a higbt, tbey fall with very different velocities. But if a coin and a fi'ather be placed in a long glass tul)e (Fig. 82), the air exhausted, and the tube turned end for end, it will be found that the coin and the feather fall in the vacuum with equal velocities. It is evident, then, that when there is a difference in the - acceleration of falling bodies at the same place it is due ^'°- *^2 not t» the force of gravitation, but to some other influence, for example, the resistance of the air.' 4i EXERCISES 1. (a) Can the masses of two bodies at different altitudes and lati- tudes be compared by using the same spring balance at the different places ? (6) Can the masses of two bodies be compared by weighine with a trip balance without knowing the force of gravity at the pLe ? ■This builrting (Fig. 81), consisthiK of a series of open galleries one above another, reaching .o a total high. „, 179 feet, Is admirably adapted to the purpose here melitioncii. ' '^ ■'The investiga„o„ by G-'Heo of the motion of falling bodies wa. one of the first steps in the development of modem science. ""'"«''« 94 DYNAMICS 2. What part of a gram-force is a dyne ? 3. Define a gram-force and a dyne. 4. A constant force acting on a free body produces what effect ? 6. To what in the acceleration produced in equal maseeg propor- tional ; i.e., if m is constant, a will vary as what ? 6. On whatcondition will equal forces produce equal accelerations f 7. Suppose that you fill a box with sand, place it on a toy cart, pull the cart by a string with a constant force along a smooth floor for a certain number of seconds, and observe the acceleration given the load (cart, box, and sand), then remove the sand and replace it with lead shot. How can you tell, by pulling the load with the same force as before, when it has the same mass as the former load ? 8. (o) When we speak of a force of 1 pound what do we mean f (6) When we speak of a force of 1 dyne what do we mean ? (c) When we speak of a mass of 1 pound what do we mean ? 9. (o) If one mass b^ four times another, how many times as .much force is necessary to produce the same acceleration in the former as in the latter? (b) IIow many times greater is the force of gravity acting on a mass of 100 pounds than that acthig on a mass of 1 pound ? (c) If a 100-pound iron ball and a 1-pound iron ball be let drop from the same hight at the same instant, which ought to reach the ground first? 10. A mass of 4 g. is moving with an acceleration of 12 cm. per second. What is the force acting ? 11. A body acted on by a force of 100 dynes receives an accelera- tion of 20 cm. per second. What is its mass ? 12. A mass of SO g. is moved by a constant force of 60 dynes. What is its acceleration ? 13. What acceleration will a force of 20 dynes produce on a mass of 10 g. ? 14. A mass of 4 kg. falls freely. What is the value of the force acting upon it ? Solution ; /= ma ■=4000x380 = 392 X WdynM. HOW CURVILINEAR MOTION IS PRODUCED 95 SECTION IX CURVILIMZAR MOTION 71 How CurvUinear Motion is produced. - Motion is a^n,^l^near when it« direction changes at every point. Acconhng to the Fi:.t Law of Motion, every'inoving body proceeds m a straight line unless con.pelled t! depart from ,t by son.e external force. Curvilinear motion can be produced only by an external force acting contmuousl- upon the body at an angle to the stmigh! path in wh:ch the body tends to ,„ove, so as constantly to change .ts direction. In c^e the body moves in a circle, this force acts at right angles to the path of the body, or toward the center of motion ; hence, this deflect- ing force has received the name of centripetal force. Thus suppo.se a l.all at A (Fig. ,s:!), su«p..n,led by a string from a pomt. rf to be struck by a bat in suel. a manner that it tends to r; ;; th r'-"" ■';• :'- *' '^ "'^*™""^'' ^™™ »»"-« '^^^ path by the tension of the string, which operates like a force drawing ''■ it toward d, it takes, in obedience to the two forces, an intermediate course. At c its motion is in the direction en, in which path it would move but for the string, in accordance with the First Law of Motion. Here, again, it is compelled to take an intermedi- ate path. Thus, at every point the tendency of the moving body is to preserve the direction it has it that point and consequently to move ,n a straight line. It does not so move becaus! at eve^ ^.nt ,t .s forced from its natural path by the pull of the string But If the string be c»t when the ball reaches the point ,; the !1 ¥ i 1 96 DYJfAMTCS .„ h« H ^"° "V^ """^ *" "•'""Se its motion, continue, in the direction m which it ia moving at that point, f. in the d.«ct.on ,A. which i, tangent t<, it, former circfar p^th If the free end of the string be held in ti,e land, the ball while revolving about the hand appears to pull the ha;d But it ! hind on h Tl " tT- "" *'"' '"^"- -' "'« ^"^ exerted ;, ha^d on the ball. This reaction is commonly called cenj/urjal f. It "^^ °w.*?'^*"' ^'"''- - 'T'^ ^''« ^"'l "f » string to a stone. Whirl it around your hand, and fcel the null How great ,s the pull? You will discover tiu!t it depends on ^^. masj of the stone, ike length of the string, and the s^vrftness of the whirl. Suppose the stone to L as massive as the earth, the length of the string to ts orbit. The pull then would represent the gmvita- t.o.i stress that l.olds tlie earth in its orbit about the sun. Law: For . body moving in a cireular orbit, the centrinet^l th™/""'rf "'' ''"'"^'^*''' ^°'<=«' "> «'« ™««« of drcir 71 ^ " '^^ "''°"'y' ^"^ •• ''"' -di- of the /=^. r farther it h., to move during a rotation ,- consequently the greacer must be it. velocity to complete a revolution in a given time. LAW OP CENTRIPETAL FORCE 97 ooQ • .1 'cii.itncj at tli(3 former n hite Rut 'vould weigh nothing. ^ "'" '^^''""*•"• S e, ,,, containing a quantity of colored liquid, h-,,,.,, Flo. 84 the globe is rotated the li,,ui,l gradually ri ., and f torial ring within tlie ,rl„l j 1 ^.*"'7'-^ " ^ ""d forms an efjua- manner the w!, J f *' ':",'"« ""= '■°"»"' "r.v. In a similar ' °^ ""• <=""' ■■' S-^^t ocean is . heaped np " at li 11 98 DYNAMICS the «,u.tor. If the earth we™ to ce«e to rotate, the water at tto «,uator would flow toward the polar region,, forming two JlJ^i'°^ ?Jl'- ^^ ™"**''" "'""''• °' differenrdenaitie^ o^Z ^^ "":'*^.».'" «'"''*' -"• fo™ concentric ring, in the tangential tendency, a, may be inferred from the law given above • ^n«>quently ,t will form the outer ring. It i, on thi, principle that cr,am .eparalor, are ope.ated. The milk is caused tc rotate rap.dly in the separator, the rx>tation separating the heavier ^.rTh t .^ ' T'°"^ '•"' °"*«' '"^^ '^- t''" lighter proper time for drawing off each liquid while in motion into separate vessels.' In public laundries clothes are dried independently of the weather by being plac,d in wire cages and rotated with great speed; the water is separated from the clothes in much the «me manner as mud is separated from a rotating carriage wheel. When a grindstone in a machine shop, or the fly wheel of a steam engine, is made to rotate so fast that the cohesion of ito part, IS no longer able to keep them moving in thei.^ circuUr S'veloIiJy":^ *"" **"' '"*""""' '' °" '""^"^^'y -«• EZIRCISXS mL.}tJ^ " *"• ^"^ <" »''« stretehlng force exerted on the rubber cord when you swtag a return ball about your hand f (6) Sup. po« that you double the velocity of the baU, how many time, do7^ increase this stretching force ? j <» uo you 2. Why do wheel, and grindstones, when rapidly rotaUng, tend to break, and the piece, to fly off? ""«. wna lo .J\, ^ ^'""?°«'*« "'^^"""•ie of the pull between a rotating body and ite center of motion depend f » By this proce«i there Is not only a great gain in the freshness of the products Obtains! bnt also in the matter of Ume, for a mS^ ™l,ete boon by the old-time method of leaving the cream to " rise." GRAVITATION IS UNIVERSAL 99 turning"! ^^fr" ',m f"*" "»'.' ""^ "" ^ "r^rtor^ ,„ 8. Account for the eunilineaT orbit, of the planeti. 6. What 1. the centrlpeul force i» planetary moUon« f tangential tendency of » railway train when going around a curr"f dei^Vthrea'^irf"'"'^''''''-^'-"'^"^'""- i| SECTION X GRAVITATIOH 73 Gravitation is Universal. _ We know that we ourselves and objects about us are pulled toward the earth by a force (weight) which is caUed (the Latin expression employed by Newton was gravita,) gravity. Sir Isaac Newton was the first to show that this force, better called ,tres», existe between bodies sepawted by any distance, however great; in other words, that there « a »tre,» between every body of matter in the univeru and every other body. The force which causes a body to fall to the ground 18 none other than that which continually corneals the moon t» accompany the earth in ite path around the sun, and which keeps the earth itself from fleeing off into space, away from the sun. This mutual action which exists between all bodies is caUed univer^l gravu tatxon Newton discovered the law which expresses the character of this action. Why bodies attract one another, however, is as much a mystery as ever. f: f| 100 DYNAMICS 74. Law of Gravitation, — The Law of Universal Gravitation is as follows: The gtavltoUon itreM between every two particle* of matter In tbe unlvene varies direcUy «s the product of their dumm, and Inverwly u the iquare of the distance between them. If the masses of two particles be represented by m and m', the distance between their centers of gravity by d, and the gravitation stress by/, this relation is expressed mathematically thus : ,1, . mm' For example, if the mass of either particle be doubled, the product {mm') of the masses is doubled, and conse- quently the stress is dcdbled. If the distance between them be doubled, then (^ = 1) the stress becomes one fourth as great. 75. Law of Weight The term weight h restricted ui Its application. It is applied only to the force with which terrettrial bodies are drawn to the earth. Since the masses of both the body and the earth are supposed to remain the same, in applying the law of gi-avitation for the determination of the relative weights of the same body at different localities, the masses of both bodies are disregarded, and formula (1) becomes, substi- tuting w (weight) for/, 1 (2)w<. d^' or, expressed in a more practical form, (S)w:w':: — -1-, LAW OF WEIGHT joj the earths center and ,. and «,' represent the corre spondu.,.,i,,^ of the body at the different llS; Jows '"' "^ '"'"""•^'^ '" "- ^-° °^ a '- - from the ,.les to the equai due to tl '" ' 'r'"'"'''' from the center of the eX! . '™'"*' "' '"»'»"<=« at the pole«. But Z h„v ' "I""" '" '"' '*" "* ''" ^^'Kht gential tendencv at Th *"'^" '■"^""'"'^ "-' (§ 72) that the t;,.- 1 W ^ "''"""' dinuni»he8 the weighi of a 1,,k1v rotation, a oody weighs at the equator Ul, + A -1 I T than at the poles. ^*' ~^ ^*- '*"" theTanhrsure^h '"V ":''^'" """ " •'""y -'«•"' ">- at nir .r " "'""''' '" '" •"•""• *""•*. I'odies become Ighteras theyare raised above the earth's surfkce. But ,1 .ne force d.n„„,shes as the square of the distance from the ce^r 4000 miles from the center, the diminution for a few mile, or r any distance which we are able to raise bodies is scare yper ceptible, hence, in all commercial transactions we may, without .mportant error, buy and sell as if the weighing always Lk plLe at the same distance from the center of the earth, in Wiich IL mass IS strictly proportional to weight (§ 7). EXERCISES ie^ol?J:V:.r.''.!f*"^'^l°' r- -'«"» - *e accelemion (6) Which varies as the mass? due to the earth's attraction ? 1 27 Lne;)Tho^rth"'"'r"' "' ""'" ''"'"*'«' '"'-« •"><'« « "".• (nearlx ^1 mues) shorter than its equatorial diameter. ' 102 DTKAMIC8 «. Why doM a 100-ponnd Iron tall bll with no gnstcr acoelerv Uon than » 1-pound ball of the Mune nuteri*! r 8. If the wnh'i mui were doubled without »ny chuge of TOlana, how would the change affect weight r 4. How many Unuw muit yon IncreaM the dietance between the centers of gravity of two uniform ipheree In order that the jraTlUtlon ■tree* tatween them may become one fourth aa great T 6. (a) If a body on the aurtace of the earth be 4000 milea from the center of the earth, and weigh at thU place 100 pound*, what would the larae body weigh If It were taken 4000 mi!e« aboTe the •arth'e aurface r (») What, 2000 mIlea above the earth f (c) What, 100 miles above the earth ? 6. If In Boston g = 980.4 cm. at sea level, what is the value of g at a point 6 mile* above sea level t 7. What retains the planets In their orbits ? & If there were but, one body of matter in existence, (o) would It have weight 7 (b) would It have maaa ? 9. What ia the character of the motion produced by a constant force acthig on a free body t 10. If the Eaklmo children Indulge in the aport of coasting, why may their sleds inn a little faster than those of the inhabitants of lower latitudes t SECTION XI THE PEHDULXIK 76. Laws of the Pendulum. — A body so supported that it can swing to and fro about a fixed axis under the action of a force ia called a pendulum. Experiment 1 — From a bracket suspend by strings leaden balls, as in Fig. 85. Draw B and C to one side, and to different bights, so that B ma • swing through an arc of, say, 5°, and C through an arc about twice as great, and let both drop at the same instant C moves faster than B, and completes a longer journey at each swing, but both complete their swing, or Tibration, in the LAWS OF THE PENOULUlf 108 ¥ SI snrit:"^'''^*^^*^ •" '-*'---»- Bxp.rim.rt 2. -Set Jl th. b.U. .winging: only B and C « u ^f '"' "" '*""*" '•" pendulum, the tutor it .wing.. Make B 1 m. long and F J m. long. With watch in hand, count the vibra- tions made by if. It completes sixty vibrations in about one minute ; in other words, it "beats seconds." A pendulum, therefore, to beat second* must be 1 m. long (more accurately, in the latitude of Boston at sea level, .093-) m., or 80.117 inches). Count the vibrations of F; it makes 120 vibrations in the same time that B makes sixty vibrations. Make G one ninth the length of B : tlie for- mer makes three vibrations while the latter makes one j consequently the time of vibration of the former is one third that of the latter. Hence, (2) the time of vibntion of • pendulum varlee m the .quaie root of ito length, or, t-.t'i-.y/l-.y/v. Since the number of vibrations made in a given time vanes inversely as the time of one vibration {i.e.,n..n'....\..\), it foUows that (3) the number of yil«tion. made by . -hn^°.''^''""'"° "' "" pendalum was discovered (1883) by Oalileo it Fio. 85 104 DYNAMICS ttat Ingth tt tb» pMidtdnm, or, «:«'::V4. Since the motion of a pendulum ig due to the force of gravity, it follows that where this force is greatest the time of vihration is shortest. Inasmuch as the force of gravity varies with the latitude of the place (§ 76), it follows that the time r.f vibnition of a pendulum at different latitudes vari s. By methods too diflTicult for school purposes it may be shown that (4) the time of TlbntUm of ■ pendulnm varie* Invenely u tlie iqiun nwt of the accdentlon (j) produfied by gnvlty, or, The relation Ix-tween the acceleration at any locality, the time of vibration of a pendulum, and the length of a pendulum is such that if any two of these quantities be known, the third can be calculated from the follow- ing formula ' : - > whence, g = —r-. The determination of the value of g at different parts of the eurth ia of sucli great interest in many ways that various govern- ments have employed skilled men to make careful pendulum observations in all acceBsible regions of the earth. 77. Simple Pendulum ; Center of Oscillation Aiiim- ple pendulum is a sizeless mass supported by a weightr less thread. Such a pendulum can exist only in the ' In this formula t represents the time of a single swinr from on« extreme position to the other. SIMI'LK rKNDUMTM lOS imBgiimtion, but the conception L iw-ful. Every real pendulum ia a compound prndulutn, wliitrl, miiy l*. Miip. posed to be comixwed of aM many itiin])le iwndulunw bound together ax there are jwrtirli-s in the i)endulum.' Thooe particles nearest the point of KU8i)enHioM tend to quicken, and those furthest away tend to c-he.k, tlie motion of tlie combination. It is ai)iMii-ent that there must 1)6 in every compound iK;n(lul.im a particle so situ- ated that its motion is neither (inickened nor checked by the combined .u.tioi. of the particles iik.ve and Inilow It The location of (his particle is called the emh-r of OBcillation. The m.l l.;„jth of a compound pendulum IS the distance of ihis jH.int from the jmint of ausj^n- sion, and it is this length that is referred to in the laws of the pendulum. Weight* (C81I...1 *„&,)„„ usually attached t<. (he lower eu.is of pendulun,rod». whi.h serve to brin^: the center of o»cill.tio,. low down ,„ the ,».,„lulu„. 1 il,„,, j.,,,,,,,,.,, „,.. ,i„„ „f ,,i,„ti„„. The time of vl.rati..,, of a ,K.„dul„„, U shortened or lengthened at W.I l.y raiMng or lowering its hob, which is usually accoin. pushed by turning a thumbscrew just l«neath the bob. EXERCISES 1. In the eiperimcnts t'ivui. above, the arcs of vibration of the I»ndu urns slowly decrease in si.e. I)„es this alter the time of vioration ? de \d*^" "*"' ""' "''"'"' ''""' ""' """' "' "'"■''""'' "' » Pei'dulnm 3. Ought the weiRht of the 1,„1, to aflcct the tiu.e of vibration of a pendulum? (.St!e § 70.) ' The lighter the threads an.l the s,„allor the balls used in the above experiments, the more .los.ly do tl,e ,».,„l„l,u„s approximate ,o simple Z,^T'^ /' is sultlH,.,„ly a,,. ,e i„ these ex,K,rime„,s to oou.lier the centera of oscillatiou of the pendulums to be at U» centers of the balta. 106 DYNAMICS 4. State the chief common uae, and the chief acientiflc u«e, of a pendulum. 6. (a) What is the length of a pendulum that beats half seconds f (6) quarter seconds P (c) that makes one vibration in 2 seconds? (d) that makes two vibrations per minute ? 6. SUte the proportion that will give the number of vibrations per minute made by a pendulum 40 cm. long. 7. How will the periods of vibration compare in the case of two pendulums the lengths of which are, respectively, 4 feet and 49 feet ? 8. Two pendulums make, respectively, fifty and seventy vibra- tions per minute. Compare their lengths. 9. How long must a pendulum be to riake one vibration in 6 seconds in Boston? 10. One pendulum is 20 inches long, and vibrates four times as frequently as another. How long is the other ? 11. What effect on the time of vibration of a pendulum bas the length of the arc ? 12. How can you quicken the vibration of a pendulum threefold ? 13. A clock loses time, (a) What change in the pendulum ought to be made ? (6) How would you make the correction ? 14. Two pendulums are 4 and 9 feet long, respectively. While the short one makes one vibration, how many will the long one make ? 16. What Is the time of vibration of a pendulum (39.09 .=- 4 = ) 9. 77 inches long ? 16. If a certain pendulum vibrate once a second, what is the time of vibration of one twenty-five times as long ? 17. (o) How will the time of vibration of a pendulum be affected by taking it to the top of a high mountain ? (6) by toking it farther from the equator, i.e., to a place of higher latitude ? 18. If a clock keep correct time in Chicago, what change In its pen- dulum must be made that it may keep correct time in New Orleans ? Wv>RK 107 SECTION XII WORK, ENEFSy, «H2 POWER 78. Work When a or a causes :i change of motion or maintains motion agi iiui rRiiatance, it is said to do work. A force to do work must effect a change of posi- tion. Force and distance are essential to work. An unbal- anced force always does work, inasmuch as it always causes a change of motion or overcomes resistance. The force that moves a body is said to do work upon it, and the body that is moved is said to have work done upon it. When the heavy weight of a pile driver is raised, work is done upon it ; when it descends and drives the pile into the earth, work is done upon the pile, and the pile ia turn does work upon the matter in its path. 79. Energy — The energy of a body is its capacity for doing work. The work done by a body, or done upon a body, is a measure of its loss or gain of energy ; hence, work and energy are measured in the same units. The act of doing work consists either in a transfer of energy from the body doing work to the body upon which work is done, or in a transformation of one kind of energy into another kind. For example, when the pile driver strikes the pile and the pile is forced into the earth, a portion of the energy of the pile driver is trans- ferred to the pile, since the pile is made to move ; another portion is transformed into heat at the point where the blow is delivered. It will be shown in a future chapter that heat is a form of energy. Work, therefore, may be defined as the act of transmitting or of tranrforming energy. 108 DYNAMICS 80. Kinetic and Potential Energy. — Everj- moving body can do work, because, by virtue of its own momen- tum it can impart motion to otber bodies ; hence, every moving body possenses energy. The energy which a body possesses in consequence of its motion is called kinetic energy. A body at rest also possesses energy whenever its position or condition is sucii that it can move and will move if allowed to do so. For example, a stone raised above the earth and resting on a shelf is capable of motion and ready to move and to do work when the shelf shall bo removed. Every youth knows that when he is on a bicycle at the top of a hill he possesses energy that will carry him to the foot of the hill without pedaling. A " head " of water is something other than water ; it is something associated with matter in virtue of its elevation. The energy of all bodies consists cither in their motion or in their capacity to move. Energy due to capacity to move is called potential energy. It is the capacity f(jr doing work which a body liits in virtue of the fact that its position is tuck that it is possible for it to move, and in virtue of the existence of a stress that tends to move it. A body possessing potential energy is often spoken of as a body having energy stnreil in it. Kxainples : A watch spring and the weights of a clock when wound up have energy stored in them whicli is doled out gradually in moving machinery. We store energy when we bend a how, condense nir, raise a hammer, and stretch a piece of ruiiber or an elastic spiral wire. When a body, e.g., a stone, is proJKct<'d vertically upward, its kinetic energy is rapidly expended in raising the stone against the force of gravity, and entirely disappears when the body reaches its Ligheot point j POTEIfTIAL KNERGY 109 but the energy is by no means lost. It has simply lieen converted into the }X)t<'ntial state ; in otlier words, it lias lu'en stored. It reappears as kinetic energy during the fall of tlif l>ody. Show that in every swing of a pendulum there are two similar trans- formations of energy. It is important to ol)serve that a l)ody acquires energy, eitlier kinetic or potential, only at the expense of wurt. 81. Potential Energy of Chemical Separation Matter may possess potential energy in virtue of chemical sepa- ration against a force called chemical affinity, and the potential energy is a meas ure ojihe work diuie in^effect- ing the separation. 1 FoLexaniple, the entire vjjue of) jcoal consists ui its potential energy, which was 8tf)redl I by the work performed through the agency of the sun's/ / energy in separating the carbon of carboiijlioxidejroml I the oxygen^ Gunpowder possesses potential energy sufficient to do a quantity of work, e.g., in blasting, that would occupy many laborers a long time. The foregoing discus.sions lead to the following con- clusion: a hody possesses potential eiieri/y when, in vir- tue of work done upon it, it occupies a position, or its constituent particles occupy positions, such that the eneri/y expended can be restored at any time hy the return of the body to its original position, or by the return of its particles to their original positions. 82. Units of Work and Energy. — The unit adopted for measuring work and energy is the work done, or energy imparted, when the force of 1 kg. acts through the distance of 1 m. It is caljed a kilogrammeter. The British unit is the work done when the force of 1 pound acts through the distance of 1 foot, and is called a 110 DYNAMICS foot-pound. The kilogrammeter (kgm.) is equivalent to 7.283 foot-pounds. 83. Formulas for calculating Work or Energy Force and distance, being the only elementa of work, are neces- sarily the quantities employed in calculating work. A given force acting through a distance of 1 m. does a cer- tain quantity of work ; it is evident that the same force acting through a distance of 2 m. would do twice as much work. ■ Hence, the general formula : in which/ is the force employed, » the distance through which the force acts, and w the work done. Often the work done upon a body is more conven- iently determined by multiplying the resittance hy the ra ipace through which it is overcome, ''■^i .. and our formula becomes, by substi- tution of r (resistance) for / (the force which overcomes it), (2) w = rt. I "B Flo. 86 Fig. 86 is a pictorial illustration of the work performed upon a weight by the muscular force exerted by the arm against the downward force of gravity in raising the weight to the top of a table. When the weight reaches the top of the table how much energy is stored in it? 84. Absolute Units of Work and Energy If, in cal- culating work by the formula w =/», the fome (/) be expressed in grams, and the distance (») through which it acts be expressed in centimeters, the work (w) will be CALCULATING KINETIC ENERGY 111 expressed in a very small gravitation unit called a gram- centimeter. Bat if force be measured in dynes and dis- tance in centimeters, the work done is expressed in an absolute unit which might properly be called a djTie- centimeter, but which is usually called an erg. An erg is the work done or energy imparted by a force of 1 dyne acting through a distance of 1 cm. Now, since 1 gmm-force is equivalent to g dynes (§ 69), it is evident that 1 gram-centimeter is eauiva- lent to g ergs. The following list of equivalents will be of service in changing gravitation units to absolute units, and vice vena : 1 kilogrammeter 1 kilogrammeter 1 gram-centimeter ■■ = 100,000 gram-centimeters. = 100,000 g ergs. = 5' ergs. 85. Formulas for calculating the Kinetic Energy of a Body when its Mass and its Velocity are known. — Sup- pose a body having a mass, jji, to be moving with a velocity, v ; its kinetic energy can do a definite quan- tity of work before the body comes to rest. Sunpose it to be moving vertically upward, its kinetic energy expending itself in raising the body. If its velocity be such that it will rise to a hight, «, tLen its energy at the start is just sufficient to do (f = ma or mg, § 69) mgs absolute units of work, or (1) E). (kinetic energy) = mgi. We may find, then, to what hight, «, a body having a velocity, v, would rise if directed vertically 'xpward, and 112 DYNAMICS from formula (1) determine its kinetic energy. Substi- tuting ff for a in formulas (2) and (3), § 44, and elimi- nating t, we find » = i^. Substituting this value for » in formula (1), we have (2) £, = TKtl* a formula which will determine the kinetic energy of a body in eryt when its mass, m, is expressed in grams, und itfl velocity, v, is expressed in centimeters per sec- ond, since the kinetic energy of a bfKly is the same whatever l)e the direction of the motion. Hence, the kinetic eneigy of a body, expressed in absolute unita, is half the product of its mass multipUed by the square of its velocity. If the result be desired in gravitational units, for example, in gram-centimeters, the number of absolute units must be divided by g, since g ergs (980) are equivalent to 1 gram-centimeter.* Accordingly, the formula (3) JS^ = ~ will determine the kinetic energy of a body in the gravitational units, gram-centimeters, kilogrammeters, or foot-pounds, accoi-d- ing as its mass, to, is expressed in grams, kilograms, or pounds, -and its velocity, v, is expressed in centimeters per second, meters per second, or feet per second, and the corresponding numerical value of gr be taken as 980, 9.8, or 32.2, respectively. • For convenience in the solution of problems we adopt 980 for the value of g. Strictly, the value of a at sea level in latitude 46° (see, 5 15) is 980.6. ' ' EXERCISES 118 XZXRaSES 1. Do the stones In the Egyptian pyramids still retain the energy that was expended in raising them to their places ? 2. The potential energy of a stone raised above the earth is rep. resented by the expression ,ng, (§ 86) ; on what three things then does it depend ? 3. What quantity of energy will a force of 10 pounds impart to a body in acting on it through a space of 05 feet, if none be lost or wasted? 4. How much work is done in raising 12 cubic feet of water 20 feet? B. How many kilogrammeters of potential energy does a mass of 800 dm.« of water possess when elevated 40 m. above the earth ? 6. (a) Suppose that an average force of 25 pounds is exerted through a space of 10 inches in bending a bow, wliat amount of energy wUl it give the bow? (h) What kind of energy will the bow, when bent, possess ? 7. (a) What quantity of energy must be imparted to a bullet whose mass is 1 ounce (j\ pound) that it may rise 257.0 feet ? (b) What change in its energy is going on while it rises? (c) When it falls to the earth what change in its encryy occurs ? 8. What amount of work is done by a man in sawing through a stick of wood, if he causes the saw to move 10 m. against an average resistance of 5 kg. ? 9. Why can you throw a stone farther than you can throw a cork ? 10. (0) How many foot-pounds of kinetic energy does a mass of 20 pounds, moving with a velocity of 60 feet per second, possess ? (6) How much work can it do 1 11. (0) Refer to formulas (2) and (3), §85, and state how many times the kmetic energy of a body is increased by doubling its velocity. (6) The kinetic energy of a body of a given mass is proportional to 12. A force of 450 pounds acte upon a body through a space of 80 feet One fourth of the work U wasted in consequence of resist- ances. How much available energy is imparted to the body ? 13. A horw draws a carriage on a level road at the uniform rate Of 6 miles an hour, (a) Does the energy of the carriage accumulate ? 114 DYNAMICS (6) Whit kind of energy does the carriage poMew ? (c) Suppose that the carriage were drawn up a hill, would Ita energy accumulate? (d) What kind of energy would it pofBesa when at re»t on the top of the hill ? (e) How would you calculate the quantity of energy It poueaeea when at rest on top of the hill ? (/) Suppose that the carriage is in motion on top of the hill, what two formulas would you employ in calculating the total energy which it iiossesses ? 14. How many kilogrammeters of kinetic energy does a body of mass 600 grams acquire in falling freely 6 seconds ? 16. How mauy gram-centimeters are stored in a watch spring If an averaKe force of 25 g. acts through a distance of 20 cm. while winding it ? 16. How many ergs of work are done in raising 2 kg. of matter 1 m. high where g = 080 ? 17. A certaui body has 000 ergs of kinetic energy. How far will this energy carry the body against a constant resistance of 20 dynes ? 18. (o) A body whose mass is 20 g. moves with a velocity of 12 m. per second. How many ergs of kinetic inirgy has it? (6) Would the answer be the same if tlie body were 4000 miles above the earth ? 19. (a) Show that momentum is a time effect of a force, and that energy is a dittanee effect of a force. (See §§66 and 85.) 20. A constant force of 20 dynes moves a body 100 cm. What amount of work is done ? 21. If the steam be shut off, whence comes the energy that keeps the train in motion for a time ? 86. Power. — In estimating simply the total quantity of work done, the time consumed is not considered. The work done by a hod carrier, in carrying 1000 bricks to the top of a building, is the same whether he does it in a day or a week. But in estimating the rate at which an agent is capable of doing work, time is an important element. The power of an agent, e.g., of a steam engine, of an animal, of a stream of water, is the rate at which it does or can do work, and is measured by the quantity EXERCISES 116 o* work it does per unit of time, and is detennined by the formula P (power) = '^(!^>. t (time) The work done by a horse in raising a barrel of flour 20 feet is about 4000 foot-pnunds ; even a mouse could do the same quantity of work in time, but he has not the power of a horse. Power is calculated in a unit called a horte-power. A horse-power is the capacity of doing 550 foot-pounds per second, or 33,000 foot-pounds per minute. The objective existence of power is curiously recognized in advertisements that we frequently see, such as " Spare power to let," etc. EXERCISES 1. For which is a truclc horae valued, his energy or hi» power ? 2. Do we spealc o£ the power or the euergy of the steam engine ? 3. Shall we say that the power, or the energy, of the horse is greater than that of man ? 4. How much work can a 2 horse-power engine do in an hour f 6. (a) What quantity of work is r«iuired to raise 60 tons of coal from a mine 200 feet deep ? (6) An engine of how many horse-power would be required in order to do it in 2 hours ? 6. A car of 3 tons mass is drawn by a horse at a speed of 180 feet per minute. The index of the dynamo meter to which the horse is attached stands at 800 pounds, (a) At what rate is the horee workmg ? (6) Express the rate in horse-power. 7. A dynamometer shows that a span of horses pulls a plow with a constant force of 1500 pounds. What power is required to work the plow If they travel at the rate of 2 miles per hour ? 8. What is the horse-power of an engine that will raise 1,360,000 pounds 60 feet in an hour ? 9. How long will it toke a 3 horse-power engine to raise 10 tons 60 feet f 116 DYNAMICS 10. How far will ■ 3 hone-power engine ralae 3000 pound* In 10 •econib f 11. The wind moves a veeael with a uniform velocity of G miiei an hour against a coiintant reaiatance of 2000 poundi. Wliat power ia luniiithed by the wind ? 12. If a 2 horse-power engine can just throw 1066 pounds of water to the top of a steeple In 2 minutes, what Is the hight of the steeple T (Disregard the resistance of the <H (lcHcril)e(l ahovu lie inter- changed, so that Dll Ih the distunce (») thiouffh wliich the force actH, and CA \s llic diMtanoo (»') thioiijfli wliicli the resiHtance movcH,/ must Ixj larger tliiiii r in propor- tion as »' is larger than «. In this cane npced is gained at the expense of force. This gives rise to tlio rommon expression, what it yuiited in tpeed i» lott in force, and vice vena. A gain of force or a gain of speed is called a mechanical advantage. 88. Special Laws of Machines While tlie general law of machines (§ 87) is always applicable, its applica- tion is not always convenient, since, for example, it necessitates putting the machine in motion in order to measure « and »' (the distances traversed, respectively, by the points of application of the force and resistance in the same time), an operation which would be very difficult and tedious in many cases. Hence, a tpeeial law, one in which the equality between the ratio of gain and the ratio between certain dimensions of the machine is stated, is often more convenient in practice. For example, in case of the lever (Fig. 88), force and tcalitance vary inveraely as their respective leverages,' or, , 1 1 illiepupil will uut fait tu obHerve tiiat in asceiiaining the relations between the force and the resistance when applied to the lever and to the wheel and axle be U dealing with inomerU* around the axis of rotation. 120 DYNAMICS in which I and V represent, respectively, the leverage of the force and that of the resistance. Again, in case of the wheel and axle (Fig. 89), 1 1 f:r = d'd' in which d represents the diameter of the wheel and d' the diameter of the axle. 89. Uses of Machines classified. — The various uses of machines may generally be classified under the following heads: 1. They may enable us to exchange intentity of force for ipeed, or speed for intensity of force. 2. They may enable us to employ a force in a direction that is more convenient -than the direction in which the resistance is to be moved, e.g., fixed pulleys, as shown at A and B in Fig. 90. 3. They may enable us to employ other forces than our own muscular force in doing work, e.g., the muscular force of animals (Fig. 90), the forces of wind, water, steam, etc. 90. Efficiency of Machines. — The efficiency of a machine is a fraction, usually stated as a per cent, which expresses the ratio of the energy given out by the machine and utilized, to the total energy expended upon the machine. The limit of the efficiency of a machine is unky, or 100 per cent, which is the Flo. 90 EXERCISES 121 efficiency of an "ideal" mi bine, in which no energy is lost. The object of improvements in machines is to bring their efficiency as near to unity as possible. For instance, if of 50 footrpounds of energy expended on a machine, 8 foot-pounds be converted by friction into heat, and 5 footrpounds be lost in consequence of the utilization of only a component of the working force, 80 that the machine is able to give out only 37 foot- pounds, its efficiency is |J = 74 per cent. If the fric- tion can be reduced one half, and an improvement can be made in the machine tliat will render the entire working force effective, then there will be wasted only 4 foot-pounds of energy, its efficiency will be raised to 1% = 92 per cent, and the quantity of work which the machine will accomplisli will be increased in the ratio of 92 : 74. EXERCISES 1. (o) When is force said to be gained by the Hse of a machine ? (!i) When is speed said to be gained ? 2. State how you would use a lever in order to gain force in the ratio of 7: 2. 3. (a) On what condition will speed be multiplied by a wheel and axle in the ratio of 6 : 2 ? (5) Where must the force and resistance be applied in this C' « ? 4. (0) With which of the t»io pulleys, i.e., the fixed or the movable pulley, is mechanical advantage gained ? (6) What purpose does the other pulley serve ? 5. (a) Where is the fulcrum or axis f,o. m of motion in a claw hammer (Fig. 91) ? (6) If the distance from the fulcrum to the center of the hand be 15 Inches, the distance of the nail from the fulcrum be 8 inches, and 122 DYNAMICS FlQ. 92 the resigtance o&ered by the nail be 80 pounds, what force muBt be exerted by the hand to start the nail ? 6. (a) What advantage is gained by a nutcracker (Fig. 92) ? (&) What is the ratio of gain ? 7. Energy is applied to a machine at the rate of 260 foot- pounds per minute, and it transmits 200 foot-pounds per minute. What is its efficiency ? 8. (a) What advantage is gained by cutting far bacit on the bladet of shears near the fulcrum (Fig. 93) ? Wiiy ? (6) Should shears for cutting metals be made with short handles and long blades, or the reverse? (c) What is the advantage of long blades ? P,o 93 9. The arm is raised by the contraction of the muscle A (Fig. 94), wliich is attached at one extremity to the shoulder and at the other extremity, B, to the forearm, near the elbow, (a) When the arm is used, as represented Fio. 94 FI0.9B In the figure, to raise a weight, what kind of a machine is it? (6) What mechanical advantage is gained by it ? (c) The ratio of gain is the ratio of what to what ? 10. What must be the ratio of the diameter of a wheel to the diameter of its axle that 60 pounds may support 1 ton (2000 poondi) t EXERCISES 123 11. Suppose the screw in the letter-press (Fig. 05) to advance i inch at each revolution, and a force uf 25 pounds to be applied to the cir- cumference of the wheel 6, whose diameter is 14 inches ; what pres- sure would be exerted on articles placed beneath the screw ? 12. Two weights, of 5 kg. and of 20 kg., are suspended from the ends of a lever 70 cm. long, (a) Where, disregarding the weight of the lever, D"jst the fulcrum be placed that they may balance ? (j>) What will be ,he pressure on the prop ? 13. ia) The pistons of a hydraidic press (§ 18) are, respectively, 2 inches and 12 inches in diameter. What is the ratio of gain of force obtained by the transmission of fluid pressure ? (b) Suppose that a force of 20 pounds be applied to the long arm of a lever whose arms are as 15 : 3, and this force causes the short arm to produce a downward pressure on the small piston, what will be the total "oward pressure exerted by the large piston ? 14. How great a force « ill be required to support a ball weighing a ton on an inclined plane whose length is twenty times its hight ? (See §63.) 16. Show why it is easier to draw a load up an inclined plane than to lift it vertically. 16. If the circumference of an axle (Fig. fiC) be 60 cm., and the point of application of the force applied to the crank travel 240 cm. during each revolution, what force will be necessary to raise / \ a bucket of coal weighing 40 kg. ? 17. Through how many meters must the force act to raise the bucket from a cavity 10 m. deep ? 18. (a) A skid 12 feet long rests with one end on a cart at a hight of 3 feet from the ground. What force will roll a barrel of flour weighing 200 pounds over the skid Into the cart ? (6) Wliat amount of work will be required ? (c) What amount of work will be required if the barrel is raised without the use of the skid? Fig. 96 124 DYNAMICS SECTION XIV SOU PSOPERTIXS OF HATTBK DUX TO UOLKU- LAK FOKCES 91. Cohesion, Tenacity, and Rigidity In solids and liquids the molecules are held together by an attractive force, called cohesion^ which prevents their separation except under the action of considerable external force. This is the force which resists an effort tending to break, tear, or crush a body. The tenacity or tenrile ttrength of solids and liquids, i.e., the resistance which they offer to i'cing pulled apart, is due to this force. It is usuallv greater in solids than in liquids, and is entirely wanting in gases. Cohesion tends to hold the molecules of a solid in fixed relative positions, thus giving tlie solid a definite shape. It gives to a solid riyidity, or ability to resist a change of shape. Different solids possess very different degrees of rigidity. 98. Cohesion in Liquids — Clean glass is wet by water. If a glass plate be dipped into water and then with- drawn, a layer of water clings to the glass. When the glass is withdrawn water is torn from water, and not glass from water. This shows that the attraction of the molecules of water for one another is weaker than the attraction between glass and water. Or if, to save words, we call the attraction between the solid and the liquid adhetion, then we may say that the cohesion between the molecules of the water is weaker than the adhesion between the glass and the water. ELASTICITY AND PLASTICITY 125 Clean glass is not wet by clean mercury, which shows that the adhesion between glass and mercury is not so great as the cohesion in mercury. Generally speaking, a solid is wet by a liquid when the adhesion of the solid to the liquid is greater than the cohesion of tiie liquid, and is not wet when the cohesion is greater than the adhesion. 93. Elasticity and Plasticity FAaUicity is that prop- erty in virtue of which a solid tends to recover its size or shape, and a fluid its size, after these have been changed by external force. If the body recover at once and completely on the removal of the stress, the body is said to be perfectly elastic. All fluids are perfectly elastic, and a few solids are approximately so, such as ivory and glass. If a solid have little or no tendency to recover its size and shape after distortion, it is said to be plastic or inelastic. Such substances are putty, wet clay, and dough. A great numlier of substances are elastic when the distorting forces are small, but break or receive a " set " when these forces are too great. They are said to be elastic "within certain limits," called the limits of elasticity. If strained beyond those limits, they become more or less plastic. The springs of a buggy sometimes become set from bearing a too heavy load and lose permanently much of their elasticity, that is, they become in a degree plastic. 94. Malleability and Ductility Solids which possess that kind of plasticity which renders them susceptible of being rolled or hammered out into sheets are said to 126 DYNAMICS be mallealle. Most metals are highly malleable. Gold may be hammered so thin as to be transparent, or to a thickness of ^-^^js-ht; oi an inch. Most substances that are malleable are also susceptible of being drawn out into fine threads, e.g., wires of different metals. Such sub- stances are said to be ductile. Platinum has been drawn into wire 0.000165 inch thick, or so fine as to be scarcely visible to the unaided eye. Wires are made by drawing a rod of metal in suocesBion through a number of holes, each a little smaller than the last, the diameter of the rod continually decreasing while its length is correspondingly increased. 95. Surface Tension. — When a piece of sheet rubber is stretched there exists between its molecules a contrac- tile stress, called tension, which tends to restore the body to its normal condition. Every liquid behaves a» if a thin film forming ita external layer were ever in a state of tension, or were exerting a constant effort to contract. This superficial film is tough or hard to break as com- pared with the interior mass. If a needle be carefully laid on the surface of still water, it will float, although the density of steel is more than seven times that of water. The tendency of a liquid surface to contract means that it acts like an elastic membrane, equally stretched in all directions, and by a constant tension. Experiment. — Form a soap bubble at the orifice of the bowl of a tobacco pipe, and, removing the mouth from the pipe, observe that the tension of the two surfaces (exterior and interior) of the bubble drives out the air from the interior until finally the bubble oontcscts to a flat sheet. CAPILLARY PHENOMENA 127 As a consequence of surface tension, every hody of liquid lendf to aimme the upherical form, since the spiiere has less surface than any other form having equal volume. The water remaining on the end of a glass rod that has been dipped in water is globular, as if a rubber bag filled with Aatcr were tied about the rod. In bodies of large mass the distorting forces due to their wight are generally sufficient to disguise the effect ; but in bodies of small mass, e.g., drops of liquids and soap bubbles, it is apparent. The hairs of a camel's-hair brush when dry present a busby appear- ance. When dipped into water the same appearance remains, but when taken out of water the surface tension of the adhering film of water draws the heirs closely together. 96. Capillary Phenomena. — If ghiss tuba (Fig. 97) of capillary (hairlike) bore be thrast into water, the water will rise in the bores considerably alx)ve the gen- eral level outside. If similar tubes (Fig. 98) be thrust Fio. 97 M Fia.98 into mercury, the mercury within the bores will be depressed below the surface outside. Phenomena of this kind are called capillary phenomena. The free surfaces of tlie liquids inside the bores are curved, the surface of water being concave and that of mercury con- vex. The size of the bores of the tubes is greatly exag- gerated in the two figures in order to show this more plainly. The smaller the bore of the tube, the greater is the elevation or depression of the liquid. 128 DYNAMICS The phenomena of capillary action are well shown by placing varioiu liquids in U-shaped glass tubes having one arm reduced to a capillary sine, as A and B in J B c Fijr. 9a. Mercury ]H>ured into A I assumes convex surfaces in both ^^^ arms, but does not rise as high ^|bJ in I M small arm as it does in the I^H y .^^ large arm. Poiur water into B, and ^H I f^i HS "" ^'"^ phenomena are reversed. ^H I r- J Ba Fig. 100 shows the forms that the ^^^ ^~^JJ) '^^ surfaces of water and mercury take when contained in the same glass tube. The following are the laws of capillary action : I. liquids rise in tubes when they wet them, and «re depressed when they do not. n. The devation or depression varies Inveisdy as the diam- eter of the bore. ni. The elevation or depression depends also upon the three substances involved in the experiment, that is, on the substance of the tube, on the Uquid, and on the substance that fills the afce above the surface of the liquid. Flu. iW Fill. 180 CHAPTER IV HEAT SECTION I KINETIC TBXORY OF HEAT — SOURCES OF BEAT 97. Heat defined As w«8 stated in § S.^^^^nol^ cules of e veiy botly are believed to be jn ini'PHjuint, ""'Hioniori^ ILihig-be true, it follows _tiiat alLniulecules osges^aneyijjm^Iia, jTbc name given to this Q pa rticular type of energy is heat. It is certain that TSUlT'aTvrm^^ ^^^^l^^"'^ '■" """ at the present day " doubts t}iat it isldMc to ihi>. motion of the moleculnn of a hodyl^ T he con clusion ia tlrnt heat it mokiadar kuu t i a energy.'^ Like the form of energy already treated, it mYoIveS thelwcTelemel^ tj^ mnfter /liy^j^ntionA^ According to this view, a body becomes wanner aft_tha-BIOtiQIW of its molecules is qnickened a nd cooler as the motion of its mole- cules is retarded. The coldest bodies we know have heat, since no molecules are ever at rest. AVe think of ice as lieing very cold, and the erroneous impression exists to Bore| y eTtenji th^t ice is heatless matter, but the fact is that no one ever found ice so cold that it could not become colder. In otiier words, the motions of the molecules of the c oldest ice in the Arctic regions mav become less rapi As late as the b«lrinnil |-f ""' ^in.>^..th «^^"" »>«-* -" ■r»n«r»llT regarded as an " igneous Jtuitt,'^' sometimes calfed " caloric. " Experi- ments performed by Couat Riimforti, Joule, and -others have demonatrated the falsity ot this view and have led to the adoption ot the ti/wttc tfttory. 129 180 HEAT J The term heat U used in two very different senses, the fhvtical and the phj/tiological In physics we deal with heat only as molecular kinetic energy . In a physi- ological sense , heji^s^considered as a leniation which we experience by coiiUict with IxKlies. Thus, we declare bodies to be cold, warm, or hot, according to the sensa- tions which we experience when we come in contact with them. Our sensationH. however, are vcrj- unreliable criterions in judging of the relative heat conditions of different bodies, for the sensations produced degen^ on many other thinfyg b>ni.l^» tt.^ ,]..g. ree of heat in the body touchetl. 98. Molar Energy Convertible into Heat. — If you Jiamnier a nail brisklv i i[ "-^-^ '-f -omPM t/.n tj y^ «» \^ handled with comfort. Stii'ks of wood may become so heated by 1)oinpr nil.hpd *^°^^^^»]- »- to take fire. w\,^ _a hammeT strilces an ah'^ its motion as a mass ceases; but the hammer and anvil^are heated, that is, the motions ^oTtRe molecules of the hammer and anvil are quickened. There is no destruction of motion. — only « ,^lnnfiT,,f in matt mntion to mo lecular motion, or, in other words, a ehajuiefrom molar or ma»» energy to molecular energy, i.e., heat. Another interesting illuatration r ' the generation of heat by the eipelMiture of molar energy is _.Vorded in the case of com- pression of air. A few drops of carl)on disulpbidj) »■- .^.»p^,^ .1 into the f;la8s barreL,4 (Fig. lO U of afire syri^ya. »n .1 the tightly fitting piston B is suddenly pushed into the bajreU The air in front of the piston is rapidly condensed and l»A/-nm«. y. hpff*-^ W ^ ignite the chemical and produce a flash o f li ght. Mhjs m otion checked usually results in Heat,.' XVTipn the brakes are applied to the wheels on a moving railroad train its OTHER SOURCES OF HEAT 131 molar energy ia conrerted into heat, and the wheel*, brake blocki, and raila are heated thereby. By -fri ction, by percuiwion , or by any process by wjiich inam motion ii arrested, - Beat it j[enera(«d. _ g^j^^aiMfc^mimmKbeD used become lieated. Meteoritea,p{liio. called^ "falling, stars," are. rendered visible l.y toeir iuteyw heat. They are piect-s "^ r1iin"'''(ftrY i'""" "''"•'' "'""™ *'^'' ""f^K'""" *"^«'' inhi tliT "itrtih'* °'"unii''i"''iii "'"' *'"'''■ """" "'"*'"""' being iniiieded by the friction of the air, produce the heat with which they u'low. , Spa rks are seen at night when th e iron slices of burses strike the stone pave- — ments! ^^^SSC^^O*""*^" when a cannon ball ati-ike s an iron-clad vessel or a target. _ 99. Other Sources of Heat. — Since heat U energy, it may originate in gome other form of energy, i.e., by the tr antformation of lome other form of enerfiH into h«(U. In the electric lamp electric energy is transformed into heat. In the com bustion of the varioua fugtg,, » ucli as wood , . . - CttaT, oilspHidTinimmating gas , chemical poten- ' tial energy is transformed into heat. And, 5... iS ^nerally, whenever heat ia generated by chemical actioni^^ uj^ ' as for example wKpt, ..nlpb.irin j^^jd in p^nrcH i^tr, watu^ or . water upon quicklime, chemical potential energy is transformed into heat. Not only is the sun the supre. \e source of heat, but it is also the source, directly or indirectly, of very n ^ ftrl y i^U the enerprv employed by man in doing work. _^ form of energy called radiant energy is continually sent for th from the sun in aU directions ; the mode of transmission and of its conversicm into heat is considered in Chapter VI. 182 HEAT ■ziKcnxt 1. Whit li the ctom of » ■■ hot box " on ■ nilwiut ear f ^ < 2. What doea coal poMDW that give* It value r " \- ^ 3. What evidence hare you diacovered that heat la a kind of energy and nut a kind of fluid r 4. What, only, can be tranaformed Into heat r 5. Are the teriiu htal and cM name* of tbingi enentlaUy different, or of different degrem of the unie thing ? SECTION II 1 r ^ TEMPEKATUKX AND THSSMOIUTKY 100. Temperature defined. — When the quantity of heat in a body increases, that is, when t h e motion of i te molecules is (quickened, the temperatur e of the body is said to rite ; and when it diminish es, the temperature is said ^gjji^. If body A tend8~Xo impart heat to body B, then A is said to have a higher temperature than B. ^Tempera t ure is a cercurv in tlie tuix! rises or falls '. until it reaches a tertain jwint, at which it remains station- ary. We then know that the mercury has the sam e tcmnemture as has tlie Miiiiiinn diiig Imily. Hence, the readinij, as it is called, of the thermometer indicates the temperature not only of the mercury, but also of the surrounding body. 103. Gndtution of Thetmometen. — The grad uation of a t)u>r mometer ia baaed on the fact tliat th e Tfinpfratiir e at n^bUJll IM melto and t hat at which yia,U:t boila under a definite preagure being" uncnangeable, tha dilltilBnuB liiUwgUl tlleiie two teiinieraturea ia eonatant. J lie hulli in (ir»t plnopH in nu-ltiiiK ice a nd allowed to atand until tlie aurface of the mercury becomea atationaVy, when a mark ia made at tliat point wliich iiidicat<'8 tlie metl ini/ puinl. Afterward 8^_|xith bulb and aten> are enveloped in at^ani at a preaaure of 760 mm. The mercury riaea in the atom until ita tem- perature reaches that of the ateani, when it becomea stationary; then another mark ia made to indicate the hoiliiin point. Then the ■pace between t he two jwints found ia divided into a c o nTenient number of equal parta called tlei/rren, and the acale la exte nded above and below these pointa aa far as is desirable . ^ The tb g'TBfni"*"'' p''^"'°''<'^ indU'atea changea of voluroe ; but aa chanjrpR of volume m this case are cans*!*! by "hanKes of temp^'rature, it ia commonly uaed for the more important purpoae of indicating iemperatvn. 184 HEAT J00°\ 6 0°Hf--- -IT.fm—- SIS' Two methods of division are adopted in this country (see a and 0, Fig. 102): by one, the space is divided into 180 equal parts, and the result is called the Fahrenhei t scale, from the name of its inventor; Wthe other, the space is divided into 10Qy4qual parts. and the resulting scale is calfed centigrade, which means one hundred fteps. In the Fah- renheit scale, which is generally employed in the United States for Ordinary household purposes, the melting and boiling points are marked, respectivelv y 32° and 212° . The centigrade scale, which is generally employed by scientists, has its melting and boiling points more conveniently marked, respec- tively, 0" and 100°. A temperature below 0° in either scale is indicated by a minus ■ Tign before the number! Thus, - 12° F. indicates 12° below 0° (or 44° below the melting point of ice), according to the Fah- renheit scale. The Fahrenheit and centi- grade scales agree at - 40°, but diverge both ways from this point. 103. Conversion from One Scale to the Other Since 100° C. =* 180° F., 6° C. o 9° F., or 1° Ck * I of 1° F. Hence, to convert centigrade degrees into Fahrenheit degrees, "we multiply the number by | ; and to convert Fahrenheit degrees into centigrade degrees, we multiply by f Now since 0° C. * 82 F., if we deduct 32° from the Fahrenheit reading we have the number of degrees by which the given temperature differs from the tempera- ture of melting ice. For example, 52° on a Fahrenheit Sf Fio. 102 EXERCISES 186 scale is not 52° above melting point, but (52° - 32° =) 20° above it. To reduce a Fahrenheit reading to a centigrade read- ing, firit ivhtract 32 from the given number, and then multiply by |. Thus, To change a centigrade reading to a Fahrenheit read- ing, first multiply-tie yiven number by », and thenadd 82. Thus, |C.-f32 = F. \ EXERCISES 1. Express the following temperatures of the centigrade scale In the Faliienheit scale : 100°; 40°; 60°; ()0°;0°; -20°; -40°; 80°; 160°. Note — The 32- ahould be added or mbtracted algrbmii-ally. Thu«, to dunge — 14* C. to lu equivalent fn the Fahrenheit scale : | x (— 14) - — ao? ; - 1^.T + 32* - 6^, the required temperature In the Fahrenheit »cale. Again, to nnd the equivalent of 24' F. in the centigrade icale :a4-32=— 8;— 8x|=-4|; hence, 24" F. it equivalent to — 4.4° + C. 2. Express the following temperatures of the Fahrenheit scale in the centigrade scale : 212° ; 32° ; 90° ; 77° ; 20° ; 10° ; — 10°- - 20° ■ -40°; 40°; 69°; 329°. 3. Explain the origin of the heat obtained by bamhig coaL / j ^5 , 4. How does all heat originate ? 5. What must be the temperature of the air that both the centi- grade and Fahrenheit thermometers shall read the same ? 6. The difference in temperature of two liquids is 36 Fahrenheit degrees ; what is the difference in centigrade degrees ? 7. (o) If the temperature of the air falls from 20° C. to - 8° C, through how many degrees does the temperature drop? (6) throagh how many Fahrenheit degrees does the temperatura drop? 186 HEAT SECTION III CALOKIHETRY '^104. Distinctifln bfitweenJttiiLfluestions "How Hot?" and "Howmudlifiatil' — The former, like the ques- ^^iT^niowsweet?" when applied to a solution of sugar, / w an,wpred onl y relatively . Tlw lattcr^ike the ques- ^-^!on "Mow muck sugar in the »n1..tinng is answered quant itiveli-^'y^BtnesH and tem^ '*-^>'"-ft ar^ pdeoen- -qfcdr!.f f h Tm^ nf the bodr< / A pint of boiling^water ■*■&* hoi as a gdlkiii of the_Mme;,i;ut the latter con- • ta i ns eight tim es^TS^'heat. ^ Temperajw^de^ends ^jh. ar^raae kineticnerau (if t/ig.-gmfeaifefc * Quantity nf hpM i, the product "f ff" nv^rane kiiu-ik frwrmi or "the moleciUes mJti^Ue'lhy the num ber of moleculeiJT^ --qSantity^Ji^it_a_bodZ>a8 cieijeiid^ therefore, upon - ^^thliaCiMii and ite temperaturty ' ' m. dermal Units. -/- The unit_used Jor_mea8uring quantity of l.»-t. palled a c a^oWya the quantit £o|Jbaat required to ra ise the te m perature of ^ ^ f f "^ '"^'"t 1 """fa" -^^J^. J-The thermal unit in the C.G.S. system ' is the aramrcalorie , sometimes called the »maUer caloru, -Ti„i.';L'X. qnant it.v of hcat rec|uired to-taJBe 1 K- S £- ,^5E;rfTomj ^ b" (J. 'i'hToperation of measuring 'heat is cmeAca lorimetry. ioTCapacTty Of Bodies for Heat. — If we place a kilogram of mercury and^a kilogram of water in separ rate vessels on a hot stov^ tttl ffl^^'IT' ^'"^ ^'^^^' "^ - iiiiMh nnnnfir t hn n ftp -"tt^"- This is because it "takes more heat to heat water than mercury, or, to use SPECIFIC HEAT isr gcientifio language, because t he capadUi of wa ter for heat is greater than that nf mpr^^^-j, " K '"= mix 1kg. nf Wfltpr nt 4n° with 1 l,^ ^f »„.„. „^ of)» ^hr teraperature of the mixture will be 30°. The heat which leaves the kilogram of water at 40" j.i falling from 40° to W is just suffi- cient to raise a kilogram of water from 20° to 30°. .But if we pc i.r 1 J. ^gTam of lead shot at 40° into a kilog ram of water at 20° Jie t«5pi!ratiire ot the watcr-A?Iir be raised to o nl y about iM,5 7r~rr j other words, a Kilogram ot lead in cnoHag frp,fi dn° to_20.57° fur- J^tenffl3reaauiia«atto..»«i«»*kilograBiQ£ W"fromW to / ^Q-SV , — a .ittle more thi.h half ^ A.^. Or, stated in another ) way, the quantity of heat that will raise a given quantity of water ' (20.57 - 20 =) 0.57 of a degree will raise an equal quantity of \ lead (40 - 20.57 =) 19.43 degrees. ^atermitranks all other su^tances except hy drogen inOs capacity i..r W^\*f\\^ n^.^r..U^. „r ,.. ,^ -i^^^j^Yfe^ ^^logram of water from 0° to lOQ-" wnnl.l r«;»a . Vii^. _grag Pf-irop from 0" to about 800°. or to a'red heat. ^°°^T^'^' ^ ^"°°"'^'" "^ "^'"'^"'' '"" """'-"r from 100° lo u- gives out as much heat as akilogram of iron gives out in co oling frnin a hf "'i '*<'"■ tn P° .^ater is a great en.mlii^r nf cUmatic temnpr»p.». On account of its great capacity for heat, water be comes heated v ery slnwlv and cook very slowly. Hence. Ue climate in the vicinity of S uou.es oi water is muc h less subject to extreme^o ^ temneratn^ than places that are remote irom water fronts. 107. Specific Heat. — The iptdfic Uat of a substance IS the ratio of the QuanfTnT ot heat ,i^^r.k t^',.^ , -^^ ^kT t^^nitureaf a given mass of the substance 1 degree M i «. - ,_ — ^ miigs of water 1 degree. g TBySBWffBWH* that the speoinc keat oi mercury is 0.^34 means that 188 HEAT it takes 0.084 ae much heat to raise a given mass of mercury a certain number of degrees as to raise an equal mass of water the same number of degrees. The specific heat of enx^substa nce is nu merically eg^ual to the number of calories required to raiseji kilogram of that substance 1 centigrade degree. For example, ~Tt""require8 6^634 of a calo rie tji ruiae thp tprp''"'*""' of 1 kg. oTmercury 1 centigr ade degree. 106. Method of detennining Specific Heat — A known mass, m, (in kilograms), of the si'^tance of which the specific heat is required is heated to a known temperar ture, t, (C.) ; then it is mixed with (or immersed in) a known mass of water, m^ at a lower temperature, t„ and as soon as equilibrium of temperat»re is established the teiuperature of the mixture, ««, is taken. Let « represent the specific heat of the substance sought. Then the quantity of heat lost by the substance is m^ {t, — t„) calories ; while that gained by the water is niy, (t„ — tj) calories. Now if no heat be lost during the operation, it is evident that m,* (t, - 1„) = m„ (t„ - t„) ; ^ _ "»» (<» ~ *») »». (*. - <«) ' For example, take the case given in § 107 ; we find for lead 1 (20.57- 20) _^^^o 1 (40 - 20.57) In accurate work allowance must be made for the heat absorbed by the vessel, called the ealorimeter, which holds Uie water. , whence, EXERCISES 189 KXXKCISEa (In the folloving exercises temperature* we given in the centigrade acale.) 1. H 800 g. of Bheet copper at 00° be placed in 600 g. of water at 10° and the resulting temperature be 20°, what is the specific heat of copper? 2. If 1 kg. of lead shot at 98° be poured into 1 1. of water at 15°, what will be the resulting temperature ? (Sp. h. of lead = 0.03.) 3. (o) If the average temperature of the water of Lake Michigan were raised some warm day from 10° to 13°, to what temperature would a lake of mercury having the same mass be raised on receiving the same amount of heat P (See Table of Specific Heat in Appendix.) (*) Which " lake breeze " would become unbearable ? 4. Why does the sand on the seashore become much warmer on a summer day than the surface of the adjacent waters? 6. A teakettle conUins 3 1. of water at 12°; how much heat will be required to raise it to the boiling point if the atmospheric pressure be 760 mm.? 6. (o) A piece of iron weighing 20 kg. loses how much heat In cooling from 80° to 40°? (6) The same quantity of water would 16se how much heat in cooling the same tmmber of degrees ? SECTION IV XmCTS OF HEAT — cmuiGB OF VOLUKB 109. Classification — The effects of imparting heat to bodies may be classified as folloTvs : (1) chemical effects; (2) electricaleffects ; (3) change -f volume V (4) change... of state. " p^ — 110. Chemical Effects. — Heat applied to a body often changres the pomposition of ita molecules.*' iM^ftMWB there la a tende ncy to combination.^ ComEustionia aa 140 HEAT 1 affflM^f hif th temperature^ a cert a in temperature be inff "" reqiSe d to start it:i The small flame of a match is suffi- "cient to cause illuminating gas and oxygen, one of the 'constituents of the air, to unite and buret into a brilliant flame. ^ In some cases heat tends to separate m(Jecules into their constituents^"/ As an exanipTe, criimSs of bread "placed on a hot stov e soon break up into cer tain gases and c arbon; ihe iormer mingle with jthe, a irj, Ifisxing - ^ black mass' of charcoal - All such changes, which Involve a change in molecular structure, belong to the domain not of physical but of chemical science. 111. Electrical Effects. — Interesting electrical phe- nomena are producible by heat, as will be shown under the head of Thermo-Electrical Currents in the chapter ^ on Electrokinetics. \" >.-..« '^^^^ ,.- ^-^r^ iji. Chang e of Volmne . — It is this effect that chiefly j>»TnniiiiiilH 2"r attentio n at present.. With few excep- tion3; all bodies, whether solids lirjuuls. or miiti ir"~l1f° in v oliilBfe When Uieir Unipei.-' tiiiifi jfl 'jj^J'^'l This result -^fTsISuIcr naturaUy «cpect when we reflect that a rjee . of temperature m ean^an increase of molecular j peed, in — Which ca^ the molejijiles must hit one another harder blow s and thereb y (fiive one another"Varther_aEaft''aBd.- jA, the same time weaEenlTTe cohesion., "" The following simple experiinenta ^111 illustrate expansion produced by heat. ^ topwlment 1. — Apparatus used : a pair of inside and outside calipers (Fig. 103), tin-' J^""*ll t"he f-*- '""■*■ *" '"«]? ' " diameter. iFit thrtnbe ti|;ht.'v h«t,ween the pronps a and 6 of the calipers; then heat the tube quite hot The tube wiU not now pasa EXPERIMENTS 141 I between the prongs until they are sepnrated a little more. Thrust the tube into cold water and cool it. It will no w pass between th e prongs. ~~— ■ Fio. 103 Fit the prongs c and e to the bore of the tube and heat the tube; the prongs now must be opened a little farther in order to fit the bore. With the statement that "heat expands" is sometimes coupled the statement that ^^cold _contracts. " The latter statement evidently is un true if by "cold " is mean t an a^ent that produces contraction. ^ Cold 18 a term of negnti on. It signifies merely a gresier or less deficiency of heat as dark- ness signifies an absence of ligbt. Since cold is not an agent that has an actual existence, we cannot with propriety say that it ever does anything. ''''■]■ rnnlinfi i.e., the diminution of molecular motion, simply makes it possible for cohesion to draw the molecules of a -*l*l7TriraiecT5se? logeiiier, and the body is said to contract. Ezpeiiment 2. — Fig. 104 represents a thin brass plate and an iron plate of the same dimensions riveted together so as to form what is called a comvtmnd hnr. Place the bar edgewise in a flame. dividing the flame in halves (one half on each side of the bar) so that both metals may be equally heated. The bar, which at first was straight, now bends, owing to the unequal expansion Q t the two metaU on receiving equal increments of temperature. Brass, which is more expansible than iron, i s now on the outer or conv« side of the bar. Kzperiment 3. — Fit stoppers tightly in th^ '""•l^- n( {yy .in.;i., thin glam flagks (or test tubes) and "th roiigh each stopper pass a glass tube about tip cm. long. T he flasks must be as nearly alike *a po88ible._ FiU one flaak with alcohol and ».h« other with water. Fio. 104 142 HEAT and OTOwd in the itoppen so as to force the liquids in the tubes a litUe way above the corks. Set the two flMk« into a basin of hot water, and note that at the instant the flasks enter the hot water the liquids sink a little i n the tubes, b ut (quickly bg gJB UjMrise, ....tll^ p4.>i.^^ H.»£1i^jj[^.ii fha tvp»"^ tlif. tubes and nursyeir i """IThen the laaks first enter_thBhfit-«atei.^ejexpMid, and thereby their capacities are increased. Meantime, as the heat has not reached the liquids to cause them to expand, they sink momentarily to accommodate themselves to the enlarged vessel. As soon, however, as the heat reaches the liquids they begin to expand, as is shown by their rise in the tubes. The alcohol rises faster than the water. Roughly speaking, alcohol is about ten times as expansive as water. Different tubttancei, in bolk the lolid and the liquid state; expa nd anequMgjm experiencing e^iat changee of temperature. _ Xxperiment 4. — Take a dry flask like that used in Experi- ment 8, insert the en? of the lub« ih a bottle of water (Fig. 106), and apply heat to the flask ; the inclosed air expands and comes out through the liquid in bubbles. After a few seconds withdraw the heat, keeping the end of the tube in the liquid; as the air left in the flask cools, ita pressnt« decreases, and the water is forced by atmos- pheric pressure up the tube into the flask and partially fills it 113. Soma Practical Consequences of ex- pansion and Contraction. — The forssaezer^g^ ' Kymatitla i»^oti "•'^■^B^'ng aP'^ nnntranting are practi cally irresistible. Iron plates in ^eSgJn^oilMii areliound tightly together in the following manner: ir on rivets, heated_ red hot, are passed tErough holes m the Fm. lOB plates and hammered till both heads closely grip the plates : the contraction of the rivets on cooling binds the plates together with great force. In the process called " shrinking on the tires " of carriage wheels the tiree ANOMALOUS EXPANSION, ETC. 148 •re expanded by heat till they slip on esaily; m they cool, they contnot and bind the wheeU fast. The enda of steel raila^iuuir ^railroads^must have a little apac e_&et ween' them , so that in hot weaiEer they will not force one another out of line and occasion fearful accidents. For a similar reason steam i pipes require the insertion of expansion joi nts. 114. Anomalous Expansion and Contraction. — Water TOsenta a partial exception to the general rule that mat- ter expands on receiving heat and contracts on losing it. If a quantity of w ater at 0° C. be heat e d, it con ^tat emperature rises, until it reaches 4° C^ when its yolume is least, -i'.& ? it has its maximum denntu. If Prr°"''° °Till, at I heated beyond this temperature ^j^ \ "abaUt 8° Ci. it« vnlumB i» tb» ^„p,^ flp (J of 1 oc. of pure water at 4° C, is 1 ^y . m ftt 0°. The mass , The following table gives the volume of 1 g. of water at cer- tain temperatures : YoLUiiK OF i G. OF Water at Atmospheric Presscrb TSHPEKATUKa St ATI VOLUMS " - 10° Ice 1.0897 cc. 0° " 1.0909 •' 0° Water 1.0001 " ..4° " 1.0000 " w t( 1.0120 " 100° ti 1.04.31 " 100° Steam 1650^ 160° ** 1870. " J The anomaly in the^ez|>anslpn_j(!f water leads to important ^ results in the economy of nature. In severely cold weather the ^ npp er layers of the water of ponds and lakes cooled by the ^ 144 BEAT 1^/ Mid wind iink and cool the who le to 4° C. A fur ther lo»» of he at raakei thajjurfaMTajw»_lij{Iit<>y»oth»t wateFtetween 4' »pq jc float* on wa ter at 4°j consequently tEe'wiler at the surface when it reaches 4° ceases to descend and cool the lower water below this polnt^ Waterjwin^ a very bad conductor of heat (j 13 7), it takes a yerTJong^tiine for the deeper laye rs of water io part with their "heat, and Boi eyen in the hardest winters,Tlie ice in temperate I ^BB'es'Ts seldom very t£ick, ami the water' at"{Ee bottom of dee p 9)1' la&es is seldom'colder Umn *lP-^ ThigTrregularity in expansion UUUun Id B6 ulheVIiquid to an a ppreciable extent. 115. Expansion CoefBdents. — Tlie expansion wliicli attends a rise of temperature depends not only upon tlie size of tlie body and upon ite change in temperature, but upon a quantity peculiar to the substance itself, called its expaniion coefficient. The so-called linear expanii(m coefficient «'» the increase of unit length per degree rite of temperature. Thus, suppose that a rod of metal of length I at temperature f be heated and its length at t,° becomes ?, ; then, representing the linear expansion coefficient by e, we have, according to defi- nition, a quantity which is nearly constant for the given sub- stance, but which has different values for different substances. (See Table of Expansion Coefficients in the Appendix.) In the expansion of fluids we have to do only with increase of volume, called volume or cubical expansion. A volume expaniion coefficient is the increase of unit vol- ume per degree ri»e of temperature. This is approxi- mately S c, or three times the linear expansion coefficient, EXERCISES 146 and may be taken a« such for moat practical purposes. Likewise, the surface or superficial expansion coeflicient is approximately 2 c. Not only do the expansion coefficients of liquids and solids vary with the substance, but the coefficient for the same suljstance varies with tlie temperature, being greater at high than at low temperatures. Hence, in giving the expansion coeffi 'ent of any substance it is customary to give the mean coeflScient through some definite range of temperature, as from 0° to 100° C. IZXItCISIS {Vwt expaiuion coefficients found In the Appendix.) 1. A certain braaa rod i« 10 feet long at 20° C. What ia iu length at 90° r An*. 10 feet, 0. 16 inch. i. A steel rail is 20 feet long at .erpetual motionis called the kinetic thtory o^ matter. SAcco rding to this theory, the molecules in gases ue_ so far sepap IraEedTTonTohe another that their motions are not gen- 'eiiny influenced by molecular attractions. Hence, in accordance with the First Law of Motioi^the mol ecule s of gases m ove in itraight line*, until they collide with one another or strike against the walls of the containing " vessel, Irom which they rebound and start on new_ paths. 117. Pressure of a Gas due to the Kinetic Energy of Its Molecttlei. — Consider, then, what a molecular storm must be raging about us, and how it^ust beat against us and against every exposed surface.'*' According to the kinetic th eory, a^as ex erte pressur e upon thejnteriof sur faces of the vesse l which confines it, in consequence of the incessant strokes of the molecules of the gas upon the surfaces (§ 29^?tiiq s trokes following one an ot her in suc h rapid successiogHhat the effect pr odu ced canno t be dis- ting uished fn)m conti nuous pressurfp ^ Upon the energy of these stroke&nTupon their fre quency must depend the amount of pressure. But we have learned that on the kinetic energy of the molecules depends that condi- tion of a gas called its temperature ^ so it is apparen t that the preiiure of a given quantity of go* varie* with itt CRITICAL TEMPERATURE 147 ( t tmptratw ct. Again, na at the same temperature the number of strokes per second must (legend upon the number of molecules in the unit of space/it is app^rtnt that the^reumre vane* teith the dentity. ^ y 118. Critical Tempcratnre. — Up t o ui. war lg77 there °""^ flf'^ i^MT' ''*'''''' had resisto. :.!! itteiunt 'i These were called**' tl>i iHTi.miK'ui.g.i.sr.-- ' ' i> at ^ pressure and thrqi^ yh the agency of impro'. •>!' Ti. ji'lam. ul "Hevices eyery ( me of these has been tR «luiii'l tv.UkiJijiuid, The expreshio!! li ;u''l air liquefy them. _But this distinction has since disapprjft'.tr!>Tr TiTTiT ■ and e ven to the Boli 100° 2]20 3730 S1.40 (1) The volume of Alcohol boll. 7»0 in.«o 3510 ini.«o a given' mau of g*a ElhcrboiUaso - 950 3080 . 554.40 at constant jnesauie is proportional to its abao- Ice melU Oo - 320 S7SO . 491.4° Ittte temperatuie. HereaiT freexce -«.80 - - -37.iPO atjv - 481 JO This is a deduc- tion from the dis- covery of Charles AlcohoUre«.em-l»Jlo - -S0a.9O 1«.50 - 256JVO given above, and is known as the Law ertinutcd to b« «bout -250o ' -U80 S30 - 41.40 of Charlet. — 8730f- -«».40 oo . -00 Likewise (2) the Fjo. 106 preasuie of a given mass of gas wboae volume is kept constant is proportional to its absolute temperature. Boyle's Law (§ 31) states that (3) at a constant tempera- tute the volume of a given mass of gas is inversely proportiona] to its pressure. 160 HEAT By a combination of Boyle's Law with Charles' Law I obtain the following comprehensive law : (4) The pto dnct at the vohune ynd fiMaore of « m*§* of gw U3Llt?J*»9lute umjgajattt. I_\ must be understood that the above laws are true only on the condition that the gas under consideration is not near the state of liquefaction. ■ZXRCISXS 1. Find, In both centigrade and Faluenheit degrees, the abeoiute temperatures at which oil of turpentine (see Table of Properties of Liquids in Appendix) boils and freezes. 2. At 0° C. the volume of a certain mass of gas under a constant pressure is 600 cc. (a) What will be its volume if iU temperature be raised to 76° C. ? (6) What will be its volume if its temperature become - 20° C. ? 3. If the volume of a mass of gas at 20° C be 200 cc, what will be its volume at 30° C. ? 4. To what volnme will a liter of gas contract if cooled from 80°C. to -16°C.? 6. One liter of gas under a pressure of one atmosphere will have what volume, if the pressure be reduced to 900 g. per square centi- meter, while the temperature remains constant ? \ '^ '^ '^^^ 6. The volume of a certain mass of air at a temperature of 17° C, imder a pressure of 800 g. per square centimeter, is 600 cc. What will be its volume at a temperature of 27° C, under a pressure of 1200 g. per square centimeter? Solution; 17° C. is equivalent to 290° abs. temp. ; 27° C. is equivalent to 300° abs. temp. Then, 200:300:: 600 x800:xx 1200. Whence, X = 344.8 cc. Am. FUSION l&l SECTION VI ■FFXCT8 OF mux COHTimiED- CHARGE OF STATE 128. Fusion. — Every change of state in matter is associated with either a disappearance or a generation gfteat^and it is usually necessary either to increase or to decrease the heat during the change. Many sub- stances are capable of existing in any one of the three state8, ^olid, liquid, or gaseous^ Which one of these states a given sub8tance"exi5S m depends usually on its temperature and the pressure upon it. ■ ^ff*^, -^gSll-^_^g ^^» cohesioni ^ consequently, the rigidity and the tenacity of solids aie generally lessened with rise of temperature. Heat ^plied to solids tends to melt or fuse them. Many substances, un der norma l _pre«8ij^change_at a definite temperature, called the funnff^otntj from^^e^solidto the liquid state, or vice verta, so that when their tempeiiSiJir are~above this point they are liquids, and when below this point they are solids. In fact, at 0° C. water substance can exist in any one of three distinct states, as a solid, a liquid, or a vapor. Under ordinary pressure ice cannot be ■ m ade warm er th an 0° C.y Experiment l..^Put a lump of ice as large as your two fists into boiling water j when it is reduced to about one fourth its original size skim it out. Wipe the lump, and place one hand on It and the other on a lump to which heat has not been applied ; yon will not perceive any difference in their temperatures. TJe temperatun of ice at Us fiuing point Joes not change while melting. 123. Regelation. — In changes of state from solids to liquids, or vice verta, we seldom concern oureelves much 162 HEAT / with the work done by or against exterior pressure. An interesting exception, however, is to be noted in the case of melting ice. The melting point of ice is lowered a very little (0.007° C. per atmospheric pressur^) by exterior pressure. This leads to some important conse- quences. If two pieces of ice be pressed together, the jjjewill melt at the point s of contac Cfand when the pressure is relieved, the water flowing around these points will freeze and thus the pieces become welded together. This operation is called reaelation, iByythis process hard snowballs are made from loose snow. If snow be subjected to great pressure in molds, it is con- verted into solid ice. It is in this way that glacier ice is formed from snow, the stnir tum at the botton> receiving the pressure of the great accumu- lation of snow above.* If a block of ice have heavy weights hung up- on it by a wire which is passed over the block (Fig. 107), the pressure will melt the ice below the wire. The water thus formed is forced above the wire and freezes as the pressure is relieved, so that the wire appears to traverse the block without cutting it. When lumps of ice are pressed through a narrow passage they crumble, melt, and re-cohere, so that the whole mass flotos, much as if it were a viscous fluid, a circumstance which is employed in explaining the ^o!0 of glaciers. < In this connection the pupil is advised to read Tyndall's Tht Formt tf Water. Fia. 107 VAPORIZATION 168 124. Vaporization.^ Water left in an open vessel gmdually Jiiesaway," tliatj&_c lian"5g? to an infliii 7le vapor and beuomea diffused through the a ir. This jHW^sJs^all^djia^matton and Its conver.se is called condensation, or liquefaction. ;;..A ^ow vaporization, which takes pliuiR only at th§ _exp2afid_iiuifaw.e{ *Jiqdil^w .calisjlTS^^iowr A t agid P100tis , i , w' iui^ inaj t ake Dlace throughout thn JaUJd, iiUt. llHUilillv h nimt ra pid nt tl.o pni.,t ..4.^w. heat is applied, is called Jo j;%, or ebullition. 125. Evaporation. J: ^(i2'«4'Xi^^2/' e!'?i>o/-a?;on (/™?«rf, _on tAe /tafMr« of t he liquid ~ ^oohi,l evaporatesjaster "" _tEan^^wateri2o« the ]a^e^^re_o[lSr^^^^Z^ws^m wateTevJtlJora!^ faster than cold watei ^n thTtZinera - ture of the air abo ve the liofuid —heatei] air will hold more vapor than cold air^onsequently evaporation is more rapid into hot air ;*Vnjh e .change of the air over the Jiquid — water evaporatesinore ijuickly on windy days than when the air is still Qore the extent of free turf ace expo»ed — a pint of water sprinkledTver a flo'STivapo- rates very qmckly^ndonjhe ^resmrejnjhe mirfaee of Jj^lisuid — auguT refiners hasten evapoi^onliy^piac- ing sugar solutions in vacuum pans where pressure is reduced by means of air pumps. Liquids tliat evapo- rate quickly are called volatile_J ufuide. Evaporation takes place at all temperatures. Even ice and snow evaporate. The laundress does not hesitate to hang clothes to dry even though she expects them to freeze quickly. Snow heaps and lilnrks of iV « become reduced in mass at a_£eezing^^ temperature. _^ 154 HEAT 1 86. Boilin g Point deiardent upon Prtfinre. — III evaporation, molecules fly from the surface of the liquid and mingle with the particles of the air ; but in boiling, the vapor, more commonly called steam, escaping too rapidly to bt'coine iramediatuly diffused in the air, drives back the air a little way. Not until the steam acquires a jTi'ssure a trifle greater tlmii that of the atmosphere can a licjuid begin to boil. The greater the external pressure to be overcome, the greater must be the pres- sure, i.e., the higher the temperature, of the steana. Injvery cate the boiling point i$ an indieati»n of the heat energy ntce»*ary to overcome cohe»ion_ injie Ugfuid and die p reimire oil iti turfaee in order th^ t)iejmUetU0 may pats off at a vapor. Experiment 2 Half fill a glass flask with water. Boil the water over a Bunsen burner; the steam will drive the air Trom tKe fl-aslf. Withdraw the burner, quickly eOJk the flask very tightly, invert it, and pour cold water upon the part containing steam, as in Fig. 108. The water in the flask, though cooled several degrws below the usual boiling point, boils again violently. The application of oAi wiiter diminishes the pressure of the steam, so that the pressure upon the water is dimini.slied, and the water boils at a temperature lowt-r than its normal boiling point. Fio, 108 Ej^Himent 3. — In a beaker half full of distilled water suspend a thermometer so that the bulb will W covered by the water and yet be at leut 2 inches above the bottom of the beaker. Apply heat to the DISTILLATION beaker, and obiervo any changpa of teinperaturo tliat may occur, both before and after boiling begins. The nnircnry in tlie ther- mometer rises continuously until the water begins to lioil, but Boon after, that is, as soon as tlieriiial elication of heat to it. It is found that {l)/pr a i/ iefn preuure Hot exiiiiiple, that of tlie atmosphere at 700 mm.) every li,[uid has a definite boilinn Point Ci illed the normal lujiliuif.^iitJoT that liquid; (2) this boiling point, ^-'miiini ■■" imfnnf nft^y hoiling lull begun; ( 3) the boiliii< j pui nt of a liquid tMirea»P» ,mtj^ th^ j'retiure. A riw nf '97 nun. in the higlit of a barometric column is attended with a rise { of about 1° 0. in the boiling point of water btjiled in \ an ojf the cliaiigi' in atmospheric pressure. At the higlit of 3 miles atiove sea level, waU^r cannot be got liot enough in an oiien vessel to coagulattf the wliite of an egg. Roughly (fwaking, a difference of altitude of UOU feet causes a variatiou o£ 1° C. in the boiling point. ^^' ^*^^**^°° This is a p rocess li y wbirb aHqiii.l . i» obtained by evaporation in_a state of £urity. If two Tlliu.Jo n.c imiabJ, for example water and alcohol, the more volatile of the two will be vaporized first, leaving •"tfie less volatile bgMnd; or if there are impurities in "^ter, for example salts in solution, the liquid evapo- rates and leaves the solid matter. At sea, fresh water for drinking purposes may thus be obtained from sea water. 166 HEAT A till for dirtillaiion on a imall »c»le may be fitted up a» In Fig. 100. A glasa flaak, C, contains the liquid to be dia- tilled. This is connected by a glass tube to a condenter, A , which has within it a coil lit tulw, B, called the worm. lid water is Biphoned from 11 vi'swl, E, into the condenser and overflows at F through the tube //. Tlii.s sertes to keep the worm cool so as to condense the passing vapor quickly. The product, called the distillate, trickles from the end of the worm at b. Fio. 109 SECTION VII LATENT HSAT 198. Latent Heat of Fusion.— E\-«!y one knowsjhat, in generitl, beatjtpplied to a body raigesjte te.mEera- ture. ■i'TVi>^excejeiiflnaLia tlus rule we haye_ just studied under the head of meltmg and boilin/j . g Aa Tyft learned in §122. the ter » »lnii.Jttat of I ^un on of a s ubstance is the uuiuber i>f oal«nca^thaLuu)>t \ be applie d to a kilogram of that substance to change I it from j> soiid to a li quid stqt^ without a chany^ of J resulting t em pera ture _That is , a given i^uantity of water falling in temperature 1° furnishes just heat enough to raise the temperature of an equal quantity of water llT JBut if a kilo gram of "VraTer at 100° t\ be^oured upon a Kilogram of small ice ■ I or snow at 0° C. and the temperature of the miX' ture after the ice is melted be taken, it will be found to be agproxi mately 10° Cj 7n ow to r aiii e the kilogram of water resulting trom the melted i(« f rom 0° C. to 1 0° C. recjuire s 10 calories of heat, which are furnished by the kilogram of hot water in cooling from 100° C. to 90° C. But the hot water cools to 10° C. It is evident, then, that the heat yielded by the water in I cnoling from 90° to 10° is rendered latent in melting the ice. ' The latent heat of fusion of ice iSj tber^Qie, approximately 80 cadorias. The latent beat of fuwon 158 IIEAT \ of other substances may be found in the Table of Prop- erties of Solids in the Ai>ijendix. 199. Transformation of Heat Reversible. — fl y^j t thaf. ^jl^jKg tiltfi tiIed, tli.^ nU-ani jwiwinK tliroUKli u tiihe into a I'.aker, U, containing a known quantity of cold water having a known temiwraturo at till' iHiginning. TIib licat rendered latent in converting tlie wat afBpipnt. Tnonna of producing extremely low temperatures. Whatever tends to hasten evaporation (see 8 125) tends to accelerate the reduction of temperaturey_Through the consumption of its own heat in the process of evaporation, the liquid itself _ becomes colder, and then reduces the temperature of all objecte in its neighborhood..^ The more volatile the liqui d employed, the more rapid is the consumption of heat, other things being equal. / Ezpciiment 2. -rr-J^iU the palm of the baud with ethei ; the ether quickly evaporates and produces a sensation of cold. Ether Ti not colder than neighboring bodies except when it is allowed to evaporate. / E;^riment 3 Wrap a wad of cotton batting about the bulb ot a ^Eliermometer, wet the batting with ether, and swing the thermometeT swiftly ^irough the air •* few times and note the fall of temperature as indicated by the thermometer. 134. Heat co nsumed by the Expansion of Gases. — If a gas ^ allnw pfl t" y^pnTiti tup' nst pressure , work is done , heat is consumed in doing it, and t he temp e r a t ure of the gas is lowered. In steamships which maSe long voyages the refrigerators constructed" for conveying perishable material like meat are kept cold by tliis process. Air is comp ressed by steam power to about one fourth its normal volume. This itself heats the air, since by this process lEe'work required for compression is converted into heat energy. DEW-POINT 168 (See § 98.) The air iajhen cooled by contact with pipes kept cooUji cplijyater Bowing tiirouj|li tlteiu7 Tlie air ia tl ien allow ed" to expand antalhe refrigerating chaiiilwr. a nd ita temperatnra i. Jowered ; for jt.mjjat he. understood tliat in order that a^in- J)re8»ed gas may resume ita normal volume against pceasure^an. amount of heat energy is rer vap.^i- it, .rpnlaiiTfr_ A given vo lume^f^air,.fQr exampla a cubic meter, can hold ^ragTTlmited ^quantity oi water vapor. This quantity d epend s on the temperature of the air. The capacity of air foFY apof Screases rapidly with the temperature, J ieing nr ' ■'.douWed.hy a rise of 10 centigrade degrees. On the . L- hand, if air containing a given quantity of water vapor be cooled, it will continually approach and finally reach saturation, since the lower the temperature, the less the capacity for water vapor. It is evident that 164 HEAT air satumted with vapor cannot have its temperature low- ered without the condensation of some of the vapor into a liquid, which will appear, according to location and con- dition of objects within it, as dew, fog, or cloud. The temperature at which this condensation occurs is called the dew-^oint. The dew-point may he defined as the temperature of tattiratioii for the quantity of water vapor actually present. The greater the quantity of water vapor present, the higher is its dew-point. Capacity for water vapor depends upon teinperature ; dew-point depends upon the quantity of water vapor present. . If the existing t^'mperature be far above dew-point, it indicates that the air can^ contain jauch more water vapor than there is in it at the time, and the air is said to be dry. The heat of a stove dries tlie air of a room without destroying any of its water vapor. In siioh a room the lips, tpngne, throat, and skin experience a disagreeable sensation ot dryness, owing to the rapid evaporation which takes place from their surfaces. / EXERCISES 1. To what is the " dampness of night air " due ? 2. How dn "air-tight stoves" and furnaces dry the air in apartments ? 3. (a) How is the "sweat" sometimes seen on cold objeoto such as ice pitchers, tumblers, etc., caused? (6) When the sweat collects quickly and abundantly what does it irdicate respecting the dew- point of the air ? (c) In such cases what slight change of temperature in the air will cause rain 9 4. Which are the more favorable to deposition of dew, windy or rtill nights? Why? 5. The air in a certain room is said to be "dry." (a) Does this indicate that the dew-point in the room is high or low 1 (6) If the temperature of the air in the room should fall, how would its humidity be affected ? (c) Would the dev^-point be changed ? THREE PROCESSES OF DIFFUSION 165 SECTION X DIFFUSION OR TRANSFERENCE OF HEAT 136. Three Processes of Diffusion. — :7liere is always a tendency to equalization of temperature ; that is, heat has a tendency to pass from a warmer body to a colder, or from a warmer to a colder part of tlio same Iwdy^ _unti l "there is an equality of temperature. There are three processes of diffusion of heat, — conduction, convec- tion, and radiation. 137. Conduction. Bzperiment 1 — I'late one end of an iron wire about 10 inches long in a lamp flame, ami hold the otlier end in the hand. Heat gradually travels from the end in the flame toward the hand. Apply your fingers successively at different points nearer and nearer the flame ; you find that the nearer you approach the flame, the hotter the wire is. The ^w; of Jieat through an unequally heated body^^ from places of higher to places of _lQ\ver temperature, is called conduction; t he bo dy through which it travels IS called the conductor. The nioTeciiIes ofUie wire in the name Tiave their motion quickened; tliej' strike their neighbors and quicken their motion ; the latter in turn quicken the motion of the next; and so on, until some of the motion is finally communicated to the hand and creates in it the sensation of heat. .^Experiment 2. — Fig. Ill represents a board on which are fastened, by means of staples, four wires: (1) iron, (2) copper, (.") bra.ss, and (4) German silver. Tlace a lamp flame wliere the wires meet. In about a minute run your fingers along the wires 166 HEAT I I Fio. Ill ( from the remote ends toward tlio flame and see how near you can approach the flume on eacli without Buffering from the heat. Make a list of tliese metals, arranging them in the order of their conductivity. S(in»H HI Iwtiilir'Hil wtwlttct-hfttt niimll more rapidly than otli ers. ThuJoiTner ar. i callud uoo d eotiJuctors, _ the latter pnnr conducton. Metala are t he .beat conductoi5i_ though they differ widely among tlienmelves, at) our experiment shows. Iron and marble, wh ich are good conductors, feel colder to the toucH of tliu hand than wood, carp et, and otlier poor conductors, because they conduct heat away from the hand faster. On the other hand, if these substances have a temperature higher than that of the hand, the latter will feel hotter than the former, because they conduct heat to the hand more rapidly. Handles of cooking utensils are made of non-conducting material to protect the hand from heat. Experiment 3. — Nearly fill a test tube with water, and hold it somewhat inclined (Fig. 112), so that a flame may heat the part of the tul)e near the surface of the water. Do not allow the flame to touch the part of the tube that does not contain water. The water may be made to boil neai its surface before any change of the temperature at the bottom will be perceived. Li(iuids_ are extremely_poor_con- ductors. Gases conduct heat j>racti- '^Uy not aTair. ^r clothing does ^not afford us heat in coH wgmher; it Is, mfleeSTcolder than our bodies. It simply checks the escape of JhiLheatof^urJjodies. 'Tills is accomplisllwd in paTT^ the poorly conducting fiEiir8~ of the. clothing, but more by the air CONVECTION IN GASES 167 ■paces in the mealies of the cloth anil by the layer of air con- fined between the clothing and on- bodies. The protection obtained from the escuiie of heat from our lionses by fliij use of double windows is little due to the thin glass which intervenes^ it is due almost entirely to the Ix^ly of confined non-conducting air inclosed between the winclnws. Siiow^is a great protection to vegetation from the severe cold of winter on account of the air confined in the spaces between the crystals. 138. Convection in Gases. — Conduction takes place gradually and slowly at liest from particle to particle, the body and its particles beinj,' relatively at rest. Con- vection takes place when the body moves or wliea thera is relative m otion between its parts, the heat in either "jS^ J'^iig conveyed from one place to another. Experiment 4 — Cover a camllu flame with it glass chimney (Fig. 113), blocking the hitter up a little way so that there may be a circulation of air beneath. Hold smoking touch-paper near Fia. 113 Fio. 114 the bottona of the chimney; the smoke seems to be drairn with great rapidity into the chimney at the bottom; in other words, the office of the chimney is to create what is called a draught of air. Experiment 5 Place a candle within a circle of holes cut in the cover of a vessel, and cover it with a chimney, A (Fig. 114). 168 HEAT Over an prificn in the cover place nnotlior chimney, li. Hold a roll of »niokiM(; tiiiu-h-i>u|ier over li. Tli« smoke ileiteiMids thii cliimncy mid jittBiM^ii through tlie vuhwI and out iit A, This illus- tratcB tin- method often adopted to produce a ventilating draught through nuneH, Let the interior of tliu tin vesnel represent a mine deep in the earth, anil the chinineyn two Hhaftii Hunk to opposite extremities of tlie mine. A fire kept liurniiig at the bottom of one shaft will cause a current of air to sweep down the other shaft and through the mine, and thus keep up a circula- tion of pure air through the mine. The cause of the ascending currents is evident. Air, on becom- ing heated, expands rapidly and becomes much rarer than the surrounding colder air; hence it rises, much like a cork in water, while cold air jiours in laterally to take its place. In this manner winds are created. Sea and land breezes are convection currents. Yentilation y or the process by which a proper supply of fresh air is nmintained in our living npartnients, is intimately connected witli convection inasmuch .is ordinarily it is through the latter that the former is secured. The heating appa ratjM^ghoiild be so arranged as to produce, in the inost efficient manner^liorivection currentsthat will expel foul air an3~iniroduce fresh air. 139. Convection in Liquids. Experiment 6. — Fill a small thin glass flask with boiling hot water colored with a teaspoon- ful of ink, put in the stopper, and lower the flask deep into a tub, pail, or other large vessel filled with cold water (Fig. 115). Withdraw the stopper, and the hot, rarer, colored water will rise from the flask, the cold water descend- ing into the flask. The two currents pa.ssiiig into and out of the neck of the flask are easily distinguished. The colored Fio. lis RADIATION 169 liquid marks dintinctly t)i« pi'tli cif tlw ln'uli'il CDiirpi'tiiiii curn'iitH tlmiiigli tlio clear li(iuiil, aiid iiiukis i-li'itr tlii^ iiii'IIiimI I>,v wlilrli lifiiit, wliiMi n|i|>lii'il at till! Iiultuiii (if n IhhIv cif I'uimiI, lii'coiiiea rapiiUy il'lfiiwil tlirnii);li the ciiti'"' laxK, iiiilwitliHtniiiliiii; that liiluiJi) are jH«>r cniicliietors. It ia tiy xiiiiilar (•unvectioii curri'iits that the wariiilii){ of hiiihl- iiigs l>y hot .vatcr is I'ffei-teil. Jiui'T. healecl in a hoiler^liv the biueiiieiit riwH throu);h [liin's to the railiatnrH iiiJliiLioyJUiLabuvei t here it y ivei lieat to the air of the room, ami, after l>eiiijr thus cooleia»ngitrontii ofUie relation Ixitwei'ii lit-iit and nioliir work. Ono of the moHFTmpofluiTl"(>f"m-ci>t (HiMJoveruii in HC'ience in the equivaliuce of heal ami work ; tliat iw, tlwt a definite fuantitt/ o f molar work, when tranijfonned withgut watte, JLVMl" definite quantity of hat ; and, conversely, that Jhii heat, when tranrformed without waite, can perform the oriffitfal (fiaiaity of molar work. 142. Transformatioii, Correlation, and Conkcrvatlon of Energy. — Tlie proof of the facts just stated was one of the most important stc'i* in the establishment of the grand twin concejitionH of modern science : (1) f^ii ^t. nil ..jBB^f.Sf-Jiaergy are K.relatedJosmi another that energy of anjf ktnd_ can be tranrforined into energy of any other ^nnd, — known as the doctrine of the correlation of KNEKOY; (2 ) iiuA-when one form of energy ditappeari itt exact equ ivalent in another form alwayi taket Ut place, to that the turn total of energy it unchanged, — known as the doctrine of the conservation of energy. The wliole drama of the universe consists in transfer- ences and transformations of energy; all natural phe- nomena are due to them, yet creation and annihilation of energy are not possible through any agent _,- known to man. Energy is often wasted in that it goes where it is not needed, but it is never annihilated. Another great law of conservation may be mentioned in this connection. Chemistry teaches that there is a conservation of matter, MECHANICAL EQtriVALKNT OF HEAT 171 »'.«., tlmt mutter in iicitluT creiitiiblo nor luin'liiliihlij through any known iigency or proctiiM. 143. Mechanical Equivalent of Heat. — AHMured that hcat^U n fonj^ of untTKy^ I)r. Jouh- o f Ennhind under- took (1840) t o iwcerUiin thu niinu-nciil ru hUion li^lafij-n tliB-uaiU of h*mt itiitl thIwB Hf moliir workJ' ^1|e jirmnged u iMiddle wht'.-l in ti vcxniI of wutfr (((Ahiit tJio weight. fe l'Wing ii tlicnnonif tr r iu thu wutiSuLfciumL J!lflLll!?-i2I'JSS^ thp water witjj . BtiiimU . tbiLiy Hrnier it ^)ecnme.T II«L"ii«5iire(l tlie work done by the dencend- uig weiglit and the torreNjjoudiug Iieut pi-odm til l>y the paddie turning in the water, and d'!te mined the ratio between tiie two quantitieH. By a Hiniilar nietliod but with improved details Row- J»n.'Lal.S»UilUQre repeated (187D) the expe.inient with^ O-'f the greatest care that liaD ever lieen exereised id ' obtained for a result the following, which differs it little from the result obtained by Joule : 1 calorie =«= 427 kgni.; that is, 427 kgm. ot work if convei-ted int^i heat would raise the temperature of 1 kg. of water tlii'ough 1 centi- grade degree. BXXRCISES 1. Let the pupil Uke a surfey of the facta he has gleaned thus far relating to heat, and argue therefrom that the modern theory of heat \» valid. 2. If a body weighing 20 kg. fall 80 m. in a vacuum, how muth heat will be generated when it is stopped f 3. How much molar work may be done by 6 calories of heat if none ia wasted t 172 HEAT Si. ■^1 • ■ .,\- A SECTION XII STEAM ENGINE 144. Description of a Steam Engine A steam engine is a macliiiie in which the elastic force of steam is the motive agent. Imismuch as tlie ehistic force of steam is entirely due to heat, the tteam etigine u properly a heat engine ; that is, it is a machine by means of which heat is continuously transformed into the energy of mass motion. The modem steam engine consists essentially of an an-angement by which steam from a boiler is conducted to each feide of a piston alternately, and then, having done its work in driving the piston to and fro, is discharged from each side alternately, either into the air or into a condenser. The steam engine furnishes to the scientific student a most interesting illustration of the transfonuation of heat into work. For the hot steam whose expansive force propels the piston falls in temperature and loses much of its energy as it does this work. To this is due the unbsilanced force which drives the parts, for there is always steam both sides of the piston, but the steam doing work and the steam that has just done work have different temperatures. 145. Tie LocomatiTe.> — Few works of man have so com- manded the admiration and excited the wonder of youth and ' For historical farts conoerninE the locomotive, the pupil is advised to read Smiles' work entitled Thf Life of Georga Slevemoti. Fur the history and the theory of the steam cn^ne in jjeneral, he m.iy read with profit an article on this subject by Ewln^ in the Enctjclopsodia Britannica, and a bibliographical sketch of James Watt in the same work. t 1 Ill I 1^ ? I = - I t-^ - = - - , t r ? 9 SSS33S • -S I ji« i g. I. I ..ill « > 'j4 K '/. i, i, K H " THE LOCOMOTIVE 178 age M the locomotive. Not a few have stood beside t)ie huge " iron horse " and wished that tliey might " see through it." The author, having tliis in mind, has ventured to digress from the beaten paths of textbook , and to produce a cut of a modern locomotive without giving a description thereof, which tlie pre- scribed limits of this book do not permit. Plate II represents a locomotive so dismantled that the pupil may see much of its interior structure, while he will be assisted in his examination by the accompanying list of names of the most important parts. T~ ^ I ^ CHAPTER V SOUND SECTION I WAVE MOTION 146. Waves This word recalls a class of phe- nomena with which every peraon is familiar. Every one has watche^ with interest trains of ridges and fur- rows traversing the surface of a pond when disturbed by the wind. Every one has seen a wave run along a clothesline when struck with a walking-stick. The stu- dent will do well in commencing the study of this sub- ject to attach one end of a cord to some fixed object, Fl(i. llfi hold the other end in his hand, stretcii the cord hori- zontally and, by quick and periodical movements of the hand up and down, produce in the cord a train of waves. He will observe (1) that a wave originates in a disturb- ance at some point in the medium ; (2) that this dis- turbance consists of a vibratory motion, caused by the up-and-down movement of the hand; (3) that the dis- turbance is propagated successively to other points in the medium ; (4) that any particular point in the cord, 174 VIBRATION FKEQUENCr 176 e.g., a (Fig. 116), simply executfs a vibmtoiy motion corresijonding to tliat of tlie liaiid, for example in the line ah. Hence, we conclude that wave motion it due to the propagation of vibratory motion to euocessive pointt in gome medium. It will be oljserved further that while the wave trav- erses the medium, the medium itself is not transferred. The ocean's billows cause the ship to rise and sink, but do not bear it onward. While, however, there is no transfer of matter, as in the flow of a river, there is ii transfer of energy; for there must be a transfer of energy wherever there is a transfer of motion. We have then arrived at a new method by which energy may be transferred, that is, by wave motion. 147. Vibration Frequency ; Amplitude ; Wave Length By one vibration of a particle we shall understand the motion of the particle from one extreme position to the other and back again. The time required to make a single vibration is called the period of vibration. The number of vibrations that occur per second is called ^ ^^ J^V'' — ^" d the vibration frequency . ' Imagine an mstantane-?;-;;;,^^^^"X,^_|-/?^^~X;---;;/^^^ r as photograph taken of a " * cord along which contniu- ou3 waves are passing. It would appear much like the curved line CD (Fig. 117). This curved line represents what is known as a simple wave line. The distance from any vibrating point to the nearest point which is at exactly the same stage of its vibration is called a 176 SOUND d iV> .*^ 9 ^ wave length, ns wx, uv, or en. The distance between tlie extreme positions of a vibrating point or the length of its journey, os, is called tlio amplitude of vibration or the amplitude of the wave. 148. Waves of Compression and Rarefaction. — Every wave consists of two parts whicii are tlie exact opposites of each other in their character, called its pha»eg. For example, a water wave consists of an elevation and a depression. In the waves which we have thus far studied the vibrations are transverse to the direction in which the wave moves. Wo m-e now to consider a class of waves whose phases consist of condenmtions or comprei- »ions and rarefactions in some medium, waves in which Fk;. lis the vibratoiy motion is in the direction in which the wave moves. Such vibrations are called longitudinal vibrations. Instead of a cord spoken of aljove, suppose we use a long spiral spring made of elastic wire. Hold one end of the spiral Li one hand and with the thumb nail of the other hand rake it quickly for a short distance lengthwise. We thus crowd close together for a little distance, B (Fig. 118), the turns of wire in front of the hand and leave the turns tehind, A. pulled wider apart. The crowded part, B, represents a condensation (or com- pression) and the stretched part, A, represents a rarefac- tion, and the two parts collectively represent the two AIR AS A MEDIUM OF WAVE MOTION 177 opposite pliascs of n wiive. Tliis wave, with its conden- sation in advance followed liy its rarefaction, runs with grant velocity along the spiral and pro.luccs a shar]) thump on the object t.. which it is attaclicd at th(' other end, and thus transmits energy, through the agency of wave motion, from tlie hand to the ohjcct. Fig. 118 represents a portion of the spiral while it is tiiivcrscd I.y u train of waves. A anil Jl represent an entire wave, while C represents the normal condition of the coil. Waves cannot lie transmitte.l through a spiral made of inehustic soft wire, for the turns after being pulled apart would not close up again. Ehutuii;, is eueutinl in a medium in order that it may tr«mnut waves of com- prelsioH and rarrfartion; and the greater its elasticity, the greater the facility and rapidity with which a medium transmits waves. 149. Air aa a Medium of Wave Motion. — lieiiiR Iiifjl.Iy elastic, air is a very suitable iiiediuin for the tran».ni,si,ion of waves! This may be illustrated in an interesting manner as follows • Fia. 11!) Place on a table a long tin tube, AH (Fig. 119), and at its orifice, a, a candle flame. Also hold a smoking paper for a few seconds just inside the end h so as to fill this end with smoke. Then strike tiie table a sharp blow with a book close to the end b. /\ 178 SOUND Instantly the candle flame ifi quenchean a physical plK.nonK.no,.. No more appropriate name than >„u„d wave can 1» applied to the physical agent with which we are to deal; it suggests at once the reality, aii.l is not sugges- tive of some vague mysterious " thing " shot throu.rl, space. Sound is a teniation peculiar to the auditory nerve, caused umally by air wave, heating upm the organ of hearing. Sound wave, are wave, in any medivm (usually air) that are capable of producing the sensation of ,ound. If we could see the air as it is traversed by soun.l waves, we should see spherical shells of condensed air |iltematingwitii shells of rarefied air, a section of which IS roughly represented in Fig. 120. The condensed por- tions correspond to localities of greater pressure, the rarehed portions to localities of less pressure. When there is an increase of pressure on the drumhead of the ear it is pushed in, and when the pressure becomes less the drumhead springs back. T 180 SOUND M I If A body vibrating in an elaitic medium, e.g., in air, doea noi necesiHirily produce sound waves; in otlier word*, not all wavei are wiuml wjiv.-s. Fur fixiini|>l.', Um cniTity nf tlie viliratiunn nia^ im 1.11 be iiisuflieieiit, or the vibrating l)os very ne" J^^^ ^ .„ Bound waves travel in wat«r about four Umes as la. ^nd in iron and in glass sixteen times as fast. _, , _^ ^, ,B. an experiment ^r,o™,«i in ^^'^l^l^^^^'^V^'^- EXERCISE 188 ■zracuM 1. The Interral of time betwvcn M<*liig » IlKhtnliift Huh uid hear- Ing Ura thunder U 3 mcoikU. How far away U tli« thiiiKltr cloud (expreMed In mete.ii), the tein|ierature of the air being !«»»(,■. f «. The flaah of light prndured by the dlwhargii of a gun ia aecn acroM a lake 2 mile* wide and the report la hranl n mcmuU afur- warda. With what velocity (expreued in feet iht wcuml) did the •ound travel ? 8. An echo of one'a voice produced by a diatant hillalde Ih heani In 6 aeconda when the temperature of the air la 0»C. How far diaunt ia the hillalde, ezpreiaed iu feetr SECTION IV -I ■mSOY OF SOUND WAVBS - LOnDHESS OF SOUIID 156. Energy of Sound Waves depends on the Ampli- tude of Vibration. — Fix your nttention upon u pirticle of air as a sound wuve pussea it. At a certain point of its vibratory excursion its velocity is at its maximum Now, since tlie energy of a moving particle vams an the square of its velocity, the ititfugiti/ of the impact which it is capable of producing upon the ear it proportional to the tquare of this maximum velocity. It can be easily proved that if llio amplitude of vibra- tion of a particle be doubled while its perioeir v ^^^^ ^^ ^ from their Source. -It is am ^^^i^j.^es very vation that the loudness "^"^^^^^ce of the waves .apidly as the distance ^rom the s^ourc^^ ^^^^^^^ ^ to the ear mcreases. ^s a ^^ ^^^^^ an ever-widening sphere, a ^^'"'1'^^ ' ,^rface; Incomes distriimted over an ^^^"^^^^^ ,, the and as a g-ater number o^a^-JP;^^^^^^ motion, the f ••-•^fX::!!r:«uenceof the less ^^^^^y;^2t:T.r..i.<^^ of a sphere varies as r^r : H^^^us" -that cs) ^^o^.^^ SPEAKING TUBES 185 w«Te ▼tries Inversely as the square of the distance from the source. The alxjve-mentioned geometrical law is known as the Law of Inver»e Sijuares, anil is applicable to many other classes of physical plienomena besides those of sound. 158. Speaking Tubes. Experiment. — Place a watch at one end of the long tin tube (Fig. IIH) and the ear at tlie otlier end. Tlie ticking sounds very loud, as tliough tlie watch were close to the ear. Long tin tubes, called speukinij tubes, jiassing through many apartments in a building, enable persons at the distant extremi- ties to carry on conversation in a low tone of voice, while persons in the various rooms through which the tube passes hear little or nothing. The rea.son is that the sound waves which enter the tube are prevented from px]>anding, so that the energy of the sound -waves is not affected by distance except as it is wasted by friction of the air against the sides of the tube and by internal friction due to the viscosity of the air. d\_ SECTION V KEENFOKCEHENT OF SOUND WAVES - VIBRATIONS ■ SYMPATHETIC 159. Reenforcement of Sound Waves. Experiment 1 Set a tuning fork in vibration ; unless it is held near the ear, you can scarcely hear the sound. Press tlie stem against a table ; the sound rings out loud enough to be heard in all parts of the room, but the sound seems to proceed from the table. When only the fork vibrates, the prongs, presenting little surface, cut ♦*>eir way through the air, producing '^M SOUND ^ the fork does to the table. Expriment 2.-Take ''^.8'''»:J;^thrust one' e.:d into a vessel ,„,^aW.inc,.^----Suove.U.eo.^e^a ,,.at.rC^and o.a ....^ ^^^^^.^^^_ ^^^^^^•T'Trt^i— very loud.. sound rapidly dies away. Columns of air, o. well a« .oundmg- pitch. „tpffected? When the prong HowisthiBreenforcementeffeeted^ „-, to the other, a xnoves from one e-trem.ty «f ^^ -c^ ;^. ^^^ ^„„. .., H sends a conden^auon d w «.e^tu^^^^ ^^ ^^^^^^^ .ensatio. stnkjng the ^u rf ac ^^^^ ^^^ ^^^^^ ^, ^^, MEASURING WAVE LENGTHS 187 reflected condensation reaches the prong just at the instant it is starting on its retreat from a" to a'; then the reflected condensation will combine with the ccmdensation formed hy the prong in its retreat to make a greater con- densation in the air outside the tulxi. Again, the retreat of the prong from a" Ui a' produces in its rear a rarefiic- tion, which also runs down the tube, is reflected, and reaches the prong at the instant it is about to return from a' to a". 'J'he return of the prong from a' to a" causes another rarefaction in its rear; these two rarefactions moving in he same direction conspire to produce an intensified rarefaction. The original sound waves thus combine with the reflected to produce resonance; but this can happen only when like phases of the two tr-.iins of waves ('oincide ; for if the tube were a quarter of a wave length longer or shorter than it is, condensations and rarefactions would concur and destroy one another. The loudness of sound of all wind instruments is due to the resonance of the air contained within them. A simple vibratory movement at the mouth or orifice of the instrument, scarcely , ,di- ble in itself (such as the viliration of a reed in reed pipes), is suffi- cient to throw the large body of air inclosed in the instrument into vibration, and the sound thus reenforced becomes audible at long distances. The human voice owes much of its tone to the resonating cavities of the mouth and nose. 161. Measuring Wave Lengths and the Velocity of Sound Waves It can be shown that if we know the vibration number of a fork, wo can find the length of the coiTssponding sound wave as well as its veloci'y. Suppose the fork to make 256 vibrations per second; the time of half a vibration is ^\^ of a second. In this 4\ 188 SOUND back again. The lengm oi velocity of the „„„a «.ve »2'" "; j^ „,„„„ 18 m„h» ».d Th.u., .uppoM tl« ii.l«»ee '■ ^^^^ f'**x;;trx " ttt li ..... - ""« Tu XSl th„ ,-.... «P-ed i» the formula wave length — ; velocity '' vibration frequency shorter the wave length. 162. Sympathetic Vibrations. 162. sympamciK. .»"'- . ♦, Vress down gently one oftlie keyset a piano so l.„a.y into the ^"-"-l^^J^;::!';::"— "» t^atca^ ::te 1. .nng, t.U ..^g ^^l' '2:;:;;^lS .ano i,y p.e.in. Raise the dampers from »"«',"'' strongly s.m.e note into the foot on the right-hand pedal, - "l;-^ J ™ ;. ,^^,,^ „„,y those the piano. Although all the ^'"^^^^^^'^J^^.^,, ,;„;, .-,., those .^respond loudly th^™ of .ihrations per that are capable ol maKinf, ■= second a» are produced by your voice. MUSICAL SOUNDS AND NOISES 189 The pulses or waves that traverse the air between the vocal orgiins and the strings, sd gentle that only the sensitive organ of the ear can perceive them, become great enough to bend the rigid steel wires when the energy of their blows, dealt at the rate of jjerhaps 512 in a second, accumulates. The large nunil)er of blows makes up for the feebleness of the individual blows. Vibrations produced in this manner are called sympa- thetic vibrations. Such vibrations Kometimes produce serious results. Instances are known where tlie vilirations of inacliinery in factories liave -caused in the walls of the liuildings sympathetic vibrations w hicli liave shaken down the buililinjjs. Military commandera order their troops to " lireak step " in crossing bridges, lest the vibrations set up might break the bridges down. SECTION VI MUSICAL SOUNDS 163. Distinction between Musical Sounds and Noises. — A sound is a sen-sation produced by a shock given to the drum of the ear. This sensation dies away rapidly but not instantaneously. When the shocks follow one another so rapidly that the sensation produced by one is not quite gone before another is caused, tlie impression transmitted to the brain is that of a continuous sound. Every one is familiar with two classes of continuous sounds, called musical sounds and noises. A musical sound or note is a continuous, uniform, and pleasing sound, such as is given out by le string of a piano ; while a noise is an irregular, fitful succession of shocks h ! I; J Ml 190 SOUND over cobblestones or by a t.ain o araphU.amre'entationo/atloi.e Via. 122 o{ sound fairly well- then -P -"f ;';J^^^ ,,,e .s /■. or grave, and m the described u. ^^e form ^^ ^^^^^^^ ^^ ^ i 1 oft1 vibrations per second ; the sounu pi JlaT«4^«To" — ••-••''^•'■"•• f.'^pto. tuned W »» -';f jril.-* 1- MUSICAL SCALE 191 The pitch of a suund produced by twice ivs many vibrations as that of another sound is called the octave of the latter. Between two sui^h sounds tiie voice rises or falls, in a manner very pleasing to the ear, by a defi- nite number of steps called musical intervals. This gives rise to the so-caUed diatonic scale, or gamut. The inter- val between two notes is the ratio of their freciuencies. The vilmition nnnilier which shall constitute a given note is purely arbitrary, and differs slightly in different countries:, but the ratios between the vibration numbers of the several notes of the gamut and (he vibiivtion num- ber of the first or fundamental note of tlie gamut are the same among all enlightened nations. The interval Iwtwcen each note in tlie scale and the funda- mental (1), the interval l)etwcen each two conHecutive notes (2), and two serieH of whole numbers which are proportional to the frequencies (.'i) are shown in the following table : •7 is>- — -=> «>- = -a «- Z= ^ g -^ 0' d' e' f er a' b' c" (1) 1 (2) (8) 24 f 1 f 27 30 IS t i 1 32 36 V 5 V 2 f U 40 45 48 261 293.62 326.26 .348 391.5 435 488.87 622 The ear is incapable of determining the number of vibrations corresponding to a given tone, but often it is capable of deter- niining with wondrous precision the ratio of the vibration num- bers of two notes; hence, all mu.sic must depend upon the recognition of such ratios, and in considering the relations between the pitches of musical notes, we have to deal with ratios of their freiiding component Tibrations. For example, at = ,-» + ro, and mn = ~ mv + mu. In diagrams, for obvious rea«on», it Ih nmcli eaHJer to repre- •ent transverse vilirations with the understanding that the results depicted apply evch wire lengthwise over a resonance box. t lurched to the shorter '-;^:^^i^^ (Fig. 125), and the tension of the wue g Fio- 125 nEATS 19fi TIN tlmM of Tibntion of itrMclwd itringt of tb* autorial vary: (1) INnetly •■ the length of the itriiigi. (2) DineUy u the equare root of their maaaet per unit of length. (S) Inveredy at the equan root of their teneloM. We will take for illuHtrntiDii the i;i>itar oa a typical ntringed instrument. It ha« aix utriiigB, three of ailk covered with Bilver wire, and three of catgut. lU raiiKe in about three ootaveii. The pitch in thifi iiiatruiiieiit in vuritd in three \ta,va: (1) ScrewA are employed t« vary the ttiiHion of the ntriiij;". (•-') To piwR from one note to another on the same Htrlng, the finger prewiea the iitring down on a "fret" and thus changea tiie length of the atring. (:i) Tlie |iltch of the lower atringa ia diminiahed l>y increaaing tlieir niasat-s. Thia ia accompliahed liy having them wound with fine silver wire. In the piono the pilch of a string depemla on ita length, moaa, and tenaion. It ia not intended that the lenaion of any one string shall change. If from any cause the tension changes, the piano ia said to be " out of tune." 169. Beats. Experiment 1 — Strike simultaneously the lowest note of a piano and its sharp (black key next above) and listen tc the reaulting sound. You hear a x>eculiar wavy or throbbing sound, caused by ail alternate rising and sinking in l(>udne8.s. These variations of intensity are called beats. Let the continuous curved line AC (Fig. 126) repre- sent a wave pnweeding from the lower key, and the (lotted line one from the upper key. Now the waves from both keys may start togetlier at vf ; iis the wave from the lower key has a greater wave length, at certain 196 BOUND * H condcnmitioiw will correnpond with interval m «t P, conucnmi momentary .ilence, too short, however, t« be percuveu. Km. VM ■ 1 l,v the e«r i» ("rrectly repre^enteil in ita the number of >«"'« '* '''1 _„ .^^ The number of vibration ^^-^i;^:':,^,^!. tone, i. e.aal . sniper ':?:s;:;^---- "-^- Uon.) at that po.n^ a.u^ be v h.^t ^^^ ^^^^ ^^^^ ^^ the note P-^ " ^e VaTm^rvaS along the -"^^ TJX i^ : ^tl string vibrates in the. string, It will l.e toun ^^^ ^.^^^ ^j^ ^ tions a^ sh- B ' 1 ig.^ ^^^^^^ lirif Jgte half Ld one fourth i. length from COMPI.KX VIBRATIONS 197 one end, iia in (2) nnil (4), tlm notcu ;,iven will l)o C" iind C", re«iK!ctively, luid tho vibnition fraiui-nciee of the Fwndwnintal ton* I'm. 127 severid Bections will Le, as we hIiouIcI cxjiect, twice and four timeH tlmt of tho opeii Htring. The iKjiiitu at which there are no vibrations are called nodet, and the portions bi'tween the niHleH au cidled a«liotu({raph by a student. THE PHONOGRAPH 201 Helmholtz analyzed sounds of different musical instru- ments by means oi a set of resonators (one of which is represented in Fig. 128) corresponding to tlie various tones used in miisic. By applying one resonator after another to the ear he was able to detect the component t»nes of sounds far too complex to be analyzed by the unaided ear. Musical instruments are of little value unless their tcnes are rich in up- per partials. The human voice in gen- eral is especially well supplied in this respect, but " O what a difference between the voice of a Patti and that of the average uncultivated savage!" Fio. 128 ,;•) Fia. 129 174. The Phonograph. — This instrument is designed to repro- dice human speech. It if constructed on the principle thi' as sound i.i profJuced by vibrations of air, any sound can be rut -oduced SOUND FiQ. l"/" by reproducing these vibrations. A hollow cyUnder of wax vl rFis l^O), U 8liri>ed over the n.etallic .^UnJ^r M. The mouth- piece B (better shown in Fi«. 130) is next placed in position. Closing the small end of the mouthpiece is an extremely thm disk of glass, C (Fig. 130), to which a gravmg point, D, is attached. , , ii. • „ Now when a person directs his voice toward the mouthpiece, the aerial waves cai.se the disk C to participate in every motion of the air, and this vibratory motion of the disk causes the iwint 1) to indent the wax. The cylinder M meanwhile; is kept rotating , uniformly by means of a spring and clock- work S, an.l at the same time the cylinder moves slowly lengthwise. When the disk is at rest the point traces on the wax cylinder a spiral groove of uniform depth. Ib.t when the disk is caused ^. vibratl the groove becomes of variable J';!''", c-resp^mdnig to the rarefactions .nd compressions of the air. Ihis groove thus formsarrmanentrecoidofthevibrationsofthed.sk. To reproduce the sonn.l, another more delicate point attached to a similar disk is made to work in the same groove, so tha when the cylinder is rotated, the p..int on the second disk pa ses over the elevations and depressions in the groove and ,s tl.us made to vibrate in the same way as did the recording point. This motion is coiummiicated to the disk, causing it to vibrate in the same manner as it did under the influence of the incident sound waves The disk communicates its motion to the air, and thus the sounds are reproduced. The oOice of the -sonator F is to give direction to the sound waves and to render them ='"'1 ^le While, commercially considered, the phonograph ,s little more than a toy, yet from a scientific standpoint it illustrates ,n a very on^Lenive manner the entire mechanism of sound. It also eprLnt, the only completely successful attempt to reproduce human speech artificially. Words spoken to the instrument Lay may be reproduced with the identical intonations and qualit=es of sound in the hearing of any succeeding generataon. PRODUCTION OK VOCAL, SOUNDS 203 SECTIOK X PBODUCTION OP VOCAl SOUNOS - AUDITION 175. Production of Vouil Sounds. — Tlii^ actual (iigaii f(,r the production of vocal »oiiii,l waves coiisiHts of two cla«tic iiieiubrancs, an (Kig. l:ll), callcil tli« rm-al ,;„;h. 'them conh are streti'licd across the top of the windpipe, whidi is a tulii! li'adiiig to the lungs, and It is to tlie vilirations caused in the cords when air from tlie lungs is forced tlirongli the slit-like ojien- ing b between them that vocal sounds are due. Tlie length and tension of these vocal cords can be altered by inua- ' cular action with great rapidity ; hence, the extreme flexibility and great range of tone, usually called compasx, of the Imman voice. The vocal cords in men are thicker tiian in women and children, so that tliey vibrato more slowly, and therefore jiroduce lower tones. The sounds produced by the vocal cords are greatly m<«lified by varying the sliape of the resonance cavity of the mouth. It is easy for one to find out for oneself, by uttering the four sounds of the vowel a one after another, that the altering of the shaiKi of the mouth produces tlie cliange of vowel sound. This is artieu- lation. Fio. 131 176. Audition. — Sound waves enter the ear passage C (Fig. 132), and, beating against the thin membrane D known as the eardrum, impress upon it the precise wave forms that are transmitted to it from the sounding body. This wave motion is transmitted to the chambers 00 of the inner ear, which are filled with a liquid. Into this liquid from the walls of these chambers project thousands of stiff elastic hairs of varying length and size. The auditory nerve TT is divided at this extremity into filaments, 204 SOUND one of «hich i. attache.1 to each hair. When the yrave motion reaches the li.iuid content, of the inner ear the hair. .mn,er.ed therein receive the impulses. , • i... Now if you raise ?M the dampers off the strings of a piano by pressing down the right-hand pedal, and sing strongly the vowel sound. «A, 00. an.l ee, for instance, against the sounding-board, stopping to listen U> the respon.*, there wiU be given back by the Fig. 1»2 Wires a surprisingly perfect ah, »«, ee, et<=. Each wire selects the particular constituent of the sound with which it is m sympathy, and the compound tone given back is an almost perfect duplicate of the original. . . * » ri,. In a similar manner we suppose the different hairs U> act Me the piano wires, and each to select that particular npple in the big wave with which it is in sympathy. The nerve filaments connected therewith transmit the impression to the brain, where in some mysterious manner these disturbances are interpreted as sound of definite pitch, quality, and loudness. 177. Limits of AudlbUity, etc. - There is a limit to the pitch which is audible to the human ear. The fallo^ving li^t of approxi- mate values of corresponding vibration frequency is submitted: LIMITS OF AlIDIBIUTY SOS Air ViDRATioNfi tfr Sfcond Range of human hearing f 40,000 30,000 4,000 2,000 512 to 2W 128 32 10 highest audible aounil. the shrill cry of a bat. highest musical note used, high ■opr;>no note. womaii'sconversational voice. man'M voice (convergatlonal). lowest musical note used, lowest audible sound. iiljcr of the tone g" of an American REVIEW EXERCISES 1. On what two things does the lenslh nf sound wave'i depend? 2. The energy of sound waves cliniinisliLs as they advance. What change in the vibration of the piu-ticles of liie medium occurs ? 3. State, respectively, the three properties of a sound wave that determine the tliree properties of a sound sensation, viz., pitch, irUen- sity, and quality. 4. What Is the lengtli of sound waves in feet, [iropagated through the air at a temperature of 20° C. by a tuning forlt that vibrates 250 times per second ? 6. What is the vibration nuu piano ? 6. If two tuning forks, vibrating respectively 256 and 258 times per second, are sounded simultaneously, what jAenomenon will occur ? 7. If a tube 30 cm long, closed at one end, respian or corpuicular theory, was supported by Newton (1672), and by most physicists up to the early part of the nineteenth cen- tury. It assumes that a luminous body (e.g., the sun, a candle flame) emits streams of minute inatenal parti- cles (corpuscles) which tmvel through space m all direc- tions with immense velocity, and that these particles by their impact upon the retina of the eye produce the sensation of sight. Since light cin traverse not only socalled empty space, but also some forms of matter, e.g., glass, water, 206 RADFATION; KADI ANT KNKK(;y 207 etc., it waa neceKsary to nHHume tliat tliew particles were able to past) between the inoleciileH of matter. Tliis theory has been found incaiml.le of exi)laininjr, and in some cases wholly inconsistent with, many phenomena tiscovered sime Newton's time, an« «''«'« f^^^'f.'^ sometimes on opposite sia«8 of the sun. Let S (Fig. 137) VELOCITY. OF LIGHT WAVES 213 represent the sun, E the earth, and J Jupiter. Romer discovered that an eclipse of the satellite is seen about 1000 seconds sooner when the earth is nearest to Jupi- ter than when it is most remote, whence he concluded ®^ Pia. 137 that tins time must be required for the light to travel the difference of path between ,1'E' and JM or the diameter of the earth's orbit. Assuming this distance to be 186,000,000 miles, the velocity of light must be about 186 000 miles per second. Various independent methods have been used to determine the velocity of .ght; suffice it to say they all agree very closely with the velocity as here given. At this rate light waves would go around the earth between seven and eight times in a second, or while sound waves would travel about one fifth of a mile. EXERCISES 1. Why are images forme,! through aperture, inyerted ? ^^reen h^iL'fh"" '"' "V"" '""*" "'P^""'"' °" "" '"«"'"'^« <>' the ■^reen from the aperture ? 3. Why does an image become dimmer as it become, larger? 214 RADIANT ENERGY — LIGHT 4. Why do we not imprint an imago of our penon on OTory object in front of wWch wo Btand? 6. Upon what fact does a gunner rely in taking eight f aba perfectly transparent body visible ? 7. At what time in tiie day U the shadow of an upright stick shortest? ... . , a What does the great velocity with which light waves travel indicate respecting the elasticity of the ether ? 9. Why ta it ditBcul', to determine the eiact Hue on the ground where the umbra of a church sUcple tenninates ? \0 What is the shape of a section of the shadow cast by a circu- lar disk placed obliquely between a luminous particle and J. screen? What is its shape when the disk is placed edgewise? U The section of the earth's umbra on the moon in an eclipse always h .^ a circular outli.te. Wliat docs this show respecting the shape of lii.' earth? . 13'.. The sensation of sound is how produced? (6) How is tJie sensation uf sight produced? (0 How are sound waves produced? Id, How are light waves produced ? (e) Which, sound waves or ether waves, originate u. molecular vibrations? (/) Sound waves travel in whatmediums? (j) Light waves travel only in what medium ? 13. (a) What is radiant energy? (b) Do all bodies emit radiant energy ? (c) Do all ether waves eflect sight ? (d) Do all bodies gen- e^^ight waves ? (e) Is a " dead " coal seen by ether waves which it generates ? SECTION TI IHTEHSITY OF ILLUMIMATIOH 189. Law of Inverse Squares. — Every one knows that a gas flame gives a stronger light than a candle flame. If a sheet of white paper be held midway between these two flames, the side next the candle flame will appear considerably darker by contrast than the side next th. gas flame. Indeed, it might require as many as sixteen candle flames to Uluminate the paper as much as the LAW OF INVERSK SQUARES 215 single gas flame, provided the distances from the paper were equal. The power of illumination is detem.ined by the amount of light receive.1 by a unit area of illumi- nated surface. We are aware that the illununation of a given surface diminishes as it recedes from thesouree of light. The Intensity of tUs Ulmnination diminishes «s the »qu«pe of the distance from its source incieases. For example suppose we assign the value one to the illumination of a visiting card when placed at a distance of 1 foot from a lamp flame; then the caitl will have an intensity of illumination equal to mie fourth if plar-ed at a distance of 2 feet, one vinth if at 3 feet, and so on. This is the Law of Inverse Squares as applied to light. This law may be illustrated thus: A square card placed 1 foot from a certain point in a candle flame, as at A (Fig. 138), receives from this point a certain quantity of light. The same light if not intercepted would go on to /?, at a distance of 2 feet, and would there illuminate four squares, each of the size of the card, but, being spread over four times the area, can illuminate each square with only one fourth the intensity. If allowed to proceed to C, 3 feet distant, it would illuminate nine such squares and would have only one ninth its intensity at A. The unit generally employed in the measurement of the illuminating power of the light emitted by a lumi- nous body is the British candle-power. It is the illumi- nating power of a sperm candle I of an inch in diameter, burning 120 grains to the hour. Flo. 138 S16 RADIANT ENERGY -LIGHT 190. Photometry. -The law given above e"*^l« «f to compare the illuminating power of one light w.th Tha of another, and to express by numbers tWr ,.^ tive illuminating powers. The process is called pho- tometry (light measuring). Ex«rta.nt.-Pl«=e an opaque rod, C (Fig. 139) vertically a of two Ughts, 4 and B, aide by Bide on the screen, in i~ no. 139 of the screen upon which the shadow a falls receives light only tm tre candlf^ and none from the gas flame A; ;»>; P^"" » iXnunated hy A alone. The rod C thus secures io^^^ ^ a Dortion of the screen which it alone lUummates Move either Ug^Zard or from the screen untilbothshadowsbecon.^^^^^^^^ intense Then measure the distances from 4 to 6 - c, and Irom bTT= I B at distance d illuminates the screen as mtensely as ^ at distance c. Hence (see § 189), A-.B^c'-.cP; or, iUe inUnsiUes vary direcU,J as tU square, oflKose distances from the screen at v,hich equal Ulumination is obtained. EXERCISES 1 (a\ SuDDOse that a lighted candle is placed in the center of each 1. (o) suppose innv » * , .„,o 20 and SO feet on a side. Coro- of three cubical rooms, respectively 10, 20 "'^ »» ^ each of the rooms. MIRRORS; IMA6ES 217 bom the cuidle win h. h„ , "* °" * ""■«'" ^^ cm. disUnt dleHi^^JS"" "^f "' ' P^P*' ^^^ "« illuminated equal-y by a ca.. die flame 60 cm. distant on one side and a eag flamp 9m 5. ., ..»dard candle, .hat is the intensity'TheVflime P "'^ "^ " SECTION III KSFLECTION OP IIGHT rpfl^^'l'f"*"', ^""'f*^- - Polished surfaces which reflect hght regnUrly (i.e., do not scatter the light) and show images of objects presented to them are called mxrror». The mirror itself, if clean and smooth, is scarcely visible. According to their shape, mirrom are called plane, concave, convex, fpherieal, parabolic, etc. Experiment 1 — Draw a straight line, t- (Fig. 140), on a largo sheet of white paper spread upon a table. Take a rectangular piece of mirror glass, Jl/ about 10 cm. by 3.5 cm., and support it vertically on one of its long edges on this Fio 140 line so that the silvered surface is just over this Une. At some point, A, stick a pin vertically. Place our eye at some pomt, E, so that you can see the image of the pin pm, ^ , TO tiat It ooinoides with the image of the first pin. ■ WFLtCTIHa _ •URTACI Slg BADIANT ENERGY -LIGHT You are now to verify the following facta : m iTtog at the Lage from different pomti. of view thrfmale does not change ite position THe trnag. Zl^atelpoliticn in ^ace independerU of the o Wen 2)But U the object (U, the pin) be moved or the Jrror be inclined to the line L, the image ^Ibo moves^ ^3) connecting poi..U..d.'by^^Bt«^^^^^^^^^ this line is perpendic- ular to the reflecting surface. (4) Measuring the distances AO and A' 0, youfindthattheobject and its image are at equal distances from the reflecting surface. Hence, we conclude that the Image 0* • P"*^ fnnt of tlie minor. 198. Law Of Reflection. -The point A (Fig. 141) emite rays in all directions. Let AO' represent one of Ze ^ys. Then the two right-angled triangles A'OO t2A7o are eq. .1, since they have one common s»de, T^ le sides A and AO are equal. Hence, the angles OfAO and (yA'O are equal. . Draw the line NCy perpendicular to the mmor at poSrJ. Then the angles i.^« ^^J^^^^T Le they are respectively equal to OA'O and (yAO. Fio. 141 DIFFUSED LIGHT 219 The angle between the normal and the incident «y ^O'iV u. called the angle of incidence. The angle betwen the normal and the reflected ray NWJi ia called the aiigle of reflection. The hiw of reflection of light may be stated as foUows • At emy poUit of , reflecting nirfice the angle of reflection i* equal to the angle of Incidence. 193. Diffused Light. «xp«iment 2._Introduee a»iimll l«,ani of Hunlight into a dark- ened room, and place in ite path a nnrror. TI.„ ligl.t i» reflected in a defi mta dn:ect.o„. If the eye be placed «. a« to ..ceive the reflected light w 11 be pamfully intenae. Substitute for the mirror a piec6 of ung^azed i«i«r. The light is not reflect by the paper Z any definite direction, but i, scattered in .,e.y directiormun.i- nating objecte in the vicinity and rendering them visible. Look- ing at the paper, you see, not an image of the sun, but the paper Itself and you may «ie it equally well from all directions. »!n„ K rT!°^ '.'" P"'*' '"'""'"' "8'" '™'" » "«fi"it« direc- tion but reflects Urn every direction j in other words, it scatters, or d.ffu.e., the light. The difference in the phenomena in the two cases i, caused by the difference in the smoothness of the two Fiu. 142 eflectmg surfaces. AB (Fig. 142) represento a smooth surface, hke that of glass, which reflecto nearly all the rays of light in the same direction, because nearly aU the points of reflection are in the same ptane. CD represente a surface of paper having the 220 RADIANT ENERGY -LIGHT ,„al. at polnU "'j-'*'--;™ " very ^-1^ Thu.. the dull ai of divergent ray« P-;-^-^^-^^ , J,„, pe^n- diculaw at the points of incidence, or the points where these rays strike the mirror, and making the angles of reflection equal to the angles of incidence, the paths PC and KC of the reflected rays are found. Every visible point of an object sends a cone of rays to Uie eye. The ^int always appear at^h^lace whence th^ point H in the direction CN. The exact Lse point, may be und by contmumg each ^"cd of Is behind the mirror until it comes to a VO^^\^fj' TrJat N. Thus, the pencils appear to emanate from fhesf i^ nte, and the whole body of light waves received t L eye seems to come from an apparent oh e<^, ND, U^iZ mirror. This apparent object is caUed an Fio. 143 REFLECTION PROM CONCAVE MIUKORS 221 image. An image ii n point or a series of points from which diverging pencils of rays come or appear to come. As of course no real image can be formed buck of a mir- ror, such an image is called a virtual or an imaginary image. It will be seen, by construction, that an inuge in a plane minor ai>pwrs as far behind the minor ai the object U In front of it, and U of the tame aiie and shape as the object IZBBCI8X8 1. If a mirror were perfect, could it be seen f 2. EipUin why it i. difficult to read the Image of a printed page In a plane mirror. ^ 3. (a) Lay a minor on a table and hold a ehanwned pencil verti- cally over it. latlie image of the iwncil erect or inrerted? (6) Incline the minor at an angle of 46° and keep the pencil vertical. What la the ponitlsn of the image? 4. Stand your book on end on a Uble and open It so Uiat the iearea make an angle of about 60°. Now place two minors in a similar poal- tion and place a pencil vertically midway between them and count the Imagea of the pencil. How can more th'ui one image be formed in each minorr 6. An object lying in front of a plane mirror la moved 3 cm. farther away from the mirror. How much does this change the dtatance between the object and iu image ? 195. Reflection from Concave Mirrors Let MM' (Fig. 144) represent a section of a concave spherical mirror, which may be regarded as a small part of a hol- low spherical shell having a polls, ed interior surface. The distance in a straight line from M to M' is called the diameUr of the mirror. C is the center of the sphere, and is called the center of curvature. G is the vertex of the mirror. A straight line, DG, drawn through the center of the curvature and the vertex is called the 1. I ria.144 222 UADIANT KNBROY-UOHT pWn«r«'»l-;'"f the mirror. A oonoavo mirror m.ybe radii of the mirror, M CA, CO, and Cli, ar« perpendic- ular to the ■mull planes which they strike. If C be a luminous point, it is evident that all light waves emaimting from Uiis point and striking the mirror will be reflected to the.r '" L^I J*; be any luminous iK)int in front of a concave mirror To find the direction that rays emanating from This point take after reflection, draw any two lin«. from this ^int, as KA and KB, represent ng two of the nfi- nite dumber of rays composing the divergent i>e>.ed that strike the mirror. Next, draw radi. U, t^e pom ^f incidence, A and B, and draw the bnes AF and BF, «Sg a.e angles of reflection equal to the angles of See. PlL arrowheads on the lines rep— g rays to indicate the direction of the moUon. The Imw ^J and BF represent the direction of the rays after "tS'be seen that the rays aft^r reflectionare con^ ver^ent, and meet at a point, F, called a foeu*. Th« SiB the focus of reflected rays that emanate from Zpo int M. It is obvious that if F were the lummous .*j^ X;L lines AB and B, would represent the r^flec^d rays, and S would be the focus of these «ys. Since the REFLECTION KROM CONCAVE MIRRORS 228 wUUon between the two imnia in such that light waves emaiuiting from uitlier one are brought by reflection to the other, theee pointo are called conjugate foci. Cnyu- gaU/oci are two point* «o related that the image of either i»f ^'' " **" "^ length of the mirror? C) D*""** "" ""**•.,„. „.„ Atwhat . o /M Tinflcribe the image. distance from ine mirror ">" «"" o- - from the mirror appear ? (*) De,ecribe the image. i \ f lil i fe SECTION IV BKFRACTIOH 197. Some Effects of Refraction. - In Fig. 149 is shown a rectangular tank having two glass sides, A and II Fio. 148 B. Direct sunlight through a window cast* a shadow 5 U« end CL of the tank. EF is an edge of the K'^FRACTION* 227 shadow. Now if the tank be filled with water (dightly clouded With „.ilk, ,0 3, t„ „„d,, ,h^ illumina Jpor^ Uon clearly .Lstinguishable from the shaded portion), the edge of the shadow will retreat to EO. That is the rays of light that graze the upper edge EC are' abruptly bent downward on entering the water, Z move m paths more nearly vertical. IxpMiment 1 - Place a coin at the bottom of a teacup. Look obhquely mto the cup in s„ch a manner that the coin i, 1^^ h dden by the edge of the cup. Now. without moving the Te fi.l the cup with water. The coin ' ' becomes visible and is seen at A'. A ray of light, AB (Fig. ISO), on leaving the water at B, is bent in the direction BE. Observe that it is turned farther from a vertical line, CD; also, that the coin and the bot torn of the cup see-n to be elevated or the water less deep than before. Compare this with a fact that every boy has learned on wading into water, that he has to roll his trouse™ higher than previously appears to be H a lead pencil be thrust obliquely into water, it will appear bent at the surface of the water, and the immersed portion will appear shortened and raised nearer to the surface. If a narrow strip of thick plate glass with a straight piece of wire just back of it (Fig. 151) be held before the eye so that rays of light from the wire wUl pass obliquely through the glass to the eye, the wire will "■■■tion will appear moved either to the right or to the left according to the inclination of the glass. But if the gla«i be not ■n- iined, the wire does not appear to be moved to either tide Fio. ISO fra. 161 KADI ANT ENEBGT- LIGHT „f liTVit travels in the same uniform The angle /i-fiA (rig. i'*'/ " /-,top thp Jo"; lIg, the a«.^e 0/ r,fra.tie ft^, moves with equal velocity « J°°8 ^J\^„t ,, e„ter, the Sf^:j^^;^^s::^.--..t.reui. INDEX OF REFRACTION 229 ito onginal velocity; so that while the point a moves to a', A moves to *', and the result is that the wave front assumes a new direction (very much in the same manner as a line of soldiers executes a wheel) and a ray or a line drawn per- pendicularly through the series of waves is turned out of its onginal direction on entering the glass. Again, the extremity c of a given wave front, cd, emerges from the glass tirst, when Its velocity U immediately quickened, so that while d advances to d', e advances to c', and the direction of the ray is again changed. It is evident that if the ray enter the new medium in a direc tion perpendicular to its surface, .>., with its wave front parallel to this surface, aU parts of the wave front will be retarded simul- taneously and no refraction will take place. Since light waves travel with different velocities in different mediums, it follows that there must be a corre- sponding difference in the lengths of the waves in the different mediums. The ratio of the wave lengths in two mediums is equal to the .•atio of the respective velocities in tiie two mediums. 190. Index of Refraction. — The deviation of Ught waves in passing from one medium into another depends upon the optical densities of the mediums and the angle of incidence. It diminishes as the angle of incidence diminishes, and is zero when the incident ray is normal to the surface. It is very important, when the angle of incidence is known, to be able to determine the direction which a ray will take on entering a new medium. Describe a circle around the point of incidence A (Fig. 153) aa a center; through the same pout draw ///per- pendicular to the surfaces of the two mediums, and to this line drop perpeudiuulars liD and C'A' from the points 280 RADIANT ENERGY -LIGHT Then suppose that the perpe ^^^ ^^ _ ^^^ ^^^ fraction ^ is called the tine of the angle DAB. Hence, f^ « the «n« 0/ «A« angle of incidence. Again, if we suppose that the perpendicular CE is fis of the radius, then the fraction f j is the «ne 0/ tAe angh of refraction. The sines Via. 163 of the two angles are to u .1. .JL. J or as 4: 3. The quotient (in this case medium. A, i«to another, B, »« 7^' ^ IIJT W.. 0/ B 6y the absoMe ^nde. of A. TXB.- O, APPHOX.M..E ABSOX..T. IK..C.S ^ ^^ 2.5 I Alcohol niamond ... • • , m Pure ifster . . ■ ■ ^-^ C»ri)on dtolptWe . . • J- j^j^ ,» qo c. and 760 mm. mint fflmn . ■ . l-M to 1.78 Air » " I.OOOM Bitot giMs • , „ ♦„ 1 Ri Mcro re '" CRITICAL ANGLE; TOTAL RKFLECTION 231 The iBciprooal, of the above indices represent the ratios of the velocity of light in these mediun« to that in a vacuum. aOL Critic! Angle; Total Reflection. _ In Fig. 164 letJS' represent the boundary surface between two mediums and ^0 and BO incident «ys in the mor^ refractive medium (e.g., gL«s); then 0I> and oe may no. 154 represent ihe same rays, respectively, after they enter he less refractive medium (.^., air). It wOl be seen tliat as tiie angle of incidence is increased the refracted ray rapidly approaches the surface OS. Now there must he an angle of incidence («.<,., COM) such that the angle f refraction will be 90O; in this case the incident Sy ^■0, after refraction, will just graze the surface OS. Thw angle (COM), which must not be exceeded if the Hiy IS to pass out into the air, is called the critical angle Any mcident ray making a larger angle with the nomal I I! 282 BADUNT ENERGY -TIGHT thw, the critical angle, «. LO, caimot emerge from the Idium. and all such rays undergo -^em^ ^^e^^^"; ea the ray iOU reflected in the direction OJ^T. Refle<> io^ttSs caae is so nearly perfect that it haB recmved leBpecial name total re/ect.<«. Total refiectumoc^r, 2elray» in the more refractive medium are .n«ci*nta^ an ar^le greater than the critical angle. In other wo^ Tght cannot pass from a denser medium mto a« wh^ w™.rim.nt 2 -Thrust the closed end of a glass test tube resembles burnished silver. Fill the test tube with water and immerse as before; the total reflection which before occurred at the interface between the glass and the air in the submerged tube """/-"'PPf "»; The critical angle for water .s 48 30 , lor flint glass 38» 41-, for diamond 28» 41 , and gene 'r.y the higher the refractive index of fuy medium, the smaller is its critical angk Light cannot pass out of diamond at a greater Hence, it must be totally reflected intemaUy, Fig. US angle than 23° 41'. and the large quantity of light thus reflected is the cause of the bril- liancy of this gem. Glass is transparent, but when pulverized or broken into very small pieces it becomes opaque and »"°^y ^'''*«'^j;^' . i„to the mass without undergoing IS X"^n"tr.iS« -ner. the whi.n«- . «iow. it. Fio. 1B6 EXERCISES 288 op«lty, and the dazzling intenaity of the light reflected from it are accounted for. A ray of light from a heavenly body, 5 (Fig. 156), undergoes a «ne. o n,fraction, a. it «,ache. «ucce.,ive\tratu„.. of the 1 W ph^of «,„.Untly increa»i„gde„.ity, and to an eye at the earth^ u ^ t'. ^ "P"*'" ^ <"""« *"'"' « point. ■«', in the liltT* * " ''""■" '"'"' "' *'■•' «mo.phe™ on ihe path of hght that traverses ,t .s such as to increa*, the apparent altitude o he heavenly bodies. It enable, u. to see a body which is . httle below the horizon, and prolong, the apparent stej of the sun moon, and other heavenly bodies above the horizon^ TwilJ » due to both .«f raction and reflection of light by the atmosphe" KXXRCISIS 1. Ftad the index of refraction of light in pairing (a) from walw into carbon dtaulphide, (6) from diamond into water. 2. Light travels with a velocity of 180,000 miles per second in » vacuum. What is the velocity of light in Uter f .hf;i, *«* ^ *'■* "'"™"' °' "fraction depend on the obliquity with which light wave, strike the «,rface of a medium? (6) D«, tte index of refraction depend r.n this ? " ' W "oes the 4. When i. one medimn said to be opUcally denser than another f SECTION V PKISHS AND UirSBS 208 Optical Prisms.- An optical prism is a portion of a transparent medium bounded by surfaces two of which are plane and inclined. Fig. 157 represents a transverse section of a common form of prism. Let AJi be a ray of light incident upon one of its surfaces On entermg the prism it is refracted toward the normal, and takes the direction £C. On emerging from the 284 BADIANT ENERGY -LIGHT prum it i« again refracted, but now from the normal in the direction CV. The object that emit- the ray wiU appear in the direction VEF. Observe that tlie ray AB, at both refractions, is bent toward the thicker part, or base, of the prism. il03. lenaef. — Any trans- parent medium bounded by surfaces of which at least one is curved is a ?en». Lenses are of two classes, converging and diverging, according as they collect rkys or cause them to diverge. Each class comprises three kinds (Fig. 168) : CUM II Fia.in Clam I Convwgliig or 1. Biconvex 1 coiiTCxleiue", 2. Pl»iKW!OBY«x > thicker In the 3. Conc»TO-«)nve« middle than at •' tbeedgea. 4. Biconcave "I Diverging or con- 5. Planoconcave I cave lenaea, thln- 6. Conveio-con- f ner In the middle cave. J than at the edges. A Straight line normal to both surfaces of a lens and passing through their centers of curvature, as AB, is Fio. 158 caUed its principal axi,. There is a point in the pnn- oipal axis of every lens called its optieal center. This point is so situated that a ray whose direction withm the lens passes through it suffers no angular deviation, EFFECT OF LENSES 2S5 but at most only a slight latenU displacement. In lenses i and <( it is halfway between their respective curved surfaces. a04. Effect of lenses — Light wdves emanating from a lumuiouB point constitute a series of concentric hollow spheres. Near Uieir source the wave fronts are much curved, but as the distance from the source inci-eases and the spheres consequently be<;ome enlai^d, the wave fronts hecome more and more nearly plane surfaces, and when the distance is very great the waves may be con- wdeied a« having practically plane wave fronts. Such are the waves received from tlie sun. Fig. 159 represents a series of such waves, portions of which are transmit- ted through a biconvex lens, and the transfor- mation from waves of plane front to waves of concave front due to refraction. It is plain that the enei^y of these transmitted waves must become concentrated at the point F, which is called the/o«M of these waves A piece of cardboard held in the path of these waves wiU be intensely illuminated at this point for a brief time; but the waves being obstructed, their energy wiU soon be transformed into heat, and a small circular hole will be burned through the card. It is, however, in many ways more convenient to Htudy the relation of the ragt than to follow up the wave front itself. Fig. 160 represents in diagram the same no. ISO 286 RADIANT ENEUGY- LIGHT Fiu. lliO phenomenn, where only tbo direetitm of propagation of individual points in the wave front is considered. It will be seen by this diagram that incident niy» parallel ^ to the principal axis of a convex lens are brought to a focus at a iioint, /', in the princiiMd axis. This point is called the principal foeu» l)e- cause it is the focus of incident rays parallel to the principal axis. It may be, found by holding the lens 80 that tlie rays of the sun may fall uiwn it parallel to the axis, and then moving a sheet of paper back and forth behind it until the image of the sun formed on the paper is brightest and smallest. The focal length is the distance from the optical center of the lens to the center of the image on the paper. Tlie shorter the focal length, the more powerful is the lens; tliat is, the Fio. 101 more quickly are the parallel rays that traverse different parts of the lens brought to cross one another. Rays emitted from the principal focus F (Fig. 160) as a lumiQous point become parallel on emerging from a CONJUGATE FOCI 287 convex lens. If the mys emanate from a point nearer tl.« leuH, they Uiverg« after egrew, but Uie divergence k le« than befon-; if f„,,„ a poi„t beyond the principd focum they converge. A concave lens causes panillel incident rays to diverge uh if they came from a point, .18 F (Fig. 161). Tliis i^int is Uienrforc its principal focus. It is, of couwe, a virtual /oeu». It is apparent that the geatnl dhct «f on-;., Unse. i. to cnm tr.nmitt«d ny, to eomrttx.; that > auc.v. >„«,«. to cauM them to (Uveix«. ao«. Conjugate Foci, — When a hnniimi.s beyond tlie prim-ipid focus (Fig. 16J; .s. ii,l> convex lens, the emergent rays con- ~ verge to another point,/",; while rays sent from F^ to tlie lens would converge to F^. Two points thus related are called emjugtUefoei. Fig. 163 shows the cor- responding changes in wave front The fact that rays which ema- nate from one point are caused by convex lenses to collect at one point gives rise to real images, as in the case of concave mirrors. 206. Law of Converging Lenses — Lenses, like con- cave mirrors, have conjugate foci at distances i>. and D, Fia. 1«3 Fia. 103 288 RADIANT ENERGY — LIGHT I from the optical centers. In converging lenses the prin- cipal focal distance and the distance of their conjugate foci (or distance of object and image) are related accord- ing to the same formula as given for concave mirrors, v«i~ F D. A Hence the law of converging lenses: The ledpioeal of the prlndprf fecal leneth to eqiul to the •nm of the redproeeto of any two conjngate focal tengths. If the object be at a greater distance than 2 F, the image is real and is on the other side of the lens at a distance greater than Jf and less than 2 F. If tlie object be at a distance greater than F but less thar. 2 F, the image is still real and at a distance greater than 2 F. 2OT. Constnictlon of Images formed by Convex Lenses. — Given the lens L (Fig. 164), whose pnncipal b Fio. 164 focu« is at F, and .object AB in front of it, any two of the many rays from A will determme where its image, a, is formed. Two rays tiiat can be traced easily are, one along the secondary axis,! AOa, and one, AA', parallel to 1 A «condary axta )• » rtmlKht line drawn oWIqnely throagh » lens .nd p^Tg thZghlUoptl«a enter. Every rjy that t»™"" '"» i;^^ ta «*^ted In* J though It h«d pM«d throngh % plmne pUte. and there- l^^ l^ llTf direction p«.Uel to the Inddent ray. .nlferlng only a lateral diiplacement. i I VIRTUAL IMAGES 289 the principal axis ; the latter will be bent so aa to pass through the principal focus Jf and will afterward inter- sect the secondary axis at some point, a; therefore this « the conjugate focus of A. Rays can be simUarly traced for S and all intermediate points along the arrow. Thus, a real inverted image is formed at ab It IS evident that if ab represent the object, thee AB wiU represent the image. In eveiy case it will be found that in which /and i-epresent con^sponding dimensions of the image and object, i-u8ix,otively, an.l 7>, and />„ their respective distiuices from the optical center of Uie lens. 208. Virtual Images. - Since rays that emanate from a point nearer the lens than the principal focus diverge after egress, it is evident that their focus must be virtual iind on the same side of tlie lens as the object. Hence, the image of «i object i>Uced ne««r the ten tlun the prii.cip.1 focM is virtual, magnified, and erect, as shown in Fig. 165 A convex lens used in this manner is caUed a limpU mtcroKope. 809. Simple Microscope — As its name implies, the microscope is an instrument for viewing minute objects The simple microscope consists of a single converging lens so placed that the object is between the principal focus and the lens. It magnifies by increasing the visual angle. The magnifying power of tlie lens is simply the ratio l-etween the apparent linear dimension of the image and the corresponding dimension of the object, e.g.. , . 240 RADIANT ENERGY -LIGHT Jt!^ AB (Fig. 165). If the lens be of short focus, as is usuaUy the case, the magnifying power is approxi- niately the latio of the distance of distinct vision' to Fia. 168 the focal length. Thus, a lens of i of an inch focal length would magnify twenty to twenty-four times. 210. Diverging Lensos. - Since the effect of concave lenses is to render transmitted rays divergent, pencils of rays emitted from ^ and iJ (Fig. 166) diverge after refraction, as if they came from A' and li', and the image Fia. 166 appears to he at A'B'. Hence, image, formed by concve to^ u« virtMl, erect, «iid smaller thui the object. 1 »„, normal eves on object to be wen most distinctly must be placed .ta!rta:roMr.:'mncL. hence, this is regarded as tbedistaneeof distinct TisioQ. ANALYSIS OF LIGHT 241 EXERCISES 1. What must be the position of an object with reference to a converging lens that its image may be real and niasnilied? 2. A luminous point is 15 cin. Inun a o.puvex lens having a fucal length of 12 cm. Find the position of its imiige. 3. (a) Find the focal length „f a lens which throws the image of an object 6 m. distant on a screen 2 m. distant. (6) Compare the size of the image with that of the object. *. W^i'l a convex lens converge the light as much when immersed in water as when it is hi air ? S. Why can you not look very obliquely into water ? le„.f: "r 7"'^/°" '<"="« "" ""Ject, a screen, and a converging lens m order that the .mage should be four time., the size of the objL' 7. About what is the focal length of a simple microscope that magnifies thirty times ? io»iope mat raag^lfyl'""' '"'"' ""'"'' "'"""' """' " ''™ "' '' ""^""^^ ^"^^^ '^-Sth (b) What IS necessary that it may have great power ? 10. To an eye wh,«e distance of distinct vUion is 25 cm how mmy di«nete.s will a lens of 1 cm. focal length magnify ? SECTION VI PRISMATIC ANALYSIS OF LIGHT 211. Analysis of Sunlight. _ For simplicity of treat- ment It lia.s been thus far assumed that a ray of lijrht when refracted is merely changed in direction. We are ..o.y to learn that a beam of white light, e.ff., a beam of sunlight, when it is refracted becomes separated into a •urge number of rays differing in ref rangibility and color. We will imagine ourselves t« be in a room from which "11 light IS excluded. Suppose that through a narrow 242 RADIANT ENERGY -LIGHT Blit or crack in a window shutter a beam of direct sun- light is admitted. If a convex lens (not shown m Fie 167) is placed in the path of this beam of light, a distinct image, AB (Fig. 167), may be projected upon he opposite wall of the room. We will next suppose a Via. 1«7 ■=.„ r tn be placed in the thin sheet of light S: i^rXslm ttriens, as shown in the figu.. You nov. have revealed to you some remarkable phlomena which were fir«t successfully .nves U^^d , >T ^ /i«4n 1757^ (1^ Not only is the ngni iSCm fJtrpVit that which before wa. a „ .ow sheet is, aft.r emerging from the P«r- out fanlike into a wedge-shaped body, with !*« thieves part itssting on the wall. (2) The image, be ore only . na row vertical band, AB, is now di.wn out into a Ion, tontal ribbon, DK (3) The imag., before whit., CAUSE OF DISPERSION 243 now presents all the c.lo™ „f the minbow, from re.l ^rough all the intermediate graxlations of o— yellow, green, and blue. ^ ' We thus learn that (1) «,hite light {, not simple in its rr^"";^'-! .*f '*« --'' of a n.i.ture of color '^^^ l colors of ,A..A ^Mte UgM is composed may he epalZ hy refractun.; (3) the separati^ is due to the d^eZt Red wh.eh :s least turned aside from a straight path, is the leas refrungible color. Then follow orange, yellow g^en, blue, and violet, in the order of their refLJbility: SeT- ^';;^;Wion of white light into it« con- ■stUuents s called dtspersion. The numl^ir of colore of wh.ch wh.t. light is composed is really indefinitely g^t, ".ut we have nances for only seven of them, l, red LIT yf -. yreen, cyan Un., ultramarine\J, and noUt; and these are called the prismatic color,. 212. Cause of Dispersion; Origin of Color. -While for convenience we find oureelves often using the word ray we must not fo^et that there is no such thi^g .7a '•.*y: we must remember that in dealing with light we ■ire deal ng with waves I ;.,»,f ^ tlie same wave length. The difference of wave length makes .teelf known to our eyes as color .aria^ioZ ^ .ht waves d.m.nish in length from the red te the violet. v^ . t'""? °" '*'" ^'■'l"''"''^ ^'*h which aerial 'v.'ves stnke the ear, so color depends upon the fre- quency with .hich ether waves strike the eye Tht 244 RADIANT ENERGY -UGHT difference between violet and red i« a difference anaJ(v gous to the difference between a high note and a low note on a piano. In a vacuum the speed of propagation appears to be the same for all waves. Hut in a refracting medium the short waves are more retarded than the longer ones, hence more refracted. This is the cause of dispersion. Each wave length has its onn refractive index, or, since vibration frequency comsi^nds to color, every simple color has its special refractive index. Light composed of waves all of the same (or nearly the same) length is called homogeneous or rmnochrormtie light The yellovv light emitted by the flame of a Bunsen lmr.«,r or alcohol lamp when powdered Ix.rax is sifted upon it k approxi- mately monochromatic. Ordinary white l^slit is a mixture of long and short ether waves. From well.e8tal>li8hed .lata, pl.yrioirt^ hav,- oaloulated the wav.- lengths corresponding U> each of the prisnuitic colors, and the results are approximately as follows : Colors of thb Spkotrum Name ok Colob Extreme red . Bed. . . ■ Orange . • YeUow . . Green . . ■ C. blue . ■ U. blue . . Violet . . . Extreme violet Wavk Lenotu i« Wav« J.RKUTH IS MILLIOSTHB OP I MILLIOIITBB Ot A CENTIMETKR ' *** I^*^" irTfff RAINBOW 245 vX 813. Rainbow. -The rainbow i. .„ example of a solar ,nec- trum on a magn.ficent scale cau«Kl by di»pe™ion and refleer„ of light within falling raindrops. «na redection bulb filled with water and hold it in the sunlight,'^^ w ,£ back upon a white screen the rainbow colors. Tit sphere of w^e represents a sort of a n,a«nifi..l raindrop. I,et u.^ exan^Lrthe results when white light fron. the sun falls upon a r ^drop Suppose SA (Fig. 1(J8) to be ramarop. incident rays. Th,.y are twice refracted by the drop and totally reflected at its back surface. If an observer faces the drop with tiie sun shining on it from behind liini so that the red comjionents A'/r when they emerge from the drop make an angle S.\E of i-J", lie will receive from thi.s drop the impression of red. For violet light tbe angle is about 40^ a.„. for other colors it has values ".termediate between the.*-. The eye at F is ,,nt i„ » ,„ ^ • .... ■ .ii«- eye ui fi 18 not 111 a position o r«^ive the violet components I"/-', but must obtail, then, trom drops ,n a circle lying within the circle of red. Hence we see ,„ the rainbow a set of concentric circles of all the colorL of the .peetrum from the red on the outside to the violet on the "Hide The center of these circles is a ,«int in 8p.,c,. exactly li.nbtrvt """ '" * """ ^"■'"'"^ *'""""^''' *'"* '"" ^"'* "'" "y" °* 214. Chromatic Aberration. _ There is in ordinary convex lenses a serious defeot, called chromatic aherrl tior, the correolion of which has demanded the highest I'kill. The convex lens lioth rrfracts and dUperses th« lijrht waves that pasi, through it. The ten.leney of f-u«e. „ u> bring to a focus the more refrangible rays H' the violet, at a nearer point than the less refrangible Fni. KiS S46 RADIANT ENEEGY — LIGHT rays, such as the red. The result is a disagreeable coloration o£ the imuges that are formed by the lens, especially by those portions of the light waves that pass through the Ions near itn edges. This evil may be ovei^ come very effectually by combining with the convex lens a plano-concave lens. Now if .-. crown-glass convex lens be taken, . ant-glass concave lens may be prepared that will coi ct the dispersion of the former without neutralizing ail its refraction, since the refraotr ive and the dispersive powere of the two kinds of glass are not proportional. A cbmpound lens composed of these two lenses cemented together (Fig. 169) consti- tutes what is called an achromatio lent. Fio. IGil 215. Spectroscope. — An instrument naed for the examination of spectrums is called a »pectro»cope. It consists usually of a prism, or " dis- persion pie<*," and two astronomical telescopes. They are arranged as in- dicated in Fig. 170, where F is the source of light, e.g., a gas flame. The narrow slit S at tlie end of th. telescope A admits a pencil of light, the rays of which are made parallel by means' of the lens L. The parallel rays fall upon the prism P, but when they emerge froiu the prism every different color has a different directiou. Fia. 170 BRIOnT-LFNE SPECTRUM 247 - The spectrum, instead of hpin-r v,„„ i viewed th.„,h the^lil^y Tw:r„rT '■ jrraphio plate at «, immres nf ♦. ' f. P''"^"'^ " I'''°t<> ^Pi>ed. Inth«1^3aluu!„;'*"7'.'*'P''"'- to the physical an,! h ., 'nfonuatum in regard '^^"^ZLTi^Z:" ""'"'"'"""" " ^"^ -" placed in the alli^/'tsllT'T;' '^'™^ '^' Instead of a c^.tinuous speoLm of " " ' "'' ^■'""^- "•*o the flame. Each of th!^ "L " T-""""'"'' """'""««J '>on>x contain. «x)i«m. th'otL t "^''*-''"'-"» •- "^ 217. Franafcrfer Lines _TI,„=„i t^' contain a !•.,«» „ u / '"" «Pectnim is found ?«i- Ibe colored pictm* of th« solar spectrum 248 RADIANT ENERGY -LIGHT in Plate I bHowb a few of these lines. Tliey were fint mapped by Fmunhofer (1814), wlio distinguislied several of tlie more prominent ones by letters of the alphabet; hence, Uie dark lines of the solar spectrum have received Uie name of Fraunhqfer linet. ai8. Explanation of Fraunhofer Lines and of AbMrp- tion Spectruma. — Suppose an electric lamp to be placed back of the Bunsen flame (Fig. 170) so that the white light of the electric lamp will pass through the flame colored yellow with some sodium salt. On examination by tlie spectroscope, there will 1)0 found a diuk line m the yellow portion of the spectrum precisely where tlie bright sodium line (see §'21G) will be if the electric Ught be extinguished. The vapor of sodium m the flame, while capable of emitting light waves of a par- ticular length, is also cai)al.le of absorbing such waves coming from another source. This of couree leaves the corresponding part of the spectrum darker than tliosc parts where the energy of the waves has not been absorlied. If salts of lithium, potassium, strontium, etc., are used in a similar manner, there will be found m every case spectrums crossed by dark lines where you would expect to find bright lines. (See Spectrums ol Lithium, etc., Plate I.) Such spectrums are obtained only when light passes through mediums capa>.le of absorbing waves of paiticu- lar lengths; hence, they are commonly called abtorptto,, tpeetrums. The dark lines in the sular fipectrum may now be account, .1 for For example, the dark line in the Bpectrum in the exa.t place where we .hovUd expect to find the bright sodium hue sho^ » INFR.URED AND LLTKA-V.OLKT WAVt:s 249 vapor th,t thi. d»rk J.ne i, found i„ tl.„ ,„,lur „H,ctrui„ Til •lark lines »re dark. liowevBr m,i„ I... 1 • • "'*"'^'"»- ^"e from which it i, concluded tl at thZ^'J " '"''»'"""'». .un-, atmcphe. ,„ th« l^t^'T'z::^;'""';" ""■ '.".i-. cop^r, nickel. alun.inun..Wdro:;r;:i::;'<::;::r 819. Infra-Redand Ultra-Violet Waves. -The noUr «pectr«. i, not UmiteA to the visible .^Jrultut extends beyond it at each extren.ity kJZ -ly«. . besides sifti.., the wave^tLn ^ 7/;;: those of another, is able to separate waves which do Z prcKluce the sensation of light from those it d rho«, waves that lie beyo„d the red end of the vilible" Th^ i, ''"'''-'' "'* """'''• *''« ^Itra-vialet waves .ey fall upon sens.tued paper. The infm-red waves - bnger and the ultraviolet shorter than the lumri part. In the infra-red portic. of the spectrum Mctocorr rboiution test chart (ANSI and ISO TEST CHART No. 2) ■ti 111 |Z8 13.6 Hi y^i^i 1.6 ^ -APPLIED IM/IGE In ^^^ 16S3 Eoit Moin Street BT^ Roclwsfer. N«« York 14609 USA :^5 f^lS) <82 - 0300 - Phone ^S (7'6) 288-5989 -Fax 250 RADIANT ENERGY — LIGHT heat-giving waves extending over fifty times the space of the vis- ible spectrnm have been carefully studied by Professor Langley. The length of some of these waves is more than thirty times thai of the loiiRest light waves. These waves show striking peculiari- ties, especially with reference to their ability to pass through cer- tain substances that are opaque to light waves. 280. Only One Kind of Radiation. — The fact that radiant energy produces three distinct effects — »«., luminous, heating, and chemical — has given rise to a prevalent idea that there are three distinct kinds of radiation. There is, however, ahsolutely no proof that these different effects are produced hy different kinds of radiation. Science recognizes in radiation no distinction but wave amplitude, wave length, and wave form. T1>e tame radiation that produce* viwm can generate heat and chemical action. The fact that the infra-red and ultra-violet waves do not affect the human eye does not argue that they are of a different nature from those that do ; it shows that there is a limit to the suscepti- bility of the human eye to receive impressions from radiation. Just as there are sound waves, some too long and others too short to affect the human ear, so there are ether waves, some too long and others too short to affect the human eye. SECTION VII COLOK 821. Color \fy Absorption. — By the color of an object is meant in part the lentation the eye gets when looking at the object. In physios it is found convenient to apply the term color to that which produces the sensation, which, as we have already learned, is a train of waves of COLOR BY ABSORPTION 251 a particular length. When in future we shall speak of TfA waves, yellow waves, etc., it will be underetood that we rrfer to waves of suitable length to produce the sensattons of red, yellow, etc. Color is not a property of any body. The red rose does not possess the property of redness. Held in dif- ferent portions of the solar spectrum it appeara red only when the red waves strike it ; in other parts of the spei trum It appears quite different This shows that the red rose IS red not because it colors the light, but on account of some relation between the substance of the rose and the-light which falls upon it. If a beam of sunlight be passed through a red glass, and the light tliat ememes from the glass be analyzed, the spectrum will show that the glass transmits copiously only red waves, that por- Uon of the spectrum where the green and the blue waves ought to appear being dark and colorless. This shows that the glass absorbs nearly all the waves except the red waves. As the glass allows only the red waves to reach the eyes, it is apparent that the glass must look red. Color of objects so determined, usually known as body color, is said to be due to selective abtorption. In the caw of an opaque object, for example the rose referred to above, the wave, of white light penetrate a little way into the object and suffer selective absorption; those waves which escape absorption are reflected out and give color to the object. So the color awribed to the rose is the very color it reject* White does not exist by itoelf j it is indeed the/i««m of the entire spectrum. The simultaneous stimulation of the retina by all the visible colors in proper proportion results in a mental impression which we call »Ai(e. No more does black exist Black IS theoretically the absence of light. 252 HADIANT ENERGY -LIGHT m Theory of Color Vision. - The generally accepted theory of color vision is that suggested by Young and deve7nped by MaxweU and Helmholtz. Itsupposes the exUt^nce of three primary color un»aUon», red, green, and violet. For each of these sensations there is pro- vided on the retina of the eye a set of nerves especially Idapted to produce it. When all these sets of nerves l^excited simultaneously and with proper intensities Z sensation of white light is produced. Combined in proper proportions they produce the intermediate sensa. \om. Thus, red and green sensations combined give yellow or orange ; green and violet give blue, etc. . 223. color BUndness.-In this defect of vision one of the three color sensations, usually that of red is assumed to be either wantmg or deficient, so that he ToZ perceived a. reduced to those Ju-b^^y^^; remaining two sensations, green and violet. This causes the red-blind person to confound reds, greens, and gmy • In some rare cases the sensation of green or of violet is the one deficient. 224. Complementary Colors. - To produce the sensa. tion of white it is not necessary that waves of al engths should enter the eye. Two sets of waves p^perly chosen will suffice. Thus, yellow and ultra- Sia^ine blue and any two opposite colors in the diag^n (Plate I) combined will produce white. Any two olors which together produce white are said to be complementary. No two of the three Pn- J c"^- spoken of above can be complementary, since the third sensation would be wanting. COLOR FATIGUE; AFTER-IMAGES 253 225. Color Fatigue; After-images. Bxp.rim.nt 1. - On a piece of white paper lay a eircniar piece p.ece of thread to the colored paper, and hold the other end i^ vL^lti r. ir' "'""" "^"* '^ -■ °^ the clr d paper, and look steadily at the center of the paper for about fif- teen seconds; then, without moving the eye.s suddenly .all the colored paper away. Instantly the,, will appear on the "hhe Xy:,:r '' '" '°""'' ''^-'^ ^•" ^"^^-^^ -"' «pi" the color of the after-.mage will bo blue ; and, in general, whatever the color o an object, its after-image will ap,«ar in the comrTe menta^. color This phenomenon is explained as follows : Wl e . we look steadily at blue for a time the nerves that are excited by waves of this color become M„,.., and less susceptible tothet • he "r* " ^""' "''" '"'' "' """- -- fully susceptible t^ the influence of waves of other colors. Hence, when we are suddenly brought to look at white, which may ,«' regard! as I compound of yellow and blue, we receive a vivfd imp:Lion from tnL'T "T"""*' "" " ""^'''' ""P"^-- f™™ the blue" hence, the predominant sensation is yellow. 226. Effect of Contrast. _ When diffei^nt colore are seen near each other at the same time their appearance differs more or less from that observed when they are seen sepa^tely Thus, a red object, e.,. a red rose, ■vppears more bnlliant if a green object, e.ff. green leaves, be seen in juxtaposition to it. Such effecte are said to be due to contrast. When any two colors given in th. ,cle (Plate I) are the? tV"*"rf ""'' " "^^" *'"y "" P'-^'' »«t each color scale. For example, if r^d and orange be brought 254 RADIANT ENERGY -LIGHT into contrast, the orange assumes more of » y«»°^/'»» hue, and the red more of a purplish hue. Colors that are already as far apart as possible, e.g., yellow and blue, do not change their hue, but merely cause each other to appear more brilliant. i827. Mixing of Color SensatloM. ,™rim.nt 2.-0n » black surface. A (Fig. 171). lay t^o .maU^ngular piece, o£ paper, one yeUow and the o her blue, smaurec g ".tout 2 inches apart. In a vertical po8.Uon between these papers, and from 8 to 6 inches above them, ^old a slip of plate glass. C. Looking obliquely down through the glass you may see the blue paper by transmitted light waves and the yellow paper by reflection. That is. you see the object itself in the former case, and the image of the object in the latter case. By a little manipulation the image and the object may be made to ov.rlap each other, when both colors will apparently disappear, and in their place the color which is the result of the mixture wiU appear. In this case it wUl be white, or rather gray, which « «»>(« of a low degree of lum«o«ty. The blending of several color sensations into one mbeautifu ly shown l^ means of Newton's color dUk (Fig. 173). which contains Fio. 171 Fio. in FlO. 1T3 Ro. m Bectors of the seven prismatic colors arranged in '^^^ ^' MIXING PIGMENTS 255 « blended in the eye. of the ob«,rver a. to produce the «„aation of gmy. Yellow (Fig. 172) mixed with blue (le« of the former being exposed, becauM it i. a more inten« color and tends to out- bjiUnce the hue) give. gray. The three prin.ary colors, red, green, and v.olet (Fig. 174; «,e al«, right lower color diagram m Kate I) combmed give gray. 228. Mixing Pigments Mixing color sensatioiis and miMig colored pigments way produce very different results. As we have seen, the blending of yellow and Uue sensations produces white. IJut if the two pig inents chrome yellow and ultramarine blue be mixed, a green pigmei.t is pn)duced. When white light pene- trates a litUe way into this mixture the yellow pigment absorb, the blue and all the colow of the spectrum below the green, imd the blue pigment absorbs the yellow and all the colors alx)ve the green, leavuig only gieen to be reflected out to the eye. The olor 8.. light of only <>"• ^^ ""■'f*''); approiimate.ly that of a «Klium flame, falU on the film Le " ,.1B (Kig. 175) repreaent a section of a transparent «hn greatly exaggerated in thickness. The incident waves along the path CD enter the film, are reflected from the rear surface at ' iwiut F, and emerge from the film in the direction GE. Other waves, no, are directly reflected at point G in the front surface of the film' along the line GE. The two trains of waves join each other at G, but one has traveled farther than the other by a little more than twice the thickness of the film Also the act of reflection from the second surface causes a reversal of plmse which results in the loss of half a wave length. From this it will be seen that the two sets of waves will emerge in different phases, and according to the amount of this differ- ence will the two trains of waves reSnforce or destroy each other. An eve placed at E, in the former case, will see a bright yellow spot at Ci in the latter case it will see a dark spot. Th» Aows that Ught added to light may produce darkness. Next let us suppose that the incident waves are white (i.e., are waves of all lengths) and that the component yellow waves inter- fere as described. In the first case given above the bright yellow spot will be seen at G ; but in the second case the extinguishment of the yellow ingredient of the white light will leave its comple- mentary blue. Hence, the eye will see at G a blue spot Newton observed these phenomena, but was unable to explain them satisfactorily by the corpuscular theory The wave th^ry being admitted, it is apparent that a method is revealed by which wave lengths of light may be measured. The quivering of the light and the rapid changes of color o£ the fixed stars, commonly called "twinkhng," is due to THE HUMAN EYE 257 interference c»u«d by the pa«»ge of light through an .tmo.ph.™ them«. ye. « Light coming to the eye from a .tar «,di.tant a. to be practically a .ingle luminous point arrive, in wave, which have tr.ver«,d .lightly unequal di,t.ncei in an iri^gularly refracting and eveMhanging atmosphere, and thu. enter the eye in irr- u- l»rly unequal pha».. Now one color i. extingui.hed, now another , l^Bt71-ZZ7^''°^'"^'^ light complementary to that momentarily IXIRCISES 1- (0) On what condition will an object appear black f (6) fo black properly .peaking a color ? (o) On what condition will an obJ«t :^::^:uT "'"^ ^ -'- ' <-> "- -»' »--- -» - ..U:^rordrtrcrr:f^:b7dtn1^"-'''^^ whft crrirCdrwetvf r "'"'^ *" '"^ """ - -'-' ACTION VIII OPTICAl IlfSTKUHENTS 230. Tt Human Eye. -Fig. 176 represente a hori- zontal section of the most wonderful of all optical instruments, the eye. Covering the front of the eye, like a watch crystal, is a transparent coat, 1, caUed the cornea. A tough membrane, £, of which the cornea is a contmuation, foims the outer wall of the eye, and is called the sclerotic coat, or "white of the eye." This coat i lined on the interior with a delicate membrane, <^, caUed the choroid coat; the latter consista of a black I'lgment, which prevents internal reflection The inmost coat, 4, called the retina, is formed by expansion 268 RADIANT ENERGY — LIGHT Fio. m of the optic nerve 0. The muwjular tissue, it, is called the irit; ita color determines the so-called "color of the eye." In the center of the iris is a circular openuig, 3, called tiie pupil, whose function is to regulate, by invol- untary enlargement and contraction, the quantity of light waves admitted to the posterior chamber of the eye. Just back of tho iris is a tough, elastic, and transparent Uxly, 6, called the eryitalline lent. This lens divides tlie eye into two chambers ; the anterior chamber, 7, is filled with a limpid liquid called the ajMeou* humor; the posterior chamber, 8, is filled with a jelly-like substance called the vitweom humor. The eye may be likened to a photographer's camera, in which the retina takes the place of the sensitized plate. Images of outside objects are projected upon this screen by means of the crystalline lens assisted by the two humors, and the impressions thereby made on this delicate web of nerve filamente are conveyed by the optic nerve to the brain. The convexity of the crystalline lens is susceptible to alteration within certain limite by muscular action so as to view near or distant objects. This alteration is called aeeommodation. An eye which can see an object most distinctly, without sense of effort, at a distance of 20 to 25 cm., is said to be a normal eye. COMPOUND MICROSCOPE 269 NeanigkUdneu oceuni wKdn th« natural focal lenRth ot the eye is ao short that the image* of all hut near obJecU are formed m front of the retina. ThU defect can t>e counteracted hy con- cave lenies placed in front of the eye. to neutralize partiaUy the refracting power of the cry.ta'line len«, and thu. to increaae iU foca length. Farrighttdneu o.cur. when the focal length of the eye i» »o great that images of near object, are formed back of the retina. In .uch cases convex lenws .hould be used to brinir the focu. forward to the retina. 8S1. Compound Microscope. — When it is desired to magnify an object more than can be done conveniently and with distinctness by a single lens, two convex lenses are used, —one, O (Fig. 177), called the objective, to form a magnified real image, a'b', of "^^^ the object ab; and the other, E, called the eyepiece, to mag- nify this image so that the ~"-,, image a'b' appears of the size a"b". Instead of looking at '"'•W * the object as when we use a simple lens, we look at the real inverted image (a'V) of the object 238. Magnifying Power. — The magnifying power of a compound microscope is the product of the respect ^ -e magnifying powers of the object glass and of the eye- piece ; that is, if the first magnify twenty times and the other ten times, the total magnifying power is 200. The magnifying power is determined experimentally by means of a micrometer scale, for a description of which the stu- dent is referred to technical works on microscopy. MO RADIANT ENERGY — UOHT 833. TelMCope. — The telescope is used to view (scope) objects afar off (tele). The refracting telescope,' like the compound microscope, consists essentially of two lenses. The ol.ject glass O (Fig. 178) forms a real diminished imago, 06, of the object AB; this image, Fio. 178 seen through the eyeglass J?, appears magnified and of the siM ed. The object glas. U of large diameter, in order to collect as much light is possible fi-om a distant object for a better illumination of the image. If this lens has 100 times as much surface as the pupil in our eye, it will gather and bring to a focus 100 times as much light from a distant planet. The small lens £ is simply a magnifier to help the eye to examine the image of a distant object forme the foils silk and then bnng the rod near an electroscope, you wiU discover no indications of electrification. But if you pkce sheet rubber or several folds of silk between your hand and the brass rod, you wUl find by testing that the brass rod, after i^ has been rubbed with silk, U electnfied. In the first case also electrification ;as geneiat^i on the brass rod when it was rubbed, but it was conducted away by your body to the earth as fast ^ It was generated, so that there was none left to affect !Z!°t f" '^". ^""^ '^ *^" intervening rubber pre- vente the electrification from escaping. The brass rod 268 ELECTROSTATICS in this case is said to be inmlated by the rubber, which is a non-conducting sulwtance. Some of the best insulating substances are dry air, ebonite, ,kellac, r«m«, paraffine, gla», >ilk», and/ur,. On the other han.l, metaU are exceedingly good conductors. Moisture injures tl.„ insulation of bodies; hence, experiments succeed best on dry days. Further, apparatus aliould alicays be kept warm. A reservoir cannot retain water unless its walls be of sufficient strength; so a body, in order to retain a charge of electricity,' must be surrounded by something that will offer sufficient resist- ance to the escape of electricity. It may be air or any of the so-called non-conductors. 243. Dielectrics. — Fig. 182 represents an empty egg- shell covered with tin foil to make it a good conductor. It is suspended from a glass rod by a silk thread, which is a non-conductor. Thus, the surface is ^^'"" an insulated conductor. Electrify a glass \ rod and bring it near the shell. The x--^"-^, shell will be attracted toward the rod. C ^ \ Next introduce a glass plate between ^'^'^ " the shell and the rod. The shell will move toward the rod as before. "We learn from this experiment that, although air and glass prevent electricity from passing from the rod to the shell, they permit an influence (an attraction) through them. The same 1 We use the term etectHcity here for the first time. In common par- lance a little-understood thing, called electricity, is said to move along th.' conductor when a discharge takes place. Of electrification, its conditions and laws, we know ranch; of electricity we know nothing,- we have no knowledge of it apart from the electrified body; hence the propriHy .. commencing our study of the science by considering the phenomena ul •Uetrificatlon. Fig. 182 INDUCTION 269 would be found to be the case if any other non- conduchng body were placed between the rod Td the shell. Inasmuch as all non-conducting substances permit an electrical influence to be exerted through them, they are culled dielectrics. ^ 244 Induction. -Fig. 183 represents two shells so Buspended that they touch each other, making p J tically one conductor. (1) Bring near to one end a sealmg-wax rod charged with - £. While the rod is m this position, carry a strip of tissue paper, C, suspended from a glass rod along the shells. The paper will be attracted to the shells, but most strongly to the ends. (2) While the rod D is still in position, separate B from A; then remove D. Test each shell with the tissue paper. Both will be found to be electrified. (i) Test each shell with an electroscope. It will be ^l-^! '''" ^ " ''^"' -''•^ + J»"d shell B (4) Finally, bring the two shells near each other. TTiey will attract each other. If the shells be allowed to touch, or be brought so near together- that a faint spark passes between them, it will be found on testing them again that both have become discharged. From these experiments we learn that when an elec- trifled body is brought near to but not in contact with an msulated conductor, the electrified body acta through Via. 183 270 ELECTROST>TICS the dielectric (in this case the air) upon the conductor, repelling electrification of the same kind to the remote Bide of the conductor, and attracting the opposite kind to the side near to it Such electrical action is called mduction. When a pith ball, for instance, is brought new to an electrified glass rod, the + B on the rod A (Fig. 184) induces - B on the side ol the ball B near to A, and repels + E to the farther side. The + EotA and the - E ot B attract each other ; Ukewise the + E ot A and the + E ot B repel eaih other; but since the like kinds are farther separated from each other than the unlike kinds, the attraction exceeds the repulsion. na.lM SECTION II XUCTRICAL POTXHTUL 349. Electrostatics and Electro-Kinetics. — Electricity may he at rest, as in a charged body, or it may be in motion, as when a charged body is discharged through a conductor to the earth. It will be shown later on that as long as a flow of electricity continues, the conductor along which it flows has properties different from those of a body upon which the charge is at rest. That branch of electrical science which treats of the properties of charges at rest is called electrottatici; and that branch which treats of electricity in motion is called electro- Mnetiei. 346. Potential. — The fundamental fact of electricity is that «« are able to place bodies in different electrical POTEKTIAL 271 <^Uxon, A charge of electricity i, « neceuary ante- cedent condUum to all electrical phenomena. We an now to du«,u«. the meaning «„d use of the very i„,portant TxCu ' "" '* '" ""P'"y«'^ ^ "I'^tri""! science. W When a charged conductor is connected with the earth, a transfer of electricity takes place between the body and the earth. (») If the body be charged with + H, we say arbi- trarily that electricity passes from the body to the earU. ; but if the body be chained with - I, we say that ekctncty passes from the earth to the body. (c) Whether electricity passes between two poi, ts of a conductor, and in which direction it passes, if at all depends upon the relative potentiah of the two points. ' W If two bodies have the same potential, no transfer of electncity takes place between them ; but if they have different potentiab, there is a transfer, and the body from wh.ch the electricity flows is said to be at a %Aer pote^tal than the body to which it flows The potential of any point « the state of that point with reference to ,U tendency to communicate electricity to, or recexve electrify from, other point,. (See definition of temperature, § 100.) The term ^o^^wtfai is relative. It is important, there- fore, to have a standaid of reference whose potential is considered to be zero, just as it is convenient in stating the elevations or depressions of the earth's surface to g.ve the distances above or below sea level, which is taken as the zero of hight For experimental purposes he earth IS usually assumed to be at zero potential. A ■ l^y charged with +£m understood to be one that has 272 ELECTROSTATICS r. higher potential than that of the earth, and a body charged with — IS one that has a lower potential than that of the earth. In like manner, when we say that the temperature of the air is 20° or - 10° C, we mean that its teuipeiature is 20° above or 10° below the standard tempe' .ilure of reference, vh., that of melting ice. Potential is analogous, in many respects, to (1) tem- perature and to (2) liquid level. For (1) if two bodies at different temperatures be placed in thermal communica- tion, heat will pass from the body at a higher to the one at a lower temperature and will continue to do so until both are at the sa^ie temperature ; (2) and if two vessels containing water at different levels be connected by a pipe, water will flow from the higher to the lower level until the water is at the same level, when the flow ceases ; so, also, (3) if two points having different poten- tials be electrically connected, that is, connected by a suitable conductor, electricity will always flow from the point at higher to the point at lower potential as long as a difference oi potential between the two points is maintained. 247. Lightning. — Franklin, by his historic experi- ment with the kite in 1752, proved the exact similarity of lightning and thunder to the light and crackling of the electric spark. Certain clouds which have formed very rapidly are highly charged, usually with -I- H, but sometimes with — E. The surface of the earth and objects thereon immediately beneath the cloud are, of course, charged inductively with the Opposite kind of electricity. The opposite charges on the earth and on BENJAMIN FRANKLIN (1706-1790) Henoirned a* an Amerimn ■tatMmsn Rnd M a icientlat of original powera Portrait after painting by DupIeaaU, In Bolton Mmenm of Pine Arta. LIGHTNING 278 the cloud hold each other prisonen by their mutual attraction, the air gurving m an intervening dielectric. A« condeniwtion progrewes in the cloud, ita potential naes (or »inkn). This procow continueu till the differ ence of poUmti.il between the cloud and the earth becomes great enough to produce a diMoharge through the air. The noiHo of thunder and of Hparlo. is duo to the sudden expansion and collapse ol the air along the path of discharge. It is the accumulation of induced chaises on elevated objects, such OS buildings, trees, etc., that offcw an intensified attraction for the opposite electricity of the cloud in consequencr of their greater proximity, and renders such objects especially liable U> be struck by lightning. The clouds gather electricity from the atmo8i,here. Our knowledge of the method by which the atmosphere becomes charged is very limited. We see what we call a " flash of lightning." What we see is not electricity but air heated temporarily so as to be self-luminous. Lightning strokes last for a very brief time, — perhaps a millionth of a second,— though the sensation produced on the retina of the eye lasts longer. IZXRCISBS 1. What cauaea one's hair to •• fly " when brushed in cold weather ? 2. Why in the eiperlmenU described above, wore Maling-wax and glass rods chosen in preference to metal rods f /M trv"^ ^ "'^ *""^ "' * '■*"'" "' electricity potential or kinetic ? (0) Whence is the electric energy derived ? 4. fiuf4? some method of showing thai there are two kinda of electrification. 274 ELECTROSTATICS 6. On what condition wiU electricity paM from one body to another body, or from a point in a given body to another point in the aame body? a (a) When glass is electrified by rubbing it with silk, does its potential become higher cr lower than that of the earth ? (6) Has seal- ing wax, after being rubbed with woolen cloth, a higher or a lower potential than that of the earth ? 7. An electroscope is charged with - X. An insulated charged body is brought near it. (a) What do you infer as to the kind of charge the body has if the foils collapse ? (6) if they diverge more ? CHAPTER VIII ELECTRO-KINETICS -ENERGY DUE TO ELECTRIC FLOW SECTION I VOLTAIC CEUS-KLECTRIC CIHCOITS 248. Introduction. -Let A (Fig. 185) represent a tumbler partly filled with sulphuric acid much diluted with water. Into the acid are plunged a strip of zinc, «, and a strip of copper, c. Each of the metal strips has a copper wire soldered to its upper end. It may be shown experimentally,! by means of an electroscope, that the instant these strips are introduced into the acid both wires become electrified. The wire joined to the copper strip becomes excited with + E, and the wire joined to the zinc with -if; or, as we learned in the preceding chapter, the potential of the former wire is raised, and that of the latter wire is lowered. It is evident, then, that if the two wires be brought into contact with each other, as shown in B, a discharge of electricity from tlie wire at higher potential to the wire it lower poten- tial will instantly follow; but, as we shall learn later • Ses the author's Prindpla of J'hynct, p. 463. 276 Flo. 18B 276 ELECTRO-KINETICS on, the discharge along the wire from the copper to the zinc is continuous, and such a discharge is known as an electric current. 249. Voltaic Cell. — An arrangement like the ahove, consisting of two solids, of which zinc is almost invari- ably one, placed in an electrolytic liquid (i.e., a liquid capable of being decomposed by a current of electricity) constitutes a voltaic cell.^ The two solids are called elements. It is necessary that one of the two eleinents should lie more actively attacked by the liquid than the other ; the one more aqted upon (the zinc) is called the electro-positive element, arid the other the electro-negative element.* 250. Electrical Circuit. — This term is applied to the entire path along which electricity flows ; it comprises the electrolyte and the wire or other conductor con- necting the elements. The operations of bringing the two extremities of the wire into contact and separating them are called, respectively, closing and opening, or making and breaking, the circuit. The free extremities 1 The voltaic cell tokes its name from Alexander Volta, who invented It in 1796. ' The following Bubstancea are arranged in order such that any one in the list is at the higher potential when put in contact with any one that follows it, bnt is at tiie lower potential when put in contact with any one before it in the list: -I- 1 ,3 S I S S o The difference of potential between zinc and carbon is equal to the sum of the differences of potentials between the intervening substances in the series. Consequently, other tilings being equal, these two substances oi all given in this list are best for giving a strong current. ENERGY OF ELECTRIC FLOW 277 Of the wires are called the electrode,, or terminah. The electrode of the negative element is called the anode, or aie po»Uive electrode, and that of the positive element io tne kathode, or the tugative electrode.'^ 251. Origin of the Energy of Electric Flow. — In the voltaic cell difference of potential is produced by simple contact of the two elements with the electrolyte/or excit- ing hqmd When the wires joii,ed to the two'element are brought into contact and .. discharge takes place, electeoal equ.hbr.um would be produced and the curi^nt would cease were there not some means by which a dif- ference of potent.al is maintained. This is accomplished by the chem.cal action all the time going on between he z.nc and the l.quid. The slow burning, or consump- t.on, of the z.nc serves to renew the difference of potential as fast as the discharges take place, and thus a continuous current w maintained whUe the circuit is closed The burning of zinc _ in other words, the transforroa. tion of the potential energy of chemical sepa.-ation which _ the zinc and acid possess into electrical energy — sup- plies the energy expended by the cell when the circuit is closed, somewhat as energy is 'The nomenclature in use, by which the zinc plate is '■ailed the eleclro-poHtive element and at the same time the 'egaltve electrode of the comhination, is at first perplexing lo the student. I*t him bear in mind that electricity always flows from a point of high potential to a point of relatively ow potential For example, let a current originating in a oltaic cell at point a (Fi^. 18«) follow the direction indicated f ^l *.""'? ' ■"*"' " """" ''" "''^"™ »■'"' reference Flo. 18fl , B • ^ "'^"•'™ *» •""' "■ " f^^^"' ♦<> P«l°' '• -n.e term anoO. ;;s ZLt """" ** """" ""' """'■ ""' "" '<'™ *«'*°*. tuer,zt ELECTRO-KINETIC^ 278 Bupplied by a steam engine through the consumption of coal. A voltaic cell «. therefore, a contnvanoebj u,hich potential energy of chemical separatum » converted directly into electrical energy- Hi. Local Action in Voltaic CjUs. - When a voltaic circuit is open and the.^ is no current the zmc ought not to be consumed, for this involves a useless consam^ tionofzincandawasteofenergy. " t^^" ^"'''^^ ''l;:^: cally pure, no chemical action takes phvce when the circuit is open. In practice, ordinary commercial mc m used, and^e zinc plate is irregularly eaten away, «l*ough °n open circuit. This consumption of zinc is said to be due TLl action. Local action is caused by the presence on the surface of the zinc plate of certain impurities, such as particles of carbon, iron, ete., which form numer- ous smaU local circuits. The zinc if thus eaten aw^ around these particles. U mercury be i-ubbed over the surface of the zinc, it dissolves a portion of tiie zinc forming with it a semi-fluid amalgam, which covers up the impurities and thus prevents local action butdoes not Lpede the ordinary action of the cell on closed circuit. 253. Polarization of the Negative Element. - The cur- rent yielded by a cell Uke that described above rapid y weakens from the moment that the circuit is closed^ This is shown by the diminution in the amount of work which the current can do. It will be noticed, also, that inmiediately .- closing the circuit bubbles of g«s are formed on the negative element. This accumulation of gas which can be shown to be hydrogen, gives nse to what is called polarizatim of the ruigative element. DANIELL CELL 279 We know that difference of potential is indispensable to a flow of electricity. Difference of potential gives rise to something analogous to a force, which causes the flow of electricity. The greater the difference of poten- tial, the greater is this agent which puts the electricity in motion; but a deposit of hydrogen on the copper raises, in some measure, the potential of this (negative) element and thereby diminishes the potential difference between the two elements. The gas also increases much the resistance to be overcome. Hence, the current is " weakened." The usual remedy for this is to employ in addition to the exciting liquid some substance which will combine with the hydrogen as soon as it is liberated. A sub- stance used for this purpose is termed a depolarizer. A mixture of a solution of ciystals of potassium dichromate in water witli a suitable quantity of sulphuric acid is used as a depolarizer in the so-called dichromate cell*. 884. ItenicU Cell. — The Daiiiell cell (Fig. 187) uses a solution which, instead of depositing hydrogen, deposits copper upon a copper negatiTe plate, and hence is free from hydrogen polarization. It con- tains a copper negative and a zinc positive plate. The copper plate is immersed in a solution of copper sulphate, and the zinc in a solution of zinc sulphate or dilute sulphu- ric acid, a porous cup separating the two "' ^^ liquids. By the electrolytic action the zinc combines with tne sulphuric acid (H^SO,), forming zinc sulphate (ZnSO,), thereby setting hydrogen free. This hydrogen, while on its way to the negative element or the copper plate, meets the copper sulphats 280 ELECTRO-KINETICS Bolution (CuSOj), which it decomposes, forming sulphuric acid again (H,SOj) and setting free the copper, which is deposited on the copper plate. Since this cell does not polarize, it is especially adapted for closed-circuit work, that is, work requiring a steady current for a great length of time. 255. Bunsen CeU. — In this cell (Fig. 188) the negative plate is carbon and the depolarizer is usually a solution of potassium dichromate. Both this and the Daniell cell are called two-fluid cells. One of the two liquids used in these cells is inside, and the other outside, a porous earthen cup, which serf es to prevent, in great measure, the two liquids from mixing. 256. LecUnchi CeU ikere is a class of voltaic cells in which the negative element is protected somewhat from polarization by means of metallic oxides. Of these the best known is the Fio. 188 Fio. 189 Leclanch* cell (Fig. 189). In this cell the carbon plate C is con- tained in a porous cup, P, and packed round with fragments of gas-retort coke and manganese peroxide. The manganese com- pound has a strong affinity for the hydrogen. Nevertheless, the EXERCISES 281 elements quickly polarize when in action. They need periodical rest to recover their normal condition. Such are calli-d itpen-circuil eelli, since they are suited for work only on lines kept oiwn or disconnected most of the time, as in telephone and bell-ringing circuits. The zinc rod Z is immersed in a solution of ammonium chloride, which is the exciting liquid. KZERCISES 1. (a) What are electrodes ? (6) What are the essential parts of a Toltaic cell ? (e) What metal is almost invariably used for the posi- tive element ? (d) Name several substances commonly used for the negative element, (e) What happens when the electrodes are brought in contact P (/) What purpose does joining the two elements serve ? 2. Why ought not the elements of a voltaic cell to touch each other? 3. What is the function of a voltaic cell ? 4. If a current passes points A, B, C, and /) in a circuit succes- sively, (a) which point is positive with reference to all the others, and which point is regative with reference to all the others ? (6) State the relation of point B to each of the other points. 6. With what propriety is the zinc clement of a voltaic cell called the p »Uite element and the negalioe deetnxte of a voltaic system ? 8. (a) What do you understand by the " polarization of the nega- tive element" ? (b) How is it caused? (c) What harm does it do? (d) How is it commonly prevented ? '. . Which, electricity or electrification, is the lemilt of work done ? 8. (a) What is meant by " local action " ? (6) Why is it objec- tionable ? (c) How is it prevented in some measure in certain cells ? 9. What kind of cells are suitable for only "open-circuit" systems ? 10. Which of the several cells that have been described will yield a current most nearly uniform or constant ? Why ? 282 ELECTRO-KINETICS SECTION II EFFECTS PBODDCIBLE BY All ELECTRIC CUSSBHT 397. Classification of Effects — The several effects producible by an electric current may be classified as electrolytic, magnetic, thermal, and phyiiologiccU. 258. Electrolysis. Exptriment 1. — Take a dilute solution o{ sulphuric acid (one part by volume to ten) and pour some of it into the funnel (Fig. 190) so as to fill the U-shaped glass tube when the stoppers are removed. Place the stoppers which support platinum electrodes tightly in the tubes. Connect with these electrodes the battery' wires. Instantly bubbles of gas arise from l>oth elec- trodes, accumulating in the upper part of the tube and forcing the liquid back into the funnel. Introduce a glowing splinter into the gas sur- rounding the -I- electrode : it relights and burns vigorously, showing that the gas is oxygen. Invert the U-tube, remove the rubber tube, • allow the gas which had accumulated about the — electrode to escape at A, and apply a lighted match to it: the gas bums ; it is hydrogen. The volume of hydrogen is just double that of the oxygen . 'xjrated in the same time. The process by which a compound substance is separated into its con- stituents by an electric current is called electrolysis, and a compound that may be thus decomposed is called an 1 A battery consisting of not less than two Bunsen, or three Daniell, cells connected in serips will Iw rpquirod. For tho pnpil's nsfl a very inex- pensive Daniell cell, sach as is now in general use in high-school laborato- ries, is recommended. KLK«TR0-MAGNET8 eleetroljfU. Tlie electrode by which the current enters the electrolyte ig called the anode, and that by which the current leaves, the kathode. Those constituents that appear at the anodes are called aniont; those that apjiear at the kathodes are called kation$. Anions are electro- negative and kations are electro-iwsitive ; hence, they are attracted to electrodes that are opixwitely electrified. Thus, oxygen, being electro-negative, is attracted to the anode, or positive electrode, and hydrogen, being electro- positive, is attracted to the kathode, or negative elec- trode. V/^hen a chemical salt is electrolyzed the base appears at the kathode, and the acid at the anode. In general, it will be found that in both the battery and the decomposing cell, hydro- gen, bases, and metals appear at the plates Ujiard which the current flows. 259. Magnetizing Effect of an Electric Current; Electro-Magnets. Experiment 2. — (a) Wind an insulated copper wire in the form of a spiral round a rod of soft iron (Fig. 101). Pass a current of electricity through the spiral, and hold an iron nail near the end of the rod. Observe, from its attraction for the nail, that the rod is magnetized. A magnet may be p->visionally defined as a body which attracts iron. (J) Break the circuit ; the nail drops, showing that the rod has lost its magnetism. The iron rod is called a coA, the coil of wire a helix, and both together an electro-magnet. In order to take advantage of the attraction of both ends, or polet, of the mMrnet, the rod is frequently bent into a U-shape (A, Flo. 191 284 ELECTRO-KINETICS Fig. 192). Often two iron rods are used, connected hy a rectangular piece of iron, em a in Jl of Fig. 192. Tliis piece of iron, called a yoke, constitutes a part of the electro-mngnet. Tl.e method of winding is such tl«t if the iron core of the U-magnet were straight- ened, or the two spools were placed together end to end, one would be a continuation of the other. For method of winding ii U-nmgnet see also Fig. 221. A piece of soft iron, 'b, placed across the ends and attracted by them, is called an armature. Fig. 193 rerrescnts n SO-ponnd weight Bupported l>y the mag- netic effect of an electric current yielded by a battery of two Bunien cells. Kiu. 1113 Fia. 198 Fni. I'M DEFLECTION OF MAGNKTIC NKKDLK 286 aw. Deflection of the Magnetic Needle by a Current. «»P«taM«t a. — (a) Place theftpparatu. (Kig. 1B») «, that t)ie magnetic ..e«.ll«. which roint, north anj ...uth, .hull 1« ..urallol to the wlr«« >»', and Wf. Introduce the anode of a single cell into gerew cup 7; and the kathode into screw cnp 7',, and pass a current northward through the upper wire. At the instant tlie cir- cuit is closed the needle swings on its axis and, after a few oscillations, comes to rest in a iH,sition which forms an angle with the wire bearing the current. (i) Break the circuit by removing one of the wiros from the Kcrow cup. The needle, under the influence of the magnetic action of the earth, returns to its original position. (c) Reverse the current by inserting the nnwle of the battery mto screw cup r, and the kathode into screw cup T,. Again there u a deflection of the needle, but the direction of the deflec tion IS reversed; that is, the north-pointing pole (.V-pole), which before turned to the west, is now deflected toward the east. (d) Place your right hand ahoo, the wire, with the palm tmmrd the wire and with the fingers pointing in the same direction as that in which the current is flowing, and extend your thumb at right angles to the direction of the current (Fig. Ifl",). You observe that your thumb points in the mmc direction as the AT-pole of the needle unrfer the current-lwaring wire. (e) Reverse the current again (so that it shall flow northward) place your right hand as before (viz., with the palm toward the wire and with the fingers pointing in the same direction as the current); your outstretched thumb still points in the m,m direc- tion as the JV-pole of the needle. (/) Introduce the anode of the battery into screw cup r and the kathode into screw cup r„ so that tl ■ current shall' flow 286 EI.RCTRU-KINETICS northward uiu/le of a needle when the direction of the current is known is this : Place tlie outttretehed right hand om or under the wire, m that the wire ahall be between the hud and the needle, with the palm toward the needle, the fln- gen pointing in the dliection of the cunent and the thumb ertended laterally it tight anglea to the direction of the current ; then the extended thumb will point in the direction of the deflec- tion of the /r-pole. It will be observed that a deflection is reversed either by reversing the current or by changing the relative positions of the wire and needle, e.g., by carrying the needle from above the wire to a position below it, or vice vena. The force exerted by the current upon the needle in deflecting it is called an electro-magnetic foree.^ ^ The science of eleiaro-iuaftnetltmi originau»l with ihe dliteovery (1819) by Oersted of the deflection of a magnetic needle by an electric current. BrMPLE 0ALVANO8COPK 287 •61. Simple OalTuoKope, or Cnrrent Detector. ««P«*mMt 4. -Introduce (h« + electriHl. of the battery into •crew cup T, (Fig. 194) «,a the - cl„ct™.ie i,„„ «„w cup T J» th., the current .h«Ii p*.. .U,v„ the wir,- in on., dir^tion and helow it in the oppcite directiun, a« in.licated l.y tlie arn.wi I hrgrr dr^eclian i, ohlaincJ Ihun «■*„ ,ke eurrrn, ,„«„ th, „«,«, onlf once. If the right-Jmnd test be applied, it will 1» Heen that tl>e tendency of the current, Jx.th when p.wHing the needle in one direction above and when puH«ing it in the oppoHite direction below, k to pr.Klu.e u deflection m one and the same direction ; con8e,,uently, the two parts of the current combine to produce a ir«5ater deflection. If a more Hensitive instmn.ent be required, that is, one in which a weaker current will p«Kluce a sensible 'Mc' . on. It V, II! be necessary to pa.s8 the current througr an .nsulate.l wire wound many tin.es around the needle. Such an ii«.truinent is called a gahanotcope, or current detector, since one of its im,K.rtant uses is to detect the presence of a current. 268. Thermal and Luminous Effects of the Electric Current. Kzperiment 5. — Construct a low-resistanco battery (i 279> of three or i^^ur cell, and intro,i«ce into the circuit a platinum wi,., No 30 about i of an inch long. The wire v,,ry quickly becomea white hot, .... ,t emits white light, which indicates a tempera- lure of approximately 1800° C. This experiment illustrates the convereion of the energy of an electric current into heat energy. In this case the energy of the cuntiut is consumed in P. 288 ELECTRO-KINjniCS overcoming the re*i*tance which the conductor or the circuit offers to its passage. Heat is developed by a current in every part of the circuit, because all sub- stances offer some resistance to a current, — in other words, because there are no perfect conductors. The small platinum wire offers much greater resistance than an equal length of a larger copper wire, whence the greater quantity of heat generated in this part of the circuit. All of the energy in any electric circuit that is not consumed in doing other kinds of work is changed into heat. 263, PhysiologiciJ £ffect8. Expeiiment 6. — Place one of the copper electrodes of a single voltaic cell on each side of the tip of the tongue. A slight sting- ing (not painful) sensation is felt, followed by a peculiar acrid taste. SECTION III ELECTRICAL QUAHTITIES AND UNITS OF MEASUREMENT 264. Strength of Current; the Ampere and the Cou- lomb. — The magnitude of the effects producible by an electric current depends upon the magnitude of the current. For this reason, almost any effect might be adopted as a basis for measuring currents. For example, the quantity of hydrogen gas or of any metal liberated at the katliode in a given time by electrolysis might be adopted, since it is strictly proportional to the magnitude of the current, or, as it is technically termed, the ttrength of the current ; the equivalent expressions are the quantity of electricity conveyed in a unit of time. ELECTRO-MOTIVK FORCE; THE VOLr 289 or, more briefly, the "rate of flow" tk •. * strength actually adopted i he stren 'iT '."^ ''"""''* whach, paased through a solution of'lit't; of T' (P^pared "in accordance with standard"^ t;^! v deposits silver at the rate of 001118^ i' This unit is called the ampele ^^ ^'' '^''^■ -.ri^^n:;^:r;-r::i^-;-^of -/ leeand when the strpncrfl, ^f *i circuit tn is 1 ampere An ^ ^^ '""""* "* *''''* Point that rr """P"'" """■"'*' therefore, is a current that dehvei. a coulomb of electricity per second." 265. Electro-Motive Force: the Vr.it r- •, flow from vessel A to vessd ^X "9^70^!'^^^^^ " " pressure be greater at the extrei^^' '^ ^""''^'* *''« of the connecting pipe c than at the extremity i^. The difference in pres- sure at these two pointe is proportional to the "head "of watering, or to the vertical hight i>^of the liquid surface Wthedi.Jene;:/^-^^^>^;™. WW ToIU. ""I*™', and w eleotro-motli. force of .bout Fio. 197 I 290 ELECTRO-KINETICS Sinularly, electricity will flow in a conductor provided there be greater electrical presmre at one end of the con- ductor than at the other end. As long as such a differ- ence of pressure is maintained, so long there will exist something that is analogous in many respects to a currentr producing force. It is for this reason called electro-motive force (E.M.F.). Electro^motive force is that which main- 'taint or tends to maintain a current of electricity through a conductor. Like a mechanical force, it has a definite direction. It does no work unless it moves electricity. Difference in electrical pressure we have hitherto assumed to be due to difference of potential. Potential difference may be due to contact of dissimilar substances, as in the voltaic cell, or to the movement of a part of the conductor in a magnetic field, as in the dynamo In every case it is due to an expenditure of energy of some kind. The volt is the name chosen for the practical unit of E.M.F. and difference of potential. It is the electrical pressure required to maintain a current of 1 ampere against a resistance of 1 ohm (§ 266). Where great accuracy is not required it will answer to consider a volt aa the E.M.F. of a DanieU cell. 266. Electrical Resistance ; the Ohm. — Every sub- stance offers resistance to the passage of a current. Those substances which offer a very powerful barrier are called insulators. The unit of resistance is called the ohm. The international ohm is "the resistance offered U an unvarying electric current by a column of mercury' ELECTRICAL POWER, .;tc. 291 at the temperature of melting ice, 14.421 g. i„ „,ass of a constant cross-sectional area, and of tL le";^;' „ ?AmL ' " ''""' '""^ '^«'«'*"'=« "f 9-3 feet of No 80 (Amencan gauge) copper wire (0.01 inch in diamet^;' Kn!flv ^'"'w.'"' ^'^'^ """^ ^'«W«1 Work or Knergy -When an electrical current of 1 ampere flows between two points in a conductor whose dTer ence o potential is 1 volt, work is done at tCl.^Z force „ J ^„it „„^ ^y ^^^^^^ .^ ^ ^^ If a coulomb of electricity flow between two pointe m a conductor whose difference of potential is 1 voTt t quantUy of work is done, or a quantity of e eltricat enej^ « absorbed, that is caUed'a Juoul^^Tl The watt and the joule are, therefore, units of elec meter t;^' "' f"'"' ^ ^'^''g*'"^ ^o the kHogram- meter, and is equxvalent to 0.1019+ kgm. Watu - voluxarnpere. Joules = .olts x oouloJs. rZlaH, are equivalent to 1 horsepower. 268. R&nm^. — ^„ ampere current U a current mai« f2^ ly an B.M.F. of 1 volt against a relllZZf t>un a current of 1 ampere against a resistance of 1 ohm. I ■1 292 nLECTRO-KINETICS A cotiductor hat a rengtance of 1 ohm when an H.M.F. of 1 volt (or a difference of potential of 1 volt between itt two end*) caiues a current of 1 ampere to pats through it. A power of 1 watt is the power of a current of 1 ampere maintained hy a difference of potential of 1 volt. A joule is the quantity of 'vork done in 1 second by a current working at the rate of 1 watt. 269. Ohm's Law. — It is apparent that the rate of flow of water from vessel A to vessel B (Fig. 197) depends wholly upon the difference of level in the two vessels, the size of the pipe, and the resistance offered by the roughness of its interior surface. In like manner, the strength of an electric current between any two points in a conductor depends wholly upon the differ- ence of potential of the two points (in other words, the E.M.F. which puts the electricity in motion), the size of the conductor, and the specific resistance of the substance of which it is composed. The three factors, current strength (C), E M.F. (or Ey and resistance (B), are interdependent. Their relations to one another are stated in the weU-known Ohm's Law, thus : The cunent ia e.iu«l to the E.M.F. divided by the reslat- «nce; or, ^ C = -; whence, ^ = JSC and .B----- B C Evidently, if any two of the three quantities are given, the third may be calculated. The following are deductions from Ohm's Law : C varies at E when E it constant. C varies inversely as B when E is constant. > In fonnnlas It Is necessary to pepresent E.M.F. by the single letter E. GALVANOMETER 393 Bemtance in any circuit (R) ,-. the ratio oftheEMF im to the current strength (C) <■»>' J^.m.j< .(t,) greater will be the angle of -^ —^ deflection, though these are not often proportional. A very simple form of this instrument is represented in sec- tional elevation and plan in Fig. 108. It consists of an insulated wire wound several times around // a magnetic needle. The needle "- IS poised on a point so as to be free to rotate. A card graduated like that of a mariner's compass 18 placed beneath the needle so that the number of degrees of deflection may be read from -f EXERCISES 1. What do yoa unde .Und by a Ur,>ng electric current? ccfdu.!?" "°'''"'" '"' ' '"-'' «- "^'ween two points of . I '•■ft *•■■! ■r: 4 294 ELECTRO-KINETICS 4. In ifhat unit Is difference of potenUal between two poInU to a conductor expreMud? 6 ,a) What ta the difference of potential between the two ele- ment of i Daniell cell? (6) What E.M.F. will a Daniell celHurn »h ? 6. (a) What iB power? (6) What U the «ame of the nnit of ^echaicil^werr ^ of electrical power? (i) What U the equiva- lence between mechanical power and electrical power ? 7. A current of 5 ampere. U maintained by an E.M.F. of 8 volU. What ta the ipower of this current? 8 The power of a cerUin current is 20 watu, and it is maintained by an E.M.F. of 10 volts. What is tue strength of the current ? 9. What E.M.F. is required to miuntain a current of 10 amperes that it may yield a horse-power ? 10. W at Is t; ,. resistance in a circuit when an E.M.F. of 1 volt matotains a current of 1 ampere ? 11. What E.M.F. is required to maintain a current of 1 ampere through a resistance of 1 ohm? 12. An E.M.F. of 15 volts will maintain a current of 3 amperes through what resistance? 13. What current will an E.M.F. of 18 volts maintain through a resistance of 6 ohms ? 14. A voltmeter (an instrument for measuring the difference «f potential between two points) applied each side of an electric lam,, ^ows a difference of potential of 40 volts. What current flow» through the lamp if it offers a resistance of 10 ohms? IR ta\ If 120 coulombs of electricity be transferred through a cir- cuit in 30 seconds, what is the average current strength? (6) Whut is the average power of the current if the E.M.F. is 2 volte? 16 If the fall of potential in an incandescent lamp be 110 volts and the strength of current maintained through it be i of an ampere, what is the resistance of the lamp ? 17. A current of 1 ampere and an E.M.F. of 70 volts »" required to feed a certata incandescent lamp. What is the resutance of the lam,, ? 18 ALeclanch«celliBU8edtoringadoorbell. The resistance..! the el'ectromagnet in the bell is 2 ohms, of the Itae '"^ + »'"';'■ '"^ «,d of the cell 1 ohm. The E.M.F. of the cell Is 1.6 volts. Wl.at current U produced when the circuit is closed? EXTERNAL AND INTERNAL RESISTANCE 296 SECTION IV MSISTAWCE OP AH ELECTHIC CMCUIT 271. External and Internal Resistance. _ An electric c.n>«.t includes the gene^utor (.^., voltatc ^ C m^nr' '""i"^' "'" oonneeto«:a„d whatever inrT mente are introduced into the circuit For convenience, the resistance of an electric circuit External reactance includes all the resistance of a cir- mt except that of the generator, while that of the latter IS termed internal resistance. When the external resistance in a circuit is considered sepanuely fron, the internal, Ohn.'s fonnu a Zt h^ converted thus (calling the former n and the latter .) Ifthe electrical dimensions of I cell be /; = 1 volt and .0 thaf^' ' 't r""^"""? ^-i'-e be short and stout, so tha iS may be disregarded, tlien the cell yields a current of 1 ampere. If by any means the '^"l s.stance of this cell can be decreased one half, it w" hen be capable of yielding a 2-ampere cur„,n if the other conditions remain the same. m. Resistance offered by Conductors. -C(Fi„ igo^ P.; W "h • I '' ' ^^>~^^. --i ^ - a Wooden p a onn on which are mounted spools of insulated' wi,^ of dififerent lengths, si.es, and kinds of met,al. I if M # •i ' 296 ELECTRO-KINETICS One of the spools of wire is represented as being con- nected in circuit with the cell and galvanometer by hav- ing the electrodes introduced into the screw cups each side of the spool. While the circuit is closed and the Fia. 199 > current is circulating through the spool and galvanom- eter, the needle of the latter is deflected a certain number of degrees. Each of the several spools is introduced separately into the circuit, and the several deflections are noted. It is found that the longer the wire i» and the finer U i», the tmaller is the deflection. A smaller deflection indicates a weaker current. Since the E.M.F. of the cell does not change, it follows that weaker cur- rents must be due to greater resistances. We therefore conclude that the resistance of wires increases with their length and fineness. When means, such as will soon be explained, are adopted for measuring the resistance of conductors and comparisons are made, the following rules are deduced: (1) Other things bdne equal, the reeirtance of « conductor is pnportiond to lu length. BESISTANCE OF A VOLTAIC CELL 297 taTWdypwportlimia to th. ««» of thdr cit)M JSmT^ iawwely m the ■qmrn of their diamMm. """"^ '"^ On introducing into the circuit, „ explained above, ^Is of wire of diflferent metala but of 'e^roal leng^ and «zes, it ,« found that the deflections differ widely. From th.8 we conclude that some metals offer less resist- ance than others; in other wohIs, that some metals are betterconductorsthanothers. For example, copper offen. about one 8«th as much resistance as iron The particular resistance of a substance under speci- fied condibom ,s caUed the ^ecijio ren,tanee of U.at substance. (See Table of Resistance of Wi« in the Appendix.) -, /'^' -"^"r'*"'" » P'««« wire would have a resistance of 0,6 olini ? 2. What is the resistance of 100 feet of No. 30 copper wire (diame- ter =0.26S mm.)? 3. What Is the resisf-xnce of .30 feet of No. 30 German-silver wire (the resistance of copper and German silver being as 1 : 12.8) f 4. State four things on which the resistance of a wire depends. 6. What is the resistance of i of a mile of No. 30 copper wire 0.26 mm. in diameter? SECTION V DIVIDED CIRCtHTS — HEASUKEMEHT OF RXSISTAHCE 274. Description of the Kesistance Box Fig. 301 represents a cylindrical box containing a series of coils of German-silver wire whose resistances range from 0.1 ohm to 50 ohms, so that the total resistance is 160 ohms. The terminals of each coil are con- nected with brass blocks A, B, C, etc. (Fig. 202). When the brass plugs 1, S, etc., are inserted between these blocks, the coils are short circuited, so that practically the whole current passes DIVIDKD CIRCUITS, SHUNTS 299 PlugN any ,Ie,ir.,a re»i«lunco w:,nin th. capacity of tl.e l,c, t may be tl.rown into the circuit. Tl.o rt.«i,tnnce box i» intrtxluced iiito tl.e circuit by con- necting the battery t«rmi.,,Ja with the screw cupii A and li (Fig. 201). 275. Divided Circuits; Shunts. — We will suppose a galvanoin- eter, G (Fig. 203), to be iiUro- duced into a voltaic . i^uit and F.o. aoi the deflection of tl.e needle noted. Then let the por- tion of the circuit between a and b bo divided by connecting these points I'y another wire so that two paths are made by v hid, the current may pass from a to 4. Immediately the deflection in the galvanometer is Fia.202 there was before the circuit was divided. The current at point a divides, and a poi^ tion flows through each bmnch from a to b Opening a new path between two points "1 a circuit is called .huntinff the circuit. Ihe wire used in shunting is called a shunt. Next we will suppose a resistance box, Vf, to be introduced into the shunt wire and th. . • . FlQ. 203 soo ELECTRO-KINETICS I •JTTOff of the shunt ia inoreaMd, the current Uirough the gal- Tanometer ia inureued, aa ia ahown by the increaaed deflectiona. Ia a dlTldad cfatah the cnmBt U dlatritaitad bttwwn tba pallia la aoMaatalareradyaatlMirtaaUtaiicaa. For example, if the reaiatance of the reaiatance box be 4 ohma, and that of the galvanometer be 1 ohm, then four iiftha of the current will traverse the latter and one fifth the former. Next we will auppoee a galvanometer, O (Fig. 204), to be introduced into circuit with a apool of wire, A, and the deflection noted. Then L let points a and b be ahunted through an- other apool of wire, B. The deflection in the galvanometer ia increaaed. Introduc- ing the ahunt virtually increases the size of the conductor between these two points, the effect of which is, of course, to diminish the reaiatance between them. The resistance of the circuit being diminished, the current ia increaaed. Qenerally, the joint realatanoe of two bianctaea of a dicnlt la tiw pndnct of thdr taspecttve raaUtancea divided by the awn of the same qnantltiaa. If any portion of a circuit be divided into three or more branches whose resistances are, respectively, r^, r,, Tf, etc., it may be demonstrated that ■K '■i '■a H in whicli R represents the joint resistance of the several branches. Fio.aiM MEASUREMENT OK RESISTANCE 801 ^ f, "." *• '■^^ "I'™"""* • 'I-nple form of Wh..Uton. bridg, .^ . WW^.,. bridge. On .wooden U«l^;„ .^JJ^'LT '"'r"""' "'"•■ * G<"»— "v,r wi«, it .tn,tch.d between the end b.r.. G U . «n.iti»e galvTomeier ^nn^ted M .hown in the flgu™. C 1. . voIUio eellT/L. «rL tr ." •*""" Jointa/^J j; ".d .Y i. the re.!,,, »nce to be measured, e.g., k .pool of wire. When the circuit i. cloeed by ln«rUng the electrode in k«w cnpMcurrentp«.e.throughoutthewhole.rr«.geme„t,«.hown by the arrow,. It will be «,en th.t between the two end U^^ FlQ. aOB 0»« i. . divided circuit, . p»rt of the current flowing through »*eh bmnch, ««.,/. ,„d ih. Furthermore, the* two bnnche. «- connected with e«=h other .t point. „ ^ , th ^h t°h X two Wnche. t ""r '"" '""^ ' "^^ "' invAtween tht wo branchem whence the instrument derive, ita n.me. In gen- wi^In^ r^"""^ •? *'"' «'"^'"«"°«'«'- By .liding thi. bridge wire along the wu* ,*, a point, p, may be found which hui the »me potent. J «i point „; then no current will traver« the bridge and there will be no deflection in the galvanometer Point J, now dmde. the German*lver wire into two partr, which 1 ^l 802 ELECTRO-KINETICS for convenience we will distinguish by the letters i and h. Pointa IB and p can have the same potential, however, only on the con- dition that the ratio of the resistance R to the resistance X is equal to the ratio of the resistance of part i to the resistance of part *. But resistance of wires is proportional to their lengths. Hence, if we measure the lengths of parts i and h, the first three terms of the following proportion will be known, from which the resistance of X may be calculated : length t : length h::R:X. SECTION VI MBTHODS OF COHBINIHG VOLTAIC CELLS 277. E.M.F. of Different Cells. — If a galvanometer be introduced into a circuit with different kinds of cells, e.g., Bunsen, Daniell, Leclanch6, etc., very different deflections will be obtained, showing that the different cells yield currents of different strengths. This may be in some measure due to a difference in their internal resistances, but it is chiefly due to the difference in their electro-motive forces. We .have learned that difference of E.M.F. is due to the difference of the chemical action on the two plates used and is whoUy independent of the size of the plates ; hence, the E.M.F. of' a large cell is no greater than that of a small one of the same kind. Consequently, any difference in strength of current yielded by cells of the same kind but of different sizes is due wholly to a difference in their resistances. The electro-motive forces of the Bunsen, Daniell, and Leclanch^ cells are, respectively, about 1.8, 1, and 1.5 volt». COMBINING CELLS; BATTKRIES SOS 278. Combining Cells; Batteries. -A number of cells connected in such a manner that the currents generated by all have the same direction constitutes a voltaic battery. The object of combining cells is to get a stronger current than one cell will afford. We learn from Ohm's Law that there are two, and only two, ways of increasing the strength of a current It must be done either by increasing the E.M.F. or by decreasing the resistance. So we combine cells into batteries, either to secure greater E.M.F. or to diminish the internal resistance. Unfortunately, both purposes can- not be accomplished by the same mutliod. 279. BatteriesofLowResistance.— Fig.206 represent* three cells having all the + plates connected with one another, and all thef - plates connected with one another, and the triplet + plates connected with the triplet - plates by the leadingK)ut wires through a galvanometer, Q. It is easy to see that since the circuit is divided by the battery into three parts, the mtemal resistance of the circuit, according to the principle stated in § 275, must be decreased threefold; in other words, the mtemal resistance of the three cells is one third of that of a single cell. This is called connecting cells in multiple, and the hvttery is called a lattery of low remtance. The resistance of the batter,; is decreased as many times as there are ceUs connected in multiple, but the E.M.F. is enml to that of one cell only Fio. 206 f pi i 804 ELECTRO-KINETICS The formula for the current strength in this ciMe is written thus : E C = - S + in which n represents the number of cells. It is evident j» from this formula that when It ia bo ineat that - is a n small part of the whole resistance of the circuit, little is added to the value of C by increasing the number of cells in multiple. 380. Batteries of High Resistance or Great E.M.F — Fig. 20T represents four cell* having the — plate of one connected with the + plate of the next, and the + plate at one end of the series connected by leading-out wires through a galvanometer with the — plate at the other end of the series. This is called connecting cells in $eriet. It is evi- dent that the current in this series traverses the liquid four times, which is equivalent to lengthening the liquid conductor four times, and of course increasing the internal resistance fourfold. But, while the internal resistance is increased, the E.M.F. qf the battery i» inereaied a* many times at there are cells in series. In many oases (always when the internal resistance is a small part of the whole resist- ance of the circuit) the gain by increasing the E.M.F. Fia.aor EXERCISES 806 more than offsete the lo«, occasioned by increased insist The formula for current strength in this case becomes (,_ nE X + nr It is evident that C is increased most by adding cells m senes when R is necessarily la,^ compared wfth nr. BwLB FOB COMBINING Celm : When the eztenul r«ii.f ^^Ui^coju^ct «U. ii. «He. ; When S ^^ ^: ^ »« U-n th. intern., r^^u^, eonn«t cdulL BXKRCISKS d«J™.T°°"*"."" '™"'* ""'*'"«' » ">« '"t four exercbe. and I S06 ELECTRO-KINETICS 10. When will a small cell give very nearly as strong a current as a large one ? 11. (■') A Danlell cell, pint sIm, whose elemente are connected hy a short, stout copper wire which ofleis no appreciable resistance, will yield a current of about i ol an ampere. H the E. M.F. of the cell be 1 volt, what is the resistance of the cell ? {b) If four such cells be con- nected in multiple by wires which offer no appreciable resistance, what current will the battery yield 7 SECTION VII Fio. aoe 881. Magnets. — Any body which attracts iron is called a magnet. A certain natural iron ore, called magnetite or lodettone, is found to possess this property. Given one magnet, it is possible to make any num- ber of others. The sim- plest method is to take a small steel bar (e.^., a darning needle) and draw one end of the magnet along it ; the bar becomes a magnet. If a magnet be laid on a bed of iron filings and then removed, a mass of filings will be found clinging to its ends as shown in Fig. 208. The magnet appears to have a center of force at or near each end, wiiile the central portion is devoid of magnetism. 283. Magnetic Poles. — If a magnetized needle (Fig. 209) be so supported at its center as to be free to rotate in a horizontal plane, it will take a position so as to point nearly north and south. That end of the needle whic^ turns toward the north, when the needle is free X Fio. 209 MUTUAL ACTION BETWEEN POLES 807 to rotate, is called the northrteeUng pole, or simply tha noHh pole. To render it at all times distinguishable from the opposite or south pole it is usually colored black. The north poles of other magnets are usu- ally marked with the letter iVr,„- the plus sign (+), and the south pole with the letter Sot the minus sign (-). A line joining the poles of a magnetic needle is called the axi» of the needle. The direction assumed by the axis of a needle free to rotate is called a magnetic mendmn of the earth. 283. Mutual Action between Poles; Magnetic Induc- tion If a second magnet be brought near to a freely ''^^ suspended magnet (Fig. 210), a mutual action between their poles will be noted as follows: Like poles repel each other; unlike polet attract each other. When a magnet causes a piece of iron or steel, in contact with it or in its neighborhood, to become a magnet, it is said to magnetize the iron or steel by induction. As attraction, and never repulsion, occurs between a magnet and an unmagnetized piece of iron or steel, jt must be that the magnetism induced in the latter is such that opposite poles are adjacent; that Fia. 210 i.^ ' 808 ELECTRO-KINETICS is, an JTor + pole induces an iS or — pole next itself, as shown in Fig. 211. ^ rio.211 It may be here remarked that if a magnet be broken into parts, the several parts will be found to be magnet- ized as shown in Fig. 211. 284. Retentivity and Resistance It is more difficult to magnetize steel than iron ; on the other hand, it is difficult to demagnetize steel, while soft iron loses nearly all its magnetism as soon as it is removed from the influence of the inducing body. That property of steel in virtue of which it retains the mi^etism which it has once acquired is called retentivity. The greater the reten- tivity of a magnetizable body, the greater is the retigtanee ^rhich it offers to becoming magnetized. The harder iteel it, the greater i» it» retentivity. Hence, very hard steel is used for permanent magnete. Hardened iron possesses considerable retentivity; hence, the cores of electro- magnets should be made of the tofteU iron, that they may acquire and part with magnetism very quickly. 285. Fonni of AitlficUl Hacneti. — Artificial magnets, includ- ing permanent magnets and electro-magnets, are usually made in the shape either of a straight bar or of the letter U, according to the use to be made of them. If we wish to use but a single pole, it is desirable to have the other as far away as possible ; then, obviously, the bar magnet is more convenient. But it the magnet is to be used for lifting or holding weights, the U-form (see Fig. 214) is far better, because the attraction of both poles is conveniently available. LINES OP MAGNETIC FORCE 309 SECTION vm ums or luoiuTic fohct-thk iiAaintTic aucvn m. Lines of Magnetic Force. - These lines are easUy studied by the use of iron filings. The field of force around a magnet is shown by placing glass over it. dusting iron filings upon the glass, and tapping it. The filings take symmetrical positions, form c™ between the poles of the magnet (Fig. 212), and show nN /k:=^ 3 . VN / A', ^\ > V, 1 . ,• / / Z ^^^fmm Flo. 213 that the line* of force connect the oppotite pole* of the m^t The fact is that each filing, when brought withm the magnetic field,» becomes a magnet by indue- tion, and tends to take a definite position which repr«- sento the resultant of the forces acting upon it from each pole of the system. If a magnetic needle be placed in the field of a magnet, it wiU take a position such that ite axis 18 tangent to the line of force passing through it. ' Snrroandlng mry nngnet then i. . lin,it«i ,p^ throneh wUA m.g«.t» u^a««» e««d., .«hnio.U, known » tU S^,;^;;^''^ 810 ELECTRO-KINETICS In Fig. 212 the unlike poles o( two magnet* are placed oppo. site each other. Fig. 313 is a diagram of lines of force of a bar i ■/ / ::;;^:^yv/ii\N>^ — -:!- .-V; ii^;^^$^:> Via. 213 magnet when its axis coincides with the magnetic meridian of the earth and its AT-pole points north ; and Fig. 214, of those of a U-shaped magnet. A mat/nelic pole is a region within a magnet toward which the lines of f<'rce converge or from which they diverge. The direction of a line of force at any point is assumed to be the • direction in which the JV-pole of . a magnetic needle would point if ,''/,'*'T^c — "7-'77T'\^ ^^^ needle were placed at that ( ( \Vt.-^','^''/' ; i '• point. The iV-nole of a magnet, \ '^N^^" '^y / as will be seen by examination of any of the figures here given, is the pole whence the lines of force emerge, and the /S-pole is the pole to which the lines of force converge. They do not stop at the jS-pole, but continue through the magnet and form complete closed circuit*. Flo. 214 PKKMEABILITV TO LINES OF FORCE 811 887 PermeabUlty to Line, of Force. _ Lines of ma«r. netic force are often regarded a« path, of magnetic flow, much a8 the wires of voltaic circuits are re.rarded as paths of electric flow. It would seem that air is a poor conductor of lines of force or, to use a technical term, its permeabUity is low : on the other hand, iron is highly permeable to lines of force. If a piece of iron be brought within a magnetic field, n,any hues of force will leave their normal paths through the air and crowd together into and pass through this medium of greater permeability. 288. Xagnrtic Action of tli, K«tt._ We hare already seen evidence of thi, action i„ giving direction to the n.agneU IX ton .„d.cate«, aa «e l.ave already learned, the di«ction of the magnetic meridian of the earth at the given place .Jj^T"'^' """^'".""PP"" • °° ^ '-H»ntal axle «o that it re:d;:r;rac:;:r ^'""' " -^"^^ ^ ^^-- ---• " -•■ » the iV-pole of a mag- net, as shown in Fig. 215, it will take a ver- tical position with its ^ S-pole down. Move the needle along the magnet; the needle will graduaUyri«, until it reaches the middle of the magnet, where it becomes horizontal. Continue moving the needle toward the S-pole of the magnet; the JV-poIe of the needle now dips, and the dip increases until it reaches the ,S.pole down* '°*^*'' *'"'" " *^"" ''^*"""'" '''"'"''*'• '"''•' '** -^-P"'* If the same needle be carried northward or southward alouft the earth's surface, it will dip in the same way a, it approaches the poUr regions, and be horizontal only at, or near, the equator. FI0.21S r u 812 ELECTRO-KINETICS FlaoM where the dipping needle MWiroe. a vertU»l podUon M« Cftlled the magnetic polet «/ Ike earli. Inawnuoh w the magnetic polee of the earth do not coincide with the geographical polee, it foUowi that in raort plaoei the needle doe« not point due north and louth. The angle which a Tertical pUne through the axil of a freely »u»pended needle makea with the geographical meridian of the place is known ai the mgU of dtelination. In other wordi, the angle of declination U the angle formed by the magneUc and the geographical meridians. Thii angle differs at different places. SliCTION IX ■AOHXTIC BBLATIOWS OF THE CVSMMBT -VMCtUO- HAOmTS 389. Magnetic Field of a Current. — If a wire be bent into the form of a circle of about 20 cm. diameter and placed vertically in the magnetic meridian, and a card- board be placed at right angles to the circle so that its Fia.216 horizontal diameter is coincident with the upper sur- face of the cardboard, and a very strong current be sent through the wire in the direction indicated by the SOLENUtO 818 •"owhW in the wire, iron filings .ifted upo„ y,, ,,^ will axmngo themselves «s shown in Fig. 216. And « the several pos.Uons taken by the needle (as indicated m the figure by arrows) show the directio J of Z H JlJ ZrZZ r""^'. "** '•''*''"°" °' *•»« "-die will ^Zt^ !;herever it nuy be placed. TAe electric S^ r IT", '^'"""^ "• '*" '■'*"•'• th^t «. the grlS s^^rCtir™^'^^^^--^^'"--'^^^ occupy the field. Fig. 217repre«enU the lines of inaf^etic force encircling a cui^ rent in o straight wire. If magnetic needles bo placed above and be- low the current, they are deflected in acconiance wit^ th. „ . the lines of force have a clockwise direction. * ^ 290. Solenoid. _ If, instead of a single circle of x, re an uu,uUted wir. be wound into a helix of se vend turn"' cullltr" ^ T^'^ ''^ *^' J"'"' -«on of the^any um,nttun.s. The passage of an electric cun^ntth«,ugi a 80 enoid g,ves it all the properties of a magnet tS -8^^t hues of force pass thn,ugh the solenda parid to Its »xis, as shown in Fig. 218. Fio. 217 n 814 KLKCTRO-KINKTIC8 A Mlenoid enciniing bb iron core constitutes »n tlectfo-nuiynet. By icOKm of iU permeabiJity the iron core greatly increane* the number o{ lines of force which poM through the solenoid. Hence, the magnetic strength of a solenoid is greatly increased by the presence of nn iron core. 891. Polarity of an Electro-Macnetic Sole- Fia. 218 I mi^, — Fig. 219 repre- sents a small voltaic cell floating on water. The leading- out wire of the cell is wound into a horiiontal solenoid. Slowly, after the cell is floated, it will take a position so that the axis of the solenoid will point north and south like a mag- netic needle. Hold the the wire, M.n^F* 228, it will tend to turn (or, if movable, the wire will tend to turn) and take a .^^^__^ position at right angles to the wire, &^-=^ ^^^^^N so that both wire and needle may be invested by a large amount of mag- netic flux having a common direc- tion. To accomplish this the needle must turn in a definite direction. Again, on examination of Fig. 229 we find that the directions Fia.2Zr W^ Fio. 228 Fio. 229 of the two sets of flux paths about the two magnets bear the same relation to one an^er «> those repre^nted in Fig. 225 encucling INDUCTION COIL 319 other. f" '"'" P^^'^ity they will repel ^h SECTION XI P«.BCCT,0, OK K^„e CU««.„ BV «„.CX,0H i-X^S::2 -r ^^ 'l^ ^^ .831. a„a h. science.1 ' """ '" ''»« ''"tory of elecWcai 896. Description of the Induction Coa T)„» tus may be defined as a device for i ~ T ^^"^ ordinar, current tron, a volSc L i ' '™"f ™""? »" poto^tial. though of educed s^Hf , ~1 two coils of insulftf*^ "^"gwi. it comiste of caUed the 1 "^^' 1 7^' T' "^"^ ^ <^'^- 230), and thereforrof loirT' °' ^'"^ '""*'- -- which fShes the r " """* "'*^ " ^°^*»^« -" Another i^dl^det o' 7. " '"'""'"^ «=""-«»• other gene«nrirc:;^'td' " ^' "" ''^^ ^ nometer, «. -^ ""'' * sensitive galva- -n^eter to'aee wh fh hZZ Z T """^ "' *"" «"'- > TheHw ' ' '^ *'' '" ''''»* direction. 820 ELECTRO-KINKTICS Simultaneoualy v»ith thU raovsraent there is a moTemrat of the needle, showing that a current must have pa»«ed through the neoondary circuit. I^t the pri- mary coil rest within the secondary. The needle will come to rest at lero, showing that the secondary current was a temporary one. Now, watching -,_ j^lg the needle, quickly pull the primary " coil out; another deflection occurs, but in the opposite direction, showing tliat a current in the opposite direction is caused by withdrawing the coil. F'»- 230 ' It is evident thivu in this case the current does not by its mere presence cause an induced current, but a change in the relative potitioM of the two circuiU, one of which bears a current, is necessary. Instead of a currentrbearing coil, a bar magnet may be intro- duced into the secondary coil and afterwards withdrawn from it. The needle is de- flected at each act, as beforb Bzpeilinent 2. — Open the primary wire at some point and place the pri- no. 231 mary coil within the secondary. On closing the circuit (Fig. 231), by bringmg mto contact the terminals, a deflection is produced. As soon as the needle becomes qui«t. break the circuit by separating the termi- naU; a deflection in the opposite direction occurs. The same phenomena occur when the primary is by any means' suddenly ttrengthened or makened. The SELF-INDUCTION 321 act by which the primary, or a magnet, causes a current in a neighboring secondary is called induetiom 297. Faraday's Law of Induction, - When, by ^ me«n. wluterer, the toW number of Bae. of fen* iiclLl^ . d«nlt 18 chMged, «n electric cumnt proporttauU to the iJto ^J^ ?" ^"'^ *° *^* "™^*- The current so produced is called an induced current. o,n?f*i ^-'"f""*^"! =^» Cmr.nt..-When any voltaic cii. cmt« broken at any po.nt, at that instant the™ may be aeen at that po.nt (egpeciaUy in a darkened room) a minute Bpark The expUnaUon i, as follows: As long as a current traverses a con- ductor It IS mvested by Unes of magnetic foree, but when the >li Pro. 232 circuit is broken the«, lines suddenly vani,h, thus prc'ucing, " explamed above, an induced current in the selfsame circuit. " 18 this induced current, commonly called an ,x,ra current, which M It passes between the terminals produces the spark. Extra currents become quite intense, and the sparks eorre,.,nndinriy brUliant when a helU, or preferably an electix^magnet, is placed 822 ELECTRO-KINETICS ■i I |l ' in the circuit. Thus, if one of the electrodes of a circuit contain- ing an electro-magnet (Fig. 232) and a voltaic cell be attached to a file and the other electrode be drawn along the file, the current ii atarted anQ stopped as each ridge is crossed and a series of bright sparks is observed. On this principle are constructed so-called "sparkers" for lighting gas. In this case automatic interrupters are used like those of induction coils. (See J 209.) 299. Sntamkoiff Coil. — A core, best made of a bundle of iron wires (AA, Fig. 233), inserted into the primary coil, greatly increases the number of lines of force or the magnetic flux about Fio.233 the coil and, consequently, greatly intensifies the secondary cur- rents. The intensity of these currents is further increased by the addition of a so-called condenser, BB. Coils which have con- densers are called Ruhmkorff coiU, in courtesy to the inventor of this attachment. Ill coils of this kind the primary remains permanently within the secondary, and the " make and break " method of inducing currents is employed. To save the trouble of making and break- ing by haud, as described in Experiment 2, the core is utilized iu MICHAEL FARADAY (1791-1867) THE TRANSFORMER 328 the eonitrnetion of ui •utonuttic interrupter. A loft-iron ham- mer, », ja connected with the eteel spring e, which ia in turn con- nected with one of the terminab of the primeiy wire. The hanuner preuea against the point of a screw, rf, and thus, through the aorew, oloaes the circuit. But when a current passes through the primaij wire the core A A becomes magnetized, draws the hammer away from the screw, and breaks the circuit. The circuit broken, the core loses its magnetism, and the hammer springs back and doses the circuit again. Thus, the spring and hammer vibrate, and open and close the primary circuit with great rapidity. Every make and every break of the primary ia accompanied by a transitoiy current in the secondary, but in alternating direc- tions. If the aecondrj-y wire be open at aome point, as at i>, a rapid succession of Sjiarks will pass between the terminahi. Secondary cunrenti: developed in high-resistance coils have, of necessity, vastly greater E.M.P. or power to overcome resistances than the primary currents which circulate in low-resistance coils. Secondary coils have been made containing wires over 200 miles long. Such coils have produced , sparks in open air 40 inches in length. Fig. 2.34.represento a Ruhmkorff coil in perspective. It has in the secondary circuit a glass tube. A, partially exhausted of air and known B8 a Geimler tube, from its inventor. Platinum wires are sealed into the glass at each end of the tube to con- duct the electric current through the glass. As the current passes through the vacuous space, the entire tube becomes illuminated with a continuous glow. 300. The Tiansformer — An induction coil is in a certain aenae a reversible machine. If a current of considerable strength circulate under small E.M.F. in the primary, then variations in its strength give rise to very weak currents of exceedingly high E Jf.F. in the secondary. Conversely, if we cause weak currents rio. 234 824 ELECTRO^KINETICS nodo- ftTf high E.H.F. to elranlate in tiie Keandary, by thdr flnetutiou than will be genented in the primvy itrong cur. ranU of mukU E.M.F. We do not in either caw onata eleotrio energy. Electric power ii the proUuot of two factors, current and electro-motive force. The induction coil enable! us to increase one of these factors at the expense of tlie other. The tramformer — sometimes called a eonrerter — is merely an induc- tion coil used to change the relation of the number of volts to the number of amperes of any current In a perficl transformer the nomber of watts !u the primary is equal to the number of watts in the secondary. Transformers are used when currents of high voltage are to be oarried great distances and delivered at a pressure that is safe to handle. With a great r«sistance in the line, due to its length or diminutive size, the loss in watts is less with a current of few Mnperes and high voltage than it is with a strong cunvnt and low voltage. Hence, high-voltage currents enable us to use smaller copper wires. The chief advantage, therefore, to be derived from high-voltage currents in transmitting electrical' power long distances, as for example from Xiagara Falls to the city of Buffalo, is economy of power and of copper, which is expensive. Currents generated by an alternating dynamo of 80,000 volts may be transmitted a distance of 60 miles over com- paratively small wires, and be transformed into currents that ai« perfectly safe for domestic purposes. SECTION XII mnrAMO-BLBCTKIC MACHIiaS 301. Principles of the Dynamo. — The dynamo, like the voltaic cell, is a device for generating electric cur- rents. The fundamental phenomenon involved in the construction of all dynamo machinery is that of the induc- tion qf eurrtnU, discovered by Faraday. The dynamo THE OrifAIfO 896 embnweB a .ytera of ooib which are nmde to move in . -«Wn.t.c field in .uch a way that the nun>ber of Ibe^J ^euc flux pacing through the.„ varie. co tin oti; Ihe magnetic flux through a coil may l-> ohan«rf Jn rr i "*•'•" <^> •'^ "«'-"» "- coil tLirflS u. whjch the denaity of the linet of for.e v^^^ Jf -^d^n_F^^36^^ eau«ing the ZTolZ na.23B Fta. 238 « n^pr^nted in K^: 286 '"^ *'' """^'•''''^-«'' 308. ConrtructtonandOpetatloiioftheDynwao Th two e«ential features of the dy„an,o a,^ r^~ " latter, a« wUh u a much 8ti.,nger field can be obtleA I 826 ELECTKO-KI N ETIC8 A machine is ciUled a magneto (see Fig. 240) when the field is produced by a permanent magnot had a difnamo when it is produced by an electro-magnet The simplest form of generator consists of a loop of wire, AB (Fig. 287), amngod so as to be rolitted between the poles of a magnet. The loop of wire in its present position incloses tlie largest possible num- ber of flux lines. As it rotates from this position, as indicated by the arrow over the loop, the number of lines of flux that pass through the loop constantly diminishes until a quarter of a turn is completed. At this point no lines pass through the loop. From what we have hitherto learned, it is apparent that during this quarter of a turn a current will circulate in the loop in the direction indi- cated by the arrows. During the next quarter turn the lines will increase, but they will pass through the loop from the opposite side, so that there is no change in the direction of the current in this quarter turn. But after a half turn is completed, and during the third quarter turn, the lines decrease and their direction through the loop is the same as during the second quarter turn ; con- sequently, the direction of the current is reversed. The current is, therefore, reversed twice in every revolution, giving rise to what is called an alternating current. The loop of wire in which currents are induced is the arma- ture. In ordinary dynamos this simple loop is replaced by a coil of many turns of wire embracing an iron core. THE COMMUTATOR 82T (*ig. 288), which ara inaulated from each other. *^0. 2M Resting on these rings are metallic sprir,„ „. „;„„.. , carbon, n and ^ called bru»he» The ZL f , loop are connected with these brushl wTe:! "' *"" tu« is rotated one of these rings tui a^tltT" higher potential than the other, but the.« c^L t * rent because they are insulated fmm'Xther T wire, Ji, just as we connect the elements of a voltein ,7 we establish an -.external cii^uiV though S S induced currente flow, as in a voltaic ci«,St u. attached to the axis of the armature In th^ two metal rings on the axle a^^cd L^o^:,!^ of a spilt ring or tube. Fig. 239'rept^U ^tti: I 1 tS8 ELECTRO-KINETICS and commutator, in which ^ and JJ are the segments of the ring. These segments are insulated from each other. The terminals of the armature coil, E and F, are connected with these segments, and the brushes C and 2> press upon the opposite segments. The connecting wire, JB, constitutes the external circuit. The two brushes exchange connections with the segments at the same instants that the current in the armature reverses, BO that brush C is always positive and brush D is always Fia. 2») Fia. 240 negative. Hence, the current through the external cii^ onit R is constantly in the same direction. Such a dynamo is called a direct-eurrent dj/namo. m vl 23 - ''^^^^^ 829 demoMtratioM. It i, th. „ ^^^^ '" '™P'« l«cture-room ^-ntHvearo/:;L?l„7---;^an „. Hi„e. that^: CC „« two armature coil, whth ?'"'''""'■<»' ""^liy. 304. EM.P.of aDynamo TV ^ '«V. <,/,«•„ ,•„ t^, Zji '"^'"«'-«V (2) the number of 305. Commercial Efficiency of « iw apparent that mechanical J..^ Dynamo. — ft jg maintaining the n.otr LILT' "^ ^ ^^"'^^ ^ it:rener"^"'^=-^^^^^^^^ ^et=S^^--;^oi.the.tio. power expended in turning the arma- ^gh,-m the best machines 90 per cent or more. ^ 306. CUMliictioa of Dynamo, n™ «»*«? dynamo wW tK i^ ' "^™"'* -I-rate generator. e.g., a batteiy. 830 ELECTRO-KINETICS Fig. 241 illuBtrates a tkunt machine, where the field coil serrea u a shunt to the external circuit. A is the main wire and B is the ghunt wire. In the shunt machine a part of the current gen- erated in the armature passes through the coils of the field magnet and thus excites it. A dynamo is said to be " self-exciting " when the whole or any part of the current which is produced is used to generate the field. The cores of the field magnets of a self-exciting dynamo, after being once excited from any source, e.g., another dynamo, always Fio. 242 ntain a little residual magnetism, so that when the armature begins to rotate a slight current is at once induced in it. This canent strengthens the field, »nd the stronger field reacto to EtECTRO-DYNAMlC FORCES 881 increa. the current. „ tha. the current soon ri.« to it. nor... ^7^LTXf:oT.^::j:''' ''^-'""-'^'''' »p«-tation. of SECTION XIII BLECXHO-DVHAmcS COBTmn.D-THE ElECTHC MOTO« Le'^B^TLlT""^ '^ Electro-Dyna^c Forces.- C^. It is placed in a .\V\ field of magnetic flux, xVxi^VV^ *'^>^ e-ff., between poles of ^ ^^\^"'^i'\'^iJ^ a magnet. Now the . >,\\V~V\"-.^ action of the electro- dynamic forces be- tween the field flux and the flux which encircles the current- bearing loop is such as to cause the loop to move from the posi- tion AB to the position A'/i' to ^M the larger poMle nuraUr of flu. lines If, when the loop reaches the position A'B', the direc- tion of the current in the loop is r.ve:.ed by mel of a commutator on the axle CB, the loop will cont,^e L motion m the same di..ction. A machine by means ot Fio. 243 In other words, the loop 882 ELECTRO-KINETICS which electric energy is transformed into mechaaical Tnergy through the instrumentaUty of electrodynamio forces is caUed an electrie motor. 308. ReversibiUty of the Dynamo. -It cannot have escaped the notice of the reader that the mechanism o retotor is the .me as that of the dyna-no. J^™^ any dynamo may be used as ^ motor ..e., <« t^^°™ enLy of electric currents into mechanical work. In "^us^ge the armature, instead of being the source ora cuLnt, is supulied with a current from some Itemal source, such a« a volUic battery or another dvSTo. If, for example, two dynamos be connected JnSes in t^he same circuit and the armature of one be ^^ta^ tie armature of the other will rotate as soon as ntent transmitted from the first attains a certam intensity. , T . / A R IVW 244) represent in diagram two dynainoB eon's'uJtTta fii^e. ' M^I^nicai power is supplied to the Fio.244 i hv the fallins weight C. In this dynamo mechanic^ dynamo A by the famng J an electric current, which energy U transformed into rt>e« ^^^ ^^ •i^Lrm^e; -r meiSlerL which raise, the weight .. SECONDARY CURRENTS 333 The energy .tored in D after it i. raised, plu, «,me additional energy to compensate for that lost in the transmission from A to B and .n the several transformations, may be used again by a reversal of transformations to raise the weight C. 309. The Blectric R.Uwny._The system of electric^iar pro- pulsion consists in the generation of an electric current at some power station by means of dynamos, its transmission over con- ductors to the electric motors on the cars, and its transformation into mechanical energy, which gives motion to the car SECTION XIV SEOOHDABY OB STORAGE CELLS - THERMO-ELECTRIC BATTERIES 310. Secondary Currents. - After decomposinff an aoid solution for a brief time between the platinum electrodes in an electrolytic cell (see § 258), if you replace the battery by a sensitive galvanometer, a deflec- tion of the needle shows that a current opposite to that which previously flowed in the circuit is now produced by the electrolytic cell. This cuirent is produced as follows: The platinum electrodes during the electro- lytic action become polarized, and energy is thus stored in the electrolytic cell. Polarization is of the nature of a counter E.M.F. It is precisely this polarization which we have to contend with in nearly all voltaic cells, and which we seek to neutralize by means of depolarizing agents. Devices for thus s'oring energy by electrolysis are called itora^e or neeondary eell$, and sometimes accumu- lator!. Note that the process is an electrical storage of 884 ELECTRO-KINETICS energy, not a storage of electricity. The energy of the chaiging current is transfonned into the potential energy of chemical separation in the storage cell. When the circuit of the storage cell is closed, this energy is recon- verted into the energy of an electric current in precisely the same way as with an ordinary voltaic cell. The storage battery offers a means of accumulating energy at one time or place and using it at some other time or place. For example, energy of a dynamo current may be stored during the daytime when the current is not needed for illuminating purpoma ; and this energy, reconverted i"*" electric energy, may feed incan- descent lamps at night at any convenient place ; or tlw charged cells may be transported to lecture halls, workshops, electric cars, etc., where powerful currents may be needed. An efficient form of storage cell in which tlie plates are made of lead and lead oxides has an E.M.F. of 'l.'i volts or more. lU resistance depends on the size and number of plates, but is often not greater than .00.') ohm ; consequently, the current which it yields is very much stronger than that of any ordinary galvanic cell. 311. Thermo-Electric Batteries. Cxptriment. — Let G (Fig. 24.5) lie a very sensitive galvanom- eter. Form two junctions l)ctweeii its copper-wire terminals and an iron wire by tightly twisting the wires together near their extremities. Let A and B be the two junctions. Immerse both junctions in sepa- rate beakers of water. (1) Raise the water in one of the beakera to the boiling point ; a current passes through the galvanometer G, caus- ing a deflection. (2) Reverse the position of the two beakers of water; the current now causes a reversed deflection. (3) Bring the cold water to the boiling point; the deflection diminishes »t«adi!v to 'em aa thermal equiUbriua is established. Fro. 24B THE ELECTRIC LIGHT 886 HEAT Thus, the thermo-electric current depends on the difference of temperature of the junctions, vanishing when that difference vanishes. Suppose the junctions to ^nn-f.^""^' ""'^ ^""°^-' ^^^ ^■^■^- ^'U ^ about 0.0016 volt. It would require about 1000 pairs of such junctions to give an E.M.F. comparable to that of an ordinary voltaic cell. The E.M P. may bo increased by combining a large number of pairs with one another in series. This is done on the same principle and in the same manner that voltaic cells are united, that is, by joining the + elec- trode of one to the - electrode of another. Kig. 24« represenu such an arrangement. The light ba» are bismuth and the dark ones anti- mony. If the difference of temperature of the two faces h- made »erv great, an E.M.F. may be obtained as grwat a« that of a voltaic lell. Such contrivances f.)r gemM-atiiig electric cur- ri'nts are called ll,e»t of them tran»for.n loss than 1 per cent of the heat energy employed. They are of interest to us chiefly because they de.-ion- strate the fact that heat energy may be directly tranrformed into electric energy. SECTION XV TH« ElECTHIC LIGHT 318. Electfk LJ«ht; Voltak Arc. -If the terminals of a powerful <\yi,nii,<, or galvanio battery be brought together, wid t}i«n separated 1 or 2 mm., the cun'ent does not cease to flow, but volatilizes a portion of the terminals. The vapor formed becomes a condueter of 886 EL£CTR0-KIN£TIC8 high resistance and, remai aing at a very high tempera- ture, produces intense liglit. The heat is so great that it fuses the most refractoiy substances. Metal termi- nak quickly melt and drop off like tallow and thereby become so far separated that the electro-motive force is no longer sufiScient for ti ; increased resist- ance, and Vi light is extin- guished, lience, pencils of carbon, being less fusiUe, are lused for terminals. The larger portion of the light emanates from the tips of the two carbon terminals which are heated to an intense whiteness. The light is too intense to admit of exam- ination with the naked eye, but if a pin'4iole image of the ter- minals be thrown upon a screen, an arch-ahaped light, known as the elentric arc, is seen extend- ing between the terminals. This is due to the transfer of light- giving particles of carbon from the positive to the nega- tive electrode. What we see is not electricity, but a luminou* cloud of matter. Fio. atT The terminala are slowly consumed by combustion; at the same time a conical-shaped cavity, called the crater, is formed at the ]>08itive terminal, while the negative terminal becomes con- ical (Fig. 247). When, in consequence of combustion, the distanos between the two pencils becomes too great for the electric oorrent INCANDESCENT ELECTRIC LAMPS 887 . ""' """''• The movemento of the carbon. ^proau^J .„eo.a«ca„, h, the ..o.^^tlZ 313. IncandMcent Electric lamp,. _xhe mcjjdescent or "glow "light is p^ueed by the heatmg of 8on,e refmctoi. «dv to a state of incandescence by the pa«s,^e of fllament« are generally used in incandes- cent lamps It i* essential that the oxygen of the air be removed from these bulbs ,,. prevent the carbons from being quickly burned; hence, veiy high vacua IZ «uccd m the bulbs. ' 6i>H^t rr"? ""•' ' '""'•^ The loop or fll~*N.t of carbon L „, joined at „» to two pLi. n>»m wire, which pa«, through the clo^d end of the gl^ tube T. „„« rf u«e the l:;' wh/^The r" '^' ^^ *'■*' '^-"" <" lip. When the lamp i, screwed into it. ^re:;h're:."""'°^''''-'''"''-^-'-^ An ordinary 16H,andIe-power lamp has a resist anc. (when hot) of abont 140 ohm ; t e d'fft ^t^ and It requires a current of 0.75 ampere oyw . watT^r't-d^rr 'x: t-^T-- Kiu. -MS One of tlwM 888 ELECTRO-KINETICS Fig. 280 reprawntt wi •lectric-light i^itero in wliich D i» nt alternator dynamo, H higli-pr«»ur« main*, Tand T tranafomiMa, M M-^ Fio.-JM L and L' low-preMure n^ains, and / and /' incandescent lamp* connected in multiple. SECTION XVI EUCTBOTYPIHO AND ELECTKOFLATIHO 314. Ilectiotyplng. — This book is printed from electrotype plates. The matter is first set up in common type from which an imprewioii, or mold, is made in wax. In the mold the eleva. tions appear as depressioiia, and vice vena. The mold is then coated with plumbago to render it a conductor, and is suspended as a kathode in a solution of copper sulphate. A copper plate is used for the anode, and the whole is placed in circuit with a low-voltage dynamo. The copper sulphate is decomposed by the electric current, and the copper is deposited on the surface of the mold. The sulphuric acid appears at ih-i ■'- electrode and, com- bining with the copper of this electrode, f jnns new molecules of copper sulphate. When the copper film has acquired about the thickness of an ordinary -risiting card it is removed from the mold. This film shows distinctly every line of the types or engraving. It is then backed with type metal to give it firmness. The plate is next fastened on a block and thus built up type high ; it is then ready for the printer. (For full directions which will enable a pupil to produce electrotypes of medals, etc., in a small way, see the author's Pkyticrew cup,,-/)/,. About a !!1 ' •-' "'"""^'^^'*''' «'"' the millimeter froin tlie end of the magnet is clampt'd a thin iron disk, A7i. An instrument con- structed in precisely the same manner may be used, and originally was used, for Fro. 253 ment is spoken into at G the disk is mil!* i '"■"' with the air vibrations, and bvTts La^, r ."'* " ""''"" causes the strength of'th: m^ t v J™ T^IZ 'f f ' »^-ngth of the magnet is, of co'urse, attended by . v. a^ "^ the number of flux lines passing th ough the oil B h '" '" produce changes in the natltSo: oMl" " """•"■' """ instrument The fl„rt,„.t; " ""Snet in this the .ceiving inlrnTrse'r S'Ttr '" r^' '" repeat whatever motions are imparted 1 the '" .™""'"' *" The vibrations of the receivinTd't J^ ! ^^"''""tting disk, ".ponding to those incideT^A l^e C^l^lr ' ''^ 342 ELECTRO-KINETICS SECTION XVIII sOktgen phenomena— bkrtziah waves - well's theory of light -MAZ- 319. Kathode Rays. — If a glass tube, into the oppo- site ends of which two wires are sealed, be exhausted to approximately one millionth of an atmosphere and the high pressure discharge of an induction coil be passed through it, many interesting phenomena occur which were investigated by Crookes and described by him in 1879. The comparatively few remaining particles of gas in the tube are attracted like so msmy pith balls to the kathode, or negative terminal, whence, after becoming electrified, they are driven off in straight lines with a velocity computed to be not less than 25,000 miles per second. On account of the rarity of the gas these excited particles dart through the tube with compara- tively few collisions, and they assume properties so novel as to justify the application of the term radiant matter, first applied by Faraday. These streams of radiant matter, now commonly called kathode rayt, are capable of turning a light paddle wheel placed in their paths within the tube. 320. Rontgen Rays Where" these charged particles strike any solid, for instance the side of the tube, the molecular impacts become the origin of a new kind of radiation that possesses some remarkable properties quite unlike, in many important particulars, those of any radi- ation which we have hitherto considered. The best kOntgkn rays 843 Intheyearl895Prof. W.K. Hontgen.of Wu^l,,.,^ i„ Bavana d.scovered that this non-IumL;. radi^tTo ^a natmg f , Crookes tube, even after i>^siuTZ„Z certam sul^tances, such a.s canlhoan], io.l, 5el 1 mu.um and „.a„y other substances which a .i t" opaque to ordumry light waves, is capable of affe'tb a photogmph.c plate beyond. Not knowing the n U 'of the resulting negatives being of the nature of shadow pictures. When we add that most metals are rather opaque to these rays, It is easy to gee how radiographs of foreign bodies imbedded in the flesh, such as needles, I)id- leia, etc., may l)e obtained, and how radiography may be of immense value to surgery in locating these bodies with pre- cision. • . •* sensitive plate is inclosed in an envelope of black t>^ t, so as to exclude all light . the plate. The hand, for Sim- ple, is placed flat on the plate and a properly constructed Crookes tnb« ; « j , above it. When the tube is exeT. b . '"^ ^ "' ' ^««' 18 exctcd by an induction coil or other Fm. 2S4 844 ELECTRO-KINETICS ■uitable apparatiu thore ROntgen rays that meet only fledi pan with littlo loss through it and thn paper to the plate, while thoM that meet bone are largely obstructed; hence, a shadow outline of the hand is pictured upon the plate, the bones appearing darker than the flesh, while such an opaque object as a gold ring casts a very dark shadow. Fig. 254 represenU a shadowgraph, or radiograph, of a hand wearing a ring. Fig. 255 represents the apparatus during the operation of taking a radiograph of a hand. The current for this purpose may be taken from a storage battery or from a street electric-light wire. There is a fundamental diflerence between the methods of ordinary photography and those of radiography. In the latter no lenses are used fof focusing, since up to the present time no Via. 268. — ^ Is the Crookes tube; B, the cnp-shaped kathode made of alpminnm ; C, the anode made of platlnnm, whence emanate the RontKon rays; D, a snpplementary tube which regulates automati- cally the degree of exhaustion within the tube A; BmAF, the primary and secondary coil's, respectively, of a Ruhmkorff coil ; O, a flnoroscope. means of refracting Rflntgen rays has been discovered; conse- quently, the picture produced is merely a record of the shadows cast by the bones. THE FLUOROSCOPE 345 32^. FlBOiOieop*. — A very important accessory to the appa- ratiu described above is an instrument calleil Ajtmrotcope. It con- liita o£ a box (Fig. 256), dark in the interior, with anoiwiiing at the small end, into which to look. At the oiipositi^ and larger end is spread some fluorescent material,' preferably barium platinum cyanide. Any body that is opaque to Kiintgen rays, if placed out- side the fluorescent screen, and between it and the Crookes bulb, casts upon the screen a shadow which may be viewed by looking in at the opening. For exam- ple, one can see a shadow pic- ture of the bones of his own hand upon the screen which is elsewhere fluorescent. In order to obtain a fluo- rescent picture of the chest of a human being, you would place an excited tube at his back (it is not necessary that the clothing be removed) and the large end of the fluoro- ecope close against his breast ; looking in at the small end and covering this aperture v/ith your face so as to exclude all light, you would see quite distinctly shadow pictures of the skeleton, and somewhat dimly the outlines of the moving organs, such as the heart, etc. 322. Hertzian Waves ; Wireless Telegraphy. — It has been proven experimentally that an electrical discharge such as occurs between the electrodes of the secondary coil of a Ruhmkorff coil is not, as it appears to the eye, a single passage of electricity but a multitude of to-and- fro discharges passing at the rate of many thousand per second. The discharge may be likened to the vibrations > Ultra-violet rays and Bontgen rays, though invisible themselves, are capable of canning certoin substances, said to be Jluonacent, to glow when exposed to them. FI0.2SS 846 ELKCTRO-KINETIC8 of an elastic rod clamped at one end. H nee, the di»- charge is said to be oteiUatory. Hertz demonstrated (1888) the presence of ether waves radiated through space at the instants when oscillatory discharges take place. These waves are called eleetro- magnetic waves. MaxweU had declared, years before, that such waves must be generated by the action of the Ruhmkorft coU, but it remained for HerU to devise a means of detecting them. Various devices have been employed by him and by others for this purpose, but the most efficient detector employed at preeent is the "coherer" invented by Edouard Branly. It consists of a glass tube, A (Fig. 257), filled with a carefully prepared mixture of metallio powders placed in circuit with a voltaic cell and a very sensitive galvanometer. The powder offers a very high resistance, but when an electric wave such as that described above reaches the coherer, it causes the particles of powder to stick together, or cohere, thus lessening the resistance and increasing the deflection in the galvanometer. The practical man at once sees in this the possibility of transmitting signals without the use of wires. Modifications of this contrivance devised by Marconi and others have recently been adopted for vrireless telegraphy. The electro-magnetic waves travel mth the speed of light, but nnlike Ught waves they will pass through the walls of a building; and the recently reported signals sent across the ocean seem to indi- cate that even the sphericity of the earth is not an insuperable obstacle to their transmiseion from continent to continent MAXWKLLS THEORY OF LFGHT 847 magnetic disturbances in the ether of rapidlyaltta" Tves r»1' . , '«'" ^''^*'' '"•' «l««t">-nagnetic waves of a hmited range of wave length. The Maxwellia.. theory is now considered verified bv ana others.i The importance of this theory from a Bcienffic outlook is g^at, inasmuch as it teaJhesTto juiervention of the same ether spn Tf i^ and mo« evident that this melm I'tt'ZllTC which energy, manifested in a great varietv !.7v K ^ Jons. pa«.s through space from"^;! L XHoIT The e,p^««.„„ ..^^^ ^ contin'uallyTqu ": ing new scope in physics. - acquir- er i^^t ;!::r:'r^«vjr"' *^"""°"-" «'»«*-'"'- APPENDIX TABUS OF METRIC MIASURIS Measube or Lemoth I HilUmeter (mm.) = O.OOI meter (ni.) = 0.03B37 Inch. 1 Centimeter (cm.) = 0.01 m. = 0.3II.S71 Inch. 1 Decimeter (dm.) = 0.1 m. = about 4 incbea. / J/«««r 1 .30.37070 inchiiH = aliout 3 feet S| inches. 1 Kiiometer (Iim.) = 1000 m. = about ( mile. Mkabi?rr or SuRrAce 1 Square millimeter (mm.») ^ 0.000001 wjuare meter (m «) = O.OOlfi square inch. I Square centimeter (cm.*) = 0.0001 m.' = 0.1660 aquure Inch. 1 Square decimeter (dm.') = 0.01 m.>. 1 Ai» = 100 m.«. Meabcre or Volume 1 Cubic millimeter (mm.«) = 0.000000001 cubic meter (m.»). 1 Cubic centimeter (cc. or cm.») = 0.000001 m.» = 0.001 cubic inch. 1 Cubic decimeter (dm.«) = aOOl m.« = lOOO cc. 1 Cubic meter = about 1..308 cubic yards. Measure or Capaci./ 1 Hllliliter (ml.) = 0.001 Uter (I.) = 1 cc. = 0.061 cubic inch 1 Centiliter (cl.) = 0.01 1. = 10 cc. 1 Deciliter =0.11. = 100 cc. ^ ■''"*' = 1000 cc. = 81.027 cubic inches = 1.0667 quarts (liquid measure). 349 850 B^ APPENDIX Incbet 1. L It - Jl — k fE d Ctibw C«otim«t«f The »re» oJ thlii figure U a »quare declmcler. A cube o( water, uiie ol wliiiM »ide» liaa llito area, U a cubic decimeter or a liter ol waUr, aiid at the temperature of 4° 0. l.a» a mm» ot a kUogram. The same vol mie of air at 0° C, and under a preMure of on ) atmoephcre, liaa a maaa of 1.203 g. The gram i» the man of 1 cc. of pure water at 4° C. APPKNDIX 861 Mbaidiik or Mass 1 Mlllignm (mg.) = o.OOl gnm j/namice defined, 65. Dymuno, 324 ; Efficiency of, 320 ; Reversibility of, 332. Dj/namomeier, 16. Dyne, 02. i Energy, 107 ; Alwolate nnits of, ' 100 ; Conservation and corre- lation of, 170 J Formulas for calculating, 110 ; Gravitational units of, 100; Kinetic and potential, 108 ; of tound waves, 183. Engine, Steam, 172. Etpiilibraiit, 66. EqvMuium, 13; Kinds of, 76; of Irodies, 74 ; Thermal, 132. Erg, 111. Ether, The, 2, 206, 347. Emporation, 163; Heat con- sumed in, 162. Expansibility, 3. Expansion, Anomalous, 143 ; CoefficienU of, 144. Extension, 2. Eye, 257. Ear, 203. Echoes, 181. Efficiency of dynamos, 320; of machines, 120. Elastic force, 15. £ioji'« Law, 202. OtciUMon, Center of, 104. Ooertonea, 108. ParaJltiogram of forces, 78. Paicart Law, 10 j principle, 23. Pendulum, Laws of, 103 ; Simple, 104. Pmumhra, 211. Phemymenon, 1. Phonograph, 201. Photometry, 214. Physical measurements, 8. Phytic*, 2. Pigment*, Mixing, 266. Pitch, 190. PUalicUy, 126. Polarity of solenoid, 314. Polarization, 278. Porosity, 5. Potential, 270. Power, 114. Kodiatit energy, 207. Kadialion, 160, 207, 208; Only one kind of, 2&0. Rainbow, 245. Ray, 200. iiays. Infra-red and ultra-violet, 240 ; Rantgen, -342. Re^orcement of sound waves, 185. Ejection from concave mirrors, 221 ; Law of, 218 ; Total, 231. Refraction, 226 ; Index of, 220. Rej/elotion, 151. iiesistance box, 297 ; Electrical, 205 ; Magnetic, 308. Besonators, 186. iZetentiviti/, 308. Rigidity, 124. JJuAinKoriTcoll, 322. Secondary or storage cells, 333. Shadows, 210. Shunt*, 200. Siphon, 43. Solenoid, 313. Sonometer, 104. Sound and soun^ waves, 179. INDEX 859 BpnUnt tnbM, 186. *«*Ie gratlty, 48; hrat, 187; roiiiUiice, 297. Sptetro»eope, 246. ' Spectrum, 243 ; AbmrpUon, 248 ; •Dijyali, 247 ; Bright-line, 247. SUMlUy of bodies, 76. Steam engine, 172. Strain, 14. Strength of current, 288. StresM, 14, 87. Sympathetic vibntlone, 188. T TOeeraph, 340. Tdegraphy, Wireless 34«. Telephone, 341. Telemope, 260. . iTOPfT'rtxre, 132; CriUcal, 147. Tenacity, 124. Tentile gtreaa, 14. Tentlon, Surface, 126. Jl^ermal unite, 186. The: 'ko-dynamice, 170. I^ermomrfer, 132. TVmet, 108. Tran^ormer, 823. Foeuumgwige, 88; Torrlcellltn, 86. Vaporization, 153. rdoc«(e», Compoeitlon of, 02; Reioiution of, 64. rOocUy, 66 ; of light waves, 212 ; of found waves, 181, 187. VentUation, 168. Vibration frequency, 176; of •trings, 194. Vibrationt, Complex, 197 ; Sym- pathetic, 188. rocaf organs and sounds, 203 VoU, 200. Voltaic cells, 276; Local action In, 278. Volt-ampere, 291. VM-couUmA, 291. Volume, 9. Urnbra, 211. UnitM of measurement, 8. 1. a^ "V^^U. ': ■-^ r- ITatt, 201. Wanes, 174; Hertzian, 346; Sound, 178; Stationary, 196. Weight, 10; Law of, 100. WheaMone bridge, 801. Work, 107; Absolute units of, 110; Formulas for calculating, 110 ; Gravitational units of, 100.