UMASS/AMHERST ^ 312Dbti0053Hb315 '*-y&-*'' r*te- This book may be kept out TWO WEEKS only, and is subject to a fine of TWO S^ CENTS a day thereafter. It will be due on the day indicated below. Digitized by the Internet Archive in 2010 with funding from Boston Library Consortium IVIember Libraries http://www.archive.org/details/electricengineer01inte INTERNATIONAL LIBRARY OF TECHNOLOGY A SERIES OF TEXTBOOKS FOR PERSONS ENGAGED IN THE ENGINEERING PROFESSIONS AND TRADES OR FOR THOSE WHO DESIRE INFORMATION CONCERNING THEM. FULLY ILLUSTJ^ATED AND CONTAINING NUMEROUS PRACTICAL EXAMPLES AND THEIR SOLUTIONS v.l ELECTRICITY AND MAGNETISM ELECTRICAL MEASUREMENTS APPLIED ELECTRICITY BATTERIES SCRANTON : INTERNATIONAL TEXTBOOK COMPANY II Ir, ^ Copyright, 1897, 1898, 1899, by The Colliery Engineer Company. Copyright, 1902, by International Textbook Company. Principles of Electricity and Magnetism: Copyright, 1894, 1895, 1900, by THE Col- liery Engineer Company. Electrical Measurements : Copyright, 1894, 1895, 1898, 1900, by The Colliery Engi- neer Company. Batteries : Copyright, 1895, 1901, by THE COLLIERY ENGINEER COMPANY. Applied Electricity : Copyright, 1894, ISQ.j, 1899, by The COLLIERY ENGINEER COM- All rights reserved. Press of Eaton & Mains NEW YORK PREFACE. The International Library of Technology is the outgrowth of a large and increasing demand that has arisen for the Reference Libraries of the International Correspondence Schools on the part of those who are not students of the Schools. As the volumes composing this Library are all printed from the same plates used in printing the Reference Libraries above mentioned, a few words are necessary regarding the scope and purpose of the instruction imparted to the students of — and the class of students taught by — these Schools, in order to afford a clear understanding of their salient and unique features. The only requirement for admission to any of the courses offered by the International Correspondence Schools, is that the applicant shall be able to read the English language and to write it sufficiently well to make his written answers to the questions asked him intelligible. Each course is complete in itself, and no textbooks are required other than those pre- pared by the Schools for the particular course selected. The students themselves are from every class, trade, and profession and from every country ; they are, almost without exception, busily engaged in some vocation, and can spare but little time for study, and that usually outside of their regular working hours. The information desired is such as can be immediately applied in practice, so that the student may be enabled to exchange his present vocation for a more con- genial one, or to rise to a higher level in the one he now pursues. Furthermore, he wishes to obtain a good working iii :iH'^']L iv PREFACE knowledge of the subjects treated in the shortest time and in the most direct manner possible. In meeting these requirements, we have produced a set of books that in many respects, and particularly in the general plan followed, are absolutely unique. In the majority of subjects treated the knowledge of mathemxatics required is limited to the simplest principles of arithmetic and mensu- ration, and in no case is any greater knowledge of mathe- matics needed than the simplest elementary principles of algebra, geometry, and trigonometry, with a thorough, practical acquaintance with the use of the logarithmic table. To effect this result, derivations of rules and formulas are omitted, but thorough and, complete instructions are given regarding how, when, and under what circumstances any particular rule, formula, or process should be applied; and whenever possible one or more examples, such as would be likely to arise in actual practice — together with their solu- tions — are given to illustrate and explain its application. In preparing these textbooks, it has been our constant endeavor to view the matter from the student's standpoint, and to try and anticipate everything that would cause him trouble. The utmost pains have been taken to avoid and correct any and all ambiguous expressions — both those due to faulty rhetoric and those due to insufficiency of statement or explanation. As the best way to make a statement, explanation, or description clear, is to give a picture or a diagram in connection with it, illustrations have been used almost without limit. The illustrations have in all cases been adapted to the requirements of the text, and projec- tions and sections or outline, partially shaded, or full-shaded perspectives, have been used, according to which will best produce the desired results. Half-tones have been used rather sparingly, except in those cases where the general effect is desired rather than the actual details. It is obvious that books prepared along the lines men- tioned must not only be clear and concise beyond anything heretofore attempted, but they must also possess unequaled value for reference purposes. They not only give the PREFACE V maximum of information in a minimum space, but this information is so ingeniously arranged and correlated, and the indexes are so full and complete, that it can at once be made available to the reader. The numerous examples and explanatory remarks, together with the absence of long demonstrations and abstruse mathematical calculations, are of great assistance in helping one to select the proper formula, method, or process and in teaching him how and when it should be used. This volume treats of the elements of electricity and magnetism, including a detailed description of primary and secondary batteries, and a full and complete discussion of the physical theory of the dynamo. As the subject matter here presented forms the groundwork of electrical engineer- ing, every effort has been made to bring out those points that are essential and impress them on the mind by means of numerous examples and illustrations. The various elec- trical measurements have been given in an unusually clear manner, so that they can readily be understood and applied to every-day wOrk, even by those who are not accustomed to making such measurements. Special attention has been paid to storage batteries, owing to their large and increasing use in connection with central stations, and primary bat- teries have been described much more fully than in ordinary textbooks. Besides being of great value to those making a specialty of electrical work, this volume will be found an excellent textbook by persons connected with electrical enterprises who wish to gain a general knowledge of elec- tricity and magnetism. As mentioned above, this volume is printed from the plates used in printing the Reference Libraries of the Inter- national Correspondence Schools. On account of the omis- sion of certain papers, the material contained in which is given in better form elsewhere, there are several breaks in the continuity of the page numbers, formula numbers, article numbers, etc. This, however, does not impair the value of the volume, as the index has been reprinted and made to conform to the present arrangement. International Textbook Company. CONTENTS. Principles op Electricity and Magnetism. Page. Introductory ....... 1449 Electrostatics - - - - - - - 1450 Electrostatic Induction - . . . . 1456 Electrodynamics - 1463 Circuits - - - - - - - - 1471 Electrical Units ------- 1472 Ohm's Law Applied to Closed Circuits - - 1491 Ohm's Law Applied to Derived Circuits - - 1500 Magnetism -------- 1517 Magnetic Lines of Force ----- 1520 Magnetic Induction - - - - - - 1524 Electromagnetism ------ 1528 Electrical Apparatus and Experiments - - 1530 Electromagnetic Reaction ----- 1541 The Electromagnet ------ 1546 Magnetizing Force and Magnetic Density - - 1550 Lifting Magnets ------- 1568 Magnets for Attraction . - . - - 1576 Electromagnetic Induction ----- 1579 Electrical Measurements. Electromagnetic Measurements - - - - 1591 Theory of the Galvanometer - - - - 1592 Galvanometer Shunts ------ 1620 Precision in Measurements ----- 1623 Electrochemical Measurements . - - - 1625 Measurement of Potential ----- 1632 vii viii CONTENTS. Electrical Measurements — Continued. Page. Measurement of Resistance ----- 1635 Temperature Coefficient ----- 1646 Insulation -------- 1649 Electrical Apparatus ------ 1659 Practical Measurements . _ - - - 1670 Instruments -------- 1670 Measurements with Commercial Instruments - 1682 Batteries. Definitions -------- 1689 Principles of Chemistry . - - - . 1690 Electrochemistry ------- 1699 Polarization and Depolarization - - - - 1709 Cells --------- 1712 Cells with a Non-Depolarizing Electrolyte - - 1714 Cells with a Depolarizing Electrolyte - - - 1718 Cells with a Liquid Depolarizer - - - - 1723 Cells with a Solid Depolarizer - - - - 1739 Cells in Which an Elementary Substance is Applied to the Cathode as a Depolarizer - 1750 Dry Batteries ------- 1751 Application of Primary Batteries - - - 1752 Accumulators ------- 1759 Uses of Accumulators ------ 1781 Installation of Accumulators - - - . - 1791 Applied Electricity. Theory of Dynamo - - - - - - 1897 Generation of E. M. F. - - - - - 1899 Graphical Representation of E. M. F. or Current 1911 The Air-Gap ------- 1922 Armature Core Losses ------ 1924 Character of Commercial Currents - - - 1927 General Principles of Armature Windings - - 1929 Open-Coil Bipolar Armatures - - - - 1938 Dpen-Coil Multipolar Armatures - - - 1950 Closed-Coil Bipolar Armatures - - - - 1954" Closed-Coil Armature Windings - - - - 1973 CONTENTS. ix Applied Electricity — Continued. Page. Ring Windings ---.... 1974 Bipolar Drum AVindings - . - . . 1982 Multipolar Drum Windings - - '- - 1994 Multiple Windings ---... 2002 The Magnetic Circuit ------ 2017 Construction of Frame - - . - . 2018 Form of Magnetic Circuit ----- 2021 Methods of' Exciting the Field - - . - 2029 PRINCIPLES OF ELECTRICITY AND MAGNETISM. INTRODUCTORY. 2201. Electricity is the name given to that which directly causes all electrical phenomena. The word is derived from the Greek word clektron, meaning amber. Although electrical science has made great advances in the last few years, the exact nature of electricity is un- known. Recent researches tend to demonstrate that all electrical pheno77tena are due to a peculiar state or stress of a medium, called ether (see Art. 1 1 26) ; that, when in this condition, the ether yoss&ss&s potential energy ov capacity for doing zuork, as is manifested by attractions and repulsions, by chemical decomposition, and by luminous, heating, and various other effects. 2202. All researches tend to prove that electricity is not a form of matter, for the only physical properties it possesses in common with material substances are indestruc- tibility and elasticity; it does not possess tveight, extension, nor any of the other physical properties of matter. 2203. Electrical science is founded upon the effects produced by tJie action of certain forces upon matter, and all knowledge of the science is deduced from these effects. The study of the fundamental principles of the science is an analysis of a series of experiments and the classification of the results, under laws and rules. It is not necessary to keep in mind any hypothesis as to the exact nature of elec- tricity; its effects and the laws which govern them are For notice of the copyright, see page immediately following th« title page. 1450 PRINCIPLES OF quite similar to those of well-known mechanical and natural phenomena, and will be best understood by comparison. 2204. Electricity may appear either to reside upon the surfaces of bodies as a charge^ under high pressure, or flow through their substance as a current^ under comparatively low pressure. That branch of the science which treats of charges upon the surfaces of bodies is termed electrostatics, and the charges are said to be static charges. Electrodynamics is that branch which treats of the action of electric currents. ELECTROSTATICS. PRODUCTION OF STATIC ELECTRICITY. 2205. When a glass rod or a piece of amber is rubbed with a piece of silk or fur, the parts rubbed will be found to have the property of attracting light bodies, such as pieces of silk, wool, feathers, gold-leaf, pith, etc., which, after momentary contact, are again repelled. These attractions and repulsions are caused by a static charge of electricity residing upon the surfaces of those bodies. A body in this condition is said to be electrified. A better experiment for demonstrating this action is to suspend a small pith-ball by a silk thread from a support or bracket, as shown in Fig. 901. Such an apparatus is spoken of as an electric pendulum. If a static charge of electricity be developed on a glass rod by rub- bing it with silk, and the rod be brought near the pendulum, the ball will be attracted to the rod, but after momentary contact will be repelled. By this contact the ball becomes electrified, and so pjq 901. \ov\^ as the two bodies retain their ELECTRICITY AND MAGNETISM. 1451 charges mutual repidsion will take place whenever they are brought near each other. If a stick of sealmg-zvax^ elec- trified by being rubbed with fur, is approached to another pendulum, the same results will be produced — the ball will fly towards the wax, and after contact will again be re- pelled. But the charges respectively developed in these two cases are not in the same condition. For if after the pith-ball has been touched with the glass rod and repelled, the electrified sealing-wax be brought in the vicinity, attrac- tion takes place between the ball and sealing-wax. Similarly, if the pendulum be charged with the electrified sealing-wax, the ball will be repelled by the wax and attracted by the glass rod. We have, therefore, to distinguish between two kinds of electrification — that produced by rubbing glass with silk and that produced by rubbing sealing-wax with fur. To make this distinction clear, the following designations have been adopted : An electric charge excited upon glass by rubbing it with silk has been termed a positive charge (+), and that developed on resinous bodies by friction with flannel or fur a negative charge ( — )• 2206. Neither charge is produced alone, for there is always an equal quantity of both charges produced, one charge appearing on the body rubbed, and an equal amount of the opposite charge upon the rubber. 2207. The inte7isity of the charge developed by rubbing the two substances together is evidently independent of the actual amount of friction which takes place between the bodies. For, in order to obtain the highest possible degree of electrification from two dissimilar substances, it is only necessary to bring every portion of one surface into intimate contact with every particle, or every portion of the other surface ; when this is done, no extra amount of rubbing can develop any greater charge upon either substance. 2208. From these experiments are derived the follow- ing laws: 1452 PRINCIPLES OF When two dissimilar substances are placed in contact^ one of them always assumes the positive afid the other the nega- tive condition^ altJiough t lie amount may sometimes be so small as to render its detection very difficult. Electrified bodies with similar charges are mutually re- pellent, while electrified bodies zvith dissimilar charges are mutually attractive. 2209. Table 71 gives a list called the electric series, where the substances are arranged in such order that each receives a positive charge when rubbed with any of the bodies following, and a negative charge when rubbed with any of those which precede it: TABLE 71. THE ELECTRIC SERIES. 1. Fur. 6. Cotton. 11. Sealing-wax. 2. Flannel. 7? Silk. 12. Resin. 3. Ivory. 8. The body. 13. Sulphur. 4. Crystals. 9. Wood. 14. Gutta-percha. 5. Glass. 10. Metals. 15. Gun-cotton. For example, glass when rubbed with fur receives a negative charge; but when rubbed with silk, it receives a positive charge. ELECTROSTATIC IIVSTRUMEIVTS. 221 0. The electroscope is an instrument for detect- ing static charges of electricity and for determining their condition, whether positive or negative; but not for meas- uring the intensity of the charges. The pith-ball suspended by a silk thread acts as a simple electroscope. A more sensitive electroscope is shown in Fig. 902, and consists of two gold leaves suspended within a glass jary, which serves to protect them from drafts of air and to support them from contact with the earth. The gold leaves a are supported side by side in the jar by a brass rod or wire b which passes through a cork in the mouth of the jar. The upper end of the brass rod is furnished with a fiat metallic ELECTRICITY AND MAGNETISM. 1453 Fig. 903. plate or ball c. An electrified body, such as the rod d, brought into the vicinity of the electroscope, will cause the leaves to repel one another, due to the fact that they are both sim- ilarly electrified. To deternime the con- ditioii of a charge by the electroscope : First, charge the gold leaves with a known charge, such as that developed upon glass when rubbed with silk. The leaves will spread apart, be- ing electrified with a positive charge. When they are thus charged, the approach of a body which is positively charged will cause them to open still more widely ; while on the approach of one negatively charged, they will close together. 2211. The torsion balance is an instrument used to measure Wi^ force exerted between two electrified bodies. It consists of an arm or lever of some light insulating material, such as a straw or piece of wood, provided at one end with a gilt pith-ball n, Fig. 903, and suspended in a glass jar by a fine silver wire. The wire passes up through a glass tube and is fastened to a brass stopper b^ called the torsion bead. The torsion head is graduated in degrees, and is capable of being revolved around upon the glass tube. Another gilt pith-ball in is fastened to the end of the vertical glass rod «, which is inserted through an opening in the top of the jar. A narrow strip of paper, also divided into degrees, encircles the glass jar at the level of the two pith-balls. Fig. 90.3. 1454 PRINCIPLES OF 221)2. To use the torsion balance: Turn the torsion head around until the two pith-balls m and n just touch each other. Remove the glass rod «, and communicate the charge to be measured to the gilt ball vi. Replace the glass rod in the jar. The two gilt balls will touch each other momentarily, and half of the charge will pass from in to n. As both balls possess similar charges, they will immediately repel each other; the ball ;/, being driven around, twists up the wire to a certain extent. The force of torsion in the wire will eventually balance the force of repulsion, and the ball n will come to rest when the balls are separated by a certain distance. In any wire, the force of torsion is pro- portional to the amount of twist, or, in this case, to the angle of torsion ; hence, the force exerted between the two balls can be measured by the angle described by the ball n. 2213. By means of the torsion balance, it is proven that the force exerted betzveen tzvo bodies statically charged with electricity varies inversely as the square of the distance betzveen them. Thus, suppose two electrified bodies one-fourth inch apart repel each other with a certain force ; at a distance of one inch the force would only be one-sixteenth as great. This law is equally true for the force of attraction between two bodies with dissimilar charges. 2214. In either case, whether of attraction or repul- sion, the force at any given distance is equ-al to the product of the two quantities of electricity on the bodies. But a unit quantity of electricity is that charge which, when placed in air at a distance of one centimeter from another equal and similar charge, will be repelled with a force of one dyne. (For values of the centimeter and dyne, see Arts. 2255 and 2262.) Therefore, if a certain body were charged with 4 unit quantities of electricity and another with 3 tinit quantities^ then the force exerted between them would be 13 times greater than if each had contained a charge of one unit. ELECTRICITY AND MAGNETISM. 1455 CONDUCTORS AND INSULATORS. 2215. Only that part of a dry glass rod which has been rubbed will be electrified ; the other parts will produce neither attraction nor repulsion when brought near an electroscope. The same is true of a piece of sealing-wax or resin. These bodies do not readily conduct electricity ; that is, they oppose or resist the passage of electricity through them. Therefore, electricity can reside only as a charge upon that part of their surfaces where it is developed. Experiments show that when a metal receives a charge at any point, the electricity immediately passes or flows through its substance to all parts. Metals, therefore, are said to be good conductors of electricity. Bodies have accordingly been divided into two classes; namely, non-con- ductors or insulators^ those bodies which offer an infinitely high resistance to the passage of electricity ; and conductors, or those which offer a comparatively low resistance to its passage. This distinction is not absolute, for all bodies conduct electricity to some extent, while there is no known substance that does not offer some resistance to its flow. 2216. Electrical resistance may be defined as a general property of matter, varying with different sub- stances, by virtue of which matter opposes or resists the passage of electricity. 2217. Conductivity is the facility with which a body transmits electricity, and is the reciprocal, or opposite, of resistance. For instance, copper is of low resistance and high conductivity; wood is of high resistance and low conductivity. Table 72 gives a list of conducting and non-conducting substances. 2218. In dividing the different substances into two classes, it should be understood that it is done only as a guide for the student. Between these classes are many substances which might be included in either, and no hard or fast line can be drawn. The list is arranged in order of 1456 PRINCIPLES OP the conductivity of the different substances, beginning with silver, which is the best conductor known. TABLE 72. CONDUCTORS AND INSULATORS IN ORDKR OF THEIR VALUE. Conductors. Insulators (N on-Conductors). Silver. Dry Air. Glass. Copper. Shellac. Mica. Other Metals. Paraffin. Ebonite. Charcoal. Amber. India-rubber. Plumbago. Resin. Silk. Moist Earth. Sulphur. Paper. Water. Wax. Oils. A general idea of these values may be obtained from the fact that water has 6,754 million times greater resistance than copper. ELECTROSTATIC INDUCTION. 2219. An electric charge will be induced \n a conductor when that conductor is brought into the vicinity of an electrified body. This effect is termed electrostatic in- duction, and the range of space in which it can take place is an electrostatic field. 2220. If the conductor A B, Fig. 904, is supported from contact with the earth by insulators, and is then brought into the elec- trostatic field of the conductor C, but not touching (T, which is electrified with a posi- tive charge, then: 1. A charge will be Fig. 904 produced on A B^ as is shown by the pith-balls spreading apart. ELECTRICITY AND MAGNETISM. 1457 2. This charge will be negative at the end A nearest C and positive at the end B farthest from C, as can be shown by an electroscope. 3. The charges at A and B are equal to each other ; for if the conductor A B he removed from the vicinity of the conductor (7 without having touched C, the opposite charges immediately neutralize each other; that is, no electrification will be indicated by the pith-balls. 4. Again, as C is brought nearer and nearer A, the charges of opposite signs on the approaching surfaces attract each other more and more strongly until C is ap- proached very near, and then a spark darts across the inter- vening space. Two charges rushing together neutralize one another, leaving the induced positive charge, which was formerly repelled to the end B of the conductor, as a per- manent charge over all the surface of A B. 5. Or, if the conductor y^ ^ be touched by a conductor connected to the earth when it is under the influence of C, the positive charge will neutralize with the earth and the negative charge will remain when A B i"?, removed from the field of C. The charge which passes to the earth from A B is called a free charge, while that charge which is held by the inductive influence of (7 is a bound charge. Both free and bound charges can be negative or positive, depending upon the sign of the charge on C. 2221. When two conducting bodies, both electrified with equal dissimilar charges, are touched together momen- tarily, the two charges will neutralize each other, no trace of either remaining ; but if they are unequal, the smaller charge will neutralize an equal amount from the larger and leave a charge which is equal to the difference between the two original charges, the sign of the remaining charge being the same as that of the larger one. Before the bodies can be separated, the remaining charge will divide equally between the two bodies. For example, two gilt balls A and B are charged respectively with -j- 30 and — 4 units of elec- tricity. When the balls are placed in contact, the — 4 1458 PRINCIPLES OF charge on B will neutralize a + 4 charge on A and leave a -(- 16 charge, which immediately divides equally between the two balls ; that is, a charge of + 8 units remains on each ball when they are separated. It is found that the effect of this electrostatic induction is greatly increased by placing some other substance, such as glass or paper instead of air, between the two bodies. 2'2>2>2» The facility with Avhich a body allows electro- static induction to act across it is called its inductive capacity. The inductive capacity varies with different sub- stances, bvit almost all non-conductors are better than air. 2:2!23. Any substance which allows electrostatic induc- tion to act across it is termed a dielectric. All dielectrics are non-conductors. Table 73 gives a list of several non- conductors in the order of their inductive capacity values, from which it will be seen that, with two exceptions, air has the lowest inductive capacity. TABLE 73. INSULATORS IN ORDER OF THEIR INDUCTIVE CAPACITY VALUES. Glass. Paraffin (solid). Shellac. Carbonic Acid. Sulphur. Air. Ebonite. Hydrogen. India-rubber. Vacuum. Petroleum. 2224. The electrophorus. Fig. 905, is an instrument devised for the purpose of obtaining an almost unlimited number of static charges of electricity from one single charge, and is based upon the principle of electrostatic in- duction. It consists of two main parts : a thin cake of resinous material cast in a round metal dish or pan B, about one foot in diameter ; and a round disk A, of slightly smaller diam- eter, made of metal and provided with a glass handle. In using the electrophorus, the resinous cake must first be ELECTRICITY AND MAGNETISM. 1459 beaten or rubbed with a warm piece of woolen cloth or fur. The disk or cover is then placed upon the cake, touched momentarily with the finger to liberate the free charge, then removed by taking it up by the handle. It is now found to be powerfully electrified with a positive charge ; so much so, Fig. 905. indeed, as to yield a considerable spark when the hand is brought near it. The cover may be replaced, touched, and again removed, and will thus yield any number of sparks ; the original charge on the resinous plate meanwhile remain- ing practically as strong as ever. !2!225. A static charge of electricity is not usually dis- tributed uniformly over the surface of conducting bodies. Experiments show that there is more electricity on the edges and corners than upon their flatter parts. The term electric density is used to signify the amount or quantity of electricity residing on a small area of any part of a body, the distribution being supposed to be uni- form over that small part of the surface. The electric density is the quotient arising from dividing the total charge of electricity in units of quantity residing upon the surface of a body, by the area of the surface in square inches. For example, a charge of 240 units of elec- tricity is imparted to a sphere, the surface area of which is 40 square inches ; then, the electric density over the surface of the sphere is ^-f-^- = 6 units of electricity per square inch. 1460 PRINCIPLES OF ELECTROSTATIC MACHINES. 2226. Electrostatic machines have been devised for the purpose of obtaining larger static charges than can be developed by rubbing a glass rod or by the electrophorus. They consist, mainly, of two parts, one for producing and the other for collecting the charges. There are three important kinds of electrostatic machines — the cylinder^ ihQ plate, and the induction machines. 2227. The cylinder machine, as usually constructed, consists of three principal parts: (1) a cylinder of glass revolving upon a horizontal axis; (2) a rubber or cushion of horsehair, to which is attached a long silk flap, and (3) an insulated metallic cylinder called a prime conductor. In Fig. 90G the cushion of horsehair a, covered with a coating of amalgam of zinc, presses against the glass cylinder b from Fig. 906. behind, allowing the silk flap s to rest upon the upper half of the glass. The prime conductor C is provided at one end with a row of fine metallic spikes, and is placed in front of the machine with the row of spikes projecting towards the glass cylinder. When the glass cylinder is revolved, a positive charge is produced vipon the glass and a negative charge upon the rubber. The positive charge is carried around upon the glass cylinder, and just before reaching a position opposite the row of spikes it acts inductively upon the prime conductor, attracting a negative charge to the near end and repelling a positive charge to the far end. When the positive charge arrives in front of the row of ELECTRICITY AND MAGNETISM. 1461 spikes, it will be neutralized by the attracting negative charge from the conductor, leaving the glass in a neutral condition ready to be excited again. A positive charge now remains upon the prime conductor, and can be utilized for other experiments. 2228. The plate macliiiie is similar in all respects to the cylinder machine, with the exception that a glass or ebonite plate is used instead of the glass cylinder, and there are usually two sets of rubbers or cushions instead of one. Each set of cushions is double ; that is, it is made in two parts, with the plate revolving between them. One set of cushions is placed at the top of the machine, and the other at the bottom, with silk flaps extending from each over a quadrant of the plate. The charge is collected on two prime conductors connected by a metal rod, and each is pro- vided with a row of fine spikes at one end. They are placed in such a position that the two rows of fine spikes project towards the glass plate at opposite sides of its horizontal diameter. The electrostatic action of the machine is in all respects the same as that of the cylinder machine. 2229. The induction machine differs widely in its action from the two machines previously described. It requires an initial charge from some exterior source to start its action. The initial charge acts inductively across a revolving glass plate and produces other charges; these charges in turn are conveyed by the moving parts to some other point, where they increase the initial charge, or fur- nish a supply of electricity to a prime conductor. The two principal machines of this class are the Holtz and the "Wimshurst. THE CONDEIVSER, 2230. It has been shown that opposite charges attract and hold one another; that electricity can not flow through glass, and yet can act across it by induction. If a piece of tin-foil is stuck upon the middle of each face of a thin plate of glass, and one of the pieces is electrified with a positive 1463 PRINCIPLES OF charge and the other with a negative charge, the two charges will attract one another, or, in other words, they are held or bound by each other. It will be found that these two pieces of tin-foil may be charged a great deal stronger in this manner than either of them could possibly be if they were stuck to the glass alone and then electrified. This property of retaining and accumulating a large quantity of static charges which two conductors possess when placed side by side and separated from each other by a non-con- ductor, is called their capacity. )2231. A condenser is an apparatus for condensing or accumulating a large quantity of static charges of electricity on a comparatively small surface, and consists of two con- ductors separated by a thin layer of some non-conducting material. One of the plates is entirely insulated from the earth, and the other is connected to it by a conductor. The capacity of a condenser depends upon (1) the size and form of the condensing plates, (2) the thinness of the insulating material between them, and (3) the inductive capacity of the insulating material. 2232. A convenient form of condenser is called the Leyden jar, Fig. 907. It consists of a glass jar J coated C Fig. 907. up to a certain height on the inside and outside with tin> foil. A brass knob a is fixed on the end of a stout brass wire, which passes downwards through a lid or stopper of dry, well-varnished wood, and connected by a loose bit of brass chain with the inner coating of the jar. ELECTRICITY AND MAGNETISM. 1463 To charge the jar, the knob is held to the prime con- ductor C of an electrical machine, the jar being either held in the hand by the outer tin-foil coating or connected to the earth by a wire or chain. When a positive charge is thus imparted to the inner coating, it acts inductively on the outer coating, attracting a negative charge in the face of the outer coating nearest the glass, and repelling a positive charge to the outside of the outer coating. This outer charge then passes through the hand or any conductor to the earth. 2233. An electrostatic battery consists of a num- ber of Leyden jars whose inside coatings are all connected together and "whose outside coatings are all connected to the earth. ELECTRODYNAMICS. POTENTIAL AND CURRENT. 2234. In dealing with electric currents, the v^oxA poten- tial will be substituted for the general and vague phrase electrical condition. The term potential, as used in electrical science, is anal- ogous yNxX^x pressure in gases, head in liquids, and tempera- ture in heat. When an electrified body, positively charged, is connected to the earth by a conductor, electricity is said to jioiv from the body /c the earth; and, conversely, when an electrified body negatively charged is connected to the earth, electricity is said to Jlow from the earth to that body. That which determines the direction of flozu is the relative electrical potential or presszcre of the two charges in regard to the earth. 2235. It is impossible to say with certainty in which direction electricity really flows, or, in other words, to declare which of two points has the higher and which the lower electrical potential or pressure. All that can be said with certainty is, that when there is a difference of electrical 1464 PRINCIPLES OF potential, or pressure^ an electric current tends to ^ow from the point of higher to that of lower potential or pressure. For convenience, it has been arbitrarily assumed and universally adopted that that electrical condition called positive \^ 2X z. higJier potential or pressure than that called negative, and that an electric current flows from a posi- tively to a negatively electrified body. 2236. The zero or normal level of water is taken as that of the surface of the sea, and the normal pressure of air as that of the atmosphere at the sea-level ; similarly, there is a zero pressure or potential of electricity in the earth itself. It may be regarded as a reservoir of electricity of infinite quantity, and its pressure or potential taken as zero. For this reason all electric currents have the ten- dency to reach this zero level, exactly as the water on the mountain top tends to flow down to the sea-level. For this reason it becomes necessary to insulate most electrical apparatus, otherwise the electric current it generates or carries will leak away to the earth. In Art. 2234 the condition which is called positive is assumed to be at a higher potential than the earth, and that called negative is assumed to be at a lower potential than the earth. It must be understood that electricity is a condition of matter and not matter itself, for it possesses " neither weight nor extension. Consequently, the statement that electricity is flowing through a conductor must not be taken too liter- ally; it must not be supposed that any material substance, such as a liquid, is actually passing through the conductor in the same sense as water flows through a pipe. The statement that electricity is flowing through a conductor is only another way of expressing the fact that the conductor and the space surrounding it are in different conditions than usual, and that they possess unusual properties. The action of electricity, however, is quite similar in many respects to the flow of liquids, and the study of electric currents is much simplified by the analogy. ELECTRICITY AND MAGNETISM. 1465 ZSST. In order to produce what is called an electric current^ it is first necessary to caitse a difference of electrical potential or pressure between two bodies or between two parts of the same body. In Art. 2208 it was stated that when two dissimilar substances are simply placed in contact, one always assumes the positive and the other the negative condition ; in other words, a difference of electrical potential is developed be- tween the two bodies. Placing a piece of copper and zinc in contact will develop a difference of electrical potential which can easily be detected. The same results will follow if the plates are slightly separated from each other and placed in a vessel containing saline or acidulated water, leaving a small por- tion of one end of each plate exposed. The exposed ends of the zinc and copper are now electrified to different degrees, or, in other words, there is a difference of electrical potential between the plates, one plate being at a higher potential than the other. When the exposed ends are connected together by any conducting material, the potential between the plates tends to equalize, and a momentary rush or discharge of elec- tricity passes between the exposed ends through the con- ducting material and between the submerged ends through the liquid. During its passage through the liquid, the electricity causes certain chemical changes to take place; these chemical reactions cause in their turn a fresh differ- ence of potential between the plates, which is followed im- mediately by another equalizing discharge, and that by a further difference, and so on. These changes follow one another with great rapidity — so rapidly, in fact, that it is im- possible to distinguish them apart, and they appear abso- lutely cojitinuous. The equalizing flow which is constantly taking place from one plate to the other is knoAvn as a con- iiiiuous current of electricity. Consequently, an electric current becomes cqntimious zvhen the difference of potential is constantly maintained. By the use of a very delicate electroscope, the exposed 1466 PRINCIPLES OF end of the copper will be found to be electrified with ^posi- tive charge and the submerged end with a negative charge ; in the case of the zinc, the opposite conditions exist, namely, the exposed end is electrified with a negative charge and the submerged end with a positive charge. The current, there- fore, will flow from the exposed end of the copper through the conductor to the exposed end of the zinc, and from the submerged end of the zinc through the liquid to the sub- merged end of the copper. VOL-XAIC ELECTRICITY. 3238. The two Italian physicists, Volta and Galvani, /O'''*'*'^^ first constructed the so-called // J simple voltaic or galvanic C|Af ^KM" cell, as shown in Fig. 908. It is ^^ |l^-T||rt an apparatus for developing a H ir^^i ill id continuous current of electricity, Ip^jJj JI^ys J^^ and consists, essentially, of a ||]||||]^^ vessel A, containing saline or IiIjIII ' ,„ J||B fe acidulated water, into which are ii^''*liH|l~^-^i^ submerged two plates of dissimi- J ill!] liill liliiiiiiilliilliiil ljlal^E lar metals, C and Z, or one "^^^^3|lill|iil^^P^^ metal and a metalloid. Fig. 908. Electrolyte is the name given to the liquid which, as it transmits the current, is decom- posed by it. The two dissimilar metals, when spoken of separately, are called voltaic elements ; when taken collectively, they are known as a voltaic couple. 2239. A voltaic battery is a number of simple voltaic cells properly joined together. Electrodes or poles of a cell or battery are metallic terminals attached to the plates, and are used to connect the cell or battery to any exterior conductor or to another cell or battery. It should be remembered that the polarity of that end of the plate or voltaic element which is acted upon by the elec- ELECTRICITY AND MAGNETISM. 1467 trolyte is always of opposite sign to its electrode. For instance, in the case of the zinc and copper, the electrode fastened to the zinc would be spoken of as the negative elec- trode of the cell, while the zinc itself would be the positive element of the cell, its submerged end being positive. CHEMICAL ACTIOIV IIV A SIMPLE CELL. 2240. When a piece of ordinary zinc is placed alone in sulphuric acid diluted with water, the zinc is attacked by the acid, and a part of it is dissolved into a salt of that metal, called sulpJiate of zinc. At the same time the liquid is de- composed and hydrogen gas is liberated from it, coming up from around the zinc in small bubbles, and the whole mass of the liquid becomes heated. If the zinc is absolutely pure, the chemical actions take place more slowly; the bubbles of liydrogen do not immediately rise to the surface, but form around the zinc, protecting it from further action of the acid. By placing another metal in the water, say a piece of copper, and connecting its exposed end with that of the zinc by a conductor, the chemical actions become exceed- ingly vigorous again. Large quantities of Jiydrogen gas are again liberated, but instead of the bubbles appearing around the zinc, they form around the copper and come to the sur- face at that place; the energy which in the former case was expended in heating the liquid now appears in the form of electric energy. Whenever the connection betAveen the ex- posed ends is broken, all chemical actions cease and remain inactive until the two metals are again connected. 2241. In any voltaic cell the element which is acted upon by the electrolyte will always be the positive element, and its electrode the negative electrode of the cell. The differences of electric potential, however, between the different pairs of metals are not all equal. In Table 74 various materials are arranged in a series, such that each substance enumerated becomes positively electrified when placed in contact with any one below it in the series. 1468 PRINCIPLES OP TABLE 74. THE ELECTROMOTIVE SERIES. 1. + Sodium. 5. Tin. 9. Gold. 2. Magnesium. 6. Iron. 10. Platinum. 3. Zinc. 7. Copper. 11. ~ Graphite (carbon). 4. Lead. 8. Silver. 2242. The term electromotive force, 2iS2ially zuritten E. M. F., is employed to denote that ivhicJi moves or tends to move electricity from one place to another. In the case of two substances placed in contact, either directly or by a liquid, the resulting electromotive force is due to the difference of potential. Just as in water-pipes a difference of level produces a pressure^ and the pressure pro- duces 2i ffozv, as soon as the water is turned on, so differ e7ice of potential produces electromotive force^ and electromotive force sets up a current^ as soon as the circuit is completed through which the electricity may flow. 2243. Any two of the substances of T^le 74 form a voltaic couple, and produce a difference of potential when submerged in saline or acidulated water; the one standing first on the list being the positive element or plate and the other the negative. For example, if iron and graphite are used, the iron will be acted upon by the liquid, and will form th& positive element; but if iroii and ^-/wi^'are used, the sine will be acted upon by the liquid, and will form the positive element. The difference of potential will be greater in proportion to distance between the positions of the two substances in the list. For example, the difference of potential developed between zinc and graphite is much greater than that devel- oped between zijic and iron ; in fact, the difference of poten- tial developed between zi7ic and graphite is equal to the difference of potential developed between zinc and iron plus that developed between iron and graphite. 2244. Electricity flowing as a current differs from static charges in three important degrees, namely, its ELECTRICITY AND MAGNETISM. 14G9 potential is much lower, its actual quantity is larger, and it is continuous. A strong voltaic battery of several cells produces only a slight effect upon a gold-leaf electroscope, and, apparently, none of its parts possesses the property of attracting light substances. 'Y:h.Q potential oi a current of electricity is com- paratively so small that a voltaic battery composed of a large number of cells is not sufficient to produce a spark of more than one or two hundredths of an inch in air, whereas a small electrostatic machine will produce sparks several inches in length. If, however, the actual quantity of elec- tricity is measured by its eft"ects in decomposing water, then the quantity produced by a simple voltaic cell as small as a thimble would give greater results than that from an elec- trostatic machine with plates two or three feet in diameter. An electric current can not be developed upon the surfaces of non-condiLcting substances by current electricity, as in the case of static charges, and it will never flow unless the conducting path is made entirely of conducting material. 2245. A number of contacts of dissimilar metals can be so arranged as to add their electrical effects together; the difference of potential then devel- oped will be greater in proportion to the number of contacts. Such an ar- rangement is called a voltaic pile. (See Fig. 909. ) It is made by placing a pair of disks of zinc (chemical symbol, Zyi) and copper (chemical symbol, Cic) in contact with one another, and then laying a piece of flannel or blotting- paper, moistened with brine, upon the copper disk. The pair of disks now form a voltaic couple. Several voltaic couples are placed together, and each pair separated by a moistened piece of Fig. 909- 1470 PRINCIPLES OF flannel or blotting-paper. One end of such a pile would then be terminated by a disk of copper and the other by a disk of zinc. The copper forms the positive electrode and the zinc the negative electrode. By joining these two electrodes together with a conductor, a current will flow from the positive to the negative tJirough the conductor, and from the negative to the positive through the contacts. THERMOELECTRIC CURRENTS. 2246. The difference of potential developed by the mere contact of two dissimilar metals varies, not only with the kind of metals and the physical condition of each, but also with their temperatiLre. The greater difference of potential developed by heat can be shown by soldering one end of a bar of copper to one end of a bar of zinc, and applying heat to the juncture so as to raise its temperature above that of the other parts of the bars. By joining the free ends together with a conductor, a current of electricity will be found to flow from the zinc through the contact to the copper; then from the free end of the copper to the free end of the zinc through the con- ductor. If the junction be cooled below the other parts of the bars, a current is produced in the opposite direction, that is, from the copper through the contact to the zinc, etc. Even the same metal in different physical conditions will develop a difference of potential if heated in a certain place. For instance, take a copper wire, part of which is straight and the remainder bent into a spiral, and heat the place where the spiral begins. Under these conditions, a difference of electrical potential will be developed between the two free ends. In general, the difference of potential is larger in. propor- tion as the difference of temperature increases. With ex- treme temperatures, however, this condition changes, and at a certain temperature of the junction no difference of potential whatever is noticed. This temperature is called the neutral temperature. When the junction is heated ELECTRICITY AND MAGNETISM. 1471 beyond the neutral temperature, inversion takes place, that is, the direction of the current changes. 2247. Electric currents produced by a change of temperature are called thermoelectric currents. On account of the small difference of potential of thermo- electric currents, they have not been found of great practical value ; in fact, they often become a source of great annoy- ance and error in accurate measurements with delicate instruments. CIRCUITS. 2248. A circuit is a path composed of a conductor, or of several conductors joined together, through which an electric current flows from a given point around the con- ducting path back again to its starting-point A circuit is broken or opened when its conducting elements are disconnected in such manner as to prevent thes; current from flowing. A circuit is closed or completed when its conducting elements are so connected as to allow the current to pass. A circuit in which the conductors have come into contact with the ground, or with some electric conductor leading to the ground, is said to be a grounded circuit, or is called an earth. The external circuit is that part of a circuit which is outside or external to the electric source. The internal circuit is that part of a circuit which is included within the electric source. In the case of the simple cell, the internal circuit consists of the two metallic plates, or elements, and the liquid, or electrolyte; an external circuit would be a wire or any con- ductor connecting the free ends of the electrodes together. 2249. A circuit divided into two or more branches, each branch transmitting part of the current, is a divided circuit ; the conductors forming these branches are said to be connected in parallel or multiple arc. Each branch taken separately is called a shunt. 1473 PRINCIPLES OF Conductors are said to be connected in series when they are so joined as to allow the current to pass through each successively. %MX\%\ 2250. A battery of voltaic cells is said to be connected in multiple arc or par- allel when the positive electrodes of all the cells ^'°- ^^^- are connected to one main positive conductor and all the negative electrodes are con- nected to one main negative conductor, as shown in Fig. 910. A battery of voltaic cells is said to be connected in series when the cells are ar- . i ranged in one circuit by Vj^^^^^^,i^,i^ji> jommg the positive elec- "' ~i "' "' "' "' trode of one cell to the ^^°- ^^^• negative electrode of the adjacent one, so that the entire cur- rent passes successively through each, as shown in Fig. 911. When the series and multiple connections are combined, the battery is said to be connected in multiple- series or parallel- it ijlf i^^t ilff series. This is accom- plished by joining several groups in multiple or parallel, the cells in each group being connected in series, as shown in Fig. 912. ELECTRICAL UNITS. 2i2'Sl. To properly measure the various factors of an electric circuit, certain definite standards or units must be adopted, to which these factors can be compared. In every electrical circuit there are particularly three factors, the true relation of which must be clearly under- stood before they can be measured. These three factors are: 1. The force tending to move the electricity. 2. The rate of flow of the electricity. r Fig. 912. ELECTRICITY AND MAGNETISM. 1473 3. The resistance which the force must overcome to pro- duce the flow of electricity. These factors are respectively termed : 1. The electromotive force (written E. M. F. or E.). 2. The current (written C). 3. The resistance (written R.). 2'2>S2'. The relation of the three principal factors will be better understood by comparison with the flow of water through a pipe. The force which causes the water to flow through the pipe is due to the Jiead ox pressure ; that which resists the flow is the friction of the water against the inside of the pipe, and varies with circumstances. The rate of flow, or the current, may be expressed m. gallons per minute, and is a ratio between the liead or pressure and the resistance caused by the friction of the water against the inside of the pipe. For, as the pressure or head increases, the rate of flow or current increases in proportion; as the resistance increases, the flow or current diminishes. In the case of electricity flowing through a conductor, the electromotive force corresponds to the pressure or head of water, and the resistance which a conductor offers to the current to the friction of the water in the pipe. The strength of an electric current or the rate of flow of electric- ity is also a ratio — a ratio between the electromotive force and the resistance of the conductor through which the cur- rent is flowing. This ratio, as applied to electricity, was first discovered by Dr. G. S. Ohm, and has since been called Otun's la'W. 2253. Ohm's La-w. — The strength of an electric current in any circuit is directly proportional to the electromotive force developed in that circuit and inversely proportional to the resistance of tJie circuit ; i. e., is equal to the quotient arising from dividing the electromotive force by the resist- ance. Ohm's law is usually expressed algebraically, thus : 1474 PRINCIPLES OF electromotive force Strength of current resistance and may be written, by utilizing the symbols given in Art 2251, ^~ K When the values of any two such quantities are known, the third can be readily found ; for, by transposing, Before giving examples of the application of Ohm's law, the value and significance of the various units will be treated upon. There are two principal systems of units employed in electrical science. They are, respectively, the funda- mental units and the practical units. FUNDAMENTAL, UNITS. 2254. The fundamental electrical units from which the practical units are derived, as shown later, are based on the three factors mass, length, and time. They are, therefore, absolutely independent of all other considerations, and the system which they form is hence termed the system of absolute units. These fundamental units are, respectively, 1. The centimeter as the unit of lengtli. 2. The gram as the unit of mass. 3. The second as the unit of time. This system is hence often termed the centimeter- gram-second system, and is written C. G. S. system. 2255. The centimeter represents ^^qqq^qqq^qqq of the distance from the pole to the equator on the surface of the earth, and is equal to .3937 inch. Hence, 1 inch equals 2, 54 centimeters, nearly. 2256. The unit of mass or quantity of matter is the gram, and represents the quantity of matter contained ELECTRICITY AND MAGNETISM. 1475 in a cubic centimeter of pure water at the temperature of its maximum density, which is 4°C,, or 39.3° F., and is equal in weight to 15.432 grains. 2>2'57. The unit of time is the second, and represents part of a mean solar day. 86,400 The secondary units derived from these fundamental units are defined as follows : 2258. The unit of area is the square centimeter, and is the area contained in a square, each of whose sides is one centimeter in length. 1 square centimeter equals .155 square inch, 1 square inch equals 6.45 square centimeters. 2259. The unit of volume is the cubic centimeter, and is the volume contained in a cube, each of whose edges is one centimeter in length. 1 cubic centimeter equals .06103 cubic inch. 1 cubic inch equals 16.387 cubic centimeters, 2260. The unit of velocity, or the rate at which a body moves from one position to another, is defined as the velocity of a body moving through unit distance (one centi- meter) in unit time (one second). The unit of velocity is, therefore, one centimeter per second. Note. — The word ^er in such expressions denotes that the quantity named before it is to be divided by the quantity named after it. Thus, to compute the velocity in centimeters per second, divide the number of centimeters by the number of seconds. 2261. The unit of acceleration is that accelera- tion which imparts unit velocity to a body in unit time, or an acceleration of one centimeter-per-second per second. The acceleration due to gravity imparts in one second a velocity considerably greater than this, for the velocity it imparts to falling bodies is about 981 centimeters per second (or about 33.3 feet per second). The value differs slightly in different latitudes. At New York City 1476 PRINCIPLES OF the acceleration of gravity is ^= 980.26 ; at the Equator, g^ 978.1 ; at the North Pole, ^= 983.1. )2262. The unit of force is the dyne, and is that force which, acting on a mass of one gram for one second, gives to it a velocity of one centimeter per second. For an example of force and the application of the unit of force, see Art. 2214. 2263. The unit of ^work is the erg, and is that amount of work performed when a force of one dyne is overcome through a distance of one centimeter ; that is, the work done in pushing a body through a distance of one centimeter against a force of one dyne ; the unit of work, the erg, therefore equals one dyne centimeter. 2264. The unit of energy is also the erg ; for the energy of a body is measured by the work it can do. The unit of energy, the erg, is therefore also one dyne centi- meter. 2265. The unit of power has no particular name in the C. G, S, system. It is defined as the rate of doing work, and is hence equal to one erg-per-second. 2266. The unit of lieat (sometimes called a calorie) is the amount of heat required to warm one gram mass of water from O'' to 1° C. 2267. The unit of electric-current strength is a current of such a strength that when passing through a cir- cuit one centimeter in length, arranged in an arc having a radius of one centimeter, it will exert a force of one dyne on a unit magnet pole placed at the center. (See Art. 2379.) 2268. The unit of quantity of an electric cur- rent is that quantity which is conveyed by unit current in one second. 2269. The unit of difference of potential (or of electromotive force) is defined as the work done on a unit of electricity ; hence unit difference of potential exists ELECTRICITY AND MAGNETISM. 1477 between two points when it requires the expenditure of one erg of work to bring a unit of -\- electricity from one point to the other against the electric force. 2270. The unit of resistance is that resistance which a conductor possesses when unit difference of poten- tial between its two ends will allow a current of unit strength (that is, one unit of quantity per second) to flow through it. PRACTICAL, UNITS. 2271. Several of the above absolute units would be in- conveniently large and others inconveniently small for prac- tical use. The following /r«(r/Z(f«/ units have therefore been adopted and named after distinguished men of science, such as Ampere, Coulomb, Volta, Ohm, Joule, and "Watt. THE AMPERE. 2272. The practical unit of electric current is the ampere. The ampere is smaller than the absolute unit of current. (Art. 2267.) 1 absolute unit equals 10 amperes. 1 ampere equals -^-^ absolute unit. 2273. The strength of an electric current can be de- scribed as a quantity of electricity flowing continuously every second, or, in other words, it is the rate of flow of electricity, just as the current expressed in gallons per minute is the rate of flow in liquids. When one practical unit quantity of electricity is flowing every second, continu- ously, then the rate of flow or the strength of the current is one ampere ; if two unit quantities are flowing continuously every second, then the strength of the current is two amperes, and so on. It makes no difference in the number of amperes whether the current flows for a long period or for only a fraction of a second ; if the quantity of elec- tricity that would flow in one second is the same in both cases, then the strength of current in amperes is the same. 1478 PRINCIPLES OF 2274. Electricity possesses neither weight nor exten- sion, and, therefore, an electric current can not be measured by the usual methods adopted for measuring liquids or gases. In liquids the strength of current is determined by measuring or weighing the actual quantity of the liquid which has passed between two points in a certain time and dividing the result by the time. The strength of an elec- tric current, on the contrary, is determined directly by the effect it produces, and the actual quantity of electricity which has passed between two points in a certain time is after- wards calculated by multiplying the strength of the current by the time. The principal effects produced by an electric current are magnetic attractions and repulsions, chemical decomposi- tion, and heating and luminous effects; of these, the two most generally used for measuring are: (1) its action before a magnetic needle, and (2) its chemical actions. These methods will be treated upon in detail in the section on Electrical Measurements ; the following, however, will give an illustration of one of the methods used in measuring electric currents, and also one mode of determining the value of one ampere : 2275. A current of electricity, when passing through water, decomposes it into its two elements, hydrogen and oxygen. The quantity of water decomposed is proportional to the strength of the current flowing, and also to the time during which it flows. For example, if a current of two amperes flowing for one second decomposes a certain quantity of water, then a current of four amperes flowing for one second will decompose txvice that quantity, and if it flows for two seconds it will decompose four times the original quantity. Consequently, a unit strength of current can be conventionally adopted by agreeing that it is that strength of current which will decompose a certain quantity of water in a certain time, and agreeing furthermore upon the quantity of water and the time. ELECTRICITY AND MAGNETISM. 1479 2276. By universal agreement, one ampere is that strength of current which will decompose .00009324 gram or .0014388 grain of water in one second. Rule. — To find the strength of an electric current in amperes by the decomposition of water ^ divide the weight of the quantity of water decomposed by the tiuie in seconds re- quired to decompose it ; if the mass of water is expressed in grams ^ divide tJie quotient by .0000982^; bnt if expressed in grains, divide by .OOlJi.388. Let W = weight of water decomposed in grams ; w = weight of water decomposed in grains ; / = time in seconds required for decomposition ; C = current in amperes. Then the strength of the current in amperes is given by the formulas: ~ tx .00009324* V"*^!*) ^""/X. 0014388- (402.) 2277. Rule. — To find the quantity of ivater zvJiich an electric current of a given strength can decompose in a given time, multiply the strength of the current in amperes by the time in seconds during which the current fiows ; if the quantity of water is to be expressed in grams, multiply the product by . 0000932^ ; but if in grains, multiply by . 0011^388. Let q =: quantity of water in grams ; q' = quantity of water in grains ; t = time in seconds of cui rent flow ; C = current in amperes. Then the quantity of water which can be decomposed by a current of C amperes in / seconds is given by the for- mulas: ^ = .00009324 6'/. (403.) q' = .0014388 C t. (404.) Example. — The current from a voltaic cell decomposes ivater at the rate of 1.29493 grains per hour ; what is the strength of current in amperes ? 1480 PRINCIPLES OP Solution. — 1 hour = 3,600 seconds. By formula 403, the strength of current _ 1.29492 _ ^-3,600 X .0014388 " '^^ ^^V^^^' ^^S" Example. — Find the number of grains of water decomposed in 8 hours by a current of .6 ampere. Solution. — 3 hours = 10,800 seconds. By formula 404, the quantity of water decomposed g' = .0014388 X .6 X 10,800 = 9.3234 grains. Ans. THE COULOMB. 2278. The practical unit of quantity of an electric current is the coulomb. The coulomb is smaller than the absolute unit of quantity of current. (Art. 2268.) 1 absolute unit equals 10 coulombs. 1 coulomb equals ^^ absolute unit. 2279. Relation of Atapere and Coulomb. — The relation of the ampere and the coulomb may be made clear by the water-flow analogy : W/ien a current of water Jlows tJirough a pipe, then the current must have a certain fixed strength, if a definite quantity of water is to be delivered at any point in a given time. When a current of electricity flows tJirough a conductor, then the ciLrrent must have a certain fixed ampere strength, if a definite number of coulombs of current is to be delivered at any point in a given time. 2280. The coulomb may be further defined as being such a quantity of electricity as zvould pass in one second tJirough a circuit in zvJiich the strength of the current is one ampere. One coulomb delivered per second therefore represents a current of one ampere. One ampere fioiving for one second zvill deliver one coulomb. j2281. If ^ = quantity of electricity in coulombs ; C —- strength of current in amperes; / = time in seconds. ELECTRICITY AND MAGNETISM. 1481 then, Q = Ct. (405.) By transposition, C ■=■— and t — -^. Example. — Find the quantity of electricity in coulombs that flows around a circuit in \\ hours, when the strength of current is 12 amperes. Solution. — By formula 405, the quantity of electricity ^ = C/ = 12 >. 1.5 X 3,600 = 64,800 coulombs. Ans. EXAMPLES FOR PRACTICE. 1. Find the quantity of electricity in coulombs that passes in a circuit in which a current of 40 amperes flows for 55 seconds. Ans. 2,200 coulombs. 2. Find the quantity of electricity in coulombs that passes in a circuit in which a current of 13 amperes flows for 15 minutes. Ans. 11,700 coulombs. 3. 36,000 coulombs of electricity pass through a closed circuit in 1 hour. If the flow is uniform during that time, what is the strength of the current ? Ans. 10 amperes. 4. How long will it take 72,000 coulombs of electricity to pass in a circuit in which the strength of current is 4 amperes ? Ans. 5 hours. THE OHM. 2282. The practical unit of resistance is the ohim. The ohm is greater than the absolute unit of resistance. (Art. 2270.) 1 absolute unit equals one-billionth ( i r.r.r. nnri nnn ) ^^ **^ ohm. 1 ohm equals 1 billion (1,000,000,000) absolute units. 2283. The ohm is the only unit in electrical measure- ments for which a material standard can be adopted. The basis of any system of physical measurements is generally some material standard conventionally adopted as the unit; physical measurements in each system are made by compari- son with the unit of that system. As a basis for the measurement of resistance, Siemens originally proposed a column of mercury having a height of 100 centimeters and a cross-section of one square millimeter, at the temperature of 0° C. ; that is, at the temperature of 1482 PRINCIPLES OF freezing water. This column of mercury he claimed had a resistance of one ohm. 2284. The idea of utilizing a column of mercury of 1 square millimeter cross-section at 0° C. as the practical unit of resistance has been universally adopted, but the height of this column has never been exactly determined. There are, therefore, various values of the unit often found quoted. The following list gives these various values in tabular form with annotations denoting their use. TABLE 75. VARIOUS VALUES OF THE OHM. Name. Height of Mercury Column. Cross-Sec- tion of Mercury Column. Use. Siemens' Unit. . 100 cm. 1 sq. mm. Out of use, because incorrect. British Associa- tion Unit, writ- ten B. A. U. . . 104.8 cm. 1 sq mm. Out of use, because incorrect. Legal Ohm (com- monly called Ohm) 106.0 cm. 1 sq. mm. In all technical meas- urements and cal- culations, as well as in this Course. International Ohm . - 106.3 cm. 1 sq. mm. Latest and most ex- act determination. Correct within---—— 0,000 part. Not yet in general use. ELECTRICITY AND MAGNETISM. 1483 2285. The relative values of these units are given by the following list: 1 legal ohm = 1.0112 B. A. U. 1 legal ohm = 1.0600 Siemens' Unit. 1 B. A. U. = .9889 legal ohm. 1 B. A. U. = 1.0483 Siemens' Unit. 1 Siemens' Unit = .9540 B. A. U. 1 Siemens' Unit = .9434 legal ohm. 2286. As stated in Table 75, the legal ohm, commonly called the otun, is used as yet in all technical measure- ments and throughout this Course, so that when the ohm is mentioned we understand thereby the resistance of a column of mercury 106 cm. (or 41.7323 inches) high, having a cross- section of 1 sq. mm. (or .00155 sq. in.) at 0° C. (or 32° F.). 2287. It very often occurs in practical work that ex- ceedingly small resistances are to be measured, for which the ohm as a unit causes unnecessary labor, because so very large. The absolute unit of resistance, on the other hand, is too small to do very well. Therefore, to facilitate calculations and measurements, a unit is used for such work having the value of one-millionth | nPtc^ ) ^^ ^^ ohm. 2288. This derived practical unit is called the tnicroliin. Therefore, to express the resistance in microhms^ multiply the resistance in ohms by 1,000,000; and, conversely, to ex- press the resistance in ohms, divide the resistance in inicroJims by 1,000,000. For example, .75 ohm = .75 X 1,000,000 = 750,000 microhms, or 750,000 microhms = .'^q^qq^O ^ '"^^ ohm. 2289. Another similarly derived practical unit is the tnegoliin, devised to facilitate calculations and measure- ments of exceedingly large resistances, and is equal to 1,000,- 000 ohms. Therefore, to express the resistance in megohms^ divide the resistance in ohms by 1,000,000; and, conversely. 1484 PRINCIPLES OF to express the resistance in ohms, multiply the resistance in megohms by 1,000,000. T. 1 o.^ ^^^ , 850,000 „, , For example, 850,000 ohms = ■ = .85 megohm, or .85 megohm = .85 X 1,000,000 = 850,000 ohms. The megohm is used mainly in the determination of ths resistance of non-conductors and insulators. EXAMPLES FOR PRACTICE. 1. Give the equivalent resistance in microhms of .00425 ohm. Ans. 4,250 microhms. 2. Give the equivalent resistance in ohms of 375 microhms. Ans. .000375 ohm. 8. Give the equivalent resistance in megohms of 4,560,000 ohms. Ans. 4.56 megohms. 4. Give the equivalent resistance in ohms of 63.5 megohms. Ans. 62,500,000 ohms. RESISTANCE. 2290. The resistance which all substances offer to the passage of an electric current is one of the most important quantities in electrical measurements. Resistance is that attribute of a conductor or of a circuit which determines the strength of the electric current that can be sent through the conductor or the circuit, around which a constant differ- ence of potential is maintained, as shown by Ohm's law, Art. 2253. 2291 . If a given conductor offers a resistance of 2 ohms to a current of 1 ampere, it offers the same amount, no more nor no less, to a current of 10 amperes. Hence we have the Rule. — TJie resistance of a given conductor is ahvays con- stant at the same temperature^ irrespective of the strength of current fiovoing through it or the electromotive force of the current. 2292. When it is required to find the resistance of a conductor of which the length is varied, though all other ELECTRICITY AND MAGNETISM. 1485 conditions remain unchanged, the following- formula may be used : r, :r, ::/,:/„ or r, = '^^ (406.) In this formula, r, = the original resistance ; r, = the required or changed resistance; /j = the original length; /^ = the changed length. 2293. As in all examples of proportion, the two lengths must be reduced to the same unit. We then have the Rule. — TJie resistance of a given conductor increases as the lengtJi of the conductor increases ; that is, the resistance of a conductor is directly proportional to its length. Example. — Find the resistance of 1 mile of copper wire, if the resistance of 10 feet of the same wire is .013 ohm. Solution. — rx = .013 ohm ; /i= 10 feet, and h= 1 mile = 5,280 feet Then, by formula 406, the required resistance .013x5,280 coc^A X. A ^3 = ^^ = 6.864 ohms. Ans. Example. — Find the resistance of 11 in. of a German silver wire, if the resistance of 100 feet of the same wire is 2.4 ohms. Solution.— i\ = 2.4 ohms ; A = 100 X 13 = 1,200 in. ; /» = 11 in. By formula 406, the required resistance EXAMPLES FOR PRACTICE. 2294, 1. Find the resistance per foot of a wire, if the resist- ance of 1 mile of the wire is 14.75 ohms. Ans. .002793 ohm. 2. If the resistance of 18 in. of a certain piece of wire is .027 ohm, what is the resistance of 1,020 feet of the same wire ? Ans. 18.36 ohms. 2295. If the sectional area of a conductor is increased, and other conditions remain unchanged, the resistance of the conductor will be decreased. For instance, if the sec- tional area be doubled the resistance is halved, and, con- versely, if the sectional area is halved the resistance is doubled. The resistance of a conductor, therefore, grows 1486 PRINCIPLES OF with decreasing sectional area, and diminishes with increas- ing sectional area. This may be expressed by the general rule : 2296. Rule. — The resistance of a conductor varies in- versely as its sectional area. The value of the resistance of a conductor for any change in its sectional area may be obtained from the following formula : r, : r, ::«,:«,, or r, = ^. (407.) In this formula, r^ = the original resistance ; r, = the required resistance ; a = the original sectional area ; a^ = the changed sectional area. Example. — The resistance of a conductor whose sectional area is .025 sq. in. is .32 ohm ; what would be the resistance of the conductor if its sectional area were increased to .125 sq. in., other conditions remaining unchanged ? Solution. — r, = .32 ohm; ^i=:.025 sq. in., and «a = .125 sq. in. Then, by formula 407, the required resistance .32 X .025 rs = ' .125 = .064 ohm. Ans. Example. — The sectional area of a conductor is .01 sq. in. and its resistance is 1 ohm ; if its sectional area is decreased to .001 sq. in., and other conditions remain unchanged, what will be its resistance ? Solution. — r, ~ 1 ohm ; ax = .01 sq. in., and a^ = .001 sq. in. By formula 407, the required resistance ^ = 1^^ = 10 ohms. Ans. .001 2297. The resistance of a conductor is independent of the shape of its cross-section. For example, this cross- section may be of circular, square, rectangular, or irregular shape; if the sectional area is the same in all cases, the resistances will be the same, other conditions being similar. When comparing the resistances of copper wires of circular cross-section, it is usually simpler to express the copper wire ELECTRICITY AND MAGNETISM. 148? by its diameter than by its area. The sectional area of any circular cross-section is, however, proportional to the square of the diameter; for the sectional area = diameter'* X .7854. We therefore have the rule: 2298. TJie resistance of a conductor of circular cross- section is inversely proportio7tal to the square of its diameter. Formula 407 may, therefore, be rewritten as follows: r, : r, :: d^ : D\ or r, = ^^. (408.) In this formula, r, = the original resistance ; r^ = the required resistance; £} = the original diameter; d = the changed diameter. Example. — The resistance of a round copper wire .12 in. in diame- ter is .64 ohm ; find the resistance of the conductor when its diameter is increased to .24 in., the other conditions remaining unchanged. Solution. — n = .64 ohm ; Z> = .12 in., and d= .24 in. Then, by formula 408, the required resistance .64 X .12^ r2 = '- ^, — • = .16 ohm. Ans. Example. — The diameter of a round wire is .1 in. and its resistance is 2 ohms ; what would be its resistance if its diameter were decreased to .02 in., and the other conditions remained unchanged ? Solution. — ri = 2 ohms ; D = .1 in., and il= .02 in. By formula 408, the required resistance 2x.l^ 2X.01 ^^ ^ EXAMPLES FOR PRACTICE^ The resistance of a piece of round copper wire .001 in. in diameter and 1 foot long is 10.8 ohms ; use the same quality of copper, and solve the following problems : 1. Find the resistance of 1,200 feet of round copper wire .102 in. in diameter. Ans. 1.2457 ohms, 2. Find the resistance of 1 mile of round copper ^ in. in diameter. Ans. 3.6495 ohms. 3. Find the resistance of 1,500 feet of square copper wire .1 in. on a side. Ans, 1,3723 ohma 1488 PRINCIPLES OF 4. Find the resistance of 100 yards of copper wire .12 in. wide by .09 in. thick. Ans. .23562 ohm. Note. — The temperature of the copper in all the above problems is assumed to be equal. 2299. The Resistance of Metals. — It was stated in Art. 2216 that the resistance varies in different sub- stances; that is, one substance offers a higher resistance to a current of electricity than another. In order to compare the resistances of different substances, however, the dimen- sions of the pieces to be measured must be equal. For, by- changing its dimensions, a good conductor may be made to offer the same resistance as an inferior one. Under like conditions, annealed silver offers the least resistance of all known metals or conductors. Soft annealed copper comes next on the list, and then follow all other metals and conductors. 2300. The resistance of a given conductor, however, is not always constant; it changes with the temperature, and also with the physical condition of the conductor. In all metals the resistance increases as the temperature rises; in liquids and carbons the resistance decreases as the tem- perature rises; and in non-conductors the resistance de- creases as the temperature rises. The amount of variation in the resistance caused by a change in temperature will be treated upon under Electrical Measurements; it is a small factor, and can be neglected for the present. 2301. A list of the common metals is given in Table 76 in the order of their relative resistances, beginning with silver as offering the least resistance. The first column of figures gives the actual resistance in microluns of 1 cubic inch of the corresponding metal at 32° Fahrenheit, or the freezing-point of water. By the resistance of 1 cubic inch is meant the resistance of a piece of the conductor, the length of which is 1 inch, and whose sectional area is 1 sq. in. Therefore, the resistance of any conductor of known dimensions which is made of one of the metals in the list can be determined by applying the formulas in Arts. 2296 ELECTRICITY AND MAGNETISM. 1489 and 2298. The second column of figures gives the rela- tive resistances of the different metals compared with silver. For example, the resistance of mercury is 62.73 times the resistance of silver, or the resistance of iron is 6,46 times the resistance of silver. TABLE 76. Name of Metal. Resistance in Microhms of 1 Cu. In. at 33° F. Relative Resistance. Silver, annealed .5921 .6292 .6433 .6433 .8102 .8247 1.1470 2.2150 3.5650 3.8250 4.9070 5.2020 7.7280 8.2400 13.9800 37.1500 51.6500 1.000 Copper, annealed 1.063 Silver hard drawn 1.086 Copper hard drawn 1.086 Gold annealed L369 Gold, hard drawn 1.393 Aluminum, annealed 1.935 Zinc pressed 3.741 Platinum annealed 6.022 Iron annealed 6.460 Nickel annealed 8.285 Tin, pressed 8.784 Lead, pressed 13.050 German Silver 13.920 Antimony, pressed Mercury 23.600 62.730 Bismuth, pressed 87.230 EXAMPLES FOR PRACTICE. 1. Find the resistance in ohms of a round column of mercury 70 inches high and .05 inch in diameter. Ans. 1.3244 ohms. 2. Find the resistance in ohms of 1,000 feet of round German silver wire .2 inch in diameter. Ans. 8. 1476 ohms. 3. Find the resistance in microhms of a cubic foot of bismuth, pressed. Ans. 4.3042 microhms. 4. Find the resistance in ohms of 1 mile of square iron wire (an- nealed) . 1 inch on a side. Ans. 34. 2353 ohms. 1490 PRINCIPLES OF 2302. In a simple voltaic cell, the intei'nal resistance, that is, the resistance of the two plates and the electrolyte, is of great importance, for it determines the maximum strength of current that can possibly be obtained from the cell. In the common forms of cells, the internal resistance may be excessively large, owing to the resistance of the elec- trolyte, the relative resistance of ordinary liquids used as elec- trolytes being from 1 to 20 million times that of the common metals. In liquids, as in all conductors, the resistance in- creases as the length of the circuit increases, and diminishes as its sectional area increases. Consequently, the internal resistance of a simple voltaic cell is reduced by decreasing the distance between the two plates or elements and by increasing their active surfaces. The internal resistance of the ordinary forms of cells varies from about .2 to 20 ohms. THE VOLT. 2303. The practical unit of electromotive force, or difference of potential, is the volt. The volt is greater than the absolute unit of electromo- tive force. (Art. 2269.) 1 absolute unit equals one one-hundred-millionths (■ -I of a volt. 100,000,000/ 1 volt equals one hundred million (100,000,000) absolute units. 2304. The volt may be further defined as being that E. M. F. %vJiicJi will cause a current of one ampere to flozv against the resistance of one ohm. 2305. The volt is the measure of the electromotive force, which has been defined and explained in Arts. 2242 and 2252. The various terms electromotive force, pressure, difference of potential, and voltage are, in general, used to signify the same thing; namely, that force which ELECTRICITY AND MAGNETISM. 1491 tends to move a current of electricity against the resistance of a conductor. 2306. The maximum difference of potential developed by any voltaic couple (see Art. 2243) placed in any electro- lyte is about 2.25 volts ; in the common forms of cells, the difference of potential developed averages from .75 to 1.75 volts. 2307. The determination of the value of the E. M. F. in any circuit is made by applying Ohm's law (see Art. 2253), which gives the E. M. F. accurately when the re- sistance and current are known. Measuring instruments, which will be described under Electrical Measurements, have been devised upon the principle of Ohm's law, to indicate the E. M. F. directly. OHM'S LAT^ APPLIED TO CLOSED CIRCUITS. 2308. Ohm's law, as shown in Art. 2253, expresses the relation between the three fundamental units of resist- ance, electrical pressure, and current. If any two of these values are known, the third is found by solving the simple equation of their relation. Before applying this law, how- ever, the following four facts should be carefully noted : 2309. I. — TJie strength of a current (C) is the same in all parts of a closed circuit, except in the case of divided circuits. II.- — In the case of a divided circuit, the sum of the cur- rents in the separate brandies is ahvays equal to the current in the main or undivided circuit. III. — TJie resistance {R) is the total resistance of the cir- cuit, that is, the sum of the resistances of the internal circuit and of the external circuit, or its equivalent. IV. — The electromotive force (E) in a closed circuit is the total generated difference of potential in that circuit. The law may now be stated by the following rules and formulas : 1493 PRINCIPLES OF 23 lO. Rule I. — The strength in amperes of a current {C) flowing in a closed circuity when the electromotive force {E) and the total resistance (R) are knozvn, is found by divi- ding the electromotive force in volts by the total resistance in ohms ; that is, ^ electromotive force ^ E , ^^^ . Current = ■ r— , or C =-^- (409.) resistance K ^ Rule II. — The total resistance (R) in ohms of a closed cir- cuit, IV hen the electromotive force {E) and the current {C) are known, is found by dividing the electromotive force in volts by the current in amperes ; that is, _. . electromotive force „ E / ^ ^ ^ \ Resistance = • , or R =—;;,. (41 0.) current 6 Rule III. — The total electromotive force [E) in volts developed in a closed circuit, when the current (C) and the total resistance (R) are known, is found by multiplying the current in amperes by the total resistance in ohms ; that is^ Electromotive force = current X resistance, or E = CR. (411.) 2311. The following examples show the application of Ohm's law as given by the formulas of the preceding article: Example. — What current can be made to flow through a circuit having a resistance of 10 ohms, if an E. M. F. of 100 volts is applied ? Solution. — ^=100; i? = 10 ; hence, by formula 409, the re- quired current C = -jTT- = 10 amperes. Ans. Example. — What resistance can be overcome by a current of 50 amperes, if the electromotive force is 500 volts ? Solution. — (7= 50; -£"= 500; hence, by formula 41 0, the required resistance R =:-=7r — 10 ohms. Ans. 50 Example. — What voltage is required to send a current of 25 amperes through a resistance of 4 ohms ? Solution. — C= 25 ; i? = 4 ; hence, by formula 41 1, the required voltage J? = 25 X 4 = 100 volts. Ans. ELECTRICITY AND MAGNETISM. 1493 Example. — The two electrodes of a simple voltaic cell are connected together by a copper wire, the resistance of which is 1 ohm. If the internal resistance of the cell is 4 ohms and the electromotive force developed is 3 volts, what is the strength of the current in the circuit ? Solution. — Let r, = the internal resistance and re — the external resistance ; that is, the resistance of the copper wire. Then, i? = r, + re = 4 + 1 = 5. By formula 409, the current E 2 C= -n = k"= •■^ ampere flowing through the circuit. Ans. Example. — The total electromotive force developed in a closed circuit is 1.2 volts and the strength of the current flowing is .3 ampere ; find the total resistance of the circuit. Solution. — By formula 410, R = — ^ = 4 ohms. Ans. . o Example. — The internal resistance of a certain dynamo-electric machine is 10.9 ohms and the external resistance is 73 ohms ; the voltage of the machine is 839 volts. Find the strength of the current flowing in the circuit. Solution.— n = 10.9 ; r^ = 73 ; J? = 10.9 + 73 = 83.9, By formula 409, C — ^^ = 10 amperes. Ans. EXAMPLES FOR PRACTICE. 1. The current from a simple voltaic cell decomposes water at the rate of 2.58984 grains per hour, and the total resistance of the circuit through which the current flows is 2 ohms. Find («) the strength of the current, and {b) the total electromotive force developed by the cell. j (a) .5 ampere. ^^^•\(b) Ivolt. 2. A battery of 10 cells connected in series generates a total elec- tromotive force of 12 volts. If the resistance of each cell is 4 ohms and the resistance of an external circuit is 8 ohms, what is the strength of current flowing in the circuit ? Ans. .25 ampere. 3. Given, Internal resistance = 4 ohms. Electromotive force = 1.5 volts. Current = .2 ampere. Find the external resistance. Ans. 3.5 ohms. 1494 PRINCIPLES OF 4. Given. Electromotive force = 24 volts. Current = .6 ampere. If the external resistance is 3 times the internal, what is the resistance of each? a^^ i External, 30 ohms. Internal 10 ohms. Ans. DROP OF POTENTIAL. 2312. Referring again to the flow of water in pipes, we may tabulate the analogies as given in Table 77, a care- ful study of which will do much to assist the understanding of what is to follow. 2313. The fourth analogy of the table states that the loss of pressure or E. M. F., due to the resistance of conductor, is termed drop of potential. This drop may be made clearer by the following : Let Fig. 913 represent a tank T of water with a hori- zontal discharge-pipe E JV, which is provided with open , Fig. 913. vertical tubes at a, b, c, etc. If the outlet at N is closed the water in the vertical tubes will rise to the height of the water in the tank ; but if the water is allowed to flow freely from the outlet at N, then the height of the water in the tubes will be represented by the inclined line at a', b\ c' , etc. The pressure or licad of the water, which is measured by the height of the water in the tubes, decreases in the direction in which the water is flowing, so that the water which leaves the discharge outlet at N has considerably less pressure than the water entering at E. ELECTRICITY AND MAGNETISM. 1495 TABLE 77. A1VAI.OGIES BETWEEN THE FLOW^ OF TVATER AJVD ELECTRICITY. Water in Pipes. Electricity in Conductors. I. XL III. IV. V. VI. Difference of level tends to make water fall from the upper level to the lower level. Difference of level hence acts as a pres sure tending to cause a flow. If not entirely obstruct ed, this pressure ac- tually produces a flow of water. Some of this pressure is lost by friction of the water against inside walls of pipe. This loss by friction is directly proportional to the length of the pipe, and inversely proportional to the diameter of the pipe. No quantity of water can flow through a pipe without suffering some loss in this man- ner; in other words there is no such thing as an absolutely fric tionless pipe. Difference of potential tends to make electric current fall from point of high po- tential to point of low po- tential. Difference of potential or E. M. F., hence acts as a pressure tending to cause a flow- If not entirely obstructed, this pressure or E. M. F. actually produces a flow of current. Some of this pressure is lost by the electrical resistance of the conductor. The loss is called di'op of potential. This loss or drop due to re- sistance is directly propor- tional to the length of the conductor, and inversely proportional to its area of cross-section. No quantity of electricity can flow through a con- ductor without suffering some loss in this manner ; in other words, there is no such thing as an absolutely resistanceless conductor. 1496 PRINCIPLES OP 2314. The same action takes place in a current of electricity flowing along a conductor, and can also be graphically shown. In Fig. 914, B represents a voltaic battery with the negative electrode connected directly to the earth at E^ and the positive electrode to a long con- ductor A L, which is also connected to the earth at E'. The battery may be regarded as a machine which raises the pressure or potential of electricity from zero (or that of the earth) to a height equal to the distance a a'; or, in other words, the distance a a' represents the total electromotive force of the battery. If the circuit is opened or broken be- tween L and E so that no current flows, then the difference Fig. 914. of potential between the conductor and the earth is the same at all points along the conductor, and is represented by the distances between the line C D and the conductor A L. But when a current is allowed to flow along the conductor, the difference of potential between the conductor and the earth decreases in tJie direction in zvJiicJi tJie current is floiv- ing. The vertical distances b b' , c c\ d d\ etc., represent this difference of potential at the points b, c, d, etc., along the conductor. The loss or drop of potential is represented by the vertical distances between the inclined line C L and the horizontal line C D. This loss or drop also represents the difference of potential between the point a and any other point along the conductor. For example, at h the differ- ELECTRICITY AND MAGNETISM. 1497 ence of potential between the conductor at that point and the earth is represented by the distance h h' ; the loss or drop of potential is represented by the vertical distance between h' and the horizontal line C D, which distance also represents the difference of potential existing between the points a and h. 2315. The graphical method of determining the dif- ference of potential is seldom used. Ohm's latv not only gives the strength of the current in a closed circuit, but also the difference of potential in volts along that circuit. The difference of potential (^') in volts between any two points along a circuit is equal to the product of the strength of the current (C) in amperes and the resistance (7?') in ohms of that part of the circuit between those two points ; or ii ' = C R\ which is an example of the use of formula 411. E' also represents the loss or drop of potential in volts between the two points. If any two of these quantities are known, E' the third can be readily found ; for, by transposing, C =-™ K. E' and R = -f^, as already given in formulas 409 and 410. Example. — Fig. 915 represents part of a circuit in which a current of 2.5 amperes is flowing. The a h e d resistance from a to (5 is 10 ' ' t ohms ; from b to c, 15 ohms, Fig- 915. and from c to d, 20 ohms. Find the difference of potential between a and b, b and c, c and d, and a and d. Solution. — Since, by formula 411, -£"' = CT?', then The difference of potential between a and (5 is 2.5 X 10 = 25 volts ; b and c is 2.5 X 15 = 37.5 volts ; c and ^ is 2.5 X 20 = 50 volts ; a and ^ is 25 + 37.5 + 50 = 112.5 volts; or, in other words, the loss or drop in potential between a and d is 112.5 volts. 2316. In a great many cases, it is desirable to have the current flow from the source a long distance to some electric receptive device, and return without causing an excessive drop or loss of potential in the conductors leading to and 1498 PRINCIPLES OF from the two places. In such circuits, the greater part of the total generated electromotive force is expended in th.e receptive device itself, and only a small fraction of it is lost in the rest of the circuit. Under these conditions, it is cus- tomary to decide upon a certain drop or loss of potential beforehand, and from that and the current calculate the resistance of the two conductors. Example. — It is desired to transmit a current of 10 amperes to an electrical device situated 1,000 feet from the source ; the total generated E. M. F. is 110 volts, and only 5^ of this potential is to be lost in the conductors leading to and from the two plants. Find (a) the total resistance of the two conductors, and (d) the resistance per foot of the conductors, assuming each to be 1,000 feet long. Solution. — 5% of 110 volts = 110 X -05 = 5.5 volts, which represents the total drop or loss of potential on the two conductors. Let ^' = 5.5 volts ; C=10 amperes, and i?' = the total resistance of the two con- ductors. Then, by formula 410, 7?' =-^ = -^ = .55 ohm. (a) Ans. The resistance per foot of the conductor is found by formula 406. In this case, ri = .55 ohm ; A = 3,000 feet ; 4 = 1 foot. Then, the 55 X 1 resistance per foot = ra = 'yqqo' — -000375 ohm. (3) Ans. EXAMPLES FOR PRACTICE. 1. In a part of a closed circuit, the drop or loss of potential caused by the resistance of the conductor is 10 volts. If the current flowing is 4 amperes, what is the resistance of that part of the circuit ? Ans. 3.5 ohms. 3. The total generated electromotive force in a circuit is 320 volts. A current of 10 amperes is transmitted to and from a receptive device situated 110 feet from the source, with a loss of potential of 10^. (a) Find the total resistance of the two conductors leading to and from the two places, and {^) find the resistance per foot of each conductor, assuming each to be alike and 110 feet long. Ans ^^^'^ 3.2 ohms. . ' ( (^) .01 ohm per foot. TOTAL AND AVAILABLE E. M. F. 2317. The difference of potential between the two electrodes of a simple voltaic cell when no current is flow- ing, that is, when the circuit is o/>en, is always equal to the total electromotive force developed within the cell; but ET.ECTRICITY AND MAGNETISM. 1499 when a current is flowing, that is, when the circuit is closed, a certain amount of potential is expended in forcing the current through the internal resistance of the cell itself. Consequently, the difference of potential between the two electrodes when the circuit is closed is always smaller than when the circuit is open. This difference of potential when the circuit is closed is sometimes called the available or ex- ternal electromotive force, to distinguish it from the internal or total generated electromotive force. 2318. The available electromotive force is equal to the difference between the total generated electromotive force and the potential expended in forcing the current through the internal resistance when the circuit is closed. From Ohm's law, this loss or drop of potential in the cell itself is equal to the product of the internal resistance and the strength of current flowing. Let E = total generated E. M. F. ; E' = available E. M. F. ; C = current flowing when the circuit is closed; r,- = internal resistance of the cell; re = an external resistance. The drop or loss of potential in the cell = Cr^ and E' = E-Cr,. 2319. For example, in a voltaic cell the total generated E. M. F. is 2 volts, and the internal resistance is 4 ohms. If the two electrodes are connected to an external resistance of 6 ohms, a current of .2 ampere will flow through the E 2 circuit, since C= ; = - -=.2 ampere. The loss r, + r, 4+G or drop of potential in the cell = C r^ = .2 X 4: = .S volt. Then, E' = E — C r^ = 2 — .8 = 1.2 volts, which is the elec- tromotive force available to force the current of .2 ampere through the external resistance of 6 ohms, since Crg= .fix 6=1.2 volts. 1500 PRINCIPLES OF OHM'S LA^W APPLIED TO DERIVED CIRCUITS. 2320. A derived or shunt circuit is a brancJi or additional circuit provided at any part of a circuit through which the current branches or divides, part flowing through the original circuit and part through the new branch. A derived circuit is in multiple circuit with the circuit from which it is derived. In the case of branched circuits, each of the branches acts as a derived circuit to the others. Any number of additional branches may thus be provided. 2321. In treating upon derived or shunt circuits, only that part of the circuit will be considered which is divided into branches and each branch transmitting part of the cur- rent; the rest of the circuit is assumed to be closed through some electric source; as, for instance, a voltaic battery. Before applying Ohm's law to derived circuits, it is nec- essary that the meaning of conductivity should be thoroughly understood. In Art. 2217 it was stated that conductivity is the inverse of resistance ; or, in other words, it is the reciprocal of resistance. Therefore, since the conductivity is greater the less the resistance, the conductivity may be defined as being equal to -^; that is, the reciprocal of the resistance. 2322. The conductivity of any conductor is, therefore, unity divided by the resistance of the conductor; and, con- versely, the resistance of any conductor is unity divided by the conductivity of that conductor. For example, if the resistance of a circuit is 2 ohms, the conductivity is repre- sented by -75- = -I ; if the resistance is increased to 4 ohms, the conductivity would be only one-half as much as in the first case, and would now be \. There is no established unit of conductivity; it is used merely as a convenience in calculation. 2323. Fig. 916 represents a derived circuit of two branches. ELECTRICITY AND MAGNETISM. 1501 Let r^ and i\ = the separate resistances of the branches, respectively; C^ and c^ = the currents in each branch, respectively ; C = the current in the main circuit. Then, r, 4^ c^ = C. When the current flows from a to b, if the resistances r, and r^ are equal, the current will divide equally between the two branches. Thus, ^ if a current of 2 amperes C ^ ^^ ^ is flowing in the main cir- \ ^ y^ cuit, 1 ampere will flow c^ * through each branch. ^^°- ^^^• When the resistances are unequal, the current will divide inversely as the respective resistances of the two branches; or, since the conductivity is the reciprocal of the resistance, the current zvill divide in proportion to their respective con- ductivities. In Fig. 916 the conductivities of the two branches are — and — , respectively. Therefore, 2 2 c r c ' c • • — * — or — = — . Example. — Given C = 60 amperes ; r, = 3 ohms ; ra = 3 ohms. Find Ci and fa- Solution. — — = — , or ~ z=—, or ^, = -^. But r, + ' 1 ' » \ 'a their joint resistance 72" = 1 -^ !l±Ii = ^^,^^ . (41 2.) 12 2 "T" ' J Rule. — The joint resistance of tivo conductors in parallel is equal to the product of their separate resistances divided by the sum of their separate resistances. Example. — In Fig. 916, given ri = 4 ohms ; ra = 6 ohms, and C= 30 amperes. Find Cx and ^2 in the separate branches and the joint resist- ance of the branches from atob. Solution. — — = — , or Cx = — r^- But ^1 + ^2 = 30, or ^ 1 = 30 — (Tj ; ^2 4 4 6 c substituting, 30 — ^2 = —~^. Reducing gives 10 c^ = 120, or c^ = 13 amperes. Ans. ^Ti = 30 — 12 = 18 amperes. Ans. jr ;-„ 4 X 6 By formula 412, the joint resistance R" = - =- =— -— = 2.4 ohms. ■^ ' -^ ;'2 + Tx 10 Ans 2326. Fig- 917 represents a derived circuit of 3 branches. JXy — ^^ Let Tj, r^, and r^ = the sepa- C ^ „{ rf \h *- X2^.Q. resistances of the three branches, respectively ; then, ci^ — , — . and — represent the Fig. 917. ^j ^2 ^3 separate conductivities of the three branches, respectively. 1 1 1 rr-\-rr-\-rr Their joint conductivity =-— + -+---. ' " ' ' '—- ' \ ' 1 ' % 123 Since the joint resistance is the reciprocal of the joint conductivity, then ELECTRICITY AND MAGNETISM. 1503 the joint resistance of the three branches in parallel from a to d. We have, therefore, the following Rule. — The joint resistance of three or more conductors in parallel is equal to the reciprocal of their joint conductivity. Example. — In Fig. 917, given r^, = 5 ohms, r^ = 10 ohms, and ra = 20 ohms. Find their joint resistance from a to ^. Solution. — By formula 413 the joint resistance „,„ _ r, r, ra ^ 5 X 10 X 20 ^ 1,000 _ "" ra rs + ri rs + r, r^ (10 X 20) + (5 X 30) + (5 X 10) 350 ~ 20 — = 2f ohms. Ans. 2>32'7, In any derived circuit, the difference of po- tential between where the branches divide and where they unite is equal to the product of the sum of the currents in the separate branches and their joint resistance in parallel, as will be apparent from consideration of Ohm's law, Art. 231 0. For example, if the currents in the three branches, Fig. 917, are 16, 8, and 4 amperes, respectively, and the joint resistance from a to I; is 2-| ohms, then the difference of potential between a and d is (16 + 8 + 4) X 2f = 28 X ^0. — 80 volts. 2328. The separate currents in thie branches of a derived circuit can be determined by finding the difference of potential between where the branches divide and where they unite, and dividing the result by the separate resist- ance of each branch. For example, in Fig. 917 assume that the difference of potential between a and d is 80 volts, and that the separate resistances of the three branches are, respectively, 5, 10, and 20 ohms. Then the current in the first branch is -V- = 16 amperes; in the second, -1-^=8 am- peres, and in the third, |-2- = 4 amperes. 2329. The separate resistances of the branches of a derived circuit can be determined by finding the dif- terence of potential between where the branches divide and 1504 PRINCIPLES OF where they unite, and dividing the result by the separate currents in each branch. For example, in Fig. 917 assume the difference of potential between a and b to be 80 volts, and the currents in the separate branches to be 16, 8, and 4 amperes, .respectively; then, the resistance of the first branch is -f-^- = 5 ohms; of the second, -§§3- = 10 ohms, and of the third, ^-^ — 20 ohms. EXAMPLES FOR PRACTICE. 1. The separate resistances of two branches X and F of a derived circuit are 13 and 29 ohms, respectively. Find their joint resistance in parallel. Ans. 8.9762 ohms. 2. The sum of the currents in two branches X and F of a derived circuit is 28 amperes. If the separate resistance of X is 7 ohms and the separate resistance of F is 4 ohms, what is the separate current in each branch ? a i Current in branch ^is 10.1818 amperes. Ans. Current in branch Fis 17.8182 amperes. 3. The separate resistances of three branches of a derived circuit are, respectively, 36, 45, and 64 ohms. Find their joint resistance in parallel. Ans. 15.2381 ohms. 4. The joint resistances of three conductors X, F, and Z, connected in parallel, is 2.5 ohms. If the separate currents in the branches are, respectively, .6, .7, and .8 ampere, what is the separate resistance of each branch ? / Resistance of branch X= 8.75 ohms. Ans. "I Resistance of branch F= 7.5 ohms. ' Resistance of branch Z =■ 6.5625 ohms. 5. The separate resistances of three branches X, V, and Z of a de- rived circuit are 2, 3, and 4 ohms. If the sum of the currents in the three branches is 26 amperes, what is the separate current in each branch ? T 12 amperes in branch X. Ans. "j 8 amperes in branch F. ' 6 amperes in branch Z. THE JOULE. 2330. The practical unit of electric energy or work is the Joule. The joule is greater than the absolute unit of energy or work, the erg (Arts. 2263 and 2264). 1 absolute unit or erg equals one-ten-millionth ( TTrT^T^Trr;?^ I part of a joule. One joule equals ten million (10,000,000) absolute units or ergs. ELECTRICITY AND MAGNETISM. 1505 ELECTRICAL, •WORK. 2331. The joule may be further defined as being that amount of energy zvhicJi is expended diiring the time of one second^ by one ampere in overcoming the resistance of one ohm. 2332. But 1 ampere flowing for 1 second = 1 coulomb (Art. 2280) ; and 1 ampere flowing through 1 ohm = 1 volt ^Art. 2304) ; therefore, 1 joule may be defined as being that amount of energy expended when 1 volt propels 1 coulomb, or when 1 coulomb is carried through a distance between which the difference of potential is 1 volt. The work done, therefore, may be said to be one volt- coulomb, just as in mechanics the work done by raising 1 pound through 1 foot is equal to the foot-pound. 2333. This volt-coulonib, however, which is called the joule, is not as great as the foot-pound, the relation being 1 joule = .7373 foot-pound. 1 foot-pound = 1.356 joules. We may now state the rule for the determination of elec- trical work as follows: 2334. Rule. — To find the amount of electrical work accomplished in joules during a given time^ multiply the quan- tity of electricity in coulombs tvJiich has passed in the circuit during that time by the loss or drop of potential. 2335. This rule may be expressed by the following formulas, for the three cases occurring in practical work: Let J = electrical work in joules; C = current in amperes ; t = time in seconds during which current flows; E= E. M. F. of circuit; R = resistance of circuit. Then, according to Art. 2334, y= coulombs X drop. But, according to Art. 2280, ampere-seconds = cou- lombs ; so that j = amperes X seconds X drop. J 506 PRINCIPLES OF But, according to Art. 231 6, drop = current X resist- ance; hence, J = amperes x seconds X amperes X resistance, which can be written, by utihzing the notation given above, as /= CY,txCY.R', or, J=ORt. (414.) This formula, then, gives the electrical work in joules when the current and resistance are known. Example. — Find the amount of work done in joules when a current of 15 amperes flows for \ hour against a resistance of 2 ohms. Solution. — ^ hour = 1,800 seconds. By formula 4 14, the electrical work done / = C2i?/ = 15xl5x3X 1,800 = 810,000 joules. Ans. 2336. When the current and electromotive force are known, we derive the formula for the electrical work as follows: According to Art. 2334, /= coulombs X drop. But drop = E and coulombs (as in Art. 2335) equal C t\ hence, J^CEt. (415.) This formula expresses the amount of the electrical work in terms of current and drop. Example. — Find the amount of work in joules done in 1 hour by a current of 25 amperes under an electromotive force of 20 volts. Solution. — 1 hour = 3,600 seconds. By formula 41 5, the electrical work /= CEt~ 25 X 20 X 3.600 = 1,800,000 joules. Ans. 2337. When the electromotive force and resistance only are known, we proceed in a similar manner. Again, according to Art. 2334, y = coulombs X drop. But coulombs (Art. 2335) = C t and drop = E\ hence. J=CtE, ELECTRICITY AND MAGNETISM. 1507 But, according to Ohm's law (Art. 231 0, formula 409), E . . C=^-r,, and inserting this value of C, we have XV. or, ■^=nr- ('''^®-' This formula expresses the amount of the electrical work in terms of the E. M. F. and resistance. Example. — What is the amount of work done in joules in 45 min- utes in a circuit having 200 ohms resistance, the electromotive force being 110 volts ? Solution. — 45 minutes = 2,700 seconds. By formula 416, the electrical work done ^ £'/ 110X110X2,700 ,.„„.^. , . /= —r=- = • jr— r = 163,350 loulcs. Ans. •^ K 200 2338. As stated in Art. 2333, the joule = .7373 foot- pound; therefore, when the work in joules is known, the work in foot-pounds is F. P. =.7373/, (417.) which may be expressed by the Rule. — T/ie eqiiivalent zvork do7te in foot-pounds, when the work in joules is known, is obtained by -multiplying the number of joules by . 7373. Example. — Express the work accomplished in foot-pounds in a circuit where a current of 8 amperes flows for 2 hours, the electro- motive force being 10 volts. Solution. — 2 hours = 7,200 seconds = /. By formula 415, the electrical work done =/= 8 X 10 X 7,200 = 576,000 joules. Expressed in foot-pounds, this will be by formula 417, F. P. = .7373 X 576,000 = 424,684.8 foot-pounds. Ans. Example. — Find the amount of work done in foot-pounds by a cur- rent of 4 amperes flowing for 15 seconds against a resistance of 3 ohms. Solution. — By formula 414, the electrical work done = /=:4x 4 X 3 X 15 = 720 joules. The mechanical work done, by formula 417, in foot-pounds is F. P= = .7373 X 720 = 530.856 foot-pounds. AnSc 1508 PRINCIPLES OF RELATIONS OF MECHANICAL, ELECTRICAL, AND HEAT ENERGY- 2339. When an electric current flows from a higher to a lower potential, electrical energy is expended and work is done. This energy is expended in overcoming the resistance of the conductor constituting the circuit. In the case of analogy IV., Art. 2313, the friction of the water against the walls of the pipe produces heat, in an exactly similar manner as heat is produced, for instance, by rubbing sandpaper over a wooden surface. In the latter case, however, the friction is very great, and the heat pro- duced is hence quickly felt by the hand, while, in the case of water against metal pipes, the friction is comparatively very small, and the heat produced thereby is not perceptible to our sense of touch. Nevertheless, the heat is there, as the principle of the conservation of energy proves (see Art. 960). This heat is dissipated into the surrounding atmos- phere; it is, therefore, not destroyed, but merely exists in another form, having gone to increase the temperature of the air. 3340. Exactly so is it with the energy expended by an electric current in overcoming the resistance of a con- ductor ; that is to say, when a quantity of electricity flows against the resistance of a conductor, a certain amount of electrical energy is transformed into lieat energy. This fact becomes very noticeable at times, for the conductor may become exceedingly hot — so hot, indeed, that unless due care is exercised the wire carrying the current may be melted by the great heat produced. 2341. The actual amount of heat developed is an exact equivalent of the work done in overcoming the resist- ance of the conductor, and varies directly as that resistance. For example, take two wires, the resistance of one being twice that of the other, and send currents of equal strengths through each. The amount of heat developed in the wire of higher resistance will be twice that developed in ELECTRICITY AND MAGNETISM. 1509 the wire offering the lower resistance. The distinguished scientist y(9?/;/r, after whom the practical unit of energy is named, made elaborate experiments to determine exactly what relation existed between the mechanical or electrical work done and the heat thereby generated. 2342. Mechanical Equivalent of Heat. — Joule found, as shown in Art. 1148, that the heat which is gen- erated by doing 778 foot-pounds of work is exactly equal to the amount of heat required to raise the temperature of 1 pound of pure water 1° F., at or near 39° F., the tempera- ture of its maximum density. This amount of heat is called one British Thermal Unit (written B. T. U.). Therefore, we have the relation 778 foot-pounds = 1 B. T. U. 1 foot-pound = .001285 B. T. U. This relation is called the mechanical equivalent of heat. 2343. Electrical Equivalent of Heat; Joule's Law. — Upon investigating the amount of heat generated by an electrical current when overcoming the resistance of a conductor. Joule found that one ampere of current flowing through one ohm of resistance during the time of one second always developed .0009477 British Thermal Unit. He found furthermore that the development of heat was proportional, 1. To the resistance of the conductor ; 3. To the square of the current strength ; 3, To the time during which the current flows ; so that if //"== B. T. U. developed in the circuit ; C = current in amperes ; R = resistance in ohms ; / = time in seconds, then the general formula for the development of heat in any electrical circuit is given by what is called Joule's La^v,. ^=.0009477 (T'ie/. (418.) 1510 PRINCIPLES OF Example. — Determine how many B. T. XJ. are developed in an elec- trical circuit having a resistance of 180 ohms, through which a current of 2 amperes flows for 1 minute. Solution. — / = 60 seconds ; C=2 ; 7? = 180 ; hence, by formula 418, the heat units developed are 11= .0009477 X 2 X 3 X 180 X 60 := 40.94 B. T. U. Ans. 2344. Referring back to Art. 2335, we find that the work in joules performed in an electrical circuit is given by a formula similar to formula 418 ; in fact, we find that the work in joules is proportional to the same factors as the heat development. This relation is best made clear by solv- ing the following Example. — Given an electrical circuit having a resistance of 2 ohms, in which a current of 2 amperes flows for 2 seconds, determine (a) the work in joules done in this circuit, and (d) the number of B. T. U. developed in the circuit. Solution. — / = 3; C=2 ; R = 2 ; then, by formula 414, the work in joules, («:)/= C2 7?/ = 3x 2x2x 2 = 16 joules. Ans. And by for- mula 41 8, {b) ^=.0009477 C^ R t = .0009477 x2x2x3X2 =.0151632 B. T. U. Ans. 2345. We therefore see that the circuit of the prece- ding example develops .0151033 heat-unit when 16 joules of work are done. Consequently, we have the relation 16 joules = .0151632 B. T. U. •, or, 1 joule = .0009477 B. T. U. ; and, conversely, 1 B.T.U.= 1,055.20 joules. Now, since we know that .7373 foot-pound of mechanical work is equivalent to 1 joule of electrical, and since 1 joule of electrical work equals .0009477 heat-unit, it is clear that we have established a complete relation between me-chanical work, electrical work, and heat energy, so that any one of these three energies can be mathematically expressed in terms of the others. These relations are expressed clearly by Table 78. 2346. The following table will be found very useful for all examples involving transformations of energy : ELECTRICITY AND MAGNETISM. 1511 TABLE 78. ENERGY EQUIVALENTS. Heat Energy. Mechanical Energy. Electrical Energy. 1.000000 B.T.U. = 778.0000 foot-pounds = 1,055.2000 joules. .001285 B.T.U.= 1.0000 foot-pound = 1.3563 joules. . 0009477 B.T.U.= .7373 foot-pound = 1.0000 joule. Example. — Given an electrical circuit having a resistance of 3 ohms, through which a current of 5 amperes flows for 1 hour, determine (a) the work done in joules; (d) how many foot-pounds this work is equivalent to; (c) the number of heat-units developed. Solution. — / = 3,600 seconds; C= 5 amperes; 7? = 3 ohms; then, by formula 414, the work in joules (rt) /= C^ 7? / = 5 X 5 X 3 X 3,600 = 270,000 joules. Ans. According to Table 78, 1 joule = .7373 foot-pound; hence, {d) 270,000 X .7373 = 199,071 foot-pounds. Ans. According to Table 78, 1 foot-pound is equivalent to a heat develop- ment of .001285 B. T. U. ; hence, {c) 199,071 X .001285 = 255.81 B. T. U. Ans. ELECTRICAL POUVER. 2347. The total amount of work done is independent of time (see Art. 954) ; that is to say, the total work is the same whether it is done in one minute or in one year. But when various amounts of work, done in different times, are to be compared to a common standard of power, the element of time must be considered. Similarly in the electrical circuit; the total number of joules of work done is independent of the time, but when there are several circuits, the work of each of which is to be compared to a standard, the element of time in which this work is done must be considered. 2348. In practical mectianical work the unit of time is always one minute, and the unit which measures the work performed in a given time is the foot-pound per 1512 PRINCIPLES OF minute. This unit is called the unit of mechanical power. Power is, therefore, rate of doing work, and hence the power exerted can always be determined by dividing the work done in foot-pounds by the time in minutes required to do it. 2349. In practical electrical work the unit of time is the second, and the unit which measures the work performed in a given time is the joule per second. This unit is called the unit of electrical po^ver, and has been named the watt. Hence, if in a certain electrical circuit, say 1,000 joules of work are done in 10 seconds, the power exerted is 1,000 -H 10 = 100 joules per second, or 100 watts. If in another circuit the same work is done in 5 seconds, the power there exerted is 1,000 -4- 5 = 200 joules per second, or 200 watts — just twice as much. Hence, we say that the power exerted in the second circuit is twice that exerted in the first ; and we understand thereby that if in both circuits work is done for the same length of time, the second circuit will do twice as much work as the first. 3350. Equation of Power for Electrical Circuit. — The equation or formula expressing the power exerted in any electrical circuit is determined as follows : According to Art. 2349, electrical power is expressed by watts = joules per second. But, according to Art. 2333, joules = volt-coulombs, and hence joules per second = volt-coulombs per second. Therefore, also, watts = volt-coulombs per second. Now, according to Art. 2280, coulombs per second = amperes. Inserting this value in the next before the last equatJOn above, we have, finally, watts = volts X amperes % ELECTRICITY AND MAGNETISM. 1513 or, if W= total watts exerted in the circuit ; £ =z volts of electromotive force ; C = current in amperes, then, IV=£C, (419.) which may be expressed by the following 2351. Rule. — hi every electrical circuit the -poiver in watts is equal to the product obtained by multiplying the cur- rent in amperes by the electromotive force in volts. Example. — What is the power in watts in an electrical circuit in which .6 ampere flows under a pressure of 110 volts ? Solution. — C=.6 ; E= 110 ; hence, by formula 419, W— ^ C = .6 X 110 = 66 watts. Ans. 2352. When \}vl^ power is to be expressed by the cur- rent and resistance., the formula is obtained as follows : According to formula 419, we have W ■= E C, and accord- ing to formula 411,^= C R ; substituting this value of E =^ C R'ln formula 419, we have W=CxCxR=C'R, (420.) which may be expressed by the following Rule. — In every electrical circuit the power in watts is equal to the prodiLct obtained by multiplying the square of the current strength in amperes by the resistance of the circuit in ohms. Example. — Determine the power expended in watts in an electrical circuit having a resistance of 183.3 ohms, through which a current of .6 ampere is flowing. Solution. — C=.6 ampere ; R = 18B.% ohms ; hence, by formula 420, fF= C'^i? = . 6 X. 6x183.3 = 65.99 watts. Ans. Note.— It will be observed that this result is the same, within decimal limits, as that obtained from the example in Art. ;2351. It is, in fact, the same circuit. 2353. When the power is to be expressed by the electro- motive force and resistance, the formula is obtained as follows: According to formula 419, we have W=EC, E and, according to formula 409, C= -^; substituting this 1514 PRINCIPLES OF E value of (7= -^ in formula 419, we have W=^E = ^, (421.) which may be expressed by the following Rule. — In every electrical circuit the power in watts is equal to the quotient obtained by dividing the square of the electromotive force in volts by the resistance in ohms. Example. — Determine the power in watts of an electrical circuit having a resistance of 183.3 ohms and an electromotive force of 110 volts. Solution. — .£"=110 volts; i? = 183.3 ohms; hence, by formula 421, ,,. E^ 110 X 110 ac^c .. A W=-j^— — ^p^ „ ■ = 66.0 watts. Ans. K loo. o Note. — Observe that this is again exactly the same as the results obtained from the examples in Arts. 2351 and 2352. It is, in fact, the same example in all three cases. ELECTRICAL HORSEPOIVER. 2354. In mechanical calculations the foot-pound per minute is found too small a unit for practical use ; there- fore a unit has been adopted having the value of 33,000 foot-pounds per minute, which is about equivalent to the power a strong horse can exert. This unit is, therefore, named the liorsepo^ver. (See Art. 955.) 2355. Similarly in electrical calculations the Joule per second, that is, the -watt, is found too small a unit for practical use ; therefore a unit has been adopted having a value exactly equivalent to the value of the mechanical horsepower. This unit is obtained by transforming 1 horse- power into watts as follows : 1 mechanical horsepower = 33,000 foot-pounds per minute. 33 000 But 33,000 foot-pounds per minute = — '—- — = 550 foot-pounds per second. Hence, 1 horsepower = 550 foot-pounds per second, or 1 foot-pound per second = :zirR . And, ooO ELECTRICITY AND MAGNETISM. 1515 according to Table 78, 1 joule ==.7373 foot-pound; hence, 1 joule per second or 1 watt = .7373 foot-pound per second, and, hence, 1 foot-pound per second = ^^ . We have, therefore, found the value of the foot-pound per second expressed both in horsepower and in watts ; so that - , ,1 horsepower 1 watt 1 foot-pound per second = —^ = , ooO •to Jo from which we find the value of 550 1 mechanical horsepower — watts = 746 watts. (422») , i o i o This value, 746 watts, is termed one electrical horse- power. 2356. The power exerted in any electrical circuit may now be expressed in horsepower units by the following Rule. — To express the rate of doing electrical work in horsepower units, find the number of watts and divide the result by 7Jf6. If H. P. = horsepower; rF= watts, W H.P.=^. (423.) Since W has the various values given by formulas 419, 420, and 421, the horsepower may also be expressed by three other equations: H.P.=^. (424.) H,.P. =^. (425.) ^•^• = 7^- (426.) 2357. "Before giving examples on the application of the foregoing formulas, it must be mentioned that a practical 1516 PRINCIPLES OP unit of electrical power in extended use is the kilowatt, having the value of 1000 watts. This unit is usually written K. W., and is related to the electrical horsepower by the following equations: 1 K. W. = 1,000 watts = 1.34 H. P. 1 H. P. = 746 watts = .746 K. W. Example. — The common incandescent electric light consists of a glass bulb containing a simple carbon conductor, the two free ends of which are connected to the source of the electric current. When the current flows through this conductor, it heats it to such a degree that it becomes white hot, or, as such a state is called, incandescent. If this conductor has a resistance of 189.06 ohms and the lamp is supplied with an electromotive force of 110 volts, determine the following points of interest : (a) What current does the lamp take ? (d) How many watts does it consume ? (r) How many B. T. U. are developed per second ? (d) How many such lamps would one electrical horse- power keep burning ? (e) What is the mechanical equivalent of the heat developed per second in the lamp? (/) For how many such lamps would 10 K.W. suffice? Note. — Regard the lamp as a simple conductor of the stated resist- ance in solving all problems relating to it. Solution.— (a) ^= 110 ; i? = 189.06 ; hence, by formula 409, C = E 110 .oo A :^ = 189:06 = --^^'^"^p^^"- ^^'• ((5) By solution (rt), C=. 582; ^=110; hence, by formula 419, fF=C^ =.582x110 = 64. 03 watts. Ans. {c) By solution {a\ C=.582 ; R- 189.06 ; / = 1 second ; hence, by formula 418, the number of British Thermal Units, H= .0009477 C^ Rf = .0000477 X .582 X .582 X 189.06 X 1 = .0607 B. T. U. Ans. {d) By solution {b), the lamp consumes 64.02 watts. According to formula 422, 1 horsepower = 746 watts ; hence, 1 horsepower will supply -TTi-^ = about 12 such lamps. Ans. '^^ ■' 64.02 (e) By solution {c), the number of B. T. U. developed per second = .060718. By Table 78, 1 B. T. U. = 778 foot-pounds ; hence, .060718 B. T, U. = .0607 X "^"^S = 47.22 foot-pounds per second. Ans. (/) According to Art. 2357, 1 K.W. =1,000 watts; hence, 10 K. W. = 10 X 1,000 = 10,000 watts. But by solution (d), 1 lamp requires 64.02 watts ; hence, 10 K. W, will suffice for ^^^^ = about 156 such lamps. Ans. ELECTRICITY AND MAGNETISM. 1517 EXAMPLES FOR PRACTICE. 1. Find the rate of doing work in watts when a current of 40 amperes flows against a resistance of 2+ ohms. Ans. 4,000 watts. 2. Express the rate of doing work in horsepower units when a cur- rent of electricity loses a potential of 20 volts in passing through a resistance of 1 ohm. Ans. .5362 horsepower. 3. How many watts in 4.5 horsepower ? Ans. 3,357 watts. 4. The power in an electric circuit is equivalent to 4 horsepower. If a current of 30 amperes is flowing, what is the electromotive force developed ? Ans, 99.4667 volts. MAGNETISM. NATURAL MAGNETS. 2358. Near the town of Magnesia, in Asia Minor, the ancients found an ore which possessed a remarkable attract- ive power for iron. This attractive power they named magnetism, and a piece of ore having this power was termed a magnet. The ore itself has since been named magnetite, and has been found to be a chemical combina- tion of about 72 parts of iron and 28 parts of oxygen, by weight. 2359. A still more remarkable discovery was made concerning this ore. It was found that when a piece of the ore was hung from a thread, it invariably swung around to such a position that one of its ends pointed north and the other south. It was also observed that the same end always pointed north. Due to this fact, small pieces of the ore so suspended were used in navigation. Ships could be steered in any direction by its aid, because the direction of the north was always shown by one end of the stone. From this fact the name lodestone (meaning ^''leading stone"') was given to the natural ore. ARTIFICIAL MAGNETS. 2360. When a bar or needle of hardened steel is rubbed with a piece of lodestone, it acquires magnetic prop- erties similar to those of the lodestone, without the latter losing any of its own magnetism. Such bars are called artificial magnets. 1518 PRINCIPLES OF Artificial magnets which retain their magnetism for a long time are called perinanent magnets. The common form of artificial magnets is a bar of steel bent into the shape of a horseshoe and then hardened and magnetized. A piece of soft iron called an armature, or keeper, is placed across the two free ends, which helps to prevent the magnet from losing its magnetism. 2361. If a bar magnet is dipped into iron filings, the filings are attracted towards the two ends and adhere there in tufts, while towards the center of the bar, half way between the ends, there is no such tendency. (See Fig. 918.) Fig. 918. That part of the magnet where there is no apparent mag- netic attraction is called the neutral line, and the parts around the ends where the attraction is greatest are called poles. An im^aginary line drawn through the center of the magnet from end to end, connecting the two poles together, is termed the axis of magnetism. 2302. The magnetic compass consists of a mag- netized steel needle, Fig. 919, resting upon a fine point, so as to turn freely in a horizontal plane. When not in the vicinity of other mag- nets or magnetized iron, the needle will always come to rest with one end pointing towards the north and the other towards the south. The end pointing northwards is the north-seek- ing pole, commonly called the north Fig. 919. ELECTRICITY AND MAGNETISM. 1519 pole, and the opposite end is called the soutti pole. This polarity applies as well to all magnets. 2363. If the north pole of one magnet is brought near the south pole of another magnet, attraction takes place ; but if two north poles or two south poles are brought together, they repel each other. In general, like magnetic poles repel one aiiotJier ; tinlike poles attract. )2364. The earth is a great magnet whose magnetic poles coincide nearly but not quite with the true geographi- cal north and south poles. By the laws of attraction and repulsion, given in Art. 3363, it is seen why a freely sus- pended magnet, therefore, will always point in a north-south direction. 2365. It is impossible to produce a magnet with only one pole. If a long bar magnet is broken into any number of parts, each part will still be a magnet and have two poles, a north and a south. 2366. Magnetic substances are those substances which are not in themselves magnets, that is, they do not possess poles and neutral lines, but, nevertheless, are capa- ble of being attracted by a magnet. A piece of soft iron will attract either pole of a magnet, or will itself be attracted towards a pole of a magnet, but when not in the vicinity of a magnet it has no defined poles. In addition to iron and its alloys, the following metals are magnetic substances: nickel^ cobalt^ manganese^ cerium^ daxdicJiromiiun. These metals, however, possess magnetic properties in a very inferior degree, compared with iron and its alloys. All other known substances are called non-magnetic substances. 2367. The space surrounding a magnet is called a magnetic field ; or, in other words, a magnetic field is a place where a freely suspended magnetic needle will always come to rest pointing in the same direction. 1520 PRINCIPLES OF 2368. to act in MAGNETIC LINES OF FORCE. Magnetic attractions and repulsions are assumed a definite direction and along imaginary lines called lines of magnetic force, or simply lines of forxe. Their position in any plane may be shown by placing a sheet of paper over a magnet, and sprinkling fine iron filings over the paper. In the case of a bar magnet lying on its side, the iron filings will ar- range themselves in curved lines Fig. 920. extending from the north to the south poles, as shown in Fig. 920. A view of the magnetic field looking towards either pole of a bar magnet would exhibit merely radial lines, as shown by the iron filings in Fig. 921. Every line of force is assumed to pass out from the north pole, make a complete circuit through the surrounding medium, and return into the south pole; from thence through the magnet to the north pole again, as shown in Fig. 922. This is called the direction of the lines of force, and the path which they take is called the mag- netic circuit. Every line of force forms a complete magnetic circuit by itself. The direction of the lines of force in any magnetic field can be traced by a small freely suspended magnetic needle, or a small compass such as is shown by in in Fig. 922. The north pole of the needle will always point in the direction of the lines of force, the length of the needle lying parallel or tangent to the lines of force at that place. If the needle be moved bodily in the direction towards which its north pole points, its center or pivot will describe a path coinciding 11 '",'^///^ Fig. 921. ELECTRICITY AND MAGNETISM. 1521 with the direction of the lines of force along that part of the magnetic field. In Fig. 922 the arrow-heads indicate the direction of the lines of force. It will be noted that in Figs. 930, 921, and 923, the magnetic lines are shown in — . 20,000=35,343. Ans. MAGNETIC UNITS. 2379. To properly define the strength of a magnet pole, a unit must be adopted by which this strength can be expressed. By universal agreement a magnet pole having unit strength is defined as a pole which meets the follow- ing conditions: 1. It must, when placed at a distance of 1 centimeter from a similar pole having equal strength repel this pole with a force of 1 dyne. 2. It must, when placed in the center of a sphere having a radius of 1 centimeter, send out such a number of lines of force that exactly 1 line of force passes through every squart centimeter of the surface of the sphere. 2380. Number of Magnetic Lines per Unit Pole. — Directly from condition 2, of the preceding article, the number of magnetic lines per unit pole may be calcu- lated. It is there stated that a sphere of 1 centimeter radius receives 1 line of force per square centimeter of surface when a unit pole is situated at its center. This is equiva- lent to saying that a unit pole has as many magnetic lines as there are square centimeters on the surface of a sphere ELECTRICITY AND MAGNETISM. 1527 having a radius of 1 centimeter. If a sphere has a radius = 1 cm., its diameter = 2 cm. By the rule of Art. 81 7, area of surface = diameter squared X 3.1416; hence, area of sur- face of our sphere = 2^ X 3.1416 = 12.5664 square centi- meters. But, as stated before, number of square centimeters of surface equal number of magnetic lines, whereby we have the Rule. — Every magnet pole of tmit strength has 12.5664 -magnetic lines. Note. — In this result, fractions of magnetic lines appear. Such fractions of magnetic lines are often obtained in magnetic calculations. They are treated in tlie same manner as other fractions are. Their significance may be made clear by the following consideration : Sup- pose we have a piece of cloth 1 inch wide and 1 inch long, that is, 1 inch square. Let us further suppose that, say, 13 pins were stuck vertically into this cloth. We could then say there are 13 pins per square inch. Assume now that one of these pins was removed, split lengthAvise in half, and the one half again stuck into the cloth. Now we would say that there were only 12i, that is, 12.5 pins per square inch of cloth. Similarly, in the rule above, when we speak of 12.5664 magnetic lines, we mean that a little over Vl\ magnetic lines are sent out from every magnet pole of unit strength. 2381 . Unit Density of Magnetism.— In Art. 2377 density of magnetism was defined as being the number of lines of force passing through unit area. To express the magnetic density definitely, however, we must have a unit whereby to measure it. This unit is derived from condition 2, in Art. 2379, where it is stated that a unit magnet pole sends 1 line of force through every square centimeter of the surface of the sphere there mentioned. In accordance with this, unit density of magnetism is a density of 1 line of force per square centimeter. Since 1 square inch equals 6.452 square centimeters, this is equivalent to a density of 6.452 lines of force per square inch, so that we have the Rule. — Unit density of magnetism is a density of 6.^52 lines of force per square inch. When every square inch cross-section of a magnetized substance has exactly the same number of lines of force passing through it, the magnetic density of the substance is said to be uniform. 1528 PRINCIPLES OF When this is not the case, the density is said to be non- uniform. 2382. Relation Bet^veen Electrical and Mag- netic Units. — In Art. 2379 a magnet pole of unit strength is defined as exerting, under the condition stated, a force of 1 dyne. In Art. 2262, however, the dyne is given as the fundamental unit of force in general. This fact makes it possible to compare magnetic forces to both electrical and mechanical forces ; for 1 dyne = unit of magnetic force; 1 dyne = unit of force in general (see Art. 2262). 1 dyne exerted through 1 centimeter = 1 dyne cm. = 1 erg = unit of work (Art. 2263). 10,000,000 ergs =-1 joule = unit of electrical work (Art. 2330). 1.356 joules = 1 foot-pound = unit of mechanical work (Arts. 2333 and 2348). We thus have given the relation between dynes, ergs, joules, and foot-pounds, or, in other words, the relation between force and work for magnetic, electrical, and mechanical quantities. Example. — Two similar magnet poles 3 centimeters apart repel each other with a force o^ 4 dynes, {a) How many ergs of work must be expended to bring the one pole up to the other one against this repul- sion ? (i) How many foot-pounds of work is this equivalent to ? Solution. — {a) To bring one pole up to the other through a distance of 3 centimeters, a force of 4 dynes must be overcome through a dis- tance of 3 centimeters. By Art. 3263, the work done equals 4x3 = 12 dyne centimeters, or 12 ergs. Ans. {d} By Art. 2330, 1 joule = 10,000,000 ergs ; hence, 1 erg = .0000001 joule. By solution (a) the work done is 12 ergs =: 12 X .0000001 = .0000012 joule. By Art. 2346, Table 78, 1 joule = .7373 foot-pound. Hence, the work done in foot-pounds equals .0000012 X .7373 - .00000088476 foot-pound. Ans. ELECTROMAGIVETISM. 2383. If a conductor conveying a current of electricity be brought near a freely suspended magnetic needle, the nee- dle will tend to place itself at right angles to the conductor, as indicated by the arrows in Fig. 927 ; or, in general, ELECTRICITY AND MAGNETISM. 1529 an electric current and a magnet exert a mutual force upon each other. From the definition given in Art. 2367, the ^ Fig. 927. Space surrounding the conductor is a magnetic field. If the conductor is threaded up through a piece of cardboard, and iron filings are sprinkled on the cardboard, they will arrange them- selves in concentric circles around the wire, as shown in Fig. 928. This effect will be observed throughout the whole length of the conductor, and is caused en- tirely by the current. In fact, every conductor conveying a t current of electricity can be imagined as completely surrounded >;;;n^" 10,000 12.0 833.3 20,000 15.0 1,333.3 30,000 18.8 1,595.7 40,000 23.0 1,739.1 50,000 30.0 1,666.6 60,000 44.0 1,363.6 70,000 65.0 1,076.9 80,000 104.0 769.2 90,000 200.0 450.0 100,000 430.0 232.6 105,000 630.0 166.6 110,000 1,035.0 106.3 CURVES OF MAGNETIZATION. 2402. The most convenient mode of representing the magnetic qualities of iron and other magnetic substances is to plot the curves of magnetization on two sheets of cross- section paper. On one sheet are plotted saturation curves which indicate the relation of the intensity of the magnetomotive force H to the magnetic density B ; on the other sheet are plotted the resulting permeability curves which indicate the relation of the permeability \i to the mag- netic density B. The cross-section paper should be divided into squares of equal dimensions of about \ inch on a side, although it will be more accurate if these squares are still further divided ELECTRICITY AND MAGNETISM. 1555 into smaller ones yV inch on a side. The sheets should be at least 11 inches wide by 14 inches high. The horizontal divisions are called abscissas, and are in- dicated by numbers placed in the margin either above or lOUUUV — ^ .< * ;- ^ - •-. f it- i 3. s *. ii- « s A ^TJ ea e ^ ft ^ U: * / /. / i- M * i 4 ^ i ~«; / / .?• « ■s s t •■5. ••>■ / / k S' ^ « 'I' ••. ■* ^- S J L / 4 > -fs^ 4 z - * 1 i ,-. fr -. ___, -— — ooovo / '- -i ^ '7^ aS f ' r I " £ h ^^ ^ &1- a'J ■• ^ ■=> 1 ■ y X ^- ^ .- - ■ / 5. '■ / - — / 7 ^ ' / / / lOOOO i / 0^ / _ _ _ _ [h _ Fig. 952. below the chart. The vertical divisions are called ordi- nates, and are represented by marginal numbers on the right or left hand of the chart. The terms abscissa and ordinate, therefore, express clearly which set of divisions, the horizontal or vertical, is referred to, instead of designating the rows of figures with reference to relative position. 1556 PRINCIPLES OF 2403. On the sheet for the saturation curves, Fig. 952 (reduced), the divisions of the abscissas represent the dif- ferent values of H, and each -l-inch division represents 50 H. 1 140000 130000 120000 \ \ v 110000 \ \ \\ \, « tooooo ^ ^ \, V \ \ 90000 \ \ N \ s. \, 80000 B \, ^ \ \ \ ■^^ 70000 \ V, \ \ \ aoooo \ s \ y \ N^ \ \ X 50000 \ '\ % \ N \ \ \ \ 5 \ 40000 \ L) ^ \ \ _J^ / / / soooo o /' / 1^ A "S 4* / s^ 4 ^^ BOOOO / ^^ ^J r ^ f ^^ 1 >o / / 4 ^ -^ ro^ 10000 / B / '^ [\1" ^0"^ 9^' A . / ^ ■ — ' ^ r"l " i" 200 400 600 800 10001200 14001600180020002200 Pig. 953. Starting with the extreme lower left-hand line as zero, the remaining lines are numbered consecutively in units of 50. The ordinates represent the different values of the magnetic density B, and each -^-inch division represents 5,000 B. ELECTRICITY AND MAGNETISM. 1557 Starting with the bottom line as zero, tne remaining lines are numbered consecutively in units of 5,000. 2404. On the sheet for the permeability curves, Fig. 953 (reduced), the divisions of the abscissas represent the different values of fi and each |-inch division represents 100 n. Starting with the extreme left-hand line as zero, the remaining lines are numbered consecutively in units of 100. The ordinates represent the different values of B, and are numbered as described for B on the sheet for saturation curves. METHOn OF PLOTTING CURVES. 2405. In the first set of readings on cast iron. Table 79, H = 64 and B = 10,000. A dot is placed on the bottom line, Fig. 952, representing 64 H. The value B = 10,000, when pointed off on the extreme left-hand vertical line, is repre- sented by two divisions, and the point falls on the line marked 10,000. This line is followed along horizontally until a point is reached which is directly over the dot on the bottom line. A heavy dot placed here will indicate the combined values of B and H at the first readings. The remaining readings in Table 79 are plotted in a similar manner, and afterwards all the heavy dots are joined together by one long curve. All the intermediate values of H and the corresponding values of B are now indicated by the curved line. For ex- ample, in the saturation curve for cast iron, where H is 350, the corresponding value of B is about 46,000 lines of force per square inch. The same method is used for plotting the rest of the saturation curves in Fig. 952 and the permeability curves in Fig. 953. ACCURACY OF CURVES. 2406. If cross-section paper with -l-inch divisions is used, the curves should be plotted and read with the help of a scale divided into tenths of an inch. Under these con- ditions, points plotted within -^^ of an inch of their correct position on the sheet will be considered as accurate. All magnetic calculations in which readings are used that 1558 PRINCIPLES OF are taken from the saturation and permeability curve sheets will be considered accurate when within %.bfo of the correct figures. CALCULATION OF THE MAGNETIC CIRCUIT. 2407. The calculation of a magnetic circuit is a more complicated problem than that of the electric circuit, but the operation is much simplified by treating the magnetic circuit in the same manner as an electric one and applying the principle of Ohm's law; it must be understood, however, that it is only the principle oi Ohm's law that is applied, and not any of the actual electrical quantities. The magnetomotive force has been described as that which produces the magnetism, but it will now be considered as that zuhich tends to drive the lines of force along the magnetic circuit against a resistance. The resistance, or that which opposes the lines of force, is called reluctance, to distinguish it from electrical resistance. 2408. The quantity of magnetism or the total num- ber of lines of force which are driven along the magnetic circuit is called the induction, and is found by dividing the magnetomotive force by the reluctance. Or, expressed algebraically, it will give the formula T- 1 . magnetomotive force Induction = • — ^^ . reluctance The numerical value for the magnetomotive force is always 3.192 X ampere-turns. 2409. The reluctance of the magnetic circuit depends upon three quantities: (1) the length of the circuit, (2) the sectional area of the circuit, and (3) the permeability of the substances which form the circuit. The reluctance : Increases as the length of the magnetic circuit increases. Decreases as the sectional area increases. Decreases as tlie permeability increases. If /represents the length of a magnetic circuit in incheSj ELECTRICITY AND MAGNETISM. 1559 A its sectional area in square inches, and fi its permeability, the reluctance of the circuit can be expressed by the formula Reluctance, R =— j-^ . (431.) A X [J' ' Writing N for the induction, a-t for the ampere-turns, and substituting the values cf the magnetomotive force and reluctance, the formula for the magnetic circuit, given in Art. 240S, becomes N= M^yiifi. (432.) In practice, the inditction, or the total number of lines of force, is established in the beginning by the requirements of the magnet, and, therefore, it is necessary to find the num- ber of ampere-turns required to drive that induction along the magnetic circuit. By transposing, the ampere-turns The magnetic circuit, however, is generally a compound one ; that is, it is composed of two or more substances. The total reluctance of the circuit would then be the sum of the separate reluctances of each substance. Let —. — 5- — ■ = R, be the reluctance of the first substance, —. — ^ = R„ be the relucta ice of the second, and so on. Then, the sum of the separate reluctances is R^ -|- R^ 4- ^tc. Therefore, the ampere-turns :?-/ are given by the formula ampere-turns a-t = ., X (R , + R, -+- etc. ). (433.) 2410. After the dimensions and induction of a magnet, have been established by the requirements, it is necessary to know the permeabilities jt^j, n^, etc., before the ampere- turns can be calculated. The permeability depends not only upon the kind and quality of the magnetic substance, but also upon the density of the lines of force. The density 1560 PRINCIPLES OP is found (see formula 427) by dividing the total numbei of lines of force which pass through a circuit by its sec- tional area. Consequently, the densities in the different substances which compose the magnetic circuit will be N N -j—, —^, etc. Then, referring to the curves in Fig. 953, the permeability of any of the different metals, corresponding to their densities, can be found. The permeability of all non-magnetic substances is always 1, irrespective of the density of the lines of force. Example. — Find the ampere-turns required to drive an induction of 55,000 lines of force through the circuit of a horseshoe magnet made Fig. 954. of cast iron, when a bar of wrought iron is placed across its two ends, but separated from them by an air-gap of ^ inch. The dimensions of the magnet and bar are shown in Fig. 954. Solution. — This magnetic circuit is a compound one, composed of three different substances: (1) the cast-iron magnet, (2) the wrought- iron bar, and (3) the two air-gaps. Let N — total induction ; /i, A, and /a = the average lengths of circuit in magnet, bar, and total air-gap, respectively ; Ax, Ai, and A^ = the sectional areas, respectively ; B;, B2, and 83 = the magnetic densities, respectively ; Ri, Ra, and R3 = the reluctances, respectively ; ^1, ^2, and iiz = the permeabilities, when the densities are Bi, 89 and 83, respectively. ELECTRICITY AND MAGNETISM. 15G1 iV By formula 433, the ampere-turns a-t = o-Tqo ^ C* + Ra + Rs)- By formula 431, the reluctance of the circuit in the cast-iron mag- /i . , , , , . . , 5 X 3.1416 net IS Ri = — ; •. The length of the circuit = A = -^ 1- 6 = 13.854 inches. The sectional ai ea = ^i = 2 X 1 == 3 square inches. By formula 427, the density Bi = -r- = -^ — = 27,500 lines of force per square inch. From Fig, 953, // is about 180, when B = 27,500 in cast iron. Then the reluctance R. = -^- = .^^, = .03848. AiXfh yxl80 The reluctance of the circuit in the wrought-iron bar is Ra = — ^2 X/«2* The length of the circuit = 4 = 5 + .25 + .25 = 5.5 inches. The sec- tional area =A.= 2 X.5 = 1 square inch. B^^ ^ = ^= 55,000 lines A2 1 of force per square inch. From Fig. 953, // is about 1,520 when B = 55,000 in wrought iron. Then, by formula 431, the reluctance, R, = , ^' = :f-4^ = .00362. AiX/^i 1 X 1,520 Since one magnetizing coil is used for the whole magnetic circuit, the two air-gaps are added together, and in the calculations a single air-gap of double length, that is, 2 X i =^ i inch, is considered. The reluctance of the circuit in the air-gap is R3 = —, — ^ . The length of the circuit = ^ = .5 inch. The sectional area = ^3 = 3x1 = 2 square inches. In the case of air, the permeability /^a = 1. / 5 The reluctance is then = —, — = k- — 5 = -SS. A^Xl^s 2X1 By formula 433, the necessary ampere-turns = "i^ 000 ^5 000 ^~ X (.03848 + .00362 + .25) = ^^^^ x .2921 = 5,038.05, which means that a magnetizing force of 5,033.05 ampere-turns will have to circulate around the magnet arms to force 55,000 lines of force through the magnetic circuit. Ans. RESIDUAL MAGNETISM. 241 1. Residual magnetism is the magnetism which a magnetic substance retains after being removed from a magnetic field. In general, soft iron and annealed steel re- tain only a small amount of magnetism, and in some cases 1562 PRINCIPLES OF the residual magnetism is imperceptible, A closed magnetic circuit of soft iron, that is, a magnetic circuit which consists of soft iron throughout its entire length, will exhibit a large amount of residual magnetism so long as the circuit remains unbroken. This tendency can be shown by a U-shaped electromagnet of soft iron, across the two ends of which is placed a well-fitted keeper. If the circuit is magnetized by a current of electricity which is suddenly turned off, the keeper will still adhere to the ends, and may even require considerable force to detach it. But when once it is de- tached and the circuit broken, the keeper will not adhere again without the aid of the current. Chilled iron and hardened steel retain residual magnetism in large quantities. Artificial or permanent magnets are made by placing a piece of hardened steel in a dense mag- netic field or in contact with another magnet. Lodestone is the result of a natural residual magnetism. HYSTERESIS. 2412. When the magnetism of an electromagnet is rapidly reversed, that is, when the direction of the lines of force is suddenly changed several times in rapid succession by changing the direction of the magnetizing current, the iron or steel becomes heated, and a certain amount of energy will be expended. This effect is due to a kind of internal magnetic friction, by reason of which the rapid changes of magnetism cause the iron to grow hot. This effect is called hysteresis (histeree'-sis). 2413. The energy expended by hysteresis is furnished by the force which causes the change in the magnetism ; in the case of an electromagnet, where the magnetism is re- versed by the magnetizing force, the energy is supplied by the magnetizing current. The complete operation of magnetizing and demagneti- zing an electromagnet in one direction, then magnetizing and demagnetizing in the opposite direction by reversing the magnetizing current, is called a cycle of magnetism. ELECTRICITY AND MAGNETISM. 1563 One cycle is made by two reversals of magnetism. For ex- ample, reversing the magnetism 40 times in one second will make 20 cycles in one second. The loss of energy by hysteresis depends (1) upon the hardness and quality of the magnetic substance in the core ; (2) upon the amount of metal magnetized; (3) upon the number of cycles per second, and (4) upon the density in the substance when the magnetizing force is not changing. 2414. Table 83 gives the power in watts expended by hysteresis in soft sheet iron when subjected to a rapid succes- sion of cycles of magnetism at different magnetic densities. The watts expended are directly proportional to the number of cycles per second and to the number of cubic inches of iron magnetized. TABLE 83. Watts Expended B per Cubic Inch, 1 Cycle per Sec. 25,800 .002320 32,250 .002715 38,700 .004340 45,150 .005320 51,600 .006370 64,500 .009040 77,400 .011920 90,300 .015180 103,200 .018780 • 109,650 .022850 116,100 .028150 Let zv = power in watts expended per cubic inch per cycle; V = volume in cubic inches; n = cycles per second ; J>F= total watts expended. Then, W=^w v n. (434.) 1564 PRINCIPLES OF Rule. — To find the pozver expended by hysteresis in sheet iron at a given stage of magnetization, multiply the watts expended at that stage, as given in Table 83, or Fig. 955, by i200O0t 110000 100000 90000 80000 70000 60000 50000 40000 3O000 20000 10000 ^ y /- / / / / / ) 1 / / / / R ^ / / / / / / / / / / ^005 .010 ,010 ,02O ,025 .030 Watts per cubic inch for one cycle. Fig. 955. ,QSS .040 the number of cubic inches of iron in the magnet and the number of cycles per second. The readings given in Table 83 are plotted on a sheet of cross-section paper in Fig. 955, and the various points are connected by a curved line. The ordinates represent the ELECTRICITY AND MAGNETISM. 1565 different densities B, and the abscissas the corresponding number of watts expended in one cubic inch of iron for one cycle per second. By referring to the curve, all the inter- mediate values of B and the corresponding watts expended can be determined. Example. — In an electromagnet, made with sheets of soft iron, there are 18 cubic inches of iron. Find the power in watts expended when the magnetizing current is reversed 70 times per second and the magnetism reaches a density of 90,000 lines of force per square inch. Solution. — 70 reversals are equivalent to 35 cycles = n. From Fig. 955, the watts expended per cubic inch for one cycle, at a density of 90,000, are equal to .015. Then, by formula 434, .the total power expended, W = .015 X 18 X 35 = 9.45 watts. Ans. LEAKAGE. 2415. All the lines of force produced by the magneto- motive force can not be confined along one path; a certain number in every magnetic circuit will stray froin the main circuit and take shorter cuts. This tendency is called xaagnetic leakage. 2416. The magnetic leakage becomes greater when the reluctance along the main circuit is not uniform at all points. The nature of magnetic leakage may be better understood by remembering that air is really a magnetic conductor, although its reluctance is much greater than that of iron or other magnetic substance. Consequently, 'when the re- luctance of the main circuit becomes large at any point, some of the lines of force find a shorter and easier path for themselves through the surrounding air. Fig. 956 represents a U-shaped electromagnet made of iron with a keeper of the same metal and sectional area. By placing the keeper tightly against the two ends, the reluctance becomes practically uniform throughout the entire magnetic circuit, and there is no perceptible leakage at any place. But if the reluctance of the circuit is changed by separating the keeper from the ends of the magnet by a small air-gap, as in Fig. 957, the conditions are altered. loG6 PRINCIPLES OF In the first place, the total number of lines of force will be reduced in all parts of the circuit, and, secondly, a cer- tain number of the lines of force will leak across from end Fig. 956. Fig. 957. to end of the magnet without passing" through the keeper. The larger the air-gap between the keeper and the magnet, the greater will be the magnetic leakage. An approximate idea of the magnetic leakage is shown in Fig. 958, where Fig. 958. Fig. 959. the keeper is placed at a considerable distance from the ends of the magnet, and Fig. 959 shows the state of the lines of force when the keeper is removed entirely. ELECTRICITY AND MAGNETISM. 1567 " 2417. Magnetic leakage may be also defined as the difference between the number of lines of force produced by the magnetomotive force and the number that are 7iseful in attracting or lifting a given weight. There are no definite laws governing magnetic leakage, and it is almost impossible to calculate the number of stray lines of force in any compound magnetic circuit. After a magnet is built, the leakage can be determined with the proper instruments and under certain conditions. In general, if the magnetic circuit is composed of mag- netic substances whose permeabilities are high and there are no large air-gaps to be crossed, the magnetic leakage will be but a small factor. 2418. If the total number of lines of force produced by the magnetizing coils and the useful number are known, the inagnetic leakage can be expressed by a per cent, of the total number produced. Thus, Let / = total number of lines of force; 4 = useful number of lines of force; /^ =: stray lines of force; / = per cent, leakage. Then, 4 ==/-/„. (435.) For example, assuming that 60,000 lines of force are pro- duced by the magnetizing coils of an electromagnet, and that only 42,000 are useful in attracting an armature or lifting a weight, then by formula 435 the number of stray lines of force I, = 60,000 — 43,000 = 18,000. 2419. The percentage of leakage is found from the formula 100 4 , / = — J— . (436.) That is to say, tJie percentage of leakage is found by dividing the stray number of lines of force by the total 1568 PRINCIPLES number produced and multiplying the quotient by 100. In the above case ^ 100 X 18,000 ^^ . . , ^= 60,000 -30^^^^kage. 2420. To find the total number of lines of force when the percentage of leakage and the number of useful lines of force are known, use the following formula: ^=m~p- (437.) Here we divide the useful lines of force by 100 minus the per cent, leakage and multiply the quotient by 100. Example. — Assuming that the magnetic leakage in an electromag- net is 25^ and that there are 75,000 useful lines of force, how many lines of force are produced by the magnetizing coils ? Solution. — By formula 437, the total lines of force _ 100 X 75,000 _ 7,500,000 _ ^ - 100 - 25 -' 75 ■ - ■^^"•"^ total lines of force produced by the magnetizing coils. Ans. EXAMPLES FOR PRACTICE. 2421* 1. 100,000 lines of force are produced by the magnetizing coils of an electromagnet and only 40,000 are useful. What is the % leakage ? Ans. QQ% leakage. 2. In an electromagnet there are 27,000 stray lines of force and 63,000 useful ; find the % leakage. Ans. 30j^ leakage. 3. The magnetic leakage in an electromagnet is 45^ and there are 110,000 useful lines of force ; find the total number of lines produced by the magnetizing coils. Ans. 200,000 lines of force. 4. If the magnetic leakage in an electromagnet is 35^ and there are 60,000 lines of force produced by the magnetizing coils, how many lines of force are useful ? Ans. 39,000 useful lines of force. LIFTING MAGNETS. 24:22* The lifting power or adhesive force of a magnet is called its tractive force, or, simply, traction. The com- mon form of electromagnet for traction is a stumpy horse- shoe magnet M with two magnetizing coils r, r, as shown in Fig. 960. The magnet is generally provided with an arma- ELECTRICITY AND MAGNETISM. 1569 ture of soft iron a, which is placed across the two poles. When the current is flow- ing in the magnet- izing coils, the full tractive force of the magnet is exerted between the arma- ture and the two polar surfaces. The maximum tractive force is found by hanging known weights W of any- material upon the armature in a suit- able manner and observing the heavi- est load it will sus- tain without sepa- rating from the magnet. The total Fig. 960. tractive force of the magnet will be the weight of the armature plus the load sustained. 2423. Another eco- nomical form of electro- magnet for traction is made in the shape of a '^r diving-bell, as shown in Fig. 961. This magnet is iron-clad; that is, the magnetizing coil is com- pletely surrounded and protected by the return magnetic circuit, and re- quires only one magnet- FiG. 961. izing coil to excite it. 1570 PRINCIPLES OP If the magnet proper M is made in one casting, the coil c is wound independently in some suitable shape ; afterwards it is thoroughly insulated by wrappings of cloth, mica, or tape, then placed around the inside core of the magnet and held in position by a ring of brass or other non-magnetic metal r wedged between the core and the outside shell. The con- nections to the coil from an outside source are inade to leads (pronounced leeds) passing from the coil up through holes in the top of the magnet. By designing the magnet low and large in diameter, the magnetic circuit can be made exceedingly short in proportion to its sectional area, thus realizing one of the conditions of an economical design. 2424. In determining the tractive force of a magnet, let A = total area of contact surface ; B = density in lines of force per square inch; P = total tractive force in pounds. That is, t/ie tractive foi'ce of a magnet increases directly as the total area of the surface in contact with the armature, and as the square of the density of the lines of force in tJie magnetic circuit where it passes across that surface. For- mula 438 is deduced from the force exerted upon a unit pole placed in a unit magnetic field, and assumes that the distribution of the lines of force is uniform throughout the entire contact surface. In actual practice it is impossible to obtain this result on account of magnetic leakage and other causes. The calculated load and the actual load lifted will generally differ — the actual being somewhat less than the calculated, due to the fact that some of the mag- netic lines leak away from the attracting surfaces. In all electromagnets designed for traction there will be two contact surfaces, one at the north pole of the magnet and the other at the south pole; or, in other words, the total lines of force developed in the magnetic circuit are used twice in producing the traction of the magnet. If the ELECTRICITY AND MAGNETISM. 1571 two contact surfaces are symmetrical and equal in area, the total tractive force of the magnet will be twice the result obtained by considering one contact surface alone; but if the contact surfaces are unlike, the tractive force exerted by each surface should be calculated separately, and the two results thus obtained added together. 2425. The most economical electromagnet designed for traction is one that will lift the greatest load in propor- tion to its ozvn iveight. To accomplish this result, the fol- lowing facts must be considered: The magnetic circuit in the magnet and keeper should be as short as possible. The sectio7ial area of the magnetic circuit should be uniform and large in p -.■oportion to the over-all dimensions. The iron or steel jcsed in the magnet and keeper should have a high permeability. The magnetic density of the contact surface should be about 110 fiOO lines of force per square inch ^ for, if the magnetism is pusJied higher than this density, the reluctance of the mag- netic circuit zvill be increased, which increases the weight of the copper tcsed in the magnetizing coils. CALCULATIOIV FOR LIFTING MAGNET. 2426. To find the magnetic density at the contact surface required to produce a given tractive force when the area of the contact surface is known : Let A = area of contact surface in square inches ; P = tractive force in pounds ; B = magnetic density of lines of force at contact surface. Then. B = 8,493 1/^. (439.) Rule. — In an electromagnet the density of lines of force at the contact surface is equal to 8,Jf93 times the square root of tJie tractive force in pounds divided by the area in square inches. 1572 PRINCIPLES OF 2427. To find the total number of lines of force in the magnetic circuit when the tractive force and the magnetic density at the contact surface are known: Let N — the induction, or the total number of lines of force. Then, i\^= 72,134,000-^. (440.) Rule. — The total number of lines of force in an electro- magnet is found by dividing the tractive force in pounds by the magnetic density at the contact surface and multiplying the quotient by 72,13Jt.,000. 2428. To find the tractive force in pounds per square inch when the area of the contact surface and the total number of lines of force are known: Let p = tractive force in pounds per square inch. JSf Rule. — The tractive force of an electromag7tet in pounds per square inch is equal to the square of tJie number of lines of force divided by 72,13 Jf.,000 times tJie square of the area of contact surface in square inches, 2429. To find the tractive force in pounds per square inch when the density at the contact surface is known: ^ ^ 72,134,000* (442.) Rule. — The tractive force of an electromagnet in pounds per square inch is equal to the square of the magnetic density at the contact surface divided by 72,13Jf.,000. 2430. To find the area of the contact surface when the total number of lines of force and the tractive force are known : ^ "^ 72,134, 000 :P* (443.) ELECTRICITY AND MAGNETISM. 1573 Rule. — The total area of eontact surface of an electro- magnet is found by dividing the square of the total number of lines of force by 72,13^,000 times the tractive force in pounds. 2431. To find the number of ampere-turns required to energize a magnet for a given traction when the permeability of the iron or steel use.d is known and the dimensions of the armature and magnet have been established: Let P= tractive force of one contact surface; then, 2 P is the total tractive force of the magnet ; /j and /j = the lengths of the magnetic circuit in magnet and armature, respectively; A^ and A^ = sectional areas of magnetic circuit in magnet and armature, respectively; ^, and//^ = permeabilities of the iron or steel used in the magnet and armature, respectively; B = magnetic density at contact surface. Then, the ampere-turns a-, = 82,598,370 X ^X {^^^^ + ^). (444.) Rule. — In the case of an electromagnet htte^ided to develop a given tractive power, the ampere-turns are equal to the tract- ive force of one contact surface multiplied by the reluctance of the circuit and by 22,598,370^ and divided by the magnetic density at the contact stirface. 2432. To find the ampere-turns required to energize a magnet for a given tractive force when the armature and magnet are made of the same quality of iron or steel and the sectional area of the magnetic circuit is the same in the armature, magnet, and contact surfaces: Let /= total length of magnetic circuit in inches; 7^= tractive force at one surface; \i, z= permeability of iron or steel used; A = cross-sectional area of magnetic circuit; JV= total number of lines of force in the magnetic circuit. / /P The ampere-turns necessary, a-t = 2,661 X —X f -j. (445.) 1574 PRINCIPLES OF Rule. — 7^0 determine the ampere -turns for an electromagnet of uniform sectional area and material wkeit the tractive force at one surface is given ^ find the square root of the tractive force divided by the area, multiply this value by 2,661 times the length of circuit in inches and divide by the permeability. As showing the relation between formulas 439 and 445 » the latter may be written : 5,493'/^ "-^= 3.192 X]I-3392>^? (446.) 2433. In designing an electromagnet for a certain tractive force, several assumptions have to be made in the beginning. The first assumption is the magnetic density in the armature, magnet, and contact surface. If wrought iron, cast steel, or soft annealed sheet iron is used, the density in the armature and magnet should be between 100,000 and 120,000 lines of force per square inch. If, however, the metal is gray cast iron, the density should be between 50,000 and 70,000 lines of force per square inch. As already stated, the density of the contact surface in any coil should be about 110,000 lines offeree per square inch. If the mag- net is made of cast iron in which the density is low, the edges of the pole-pieces should be chamfered off to increase the density of the contact surface. This chamfering will slightly increase the reluctance of the magnetic circuit at that point, but the amount will be small and can be neglect- ed. The next assumptions are the over-all dimensions of the magnet. The relation between the tractive force for which the magnet is to be designed and the magnetic densities determines the sectional areas of the armature and magnet, but does not give any information regarding the over-all dimensions. Several trials may be necessary to de- termine the most economical dimensions. In the first trial, ample space should be left for the magnetizing coils, and if this space is found to be too small or larger than necessary, the over-all dimensions should be changed and the magnet recalculated. ELECTRICITY AND MAGNETISM. 1575 Example. — Design an electromagnet for a maximum tractive force of 672 pounds. Solution. — From formula 4-43 the tractive force in pounds per square inch p = i-.:, oa (\(\c\ • Using a density of 110,000 lines of force at the contact surface gives p = ., , ..', ,„„. = 167.74, or about 168 pounds * -^ 72,184,000 '■ per square inch. The total tractive force divided by the tractive force per square inch gives the total area of the contact surfaces. There- fore, -^11 = 4 square inches for the area of the two contact surfaces, or 2 square inches for the area of one contact surface. The total lines of force in the circuit are 110,000 X 3 = 220,000. In the first trial, imagine a bar of wrought iron 8 in, long, 2 in. wide, and 1 in. thick, bent in the direction of its least dimension into the form of a horseshoe with straight sides, so that the distance between the centers of the poles is 3 in. The armature maybe a bar of wrought iron 4 in. long, 2 in. wide, and 1 in. thick. The sectional area of the magnetic circuit is 2 square inches in magnet, armature, and contact surface, and the density is 110,000 lines of force per square inch. From Table 82, when B = 110,000 the permeability in wrought iron is 106.3. The mean length of the magnetic circuit in the magnet is 8 in., and in the armature it is 3 + -J- + -J- = 4 in. ; hence, the total length / is 8 + 4 = 12 in. By formula 445, the ampere-turns «-/ = 2:661 v . y a/'-— — 106.3 ^T 2 ~ 12 2,661 Xjwr^jX 12.961 = 3,893.42, or about 3,893 ampere-turns required to magnetize the magnetic circuit under these conditions. Assuming the current to be 10 amperes, then 3,893 -=-10 = 389.3, or say 389 turns of a conductor to be wound around the magnet. A cop- per wire covered with two layers of cotton thread can be used for the conductor. A size of wire must be used which will not heat excessively when a current of 10 amperes is flowing through it. From experiment, it is found that a copper wire. 091 in. in diameter will carry 10 amperes with safety. After the wire has been covered with two layers of cot- ton, the diameter will be about .1 in. The wire should be wound in tAVo coils, one on each pole of the magnet. If each coil is wound in layers extending 2 in. from the polar surfaces, there will be 2 -r- .1 = 20 turns of wire lying side by side, or 20 turns in each layer in each coil. The total number of turns in each coil should be -^^ = 194.5, or say 195. The number of turns divided by the turns in one layer will give the number of layers; therefore, ^^^- = 9.75 layers in each coil. The maxi- mum depth of wire will be 10 layers or 1 in. on each coil, which exactly fills up the space between the two poles after both coils have been wound. It is better practice, however, to design the magnet with some space between the two coils ; in the preceding example a space of from i inch to | inch might have been allowed between the two coils. 1576 PRINCIPLES OP MAGNETS FOR ATTRACTION. SHORT-RANGE MAGNETS. 2434. Electromagnets designed for attracting theii armatures through a distance can be divided into two sub- classes, namely, short 2Si6ilong r^/z^^" magnets. Short-range mag- nets are used in places where the armature is required to move rapid- ly through a short dis- tance, exerting compar- FiG. 9G2. atively little force ; as, for example, in telegraph apparatus, electric bells, arc lights, etc. Such magnets are usually of the horseshoe type, as shown in Fig. 9G2, which represents an electro- magnet for a telegra-ph relay. In this particular mag- net the cores are made of two round bars of soft iron M^ f in. in diameter and 2 in. long. The cores are screwed into a yoke of soft iron b, f in. wide by \ in. thick and 2 in. long. The magnetizing coils are wound over vulcanized rubber bobbins or spools, and contain, all told, about 8,500 convolutions, or turns, of insulated copper wire .009 in. in diameter. The total resistance of the wire in the two mag- netizing coils is about 150 ohms. A vulcanized rubber shell or cover c is slipped over each coil when wound, to protect it from dust and bruises. 2435. Fig. 963 represents another form of magnet used for rapid vibrations of the ar- mature. The cheapness of winding only one coil instead of two and its simplicity of construction recommend it for a large variety of practical uses. Fig. 963. The principal disadvan- ELECTRICITY AND MAGNETISM. 1577 tage is the large amount of magnetic leakage caused by an unbalanced magnetic field. There is a large variety of short- range electromagnets adapted to special uses, -but all the various types are modifications of the same general principle. The magnitude of the force which short-range electro- magnets are usually required to exert is comparatively small ; in most cases the armature moves only a fraction of an inch against the tension of a light helical spring. Conse- quently, it is unnecessary to calculate the magnetic circuit and the force of attraction. The size and amount of wire to be used for the magnetizing coils depend upon the local con- ditions, and the most satisfactory results are obtained by experimental trials in each particular case. LOIVG-RANGE MAGNEXS. 2436. The most economical form of long-range mag- nets is the coil-and-plunger magnet ; that is, a magnet in which a part or the whole of the armature moves inside the magnetizing coils. The simplest, although the most in- efficient, type of such magnets is a straight bar of iron mov- ing freely into one magnetizing coil or solenoid. The bar will always be attracted towards the center of the solenoid, with its neutral line coincidine with that of the solenoid. The range of action is long, but the force exerted is com paratively weak. Fig. 964 represents an effective type of coil-and-plunger 1578 PRINCIPLES OF magnet, and one capable of exerting heavy pulls through long ranges. The magnetic circuit is divided at about the center of the coils c, c, and half of each core is attached to the armature a. The advantage thus gained consists in causing the greatest reluctance to take place where the mag- netizing force is the strongest, and, hence, the tendency to magnetic leakage is reduced. A coil-and-plunger magnet of this type weighing about 65 pounds will give an initial pull of approximately 50 pounds when the air-gap between the cores of the armature and the cores of the yoke is 3 inches. As soon, however, as the armature starts to move into the coils, the reluctance of the magnetic circuit and the mag- netic leakage are reduced ; consequently, the density of the magnetic field increases, which in turn increases the attract- ive force. If the magnetizing force remains unchanged, the attractive force when the armature has moved through only part of the distance will be several times the initial attractive force. 2437. A combination of the coil-and-plunger and iron- clad types with one magnetizing coil gives an efficient mag- net for powerful pulls over short ranges. The inside core in, in- stead of protruding above the top of the magnetizing coil as in ordinary short-ranged iron- clads, rises to only about half the height of the coil, as shown in Fig. 905. The other half of the core n is attached to the armature a, and moves inside the magnetizing coil c. This Fig. 9G5. . , . , , IS wound m a metal spool or bobbin, which is rigid enough to serve as a guide for the armature. The range of action is limited on account of the enormous magnetic leakage taking place across the top of the coil when the air-gap becomes large. ELECTRICITY AND MAGNETISM. 1579 ELECTROMAGNETIC IIVDUCTION. 2438. It has been shown that a magnet and a con- ductor carrying a current of electricity exert a mutual force upon each other ; or, in other words, each tends to produce motion in the other. In general, when a conductor carry- ing a current of electricity is placed in a magnetic field, the conductor will tend to move in a definite direction and with a certain force, depending upon the strength and direction of the current and upon the direction and density of the lines of force. Direction gj motion- 2439. To determine the direction of motion of a conductor carrying a cur- rent of electricity ^vlien placed in a magnetic field : Rule. — Place thumb, forefinger, and middle finger of the left hand each at right angles to the other two, as shozvn in Fig. 966 ; if the forefinger shozvs the direction of fig. 966. the lines of force and the viiddle finger sJiozvs t lie direction of the current, then the thumb will show the direction of motion given to the conductor. The direction of motion produced in the conductor can also be graphically shown. The diagram. Fig. 967, indi- cates a cross-section of a mag- netic field; the dots repre- sent an end view of the lines of force, and the heavy line a conductor conveying a cur- rent of electricity. If the direction of the lines of force is dowmvards, that is, pier- y cing the paper, and if the cur- J rent flows in the direction in- FiG. 967. dicated by the arrow-heads, C, liBi ^ ^B ^■^ K 7^ 1580 PRINCIPLES OP then the conductor will be moved bodily to the right^ as indicated by the two arrows. 2440. This action is also true of an electric arc passing through a magnetic field, that is, a current of electricity passing or jumping in the form of a con- tinuous spark between two electrodes across an air-space which is traversed by lines of force, as indicated in Fig. 968. ^IH The arc or spark will be impelled to one 5^5^ ^ll side in the same direction as the conductor in the previous case. If the electrodes remain in a fixed position relative to the Vj magnetic field, the arc will be blown out ; ^ that is, the spark will be extinguished and Fig. 968. ^j^Q current will cease to flow in the cir- cuit. In both cases the motion is caused by the mutual action of the lines of force in the magnetic field and those produced by the current itself, as shown in Fig. 969, where the current is assumed to be flowing downwards. The lines of force in the magnetic field tend to coincide in direction with those around the current, and in doing so they exert a crowding effect on the current, which, in the first case, produces motion in the conductor, and in the second a ten- sion upon the arc. N S 2441. The converse Fig. 969. of this effect is also true, namely, when a conductor forming a closed circuit is moved across a magnetic field at right angles to the lines of force^ a ciirrent is induced in the con- ductor. This statement will be better understood by comparing the action in Fig. 967 with that in Fig. 970. In the former case, when a current is flowing in the direction indicated by the arrow-head the conductor will move bodily to the right. In Fig. 970, however, when the conductor is ELECTRICITY AND MAGNETISM. 1581 Wz M moved to the right by some exterior means a current is induced in it which tends to flow in an opposite direction to the current which pro- ^ >^ duces the same motion in the former case. This generation of current may be explained by saying that the motion of the con- ductor across the lines of force from the magnet sets up an electromotive force in the conductor, which, when the circuit is completed, causes a current to flow. ^ ■■■. ^ The direction of the current ^' i°- 9™- induced in the conductor will be at right angles to the lines of force and to the direction of motion of the conductor. 2442. To determine the direction of induced currents : Rule. — Place thumb, forefinger, and middle finger of the right hand each at right angles to the other tzvo ; if the fore- finger shozi's the direction of the lines of force and the thumb shozus the direction of motion of conductor, the middle finger will shoiv the direction of the induced ctirrent. (See Fig. 971.) 2443. The positive end of a conductor in which a current is gen- erated by moving across a magnetic Fig. 971, field is that end towards which the current tends to flow ; the negative end is that from which the current tends to flow. 2444. An electric current will be induced in a coiled conductor when a pole of a magnet is suddenly inserted into the coil. The current will be continuous so long as there is a change in the member of lines of force passing through the 1583 PRINCIPLES OF coil, but the current will cease to flow when the number of lines of force becomes constant, that is, when the lines of force inside the coil do not increase or diminish in number. In reality, currents produced in a conductor cutting lines of force and currents induced in a coiled conductor by a change in the number of lines of force which pass through the coil are due to the same motion, for every conductor carrying a current of electricity forms a closed coil, and every line of force is a complete magnetic circuit by itself. Con- sequently, when any part of a closed coil is cutting lines of force, the lines of force are passing through the coil in a definite direction, and changing at the same rate as the cutting. In calculations, however, it is more convenient to make a distinction between the two cases, and to consider that the current or, more strictly, the E. M. F., in the first case is generated by a conductor of a certain length cutting the lines of force at right angles; while, in the second case, the current in a closed coil is induced by a change in the number of lines of force passing through the coil. 2445. The action of induced currents can be shown by a closed coil of any conducting material moving in a mag- FlG. 972. netic field. If it is moved in a uniform field along the lines of force, as in Fig. 972, so that only the same number of lines of force pass through it, no current will be generated. Or, if the coil be moved across the lines of force in a uniform ELECTRICITY AND MAGNETISM. 1583 field, Fig. 973, as many lines of force are left behind as are gained in advancing, and there will be no current generated in the coil. Rotating the coil on a central axis, like the rim FIG. 973. of a pulley, will not generate a current, because there is no change in the number of lines of force passing through the loop. But if, as in Fig. 974, the coil be tilted in its motion across the uniform field, or rotated around on any axis in N Fig. 974. its own- plane, then the number of lines of force that pass through it will be altered and a current will be developed. Where the magnetic field is not uniform, the removal of the coil bodily from a place where the lines of force are dense to where they are less dense, as from position 1 to position 2 1584 PRINCIPLES OF in Fig. 975, will cause the generation of a current in the coil ; or if the coil is moved to a place where the direction Fig. 975. of the lines of force is reversed, the effect will be the same. 2446. To determine tlie direction of induced currents in a closed coil : Rule. — If the effect of the movemejit is to diminish thi number of lines of force that pass through the coil, the cur- rent will flow around in the conductor in the direction of the hands of a watch as viewed by a person looking along the ^nagnetic field in the direction of the lines of force ; but ij the effect is to increase the niunber of lines of force that pass through the coil, the current will flow aroimd in the opposite direction. 2447. In the explanations just given, it was stated that currents are generated by moving the conductor in a magnetic field. It must be remembered, however, as shown in the beginning, that a current is merely the equalization of a difference of potential. Strictly speaking, therefore, it is not actually a current, but electromotive force, that is developed by induction in the moving con- ductor ; for, on opening the circuit, the electromotive force will still exist, but no current can flow. The word current is used merely to avoid complication. ELECTRICITY AND MAGNETISM, 1585 Fig. 976. EXPERIMENTS W^ITH ELECTRICAL APPARATUS. 2448. (Art. 2439.) Take a piece of wire about 12 inches long ; about an inch each side of the center make a right-angle bend ; bare the ends of the wire and bend about an inch of each end into a loop. This will make a sort of trapeze of wire, as shown at .-i A, Fig. 976. Bare the ends of two wires leading from the battery (via the revers- ing switch), scrape them bright to ensure good contact, and support them in the same line about 2 inches apart, so that the bent wire may hang from them, as shown in the figure, where vS" and vS represent the supports of the wires. Now, hold- the horseshoe magnet M, Fig. 976, in such a position that the bent wire may swing freely between its poles, and with the switch complete the circuit, [a) What happens ? {b^ Reverse the current through the hanging loop ; what happens ? (r) How can you foretell which way the wire will swing ? (Art. 2439.) Replace the bent wire in the above ex- periment with a wire bent into a coil of about three turns, large enough to slip freely over one pole of the magnet, and suspend this coil, as before. Repeat the first two experi- ments, using this coil instead of the wire trapeze. Are the effects noted above altered any ? Why ? DETERMINATION OF E. M. F. 2449. The electromotive force generated in a con- ductor cutting lines of force at right angles is proportional to the rate of cutting. The rate of cutting is found by dividing the number of lines cut by the time taken to cut them. 1586 PRINCIPLES OF One absolute unit of potential !•& generated in a conductor when it is cutting lines of force at the rate of one line of force per second. By definition, one volt is equal to 100,000,000 (10^) absolute units (see Art. 2303) ; consequently, in order to generate an electromotive force of one volt, the rate of ciitting must be 10^ lines of force per second. This can also be expressed algebraically. Let E = the electromotive force in volts ; N = the total number of lines of force cut by the con- ductor ; t = time in seconds taken to cut the lines of force. Then, £ = Ji^r (447.) That is, t/ie electromotive force in volts generated in a mov- ing conductor is found by dividing the total number of lines of force cut by the conductor by the time taken and by 100,000,000. If the total number of lines of force remains unchanged, the electromotive force developed is the same, whether the lines of force proceed from a permanent magnet or electro- magnet. 2450. According to Ohni's lazv, the current obtained from conductors cutting lines of force, is equal to the quo- tient arising from dividing the total electromotive force generated by the total resistance of the circuit through which the current passes. In general, the total resistance is the resistance of the conductor cutting the lines of force, or the resistance of the internal circuit, plus the resistance of any conductor or conductors which complete the external circuit. If E represents the total electromotive force in volts, r^ and r^ the resistance in ohms of the internal and external circuits, respectively, and C the current in amperes, E then C = ■ ; . It will be seen from the above expression that a large or small induced current can be obtained from conductors ELECTRICITY AND MAGNETISM. 1587 cutting lines of force by simply changing the combined resistance of the internal and external circuits. There is, however, a maximum limit to the amount of current obtained in this manner. The lines of force which are pro- duced around the conductor by the current itself will always act in opposition to the lines of force producing the electro- motive force, and will tend to distort or crowd them away from their original direction. The number of lines of force produced around the conductor by the current is directly proportional to the strength of the current ; and, conse- quently, as the current becomes larger and larger, the lines of force cutting the conductor become more and more dis- torted and crowded away from their original direction, until the conductor no longer cuts all the lines of force, and, there- fore, the electromotive force generated becomes smaller. A general rule to get rid of this effect is to make the density of the magnetic field large in proportion to the current. PRODUCTION OP INDUCED E. M. F. 2451. There are three ways of producing an electro- motive force by induction in a coiled conductor, namely, by electromagnetic induction^ by self-induction, and by mutual induction. 2452. In electromagnetic induction the change in the number of lines of force which pass through the coil is due to some relative motion between the coil and the magnetic field; as, for example, by thrusting a magnet pole into the coil, or by taking the magnet out from the coil, or by suddenly turning the coil in a magnetic field. 2453. In self-induction the change in the number of lines of force is caused by sudden changes in a current which is flowing through the conductor itself and supplied from some exterior source. If this exterior current is sud- denly increased, it will produce a change in the number of lines of force ; the change in turn induces an electromotive force in the conductor which opposes the exterior current in the coil and tends to keep it from rising. The exterior 1588 PRINCIPLES OF current will eventually reach its maximum strength in the coil, but its progress will be greatly retarded by the induced electromotive force. If, on the contrary, the exterior cur- rent is suddenly allowed to decrease, it will produce a change in the lines of force; this change induces an electromotive force in the coil which acts in the same direction as that of the exterior current, and tends to keep it from decreasing. As in the previous case, the exterior current will eventually decrease to its minimum strength, but it will fall gradually, and a portion of a second will elapse before it becomes con- stant. In fact, the current flowing through a coiled con- ductor acts as if possessing inertia ; any sudden change in the strength of the current will produce a corresponding electromotive force which will tend to oppose that change and keep the current in its original strength. r^mH 24:54:, In mutual induction, two separate coiled con- ductors, one carrying a current of electricity, are placed near each other, so that the magnetic circuit produced by one will be enclosed by the other, as shown in Fig. 977, in which the current is Fig. 977. flowing around coil P. The coil (P) around which the current is flowing is called the primary or exciting coil ; the other (5) is the secondary coil. Any change in the strength of the current flowing around \)s\Q primary coil will produce a corresponding change in the lines of force in the magnetic circuit, and, consequently, an electromotive force will be induced in the secondary coil. If the current in the primary coil is increasing^ the electro- motive force induced in the secondary coil will cause a cur- rent to flow around in the opposite direction to the current in the primary coil. If the current in the primary coil is decreasing^ then the induced electromotive force in the secondary coil will cause a current to flow around in the same direction as the current in the primary coil. ELECTRICITY AND MAGNETISM. 1589 2455. An induction-coil is an apparatus devised on the principle of mutual induction for producing pulsating currents of electricity of high electromotive force. Induc- tion-coils are sometimes called Ruhmkorff coils, from the name of a celebrated manufacturer of them. They consist, essentially, of two coils, primary and secondary, wound around a core consisting of a bundle of iron wires. In Fig. 978 the secondary coil is composed of a large number of ^B Fig. 9 turns of fine insulated wire, while the primary coil P con- tains only a few turns of thick insulated wire. The primary circuit is automatically opened and closed at a and i, in the following manner: t represents a spring which tends to keep the circuit closed between the armature a and the contact pin /. As soon, however, as the circuit is closed by the action of the spring, the current from the battery B begins to circulate around the core in, thereby producing an electromagnet and attracting the armature a away from the contact pin i. Upon opening the circuit between a and ?', the magnetism in the core begins to weaken, the spring once more closes the circuit, and the entire operation is again repeated. These actions take place in rapid succes- sion, several times a second, constantly producing a change in the lines of force passing through the core, and thereby inducing a current in the secondary coil. 2456. Fig. 979 shows the commercial form of Ruhm- korff coil. The primary coil is wound around the core of soft iron wires, and its two ends brought out at/, /'. The 1590 PRIN. OF ELECTRIC. AND MAGNETISM. secondary coil, consisting of several miles of fine insulated wire, is wound over the primary coil, and its ends attached to the insulated electrodes s, s'. The current in the primary coil is obtained from a voltaic battery connected to Fig. 979. the terminals at t, t\ and is interrupted by means of a mercury break at A and B. The apparatus is also provided with a commutator C, which commutes or changes the direc- tion of the current in the primary coil. AVhen a battery which develops an electromotive force of a few volts and comparatively large currents is connected in the primary circuit as described, a torrent of sparks passes between s and s\ under an electromotive force of several thousand volts. ELECTRICAL MEASUREMENTS. ELECTROMAGNETIC MEASUREMENTS. 24:57, A current of electricity is not a material sub- stance, and, therefore, has no dimensions (length, area, or weight) by which it might be measured. A ciirrent oj electricity must, therefore, be measured by the effects which it prodiices. 2458. These effects manifest themselves as follows : When a current of electricity is flowing in a conductor, the energy expended in overcoming the resistance of the conductor manifests itself as heat. The amount of this energy is equal to the square of the current times the resistance (see Art. 2341); therefore, the heat generated in a circuit will be proportional to the square of the current if the resist- ance be constant, or to the resistance if the current be con- stant. When a current of electricity flozvs through a conducting liquid, the liquid is decomposed. This decomposition is due to a chemical action of the current, known as electrolysis, and is distinct from the. heating effect. The decomposition either liberates a certain amount of gas or deposits one or more of the elements of the liquid upon one of the elec- trodes. The amount of liquid decomposed is directly pro- portional to the quantity (coulombs) of current ; hence, the rate of decomposition, or the amount of liquid decomposed per unit of time, is proportional to the strength of the cur- rent in amperes. When a current of electricity floivs through a conductor, a field of magnetic force is set up around the conductor zvhich For notice of copyright, see page immediately following the title page. 1592 ELECTRICAL MEASUREMENTS. • tends to produce a relative motion in any other magnetic field in the vicinity ; as, for instance, that emanating from a magnet pole. The force acting on such- a pole will be directly proportional to the strength of the current, to the length of the conductor, to the strength of the magnet pole, and inversely proportional to the square of the dis- tance between the conductor and the magnet pole. An instrument which measures a current by its electro- magnetic effect is called a galvanometer. THEORY OF THE GALVANOMETER. 2459. As the units of electrical measurements are based upon the so-called "absolute" or " C. G. S." system (see Art. 2254), measurements of current by means of electrolytic effect can be made only when the, effect of unit current has been previously determined. By the electro- magnetic action the absolute value of a current may be derived as folloAvs : As stated in Art. 2458, the force exerted en a unit pole by a neighboring current is proportional to the strength of the current, to the length of the conductor, to the strength of the pole, and inversely proportional to the square of the distance from the conductor to the unit pole. Then, to exert unit force on the unit pole, it is necessary to employ unit current, and a conductor of unit length, that is, one centimeter long, which must be bent to an arc of unit (one centimeter) radius, in order that each part of the conductor be at unit distance from the unit pole. Under these conditions, a current of one C. G. S. unit flowing through the conductor will act on a unit pole at the center of the arc to which the conductor is bent with a force of one dyne. Thus the absolute value of one C. G. S. unit of current may be determined. 2460. When a magnetic pole is placed near another magnetic pole, the attraction (or repulsion) of the two poles is proportional to the product of the strengths of the two ELECTRICAL MEASUREMENTS. 1593 poles, and inversely proportional to the square of the dis- tance between them ; so, two equal magnetic poles, which, when placed at a unit distance (one centimeter) apart, exert a force of attraction or repulsion on one another of one dyne^ are said to be of tinit strength. 2461. In Art. 3273 it was pointed out that the C. G. S, unit of current is ten times greater than the prac- tical unit, the latter being more convenient to use. Simi- larly in Arts. 2282 and 2303 the C. G. S. and practical values of the units of resistance and electromotive force were given. It would be very difficult to construct apparatus that would fulfil the conditions given in Art. 2459. It is much easier to vise a conductor bent into a complete circle, and as the effect of changing various dimensions is known from the relations given in Art. 2459j a formula may be constructed which will give the effect on a magnet pole of a current flowing through a conductor of any length bent to any radius. Let r represent the radius in centimeters to which the conductor is bent; now, if the conductor be of sufficient length to be bent into a coil of more than one turn having a radius r, the length of eacJi turn of the bent conductor is Tz d^= 2 TT r centimeters, and the total length of the con- ductor ■^z'^TLrt centimeters, where / represents the number of turns that the conductor makes when bent into the coil. The distance between the conductor and the center of the coil is obviously equal to r centimeters ; then the force that a current of 1 C. G. S. unit flowing through the coil would exert on a unit magnet pole placed at the center of the coil = • — -^ — • dynes, being directly proportional to the length of the conductor, and inversely proportional to the square of the distance between the magnet pole and the conductor. (Art. 2458.) This force being also directly proportional to the strength of the current, a current of A C. G. S. units will exert a 1594 ELECTRICAL MEASUREMENTS. force oi A X ^ — dynes; or, representing the force exerted on the magnet pole in dynes by/", 27:A ri - p— • Dividing both terms of the fraction by r, /=^, (448.) which is the formula required. 2462. It is not convenient to directly measure the force exerted on a unit pole by a current circulating in a coiled conductor. If, however, any magnet pole can be influenced by a known constant force in one direction, then, by exerting upon it another force, due to a current circulating in a coil, but acting in a different direction, the resultant of the two forces may be accurately determined and the value of the second force measured. This known constant force is furnished by the earth itself, which is a magnet of such enormous size that for short distances the direction of its lines of force may be considered as perfectly parallel. The actual direction of the earth's field is not horizontal, but at an angle to the hori- zontal, so the actual field may be said to be made up of two components — a horizontal and a vertical component. The horizontal component is most frequently made use of in measurements, as in this case. A small bar magnet placed across the earth's field of force will have equal and opposite forces acting on its poles or ends, since the lines of force act in a parallel direction ; this results in turning the magnet about its center, if the magnet is free to move, until the forces act in a direct line with the center, when it can no longer move. This is illustrated by the magnet in the common compass. The force of the earth's field tends to keep the magnet parallel to the lines of force of the earth's field, and, consequently, the magnet points 7iorth and south. ELECTRICAL MEASUREMENTS. 1595 2463. Fig. 980 illustrates this action. The direction of the earth's field of force is represented by the line a b. A bar magnet, N S, placed across this line at an angle with it will have equal and opposite forces acting upon the poles N and S, as shown by the arrows. These forces may be considered as parallel to the line ad; so, if the magnet be free to turn about its center, these forces will bring it to a state of rest when the line a b passes through the magnet from N to S. If the magnet A^^S" be acted upon by another force at an angle with a b, the magnet will come to rest at a point where the two forces balance. In Fig. 981 the magnet N S \s acted upon by the earth's field along the line a b, the direction of the force on the N pole of the magnet being along the line d N^ and that on the 5 pole along the line a S, as indicated by the arrow-heads. In addition, another force is acting along the line X J', at right angles to a b, the direction of the force on the N pole being along the line c N, and on the vS pole being along the line d S, as indicated by the arrows. Under the influence of these two forces the magnet is deflected into the position shown, where it re- mains at rest, making the angle 7/1° with the line a b. Calling the horizontal component of the strength of the earth's field 77, the strength of the force acting along the line X y, /, and the strength of each pole of the magnet N S,p, then the forces acting on the N pole of the magnet are equal to H Y. p in the direction d N^ and f y. p \n the 1596 ELECTRICAL MEASUREMENTS. direction c N\ the forces acting on the S pole are equal to // X / in the direction ^ c^ and f X p in the direction d S. The force // X / acting in the opposite directions on the two poles of the magnet form a couple tending to rotate the magnet about its center o. The moment of this couple is equal to one of the forces multiplied by the perpendicular distance between their lines of action. (See Art. 906.) That is, the moment of the couple produced by the force H p is equal to H p X c N^ and its direction is right-handed. Similarly, the force f p produces a couple which tends to produce left-handed rotation of the magnet, and the moment of this couple is fp X S c. Since the magnet is in equilib- rium, that is, at rest, these two moments are equal, and fpxSc= H p XcN, or/ xSc = Hxc N. Since this last equation does not contain /, it follows that the deflection of the magnet is independent of the strength of the magnet. Since /X Sc=/IXcN,f=II^. In Art. 754, rule 5, it is stated that the tangent of an angle is equal to the side opposite divided by the side adjacent. In Fig. 981, riV is the side opposite the angle 7n°, and Sc cN the side adjacent. Therefore, -^-^ is the tangent of the angle w°, and the force f is given by the formula f= Hxt2inm°. (449.) H being constant, f varies as the tangent of the angle through wJiicJi the magnet is deflected. An instrument which measures current on this principle is called a tangent galvanometer. 2464. The horizontal component (//") of the earth's field has been accurately measured at various places, and the following table gives the values for some well-known localities : ELECTRICAL MEASUREMENTS. TABLE 84. 1597 HOKIZOIVTAL COMPONENT OF THE EARTH'S MAGNETISM^ Localil/. Value of Compo- nent. Lines of Force per Square Centi- meter. London, England Paris .180 .188 Berlin .178 Rome .240 Montreal .147 Niagara ... Halifax .167 .159 Boston .170 New York .184 Philadelphia .194 Washington .200 Chicago .184 Cleveland .184 San Francisco .255 TANGENT GALVANOMETER. 2465. It is necessary that the lines of force that in- fluence the magnet be practically parallel within the range covered by the swing of the magnet. With the earth's field this is the case, as has been pointed out in Art. 2462 ; but with a coiled conductor, this only holds true of a very small space relative to the diameter of the coil, at the center of the coil. A tangent galvanometer must, therefore, have a magnet of short length as compared with the diameter of the coil. A magnet f in. long can be used with a coil of 8 in. diameter with accurate results. The deflections of a magnet as short as this could scarcely 1598 ELECTRICAL MEASUREMENTS. be read directly. A very thin light pointer is, therefore, at- tached to the magnet, usually at right angles to it, which extends out over a scale upon which the deflections may be read. Fig. 982 gives a top view of a simple tangent galvanome- ter in which N S is the coil of wire and F is the pointer at- tached to the permanent magnet M. Two scales are shown, one on each side of the coil. One is divided into degrees, and the divisions on the other are proportional to the tan- gents of the angles represented by the divisions on the degree scale. 2466. In order that a variety of current strengths may be measured with the same instrument, it is customary to wind the coil in two or more parts, of varying number of turns and size of wire. The terminals of these parts of the coil are led out to binding-posts, ^, h, b, b, Fig. 983, on the base of the instrument, so that either one or all the parts of the coil may be used. Even this method of winding does not give much range to the instrument. Another way of regulating its indications is to vary the effective earth's ELECTRICAL MEASUREMENTS. 1599 field, which may be accomplished by placing a permanent bar magnet, called a controlling magnet, in the plane of the coil and parallel to it. Fig. 983 shows a tangent galva- nometer, with an adjustable control- ling magnet m. If this controlling magnet be so placed that its ^ pole corresponds in direction with the N' pole of the magnet of the instrument, its field will be added to the earth's field, so that a given current will give a smaller deflection than if the con- trolling magnet were removed. If the polarity of the controlling magnet be reversed, the opposite effect will re- sult, and the instrument will give a deflection with a very small cur- rent. FIG. 983. 2467. Controlling magnets are used on many forms of galvanometers; there is a difficulty, known as drift, which attends their use, especially when used to make the galvanometer very sensi- tive. This difficulty is due to the fact that the direction of the earth's field is continually changing slightly, and its effect is to make the zero-point of the instrument vary from time to time. This effect may be shown by the dia- gram in Fig. 984. In («), n o represents the direction and magnitude of the force due to the earth's field, and ii in the direction and magnitude of the force due to the controlling magnet. The resultant n s is then the direction which the magnet of the instrument would assume. Now if the direction of the earth's field change through a slight angle to the position shown in (l?), the re- sultant is then the line n^ s^, and its direction is at an angle 1600 ELECTRICAL MEASUREMENTS. of nearly 180° to the resultant 11 s. If the controlling mag- net had not been used, there would have been a slight " drift," but the use of the controlling magnet to lessen the effective field very much magnifies the effect of any change in the direction of the earth's field. 2468. When a controlling magnet is used, it is neces- sary to find the deflection that a certain known current will produce, as the actual value of II is no longer known. Knowing the deflection with a given current, other currents may be measured, as the galvanometer is still governed by the same law, and formula 449 may be changed to read C = A' tan 7n°, (450.) where 6^= current in amperes and /x" = a constant, called the galvanometer constant^ by which the tangent of the angle of deflection must be multiplied to get the value of the cur- rent flowing. This process of finding the constant of a galvanometer or other measuring instrument by comparing it with a known standard is called calibration. The formula for the value of/" with this form of tangent galvanometer is the same as before, viz., _/"=// tan 111° , but the value of H is now the intensity of the earth's field //wi" or oninus (according to its polarity) the intensity of the field due to the controlling magnet. After having found the galvanometer constant ^ this value of H may be calculated. 2469. The following examples illustrate the application of the formulas of the tangent galvanometer: Example. — What will be the force in dynes exerted on a unit magnet pole placed at the center of a coiled conductor of three turns bent to a circle of 13 cm. radius, by a current of 3 C. G. S. units ? Solution. — Use formula 448, / = . 3 TT = 6.3833; A = 2; / = 3; Ai = Q; r=13. ^ 6.3833x6 37.6993 0^.-,/.^ Then, /= to^— = ■ — to — — 3-1416 dynes. Ans. 13 13 Example. — A tangent galvanometer has the following dimensions: Mean diameter of coil, 7| in. ; number turns first section, 3; number turns second section, 1. If this instrument is set up in Boston, and a ELECTRICAL MEASUREMENTS. 1601 current of 2 amperes* is sent through the first section of the coil, what will be the deflection of the magnet in degrees ? Solution. — Use formula 448, /= . Diameter of coil = 1^ in. = 20 cm. ; turns = 3; amperes = 2; C. G. S. units = .2. _ , . 2X3.1416X.2X3 3.76992 o^.qqo ^ ^ . -i Therefore, / = -j = — --r — = .376992 dyne due to coil. Also, from formula 449, /= Hx tan ;«°. Transposing, tan jn" = ■£-. JI=.11iO. (Table 84.) rru f . o .376992 „_._ Therefore, tan m = — .„^ = 2.2176. .1 (U Referring to the table of Natural Tangents, the tangent of the angle 05° 46' is 2.22164. This is as nearly correct as the deflection could be read on the scale. Ans. 65° 46', nearly. 24'70. Example. — Another galvanometer is constructed exactly' like that referred to in Art. 3469, but with a controlling magnet attached to increase its range. The two galvanometers are connected together by wires, so that the second seciwjt of the coil of the Jlrsi galvanometer (called No. 1) is in series with the first sectwtt of the galvanometer with the controlling magnet (called No. 2). On sending a current through the two instruments, the deflection of No. 1 is 52°, while the deflection of No. 2 is but 38°. (a) What current is passing through the galvanometers, and {b) what is the value of .the galvanom- eter constant of No. 2, if the experiment is made in Philadelphia ? Solution. — (a) Consider No. 1 only. From formula 449, /= Hta.nm°. As H— ,194, 7n° = 52°, and tan m" = 1.28, nearly, /=.194x 1.28 = .24832. Also, from formula 448, /= ^^^^, or ^^11^=. 24832; hence, 6 2832 V v4 V 1 -^ j^ ^^ = .24832; .62832^ = .24832, and A = .3952 C. G. S. units of current. As A equals C. G. S. units, this result must be multiplied by 10 to give practical units = 3.952 amperes. Ans. (d) In No. 2 the current is 3.952 amperes and the tangent of the angle of deflection ~ tan 38° = .7813, nearly ; substituting in formula * Whenever the word ampere is used alone, the practical unit (one-tenth of the C. G. S. unit) is understood. The C. G. S. unit, when used, is called the C G. S. unit. 1602 ELECTRICAL MEASUREMENTS. 450, C= A^tan m° ; (:'= 3.953, and tan m" = .7813, 3.952 = A'X .TOIS, 8.952 .7813 A' =5.058. Ans. Remark. — This value of A' is only good for the first section of the galvanometer coil, which consists of three turns. If the value of H in formula 449,/= H tan ;«% be calculated for this galvanometer, then changes may be made in the number of turns of the coil used, without recalculating a galvanometer constant, if the controlling magnet be unchanged. In the example above given, the value oifirv No. 2 is obviously three times that in No. 1, as the same current passes through three times the length of wire. Therefore, /= 3 X .24832 = .74496, and tan m° — tan. f 744qfi 38° = .7813, nearly. As ■' , = H, then, ' JT: " = AT = .9535. ■' tan;« .7813 This value of H represents the combined. value of the field due to the earth and that due to the controlling magnet. As will be seen, the intensity of this field is nearly five times that of the earth alone ; so galvanometer No. 2 may be used to measure currents of about five times the strength that No, 1 will measure under the same conditions. EXAMPLES FOR PRACTICE. 2471. 1. A coil of wire is wound 20 cm. in diameter and con- sists of 5 turns. Through this coil a current of 12 amperes is passed. What will be the force exerted on a unit magnet pole at the center of the coil ? Ans. 3.77 dynes. 2. Using the galvanometer (Art. 3469), a current of 5 amperes is passed through the second section of the coil, {a) What will be the deflection in degrees ? {b) What would be the deflection if the instru- ment were in Washington instead of Boston ? (c) What current would a deflection of 46° indicate, using the first section of the coil and taking the measurement in Chicago ? i (a) 61° 35', nearly. Ans. ] \b) 57° 31', nearly. ( {c) 1.01 amperes, nearly. 3. A galvanometer with a coil 12 in. diameter having 12 turns of wire gives a deflection of 42° when a certain current is passed through the instrument being set up in Montreal. What is the value of this current in amperes ? Ans. .267" ampere. SINE GALVAIVOMETER. 2472. Another form of galvanometer, shown in Fig. 985, employs much the same principle as the tangent gal- vanometer, except that its coil C is movable about a verti- cal axis. ELECTRICAL MEASUREMENTS. 1603 This instrument being set up with the plane of its coil in the earth's magnetic meridian, and the pointer (which, as in the tangent galvanometer, is usually fixed at right angles to the magnet) at zero, a current is sent through the coil by- means of the wires W, which deflects the magnet. The coil is then turned in the same di- rection that the magnet is de- flected, until in such a position that the magnet comes to rest with the plane of the coil coin- ciding with the direction of the magnet. This point is usually determined by a mark on a part of the support of the coil, which must be made to register with the pointer attached to the magnet. The angle through which the coil has been turned is read by a vernier from a scale of degrees .S attached to the base of the instrument, and tJie sine of this angle multiplied by the proper constant gives the fig. 985. current flowing in the coil^ whence the name. 2473. The theory of the sine galvanometer may be demonstrated as follows: In Fig. 986, NS is a magnet which is acted on by the earth's field along the line a b, the direction of the force on the N pole being represented by the line Nc. Another force is also acting on the magnet at right angles to its axis NS, along the line xy. This force acts on the N pole in the direction represented by the line N d. As the forces acting on the S pole are equal to those acting on the N pole, only the latter need be considered. As before, call the horizontal component of the strength of the earth's field H, the strength of the force acting along the line .arj, /,and the strength of the pole of the magnet,/. 1604 ELECTRICAL MEASUREMENTS. Let the line N c represent the amount and direction of the force H p due to the earth's field, and the line N dxho. amount and direction of the other force; then, by comple- ting the parallelogram of forces (see Art. 875) the re- sultant of the two, N c, is found. This resultant N e repre- sents the direction and amount of the single force that would deflect the mag- net to the position shown, where it makes the angle vi° with the line N c^ which is parallel to a b. It is evident that the lengths N c and A^0.; Rule. — To determine the strengtJi of a ciirrent by decom- position of water y subtract from the original zveight of the apparatus its weight after the current has passed tJirough ; divide this result, expressed in grams or grains, by the length of time the current ivas passing, in seconds, multiplied by the number of grams or grains of water which can be decomposed by 1 ampere in 1 second. Example. — The original weight of the apparatus was 980.5 grams ; the current was passed through for 38 minutes, and the weight was then found to be 979.6 grams; what was the strength of the current in amperes ? 1628 ELECTRICAL MEASUREMENTS. Solution. — In this example, Wi = 980.5 grams ; w-^ = 979.6 grams 88 minutes = 2,280 seconds = /. Then, by formula 455, 980.5-979.6 .9 . _„„ , . ^= .00009324X2,280 = :2i25872 = ^•'''+ ^"^P^^^^" ^"^- It will now be readily seen that if a galvanometer be con- nected in series with the apparatus for decomposing the water, and the deflection noted, its galvanometer constant may be easily calculated. EXAMPLES FOR PRACTICE. 1. If the loss in weight of apparatus be 3.462 grains after a current has passed through for 40 minutes, how many amperes have been passing ? Ans. 1.0025 amperes. 2. If .756 ampere is passed through the apparatus for 1 hour, what will be the loss of weight of the apparatus {a) in grams ? {b) in grains ? Ans. i(-)-2537+. ({b) 3.9158 -h. Note. — In decomposing water, a battery of sufficient number of cells to give about 3 volts should be used. The cells should give a constant current. 2496. If a solution of copper sulphate (blue vitriol) be used instead of acidulated water, the decomposition of the liquid by the current will cause a deposit of copper on the negative plate. The weight of copper deposited in' a given time is proportional to the current flowing, and 1 ampere will deposit .0003286 gram of copper in 1 second. Moderate variations in the proportions of copper sulphate in the solution or the temperature do not affect the result appreciably. The above figure is given for a half saturated solution of copper sulphate [that is, about 1 part (by weight) of copper sulphate to 5 parts of water] at a temperature of 73° F. A reduction of temperature to 54° F. would not alter the figure given by more than .03^, In making measurements of the amount of copper depos- ited, electrodes of copper should be used, of such size that there shall be from 8 to 15 square inches of surface to be deposited upon for each ampere of current. When the copper is deposited from the copper sulphate solution, sulphuric acid is set free, which dissolves a portion ELECTRICAL MEASUREMENTS. 1629 oi the positive plate, forming copper sulphate, thus keeping the amount of copper sulphate in solution practically con- stant. The positive plate does not lose in weight in direct proportion to the current passing, so in measurements of this description the gain in weight of the negative plate only is measured. 2497. Apparatus prepared according to the following description will afford a means of measuring the current, which requires even less apparatus than the weight method of water decomposition, but the precautions therein noted should be taken to insure reliable results. Trough. — The vessel or trough used should be of wood or other insulating material, of sufficient size to allow the square part of the plates to hang entirely below the surface of the liquid. 2498. Plates. — It would be best to use three plates, one negative or £^am plate, suspended between two positive or loss plates, which should be of the same shape and mate- rial as the gain plate, but somewhat smaller and thicker The gain plate should be of very thin copper, so that its gain in weight will be enough to make considerable differ- ence between its weights before and after the test. The plates should be cut approximately square and the corners clipped off. It is rather better to make them circu- lar, but this form is often not as convenient to prepare, and is not at all necessary. From one side of the plate a narrow strip should be left projecting, long enough to bend into a hook by which to hang the plate on the scales or in the liquid. Three pieces of heavy bare copper wire or rod should be provided, long enough to reach across the top of the trough ; on resting these on the edges of the trough a short distance apart, the electrodes may be readily hung from them and the necessary connections made to them from the battery. The positive plates should be rubbed bright on both sides with fine sandpaper. The negative plate should be 1630 ELECTRICAL MEASUREMENTS. carefully rubbed smooth and bright with very fine sandpaper or emery, taking great care not to touch the part of the bright surface that will be below the surface of the liquid with the bare fingers or any greasy substance. A piece of clean paper or cloth should be used to handle the plate with. After carefully brightening the plate, it should be washed and dried carefully several times, and then accurately weighed. This preparation of the gain plate should not be made until all the rest of the apparatus is ready, as a long expo- sure to the air will oxidize the bright surface of the copper. 2499. Liquid. — Make the liquid by dissolving 1 part (by weight) of crystals of copper sulphate in 5 parts (by weight) of water, and adding about 1 per cent, of strong sulphuric acid. (One per cent, is about 3 teaspoonfuls to the quart.) This excess of acid serves to dissolve such impurities as may exist in the copper sulphate. A conducting liquid thus prepared for electrolysis or for use in a battery is known as an electrolyte. (See Art. 2238.) Other salts of metals in solution besides the above may be used as the electrolyte, with corresponding metals as electrodes. 2500. Battery and Connections. — A battery of two cells in series will be sufficient if small currents are desired. Cells should be used giving approximately a constant current. If constant-current batteries are not avail- able, use three or four cells of some other type, and insert a resistance which may be varied to keep the cur- rent constant. The various forms of cells will be described later. Connec- tions should be made by means of insulated wires, as shown in Fig. 995, where 5 = switch for making and breaking the circuit ; B = battery; keeping the current constant; G = Fig. 995. R = resistance galvanometer; for 7"= trough containing plates and liquid-, ELECTRICAL MEASUREMENTS. 1631 W, IF, JV = copper wires across top of trough from which plates are hung. 2501. After preparing the solution and setting up the apparatus, the positive plates should be hung in place, then the negative plate should be prepared and weighed; as soon as possible hang the negative plate in place; put in sufficient liquid to completely cover the plates; then, close the switch, noting the exact instant when the circuit is made. The de- flection of the galvanometer needle should be noted from time to time, and any change in the deflection corrected by changing the resistance R. After sufficient time has elapsed, open the switch, again noting the exact time. As soon as possible, take out the negative plate, wash and dry it carefully several times, and accuratel}^ weigh it. Then, find the amperes that have been flowing by the fol- lowing formulas : Let Wj = the original weight of gain plate ; w^ = the weight after the current has passed; it = time in seconds during which the current flows; C = strength of current in amperes. Then, if the weights are in grams, ~ .0003286 f ^^^^--^ If the weights are in grains, .005068/- 14»»-; Rule. — In order to determine the strength of ciirre7if by measurement of copper deposited, subtract the original zveiglit of the gain plate, in grams, from the weight as found after the experiment; divide this result by the length of time the current was flowing in seconds utultiplied by the number of grams of copper which can be deposited by 1 ampere in 1 second. After finding the current which has been passing, the galvanometer constant can be found from formulas 448 and 450. 1632 ELECTRICAL MEASUREMENTS. Example. — The negative plate io a sheet of copper about 2^ in. square and about -jV in. thick. After cleaning, it weighs 29.62 grams. The current being allowed to pass for 75 minutes, the plate weighs 31.33 grams. A tangent galvanometer in circuit gave a deflection of 42°. (a) How many amperes were passing, and {i>) what was the gal- vanometer constant ? Solution. — (a) In this example, Wi=: 29.62 grams; 'Z£'a= 31.33 grams; /f = 75 X 60 = 4,500 seconds. Then, by formula 457, the current 31.33- 29.62 , .^„. . ^ = .0003286X4.500 = ^'^^'^ ^"^P"^"^' ^'^^ {d) Use formula 450. €■= K tan m*. Tan 43° = .9004. Then, z = K\ tan 771 Note. — The weight of copper deposited per ampere per second may be taken in grains (Troy) instead of grams, and the result worked out in the same way. 1 gram = 15.432 grains (Troy). Example. — Change the weights in the above example to grains and work out the results. MEASUREMENT OF POTENTIAL. 2502. If two points between which a difference of potential exists are connected together by a conductor, a current will flow from one to the other, its value depending on the resistance of the conductor and the difference of potential between the two points. If this conductor be the coil of a galvanometer, it is obvious that the divisions on the scale may be marked to read volts instead of amperes. In Fig, 996 a current flows from the battery B through the resist- "5^ ance abed. There FIG. 996. will, therefore, be a certain fall of potential along abed, and it may be desired to measure the difference of potential between b and c. ELECTRICAL MEASUREMENTS. 1633 2503. If a galvanometer whose resistance is approxi- mately that of the part of the circuit b c x?, connected to the points b and c, the current flowing from a to b will divide at b, and a part flow through the galvanometer G. The whole current will again flow from c to d. If the resist- ance of the galvanometer is known, the current flowing through it, as measured by the deflection of the needle, is also a measure of the difference of potential between b and c, but this difference of potential is not the same as it was before the galvanometer was connected. The galvanometer being placed in parallel with a part of the circuit reduces the total resistance of the circuits, and as the distribution of resistance between a and d? is changed, the distribution of the fall of potential will also be changed. In order, therefore, to measure the difference of potential between b and c, the instrument used should be so con- structed that it will not measurably alter the conditions of the circuit. If the galvanometer G in Fig. 996 have a very high resistance as compared with b c^ so that the current passing through it will be a very small percentage of the total current in the circuit, the conditions will not be altered sufficiently to introduce any serious error. 2504. When a difference of potential exists between two points between which no current is flowing, as a battery with no external circuit made, it is usually the case that any considerable current flowing will reduce this difference of potential, owing to the internal resistance of the battery or other generator of the E. M. F. To measure this difference of potential again requires a galvanometer of such resistance that a very small current will flow through it, in order that the conditions of the cir- cuit shall not be sensibly changed; so that commercial measuring instruments that are constructed on the galva- nometer principle are divided into two classes : 1. Instruments of low resistance, so arranged that a con- siderable current is required to give readable deflections, usually with the scales so marked as to give the deflicction 1G34 ELECTRICAL MEASUREMENTS. of the needle the proper value in amperes of the current passing through the instrument. These are called am- pere-meters, or more briefly ammeters. 2. Instruments of high resistance, so arranged that very small currents will give readable deflections, and with the scales usually so marked as to give the deflection of the needle the proper value in volts of the difference in poten- tial between the points to which the instrument is connected. Such instruments are called voltmeters. 2505. Fig. 997 illustrates a method of measuring dif- ferences of potential, in which the principle of operation necessitates that no cur- rent be flowing through the galvanometer G. In the figure, abed is a re- sistance through which a current is flowing, sup- plied by the battery B. It is desired to measure the difference of potential be- + lilitililTlili ^- tween Z* and measured by the voltmeter V M. Example. — 1. If the current flowing from a to d he 2.2 amperes, and the drop from b to c he ^.25 volts, what is the resistance of the part of the circuit bcl E_ C V.M. Solution. — By formula 41 0, 7? 6.25 £•=6.25. (7 = 2.2. i? = 3.2 = 2.841 ohms. Ans. 2. If the current be found to be 21.25 amperes, and the drop in potential 4.6 volts, what is the resistance ? Ans. .2165 ohm. 2507. This method of measuring resistance is often not convenient, and many times impossible to use. Another 1636 ELECTRICAL MEASUREMENTS. method is to compare the unknown resistance with one or more known resistances in several ways. It may be done by connecting a known and the unknown resistance in series, and, on sending a current through the two, measure ing the drop in volts across each. The resistances will be directly proportional to the fall of potential, and the current need not be meas- ured. In Fig. 999, B is the bat- tery, the current from which flows through the known resistance a b and the unknown resistance b c. Voltmeters V M and K, J/, measure the fall of potential across each. The same voltmeter might readily be used for both readings. Example. — 1. If the resistance ab\s known to be 2 ohms, and the drops as measured by V M and Vi Mi are 4.25 volts in ad and 6.13 volts in b c, what is the resistance oi b cl Solution. — As the resistances are directly proportional to the drops of potential, Fig. 999. 4.25 or, 2x6.12 4.25 6.12 12.24 4.25 ohms. Ans. Example. — 2. If the drop through the known resistance is 6.28 volts and through the unknown 2.25, what is the unknown resistance if the known is 3.5 ohms ? Ans. 1.254 ohms. 2508. Another way to attain the same result would be to connect the known and the unknown resistance in parallel, and measure the current in each. The currents would be in inverse pro- portion to the resistances. In Fig. 1000 the current from the battery B di- vides at .r, a part flowing through the known resist- ance a b and the balance through the unknown Fig. looo. ELECTRICAL MEASUREMENTS. 1637 resistance c d. Ammeter A M measures the current \n ah and ammeter A^ M^ measures the current in c d. It is to be noted that the ammeters and their connecting wires should be of such low resistance as not to add mate- rially to the resistance of either branch of the circuit. Example. — If ammeter AM indicates 3.6 amperes and ammeter Ax Mx indicates 4.3 amperes, what is. the resistance oi c d \i ab is 10.5 ohms ? Solution. — As the currents are inversely proportional to the resist- ances, 4.2 : 3.6 :: 10.5 : x\ 3.6X10.5 37.80 ^ , . or x = ^ — = -^ = 9 ohms. Ans. 2509. In Fig. 1000 the drop along c d must be the same as that along^ d (neglecting the ammeter resistances). If any point in c d he selected, a point in a if can be found that will have the same difference of potential between it and x that the point in c d has. If a galvanometer is connected across from the point in ^ ^ to the point in a d, no current will flow through it, as there is no difference of potential be- tween the points. Fig. 1001 rep- resents this condition. It is obvious that the resistance from a to 7Z must be the same proportion of the total resistance a b that the resistance from c to m is of c d, in order that the drop in a n shall be the same as in c in. If the point n be moved to any point in a b, the point m must be correspondingly moved on c d, in order that there may be no current flowing though G, and that the proportion a 11 : a b \\ c 111 : c d may still hold good. It is also evident that the same proportion holds good for K b and in d \ i. e.^ n b '. a b w in d \ c d. From the above proportions, an '. c in :: a b : c d, and n b : m d w a b : c d. Therefore, an : c in v. n b : in d. 1638 ELECTRICAL MEASUREMENTS. That is, the resistance of a n is to the resistance of c in as the resistance of n b is to the resistance of in d. From this proportion, it is evident that if a ii, c in, and in d be known, the resistance of ii b may be readily calculated. This affords a ready means for measuring resistance, which, as will be shown, is very flexible and universally applicable. 25 lO. In Fig. 1002, M, N, and /'are three known resist- ances, which may be varied by known amounts. An un- known resistance X is connected to c and b, completing the c branch a c b oi the circuit from a to b. Through this circuit a current flows from the battery B. Any one of the three resistances M, N, and P may be adjusted until the galva- nometer G indicates that the points c and d are at the same potential; then, from the proportion given in Art. 2509, M:N'.:X:P. It is obvious that if M be equal to N, Jf will be equal to P, while if X be a very high or very low resistance it may be measured equally well by changing the ratio oiMtoN. In any case, M X^j^xR (459.) This method of measuring resistance is known as the Wlieatstone bridge method, and the instrument used is called a Wheatstone bridge, or, more commonly, a bridge. ELECTRICAL MEASUREMENTS. 1639 In practice, the arms J/, N, and P of the bridge are made up of a number of carefully prepared resistance coils, ac- curately adjusted to different resistances, fixed in a box, on the top of which are arranged blocks of brass, which form the terminals of the coils. The brass blocks are so situated that by inserting a metallic plug between any two of them the corresponding resistance coil is cut out, or sJwrt-circiiited ; that is, the current passes from block to block through the plug instead of going through the coil, as this path offers practically no resistance to the current. In this way the resistance of the arms of the bridge is changed. Fig. 1003 shows a section of a box of coils showing the brass blocks and the method of cutting out the coils, a, b, c, 52'3» As the number of paths for the current through the insulation increases with the length of the line, the in- sulation resistance of the line decreases as the length of the line increases ; so the total insulation resistance multiplied by the length of the line gives the insulation resistance per unit of length. The usual unit of length for overhead tele- graph and telephone lines is one mile. Example. — What is the insulation resistance per male in the above example if the line be 7.5 miles long ? Solution.— 26,700 X T.5 = 200,250 ohms, or .2 megohm, practically. Ans. This is about the insulation resistance required for ordi- nary telegraph and telephone work. The above method of testing requires a sensitive galva- nometer of fairly low resistance, and gives approximately precise results for resistances not exceeding about 30,000 ohms. If the resistance much exceeds this limit, a shunt may be used with the galvanometer of any convenient multiplying power; for example, 100. The deflection through the known resistance being noted, the shunt should be removed for the line resistance measurement. Thus, a current through the insulation resistance of — -— of the current through the 71 -\-\ known resistance (in the above case -j^xr) '^'^ give the same ELECTRICAL MEASUREMENTS. 1653 deflection, and the line insulation resistance will be a corre- sponding multiple of the known resistance. To obtain more accurate results, allowance must be made in each case for the resistance of the galvanometer and bat- tery. Usually, these are not a sufificient per cent, of the total resistance of either circuit to affect the result much. 252/4:0 Another good method of measuring insulation resistance is to make this resistance one arm of a Wheat- stone bridge, as represented in Fig. 1009. By making the #~ Fig. 1009, resistance of AI great in proportion to N, resistances as high as 2,000,000 ohms may be measured with a bridge as ordi- narily arranged. (See Fig. 1004.) * 2525. By grounding the distant end of the line L, the resistance of the conductor which makes up the line may be measured by the same methods. Grounding a cir- cuit consists in connecting it electrically with the earth, usually by means of a metal plate buried in moist earth, or to the pipes of a water or gas system. Grounding is conven- tionally represented as at E^ Figs. 1008 and 1009. The re- sistance of the earth is so slight that for small currents it may be usually neglected, if the grounding is well done. 2526. The insulation resistance of apparatus for elec- tric light and power work must be considerably greater than that for telegraph and telephone use, and the wire used is, except in special cases, covered with insulation instead of being bare. 1654 ELECTRICAL MEASUREMENTS. This insulation must not only have a high specific resist ance, but it must be able to meet various other require- ments. In wire for overhead construction, for example, the insulation must stand the abrasion of tree branches, etc., be reasonably fireproof, water-proof, able to withstand the action of the weather, and flexible enough to allow the wire to be reeled or strung in place without injury to the insulation. It is obvious that many substances of high specific resist- ance, such as glass or porcelain, would not fill some of the above conditions. In fact, there is scarcely any one sub- stance that would answer. The best grades of insulated wire are usually made with a layer of rubber, or some com- pound composed largely of rubber, surrotmding the wire, and protected by an additional covering of braided cotton or similar device, soaked in some reasonably fireproof and weather-proof compound. In order to thoroughly test the insulation resistance, con- tact should be made with the whole outer surface of the insulation. This is best done by immersing the wire in a tank of water, slightly salted to make it conducting, as shown in Fig. 1010. The tank is of metal, and the insulation resistance is measured between the water surrounding the wire and the wire itself, as shown at a b. Connection with the water is made by a binding- post attached to the metal tank, or if the tank be glass or china, a metal plate is used, dipping in the water. 2527. A long piece of wire prepared for test in this way would have a large area of insulating material between two conducting bodies, i. e., the wire and the water. On connecting the wire and water to the poles of a battery, a charge of electricity will spread itself over the inner and outer surfaces of the insulation, which will cause a momen- tary rush of current from the battery. Another phenomenon which also appears is that known to telegraph engineers as Fig. 1010. ELECTRICAL MEASUREMENTS. 1655 electrification. The exact nature of this phenomenon is not known, but it has been held by eminent authority to be 2i polarization of the insulation, and its effect is to cause a con- tinuation of the first rush of current due to the static charge, that gradually grows smaller and smaller, until after the lapse of some few minutes the current becomes steady. On disconnecting the battery and replacing it with a piece of wire, a back current will flow through the wire from surface to surface of the insulation until it is depolar- ized. In testing the insulation resistance of long pieces of wire in water, these effects may interfere materially with read- ings, especially if the Wheatstone bridge method be used. With the following methods of testing, however, it is usually sufficient to wait, after closing the current, until the current has become steady before taking readings. In testing long cables for submarine use, or long pieces of wire, it is sometimes customary to take the resistance readings after the electrification has continued for a certain definite time, usually 1 minute. This is always so stated in the results of the test, thus: " Insulation resistance per mile after 1 minute's electrification, 400 megohms. " Where the surface area of the insulation is small, the elec- trification is hardly perceptible, and ordinarily will have no effect on the readings, even if a bridge be used. 2528. The following method is like that described in Art. 2522, Fig. 1008, except that as the insulation resist- ance of a short length of well-insulated wire would be quite high, it would probably be necessary to use a shunt with the galvanometer. Fig. 1011 is a diagram of connections for such a measure- ment. The shunt S is connected in parallel with the gal- vanometer G by inserting a metal plug between the metal blocks at a. The switch K connects either the metal tank T or the known resistance R with the battery B. The best method of procedure is to first read the deflec- tion through the insulation resistance of the wire P^witb 1656 ELECTRICAL MEASUREMENTS. the shunt disconnected. Then connect in the fhunt and read the deflection through the known resistance R, chan- ging the shunt vS" until the deflection is approximately the G V Fig. 1011. same as before. Then, knowing the multiplying power of the shunt used, the insulation resistance of the wire may be calculated as in Art. 2522. Example. — In a tangent galvanometer the resistance is 600 ohms; deflection through insulation = 38° ; with a shunt of 8 ohms, deflection through resistance = 42° ; resistance i? = 10,000 ohms. What is the insulation resistance ? Solution. — Multiplying power of shunt = ^^ + 1 = 76. The deflection through the resistance = (/° =42, and the deflection through the insulation = ^°i= 38. Then, tan ^" = .9004; tan S37, If the student has access to an electric-light station he can measure the resistance of the various circuits of the dynamos or other appliances, or of the lines, at times when the station is not running, or can measure such other resistances, of between. 05 and 200 ohms, as the opportunity may allow. Other standard resistances may be prepared on the same lines as those furnished with a bridge; if made of higher or 1670 ELECTRICAL MEASUREMENTS. lower resistance than those furnished, they will increase the range of resistances that may be measured, although accu- rate measurement of high resistances (500 ohms or over) should not be expected. The best method of calibrating the tangent galvanometer is to compare it with a standard direct reading instrument — a Weston ammeter, for example. If this can not readily be done, it may be calibrated by the copper sulphate electroly- sis method described in Art. 2496 and following. The weight measurements should be carefully made on a delicate pair of scales. Any good apothecary has such a pair of scales, and would probably perform- the weighings for a small sum. In this method of calibration, copper wires may be sub- stituted for the copper plates described in Art. 2498, they being easier to clean and handle. Two wires should be used, coiled into open spirals, one about twice the diameter of the other; the smaller should be placed inside the larger, and connected to the negative pole of the battery, thereby becom- ing the electrode to be weighed. Many other useful applications of this apparatus which might be mentioned will occur to the student as he advances in the Course. PRACTICAL MEASUREMENTS. INSTRUMENTS. 2538. Most of the apparatus and tests so far described are more for laboratory use than for the shop or station, and now such accurate and reliable portable measuring in- struments are made that many measure- ments before referred to may be made with as great a degree of precision and much Fig. 1020. greater facility than ELECTRICAL MEASUREMENTS. 1671 with the various galvanometers and other apparatus already described. Some of the best forms of portable instruments tiG. 1U21. made are those known as the Weston instruments, general form is shown in Fig. 1020. These instruments are made on the principle of the D'Arsonval galvanom- eter (Art. 2476), as shown in the sec- tional view, Fig. 1021. Fig. 1022 shows the magnetic circuit of this form of instru- ment. The permanent magnet A A has soft iron pole-pieces P, P fastened to it by the m. screws S, S, and bored Fig. 1023 Theii 1672 ELECTRICAL MEASUREMENTS. out to make a cylindrical opening. In the center of this open- ing is a stationary soft iron cylinder C, supported in place by a screw J/ passing through a lug on the brass plate B. This cylinder being of less diameter than the opening through the pole-pieces, there is left a narrow gap between the pole-pieces and the iron core, as shown. The lines of force from the permanent magnet pass across this space, making a strong and uniform magnetic field. The movable part of the instrument is shown in Fig. 1023. It consists of a rectangular coil C of fine wire wound on an Fig. loas. aluminum or thin copper bobbin, which is suspended verti- cally between two delicate jeweled bearings. Two flat horizontal spiral springs 5, 5 oppose the tendency of the coil to rotate, and at the same time conduct the current to the suspended coil. A thin aluminum pointer P, attached at right angles to the coil, moves over a scale and indicates the deflection of the coil from its normal position, which is as shown in Fig. 1021. On a current being sent through the coil by means of the springs vS, 5, there is a tendency for the coil to move through the magnetic field (Art. 2438), which it will do until the torsion of the spiral springs equals the force with which the coil tends to move, when the coil will come to rest, and the pointer will indicate the angle of deflection of the coil. The magnetic field being practically uniform, the angle of ELECTRICAL MEASUREMENTS. 1673 deflection is closely proportional to the current in the coil, so the scale divisions are very uniform, as is shown by Fig. 1024, which is a scale about three-fourths size. The copper or aluminum bobbin on which the coil is wound, in moving through the magnetic field, has an electromotive 60 70 80 _ 90 I "JO Fig. 1024. force set up in it which causes a current to circulate around the bobbin as long as the bobbin moves. This current cir- culates in thie opposite direction to the current in the coil; hence, it tends to oppose the motion of the coil. As this tendency exists only when the bobbin is moving, it has the effect of preventing the needle from swinging too far over the scale, thus bringing it quickly to rest at the proper point. This damping effect is due almost entirely to the currents in the bobbin. The friction is so slight that it has practically no effect on the position the needle will take. This is shown by the fact that the needle having been deflected by a cur- rent will respond to very minute variations in that current; that is, the instruments are very sensitive. An instrument whose moving system possesses this feature of coming to rest quickly at the proper point is known as a dead-beat instrument ; this is a very important feature, for it assists the rapidity of taking measurements very materially. The moving system is practically the same for all direct-cur- rent Weston ammeters and voltmeters. If the instrument is designed for a voltmeter, a high resistance, located in the back of the case, is connected in series with the movable coil; if for an ammeter, the coil is connected in parallel with a short, thick piece of copper or some alloy, so that only a small part of the current passes through the movable coil, and the resistance of the instrument is extremely low. By 1674 ELECTRICAL MEASUREMENTS. reason of this extremely low resistance of the ammeters and the high resistance of the voltmeters, they consume very little energy indeed, and may be left continuously in circuit without undue heating. For example, a 15-ampere Weston ammeter has an internal resistance of .0022 ohm; when measuring a 10-ampere cur- rent, the drop (C R) is .022 volt, and the watts expended (C E) = .22, or about one thirty-four-hundredth I J of a horsepower. The resistance of a 150-volt voltmeter is about 19,000 ohms. Measuring 110 volts, the instrument would take = .0058 ampere, nearly, with a consumption of energy of .638 watt, nearly, or about of a horsepower. 1,200 The conducting parts of the instrument are made of an alloy having a very low temperature coefficient, so that moderate changes in the temperature of the instrument do not affect its readings appreciably. Beneath the needle just inside the scale is a mirror. On looking down on the needle, by getting the needle directly over its reflection in the mirror, errors due to not getting the needle in line with the scale (known as parallax) are eliminated. These several good features make these instruments very reliable and convenient for making all sorts of electrical measurements, and as they may be obtained in a great variety of ranges, their use is very general. There are many other forms of portable instruments made, most of them being constructed on the same general principle as the Weston, and they may often be used in making various measurements to good advantage. SIEMENS DYNAMOMETER. 2539. Another instrument which is largely used for measuring currents is the Siemens dynamometer. This in- strument is constructed on the same fundamental principle that the Weston and many other electromagnetic instru- ELECTRICAL MEASUREMENTS. 1675 ments are, namely, that a conductor carrying a current will tend to move, if in a magnetic field, with the direction of the lines of force at an angle to the direction of the current. The working parts of this instrument, one form of which is shown in Fig. 1025, consists of two rectangular coils of wire, one, i% fixed, the other, M, mova- ble. The normal po- sition of the movable coil is with its plane at right angles to the plane of the fixed coil, and it is sus- pended in this posi- tion by a fiber. To the top of the coil is also attached a light helical spring S, the other end of which is attached to a milled nut T. On turning this nut the spring will be tightened, Fig. 1025. thus acting to move the coil. The two coils are connected in series, connection being made to the movable coil by means of mercury cups C, C, into which the ends of the coil dip. On sending a current through the two coils in series, the mutual action of the two coils tends to move them into par- allel planes. The effect is to rotate the movable coil about its vertical axis; by turning the milled nut, a tension may be put on the spring which will return the coil to its origi- nal position. The force exerted by the spring on the coil is proportional to the angle through which the milled head attached to the spring is turned; so, by a pointer P, at- tached to the milled head, the force required to pull the coil back to its central position may be indicated. A pointer /, attached to the movable coil, is opposite a rm=.^^ Hc^ r#r™=----^^^^""' ?■ V j 1 \/ V 1676 ELECTRICAL MEASUREMENTS. zero mark on the scale when the movable coil is at right angles to the fixed coil. As the two coils are in series, doubling the current in one coil doubles it in the other, so the mutual force of both coils is doubled, and the force acting on the movable coil is quadrupled ; that is, the force on the movable coil, hence the torsion in the spring necessary to bring the pointer on the coil back to zero, is proportional to the square of the current. These instruments are seldom made direct reading, but are furnished with a table which gives the deflections corre- sponding to various current strengths. Intermediate values may be interpolated or calculated. The fixed coil is usually wound in two parts of unequal number of turns and size of wire; either coil may be used, thus varying the range of the instrument. This form of in- strument is especially useful, as it may be used equally well for alternating current as for direct, since there is no iron or other magnetic material used in its construction. EDISON CHEMICAL. METER. 2540. As stated, most of the measuring instruments in commercial use depend on the electromagnetic effect of a current for their action; perhaps the only electrochemical current meter that is in commercial use is the Edison chem- ical meter, which is extensively used by the Edison Illumi- nating Companies. In this instrument a fixed proportion of the current passing through the meter is shunted through an electrolytic bath consisting of two zinc plates dipping in a solution of sulphate of zinc. The plates, solution, and con- nectors are all mounted in little glass jars, and two jars are set up in each meter, one to act as a check on the other. At the end of a certain fixed time (usually thirty days) the jars and their contents are replaced by others, and the am- pere-hours of current that have been used by the customer calculated from the gain in weight of the negative plate. By various ingenious devices in the several parts of the meter, the effects of various sources of error are almost ELECTRICAL MEASUREMENTS. 1677 entirely removed. Great care, however, must be exercised in removing the jars and caring for their contents. Fig. Fig. 1026. 1026 gives a view of the latest type of Edison chemical meter. CARDEIV VOLTMETER. 2541. The representative instrument of the class that measures the heating effect of the current is the Cardew voltmeter, illustrated in Fig. 1027. In this instrument a long wire w, usually of some platinum alloy, is stretched from end to end of the long tube a ; each end is fastened to the dial end of the tube ; the wire then passes over pulleys at the end of the tube and back to the dial end, where a spring attached to the middle of the wire keeps it stretched taut. On a current being sent through the wire, the heat caused by the passage of the current 1678 ELECTRICAL MEASUREMENTS. expands the wire; the addition to its length is taken up by the spring-, and the motion of the middle of the wire which is attached to the spring is transmitted to a needle b by suitable multiplying gear, so that the motion of the needle over the dial is a measure of the amount of expansion of the wire. The wire is usually of small diameter and considerable specific resistance, so that it in itself has resistance enough to allow the in- strument to be used as a voltmeter for poten- tials less than about 100 volts without external resistance. This voltmeter may be used either for alternating or direct currents, is remark- ably dead-beat, and simple in construction. Its internal resistance is low for a voltmeter, and, in consequence, it takes considerable current, enough in many instances to seriously affect some conditions of an experiment. This in- strument has no particular law of deflections FIG. 1027. by which the scale is divided; the principal di- visions are determined by comparing the instrument with a standard, and the intermediate divisions interpolated. There are several other instruments made on this prin- ciple, commonly known as hot-wire instruments ; the Cardew is the best known. ^w "WATTMETERS. 2542. The energy expended in a circuit being the product of the current and the electromotive force, these factors may be measured separately, and multiplied together to obtain the number of watts expended. Instruments have been designed, however, which automatically perform this multiplication, thus measuring watts directly, one of the best known being the Siemens wattmeter. This instrument is of the same general form as the current-meter, Fig. 1025, the difference between the instru- ments being that in the wattmeter the two coils are not ELECTRICAL MEASUREMENTS. 1679 consequently the total Fig. 1028. in series. This instrument measures at all times the product of the current in any circuit and the difference of potential between the ends of that circuit. The stationary coil is in series with the outside circuit: current flows through it. The movable coil is in series with a resist- ance great enough to prevent the full differ- ence of potential be- tween the mains send- ing more than a small amount of current ^ through the movable (S(S?)(^ d coil. This coil and the resistance are then con- nected in parallel with the rest of the circuit, as shown in Fig. 1028, where F is the fixed coil of the instrument; J/, the movable coil; 7?, the resistance that is connected in series with M\ D, the source of electricity, and C the; exter- nal circuit, the energy expended in which it is desired to measure. It is evident that if the drop in volts through the circuit C be constant, the current through M will also be constant. The force acting on the movable coil will then vary directly as the current in the coil F; the potential being constant, the watts expended in the circuit will also vary directly as the current. If the current in the coil F is constant, variations in the E. M. F. will vary the current in the coil M in the same proportion, and the force on the coil 71/ will then vary directly as the E. M. F. ; the current in the circuit C being constant, the watts will also vary directly as the E. M. F. So, in either case, the force acting on the movable coil (consequently the force required to bring it to zero position) varies directly as the watts. When varia- tions occur in both current and potential simultaneously, the same holds true, and the force required to bring the coil to the zero position is proportional to the watts. 1680 ELECTRICAL MEASUREMENTS. The general appearance of the wattmeter is almost pre- cisely the same as that of the current dynamometer. The resistance used with the movable coil is usually made a. separate piece of apparatus; when made so that it has no self-induction^ the wattmeter may be used for measuring the energy expended in alternating-current circuits. THE THOMSON RECORDING WATTMETER. 2543. The Siemens wattmeter gives the instantaneous value of the watts expended in the circuit. The Thomson wattmeter is, as its name indicates, a recording meter, and its readings give the product of the watts and time, i. e., the watt-hours. The construction is simple; the principle is, broadly, that of the Siemens dynamometer. The movable coil is not held to zero position, but revolves, and does not surround the fixed coil, but revolves between two fixed coils. The movable coil is really a small drum-wound armature^ provided with a small coinmutator made of silver to prevent oxidation. The effect of using the commutator is to make the effective plane of the coil (armature) take a position at right angles to the plane of the fixed coils. The connections of this instrument are made on the same principle as those of the Siemens wattmeter. The fixed coils are in series with the circuit, and the movable coil and a resistance in series with it are in parallel with the circuit. The amount of energy expended in the circuit is measured by the rotation of the movable coil, a worm on the shaft on which the movable coil is mounted engaging with a set of gears which operate a dial similar to a gas-meter dial, so that the energy expended in a certain given time in the cir- cuit may be read directly from the dial in watt-hours. The friction of the apparatus being exceedingly small, the retarding force on the coil that opposes its tendency to rotate is imparted by a thin copper disk attached to the shaft on which the movable coil is mounted. This disk is rotated between the poles of strong permanent magnets; the lines of force from the magnets cutting the disk set up electromotive forces between adjacent points on the disk; ELECTRICAL MEASUREMENTS. 1681 the disk being of copper, the resistance between those points is very low, so that a considerable current may flow. This current tends to retard the rotation of the copper disk, and this tendency increases directly as the speed. As in the Siemens wattmeter, the force acting to rotate the movable Fig. 1029. coil increases directly as the watts; therefore, the number of revolutions of the moving system of the meter will be directly proportional to the watts expended in the circuit; This meter may be used for either alternating or direct cur- rents, and gives very accurate results. Fig. 1029 represents the Thomson meter with the cover removed. SH ALLEN BERGER METER. 2544. This meter is constructed on a similar principle to the Thomson meter, but is designed to be used only on alternating-current circuits, as is also the Duncan meter. Other recording meters are in use, but are usually compli- cated in construction and rather unreliable in operation. 1682 ELECTRICAL MEASUREMENTS. In addition to the Siemens wattmeter, there have recently been introduced general forms of portable direct-reading wattmeters, which are giving good satisfaction, and are more convenient to use than the Siemens form. SWITCHBOARD INSTRUMEIVTS. 2545. In lighting and power stations and similar places, it is often desirable to know the approximate number of amperes, volts, or watts delivered by a machine or machines, and for this purpose instruments have come into use which, while not sufficiently accurate for making reliable measure- ments to a great degree of precision, are very useful in indicating approximately the output of a machine or the load on a circuit. The scales of such instruments are usually large and open, so they may be read from a dis- tance. Many forms of such instruments are made by different manufacturers ; their principle of operation is usu- ally the electromagnetic effect of the current, but their de- tails of construction will not be described here. MEASUREMENTS WITH COMMERCIAL INSTRUMENTS. 2546. Most of the measurements previously described as being made with some form of galvanometer can be made with good commercial instruments — the Weston, for example. In the Weston instruments, the terminals of the ammeter are both on the same (right) side of the instrument (see Fig. 1020), and are made large and heavy, while in the volt- meters the terminals are on opposite sides, are made small, and are usually covered with rubber, in order that they may be handled without danger from shocks. Some of the voltmeters are made with the resistance coils in two sec- tions, of such relative value that, when only one section is in circuit, the scale readings are some convenient submulti- ple of the readings when both sections are used. In this case the instrument is provided with an extra binding-post ELECTRICAL MEASUREMENTS. 1683 on the left side, and the scale divisions have two values; for instance, the voltmeter with a range of 150 volts may- have the resistance so divided that by using the third bind- ing-post the range will be 15 volts and the scale divisions will have yV their former value. Measurements of current strength or difference of poten- tial are very simple. To measure the number of amperes flowing in a circuit, it is only necessary to connect an ammeter of proper capacity in series with the rest of the circuit, as shown in Fig. 1030, and read the amperes directly from the posi- tion of the pointer on the scale. The resistance of the ammeter, as pointed fig. io30. out, is so low that it will not affect the total resistance of the circuit appreciably. The difference of potential between two points in a circuit, or the E. M. F. of a battery, or other source of E. M. F., may be readily measured by connecting the terminals of a voltmeter to the proper points of the circuit and read- ing the voltage direct, as shown in Fig. 1031. By using instruments of the proper range, very low or very high resistances may be measured. Fig. 1032 shows a way of measuring a very low resistance — in this case a section of copper rod. Here a current from the bat- tery B, measured by the ammeter A, flows through the section of copper rod R, and the drop between the points C and D is fig. 1032. 1684 ELECTRICAL MEASUREMENTS. measured by the voltmeter V. As the drop through a short section of copper rod would be very slight, except with an enormous current, a voltmeter capable of measuring very small differences of potential must be used. They may be had to measure from to ,05 volt, such an instrument being known as a millivoltmeter. Example. — If, in the above figure, the reading of the ammeter be 34.5 amperes, and that of the millivoltmeter be .00875 volt, what is the resistance of the copper rod between C and B ? .00875 Solution. — -=f 35.4 = .000247 ohm. Ans. J5i ls> ^ r.M. \-^I\I\l\ 'l/WW High resistances may be measured in a similar manner by using a low-reading ammeter (mil-ammeter) and a high- reading voltmeter. The high-reading voltmeters may also be used to measure very high resistances, such as insulation I I I I resistances; the method of connecting up for such a test is shown in Fig. 1033. Here jI^ is the insulation to be measured, B C a. battery or other source of E. M. F., which should be as high as convenient, as long as it is within the range of the in- strument, V M the volt- meter, and K a switch for shunting the resistance R. As the resistance of the switch K is practically nothing, it is evident that when it is closed the voltmeter is connected directly to the terminals of the battery and will measure its E. M. F., and when the switch K is open the resistance R is in series with the voltmeter. The formula for finding the value of R in ohms is R = r{^-lS^, (466,) where d =■ deflection of voltmeter with the resistance R not in circuit, d^ = deflection of voltmeter with resistance R in circuit, and r -•. resistance of voltmeter. This formula is obtained as follows: The E. M. F. of the Pig. 1033. ELECTRICAL MEASUREMENTS. 1685 battery B C being constant, the drop through the voltmeter only or the voltmeter and resistance in series will be the same, that is, C r = C^R-\- C^ r. As the deflection of the voltmeter needle is proportional to the current, this may be written dr = d^R-[- d^r\ or, dr — d^r = d^R\ dr d^r „ dr jy hence, ^\~^ — l)=-^» which is the formula given. In the simple case where the resistance to be measured is just equal to the voltmeter resistance, it is evident that the deflection of the voltmeter with the resistance in series with it would be half that when the voltmeter alone is in circuit, which satisfies the equation as follows: Given, rX{\ — l)=R. Then, rxl=Ry and r = R. Example. — If the E. M. F. of the battery, as measured by the volt- meter, is 100 volts, and the deflection, when the resistance to be measured is in circuit, is 40 volts, what is the value of that resistance in ohms if the resistance of the voltmeter is 18,000 ohms ? Solution.— In this case ^=100, di = 40, r= 18,000. Then, by formula 466, J? = 18,000(^3:7- _ 1) = 18,000 X 1.5 = 27,000 ohms. Ans. 2547. It will be seen that this method of testing insula- tion is on exactly the same principle as that shown in Fig. 1008 (Art. 2522), the known resistance in this case being that of the instrument itself. Slight variations in the E. M. F. of the source of supply do not afifect the result very materially, and when an approximately constant known E. M. F. is available, such as an electric-lighting circuit, in- sulation tests may be made with great facility by merely connecting the voltmeter in series with the E. M. F. and 1686 ELECTRICAL MEASUREMENTS. the insulation resistance. On the assumption that the E. M. F. has a constant (known) value, a table may be prepared showing the insula- tion resistance corresponding to various deflections of the voltmeter. This affords a ready means of testing the insulation resist- ance of lighting circuits where the E. M. F. of the dynamos is constant, if the voltmeter is of high resistance; by con- necting the voltmeter be- tween one side of the circuit and the ground, the deflection of the needle will give the insulation resistance of the otJier side of the line, or will show the presence of a "ground," as represented in Fig. 1034. Both sides may be tested in this manner, and it is usual to provide a small switch or other convenient apparatus for readily making the desired con- nections. Fig. 1034. Fig. 1035. 2548. For many electrical measurements, it is neces- sary to know the rate of revolution of certain moving parts ELECTRICAL MEASUREMENTS. 1687 Fig. 1036. of machinery. The number of revolutions made by the machinery in one minute or other length of time does not necessarily give its rate of revolution, so that for ac- curate work the ordinary revolution counter is scarcely suitable. Instruments called tachometers are made which indicate by the posi- tion of a needle on a dial the rate of revolution of the ap- paratus to which they are connected. The principle of these instruments is similar to that of a centrifugal en- gine governor; two weights are thrown out from their center of rotation by centrif- ugal force, and their ten- dency to move is overcome by a spring. By suitable gearing the motion of the weights is made to actuate a pointer which moves over a suitably divided dial, thus indicating the rate of rota- tion of the weights. Fig. 1035 shows a form of tachometer which, being belted to a pulley of suitable diameter by a light belt, will give the rate of revolution of that pulley. The form shown in Fig. 1036 is intended to hold in the hands. A three-sided 1688 ELECTRICAL MEASUREMENTS. point on one of the spindles of the instrument is intended to be thrust into the center mark of a revolving shaft, when the rate of revolution of that shaft is indicated on the dial. It is usual to make three little ridges in the sloping sides of the center mark of the shaft with a three-sided punch (sup- plied with the instrument), to insure that the point on the tachometer shaft will not slip when the instrument is applied. 2549. Electrical measurements may be broadly stated to be measurement of current. The principal methods of measuring current and their general applications have been described, but for particular cases these methods often require much modification in detail, and to arrive at cer- tain results many combinations of such methods may be made, according to the requirements of the case in hand. Some of these combinations and modifications for special cases will be described where necessary in succeeding sections. BATTERIES. DEFINITIONS. 2550. An electric battery is a combination of a num- ber of separate electric sources. Thus, a voltaic or galvanic battery (see Arts. 2238 and 2239) is a combination of a number of separate voltaic cells properly joined together. The term battery is also applied to a combination of Leyden jars (see Art. 2232) properly joined together so as to form a so-called Leyden battery. A battery of this kind, however, has very little practical value, in the present state of the art, compared to the value of the two great classes of batteries treated of in this discussion, namely: I. Primary batteries. II. Secondary or storage batteries, sometimes called accumulators. 255 1 . A primary battery is a combination of a num- ber of primary cells so as to form a single source. 2552. A secondary or storage battery is a com- bination of a number of secondary cells so as to form a single electric source. 2553. Primary batteries, as well as secondary batteries, depend for their operation upon the chemical action which takes place between certain different substances when brought into contact with each other. The whole theory and operation of cells and batteries being thus dependent on chemical action, it is necessary to give here some prin- ciples of chemistry, which is that science which treats of the composition of matter, of the changes produced therein by the action of heat and other natural forces, and of the action and reaction of different kinds of matter upon each Other. For notice of copyright, see page imnaediately following the title page. 1690 BATTERIES. PRINCIPLES OF CHEMISTRY. 2554. Chemical action is that which produces a change in the chemical condition of matter, and may be action of decomposition, i. e., spHtting a substance up into other distinct substances; or action of recomposition, i. e. , uniting two or more different substances into a new one. 2555. Decomposition can not go on indefinitely; if a substance be split up by decomposition, and the resulting substances (if possible) be again split up, and so on, a point will be reached where substances are found which by no known process can be further decomposed. Such substances are called elements. 2556. A chemical compound is the union of two or more elements to form a new substance. Compounds may be formed by the union of two or more compounds; but this is merely a new union of the elements which originally formed the uniting compounds. 2557. There have so far been discovered about seventy- two substances which seem to be elements. About half of these are very rare ; the balance, the more important, are given in Table 89. To prevent constant repetitions of their names, and to aid in expressing the composition of sub- stances, there has been assigned to each element a symbol^ consisting of the initial letter, or the initial letter and another letter of its Latin name, which is often different from its com- njon name. These symbols are given in column 2, Table 89. 2558. The exact nature of chemical action is not known, any more than is the exact nature of electricity or heat; but it is similar to other physical phenomena in that chemical action is a manifestation of energy. This energy is appar- ently stored up in the atoms of the elements 2^^ potential energy, and causes such atoms to have an affinity for, or tendency to combine with, other atoms, this affinity being greater or less according to the relative amount of potential energy stored in the combining atoms. Under the proper conditions, these affinities cause the atoms to combine, BATTERIES. 1691 which allows their potential energy to appear as kinetic energy, usually in the form of heat. Thus, chemical com- bination develops kinetic energy, while to perform chemical decomposition, kinetic energy must be supplied. 2559. The heat given out by the formation of a com- pound is known as the heat of formation of that substance. The amount of this heat has been measured in the case of some substances, and tables giving these values are published in most works on chemistry. Note. — The heat of formation is usually expressed in calories (per gram of the substance), the calorie used being the lesser, or grain- degree, calorie which is the heat required to raise 1 gram of water 1° C. It is obviously .001 of the calorie defined in Art. 1 130. 2560. An element is the ultimate substance to which any compound can be chemically subdivided. As has been explained in Art. 1089, all matter (every substance) is (mechanically) composed of molecules, they being the small- est /(:zr//<:/^.s' into which the substance can be mechanically subdivided without being resolved into its elements. The molecules are each made up of a number of atoms of the elements of which the substance is composed, and in any given substance each molecule is always composed of the saine total member of atoms of its elements combined in the same proportions; if the proportionate number of atoms of any element is changed, a new substance is formed. When an element exists uncombined, its atoms do not exist alone, but group together into molecules, just as the atoms of the different elements group together to form the molecules of the compound. 2561. By very careful analysis and measurement, it has been determined that elements always combine in certain fixed proportions or multiples of those proportions; from this fact, it is possible to assign to each element a number, which number, or a multiple of it, will represent the propor- tion, by weight, of that element which enters into any com- pound. To this number is assigned the name atomic weight, and these numbers represent the relative rveights 1692 BATTERIES. of the atoms of the elements. The actual weight of an atom has been calculated, but is unimportant here. Hydrogen being the lightest of the elements, the weight of its atom is taken as the unit, and the atomic weights of all other elements calculated therefrom. The atomic weights of the more common elements will be found in col- umn 3 of Table 89. TABLE 89. THE PRINCIPAL ELEMENTS. Name of Element. Aluminum Antimony- Arsenic .. . Barium. . , Bismuth . . Boron .... Bromine . . Cadmium. Calcium.. . Carbon . . . Chlorine . , Chromium Cobalt . . . Copper.. . . Fluorine . . Gold Hydrogen . Sym- bol. Al Sb As Ba Bi B Br Cd Ca Atomic Weight. 27.00 120.00 75.00 137.00 208.90 11.00 79-95 112.00 40.00 t 12.00 CI 35-45 Cr 52.10 Co 59.00 Cu 63.40 Fl 19.00 An 197.30 H 1. 00 Valency. Ill V V II V III I VII II II IV I VII II VI i n ^ VIII i I ( II I VII j I I III I Chemical Equiva- lent. 9.00 24.00 15.00 68.50 41-78 3.66 79-95 11.42 56.00 20.00 3.00 35-45 5-07 26.05 7-44 29.50 7-38 63.40 31.70 19.00 2.57 197.30 65-77 Electro- chemical Equivalent. Grams per Coulomb. .00009324 .00024860 .00015540 .00070960 .00043280 .00003792 .00082100 .00011840 .00058020 .00020720 .00003098 .00036730 .00005252 .00026990 .00007708 .00030560 .00007646 .00065680 .00032840 .00019680 .00002663 .00204400 .00068140 .00001036 BATTERIES. 1693 TABLE 89 — Continued. Name of Element. Sym- bol. Atomic Weight. Valencv. Chemical Equiva- lent. 6. Electro- chemical Equivalent. Grams per Coulomb. Iodine. Iron . Lead Magnesium Manganese. Mercury , Nickel .... Nitrogen. . . Oxygen .... Phosphorus Platinum.. . Potassium.. Selenium. . . Silicon. . . . Silver Sodium .. . Strontium. Sulphur . . Telluriufn Tin Zinc Fe Pb Mg Mn Her Si Ag Na Sr 125-85 56.00 206.95 24.30 Ni 58.00 N 14.03 16.00 P 31.00 Pt 195.00 K 39-11 Se 79.00 28.40 107.90 23-05 87.60 5 32.06 Te 125.00 Sn 119.00 Zn 65-30 j I ( VII II IV II IV II II VII I II i II (VIII V i II \ VI V II IV I j II I VI IV I I II i II ( VI II II IV II 125.85 17.98 28.00 14.00 103.48 51-74 12.15 27.50 7.86 200.00 100.00 29.00 7-25 2.81 8.00 2.67 6. 20 97-50 48.75 39-11 39-50 13-17 7. 10 107.90 23-05 43.80 16.03 5-34 62.50 59-50 29-75 32-65 .00130300 .00018630 .00029010 .00014500 .00107200 .00053600 .00012590 .00028490 .00008143 .00207200 .00103600 .00030040 .00007510 .00002911 .00008288 .00002766 .00006423 .00101000 .00050500 .00040520 .00040920 .00013640 .00007355 .001 1 1800 .00023880 -00045370 .00016610 .00005532 .00064750 .00061640 .00030820 .00033820 The names of the non-metallic elements are printed in italics. 1694 BATTERIES. 2562. In indicating the elements wiiich make up any substance, the symbols of those elements are commonly used ; also, to indicate the number of atoms (if more than one) in the molecule, a small number is suffixed to the symbol. The expression of the chemical constitution of a substance by means of the symbols, with the relative number of atoms of each element suffixed, is called the chemical formula of that substance. Thus, a substance (water) whose formula is H/J is com- posed of hydrogen and oxygen, and each molecule of water is composed of two atoms of hydrogen and one of oxygen. The atomic weights of H and O (from Table 89) are 1 and 16, respectively. Therefore, any weight of water is com- posed of 2 X 1 = 2 parts by weight of hydrogen and 16X1 = 16 parts by weight of oxygen. It follows, then, that the weight of 1 molecule of water will be 2 + IG = 18 ; if 1 gram of water were decomposed there would result -^-^ = .1111 + gram of hydrogen and || = .8889— gram of oxygen. (Compare this with Art. 2493.) 2563. An apparent exception to the above statements is the metal mercury, which seems to unite with most of the other metals in all proportions, forming amalgams of the metals. These amalgams, however, are generally considered to be merely mechanical mixtures, and not true chemical compounds. Some metals, such as zinc, gold, silver, lead, and others, form amalgams at ordinary temperatures, it be- ing merely necessary to clean the surface of the metal thor- oughly before placing it in contact with the mercury. An amalgamated metal in a chemical formula is indicated by placing the symbol Hg after and above the symbol of the metal amalgamated; thus, Zn^^' 2564. As the same elements occur in many different substances, it is evident that they must be capable of repla- cing each other; that is, in a molecule of a given substance the atoms of one element present can be replaced by a certain number of atoms of another, thus forming a new compound. This number is not necessarily the same as the number of BATTERIES. 1695 atoms of the element replaced. For example, one atom of carbon [C) can replace \.\i& four atoms of hydrogen (//) con- tained in two molecules of water {'iH^O), forming CO^. From this it follows that the zveight of one clement which zviU replace nnit %veig]it of another element in a compound is not always the same as the ratio of the atomic weights of the tivo elements. The weight of the replacing element may be said to be the (chemical) equivalent of unit weight of the replaced element. Taking for the standard replaced element the lightest, hydrogen, and calling its unit weight 1, the least weight of any other element which will replace 1 part by weight of hydrogen in a compound, or will unite with 1 part by weight of hydrogen, is its actual chemical &i\\x^^&.- l^w^ty or combining zveight. (See column 5, Table 89.) The chemical equivalent of hydrogen is evidently the same as its atomic weight, 1. Now, in binary compounds (compounds consisting of only two elements) containing hydrogen, the proportion of the hydrogen in the compound is never less than 1 atom of 7/ to 1 atom of the other element, though often more; consequently, from the definition, the chemical equivalent is never greater than the atomic weight, and may be less. 2565. The ratio of the atomic weight to the chemical equivalent of an element is thus equal to or greater than 1. In fact, as it is considered that there are comparatively few atoms of each element in any molecule, this ratio is always small, and always a whole number. This ratio is also the number of atoms of hydrogen which would be required to re- place one atom of the given element, and is called the va- lency, or atomicity, of the element. The valency of the more common elements is given in column 4, Table 89. It can also be shown from the above statements that the number of atoms of one element required to replace a given number of atoms of another element which are in combination with a given number of atoms of a third element is inversely pro- portional to the respective valencies of the replaced and re- placing elements. 1696 BATTERIES. For example, each molecule of water {H^O) contains two atoms of //and one of O. If the (9, whose valency is II, is replaced by CI, whose valency is I, each of the two atoms of H will combine with one atom of CI, forming, not H^Cl^^ but two molecules of HCl (written ^HCl). Thus, two atoms of CI of valency I are required to replace one atom of oxygen of valency II, 2566. Elements sometimes combine in other propor- tions than the above statements would allow; but such sub- stances are seldom stable, readily uniting with additional atoms of the proper elements until the proportions are as indicated by the valencies. However, some elements seem to have two different valencies, as will be noticed in column 4, Table 89; the lower valencies give the more stable com- pounds. It should be remembered that the above principles of atomic weight, valency, etc., are not the expression of any chemical theory, but the result of long and careful ob- servation and measurement; this, however, is not infallible, and apparent violations of the foregoing, statements will be encountered, though they may be generally used with con- sistent results. 2567. At ordinary temperatures and pressures, five of the elements, hydrogen, oxygen, nitrogen, fluorine, and chlorine, are gases; mercury and bromine are liquids; while all the rest, including all metals excepting mercury, are solids. All the solids except carbon have been liquefied at various temperatures. Few elements, except the more common metals and oxy- gen and nitrogen, are extensively used or found in an un- combined state; they usually occur in various combinations,, which are divided into three classes: acids, bases, and salts. 2568. An acid may be defined as a compound con- taining hydrogen, which hydrogen may be replaced by a metal when presented to it in the form of an oxide or hy- drate. The combination of oxygen with any other single element is called an oxide. A hydrate is the substance BATTERIES. 1697 formed by the union of an element, or, more often, a me- tallic oxide, with the elements of water. This should not be confounded with a solution, which is merely a mechan- ical mixture of some solid with water, or similar liquid. Acids are usually sour to the taste, and will readily cause chemical action. Most acids contain oxygen, being formed from the union of an oxide of a non-metal and water; but in some few acids oxygen is absent. Table 90 gives a list of the more common acids, with their chemical formulas and other data. TABLE 90. COMMON ACIDS. r. Name of Acid. 3. Chemical Formula. r. Specific Gravity. 3. Pure Acid. 4. Commercial Acid. (Average.) Hydrochloric Hydrobromic Nitric HCl HBr HNO^ H^CrO, 1.227 1.515 1.530 1.846 1.14 to 1.16 1.33 to 1.41 Sulphuric 1.70 to 1.83 Chromic Note. — HCl and HBr are in reality gases, which dissolve readilj- in water, forming the liquid known by the above names. The specific gravity given is that of the solution (maximum). 2569. A base is a compound, usually an oxide or hydrate, of a metal, which metal is capable of replacing the hydrogen of an acid when the two are in contact. Some particularly active bases are known as alkalies^ which are soluble in water. The principal alkalies are sodium hydrate, NaOH, potassium hydrate, KOH, and ammonium hy- drate (aqua ammonia), NH jOH. 2570. A salt is the substance resulting from the re- placement of the hydrogen of an acid by the metal of a base, The action of the stronger acids and bases on each other is 1698 BATTERIES. very violent. By some chemists the acids are considered to be salts of hydrogen. Some combinations of non-metallic elements act in many ways similar to the metals, and can form oxides and hydrates and bases, and replace the hydrogen in acids, and tnese groups of elements should be included in the above denni- tions. Such a group is NH^^ which is sometimes called amnionium. There are several other similar groups. They act and may be handled as elements; their valency is the difference between the valency of the separate elements. Thus, in the above case, NH^^ the valency of N is V, while that of 77, is 4 X I = IV; hence, the valency of NH^ — V - IV = I. 2571. In chemistry, substances are given names in accordance with their composition, although many of the more common substances have popular names. For ex- ample, the crystals of copper sulphate are popularly known as blue vitriol. Ordinary compounds of a metal and non- metal are named from both components. The Latin name of the metal is given first, and for its last syllable, uni, is substituted ic\ to this is added the name of the non-metal, with its last syllable changed to ide. Thus, a compound of iron and sulphur is named y^rrzV sulphide. In the case where an element has two valencies, distinc- tion is made between the two compounds which may be formed from the same elements by substituting the termi- nation oiis for ic in the name of the metal, when referring to the compound having the lower proportion of the non- metallic element, which is usually oxygen. For example, copper forms two oxides: ciipric oxide, CtiO, and enprous oxide, Cu^O. The prefixes per and proto are sometime3 used instead of the terminations ic and 07is, respectively. The names of acids are derived from their principal constit- uent (aside from the hydrogen) by changing the last sylla- bles of its name to ic. Thus, the principal acid formed from sulphur is called stilphuric acid {H^SO^. The acids which do not contain oxygen are distinguished by the prefix hydro^ as hydrobromic acid {HBr.\ (See Table 90.) BATTERIES. 1699 2572. The names of the salts resulting from the action between bases and acids are derived from the name of the acid by taking the first syllable of the principal constituent of the acid and adding ate. Thus, salts formed from bases and sulphuric acid are named sulphates, and from nitric acid, nitrates. In the case where oxides are formed with non-metals of more than one valency, the acids formed from such oxides by their union with water take the ic and oils terminations, just as the metallic compounds do. For example, there are two oxides of sulphur, SO^ and SO^. The acid formed from the first is known as sulphurous acid, and from the second sulpJiiiric acid. The salts of an acid ending in ic have the termination ate, .as stated above, while the salts of the Otis acids end in ite. It is evident, from the use of the terminations, that the ate salts and the ic oxides contain greater proportions of oxygen ; ite salts and ous oxides are usually unstable, readily combining with oxygen to form the higher salts or oxides. ELECTROCHEMISTRY. 2573. A current of electricity passing through a con- ducting liquid will decompose the liquid, the amount of the various elements set free being proportional to the quantity of electricity passing through the liquid. (Art. 2493.) The amount (weight) of any element which will be liber- ated by a given quantity of electricity X'S, proportional to the cJiemical equivalent of that element ; hence, from the amount of hydrogen (or other element whose valency is always I) set free by unit quantity of electricity, the amount of any other element that will be set free by the same quantity of electricity may be calculated. The chemical equivalent of hydrogen being 1, the amount of hydrogen liberated by one coulomb of electricity becomes a multiplier, and by multi- plying the chemical equivalent of each element by this mul- tiplier the electrochemical equivalents, or the weight of each element liberated per coulomb, results. (See col- umn 6, Table 89.) 1700 BATTERIES. 2574, There is reason to believe that all chemical action generates E. M. F. ; but in order that this E. M. F. may be utilized, the chemical action must take place in and between conducting bodies. In order that the E. M. F. may be continuously main- tained — that is, that the chemical action be continuous — at least one of the bodies acted upon must be a liquid. This liquid is called the electrolyte (see Art. 2238). An electrolyte does not necessarily contain water; it may even be made by melting one of the elements of the cell. 2575. The simplest form of a cell consists of at least two bodies, of which one at least must be a liquid, in and between which two bodies the chemical action goes on which generates the E. M. F. In order that this E. M. F. may be utilized to cause a current to flow, provision must be made for connecting an external circuit with the two bodies between which the action takes place. Such a cell is usually composed of an electrolyte (often called the exciting liquid), into which are placed two con- ducting bodies; at least one of the bodies is metallic, and it is between this body, called the anode, and the electrolyte that the chemical action takes place. Strictly speaking, the surface of contact between the liquid and the metal is the place of action, and would more properly be called the anode. The other body, called the cathode, serves mainly as a means of connecting the external circuit to the electrolyte, the other end of the circuit being connected to the anode. Connection is actually made to the parts of the anode and cathode which project from the cell, these being then called the electrodes of the cell. This is the usual construction, although in some cells the chemical action takes place be- tween two different liquids, in which case whatever solid conducting bodies are used act merely as connectors or terminals. Examples of such cells will be pointed out in the descrip- tion of the various types. BATTERIES. 1701 2576» The chemical action which takes place is as fol- lows : When the two elements of the cell are placed in the electrolyte, the fact of there being 2i chemical affinity het^QQn the various substances in the cell sets up a difference of potential, which appears as between the terminals of the cell; this affinity may or may not set up a chemical action, but so long as the external circuit is open, whatever action may occur is only local, and its energy appears as heat. The reason that no chemical action occurs is that the atoms, having combined, have given up most of their potential energy, and so remain in the combinations they have as- sumed; as soon, however, as the external circuit is closed, the difference of potential which exists equalizes itself, and causes a momentary current to flow through the external circuit yr^7;2 the cathode to the anode, the cathode being at the higher potential. This current decomposes the electrolyte, breaking up the compounds therein and restoring to the various atoms their potential energy. Some of these atoms then unite with the material of the anode, and the E. M. F. is maintained, causing the flow of current to be continuous. ELECTROCHEMICAL CALCULATIONS. 2577. In the following we shall show the exact relation existing between the current and the chemical work; that is to say, we shall show how to calculate the amount of chemical work which a given current can perform, and, con- versely, the quantity of current evolved when a definite amount of chemical work is done. 2578. Whenever an electrolyte is decomposed by a current, the resolved elements have a tendency to reunite. This tendency is termed chemical affinity. Thus, when an electric current has been sent through a solution of zinc sulphate {ZnSO^), and the solution has thereby been split up into zinc, oxygen, and sulphur, then, as soon as the current ceases to flow, the zinc exhibits a tendency to recombine chemically with the disintegrated solution. This 1703 BATTERIES. tendency represents the strong chemical affinity of zinc for oxygen and sulphur. Also, when acidulated water has been decomposed electrically, the separated oxygen and hydrogen tend to reunite. 2579. This tendency to reunite is strikingly shown by an electromotive force which is set up in the solution after the decomposing current ceases. This E. M. F. can be shown to exist by connecting a galvanometer in circuit with the decomposed solution. The deflection of this instrument will show that this E. M. F. due to chemical affinity acts in the opposite direction to the E. M. F. of the decomposing current. In other words, it is an opposing electromotive force. 2580. Careful measurement has shown that when hydrogen and oxygen combine with each other, an electro- motive force of 1.47 volts is set up. From this it follows that no water can be decomposed unless an electromotive force of at least 1.47 volts is utilized; for it requires this much alone to offset the opposing E. M. F. of recombination. 2581. With every electrolyte there is a similar- mini- mum E. M. F. necessary to produce continuous decomposi- tion. This E. M. F. can be calculated for any electrolyte if the heat of formation and the electro-chemical equivalent of its constituents are known. The heat of formation is the thermocliemical equivalent of the substance. By the thermochemical equivalent is meant the amount of heat liberated by the chemical combination of the molecular weight of one substance with another. This energy is usually expressed in gram-calories; that is, the amount of heat necessary to raise the temperature of one gram of water 1° Centigrade. This thermochemical equivalent is a value found by careful experiment. Thus, one gram of zinc, for instance, converted into zinc sulphate (ZnSO ^, is known by experiment to give off about 4,000 heat-units as it combines. In Table 91 the heat of formation of various substances with oxygen is given. BATTERIES. 1703 TABLE 91. HEAT OF COMBINATIOIV WITH OXYGEN. 1 Gram of Hydrogen . Carbon. . . . Sulphur. . , Phosphorus Zinc. ..... Iron Tin Copper . . . Calories or Gram Degrees of Heat Produced. 34,000 8,000 2,300 5,747 1,301 1,576 1,233 602 2582. Electrochemical Equivalent. — Experiment has shown that when 1 C. G. S. iinit of current (Art. 2268) passes through water, it liberates .0001036 gram of hydrogen. Now, since 1 C. G. S. unit of current equals 10 practical units or coulombs (Art. 2278), it is evident that 1 coulomb will liberate only J^ of this weight of hydrogen, or 1 coulomb liberates .00001036 gram of hydrogen. This quantity of hydrogen is always liberated by 1 coulomb of current, and similarly 1 coulomb of current will liberate a certain definite weight of any other electrolytic substance. The weight thus liberated by 1 coulomb, or by 1 ampere flowing for 1 second, is termed the electrocUemical equivalent of the substance, and may be found tabulated for the most important elements in column 6 of Table 89. 2583. Total l?^eight Liberated by Chemical Action. — Experiment has furthermore shown that the total weight of any substance liberated by chemical action is directly proportional to the quantity of current flowing, so that if z = electrochemical equivalent of any substance; Q ■=■ number of coulombs; W =^ weight in grams of liberated substance; then, W==Q^z. (467.) 1704 BATTERIES. Example. — A current of .5 ampere was passed through an acidulated solution of water for 10 minutes. "What weight of hydrogen was evolved ? Solution. — / = 10 minutes = 600 seconds. (7=. 5 ampere. Then, by formula 405, Q = C/ = .5 X 600 = 300 coulombs. Referring to column 6, Table 89, we find for hydrogen ^^ = .00001036; hence, by formula 467, IV= 300 X .00001036 = .003108 gram of hydrogen. Ans. 2584. Heat Formation by Chemical Action. — In Art. 2581 the formation of heat during chemical action was explained. Experiment has shown that the total heat generated during chemical action is proportional to the weight of the substance liberated; so that if /i = calories evolved per gram of substance; IV = weight in grams of substance liberated; U = total calories evolved ; then, - H— Wx h\ but, inserting the value of W as given by formula 467, we have as the total heat evolved in calories H^Qxzxh. (468.) 2585. Relation of Heat and V^ork. — It can be shown by a simple calculation, knowing the inechanical equivalent of heat, that 1 calorie is equivalent to 4.2 joules of work. This being the case, formula 468 may be written to express the total joules ^ of energy required to liberate a given weight of any substance; for, if y^=: total joules of energy, then, by utilizing the notation of Art, 2584, /=4.2 Qx^Xh. (469.) 2586. It is possible to express this work in another manner. By referring to Art. 2332, it will be seen that the work done in joules in any electrical circuit can be expressed by the product of volts and coulombs of that cir- cuit; or, if E = volts; Q = coulombs ; / = joules; then, J^ExQ. (470-) BATTERIES. 1705 2587. Calculation of E. M. F. Produced by Chemical Action. — Comparing formulas 469 and 470, we see that they are different expressions for the same quantity y, namely, the electrical work in joules done in the circuit; or, / = 4. 2 Qyis X h^ and 'j=ExQ. But, when two quantities are each equal to a third, they are equal to each other; hence, ^X = 4.2 X^X/^. Dividing both sides of this equation by Q gives us an ex- pression for the electromotive force in volts, namely, ^^4.2/^X^. (471.) This important result may be expressed in words as follows: The electrovwtive force in volts of any chewical reaction is equal to the product of the electrochemical equiva- lent of the separated substance, the heat of combination of the substance per gram degree, and tlie constant Ji..2. Example. — Calculate the opposing E. M. F. set up by the hydrogen tending to unite with the oxygen during the decomposition of water. Solution. — Refer to Table 89, column 6, where for hydrogen 2 = ,00001036, and to Table 91, column 3, where for hydrogen /z = 34,000; then, by formula 471 , £ = 4.2 X 34,000 X .00001036 = 1.479 volts. Ans. Note. — In the same way we may calculate the opposing E. M, F. set up and effecting any particular electrolysis. 2588. In the above, the E. M. F. is calculated on the assumption that all the chemical energy developed is con- verted into electricity, and that none of the energy appears as heat. Practically, however, some heat is generated in almost every case during the electric activity. This is only a secondary consequence of the electric resistance of the cell. If the cell offers a negligible resistance, then the amount of heat electrically developed by the current would also be negligible, and all the chemical energy developed by chemical changes in the cell would be liberated outside the cell, that is, in the external circuit. 1706 BATTERIES. 2589. It should be remarked, however, that owing to the incompleteness of our knowledge of thermo- chemical equivalents, and of the exact nature of the electro- chemical actions in the cell, the E. M. F. of a cell can only in a few instances be practically predetermined. ELECTROCHEMICAL THEORIES. 2590. If more than one set of actions can take place in a cell, the effect of the various actions on the E. M. F. of the cell may be determined by properly applying formula 471 to each action; the E. M. F. of each action may be then added or subtracted to get the resulting E. M. F., according to the nature of the action. If the substance forming the anode has an affinity for one or more elements of the electrolyte, and the substance form- ing the cathode has an affinity for the other element or ele- ments of the electrolyte, it is evident that the tendencies of these elements to combine with the anode and cathode, re- spectively, will assist each other, and the E. M. F. of each action will add together in giving the resulting E. M. F. of the cell. If the substances forming the anode and cathode, respect- ively, have each an affinity for tJic same element or elements of the electrolyte, it is again evident that the tendency of these elements to combine with the anode will be partly balanced by their tendency to combine with the cathode; hence, the E. M. F. which would result from either action alone must be subtracted from the other to obtain the resulting E. M. F. This explains the case spoken of in Art. 2243, where it is stated that a cell with zinc and iron as elements will give a less E. M. F. than a cell using zinc and graphite (carbon). In the zinc-iron cell a part of the electrolyte has an affinity for both the zinc and the iron, while in the zinc-graphite cell the electrolyte has no affinity for the graphite, and the full E. M. F. of the action on the zinc appears. The mean- ing of the Electromotive Series (Art. 2241) should now be clear, . > BATTERIES. 1707 2591. The action which takes place in a cell if the electrolyte be an acid is the decomposition of the acid, the liberation of the hydrogen, and the formation of a salt of the metal of the anode by its union with the balance of the acid. If the electrolyte be a solution of some salt, the action is more complicated, and is about as follows : The water of the solution is decomposed, its oxygen uniting with the anode, forming an oxide, and the hydrogen is liberated, as before. The oxide which is formed then unites with the salt in solution, forming salts of the metal oxidized; these formations increase the E. M. F. which the cell would have were water alone the exciting liquid and the oxidation of the anode the only action. 2592. Thus it is seen that in almost all the chemical actions which occur in batteries, the attacking of the anode results from the decomposition of the electrolyte, hydrogen being liberated. This decomposition of the electrolyte takes place throughout the space between the anode and cathode; the hydrogen, however, does not appear through- out the electrolyte, but only at the surface of the cathode; for as soon as the electrolyte is decomposed into its elements, the union of the metal of the anode with the ele- ments of the electrolyte with which it can combine can only take place with the atoms of the particular molecules which were at the surface of the anode; the free hydrogen atoms of these molecules then unite with the free elements of what was the next layer of molecules, reforming the original electrolyte; the displaced hydrogen atoms of these newly formed molecules unite with the free elements of the next layer of molecules, and so on all across the liquid, until at the point where the current leaves the liquid (the cathode) there are left the free hydrogen atoms of the last layer of molecules. These then appear at the surface of the cathode, providing the cathode is not a substance with which these free atoms may unite. 2593. The accompanying diagrams represent this ac- tion in the case of the zinc {Zn), sulphuric acid {H^SO^), 1708 BATTERIES. and copper {Cu) cell, given in Art. 2240. One single line of the molecules of the electrolyte between the zinc and the copper plate is represented at a, Fig. 1037. Each molecule of the acid is made up of one atom of vS and four of O, united with a molecule consisting of two atoms of H. in [5o:ni?i? i[i^i? I ? i[io:] i-? i? iiisnlT TTliaonRnTl (io3 H H [^ [Z] [zi [1^ m [iDii^m [Z] [^m cz [^ [ff] [^ m [Zl [^ m m [^ S E [^ m [Z] (^ \SOt \ H \ B~\ \SOt I g I H~\ I aOt\ B I H~l \SOt\ B | H~\ 1 50«| B | B^ I g I l-g I \SO,\ H I hH liSQ^I -g I -H~l ISQ^I B \ B~\ |.SQ^| g | B~\ [go7 Fig. 1037. No current is supposed to be flowing through the liquid. For convenience, it is assumed that the molecule of S0^ is not decomposed by the current; actually, it probably is, but since in its action with the zinc it unites with it as a whole, the assumption is allowable. In d, Fig. 1037, the molecules are represented as decom- posed by a current, and each individual molecule of SO^ and atom of H is separate. Now, the molecule of SO^ at the right has a greater affinity for, or tendency to combine with, the zinc than it has to combine with the free atoms of //', and does so, as represented at c, Fig. 1037, and the re- maining molecules of SO^, not being in contact with the zinc, unite with the free atoms of //^ all the way across the liquid, until at the copper plate there are no free molecules of SO^ left to combine with the last atoms of //"in the line; consequently, the free atoms of H appear in the form of BATTERIES. 1709 gas at the copper plate. Of course the newly formed mole- cules of H^SO^ are immediately decomposed and reunited, which process continues Avith inconceivable rapidity, the result being a practically continuous formation of ZnSO ^ at the anode and the liberation of H at the cathode as long as any current flows through the electrolyte. Now, it is evident that all the energy required to decompose all but one molecule in any line of molecules across the electrolyte is immediately given up by the reunion of the free atoms. For this reason the distance between the anode and the cath- ode, or their size, does not affect the amoitnt of electrolyte decomposed by a given force, nor the energy required to per- form the decomposition. POLARIZATION AND DEPOLARIZATION. 2594. If at or near the cathode there is some sub- stance, such that the free hydrogen left by the decomposi- tion of the electrolyte may unite with it, the energy liberated by such formation will add to the E. M. F. of the cell. If this free hydrogen can not unite with some substance at the cathode, it collects on the surface in bubbles as a gas. In addition to the reduction of the E. M. F. of the cell due to decomposition of the electrolyte, the formation of hydrogen also acts disadvantageously, as it forms in a layer on the surface of the cathode, which enormously increases the internal resistance of the cell, thus diminishing the current which the E. M. F. of the cell can send through any given external resistance. The formation of hydrogen on the surface of the cathode is known as polarization, and its removal, by any means, mechanical or chemical, is called de- polarization, the agent used being called the depolarizer. 2595. If merely mechanical means of depolarization be used, the result is to prevent the increase of internal resistance of the cell; by causing the liberated hydrogen to recombine at the cathode, by chemical means, not only is the internal resistance not increased, but the actual E. M, F. of the cell is increased. 1710 BATTERIES. 2596. Various mechanical devices for depolarizing cells have been used ; the cathode has been arranged to be agitated in the liquid, or to be entirely 'removed from the liquid at intervals; or the cathode, and in some instances both electrodes, have been made in the form of disks, dipped for about half their diameter into the electrolyte. On rotating the disks, the hydrogen is prevented from form- ing on the cathode by its motion. The power for performing these various movements has usually been derived from clockwork, and in some instances from the current given out by the battery. It is evident that such devices are commercially of little value, especially as chemical depolarizers may be easily used. 2597. The depolarization by chemical means may be accomplished by surrounding the negative element (cathode) with a solid or liquid substance, with which the free hydro- gen may combine. This combination usually merely dis- poses of this element, and prevents the bad effects of a deposit on the cathode. Under these circumstances the compound formed at the cathode is usually water, the de- polarizer being a substance rich in oxygen, with which the hydrogen combines. This water has the effect of diluting the electrolyte, already weakened by the combination with the anode; but, by properly selecting the depolarizer with reference to the electrolyte, the chemical combination at the cathode may be such that it will, either directly or by further combination, replace the part of the electrolyte which has combined with the anode, thus keeping the elec- trolyte of the same composition and strength throughout the life of the anode or of the depolarizer. Instances of both these classes of chemical depolarization will be noted in the description of the various cells. 2598. The rate at which any depolarizer will depolarize depends on many conditions; and no depolarizer will keep the E. M. F. of a cell constant for all currents, for, after a certain limiting current has been reached, the limit depend- ing on the sizes of the various parts of the cell, the formation BATTERIES. 1711 of the free element of the electrolyte is more rapid than its absorption by, or recombination with, the depolarizer, and the surplus will collect on the cathode. In the case of depolarizers which, by the formation of water, dilute the electrolyte, the E. M. F. will become less with continued use of the cell, even if the current output be small. These facts should be remembered in dealing with the various depolarizers. 2599. From the preceding remarks, it appears that in order to give a high E. M. F., the metal chosen for the anode must be one whose salts have a comparatively high value for their heat of formation. Such metals are potassium, sodium, strontium, calcium, and magnesium; potassium salts having the highest heat of formation, the others, in the order given, having lower. 2600. Having a high heat of formation means, however, that the metal has a great affinity for the elements necessary to form its salts or oxides; this being the case, they are liable to combine with such elements whenever the opportu- nity presents itself, taking them from the air, from water, or from salts of other metals which have a lesser affinity for the salt-forming elements. Consequently, the metals in the list given could not be used in the presence of acids or solution of salts, or even of water, without decomposing the liquid and rapidly forming salts or oxides, the whole of the energy of the action appearing as heat. In order, then, to have a practicable cell, the metal should not be attacked by the ex- citing liquid except as the exciting liquid is decomposed by the passage of the current. This is the reason for the ex- tensive adoption of zinc, that being a metal whose heat of formation is comparatively high, at the same time not high enough to cause its salts and oxides to be formed with any degree of rapidity unless the necessary elements are pre- sented to it in a free state, as they are in a voltaic cell by the decomposition of the electrolyte. Besides, zinc is actually the cheapest of the metals, ex- cepting iron, and, in proportion to the amount of kinetic 1712 BATTERIES. chemical energy possessed, is cheaper than any other metal which could be used. 2601. Batteries, as sources of electrical energy, are used mainly in cases where a current is required very inter- mittently, such as in ringing bells, lighting gas, etc., or where a small but steady current is required for long periods of time, as in telegraphy and telephony, or for laboratory and testing purposes. Their general use on a large scale, as sources of electrical energy for lighting or power purposes, is prohibited, at least at present, by the comparatively great cost of the material consumed, and the expense of installa- tion and maintenance. For example, the bichromate battery is about the cheapest in point of cost of materials consumed, and in this the ma- terials alone would cost about 28 cents per horsepower per hour on a large scale, while the cost of electrical energy, using dynamos, is about 5 or 6 cents per horsepower per hour, ordinarily, and in many cases is much less. The cost of material in the silver chloride battery is about $135 per horsepower per hour. This high cost of the power does not, however, prevent batteries from being largely used for the purposes outlined above, and their practical application is an important part of electrical engineering. CELLS. CLASSIFICATION. 2602. The various classes of voltaic cells may be divided as follows: Cells in ^iVhich There Is No Depolarizer. — This is the simplest form of cell, and, on account of polarization, cells of this class, commonly called open-circuit cells, are not used for other than intermittent work. 2603. Cells TVitti a Depolarizing Electrolyte. — In this class of cells the electrolyte is of such a nature that either no hydrogen is formed or the liquid contains a sub- BATTERIES. 1713 stance with which the hydrogen unites. As this action tates place mainly at the cathode, there is little distinction, as far as action goes, between this latter type and cells with a liquid depolarizer. 2604. Cells W^ith a Liquid Depolarizer. — In this class of cells, however, the cathode is surrounded by a de- polarizing liquid, which is prevented, by mechanical means, from mixing with the electrolyte. The means usually employed are either to separate the two liquids by a porous partition, which allows of their elec- trical contact without mechanical mixture of the two, if their respective specific gravities be nearly the same ; or, if these differ considerably, gravity will keep the two liquids apart, one over the other in the containing vessel. 2605. Cells With a Solid Depolarizer. — This class is identical in action with the class preceding, the depolarizer, however, being a solid instead of a liquid. If the solid depolarizer is granular, or in the form of pow- der, it is often necessary to employ a porous partition between the cathode surrounded by the depolarizer and the electrolyte. This is merely to keep the depolarizer in place, and is dispensed with if the depolarizer is formed into a paste or solid body upon the cathode. In fact, the depo- larizer may itself form the cathode, if it be a solid conduct- ing material, the office of the cathode being primarily to establish a connection between the electrolyte and the exter- nal circuit. 2606. Cells in Whicli an Elementary Substance Is Applied to the Cathode, Acting as a Depolarizer. — This substance may be applied mechanically or chemically. In the former case, the body, in the form of a gas or liquid^ is made to appear at the cathode by pumping or forcing it to that place from some external source of supply. In the chemical method, the cathode is surrounded by solid or liquid substances, which by their action on each other evolve some elementary body which combines with the free element of the decomposed electrolyte. 1714 BATTERIES. This is distinct from tlie action of cells with a liquid or a solid depolarizer, as the production of the elementary de- polarizing body substance is independent of the electrical action of the cell, going on all the time, whether the cell is in tise or not, variations in the current output of the cell having no influence on its production. Voltaic cells are ordinarily classed as " single-fluid " and *"' two-fluid " cells ; but as such a classification has little reference to this principle of operation, it will not be used in this discussion. The number of different kinds of cells that have been made is very large indeed, but they can all be subdivided into one of these general classes. Only a few typical cells of each class will be described. CELLS WITH A NON-DEPOLARIZING ELECTROLYTE. 2607. This class of cells includes the cells of the Volta type, which consists generally of an electrolyte of acid or saline solution, into which are placed two or more plates of metal, one of which (usually of zinc) is acted on by the electrolyte. 2608. A simple form of this cell is illustrated in Art. 2238. Its materials are zinc, dilute sulphuric acid, and copper, which give an E. M. F. of about .9 volt. Many modifications of the form of this type of cell have been suggested and used, such as making the elements in strips and rolling them around each other in a helical form, with insulating material between, etc. ; but all are open to the objection of rapid polarization. 2609. In place of copper as a cathode many other elements have been used, notably the Smee cell, using platinum or platinized silver, and cells of various makes in which the cathode is of iron. In cells of this and other types, impurities in the zinc set up local actions, which diminish the E. M. F. of the cell and cause a wasting of the zinc. These local actions are almost BATTERIES. 1715 wholly prevented by amalgamating the zinc, which is usually done. If a good quality of drawn or rolled zinc is used, this pre- caution is hardly necessary. 261 0. Not long after the first use of the zinc, sulphuric acid, and copper battery, it was found that the copper or other metallic cathode could be advantageously replaced with porous carbon, and many cells were so constructed. The E. M. F. of such a cell is about 1.35 volts ordinarily. To prevent the electrolyte from becoming exhausted too quickly, there is sometimes placed in the cell a porous earthenware pot or cup, filled with strong sulphuric acid. As the dilute acid outside the porous cup becomes weaker, the stronger acid oozes through the sides of the porous cup and keeps up its strength. In some instances the carbon cathode has itself formed the porous cup. An objection to the use of porous cups in this type of cell is that its pores are liable to become clogged by deposits of zinc sulphate from the solution. 2611. Other acid electrolytes have been used in this type of cell. With either nitric or hydrochloric acids (diluted) the E. M. F. is not sensibly different from that with sulphuric acid as the electrolyte. 2612. Of the saline electrolytes, the best exciting liquid is considered to be a solution of ammonium chloride (sal ammoniac). The E. M.- F. of a zinc, ammonium chlo- ride, and carbon cell is about 1.15 volts. 2613. There are a great number of cells of this type in- use for ringing bells, gas lighting, and doing other intermit- tent work. They are all alike in principle, but their mechanical construction differs somewhat. In the Law open-circuit cell, the carbon electrode is in the form of a hollow cylinder, enclosing a smaller hollow cylinder, each with a wide slit in one side. These cylinders hang vertically in the electrolyte, and the zinc hangs in the space formed by the slits in the side, being suspended from the cover of the 1716 BATTERIES. cell. This is an excellent form of cell, being well worked out in its mechanical details. 2614. In the Little Giant cell, the hollow carbon cylinder is continuous, except for a hole in the side for the circulation of the electrolyte, and the zinc, in the form of a rod, is suspended in the center of the carbon cylinder. The top of the cylinder is extended to form the cover of the cell, and the zinc is insulated from it by a porcelain bushing. 2615. The Hercules cell employs a corrugated solid carbon cylinder, the zinc element being made of sheet zinc bent into a cylinder surrounding the carbon. 2616. Many other forms of carbon or zinc elements may be and are used. The particular shape of the carbon has comparatively little to do with the satisfactory working of the cell, care and good design in the construction being more important. The element should be of such shape as not to be easily broken in transit, and, being usually molded into shape under pressure, should be of such proportions that it is cheap to make. 2617'. In all the cells of this type the carbon is made as porous as possible, and of such shape that the surface exposed to the liquid is very large compared with the sur- face of the zinc. Thus, the average area of the internal circuit of the cell is made large, and at the same time ad- vantage is taken of the slight depolarization, occurring with a porous carbon of large surface, due to the oxygen which porous carbon absorbs from the air, with which some of the evolved hydrogen combines. The E. M. F. of this type of cell is, therefore, slightly higher than those which employ a non-oxidizable metallic cathode, such as platinum. This depolarizing action takes place sloAvly, and, therefore, hy- drogen will form on the cathode if a considerable current be taken from the cell, thus increasing the internal resistance. In intermittent work this is not objectionable, as the hydro- gen is soon absorbed when the external circuit is opened. BATTERIES. 1717 2618. Another salt which has been much used in solu- tion as an electrolyte is sodium chloride (common salt). The heat of formation of sodium chloride being greater than that of ammonium chloride, the energy required to decom- pose the electrolyte is greater; therefore, the E. M. F. of cells using this electrolyte is slightly lower, that of a zinc, sodium chloride, and carbon cell being about 1.08 volts. However, this electrolyte being very cheap and of com- mon occurrence, many makers of batteries have employed it. It has also been proposed to use sea-water as an electro- lyte, by placing in the ocean immense plates of zinc and copper or carbon. This has never been commercially ac- complished, for the consumption of zinc makes the cost of the electrical energy too great for this method to compete with others now in use. 2619. Electrical buoys have been constructed, in which plates of carbon or copper and zinc enter or leave the water as the buoy is rocked by the waves, thus causing a light to flash or a bell to ring intermittently. 2620. Various other salts in solution have been used as electrolytes, such as ammonium nitrate, alum, potassium sulphate, zinc sulphate, zinc chloride, potassium hydrate (caustic potash), etc. The E. M. F. of cells using solutions of these various salts as electrolytes may be found from the values given in Table 93. 2631. The effect of substituting various metals for the zinc in this type of cell may be found from Table 92, which gives the E. M. F. of the action of dilute sulphuric acid on various metals. The values given in this table may be taken for the E. M. F. of cells using a platinum or carbon cathode; if other metals which appear in the table be used as the cathode, the E. M. F. of the action of the acid upon them must be subtracted to get the E. M. F. of the cell. (See Art. 2590.) With other electrolytes, the substitu- tion of other metals for zinc reduces the E. M. F. in about the same proportion as in the table. 1718 BATTERIES. TABLE 92. E. M. F. OF THE FORMATION OF VARIOUS SULPHATES. Metal. Formula of Sulphate. E. M. F. Volts. Potassium ZnSO^ CdSO, PbSO^ FcSO, CuSO, Ag.^0, None 2 35 Zinc 1 35 Cadmium 1.05 Lead .90 Tin 88 Iron .83 Aluminum .70 CoDoer , . . . . .47 Silver .30 Platinum .00 TABLE 93. E. M. F. OF ZINC (PURE) WITH VARIOUS ELECTROLYTES. Electrolyte. Acids. E. M. F. Volts. Electrolyte. Saline Solutions. E. M. F. Volts. HSO, 1.35 1.40 1.43 NaCl 1 08 HCl ZllSO 1 32 HNO, NH CI. 1 15 NaOH 1.35 KOH 1 38 Ordinary //„ (9 0.90 CELLS WITH A DEPOLARIZING ELECTROLYTE. 2622. The best known cells of this type are the so- called bichromate cells. These consist, broadly, of a zinc- carbon couple, with an electrolyte composed of a solution of some acid or other exciting liquid, mixed with a proportion of the bichrojnate salts of some metal. The bichromate salts are a peculiar series of salts formed by the oxide of BATTERIES. 1719 chromium having the formula Cr^O^, which is an unstable oxide, appearing only in combination with some other metal, such as potassium or sodium, forming the bichromate salts of those metals. The mixture usually employed as an elec- trolyte is sulphuric acid and potassium bichromate, K„Cr^O^, although sodium bichromate, Na^Cr^O^, is somewhat supe- rior for the purpose, which is to act as a depolarizer. This office the bichromate salts perform perfectly, as they have a large proportion of oxygen, as is seen from their formulas; consequently, the hydrogen liberated by decom- position of the electrolyte is consumed as fast as generated, forming water and a salt known as chrome alum, which forms in crystals of a purplish color. This results in a high E. M. F. (usually about 2 volts). 2623. The chemical actions in this class of cells are complicated; one result is the formation of chromic acid by the action of the acid in the electrolyte on the K^Cr^O^, which will slowly attack the zinc whenever in contact with it, whether there be any current flowing or not. This leads to the device — which is almost universally adopted — -of lift- ing the anode, or both elements, from the liquid when the cell is not in use. Cells which are in continuous use are liable to have their internal resistance increased by a deposit of the crystals of ^^-* chrome alum on the cathode, these crys- tals being poor conductors. In certain forms of cells the construction is such that this is not liable to occur. 2624. Afamiliar type of bichromate cell is the Grenet cell, shown in Fig. 1038, which consists of a bottle-shaped glass jar with a hard rubber or porcelain cover. From this cover two flat carbon plates C, C are suspended, parallel to and a short distance, from each other, as shown; between them hangs a zinc plate Z supported by a sliding rod R, which fig. loas. 1720 BATTERIES. may be drawn up until the zinc is entirely out of the liquid; it is held in any position by the thumb-screw T. On the top of the brass rod is a binding-post B^, the other terminal of the cell being the binding-post B^ which is connected to the two carbon plates. The electrolyte is composed of 3 parts of potassium bichromate, dissolved in 18 parts of water, to which is added 4 parts of sulphuric acid. . The E. M. F. of such a cell is 1.93 to 2 volts. At ordinary temperatures, variations in the proportion of bichromate in the solution, within moderate limits, do not vary the E. M. F. or the internal resistance very much. Variations in temperature vary the internal resistance, but not the E. M. F., the internal resistance decreasing as the temperature increases. With the above proportion of sul- phuric acid and bichromate in the solution, the sulphuric acid is first exhausted. Theoretically, for an equal life of both substances in the electrolyte, the correct proportions should be z- r r^ o a I P^""^^ ^^ weight, which proportion is often used. In fact, however, it is more necessary to keep up the strength of the depolarizer, that is, the bichromate, so the first given proportion will really give better results. 2625. A great variety of batteries of this type has been made, especially abroad, where they are called Pog- gendorfs cell; they do not differ in principle or material from the Grenet cell, but in inechanical details are more suited to general work. They are usually built with several cells, the various elements being connected in series to give an E. M. F. of 6 to 10 or more volts. All the elements are simultaneously raised out of or lowered into the liquid by a lever or windlass arrangement, as shown in Fig. 1039, which represents a battery of five cells all alike. The ele- ments are of zinc and carbon, there being three plates of zinc, Z, and four of carbon, (7, in each cell. The plates are BATTERIES. 1721 all suspended from a wooden cross-bar, so that they may be simultaneously raised or lowered by winding or unwinding Fig. 1039. the chains H, H upon the rod R^ which is turned by means of the crank K. The elements may thus be raised from the liquid con- tained in the jars J when the cells are not in use. The elements of each cell are provided with two binding-posts B, B, one of which is connected to the carbon and the other to the zinc plates. The various cells may then be used separately, or connected together in parallel or in series, as desired. 2626. An ingenious arrangement of bichromate cells for cautery work is that due to Chardin. In his battery the elements are normally held out of the liquid by a spring; by pressing a foot lever they may be gradually lowered into the liquid. When just the ends of the elements are in the liquid, the internal resistance of the battery is considerable; but as the elements are lowered, this resistance decreases largely. 1723 BATTERIES. By varying the distance which the pressure on the foot lever causes the elements to dip into the liquid, a sensitive and easily managed method of control of the output of the battery is secured. ■ 2627. Another type of bichromate cell consists of a closed vessel divided into two parts by a horizontal per- forated partition. In one part the zinc and carbon elements are located. Enough liquid to fill one of the parts of the vessel is introduced; when the vessel is standing on one end, all the liquid is below the partition and the elements above, and in order to render the cell active, it is only necessary to turn the vessel completely over, when the liquid flows through the perforated partition and comes in contact with the zinc and carbon. 2628. Among the cells which may be said to belong to this class is a type of cell in which no free hydrogen or other gas is evolved in the decomposition of the electrolyte. Such electrolytes, which might more properly be called non-polarizing, are the solutions of some of the salts of metals having more than one valency. The salt containing the greater amount of the non-metallic element (the zV salt) is used as the electrolyte; on being decomposed, a salt of the metal of the anode is formed with a part of its non- metallic element, and the remainder is recombined to form the salt having the lesser proportion of the non-metallic element (the ons salt). 2629. An example of this type of cell is the Pabst cell, in which wrought iron and carbon are used as elements, and a solution of ferric chloride as the electrolyte. The ferric chloride is decomposed into ferrous chloride and free chlorine ; the latter unites with the iron anode, resulting in an E. M. F. of .78 volt. 2630. Similar cells are also made, using a solution of ferrous sulphate as an electrolyte, the action being similar. There are other salts, with solutions of which zinc will combine without hydrogen being released, such as sulphite BATTERIES. 1723 of potassium or of sodium, and non-polarizing cells are constructed, employing solutions of these salts as elec- trolytes. 2631. Most single fluid cells in which the electrolyte is depolarizing are open to the objection that the zinc is attacked by the electrolyte at all times, whether the exter- nal circuit be closed or not; besides this, with the exception of the bichromate cells, the materials of the electrolyte are usually expensive, and not readily obtainable, and the com- mercial use of such cells is limited. CELLS WITH A LIQUID DEPOLARIZER. 2632. Nitric acid, being rich in oxygen, is largely used as a depolarizing liquid in this class of cells. Its use is objectionable from the fact that when deprived of a part of its oxygen, it gives off a gas, nitric oxide, which, on combining with the oxygen of air, becomes nitro- gen peroxide, NO^, a disagreeable and even dangerous cor- rosive gas; consequently, the best of ventilation is essential where cells with this depolarizer are used. 2633. The principal cells using this depolarizer are the Grove and Bunsen cells, and some of their derivatives. In the Grove cell the positive element is zinc; the negative, platinum. The platinum element is placed inside a porous cup and surrounded with nitric acid; outside the porous cup is the exciting liquid, sulphuric acid diluted with water. The E. M. F. of the Grove cell is 1.9 volts at ordinary temperatures. 2634. The Grove cell is a very old type, and has been made in many forms, but the expense of using the platinum element has led to the adoption of the Bunsen cell, which substitutes a carbon element for the platinum. With com- mercial nitric acid, specific gravity about 1.33, the E. M. F. of the Bunsen cell is 1.89 volts ordinarily; if pure (fuming) nitric acid, specific gravity 1.53, be used, the E. M. F. is 1724 BATTERIES. increased to about 1.96 volts. About .35 volt is due to the action of the depolarizer. 2635. Variations in the density of the nitric acid thus affect the E. M. F. of the cell only slightly, until the specific gravity of the solution falls to about 1.23; but at a density below this the acid has little or no effect as a depolarizer, although the liquid still contains about oOfo of nitric acid. As the commercial acid is most frequently used in the cell, only a small proportion of water is required to dilute it to a point where it can not be used. In fact, where commercial acid is used, only about 13^ of the actual amount of the pure acid in the solution can be utilized, if nitric acid alone be the depolarizer. The water formed at the cathode by the process of de- polarization, therefore, is disadvantageous on account of its dilution of the depolarizer. Several investigators have mixed sulphuric acid with the nitric, in various proportions, with good results. Sulphuric acid has a strong affinity for water, and will combine with it in considerable quantity ; consequently, the water formed at the cathode is absorbed by the sulphuric acid, leaving the nitric acid at its full strength. 2636. Variations in the density of the exciting liquid also affect the E. M. F. of the cells to some extent, but not so much so as variation in the density of the depolarizer. The density ordinarily used is about 1.09 sp. gr. (13^ by weight of acid). At this point the E. M. F. of the action of the exciting liquid on the zinc is about 1.53 volts. As the action of pure water alone on zinc will give an E. M. F. of about .9 volt, variations of the density of the exciting liquid from 13^ (by weight) of acid down to pure water will reduce the E. M. F. about .6 volt. Increasing the density of the liquid to about 1.23 gives a maximum E. M. F, (of the action of the acid on the zinc only) of about 1.6 volts; any further increase in the density does not in- crease the E. M. F. appreciably. To obtain the E. M. F. of the cell, to the above figures should be added the E. M. F. BATTERIES. 1725 due to the action of the depolarizer, about .35 volt, as stated above. It is somewhat difficult to maintain sulphuric acid which has free access to the air at a density much above about 1.10, on account of the absorption of water from the air by the acid, and acid of about this density is ordinarily used. 2637. The proportions of the two acids in the cells are about 3 of exciting liquid to 1 of depolarizer, the depolarizer being of a specific gravity of about 1.33; with these propor- tions the cell will maintain its E. M. F. (within about lOfo) for several days on a closed circuit. The average internal resistance (as ordinarily constructed) is about 2 ohms. 2638. Many modifications of the Grove and Bunsen cells have been made, some consisting merely in changes in the mechanical arrangement of the parts, others substituting various depolarizers, exciting liquids, or elements. For example, a carbon cup fitted with a tight cover has been used as cathode. On this being filled with nitric acid, the gas given off by the acid produces a pressure inside the cup, which forces the acid out through the pores of the car- bon to the surface, where its depolarizing action takes place. This suppresses a part of the disagreeable fumes of the acid. To accomplish this same result, it has been proposed to cover the cell with an inverted vessel containing scrap tin, which will absorb the fumes. A layer of turpentine floating on the acid will prevent a large part of the fumes from being given off, as they combine with the turpentine. 2639. When iron or steel is placed in strong nitric acid it is not attacked, although this acid is a powerful oxidizing agent; but when the acid is diluted to about 1.20 sp. gr., or lower, the iron is strongly attacked. Consequently, with a strong solution of nitric acid" as a depolarizer, iron (usually cast iron) may replace the carbon element of the Bunsen cetl, with good results, the E. M. F. being about 1.7 volts. Care must be taken, however, that the density of the depolarizer does not fall too low, or the 1726 BATTERIES. negative element will be consumed. In fact, a cell of this class may be constructed with only iron and nitric acid as elements, in the following order: Iron (anode), dilute nitric acid, porous cup, strong nitric acid, and iron (cathode). 2640. A cell similar to the foregoing, except that the negative element is carbon instead of iron, known as the Maeche cell, gives an E. M. F. of 1.5 volts, and has the ad- vantage of giving off a much less quantity of nitrous vapor than the Bunsen. By substituting ordinary water for the dilute acid in the Maeche cell, the E. M. F. is reduced to about 1.2 volts; but owing to the difference in specific grav- ity of the two liquids (nitric acid and water), they soon mix somewhat through the walls of the porous cup. 2641. The E. M. F. of this type of cell is really gener- ated in two parts: one at the surface of the anode, due to the action of the electrolyte on the anode, and the other at or near the cathode, due to the action of the depolarizing liquid on the hydrogen evolved. (See Art. 2590.) Vary- ing the material of the anode or the electrolyte will then affect that part of the E. M. F. just as in a cell of the class given in Art. 2602, and the amount by which the E. M. F. is reduced or increased may be found from the values given in Tables 92 and 93, making due allowance for the E. M. F. due to the depolarizing action. The effect on the E. M. F. of varying the depolarizer may likewise be calculated from the values given in Table 94. TABLE 94. DEPOLARIZIIVG EFFECT OF VARIOUS SUBSTANCES. Substance. Solids. E. M. F. Volts. Substance. Liquid. E. M. F. Volts. yJ/;/ 6*2 (ordinary) Pb .33 .81 HNO^ (c o n c e n- trated) .35 •^ "i^x H CrO .47 ■'■■L^^i ^ ^ CI gas dissolved in water .04 BATTERIES. mi 2'^4:2>. The foregoing values for the E. M. F. in Tables 92, 93, and 94 are about the average of the somewhat vary- ing results of different experimenters. The values also vary somewhat with different tempera- tures and degrees of concentration of the liquids; they will be seen to be approximately correct if compared with exist- ing cells. It will be seen from this table that either chromic acid or chlorine water (chlorine gas dissolved in water) used as a depolarizer would give a higher E. M. F, than nitric acid; but as these liquids decompose in the presence of air, they can not be commercially used, just as in the case of sodium or potassium as anodes. (See Art. 2599.) 2643. Another important type of cell of this class is the bichromate cell, which differs from that described in Art. 2603, in that the bichromate solution is not mixed with the electrolyte, but is separated from it by a porous partition, with the effect that the zinc is not seriously attacked on open circuit. As to the E. M. F., chemical action, etc., this type is not sensibly different from the bichromate cells described in Art. 2603. The bichromate solution is usually, with the cathode, placed in the outer vessel, the zinc and exciting liquid being inside the porous cup; the exciting liquid being usually sulphuric acid diluted with water to about 1.10 sp. gr. , although solutions of sodium chloride or ammonium chloride are used. 2644. The depolarizing liquid is usually of the com- position given in Art. 2624, under the name electropoion fluid. A bichromate mixture is prepared by dealers in battery material, as follows (all parts by weight) : Sulphuric acid, 2 parts, is mixed with water, 4 parts; in another vessel, 1 part of potassium bichromate is dissolved in 3 parts of boiling water, and while hot is mixed with the liquid first prepared. This liquid, when cold and more or less diluted, is suitable for use in most bichromate cells. » 1728 BATTERIES. 2645. The Fuller bichromate cell, one form of which is represented in Fig. 1040, is a very excellent cell of this type, being economical in operation. It consists of a glass jar containing the de- polarizer (electropoion fluid diluted about one-half), into which is hung the carbon cathode C. In the center of the jar is placed the porous cup P, into which is poured a little mercury, and the zinc, which is in the form of a rod or wire W, with a conical lump Z cast on the 1:-^ end, placed in position. The mercury serves to keep the zinc well amalgamated. The exciting liquid is Fig. 1040. either very dilute sulphuric acid, or, more commonly, pure water. The E. M. F. is 2.14 volts, and the internal resistance (of the type shown in Fig. 1039) usually about 1 ohm, depending, however, on the thickness and character of the porous cup. This type of cell is largely used for telegraphic purposes in England. 2646. Bichromate cells are often constructed in which the liquids employed have such a difference in their specific gravities that they may be placed one over the other in the cell, no porous partition being required to keep them from mixing. 2647. The Partz cell, one form of which is illustrated in Fig. 1041, is an example. This cell is a bichromate cell (see Art. 2643), which uses a solution of sodium chloride, or of magnesium sulphate, as an electrolyte, surrounding the zinc Z, and a bichromate solution as a depolarizer, sur- rounding the carbon cathode C. The depolarizer, having a higher specific gravity than the electrolyte, remains at the BATTERIES. 1729 bottom of the jar, and the two liquids are kept separate. As the depolarizer is weakened by use, it is from time to time strengthened by the intro- duction of crystals in the glass tube 7", which is sus- pended in the cell, having a small opening below the normal level of the bichro- mate solution. The crys- tals used ' are what the manufacturers call sulpho- chromic salt, which is formed by the action of sulphuric acid on some bichromate solution, and when dissolved in water gives the same results as the electropoion fluid (Art. 2644). With the cell shown, which employs a 6-in. X 8-in. jar, the internal re- sistance is about 1 ohm with a solution of magnesium sul- phate, and about .5 ohm with a solution of sodium chloride, the E. M. F. being the same, 1.9 to 2 volts, in either case. This cell is good for either open or closed circuit work, as the depolarization is very complete; at the same time, the local action on open circuit is almost imperceptible. The chrome alum solution which forms, being heavier than the bichromate solution, descends to the lower part of the cell, so that the crystals form beneath the carbon plate, which is slightly raised from the bottom of the jar; conse- quently, the formation of these crystals does not appre- ciably increase the internal resistance of the cell. Fig. 1041. 2648. Another form of gravity bichromate, known as the Kousmine cell, has its liquids arranged in the reverse order to the above. The electrolyte is sulphuric acid 1730 BATTERIES. diluted to about 1.15 sp. gr. or less, and surrounds the zinc anode at the bottom of the jar. The depolarizer is a very ■weak solution of potassium bichromate, which floats on the sulphuric acid, being much lighter, and surrounds the carbon cathodes at the top of the jar. The heavy solution of chrome alum falls to the bottom, as in the Partz cell. The E. M. F. and actions of this cell are the same as in other bichromate cells, but its life is not long, the bichro- mate solution being soon exhausted by use. 2649. It can be readily seen that in cells of this class, consisting of the anode, exciting liquid, porous partition, depolarizing liquid, and cathode, a great number of differ- ent styles of cells may be constructed, by varying any of the four principal constituents, and a great many such variations have been made or suggested. As pointed out in Arts. 2599 and 2600, zinc is really the best and cheapest material for the anode; consequently, substituting other metals has not usually benefited the cell, except in special cases. The effect on the E. M. F. of such substitution may be readily found from Table 92, as before. Great varieties of solutions have been used as electrolytes or depolarizing liquids ; some with good results, and others without apparent reason, except to make a new cell. 2650. M. D'Arsonval, a French physicist, has made a series of cells, in which, by the action of the two liquids upon each other at their junction in the porous cup, an insoluble but conducting body is deposited in the pores of the porous cup, which prevents the gradual mixing of the liquids that usually takes place. For example, one of these cells is made up as follows: Zinc, solution of sodium hydrate (caustic soda), porous cup, ferric chloride, and carbon. The E. M. F. of this cell is about 2.7 volts; the action of the hydrogen on the ferric chloride reduces it to ferrous chloride and hydro- chloric acid; at the same time ferric hydrate (which is in- soluble, but a conductor) is formed in the pores of the porous cup. ^ BATTERIES. 1731 2651. Various chloride salts have been used as depolar- izers in cells of this class, the action being usually the reduction of the chloride to one containing a greater pro- portion of the metallic element, or else the entire reduction of the chloride, depositing the metallic element on the cathode; in either case the action of the hydrogen on the free chlorine forms hydrochloric acid. 2652. Many of the nitrate and sulphate salts have also been used as depolarizing liquids, and with a variety of electrolytes, generally acid; but the principal type of this class of cell, other than the Bunsen and the bichromate, is the type which employs as an electrolyte a salt of the metal of the anode, and as a depolarizer a salt of the metal of the cathode. The depolarizer is usually a salt formed by the same acid that formed the electrolyte salt; that is, if the electrolyte be a sulphate, the depolarizer is also a sulphate, etc. In this case the action is as follows: The passage of the current decomposes both liquids, and the hydrogen from the decomposed water unites with the non-metallic elements of the decomposed liquids, forming the acid from which the salt was formed, the metallic element of the de- polarizer being deposited on the cathode; this acid attacks the anode, reforming the salt of which the electrolyte is composed. The electrolyte, therefore, is continually added to, while the depolarizer is continually reduced. 2653. Neglecting the intermediate reactions, which generally do not affect the E. M. P., it is evident that the E. M. F. of this type of cell is due to the energy given up by the formation of the salt of which the electrolyte is com- posed, less the energy required to decompose the salt of which the depolarizer is composed. Now, whatever may be the actual energy of the formation of the various salts, the difference between the energies of formation of the same salts of any two metals is the same, whatever the particular salt may be ; for example, the difference between the heat of for- mation of zinc sulphate and that of copper sulphate is the 1732 BATTERIEa same as the difference between the heats of formation of zinc nitrate and copper nitrate. 2654. It naturally follows, that with given metals for the anode and cathode, the E. M. F. should be the same, whatever salt of the two metals be used as electrolyte and depolarizer, respectively. This is borne out in practice, as experiments have shown the E. M. F. under these circum- stances to be practically the same. In order, then, to obtain a high E. M. F., it is necessary to use as an anode a metal whose salts have a high heat of formation, and as a cathode a metal whose salts have a low heat of formation, just as in the other classes of cells. For commercial use, the same considerations apply as to the other classes; that is, the materials used in the cell must be easily and cheaply obtained, even if they do not result in the highest possible E. M. F. The cells which best realize this condition are the Daniell cell and its derivatives. 2655. The Daniell cell uses for the anode, zinc; for the electrolyte, a solution of (usually) zinc sulphate, ^;25' (9^; for the cathode, copper; and for the depolarizer, a solution of copper sulphate, CitSO ^. Sometimes, in setting up the cell, dilute sulphuric acid is used instead of the zinc sulphate, but this soon forms a solution of zinc sulphate; hence, the result is the same as if the zinc sulphate were used origi- nally. The E. M. F. of the Daniell cell is given several values by different investigators, ranging from 1.059 to 1.079 volts. The London Post Office uses this cell as a standard, and calls its E. M. F. 1.07 volts. The original form of the Daniell cell consisted of a glass jar, into which the zinc, in the form of a cylinder, was placed. Inside the zinc was a porous cup containing the cathode, a strip of sheet copper. The porous cup was filled with the CuSO ^ solution and the outer jar with the ZnSO^ solution. 2656. To prevent the gradual weakening of the depo- larizer, it is usual to put a considerable amount of copper sulphate crystals (commonly known as blue vitriol) into the BATTERIES. 1733 porous cup. As the liquid weakens, the crystals are grad- ually dissolved. Several modifications of the form of the original Daniell cell are in use, many of them designed to keep up the supply of copper sulphate as it is weakened. 265T. One such design, known as the globe or bal- loon cell, is shown in Fig. 1042, where Z is the zinc anode, P the porous cup, in which is the copper cathode C. To keep up the strength of the depolar- izer, a glass globe G is filled with crystals of copper sulphate vS" and a little water, in which--;_ the copper sulphate gradually dissolves ; the solution, being heavier than the water, falls to the bottom of the neck of the globe and replenishes the solu- tion in the porous cup. The neck of the globe extends down into the porous cup below the level of the liquid, so that the water may be retained in the globe. The globe rests on a ring of some soft material R^ making a comparatively tight joint between the globe and jar, which prevents evaporation to a considerable extent. As ordinarily constructed, the globe holds about two pounds of copper sulphate crystals, which will usually last about six months. A cell similar to the above is used extensively for telegraph purposes in Russia. 2658. The specific gravity, at ordinary temperature, of a saturated solution of ZnSO ^ is about 1.44, while that of a saturated solution of CiiSO^ is about 1.20; hence, if saturated solutions of these salts are used, the zinc sulphate solution will be considerably heavier than the other; it has been found, however, that the best results are obtained from a saturated solution of copper sulphate, used with a solution Fig. 1042. 1734 BATTERIES. of zinc sulphate diluted to a specific gravity of about 1.10. The considerable difference in weight between the two solutions has led to their arrangement, one over the other, in the cell, the heavier copper sulphate being at the bottom. 2659. In the Hussey and the Gethin cells a porous partition is used to separate the two liquids, in the form of a porous cup, located in the upper part of the jar. This cup holds the zinc and the electrolyte; beneath it is the copper, made in the form of a cross of sheet copper, which is surrounded by crystals of copper sulphate. 2660. Since the proportion of the two liquids in the jar varies from time to time, the porous partition does not always mark the point of separation of the two liquids, and it increases the internal resistance of the cell; consequently, the batteries of this type that are more generally used are those which do not use any porous partition at all, depend- ing on the difference in the specific gravities of the two liquids to keep them apart. Such cells are called gravity cells, or gravity Daniell cells, and are very extensively used for telegraph and fire- alarm work in this country. 2661. As long as a current is flowing through the cell, the chemical action keeps the boundary-line of the two liquids sharply defined ; but when the current ceases to flow the solutions gradually intermix, and the copper sulpJiate^ coming in contact with the zinc anode, sets up local actions, which cause a deposit of copper on the zinc, and a con- sumption of the zinc itself. To prevent this action, these cells should be used only on a circuit which is closed practi- cally all the time, which is the case with telegraph and fire- alarm lines. 2662. Practically the first cell of this type to be used was the Callaud cell, illustrated in Fig. 1043. In this cell the zinc Z is in the form of a cylinder, suspended by hooks from the edge of the jar. The copper (7 is a flat strip bent into a circle, which rests on the bottom of the jar. Con- BATTERIES. 1735 nectlon ■ is made between it means of a wire JV, which is insulated with some rubber compound where it passes through the liquids. The posi- tion of the two liquids is shown in the illustration, the zinc s ul pha te {ZnSOJ being at the top, as stated. This form of cell has been modified quite largely, it being now the practice to use lar^e cast zincs and the external circuit by w + FIG. 1044. instead of the cylin» der of sheet zinc used in the Callaud form, which allows of a longer life for each cell. 2663. The form of gravity Daniell cell most used in this country is the familiar croAvfoot cell, illustrated in Fig. 1044, where Z is the zinc, from the shape of which the cell gets its name; C is the copper, which is connected to the external 1736 BATTERIES. circuit by the wire JV, which is insulated where it passes through the liquid. When the cell is set up the copper cathode is surrounded with copper sulphate crystals. The standard form of this cell is of the following dimensions: Jar, 6 inches diameter, 8 inches high. Copper, made from three pieces of thin sheet copper 2 inches wide and 6 inches long riveted together in the middle; the outside pieces are then spread out, making the copper of a six- pointed star shape. To the middle strip is riveted a piece of No. 16 insulated copper wire. (See Fig. 1044.) The zinc is of the shape shown in the illustration, and weighs 3 lb. About 2 pounds of sulphate of copper crystals are required to charge the cell. 2664. The usual practice in charging is to set up the elements in the cell, put in the copper sulphate, and fill up with clean water until the zinc is covered; the cell is then allowed to stand for about 24 hours. By the action of the zinc on the copper sulphate solution, zinc sulphate is soon formed around the zinc, and the cell is ready for use. If desired for immediate use, a solution of zinc sulphate may be prepared and poured into the jar with the copper sulphate solution; in this case the zinc should not be placed in position until the two liquids have separated, which will be indicated by the upper part of the liquid becoming nearly colorless, while the lower part is of a deep blue color. 2665. The average internal resistance of a crowfoot cell of this size is about 3 ohms, and its E. M. F. is the same as the other forms of Daniell cell, 1.07 volts. 2666. The maintenance of this type of cell is simple, it only being necessary to renew the supply of copper sul- phate crystals when the solution becomes weak, which is indicated by the fall of the blue-colored liquid below the top of the copper cathode; besides this, the density of the zinc sulphate solution should be occasionally measured with a hydrometer, and if too dense (above about 1.15 sp. gr.) a part should be removed and replaced by water. BATTERIES. 1737 2667. With the crowfoot form of zinc there is consid- erable waste, due to the size of the **stub" which is left when the zinc has been consumed so that it can not be used. Several forms of zincs have been designed to prevent this waste as far as possible. 2668. One form, used by the Baltimore (Md.) Fire De- partment, is cast into a ring with upwardly projecting lugs, which have shoulders upon them, by which the zinc is sup- ported by the edge of the bat- fig. 1045. tery jar. This form of zinc is illustrated in Fig. 1045. The ring itself being entirely below the level of the liquid in the cell, it can be almost entirely consumed. 2669. Fig. 1046 illustrates another similar form, known as th.Q pinnacle zinc, from the fact that it is supported on a vertical rod of insulating material, which is fast- ened at the lower end to the copper. This rod projects up through the liquids and enters the cavity in the center of Fig. 1046. Fig. 1047. the brass supporting piece B, which is fastened to the zinc Z by the screws S, S. The complete cell is shown in Fig. 1047, 1738 BATTERIES. Z being the zinc, C the copper, and P the rod of insulating material which supports the zinc by means of the supporting piece B. 2670. Another form of zinc in which there is no waste whatever is the D'Infreville wasteless zinc, illustrated in Fig. 1048. Fig. 1048. This zinc is cast with a conical lug C on the top, and a corresponding cavity in the under side of the zinc (see Fig. 1049). When the zinc is nearly consumed, it is removed from the support B^ and the lug (7 inserted in the cavity of a new zinc, which is then put in place in the support B. The old zinc is then underneath, and FIG. 1049. is entirely consumed. Fig. 1049 shows a cross-section of this form of zinc, showing a new zinc A, a partly consumed zinc B, and the stub of a third C. The support B (Fig. 1048) also serves as a connector, the end of the connecting wire being sprung in between the two brass strips of which the connector is made, as shown at W. 2671. The Daniell cell, in various forms, has been used as a standard cell in laboratory work and for testing pur- poses. It is well adapted to such work, if too great a degree of accuracy is not required, as the E. M. F. is practically unaffected by moderate changes in temperature or in the den- BATTERIES. ItSQ sity of either solution used, or by the length of time the cell is in operation. For ordinary work the E. M. F. of such a standard cell may be taken at the value given; that is, 1.07 volts. (See Art. 2655.) CELLS WITH A SOLID DEPOLARIZER. 2672. The depolarizers which are used in this class of cell are generally substances containing a large proportion of oxygen, with which the free hydrogen unites, forming water; the balance of the depolarizer is sometimes dissolved in this water, but more often remains at the cathode in a Bolid form, the water merely serving to dilute the electro- lyte. In the first case the solution formed usually acts to keep up the strength of the electrolyte. (See Art. 2597.) 2673. Some few of the non-metallic elements which exist in the solid state will unite directly with hydrogen, and might be used as depolarizing cathodes; such a substance is the metalloid tellurhini. Such elements are rare and are not used in commercial forms of cells. ^Q74r. Among the most widely used depolarizers are the oxides of manganese, copper, and lead, and the chlorides of some of the metals. The several sulphates of mercury also have a large pro- portion of oxygen, and are used for this purpose. 2675. The Leclanche cell is a well-known and widely used cell of this type. Its positive element (negative elec- trode) is zinc, usually in the form of a rod ; the electrolyte is a saturated solution of ammonium chloride, NH JOI (sal ammoniac), and the negative element is carbon, surrounded by manganic oxide, MnO^ (black oxide, or peroxide, of manganese), which is the depolarizer. This being in the form of a coarse powder, it is usually contained in a porous cup, which allows free access of the electrolyte to the depolarizer and negative element. Fragments of crushed coke (or carbon in other forms) are 1740 BATTERIES. often mixed with the manganic oxide to decrease the resist- ance of the contents of the porous cup. Fig. 1050 shows the usual form of this type of cell. The porous cup P contains the manganic oxide and the carbon electrode, which pro- jects from the top of the cup, and to which a binding- post B is attached. The glass jar is circular, with a contracted top, in which a slight recess is formed to contain the zinc Z. The top of the zinc is provided with a binding- screw i?j, which serves as the negative terminal of the cell, B being the posi- tive. FIG. 1050. The top of the jar is coated with parafHn to prevent the crystals of sal ammoniac •' creeping " over the top of the jar as the liquid evaporates. 2676. The cell illustrated in Fig. 1050 is of the follow- ing dimensions: Jar, 4|- in. diameter, 6 in. high. Zinc, f in. diameter, 6^ in. high. Porous cup, 3 in. diameter, h\ in. high. Carbon, 6 in. X If in. Y^^'wi., about. The weight of the zinc rod is about 3 ounces, about two- thirds of which is below the level of the liquid. There are about 16 ounces of peroxide in the porous cup, and it re- quires nearly 6 ounces of ammonium chloride to make suf- ficient solution for this size of cell. For each ounce of zinc consumed in the cell, 2 ounces of manganic oxide and 2 ounces of ammonium chloride must also be consumed ; so, from the amount of these materials BATTERIES. 1741 contained in the cell, It follows that there is enough peroxide in the porous cup to last while four zincs are being con- sumed, while the ammonium chloride will not last longer than 1|- zincs. As the zincs are usually replaced when eaten away to about -J in, or -^j- in. diameter, the solution need not be replaced until two zincs have been consumed, and the contents of the porous cup will last as long as five or six zincs. The consumption of zinc in the Leclanche cell is about 23 ampere-hours per ounce of zinc, and as about If ounces of each zinc rod may be consumed, the life of each zinc is then about 40 ampere-hours. The E. M. F. of this type of cell is about 1.48 volts, and its internal resistance about 4 ohms. 2677. It is usual to seal the carbon and depolarizer into the porous cup by some compound, such as sealing-wax, leaving small tubes or holes, by which whatever gas not ab- sorbed by the depolarizer may escape. This sealing neces- sitates the entire renewal of the porous cup, with contents, when the depolarizer is exhausted; to obviate this expense, some makers use a carbon porous cup and place the zinc in- side, at the center, the space between the zinc and carbon being filled with peroxide. 2678. A form of Leclanche cell, made by the Law Battery Co., also replaces the clay porous cup by one made of carbon, but in this case the zinc is outside the carbon, as in the regular form. The carbon cup is made with a screw cover, also of carbon, which renders the replacing of the de- polarizer a simple matter. This construction reduces the cost of maintenance of the cell, but increases the first cost. 2679. Another widely used form of Leclanche cell is the Gonda Leclanche, which uses no porous cup whatever; the manganic oxide is mixed with granulated carbon and some gummy substance, and compressed into cakes under great pressure. These cakes are attached to the sides of the carbon plate, and act in the same manner as the depolarizer in the regular form. 1742 BATTERIES. 9 o n I z J -< 1 i '^i 1 -3 '111 C w G G i ■'. 1 i M —J » ) R Fig. 1051 shows the construction of the elements of such a cell. The two cakes of depolarizer (called gondas) G, G are clamped one on each side of the carbon plate C by the soft rubber bands R, R, which also serve to hold the zinc rod Z in place. The zinc lies in a groove in a block of wood or clay W, which serves to keep the zinc away from the gondas. This block is some- times done away with by supporting both zinc and carbon from a plate of insulating material, which also acts as a cover to the jar. In still other forms, the depolarizer is molded into a cylin- ^ der, in the center of which the zinc is supported. A second zinc electrode is some- times used in this latter form, consist- FiG. 1051. ing of a cylinder of sheet zinc encircling the cylindrical gonda, a common terminal being connected to both zincs. The liquids and action of the gonda form are the same as in the regular Leclanche cell. 2680. Commercial sal ammoniac often contains a con- siderable amount of impurities, in the shape of other salts, which materially reduce the life of the electrolyte; not suf- ficiently, however, to warrant the cost of using the chemi- cally pure salt, as prepared by chemists. 2681. Ammonium chloride has been found to be the only salt which works well with manganic oxide as a de- polarizer, so the many other forms of cell that have been constructed, using this depolarizer, differ materially from the Leclanche type only in the mechanical arrangement of the parts. 2682. The principal chemical actions in this type of cell are the formation of zinc chloride and ammonia, and the reduction of the amount of oxygen combined with the man- BATTERIES. 1743 ganese. Besides these, there are other more complicated reactions which occur, but which do not affect the E. M. F. of the cell materially. 2683. Another solid depolarizer which is used in im- portant commercial cells is cupric oxide, CuO. The La- lande and Chaperon cell uses an iron or copper nega- tive element surrounded with a layer of cupric oxide. The positive element is zinc, the electrolyte a solution of potas- siiiin hydrate (caustic potash). On closing the external cir- cuit, the potassium hydrate solution attacks the zinc, form- ing a compound oxide of potassium and zinc, known ^.spotas- siuin zincate, and liberating hydrogen, which combines with the oxygen of the cupric oxide, forming water, and depositing metallic copper on the cathode. If the surface of a solution of caustic potash is exposed to the air, it will gradually form potassium carbonate; to pre- vent this action, cells of this type are either entirely en- closed or the surface of the liquid is covered with a thin layer of heavy oil. Fig. 1052 shows one form of Lalande and Chaperon cell, in which the iron vessel V forms the negative ele- ments, the positive terminal being a lug A cast on the side of the vessel. The cupric oxide B is in a layer at the bot- tom of the vessel. The zinc i? is suspended from a rod K^ which passes through a rubber stopper G, terminating in a binding-post F. The rubber stopper is provided with a valve H, which allows such gases as are evolved to escape. fig. io58. 1744 BATTERIES. Several other forms, of greater or less capacity, are man- ufactured. The E. M. F. of this type of cell is about .7 volt, and its internal resistance is usually low. 2684. The Edisoti-Lalande cell is a modification of the Lalande-Chaperon. The cupric oxide is molded under pressure into plates of the requisite size, being first mixed with magnesic chloride, which, when the molded plates are heated, serves to bind the mass together. These plates are held in copper frames, which enclose the edges of the plates. The positive element in this cell is zinc, and the electrolyte a solution of potassium hydrate, as in the Lalande-Chaperon cell. Two plates of zinc are used in most of the forms of this cell, one on each side of the cupric oxide plate. A form of this cell is shown in Fig. 1053, which repre- sents a 150-ampere-hour cell. The cupric oxide plate C is suspended in a cop- per frame i% F be- tween the two zinc plates Z, Z, which are hung from each side of a lug on the por- celain cover of the jar. The sides of the copper frame of the oxide plate are car- ried up through the cover supporting the plate, and form ter- minals B, B, either of which may be used as the positive ter- minal of the cell. The copper frame is protected from the action of the liquid where it passes up through by tubes of insulating material r, T. A binding-post B^, on the bolt which supports the two zinc plates, serves as the negative terminal. Fig. 1053. BATTERIES. 1745 A heavy paraffin oil is used in this cell to prevent the action of the air on the solution ; the oil layer is represented in Fig. 1053. The cell shown is 5^ in. X 8^ in., outside dimensions, and will give a current of 3 amperes at a potential of about .7 volt for 50 hours, which is equivalent to about 100 watt- hours, with one "charge " of zinc, caustic potash, and oxide. The internal resistance of the above cell is about .07 ohm; the weight of the oxide plate is about ^ pound. This type of cell is made in various sizes, ranging from a 15 ampere- hour cell for telephone and similar work, to 900 ampere- hour cells for running lamps, small motors, etc. 2685. There are several oxides of lead which have been used as depolarizers in single liquid cells: plumbic ox- ide, PbO, known as litharge, which is in the form of a yel- lowish powder; peroxide of lead, PbO^, and a combination of the oxide and the peroxide, Pb^O^, known as minium, or red lead, which is a brilliant red powder. 2686. As seen from its formula, the peroxide contains the most oxygen, and is rather the best depolarizer; for example, in the zinc, dilute sulphuric acid, and carbon cell, surrounding the carbon with lead peroxide increases the E. M. F. to 2.2 volts; the action of the sulphuric acid on the peroxide, however, forms a small quantity of lead sulphate, which is insoluble, and increases the internal resistance of the cell somewhat. Lead peroxide is extensively used in accumulators (storage- batteries) as a depolarizer. 2687. It is also used in a cell (made in Europe) which is interesting from its use of identical electrodes; that is, both anode and cathode are of carbon, arranged as follows: The cathode is a cylindrical rod of carbon surrounded with lead peroxide, which is kept in place by a canvas bag. The anode is a perforated carbon cylinder, made to slip over the cathode and its surrounding canvas. The whole is then put in a glass jar and surrounded by fragments of crushed coke; the jar is then half filled with a strong solution of sodium 1746 BATTERIES. chloride. The lead peroxide is reduced to lead by the action of the hydrogen; the oxygen (due to the decomposition of the water) combines with the carbon anode. This process goes on slowly, so that if much current be drawn from the cell it will polarize by the formation of the oxygen on the surface of the anode. If used for furnishing feeble currents, this cell will last a long time; its E. M. F. is about .6 or .7 volt. 2688. AH cells using the above-mentioned solid depo- larizers may be regenerated by passing a current from some other source through them in the opposite direction to that of their own current; the effect of such a current is the decomposition of the various substances formed by the original action of the cell and their recomposition into the original substances of which the cell was composed. If the mechanical construction of the cells is such that these sub- stances return to their original position in the cell, they will again act as a voltaic couple from which a current may be obtained. 2689. This constitutes a storage, or secondary- battery, or accumulator. It is evident that such a cell is nothing but a primary voltaic cell, which, when exhausted, may be restored by the passage through it of a current from an external source; there is no real storage of electricity, so the name storage- battery is hardly correct; the last name, accumulator, is more appropriate to the action of such a cell. Accumulators will be treated of more fully later. 2690e The principal chlorides used as depolarizing agents are the chlorides of mercury and of silver. If the carbon of a zinc, ammonium chloride, and carbon cell be placed in a porous cup and surrounded with a paste of mercurous chloride, the chemical action is as follows: The ammonium chloride attacks the zinc, forming zinc chloride, and freeing ammonia and hydrogen, which attack the mercurous chloride and reform ammonium chloride, leaving free mercury at the negative pole. BATTERIES. 1747 The ammonium chloride solution is thus kept up at its full strength until the mercurous chloride is entirely ex- hausted, and the hydrogen is recombined as fast as formed. Such a cell has an E. M. F. of 1.45 volts, which is main- tained as long as the depolarizer lasts, if excessive currents are not used. 2691. The chloride of silver is used in a similar man- ner. Cells employing this depolarizer use as a negative element a silver wire or plate coated with silver chloride. The positive element is usually zinc, and the electrolyte a dilute solution of one of the chloride salts. With ammonium chloride, the E. M. F. is 1.03 volts; with zinc chloride, 1.02 volts, and with sodium chloride (common salt), 0.97 volt. Silver chloride cells are quite extensively used in medical and testing work, on account of the constancy of their E. M, F. As in this work only very feeble currents are required, this type of cell is usually made small and of compact form, especially as the use of the silver element would make a large cell very expensive. The chemical action is of the same order as that of the mercurous chlo- ride cell just described; that is, the chlorine part of the electrolyte is continually replaced from the depolarizer. 2692. The various sulphates of mercury which are used as depolarizers are the mercuric sulphate, the mer- curous sulphate, and a sulphate containing a still higher percentage of mercury, known as turbith (or turpeth) min- eral. Either sulphate may be used in the zinc, dilute sul- phuric acid, and carbon cell without materially affecting the E. M. F., which, under these circumstances, is 1.3 to 1.5 volts. These sulphates, being slightly soluble, are usually em- ployed in the form of a paste, made with water or the exciting liquid. In ordinary work the mercury sulphates are not extensively used, not only on account of the high cost of these salts, but because of their poisonous qualities. 1748 BATTERIES. Still, these sulphates are excellent depolarizers, and are used in standard cells. 2693. The Latimer-Clark cell, in which the electro- lyte is a paste of mercurous sulphate, formed with a solution of zinc sulphate, and the elements are zinc and pure mer- cury, is largely used as a standard in laboratory work, its E. M. F. being extremely constant, if proper precautions are taken in its construction. With chemically pure zinc and mercury, and a very carefully prepared electrolyte, the E. M. F. of a standard Clark cell at 15° C. is 1.434 volts. This E. M. F. varies very slightly with the temperature, the temperature coefficient being .077^ per degree Centigrade, so that the E. M. F. at any temperature may be expressed by the following formula: Let / = temperature in degrees Centigrade at which measurement is made; E=- electromotive force of cell; then, E = 1.434 [1 -.00077 (/ ~ 15)] volts. (472.) Thus, for example, formula 472 gives 1.4507 volts for this cell at the temperature of freezing water, 0° C, and 1.4155 volts at 33° C. The greatest accuracy is demanded in the construction of this cell and in the determination of its temperature coef- ficient, because the cell is used as a standard in the measure- ment of unknown electromotive forces. These cells are used as standards of E. M. F. only. They do not supply anything but very minute currents; so they are made of conveniently small size, and the most approved forms have a carbon or graphite resistance of about 10,000 ohms connected permanently in series with the cell, to pre- vent its accidental short-circuiting and consequent failure. These cells are very valuable on account of their constancy, but the element of temperature which enters in makes them somewhat difficult to use with great precision, as thermometers are, as a rule, inexact, their measurements depending largely on their physical condition. BATTERIES. 1749 2694. By substituting oxide of mercury for the sul- phate, and using a weak (10^) solution of zinc sulphate as the electrolyte, the temperature coefficient is, it is claimed, only .01^ per degree C. This is the Gouy standard cell, which has an E. M. F. of 1.39 volts at 12° C. 2695. A cell has been designed by Mr. Edward Wes- ton, which, it is claimed, has no temperature coefficient whatever within reasonable limits. This cell uses for the positive element the metal cadmium in the form of an amalgam, and for the negative, sulphate of mercury mixed with pure mercury. The electrolyte is a solution of some cadmium salt, preferably the sulphate. The E. M. F. of this form of cell is 1.019 volts, nearly. The mechanical construction of this cell makes it well suited for general use as a standard cell, it being entirely sealed into and enclosed by a solid casing. The cell itself is similar to one of the usual forms of standard cells, consisting of two short glass tubes, open at the end, and connected together near the top by a short tube, as represented in Fig. 1054, in which 7", T are the two tubes connected together by the short tube S. In the bottom of the tubes are the elements P and tV, to which connection is made by means of the wires W, IV, which are sealed into the glass. These wires are led to binding-posts conveniently mounted on the case. The space above the ele- ments is filled with the electro- lyte, and the top of the tubes fig. io54. fitted with corks C, C, which are afterwards sealed in place, preferably with some resinous compound. The elements, being in a semi-liquid condition, are each kept in place by a 1750 BATTERIES. piece of cloth F, with a perforated cork M laid over it. When this is forced down the tube to the surface of the element, the cloth keeps the element in place, and the cork holds the cloth, the perforations allowing free access of the liquid to the elements. This is the general form in which most standard cells are made, although the various makers usually introduce slight changes in the mechanical construction, 2696. The Bailie and Fery cell is also used as a standard cell. Its action is similar to those just described, the depolarizer being lead chloride, deposited in crystalline form on a lead cathode. The positive element is amalga- mated zinc, and the electrolyte a solution of zinc chloride. The E. M. F. of this cell is .5 volt, and its temperature co- efficient is low, being about .02^ per degree C. CELLS IN ^¥HICH AN ELEMENTARY SUBSTANCE IS APPLIED TO THE CATHODE AS A DEPOLARIZER. 2697. This class of cells is not large, and has no extended commercial application, at least in this country. The principal elements used for depolarizers are those com- prised in that group known as halogens; that is, chlorine, bromine, iodine, and fluorine. AlFthese elements will com- bine with hydrogen directly, forming acids; of these the formation which liberates the greatest amount of energy is that of hydrogen and chlorine {HCl, hydrochloric acid); this element (chlorine), therefore, is most used in this class of cells, as it results in a high E. M. F. Chlorine being normally in the form of gas, it is sometimes generated by chemical action in suitable apparatus outside the cell, and allowed to pass through the cell or battery of cells near the cathodes, acting as a depolarizer and forming hydrochloric acid. In other cases, the materials whose chemical reactions produce chlorine are brought together at the cathode, and the chloride produced acts as in the previous method. BATTERIES. 1751 As a rule, some or all of the other products of the chemi- cal actions must be removed as fast as produced, to make room for a fresh supply of chemicals ; in any case, as stated in Art. 2606, the supply of depolarizing element is inde- pendent of the output of the cell, and must be regulated by hand. On the whole, cells of this class would be expensive to construct and maintain, and capable only of limited and special application. 2698. Strictly speaking, cells which have been in- cluded in the class given in Art. 2602, whose carbon cathode is made of large surface and very porous, should be included in this class (see Art. 2617); but their depolari- zation is very incomplete, and is rather accidental than a pronounced feature of the design; hence, they are placed in the former class. DRY BATTERIES. 2699. This name is applied to cells, usually belonging to the class mentioned in Art. 2605, in which the electro- lyte is carried in the pores of* some absorbent material, or combined with some gelatinous substance, so that the cell may be placed in any position without spilling the liquid. 2700. These cells are usually made in small sizes, with zinc and carbon elements, the zinc usually forming the out- side of the cell, being made into a sort of cylindrical can, in the center of which is the carbon, surrounded by its depo- larizing compound. The space between them is filled with some absorbent material, such as "mineral wool," asbestos, sawdust, blotting-paper, etc., and the whole is then soaked in the exciting liquid ; or the exciting liquid is mixed with a hot solution of some gelatinous body, such as isinglass or "Irish moss," which mixture is poured into the cell; on cooling, it forms a soft jelly. The first method of prepara- tion is most used. 2701. It is evident that only a comparatively small amount of liquid can come in contact with the zinc at one 1752 BATTERIES. time, so the current output must be small; in fact, they arc not adapted for anything but intermittent work. It is quite necessary, however, that they have a depolarizer, as otherwise they must be made open to allow the hydrogen to pass off, which would also allow the small amount of water they contain to evaporate; to prevent this latter action, these cells are sealed with some resinous compound. 2702. Owing to the presence of the absorbent material, the actual amount of liquid in these cells is comparatively small; consequently, they are soon exhausted. The sealing^ being seldom perfect, often allows the water to evaporate, in which case the cell ceases to act; a cell of this description may often be made to work when apparently exhausted by drilling a small hole in the seal and injecting a little water. 2703. The materials used in dry batteries are usually kept secret by their manufacturers; they all, however, answer to the above description as to construction, and the best types employ the same materials as the Leclanche bat- tery; that is, a zinc anode, ammonium chloride electrolyte, manganic oxide depolarizer, and carbon cathode. In spite of its defects, this form of cell is extremely con- venient on account of its portability, and in many cases can be profitably used. 2704. Silver chloride cells (see Art. 2691) are made in a sealed form, and have all the advantages of a dry bat- tery; the materials of the battery are enclosed in a capsule of semi-flexible material, which allows of the necessary con- tractions and expansions of the apparatus. In this form these cells are very convenient for testing and similar purposes. THE APPLICATION OF PRIMARY BATTERIES. 2705. Although the cost of electricity generated by chemical action is greater than that generated by dynamo- electric machinery, there are many cases in which, from lack of motive power, or from the small amount of current required, primary batteries may be successfully used. In BATTERIES. 1753 such cases, the cost of materials consumed in producing the electrical energy is entirely offset by the little attention required and the constancy of the source of supply; and in many cases where current is used intermittently, the cost of the current from a battery in which the materials are con- sumed only as the current is used would actually be less than the cost of the power for driving an equivalent dynamo all the time. 2706. The most important applications of primary bat- teries are to telegraph, telephone, and electric fire-alarm systems, where a constant but small current is required more or less continuously, although in large central offices, where the necessary current represents a considerable amount of energy, dynamos are replacing the batteries to some extent, on account of the saving in space. For this (telegraph, telephone, and fire-alarm) work, gravity batteries of the Daniell type are more commonly used, as they possess the advantages of long life and little attention. 2707. For telephone work, the currents used are very minute indeed, and almost any good cell in which there is no local action and in which the depolarization is complete (at least for small currents) will give good results. The E. M. F. required is 1.5 to 2 volts; consequently, in some cases single cells which give about this E. M. F. may be employed. 2708. In fire-alarm work a steady current of (usually) .04 ampere is used, the potential varying with the length of the circuit. Gravity Daniell cells are used largely in this work, the zincs being made large and heavy to insure long life and, consequently, little attention. 2709. Several systems of block signaling on lines of railroads also employ electrical devices of such a character that gravity Daniell cells are well suited for furnishing the current for their operation, and are quite extensively used for such purposes. 1754 BATTERIES. 2710« There are a great number of devices which require the application of a current intermittently; some, such as electric bells and other signals, electric gas-lighting apparatus and the like, are used infrequently and irregu- larly, and the amount of electricity required is small, so that almost any voltaic cell will do, depolarizing or not, provided there is no local action to cause waste when not in use; therefore, cells with liquid depolarizers (see Art, 2604) are not well adapted to this work, as in the long periods in which these cells are not called upon to furnish current the two liquids will mix and usually cause local action. 271 1. The cells most used for this work are the various zinc-carbon batteries, both of the class described in Art. 2602, with non-depolarizing electrolytes, and of the class described in Art. 2605, with solid depolarizers; of the lat- ter, some form of Leclanche cell usually gives the best re- sults. In hotels and large buildings where the bell or signal service is practically continuous, depolarizing cells are re- quired, such as large Leclanche cells, bichromates (with separate fluids), if of good modern construction, Edison- Lalande, and the like. 2712. Electric currents are much used in physicians* and surgeons' offices; currents of a few milliamperes in strength, but of from 75 to 100 volts E. M. F., are applied for curative purposes, while currents of 10 to 20 amperes in strength are used for heating cautery loops in surgical operations, requiring an E, M. F. of from 4 to 8 volts. Miniature incandescent lamps, usually operated from the battery which furnishes current for the cautery, are also used to examine the interior of the body. 2713. The first appliance obviously requires a large number of cells of a small size; for occasional use, and where first cost is not such an object as compactness, a battery of small silver chloride cells is very convenient, while for more frequent use, requiring larger cells, some cheaper form of depolarizing cell is used. Obviously, if the cells selected have a high E. M. F. (say 2 volts), a less number will be required than if the cells are of BATTERIES. 1755 a low E. M. F. ; however, as in some instances the regula- tion of the current is obtained by switching in or out some of the cells, this regulation will be more uniform and gradual if the E. M. F. of each cell is low. 2714. For furnishing the larger currents for cautery work, large cells should be selected, those which are so arranged as to have a minimum internal resistance being best. As the use of porous cups in a cell increases the in- ternal resistance largely, cells which employ them are not well suited for this work. Bichromate cells are very convenient for this purpose, as their internal resistance is low and the E. M. F. high and steady. It is usually convenient to use the form of bi- chromate cell in which the elements are raised from the liquid when the cell is not in use, as the purpose for which the current is used involves personal and immediate atten- tion to all parts of the apparatus. 2715. The most extensive application of cells of the Bunsen type is to electroplating and similar work, and cells of large size are made especially for this purpose. Such work being usually carried on in establishments es- pecially fitted up for the purpose, the various unpleasant features of the Bunsen cell, which make them objectionable for many purposes, may be readily provided for, and their high and constant E. M. F. utilized. 2716. The minor applications of primary batteries are almost innumerable. A study of the requirements of such cases will usually determine the best type of cell to use, but attention should also be paid to the mechanical construction of the cells selected, as on this point often depends their life and suitability for the work they are called upon to do. The binding-posts should be firmly and substantially fixed to the elements, and should be thoroughly protected from possible contact with the electrolyte, as the resulting action will so corrode the joint between the two as to destroy the contact, besides possibly eating away the connecting wires and breaking the circuit. 1756 BATTERIES. Of the material of the positive element, as much as possi- ble should be below the level of the liquid, as when that is consumed the balance must be thrown away, and this may represent a considerable loss. Altogether, the cell should be substantial and compact, not liable to local action, and arranged so that its parts may be readily renewed with the least possible waste. 2717. In general, it must be remembered that the consumption of material in a primary cell (assuming no local action) is proportional to the output in ampere-hours; the energy output depends not only on the amount of ma- terials consumed, but on the E. M. F. of the cell and its internal resistance, so that, other things being equal, the higher the E. M, F. of a cell and the lower its internal resistance, the greater its output for a given cost of materials. 2718. As stated, the most economical metal to use for the positive element is zinc, and the amount of zinc con- sumed in a cell may be readily determined from the output in ampere-hours and the chemical equivalent of zinc (again assuming no local action) ; but to find the total cost of the energy, to this must be added the cost of the depolarizer consumed, if any, and the cost of labor in renewing the ma- terials and caring for the cells. 2719. The substances resulting from the chemical ac- tions which take place often have a market value; usually, however, the expense of collecting or preparing such sub- stances for sale will be greater than the price they will bring, so that in ordinary cases this should not be taken into account. 2720. It is evident that all the E. M. F. of a cell is not available to send a current through the external circuit, but that a part is expended in overcoming the internal re- sistance. If the resistance of the external circuit is very great, this drop is of little importance; while if the external resistance BATTJilRIES. 1757 is very small, the internal resistance practically determines the amount of current flowing. 2>72>1. The various methods of connecting up the cells of a battery, in parallel, series, or parallel series, are given in Art. 2250. If several cells, all of the same size and kind, are con- nected in series, their total internal resistance will equal ^/le resista7ice of one cell multiplied by the miinber of cells, and their total E. M. F. will equal the E. M. F. of one cell mul- tiplied by the number of cells ; if they are all connected in parallel, their total resistance will be equal to the resistance of one cell divided by the number of cells, while their total E. M. F. will be equal to that of a single cell. From this it follows that if the external resistance is very small, increas- ing the number of cells in series will not increase the cur- rent in the external circuit appreciably, as the resistance increases nearly as fast as the E. M. F. ; while if the exter- nal resistance is great, increasing the number of cells in parallel will not appreciably increase the current flowing, as the total resistance is not much altered, while the E. M. F. remains the same. 2722. For a given external resistance and a battery of a given number of cells, the maximum current will flow when the cells are so grouped that their internal resistance just equals the external; so that, in installing a battery, the resistance of the circuit and of the cells should be ascer- tained, and the cells grouped accordingly. This may be E proved, numerically, as follows: C = -^. Let m cells be in series in / rows, or a total of m X / cells. Let E be the electromotive force and R the internal resistance of each cell, and r the resistance of the outside circuit. Substi- m E tuting in above formula, C = -, ^ tt — ; — id). Then, {in R -\- I) -\- r ^ ' m R C is greatest when — - — [- r is smallest ; that is, when m and / are chosen such that -j- R, the total internal resistance. I'^'SS BATTERIES. equals or approximates to r. Let us assume m x I ^= 12, ^ = 2, r = 3, i? = 2. Substituting in formula (<«), and taking the following values of /, , , .. 12 X 2 24 - ^=1^ ^- (,o_X2) + 3 = 24 + 3 = -^""^P^^^- Total internal resistance = — = 24 ohms. J ■ ^ 6X2 12 ^-^- ^= (|X2) + 3 = 6T3^'-'""^P^^^^- Total internal resistance = 6X2-^2 = 6 ohms. / o /- 4X2 8 , , Total internal resistance = 4x2-4-3 = 2f ohms. »./-. oX2 6 _ Total internal resistance = 3x2-4-4= 1|- ohms. It is thus seen that the largest current is obtained when the internal resistance approaches nearest to the value of the external. Ordinarily, in telephone, telegraph, and fire-alarm work the external resistance is high, while for ringing bells, gas- lighting, and similar work the resistance is low; batteries for these purposes should be grouped accordingly. 2723. The internal resistance of a cell can not be measured in the same way as the resistance of a piece of wire, that is, by sending a measured current through it from some external source, measuring the drop in volts and calculating the result from Ohm's law ; for the E. M. F. of the cell itself would either add to or subtract from (depend- ing on the polarity of the current) the drop due to the cur- rent, and, hence, the calculated results would be at fault. 2724. A simple way to measure this internal resistance is to cause the cell itself to furnish a current through some known resistance. Then, by measuring the E. M. F. at the BATTERIES. 1759 terminals of the cell with a voltmeter, when the current is flowing and on open-circuiting the cell, the difference between the two readings will show the drop in volts due to the flowing of this current against the internal resistance of the cell. For example, if a cell gives an E. M. F. of 1.5 volts on open circuit, and on being connected to an external resist- ance of 2 ohms the E. M. F, at the terminals drop to 1.25 volts, the drop in the cell is obviously .25 volt. The cur- rent is C = ^ = ^^— = .625 ampere; therefore, the internal resistance of the cell is i^ = -^ = -^-— - = .4 ohm. C .d2o ACCUMULATORS. 27,25. A storage-battery, or, preferably, an accumu- lator, is an apparatus consisting of certain materials so arranged that when they have undergone chemical action, due to the influence of a current of electricity, the combina- tion has acquired the properties of a voltaic cell, and is en- abled to discharge into a closed circuit a current of electricity approximately the same as the original charging current. Many forms of primary batteries may, when exhausted, be more or less regenerated by passing through them a cur- rent, from some external source, in the opposite direction to the current they themselves produce. It is customary, how- ever, to consider as accumulators only those cells whose original construction is similar to an exhausted battery; that is, they can not be used as sources of electricity until they have been cJiarged by passing a current through them. 2726. A great deal of confusion exists as to the use of the terms positive and negative in speaking of the plates of a secondary cell ; for in charging the cell the current is in the reverse direction to that which flows when the cell is acting as a voltaic cell and discharging. It is customary, however, to speak of the plate at which the current enters the cell (while charging) as the positive plate. In fact, 1760 BATTERIES. whether charging or discharging, his plate is at a higher potential than the other, which justifies the above use of the term, although with respect to the chemical actions in the cell the positive and the negative plates are reversed in the two operations. 2727. Accumulators may be divided into two general classes : (1) lead accumulators, and (2) bimetallic accumulators. The larger proportion of cells now in use are of the first class. 2728. Lead Accumulators. — The original lead ac- cumulators, as made by Plante, consist of two plates of lead, usually rolled together in a spiral, and separated by strips of rubber or other suitable insulating material; these are placed in dilute (about 10^) sulphuric acid. On sending a current from some external source through this cell, the water becomes decomposed, and the oxygen combines with the positive plate, forming lead oxide or peroxide, while the hydrogen collects at the negative plate. On disconnecting the source of the applied current, and completing the external circuit of the cell, the water again is decomposed, the oxygen uniting with the hydrogen col- lected at the negative plate, and also with the lead plate itself, and the hydrogen uniting with the oxygen of the oxide of lead at the positive plate, thus producing a current in the opposite direction to the applied current. 2729. Owing to the fact that the formation of the layer of oxide prevents further oxidation, the amount of chemical change due to the applied current is small, so the secondary current from the cell is of short duration ; after this current has ceased, however, the surface of the positive plate is much increased, owing to the removal of the oxygen from the lead oxide, leaving the metallic lead in a spongy form. On again sending a current through the cell a further oxidation of this (positive) plate takes place, and by continuing this process, reversing the current each time it is sent through, both positive and negative plates become porous to a considerable depth, thus very much increasing BATTERIES. 1761 the surface on which the oxidation can take place. This process might be carried on until the whole plate is re- duced to spongy lead ; in that case the plate would not hold together, so a sufficient amount of the original plate must be left for mechanical strength. After the plates are so formed^ they are ready to be used as an accumulator. 2730. This forming process, however, is too long and expensive for commercial success, though it is considerably hastened by roughening the surface of the lead plates with nitric acid before commencing the process; it was soon superseded by the process invented by Faure, of coating the surface of the plates with some substance which by the first charging current is converted into lead peroxide on the posi- tive plate and into spongy lead on the negative. This sub- stance may be lead oxide (litharge), lead sulphate, minium {Pb^O^), lead peroxide, or mixtures of these substances. 2731. These substances are applied in various ways; one method is to make a paste of the substance (in this case usually minium), that for the negative plate being made with sulphuric acid, which changes the PbJD^ into PbSO ^ (lead sulphate) and water, while that for the positive plate is made with water only. These pastes were originally ap- plied directly to the surface of the plain lead plate; but as they proved to be only slightly adhesive, the plates were prepared by scratching or otherwise roughening the surface, which process has been gradually extended until the lead plates are now cast into grids, or latticework plates, in the spaces of which the paste is applied, or forced by hydraulic pressure. Some manufacturers do not use a paste of the active material, but employ the minium, litharge, or lead sulphate in the form of dry powder, forcing it into the grid under such enormous pressures that the powder is solidified. 2732. The grids are usually designed to hold the active material securely in position; to this end they are made with perforations which are not of the same area through- out the thickness of the plate, but wider or narrower in the 1763 BATTERIES. ' center, so as to hold the filh'ng of active material by the dovetailing action of their shape, as will be shown later. • 2733. After the grids have been filled with active material, they are set up in pairs in suitable vessels, and surrounded by an electrolyte consisting of sulphuric acid diluted to about 1.17 sp. gr., which density corresponds to about 20^ of acid in the liquid. A charging current is then sent through the cell from some external source ; the action of this current decomposes the water, the oxygen of which further oxidizes the lead oxide (litharge or minium) to per- oxide, at the positive plate, the hydrogen going to the nega- tive plate, where it reduces the lead sulphate to spongy lead by uniting with the SO^^ forming sulphuric acid. Thus, the active material becomes lead peroxide in the positive plate and spongy lead in the negative. By many investi- gators this lead peroxide is thought to be Jiydrated lead peroxide ; that is, it contains a certain amount of hydrogen and oxygen in excess of the normal peroxide, and is repre- sented by the formula H^Pb^O^. This, as well as many of the actions which occur in accumulators, is not clearly established as yet. 2734. Continuing the charging current, when all the active material is thus converted, produces no further effect, except to continue to decompose the water; the re- sulting gases pass off through the water, giving it a milky appearance. This phenomenon is known as gasing or boiling, and is an indication that the cells are fully charged. Continuing the charging current beyond this point, that is, overcharging the cells, does no harm to the plates, but the energy repre- sented by the current is wasted. 2735. On discontinuing the charging current at the gasing point, and completing the external circuit of the cell, a current will flow in the opposite direction to that of the charging current, the resulting chemical action being to reduce the lead peroxide to lead oxide at the positive plate, and the spongy lead to lead sulphate at the negative; a BATTERIES. 1763 secondary action is the formation of a part of the lead oxide at the positive plate into lead sulphate. The sulphates thus formed are not all of the same proportions; one exists as red, another as yellow, and a third as white crystals, of which the white sulphate is best known, as it is formed when the cell is considerably discharged, and is extremely troublesome. This discharge may be continued until all chemical action ceases, and the E. M. F. consequently falls to zero; but this is not advisable, since, if the discharge is carried beyond a certain point, the red or yellow sulphates, probably by combination With the litharge {PbO), form the white insoluble sulphate, which has a higher proportion of lead than the others; this, being a non-conductor, materially increases the internal resistance of the cell, and when it is removed it usually carries some of the active material with it, as it is very adhesive. 2736. When the cells have been properly charged, the positive plate is of a brown or deep red color, while the negative is a slaty gray. The presence of the insoluble sulphate is made apparent by the formation of a white coating or glaze over the plates, which are then said to be sulphated. If the cells are discharged and left to stand with the electrolyte in place, sulphating takes place rapidly. 273T. It will be noticed that sulphuric acid is formed during thecharge, and decomposed during discharge ; thus the proportions of it in the electrolyte, consequently the density of the electrolyte, vary with the state of charge of the cell; starting with a specific gravity of 1.17, when the cell is fully charged the specific gravity will be found to be about 1.22, indicating the presence of about 25^ of sulphuric acid in the electrolyte. 2738. The chemical actions of charging or discharging do not take place simultaneously, as is shown by the varia- tions in E. M, F. under different conditions of charge or discharge, nor are they probably the only actions which occur. 1764 BATTERIES, 2739. The E. M. F. of this type of cell is approximately 2 volts, being 2.04 when slightly discharged, which gradually falls to 1.90 volts when nearly discharged. Beyond this point, further discharging causes the E. M. F. to fall more rapidly, the decrease after 1.8 volts being very rapid. (See Fig. 1055.) 2740. The rating of accumulators is usually based on their capacity when discharged to an E. M. F. of 1.8 volts; but in spite of this rating, the result of a long series of tests shows that in practice they should not be continuously dis- charged to below 1.9 volts, as below this point sulphating is very liable to occur, and, the nature of the chemical action being changed, it also leads to the distortion of the positive plate, which is known as buckling. As the plates are located very close together in the cells to reduce the internal resistance, buckling is liable to cause the plates to touch, thus short-circuiting the cell. 2741. The cause of buckling seems to be the formation of sulphate in the plugs of active material which fill the spaces of the grids, thus causing the plugs to expand; lead having very little elasticity, the grid is forced out of shape. As usually constructed, the edges of the grid are heavier than the intermediate portion, so that the effect of the dis- tortion is to bulge the plate in the center. If the plates are not discharged too far and too rapidly, the expansion of the active material is gradual, causing the grid to stretch evenly ; this makes the plates " grow," or increase in area, sometimes as much as 10 per cent. 2742. The quantity of electricity which may be taken from a completely charged cell depends upon the amount (weight) of material altered by the chemical action, as in a primary cell; while the rate at which this material is altered, consequently the rate at which the electricity can be taken out (the rate of discharge in amperes), and, to a large extent, the amount of material altered, depends upon the surface of the active material exposed to the chemical action. BATTERIES. 1765 2743. Cells of this type are then rated at a certain number of ampere-hours capacity, depending on both the weight and the surface area of the active material in the cell, and a certain economical discharge rate is also recom- mended, depending on the surface of the plates exposed to the electrolyte. If this discharge rate be continually exceeded, the chem- ical action goes on too rapidly, the white sulphate is formed in the active material of the positive plate, finally causing disintegration of the active material and buckling of the plates, even if the discharge is not carried beyond the point (1.9 volts E. M. F.) given above. With the ordinary con- struction, the normal discharge rate is about .0165 ampere per sq. in. of surface of positive plate, and the discharge capacity about 4.5 ampere-hours per pound of plate (both positive and negative plate included). 2744. Fig. 1055 shows the manner in which the E. M. F. of an accumulator falls as the discharge proceeds. In this L^ — — __^ -1, N \ ~1, >^ I s. \ -1 •cs -I KJ ~1. Tl ME in TlOl JUS. 1 1 i 4 t ' ( T 12 1 FIG. 1055. case the cell was connected to a variable external resistance, such that about the normal discharge current, as advised by the manufacturers, was maintained throughout the test in the 1766 BATTERIES. external circuit. The oxidation of the slight layer of hydro- gen left on the negative plate from the discharge causes the E. M. F. to be high at first, butas this is quickly disposed of, the E. M. F. falls in the first ten minutes or so to 2.04 volts; on continuing the discharge, the E. M. F. falls slowly and evenly until after about 8^ hours of discharging the E. M. F. falls to 1.9 volts. If the discharge is continued beyond this point, the nature of the chemical action changes somewhat, and the fall of E. M. F. becomes more rapid, at 10 hours being 1.8 volts, and at 11 hours being only 1.63 volts, 2745. This falling off of the E. M. F. is due to the weakening of the acid solution and to the gradual reduction of all the spongy lead on the one plate and the peroxide on the other to sulphate. As this reduction can only go on at the points where the acid is in contact with the spongy lead or the peroxide, it is evident that the interior portions of the active material are affected much more slowly than the surface, as the acid penetrates the active material only at a comparatively slow rate. On this account, discharging at slow rates allows the active material to be more uniformly and thoroughly re- duced, thus giving a greater output. This also accounts for the fact that on discontinuing the discharge at any point the E. M. F. will soon rise to practi- cally its original value, 2.04 volts; for unless the cell is entirely discharged there is always some unconverted active material in the interior of the plate, which serves to give the original E. M. F. when reached by the acid. If the dis- charge is resumed, this acid is soon exhausted, and the E. M, F. rapidly falls to the value it had when the discharge was stopped. 2746. In the above case, the product of the amperes and the hours will give the output of the accumulator in ampere-hours; if the discharge rate had been greater, the output in ampere-hours would have been diminished, the discharge being continued until the E. M. F. falls to the BATTERIES. 1767 same value In each case. Conversely, if the discharge rate had been lower, the output would have been increased. For example, assume the limiting E. M. F. to be 1.9 volts. In a certain cell, with a discharge current of 30 amperes, the E. M. F. reaches its limit in 10 hours, giving an output of 300 ampere-hours. If the discharge current were 40 amperes, the limiting E. M. F. would be reached in about 6|- hours, giving an out- put of only 260 ampere-hours; while if it were 20 amperes, the limiting E. M. F. would not be reached for about 17i hours, giving an output of 350 ampere-hours. For the sake of uniformity, the rating of the capacity of accumulators is made on the basis of a discharge current which will cause the E. M. F. to fall to 1.8 volts in 10 hours, although most manufacturers give tables showing the com- parative capacity of the various sizes of cells at other rates of discharge. 2747. The rate of charge (charging current) for accu- mulators of this class should be about the same as the nor- mal (10-hour) discharge rate, although much smaller cur- rents, continued for a proportionately longer time, may be used. 2748. Although "storage-batteries " do not store elec- tricity, they certainly do store energy by converting the kinetic energy of the electric current into chemical potential energy, which may be realized as kinetic energy again. The efficiency of the accumulator (or of any other means of stor- ing or transforming energy) is the output divided by the input. This quotient is always less than 1, as the accumu- lator is not a perfect storer of energy ; that is, there are certain losses in the transformation of kinetic electrical to potential chemical energy, and vice versa, besides the loss of the energy required to force the current through the cell, that is, the loss due to the resistance of the plates and elec- trolyte. 2749. The input and output of an accumulator may be expressed either in ampere-hours (the quantity of 1768 BATTERIES. electricity) or in watts (the rate of doing zuork of the cur- rent). If secondary cells of this class be fully charged at normal rate, after a discharge to 1.8 volts, and then dis- charged to the same point, also at normal rate, the ampere- hour efficiency will be ordinarily from .87 to .93, or 87^ to 93^. If charged and discharged to the same point at very slow rates, this efficiency may rise to 96^ or 97^. 2750. The watt efficiency at normal rates of charge and discharge is lower, being from 65^ to 80^, depending on the construction of the cell. In larger cells of modern con- struction, the watt efficiency is as high as 84^. 2751. The cause of the loss represented by the fore- going figures is, for the ampere-hour efficiency, due to the fact that the charging current must perform several chemi- cal decompositions, of which the elements either do not recombine in the cell or, recombining, do not give up their potential energy in the form of electrical energy. This loss varies with the rate of charge and discharge, as indicated by the figures given, but for a given rate it is practically fixed, the mechanical arrangement of the cells having little effect upon it. 2752. The greater loss shown in the watt efficiency figures is due to the fact that the E. M. F. of charge is higher than that of discharge, due in part to the E. M. F. required to perform the wasteful chemical actions referred to above, but largely to the drop in volts caused by the passage of the current against the resistance of the plates and electrolyte. This drop adds to the E. M. F. required to perform the chemical decomposition in charging, and sub- tracts from the E. M. F. due to the chemical recompositions, and its amount depends more on the. construction of the cell than does the loss represented by the ampere-hour effi- ciency, as it varies with the shape and size of the plates, their distance apart, their state of charge (on account of variations of the resistance of the electrolyte as the percent- age of acid varies) and other conditions. This loss due to the internal resistance in well-designed BATTERIES. 1769 cells usually amounts to about 8^, at normal rates of charge and discharge ; the loss is correspondingly less at low rates and more at high rates, being proportional to the square of the current flowing. In a good modern cell exposing about 1,100 sq. in. of positive plate surface, the internal resistance is about .005 ohm when charged. Cells of greater capacity than the above (which is listed as 350 ampere-hours) would have a proportionately lower resistance. 2753. The above efficiency figures, as stated, are given for a discharge to 1.8 volts E. M. F., the usual manufac- turers' rating; if the cells are not discharged to so great an extent, both ampere-hour and watt efficiencies are higher. 2754. The E. M. F. required to send a given charging current through a secondary cell varies with the state of —2 Cr, ^_ - pi / / •<:* ■2-^ ^ y , ^ ^ r 1 T. rjsIE i,n HO URS a I { * i '. I 1 " 1 r Fig. 1056. charge of the cell. Fig. 1056 shows the E. M. F. required to charge the same cell that gave the discharge E. M. F. curve (Fig. 1055), being in this case charged at the same rate as previously discharged. This curve shows that the charging E. M. F., after a quick rise in the first few minutes to about 2.06 volts, gradually rises during the first 6 or 7 hours, after which the rise is more rapid, until after 11 hours of charging it becomes 1770 BATTERIES. 2.5 volts; at this point gasing begins and the cell is practi- cally charged. On continuing the charging current, the E. M. F. rises a little more, and then remains practically constant at about 2.55 volts; as the only action which now takes place is the decomposition of the electrolyte, giving ofif gas, further charging would only result in a waste of energy; although long-continued overcharging at a mod- erate rate will gradually remove any formations of white sulphate that may exist. (See Arts. 2734 and 2736.) 2755. From this curve it appears that the cell became completely charged in practically 11 hours; as the discharge curve (Fig. 1055) shows that with the same number of amperes the discharge is complete (to 1.8 volts) in 10 hours, the ampere-hour efficiency of this cell is W^ or 91^, prac- tically. 2756. If an accumulator of this class is not discharged at an excessive rate nor to more than 1.9 volts E. M. F., the positive plates should last for about 1,200 or more dis- charges; while if discharged each time to below 1.8 volts, or at excessive rates, the life of the positive plate will not ordinarily be more than 400 or 500 discharges. The nega- tive plates, with good care, will usually outlast four or five positive plates. Some of the more modern cells of this class will show better results than the above, which, however, are good average figures. 2757. The usual construction of cells of this class is as follows : The plates and electrolyte are contained in a vessel of approximately cubical form; this vessel is of glass, if the cells are not intended to be portable, the glass allowing the examination of the condition of the plates while the cell is in operation. If the cells are intended to be portable, the vessel is usually made of hard rubber or gutta-percha, ot of wood lined with hard rubber or lead. Very large accu- mulators for central-station use are usually set up in lead- lined wooden tanks. BATTERIES. 1771 2758. The plates are usually approximately square, and from ^ inch to ^ inch thick, according to size. To get a large surface area without using single large plates, and to allow of one size of plate being used for cells of various capacities, each cell contains a number of positive and nega- tive plates, arranged alternately side by side a short distance apart. The number of negative plates is always one more than the number of positive plates, so that eac/i side of each positive plate has presented ^ to it the surface of a nega- 'nX tive. All the positive plates are connected together by a y- connecting strip, usually at one corner of the plate, and ^' all the negatives are similarly y. connected. The arrangement of a typical accumulator cell ^' is represented in Fig. 1057, ^v- where N, N, N, N, N are the negative plates and P, P, jP, P the positive. From a corner of each plate a lug projects; the lugs on the negative plates are joined to a con- necting strip, as represented at T, and the lugs on the positive plates are similarly joined to a connecting strip T'. The joints are made by a process called "burn- ing," which consists in melt- ing the lugs and strip together by a flame of hydrogen. This hydrogen flame absorbs the oxygen from the film of lead oxide with which the lead is usually covered, thus making a clean and solid joint. These connecting strips are extended beyond the limits of the cell, and serve to connect the various cells of the battery together, as shown at C, the connection being made by a brass bolt, which clamps the connecting strips together firmly. 1773 BATTERIES. 2759. The plates are placed in the jary, resting on a wooden support made from two strips of wood (usually boiled in paraffin) of triangular section S, S. These support the plates at such a height that any loosened particles of active material fall below the level of the bottom of the plates, thus preventing possible short-circuiting. When in position, the electrolyte is poured in until it reaches the line L L, thus covering the plates. To prevent the plates from touching each other, it is usually the practice to sepa- rate them by blocks or strips of insulating material, the exact arrangement varying with the different manufac- turers. 2760. Owing to the expense oi forming t\\.Q. plates by the Plante process, cells of the construction invented by Faure, known as "pasted plate" cells, have been very extensively used. Those principally used abroad are known as the Faiti'e-Sellon-Volkmar cells, from the company owning the principal French patents. 2761. Sections of the grids principally used by this company are shown in Figs. 1058 and 1059. The first is cast of lead alloyed with a little antimony to give stiffness EHcdn nnmn nnmn nnnn Fig 1058. Fig. 1059. to the grid, and oxide paste is forced into the openings in the grid {n^ n, n). The section, taken at the line a b^ shows the shape of these openings. BATTERIES. 1773 2762. The second grid is made of two plates cast sepa- rately and afterwards riveted together with lead rivets. In this grid, as shown by the section, the openings for the paste (;z, it, n) are larger in the center of the plates than at the faces, thus securely holding the plugs of active materials. 2763. Grids similar to those shown in Fig. 1057 are used in the E. P. S. accumulator in England and in the cells made by the Electric Accumulator Co., the Julien Co., in the United States, and by other manufacturers. 2764. In Germany, where the accumulator has been most extensively employed, more complicated forms of grids are used. One of these is shown in Fig. 1060; it consists of Fig. 1060. a double lattice united at the edges of the plate, and kept at a little distance apart, as shown in the section, by small columns at the points where the members of the two lattices cross, as represented at c c. This plate is cast at one operation. This form of plate holds a large quantity of active material, and is quite stiff. Even more complicated, grids are used, some consisting of three layers of lattice- work, separated by columns, 'as in the grid just described. 2765. Fig. 1061 represents a section of the Tudor grid, a form of pasted-plate grid which has many good features; it is composed of a number of small square or rectangular grooved grids G^ about 6 inches square, with 1774 BATTERIES. the active material pasted or forced in the grooves as in the ordinary form (see section, Fig. 1061). Six or more of these small grids are then fastened by a lug on one edge, as at C, to the bars of a cast lead supporting frame i% which has openings between the bars slightly larger than the small grids which they enclose. The small grids are thus free to expand or contract without interfering with the plate as a whole, thus preventing to a large extent buckling and dis- integrating of the plate, and any damaged grid may be replaced without disturbing those remaining. 3766. Accumulators employing this form of grid are largely used in central stations in Germany, and also form one of the largest accumulator installations in the United States, that of the Edison Electric Illuminating Co., of Boston, Mass., which consists of two sets of 70 cells each, each set having a capacity of about 3,500 ampere-hours. Other forms of grids are also made by the same company, and are also known as Tudor grids. 2767. Fig. 1062 illustrates the grid used in the Sor- ley cell, made in the United States. It is made of strips _n n » § _ _ of lead s, s, s of uniform width and thickness, which are bent into the shapes shown, and are held in place by other strips around the edge of the plate. These strips are led out at the upper edge to form a termi- nal. The oxide paste is forced into the openings between the strips at n, jz, 7i, as in the cast grids. The advantage claimed for this type of grid is that it allows of free contraction and expansion of the active material. 2768. A form of grid which is cast around the plugs of active material is represented in Fig. 1063. This grid was invented by Reckenzaun for use in street-car propul- sion; the active material is prepared in cylindrical plugs, Fig. 1062. BATTERIES. 1775 r / \ l----^ -rr:^ 1 J 1 1 ---\ f— - - I . ...] I ^ - - -1 1 - -- i —J 1—- ( 1 1 *T^ r ' \ \ t H' V y' i !t Fig. 1063. shown at c, which are laid in a corrugated mold, and the melted lead alloy poured in around them. They are thus held quite firmly in place, ^ while exposing a considera- ble surface to the electro- ^^^=,^^^ ^^^^,,,^,^^3^ lyte. " As can be seen from |„. Itttzi \ - 1 Q the section, taken along the i i-Tzn i- J t . line a b^ the cylindrical form of the plugs holds them in place, even if the plate be bent considerably. 2769. None of the pasted-plate cells, however, is as substantial as those in which the active material is formed from the plate itself, as in the Plante cell. The principal objection to the Plante process being the length of time required to alter the surface of the plates from a smooth to a spongy condition, attempts have been made to construct plates which are porous at the start, such as compressing lead dust, or fine threads of lead made by blowing a stream of air through melted lead, etc., deeply grooving or even slitting the plates to increase the surface; none of these processes has resulted in a plate which is substantial enough for commercial use. 2770. A form of cell in which it is claimed the plates combine the cheapness of preparation of the pasted plate with the greater solidity and longer life of the Plante plate is the chloride accumulator made in this country by the Electric Storage Battery Co., of Philadelphia. 2771. The plates of this type of cell are made as fol- lows: A mixture of zinc chloride and lead chloride is melted and run into molds, which form it into cylindrical pellets or pastilles, which have a bevel /\ shaped edge, being thus larger in the center than at the faces. These pellets are placed in a second mold, being held in position by steel pins, and an alloy of lead and antimony is melted and forced in between the pellets under heavy pressure. When this 1776 BATTERIES. cools it forms a plate, binding all the pellets of zinc and lead chloride together. 2772. This plate can not be used in this form in an accumulator; a number of these are first set up in a bath of dilute zinc chloride with plates of zinc, to which the lead plates are connected. These plates then act as the elements of a primary battery, and the resulting chemical action dis- solves out the zinc chloride from the pellets, and converts the lead chloride into metallic lead, which assumes a crystal- line form. The plate is now practically a continuous lead plate, solid and dense in some parts and porous in others. 2773. The plates in this condition are suitable for negative plates; those required for positive plates are then set up with plain lead plates in a bath of dilute sulphuric acid, and a forming current sent through them from the prepared plates to the plain. This current causes the porous parts of the plates to be formed into lead peroxide and sulphate ; the plate is now the equivalent of a pasted plate, and is an improvement through having its active material firmly bound in place in the com- pressed grid. Fig, 1064 shows a part of one of these plates; the section, taken along the ^ line a b, shows the shape of Fig. 1064. these plugs. The holes in the plugs are caused by the pins by which they are supported in the mold. 2774. The requisite number of these prepared plates are then set up together to form a cell, alternate positives and negatives being connected to common conductors, as in other types of cells. (See Fig. 1057.) The plates are each surrounded by a sheet of asbestos paper, and are separated from each other by a thin wooden BATTEHIES. 1777 strip so thoroughly perforated with large holes that it really fills little of the space between the plates; this wooden strip serves as a distance-piece, keeping the plates a certain fixed distance apart. 2775. The E. M. F. and action of this form of accu- mulator are the same as that of the Faure (pasted) type or the Plante. It is claimed by the manufacturers that, from the solidity of the construction, buckling and loosening of the active material are practically impossible, so that the cells may be discharged to a low E. M. F. or at high rates without serious injury. Its output per pound of element is greater than that usually assigned to lead accumulators, be- ing about 5 ampere-hours per pound of plates (both positive and negative) at normal discharge rates. 2776. Most of the larger installations of accumulators in central stations in this country have been of this type of cell, and they are in use in France on street-cars, and also in England. The majority of German installations are of the pasted-plate type. 2777. There are, as in primary cells, a great number of forms of accumulators in use, both of the Plante type and the Faure ; they differ from those described only in details of construction, such as the arrangement of the plates, ver- tically or horizontally, the form of the grids, etc., and need not be described here. BIMETALLIC ACCUMULATORS. 2778. In this class of cells the elements consist of two different metals, the electrolyte being a salt of one of the metals. There have been several combinations of materials pro- posed for cells of this type, but the only cells which have actually been used to any extent are the zinc-lead, copper- lead, and copper-zinc cells. 2779. The zinc-lead cell usually consists of plates of zinc and lead in a solution of zinc sulphate. On sending a 1778 BATTERIES, charging current through this cell (the zinc being the nega- tive plate) the zinc sulphate is decomposed, depositing zinc on the zinc plate and forming free sulphuric acid with the hydrogen of the water, which is also decomposed, its oxygen uniting with the lead plate, forming peroxide of lead. On open circuit and while charging, the free sulphuric acid in the solution slowly attacks the deposited zinc, reforming zinc sulphate, so that the efficiency of this form of cell is low, and it will not retain a charge more than a few days. The E. M. F. is high, being about 2.35 volts. 2780. The more modern forms of this cell employ a tinned-iron plate, amalgamated, or a lead plate, in place of the zinc plate. On charging the cell the zinc is deposited on the surface of the tinned-iron or lead plate, where it acts as the negative plate on discharge. (See Art. 2726.) 2T81. By substituting copper sulphate for zinc sul- phate, and copper plates for the zinc or other negative plates in this type of cell, the acid formed during charge can not attack the copper, so that this loss is obviated; the E. M. F., however, is but 1.25 volts under these circum- stances, so the watt output is materially reduced. 2782. Owing to the variations in the composition of the electrolyte, the internal resistance of cells of the types before described is variable, being lowest when charged and increasing during discharge as the sulphuric acid forms sulphate of copper or zinc. 2783. The copper-zinc accumulators are in greater commercial use than the other forms of bimetallic cells, the best known being the Phillips-Entz accumulator, which was made by the Waddell-Entz Electric Company. This accumulator employs the same active materials as the La- lande-Chaperon or Edison-Lalande primary cell (see Arts. 2683 and 2684), modified in mechanical construction to adapt them for accumulator use. 2784. The positive plate is made of porous copper on a solid foundation, prepared in the following manner,* A BATTERIES. 1779 copper wire is surrounded with a paste made of finely ground copper oxide and sulphur; around this is woven a netting of fine copper wire, and the whole is then heated nearly to red heat, which causes the sulphur to unite with the oxygen of the copper oxide and pass off as gas, leaving the copper on the central wire in a very porous state. This cable is covered with a thin layer of loosely woven cotton thread, which forms a porous partition, and is then wound or braided into a mat or plate, forming the positive plate, the negative plate being a thin sheet of steel, thoroughly amalgamated; a number of these plates are mounted, alternately positive and negative, in a jar made of sheet steel, and surrounded by the electrolyte, which is a solution oi potassium zincate 2ind potassium hydrate. (See Arts. 2683 and 2689.) The jar is covered with an air-tight steel cover, to pre- vent the carbon dioxide (carbonic acid gas) in the air from coming in contact with the potassium hydrate solution; this cover is provided with a gas-valve to allow the gases formed in the cell to pass off. 2785. On charging the cell as thus constructed, the chemical reactions are complicated, but result in the deposition of the zinc from the potassium zincate on the steel plate and the sides of the jar, and the oxidation of the porous copper. On discharge the action is the same as in the Lalande-Chaperon primary cells; that is, the zinc is dis- solved, the potassium zincate is reformed, and the copper oxide reduced to metallic (spongy) copper. 2786. The efficiency of this type of accumulator is about the same as that of the lead accumulators, while its output is very much greater, weight for weight, the ampere^ hour output being about 5 times that of a lead cell, or about 20 ampere-hours per pound of plates. The E. M. F. of this form of accumulator being much lower than that of the lead accumulator, averaging 0.75 volt during discharge, the comparison on a basis of watt output is not so favorable; still, the zinc-copper accumulator will show an output of about 15 watt-hours per pound of plates, while the lead 1780 . BATTERIES. accumulators seldom exceed an output of from 7 to 10 watt- hours per pound of plates, the latter figure being seldom reached at normal rates of discharge. 2787. The efficiency and internal resistance of the. copper-zinc accumulator vary quite largely with the tem- perature, on account of the considerable variations in the density of the electrolyte; on this account the cells are ordinarily charged and discharged at a temperature of about 54° C. (130° F.), at which point the resistance is about the same as in a similar lead accumulator. 2788-. These cells are not much affected by the rate of discharge, there being no such occurrence as sulphating or buckling; but on account of the difficulty of depositing the zinc in a solid form, the charging must be done at a slow rate, and the action of the cells is improved by intermittent charging. The E. M. F. required to charge one of these cells varies from 0.90 volt at the start to 1.05 volts at the finish. 2789. In spite of the porous partition (cotton thread) which surrounds the positive plate, local action is liable to occur, on open circuit, so that these cells will not retain their charge for more than a few days, while a lead accu- mulator will scarcely lose 25^ of its charge in as many months. 2790. On account of these features the copper-zinc accumulator can be successfully used only in installations where it is charged and discharged daily, thus preventing local action, and when it can have the necessary appliances, care and attention in charging, to insure proper charging rate, temperature, etc. ; so, in spite of its large output per unit of weight, it can hardly come into general use. How- ever, for traction work, that is, for use on street-cars and other vehicles in constant use, where the accumulators must be able to stand variable and very frequently heavy dis- charge rates, and must also be as light as possible, this form of accumulator possesses especial advantages, and is, con- BATTERIES. 1781 sequently, better suited to the work than the lead accumu- lator. 2T91. Other forms of bimetallic accumulators have been proposed, and in some cases used, among which may- be classed several forms of primary cells, such as the Dan- iell, Leclanche, and others, which may be "regenerated" by passing a current through them; these have never been of commercial value, and do not require further attention. THE USES OF ACCUMULATORS. 2792. In central stations furnishing electric current for lighting and other purposes, the demand for current varies very largely at different periods in the day; for example, a lighting station in a large city would probably be called upon to furnish, from 7 to 8 p. m., 10 times the amount of current that was required from 7 to 8 a. m. , and in smaller stations the disproportion is even greater. As economy of operation demands that the engines and dyna- mos be worked at or near their full capacity, especially if the engines be compound or triple expansion, these condi- tions can both be met only by dividing the machinery into a large number of small units, or by having some system of storage of the electrical energy. In the first case, the small units require more attention, and are much less efficient than larger ones, and most modern large stations have their machinery divided into a few large units, employing large compound or triple-expansion engines. 2793. In these stations accumulators are being intro- duced on a large scale, and are installed according to one of two plans, as follows: 1, The dynamos and engines are not capable of carrying the full current required at certain parts of the day, for ex- ample, in the evening, but are of a size sufficient to fur- nish the current for the average rate required during the 24 hours. In this case, accumulators are installed which have a capacity sufficient to furnish the required excess of 1782 BATTERIES. current over the average. At times when the output of the station is less than the average rate, the current is used to charge the accumulators, thus keeping the output of the engines and dynamos at its maximum, which is the condi- tion of greatest economy in operation. On account of the loss in charging and discharging the accumulators, the machinery must really have a capacity slightly greater than the average output of the station ; but in any case the total amount of machinery, including engines, boilers, and dyna- mos, that must be installed is far less than if accumulators were not used, as in such case the total capacity of the machinery must evidently equal the maximum output of the station. 2. The second plan is to install accumulators of sufficient eapacity to furnish all the current of the station for a part of the day when the output is less than the average; in this case, the engines are shut down for a considerable part of the day, the accumulators furnishing the entire output of the station during this time; when the demand for current begins to increase, the machinery is started up, and then furnishes the entire output of the station for the balance of the day, charging the accumulators when the station output is less than the capacity of the machinery. In this case the capacity of the accumulator plant is relatively less than in the former, and as the cost of accumulators is high, this may cause a saving over the first plan, although the mechanical efficiency of the station may be somewhat lower than in the first case. 2794. The result of applying accumulators to a large station is shown in Figs. 1065 and 1066. In both, the con- tinuous line represents the actual output in amperes of a certain large station in New York, for a certain day. 2795. If this station were designed to use accumula- tors according to the first plan, the result would be about as represented in Fig. 1065. Here the dotted line repre- sents the output of the dynamos (in amperes) ; the differ- ence between the ampere output of the dynamos and that BATTERIES. 1783 of the station is either absorbed or given out by the accumulators, as the station output is less or greater than the dynamo output. From the curve it appears that the accumulators are absorbing current (that is, being charged) from about 11.45 p. m. to about 4.30 p. m. (of the next day), while during the balance of the 24 hours the accumulators are giving out current, that is, discharging. The output of the dynamos is nearly constant, at about 850 amperes, the " 2000 r -1 \ 1 1800 X \ JfiO 1 i \ 140 \ J i i i 120 ) T fi-S^ %'-^ 100 r^r\ \ 4 ^ \\~^ — _A ccnmn LATOBi CHABaiNG — — |— ; -- ^•t ' \ ' ; r '^<^. ■m- — ~ -., — 4-- — -^- -'-< -\-\- \'- r~i ■'\ ^ — :/ ACCUM ULA Tons DISCHAKGIXG -»J\ a' 600, Sn~- i /I J kv^ \\\\ J ■-- 10 t Fig. 1123. as follows: Let B = the density of the magnetic field, L = the length of the conductor, and iJ/= the length of its path, or its velocity. Then, the area moved over by the con- ductor (in unit time) is L M, and the total number of lines cut by the conductor is B -^ M- Then, substituting this value for N in the above formula, E = — -— ^ — . As in this case 10' ^^ / = 1, unit time being assumed, this may be written E^^f, (473.) which gives an expression whereby the E. M. F. generated in a conductor moving in a magnetic field under the con- ditions given above may be found. The density B, being the number of lines of force per unit of area, i. e., per square inch, or per square centimeter, it is 1900 APPLIED ELECTRICITY. evident that the product L M must be expressed in the same units in order that the equation N =^ L i^ should hold true. Example. — Suppose the conductor a b \n. Fig. 1123 to be 1 foot 8 inches long, and that it is moved in a magnetic field whose density is 50,000 lines of force per square inch at such a (uniform) velocity that at the end of 1 minute it would have moved 2,250 feet. What is the E. M. F. generated in the conductor ? Solution. — As the density is expressed in lines of force per square inch, the other dimensions must be reduced to the same unit, i. e., inches. The length of the conductor L is then 20 inches, and the velocity, 2,250 or distance through which it would move in 1 second, = M — 37.5 ft., or 37.5 X 12 = 450.0 in. 60 Hence, from formula 473, E ^ ^ ^J^ , where B = 50,000, L = 20, and M = 450, E 10« 50,000 X 20 X 450 450,000,000 10* 10^ = 4.5 volts. Ans. 3019. The formula given in Art. 3018 does not hold good as it stands if the conditions governing the direction of the motion of the conductor are not as before stated, which are, that the conductor must lie in a plane at right angles to the lines of force and move in a direction at right angles to its own length and to the direction of the lines of force. It is evident that a conductor might readily be moved in a direction which would not conform to all or any of the above conditions; the formula, to be generally ap- plicable^ must then be modified to suit such cases. Tkkki'kkii / K 3020. Fig. 1124 represents a case where a conductor a lies in a plane at right angles to the lines of force (so that we are looking along its length, and consequently see only the round section, as shown), and is moved ^^ in a direction at right angles to its own length, but at the angle /, which is not a right angle, to the direction of the lines of ^ force flowing between the poles A^ and 5 of Fig. 1124. a magnet. If the conductor move from a APPLIED ELECTRICITY. 1901 to a in unit time (say one second), the area swept over by the conductor in unit time is a rectangle, and the area is measured by the product L M of the length of the conductor L and the length of its path in unit time, or its velocity, M\ but the total number of lines cut by the conductor is not the product of the density B and the area L M, since the density is measured on a plane at right angles to the lines of force, and the area L Mis at an angle to this plane. From an inspection of Fig. 1124, it will be seen that the conductor will cut exactly the same number of lines of force if moved from any point on the line a n (whicli is parallel to the lines of force) to the point a' ; in other words, whatever the value of the angle /, the number of lines of force cut by the conductor in moving from a to a' will be the same. By making this angle a right angle, as at n, the path of the conductor along the line 7t a' will be at right angles to the lines of force, and all the conditions prescribed in Art. 3018 will be fulfilled. The length of the line n a' is, however, not equal to the length of the line a a'; but as the former length must be used in calculating the total number of lines cut, and the latter is the length which is known, an expression for the length 71 a' in terms of the length a a' must be found. From the construction of the figure, the triangle a n a' is a right- angled triangle, with the length of the hypotenuse a a' and the adjacent angle/ given; the length of the side 7t a' opposite the angle / is found by trigonometry to be a a' sin p°, which is the desired value. ' 3021. Calling the length of the conductor L and the length of its path M, as before, it follows from the above that the total number of lines of force cut by the conductor is given by the formula N=^ LM sin p°. (474.) With given values of B, L, and M, it is evident that iV is a maximum when/" = 90°, as then sin/° = 1, and B L J/ sin /° = B Z M^ corresponding to the case given in Art. 301S, 1902 APPLIED ELECTRICITY. while if Z" = 0°, then sin /° = and ^ L M sin /° = 0, which means that if the conductor be moved in a direction at an angle of 0°, i. e., parallel to the lines of force, no lines will be cut by it and no E. M. F. generated. A method of considering the relation between the length n a' and the length a a', which is very useful in some cases, is to regard the length n a' as the projection of the length a a' on a plane at right angles to the lines of force. The application of this method will appear in other parts of this section. 3022i. In a similar manner other variations from the conditions given may be considered. Fig. 1125 represents ^ the case where the conductor a b lies in a plane at right angles to the lines of force, and is moved in the same plane, but in a direction b b' at an angle 5, which is not a right angle, to its length a b. The shape of the area swept over in moving from a b to a' b' is evi- dently a rhomboid, of which the area is equal to the product of the base b b' and the altitude a n. This altitude being perpendicular to the base b b\ the triangle a b n\s 3i right triangle, and, by trigonometry, side a n —.a b sin s. Consequently, the total number of lines of force cut by the conductor a b oi length L in moving over a dis- tance b b' — iJ/ through a field whose density = B, is N=E M Lsms. (475.) Again, with given values of B, L, and M, the value of N is a maximum when s = 90°, for sin 90° = 1 and B if Z sin s=E 31 L\ and where s = 0°, sin s = and B M L sin s = 0, which means that if the conductor is moved at an angle of 0°, i. e., parallel to its own length, no lines of force are cut by it, and no E. M. F. is generated fn the conductor. In this case, again, the length a n is the projection of the 'r-\^r': J>;;;-': ■ '/. .. '-■..', ■7 ■..•■.••■/■•■ 1 •'.■ •■■,'•■■'''' ' Fig. 1125. APPLIED ELECTRICITY. 1903 ttr --— — -- \i: actual length of the conductor a b om. plane at right angles to the direction of its path. 3023. Fig. 1126 represents the plan and elevation of the case where a conductor a b \s situated in a magnetic field at an angle r to the lines of force, as represented in the elevation, and is moved through the field in the direction a a' or b b' at right angles to the lines of force and to its own length, as represented in the plan. The area swept over by the conductor is equal to the product of its length a b (see elevation) and the length of its path a a' (see plan), but, as before, the product of this area and the density of the lines of force is not equal to the total number of lines of force cut, as the area is not measured at right angles to the lines of force. The number of lines of force cut, how- ever, is measured by the product of the %'y'^'':''':'''''-':''^ density, the length of the path of the con- -i-:.: ' .\:.:^:.:,::.:v^^k\ ductor, and th.Q projection of its length on a pie. nae. plane at right angles to the lines of force. This projection is represented by an, Fig. 1126, and the triangle a b ii being a right triangle, side a n — a b sin r, as before, and the total number of lines cut is iV=BJ/Zsinr. (476.) With given values of B, Z, and M, N will again have a maximum value when r = 90°, as sin 90° = 1 and E M L sin r=S L M; and when r = 0°, and sin r = 0, B M L sin r = 0, which means that if the conductor is located in a plane at an angle of 0°, i. e., parallel to the lines of force, no lines of force will be cut; hence, no E. M, F. will be generated by a movement of the conductor. 3024. For any case where the conditions governing the motions of the conductor differ in more than one re- spect from those given in Art. 3018, a formula may be 1904 APPLIED ELECTRICITY. constructed by combining formulas 474, 475, and 476. Thus, the total lines of force cut by any conductor of length L situated in a uniform magnetic field of density B, lying in a plane at an angle of r° with the lines of force, and moved with a velocity M through the field in a direction at an angle of s° with its length, and at an angle of /° with the lines of force, will be given by the formula yV= B Z sin r° sin s° M sin /°, and the E. M. F. resulting from this motion will be given by the formula B L sin r° sin s° M sin p" 10^ (477.) It is evident that with given values of B, Z, and J/, the value of N^ hence of E^ will be a maximum when the angles r, i", 2in^ p are each equal to 90°, while if any of these angles is equal to 0°, the value of iVand E will be 0. It follows, then, that to get the maximum E. M. F. with a given length of conductor, these angles should all be as near 90° as possible, which is the case in almost all dynamos, as will be pointed out. 3025. Thus far a field of uniform density has been assumed; but from the statements which have been made the effect of variations in the density of the field may be readily found. It should be remembered that as the E. M. F. generated in a moving conductor is proportional to the rate of cutting lines, it is not necessary that the conductor should actually move over any particular area in order that an E. M. F. be generated in it; it is only required that the conductor move at such a velocity that {/"that velocity were maintained for one second, the conductor would cut a certain number of lines of force, as measured by the area which would be swept over. This area is obviously the same whether it encloses lines of force or not; so if at any one point in a conductor's path the density is known, the number of lines of force which would be cut by the conductor in moving over that area if the density were uniform at its known value would evi- APPLIED ELECTRICITY. 1905 dently be the product of the known density and the area, and the E. M. F. generated at the instant when the con- ductor is passing through the part of the field where the density is of the given value may be found from the for- mula. 3026. The considerations just mentioned apply if the velocity is not constant, for if the velocity at any instant is known, the area which would be moved over by the conduct- or in one second ?/ the velocity were constant at the known value, measures the number of lines which would be cut in one second, and hence the rate of cutting or the E. M. F. generated. In actual practice the velocity of conductors in any par- ticular case is almost invariably constant, while the density of the field is seldom uniform. Example. — A conductor 3 feet 3 inches long is dropped vertically through a magnetic field whose lines of force are horizontal, but of varying density. At a certain point a the velocity is known to be 40 feet per second, and at the same point the density of the magnetic field is known to be 28,000 dines of force per square inch. What E. M. F. is generated in the conductor when at the point a ? Solution. — The velocity of the conductor at this point is 40 X 12, = 480 in. per sec. The conductor being 3 ft. 3 in. = 39 in. long, if moved at this velocity for one second would sweep over an area of 480 X 39 = 18,720 sq. in., which area would enclose 18,720x28,000 = 524,160,000 lines of force, if the density were uniform at the known value through- N out the area. From the formula E=^ :-—, 10** „ 524,160,000 ^-._ . . E= ^-T--! = 5.241'6 volts. Ans. 10** THE EFFECT OF CURREIVT IN THE CONDUCTORS. 3027. Thus far, only the production of the E. M. F. has been considered. If this E. M. F. is allowed to act on a closed circuit, so that a current will flow, certain effects will be produced, which must be taken into account. First, the passage of the current through the conductor implies a loss or drop of potential equal in value to the product of 1906 APPLIED ELECTRICITY. the current and the resistance of the conductor. (Art. 2315.) The difference of potential between the terminals of the conductor in which the E. M. F. is generated is then less than that E. M. F., by an amount equal to the drop. Calling c the E. M. F. generated, or the internal E. M. F., E the difference of potential between the terminals, Ri the internal resistance of the source of ^, and C the current flowing, then, E =■ e — C R,-. The total amount of energy- expended in the circuit w is evidently the product of C and e;i.e.,w=zCe. Of this, C X C Ri= C Ri is expended within the source of the E. M. F. itself, leaving C e — C^ Ri= C E = W, the energy expended in the external circuit, or the otit- piit. It is evident that as C^ R^ is entirely expended in heating the conductors in which the E. M. F. is generated, it is wasted as far as any practical application is concerned, and should, therefore, be made as small as possible, in order that C E can be as large a proportion as may be of the total energy developed, C e. On this account, the internal circuits of dynamo machines are made of copper, that being the metal which has the greatest conductivity for a given tost and bulk. 3028. In addition to this drop of potential, the pres- ence of the current introduces reactions between the mag- netic field in which the conductors are moved and the field due to tho current itself. (Arts. 2438 and 2439.) These reactions result in a tendency for the conductor to move, relative to the lines of force of the field, in a direction at right angles to its own length and to the direction of the lines of force. The amount of the force is proportional to the amount of current and also to the density of the magnetic field, meas- ured in a plane at right angles to the direction of the lines of force. If the length of the conductor lies in this plane, the force acting on each centimeter of its length, when the field is of unit density (one line of force per square centimeter) and a current of one absolute (C. G. S.) unit is flowing through it, is one dyne. From this it follows that, calling APPLIED ELECTRICITY. 1907 A the current in absolute units, B the density of the field in lines of force per square centimeter, and L the length of the conductor that is within the limits of the field in cen- timeters, the force on the whole conductor in dynes, /=A BL (478.) 3029. This force acts in a direction at right angles to the length of the conductor and to the direction of the lines of force; it is evident, however, that /"may be resolved into components in any other direction, by a method similar to that used in finding the E. M. F. generated in a moving conductor. If this is done, it will be found that similar results are obtained; namely, that the component of the force/" in any direction is equal to the value of /" given by the above formula multiplied by the sines of the angles which the direction of the component makes both with the length of the conductor and with the direction of the lines of force, and of the angle which the length of the conductor makes with the lines of force. From this it follows that if any one of these angles is equal to 0°, the component to that direction is also 0; that is, there is no tendency for the conductor to move in a direction parallel to its own length or parallel to the lines of force, nor in any direction if the length of the conductor is parallel to the lines of force. It will be seen that the maximum component of the direc- tion of the force is in the same direction as the motion required to produce the maximum E. M. F. in the con- ductor; and, further, in any other direction the force is reduced in the same proportion as the E. M. F. would be re- duced from the maximum by movement in the same direction. 3030. If, then, the E. M. F. generated in a moving conductor is allowed to cause a current to flow, the reac- tion of the current in the magnetic field will cause the con- ductor to tend to move in a direction opposite to its motion in generating the E. M. F. (See Arts. 2439 and 2440.) In order to move the conductor, it is necessary, then, to apply to it a force (neglecting inertia, friction, etc.) equal to 1908 APPLIED ELECTRICITY. the component of the reaction between the current and the field that is in the direction in which the conductor is moved. The product of this force and the distance through which the conductor is moved is evidently the mechanical work done upon the conductor; hence, the product of the force and the distance through which the conductor is moved in unit time is equal to the rate at which energy is expended in moving the conductor. In C. G. S. units, then, zu = A B L M, where w is the rate of doing work in er^s per second ; y^, B, and Z have the same values as before, and J/ is the distance through which the conductor is moved in one second, in centimeters. As 10^ ergs per second equal 1 watt, dividing both sides of the equation by 10' gives the power directly in watts, or W= ■. By dividing the upper term of the fraction by 10, C, the current in amperes, may be substituted for A, J U r 1 Ml .U J 7T/ CBLM and the formula will then read yy = — -^ 10' Formula 477, which gives the E. M. F. generated in the moving conductor, may, on the assumption here made that the angles between the path of the conductor and its length, and the direction of the lines of force, are all 90°, be written E = — J in which B, L, and Af have each the same value as in the above formula; which, therefore, may be written This means t/iat the work done in moving a conductor tJiroiigh a magnetic field [neglecting friction and inertia^ is equal to the zvork done by the resulting E. M. F. and curretit; which also follows from the law of conservation of energy. 3031. From this it will be seen that it is necessary to supply mechanical power to the armature of a dynamo in order that it may supply a current, and the manner in which this power is expended should also be clear. In commercial apparatus, it is evident that aside from the power required to move the conductors, an additional APPLIED ELECTRICITY. 1909 amount of power must be supplied for overcoming the fric- tion and all other sources of loss that may exist in the mechanism which is used for moving the conductors; further, the amount of electrical energy that appears in the external circuit is less than the total energy generated, by the amount expended in heating the conductors in which the E. M. F. is generated, as has already been pointed out. The ratio of the energy appearing in the external circuit, or the output of the dynamo, to the total amount generated, is called the electrical efficiency of the dynamo; the ratio of the output to the input, the input being the total amount of energy mechanically applied to the conductors to move them, including all losses in the mechanism used, is called the commercial efficiency of the machine. Both values are usually given in per cent, of the input; it is evident that this percentage must be less than 100, and in commercial machines it ranges from 75^ to 95^, or higher, depending upon the size and design. In finding the efficiency, both output and input must be reduced to the same units. 3032. If, instead of mechanically moving the con- ductors through the magnetic field, they be located therein with their lengths at an angle to the lines of force, and an E. M. F. from some external source be applied to the ter- minals of the conductors, a current will flow through them, and the reaction between the field produced by the current and the field in which it is located will produce a tendency of the conductors to move relatively to the magnetic field, just as when the current is produced by the E. M. F. gen- erated in the conductors themselves. This tendency is exerted in a direction at right angles to the lines of force and to the length of the conductor, producing a force act- ing in that direction, which may be resolved into compo- nents acting in any other direction. If the conductor be free to move in any direction, then this force will cause it to move, provided its component in that direction is greater than 0, and the rate at which work 1910 APPLIED ELECTRICITY. will be done by the conductor in moving will be equal to the product of the value of the force in the direction of motion and the distance moved in unit time, i. e., the velocity. This apparatus is then an electric motor, capable of doing external mechanical work. 3033. The motion of the conductors through the field under these conditions will set up in them an E, M. F. which is opposite in direction to the E. M. F. which is sending the current through the conductors. (See Arts. 2439 and 2440.) It is evident, then, that in order to keep up the strength of the current in the moving conductors, the E. M. F. ap- plied to their terminals must be equal to the E. M. F. gen- erated, plus the drop or fall of potential in the conductors. 3034. It has already been shown that the energy repre- sented by the product of the force on the conductor and the velocity of the conductor is equal to the energy represented by the product of the current flowing and the E. M. F. generated by the motion of the conductor. Calling e the E. M. F. generated in the winding and C the current flow- ing, as before, the mechanical work done by the moving conductor is e C. The energy represented by C"^ Ri {R^ being the internal resistance of the conductors), as in the case previously considered, appears only as heat. The sum of these two, then, equals the total amount of energy which must be put into the apparatus to move the conductors; that is,.^ C+C Ri= B C, E being the E. M. F. applied to the terminals of the winding. (Compare this with Art. 3030.) 3035. It appears, then, given a conductor, or several conductors, situated in a magnetic field, with their lengths at an angle to the lines of force, that the conductors may be moved by the application of a mechanical force so that an E. M. F. will be generated in them, and this E. M. F. may be utilized in sending a current through an external circuit; this is the dynamo, in which the mephanical energy supplied APPLIED ELECTRICITY. 1911 is converted into electrical energy. Or, an E. M. F. may be applied to the terminals of the conductors, causing a current to flow through them, which will cause them to move through the field ; this is the motor, in which the electrical energy supplied is converted into mechanical energy. It will be seen that precisely the same features are required for both kinds of apparatus, and the same actions go on in both, the distinction being that what is the oiitpitt of one is the input of the other. If the conductors had no resistance, and there was no friction or any other loss in the mechanism used to transmit the mechanical energy to or from the con- ductors, then the input would equal the output, and the efficiency would be 100^. This is manifestly impossible, so that the input must exceed the output by the amount of energy lost in heating the conductors and in the mechanism used to move the conductors, or that is moved by the con- ductors; that is, the efficiency is ahvays less than 100^, in either dynamos or motors, and the various losses are of the same kind in both cases. This subject will be taken up more in detail later. The development of the various systems of armature winding from the principles that have been given will now be taken up. GRAPHICAL REPRESEIVTATIOIV OF E. M. F. OR CURRENT. 3036. The value of the E. M. F, generated in a mov- ing conductor during successive instants may be graphically represented by a "curve " on cross-section paper, the method usually adopted being to make the ordinates represent the E. M. F. and the abscissas either intervals of time or, what usually amounts to the same thing, distances passed over by the conductor. In the case of a conductor moving in a straight line at a constant velocity through a uniform mag- netic field of unlimited extent, the E. M F. generated at any instant is constant, and would, therefore, be represented by a straight line parallel to the axis of abscissas, and at a 1912 APPLIED ELECTRICITY. certain distance from that axis, depending upon the value of the E. M. F. generated and the scale selected to represent it. Thus, the graphical representation of the E. M. F. generated in the conductor, as given in the example in Art. 3018, would be a straight line parallel to the axis of ab- 6 — J — 4 2 1 2 ' 3 4 5 6 7 8 _ Seconds Fig. 1127. scissas and at a distance from it equal to 4.5 volts on the scale of the ordinates, as shown in Fig. 1127. The direction of the E. M. F. may be found from the rule given in Art. 2442, the E. M. F. being considered as hav- ing the direction in which the current which it would pro- duce is considered to flow. By applying this rule, it will be seen that if either the direction of the lines of force or the direction of motion of the conductor be reversed, the direction of the E. M. F. is also reversed, but if bot]i be reversed, the direction of the E. M. F. is unchanged, 3037. If the direction of the motion of a moving con- ductor is instantly reversed, but the velocity maintained constant, the E. M. F. generated in that conductor will be reversed in direction, but unchanged in value. In order to represent this condition graphically, it is necessary to make some distinction whereby the change in the direction of the E. M. F. will be indicated. This is done by plotting the E. M. F, curve on both sides of the axis of the abscissas; assigning to one side the values of the E. M. F. when in one direction, and to the other its values when in the opposite APPLIED ELECTRICITY. 1913 direction, both to the same scale. It is customary to plot the curve of the E. M. F. or current when in a positive di- rection with respect to some given part of the circuit above the axis of the abscissas, so that this part of the curve is considered as -\- in direction. Thus, if the conductor giving the curve represented in Fig. 1127 had been moved in one direction for 2 seconds, then instantly reversed and moved in the opposite direction N 6q^ 6 4 2 A C E G 1 2 3 4 5 6 7 2 4 ' 6 ■ Time Seconds Fig. 1128. at the same velocity for 2 seconds, then reversed again and so on, the curve of the E. M. F. would be as represented in Fig. 1128. Here from A to C the curve is the same as Fig. 1127, 4.5 volts in one (the -\-) direction ; at C (the end of the 2d second) the direction of the motion, also. the E. M. F., is reversed, and is represented by the line drawn on the other side of the axis of the abscissas from C to E, where the E. M. F. is again reversed, and so on. As at the instant the E. M. F. is reversed it passes through all the intermediate values between 4.5 volts in one direc- tion and 4.5 volts in the other, a line must be drawn to 1914 APPLIED ELECTRICITY. indicate all these values, as shown ; the reversal being assumed to be instantaneous, this line coincides with the ordinate which passes through the abscissa which represents the time at which the reversal took place, as at 2 seconds, 4 seconds, 6 seconds, etc. 3038. If the change from the maximum E. M. F, in one direction to the maximum in the other were not instan- taneous, this line would not coincide with one of the ordi- nates; for example, assume that this same conductor was not moved at a constant velocity, but with a uniform acceler- ation of such an amount that, starting from zero, the velocity at the end of the 1st second was the same as the constant value assumed in the previous case ; then the E. M. F. generated at successive instants during this 1st second would be represented, as in Fig. 1129, by a straight line 6 # 1 \ 1 \ \ \ ^ / 1 \ 1 \ ^■^ / \ /. \ C t: G 63" 6 1 2 \ 3 1 4 •S 6 \ 7 2 \ 1 \ "A 1 1 4 / 1 / 1 6 Time Seconds Fig. 1129. commencing at volts at time and rising to 4.5 volts at the end of the 1st second. If from this point the velocity of the conductor is retarded at the same rate as it was previously accelerated, its velocity at the end of the 2d second would be and the curve of the APPLIED ELECTRICITY. 1915 E. M. F. generated during the 2d second would again be a straight line, commencing at 4.5 volts at the end of the 1st second and falling to volts at the end of the 2d second. If the conductor is now moved in the opposite direction and the same cycle of acceleration and retardation gone through with, the curve of the E. M. F. generated during this cycle of motions will be of exactly the same shape as that for the previous cycle, but will lie on the opposite side of the line, as is represented by the part C E oi the curve shown in Fig. 1129. Continuation of this cycis of motion gives a series of repetitions of this curve, as represented in Fig. 1129. 3039. A similar curve would result if the velocity of the conductor had been kept constant, as in the case in Art. 3037", but the density of the field had been uniformly varied along the path of the conductor from to a maximum, and then to again. Both of these cases assume that the change from acceler- ating to diminishing velocity, or from increasing to decreas- ing density, is instantaneous, as indicated by the sharp peaks of the E. M. F. curve. In any apparatus as actually con- structed these changes would be more gradual, which would result in more or less rounding the peaks of the curve. 3040. If a conductor is moved in a straight line through a succession of magnetic fields of alternate polarity, as rep- resented in Fig. 1130, the curve of the E. M. F. generated Pig. 1130. will be of similar character to those shown in Figs. 1128 and 1129; that is, the E. M. F. will be maintained in one direc- tion as long as the conductor is moving through a field of 1916 APPLIED ELECTRICITY. one polarity, but as soon as the direction of the lines of force is reversed, the E. M. F. is also reversed . (Art. ,3036.) The actual shape of the waves of the curve will depend, as in the previous cases, upon the variation in the uniformity of the density of the field or of the velocity. The manner of finding the E. M. F. generated in any conductor moved in any straight line through a magnetic field of any condition of density should now be clear. It is evident, however, that motion in a straight line or in any irregular line is not in general desirable for dynamos; motion in a straight line can not be indefinitely continued, for that would require a field of unlimited extent, and sud- den changes in the direction of motion of the conductor do not usually permit of good mechanical construction. To avoid both the infinite field and the sudden changes in the direction of motion, the conductor may be moved in a circu- lar path, which is mechanically convenient and allows of the use of a field of limited extent; the effect of such motion will now be considered. 3041. In the case of a conductor moving in a circular path through a field of uniform density, if the lines of force are at every point radial to the path of the conductor, as represented in Fig. 1131, the angle which the direction of motion of the conductor makes with the lines of force at every instant is constant; the E. M. F. generated in the con- ductor is, therefore, con- stant as long as a constant velocity is maintained. In order to obtain the distribution of the lines of force required in the above case, one pole of the magnet i^S S S S) Fig. iiai. must be made in the form APPLIED ELECTRICITY.. 1917 of a hollow cylinder, concentric with and enclosing the path of the conductor {a n a') and the other pole [N N JVN). In the space between these two poles the lines of force will be radial in direction and uniform in density if the rest of the magnetic circuit is properly designed. 3042. If the direction of the length of the conductor is radial, instead of parallel to the axis, as in the above case, by making the lines of force parallel to the axis and uniform in density all along the path of the conductor, the angle between the lines of force and the direc- tion of motion of the conductor will at all instants be the same; hence, the E. M. F. will be of the same character as before. This arrangement of the lines of force may be obtained by making the pole faces circular in shape and placing them in two parallel r'- planes with the center of the i ' pole-pieces coinciding with the ^'°- ^^^^• axis of rotation of the conductor, as represented in Fig. 1132. The arrangement of the balance of the magnetic circuit is not indicated in this figure. A part of the north pole- piece is broken away in the elevation to show the con- ductor a 0. THE SINE CURVE. 3043. Fig. 1133 illustrates a case of circular motion which differs in many features from the first two considered. Here the lines of force are parallel to each other and at right angles to the axis of rotation; consequently, the angle between the direction of motion and the direction of the lines of force changes at every instant. From this it fol- lows that the E. M. F. also varies during successive in. stants. Although the direction of motion of the conductor changes, at any one point it may be considered to be along 1918 APPLIED ELECTRICITY. a straight line tangent to the circle at that point, and a cer- tain length may be assigned to this line which will represent the velocity of the moving con- ductor. Thus, at the instant when the conductor is at the point a (Fig. 1133) of its path, the line representing its direc- tion of motion at that point makes an angle of 0° (is par- allel) with the lines of force; hence, no E. M. F, is generated at this point. As the conduct- or moves along its path, this angle becomes greater until at a point 90° from a the angle is also 90°, and the E. M. F. gen- erated is a maximum. Further Fig. 1133. continuation of the motion for another 90° decreases the angle until it is again 0°, and the E. M. F. is again zero. The remainder of the revolution repeats this cycle of changes of the angle, but, as the conductor is moving in the opposite direction relative to the lines of force, the E. M. F. is reversed in direction. From this it follows that the curve of this E. M. F. would form a series of waves on each side of the axis of the abscissas, as in the cases de- scribed in Arts. 3037 and 3038. 3044. The shape of the waves of this curve may be found by calculating the E. M. F. generated at successive intervals of time; this E. M. F. will evidently be propor- tional to the sine of the angle which the direction of motion makes with the lines of force (see Art. 3020), so that by constructing at any point on the circle a right-angled tri- angle which includes the above angle, the side opposite this angle may be used as the length of the ordinate represent- ing the E. M. F. generated at that point. APPLIED ELECTRICITY. 1919 This process is represented in Fig. 1134, where b repre- sents a certain point in the path of the conductor a at which it is desired to know the E. M. F. generated. The line h r, tangent to the circle at the point b, represents the direc- tion of the motion of the con- ductor at this point, and makes the angle / with the direction of the lines of force, repre- sented by the line ?' t. The line / b, at right angles to r t, is, then, the sine of the angle/; hence, it is a measure of the E. M. F. generated in the con- ductor at the point b, and by repeating this process for suc- cessive points around the circle a series of values will be ob- tained which may be used as ordinates of the E. M. F. curve, as stated. From the construction of the figure, the line o b \s per- pendicular to the line b r, and the line o a is perpendicular to the line r t; hence, the angle d included between the lines a and ^ ^ is equal to the angle / included between the lines b r and r t, and the E. M, F. is, therefore, propor- tional to the sine of the angle d, or to the length of the line b n. This length {b li) may or may not equal the E. M. F. when laid out on any scale, but will always be proportional to it. Hence, the E. M. F. generated at any instant in a con- ductor moving in a circular path through a magnetic field of uniform density whose lines of force are at right angles to the axis of rotation and parallel to each other is propor- tional to the sine of the angle through whicJi the conductor has been rotated from a point where its direction of motion is parallel to the lines of force. Fig. 1134. [920 APPLIED ELECTRICITY. 3045. If the velocity of the conductor is uniform (as is assumed above), the conductor will move through equal angles in equal intervals of time; hence, the abscissas of the E. M. F. curve may represent either the intervals of time required for the conductor to move through the various angles or the angles themselves. The ordinates may repre- sent the sines of the same angles, the E. M. F. being pro- portional to them. This curve may be conveniently drawn by laying off on a circle a series of points representing suc- cessive positions of the conductor after equal intervals of time, as represented at «, /^, ^, . . . . a' in Fig. 1135 {a)^ 45° 90^ laS" 180 or Angle in Degrees a a' being a diameter at right angles to the lines of force. The vertical height of any of these points above the diameter a a! is, then, the sine of the angle through which the conduct- or has been moved, and these heights may be projected on the ordinates of properly arranged cross-section paper, as represented in Fig. 1135 (^), giving the curve a, b, c^ . . . . a\ as shown. The curve for the remainder of the revolu- tion, a' in a, may be laid out in the same way, and would evi- dently be of the same shape, but would be on the opposite side of the axis of the abscissas. This form of curve is called a sine curve, or sinusoid, from its method of con- APPLIED ELECTRICITY. 1921 struction, and possesses several peculiar features, as will be pointed out. 3046. Value of E. M. F. — From the explanation given in Art. 3024, it will be seen that the E. M. F. gen- erated in the conductor in the above case at any instant may- be found from formula 477 ; r° and s° being in thi& ease each equal to 90°, sin r° and sin s° are each equal to ), and may be omitted, making the formula read ^_ BZJ/sin /" 10^' It is evident that during one complete revolution the con- ductor passes over a distance equal to 2 tt r, r being the radius of its circular path, or o a (Fig. 1135). Then, if the speed of the conductor is vS revolutions per S / S minute, its velocity is equal to ^^^^(T^^^i^g the revolu- tions per second), and this value may be substituted for M' in the above formula, which would then read BZ 27rr--sin/° j^ dO £= — 10" All the lines of force cut by the conductor in each revolu- tion are included in the area obtained by multiplying to- gether L and 2 ?'. This being the case, the total numbei of lines cut by the conductor, which is represented by A^, is equal to B Z. 2 r. N From this, — - = B L, which value may be substituted for 2 r ■' BZ in the previous formula, which then reads as follows: N S ^_ 27'"^60^^^^° ^ " 10" Simplifying this, it becomes ^ ~ 10* X 60 • 1922 APPLIED ELECTRICITY. When E is at its maximum value, ^,„, ^° ;= 90° and sin/° = 1 ; hence, ^- = i#i4o- (479.) THE AIR-GAP. 3047. If the field through which the conductor moves in its circular path, having a radius o a, exists between two parallel pole faces, as represented in Fig. 1135, it is evident that the distance between the pole faces must be a little greater than 2 ^ «, in order that the conductor may not touch the pole faces in its rotation. This distance between the pole faces introduces an air-gap of great length compared to its area, thus requiring a con- siderable expenditure of M. M. F. (magnetomotive force) in forcing the field across the gap. The average length of this air-gap may be reduced by making the pole faces concentric with the path of the con- ductor, but as in this case the length of the air-gap is no longer uniform, the density of the field' in the gap will not be uniform; and, further, the increased density is situated at a point where it has the least effect; i. e., at the point where the conductor is moving in a direction nearly or quite parallel to the lines of force, as repre- sented in Fig. 1136. 3048. As there is actually required for the movement of the conductor only a thin cyl- indrical space near the pole faces, the length of the air-gap may be reduced very largely by filling in the space not required for the movement of the con- FiG. 1136. ductor with a cylindrical core of iron. The distribution of the lines of force will now be APPLIED ELECTRICITY. 1923 materially different from that shown in Fig. 1136; the length of the air-gap being practically uniform and much shorter, the direction of the lines of force will be in nearly the shortest distance across the gap, i.e., will be nearly radial, and the density will be practically uniform and, with the same M. M. F., much higher. The actual distribution of the lines of force will be about as represented in Fig. 1137. It will be noted that some of the lines of force do not pass into the core at all, and are even entirely outside the path of the con- ductor. These leakage lines (see Art. 2415) are always present in any magnetic circuit which includes an air- gap, although they have not thus far been repre- sented. Their influence fig. 1137. on the design of the magnetic circuit may be neglected for the present, but will be fully discussed later. 3049. If the lines of force in the air-gap were abso- lutely radial and of uniform density throughout, the direc- tion of the motion of a conductor moving through this air- gap would at any instant be at right angles to the lines of force, and (assuming a constant velocity) the E. M. F. would be constant in value, but, of course, reversed at the end of each half revolution. The E. M. F. curve would, therefore, be similar to that shown in Fig. 1128, Art. 3037. This differs from the case described in Art. 3041,in that the direction of the motion of the conductor with respect to the direction of the lines of force is not constant, but is re- versed at the end of each half of a revolution, which causes the E. M. F. to be reversed, as stated- 1924 APPLIED ELECTRICITY. The actual distribution of the lines being different from this just described, the curve is actually more like the sine curve (Fig. 1135), but with a more flattened top, conse- quently a more rapid increase from zero to values near the maximum. ARMATURE CORE LOSSES. 3050. A very convenient method of moving the con- ductor through the magnetic field is to mechanically attach it to the surface of the cylindrical core, which may then be rotated around its axis by any convenient means. The motion of the core does not of itself affect the distribution or the density of the lines of force ; but in order to maintain the motion of the core, certain losses, due to hysteresis and to eddy currents circulating in the core, must be overcome. 3051. The hysteresis is due to the continual change in the direction of the lines of force through the core, as it rotates, amounting to one complete reversal in each half revolution ; the amount of the hysteresis loss depends upon the quality of the iron of which the core is made, the density of the lines of force in the core, the number of reversals of magnetism per unit of time, and the amount of iron affected. (Art. 2413.) 3052. The eddy-current loss is due to the fact that, the iron of the core being a conductor, the E. M. F. gen- erated in it by its rotation in the magnetic field causes cur- rents to circulate through the mass of metal in the core ; these currents do not differ from the currents flowing in the conductors attached to the surface of the core, but as they do not appear in the external circuit, they represent so much wasted energy. 3053. The E. M. F. of these eddy currents is neces- sarily low ; but if the core is a solid mass of metal, the re- sistance offered to these currents is extremely small, so that the small E. M. F. may cause enormous currents to flow, which would thereby be the source of a great loss of energy. APPLIED ELECTRICITY. 1925 The direction of these currents may be found by applying the rule given in Art. 2442, when it will be seen that if the direction of the current in a section of the core under one pole is from front to back, under the other pole it will be from back to front, so that these currents will circu- late around the core, as represented in Fig. 1138, in which only the lower half of the core is represented, the paths of the eddy currents being indicated by the lines with the arrow-heads. In order to reduce the value of the eddy currents as much as possible, it is evidently necessary to reduce their E. M. F. and to increase the resistance of their path. This is usually accomplished by building up the core of a number of thin iron disks, as represented in Fig. 1139, arranged parallel to the lines of force and at right fig. iiss. angles to the axis of rotation, and insulated from one another. Instead of being one single conductor of large section, the core is now made up of a number of conductors of less section and shorter length ; the E. M. F. generated in each conductor is, there- fore, much less, and the current produced Fig. 1139. thereby is relatively much smaller than in the case of the solid core, so that the loss of energy is reduced. 3054. This process of dividing the core into thin plane sections is called lamination, the separate sections forming 1926 APPLIED ELECTRICITY. the laminae. Lamination does not affect the magnetic qualities of the core, since all the sections are continuous in the direction of the lines of force. , Building up the core of lightly insulated iron wire will also prevent eddy currents, but as in this case the iron of the core is not magnetically continuous, the reluctance of the core as a whole is much greater than that of the iron of which it is composed. The laminated structure is, there- fore, most extensively used. 3055. As in the case mentioned in Art. 3042, the direction of the length of the conductor may be radial instead of parallel to the axis of rotation. In that case the cylindrical core would take the form of a disk, and the lines of force would enter and leave the core at the end faces instead of the cylindrical face, as represented in Fig. 1140, a h being the conductor supported on the core C, which rotates about the axis o o' . Fig. 1140. The curve of the E. M. F. generated under these circum- stances would be similar to that mentioned in Art. 3049, i. e., similar to a sine curve, but with flatter peaks to the waves. From an inspection of the figure, it will be seen that if the core were made up of disks arranged at right angles to the axis of rotation as in the previous case, the laminae would not act to reduce the B. M. F. available for the production oi APPLIED ELECTRICITY. 1927 eddy currents; so this type of core is usually constructed of a long strip of thin iron, wound in a helical form, with strips of insulating material between the layers. This makes a core of the requisite form that is magnetically continuous in the direction of r.he lines of force, and is free from excessive eddy currents. CHARACTER OF COMMERCIAL CURRENTS. 3056. Any electric current in commercial use may be classified either as a direct current or an alternating current. The abbreviations for these are D. C, direct cur- rent, and A. C, alternating current. A direct current may be defined as a current which ahvays flozvs in the same direction through the conductor or circuit. A direct current may be continuous, so-called, or pul- sating. A strictly continuous current is one in which the E. M. F. has an absolutely constant value during succeeding intervals of time, which would, therefore, cause a perfectly steady current to flow through a circuit of constant resist- ance. The curve of a continuous current would then be a straight line parallel to the axis of the abscissas, as represented in Fig. 1127. Incandescent dynamos or constant potential dynamos are familiar examples of machines that furnish continuous currents. 3057. The pulsating current is practically unknown in the commercial world, and although the current from a Thomson-Houston arc machine may be called a pulsating current, yet it is never mentioned as such. As will be explained farther on, a pulsating current is one which always flows in the same direction, but the electromotive force constantly varies, so that the current consists of dis- tinct impulses or rushes of current. In Fig. 1141, {a), {b), and {c) represent three possible curves of pulsating currents; in {a) the fluctuations of the E. M. F, or current occur between a m^ximurn and zero, while in {^b) 1928 APPLIED ELECTRICITY. the minimum is about .7 of the maximum; {c) represents a slightly different type of curve, in which the mini- mum is about .85 of the maxi- mum. It will be seen that either of the last two quite closely approaches a strictly continuous current. ^ f N /■ "^ ^ N r N . J V I J I J Time (a) 1 ^ N \^ / ^ ^ \ y ^ 1 Time (b> ^ Time 3058. An alternating current may be defined as a current which is continually reversed in direction; conse- quently, its E. M. F, and current alternate between two opposite maximum val- ues; the curve of the E. M. F. or current would, there- fore, lie on both sides of the ^(.^ axis of the abscissas. A dy- FiG. 1141. namo which generates an al- ternating E. M. F. is called an alternator. The E. M. F. generated in a conductor whose direction of motion with respect to the direction of the lines of force is periodically reversed would, therefore, be an alternating E. M. F., as shown by the curves in Figs. 1128, 1129, and 1135. If the conductor so moved cuts the lines of force in each direction in the same time and at the same rate, the curves of the E. M. F. generated by the motion in each direction will both be of the same shape, and will lie equally on both sides of the axis of the abscissas, and a continuation of the F / \ / \ / \ A V V y E O V / 1 K V y M K 1 "ijwe Fig. 1148. cycle of motions, under the same conditions, will give an E. M. F. curve that is merely a series of repetitions of the APPLIED ELECTRICITY. 1929 curve representing the E. M,. F. generated during the first cycle of motions. Such an E. M. F. (or its resulting cur- rent) is called a cyclic, periodic, or tiarmonic alternating E. M. F. (or current). A curve showing a form of such an E. M. F. is given in Fig. 1142, the axis being A M; the positive impulses are above, at V, and the negative impulses at JC. The curve crosses the axis at the points C, B, G, etc. GENERAL PRIIVCIPLES OF ARMATURE WINDINGS. 3059. It should be clear that rotary motion of a con- ductor in a magnetic field may be divided into two gen- eral classes: (1) where the arrangement of the field with regard to the path of the conductor is such that the direc- tion of the motion is always the same, relative to the direc- tion of the lines of force, and (2) where the arrangement is such that the direction of motion is periodically reversed, relative to the direction of the lines of force. A further distinction between these two classes is that in the first class each line of force is cut oily once in each rev- olution, while in the second class each line of force is cut twice in each revolution. This has given rise to the names unipolar and bipolar (or multipolar) induction for the two classes; i. e., the E. M. F. generated in a conductor so arranged as to come under the first class would be said to be due to iinipolar induction, etc. These terms have been extended to the machines themselves, so a machine in which the E. M. F. is generated by unipolar induction is called an unipolar dynaino; if the E. M. F. is generated by bipolar induction, it is called a bipolar dynamo, and so on. This application of the term tcnipolar is hardly correct, since an "unipolar dynamo" must necessarily have two poles. Its application to induction, however, is more accu- rate, because, aside from its influence on the design of the magnetic circuit, the presence of more than one pole is not necessary in considering this class of induction; that is, as 1930 APPLIED ELECTRICITY. each line of force is cut only at one point, it does not mat- ter what course it takes after being cut. With bipolar or multipolar induction, it is necessary that the lines from each magnet be grouped together in the same manner at the two separate points of their own path at which they are cut by the conductor, which is most conveniently done by making these points the surfaces of the poles of the magnet. Still, the distinction is usually applied to the machines themselves. 3060. It has been shown that with either unipolar or bipolar induction the conductor may occupy one of two radically different positions; namely, the direction of its length may be parallel or radial to the axis of rotation. In either case, with unipolar induction, as illustrated in Arts. 3041 and 3042, Figs. 1131 and 1132, it is evident that the E. M. F. generated in the conductor is a direct E. M. F. in the sense of being continuous in direction, while with bipolar induction, as illustrated in the cases given in Art. 3043 and those following, the E. M. F. generated in the conductor is an alternating E. M. F. 3061. In order to electrically connect a stationary ex- ternal circuit with the moving conductor, some form of sliding or rubbing contact is necessary, which usually takes the form of stationary strips of copper, carbon, or other con- ducting material called brushes, which form the terminals of the external circuit, and which rest upon bare metallic surfaces which are electrically connected to the conductors and mechanically attached to but insulated from the shaft by which the armature core, conductors, and collecting de- vices are driven. In case it is desired to make continuous connection throughout the revolution with the conductor, these bare metallic surfaces are made continuous, i. e., in the form of rings, and the device is then called a collector, while if it is desired to make the connection between the conductors and the external circuit during a part of a revo- lution only, the bare metallic surfaces are made segmental. It is never the case that the external circuit is entirely dis- APPLIED ELECTRICITY. 1931 connected from all the conductors of the armature at the same time, so that if any particular conductor is discon- nected from one of the terminals of the external circuit at any time during the revolution, another must be substi- tuted. This results in a collecting apparatus consisting of a series of separate metallic segments arranged in cylindrical form, each connected to some part of the winding, forming a device called a commutator. From the nature of the device, the character of the dif- ference of potential which appears between the terminals of the external circuit (the brushes), if a collector is used, is the same as the character of the E. M. F. generated in the conductors; i. e. , it is subject to the same fluctuations in value or reversals of direction. If a coniDmtator is used, this is not necessarily the case; in fact, is not likely to be, since the connection with any particular conductor is not maintained throughout that conductor's cycle of motion, so that the character of the E. M. F. generated is not reproduced in the difference of potential existing between the brushes. This is an impor- tant distinction, since it is the character of this difference of potentiai which directly determines that of the current in the external circuit, and not the character of the E. M. F. generated. 3062. It has been pointed out that, in order to gener- ate a sufficiently high E. M. F. for commercial applications, a number of conductors must be used, so connected together that their E. M. F. 's will add together to the desired amount. These conductors may obviously be located in the same magnetic field, and rotated under the same conditions; then, the E. M. F. of each will pass through exactly the same cycle, with a phase difference depending upon their relative positions in the field at any instant. From a study of these features, the proper methods of connecting the con- ductors to each other and to the external circuit to attain any desired result may be deduced. Fig. 1143 represents 16 conductors, a, b^ c^ . . . . J>, 1932 APPLIED ELECTRICITY. equally spaced around the periphery of the core C. The direction of the lines of force being from N to 5, and the direction of motion being as indicated by the arrows, the direction of the E. M. F. in the con- ductors under the N pole face is from back to front, while in those under the 5 pole face it is from front to back, as will be seen if the hand rule (Art. 2442) is appHed. Fig. 1143. This is indicated by marking the conductor with a + or a solid black dot, as shown. Conductors in the positions a and z, being in such a position that no lines of force are cut by them, have no E. M. P., and are not marked. 3063. In connecting two or more conductors in series, it is evident that the maximum E. M. F. will result when the E. M. F. 's of the two conductors coincide in phase, for, otherwise, at a part of their cycle the E. M. F.'s in the two conductors would oppose each other; the same result may be obtained if the phases are displaced 180°, for then the two conductors will each have a maximum E. M. F. gen- erated in them at the same instant, and al- though these two E. M. F.'s would be repre- ^& sented in a clock diagram as acting in opposite directions, the conductors may be so connected that the E. M. F.'s will add together. This is represented by the diagram. Fig. 1144, where a b and c d represent two conductors, in which the E. M. F.'s generated are in opposite direc- ^ tions, as indicated by the arrow-heads, but by fig, ii44. APPLIED ELECTRICITY. 1933 connecting the ends b and c together the difference of potential between a and d is equal to the sum of the two E. M. F.'s. Applying these principles to the case illustrated in Fig. 1144, it is evident that the proper conductor with which any one of the conductors — for example, conductor e — should be connected in series is either the conductor diametrically opposite it, in this case conductor ;;z, or either of the con- ductors immediately adjacent to it, in this case either con- ductoryor d. Note. — The figure being very much out of proportion, the angular distance between these adjacent conductors would seem to be sufficient to cause a considerable difference in their phase ; in practice, however, the angular distance between adjacent conductors would be very- small, and the difference in phase of the E. M. F.'s generated in them almost inappreciable. 3064. Applying the principle illustrated in Fig. 1144, opposite conductors would be connected by conductors ex- tending across one of the end faces of the core. But in connecting adjacent conductors in series a different method must be followed, since the ends which are similarly situated on the core must be connected together, as illustrated in Fig. 1145, where a b and c d represent two conductors, in each of which the E. M. F. generated is in the same direction, as indicated by the arrow-heads. In order to connect these two conductors in series, so that the E. M. F.'s will add, the ends b and d (or a and c) must be connected together, as represented, in which case the difference of potential between a and c (or b and d, if a and c are con- nected) would be equal to the sum of the two E. M. F.'s generated. 3065. Now, in the armature, the above connection mani- festly can not be made across the end faces of the drum; neither can it be made directly across the cylindrical face, for in the latter case an E. M. F. would be set up in the con- necting wire, opposite in direction to the E. M. F. of the 1934 APPLIED ELECTRICITY. :S^:1i &-"" ,-- — — ■«--i- ■IZ^ "" ■^.,,,^ -<-V- -i^ "- •-^ ^^^ -<--V Sr^--' ;:;;: <- -Va- ~-- ::\^ ,¥- 1^ -* conductors. The only reasonable way in which this style of connection can be made is to make the armature core in the form of a cy/- indrical ring, and pass the connecting ' wires through the hole in the center of the ring, as illus- trated in Fig. 1146. Here the conductor c is connected to the conductor d by Pi^- ^^40. a wire passing down the back face of the ring, through the hole in the center at X and up the front face to d. The lines of force pass from pole to pole through the iron of the core, as represented in Fig. 1146, and hence are not cut by this connecting wire x, which, therefore, has no E. M, F. generated in it. 3066. These two general methods of connecting con- ductors in series are called drum >vinding and ring winding, respectively, from the shape of the cores used. The first practical use of the ring winding was due to Gramme, hence it is often called the Gramme winding. It was invented by Paccinotti. The drum winding was originated by Siemens. 3067. In building up a drum armature core, the disks of which it is composed may be slipped directly on the driving shaft, forming a solid mass of metal; but in the ring core it is necessary to provide a support for the ring- shaped disks, which shall have sufficient strength to drive the armature core and at the same time provide a sufficient opening between the shaft and the inside of the core to admit the connecting wires of the winding. Such a support is called a spider, and usually consists of two castings, made APPLIED ELECTRICITY. 1935 with a central hub bored out for the shaft, from which hub a number of thin arms radiate and support the armature core, the connecting Avires being wound in between these arms. 3068. It will be seen that if the conductors are ar- ranged radially on the end faces of the core, with the pole- pieces facing these surfaces (see Art. 3055), the same two systems of winding may be followed when connecting the conductors in series. In this case the connecting wires are arranged on the cylindrical surface (or surfaces in a ring winding) instead of the radial surfaces. To get the best re- sults, these armatures are made in the form of a disk; the distinctive features of the ring or drum winding are not altered by this change in the form of the core, but the me- chanical construction is materially different. In order to distinguish between the two forms of cores, those in which the lines of force enter and leave the cores at the cylindrical surface are called cylinder armatures, whether the winding be ring or drum, and those in which the lines of force enter and leave at the end face (or faces) are called disk armatures. (vSee Arts. 3041 and 3042.) 3069. Fig. 1147 illustrates these two methods of con- necting conductors in series for cylinder amatures, (/i) being the ring and (i>) the drum winding. In each the upper half of the core is removed, showing the loop formed by the con- ductors and the connections between them. In order to connect the free ends of "the loop to the collecting device, or to other conductors, other connecting wires are added, as represented at 1, 2. It will be seen that in either form of winding the active conductors and the connecting wires form a coil of one or more turns. In practice these coils are usually formed from a single piece of insulated wire, of suit- able length, wrapped around the core a sufificient number of times to make the coil of the requisite number of turns. Each coil so wound covers a certain fraction of the surface of the armature core; in the case of the drum winding, this 1936 APPLIED ELECTRICITY. fraction of the surface is divided into two parts that are on opposite sides of the core, while in the ring winding it is Fig. 1147. altogether on one side. The amount of surface of the core covered by the coil may be called the width of the coil. DIRECT-CURRENT ARMATURE WIND- INGS. UNIPOLAR ARMATURES. 3070. In order that an E. M. F. which acts continually in one direction may be generated in a moving conductor, it is necessary that the direction of motion of the conductor be always the same with reference to the direction of the lines of force of the magnetic field in which the motion takes place. Motion in a straight line is here obviously impossi- ble, since it could not be continued for any length of time ; motion in a circular path is, therefore, the only kind that ansvvers the requirements. In Arts. 3041 and 3042 two methods of moving a con- ductor in a circular path in a constant direction relative to the lines of force are described and illustrated. These are examples of wiipolar induction. (See Art. 3059.) In either of the above methods, it is evident that a number of APPLIED ELECTRICITY. 1937 conductors may be used, distributed along their circular path, and in each the same E. M. F, will be generated. In order to obtain a high E. M. F., it would then be desirable to connect these various conductors in series, in such a way that all their E. M. F.'s would be added together. If this is attempted, it will be found that, owing to the fact that the lines of force form closed loops, it is impossi- ble to permanently connect the active conductors in series in any manner so that the connecting wires will not cut the lines of force in such a way as to set up in them an opposing E. M. F. of exactly the same value as that generated in the armature conductors proper. The final effect of connecting any number of armature conductors in series is, therefore, at most only the E. M. F. of a single conductor. The only way, then, in which the conductors may be con- nected is by means of sliding contacts, whereby the con- necting wires may be stationary with respect to the moving armature conductors. It is evident that this method is of limited application, since the connections for a large number of conductors would become too complicated. 3071. With unipolar induction, then, the maximum E. M. F. possible is that of a single conductor; it is evident, however, that if a number of separate conductors are used, they may all be connected in parallel, which, while it does not increase the E. M. F., does increase the possible current output, since it decreases the internal resistance of the arma- ture winding. A number of such conductors connected in parallel are equivalent to a single wide conductor; in the case illustrated in Fig. 1131, this would be equivalent to a tube, of a thick- ness sufficient to allow it to rotate freely between the poles A^and 5, while in the case illustrated in Fig. 1132 it would be equivalent to a disk rotating between the poles N and S. It is in one or the other of these forms that the armatures of unipolar dynamos, which have a limited application in cases where a large current at a low potential is required, are constructed. 1938 APPLIED ELECTRICITY. OPEN-COIL BIPOLAR ARMATURES. 3072. The E. M. F. generated in the separate coils of an armature winding which is revolved between the oppo- site poles of a bipolar magnet is naturally alternating in character, since its direction when passing through one field is opposite to that which it has when passing through the other. When connected to the external circuit by means of col- lector rings, this alternating E. M. F. is impressed directly on the external circuit; but by using a suitably arranged commutator, the connections between the coils of the arma- ture winding and the external circuit may be reversed at proper intervals, so that the current in the external circuit will be uniform in direction. A simple way of accomplishing this result with a single coil is shown in Fig. 1148, in which a coil of three con- ductors, a b c, is wound on a ring core and connected to the two commutator segments S' and S", each of which covers nearly one-half the circumference of the commutator. On APPLIED ELECTRICITY. 1939 these two segments rest the two brushes -}-B and —B, they being placed opposite each other and making contact with the segments S' and S" on the neutral line x _y. 3073. When the coil is in the position shown, it being rotated in the direction indicated by the arrow, the E. M. F. generated in the coil will be acting in the direction indicated by the arrow-heads, thus making the top brush positive. When the coil reaches the neutral space, the brushes will each momentarily make contact with both commutator segments, by bridging the space which separates them ; but as in this position there is no E. M. F. generated in the coil, this has no effect. On further motion of the coil under the opposite pole-piece, by which its E. M. F. is reversed in direction, the top brush comes in contact with segment S' and the bottom brush with segment S". Since the direction of the E. M. F. in the coil has been reversed, this reversal of the connection between the brushes and segments results in keeping the difference of potential between the brushes in the same direction as before. It is evident that this difference of potential is not at all constant, but varies from a maximum to zero and then to maximum again; the curve of its various instantaneous values would be a series of waves, all on one side of the base line. In other words, such an arrangement as has been described would cause a pulsating current to flow in the ex- ternal circuit. (See Art. 3056.) 3074. Another coil can be wound on the core directly opposite the first, and connected in series or in parallel with it. The width of the coils can not be greater than the width of the neutral spaces, without causing opposing E. M. F.'s during parts of a revolution; consequently, only a part of the surface of the armature can be utilized, and at best there is a part of the time that the E. M. F. of the winding is zero. However, other pairs of coils may be wound on the sur- face of the core, in positions intermediate between those of 1940 APPLIED ELECTRICITY. the original pair; these pairs may then each have its own commutator and brushes, and as the maximum and zero of values of the E. M. F.'s of the new windings occur at differ- ent periods of time from those of the first pair, the E. M. F.'s may be combined so as to prevent the E. M. F. acting in the external circuit from falling to zero. 3075. Fig. 1149 shows the arrangement, for both ring and drum winding, of two sets of coils A A' and B B\ each Fig. 1149. set containing four active conductors, those of one set occupying a position on the core 90° from those of the other. Both sets are supplied with their two-segment commutators, which for convenience are represented as being concentric, A A' being connected to a and a\ and B B' to b and b'. Brushes 1 and 2 rest on segments a and a', and brushes 3 and 4 rest on segments b and b'. 3076. The maximum E. M. F. of each of these sets is the same, but that of the one occurs \ revolution ahead of the other, so that the curves representing the instantaneous values of the E. M. F.'s of these two sets of coils for one revolution would be about as represented in Fig. 1150, where curve 1 is the E. M. F of coils A and A', and curve 2 is the E. M. F. of coils B and B', for a complete revolution, start- ing from the position of the coils represented in Fig. 1149. If the two sets of coils are connected together in series by APPLIED ELECTRICITY. 1941 means of an external connection between, say, brushes 2 and S, then the difference of potential between brushes 1 and ^ at any instant is equal to the sum of the E. M. F.'s of the --, ~-- ~^ is \ / f3 \ Is \ 1 \ 1 / 1 \ 1 \ + J \ / \ \ 1 / \ \ \ 1 71 f\ > 7i \ ' > C ii \ /- % /. \ 7 1 \ / \ 1 / \ J V J V J V J \ i r y f}" li iO" 270" 360 Fig. 1150. two sets of coils at that instant. The result of the addition for the entire revolution is represented by the dotted curve 3, Fig. 1150. It is readily seen that for about one-fourth of each wave the E. M. F. of one set of coils is nearly at its zero value, and, therefore, contributes but little to the total E. M. F. of the armature; the resistance of this set of coils must, nevertheless, be overcome, since it forms a part of the circuit. 3077. Instead of connecting the sets of coils in series, they may be connected in parallel; but with the coils con- nected as shown in Fig. 1149, this would result in having the more active set of coils short-circuited by the set that is less active, which would very materially reduce the differ- ence of potential between the brushes. There is, however, a part of the revolution when the E. M. F.'s of the two sets of coils are nearly enough the same to allow of their being connected together in parallel, and by widening the gap be- tween the ends of the segments of the commutator, each set of coils may be entirely disconnected from its brushes during the part of its revolution when its E. M. F. is much lower than that of the other set. 1943 APPLIED ELECTRICITY. This arrangement of the commutator segments for the windings shown in Fig. 1149 is represented in Fig. 1151, in which a and a' are the segments connected to coils A and A\ and b and b' are the segments con- nected to coils B and B\ as be- fore. Fig. 1151. represents the E. M. F 3078. It is evident that curves showing the difference of potential between either pair of brushes would comprise that part of curves i or ^ (Fig. 1150) that of the winding during the time that the brushes are in contact with the commutator segments. The curves in Fig. 1152 represent the difference of potential which would exist between the brushes if the arrangement shown in Fig. 1151 were used with the windings shown in Fig. 1149, curves i, i, etc., showing the difference of potential between brushes S and .^, and curves 2, 2, etc., showing the difference of potential between brushes 1 and 2, starting from the position of the commutator represented in Fig. 1151. It is apparent that with this arrangement the windings might be connected in parallel by connecting together brushes 1 and S and 2 and 4 (Fig. 1151). In that case, the difference of 90^ 180° Fig. 1152. 270° 360" potential between the brushes would be the E. M. F. of one winding until the other is connected in parallel with it, which connection would cause the difference of potential to drop a little, since the winding which is newly connected has a slightly lower E. M. F. than the other. The result of APPLIED ELECTRICITY. 1943 this is that the curve is depressed a little during the time that the coils are in parallel, as represented by the dotted lines in Fig. 1152. 3079. From this curve (Fig. 1152) it will be seen that at the moment when the two sets of coils are thrown in parallel by the brushes, the E. M. F. in the two sets is not the same, that of the set which had just before alone been connected to the brushes being higher than that of the other. A little later, at the moment when one of the sets is disconnected from the circuit by one set of brushes leav- ing its segments, the coil which is disconnected has a less E. M. F. than the other. If the coils had little inductance, this would result in the greater E. M. F. of the one set of coils sending a current around through the other set against the E. M. F. gener- ated in it, which current would not appear in the external circuit, and would, therefore, represent so much wasted energy. 3080. This local current would evidently be greatest when the difference between the E. M. F.'s of the two sets of coils is greatest; that is, at the moment when the two sets of coils are connected in parallel, and at the moment one of the sets is disconnected from the brushes. Then, when the one set of coils is disconnected from the other, this local current would be suddenly broken, which would result in sparking. In an armature as actually constructed, however, the inductance of the coils is sufficient to prevent these local currents; when a coil is first connected in parallel with another, its inductance prevents a sudden rush of current through it, and allows it to take up its share of the current output gradually. As the coil approaches the point where it is to be disconnected from the circuit, and the E. M. F. generated in it becomes less than that of the coil with which it is connected, its inductance serves to keep up its E. M. F., so that its current gradually grows less, until at the time when it is disconnected from the circuit, if that time is 1944 APPLIED ELECTRICITY. properly chosen, its current output is practically zero, and little or no spark results from breaking its connection with the circuit. 3081. In Fig. 1151 the two sets of segments have, for convenience, been represented as concentric; in practice, however, the two sets would be made of the same diameter and placed side by side. If made in this way, the separate brushes 1 and S and 2 and ^ Fig. 1151, may be replaced by two wider brushes, wide enough to bear on either or both sets of segments. This is represented in Fig. 1153, in which a and a' and b and b' are the two pairs of commutator segments, and 1 and 2 are the brushes, which are wide enough to bear on either or both pairs of seg- ments, according to the position of the commutator. 3082. It will be seen that this arrangement of coils and commutator gives a direct but pulsating current, in which the pulsations are not excessive. As pjq ;[j5g_ has been pointed out, however, the width of the coils should not be greater than the width of the neutral spaces, so that even with two sets of coils the entire armature surface can hardly be utilized. More than one complete winding, however, can be placed upon the same core, and if each is provided with its own commutator, they may be coupled up in series or in parallel, as desired. Such a winding as has been described, in which separate sets of coils are used, and which are connected together in various combinations and connected to or disconnected from the circuit during the rotation of the armature, is called an open-coil >vinding. 3083. Only two or three forms of open-coil windings are m commercial use at the present time. That which has APPLIED ELECTRICITY. 1945 been described is used in the Brush, dynamos, the ordinary sizes of machine using two separate windings, each with its commutator, as represented in Fig. 1154. In this machine the pole-pieces face the sides of the armature, as represented by the heavy dotted lines. The segments of the two separate commutators are for con- venience represented as concentric, with the brushes resting on their edges ; whereas, actually, they lie side by side, Fig. 1154. forming two separate commutators of the same diameter, each having four segments, and the brushes rest on their circumference. One winding consists of two pairs of coils A and A' con- nected in series, and B and B' also connected in series, the two pairs being located at right angles to each other, as represented. This winding is connected to its commutator, coil A to segment a, coil A' to segment a' , coil B to segment b, and coil B' to segment b', as represented. Brushes 1 and 2 rest 1946 APPLIED ELECTRICITY. on this commutator, making contact on the line x j/ of maximum action of the coils. The second winding consists of two pairs of coils C and C and D and D', located at right angles to each other and half way between the coils of the first winding. These coils are connected in series and to the segments of the second com- mutator, coil C to segment c, coil C to segment c', coil D to segment d, and coil D' to segment d', as represented. Brushes S and 4 rest upon the segments of this commutator on the same line of maximum action of the coils. 3084. Taking each winding separately, it will be seen that its two sets of coils pass through the following combi- nations : One set of coils only connected to the brushes ; then the two sets, connected in parallel, both connected to the brushes; then one set only; then both sets in parallel, and so on. The maximum E. M. F. occurs when the single set of coils is connected, and is directly in the line of maximum action ; the minimum occurs -| of a revolution ahead of this point, when both sets of coils are in parallel, and are equally distant from the line of maximum action. (See Fig. 1152.) This being the case, it is evident that as the coils of one winding are half way between the coils of the other, the maximum E. M. F. of one winding occurs at the same instant as does the minimum E. M. F. of the other. On account of this, when the two windings are connected in series, the fluctuations of the current are much reduced. This connection of the two windings is obtained by con- necting the positive brush {3, Fig. 1154) of one winding with the negative {3, Fig. 1154) of the other, the external circuit being connected between the two remaining brushes (1 and 4, Fig. 1154). In the larger sizes of these machines, three and even four separate windings are used, each with its commutator and all connected in series. 3085. Instead of using overlapping segments, the same results may be obtained with segments which are placed APPLIED ELECTRICITY. 1947 end to end, by making the brushes have a large arc of contact, or, what amounts to the same thing, using two brushes on each side, spaced a distance equal to the desired arc of contact and connected permanently together. This is represented in Fig. 1155, a and a' being the segments connected to winding A A' (Fig. 1149), and b and b' being the segments connected to wind- ing B B' (Fig. 1149). It will be seen that the pairs of brushes 1 and 3 and Jf and 2, being per- manently connected together, act as one wide brush. In the position shown, both sets of coils are in parallel ; if the com- mutator is rotated in the di- fig. 1155. rection of the arrow, segments a and a' will pass out from under brushes 3 and Jf, leaving only segments b and b' con- nected to the winding, and, therefore, only coils B and B' in circuit. Further rotation will bring segments a and a' under brushes 1 and ^, respectively, throwing coils yi and A' and B and B' in parallel again, and so on. It will be seen that this arrangement gives the same results as that pre- viously considered. 3086. Instead of two sets of coils, three may be used, situated 120° apart on the armature. In this arrangement, which is used in the Thomson- Houston open-coil dynamos, only one end of each set of coils is carried to a commutator segment, there being, there- fore, but three segments; the other end is connected to a common junction of the three ends. The commutator segments are each a little less than 130° in span, being placed end to end and separated by a small air-gap. The brushes used are divided into pairs, as described in Art. 3085 ; that is, the equivalent of two wide brushes is used, the arc of contact being about 60°, or about half the span of one segment. 1948 APPLIED ELECTRICITY. Both ring and drum windings are used for the armatures; Fig. 1156 gives a diagram of the connections, etc., of the drum-wound armature. A A', B B\ and C C are the three coils, wound on the core in planes making angles of 120° with each other. One end of each of the coils is joined to a metal ring (not represented in the figure) on the back of Fig. 1156. the armature, which forms a common connection for the three. The other ends are joined to the commutator seg- ments, that of A A' to segment a, that of B B' to segment b^ and that of C C to segment ^, as represented, i, ^, ^', which rest on segments c and d, and brushes S and viiid[ing. As in the bipolar winding, the pitch may be the same, both front and back, in which case it must be odd, or the front and the back pitch may differ by 2, in which case they must both be odd, making the average pitch even. 31 60. It has been pointed out that the wave winding advances in a series of waves or steps, and it is evident that, after making a number of steps equal to the number of poles, the winding must come to the second winding space from that containing the conductor with which the wind- ing started. From this it follows that the total number of winding spaces possible with this form of winding is equal to the product of the number of poles and the average pitch, ± 2, or, as expressed in the symbols previously used, ^v = %py ±^. (484.) It will be noted that this is the same formula as that used for the bipolar drum winding, in which both pitches were given the same direction (formula 483), with the addition of the term/. (See Art. 3148 and Fig. 1171.) 1998 APPLIED ELECTRICITY. 3161. Fig. 1175 is a diagram of a four-pole wave wind- ing, in which y = 9. Therefore, w = 2/ j ± 2 = 34 or 38. The former number (34) is used in this diagram. It will be seen from this diagram that the wave winding results in a two-circuit winding, requiring only two brushes, Fig. 1175. This holds true just as the two-circuit multipolar rings, whatever the number of poles of the field. The advance of this winding is in the same direction as the pitch. If +2 had been used in the formula, 38 conduct- ors would have been required, and the advance would have been opposite in direction to the pitch. If the average pitch had been taken as 8, using +9 for the back and +7 for the front pitch (or vice versa), the APPLIED ELECTRICITY. 1999 same number of conductors might have been used; i.e., w = 2/j/ ± 2 = (2 X 2 X 8) ± 3 = 30 or 34. For bar-wound armatures, it is better to use +3 in the formula, and the same pitch on both ends, if the number of conductors required will allow, since that will give the most economical system of end connections. From Fig. 1175 it will be seen that each brush alternately short-circuits two coils that are in series, and the point where these two coils are connected is the commutator seg- ment that is as nearly as possible opposite the brush that is short-circuiting the coils. 3162. Sometimes it is desired to use a two-circuit armature, but the ordinary form would give too great a dif- ference of potential between segments. Since in this form of winding there are/ coils included between every adjacent pair of commutator segments, an additional commutator segment may be inserted, in such a case, between each pair of segments of the winding as already given, each of these interpolated segments being connected with the segment of the original commutator that is directly opposite it. This is illustrated in Fig. 1176, which shows a four-pole wave wind- ing with 30 conductors, in which the pitch (both front and back) is -[-7. A number of commutator segments equal to the number of conductors (30) is used ; alternate segments are connected to the winding, and each of the rest is con- nected to the segment directly opposite, which is one of those connected directly to the winding. The result of this interpolated segment construction is that, unless the brushes are wider than one segment, only one coil, consisting of two conductors, is short-circuited at a time, and the difference of potential between adjacent segments is only that gen- erated in one coil, instead of that generated in/ (2) coils, as would be the case if the interpolated segments were not used. 31 63. When in the position shown in the figure, the coil formed of conductors 1 and 8 is short-circuited by the — brush. If the armature is rotated in the direction indicated 2000 APPLIED ELECTRICITY. by the arrow, the next coil to be short-circuited is that formed of conductors 9 and 16, by the 4-brush; the next is the coil formed by conductors ^^ and 17, by the —brush; Fig. 1176. and so on, as the armature rotates. (Compare this with Art. 3132.) Only two of the cross-connectors carry the current at any one time, as indicated by the arrow, Fig. 1176. 3164. With more than two pairs of poles, an additional set of interpolated segments must be used for each pair of poles increase over two, and these must be located ^ apart on the commutator, and connected together. This makes such APPLIED ELECTRICITY. 2001 a complicated system of connections that the interpolated segment construction is seldom used for fields with more than four poles, although, when the number of pairs of poles (/) is even, one set of interpolated segments connected to the segments directly opposite may be used, thus halving the difference of potential between segments and the number of conductors short-circuited at a time. Hence, with an eight- pole field, one set of interpolated segments would reduce the difference of potential between adjacent segments to the E. M. F. generated in two coils. 3165. From the formula for the number of winding spaces in the wave winding, zu = '^p y ± 3, it will be seen that w is always twice an odd number when/" is even, as in 4, 8, or 12 pole machines; while w may be twice either an odd or an even number when/ is odd, as in 2, 6, or 10 pole machines. From this it follows that with bar-wound arma- tures arranged for two-circuit single winding, w must be such a number that the number of conductors per slot and 2/, the number of poles, cannot have a commor^^ factor greater than 2. For example, four conductors per slot can not be used in an 8-pole machine, as 4 and 8 have a common factor greater than 2. Four conductors per slot can, how- ever, be used with six poles. It would seldom be the case that a greater number of conductors per slot than four would be desired, owing to mechanical difficulties in con- structing the winding. Unless an interpolated segment commutator is used, the w number of commutator segments is equal to -— , hence is 2 odd when/ is even, and may be either even or odd when/ is odd. 3166. In multipolar drum armatures, end connec- tions similar to those described in Art. 3152 are almost invariably used, especially as almost all the larger sizes of drum-wound armatures employ bars for the active con- ductors and flat strip end connectors, the armature coils then consisting of but two active conductors each. 2002 APPLIED ELECTRICITY. In case it is desirable to use more than two active con- ductors per coil, the type of winding described in Art. 31 53, in which the coils are wound to shape on a separate form and afterwards placed in position on the core, may be very advantageously used, especially with slotted armatures. MULTIPLE WIIVDINGS. 316T. Sometimes in large machines for large current output the size of the conductors required and the volume of current that must be commuted at the brushes are both inconveniently large with the ordinary forms of winding, as already described. To avoid these difficulties, two or more separate windings on the same armature may be employed, each of which will then furnish its share of the required current. A separate commutator may be employed for each winding, in which case the corresponding brushes of each commutator must be connected in parallel; but as this leads to undesirable complications, it is much better to combine the various commutators into one, by inserting the succes- sive segments of one commutator between the similar seg- ments of the other. The various windings are then con- nected in parallel by using a wide brush, which must evidently be of sufficient span to be always in contact with at least one segment that is connected to each winding, so that if there are in separate windings, each brush must have a span not less than that of in segments. Under these conditions, the coils of the successive windings will be short- circuited one at a time, and the volume of current commu- tated will be only — of that which would be short-circuited in if a similar form of single winding were employed for the same current output. Such a winding as has been described is known as a mul- tiple ^winding, to distinguish it from those forms in which the conductors are so connected as to form a single closed- coil winding. Any specific winding is usually spoken of as a double, APPLIED ELECTRICITY. 3003 triple^ etc., winding, according to the number of separate windings employed. 3168. If a given number of conductors which, when connected up into any particular form of single closed-coil winding, will give an E. M. F. of V volts, are so connected as to give in separate windings of the same form, all con- nected in parallel, there will be but — as many of the con- ductors connected in series as in the single winding, hence V the E. M. F. will be only — volts. To apply the formulas given for finding the E. M. F. developed in a winding con- sisting of a certain number of conductors (formulas 480 and 482), it is only necessary then to introduce the term ;;/ (the number of separate windings) into the denominator of the formula, so that for multiple-wound iniiltiple-cimiit windings the formula becomes and for multiple-wound two-circuit windings it becomes p_ cpNS 3169. The principle of multiple winding may be ap- plied to any form of closed-coil winding, if desired, and, further, by properly selecting the number of coils and their order of succession, the end of one winding may be joined to the beginning of the next, and so on, thus forming a single reentrant system of the whole series of conductors. This may also be modified, as will be pointed out, to make the windings form a number of separate reentrant systems which will be some whole factor of ;;/. That is to say, the conductors of a multiple-wound armature having vi wind- ings may be combined as m separate reentrant sj'stems, 1 reentrant system, or a number of separate reentrant sys- tems equal to some whole factor of m. In practice, it is 2004 APPLIED ELECTRICITY. seldom that in exceeds 3 or 4, although it may be any whole number within reasonable limits. The application of the principle of multiple windings to the various types of armature windings will now be taken up. MULTIPLE-WOUND MULTIPLE-CIRCUIT RING "WINDINGS. 31 70. The multiple-circuit winding is the simplest form of ring winding, and, as has already been pointed out, it may be used in fields having any number of pairs of poles without changing the connections. Since the adjacent coils of a single-wound ring are con- nected together, and for multiple windings the separate Fig. 1177. coils of each winding are supposed to lie between successive coils of the others, it follows that, in connecting up the coils of a ring winding to form vi separate windings, each coil is connected to the inth. coil on each side ; that is, in — 1 coils are skipped over in connecting successive coils of the wind- APPLIED ELECTRICITY. 3005 ing. This is shown in Fig. 1177, which represents a two-pole multiple-wound multiple-circuit ring armature of 36 coils, in which 7/i = 2. Consequently, in connecting successive coils, 2 — 1 = 1 coil is skipped once, and alternate coils are connected in each winding. Coils numbered i, 2, S, etc., represent the one winding, and coils 1\ 2\S\ etc., represent the other. 3171. It will be seen that, in connecting alternate coils of the even number (36) which is used in this case, the end of the 18th coil is connected to the first coil, thus forming one reentrant system, so that a fresh start must be made to form the second winding, which, therefore, forms a second reentrant system. Fig. 1178. This results from the fact that the total number of coils is divisible by the number of windings, without a remainder. If the number of coils is so chosen that there is a remain- der, then, after passing through alternate coils once around the armature, the end of the last coil connected will not con- 2006 Applied electricity. nect with the beginning of the coil from which the winding was started, but with one on one side or the other of it, thus starting the second winding, which ends at the begin- ning of the first coil of the first winding; the two windings thus form a single reentrant system. This is illustrated in Fig. 1178, which represents a two-pole multiple-circuit multiple-wound armature having 33 coils, in which 111 = 2, as before. The coils are numbered from 1 to 33, inclusive, in the order in which they are connected. It will be seen that, after passing through alternate coils once around the armature, thus passing through 17 coils, the next coil in succession is coil 18, immediately to the right of coil 1, which is then the beginning of the second winding, which ends with coil 1. 3172. To make a single reentrant winding, when in = 2, the number of coils must be odd. This being the case, the number of commutator segments is odd, and but one coil is short-circuited at a time, unless the brush has a span greater than that of two segments. In the case illustrated in Fig. 1178, coil 26 is short-circuited by the— brush; a moment later, the -{-brush will short-circuit coil 18, then the —brush will short-circuit coil 10, then the -{-brush coil 2, and so on. 3173. In general, for this class of windings (which, as already stated, may be applied to fields having any reason- able number of pairs of poles), if the number of coils, s, is a multiple of the number of windings, ;//, the conductors will connect together into in separate reentrant systems ; while, if the number of coils is mutually prime with vi, the con- ductors will join together into a single reentrant system. For example, a multiple-circuit multiple-wound armature where m = 3 is to have in the neighborhood of 50 coils. If 48 or 51 coils is the number used, three separate reentrant systems will result, each containing -*3^- = 16 or -y- = 17 coils. If 49 or 50 coils are used, a single reentrant system will re- sult. When m = 4, or any even number, the number of APPLIED ELECTRICITY. 2007 reentrant systems that will result with any given number of coils, s, will be equal to the greatest common factor of m and s. Thus, when ;;/ = 4 with 48 coils, the greatest com- mon factor being 4, that number of separate reentrant sys- tems will result; with 49 coils, the greatest common factor is 1, and one reentrant system will result. With 50 coils, however, the greatest common factor is 2, so that two sepa- rate reentrant systems will result, each made up of 2 of the 4 windings. (Compare this with Art. 3171.) MULXIPLE-IVOUND T^VO-CIRCUIT RING WINDINGS. 31 74. The application of the principle of multiple wind- ings to this form of armature winding is not materially dif- ferent from the cases just considered. In the single winding, described in Arts. 3129 to 3133, the number of coils in the winding is found from formula 481,^=/J±1, the last term (±1) being introduced in order that the winding should form a single two-circuit winding. To apply this formula to multiple-wound two- circuit windings, it is only necessary to substitute in, the number of separate windings desired, for 1, which gives the following formula : s=py±m. (487.) If jK (the pitch) is a multiple of in, then s will also be a multiple of ?«, and, as in the multiple-circuit windings, m separate reentrant systems will result ; while if j and m are mutually prime, then s will not be a multiple of in, and a single reentrant system will result. In fact, the number of separate reentrant systems which will result with any given number of coils will be equal to the greatest common factor of in and y. 3175. For example, a four-pole two-circuit ring wind- ing, with a pitch of 11 and 3 windings (j = 11, in = 3) could have s =p y ± 3 = 22 ± 3 = 25 or 19 coils, and 11 and 3 be- ing mutually prime, a single reentrant system would result with either number. Fig. 1179 represents the above case, 2008 APPLIED ELECTRICITY. 25 being the number of coils used. It will be seen that this winding is of the same type as the single winding illustrated in Fig. 1166. In this case the coils are numbered from 1 to 25; in addition, the numbers 1', 2\ S', etc., show the order in which the successive coils are connected. This being a Fig. 1179. triple winding, the brushes are made of the same span as three segments; the +brush short-circuits coils 8 and 19, and the —brush short-circuits coils 2 and 13, the rest of the coils having arrow-heads showing the direction of the current in them. Each of the three windings of this example being a two- circuit winding, there are six circuits through the armature. On tracing these out, starting from the —brush, it will be APPLIED ELECTRICITY. 2009 found that the various coils are divided among the circuits as follows: ' j 1 — 12 — 23 — 9 — 20 ) "^ •j 15- 4_18-7 j (25 — 11 — 22 I I 4- j 24 - 10 - 21 ) ^ ( 16- 5 ) , This indicates an extreme irregularity in the number of coils in each circuit, but this is only due to the small num- ber of coils necessarily used in the diagram. In any wind- ing as actually used the irregularity would be almost inappreciable. Fig. 1180. 3176. Fig. 1180 is a diagram of a four-pole two-circuit double-wound armature of the same type as that illustrated 2010 APPLIED ELECTRICITY. in Fig. 1167. For this type of two-circuit ring winding, formula 487 is used; but to obtain an even distribution of potentials around the coramutator only the —sign should be employed; i. e., s=p j — in. In this case j= 11; hence, J- — 22 — 2 = 20. As y and in are in this case also mutually prime, the winding forms a single reentrant system. As in Fig. 1179, the coils are numbered i, 2, 3, etc., and the num- bers 1', 2\ 3', etc., show the succession in which the coils are connected. Coils 1, 12, and 3, and their connections, are drawn in heavier lines than the rest, to better show the plan of connection. Although this is a double winding, the brushes must be made of a span equal to at least that of 3 segments, as shown, in order that they may be in connection with both Avindings all the time. This width is necessary because each coil is connected to two adjacent segments. In the position shown, the -fbrush short-circuits coils 1 and 11, and the —brush short-circuits coils 16 and 6; the direction of the current in the remaining coils is indicated by the arrow-heads, as before. The four circuits of this armature are made up as follows, starting from the —brush: ' j 17-8-19-10 ) ~ (15-4-13- 2 f j 7 - 18 - 9 - 20 I I — 14 _ 3-12 f This winding is much more regular than that shown in the previous figure, but this is not an essential feature of this form of winding, being due to the even number of coils and windings. 3177. In case it is desired to make the cross-connec- tions a part of the commutator construction, which is usually more desirable, the angular span of the cross-connections should be the same throughout, in order that the cross- connections may be symmetrical. With the winding as shown, this is not the case, for the leading segment of coil 1 is connected to the lO^A segment APPLIED ELECTRICITY. 2011 to the right, while the following segment of the same coil is connected to the 21st segment, also to the right. If, instead of connecting the two ends of each coil to ad- jacent segments, they are connected to two segments which are separated by a third, the inequality in the spans of the cross-connections disappears, and they become symmetrical. This, however, causes the leads from the armature coils to the commutator segments to cross, requiring extra pre- cautions in insulating. In case the winding were triple, quadruple, etc., the two ends of each coil would be connected to two segments sepa- rated by 2, 3, etc., others; that is, in general, the two com- mutator segments to which each coil of the in windings is connected would be separated by ni — 1 other segments, if it be desired to make the cross-connections a part of the commutator construction. MULTIPLE- W^OUND MULTIPLE-CIRCUIT DRUM "WIIVDIIVGS. 3178. The conditions governing the multiple-circuit multiple-wound ring windings also apply to this class; in addition, the influence of the difference between the ring and the drum form of coil must be taken into account. As each coil of the drum winding is made up of two active parts, each occupying a winding space, the number of winding spaces, w, must be even. The back pitch, which determines the number of winding spaces included between the two active parts of a coil (see Art. 3139), needs only to be made of such value that the two parts of the coil shall not be in any one field at the same time, which implies that the angular span of the coil should not be much greater or less than -^r—» Zp The front pitch, which determines the numbei: of winding spaces included between similar parts of two successive coils, is determined by the number of separate windings used. In the multiple-circuit single-ivound drum winding, the front pitch = back pitch ± 2; that is, a winding space, belonging to another part of the winding, intervenes between the adjacent parts of successive coils. 2012 APPLIED ELECTRICITY. In the multiple windings, in addition to the winding space for another coil of the same winding, there must also be included between the adjacent parts of successive coils two winding spaces for each of the other windings. Conse- quently, the difference between the front and back pitches must be 2 in. In practice, the front pitch is made less than the back pitch for reasons already given. (Art. 3145.) Both pitches must be odd, and the front pitch must be opposite in direction to the back pitch. 3179. As in the multiple-circuit multiple- wound ring windings, the number of separate reentrant systems formed by the windings will equal the greatest common factor of the number of coils and the number of windings; the number of coils being equal to one-half the number of winding spaces, the number of reentrant systems is equal "IV to the greatest common factor of — and in. Any even 2 number of winding spaces may be used, whatever the number of poles. In order to prevent opposing E. M. F.'s in a coil, the number of winding spaces should be about equal to the product of the number of poles and the average of the front and back pitches. (Compare Art. 3156.) It is usually rather better to make the number of winding spaces a little greater than this product, as in this case the end connec- tions are a little shorter. 31 80. Fig. 1181 shows a diagram of a four-pole mul- tiple-circuit double-wound drum armature having 20 coils (w = 40). The back pitch is taken as +13 ; hence, the front zv pitch = -(13 - 2 in) = - (13 - 4) = - 9. y (20) being a multiple of in (2), this gives two separate reentrant systems. A single conductor is represented in each winding space, numbered i, 2, 3, etc. ; the order in which the conductors making up the first of the two windings are connected is indicated by the numbers i', 2 ', 3', etc., and the order of connection of the conductors of the second winding is indi- APPLIED ELECTRICITY. 2013 cated by the numbers 1" , 2", 8", etc. Each brush short- circuits a single coil, and the short-circuited conductors Fig. 1181. 2, 9, 12, 19, 22, 29, 32, and 89 are indicated by the absence of the arrow-heads, which on the rest of the conductors indicate the direction of the current in them. MULTIPLE-TV^OUIVD TTI^O-CIRCUIT DRUM WINDINGS. 3181. The principles and formulas given for two-cir- cuit single-wound drum windings require only slight modi- fications to adapt them to this class of windings. The front and the back pitches being in the same direction may be alike or may differ by 2. In either case, each pitch must be odd ; so, if both pitches are alike, the average pitch 2014 APPLIED ELECTRICITY. must be odd, but if they differ by 2, the average pitch may be even. In the single-wound two-circuit drum winding it was pointed out that, in passing through the winding, the second winding space to one side or the other of that at which the start was made would be arrived at after passing under each pole in succession, and from this the formula given for the number of winding spaces was derived. In the multiple-wound two-circuit drum windings, in ad- dition to this one winding space belonging to the sa7n^ winding, two others for each of the other windings of the armature must also intervene between the winding space started with and that passed through after making one series of steps around the armature. From this it follows that the total number of winding spaces allowable will be given by the formula w = 2p y ±2m, (488.) y being the average pitch, and/ and in being the number of pairs of poles and the number of windings, respectively, as before. As in all two-circuit windings, only two brushes are necessary, although two for each pair of poles may be used if desired. The number of separate reentrant systems formed will be equal to the greatest common factor of m (the number of windings) andy (the average pitch). 3182. In Fig. 1183 is shown a diagram of a four-pole, double-wound, two-circuit drum armature, having the same number of coils (20) as the multiple-circuit armature illus- trated in Fig. 1181. In this case the pitch, both front and back, is taken as 9, and the number of winding spaces found from formula 488, as follows: w = 2/ J ± 2 w = 36 ± 4 = 40 or 32. In this case 40 winding spaces was the nvimber used. As before, one conductor in each winding space is represented, they being numbered 1, 2, 3, etc. Since the greatest com- mon factor oi y (9) and m (2) is 1, this winding results in a APPLIED ELECTRICITY. 2015 single reentrant system, the order in which the conductors are connected being indicated by the numbers i', 2', 3', etc. Two brushes are shown, the +brush short-circuiting the coils formed from conductors 13, 22, 31, and 40, and the — brush short-circuiting the coils formed from conductors 3, 12, 21, and 30, these being indicated by the absence of the Fig. 1182. arrows which, with the other conductors, indicate the direc- tion of the current in them. The path of the current through the four circuits of this armature, starting from the — brush, is as follows: j 1-10-19-28-37- 6-15-24-33-2 ) ■j 32-23-14- 5-3G-27-18- 9 ) j 39- 8-17-26-35- 4 ) 1 34-25-16- 7-38-29-20-11 ) + 2016 APPLIED ELECTRICITY. It will be seen that some irregularity is indicated,. owing to the coils short-circuited by the —brush being taken wholly from the second winding. With the necessarily large number of conductors used in practice, the difference between the number of conductors in the different branches of the winding forms such a small percentage of the whole number employed as to make its effect negligible. 3183. One of the principal advantages of multiple winding as applied to drum armatures appears when bar windings (a single conductor per winding space, with sepa- rate end connections) are used. In this form of winding, the bars are usually set in slots cut in the periphery of the armature core, and it is very de- sirable that the number of slots adopted for any particular size of armature be such that they may be used for windings giving different voltages, without change. Thus, for exam- ple, of the two windings illustrated in Figs. 1181 and 1182, the two-circuit winding (Fig. 1182) will evidently give twice the E. M. F. that the multiple-circuit winding (Fig. 1181) will with the same number of revolutions and in a magnetic field of the sam.e. strength, the only change made in the winding being in the span and arrangement of the end con- nectors. The same result may be attained by changing the multiple-circuit winding from a multiple-wound to a single- wound armature, which would be accomplished in this case (Fig. 1181) by reducing the back pitch to 11, or increasing the front pitch to —11. The two-circuit winding can not be so changed, however, in a four-pole machine, as an odd number of coils is required for the single winding (Art. 3165); but when the number of pairs of poles is odd, as in a six-pole machine, an even number of coils may be em- ployed for the single winding, and this may be changed to a double winding by changing the end connections, if desired, and the features of the two-circuit winding retained. 3184. For example; suppose that, having decided on a certain number of revolutions and a certain number of lines of force in the field, it is found that 358 conductors are APPLIED ELECTRICITY. 3017 required for a six-pole, single-wound, two-circuit, bar-wound drum armature, to give 500 volts. From formula 484, w = 2/j±2, the required pitch may be found; since zv=. 358 and / = 3, 358 = 6 X J ± 3, from which y = ^^ = 59.3 + or ^^ = 60, which latter value would necessarily be used, fractional pitches being an ab- surdity. As the front and back pitches must each be odd, to have the average pitch 60, the front and back pitches may be 59 and 61, respectively. In case it was desired to use the same armature for a 250- volt machine, the same number of conductors might be used, by so changing the pitch as to make a double winding. The proper pitch to use would be found from formula 488, ■w = 2 p y ± 2 7u; zv = 358 as before, / = 3, and 7U = 2, and 358 = 6 X/± 4; hence, j = 3|_4 = 59^ or -^ = 60.33+. 59 would be taken as both front and back pitch. It would thus be only necessary to slightly change the end connect- ors for the l>ack pitch, to use the same armature for either a 250-volt or a 500-volt machine. THE MAGNETIC CIRCUIT. 3185. As far as the generation of the E. M. F. of the dynamo is concerned, it is only essential that the lines of force of the magnetic field be present at the points where they are cut by the conductors, and have the proper direc- tion and distribution. However, since each line of force is continuous, forming a closed circuit, provision must be made for a complete path for the lines of force to and from the points where they are cut by the conductors, and through the magnetizing coil or coils wherein they are gen- erated. Of course, they might be left to find their own cir- cuit through the surrounding air, but in order to realize the large number of lines of force required with the expenditure of a reasonable amount of magnetizing force, it is necessary that the path of the lines of force be of as great a perme- ability as possible; i. e., through an iron or steel magjietic circuit. 2018 APPLIED ELECTRICITY. In addition to the armature and its winding, a bipolar or multipolar dynamo must then have an iron or steel frame, or Jield-jnagiiet, which, completes the magnetic circuit out- side the armature. This frame is made up of one or more pairs of pole-pieces, from (or into) which the lines of force pass to (or from) the armature through the spaces between the faces of the pole-pieces and the surface of the armature core, which are called the air-gaps ; it must also have a part upon which the magnetising eoils are wovmd, which part is called the field core. The part of the frame that joins together the field cores, if more than one is used, or that joins the pole-pieces and the field cores, is called the magnetic yoke. CONSTRUCTION OF FRAME. 3186. It will be seen that the object of the frame, as a whole, is to so guide the lines of force that are generated by the current in the magnetizing coils that they will enter and leave the armature at the proper points, forming the mag- netic field in the air-gaps of the required distribution and density. It is not essential to the operation of the machine that the frame be of any given form or size, so long as the lines of force are properly delivered to the armature; economy in materials or labor, mechanical strength, and other consider- ations determine the form and size of frame to be adopted. 3187. Since the magnetic circuit may be considered analogous to the electric circuit, it will be seen that in order to obtain a large number of lines of force with a moderate magnetizing force, the reluctance of the circuit must be low; that is, the iron should be of considerable cross-section and the circuit of mioderate length. It should be remem- bered that, since the permeability of the best of iron is only, perhaps, 1,500 times that of air, a considerable number of lines of force that pass through the magnetizing coil com- plete their circuit around through the air without passing APPLIED ELECTRICITY. 2019 through the air-gaps. To reduce this magnetic leakage as far as possible, surfaces between which there is a great difference of magnetic potential should be kept as far apart as the design of the magnet will allow, and made of as small area as possible. In any case, some ~ leakage is bound to occur, and this must be provided for by making those parts of the frame through which the leakage lines pass of sufficient area for both the useful and the leakage lines. The conditions which govern the leakage will be more fully discussed later; in general, the area of the iron in the frame must be sufficient for from 15 to 50^ more lines of force than are used in the armature. DENSITY OF LINES OF FORCE. 3188. Referring to Fig. 952, it will be seen that the saturation curves there shown all rise in a nearly straight line for some distance from 0, then curve away from the axis of the ordinates and follow another approximately straight line, which makes a much greater angle with the axis of the ordinates than does the first-mentioned line. This effect is much more marked in the case of wrought iron and cast steel than with cast iron, but in any case it will be seen from this feature of the saturation curves that the most economical density at which to work the iron of the magnetic circuit is that in the vicinity of the bend or "knee " of the curve. A much lower density could not be economically used, because a considerable increase in the number of lines of force could be obtained with comparatively little increase in the magnetizing force required ; and on this account accidental small changes in the magnetizing force would produce a considerable change in the number of lines of force, so that the magnetic circuit of the machine would be in an unstable condition. A much higher density would not be economical, because the increase in the number of lines of force could be obtained only by a very considerable increase in the magnetizing force. 2020 APPLIED ELECTRICITY. 3189. Applying these statements to the curves given in Fig. 952, it will be seen that, in general, cast steel and wrought-iron forgings should be worked at densities of be- tween 80,000 and 100,000 lines of force per square inch, while sheet iron may be worked higher, between 90,000 and 110,000 lines of force per square inch. With cast iron, the curves being flatter, the allowable range is somewhat greater, the usual range in practice being from 25,000 to 50,000 lines of force per square inch, the latter value being used only in the case of the best grades of soft, gray cast iron. The best densities to use are, therefore, not those that give the maximum permeability of the iron used, as at that point the iron would be in the unstable condition referred to previously. 31 90. From the above and from the curves referred to, it appears that for the same expenditure of magnetizing force a cast-iron magnetic circuit must have about twice the sectional area of one of cast steel or wrought iron, in order to realize the same number of lines of force, so that the cast- iron magnetic circuit would be about twice as heavy as one of steel or wrought iron; its less cost per pound, however, may often counterbalance this extra weight, and, in fact, the choice of materials for the frame, as well as almost all the other features of a dynamo, depends upon the local con- ditions governing each particular case. 3191. The density used in the air-gaps varies, but the best practice fixes it at somewhere in the neighborhood of 30,000 lines of force per square inch; this depends, however, on many other features of the design, as will be pointed out later. In any case, the amount of the magnetizing force that is required to force the magnetic flux through the air-gaps is a large proportion of the total amount, since the permeability of the air-gaps is 1, which much more than compensates for their comparatively short length. APPLIED ELECTRICITY. 2021 FORM OF MAGNETIC CIRCUIT. 3192. The form of the magnetic circuit is subject to many variations; there are, however, two general classes into which they may all be divided. In the first, a single source of magnetizing force for each pair of poles (which may reside in one or more magnetizing coils) sends the lines of force around through a magnetic circuit, of which the air- gaps and armature directly form a part. Such an arrange- ment is said to have salient poles. In the second type, at least two magnetizing forces are necessary for each pair of poles; these magnetizing forces act in opposite directions upon a complete magnetic circuit, and the opposing lines of force cause consequent poles to appear at points on the mag- netic cfrcuit, which points are properly provided with pole- pieces, between which the armature is located. Such an arrangement is said to have consequent poles. 3193. One of the simplest forms of salient-pole bipolar field-magnets is represented in Fig. 1183. In this form the magnetizing force is supplied by the single coil shown in section at W and W. ' This surrounds the field core C^ to which are attached the magnet yokes 3f and Af, which termi- nate in the pole-pieces iV and 5. Be- tween these pole-pieces the armature A revolves. The mean paths of the lines of force through the magnetic circuit (neglecting leakage lines) are fig. 1183. indicated by the dotted lines having the arrow-heads, which indicate the direction of the lines of force, assuming the polarities of the pole-pieces to be as indicated by the letters N and 5". In this figure the field core is represented as being vertical, and this type of magnet is so used in certain ma- chines of English make. It may, however, be either vertical or horizontal, and be above, below, or on either side of the armature, as desired. The Jenney motors, the Wood bi- polar machines, the Holtzer-Cabot small motors, and others 2022 APPLIED ELECTRICITY. made in this country use this type of magnets with the coil horizontal and below the armature. Further, the armature shaft may either have the direction indicated or be at right angles to that direction, if desired, without changing the character of the field-magnet. The mechanical construc- tion in this last case would evidently be bad, and, in general, this is the principal feature which determines the disposition of the magnet frame with regard to the armature. 3194. A form of consequent-pole field-magnet which is derived from that just described is shown in Fig. 1184. This form of field-mag- net is known as the " Manchester type," and is used by the Mather Electric Co., the West- inghouse Co., and others in this country. This is practically the same form of magnet as Fig. 1184. that shown in Fig. 1183, with the addition of a second similar magnet situated on the opposite side of the armature A, as indicated by the letters N', M\ C, M\ and S'. Assuming that the same total number of lines of force passes through the armature in each case, it follows that with the consequent-pole magnet (Fig. 1184) each half of the magnetic circuit contains half the total number of lines, and needs, therefore, to be of but half the sectional area of the frame of the salient-pole magnet, which carries all the lines of force, as is indicated by the relative proportions of the two magnets. (See Figs. 1183 and 1184.) Conse- quently, the weight of the frame in either case is about the same. 3195. In the consequent-pole magnet, the magnetic circuit in each half is approximately the same length but of half the area as that of the salient-pole magnet; its reluc- APPLIED ELECTRICITY. 2023 tance is about twice as great, but since it carries half the number of lines of force, it follows that the magnetizing force required for each half oi the consequent-pole magnetic circuit is the same as that required for the whole of the salient-pole magnet. However, the magnetizing coils on the consequent-pole magnet are of smaller diameter than those used in the salient-pole magnet, so that the weight of copper used for the magnetizing coils of the former type of magnet is not double that required for the latter type. The actual ratios of weights of copper and iron may be readily calculated for any particular case, but there are other conditions that influence the choice of the form of magnet to be used, which must be taken into account. 3 1 96. Fig. 1185 shows the adaptation of these two forms of field-magnets to a multipolar machine. In the figure, the part to the left of the vertical diam- eter represents the salient-pole magnet, and that to the right represents the con- sequent-pole magnet, each being laid out as for an eight-pole magnet. The salient - pole magnet consists of a number of separate magnets, each with its magnetizing coil. It is, therefore, nec- essary to supply some separate support for these magnets. In the consequent-pole magnet, however, the whole frame is continuous, each pole-piece being sup- ported by a field core on each side, the frame, therefore, being of sufficient mechanical strength for its own support. Fig. 1185. 2024 APPLIED ELECTRICITY. In the latter form, the mean length of the magnetic circuit for each pair of poles is less than with the salient-pole mag- nets, which results in a slight saving in magnetizing force, other things being equal. Of the above types of magnets for multipolar machines, the salient-pole type is used in the " Perrett " machines, built by the Electron Manufacturing Co., and the con- sequent-pole type is used by the Standard Electric Co., in this country, and in several types of machines made abroad. 3197. The two simple forms of field-magnets which have been described may be. considerably modified by changing the position or increasing the number of the field coils. For example, the magnetizing coil of the salient-pole magnet (Fig. 1183) may be wound over the entire frame from pole-piece to pole-piece, as in the " ring-type " machine of the Mather Electric Co. Similarly, the magnetizing coil on each half of the consequent-pole magnet (Fig. 1184) may be wound over the entire frame from pole-piece to pole- piece, as in the " C & C " machines. In both these examples, the field cores are made approximately circular in outline. Further, by dividing the magnetizing force between two coils, and locating these coils in the part indicated as the magnet yoke in Fig. 1183 (J/ and J/), a type of field - magnet results which is commonly known as the horseshoe type, as illus- trated in Fig. 1186. It will be seen that in these two forms the magnet yoke (M) of each corresponds to the field core of the other. This Fig. 1186. type of field-magnet is very extensively used for bipolar machines, the Thomson-Hous- ton, Crocker- Wheeler, Connecticut, Keystone, and other makes of machines using it in the position shown, i. e., with the magnet frame beneath the armature. APPLIED ELECTRICITY. 2025 The General Electric Co. in their Edison machines, the Commercial Electric Co., the Eddy Electric Manufacturing Co., and others, use the same form of magnet in the reverse position, i. e. , with the magnet frame above the armature. The Excelsior arc machine employs the same type of magnet, but with the armature shaft parallel to the field cores, passing, therefore, directly through the magnet yoke. The pole-pieces are necessarily modified in shape to suit the changed position of the armature, and are extended to embrace three sides of the armature, which is ring wound. 3198. The consequent-pole magnet that results from combining two horseshoe magnets of the types illustrated in Fig. 1186 is shown in Fig. 1187. Here the various letters have the same reference as in the previous figures. As in that previously described, the consequent-pole ar- rangement requires only half the cross-section of metal in each half of the magnetic circuit, but the total amount used is about the same. This is also a commonly used type of bipolar field-magnet. Among others, it is used in the Wood arc machine of the larger sizes, in the position represented in the figure, i. e., with the field cores {C, C, C, C) vertical. The Weston and the Schuyler arc machines use fig. US'? the same form of field-magnet, but with the field cores horizontal, and it has also been used in this same position for various special machines built by the General Electric Co. and others. The smaller sizes of the Wood arc machine use this form of magnet with the field cores horizontal, and with the shape of the pole-pieces modified so as to allow of the armature shaft being parallel to the field cores, it passing through and 2026 APPLIED ELECTRICITY. having its bearings in the yokes {MandM). The Brush arc machine uses a similar construction, but the armature is made in the form of a ring-wound disk, and the pole faces face the end faces of the armature, as represented in the diagram. Fig. 1188. The magnet in this case might be considered to be two separate bipolar, salient- pole, horseshoe magnets. •AVAwar VAVi |W/ftW.V.*4 - ffi •••••••••• s^ WWAW AVMAVft ^JWWWW 3 1 99. By carrying the magnetizing coils still fur- ther along the frame, until they are as close as possi- ble to the ends of the pole- pieces, still another type of field-magnet results, as represented in Fig 1189. As shown, this is a very heavy and clumsy magnet, requir-. ing a large amount of material on account of the length of the magnet yoke, MM. If, however, half the material in this yoke be located on the other side of the armature, so that the magnetic circuit through the frame from field core to field core consists of two branches, a much neater and FIG. 1188. Fig. 1189. lighter magnetic circuit, that is quite extensively used, results, as represented in Fig. 1190. This form of circuit still has salient poles, since the poles are produced by the direct action of the magnetizing forces,, and not by the opposition of two magnetizing forces. APPLIED ELECTRICITY. 3027 M M It has the advantage that the magnetizing coils and armature are enclosed by the frame, thus affording them mechanical protection. This type of magnet is used (in the position shown) by the makers of the " Detroit " dyna- mos, by the Western Electric Co., and by others in this country and abroad. The Thomson-Hous- ton arc-lighting dyna- fig. ii90. mos also employ this type of field-magnet, the form being modified by making the magnet yokes of a series of round, wrought-iron bars, which connect together circular flanges on the ends of the field cores, thus making the general outline cylindrical. Eickemeyer has used it for very compact machines in which the magnetizing coils actually enclose the armature, the field cores being very short. The same form of magnet, but with the magnetizing coils above and below the armature, was used in the old Hoch- hausen dynamos, also by the Thomson-Houston Company for their old " S. R. G." railway motors, and by others. 3200. With this arrangement of the magnetizing coils, a consequent-pole bipolar magnet is not possible; but by reversing one of the coils so that the two magnetomotive forces are opposite, two conse- quent poles will be formed on the magnet yokes M and M, Fig. 1190, at a point opposite the neu- tral spaces of the bipolar Fig. 1191. form; and by locating 2028 APPLIED ELECTRICITY. suitable pole-pieces at these points, a four-pole magnet results, as represented in Fig. 1191. It will be seen that this mag- net has one pair of salient poles N and N, and one pair of consequent poles 5 and vS. This gives a very compact form of four-pole magnet, and is used in several types of railway motors, in the "Eddy" slow-speed stationary motors, and by other makers. The "Wenstrom" dynamos also employ a somewhat modified form of this type of field- magnet, the magnet yoke being barrel-shaped and com- pletely enclosing the magnetizing coils and pole-pieces, spaces being left in the sides for the removal of the armature. 3201. By winding magnetizing coils around the con- sequent poles of the type of magnet illustrated in Fig. 1191, they become salient poles, giving still another type of field-magnet, illustrated in Fig. 1192. The same letters of reference are used in this figure as in the previous ones. This is a very useful form of field-magnet, and is that most generally used in this country for multipolar machines of any number of poles, almost every maker using it for multipolar generators and alternators. The various magnet yokes form a complete ring, which is often, especially when six or Fig. 1192. , more poles are used, made circu- lar in outline. A modification of this form of magnet is used by the Siemens & Halske Company, in which the field cores project radially outward from a common hub, instead of inward, the armature revolving outside the poles of the magnet. 3202. The number of possible forms of field-magnets is very great, although they may all be classed as either salient or consequent pole magnets, or combinations of the two. Many of the forms of magnets which have been and APPLIED ELECTRICITY. 2029 are used seem to have been designed merely with a view to getting something different from any other maker, and considerations of economy of material or of mechanical fitness, which should prevail in the selection of a design, have been largely neglected. These forms described are the basis of the designs of field-magnets in modern construction. METHODS OF EXCITING THE FIELD. 3203. The requisite number of ampere-turns for exciting the field of a dynamo-electric machine may be obtained in a variety of ways. In the first place, the cur- rent which flows through the magnetizing coils may come either from some separate external source, the machine being then said to be separately excited, or it may be furnished by the ar- mature of the machine itself, it being then said to be self- excited. In some cases a combination of separate and self-ex- citation may be used. A diagram illustrating separate excitation is given in Fig. 1193. The current required is in this case supplied by the primary or secondary battery B, fig. 1193. although another dynamo may be used, if desired. In order to adjust the current in the magnetizing coils to the proper value, or to vary it if necessary, an adjustable resistance r is included in the field circuit. The armature has no connection whatever with the field circuit, but supplies the external circuit, Re^ directly. 3204. It is evident that with self-excitation a small or a large current may be used in the magnetizing coils, accord- 2030 APPLIED ELECTRICITY. Ing to the nature of the source of the current, a large or a small number of turns being used in the magnetizing coils to give the necessary magnetizing force. Alternators are usually separately excited, since the cur- rent given out by the machine, being alternating, can not be used directly for the purpose. Separate excitation has also the advantage that variations of the output of the armature of the machine, caused by changes in the speed or of the current, do not directly affect the field excitation. SERIES WINDING. 3305. There are three general methods by which self- excitation is accomplished. In the first, the whole of the current flowing through the armature also flows through the magnetizing coils; such a machine is said to be series -wound, from the fact that the armature and magnetizing coils are con- nected in series. This ar- rangement is represented in the diagram shown in Fig. 1194. With this arrangement, the magnetizing force act- FiG. 1194. ing on the magnetic circuit, consequently the number of lines of force in the magnet, varies with the current which the machine furnishes to the external circuit; therefore, when the armature is running at a constant speed, the E. M. F. which is generated in it varies as the current varies, though not necessarily in the same proportion. This is not usually desirable, since most applications of direct current require that either the E.M.F. or the current be maintained approximately constant. 3206. To realize either of the above conditions in a series-wound dynamo, it is necessary to adopt some method APPLIED ELECTRICITY. 2031 of regulation, whereby either the effect of variations in the current on the magnetizing force of the field may be neu- tralized or the effective E. M. F. of the armature may be altered to suit the conditions. The former result may be obtained by placing an adjustable resistance in parallel with the magnetizing coil, as represented in Fig. 1195. In this diagram, 5 F represents the magnetizing coil, or series field, and R is the adjustable resistance, connected in parallel with the magnetizing coil, as described. It will be SF Fig. 1195. seen that the current divides between the two branches of this part of the circuit, and by varying the resistance R the proportion of the whole current that flows through the magnetizing coil 5i^may be varied as required. The method of varying the effective E. M. F. that is used in the Thomson-Houston open-coil armature has already been described (Art. 3086). Another method of accom- plishing the same result with closed-coil armatures is to shift the brushes away from the neutral point, which entails special construction and precautions against destructive sparking, etc. 3207. Series winding is very little employed in dyna- mos, except for machines designed to give a constant cur- rent, such as is used for operating lamps or other devices that are connected in series. For motors, however, series winding is very useful, since when starting up under heavy load, or whenever taking a current in excess of the normal 2033 APPLIED ELECTRICITY. amount, the field strength is increased, which increases the. amount of the reaction between the armature winding and the field, that is, increases the turning force of the armature. SHUNT A^INDIXG. 3208. The second method of self-excitation consists of forming a separate circuit of the magnetizing coils, which are connected directly between the brushes, or in shunt to the external circuit, this style of winding being, therefore, known as shunt ^winding. This is illustrated in Fig. 1196. It will be seen that the magnetizing-coil circuit is in a measure independent of the external circuit {Re), it being exposed at all times to the full difference of potential that exists between the brushes {-{-B and —B) ; from this it follows that changes in the current flowing in the external circuit do not affect the magnetizing force acting on the field, except as they may change the difference of potential between the brushes. Changes in the current of the external circuit do affect this quantity in several ways, namely, by varying the drop due to the resistance of the Fig. 1196. armature winding, by varying the counter inagnetomotive force of the armature winding, and by varying the length of the path of the lines of force by the variations in the amount by which they are distorted by the cross magneto- APPLIED ELECTRICITY. 2033 motive force. (See Arts. 3115 and 3118.) This last is comparatively unimportant, but the other two require care- ful consideration in the design of dynamo machinery, as will be pointed out. 3209. In a shunt-wound motor the conditions are dif- ferent, the magnetizing-coil circuit being supplied directly from the mains; the magnetomotive force then depends simply upon the difference of potential between the supply mains, which is usually kept constant, so that in general a shunt-wound motor may be considered to have a constant magnetizing force acting on its field-magnet. COMPOUND IVIIVDING." 3210. From the above statements it will be seen that in order to maintain a constant difference of potential be- tween the brushes of a dynamo (assuming a constant speed), the magnetomotive force of the magnetizing coils must be increased as the current increases, both to increase the number of lines of force so as to increase the E. M.- F. generated, and to make up for the counter magnetomotive force of the armature winding. One way to accomplish this result is to place an adjustable resistance (r. Fig. 1196) in the magnetizing-coil circuit, which may be gradually cut outvas the current output increases, thus reducing the resistance of the magnetizing- coil circuit, and increasing thereby the current flowing through it. This, however, requires personal attention, automatic devices for vary- ing the resistance not being satisfactory, and in case the current from the dynamo fluctuates rapidly, it is diffi- cult to operate the resistance with sufficient rapidity. Since the amount by which the mag- Pie ^g^^ +r 2034 APPLIED ELECTRICITY. netomotlve force of the magnetizing coils must be varied is closely proportional to the current flowing, which follows from the nature of the causes which require the variation, it is possible to obtain the required variation by providing additional magnetizing coils through which the main cur- rent passes. This is known as compound ^vinding, and is illustrated in Fig. 1197. 321 1. It is evident that this is a combination of series and shunt winding, the shunt winding furnishing a constant magnetizing force and the series winding an additional mag- netizing force which is proportional to the current output of the machine. This latter winding is so proportion'ed that it furnishes the proper increase in the magnetomotive force, as the current increases, to make up for the dropping off of the difference of potential between the brushes that would otherwise occur. For certain classes of work, a little more than this amount is provided, so that the difference of po- , tential between the brushes rises slightly as the current out- put increases. In such a case the machine is said to be over-compounded. 3212. Compound winding is seldom used for motors, as either a series or a shunt winding serves for almost all con- ditions of operation. Nevertheless, for application to such machinery as printing-presses, a compound winding is ex- tremely useful, as the series turns produce a powerful field at starting and at slow speed, and they may gradually be cut out or connected in various combinations to produce different working speeds without the necessity of inserting an external resistance in the armature circuit, except for starting up, when a resistance may be temporarily used. BUILDING UP THE FIELD. 3213. Any iron, after being magnetized, retains a certain amount of residual magnetism, so that there will be a small E. M. F. generated in the armature winding when the armature is rotated and the field circuit left open; this APPLIED ELECTRICITY. 2035 is utilized to start the current in the magnetizing coils. In the case of a shunt-wound dynamo, when the machine is started and the magnetizing-coil circuit closed, the small E. M. F. generated in the armature by the residual magnet- ism sends a small current through the magnetizing coils, producing a small magnetizing force. If this magnetizing force tends to send lines of force through the magnetic cir- cuit in the same direction as the residual magnetism, the number of lines of force will be increased; this will increase the E. M. F., which increases the current in the magnet- izing coils, and still further increases the number of lines of force and the E. M. F., which process continues until further increase in the magnetizing force results in so little increase in the number of lines of force that the E. M. F. generated becomes steady, the windings being so designed that this shall be the E. M. F. at which it is desired to run the machine. It will be seen that if the external circuit is open, all of the current that the E. M. F. (due to the residual magnet- ism) produces flows through the magnetizing coils; if, how- ever, the external circuit is closed, only a part of the current flows through the magnetizing coils, so that the field will "build up " more slowly than with the external circuit open, and, in fact, will not build up at all if the external resistance is low as compared with the armature resistance. From this it follows that a shunt-wound machine should be started up with its external circuit open. A series-wound machine, on the contrary, must have its external circuit closed in order that any current may flow through the magnetizing coils, and the lower the resistance of the external circuit the more quickly will the machine build up. From the above it will be seen that a compound-wound dynamo may be started with its external circuit either open or closed, since it has both series and shunt wound coils. Usually, however, such machines are started and brought to their full E. M. F. with the external circuit open. 3036 APPLIED ELECTRICITY. 3214. At starting, while the current is increasing in the magnetizing-coil circuit, the inductance of the magnet- izing coils increases its apparent resistance, and a part of the energy supplied to the coils is stored up in the magnetic field which is being established. As soon as the current in the magnetizing coils reaches its maximum value, however, and so long as it remains constant at this value, there is no reactance present, and the entire amount of energy delivered to the coils is expended in heating the wire ; that is, it re- quires (directly) no energy to maintain a magnetic field at a constant value, the field depending on the ainpei'e-tiirns that are acting on the magnetic circuit. It is obvious, how- ever, that in order to force the current through the wire of which the magnetizing coil is composed, energy must be expended, but this energy appears entirely as heat, and, con- sequently, is wasted as far as any practical application of it is concerned. The number of watts expended in sending the current through the magnetizing coils should, therefore, be made as small as the design of the machine will permit, both to prevent any excessive waste of energy and to prevent possible damage by the heat liberated. In practice, the loss of energy from this cause varies from about 2 per cent, of the total output of the machine in larger sizes, to 5 or more per cent, in the smaller. 3215. In shunt- wound machines the magnetizing coils are exposed to the full difference of potential that exists be- tween the brushes of the machine, and, consequently, should use only a small amount of current in order that the loss in watts should be the required small percentage of the output. From this it follows that the wire used for the magnetizing coils should be of small size and of considerable length, making a large number of turns around the magnets, both to give the necessary resistance to keep the current at its proper value and to allow of this small current furnishing the requisite number of ampere-turns. In series-wound machines, however, as the total current flowing gives the magnetizing force, the magnetizing coils need to have com- APPLIED ELECTRICITY, 2037 paratively few turns, which should be of correspondingly large wire, in order that the watts loss (which is equal to C R) should be kept within the desired limits. It will be seen that in series-wound dynamos the difference of potential between the terminals of the machine is less than that which appears between the brushes by the amount of the drop in the magnetizing coils. The above remarks concerning the magnetizing coils of shunt and series wound dynamos also apply to those of com- pound-wound machiiies, since they are made up of a shunt and a series winding. INDEX. Abscissas .... Absolute unit of potential " units . Acceleration, Unit of Accumulator . " cells, Construction of " " Method of set- ting up . " Chloride " Discharge rate of " Efficiency of " . grids . " Internal resistance o " Lead . " * Phillips-Entz . " plants. Failure's of " plates, Life of . Accumulators, Bimetallic " Copper-zinc . " for street cars " in power stations " Installation of " Use of Acid Acids, Table of Advance of winding Affinity, Chemical . Air-gap .... Alternating currents Alternator Amalgams of mercury . Ammeter, Edison chemical " Weston . Ammeters Ammonium Ampere .... " and coulomb. Relation be tween . . . , 1674 age. Page. 1555 Ampere-hour efficiency of accumu- 1586 lator . . . . 1768 1474 " hours 1765 147s " meters . . . . 1634 1746 " turns 1543 I7S9 " " required to energize 1770 magnet . Analogy between flow of water 1573 1793 and electricity . . . . 1495 177s Apparatus for measuring current 1629 176s Area, Unit of 1475 1767 Armature 1518 1770 " ...... 1898 1768 " core losses 1924 1760 " reaction . . . . 1969 1778 " winding . . . . 1898 1797 " windings, Closed-coil . 1973 1770 '• " D i r e c t -cur- 1777 rent . 1936 1778 , " " General prin- 1786 ciples of 1929 1786 Armatures, Closed-coil bipolar 1954 1791 " Cylinder 1935 1781 Disk . . . . 1935 1696 " Iron-clad 1995 1697 " Open-coil bipolar 1938 1987 " " multipolar . 1950 1 701 " Unipolar 1936 1922 Artificial magnets . : . . 1517 2018 Atomic weights of chemical ele- 1927 ments 1695 1928 Atomicity of chemical elements . 1695 1694 Available electromotive force 1498 1676 Axis of magnetism . . . . 1518 B. Back pitch of winding Bailie and Fery cell Balance, Torsion Ballistic galvanometer Page. 1750 1453 INDEX. Page. Ballistic galvanometer used in measuring magnetic qualities of iron Balloon cell Bar magnet " winding Base (chemical) Battery connected in multiple arc or parallel " connected in multiple or parallel series " connected in series . " Electric " Electrostatic " Grouping of cells of, fo maximum current . " Le5fden " Method of connecting cell of ... . " Primary " Secondary . " Storage " Voltaic Batteries, Application of Dry .... Bichromate cells Bimetallic accumulators " " EflScienc of . Binary compounds . Bipolar armatures. Closed-coil " " Open-coil " drum windings Bound charge . Bridge, Wheatstone British thermal unit Broken circuit . Brushes Buckling of accumulator Building up field Bunsen's cell C. G. S. system of units . Calculation of magnetic circuit Calibration of galvanometer . Callaud cell Calorie Capacity . " Inductive . Cardew voltmeter . Cathode Cell, Bailie and Fery " Bichromate Cell, Bunsen " Callaud I6II " Chaperon 1733 " Chemical action in . 1532 " Daniell IQ95 " " crowfoot 1697 " D'Arsonval .... " Edison-Lalande 1472 " Fuller bichromate . " Galvanic 1472 " Gethin 1472 " Globe or balloon 1689 " Gonda-Leclanche . 1463 " Gouy standard " Gravity 1757 " Grenet 1689 " Grove " Hercules 1757 " Hussey ..... 1689 " Internal resistance of 1689 " Kousmine .... 1689 " Lalande 1466 " Latimer-Clark 1752 " Leclanche .... 1751 " - Little Giant .... 1718 " Maeche 1727 " Pabst 1777 " Partz " Poggendorf .... 1779 " Smee 169s " Sorley . . . . . 1954 " Voltaic 1938 " Zinc-lead 1982 Cells, Bichromate .... 1457 " Classification of . . . 1638 " Grouping of, for maximum 1509 current .... 1471 " Methods of connecting 1930 " of Volta type 1764 " with depolarizing electro- 2034 lytes . 1723 " " " electro- lytes . Page. " " elementarysubstances 1474 applied to cathode . 1558 " " elementarysubstances 1600 applied to cathode . 1734 " " liquid depolarizers . 1476 " " " " 1462 " " non-depolarizing elec- 1458 trolytes 1677 " " solid depolarizers 1700 " " " " 1750 " without depolarizers 1718 Centigrade and Fahrenheit scales, 1727 Relations between 1649 INDEX. Xlll Centimeter . . . . . Chaperon cell ..... Character of commercial currents Chardin's arrangement of bichro- mate cells . . Charge, Bound " Free " Negative . . . . " Positive . . . . Charging accumulators, Precau- tions to be observed in " current of accumulator, E. M. F. of , Chemical action .... " " Electromotive f orceproduced by Heat formation by in galvanic cell " voltaic cell Nature of Weight of s u b - stances liberated by. affinity compounds elements . Table of equivalent formula . nomenclature Chloride accumulator Chord winding Circuit " Broken . " Closed . " Completed " Divided " External " Grounded " Internal " Magnetic " Open Shunt . Circuits, Magnetic " Telegraph Closed circuit . " coil armature windings " " bipolar armatures " " winding Coefficient, Temperature Coil-and-plunger magnet " Exciting . " Induction . " Primary " Ruhmkorff " Secondary Page. 1474 1743 1927 1721 1457 I4S7 1451 1451 1794 1769 1705 1704 1 701 1467 1703 1 701 i6go 169s 1471 1471 1471 1471 1471 1471 1471 1471 2017 1471 1471 1521 1799 147T 1973 1954 i960 1646 1577 1588 1589 Coils, End connections of Collector .... Combining weight . Commercial efficiency of dynamo Commutation of current Commutator Compass . " Magnetic . Compound winding '* wound dynamo Compounds, Chemical Condenser Conductivity " Joint . Conductors " and insulators, Table of i Consequent poles Conservation of energy Continuous currents Controlling magnet of galvanom eter .... Copper-zinc accumulators Core, Field " Lamination of " losses Coulomb . " and ampere, Relation be tween Counter-magnetomotive force Cross-magnetomotive force . Current and static charge, Differ^ ence between . " Apparatus for measuring " Commutation of Effects of . " Electric " Graphical representation of ... . " in conductors, Effect of " strength. Determination of, by decomposition of water .... " strength measured by cop- per deposit Currents, Alternating " Commercial " Continuous " Direct " Pulsating " Thermo-electric Curve, Sine Curves, Accuracy of " Method of plotting 1930 169s 1909 1962 1931 1532 1518 2033 2033 1690 1461 1455 1500 1501 145s 1522 2021 1508 1927 1599 1778 2018 1925 1924 1480 1480 1972 1972 1962 1478 1591 1463 1911 i9°5 1631 1631 1927 1927 1927 1927 1927 1470 1917 1557 ISS7 INDEX. Curves of magnetism '■ Permeability " Saturation . Cycle of magnetism Cyclic alternating E. M. F. Cylinder armatures " machines . D. Daniell cell " crowfoot cell D'Arsonval cell " galvanometer Dead-beat instrument Decomposition, Chemical Density, Electric " Magnetic . " of lines of force Depolarization .... " Mechanical devices for " Rate of . Depolarizers .... " of chlorides of me cury and silver " " oxides of lead " " sulphate of nier^ cury . Depolarizing effects of varioussub stances Derived circuits, Ohm's law ap plied to Desiccator .... Dielectric D'Infreville ■wasteless zinc . Direct-current armature winding " currents Direction of inducedcurrents, Ruli for . " of motion of conducto Rule for Discharge rate of accumulator Disk armatures Divided circuit Drop of potential Drum winding .... " windings. Multipolar . Dry batteries .... Duncan meter .... Dynamo, Compound-wound . " Over-compounded . " Self-excited " Separately excited . " Series-wound . " Shunt-wound . Pag^e. 1554 '554 1554 1562 1929 1935 1460 Page. 1735 1730 1606 1673 i6go 1459 1524 1500 2019 1709 1710 1710 1709 1746 1746 1746 1726 1500 1626 1458 1738 Dynamo, Theory of Dynamometer, Siemens . Dyne 1581 1579 1765 1935 1471 1494 1934 1994' 1751 1681 2033 2034 2029 2029 2031 Z032 E. M. F., Graphical representation of " in closed-coil armatures. Calculation of " of charging current " " the formation of vari ous sulphates . " " zinc with various elec trolytes Earth (grounded) circuit Earth's magnetic field, Horizontal component of . . . Eddy currents .... Edison chemical ammeter " Lalande cell Efficiency of bimetallic accumula tors " Commercial . " Electrical " of dynamo Electric battery " current " " Unit of . " density " motor .... " pendulum . " quantity, Unit of " series .... Electrical and magnetic units. Re- lation between . " apparatus, Description of 1674 1476 " Experiments with . " Experiments with . " Experiments with . " Experiments with . circuits compared with flow of water through a pipe efficiency of dynamo equivalent of heat . horsepower instruments measurements. Practical mechanical, and heat en- ergy. Relations of power . . . . 1901 1769 1718 1718 1471 1595 1924 1676 1744 1779 1909 1909 1973 1689 1463 1476 1450 1910 1450 1476 152a 1531 1660 1536 1548 1585 1666 1473 1909 1509 1514 1670 1670 INDEX. Electrical resistance " units " work Electricity and flow of water Analogy between " Nature of " Static " Voltaic . Electrification .... Electrochemical calculations " equivalent . " equivalents . " measurements " theories Electrochemistry Electrodes of cell or battery . Electrodynamics Electrolysis Electrolytes Page. 1455 1472 1505 1495 1449 1450 1466 1655 1701 1703 1699 1625 1706 1699 1466 1450 1462 1591 1466 1700 164s 1546 1571 1547 " Resistance of Electromagnet .... " Calculation of " Horseshoe " Iron-clad Electromagnetic induction " measurements " reaction Electromagnetism . Electromagnets, Classes of . Electromotive force " force, Available " force, Determina- tion of . " force, Generation of " force produced by chemical action, ^ Calculation of " force, Total " Unit of " " Value of " series Electrophorus . Electropoion fluid . Electroscope Electrostatic battery field . " induction " instruments " machines . " " Cylinder " " Induction " " Plate Electrostatics 1450 Elements, Atomic weight of . . i6gi 1579 1591 1541 1528 1548 15^8 158s 1705 1498 1476 192 1 1468 1458 1727 1452 1463 1456 1456 1452 1460 1460 1461 1461 Elements, Chemical Table of . " Voltaic . End connections of coils . Energy, Conservation of " equivalents, Table of " Unit of . . . Equivalents, Electrochemical Erg Exciting the Field, Methods of Experiments with electrical appa ratus " " electrical appa- ratus " " electrical appa ratus " " electrical appa- ratus " " electrical appa- ratus. Sugges- tions for External current Field, Building up of " core .... " Electrostatic . " Magnetic " magnets. Types of " Methods of exciting Force, Electromotive " Magnetizing . " Magnetomotive . Unit of . Forming accumulator plates . Frame of dynamo. Construction Free charge .... Front pitch of winding . Fuller bichromate cell . Fundamental units . Page. iggi 1508 IS" 1476 i6gg 1703 1476 2029 1536 Q. Galvanic cell Galvanometer Ballistic . Calibration of . 1600 constants . . 1600 D'Arsonval . . 1606 Reflecting . . 1605 Sine .... 1603 Tangent . . . 1597 Theory of . . 1592 Generation of electromotive force 1899 1585 1471 Page. 2034 2018 1456 1519 2028 2029 1468 1550 1543 1476 1772 201S 1457 1983 1728 1474 Page. 1466 1592 1620 1661 XVI INDEX. Gethin cell Globe cell .... Gonda-Leclanche cell Gouy standard cell . Gram Gi'.amme winding Graphical representation of E or current Gravity cell . . Grenet cell Grid, Reckenz.aiin . Grids, Accumulator Grounded circuit Grounding a circuit Grove cell .... Page. 1734 1733 1641 1749 1474 1934 1 911 1734 1719 1774 1770 1471 1653 1723 H. Halogens Harmonic alternating E. M. F. Heat and work, Relation between " Equivalent of . " formation by chemical action " Mechanical equivalent of " of formation .... " " " of various sub- stances with oxygen . " Unit of Hercules cell Holtz machine ..... Horizontal component of earth's field Horsepower, Electrical . Horseshoe magnet .... Hussey cell Hydrate Hysteresis Power expended by 1750 1929 1704 1509 1704 1509 1703 1476 1716 1595 1514 1532 17.34 1696 1562 1924 1564 I. - Page. Induced currents in closed coil, Di- rection of . . 1584 " " - Rule for direction of . . . 1581 " . E. M. P., Production of . 1587 Induction-coil ... . . . 1589 " Electromagnetic . . 1579 " Electrostatic . . . 1456 " "■ machine . 1461 " Magnetic . . . 1524 " Mutual .... 1588 " Self 1587 " Unipolar .... 1936 Inductive capacity .... 1458 Input of dynamo , . . . 1973 Installation of accumulators Instruments, Electrical . " Electrostatic " Switchboard Insulation .... ", resistance " " Measurement of " resistance of apparatus for electric-light and power work " resistance of telegraph lines Page_ 1791 1670 1452 1682 1649 1649 1655 Insulators,. " in order of their induct ive capacity " Resistances of Internal circuit " resistance of accumulator " " cell " " " voltaic cell Iron-clad armature . " Methods of testing . 1653 1650 1455 1645 1471 1768 1758 1490 1995 1611 J. Page. Joint resistance of conductors . 1501 Joule 1504 Joule's law 1509 K. Page. Keeper 1508 Kilowatt 1516 Kousmine cell 1729 Lalande cell Lamination of core . Latimer-Clark cell . Law, Joule's " Ohm's " open-circuit cell Laws of static charges Lead accumulators . Leads Leakage, Magnetic . Leclanche cell . Leyden battery " jar Life of accumulator plates Lifting magnets " " Calculation for Lines of force. Density of " " " Magnetic . " " " Rule for direction o' Litharge Little Giant cell Page. 1743 1925 1748 '509 1473 1715 1452 1760 i960 1565 1739 1689 1462 1770 1568 1571 2019 1520 ■ 1530 174s 1716 INDEX. XVll Lodestone . Long-range magnets Loop winding . M. Machines, Electrostatic . Maeche cell .... Magnet for attraction . " calculation for . " Coil-and-plunger " Controlling Magnetic and electrical units, Re lation between " circuit " " Calculation of " " Closed . " " Compound . " " Form of " " Sectional area o " " Simple . " compass . " density Page. • 1517 • 1577 • '995 Page. 1460 1726 1576 1571 1577 1599 1528 1 52 1 2017 1558 1523 1523 2021 1523 1522 1518 1524 15S0 Page. " " and permeability of iron and steel " fields " induction . " leakage " lines in solenoid " " of force . " " per unit pole " permeability . " poles, Attraction b e tween " " Strength of " qualities of iron, meas- ured by ballistic gal vanometer " satviration " substances " units . " yoke . Magnetism " Cj'cle of " Quantity of " Residual " Unit density of Magnetite . Magnetization, Curves o Magnetizing force . Magnetomotive force " " Counter " " Cross . " " Intensity of Magnets, Artificial . . 1553 1519 1524 1565 1545 1520 1526 1545 1592 1526 i6ri 1552 1519 1526 2018 1517 1562 1524 1561 1527 I5'7 1552 1550 1543 1972 1972 1544 1517 Magnets, Lifting " Long-range " Natural " Permanent " Short-range " Tractive force of Mass, Unit of . . . Maximum current of battery Measurements, Electrochemical " Electromagnetic " of potential . " Precision in . " with commercial instruments Mechanical, electrical, and heat en ergy. Relations of " equivalent of heat Megohm Metals, Resistance of Meter, Duncan . " Shellenberger Microhm . Minimum . Multiple arc, Battery connected in " circuit windings " windings . " wound multiple-c ircui drum windings " " multiple-circuit ring windings " " two-circuit drum windings " " two-circuit ring windings . Multiplying power of shunts . Multipolar armatures. Open-coil " drum windings Mutual induction N. 1577 1517 1518 1576 1568 1474 1757 1625 1.59 1 1632 1623 1682 1509 1483 1483 1745 1472 1977 2002 2007 1621 1950 1994 1588 Negative charge Neutral line of magnet . " temperature Nitric acid as a depolarizing liquid 1723 Page. • 1451 . 1518 ■ 1470 O. Page. Ohm, Legal . .... . 1483 " Various values of . . . 1482 Ohm's law . ; . . . 1473 " " applied to closed cir- cuits . 1491 " " " " derived cir- cuits . 1500 Open circuit .. . ... . 1471 '■ " cell. Law . . . 1715 XVlll INDEX. Page. Open-coil bipolar armatures . . 1938 " multipolar armatures . 1950 " •winding- .... 1944 Ordinates ...... 1555 Output of dynamo .... 1973 Oxide ....... i6qi Pabst cell . Parallax Parallel or multiple arc, Battery connected in " " multiple arc, Conduc tors connected in Partz cell Pendulum, Electric Periodic alternating E. M. F. Permanent inagnets Permeability and magnetic den- sity of iron and steel " curves " Magnetic . Peroxide of lead - Phillips-Entz accumulator Pile, Voltaic Pinnacle zinc Pitch of winding Plate electrostatic machine Poggendorf cell Polarity of solenoid . Polarization Poles, Consequent . " of cell or battery . " " magnet " " magnetic compass " Salient . Positive charge Potential .... " Absolute unit of " Drop of " Measurement of Power, Electrical Unit of . Precision in ineasurements Primary batteries, Applicati " battery " coil Prime conductor Pulsating currents . R. Rate of cutting lines of force Reaction, Armature " Electromagnetic Reckenzaun grid Page. 1722 1674 on of 1472 1471 1728 1450 1929 1518 1553 1554 1545 1745 1778 1469 1737 1978 1461 1720 1542 1709 2021 1466 1518 1518 2021 1451 1494 1632 1476 1623 1752 1460 1927 Page. • 1585 . 1969 • 1541 • 1774 Recomposition (chemical) Reflecting tangent galvanometer Relations of mechanical, electrical and heat energy " " thermometric scales Reluctance Residual magnetism Resistance " coils " " Standard " Electrical " Insulation " of metals " " various electrolytes " " " insulators " Specific . Unit of . . . Reversal method of testing iron Revolution counter . Ruhmkorff coil .... Salient poles Salt (chemical) . Saturation curves . " Magnetic Secondary battery . " cells " coil . " units Self-induction . Series, Battery connected in " Conductors connected " Electric " Electromotive " winding " wound dynamo Shellenberger meter Short-range magnets Shunt, Galvanometer " Multiplying power of " winding " wound dynamo Siemens dynamometer " wattmeter. Sine curve " galvanometer Slide-wire bridge Smee cell . Solenoid " Magnetic lines in " T'olarity of Solution Sorley cell Sparking limit . Page. 1690 1605 1649 1558 1561 1484 1660 1643 1455 1649 1488 164s 164s 1643 1477 1614 Page. 2021 1697 1534 1552 1689 1746 1475 1587 1472 1472 1452 1468 2030 2031 1681 1576 1620 1621 2032 2032 1674 1678 1917 1603 1660 1714 1542 154s 1542 1697 1774 1972 INDEX. Pag-e. Specific resistance .... 1643 Standard resistance coils . . 1643 Static charge and current, DifTer- ance between . . . 1468 " charges. Laws of . . . 1452 Statical electricty. Production of . 1450 Step-by-step method of testing iron 1614 Storage batteries (see also accumu- lators) . . i68g " " Space 1 for . Switchboard instruments 1746 1759 I7Q2 1682 T. Pag-e. Tachometers 1687 Tangent galvanometer . . . 1597 " " Reflecting 1605 Telegraph lines, Insulation resist- ance of ..... . 1650 Telephone lines, Insulation resist- ance of ..... • 1650 Temperature coefficient . . . 1641 " coefficients for vari- ous metals . . 1647 " Neutral . . . 1470 Theory of the galvanometer . . 1592 Thermal unit, British . . . 1509 Thermochemical equivalent . . 1702 Thermoelectric currents . . 1470 Thermometric scales. Relations between ...... 1649 Thomson recording wattmeter . 1680 Time, Unit of 1475 Torsion balance . . . . 1453 " " Use of . . . 1454 Total electromotive force . . 1498 Tractive force of magnet . . 1568 " " " " how cal- culated 1571 Tudor Grids 1773 Two-circuit windings . . . 1976 U. Page. Unipolar armatures . . . 1936 " induction .... 1936 Unit of acceleration . . . 1475 " " area ..... 1475 " " diiTerence of potential . 1476 " " electric-current quality . 1476 " " " strength . 1476 " " electromotive force . . 1476 " " energy 1476 " " force 1476 " " heat 1476 Unit of mass " " potential. Absolute " " power . " " resistance " " time " " velocity " " volume " " work Units, Electrical " Fundamental " Magnetic " Secondary V. Valency of chemical eleinents Velocity, Unit of . . . Volt Voltaic battery cell .... " " Internal resistance of " " Simplest form of " couple . " electricity " eleinents " pile Volt-coulomb . Voltmeter . " Cardew " Weston Volume, Unit of W. Watt " efficiency of accumulator Wattmeter, Siemens " Thomson recording Wave winding .... Weston ammeter and voltmeter Wheatstone bridge . Wimshurst machine Winding, Advance of Bar .... " Chord " Closed-coil " Compound " Drum " Gramme ■' Loop . " Open-coil Pitch of Ring . " Series " Shunt " Wave Windings, Armature " Bipolar drum Page. 1474 1686 1476 1477 M7S 147s ^475 1476 1472 1474 1526 1475 Page. 1695 147s 1490 1466 1466 1490 1700 1466 1466 1466 1469 1505 1634 1677 1674 1475 Pag-e. 1514 1768 1678 1680 1997 1674 1987 1995 1988 i960 2033 1934 1934 199s 1944 1978 1934 2030 2032 1997 1929 1982 XX IND Page. EX. Page. Windings, Close id-coil 1973 Windings, Multipolar drum . ■ 1994 " Direct-current 1936 Ring ■ 1974 Mult: iple . . . . 2002 " Two-circuit . • 1976 " " circuit 1977 Work and heat, Relation between 1704 " " wound, multi- " Electrical • 1505 ple-c ire u i t, " Unit of ... . ■ 1476 drum . 2011 " wound, multi- Y. Page. ple-ci r cu i t, Yoke, Magnetic . 2018 ring 2004 " " wound, two- Z. Page. circuit, drum 2013 Zinc, D'Infreville wasteless . ■ 1738 " wound, two- " lead accumulator cell . • 1777 circuit, ring 2007 " Pinnacle .... • 1737 V5